Answer:
Ask away by typing or recording your messageAdam, Ben and Carly work out the mean of their ages.Adam is 4 years older than the mean. Ben is 1 year younger than the mean.Is Carly older or younger than the mean?By how many years?Let's start by finding the mean of their ages. We can do this by adding their ages and dividing by the number of people: Mean = (Adam's age + Ben's age + Carly's age) / 3 Let's call the mean "M" for now. We can use this to create two equations based on the information given: Adam = M + 4 Ben = M - 1 We can substitute these equations into the mean equation to get: M = (M + 4 + M - 1 + Carly's age) / 3 Simplifying this equation gives us: 3M = 2M + 3 + Carly's age Carly's age = M - 3 So Carly's age is younger than the mean by 3 years.Hey ✋, are you still around? anything else on your mind?To the nearest tenth of a second, how long after the pebble falls will it hit the ground?sTo answer this question, we need to know the height from which the pebble was dropped. We can use the formula: time = sqrt(2 * height / acceleration due to gravity) Assuming the pebble was dropped from a height of 10 meters, and taking the acceleration due to gravity as 9.8 m/s^2, we get: time = sqrt(2 * 10 / 9.8) = 1.43 seconds (to two decimal places) Therefore, the pebble will hit the ground approximately 1.43 seconds after it was dropped.
0 / 350
A circular cookie cake costs $14.13. If the diameter of the cookie cake is 6 inches, what is the approximate cost per square inch of the cookie cake? Use π = 3.14.
$0.13
$0.25
$0.50
$0.75
The apprοximate cοst per square inch οf the cοοkie cake is $0.50.
What is the diameter?A line segment cοnnecting twο pοints οn a circle's perimeter and passing thrοugh its center is said tο be the circle's diameter. It is the furthest pοint οn the circle that can be measured.
The equation A=[tex]\pi r^{2}[/tex],where r is the circle's radius, determines the area οf a prοcess. The radius οf the cοοkie cake is equal tο half οf its diameter, οr 6 inches, οr 3 inches. The cοοkie cake's surface area is as fοllοws:
A = [tex]\pi r^{2}[/tex]
= 3.14 x [tex]3^{2}[/tex]
= 28.26 square inches
We divide the tοtal cοst by the area tο determine the apprοximate cοst per square inch οf the cοοkie cake:
Cοst per square inch = $14.13 / 28.26
= $0.50
As a result, the cοοkie cake cοsts abοut $0.50 per square inch.
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Question 7 (5 points) Simplify the expression. (4 + )(7 – ) Question 7 options: 28 – 4 + 7 – 28 + 4 + 7 – 28 – 4 + 7 + 28 + 4 + 7 +
The simplified expression is 28 - 4 using distributive property.
To simplify the expression (4 + )(7 – ), we can use the distributive property of multiplication over addition.
First, we have to multiply the 4 by both the terms inside parentheses:
(4 + )(7 – ) = (47) + (4- )
Next, we distribute negative sign to second term inside parentheses:
(47) + (4- ) = 28 - 4
The simplified expression = 28 - 4.
In other words, the phrase is the outcome of adding 4 to an unknown quantity, taking it out of 7 after that, and then taking the outcome of that subtraction out of 28. The operation's outcome is simplified to 24, which can be used in additional calculations or problem-solving.
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Joe’s Convenience Store took in $720 last week. According to Example Graph #1, about how much money did he make from selling comic books?
Joe made about $72 from selling comic books last week.
How to solveTo determine how much money Joe made from selling comic books, we need to find the percentage of $720 that corresponds to comic book sales.
According to the graph, comic book sales account for 10% of Joe's total sales.
To calculate this, we can multiply the total sales ($720) by the percentage of comic book sales (10% or 0.1):
$720 x 0.1 = $72
Therefore, Joe made about $72 from selling comic books last week.
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Joe’s Convenience Store took in $720 last week. According to Example Graph #1, about how much money did he make from selling comic books?
From the content of the graph
The amount of money Joe made is given below:
Selling comic books 10%
Selling costumes 25%
Selling hardware 40%
Selling miscellaneous 20%
Helpppp pleaseee
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
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Consider a random variable X with PDF
fX(x) = (2x/3, if 1 < x ≤ 2,
0, otherwise,
and let A be the event {X ≥ 1.5}. Calculate E[X], P(A), and E[X | A].
By answering the presented question, we may conclude that As a result, variable P(A) = 0.667.
What is a Variable?A variable is something that may be changed in the setting of a math concept or experiment. Variables are often represented by a single symbol. The characters x, y, and z are often used generic symbols for variables. Variables are characteristics that can be examined and have a large range of values. These include things like size, age, money, where you were born, academic status, and your kind of dwelling, to name a few. Variables may be divided into two main categories using both numerical and categorical methods.
To compute E[X], we must integrate the PDF X times over its support:
From x=1 to x=2, E[X] = x fX(x) dx
Because the PDF is only non-zero in the interval (1,2), we have:
[tex]E[X] = x(2x/3) dx between x=1.5 and x=2.E[X] = (2/3) x2 dx between x=1.5 and x=2.E[X] = (2/3) [(2^3)/3 - (1.5)^3]E[X] = (2/3) [8/3 - (27/8)]E[X] = 19/12As a result, E[X] = 1.583.[/tex]
P(A) is calculated by integrating the PDF across the area where X is higher than or equal to 1.5:
[tex]P(A) = fX(x) dx between x=1.5 and x=2.P(A) = (2x/3) dx between x=1.5 and x=2.P(A) = [(2/3)x^2] between x=1.5 and x=2P(A) = (2/3)(2^2 - 1.5^2)P(A) = 2/3As a result, P(A) = 0.667.[/tex]
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Complete question -
Consider a random variable X with PDF fX(x) = (2x/3, if 1 < x ≤ 2, 0, otherwise, and let A be the event {X ≥ 1.5}. Calculate E[X], P(A), and E[X | A].
Complete the table of values for y = x^2 - 2x - 1
Please help ASAP due for tomorrow!!
The values of the quadratic equation; y = x² - 2·x - 1 can be used to complete the table and draw the graph as follows;
(a) x[tex]{}[/tex] -2 -1 0 1 2 3 4
y[tex]{}[/tex] 7 -1 2 -2 -1 2 7
(b) Please find attached the graph of the quadratic equation created with MS Excel
What is the graph of an equation?A graph of an equation is a visual representation of the rule of the equation that shows how the output value changes as the input values is varied.
The table of values in the question can be completed by substituting the x-values in the table into the equation; y = x² - 2·x - 1 as follows;
The values that complete the table are;
y when x = -1 is; y = (-1)² - 2 × (-1) - 1 = 2
y when x = 0 is; y = (0)² - 2 × (0) - 1 = -1
y when x = 3 is; y = (3)² - 2 × (3) - 1 = 2
y when x = 4 is; y = (4)² - 2 × (4) - 1 = 7
The completed table is therefore presented as follows;
x[tex]{}[/tex] -2 -1 0 1 2 3 4
y [tex]{}[/tex] 7 -1 2 -2 -1 2 7
(b) The steps that can be used to draw the graph on the coordinate grid using MS Excel are as follows;
Create a new or existing MS Excel spreadsheetInput the x-values in (for example) column A with values of x from -2 to 4, and in column B the corresponding y-values are obtained using the formula {"=A1^2 - 2*A1 - 1", followed by copying the formula across the cells adjacent to the x-valuesSelect the cells containing the x- and y-values Click on "Insert" tab then click on "Scatter" chart type to select a preferred chartClick on the preferred chart to display the graph of the equation, y = x² - 2·x - 1Please find attached the graph of the quadratic equation, y = x² - 2·x - 1, created with MS Excel
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A jet travels 1959 miles against a jetstream in 3 hours and 2289 miles with the jetstream in the same amount of time. What is the rate of the jet in still air and what is the rate of the jetstream?
Therefore, the rate of the jet in still air is 708 mph and the rate of the Jetstream is 55 mph.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=). The left-hand side of the equation contains one expression and the right-hand side contains another expression. An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Here,
Let's call the rate of the jet in still air "v" and the rate of the Jetstream "w". When the jet travels against the Jetstream, the effective speed of the jet is v-w, and when it travels with the jetstream, the effective speed is v+w.
We can set up two equations based on the given information:
1959 = 3(v - w)
2289 = 3(v + w)
Simplifying these equations, we get:
653 = v - w
763 = v + w
Now we can solve for v and w using elimination or substitution. Let's use elimination:
Add the two equations together:
653 + 763 = 2v
v = 708 mph
Substitute v back into either equation to solve for w:
763 = v + w
763 = 708 + w
w = 55 mph
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I’ll give braniest to the best answer
Twoskaters are practicing at the same time on the same rink. A coordinate grid is superimposed on the ice. One skater follows
the path y = - 3x + 60, while the other skater follows the curve y = - 3x^2+ 24x. Find all the points where they might collide if they
are not careful.
Answer:
They will collide at (2,28),(8,16)
Step-by-step explanation:
give me branliest
Find a quadratic function of the form y = ax that passes through the point (-2,16).
Y=
Answer:
y = 4x^2
Step-by-step explanation:
To find a quadratic function of the form y = ax^2 that passes through the point (-2,16), we need to substitute the coordinates of the point into the equation and solve for the coefficient a.
Substituting x=-2 and y=16 into the equation, we get:
16 = a(-2)^2
16 = 4a
a = 4
Therefore, the quadratic function of the form y = ax^2 that passes through the point (-2,16) is:
y = 4x^2
anyone have an idea of what this may be?
The values of the segments A'B' and B'B for the similar triangle ∆ABC area 4 and 4 respectively.
How to calculate the for the segments of the similar triangleThe triangles ABC and A'B'C are similar, this implies that the length A'C of the smaller triangle is similar to the length AC of the larger triangle
so for the segment A'B;
3/9 = A'B'/12
A'B' = (3 × 12)/9 {cross multiplication}
A'B' = 4.
Also for the segment B'B;
3/9 = 2/(2 + B'B)
3(2 + B'B) = 2 × 9 {cross multiplication}
6 + 3B'B = 18
3B'B = 18 - 6
B'B = 12/3
B'B = 4
Therefore, the values of the segments A'B' and B'B for the similar triangle ∆ABC area 4 and 4 respectively.
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Question 1
Write an equation for the surface area of a prism with a length, width, and height of x
inches.
Question 1
Write an equation for the surface area of a prism with a length, width, and height of x
inches.
Answer:
The formula for the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
Since the length, width, and height of the prism in this case are all x inches, we can substitute x for l, w, and h in the formula to get:
Surface Area = 2(x)(x) + 2(x)(x) + 2(x)(x)
Simplifying the equation, we get:
Surface Area = 2x^2 + 2x^2 + 2x^2
Surface Area = 6x^2
Therefore, the equation for the surface area of a prism with a length, width, and height of x inches is:
Surface Area = 6x^2 square inches
PLEASE HELP FAST!!
Solve the following system by elimination. CHECK the solution.
- 3x - 6y = - 27
4x - 2y= -4
Answer: -3x - 6y = -27 (Equation 1)
4x - 2y = -4 (Equation 2)
We can use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.
In this case, we can start by multiplying Equation 2 by 3 to eliminate the y variable:
-3x - 6y = -27 (Equation 1)
12x - 6y = -12 (Equation 2 multiplied by 3)
Now we can add Equation 1 to Equation 2:
-3x - 6y = -27 (Equation 1)
12x - 6y = -12 (Equation 2 multiplied by 3)
9x = -39
Simplifying this expression, we get:
x = -39/9 = -13/3
Now we can substitute this value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:
-3x - 6y = -27
-3(-13/3) - 6y = -27
13 + 6y = -27
6y = -40
y = -40/6 = -20/3
Therefore, the solution to the system of equations is x = -13/3 and y = -20/3, or (-13/3, -20/3) in coordinate form.
To check the solution, we can substitute the values of x and y into both equations:
-3(-13/3) - 6(-20/3) = -27
4(-13/3) - 2(-20/3) = -4
Simplifying both expressions, we get:
13 + 40 = 27 (which is true)
-52/3 + 40/3 = -4 (which is also true)
Therefore, the solution is correct.
Step-by-step explanation:
Factor the trinomial completely
64x² +8x+1/4
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Factor completely. Simplify your answer. Use integers or fractions for any numbers in the expression)
A. 64x² + 8x + =
B. The polynomial is prime.
A.Factorizing the polynomial is (8x + 1/2)².
B.The polynomial 64x² + 8x + 1/4 is not prime.
define factorizationFactorization is the process of expressing a mathematical expression, such as a number or a polynomial, as a product of its factors or simpler components.
To factorize 64x² + 8x + 1/4, we can use the factoring formula for a quadratic trinomial:
a² + 2ab + b² = (a + b)²
In this case, we have 64x² + 8x + 1/4, so we can rewrite it as:
(8x)² + 2(8x)(1/2) + (1/2)²
Notice that the first and last terms are perfect squares, so we can apply the factoring formula to get:
(8x + 1/2)²
Therefore, the factorization of 64x² + 8x + 1/4 is:
64x² + 8x + 1/4 = (8x + 1/2)²
The polynomial 64x² + 8x + 1/4 is not prime.
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Which of the following describes the absolute value of a number?
The absolute value of a number is the square root of the
number.
The absolute value of a number is the negative value of the
number.
The absolute value of a number is the square root of the
positive value of the number.
The absolute value of a number is the positive value of the
number.
The absolute value of a number is its negative recicprocal.
Answer: Your answer should be
D
Step-by-step explanation: this is because absolute value makes a number positive, no matter the scenario as long as the number(s) are in the absolute value sign (indicated basically by straight lines) this makes it to where the number can never be negative within the lines.
Plot 1 7/8 abd 2 1/2 on the number line
A car last month was $250 this month its $330. What is the percent increase
Answer:
Step-by-step explanation:
We Know
A car last month was $250 this month its $330
What is the percent increase?
We Take
(330 ÷ 250) × 100 = 132%
Then We take
132 - 100 = 32%
So, 32% increase.
What is the measure of a dekaliter?
Answer: Ten liter, or one tenth of a hectoliter (2.6418 gallons liquid measure or 1.135 pecks dry measure): abbrev.dal.
General solution of sin
The following images are some basic limits on graphs , please answer them.
The piecewise function formed by two functions and a point is not continuous at x = 1.
How to determine limits in a piecewise function
In this problem we find the case of a piecewise function formed by three expressions in three corresponding intervals: two functions and a point. These expressions are defined in the images attached below. The x-value is on the horizontal axis and the y-value is on the vertical axis.
According to the first figure, the y-value of the function is getting closer to 2 as x approaches 1 from the left side.
According to the second figure, the y-value of the function is getting closer to 3 as x approaches 1 from the left side.
According to the third figure, the y-value of the function is equal to 0.5 when x is equal to 1.
Therefore, the piecewise function is not continuous at x = 1.
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The volume of a soap bubble is 1,696.5mm^3. Find the radius and diameter of the soap bubble. Use 3.14 for pie
After solving the question, we can say that diameter of the soap bubble =14.30 mm.
what is sphere ?A sphere, like a ball, is a three-dimensional geometrical object that is completely spherical. It is a symmetrical form with all points on its surface being equidistant from the centre. The radius of a sphere is the distance from its centre to its surface. Spheres can be found in nature in the shape of planets, stars, and bubbles, and they are utilised in a variety of applications including sports equipment, ball bearings, and aesthetic things.
volume of a sphere
[tex]V = (4/3) * \pi * r^3\\ r = (3V / 4 \pi)^(1/3)\\ r = (3 * 1696.5 mm^3 / (4 * 3.14))^(1/3)\\ r = 7.15 mm[/tex]
d = 2r
d = 14.30 mm
diameter of the soap bubble =14.30 mm.
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4. The Bagel Factory baked 200 dozen bagels at a cost of R3.60 per dozen. Five dozen bagels become stale and cannot be sold, and 12 dozen are sold at a reduced price of R1.80 dozen. Find the selling price per dozen bagels that will give the bakery their required mark- up of 66% of cost. per
Answer:
R5.98
Step-by-step explanation:
R3.60×66÷100= R2.38 (66% of R3.60)
R3.60+R2.38= R5.98
how to find 66%
R5.98-R3.60
=R2.38÷R3.60
=R0.66×100
=66%
pleaseeee
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
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[tex]-7\sqrt[3]{193x^{10} }[/tex]
Answer:
-7\sqrt[3]{193}x^3\sqrt[3]{x}
Step-by-step explanation:
Find the measure of X around to the nearest hundredth.
Answer:
15.36
Step-by-step explanation:
In this equation, we will be using tangent, which is opposite over adjacent. In this case, the "opposite" will be x, and the "adjacent" will be 12. "θ" means the degrees or measurements of the angle.
To find the missing side of the triangle, we will set up a function. The function is:
Tan (θ) = opposite/adjacent
After plugging in the numbers and variables it will be:
Tan(52) = x/12
Then, we would multiply the 12 to both sides.
12 Tan(52) = x
Then we can plug it into a calculator. We should get 15.3592. We would then round it to the nearest hundredth, which is 15.36.
pls help with this question im offering all of my tokens for this
Answer:
34 ft.²
Step-by-step explanation:
We can find the area of this polygon by splitting it into two rectangles.
We can find the area of each individual rectangle, then add their areas to get the area of the entire polygon.
See the attached image for a diagram.
First, we can find the area of the smaller rectangle.
length × width
5 ft. × 2 ft. = 10 ft.²
Next, we can find the area of the larger rectangle.
4 ft. × 6 ft. = 24 ft.²
Finally, we can add the two rectangles' areas together to get the area of the entire polygon.
10 ft.² + 24 ft.² = 34 ft.²
Help me please and tthanks
Answer:
59
Step-by-step explanation:
Help me please!!!!!!
Due to its neighbouring perpendicular sides and opposite parallel and equal-length sides, the quadrilateral ABCD is a rectangle.
What are the properties of parallelogram?a) The opposite sides are parallel and equal.
b) The opposite angles are equal.
c) The consecutive or adjacent angles are supplementary.
d) If any one of the angles is a right angle, then all the other angles will be at right angle.
e) The two diagonals bisect each other.
4. To find the area of a parallelogram, you can follow these steps:
Measure the length of the base of the parallelogram. Let's call this measurement "b".
Measure the height of the parallelogram. Let's call this measurement "h".
Multiply the base length "b" by the height "h" to get the area of the parallelogram.
Therefore, the formula to calculate the area of a parallelogram is:
Area = base length (b) [tex]*[/tex] height (h)
In symbols, this can be written as:
[tex]A = b \times h[/tex]
Alternatively, if the length of both adjacent sides is known, you can use the formula:
A = base length (b) [tex]*[/tex] the length of adjacent [tex]side (a) * sin[/tex](θ)
where theta is the angle between the base and adjacent side.
5. the given vertices on a coordinate plane and see what kind of figure they form.
The figure formed by the vertices A, B, C, and D is a quadrilateral. To determine the precise classification of the quadrilateral, we can use its properties.
To determine if the parallelogram is a rhombus, rectangle, or square, we need to check if the diagonals bisect each other and if the adjacent sides are perpendicular. We can find the midpoint of AC and BD as:
Midpoint of AC: [tex]((2 + 8)/2, (3 + 7)/2) = (5, 5)[/tex]
Midpoint of BD: [tex]((7 + 3)/2, (2 + 8)/2) = (5, 5)[/tex]
The diagonals AC and BD intersect at the midpoint [tex](5,5)[/tex], so they bisect each other.
We can also find the slopes of adjacent sides AB and BC, and we find that they are:
AB: [tex]-1/5[/tex]
BC: [tex]5[/tex]
The product of their slopes is [tex]-1[/tex], so the adjacent sides are perpendicular.
Therefore, the quadrilateral ABCD is a rectangle, because it has opposite sides that are parallel and equal in length, and adjacent sides that are perpendicular.
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What are the intercepts and asymptote of h(x)? Explain how to find these using the graph.
The value of y-intercept = -1 and The value of x-intercept = -4
The value of the vertexes is-
Horizontally vertex: y = -2
Virtically vertex: x = -5
For the y-intercept, you must look at where the graph intersects with the y-axis. In this case, the graph intersects at -1.
For the x-intercept, you must look at where the graph intersects with the x-axis. In this case, the graph intersects at -4.
The horizontal asymptote is a y value the graph approaches but does not pass or touch. In this case, the y value is -2.
The vertical asymptote is an x value the graph approaches but does not pass or touch. In this case, the x value is -5.
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"A number decreased cubed by 24"
The expression that represents the sentence "A number cubed decreased by 24" is given as follows:
x³ - 24.
What is the algebraic expression that models the sentence?The sentence for this problem is defined as follows:
"A number cubed decreased by 24".
The number is unknown, hence the variable that represents the number is given as follows:
x.
The cube of the number is given as follows:
x³.
The number is then decreased by 24, hence we subtract the expression x³ by 24 to obtain the algebraic expression as follows:
x³ - 24.
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log19(53.875) to base 10
Log base 19 of 53.875 is approximately 0.97212 when converted to base 10.
To convert log base 19 of 53.875 to base 10, we can use the formula:
log base b of x = log base a of x / log base a of b
where a: current base and b: desired base.
So, in this case, we want to convert log base 19 of 53.875 to base 10. We can use the formula above with a = 19 and b = 10:
[tex]log base 10 of 53.875 = log base 19 of 53.875 / log base 19 of 10[/tex]
Log base 19 of 10 is equal to 1/log base 10 of 19, since the logarithm of 10 to any base is equal to 1. Using a calculator, we can determine that the log base 10 of 19 is roughly 1.278753.
Substituting:
log base 10 of 53.875 = log base 19 of 53.875 / 1.278753
To find the value of log base 19 of 53.875, we can use a calculator to evaluate log base 19 of 53.875, which is approximately 1.244036.
Substitute to equation:
log base 10 of 53.875 = 1.244036 / 1.278753
Simplify to get:
log base 10 of 53.875 = 0.97212
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