If a reflection takes triangle CAT to C'A'T', what is A'C'?

triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of 3 units, side TC has a measure of 4 units, and side AC has a measure of 5 units

3
4
5
Cannot be determined

Answer:

3x² - 12x - 36

= 3(x - 6)(x + 2)

Step-by-step explanation:

3x² - 12x - 36      Find any common factor. All terms are divisible by 3.

= 3(x² - 4x - 12)    Find two numbers that sum to -4 and whose product is -12. Replace -4 with these two numbers.

= 3(x² - 6x + 2x - 12)   Group the terms splitting from the middle

= 3( (x² - 6x) + (2x - 12) )   Find the common factor in each group.

= 3( x(x - 6) + 2(x - 6) )      The groups have a common factor (x - 6).

= 3( (x - 6)(x + 2) )           Remove the extra brackets

= 3(x - 6)(x + 2)             Fully factored

Answer:

-9.4, -0.5, 0.75, 1.25, 7/4

Step-by-step explanation:

These are the values of all the numbers in order.

Have a good day!!!

To plot the given numbers -0.5, 7/4, 1.25, 0.75, -9/4 on a number line, convert them into decimal form and mark these points on a line between appropriate integers. Hence, the points are -2.25 (between -2 and -3), -0.5 (between 0 and -1), 0.75 (between 0 and 1), and 1.25 and 1.75 (between 1 and 2).

To plot the given numbers -0.5, 7/4, 1.25, 0.75, -9/4 on a number line, we first need to convert them all into the same form. Converting everything into decimals, we have -0.5, 1.75 (which is 7/4), 1.25, 0.75, and -2.25 (which is -9/4).

Start by drawing a straight horizontal line and mark the points for integers. For example, if the numbers range from -3 to +2, mark these integers on your line. Next, find the points that correspond to the decimal numbers. Suppose you've marked the numbers from -3 to 2, your plot would look like the following:

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Answer:

(-∞,∞) or {y|y∈R}

Step-by-step explanation:

Answer:

Step-by-step explanation:

Exponential functions have the form

f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.

Answer:

Exponential functions have the form

Step-by-step explanation:

Answer:

Part a) The equation for the volume of the film canister is

[tex]32\pi=\pi r^{2}(8)[/tex]

Part b) The radius of the film canister is [tex]2\ cm[/tex]

Step-by-step explanation:

The complete question is

A film canister in the shape of a cylinder has a height of  8 centimeters and a volume of 32π cubic centimeters.

a. Write an equation for the volume of the film canister.

b. What is the radius of the film canister?

Part a) Write an equation for the volume of the film canister

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

where

r is the radius of the circular base

h is the height of the cylinder

we have

[tex]V=32\pi\ cm^3[/tex]

[tex]h=8\ cm[/tex]

substitute

[tex]32\pi=\pi r^{2}(8)[/tex] ----> equation for the volume of the film canister

Part b) What is the radius of the film canister?

we have

[tex]32\pi=\pi r^{2}(8)[/tex]

[tex]32\pi=8\pi r^{2}[/tex]

Simplify

Divide by 8π both sides

[tex]4=r^{2}[/tex]

square root both sides

[tex]r=2\ cm[/tex]

The equation for the volume of the film canister is V = 3.142 × r² × 8.

Use the formula V = πr²h, where V represents the volume, r is the radius, and h is the height.

Substitute the given values into the formula to calculate the volume.

For a given height of 8 centimetres, the volume formula becomes V = 3.142 × r² × 8.

A function is a relationship between inputs where each input is related to exactly one output.

The coordinates of the table are: (22, 26), (20, 22), (16, 20), (14, 18),

(10, 14).

The graph of the coordinates formed from the table must show a linear graph.

This means a straight line.

The graph is shown below and it is not a straight line.

The function represented in the table is not linear.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

A function is represented by the values in the table.

x      y

22   26

20   22

16    20

14     18

10     14

Now,

We can find the coordinates of the given function.

(22, 26)

(20, 22)

(16, 20)

(14, 18)

(10, 14)

The graph of these coordinates must show a linear graph.

This means a straight line.

The graph is shown below and it is not a straight line.

Thus,

The function represented in the table is not linear.

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Answer:

Step-by-step explanation:

midpoint theorem : (mx₂+nx₁/m+n , my₂+ny₁/m+n)

(-3, k) = ( -3*-2 + k*-5/-3+k  , -3*3 + k*-4/-3+k)

(-3, k) = (6-5k/-3+k , -9-4k/-3+k)

Compare x values of  both side ;

-3 = 6-5k/-3+k

-3 *( -3+k) = 6-5k

-3*-3 +k *-3 = 6-5k

9 -3k = 6- 5k

5k -3k = 6 - 9

2k = -3

k= -3/2

Answer:

$896.70

Step-by-step explanation:

Amount( A) Devi earned can be calculated from the formula below

[tex]A =P ({ 1 + \frac{r}{m} })^{mt}[/tex]

Where,

P= principal=$750

r=rate=6%=0.06

m=compounding frequency=4

t=time=3yrs

[tex]A =750 ({ 1 + \frac{0.06}{4} })^{(4 \times 3)}[/tex]

[tex]A =750 ({ 1 + 0.015)}^{12}[/tex]

[tex]A =750 \times ({ 1.015)}^{12}[/tex]

[tex]A =750 \times 1.1956[/tex]

[tex]A = 896.70[/tex]

Answer:

135

885-750 is 135 on financial literacy

Answer: 37%

Step-by-step explanation:

Initial Population                                        = 100,000

 Population after 5 years                            = 137,000

Population increase                                    = 137,000 - 100,000

                                                                     = 37,000

Therefore % increase                                  = 37,000/100,000 x 100

                                                                     = 37%

Answer:

t=3

Step-by-step explanation:

6t= 36+7-25

t=18/6

Answer:

C

Step-by-step explanation:

The ratio of frames : containers can be calculated using values from table.

3 : 12 = 7 : 28 = 9 : 36 = 1 : 4 ← in simplest form, thus

Number of containers is 4 times the number of frames

Thus for 5 picture frames the number of containers = 5 × 4 = 20 → C

Answer:

x = 1 is not part of the domain

Step-by-step explanation:

The denominator of g(x) cannot be zero as this would make g(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve

x - 1 = 0 ⇒ x = 1 ← restricted value

The number x = 1 is not part of the domain of the function g(x) = (x+2)/(x-1) because setting x to 1 would result in division by zero, which is undefined. Thus, x = 1 is an asymptotic value and is excluded from the domain.

The number that is not part of the domain of the function g(x) = \frac{x+2}{x-1} is x = 1. Knowing that the domain of a function includes all the values that x can take on for which the function is defined, we can identify values that are not in the domain by looking for any values that would cause the function to be undefined. In the case of g(x), since it involves a division by x-1, we need to make sure that the denominator does not equal zero since division by zero is undefined in mathematics.

To find out when the denominator is zero, we set x-1 = 0 and solve for x. The solution is x = 1, which means that x cannot be 1, since it would make the function undefined. Therefore, x = 1 is not part of the domain of g(x).

As described in FIGURE 4.4 from OpenStax under a CC BY 4.0 license, functions like y = \frac{1}{x} have asymptotes or limits that indicate values that are not part of the domain. g(x) has a similar characteristic, where x = 1 is an asymptote.

Answer:

[tex]\large\boxed{x=\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right\\\\|x-4|=\left\{\begin{array}{ccc}x-4&for&x-4\geq0\to x\geq4\\-(x-4)&for&x<4\end{array}\right[/tex]

[tex](1)\ x<4\\\\-(x-4)-5=3(x-1)\qquad\text{use the distributivep property}\\\\-x-(-4)-5=3x+(3)(-1)\\\\-x+4-5=3x-3\qquad\text{combine like terms}\\\\-x+(4-5)=3x-3\\\\-x-1=3x-3\qquad\text{add 1 to both sides}\\\\-x-1+1=3x-3+1\\\\-x=3x-2\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-2\\\\-4x=-2\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{-2}{-4}\\\\x=\dfrac{1}{2}\in(1)[/tex]

[tex](2)\ x\geq4\\\\x-4-5=3(x-1)\\\\x+(-4-5)=3x-3\\\\x-9=3x-3\qquad\text{add 9 to both sides}\\\\x-9+9=3x-3+9\\\\x=3x+6\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\x-3x=3x-3x+6\\\\-2x=6\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{6}{-2}\\\\x=-3\notin(2)[/tex]

Answer:

$206.4

Step-by-step explanation:

8.6*24=206.4

65 student tickets were sold

Solution:

Given that movie theater sells student tickets for $ 6 and adults for $ 8

Let "s" be the number of student tickets sold

Let "a" be the number of adult tickets sold

Cost of 1 student ticket = $ 6

Cost of 1 adult ticket = $ 8

Given that theater sold 140 tickets

Number of student tickets sold + number of adult tickets sold = 140

s + a = 140 ------ eqn 1

The theater generated $ 990

number of student tickets sold x Cost of 1 student ticket + number of adult tickets sold x Cost of 1 adult ticket = 990

[tex]s \times 6 + a \times 8 = 990[/tex]

6s + 8a = 990 ------ eqn 2

Let us solve eqn 1 and eqn 2 to find values of "s" and "a"

From eqn 1,

s = 140 - a ----- eqn 3

Substitute eqn 3 in eqn 2

6(140 - a) + 8a = 990

840 - 6a + 8a = 990

2a = 150

a = 75

Substitute a = 75 in eqn 3

s = 140 - 75

s = 65

Therefore 65 student tickets were sold

Answer:

AC = 12 units.

Step-by-step explanation:

Δ ACD is right-angled. ( as CD ⊥ AB).

cos 45° = CD / AC = 6√2 / AC

AC = 6√2 / cos 45°

AC = 6√2 / 1 /√2

= 6√2 *√2

= 6 * 2

= 12   (answer)

HOPE THIS HELPED ;3

Final answer:

The final line of Mariana's work would show identical sides after simplification, resulting in an equation like 0 = 0 or x = x, indicating an infinite number of solutions.

Explanation:

If Mariana solved a linear equation and found that it had an infinite number of solutions, the final line of her work would show that both sides of the equation are identical after simplification. For instance, if the original equation was 2x + 3 = x + x + 3, upon simplifying both sides, she would end up with x + x = x + x, which is an identity (indicating that any value for x would satisfy the equation). Therefore, the final line could have been a simplified equation that resulted in a statement like 0 = 0 or x = x after all terms cancel out.

Answers:

b) [tex]x(25x-1)[/tex]

c) [tex]x^{2}-4(x-3)[/tex]

d)[tex]4x(x-5)+25[/tex]

e)[tex]2(3x^{2}+11x+14)[/tex]

Step-by-step explanation:

b) We have the following expression:

[tex]25x^{2}-x[/tex]

Applying common factor [tex]x[/tex]:

[tex]x(25x-1)[/tex]

c) We have the following expression:

[tex]x^{2}-4x+12[/tex]

Applying common factor [tex]4[/tex]:

[tex]x^{2}-4(x-3)[/tex]

d)We have the following expression:

[tex]4x^{2}-20x+25[/tex]

Applying common factor [tex]4x[/tex]:

[tex]4x(x-5)+25[/tex]

e)We have the following expression:

[tex]6x^{2}+22x+28[/tex]

Applying common factor [tex]2[/tex]:

[tex]2(3x^{2}+11x+14)[/tex]

Samantha measured [tex]13\frac{1}{8}[/tex] inches for the entire month

Step-by-step explanation:

Samantha is measuring the snowfall in a snow Gog for her science project

We need to find how much snowfall Samantha measured for the entire month

∵ She measured [tex]3\frac{3}{4}[/tex] inches of snow in the 1st week

- Change the mixed number to improper fraction

∵ [tex]3\frac{3}{4}=\frac{(3)(4)+3}{4}=\frac{12+3}{4}=\frac{15}{4}[/tex]

∴ She measured [tex]\frac{15}{4}[/tex] inches of snow in the 1st week

∵ She measured twice as much snow as the 1st week in the 2nd week

- Multiply the value of the 1st week by 2

∵ [tex]\frac{15}{4}[/tex] × 2 =  [tex]\frac{30}{4}[/tex]

∴ She measured [tex]\frac{30}{4}[/tex] inches of snow in the 2nd week

∵ She measured half as much snow as the 1st week in the 3rd week

- Multiply the value of the 1st week by 1/2

∵ [tex]\frac{15}{4}[/tex] × [tex]\frac{1}{2}[/tex] =  [tex]\frac{15}{8}[/tex]

∴ She measured [tex]\frac{15}{8}[/tex] inches of snow in the 3rd week

∵ It did not snow at all in the fourth week

- Add the values of the three weeks above to find the amount

  of snowfall she measured for the entire month

∵ The amount of snowfall = [tex]\frac{15}{4}+\frac{30}{4}+\frac{15}{8}[/tex]

- To add the fraction you must make all the denominator same number

  so multiply the 1st and 2nd fractions by 2 up and down to make all

  the denominator equal 8

∴ The amount of snowfall = [tex]\frac{30}{8}+\frac{60}{8}+\frac{15}{8}[/tex]

- Add the numerators and put the sum over 8

∴ The amount of snowfall = [tex]\frac{105}{8}[/tex]

- You can change the improper fraction to mixed number by divide

  105 by 8 and put the reminder over 8

∵ 105 ÷ 8 = 13 and 1/8

∴ The amount of the snowfall = [tex]13\frac{1}{8}[/tex] inches

Samantha measured [tex]13\frac{1}{8}[/tex] inches for the entire month

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Answer:

53q+10

Step-by-step explanation:

(-3q+3)+7(8q+1)

-3q+3+56q+7

53q+3+7

53q+10

Answer:

[tex] - 3q + 3 + 56q + 7 \\ 53q + 10[/tex]

Good luck!

Intelligent Muslim,

From Uzbekistan.

Answer:

It's 6 units

Step-by-step explanation:

i took the test

Answer:

17 rafts are needed for 136 people.

Step-by-step explanation:

Given:

Total number of people waiting for river raft ride = ?

Number of people the raft holds = 8

To Find:

The number of rafts needed =?

Solution:

Let X be the total number rafts needed to accommodate  all the 136 people waiting for the River Raft ride.

So now X will be

X= [tex]\frac{\text{Total number of people}}{\text{number of people a raft can hold}}[/tex]

X= [tex]\frac{136}{8}[/tex]

X = 17

Balancing of equations as shown in the attached document requires that the number of atoms, of an element, on the left of the equation is equivalent to the number of the atoms of the same element on the right of the equation. This is in observation of the conservation of mass rule of thermodynamics. Mass and energy cannot be destroyed nor created, it can only be transformed from one form to another. In this case, mass remains the same in the system since this is a chemical reaction- only the bonds between atoms are being rearranged.

Answer:

40

Step-by-step explanation:

80% of the test = 32 questions

100% of the test = x questions

Cross multiply

80*x = 100 * 32   Combine the right

80x = 3200         Divide by 80

x = 3200/80

x = 40

There are 40 questions on the test.

100 children tickets and 200 adult tickets were sold.

Step-by-step explanation:

Given,

Cost of one student ticket = $4

Cost of one adult ticket = $6

Total sales = $1600

Number of tickets sold = 300

Let,

x represent the number of children tickets sold.

y represent the number of adult tickets sold.

According to given statement;

x+y=300      Eqn 1

4x+6y=1600   Eqn 2

Multiplying Eqn 1 by 4

[tex]4(x+y=300)\\4x+4y=1200\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](4x+6y)-(4x+4y)=1600-1200\\4x+6y-4x-4y=400\\2y=400[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{400}{2}\\y=200[/tex]

Putting y=200 in Eqn 1

[tex]x+200=300\\x=300-200\\x=100[/tex]

100 children tickets and 200 adult tickets were sold.

Keywords: linear equation, elimination method

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Answer:

Explanation:

1. Using the minimun number of sheets  of paper in the interval [300, 400]

a) Cost: $ 2.00 / 100 sheets

b) 300 sheets / day × $ 2.00 / 100 sheets = $ 6.00 / day

c) Approimately 20 school days per month:

2. Using the maximum number of sheets of paper in the interval [300, 400]

a) Cost: $ 2.00 / 100 sheets

b) 400 sheets / day × $ 2.00 / 100 sheets = $ 8.00 / day

c) Approimately 20 school days per month:

3. Middle value:

Calculate the middle value between $160.00 and $120.00

Thus, the answer is the option A.

The team moved the ball -3 yards per play.

Step-by-step explanation:

Given,

Total yards lost = 12 yards

Total plays = 4 plays

As the yards are lost, therefore, we will use negative sign.

Yards per play = [tex]\frac{Number\ of\ yards}{Number\ of\ plays}[/tex]

Yards per play = [tex]\frac{-12}{4}[/tex]

Yards per play = -3

The team moved the ball -3 yards per play.

Keywords: division, unit rate

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Answer:

-2

Step-by-step explanation:

The equation is -12/c=6

by solving for c you get,

-12/c=6

Then multiply both sides by the LCM c to get, -12=6c

Divide both sides by 6 to get,

-12/6=6c/6

-2=c

Verification:

-12/-2=6 since when a negative number divides a negative number the answer is a positive value

Answer:

2 years are the 18.2% of 11 years.

Step-by-step explanation:

For calculating what percentage of 11 years is 2 years, we have to do the following calculations:

Fraction used to represent the question = 2/11

Now, we divide 2 by 11, where 2 is the dividend and 11 the divisor:

2/11 = 0.1818....

Converting 0.1818 to percentage:

0.1818 * 100 = 18.2% (Rounding to the nearest tenth)

2 years are the 18.2% of 11 years.

Answer:

Step-by-step explanation:

4 1/2 minutes = 4.5 minutes

2 / 4.5 = 0.44 laps per minute

OR

4.5 / 2 = 2.25 minutes per lap

not sure which one ur looking for...but both are unit rates

The unit rate of Jordan's swimming speed is approximately 0.44 laps per minute. This is calculated by dividing the number of laps (2) by the total time (4.5 minutes).

To identify the unit rate in this scenario, we first need to understand what we are finding. The unit rate means how much of something is done in one unit of time, in this case, how many laps Jordan can swim in one minute. Since Jordan can swim two laps in 4 1/2 minutes, we want to find out how many laps he can swim in one minute. We divide the total laps (2) by the total time (4.5). This will compute to approximately 0.44. Hence, Jordan can swim around 0.44 laps in one minute.

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