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The coordinates of the image after reflection over line y = 1 is

preimage         Image

J(2, 4                J' (2. -2)

K(-4,-2)              K' (-4. 4)

L( − 1, 0)             L' (-1, 2)

Reflection is one of the movements in transformation that involve creation of mirror image

The reflection to be done is over line y = 1

Transformation rule for reflection over line y at origin (0, 0)) is

(x, y) → (x, -y)

However, reflection over line y = 1 which is (0, 1) is  done as follows

J(2, 4) ⇒ (2, 4 - 1) ⇒ (2, 3) ⇒ (2, 1 - 3) → J' (2, -2)

from 4 to 1 = 4 - 1 = 3 units

reflecting 3 units over y = 1

1 - 3 = -2

J' (2, -2)

K(-4,-2) ⇒ (-4, -2 - 1) ⇒ (-4, -3) ⇒ (-4, 1 - -3) ⇒ K' (-4, 4)

from -2 to 1 = -2 - 1 = -3 units

reflecting -3 units over y = 1

1 - -3 = 4

K' (-4, 4)

L (-1, 0) ⇒ (-1, 0 - 1) ⇒ (-1, -1) ⇒ (-1, 1 - - 1) ⇒ L' (-1, 2')

from 0 to 1 = 0 - 1 = -1 unit

reflecting -1 unit over y = 1

1 - -1 = 2

L' (-1, 2)

see graph for more information

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Given the expression below

The general form of a quadratic equation is

Using the completing the square method,

Where b =10 from the given equation

For part A, the numerical value to be added is 25

Hence, for part A, the answer is 25-25

By completing the square

Hence, for part B, the answer is (x+5)²-38

The value of the angle m∠DAC is 74° as AB bisects ∠DAC .

We know from the properties of angles that the angle bisector will bisect the angle into two equal parts.

∠DAC is bisected by the straight line AB. This forms two angles ∠DAB and ∠BAC .

∠DAC =∠DAB + ∠BAC

now, ∠DAB = ∠BAC

given that ∠DAB = 37

Hence m∠BAC = 37

now,

∠DAC = ∠DAB + ∠BAC

m∠DAC = 37° + 37°

m∠DAC = 74°

A line that divides an angle into two equal angles is known as an angle bisector in geometry. A device that splits an object or form into two equal halves is referred to as a "bisector." A ray that divides a given angle into two identical segments of the same length is called an angle bisector.

Therefore the value of m∠DAC is 74° .

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1) Since these triangles are congruent, then we can write out the following for congruent triangles have congruent sides:

2) Still based on that principle, we can plug v=2 into any of those formulas to get the measure of QS and TV. So let's pick the simpler one:

As we can see these segments are congruent.

Answer:

[tex] \rm x = 8 \pm 6i [/tex]

Step-by-step explanation:

Given equation: x² - 16x = -100

x² - 16x + 100 = 0

By comparing given equation with standard quadratic equation i.e. ax² + bx + c = 0 we get:

a = 1

b = -16

c = 100

Quadratic formula:

[tex] \boxed{ \rm x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} } [/tex]

Now, substituting the values in the quadratic formula:

[tex] \rm \implies x = \dfrac{ - ( - 16) \pm \sqrt{ {( - 16)}^{2} - 4(1)( 100) } }{2(1)} \\ \\ \rm \implies x = \dfrac{ 16 \pm \sqrt{ 256 - 400} }{2} \\ \\ \rm \implies x = \dfrac{ 16 \pm \sqrt{-144 } }{2} \\ \\ \rm \implies x = \dfrac{ 16 \pm 12i }{2} \\ \\ \rm \implies x = 8 \pm 6i [/tex]

Answer:

x has no real solutions.

x = 8 + 6i, x = 8 - 6i

Step-by-step explanation:

First, move the all the terms to one side of the equation.

x^2 - 16x + 100 = -100 + 100

x^2 - 16x + 100 = 0

Then, based on our knowledge of the standard form of a quadratic equation: ax^2 + by + c = 0, we can plug the coefficients in front of the variables into the formula, which looks like [tex]x=\frac{-b+or-\sqrt{b^2-4ac} }{2a}[/tex].

Our a here is 1,

The b is -16,

The c is 100.

plugging it in:

[tex]\frac{-(-16)+or-\sqrt{(-16)^2-4*1*100} }{2*1}[/tex]

simplifies down to:

16/2 + or - (√(256 - 400))/2

= 8 + or - √(-36)

Here, we have a negative square root, meaning there will be no roots for this equation in the real number system.

If you include imaginary/complex numbers, this equation will have roots.

x = 8 + or - √(-36)

x = 8 + or - 6√(-1)

x = 8 + or - 6i

so the final answer:

x = 8 + 6i, x = 8 - 6i

An equation which is most likely used to determine the acceleration from a velocity vs. time graph is: B. m = (y₂ - y₁) / (x₂ - x₁).

A velocity vs. time graph can be defined as a type of graph that is used to graphically represent the rate of change of velocity of an object with respect to time.

In Mathematics, the velocity of a physical object is plotted on the horizontal axis (y-coordinate) time is while plotted on the vertical axis (x-coordinate) of a velocity vs. time graph.

Mathematically, the acceleration of a physical object on a velocity vs. time graph can be calculated by determining the rate of change (slope) as modeled by this formula:

Acceleration, m = change in velocity/change in time

Acceleration, m = (y₂ - y₁) / (x₂ - x₁).

Where:

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Complete Question:

Which equation is most likely used to determine the acceleration from a velocity vs. time graph?

answer choices

A. a = t/delta v

B. m = (y₂ - y₁) / (x₂ - x₁)

C. a = delta v/t

D. m = (x₂ - x₁) / (y₂ - y₁)

Answer:

B. m = StartFraction v subscript 1 - v subscript 2 Over x subscript 2 minus x subscript 1 EndFraction.

Step-by-step explanation:

Got 100% on the test. Y'all have a good day! :D

SOLUTIONS

(a) What is the product of 3x - 4 and 5x² - 2x + 6? Write your answer in standard form.

The product is

The product will be

The product of 4 - 3x and 5x² - 2x + 6 will be equal to the -1 multiply be the product of 3x - 4 and 5x² - 2x + 6, thus the two product are same

Checking

Hence the two answer are the same.

Answer:

3(4−x)²

Step-by-step explanation:

Answer:

3(4-x)^2

Step-by-step explanation:

factor

Answer:

0.33

Step-by-step explanation:

The specific number (females prefer cycling = 0.15) and the fitting total. There are 2 possibilities for that total :

all females

all people preferring cycling

the way it was phrased I would say the reference is all females.

the conditional relative frequency is then

0.15 / 0.46 = 0.326=0.33(rounded)

Hence the conditional relative frequency that a female prefers running is 0.33

Answer: 5 1/2 feet

Step-by-step explanation: 6 1/2ft - 1ft = 5 feet

Good Question! Jk

For a given simultaneous equation,

The point at which both the lines intersect gives us the solution.

Thus,

the point A gives the solution of the system of equation.

Answer is A.

The value of y when x=12 is 600

The values of y vary directly with x

y α x

y = kx

where k is the proportationality constant

The values of y=425 when x=8.5

y = kx

425 = k (8.5)

k = 50

We need to find the value of y when x=12

y = kx

y = 50 x 12

y = 600

Therefore,  the value of y when x=12 is 600

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The value of the composite function is found as 68/5.

The function is given as;

g(x) = 32/(x+3)

Write the function as 'y'

y = 32/(x+3)

Replace the value of x with y.

x = 32/(y+3)

Solve for y.

x(y + 3) = 32

xy = 32 - 3x

y = (32 - 3x)/x

Thus, g⁻¹ (x) = (32 - 3x)/x is the inverse of the function.

Now, find the value composite function;  (g⁻¹ o g) (5).

(g⁻¹ o g) (5) =  (32 - 3x)/x . 32/(x+3)

Put x = 5

(g⁻¹ o g) (5) =  (32 - 15)/5 . 32/(5+3)

(g⁻¹ o g) (5) = 17×4/5

(g⁻¹ o g) (5) = 68/5

Thus, the value of the composite function is found as 68/5.

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Given:

Percentage discount = 15%

Let's find the expression that does not represent the cost of an item in the store.

Let c represent the original cost of an item.

To find the c

Solution

For this case we can do the following:

The scatterplot shows the weakest negative linear correlation is On a graph points are grouped closely together and increase. Option A.

The scatterplot showing the weakest negative linear correlation is the following scatterplot. The dots are scattered along the decreasing trend line. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that an increase in one variable tends to increase the other variable.

A negative correlation means that as one variable increases the other tends to decrease. Plotted points indicate correlations between variables if any. The scatterplot above is an example of a weak negative correlation. In this graph, y values ​​decrease as x values ​​increase, but the pattern does not resemble a straight line.

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The value of -175-15- (-204) is 14

We learn to add and subtract two or more integers or any other mathematical values using the two basic arithmetic operations of addition and subtraction. The plus sign (+) stands for addition, whereas the negative sign (-) stands for subtraction (minus sign). The opposite of addition is subtraction and vice versa.

The following are rules for addition and subtraction:

=>  [tex]+ \times + = +[/tex]

=>  [tex]- \times - = +[/tex]

=>  [tex]+ \times - = -[/tex]

=>  [tex]- \times + = -[/tex]  

Here we have

-175-15- (-204)

=> - 175 - 15 + 204

=>  - 190 + 204

=>  14

Therefore,

The value of -175-15- (-204) is 14

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Answer:

Step-by-step explanation:

We have similar figures given.

The ratio of corresponding sides of similar figures is same as per definition of similarity.

Use this property and solve each question.

Considering x is positive, PS and MN are longer legs of right triangles.

Answer:

The answer is -3x + 6y = 36

Step-by-step explanation:

19)

The given system of equations is,

The above system of equations can be written in matrix form as,

Here,

Therefore, equation (1) can be written as,

Therefore,

Now, we need to calculate the inverse of A.

(Note:

Let a 2x2 matrix P is of the form given below.

The inverse of the matrix P is,

)

Similar to the inverse matrix of 2x2 matrix P, the inverse matrix of A can be written as,

Now, put the values in equation (2) to find the solution to the system of equations.

Therefore, the solution to the system of equations using inverse matrix is x=2 and y=-1.

Answer:

Table 1 is the only table which represents PROBABILITY DISTRIBUTION table.

Step-by-step explanation:

c, d, and e. this is because c equals 21, d equals 27, and e equals 9

The simplification of four fourths over nine written as 4/4 ÷ 9 is given by 1/9

Fraction refers to a number which consists of a numerator and a denominator.

A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.

Given: four fourths over nine

= 4/4 ÷ 9

= 1 ÷ 9

= 1/9

Or alternatively

4/4 ÷ 9

= 4/4 × 1/9

= (4 × 1) / (4 × 9)

= 4/36

= 1/9

In conclusion, the fraction four fourths over nine is simplified as 1/9

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We are given log ( 10^3)

We can use one of the properties of logs

log u^n = n log u

Rewriting log ( 10^3) using this property

log ( 10^3) = 3 log 10

log has an implied base of 10

log 10 = 1

3 log 10 = 3 *1 =3

The two correct choices are

A. 3 * log 10

D. 3

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

The perimeter of the floor in the scale drawing is 58 inches.

The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.

The letter "p" stands for the perimeter, which is equal to twice the width plus twice the length of the rectangle.

Given, the length of rectangular classroom is 36 feet

and the width is 22 feet.

The scale drawing has a length of 18 inches.

Here we can see that two different units are used.

So, we need to convert feet to inches.

1 foot = 12 inches

Now we will convert the length in inches,

36 feet = 36*12 inches

            = 432 inches

Now we will convert the width in inches,

22 feet = 22*12

            = 264 inches

Now, we will calculate by how many times the length has been scaled down:

[tex]\frac{432}{18} = 24[/tex]

So, the length has been scaled down to 24 times.

Now, we will scale down the width 24 times:

[tex]\frac{264}{24} = 11[/tex]

So, the width of the scale drawing is 11 inches.

Now, we will find the perimeter of the scale drawing:

Perimeter = 2(scale down length + scale down width)

                = 2(18+11)

                =2*29

                =58 inches

Therefore, the perimeter of the scale down drawing is 58 inches.

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The value of the expression ''93 to the power of 7'' will be;

⇒ 60,170,087,060,757

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is,

''93 to the power of 7''

Now,

Solve the expression as;

93 to the power of 7 = 93⁷

                                = 93 × 93 × 93 × 93 × 93 × 93 × 93

                                = 60,170,087,060,757

Thus, The value of the expression ''93 to the power of 7'' will be;

⇒ 60,170,087,060,757

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Answer:

[tex]y=-\frac{1}{2} +1[/tex]

Step-by-step explanation:

We have to choose two points in the graph:

P₁ = (0, 1)     → x₁ = 0  &  y₁ = 1

P₂ = (2, 0)   → x₂ = 2  &  y₂ = 0

Now any of those point can be the P₀ I'll choose P₁ as P₀

P₀ = (0, 1)     → x₀ = 0  &  y₀ = 1

[tex]y - y_o=\frac{y_2-y_1}{x_2-x_1}(x-x_0)\\ \\y-1 = \frac{0-1}{2-0}(x-0)\\ \\y-1=\frac{-1}{2}(x) \\\\y-1=-\frac{1}{2}x\\ \\y=-\frac{1}{2}x+1[/tex]

Answer:

6 8/17

Step-by-step explanation:

17 x 6 is 102 so that can go into 110

Then you do 110-102 to find how many are left over 110-102= 8 so there are 8 left over so that goes into the numerator so the answer is 6 8/17 The denominator stays the same unless you can simply but in this case you can’t.

The graph given is has the cubic function as the parent function.

The cubic function is shown below: