50 POINTS
Triangle ABC and triangle CDE are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of CE?

A)
6 − 2
9 − 3
=
8 − 6
12 − 9

B)
6 − 2
9 − 3
=
12 − 6
8 − 9

C)
8 − 6
9 − 3
=
6 − 2
12 − 9

D)
9 − 3
6 − 2
=
8 − 6
12 − 9

Answer:

The number of faces is 29

Step-by-step explanation:

we know that

The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

[tex]V- E + F= 2[/tex]    

we have

[tex]V=16[/tex]

[tex]E=43[/tex]

substitute and solve for F

[tex]16- 43 + F= 2[/tex]

[tex]-27+F= 2[/tex]

[tex]F= 2+27[/tex]

[tex]F= 29[/tex]

Answer:

20 cm

Step-by-step explanation:

If the scale says that the building uses the scale or 1 cm: 6 meters. You pretty much just take 120 and divide by 6. You take that answer and turn the units in cm.  

Answer:

a = 12 ft, b = 12 ft

Step-by-step explanation:

The triangle is 45 45 90 right triangle

so a = b

Ratio of leg : hypo. = a : a√2

Given hypo = 12√2, so legs a = b = 12

Answer

a = 12 ft, b = 12 ft

Answer:

Step-by-step explanation:

The triangles are similar. Therefore the corresponding sides are in proportion:

[tex]\dfrac{x}{40}=\dfrac{4}{32}[/tex]               cross multiply

[tex]32x=(40)(4)[/tex]

[tex]32x=160[/tex]             divide both sides by 32

[tex]x=5[/tex]

Answer:

Step-by-step explanation:

2^(-3) = 1/2^3 = 1/8

A minus means put the number in the numerator if it was in the denominator.

A minus means put the number in the denominator it was in the numerator.

If there is no denominator, create one.

[tex]\bf girls:boys\qquad 5:7\qquad \cfrac{girls}{boys}=\cfrac{5}{7}\qquad ~\hspace{8em}\cfrac{\stackrel{\textit{girls}}{g}}{\underset{\textit{22 more than \underline{g}}}{g+22}}=\cfrac{5}{7} \\\\\\ 7g=5(g+22)\implies 7g=5g+110\implies 2g=110\implies g=\cfrac{110}{2}\implies g=55[/tex]

Answer:

Step-by-step explanation:

We write only the coefficients of the given equation inside the upside down symbol of division.

We first do synthetic substitution and then verify the result by putting g(4) and g(-5) in the original equation. Both should have the same result.

The questions are solved on the image attached.

Answer:

709, 1,708

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The answer is 1/2 because there are 3 even numbers and there are a total of six numbers which is 3/6 and when simplified it is 1/2.

Hoped this helped!

Answer:

1.25 cups or 1 1/4 cups

Step-by-step explanation:

Note that half of 12 muffins is 6 muffins.

If making 12 muffins requires 2.5 cups of flour, then halving both measurements results in       1.25 cups of flour per 6 muffins.

Answer:

Choosing a boy randomly in a class of 10 boys and 10 girls

Step-by-step explanation:

The probability of  choosing a boy randomly in a class of 10 boys and 10 girls is calculated as;

(number of boys)/ (total number of students in the class)

= 10/(10+10) = 10/20 = 1/2

The probability of drawing a heart randomly out of a pile of 4 hearts and 8 spades is calculated as;

4/(4+8) = 4/12 = 1/3

The probability of correctly choosing a random number between 1 and 10 is simply 1/10 since the numbers are have a uniform distribution and thus equally likely to be selected.

The probability of choosing a girl randomly in a class of 8 girls and 12 boys is calculated as;

(number of girls)/ (total number of students in the class)

= 8/20 = 2/5

Thus choosing a boy randomly in a class of 10 boys and 10 girls is the event which has a probability closest to 1.

Final answer:

Out of the given events, choosing a boy randomly in a class of 10 boys and 10 girls has the highest probability, which is 0.5. Therefore, this event's probability is closest to 1.

Explanation:

To answer which event has a probability closest to 1, we need to calculate the probability of each event:

Choosing a girl randomly in a class of 8 girls and 12 boys has a probability of
     8 girls / (8 girls + 12 boys) = 8/20 = 2/5 or 0.4.

Comparing these probabilities, choosing a boy randomly in a class of 10 boys and 10 girls has the highest probability, which is 0.5. Therefore, this event has a probability closest to 1.

Answer:

(4+3)x(7-1)=42

The correct position of the brackets is [tex](4+3)*(7-1)=42[/tex].

The given equation is:

               [tex]4+3*7-1=42[/tex]

          ⇒[tex](4+3)*(7-1)=42[/tex]

Let us consider LHS,

[tex](4+3)*(7-1)[/tex]

[tex]=7*(7-1)[/tex]

[tex]=7*6[/tex]

[tex]=42[/tex]

[tex]=RHS[/tex]

Hence, the above position of the bracket in the given statement is making it true.

Therefore, the correct position of the bracket is [tex](4+3)*(7-1)=42[/tex].

Brackets, in math, are a set of marks like parentheses that are used to enclose a set of terms. These terms may be within an algebraic expression, and in this case, the brackets are used to separate terms and denote the order of operations.

Square brackets (also called brackets, especially in American English) are mainly used to enclose words added by someone other than the original writer or speaker, typically in order to clarify the situation: He [the police officer] can't prove they did it.

Different symbols like these: (, ), [, ], {, and } in your math books. These symbols are called brackets. Brackets in mathematics serve a very important purpose; these symbols help us group different expressions or numbers together.

Learn more about brackets, refer to:

https://brainly.com/question/17654845

#SPJ2

Answer:

245 yards

Step-by-step explanation:

Answer:

245 yards

Step-by-step explanation:

You could say the tee is at (0, 0) and the hole lies on the x-axis.

The path of the ball is the straight-line so, y = tan(24°)x

215cos(24°) = 196.4

215sin(24°) = 87.4

The ball lands at coordinates (196.4, 87.4).

They say the ball lands 100 yards from the hole, the hole is on a circle of radius 100 that is centered at (196.4, 87.4).

Equation of the circle:

(x-196.4)² + (y-87.4)² = 100²

Since the hole is on the x-axis, it lies at the intersection of the circle and the line y = 0 so:

(x - 196.4)² + (0 - 87.4)² = 100²

x = 244.92

The distance between tee and hole is 245 yards.

Answer:

2.225

Step-by-step explanation:

to get your answer you would multiply .025 by 89

Please give brainliest!!!

Answer:

2.225

Step-by-step explanation:

2.5% converted to a decimal is 0.025

2.5% of 89 really means 2.5%*89 because in math, of means multiply.

89*0.025=2.225

You have to multiply by the decimal because the percent is a proportion in reality.

Think about it this way:

Since 2.5% of 89 is 2.225, 97.5% of 89 has to be 89-2.225, which is 86.775

and it is:

89*0.975=86.775

This is because the percentage is equal to 1 in whole.

0.025+0.975=1 or 2.5%+96.5%=100%

Answer:

14.1 in³

Step-by-step explanation:

Your expression for the volume was correct, except that it lacked units of measurement.

The volume is V = (1/3)π(1.5 in)²(6 in) = 14.1 in³

The volume of the cup will be 14.1 cubic inches. Thus, the correct option is B.

Let h be the height of the cone and A be the base area of the cone. Then the volume of the cone will be given as,

V = 1/3 × πr²h

A paper cup in the shape of an inverted cone is 6 inches tall and 3 inches in diameter.

The volume of the cup is calculated as,

V = 1/3 × π(1.5)²(6)

V = 14.1 cubic inches

Thus, the correct option is B.

More about the volume of the cone link is given below.

https://brainly.com/question/1984638

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Answer:

Answer:

yes

Step-by-step explanation:

to find the surface area, you need to find the area of all 6 sides using the dimensions given. each visible side has an opposite side that has the same dimensions.

1) 6*2=12

2) 6*2=12

3) 9*2=18

4) 9*2=18

5) 9*6=54

6) 9*6=54

then, you have to add all 6 sides together.

12+12+18+18+54+54

24+36+108

60+108

168 cm squared is the surface area

Answer:

90%

Step-by-step explanation:

If you are going to find out the percent of the car that do not have 4 wheel drive, you take the total amount of car that passed though the stoplight which is 100% . You take this 100% and then subtract the 10% to get the final answer 90%. 90% of the cars do not have 4 wheel drive.

To find the percentage of cars without four-wheel drive, subtract the percentage of cars with four-wheel drive from the total. Since 10% of cars have four-wheel drive, 90% do not.

If 10% of the cars have four-wheel drive, then the percentage of cars without four-wheel drive is the remainder when the total percentage (100%) is reduced by the percentage of those that do have four-wheel drive.

To calculate this, we subtract the percentage of cars with four-wheel drive from the total percentage:

100% - 10% = 90%

Therefore, 90% of the cars do not have four-wheel drive.

ANSWER

The image is located at (5,-6)

EXPLANATION

The rule for reflection over the y-axis is to negate the x-coordinates.

This implies that,

[tex](x,y)\to (-x,y)[/tex]

If the point located at (-5, -6) is reflected over the y-axis, the coordinates of the image is obtained by negating the x-coordinate.

Therefore

[tex]( - 5, - 6)\to (5, - 6)[/tex]

The image is located at (5,-6)

Answer:

The correct answer option is (5, -6).

Step-by-step explanation:

We are given the following coordinates of a point:

[tex] ( - 5 , - 6 ) [/tex]

If this point is reflected through y axis, what will be the coordinates of its image?

Reflection through y-axis means that the sign of the x coordinate will be changed so we get:

[tex] ( - 5 , -6 ) [/tex] [tex] \implies [/tex] (5, -6)

Answer:

The answer is the attached figure

Step-by-step explanation:

* Lets revise the equation of the circle

- The center-radius form of the circle equation is

  (x – h)² + (y – k)2 = r², where the center is the point (h, k)

  and the radius is r.

- This form of the equation is helpful, since you can easily find the

  center and the radius.

* Now lets solve the problem

- The equation of the circle is (x + 2)² + (y - 0.5)² = 16

* Lets compare it with form above

∵ (x - h)² = (x + 2)²

∴ -h = 2 ⇒ × -1

∴ h = -2

∵ (y - k)² = (y - 0.5)²

∴ -k = -0.5 ⇒ × -1

∴ k = 0.5

∴ The center of the circle is (-2 , 0.5)

∵ r² = 16 ⇒ take √ for both sides

∴ r = √16 = 4

∴ The radius of the circle is 4 units

* Now lets look to the answer to find the circle whose center is

 (-2 , 0.5) and radius 4 units

∴ The answer is the attached figure

* From the graph:

- The center of the circle is (-2 , 0.5)

- The horizontal diameter is between -6 and 2, then the length

 of the diameter = 2 - -6 = 8

∵ The radius = 1/2 the diameter

∴ The raduis = 1/2 × 8 = 4 units

Answer:

it is the second answer choice

Step-by-step explanation:

hope it helps!

Hello!

-7 will be your answer.

Let’s first substitute in each of the choices below.

-17+-5 Does Not equal -12 so we know it’s not The first one

-7+-5=-12 We have our Answer but let’s just check the others just so we know.

7+-5 is the same thing as 7-5 so it will be 2.

And 17+-5 is the same thing as subtracting 5 so that will be 12.

Our answer is the second one

ANSWER

B. The functions f(x) and g(x) because f(g(x))=g(f(x))=x

EXPLANATION

The given functions are:

[tex]f(x) = 2x - 2[/tex]

and

[tex]g(x) = \frac{1}{2}x + 1[/tex]

If f(x) and g(x) are inverses, then

f(g(x))=x

[tex]f(g(x))=f( \frac{1}{2} x + 1)[/tex]

[tex]f(g(x))=2( \frac{1}{2}x + 1) - 2[/tex]

Expand the parenthesis to obtain,

[tex]f(g(x))=x + 2- 2[/tex]

[tex]f(g(x))=x[/tex]

Also,

[tex]g(f(x)) = g(2x - 2)[/tex]

[tex]g(f(x)) = \frac{1}{2} (2x - 2) + 1[/tex]

[tex]g(f(x)) = x - 1+ 1[/tex]

[tex]g(f(x)) = x [/tex]

Hence f(x) and g(x) are inverses

Answer: Option B

Then The functions f(x) and g(x) are inverses because [tex]f(g(x))=g(f(x))=x[/tex]

Step-by-step explanation:

To answer this question we must make the composition of f (x) and g (x)

We found

[tex]f (g(x))[/tex]

We know that

[tex]f(x) = 2x-2\\\\g(x) = \frac{1}{2}x + 1[/tex]

By definition if two functions f and g are inverses then it follows that:

[tex]f(g(x)) = g(f(x)) = x[/tex]

So if [tex]f(g(x)) = x[/tex] f and g are inverse

To find  [tex]f(g(x))[/tex] enter the function g(x) within  the function f(x) as shown below

[tex]f(g(x))= 2( \frac{1}{2}x + 1)-2\\\\f(g(x))= x + 2 -2\\\\f(g(x))= x[/tex]

Now

[tex]g(f(x))= \frac{1}{2}(2x-2) + 1\\\\g(f(x))= x-1 + 1\\\\g(f(x))= x[/tex]

Observe that

[tex]f(g(x))=g(f(x))=x[/tex]

Then The functions f(x) and g(x) are inverses because [tex]f(g(x))=g(f(x))=x[/tex]

This is least to greatest

2 2/5 or 2.40

2.45

2 2/3

2 2/5 , 2.45 , 2 2/3

Answer:

2 2/3

Step-by-step explanation:

2 2/3 = 2.666...

2.45 = 2.45

2 2/5 = 2.4

From least to greatest:

2 2/5, 2.45, 2 2/3

The greatest of the three numbers is 2 2/3

Answer:

Base = 5 cm

Height = 20 cm

Step-by-step explanation:

Points to remember

Area of triangle = bh/2

Where b - base of triangle

h - Height of triangle

To find the Height and Base of given triangle

It is given that,area of a triangle piece of stained glass is 50 centimeters

the height of the triangle is four times the base

h = 4b

Area = bh/2

50 = (b * 4b)/2

100 = 4b²

b² = 100/4 = 25

b =√25 = ±5

b = 5 then h = 4b = 4 * 5 = 20

Base = 5 cm and Height = 20 cm

ANSWER

base=5 cm, height = 20cm

EXPLANATION

The area of a triangle is

[tex]A = \frac{1}{2} bh[/tex]

From the question, A=50 and h=4b

We substitute into the formula to get;

[tex] \frac{1}{2} b \times 4b =5 0[/tex]

This implies that,

[tex]2 {b}^{2} = 50[/tex]

[tex] {b}^{2} = 25[/tex]

Take positive square root to get;

[tex]b = \sqrt{25} [/tex]

[tex]b = 5[/tex]

The base is 5 cm and the height is 20 cm.

Answer:

[tex]\large\boxed{x^{-10}y^8=\dfrac{y^8}{x^{10}}}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\left(x^{-4-(-9)}y^{1-5}\right)^{-2}=(x^5y^{-4})^{-2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=(x^5)^{-2}(y^{-4})^{-2}=x^{(5)(-2)}y^{(-4)(-2)}=x^{-10}y^8\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{y^8}{x^{10}}[/tex]

Answer:

Step-by-step explanation: its b

First, you'd have to decompose the shape. The way I decomposed it was by splitting the shape into a small rectangle and a large one. The formula for the rectangles is 6 times 3 and 6 by 9. You multiply 6 by 3 and get 18; then you multiply  6 by 9 and get 54. Lastly, you simply add 18 and 54. This gives you an answer; 72.

Answer:

Reasonable domain is [1.375,3].

Step-by-step explanation:

Given function is [tex]f\left(t\right)=-16t^2+44t+12[/tex].

Now we need to find about what is the reasonable domain of the graph of the function [tex]f\left(t\right)=-16t^2+44t+12[/tex] when the basketball falls from its maximum height to the ground.

Compare with [tex]at^2+bt+c[/tex], we get a=-16 and b=44

then t-coordinate of vertex [tex]t=-\frac{b}{2a}=-\frac{44}{2\left(-16\right)}=1.375[/tex]

Then that means maximum height of the ball occurs when time t=1.375 seconds.

Now let's find time when ball falls on ground so set f(t)=0

[tex]f\left(t\right)=-16t^2+44t+12[/tex]

[tex]-16t^2+44t+12=0[/tex]

[tex]4t^2-11t-3=0[/tex]

[tex]\left(4t+1\right)\left(t-3\right)=0[/tex]

[tex]4t+1=0[/tex] or [tex]t-3=0[/tex]

[tex]4t=-1[/tex] or [tex]t=3[/tex]

[tex]t=-0.25[/tex] or [tex]t=3[/tex]

Time can't be negative so we use t=3 only

Hence reasonable domain is [1.375,3].

Answer:

26 is your answer.

Step-by-step explanation:

Perimeter is adding all the numbers around the shape up like: 11 + 3 + 6 + 3 + 3 = 26

Hope i have helped you!

Answer:

40  ft

Step-by-step explanation:

The perimeter of the shape is 1) the perimeter of the rectangle with sides of 11 and 3 ft plus 2) two sides of 6 ft each.

1) the perimeter of the rectangle: 22 + 6 = 28

2) the perimeter of two sides: 2x6= 12

3) The perimeter of the shape: 28 +12 =40

Answer:

48=14+2w

An equation for this with no values would be 2w+2l=p

Step-by-step explanation:

I hope this helps if it does please add brainliest

Answer:

A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Common examples of "unit rate" follow:

miles per hour (mph).  How many miles are covered in 1 hour of driving?

25 cents/pen:  each pen costs 25 cents each.

Suppose I know I can pack 1/4 box in 20 minutes.  How many boxes can I pack in 1 hour?  That would be a unit rate.  To find it, write out the ratio

1/4 box                                                                                 60 min

-------------   and multiply this by the conversion factor    ---------------

 20 min                                                                                  1 hour

... which results in  3/4 box per hour (a unit rate)