The coordinates of the vertices of △ABC are A(−1, 1) , B(−2, 3) , and C(−5, 1) . The coordinates of the vertices of △A′B′C′ are A′(−1, −4) , B′(−2, −6) , and C′(−5, −4) .



Which statement correctly describes the relationship between △ABC and △A′B′C′ ?

△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 3 units down followed by a reflection across the x-axis, which is a sequence of rigid motions.
△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 5 units down followed by a reflection across the x-axis, which is a sequence of rigid motions.
△ABC is not congruent to △A′B′C′ because there is no sequence of rigid motions that maps △ABC to △A′B′C′ .
△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a reflection across the x-axis followed by a translation 3 units down, which is a sequence of rigid motions.

Answer:

$0.80

Step-by-step explanation:

The total number of nuts in all the cans is found by multiplying the number of cans (45) by the number of nuts in each can (338). Hence, the total number of nuts, n, in all of the cans is 15210.

This problem is related to simple multiplication. Here, you have 45 cans of nuts and each can contains 338 nuts. So if you want to find the total number of nuts in all the cans, you need to multiply 45 (total number of cans) by 338 (number of nuts in each can).

The multiplication is as follows:

45 * 338 = 15210

So, the total number of nuts, n, in all of the cans is 15210.

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Answer:

10.0 is the correct answer  

Step-by-step explanation:

Given : FA is a ray.

Find out the pair of angles share the common side FA.

To proof

As shown in the diagram

∠ BAF and ∠DAF  are th.e pair of angles shares FA as a common side

REASON

Adjacent Angles are those angles that share a common side, a common vertex, and no common interior points.

as ∠ BAF and ∠DAF  shares common vertex A and  common side FA.

Therefore

∠ BAF and ∠DAF  are th.e pair of angles shares FA as a common side

Answer:

The value of x is 0.09

Step-by-step explanation:

Here, the given function is,

[tex]f(x)=\log(-20x+12\sqrt{x})[/tex]

Differentiating with respect to x,

[tex]f'(x)=\frac{1}{-20x+12\sqrt{x}}(-20+\frac{12}{2\sqrt{x}})[/tex]

[tex]=\frac{-20+\frac{6}{\sqrt{x}}}{-20x+12\sqrt{x}}[/tex]

[tex]=\frac{-10+\frac{3}{\sqrt{x}}}{-10x+6\sqrt{x}}[/tex]

[tex]=\frac{-10\sqrt{x}+3}{2\sqrt{x}(-5x+3\sqrt{x})}[/tex]

Again differentiating with respect to x,

[tex]f''(x)=-\frac{(-10\sqrt{3}+3)(-15x+3\sqrt{3})}{4x\sqrt{x}(-5x+3\sqrt{x})}[/tex]

For maxima or minima,

[tex]f'(x) = 0[/tex]

[tex]\implies \frac{-10\sqrt{3}+3}{2\sqrt{x}(-5x+3\sqrt{3})}=0[/tex]

[tex]\implies x \approx 0.09[/tex]

At x = 0.09,

f''(x) = negative,

Hence, for x = 0.09, f(x) is maximum.

The sofa's original price is calculated by using the formula: original price = sale price/percentage in decimal format. In this case, the percentage is 68%, and hence the original price would be 357 / 0.68 which is equal to $525.

This is a percentage problem. If the sale price of $357 represents 68% of the original price (because 100% - 32% is 68%), we can find the original price of the sofa using the formula: original price = sale price/percentage in decimal format.

Therefore, the original price would be 357 / 0.68 = $525

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Answer: A is the right answer .Probability of the book chosen is a biography is [tex]\frac{2}{15}[/tex].

Step-by-step explanation:

According to the given graph or pie chart

The number of biography books=4

Total books= Romance books+ Science fiction books+ Biography books+Adventure books =2+14+4+10=30

Let B be the event of choosing a biography book then

Probability of the book chosen is a biography P(B)=[tex]=\frac{biography\ books}{total\ books}=\frac{4}{30}=\frac{2}{15}[/tex]

Therefore, Probability of the book chosen is a biography is  [tex]\frac{2}{15}[/tex].

From the graph, it is found that there is a [tex]\mathbf{\frac{2}{15}}[/tex] probability that the book chosen is a biography, and the correct option is given by option A.

In this problem:

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

Thus:

[tex]\mathbf{\frac{2}{15}}[/tex] probability that the book chosen is a biography, and the correct option is given by option A.

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Answer: It's 115 I took the k12 test

Step-by-step explanation:

Fred's initial deposit, considering a 3.4% interest rate compounded daily over nine years, was approximately $1258.16.

To find Fred's initial deposit, we need to use the formula for compound interest:
A = P(1 + r/n)ⁿᵗ, where:

Here, we know:

We need to find P. Rearrange the formula to solve for P:

P = A / (1 + r/n)ⁿᵗ

Substitute the known values:

P = 1728.57 / (1 + 0.034/365)³⁶⁵×⁹

First, calculate the daily interest rate

0.034 / 365 = 0.00009315

Next, calculate the exponent:

(365 × 9) = 3285

Now, compute (1 + daily interest rate) raised to the power of 3285:

(1 + 0.00009315)³²⁸⁵ = 1.37423

Finally, divide the final amount by this value:

P = 1728.57 / 1.37423 = 1258.16.

you could pick:

 A & B

 A & C

B & C

B & A

C & A

C & B

The total number of possible outcomes is 6 and this can be determined by using the given data.

Given :

The following steps can be used in order to determine all the possible outcomes for this experiment:

Step 1 - According to the given data, the total number of items in the box is 3.

Step 2 - The total number of outcomes for this experiment is given by:

Total outcomes = 3!

Step 3 - Simplify the above expression.

Total outcomes = 3 [tex]\times[/tex] 2 [tex]\times[/tex] 1

                          = 6

Step 4 - Now, the list of all the outcomes for this experiment:

A and B

A and C

B and C

B and A

C and A

C and B

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Answer:

the number of cakes that can be produced is only 34.  

Step-by-step explanation:

   total flour needed = flour need for batter + flour needed for topping

,

  total flour needed = 2 2/9 cups + 1/2 cup = 49/18 cups

after, we divide the total amount of flour by the answer obtained above to determine the number of cakes that can be made.

   number of cakes is the total amount of flour  needed per cake

     number of cakes is  95 cups / (49/18) = 34.89 cakes

the number of cakes that can be produced is only 34.

Answer:

45 pounds

Step-by-step explanation:

Answer:

The Answer is 37.5

Step-by-step explanation:

Answer:

The expression is 16 + p

Step-by-step explanation:

Algebraic expression is a mathematical phrase that contains numbers and variables with an operation ( addition or subtraction etc. )

Given,

The number of photos Latonya has on her phone = 16,

While p represents the number of photos Luis has in his wallet,

Where p is a variable,

So, the total number of photos = Latonya's photos + Luis's photos

= 16 + p

Hence, the required expression is '16 +p'

Answer:

a

Step-by-step explanation:

if dont want to read

Table 1 shows the possible amounts of cookies and cupcakes in a box, given the ratio of 5 : 4.

What is Ratio?

A ratio indicates how many times one number contain in another number.

Given that;

The ratio of the number of cookies to the number of cupcakes in a box is  5 : 4.

Now, In the table 1;

The ratio are given as,

5 : 4

10 : 8

20 : 16

40 : 32

Since, The ratio are 5 : 4.

Simplify all the ratio as;

10 : 8 = 10/8

        = 5/4

        = 5 : 4

And, 20 : 16 = 20/16

                   = 10/8

                   = 5/4

                   = 5 : 4

And, 40 : 32 = 40/32

                    = 20/16

                    = 10/8

                    = 5/4

                    = 5 : 4

Thus, Table 1 shows the possible amounts of cookies and cupcakes in a box, given the ratio of 5 : 4.

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Answer:

a. $10,122.00

Step-by-step explanation:

By definition the deferment period is a time during which a borrower does not have to pay interest or repay the principal on a loan.

In this case the balance should be the initial value $17,190, but Felicia made 12 payments of $589 each one.

So, $589 x 12 = $ 7,068.

$17,190- $ 7,068 = $10,122

Answer:

advantages of buying:

-you own your own property

-the value of your property may increase over time

-you can improve or decorate your house as you wish

advantages of renting:

-your landlord is responsible for repairs

-you need to pay fewer up-front cost

-paying rent on time helps you build a good credit history

-renting is better if you dont plan to stay long

-you can have roomates to share costs

Answer:

[tex]x=-3+\sqrt{3}[/tex]    , [tex]x=-3-\sqrt{3}[/tex]

Step-by-step explanation:

x2 + 6x + 7 = 0

Solve the equation for x

To solve this we apply quadratic formula

[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

a= 1 , b= 6 , c= 7

Plug in all the values in the formula

[tex]x=\frac{-6+-\sqrt{6^2-4(1)(7)} }{2(1)}[/tex]

[tex]x=\frac{-6+-\sqrt{36-28} }{2(1)}[/tex]

[tex]x=\frac{-6+-\sqrt{8} }{2(1)}[/tex]

[tex]x=\frac{-6+-2\sqrt{2} }{2}[/tex]

Divide each term by 2

[tex]x=-3+- \sqrt{3}[/tex]

so we got two value for x

[tex]x=-3+\sqrt{3}[/tex]    , [tex]x=-3-\sqrt{3}[/tex]

Answer:

The distribution is skewed (either to the left or to the right).

Step-by-step explanation:

Skewness is the measure of how symmetric the distribution of the data is around its mean. It can be skewed either to the left or to the right (meaning that one of the "tails" of the distribution is longer than the other). This means that the mass your data set's observations tends to accumulate more around one extreme of the distribution than around the other.

A strictly symmetric, normal distribution would have a skewness measure of 0.

Answer:

Artaud is 12 years old

Step-by-step explanation: