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Examine the diagram.


Name two corresponding angles to ∠1.
∠6 and ∠15
∠5 and ∠6
∠13 and ∠15
∠5 and ∠13

Answer: Domain (-∞,∞) ; range: (0,∞)

Step-by-step explanation:

1. The exponential functions with the form [tex]f(x)=ab^{x}[/tex] has domain of all real numbers, becaure there is no values in the set of real number for which the value of [tex]x[/tex] is not define. When [tex]x[/tex] approches to ∞, the function approches to ∞.

2. When [tex]x[/tex] approches to -∞, the function approches to 0 but never touches it. This means  that [tex]y[/tex] is always greater than zero ([tex]y>0[/tex]). Therefore, the range of the function is (0,∞).

Answer:

Lesson 1 unit 5 exponential, logarithmic, pricewise functions

Step-by-step explanation:

1. A and D

2. C

3. B

4.c

The figures in a plane can be reflected, rotated, translated or dilated to produce new figures or images.

A transformation that moves all points to the same distance and in the same direction. The final figure looks the same, just moved over. It does not flip or gets rotated. It also does not change size.This type of translation is called glide reflection. Its the summation of translation and reflection.

Answer:

Glide Reflection

Step-by-step explanation:

c is the correct equation

given ΔABC is similar to ΔPQR

then the ratios of corresponding sides are equal.

the sides a, b and c inΔABC correspond to the sides p, q and r in ΔPQR

thus the following ratios are equal

[tex]\frac{a}{p}[/tex] = [tex]\frac{b}{q}[/tex] = [tex]\frac{c}{r}[/tex]

from this we can see that [tex]\frac{c}{r}[/tex] = [tex]\frac{a}{p}[/tex] → c

A 2x + 6 is the quotient

Answer:

The quotient in polynomial form is 2x+6

Step-by-step explanation:

use the synthetic division

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

-1             2          8        6

               0          -2       -6            

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

               2          6         0

Now we use the quotient we got.

quotient is 2  and 6. Remainder is 0

In quotient we have only two numbers

So we write it as 2x+6

The quotient in polynomial form is 2x+6

Answer:

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

Step-by-step explanation:

we have to multiply 15 and 4.

then find the factors of this product.

we get,

15 x 4=60

Now, factors of 60 which make 4 are 6 and 10

because   6-10=-4

So,

[tex]15 x^{2}-4x-4\\ =15x^{2} -10x+6x-4\\[/tex]

Now, we have to take common factor pairwise.

Taking 5x as common factor from first pair and 2 from second pair,

we get

[tex]15x^{2} -10x+6x-4\\=5x(3x-2)+2(3x-2)\\=(3x-2)(5x+2)[/tex]

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

consider the factors of the product 15 × - 4 = - 60

which sum to give the coefficient of the middle term ( - 4 )

the factors required are - 10 and + 6

split the x- term using these factors

15x² - 10x + 6x - 4 ( factor by grouping )

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

Take out the common factor (3x - 2)

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

a no the corresponding angles are not congruent

∠A ≠ ∠E and ∠D ≠ ∠H

Answer:

No, the corresponding angles are not congruent.

Step-by-step explanation:

In the bigger model, the corresponding angles are 1 degree bigger

Given rational expression is

[tex]-\frac{8x}{8x^2+2x}[/tex]

Now we need to find the restricted values if any for this rational expression.

Restricted values means the possible values of the used variable (x) that will make denominator 0 as division by 0 is not defined.

So to find the restricted values, we just set denominator equal to 0 and solve for x

[tex]8x^2+2x=0[/tex]

[tex]2x(4x+1)=0[/tex]

2x=0 or 4x+1=0

x=0 or 4x=-1

x=0 or x=-1/4

Hence final answer is x=0, -1/4

To find the restricted values of a rational expression, set the denominator equal to zero and solve for x.

To find the restricted values of the rational expression, we need to determine the values of x that will make the denominator of the expression equal to zero. When the denominator is zero, the expression is undefined.

In this case, the denominator is 8x2 + 2x. We set this equal to zero and solve for x:

8x2 + 2x = 0

Factor out 2x:

2x(4x + 1) = 0

Set each factor equal to zero:

2x = 0, 4x + 1 = 0

Solve each equation:

x = 0, x = -1/4

Therefore, the restricted values of x for the given rational expression are 0 and -1/4.

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B

the range of the function are the values that the domain map to

here range { - 4, 1, 7 , 15 }

The range is the output values (also known as the y values)

-4, 1, 7 ,15 or letter B

Answer:

Unit rate is 2.69 cups of water for 1 cup of lime juice.

Step-by-step explanation:

Rate of water (cups) per lime juice (cups) means how much water (cups) is added to 1 cup of lime juice to make limeade.

This can be calculated as,

Unit rate = Number of water (cups) / Number of lime juice (cups)

Unit rate = [tex]\frac{35}{13}[/tex]

Unit rate = 2.69 cups of water for 1 cup of lime juice.

g=1

Add like terms on both sides. That would lead to 2+6g=11-3g

Add -6g to both sides or add 3g  to both sides so that g is on one side. Also get the whole numbers on the opposite side to get 9g=9 or -9g=-9. That makes g=1

(11)

the equation of a line in point- slope form is

y = mx + c ( m is the slope and c the y-intercept

thus y = 4x + 3 ← in slope-intercept form

the equation of a line in point- slope form is

y - b = m(x - a ) ( m is slope and (a, b ) a point on the line )

thus y - 3 = 4 ( x - 0 ) or y - 3 = 4x ← in point- slope form

the equation of a line in standard form is

Ax + By = C ( a is a positive integer and B, C are integers

rearrange y - 3 = 4x into this form

4x - y = - 3 ← in standard form

(12)

y = - 2x - 1 ← in slope-intercept form

y + 1 = - 2x ← in point- slope form

2x + y = - 1 ← in standard form

Answer:

$996

Step-by-step explanation:

The rectangular plot has an area that is the product of its length and width. We are given the width as 12 feet, and the area as 240 ft², so we can find the length from ...

... A = L×W

... 240 ft² = L×(12 ft)

... 240 ft²/(12 ft) = L = 20 ft

Opposite sides of the rectangle are the same length, so the cost of fence for a side of a given length will be the sum of the costs of the opposites sides.

The 12 ft side has one segment that is $18 per foot, and one that is $15 per foot. For the 20 ft sides, both are $15 per foot. Then the total cost can be figured from ...

... (12 ft)·($18/ft + $15/ft) + (20 ft)·($15/ft +$15/ft) = 12·$33 +20·$30 = $996

Steps:

subtract 3 from both sides:

2x²-5x+1 - 3 = 3 - 3

Simplify:  

2x² - 5x  - 2 = 0

Solve with the quadratic formula :

for a =  2 , b = - 5 ,  c =  - 2

x₁ =  -  ( - 5 ) +√ ( -5 )² - 4 * 2 ( - 2 )  / 2 * 2 =

x₁ =  5 + √ 41 / 4

x₂ = -  ( - 5 ) - √ ( -5 )² - 4 * 2 ( - 2 )  / 2 * 2

x₂ = 5 - √ 41 / 4

∠ a and ∠ d ( 2 arcs at angles indicate corresponding angles ) ;

∠ b and ∠ c ( single arc at angles indicate corresponding )

Answer:

What does the multiplication property of equality allow us to do while solving equations?

C. The multiplication property of equality allows us to multiply both sides of the equation by the same value to maintain equivalent equations.

~batmans wife dun dun dun...

The multiplication property of equality in Mathematics allows us to multiply both sides of an equation by the same value without affecting the equality. This property is useful for simplifying equations and finding unknown variables.

The multiplication property of equality is a crucial concept in solving equations. It states that if you have an equation, you can multiply the same quantity to both sides of the equation without affecting the equality. Essentially, what it says is captured in option C: The multiplication property of equality allows us to multiply both sides of the equation by the same value to maintain equivalent equations.

For example, if we have an equation 2x = 8, we can apply the multiplication property of equality by multiplying both sides of the equation by 1/2 (the reciprocal of 2) to find the value of x, without changing the balance of the equation. So, 2x * 1/2 equals 8 * 1/2, simplified gives us x = 4. This helps in simplifying complex equations and reaching the solution.

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the function has only 2 points of discontinuity. Both a jump and removable discontinuity

The data shown in the graph states that the graph is continuous at point  [tex][-2,1][/tex]  and  [tex][-1, 2.5][/tex] and discontinuous at [tex](-2,2)[/tex] and [tex](-1,3)[/tex].

The graph is a systematic representation of data in pictorial form. The definition of continuity states that the function is defined at that point, and discontinuity defines that the function is not defined at that point.

The information provided in  the given graph states that the function is defined at the point[tex][-2,1][/tex] and[tex][-1, 2.5][/tex] and discontinuous at [tex](-2,2)[/tex] and [tex](-1,3)[/tex] which is represented in the form of holes.

The graph is continuous at point  [tex][-2,1][/tex]  and  [tex][-1, 2.5][/tex] and discontinuous at [tex](-2,2)[/tex] and [tex](-1,3)[/tex].

Learn more about continuity here:

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x³ - 3x² + 4x - 2

complex roots occur in conjugate pairs

1 + i is a root then so is 1 - i

the factors of the polynomial are therefore

f(x) = (x - 1 )(x - (1 + i))(x - (1 - i))

     = (x - 1 )(x² - 2x + 2 ) ( expand factors and simplify )

     = x³ - 3x² + 4x - 2

Answer:

f(x) = x3 – 3x2 + 4x – 2

Step-by-step explanation:

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\(\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad(\stackrel{x_2}{4}~,~\stackrel{y_2}{-6})\qquad \qquadd = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\d=\sqrt{[4-(-2)]^2+[-6-2]^2}\implies d=\sqrt{(4+2)^2+(-6-2)^2}\\\\\\d=\sqrt{6^2+(-8)^2}\implies d=\sqrt{100}\implies d=10[/tex]

EF = 10

to calculate the distance use the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (4, - 6 )

EF = √(4 + 2 )² + (- 6 - 2 )² = √(36 + 64 ) = √100 = 10

{(−7, 2), (−2, 2), (0, 1), (4, 5)} = B

Element x contains negative 4, negative 3, negative 1, and 1. Element Y contains negative 3, negative 1, and 4. = C

i hope this helps, i got kinda confused :/

Answer:

1) Domain -7, -2, 0, 4

Range 1, 2, 5

2) Domain -4, -3, -1, 1

Range -3, -1, 4

Step-by-step explanation:

1) Given relation,

{(−7, 2), (−2, 2), (0, 1), (4, 5)}

That, has the input values, -7, -2, 0, 4,

And, has the output values 2, 1, 5

We know that the set of all possible input values of a relation is called the domain of the relation,

While the set of all possible output values is called the range of the relation,

Thus, the domain of the above relation would be,

{ -7, -2, 0, 4 }

And, the range of the function,

{ 1, 2, 5 }

2) In the second relation,

Negative four maps to negative 1. Negative three maps to negative 3 and 4. Negative one maps negative 1. One maps to 4.

Let g(x) be the relation,

⇒ g(x) = {(-4, -1), (-3, -3), (-3, 4), (-1,-1), (1,4)}

Input values are -4, -3, -1, 1,

⇒ Domain = { -4, -3, -1, 1 }

Also, output values are  -1, -3, 4,

⇒ Range = { -3, -1, 4 }

[tex] \: \: \: \: \: \: \: \: \: \: \: \bold{ - 2x = - 9 - 5}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ - 2x = - 14}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = \cfrac{ - 14}{ - 2}} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = \cfrac{14}{2} }[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = 7}[/tex]

Note: For a problem like this, we must first subtract the number that is 5, then we must know that two negatives make a positive and that we must add 9 and 5 to give us 14, then we must put it as a fraction since it makes it easier for us to finish the problem, next it is known that two negative signs make a positive thus eliminating the less Parentheses and finally we divide so that we get a result of[tex]\bold{ x = 7}[/tex]

To solve a function like this, simply put the numerical value in place of the unknown variable for which you have to find the solution, for instance '-3' in this case.

g(x) = 2x-2

so to find g(-3), we just need to replace the x in the given expression by '-3'. Working is shown below:

g(x) = 2x-2

putting '-3' in place of x

g(-3) = 2(-3) - 2

g(-3) = -6 -2

g(-3) = -8

13 .3333... = 13 [tex]\frac{1}{3}[/tex] %

percentage increase is calculated as [tex]\frac{increase}{original}[/tex] × 100%

increase = 255 - 225 = 30 and original = 225

[tex]\frac{30}{225}[/tex] × 100% = 13.33.... % = 13 [tex]\frac{1}{3}[/tex] %

we are given

[tex]\frac{(1.6\times 10^{8})(5.8\times 10^{6})}{(4\times 10^{6})}[/tex]

Since, we have to write this in scientific form

so, we will make all 10^x terms together

and all other terms together

so, we get

[tex]=\frac{(1.6\times 5.8) (10^{8}\times 10^{6})}{(4\times 10^{6})}[/tex]

we can multiply terms

[tex]=\frac{(9.28) (10^{8+6})}{(4\times 10^{6})}[/tex]

[tex]=\frac{(9.28) }{4} \times 10^{8+6-6}[/tex]

[tex]=2.32 \times 10^{8}[/tex]

so, option-B...........Answer

Answer:

2.32 x 10^8

Step-by-step explanation:

2.32 x 108

108 + 6 - 6 = 108

and

(1.6)(5.8)

(4)

=  

9.28

4

= 2.32

thus,

2.32 x 108

5 nine-hour days is a total of 5×9 = 45 hours.

If 45 hours are worked in 4 days, the daily average is

... 45/4 = 11 1/4 . . . hours

They will need to work 11 hours 15 minutes daily if they switch.

We don't actually know what the problem originally was, so we don't know what the error was or what the correct answer should be.

If the numbers on the left are given, and the problem is to find the number on the right, then ...

Paolo added 0.2 instead of subtracting it.

-0.43 -0.2 = -0.63 . . . . . correct answer

_____

If the left and right numbers are given and the problem is to find the one in the middle, then ...

Paolo incorrectly calculated 0.43 -0.23, getting -0.2 instead of +0.2.

-0.43 +0.2 = -0.23 . . . . correct answer

_____

If the problem is to find the term on the left, then ...

Paolo incorrectly added 0.2 and -0.23, getting -0.43 instead of -0.03.

-0.03 -0.2 = -0.23 . . . . correct answer

If they're making 75 pies an hour, and working 8 hours a day, you would multiply 8 by 75. 8x75=600. Hope this helps!

Answer:

-5/3

Step-by-step explanation:

The slope of the line between two points is the "rise" divided by the "run". That is, it is the ratio of the vertical change to the horizontal change.

It is usually convenient (but not necessary) to choose the horizontal change to be positive when finding slope from a graph.

When finding slope from a pair of point coordinates, you can do the math with the points in any order. The x- and y-values need to correspond, meaning if you subtract the first y-value from the second, you must also subtract the first x-value from the second.

slope = (change in y)/(change in x) = ∆y/∆x

... = (3-8)/(-4-(-7)) . . . . . . . . (difference of y-values)/(difference of x-values)

slope = -5/3

24 rows of seats

let n be the number of rows

then the number of seats per row = n + 4

number of seats = number of rows × number of seats per row

n(n + 4 ) = 672

n² + 4n - 672 = 0 ← in standard form

the factors of - 672 which sum to + 4 are + 28 and - 24

(n + 28)(n - 24) = 0

equate each factor to zero and solve for n

n + 28 = 0 ⇒ n = - 28

n - 24 = 0 ⇒ n = 24

number of rows n > 0

number of rows = 24 and number of seats per row = 28

24 × 28 = 672 as a check

Answer: 9x - y = -7

Step-by-step explanation:

Ax + By = C

9x + 7 = y

9x + 7 - y = 0

9x - y = -7

Hope this helps! :)

9x - y = - 7

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

rearrange y = 9x + 7 into this form ( subtract y from both sides )

0 = 9x - y + 7 ( subtract 7 from both sides )

9x - y = - 7 ← in standard form