If ABCD is dilated by a factor of, the
coordinate of A' would be:
C
3
2
1
B
-4 -3 -2 -10
3 4 5 6 7
8 9 10 11
-1
-2
3
A
D
A' = ([?], [ ])
T
ת
2

There's a fixed difference of 6 between terms (9 - 3 = 6, 15 - 9 = 6, and so on). The first term of the sequence is 3, so the [tex]n[/tex]-th term is

[tex]3 + 6(n-1) = 6n - 3[/tex]

If there are 24 terms in the sum, then the last term is 6×23 - 3 = 135.

Let [tex]S[/tex] be the sum,

[tex]S = 3 + 9 + 15 + \cdots + 123 + 129 + 135[/tex]

Reverse the order of terms:

[tex]S = 135 + 129 + 123 + \cdots + 15 + 9 + 3[/tex]

If we add up the terms in the same positions, we get twice [tex]S[/tex] on the left side, while on the right side we observe that each pair of terms will sum to 138.

[tex]S + S = (3 + 135) + (9 + 129) + (15 + 123) + \cdots + (135 + 3)[/tex]

[tex]2S = 138 + 138 + 138 + \cdots + 138[/tex]

and since there are 24 terms in the sum, the right side is the sum of 24 copies of 138. In other words,

[tex]2S = 24 \times 138[/tex]

and solving for [tex]S[/tex] gives

[tex]S = \dfrac{24\times138}2 = \boxed{1656}[/tex]

Answer:

See below ~

Step-by-step explanation:

Linear pairs add up to 180 degrees.

⇒ 4x - 10 + 3x + 43 = 180

⇒ 7x + 33 = 180

⇒ 7x = 147

⇒ x = 21

∠A = 4(21) - 10

∠A = 84 - 10

∠A = 74°

∠B = 3(21) + 43

∠B = 63 + 43

∠B = 106°

12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.

An equation is an expression that shows the relationship between two or more variables and numbers.

It took 4 days for 4 butterflies to give birth to 4 larvae. After 4 days, each butterfly produces a larvae

Hence for 12 butterflies in 12 days:

number of larvae = 12 butterflies * (12 days /4 days per larvae) = 36 larvae

12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.

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Answer:

2

Step-by-step explanation:

y=k/x

58=k/9

k=58×9

k=522

y=522/x

when x=261

y=522/261

y=2

The graph represents the trigonometric function y = cotx option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have shown a trigonometric graph in the picture.

As we know:

At x = 0

tan0 = 0

But cotx at x = 0 does not defined.

The csc x and sec x are the reciprocal of sinx and cosx and the sinx and cos have a sinusoidal graph.

Thus, the graph represents the trigonometric function y = cotx option (C) is correct.

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By using the binary operator of addition, the result of summing f(x) = 4 · x² + 7 · x - 3 and g(x) = 6 · x³ - 7 · x² - 5 is equal to (f + g)(x) = 6 · x³ - 3 · x² + 7 · x - 8.

Binary operators is a operator that connects two functions. There are five binary operators between two functions: (i) Addition, (ii) Subtraction, (iii) Multiplication, (iv) Division, (v) Composition.

In this question we must apply the addition between two quadratic functions. In addition, we know by algebra that the sum of a quadratic function and a cubic function is equal to a cubic function. Hence, the resulting expression is:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = (4 · x² + 7 · x - 3) + (6 · x³ - 7 · x² - 5)

(f + g)(x) = 6 · x³ - 3 · x² + 7 · x - 8

By using the binary operator of addition, the result of summing f(x) = 4 · x² + 7 · x - 3 and g(x) = 6 · x³ - 7 · x² - 5 is equal to (f + g)(x) = 6 · x³ - 3 · x² + 7 · x - 8.

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Answer:

20 % discount

Step-by-step explanation:

Lilian got 4 dollars off of the original price    (20 - 16 = 4 )

4 / 20  * 100% = 20% off

The percentage of discount that Lillian gets because of sale is 20%.

Percentage is a measurement to find value of given number out of hundred.

Given that,

The price of phone on tag = $20.

Lillian paid for phone = $16.

To find the percent discount on phone,

First find amount of discount = 20 - 16 = $4.

The percentage of discount = (4 / 20) x 100 = 20 %

Lillian gets 20% discount on new mobile.

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Using the area of a sector formula, we get the area to be:

[tex]\pi (10)^{2} \left(\frac{45}{360} \right)=\boxed{12.5\pi \text{ cm}^{2}}[/tex]

The value of (f/g)(-1) is 0, value of (g . f) (2) is  -3√3, the value of (g - f)(-1)  is √15, and the value of (g + f) (2) is √3 - 3

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have two functions:

f(x) = 1 - x²

g(x) = √(11 - 4x)

f(-1) = 0

g(-1) = √15

f(2) = -3

g(2) = √3

(f/g)(-1) = f(-1)/g(-1) = 0/√15  = 0

(g . f) (2) = g(2)f(2) = (√3)(-3) = -3√3

(g - f)(-1) = g(-1) - f(-1) = √15 - 0 = √15

(g + f) (2) = g(2) + f(2) = √3 + (-3) = √3 - 3

Thus, the value of (f/g)(-1) is 0, value of (g . f) (2) is  -3√3, the value of (g - f)(-1)  is √15, and the value of (g + f) (2) is √3 - 3

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Answer:

x^2-2x-3

Step-by-step explanation:

(x+1)(x-3)

x(x-3)+1(x-3)

Answer:

D. 11

Step-by-step explanation:

Take the two horizontal line measurements and subtract them.

13-9=4

That is how much it changed between these two numbers. Since x is exactly halfway between, simply divide 4 and 2.

4/2=2

Now, add that to 9 or subtract it from 13.

9+2=11

or

13-2=11.

Hope this helps!

If not, I am sorry.

Answer:

D. 11

Step-by-step explanation:

Since segment AC bisects segments ED and BF, the length of AC is the average of the lengths of EB and DF.

AC = x = (EB + DF)/2 = (9 + 13)/2 = 22/2 = 11

Answer: D. 11

Answer:

566

Step-by-step explanation:

I got it right..................

Answer:

18x + 14

Step-by-step explanation:

First, we need to distribute the 5:

 5(4x + 7) - 2x = __ + 21

 20x + 35 - 2x = __ + 21

Now, we can combine like terms:

 20x + 35 - 2x  = ___ + 21

  18x + 35 = ___ + 21

> subtract 21 from both sides to isolate "___"

 18x + 35 = __ + 21

          -21             -21

18x + 14 = ___

now that we have a solution, we should check that it works:

5(4x + 7) - 2x = ____ + 21

5(4x + 7) - 2x = 18x + 14 + 21  

{simplify both sides:}

20x + 35 -2x = 18x + 35

18x + 35 = 18x + 35

(TRUE)

So, we know our solution is 18x + 14

hope this helps!!

Answer:

see explanation

Step-by-step explanation:

the vertices of S under the translation [tex]\left[\begin{array}{ccc}0\\-3\\\end{array}\right][/tex] are

(2, 3 ) → (2, 0 )

(6, 3 ) → (6, 0 )

(4, 5 ) → (4, 2 )

Under an anticlockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) then the above coordinates become

(2, 0 ) → (0, 2 )

(6, 0 ) → (0, 6 )

(4, 2 ) → (- 2, 4 )

which are the coordinates of the vertices of the image T

then the rotation is 90° anticlockwise about the origin , point (0, 0 )

Answer:

Below

Step-by-step explanation:

the vertices of S under the translation  are

(2, 3 ) → (2, 0 )

(6, 3 ) → (6, 0 )

(4, 5 ) → (4, 2 )

Under an anticlockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) then the above coordinates become

(2, 0 ) → (0, 2 )

(6, 0 ) → (0, 6 )

(4, 2 ) → (- 2, 4 )

which are the coordinates of the vertices of the image T

then the rotation is 90° anticlockwise about the origin , point (0, 0 )

Answer:

Can you give exanation

I don't understand

Answer:

y=3x-1

Step-by-step explanation:

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

Answer:  [tex]\textsf{y = -2/5x}[/tex]

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

Given:  [tex]\textsf{Passes through (5, -2) and slope of -2/5}[/tex]

Find:  [tex]\textsf{The equation that follows the details provided}[/tex]

Solution: We first need to plug into the point-slope form and after simplifying, distributing, and solving for y we will complete our equation.

Plug in the values

Distribute and simplify

Subtract 2 from both sides

Therefore, the final equation that follows the information that was provided is y = -2/5x.

Answer:

3

Step-by-step explanation:

because I sense three and You need

Considering it's horizontal asymptote, the statement describes a key feature of function g(x) = 2f(x) is given by:

Horizontal asymptote at y = 0.

They are the limits of the function as x goes to negative and positive infinity, as long as these values are not infinity.

Researching this problem on the internet, the functions are given as follows:

The limits are given as follows:

[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 2(2)^x = \frac{2}{2^{\infty}} = 0[/tex]

[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 2(2)^x = 2(2)^{\infty} = \infty[/tex]

Hence, the correct statement is:

Horizontal asymptote at y = 0.

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Answer:

1/5 divided by 4 equals to 0.05

[tex] \frac{ {3}^{6} \times {5}^{3} }{ {9}^{2} \times {5}^{2} } \\ \\ \frac{ {3}^{6} \times {5}^{3 - 2} }{ {3}^{4} } \\ \\ {3}^{6 - 4} \times {5}^{1} \\ \\ {3}^{2} \times 5 \\ \\ 9 \times 5 \\ \\ 45.[/tex]

Answer:

the algebraic expression is ; x-7=5

Answer:

[tex]\fbox {D. 3,200.4 mm}[/tex]

Step-by-step explanation:

Given :

[ 1 inch = 2.54 centimeters ]

Unit conversions to keep in mind :

Solving

Step-by-step explanation:

(3+3+3*2)+(2*3-2-4*2)

The value of the addition of the two polynomials is 3x³ - x² + 1.

The addition of polynomials involves combining like terms of two or more polynomials to create a new polynomial. A polynomial is an expression consisting of variables, coefficients, and exponents, connected by addition and subtraction operations.

To add the given polynomials:

(3 + x³ + 3x²) + (2x³ - 2 - 4x²)

First, let's group the like terms:

(x³ + 2x³) + (3x² - 4x²) + (3 - 2)

Combine the coefficients of the like terms:

3x³ + 3x² - 4x² + 3 - 2

Simplify the expression:

3x³ - x² + 1

Therefore, the sum of the given polynomials is: 3x³ - x² + 1.

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Answer:

Step-by-step explanation:

area of square + 1/2 area of 1 triangle * 4

The statement C is true about the proportional relationship that is modeled by Peter’s equation. Peter walks at a rate of 13/4 miles per hour.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

The complete question is

"Peter uses the equation Y=13/4x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by the peat there's the equation?

A: Peter walks a rate of 4/13 miles per hour.

B: Peter walks at a  rate of 4 miles per hour.

C: Peter walks at a rate of 13/4 miles per hour.

D: Peter walks at a rate of 13 miles per hour."

Given equation;

Y=13/4x

Where,

y represents the number of miles

x is the time period

The equation shows Peter walks at a rate of 13/4 miles per hour.

Hence statement C is true about the proportional relationship that is modeled by Peter’s equation.

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