algebra2 help please ​

the scale factor is 2.

because

if you look at the length AL in the smaller shape, it is 2 squares.

now if you look at the length AL in the enlarged shape, it is 4 squares.

to find the scale factor, do 4 ÷ 2 which is 2.

therefore the scale factor is 2

Answer:

The correct option is 2. The scale factor is 2.

Step-by-step explanation:

The coordinates of preimage are A(1,2), T(0,0), K(4,1) and L(3,2).

The coordinates of image are A'(2,4), T'(0,0), K'(8,2) and L'(6,4).

If a figure dilated by scale factor k with center at origin then the rule of dilation is

[tex](x,y)\rightarrow (kx,ky)[/tex]

[tex]A(1,2)\rightarrow A'(2,4)[/tex]

[tex]k=\frac{\text{x coordinate of image}}{\text{x coordinate of preimage}}[/tex]

[tex]k=\frac{2}{1}[/tex]

[tex]k=2[/tex]

Therefore the scale factor is 2 and the correct option is 2.

Answer:

28π and 196π

10π and 25π

2500π

A = C/4π

Step-by-step explanation:

The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. The area of the circle is the amount inside the circle and is found using A = πr². Substitute the relevant values in each situation into the formulas to find the circumference and area.

if the radius of a circle is 14 units, what is its circumference? what is its area?

Substitute r = 14.

C = 2πr = 2π(14) = 28π

A = πr² = π(14)² = 196π

if a circle has diameter 10 units, what is its circumference? what is its area?

Substitute r = 5.

C = 2πr = 2π(5) = 10π

A = πr² = π(5)² = 25π

if a circle has circumference 100π units, what is its area?

Substitute C = 100π to find the radius. Then substitute the radius into the are formula.

C = 2πr

100π=2πr

100 = 2r

50 = r

A = πr² = π(50)² = 2500π

if a circle has circumference c, what is its area in terms of c?

Cole the circumference formula for r. Then substitute the expression into the area formula.

C = 2πr

r = C / 2π

A = πr² = π(C/2π)² = πC/4π² = C/4π

1. Circumference: [tex]\(28\pi\)[/tex]units, Area: [tex]\(196\pi\)[/tex] square units.

2. Circumference: [tex]\(10\pi\)[/tex]units, Area: [tex]\(25\pi\)[/tex]square units.

3. Area: [tex]\(2500\pi\)[/tex]square units.

4. Area: [tex]\(\frac{C^2}{4\pi}\)[/tex]  square units.

Let's go through each question one by one, using the formulas for the circumference and area of a circle.

1. If the radius of a circle is 14 units, what is its circumference? What is its area?

  - The circumference [tex]\( C \)[/tex] of a circle is given by the formula:

[tex]\[ C = 2\pi r \][/tex]

    where [tex]\( r \)[/tex] is the radius.

    Given [tex]\( r = 14 \)[/tex] units, we have:

[tex]\[ C = 2\pi \times 14 = 28\pi \text{ units} \][/tex]

  - The area [tex]\( A \)[/tex]of a circle is given by the formula:

[tex]\[ A = \pi r^2 \][/tex]

    Given [tex]\( r = 14 \)[/tex] units, we have:

[tex]\[ A = \pi \times 14^2 = \pi \times 196 = 196\pi \text{ square units} \][/tex]

2. If a circle has diameter 10 units, what is its circumference? What is its area?

  - The diameter [tex]\( d \)[/tex] is related to the radius by [tex]\( d = 2r \)[/tex]. Therefore, the radius [tex]\( r \)[/tex] is:

[tex]\[ r = \frac{d}{2} = \frac{10}{2} = 5 \text{ units} \][/tex]

  - Using the circumference formula [tex]\( C = 2\pi r \):[/tex]

[tex]\[ C = 2\pi \times 5 = 10\pi \text{ units} \][/tex]

  - Using the area formula [tex]\( A = \pi r^2 \):[/tex]

[tex]\[ A = \pi \times 5^2 = \pi \times 25 = 25\pi \text{ square units} \][/tex]

3. If a circle has circumference [tex]\( 100\pi \)[/tex] units, what is its area?

  - Given the circumference [tex]\( C = 100\pi \),[/tex] we can find the radius [tex]\( r \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]

[tex]\[ 100\pi = 2\pi r \][/tex]

    Dividing both sides by [tex]\( 2\pi \):[/tex]

[tex]\[ r = \frac{100\pi}{2\pi} = 50 \text{ units} \][/tex]

  - Using the area formula [tex]\( A = \pi r^2 \):[/tex]

[tex]\[ A = \pi \times 50^2 = \pi \times 2500 = 2500\pi \text{ square units} \][/tex]

4. If a circle has circumference [tex]\( C \),[/tex] what is its area in terms of [tex]\( C \)[/tex]

  - Given the circumference [tex]\( C \),[/tex] we can express the radius [tex]\( r \)[/tex] in terms of [tex]\( C \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]

[tex]\[ r = \frac{C}{2\pi} \][/tex]

  - Using the area formula [tex]\( A = \pi r^2 \)[/tex] and substituting [tex]\( r = \frac{C}{2\pi} \):[/tex]

[tex]\[ A = \pi \left( \frac{C}{2\pi} \right)^2 = \pi \left( \frac{C^2}{4\pi^2} \right) = \frac{\pi C^2}{4\pi^2} = \frac{C^2}{4\pi} \][/tex]

Answer:

P(n) = 0.5

Step-by-step explanation:

For two events which are independent, we use the multiplication rule which states P (A and B) = P(A) * P(B). Substitute P(m) = 0.4 and P(m and n) = 0.2 into this formula.

P (m and n) = P(m) * P(n)

0.2 = 0.4*P(n)

Divide by 0.4 on both sides.

0.2 / 0.4 = P(n)

0.5 = P(n)

Answer:

  72

Step-by-step explanation:

1 out of 10 do not recommend naps, so 9 times as many do recommend naps.

  9 × (8 doctors) = 72 doctors . . . . . recommend naps

Answer:

264 cubic meters

Step-by-step explanation:

The sea turtle habitat at the zoo has a total volume of 264 cubic meters.

To find the total volume of the sea turtle habitat, which consists of two connected aquariums, you can calculate the volume of each aquarium separately and then add them together.

For the first aquarium:

- Length = 6 meters

- Width = 4 meters

- Height = 2 meters

The volume of the first aquarium is calculated as:

Volume_1 = Length * Width * Height

Volume_1 = 6 m * 4 m * 2 m

Volume_1 = 48 cubic meters

For the second aquarium:

- Length = 8 meters

- Width = 9 meters

- Height = 3 meters

The volume of the second aquarium is calculated as:

Volume_2 = Length * Width * Height

Volume_2 = 8 m * 9 m * 3 m

Volume_2 = 216 cubic meters

Now, to find the total volume of the sea turtle habitat, you add the volumes of the two aquariums together:

Total Volume = Volume_1 + Volume_2

Total Volume = 48 cubic meters + 216 cubic meters

Total Volume = 264 cubic meters

So, the total volume of the sea turtle habitat at the zoo is indeed 264 cubic meters, as provided.

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Answer:

16.033 min

Step-by-step explanation:

We can write Newton's Law of Cooling as

T = Tₐ + (T₀ - Tₐ)e^(-kt), where

Tₐ = ambient temperature of the surroundings

T₀ = initial temperature of the object

k = the cooling constant

t = the time

(1) Calculate the cooling constant

Data:

T =   110 °F

T₀ = 180 °F

Tₐ =  70 °F

 t =   20 min

Calculation:

110 = 70 + (180 - 70)e^(-k×20)

40 = 110e^(-20k)

0.363 64 = e^(-20k)

-1.0116 = -20k

k = 0.050 580 min⁻¹

(2)After adding cream

(a) Calculate T₀  

2 oz × 40 °F + 12 oz × 180 °F = 14 oz × T₀

80 °F + 2160°F = 14T₀

2240 °F = 14T₀

T₀ = 160 °F

(b) Calculate the time to cool to drinking temperature

110 = 70 + (160 - 70)e^(-0.050 580t)

40 = 90e^(-0.050 580t)

0.444 44 = e^(-0.050 580t)

-0.810 93 = -0.050580t

t = 16.033 min

It will take 16.033 min for the mixture to reach drinking temperature

To determine the time it takes for the mixture to reach drinking temperature, we first calculate the initial temperature of the mixture after adding 2 ounces of 40°F cream to the 180°F coffee, which turns out to be 165°F. Then, according to Newton's Law of Cooling, the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F would be the same as the time it took for the original coffee to cool from 235°F to 180°F, given the cooling constant doesn't change when we add the cream. Therefore, the mixture will take approximately 20 minutes to reach drinking temperature.

To determine the time it takes for the mixture to reach drinking temperature, we first need to calculate the initial temperature of the mixture. When you add 2 ounces of 40°F cream to the 180°F coffee, the temperature of the mixture instantly becomes the weighted average of the temperature of the coffee and of the cream. Thus, we have:

(12 * 180 + 2 * 40) / (12 + 2) = 165°F.

Now we need to calculate the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F. According to Newton's Law of Cooling, the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. If we assume that the proportionality constant (or the cooling constant) doesn't change when we add the cream, then the time it takes for the mixture to cool from 165°F to 110°F will be the same as the time it took for the original coffee to cool from 235°F (165 + 70) to 180°F (110 + 70), which is 20 minutes. We can conclude that the mixture will take approximately 20 minutes to reach drinking temperature.

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Answer:

230.4

feet

Explanation:

arc length  

=

circumference  

×

fraction of circle

×

×

×

×

=

2

π

r

×

165

360

×

×

×

×

=

2

×

π

×

80

×

165

360

×

×

×

×

=

230.4

feet to nearest tenth

Step-by-step explanation:

The length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft

Since the distance between the two cars is the length of an arc, we need to know what the length of an arc is.

The length of an arc is given by L = Ф/360 × 2πr where

Given that for the ferris wheel

Substituting the values of the variables into the equation, we have

L = Ф/360 × 2πr

L = 140°/360 × 2π × 30 ft

L = 14/36 × 60π ft

L = 14/3 × 5π ft

L = 70π/3 ft

L = 219.91 ft/3

L = 73.3 ft

So, length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft

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1+y (greater than or equal to symbol) 6

Answer:

I dont really know the answer.. but ill try; if its wrong I am so sorry;

Step-by-step explanation:

First you must get the area of a circle, which is; A= pi r squared

and all you have to do is fill it in like this;

A= 3.14 x 2.0

           ^

    A= 6.28

The first month has the equation raised to 11 which is the number of months left in the period.

So each month the equation would be the same except it would be raised to 1 less than the previous month.

Month 2 = 50(1.003)^10

Month 3 = 50(1.003)^9

Month 4 = 50(1.003)^8

Month 5 = 50(1.003)^7

Month 6 = 50(1.003)^6

Month 7 = 50(1.003)^5

Month 8 = 50(1.003)^4

Month 9 = 50(1.003)^3

Month 10 = 50(1.003)^2

Month 11 = 50(1.003)^1

Month 12 = 50(1.003) ( the last month would not be raised to anything)

Answer:

600

Step-by-step explanation:

its 50 X 12

thats how you would solve that

What is the length of the actual car in feet and inches? 4/5 ft 48/72in

Answer:

The answer is five.

Step-by-step explanation:

A pyramid with a square base has one square face and there are four triangle faces, so there are five in total.

I hope this helped! :-)

Number of faces of pyramid with a square base is 5.

Hence option A is correct.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Since we know that

A pyramid having square base have,

Number of square face = 1

Number of triangular face = 4

Hence total face in this triangle is,

= 1+4

= 5

Hence total faces = 5.

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distributive property because u need to mulptiply the number outside with the parentheses

Answer:

A)Distributive property

Step-by-step explanation:

This is because you need to multiply

Destructimous had 6 ultra power blasts.

The total number of blasts Destructimous has is:

Total blasts = Sonic blasts + Heat rays

Total blasts = 7 + 13

Total blasts = 20

Now, we know that Destructimous has a 2/7 chance of using its ultra power blast. To find out how many ultra power blasts it fires, we calculate 2/7 of the total blasts:

Ultra power blasts = (2/7) * Total blasts

Ultra power blasts = (2/7) * 20

Ultra power blasts = 40/7

Now, since we can't have a fraction of a blast, we need to round this number to the nearest whole number. In this case, 40/7 is approximately 5.71, so when rounded, it's 6.

So, Destructimous had 6 ultra power blasts.

-------------------------------------

To assess the evidence of Hypothesis testing, the students need to determine the likelihood of the proportion of Millennial students at their campus that live at home with their parents being 36% or higher.

The question here is regarding the testing of a population proportion using statistical hypothesis testing, specifically a one-sample z-test. The null hypothesis (H0) is that the population proportion is equal to a specified value, in this case, 36%). The alternative hypothesis (Ha) is that the population proportion is greater than the specified value (more than 36%).

The question we need to answer is 'If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%?'

The scenario suggests an indication towards a right-tailed z-test as we're looking to see if the data indicates a proportion >36%. However, as with all statistical tests, one should be cautious about drawing definitive conclusions without additional context and understanding the potential for sampling variability and error.

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Answer:

D.

Step-by-step explanation:

50-20=30 (because of the initial cost)

Then multiply 30*0.5=60

so she can buy less than or equal to 60

Answer:

D. S ≤ 60

Step-by-step explanation:

Ella has $50.00 and the registration fee is $20. This means that she would have $30.00 to buy songs and each song costs $0.50, so:

$30.00/$0.50= 60

The number of songs that she would be able to buy is 60.

According to this, the inequality that gives the maximum number of songs that she can buy is S ≤ 60 as it indicates that the maximum number of songs (s) that she can buy is less than or equal to 60.

Answer:

There are 16 terms in the sequence.

Step-by-step explanation:

The given sequence is

14348907, ..., 9, 3, 1

The first term of the sequence is

[tex]a_1=14348907[/tex]

The last term of the sequence is [tex]l=1[/tex]

The common ratio is [tex]r=\frac{1}{3}[/tex]

The nth term of this sequence is;

[tex]a_n=a_1(r)^{n-1}[/tex]

We plug in the common ratio and the first term to get;

[tex]a_n=14348907(\frac{1}{3})^{n-1}[/tex]

The find the number of terms in the sequence , we plug in the last term of the sequence.

This implies that;

[tex]1=14348907(\frac{1}{3})^{n-1}[/tex]

[tex]\frac{1}{14348907}=(\frac{1}{3})^{n-1}[/tex]

[tex]\Rightarrow 3^{-15}=3^{-(n-1)}[/tex]

Since the bases are the same, we equate the exponents;

[tex]-15=-(n-1)[/tex]

[tex]15=n-1[/tex]

[tex]15+1=n[/tex]

[tex]n=16[/tex]

Answer:

Step-by-step explanation:

First att all, let's take angle B... It's bigger than 180° and smaller than 360. Then: 180 < 6x < 360. So 6x = 288°. The only alternative what's correct is the first one.

I hope I helped you

Answer:

x = ±√2

Step-by-step explanation:

         x - 1 =     1/(x + 1)

(x -1)(x + 1) =     1     Multiplied each side by x + 1

       x² - 1 =     1     Difference of two squares

           x² =     2     Add 1 to each side

           x  = ±√2

x-1 is the reciprocal of x+1 when x = -√2 or x = √2.

Check:

(a) x = -√2

  -√2 - 1 = 1/(-√2 + 1)

-(√2 + 1) = (√2 +1)/[(-√2 +1)(√2 + 1)]

-(√2 + 1) = (√2 +1)/(-2 +1)

-(√2 + 1) = (√2 +1)/(-1)

-(√2 + 1) = -(√2 +1)

(b) x = √2

√2 - 1 = 1/(√2 + 1

√2 - 1 = (√2 - 1)/[(√2 + 1)(√2 - 1) ]

√2 - 1 = (√2 - 1)/(2 - 1)

√2 - 1 = (√2 - 1)/1

√2 - 1 = √2 - 1

OK.

Answer:x = ±√2

Step-by-step explanation: this is because reciprocal means the numerator and denominator switches

So the equation is x-1=1/(x+1)

And you solve for it thats how u get the answer

Answer:

The mean is 5

the median is also 5

and the mode is 1

Step-by-step explanation:

Answer:60,61,73,75,79,81,81,81,92,96,98

Step-by-step explanation: Mean:80

                                             Median:81

                                            Mode:81

Answer:

There are 21 luxury vehicles in 3 shipments sent to a dealership . Which of the following expresses the ratio of shipments to luxury vehicles?

A. 21/3

B. 21 to 3

C. 21:3

D. 3:21

Step-by-step explanation:

Answer:

The answer is D. 3:21 Hope this helps!

1.5 • 3.142= 4.713 should be the answer

Answer:   4.5π  ≈  14.14 cm²

Step-by-step explanation:

[tex]Area_{\ circle}=\pi \cdot r^2\\\\Area_{\ semicircle}=Area_{\ circle}\div 2\\\\\\A=\dfrac{\pi \cdot 3^2}{2}\\\\\\.\quad =\dfrac{9}{2}\pi\\\\\\.\quad =4.5\pi\\\\\\.\quad =14.14[/tex]

Answer:

[tex]\large\boxed{x=\dfrac{27}{2}\to x=13\dfrac{1}{2}\to x=13.5}[/tex]

Step-by-step explanation:

[tex]\dfrac{2}{3}x-2=7\qquad\text{add 2 to both sides}\\\\\dfrac{2}{3}x-2+2=7+2\\\\\dfrac{2}{3}x=9\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{2}{3\!\!\!\!\diagup_1}x=3\cdot9\\\\2x=27\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{27}{2}\\\\x=\dfrac{27}{2}\to x=13\dfrac{1}{2}\to x=13.5[/tex]

Answer:

280 degrees.

Step-by-step explanation:

To convert radians to degrees we multiply by 180/pi:

angle O = 14pi/ 9 * 180 / pi

=  14*180 / 9

=  280 degrees.

The angle 0=14pi/9 radians can be converted to degrees by using the conversion factor 1 radian = 57.3°. Multiplying the given angle in radians by the conversion factor results in an equivalent angle of 280° in degrees.

To convert the angle from radians to degrees, we use the conversion factor 1 rad = 57.3°. The problem provides the angle 0 = 14pi/9 radians. By using the conversion factor, the process of conversion would be as follows:

Therefore, the angle 0=14pi/9 radians is equal to 280° in degrees.

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Answer:

no simplify. answer is:

b. log(1/7)

ANSWER

d.

[tex] \frac{1}{7} [/tex]

EXPLANATION

We want to simplify

[tex] {10}^{ log( \frac{1}{7} ) } [/tex]

Recall that the common logarithm has a base of 10.

This implies that,

[tex] {10}^{ log( \frac{1}{7} ) } = {10}^{ log_{10}( \frac{1}{7} ) } [/tex]

Recall again that:

[tex] {p}^{ log_{p}(q) } = q[/tex]

Therefore,

[tex] {10}^{ log( \frac{1}{7} ) } = {10}^{ log_{10}( \frac{1}{7} ) } = \frac{1}{7} [/tex]

I am thinking the answer is 225. Sorry if I'm wrong!

Answer:

15  cookies

Step-by-step explanation:

We have 20 cookies and we know that three quarters of them were burned. To find the number of cookies burned, divide the 20 cookies into 4 equal parts.

This will give you 4 parts of 5 cookies.

[5] + [5] + [5] + [5]

Then they tell us that 3 quarters were burned. This means that of these 4 parts [5] + [5] + [5] + [5], 3 were burned. Then take 3 of these parts and add them.

[5] + [5] + [5] = 15 cookies.

This is the same as multiplying:

[tex]20 * \frac{3}{4} = 15[/tex]

right isosceles

rs:34&rs=rt+st

rt:17

st:17

ab=[(x(a)-x(b))+(y(a)+y(b))]

Answer:

Isosceles.

Step-by-step explanation:

We are going to check it with the distance formula

d(R,T) = [tex]\sqrt[2]{(3-4)^{2}+(-3-1)^{2}}[/tex]

= [tex]\sqrt[2]{(-1)^{2}+(-4)^{2}}[/tex]

= [tex]\sqrt[2]{1+16}[/tex]

=  [tex]\sqrt[2]{17}[/tex].

d(T,S) = [tex]\sqrt[2]{(4-8)^{2}+(1-0)^{2}}[/tex]

= [tex]\sqrt[2]{(-4)^{2}+(1)^{2}}[/tex]

= [tex]\sqrt[2]{16+1}[/tex]

=  [tex]\sqrt[2]{17}[/tex].

d(S,R) = [tex]\sqrt[2]{(8-3)^{2}+(0-(-3))^{2}}[/tex]

= [tex]\sqrt[2]{(5)^{2}+(3)^{2}}[/tex]

= [tex]\sqrt[2]{25+9}[/tex]

=  [tex]\sqrt[2]{34}[/tex].

Then, as the triangle has two sides with the same length, the triangle is isosceles.

Answer:

56 in.

Step-by-step explanation:

By proportion  8/5 = L/35  where L is the length of the picture.

5L = 8*35

L = 8*35/5

L = 56 in.

The length of a similar picture frame is Option (a) 56 in.

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A ratio indicates how many times one number contains another. It is expressed as a:b where a and b are parameters for any given set of relation.

Given length to width ratio is 8:5.

We have to find the length of similar picture frame which has a width of 35 inches.

Let length of the picture frame be L inches.

Using ratio equation for solving, we have

   8:5 = L:35

⇒ 8/5 = L/35

∴  L = (8/5) * 35 = 56 inches.

Therefore the length of a similar picture frame is Option (a) 56 in.

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