Dilate a triangle with vertices (0,0), (0,2) and (2,0) using the scale factor k=3. What is the value of the ratio (new to original) of the perimeters? the areas?

The ratio of the perimeters is ___.

The ratio of the areas is ___.

Dilate A Triangle With Vertices (0,0), (0,2) And (2,0) Using The Scale Factor K=3. What Is The Value

Answers

Answer 1

Answer:

Part a) The ratio of the perimeters is [tex]3[/tex]

Part b) The ratio of the areas is [tex]9[/tex]

Step-by-step explanation:

Part A) What is the value of the ratio (new to original) of the perimeters?

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x-----> the perimeter of the new triangle

y-----> the perimeter of the original triangle

[tex]z=\frac{x}{y}[/tex]

we have

[tex]z=3[/tex]

substitute

[tex]\frac{x}{y}=3[/tex]

Part B) What is the value of the ratio (new to original) of the areas?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> the area of the new triangle

y-----> the area of the original triangle

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=3[/tex]

substitute

[tex]\frac{x}{y}=3^{2}[/tex]

[tex]\frac{x}{y}=9}[/tex]

Answer 2

Answer:

Part a) The ratio of the perimeters is 3

Part b) The ratio of the areas is 9


Related Questions

A Circle Has a radius of six inches what is the exact length of an arc formed by a central angle measuring 45 degrees

Answers

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=6\\ \theta =45 \end{cases}\implies s=\cfrac{(45)\pi (6)}{180}\implies s=\cfrac{3\pi }{2}\implies s\approx 4.7[/tex]

How many tables are needed ~~~~~PLEASE HELP

Answers

Answer:

it would be 5 tables

Step-by-step explanation:

1:6

2:10

3:14

4:18

5:22

just count by 4

what’s the area
A. 64
B. 44
C. 30.25
D. 13.75

Answers

Answer:

B) 44

Step-by-step explanation:

Let's start with the triangles. Normally, when dealing with triangles, you would use the formula (B*H*1/2), but since there's two identical triangles, we can just do (B*H) and get the area for both:

2.5*5.5=13.75

Then to solve for the square, it is also (B*H):

5.5*5.5=30.25

At this point, to solve for the total area, you just add the areas together:

13.75+30.25=44

Hope this helps!

Answer: B. 44

Step-by-step explanation: The area of a rhombus is base times height. The height is 5.5 cm, and the base is 8 cm. To find the base, add 2.5 and 5.5.

8 x 5.5 = 44

The area is 44 cm^2

If g(x)=x^2+2find g (3)

Answers

Answer:

3^2 = 9

9+2 = 11

g(3)= 11

Step-by-step explanation:

ANSWER

[tex]g(3) = 11[/tex]

EXPLANATION

The given function is

[tex]g(x) = {x}^{2} + 2[/tex]

We substitute b x=3 into the function to obtain;

[tex]g(3) = {3}^{2} + 2[/tex]

Simplify;

[tex]g(3) = 9 + 2[/tex]

[tex]g(3) = 11[/tex]

Select the correct answer.

What would be the tax amount to be paid on $22,000 taxable income according to the marginal tax rate (tax rate below $9,225 is 10%, and between $9226 and $37,450 is 15%)?

A: $2536.50
B: $3123.25
C: $2838.75
D: $1225.25

Answers

Answer:

I'd go with B because it's closest, not sure if some context is missing to get an exact answer....

Step-by-step explanation:

22000 falls in the 15% tax rate bracket

Tax=income•rate

Tax=22000•(15/100)

Tax=3300

Answer:

The answer is C

Step-by-step explanation:

what is 4 apples per pound

Answers

Answer:

It actually really depends on the size of the apples, say 1 pound of aan apple should be approx 3 medium-sized apples, so maybe for 3 pounds of an apple it would be around 9 medium sized apples.

Depends on size of the apples

Given h(f)=-2(t+5)^2 +4, find h(-8)

Answers

Answer:

h(-8) = 22

Step-by-step explanation:

Plug  -8 in for t and simplify...

h(-8) = 2(-8 + 5)² + 4

    h(-8) = 2(-3)² + 4

        h(-8) = 2(9) + 4

          h(-8) = 18 + 4

             h(-8) = 22

Answer:

Step-by-step explanation:

Given h(f)=-2(t+5)^2 +4

There is an intermediate step which is

h(f) = -2(f + 5)^2 + 4

h(-8) = -2(-8 + 5)^2 + 4

h(-8) = -2(-3)^2 + 4

h(-8) = -2(9) + 4

h(-8) = -18 + 4

h(-8) = - 14

Ameri is standing 50 feet from the base of a building from where he stands the angle formed between the top of the building in the ground at his feet is 60 how tall is the building

Answers

Answer:

The answer would be...

Step-by-step explanation:

50 square root of 3 ft

Answer:

The answer is C.50 StartRoot 3 EndRoot ft

Step-by-step explanation:

FACTOR THE TRINOMIAL: x^2+6x+5
PLZZ HELP AND ANSWER W/ STEPS

Answers

Answer: (x + 1)(x + 5)

Step-by-step explanation:

Need to find two numbers whose product is the c-value (5) and whose sum is the b-value (6).

x² + 6x + 5

              ∧

            1 + 5 = 6    this works!

So the factors are:   (x + 1)(x + 5)

Which if the following best describes a pair of angles that combine to form a straight angle.

A. Vertical Angles
B. Supplementary Angles
C. Complementary Angles
D. Linear Pair

Answers

Answer:

The answer to this is B, because supplementary angles sum up to 180 degrees, which means it is a straight angle.

Answer:

Option B and D

Step-by-step explanation:

Given are four options and we have to select the one which form a straight angle.

The given options are

A. Vertical Angles  ... Vertical angles are formed when two lines intersect and hence cannot combine to form a straight angle.  Incorrect option.

B. Supplementary Angles ... Supplementary angles are a pair of angles which add upto 180 degrees and hence they form a straight angle. Correct option

C. Complementary Angles  ... These pair add up to 90 degrees and cannot combine to form a straight angle.  ..  Incorrect

D. Linear Pair ... A linear pair is a pair of angles formed on a straight line and hence correct option.

Which of these functions has an inverse function? Select all that apply.
y = x
y = x^2
y = x^3
y = x^4

Answers

ANSWER

y=x

y=x³

EXPLANATION

A function, f(x) has an inverse if and only if

[tex]f(a) = f(b) \Rightarrow \: a = b[/tex]

Thus, the function is one to one.

For y=x or

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

[tex]f(a) = f(b) \Rightarrow \: a = b[/tex]

Hence this function has an inverse.

For the function y=x² or f(x)=x².

[tex]f(a) = f(b) \Rightarrow \: {a}^{2} = {b}^{2} \Rightarrow \: a = \pm \: b[/tex]

This function has no inverse on the entire real numbers.

For the function y=x³ or f(x)=x³

[tex]f(a) = f(b) \Rightarrow \: {a}^{3} = {b}^{3} \Rightarrow \: a = b[/tex]

This function also has an inverse.

For y=x⁴ or f(x) =x⁴

[tex]f(a) = f(b) \Rightarrow \: {a}^{4} = {b}^{4} \Rightarrow \: a = \pm \: b[/tex]

This function has no inverse over the entire real numbers.

Answer:

The function [tex]x=y[/tex] and [tex]y=x^{3}[/tex] are inverse function.

Step-by-step explanation:

Function inverse definition:

If a provided function f(x) is mapped x to y, then the inverse of the provided function f(x) is mapped y to x.

Or  [tex]f(x)=f(y)\Rightarrow x=y[/tex]

Now, consider the function y = x.

Interchange the variables x and y.

[tex]x=y[/tex]

Now, solve [tex]x=y[/tex] for [tex]y[/tex].

[tex]x=y[/tex]

Therefore, this function has an inverse.

Consider the function [tex]y=x^{2}[/tex].

Interchange the variables x and y.

[tex]x=y^{2}[/tex]

Now, solve [tex]x=y^{2}[/tex] for [tex]y[/tex].

[tex]\pm \sqrt{x} =y[/tex]

Therefore, the function has no inverse.

Consider the function [tex]y=x^{3}[/tex].

Interchange the variables x and y.

[tex]x=y^{3}[/tex]

Now, solve [tex]x=y^{3}[/tex] for [tex]y[/tex].

[tex]\sqrt[3]{x}=y[/tex]

Therefore, the function has inverse.

Consider the function [tex]y=x^{4}[/tex].

Interchange the variables x and y.

[tex]x=y^{4}[/tex]

Now, solve [tex]x=y^{4}[/tex] for [tex]y[/tex].

[tex]\pm \sqrt[4]{x}=y[/tex]

Therefore, the function has no inverse.

Hence, the function [tex]x=y[/tex] and [tex]y=x^{3}[/tex] are inverse function.

if you horizontally stretch the quadratic parent function, f(x)=x^2, by a factor of 3, what is the equation of the new function?

Answers

Answer: [tex]g(x)=\frac{1}{9}x^2[/tex]

Step-by-step explanation:

By definition, he quadratic parent function [tex]f(x)=x^2[/tex] is the simplest form of a quadratic function.

By definition, if the fucntion is multiplied by the factor b and:

 |b|>0  the function is stretched.

If 0<|b|<1 the function is compressed.

Then the new function will have the form:

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

Therefore, keeping the above on mind, if b=3, then the new function is:

[tex]g(x)=(\frac{1}{3}x)^2[/tex]

[tex]g(x)=\frac{1}{9}x^2[/tex]

Answer: g(x)=(1/3(x))^2

Step-by-step explanation:

Find the missing part. l = 8, w = 4, h = 2 Find the diagonal (d) of the base.

Answers

pythagoras

a^2 = b^2 + c^2

a^2 = (8)^2 + (4)^2

a^2 = 64 + 16

a^2 = 80

[tex]a = \sqrt{80} [/tex]

Answer:

The length of the diagonal (d) = 4[tex]\sqrt{5}[/tex] units.

Step-by-step explanation:

We are given the length (l) = 8, width (w) = 4 and height (h) = 2.

Now we have to find the diagonal of the base.

The given figure is a rectangle box. The base of the rectangular box is a rectangle with the length (l) = 8 and the width(w) = 4

The length of the diagonal (d) = [tex]\sqrt{l^2 + w^2}[/tex]

d = [tex]\sqrt{8^2 + 4^2}[/tex]

d = [tex]\sqrt{64 + 16}[/tex]

d = [tex]\sqrt{80}[/tex]

d = [tex]\sqrt{16} \sqrt{5}[/tex]

d = 4[tex]\sqrt{5}[/tex]

So, the length of the diagonal (d) = 4[tex]\sqrt{5}[/tex] units.

Lines
AB
and
AC
tangent to circle k(O) at B and C respectively. Find BC, if m∠OAB=30°, and AB=5 cm.

Answers

Answer:

5 cm

Step-by-step explanation:

If AB is tangent to the circle k(O), then radius OB is perpendicular to segment AB.

If BC is tangent to the circle k(O), then radius OC is perpendicular to segment AC.

Consider two right triangles ABO and ACO. In these triangles:

AO is common hypotenuse;∠OBA=∠OCA=90°, because AB⊥OB, AC⊥OC;OB=OC as radii of the circle k(O).

By HL theorem, triangles ABO and ACO are congruent. Then

∠OAB=∠OAC=30°;AC=AB=5 cm.

Hence, ∠BAC=∠OAB+∠OAC=30°+30°=60°.

Consider triangle ABC, this triangle is isosceles triangle. In isosceles triangles angles adjacent to the base are congruent, thus

∠CBA=∠BCA=1/2(180°-60°)=60°.

Therefore, triangle ABC is an equilateral triangle, so BC=AB=AC=5 cm.

What is the slope of the line with the equation 3y+5x=4
Question 4 options:

-5


−53

35

3

Answers

I think none of these are right. It's Y=-5/3x +4/3

ANSWER

[tex] - \frac{5}{3} [/tex]

EXPLANATION

The given line has equation

[tex]3y + 5x = 4[/tex]

Rewrite the equation in the form:

[tex]y = mx + b[/tex]

Add -5x to both sides.

[tex]3y + 5x - 5x = - 5x + 4[/tex]

[tex]3y = - 5x + 4[/tex]

Divide through by 3.

[tex]y = - \frac{5}{3}x + \frac{4}{3} [/tex]

Comparing to the slope intercept formula,

[tex]m = - \frac{5}{3} [/tex]

The slope is

[tex] - \frac{5}{3} [/tex]

Mr. broun paid $3.30 in tax on a $55 motel bill. What percent of $55 was the Tax?

Answers

Answer:

That would be 6%.

Answer:

6%

Step-by-step explanation:

55(x)= 3.30

3.30/55 = .06

x=.06 which equals 6%

A very small town has only five residents with the following incomes (all in thousands): $33, $24, $22, $45, $99. Find the median income.

Answers

Answer:$33,000

Step-by-step explanation:

Answer:

a.33,000

Step-by-step explanation:


[tex] {x}^{2} - 64[/tex]

Answers

(x-8) (x+8) is the answer

Factored into binomials, this would be (x + 8)(x - 8).

The jacket is on sale for $36 which Is 80% of the original cost. What is the original price of the jacket?

Answers

43.20 dollars because it is 36$ + 80%

Answer:

45

Step-by-step explanation:

percent x whole = part

80%w = 36

.8w=36

divide .8 by both sides

w=45

Simply the expression 6x^2(3x)

Answers

Answer:

[tex]\large\boxed{6x^2(3x)=18x^3}[/tex]

Step-by-step explanation:

[tex]6x^2(3x)=(6\cdot3)(x^2x)\qquad\text{use}\ a^na^m=a^{n+m}\\\\=18x^{2+1}=18x^3[/tex]

what is the surface area formula for this shape and if you could explain that would help me a lot ​

Answers

Answer:

I think it's A

Step-by-step explanation:

The reason is because the circle is pi r ^2 but the wedge is some kind of fraction of a circle with degree 1, like area times circumference. The question should say, which of the following is the most probable formula for SA.

Answer:

[tex]\large\boxed{C.\ S.A.=\pi r^2+\pi rl}[/tex]

Step-by-step explanation:

It's a net of a cone.

The formula of a surface area of a cone:

[tex]S.A.=\pi r^2+\pi rl[/tex]

What is the pattern in the values as the exponents increase?

Answers

Answer:

Multiply the previous value by 2

Step-by-step explanation:

As the exponents increase,

(that is, they go from negative to positive)

-5,-4,-3,-2, -1,0

------------------------>

We see that each previous value is multiplied by a factor of 2

We can see the graph of the values in the picture below

Please help I will give brainliest please show work and find the volume of this odd looking pyramid

Answers

Answer:

206  2/3 ft³

Step-by-step explanation:

The volume of this solid is given by V = (1/3)(base area)(height).

Here, V = (1/3) (62 ft²) (10 ft ) = 206  2/3 ft³

Besides 6 and 1, what is one factor of 6?

Answers

Three times two equals six

Another factor of 6, besides 6 and 1, is 3. Factors are numbers that divide into another number without leaving any remainder. Both 2 and 3 are factors of 6 since 2 multiplied by 3 equals 6.

Besides 6 and 1, another factor of 6 is 3.

Factors are whole numbers that divide evenly into another number. For the number 6, the factors are 1, 2, 3, and 6. The process of factoring involves finding all numbers that you can multiply together to get the number in question. In this case, 2 multiplied by 3 equals 6.

We can also verify this by noting that dividing 6 by 3 gives us 2 with no remainder, confirming that 3 is indeed a factor of 6.

Write 33% as a fraction in simplest form

Answers

Answer: the answer to 33% is around 1/3

Step-by-step explanation:

Answer:

33/100

Step-by-step explanation:

There is no way to simplify

What is the third quartile of this data set? *I NEED THE HELP ASAP* thx

Answers

I think the answer is 44

A dinner plate has a diameter of 14 inches. Approximately how many square inches is the area of the plate?

Answers

Answer:

153.94 square inches

Step-by-step explanation:

A = Pi(r)^2

A = Pi(7)^2

A = Pi(49)

A = 153.93804

Answer: 153.938 [tex]in^{2}[/tex]

Step-by-step explanation:

π = 3.14 and d = diameter

* Hopefully this helps:) Mark me the brainliest:)

∞ 234483279c20∞

The bases of a trapezoid are 20 and 32 feet. The height of the trapezoid is 6 feet

Answers

Answer:

The Answer is 156

Step-by-step explanation:

A=(B1+B2)H/2

1) to find the area of a trapezoid you must First add the 2 bases

20+32= 52

2) Then Multiply the 2 bases sum by the Height

52 x 6 = 312

3) divide the product 312 By 2

312/2= 156

That is Your answer!

Hopes this helps!

For the area of a trapezoid use formula: Area = (BaseX+BaseY) times Height divided by 2.

so for this problem you’d plug in (20+32) times 6 then divide it by two.

20+32=52 times 6 equals 312

Divide by 2 and you get 156.

Area= 156

I need to answer this and also EXPLAIN how I got it. Help pls

Answers

Answer:

1+4*2=10

Step-by-step explanation:

1 + 4 is equal to 5 then multiply 5 by 2 and you get 10

Answer: x=−4y+10

Step-by-step explanation:

Let's solve for x.

x+4y=10

Step 1: Add -4y to both sides.

⇒x+4y+−4y=10+−4y

⇒x=−4y+10

Answer:

x=−4y+10

* Hopefully this helps:) Mark me the brainliest:)!!

Which expression represents the number of coins Sarah has.

Sarah has 16 coins, but spends some of them during the day.

A. C - 16
B. 16c
C. 16 - c
D. 16 + c

Answers

This answer gone be c.16-c

Answer:

is it 16 c or not

Step-by-step explanation:

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