Find a translation that has the same effect as the composition of translations

Answer: 16x^2+144x+18

Step-by-step explanation:

The sum of two given expressions is 16x²-6x+14.

Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.

The given expressions are 8x²-x+9 and 8x²-5x+5.

Now, sum =8x²-x+9+8x²-5x+5

Group like terms and simplify, we get

(8x²+8x²)+(-x-5x)+(9+5)

= 16x²+(-6x)+14

= 16x²-6x+14

Therefore, the sum of two given expressions is 16x²-6x+14.

Learn more about the addition of algebraic expressions here:

https://brainly.com/question/21443100.

#SPJ2

Answer:

y= -3x+1

Step-by-step explanation:

Triangle RST is rotated 180° about the origin, and then translated up 3 units.  Then , ΔRST ≅ ΔBAC

We know that  To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).

Thus, The coordinates of triangle RST becomes

R (1,1) → R'(-1,-1)

S (3,4) → S'(-3,-4)

T(-5,0) → T'(5,0)

Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)

R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B

S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A

C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C

As rotation and translation both are rigid transformation that maps only congruent figures.

Therefore, ΔRST ≅ Δ BAC

learn more about of triangle here

https://brainly.com/question/11505183

#SPJ4

The evaluation of the composite function (g o f)(0) is -4

A composite function is generally a function that is written inside another function.

Therefore, let's solve the composite function below:

f(x) = 1x

g(x) = x - 4

Let's find (g o f)(0)

Therefore,

(g o f)(x) = g(f(x))

Hence,

(g o f)(0) = g(f(0))

f(0) = 1(0) = 0

Therefore, let's substitute f(0) in g(x)

(g o f)(0) = 0 - 4

(g o f)(0) =  - 4

learn more on function here: brainly.com/question/24181440

#SPJ1

Answer:

y=40 z= 5h+15

5 hours to make the same amount of money

Step-by-step explanation:

40-15=25

25/5=5

hope this helped

Considering that R and S are points on the number line If RS= 10 and R lies at 13 then s will lie at

A number line is a sequence of numbers arranged at a particular pattern in a straight line

Information gotten form the question have it that"

RS= 10

R lies at 13

In a number line if R lies in point 13 and RS = 10 then we solve as follows

R + | 10 |

13 + 10 = 23

13 - 10 = 3

Hence R lies at point 3 or 13

Learn more on number line: https://brainly.com/question/12399107

#SPJ1

The angle which the pendulum travels is 0.61 radian

Two parallel, identical bases connected by a curving surface form a 3D solid shape known as a cylinder. Similar to a disk in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases.

Given that :A pendulum is 45cm long. When the pendulum swings it travels along the arc of the circle and covers a distance of 27.5cm.

  Central Angle =[tex]\frac{length of arc}{Radius}[/tex]

= [tex]\frac{27.5}{45}[/tex]

=0.61 radian

The angle which the pendulum travels is 0.61 radian

To learn more about central angle of circle visit :

brainly.com/question/23247585

#SPJ9

Answer:

16

Step-by-step explanation:

→ Add the fractions

[tex]2\frac{1}{4} +\frac{1}{2} =\frac{9}{4} +\frac{1}{2} =\frac{9}{4} +\frac{2}{4} =\frac{11}{4}[/tex]

→ Equate to 44

[tex]\frac{11}{4} x=44\\[/tex]

→ Multiply both sides by 4

11x = 176

→ Divide both sides by 11

x = 16

Answer:

y = 5

Step-by-step explanation:

the equation of a horizontal line, parallel to the x- axis is

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (- 5, 5 ) and (0, 5 ) with y- coordinates 5 , then

y = 5 ← equation of line

If the Great games company sells 9/20 of its games through its online stores, then the percentage of the games are sold online is 45%

The fraction of games sells through the online store = 9/20

Here we have to convert the simple fraction to the percentage

Simple fraction is a fraction that consist of whole number numerator and denominator. The top term in the simple fraction is called the numerator and bottom term is called denominator

The percentage is defined as the number that is expressed as the fraction of 100. It is represented by the percentage sign "%"

To convert  simple fraction to percentage, multiply the simple fraction by 100

The percent of games are sold online = (9/20)×100

= 45%

Hence, if the great games company sells 9/20 of its games through its online stores, then the percentage of the games are sold online is 45%.

Learn more about percentage here

brainly.com/question/17151247

#SPJ1

Answer:

Step-by-step explanation:

1 to the 10th power is 1.

The distance from the midpoint to the origin is [tex]\sqrt{5}[/tex].

What is midpoint?

Midpoint is the point that is in the middle pf the line, and to calculate midpoint the formula is

[(x)1 + (x)2]/2, [(y)1 + (y)2]/2

given coodinates are (-2, -4) and (0, 8)

midpoint = (-2+0/2, 8-4/2)

=(-1, 2)

to find the distance from the midpoint to origin.

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

the points are (-1,2) and (0,0)

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

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

To know more about midpoint, visit:

https://brainly.com/question/1571794

#SPJ9

Answer:

Yes, you have to distribute.

Step-by-step explanation:

2+5(x+3)-3(x-4)=x+2(2x+4)

2+5x+15-3x+12=2(2x+4)

Add the Numbers

2+5x-3x=2(2x+4)

Combine Like Terms, Then you can rearrange the terms for simplification. You should end up with an exation looking like this:

2x+29=5x+8

Subtract 29 from both sides. Simplify, then subtract 5x from both sides.
2x-5x=5x-21-5x
Simplify, then Divide both sides by the same factor. Simplify once more then you should have
x=7

Hope this helps ;)

The measure of angle A is found as 115 degrees.

For the given question, the values of the angles are given.

A=(3x-35)

B=(x-35)

c=x

We know that the sum of all angles in a triangle is 180.

A + B + C = 180

Put the values;

3x-35 + x-35 + x = 180

Simplifying;

5x - 70 = 180

5x = 250

x = 50

Put the values in the angles;

Angles A = 3×50 - 35

Angles A = 115

Thus, the measure of angle A is found as 115 degrees.

To know more about the triangles, here

https://brainly.com/question/17335144

#SPJ13

Answer:

Step-by-step explanation:

We are looking for a new number which is 350 more than 400.

We will get the new number by adding 350 to 400.

We write it down as:

400+350=750

Therefore your answer is; 750

Answer: 750

Step-by-step explanation: You add both of them 350+400...

Answer:

0.026 is the value of x.

Step-by-step explanation:

sinx=p÷h

sinx=5.3÷8.2

sinx=sin0.02......

x=0.02°

Answer:

88

Step-by-step explanation:

multiply 13 by 2 = 26

then add by 1 52 and 15

= 94

then subtract 94-6

88

Remember use Dmas while solving

The best description for the sequence of transformation used is; Rigid Transformations.

In mathematics, a rigid transformation is defined as a geometric transformation of a defined Euclidean space that does not change or preserves the Euclidean distance that is between every pair of points. Examples of this rigid transformations are rotations, translations, reflections e.t.c

Now, from the given transformation, the first thing to notice is that the transformation does not change the distance between pair of points in the diagram. Secondly, it is neither only a translation nor reflection as it is more than  one transformation that was used and so it can be described as a rigid transformation.

Read more about Transformation at; https://brainly.com/question/4289712

#SPJ1

A measure of the probability that the sample's average IQ is below 987 is 44.70 %.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean.

The Z-standard score's deviation measure, which the p-value is, can be regarded of as a percentile expression. So they do have p-values.

Given: IQ scores are frequently described as having a normal distribution with a mean of 100.0 and a standard deviation of 15.0. A sample of 57 persons is chosen at random.

Z-score = (X- μ)/σ

             = (98-100)/15

             = -0.1333

P value for this z score equals 0.4470 which is 44.70 %

Therefore, the probability that the average IQ of the sample's population is lower than 987 is 44.70 %.

Learn more about p-value here:

https://brainly.com/question/4621112

#SPJ9

Mandy must to walk a distance of 24.73 units towards Mark.

Given:

Mark is standing at 35th Street and 21st Avenue, so his location can be determined using the coordinates (35,21)

Mandy is positioned at 59th Street and 15th Avenue, hence her position's coordinates are as follows: (59,15).

We must now determine the distance Mandy must travel if Mark stays where he is and walks to meet him.

We can use the distance formula to determine this:

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

Here,

(x₁, y₁) =  (35, 21)

(x₂, y₂) = (59, 15)

Then,

D = [tex]\sqrt{(59-35)^{2}+(21-15)^{2} }[/tex]

D = [tex]\sqrt{24^{2} +6^{2} }[/tex]

D = [tex]\sqrt{576+36}[/tex]

D = √612

D = 24.73

That is,

Mandy must to walk a distance of 24.73 units towards Mark.

Learn more about distance here;

https://brainly.com/question/28996289

#SPJ1

This operation is equivalent to:

It is like a function inside a function. So, we can look for parts in h(x) that are common and call that the function inside.

As we can see, h(x) have terms with x + 4, so if we call:

We can see that h(x) becomes:

And if we substitute g(x) by x, we will get the expression of the ouside function f(x):

This way, we have:

So, the functions are:

Answer: 120

Step-by-step explanation:

[tex]\displaystyle\\10.8:0.09=\\\\\frac{10.8}{0.09}=\\\\\frac{10.8(100)}{0.09(100)}=\\\\\frac{1080}{9} =\\\\\frac{9(120)}{9}=\\\\120[/tex]

The quadrilateral named D, H, and E will be the scaled copies of the unlabeled rectangle.

A quadrilateral may be defined as a closed figure having four sides whereas a rectangle is a type of quadrilateral which has four sides in which any two sides are equal and the other two sides are also equal. The interior angles are 90°. The scale factor may be defined as the ratio of two dimensions such that one figure is large, and another is small. The scale factor is done due to the unpractical measurement of any figure. For example, if a figure is a scale copy of the scale factor of 6/2 it means 2 is converted into 6. Now, from the question If any figure is a scaled copy, then all dimensions must be enlarged with the same factor it means length and width both must be enlarged with the same factor. So, the unlabeled rectangle has 4 grid lengths and 2 grid widths. In H length is 8 grids and width are 4 which is the multiplication of 2 by 4 and 2. Quadrilateral D and E also follow the same.

To learn more about scale factors:

brainly.com/question/22312172

#SPJ9

The reflection of a coordinate about the y = x  will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5).

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

It is known that,

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

Therefore,

A(0, -3) → A'(-3,0)

B(2, 2) → B'(2,2)

C(5,0) →C'(0,5)

Hence "The reflection of a coordinate about the y = x  will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5)".

To learn more about the transformation of graphs,

brainly.com/question/3099136

#SPJ1

The volume of the cube is 27[tex]z^{15}[/tex]

A cube is a three dimensional shape having 6 square faces , all the faces are of equal length , breadth and height.

Here we have to find the volume of a cube

The length of the side is 3[tex]z^{5}[/tex].

The formula for the volume of the cube = a³

where a is the length of the side.

Substituting the value of a we get,

The volume of the cube = (3[tex]z^{5}[/tex])³

                                        = 27[tex]z^{15}[/tex]

Therefore the volume of a cube is 27[tex]z^{15}[/tex].

To know more about the volume of a cube refer to the link given below:

https://brainly.com/question/19891526

#SPJ1

Hello!

So, we are given the following to solve:

[tex]\frac{1}{2}- \frac{9}{4}x=- \frac{2}{3}[/tex]

To solve this, subtract  [tex]\frac{1}{2}[/tex] from both sides.

[tex]\frac{1}{2} -\frac{9}{4}x- \frac{1}{2} =-\frac{2}{3} -\frac{1}{2}[/tex]

Simplify.

[tex]-\frac{9}{4}x= -\frac{7}{6}[/tex]

Multiply both sides by 4.

[tex]4(-\frac{9}{4}x)=4(-\frac{7}{6})[/tex]

Simplify.

[tex]-9x=-\frac{14}{3}[/tex]

Divide both sides by -9.

[tex]\frac{-9x}{-9}= \frac{-14/3}{-9}[/tex]

Finally, simplify.

[tex]x=\frac{14}{27}[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

art I 5.00% per annum ------------- Amount invested =x

Part II 9.00% per annum ------------ Amount invested = y

8000

Interest----- 520.00

Part I 5.00% per annum ---x

Part II 9.00% per annum ---y

Total investment

x + 1 y= 8000 -------------1

Interest on both investments

5.00% x + 9.00% y= 520

Multiply by 100

5 x + 9 y= 52000.00 --------2

Multiply (1) by -5

we get

-5 x -5 y= -40000.00

Add this to (2)

0 x 4 y= 12000

divide by 4

y = 3000

Part I 5.00% $ 5000

Part II 9.00% $ 3000

CHECK

5000 --------- 5.00% ------- 250.00

3000 ------------- 9.00% ------- 270.00

Total -------------------- 520.00

There are 8 tenths in 4/5, There are five fifths in 1/10, there are 2 tenths in 1/5, there are 25 fifths in 5.

The digit that follows the decimal has the place value of tenth. It stands for the digit's 1/10 position.

The fifth of a number is obtained by multiplying five occurrences of the number n together: n5 = n n n n. A number's fourth power or its square by its cube can likewise be used to create fifth powers.

a) Given 4/5, multiply the numerator and denominator by 2 to obtain the tenths. We get =4/5 2/2 =8/10 =8(1/10). Similarly, in 1/5, calculate the tenths in 1/5.

c) 525/25 = 25 is the fifth in 5.

To know more about fifths and tenths, visit:

https://brainly.com/question/1254522

#SPJ9