Answers
THE GRAPH SHOWING (X=2,5) (Y=10,9) (Z=6,1) Thus, taking YZ as the base, the area of the triangle XYZ is 2√(98)square units.
DEFINE THE TRIANGLE'S AREA?The total area filled by a triangle's three sides in a two-dimensional plane is what is known as the triangle's area. The basic formula for calculating a triangle's area is A = 1/2× b× h, which equals half the product of the triangle's base and height.
We can use the following formula to determine a triangle's area given its coordinates:
Area is equal to half of |x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|.
where the triangle's vertices' coordinates are (x₁,y₁), (x₂,y₂), and (x₃,y₃).
As YZ serves as our base in this instance, we must first determine its length. When we apply the distance formula, we obtain:
√((1-9)2 + (6-1)2) Equals √YZ (98)
Finding the perpendicular distance from X to YZ will allow us to determine the height of the triangle now that we know YZ. This distance is equivalent to 2-6 = -4, which is the x-coordinate of X less the x-coordinate of Z.
As a result, the triangle's area is:
Area is equal to 1/2 × YZ × height
= 1/2×√(98)× |-4|
= 2 √ (98)
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Related Questions
Bruce is going to call one person from his contacts at random. He has 25
2525 total contacts. 20
2020 of those contacts are from his neighborhood.
What is P(call a person not from his neighborhood
)
P(call a person not from his neighborhood)start text, P, left parenthesis, c, a, l, l, space, a, space, p, e, r, s, o, n, space, n, o, t, space, f, r, o, m, space, h, i, s, space, n, e, i, g, h, b, o, r, h, o, o, d, end text, right parenthesis?
If necessary, round your answer to 2
22 decimal places.
Answers
Bruce is going to call one person from his contacts at random and Probability to call a person not from his neighborhood = 1/5 or 0.2
Total number of contacts = 25
Total number of contacts that are from his neighborhood = 20
Find the probability of calling one person not from his neighborhood.
Find the number of contacts not from his neighborhood.
Total contact = 25
Total from his neighborhood = 20
Total not from his neighborhood = 25 - 20
Total not from his neighborhood = 5
Find the probability of calling one person not from his neighborhood:
Total contact = 25
Total not from his neighborhood = 5
P(call a person not from his neighborhood) = 5/25
P(call a person not from his neighborhood) = 1/5 or 0.2
or we can say that,
probability = number of favorable outcomes
number of possible outcomes
there are five favorable outcomes (the 25-20=5) people not from his neighborhood
there are 25 total possible outcomes (the 25 total contacts)
P (call a person not from his neighborhood) = 5/25= 0.2
Therefore, the probability is 0.2
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Write a cubic function in standard form that has x-intercepts at (-1,0) (2,0) (4,0) and a y intercept at (0,-24)
Answers
After answering the presented question, we can conclude that Therefore, the cubic function in standard form that has x-intercepts at (-1,0) (2,0) (4,0) and a y-intercept at (0,-24) is [tex]f(x) = 3x^3 - 21x^2[/tex] [tex]+ 14x + 24.[/tex]
what is function?In mathematics, a function appears to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.
To find a cubic function in standard form, we can start by using the intercept form of the cubic equation:
[tex]f(x) = a(x-x1)(x-x2)(x-x3)\\f(x) = a(x+1)(x-2)(x-4)\\-24 = a(0+1)(0-2)(0-4)\\-24 = a(-8)\\a = 3\\[/tex]
So the cubic function in standard form that satisfies the given conditions is:
[tex]f(x) = 3(x+1)(x-2)(x-4)\\f(x) = 3x^3 - 21x^2 + 14x + 24\\[/tex]
Therefore, the cubic function in standard form that has x-intercepts at (-1,0) (2,0) (4,0) and a y-intercept at (0,-24) is [tex]f(x) = 3x^3 - 21x^2[/tex] [tex]+ 14x + 24.[/tex]
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Solve 9/n = 75/100 for the unknown quantity, n.
Answers
Answer:
n = 12
Step-by-step explanation:
Given equation:
[tex]\dfrac{9}{n}=\dfrac{75}{100}[/tex]
We can solve the equation for the unknown quantity, n, by cross-multiplying, which means multiplying both sides of the equation by the product of the denominators.
The denominator of a fraction is the part below the division bar.
The denominators of the given equation are n and 100, so their product is 100n.
Multiply both sides by 100n:
[tex]\implies \dfrac{9}{n} \cdot 100n=\dfrac{75}{100}\cdot 100n[/tex]
Simplify and cancel the common factors:
[tex]\implies \dfrac{9\cdot 100n}{n} =\dfrac{75\cdot 100n}{100}[/tex]
[tex]\implies 9\cdot 100 =75\cdot n[/tex]
[tex]\implies 900 =75n[/tex]
To solve for n, divide both sides of the equation by 75:
[tex]\implies \dfrac{900}{75} =\dfrac{75n}{75}[/tex]
[tex]\implies 12=n[/tex]
Therefore, the unknown quantity, n, is 12.
Answer:
[tex]n = 12[/tex]Step-by-step explanation:
To find:-
The value of "n" .Answer:-
The given equation to us is ,
[tex]\longrightarrow \dfrac{9}{n}=\dfrac{75}{100} \\[/tex]
Simplify the RHS of the equation. This can be done by dividing the numerator and denominator by 25 as it is the HCF of 75 and 100 . So we have;
[tex]\longrightarrow \dfrac{9}{n}=\dfrac{75\div 25}{100\div 25} \\[/tex]
Simplify,
[tex]\longrightarrow \dfrac{9}{n} = \dfrac{3}{4} \\[/tex]
Flip the numerator and denominator on both the sides , as ;
[tex]\longrightarrow \dfrac{n}{9} =\dfrac{4}{3} \\[/tex]
Multiply both the sides by 9 as ,
[tex]\longrightarrow \dfrac{n}{9}\times 9 =\dfrac{4}{3}\times 9\\[/tex]
Simplify,
[tex]\longrightarrow \boxed{\boldsymbol{ n = 12}} \\[/tex]
Henceforth the value of n is 12 .
Y varies inversely with the cube of x and y=9 when x=2
Answers
[tex]Therefore, when[/tex] [tex]x=4,y=1.125[/tex]. Y varies inversely with the cube of x and y=9 when x=2.
What is cube?A cube is a three-dimensional geometric shape that has six square faces, all of which are congruent to each other, and eight vertices (corners) where three faces meet. It is a regular polyhedron, which means all its faces are congruent and all its angles are equal.
A cube is often used in mathematics, geometry, and engineering because of its regular shape, which makes it easy to calculate and work with. It is also a common shape in everyday objects, such as dice, Rubik's Cubes, and boxes. The volume of a cube is calculated by multiplying the length of any of its sides by itself twice, while the surface area is found by multiplying the length of any of its sides by six.
If y varies inversely with the cube of x, we can write this relationship as:
[tex]y = k/x^3[/tex]
where k is a constant of proportionality. To solve for k, we can use the given information that y=9 when x=2:
[tex]9 = k/2^3[/tex]
Simplifying the equation, we get:
[tex]k = 9 * 2^3[/tex]
[tex]k = 72[/tex]
Now that we have determined the value of k, we can use the equation to find the value of y for any value of x. For example, if x=4, we have:
[tex]y = 72/4^3[/tex]
[tex]y = 72/64[/tex]
[tex]y = 1.125[/tex]
[tex]Therefore, when=4,y=1.125[/tex]
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What is true about the preimage of a figure and its image created by a translation?
Question content area bottom
Part 1
Select all that apply.
A.
Each point in the image has the same x-coordinate as the corresponding point in the preimage.
B.
Each point in the image has the same y-coordinate as the corresponding point in the preimage.
C.
The preimage and the image have the same size.
D.
The preimage and the image are congruent.
E.
Each point in the image moves the same distance and direction from the preimage.
F.
The preimage and the image have the same shape.
Answers
A pre-image is a transformation representing a flip of a figure. For reflection:
The preimage and the image have the same size.
An image created by a reflection will always be congruent to its pre-image.
Corresponding angles and segments are always congruent in a reflection of a figure.
An image and its pre-image are always the same distance from the line of reflection.
Transformation
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection, and dilation.
A reflection is a transformation representing a flip of a figure. Reflection preserves the shape and size of the figure. Also, An image and its pre-image are always the same distance from the line of reflection.
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Pls Answer Fast!! Whoever gets it write first I will give a brainly!!!
Answers
Answer: I think you forgot to attach the question
Step-by-step explanation:
first five terms of
t(1)=4
t(n+1)=t(n)-3
Answers
the first five terms of the sequence t(1)=4 and t(n+1)=t(n)-3 are: 4, 1, -2, -5, -8.
To find the first five terms of the sequence defined by the formula t(1) = 4 and t(n+1) = t(n) - 3, we can use the recursive formula to find each term in the sequence:
t(1) = 4
t(2) = t(1) - 3 = 4 - 3 = 1
t(3) = t(2) - 3 = 1 - 3 = -2
t(4) = t(3) - 3 = -2 - 3 = -5
t(5) = t(4) - 3 = -5 - 3 = -8
Therefore, the first five terms of the sequence are: 4, 1, -2, -5, -8.
A recursive formula is a formula used to define a sequence, where each term of the sequence is defined in terms of the previous terms. In other words, to find a particular term in the sequence, you need to know the value of the previous term. This can be useful for generating sequences with complex patterns, such as the Fibonacci sequence. However, recursive formulas can also be more difficult to work with than explicit formulas, which give a direct formula for calculating any term in the sequence without relying on previous terms.
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Explain to Tony how he can get the answer without doing any work. Write the special pattern he will need to use and explain how to use it to find each term of the trinomial.
HELP!!!!!!!!!!!!!!!!!!!!! I NEED THIS ASAP
Answers
The expanded trinomial is 25z^2 - 10zy + y^2. Tony can use the special pattern for expanding a binomial in the form (a + b)^2 = a^2 + 2ab + b^2.
In this case, he can write (5z - y)^2 as:
$(5z)^2 + 2(5z)(-y) + (-y)^2$
Simplifying each term, we get:
25z^2 - 10zy + y^2
Tony can use this pattern to find each term of the trinomial without having to multiply the entire expression. He simply needs to square the first term, multiply twice the product of the first and second terms, and square the second term, which will give him the three terms of the trinomial
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Find the equation of the exponential function represented by the table belowFind the equation of the exponential function represented by the table below:
x y
0 4
1 12
2 36
3 108
Answers
The equation of the exponential function is[tex]4 * 3^{x}[/tex].
What is exponential function?
An exponential function is of the form:
[tex]f(x) = a^{x}[/tex]
here "a" is a constant called the base, and "x" is the variable. The base "a" is typically a positive real number, but it can also be a negative number or a complex number. The function is called exponential because the variable "x" appears in the exponent.
We can see that as "x" increases by 1, "y" is multiplied by a constant factor of 3. This suggests that the exponential function has a base of 3. To find the equation, we can use the general form of an exponential function:
[tex]y = a * b^{x}[/tex]
where "a" is the initial value or y-intercept, and "b" is the base.
We can use the given values of (x,y) to form a system of equations:
[tex]a * 3^{0} = 4[/tex]
[tex]a * 3^{1} = 12[/tex]
[tex]a * 3^{2} = 36[/tex]
[tex]a * 3^{3} = 108[/tex]
Simplifying each equation, we get:
a = 4
3a = 12
9a = 36
27a = 108
Solving for "a", we get:
a = 4
Substituting this value of "a" into the equation, we get:
[tex]y = 4 * 3^{x}[/tex]
So the equation of the exponential function represented by the table is y [tex]= 4 * 3^{x}.[/tex]
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I need help with problem
Answers
Answer:
it’s the first one- 9x-3=60
Step-by-step explanation:
Select all expressions that are equivalent to
0.75x + 0.25(x + 12.4) + (x – 2.1)
Answers
Answer:
Step-by-step explanation:
answer is 0.5
Andre uses the expression (x - 5)2 + 7 to define f. Noah uses the expression (x + 5)² - 7 to define
f. Which of the students is correct?
Andre
Noah
Neither is correct
Both are correct
Answers
Answer:
It looks like (x - 5)^2 - 7 is correct.
Step-by-step explanation:
The vertex form of this type of function is
a(x - b)^2 + c where a is some constant and (b, c) is the vertex.
In this case the vertex is at (5, -7) so we can write f as:
a(x - 5)^2 - 7.
From the diagram it looks like when x = 0 f lies between 16 and 20 so that makes a = 1
what is the long method of 23 ÷ 650
Answers
Answer: The long division method is a way to solve division problems by hand. Here are the steps to do long division:
Write the dividend (the number being divided) inside a long division bracket, and write the divisor (the number doing the dividing) outside of the bracket.
Divide the first digit of the dividend by the divisor. Write the answer (the quotient) above the dividend, and write any remainder (what’s left over) below the first digit of the dividend.
Bring down the next digit of the dividend next to the remainder.
Repeat step 2 until you’ve brought down all of the digits of the dividend.
The final answer is your quotient with any remainder written as a fraction.
please help asapppppp
Answers
The equations [tex]y=2x-3 [/tex]and [tex]y=x+6[/tex],
we can use them to find the point of intersection between the two lines. This point of intersection represents the solution to the system of equations.
Setting the two equations equal to each other, we get:
[tex]2x - 3 = x + 6[/tex]
Simplifying this equation, we can see that x = 9.
Now we can substitute x = 9 into either of the original equations to find the corresponding value of y.
Let's use the equation [tex]y=2x-3[/tex]
[tex]y = 2(9) - 3 = 15[/tex]
Therefore, the solution to the system of equations y=2x-3 and y=x+6 is the point (9, 15).
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a service facility consists of one server who can serve an average of 2 customers per hour (service times are exponential). an average of 3 customers per hour arrive at the facility (interarrival times are assumed exponential). the system capacity is 3 customers. a on the average, how many potential customers enter the system each hour? b what is the probability that the server will be busy?
Answers
(a) The average number of potential customers entering the system each hour is 2.5 customers per hour.
(b) The probability that the server will be busy is equal to the utilization factor, which is 0.67.
How to find potential customers enter the system each hour?a) The average number of potential customers entering the system each hour can be calculated using Little's law, which states that the long-term average number of customers in a stable system is equal to the long-term average arrival rate multiplied by the long-term average time a customer spends in the system.
In this case, the arrival rate is 3 customers per hour, and the average time a customer spends in the system is equal to the average time between arrivals plus the average service time, which is 1/3 + 1/2 = 5/6 hour.
Therefore, the average number of potential customers entering the system each hour is 3 x 5/6 = 2.5 customers per hour.
How to find the probability that the server will be busy?b) The probability that the server will be busy can be calculated using the formula for the utilization factor, which is equal to the long-term average service rate divided by the system capacity.
In this case, the service rate is 2 customers per hour, and the system capacity is 3 customers. Therefore, the utilization factor is 2/3 = 0.67. The probability that the server will be busy is equal to the utilization factor, which is 0.67.
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Find the value of x. Round to the nearest tenth .
Answers
Answer:
x ≈ 16,8
Step-by-step explanation:
Use trigonometry:
[tex] \tan(40°) = \frac{x}{20} [/tex]
Cross-multiply to find x:
[tex]x = 20 \times \tan(40°) ≈16.8[/tex]
an ice cream shop is testing some new flavors of ice cream. they invent 25 2525 new flavors for customers to try, and throw out the 13 1313 least popular flavors. the shop makes 80 8080 cartons of each of the remaining flavors. it takes 2 22 cartons to get one liter ( l ) (l)(, start text, l, end text, )of ice cream. how much total ice cream is in the cartons?
Answers
The total number of ice cream which is in the cartons if cartons to get one liter (L) of ice cream is 480 Liters.
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently utilised in everyday life. When we need to combine groups of similar sizes, we utilise multiplication.
We have,
throw out the 13 least popular flavors,
Total flavors
25 - 13 = 12
80/2 = 40 liters.
The remaining 12 flavors and 40 liters each so,
total ice cream = 12 x 40 = 480 liters.
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Complete question:
An ice cream shop is testing some new flavors of ice cream. They invent 25 new flavors for customers to try. and throw out the 13 least popular flavors. The shop makes 80 cartons of each of the remaining flavors. It takes cartons to get one liter (L) of ice cream. How much total ice cream is in the cartons?
Select the correct answer from the drop-down menu.
A sphere has a radius of 24 centimeters. What is its volume?
Answers
Answer: The volume of the sphere is 57876.48
Step-by-step explanation:
The formula you need for volume of a sphere is:
V = [tex]4/3\pi r^3[/tex]
You will enter the applicable numbers and multiply.
4/3 * 3.14 * 24 * 24 *24
When we multiply all numbers, the volume of a sphere with a radius of 24 centimeters is 57,876.48
b^2-c^2-10(b-c) factor completly
Answers
Answer:
[tex](b - c)(b + c - 10)[/tex]
Step-by-step explanation:
[tex] {b}^{2} - {c}^{2} - 10(b - c)[/tex]
What does factorising mean?
Factorising is a way of writing an expression as a product of its factors using bracketsWhat does expanding brackets mean?
Expanding brackets is multiplying every term inside the bracket by the term on the outside (remember, if you multiply a negative number by another negative number, the product will be positive)Now, expand the brackets in this expression:
[tex] {b}^{2} - {c}^{2} - 10b + 10c[/tex]
Apply the difference of squares formula to factor the expression even more (also, factor out -10 from the expression by putting it in front of the brackets):
[tex](b - c)(b + c) - 10(b - c)[/tex]
Now, factor out (b - c) from the expression:
[tex](b - c)(b + c - 10)[/tex]
Solve this problem by solving for x
Answers
Answer:
x = 3
Step-by-step explanation:
Check attachment. I did this lesson in class so I know.
please help my math work is so hard
Answers
Answer:
m∠1 = 48°
m∠2 = 132°
Step-by-step explanation:
We Know
m∠1 + m∠2 = 180°
Let's solve
(x + 26) + 6x = 180
x + 26 + 6x = 180
7x + 26 = 180
7x = 154
x = 22
Now we put 22 in for x and solve m∠1 and m∠2 !
m∠1 = (x + 26)
m∠1 = 22 + 26
m∠1 = 48°
m∠2 = 6x
m∠2 = 6(22)
m∠2 = 132°
if 21 of the people in the picture group and 13 of the people in the actual candy group failed to detect the switch, would you conclude that there is convincing evidence that the proportion who experience choice blindness is different for the two treatments (choice based on a picture and choice based on seeing the actual candy)? test the relevant hypotheses using a 0.01 significance level. (let p1 be the proportion who experience choice blindness based on a picture treatment, and p2 be the proportion who experience choice blindness based on seeing the actual candy treatment.)
Answers
The calculated z-value of 2.45 is less than the critical value of 2.58, we fail to reject the null hypothesis.
To test whether there is convincing evidence that the proportion of people who experience choice blindness is different for the picture group and actual candy group, we need to conduct a hypothesis test.
Let p1 be the proportion who experiences choice blindness based on a picture treatment, and p2 be the proportion who experiences choice blindness based on seeing the actual candy treatment.
Our null hypothesis is that there is no difference between the two proportions:
H0: p1 = p2
Our alternative hypothesis is that there is a difference between the two proportions:
Ha: p1 ≠ p2
We will use a two-sample z-test to test this hypothesis. The test statistic is:
z = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2))
where p = (x1 + x2) / (n1 + n2) is the pooled sample proportion, x1, and x2 are the number of people who experienced choice blindness in the picture and actual candy groups, respectively, and n1 and n2 are the sample sizes.
Using the given information, we can calculate the sample proportions as:
p1 = (21/50) = 0.42
p2 = (13/50) = 0.26
The pooled sample proportion is:
p = (21 + 13) / (50 + 50) = 0.34
The sample sizes are n1 = n2 = 50.
Substituting these values into the formula for the test statistic, we get:
z = (0.42 - 0.26) / sqrt(0.34*(1-0.34)*(1/50 + 1/50)) = 2.45
Using a standard normal distribution table, we can find the critical values for a two-tailed test with a significance level of 0.01:
[tex]z_crit = ±2.58[/tex]
Since our calculated z-value of 2.45 is less than the critical value of 2.58, we fail to reject the null hypothesis. Therefore, we do not have convincing evidence to conclude that the proportion of people who experience choice blindness is different for the picture group and actual candy group at a significance level of 0.01.
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GRADE 8
The following figure shows triangle XYZ. The length of XY is 19 units, and the length of YZ is 181 units.
Y
19
X
181
What is the value of
Z
Note: Figure not drawn to scale.
? Enter your answer as a fraction in the spaces provided.
YZ
Answers
The value of [tex]\frac{XZ}{YZ}[/tex] include the following: C. [tex]\frac{180}{181}[/tex]
What is Pythagorean theorem?In Mathematics and Geometry, Pythagorean's theorem is represented by the following mathematical equation:
a² + b² = c²
Where:
a, b, and c represent the side lengths of a right-angled triangle.
In order to determine the length of XZ in right-angled triangle XYZ, we would have to apply Pythagorean's theorem.
YZ² = XY² + XZ²
181² = 19² + XZ²
XZ² = 32,761 - 361
XZ = √32,400
XZ = 180 units
For the ratio, we have:
Ratio = XZ/YZ
Ratio = 180/181
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
a polynomial is factored using algebra tiles. an algebra tile configuration. 0 tiles are in the factor 1 spot and 0 tiles are in the factor 2 spot. 15 tiles are in the product spot in 3 columns with 5 rows: 1 is labeled x squared, 2 are labeled x, the 4 tiles below x squared are labeled negative x, and the 8 tiles below the x tiles are labeled negative. which polynomial was factored?
Answers
The polynomial that was factored using algebra tiles with an algebra tile configuration of 0 tiles in the factor 1 spot and 0 tiles in the factor 2 spot, and 15 tiles in the product spot in 3 columns with 5 rows with 1 labeled x squared, 2 are labeled x, the 4 tiles below x squared are labeled negative x, and the 8 tiles below the x tiles are labeled negative is: x² - 2x - 8.
When you factor a polynomial using algebra tiles, you arrange the tiles in the form of a rectangle. The area of the rectangle gives the product of the two binomials, while the sides of the rectangle give the sum of the two binomials.In this case, there are 15 tiles in the product spot, so the two factors must have a total of 15 terms.
However, since there are 0 tiles in both the factor 1 and factor 2 spots, both binomials must have a constant of 0. Therefore, the only possible arrangement for the tiles is: 1 x² tile, 2 x tiles, 4 negative x tiles, and 8 negative tiles.Now, we need to arrange these tiles in the form of a rectangle. The only possible arrangement is a rectangle with a length of 5 tiles (3 columns) and a width of 3 tiles (1 x² tile and 2 x tiles). The 4 negative x tiles are placed below the x² tile, and the 8 negative tiles are placed below the x tiles. This gives the polynomial: x² - 2x - 8.
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Write a function that models the data.
Answers
Quadratic function that models the given data points: [tex]y &= -7.5x^2 + 13.5x + 42[/tex].
How to write a function that models the data?
To model the data shown in the graph, we need to find a function that best fits the given data points. A polynomial is a common type of function used for this purpose. In this case, we can use a second-degree polynomial (a quadratic function) to fit the data.
[tex]y &= ax^2 + bx + c[/tex]
where a, b, and c are constants governing the shape and position of the parabola.
To find the values of a, b, and c that fit the given data points, we can use a system of equations. We can substitute the x and y values of each point into the equation of the quadratic function and get three equations:
[tex]a(0)^2 + b(0) + c &= 42 \\a(1)^2 + b(1) + c &= 21 \\a(2)^2 + b(2) + c &= 10.5 \\[/tex]
Simplifying these equations, we get:
c = 42
a + b + c = 21
4a + 2b + c = 10.5
Substituting c = 42 into the second equation, we get:
a + b = -21
Substituting c = 42 into the third equation and simplifying, we get:
4a + 2b = -73.5
Solving these two equations simultaneously, we get:
a = -7.5
b = 13.5
Substituting these values into the equation of the quadratic function, we get:
[tex]y = -7.5x^2 + 13.5x + 42[/tex]
This function models the data shown in the graph. We can verify this by plotting the function and the data points on the same graph and checking that they match.
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6. A square with a side of x is inside a square with a side of 4, as pictured below. Which expression represents the area of the shaded region in terms of x?
Answers
For given Squares, The area of Shaded region will be 16-x².
What are squares?
In geometry, a square is a two-dimensional shape that has four sides of equal length and four right angles (90-degree angles). Each side of a square is parallel to its opposite side, and the diagonals of a square bisect each other at right angles. The formula for the area of a square is A = s², where A is the area and s is the length of one side.
Now,
As Area of Square= side²
Area of shaded region=Area of Bigger square - Area of White Square
and Side of bigger square=4
Side of White Square = x
Then
A (Area of shaded region) = 4²-x²
A=16 - x²
Hence,
The area of Shaded region will be 16-x².
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HELP PLEASEEEEEEE NEED HEP NOWW
Answers
Answer:
99°
Step-by-step explanation:
180° - 36° - 63° = 81
360° - 180° - 81° = 99°
Emily and her four friends are splitting the cost of a vacation.
Each person cannot pay more that $200.
What could be the total cost of the vacation?
Answers
The total cost of the vacation could be any amount up to $1000, but it cannot exceed $1000.
What is finite and infinite set?A set with a particular, constrained number of elements is said to be finite. For instance, because it only has five items, the set "1, 2, 3, 4, 5" is a finite set. On the other hand, a set with an infinite number of items is called an infinite set. For instance, because it has no beginning or end, the set of all positive numbers 1, 2, 3, 4,... is an infinite set.
For the given amount of $200 split in 5 people the total cost of the vacation cannot exceed:
(5 people x $200/person = $1000).
Hence, the total cost of the vacation could be any amount up to $1000, but it cannot exceed $1000.
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in an evaluation of a stress management program, researchers randomly assigned subjects to two treatment groups and a control group. the results of the study showed that the two treatment groups multiple choice question. had fewer illnesses like colds and flu. had fewer strokes. had a reduction in blood pressure. reported fewer emotional outbursts.
Answers
The purpose of the study was to determine whether the stress management program had any effects on various health outcomes.
Researchers tested a stress program with 3 groups; treatment groups had fewer illnesses, strokes, lower blood pressure, and emotional outbursts. The researchers conducted an evaluation of a stress management program, in which they randomly assigned subjects to one of three groups: two treatment groups and a control group. The purpose of the study was to determine whether the stress management program had any effects on various health outcomes.
The results of the study indicated that both treatment groups experienced a number of positive health outcomes compared to the control group. Specifically, the treatment groups had fewer illnesses like colds and flu, fewer strokes, a reduction in blood pressure, and reported fewer emotional outbursts.
The findings of this study suggest that a stress management program may have multiple benefits for individuals' health, including reducing the risk of certain illnesses and improving emotional well-being. However, further research is needed to confirm these findings and to determine whether these effects are sustained over time.
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9,100 dollars is placed in a savings account with an annual interest rate of 5%. If no money is added or removed from the account, which equation represents how much will be in the account after 6 years?
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Answers
An equation represents how much will be in the account after 6 years is M = 9,100*[tex](1 + 0.05/1)^{1*6}[/tex]
What is an account ?
The formula to calculate the amount in a savings account after a certain number of years with no deposits or withdrawals is:
M = P*[tex](1 + r/n)^{n*t}[/tex]
Where:
P = Principal (initial amount)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Time in years
In this case, P = $9,100, r = 0.05 (5% as a decimal), n = 1 (interest is compounded annually), and t = 6 (years).
Using these values, we can calculate the amount in the account after 6 years as follows:
M = 9,100*[tex](1 + 0.05/1)^{1*6}[/tex]
M = 9,100*[tex](1.05)^{6}[/tex]
M = 9,100(1.3401)
M = $12,175.91
Therefore, the correct equation is:
M = 9,100*[tex](1 + 0.05/1)^{1*6}[/tex]
What is an interest?
Interest is the cost of borrowing money, usually expressed as a percentage of the amount borrowed, and is paid by the borrower to the lender. It can also be the amount earned on an investment or savings account.
Interest rates can vary depending on a variety of factors, including the current economic conditions, inflation, the borrower's creditworthiness, and the length of the loan or investment term.
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Complete question is: 9,100 dollars is placed in a savings account with an annual interest rate of 5%. If no money is added or removed from the account. An equation M = 9,100*[tex](1 + 0.05/1)^{1*6}[/tex] represents how much will be in the account after 6 years.