Answer:
x = − 2 + √ 7 , − 2 − √ 7
Step-by-step explanation:
Answer:
x = +/- 2 +/- √7
Step-by-step explanation:
solve for x, Give your answer as a fraction or decimal rounded to the nearest hundredth.
Using the fact that the triangles are similar, we will see that:
x = 5.626
How to find the value of x?On the image we can see two triangles, such that one is inscribed on the other.
Just because of that, it is obvious that the two triangles are similar.
And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:
3/x = 8/15
The quotient is "left side over the bottom side"
We can solve that equation for x:
3/x = 8/15
3 = (8/15)*x
(15/8)*3 = x
45/8 = x
5.625 = x
That is the value of x.
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When it was raining, Elliott drove for 120 miles. When the rain stopped, he drove
20 mph faster than he did while it was raining. He drove for 300 miles after the
rain stopped. If Elliott drove for a total of 10 hours, how fast did he drive while it
was raining?
Answer:
[tex]\boxed{22}.[/tex]
Step-by-step explanation:
Since Elliott drove for a total of 10 hours, and he drove for 120 miles while it was raining and 300 miles after the rain stopped, we know that he drove for a total of 120 + 300 = <<120+300=420>>420 miles.
If he drove for a total of 10 hours and covered a distance of 420 miles, then his average speed was 420 miles / 10 hours = <<420/10=42>>42 mph.
Since Elliott drove 20 mph faster after the rain stopped than he did while it was raining, then we know that his speed while it was raining was 20 mph slower than his average speed of 42 mph. That means his speed while it was raining was 42 mph - 20 mph = <<42-20=22>>22 mph.
Given: quadrilateral MATH; M(-5,-2), A(-3,2),
T(3,2) and H(1,-2)
Prove: MATH is a parallelogram
State the formula you will be using.
Show all work.
Answer:
MATH is not a parallelogram
Step-by-step explanation:
(sqrt means squareroot)
To prove that quadrilateral MATH is a parallelogram, we can use the following formula:
A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent.
In other words, if the lengths of the sides opposite each other in a quadrilateral are the same, then the quadrilateral is a parallelogram.
To prove that MATH is a parallelogram, we need to show that both pairs of opposite sides are congruent.
The first pair of opposite sides consists of segment MA and segment TH. To show that these sides are congruent, we can use the Distance Formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points that define the line segment.
Substituting the coordinates of points M and A, we get:
d = sqrt((-3 - (-5))^2 + (2 - (-2))^2)
= sqrt((-3 + 5)^2 + (2 + 2)^2)
= sqrt(8^2 + 4^2)
= sqrt(64 + 16)
= sqrt(80)
= 8.944
Substituting the coordinates of points T and H, we get:
d = sqrt((1 - 3)^2 + (-2 - 2)^2)
= sqrt((-2)^2 + (-4)^2)
= sqrt(4 + 16)
= sqrt(20)
= 4.472
Since 8.944 is not equal to 4.472, we cannot conclude that MA and TH are congruent. Therefore, MATH is not a parallelogram.
Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?
Find the total tax using the expanded expression. Did you get the same answer as you did by evaluating the original expression?
PLEASE HELP
Answer:
Are you on I X L?
Step-by-step explanation:
I apoligize but try googling 5% of 50
Answer:
the total tax is 4.50 dollars, yes it is the same because they are basically the same equation.
Step-by-step explanation:
What does r equal?
Answer: r = ________
Draw the image of quadrilateral ABCD under the translation (x, y) to (x-7, y+1).
help me please!
What is the area when the diameter is 16?
201.06 square units (rounded to 2 decimal places) is the area of the given circle.
The formula for the area A of a circle is A = πr², where r is the radius of the circle and π is the famous, well-known irrational number pi equal to 3.14159 (rounded to 5 decimal places).
Given that the circle's diameter is 16, and that a circle's radius is equal to half its diameter, the following conclusions can be drawn:
r = d/2
= 16/2
= 8
A=πr2
AND HALF THE DIAMETER IS THE RADIUS (r)
r=8
A= πr2 = π (8) squared = 64 * π = 200.96
or,
Now, substituting the values of r and π into the formula for the area of a circle, we get
A = πr²
= (3.14159)(8²)
= (3.14159)(64)
= 201.06 square units (rounded to 2 decimal places) is the area of the given circle.
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I will mark you brainlist!
Answer:
1. 2 runners
2. 25 runners
3. 24%
4. 15 runners
5. 60%
6. uh I think it's asking the same thing as 3, so 24%?
please help i will give brainlist!!
Answer:
1157.09
Step-by-step explanation:
Find m/R.
P
(3x + 5)°
2
(8.x-12)
S
8x-12+3x+5=180(sum of straight angles)
8x+3x-12+5=180
11x-19=180
11x=180-19
11x=161
x=161÷11
Step-by-step explanation:
sum of straight angles are 180
XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3 find the length of arc XZ
4π
Step-by-step explanation:As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:
A = [tex]\frac{1}{2}[/tex] x b x h -------------(i)
Where;
A = 18[tex]\sqrt{3}[/tex]
b = XZ = base of the triangle
h = YZ = height of the triangle = 6
Substitute these values into equation(i) and solve as follows:
18[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2}[/tex] x b x 6
18[tex]\sqrt{3}[/tex] = 3b
Divide through by 3
6[tex]\sqrt{3}[/tex] = b
Therefore, b = XZ = 6[tex]\sqrt{3}[/tex]
Now, assume that the circle is centered at O;
Triangle XOZ is isosceles, therefore the following are true;
(i) |OZ| = |OX|
(ii) XZO = ZXO = 30°
(iii) XOZ + XZO + ZXO = 180° [sum of angles in a triangle]
=> XOZ + 30° + 30° = 180°
=> XOZ + 60° = 180°
=> XOZ = 180° - 60°
=> XOZ = 120°
Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;
[tex]\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}[/tex]
[tex]\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}[/tex]
[tex]\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}[/tex]
[tex]\frac{1}{12} = \frac{1}{2|OZ|}[/tex]
[tex]\frac{1}{6} = \frac{1}{|OZ|}[/tex]
|OZ| = 6
The radius of the circle is therefore 6.
Now, let's calculate the length of the arc XZ
The length(L) of an arc is given by;
L = θ / 360 x 2 π r ------------------(ii)
Where;
θ = angle subtended by the arc at the center.
r = radius of the circle.
In our case,
θ = ZOX = 120°
r = |OZ| = 6
Substitute these values into equation (ii) as follows;
L = 120/360 x 2π x 6
L = 4π
Therefore the length of the arc XZ is 4π
Mr. Starnes and his wife have 6 grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them.
a. Give a probability model for this chance process.
b. Find the probability that at least one of the two girls (Piper and Sedona) get to go to the show.
Probability that one of the girls (Piper as well as Sedona) will be able to attend the performance is one in five.
Explain the term Probability?Any probability is a mathematical representation of the likelihood or chance that a specific event will take place. All these proportions ranging from 0 to 1 and percentages varying from 0% through 100% can be used to describe probabilities.For the stated question-
There are 6 grandkids.There are two girls.Out of the six grandchildren, two are to be chosen.
There are 6C2 different ways to choose 2 out of 6 grandchildren.
6C2 = 6! / (6 - 2)!*2!
6C2 = 15
There are 15 different ways to choose two grandchildren out of six.There are 2C1 different ways to choose 1 of the 2 girls.
2C1 = 2
There are two different ways to choose one of the two girls.
Number of methods for choosing both girls = 2C2
Number of methods for choosing both girls equals one.
Probability of choosing 1 of the 2 grandchildren is 1/15.
The likelihood of choosing both girls is 2/15.
Probability that one of the females (Piper and Sedona) will be able to attend the performance is:
= 1/15 + 2/15.
= 3/15.
Thus, Probability that atleast one of girls (Piper as well as Sedona) will be able to attend the performance is one in five.
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3. Target is selling two popular toys this year for kids. Toy x is a Power Treads and toy y is an
America Girl Doll. Target pays $8 each for the Power Treads and $14 each for the America Girl
Doll. One unit of Power Treads yields a profit of $2 while an America Girl Doll yields a profit of
$3. Target estimates that no more than 2,000 toys will be sold-every month and does not plan
to invest more than $20,000 in inventory for these toys. How many units of each type of toys
should be stocked in order to maximize the monthly total profit?
What are the vertices? What are the constraints? What is the profit equation?
Answer:
10
Step-by-step explanation:
heyy! i’ll give brainliest please help.
Answer:
The answer is B.
Step-by-step explanation:
Its B because the lower the altitude the higher the pressure, and in this case the air towards the ground is being moved up, which is letting cold air sink back down.
find the geometric means of the following sequence -7, ?, ?, ?, ?, -1, 127, 357
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Given:
The quadratic equation is:
[tex]10m^2-7m+3=0[/tex]
To find:
The solutions for the given equation by using the quadratic formula.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]10m^2-7m+3=0[/tex]
Here, [tex]a=10,b=-7,c=3[/tex]. Using the quadratic formula, we get
[tex]m=\dfrac{-(-7)\pm \sqrt{(-7)^2-4(10)(3)}}{2(10)}[/tex]
[tex]m=\dfrac{7\pm \sqrt{49-120}}{20}[/tex]
[tex]m=\dfrac{7\pm \sqrt{-71}}{20}[/tex]
[tex]m=\dfrac{7\pm i\sqrt{71}}{20}[/tex] [tex][\because \sqrt{-a}=i\sqrt{a},a>0][/tex]
Therefore, the solution set of the given equation is [tex]\left\{\dfrac{7- i\sqrt{71}}{20},\dfrac{7+ i\sqrt{71}}{20}\right\}[/tex]. Hence, the correct option is D.
two cards are drawn from a shuffled deck of 52 cards. what is the probability that the first card is a king and the second is a heart
On solving the provided question, we can say that the required probability is = 13/204.
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
probability of 1st card = 1/4
since the card is not replaced
total number remaining cards = 51
second card 13/51
the required probability is = 13/204
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What is the name of longest side of triangle?
Answer: Hypotenuse
Step-by-step explanation:
The Hypotenuse is known as the longest side of a triangle.
Ervin scores half as many points in a game as Larry. If Larry scored x points, how many points did Larry score if Ervin scored 16?
The score of Larry is 32 points.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
Ervin scores half as many points in a game as Larry.
If Larry scored x points,
then the points of Ervin are x/2 points.
Here, x = 16,
So,
Ervin's points = Larry's points
The equation is,
16 = x/2
x = 16(2)
x = 32 points
Therefore, 32 points are the score of Larry.
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if 4 times a number is increased by 6, the result is less than 15 than the square of the number. find the number
Answer:
n = 7
n = -3
Step-by-step explanation:
4n+6 = n²-15
4n = n² - 21
n² - 4n - 21 = 0
(n-7)(n+3) = 0
n = 7
n = -3
Pretty easy middle school math
Answer:
3
Step-by-step explanation:
If we use pythagoras theorem we know a^2+b^2=c^2
c being the hypoeneuse
so we half the 8 to get the dimensions of the right angle so the bottom side is 4cm and then we use the hypotenuese which is 5 and plug it in so
a^2+4^2=5^2
a^2+16=25
-16 from both sides
a^2=9
square root both sides
a=3
Identify a method of developing systems that is well-suited to traditional project management tools and technique
The waterfall model has equivalent flexibility to other approaches. suitable for conventional project management tools and methods.
The waterfall model of the software development life cycle is the greatest technique for creating systems.
This includes the following elements:
1. The requirements phase, which takes into account the needs needed to build the product
2. The product's design is created
3. The programmers who wrote the code to put the product into action built the product.
4. The product is examined and all flaws are fixed to ensure that it responds correctly to inputs.
5. The systems are periodically maintained to ensure continued operation and proper output
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Does anyone know how to do this
The experimental probability of spinning a number less than 3.
7/25.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The total number of spuns.
= 8 + 6 + 9 + 11 + 9 + 7
= 50
Total number of spuns of the spinner less than 3.
= 8 + 6
= 14
The probability of spinning a number less than 3.
= 14/50
= 7/25
Thus,
The probability is 7/25.
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The sports store sells 5 t-shirts and 10 pairs of shorts for 132.50. The next day they sell 3 t-shirts and 5 pairs of shorts for 69.50. What is the cost of a t-shirt?
Answer:
A) 5t + 10s = 132.50
B) 3t + 5s = 69.50
We multiply B) by -2
B) -6t -10s = -139.00 then we add A)
A) 5t + 10s = 132.50
-t = -6.50
t-shirt price = 6.50
Source: http://www.1728.org/unknwn2.htm
Step-by-step explanation:
George invests $2000 in an account with an interest rate of 5%. Which best represents this?
Y=2000(1.05)^x
Y=2000(.05)^x
Y=2000+ 0.5^x
Y=2000(.95)^x
Answer:
Y=2000(1.05)^x
Step-by-step explanation:
This is because 2000 is the fixed beginning value and should stay by itself.
While the interest rate of 5% is 1.05 because the amount of money George will have will be going up based on the fixed beginning value.
HELP! (25 POINTS AND CROWN FOE THE RIGHT ANSWER!!)
The area of the rectangle is 15cm, the length is xt2cm, the width is xcm , find the value of x
You now have the total length for the remaining 2 sides. This number divided by 2 is the width.
How do you find the length and width of a rectangle when given the area?When given an area of A and a length of h, its width w is equal to A/h.
Its width is w = P/2h if you have the perimeter P and length h.
If you know the length h and the diagonal d, you can calculate the width using the formula w = (d2h2).
The height, area, diagonal, or perimeter of your rectangle are the two measurements that the width of a rectangle calculator uses to calculate the width of your rectangle. We'll also demonstrate various formulas for calculating the width of a rectangle based on the information at hand. The width of a rectangle can be determined in a variety of ways, depending on the information at hand.
A=w×h
P=(w+h)×2
d = w 2 +h 2
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What is the area of a rectangle with a length of 14.4 inches and a width that is one-third of the length?
A. 43.2 in.
B. 51.84 in.
C. 69.12 in.
D. 103.68 in.
If you give the answer, please make sure it is correct and one of the answers on the group of answer choices! Thank you! :)
The area of the rectangle is 69.12 square inches.
What is the area of the rectangle?
We know that for a rectangle of length L and width W, the area is given by the formula:
A = L*W
Here we know that the length is 14.4 inches, then:
L = 14.4 in
And the width is one-third of that length, then we can write:
W = (1/3)*L
Replacing the value of L, we will get:
W = (1/3)*14.4 inches
W = 4.8 inches.
Then the area of the rectangle is:
A= (4.8 in)*(14.4 in) = 69.12 in²
That is the area of the rectangle.
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Ray had a block of wood in the shape of a rectangular prism. The block and it's dimensions are shown below:
Answer:
[tex](a)\ Area = 24in^2[/tex]
[tex](b)\ Area = 60in^2[/tex]
Step-by-step explanation:
Given
See attachment for the dimension of the block
Solving (a): Area of the front face
From the attachment, the front face has the following dimension.
[tex]Length = 4in[/tex]
[tex]Width = 6in[/tex]
The area is calculated as:
[tex]Area = Length *Width[/tex]
[tex]Area = 4in * 6in[/tex]
[tex]Area = 24in^2[/tex]
Solving (b): Area of the top and bottom faces
The top and bottom faces have the same dimension
From the attachment, the top face has the following dimension.
[tex]Length = 5in[/tex]
[tex]Width = 6in[/tex]
The area of the top is calculated as:
[tex]Area = Length *Width[/tex]
[tex]A_1 = 5in * 6in[/tex]
[tex]A_1 = 30in^2[/tex]
The area of the top and the bottom faces is:
[tex]Area = 2 *A_1[/tex] ---- because the top and bottom faces have the same dimension
[tex]Area = 2 *30in^2[/tex]
[tex]Area = 60in^2[/tex]
Find the measure of x.
48°
Answer:
c
Step-by-step explanation:
use that the sum of angles in a triangle is 180°
you know 2 angles so you can find the third
x= 180 -90-48 =42°
Answer:
c. x = 42 degrees
Step-by-step explanation:
A right triangle is 90 degrees
90 - 48 = 42
So, the measure of x is 42 degrees