Select the correct answer.
Consider the function given below.
f(x) = lx-5l +2
Which of the following statements about the y-values of the graph of the function is true?
A. The y-values are all greater than or equal to 5.
B. The y-values are all greater than or equal to 2.
C. The y-values are all less than or equal to 2.
D. The y-values are all less than or equal to 5.

Answer: y= (2/3)x - 2

Step-by-step explanation:

The biggest way to remember equations like these is to know rise over run which means however many times it goes up until it intersects with both x and Y will be on the top of the fraction and however many times it goes to the right until it intersects with both x and y will be on the bottom of the fraction. So since it hits (0, -2) then intersects at (3,0) it will be 2/3x and the Y is where X equals zero so it would be -2. Hope that helps!

Answer:

y  =  [tex]\frac{2}{3}x - 2[/tex]

Step-by-step explanation:

Step 1:

Choose two points on the graph, (x1, y1) and (x2, y2), to find the slope.

Find the ratio between change in y-values and change in x-values.

m = (y2 - y1) / (x2 - x1)

Points I picked:

(x1, y1) = (0, -2)

(x2, y2) = (3, 0)

Then,

m = (0 - (-2)) / (3 - 0)

m = 2/3

Step 2 :

Find the y-intercept from the graph. That is the point at which the line intersects the y-axis.  

The y-intercept is -2.

b  =  -2

Step 3 :

Use the slope (m) and y-intercept (b) to write the equation in slope-intercept form:

y = mx + b

Substitute m = 2/3 and b = -2

y  =  2/3 x - 2

Answer:

the graphical explanation please

4

Step-by-step explanation:

[tex]{ \tt{ \frac{5}{1} \times \frac{4}{5}}} [/tex]

[tex]{ \tt{ \frac{5 \times 4}{5}}} [/tex]

[tex]{ \tt{ = \frac{20}{5}}} [/tex]

[tex] = { \green{ \boxed{ \pink{ \sf{4}}}}}[/tex]

We're assuming Deshaun is driving at a constant speed/at the same rate,

He drove 469 miles in 7 hours -> his speed = 469 : 7 = 67 (mph)

Therefore, it would take him 335 : 67 = 5 hours to drive 335 miles.

He earned $71.5 if he earn $11 /hr. I worked for 6 and a half hrs yesterday.

An hour (symbol: h; also abbreviated as hr) is a measure of time that is traditionally thought of as one-fourth of a day and that, according to science, lasts between 3,599 and 3,601 seconds, depending on how quickly the Earth rotates. There are 24 hours in a day and 60 minutes in an hour. 60 minutes is one of the 24 equally spaced out segments of a day.

Given,

Earns $11/hr

Worked for 6 hours and 30 minutes

Multiplying:

$11 × 6.5 hours

$ 71.5

He earned $71.5 if he earn $11 /hr. I worked for 6 and a half hrs yesterday.

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The populations, considering an exponential function, are given as follows:

An increasing exponential function is modeled according to the rule presented as follows:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which the variables of the function are:

In this problem, the parameters are given as follows:

A(0) = 16, r = 0.2.

Hence the function, written as P(t), is:

[tex]P(t) = 16(1.2)^t[/tex]

The numeric values are found replacing the lone instance of t by the value at which we want to find the numeric value, hence:

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The graph of the linear equation can be seen in the image at the end.

Here we have the linear equation:

y = -2x - 1

To graph this, we need to evaluate from x = -2 to x = 2, this means replacing the value of x by the correspondent number.

if x = -2, then:

y = -2*(-2)  - 1 = 4 - 1 = 3

So we have the point (-2, 3)

if x = -1

y = -2*-1 - 1 = 2 - 1 = 1

We have the point (-1, 1)

If x = 0

y = -2*0 - 1 = -1

We have the point (0, -1)

If x = 1

y = -2*1 - 1 = -3

We have the point (1, -3)

If x = 2

y = -2*2 - 1 = -5

We have the point (2, -5)

Now we just need to graph these 5 points on a coordinate axis and then connect them with a line, the graph of the linear equation can be seen below.

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The equation of the line is ,y= -9x+5.

Acc to our question-,

We should use the slope-intercept formula to solve this problem.

The point-slope formula states:= [ y = mx + c]

Where m is the slope and c is the y-intercept for the point (0,y1)

Substituting the information provided we get the equation: y= -9x+5.

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( 60+12x )/5 fish fisherman will catch in 5+x days .

The unit method is a method of solving a problem by first obtaining the value of a single unit,  then multiplying the value of the single unit to obtain the necessary value.

Assume you go to the market to buy six apples. The shopkeeper told you that he sells 10 apples for 100 rupees. In this case, the apple is the unit and the apple price is the value. Knowing the units and values ​​is important when solving problems using unitary methods.

For simplicity, always write what you calculate on the right and what you know on the left. In the problem above, we know the amount of apples, but we don`t know the value of the apples. Note that the concept of ratio and ratio is used for problems related to this method.

5 days ------------> 12 fish

1 day --------------> 12/5 fish

5 + x days --------------> 12/5 x (5+x)

                                   = ( 60+12x )/5 fish

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The value of x will be= 90 degress.

acc to our question-

hence,The value of x will be= 90 degress.

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Answer:

D.

Step-by-step explanation:

just click the rotate button until it matches one of the answers

The percentage of card  which is not divisor of 45 is 23.077%

Always write the things that need to be estimated on the right side and the variables that are known on the left side to simplify the task. In the important in the current, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are addressed using the concepts of ratio and proportion.

What does the term "percent" mean?

A fraction of one hundred is used to express a quantity or ratio as a percentage. The acronyms "pct," "pct," and occasionally "pc," as well as the percent symbol, "%," are also frequently used.

A % is a numeric expression that lacks both dimensions and a measurement system. The formula to determine the proportion of one number to another is percentage = (Original number/Another number) x 100.

In mathematics, a percentage is a number or ratio that represents a portion of 100. In percentages, 100% is meant. It contains no units.

A %, also known as a decimal or a fraction, is a figure that indicates how many out of 100 we are discussing. For example, "three for the price of one" is a percentage.

Given That:

In the deck of 52 cards You pick randomly 5 , 6 , 7 , 8
so each card has 4 variant
now for getting probability of not getting a divisor of 45 is
total outcomes = 52
observable outcomes = 4+4+4 = 12
its because 5 is a divisor so we didn't include it
hence the probability is 12/52
Percentage of this probability is 0.23077 x 100 = 23.077%

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Answer:

116.

Step-by-step explanation:

Your welcome <3.

Answer:

116

Step-by-step explanation:

Examining the figure, the correct options are

Two angles are said to be congruent when they are equal to each. The symbol to represent congruency is ≅

The following angles are congruent in the figure

Corresponding angles refers to angles that are in a position that are in matching position to another angle.

Corresponding angles are said to be equal when there are parallel lines intersected across by a line called transversal line.

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The dimensions of this rectangular tank that has the minimum surface area are 42 feet and 21 feet.

First of all, we would determine the surface area of this rectangular tank with a square​ base by using this formula:

h = V/s²

Where:

For the surface area of this rectangular tank with a square​ base, we have:

Surface area, A = base area + 4(lateral area)

Surface area, A = s² + 4(s × h)

Surface area, A = s² + 4(s × V/s²)

Surface area, A = s² + 4V/s

Next, we would take the first derivative of the surface area as follows:

A' = 2s - 4V/s²

Substituting the given parameters into the formula, we have;

A' = 2s - 4(37044)/s²

For the minimum surface area dimension, the first derivative of the surface area would be equated to zero:

2s - 148,176/s² = 0

148,176/s² = 2s

148,176 = 2s³

s³ = 74,088

s = ∛74,088

s = 42 feet.

For the height, we have:

Height, h = V/s²

Height, h = 37044/42²

Height, h = 37044/1764

Height, h = 21 feet.

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Answer:

3x^2-2x+3+1/x+2

Step-by-step explanation:

The linear equation we need to solve is:

$25.50*w = $309.99 - $131.49

And the solution is w = 7.

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $131.49, and save another $25.50 per week, then the amount you have after w weeks is:

f(w) = $131.49 + $25.50*w

So the linear equation we need to solve is:

$131.49 + $25.50*w = $309.99

To solve this we need to isolate w.

$131.49 + $25.50*w = $309.99

$25.50*w = $309.99 - $131.49

w = ($309.99 - $131.49)/$25.50 = 7

So they can buy the chair after 7 weeks.

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Answer:

A fruit seller buys 712 fruits of which 3/4 are apples. The apples that he bought 1/3 were found to be rotten if he sold all the good apples at Rs.5 1/4 each.

Step-by-step explanation:

Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.

Martin now has: 6 + m

The coordinates of G(4, 4) , H (0, 2),  J(8, 0)

In order to construct the three sets of relationships between the coordinates of each triangle's three sides' ends and the shared midpoint, we must first set up the three sets of relationships.

G(x(G), y(G))

K(2, 3) (2, 3)

M(6, 2) (6, 2)

H(x(H) and y(H))L (4, 1)

J(x(J), y(J))

K(2, 3) at the midway of side GH

According to the x-component:

x(H) = x(G - x(H))/2

x(G)-[x(H)-x(G)] = 2*x(H)

x(H) + x(G) = 4

x(H) = 4 - x(G) (G)

According to the y-component:

y(H) plus [y(G) - y(H)]/2 = 3.

2*y(H) plus [y(G-y(H)] = 6

y(H) + y(G) = 6

y(H) = 6 - y(G) (G)

Midpoint L(4) and side JH(1):

According to the x-component:

(x(H) + [x(J) - x(H)]/2) equals four.

2*x(H) plus [x(J)-x(H)] = 8

x(H) + x(J) = 8

x(H) = 8 - x(J) (J)

According to the y-component:

y(H) = y(J - y(H)]/2 + y(J) = 1

y(J) - y(H) = 2*y(H)

y(H) + y(J) = 2

y(H) = 2

Side GJ with M(6, 2) as the midpoint:

For the x - component, the formula is: x(J) = [x(G) - x(J)]/2 = 6 2*x(J) = [x(G)- x(J)] = 12 x(J) = 12 - x (G)

y(J) + [y(G) - y(J)]/2 = 2 2*y(J) + [y(G)- y(J)] for the y-component. = 4 y(J) = 4 - y + y(G) = 4 y(J) (G)

The x and y coordinates may now be easily separated, and we can use algebra to isolate each one and determine its location.

x(H) = 4 - x(G), 8 - x(J), and 12 - x(J) (G)

Because x(H) = x (H)

4 - x(G) = 8 - x(J) (J)

8 - x(J) - 8 - x(G) - 4 = -x(J) x(J) x(J) = 4 + x (G)

Using 1.c above and this relationship now x(J) = x(J), so:

-2 * x(G) = -8 x(G) =, 4 12 - x(G) = 4 + x(G) 12 - x(G) - x(G) - 12 = 4 + x(G) - x(G) - 12

Given that x(J) = 4 + x(G) above, x(J) = 4 + 4 = 8 and x(H) = 4 - x(G) = 4 - 4 = 0 respectively.

Let's now perform the identical procedure using the y-coordinates.

y(H) = 6 - y(G), y(H) = 2 - y(J), y(J) = 4 - y(G),

and since y(H) = y(H), 6 - y(G) = 2 - y(J), -y(G) = 2 - y(J) - 6 = -y(J) - 4 y(G) = y(J) + 4 Now that y(J) = 4 - y,

we may substitute (G).

y(H) = y(G) - 2 and y(H) + 4 - y(G) = 2

and y(H) + 4 - y(G) = 2 - 4 and y(G)

Since y(H) = 6 - y(G)

according to 1. above, y(H) = y(G) - 2 + 6 - y(G) 2 * y(H) = 4 y(H) = 2 y(H) = 2 - y(J) 2 = 2 - y(J) y(J) = 4 - y(G) 0 = 4 - y(G) y(G)

H(x(H), y(H)), G(x(G), y(G)), and J(x(J), y(J)) are the results.

To determine the coordinates of the angles or triangle's tips, we used the midpoints of each side.

The coordinates are: H (0, 2) G(4, 4) J(8, 0)

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Answer:

Step-by-step explanation:

42feet

The value of the number 9.15 x 10° written in standard form is equal to 9.15.

As given in the question,

Given number is equal to :

9.15 x 10°

Given number 9.15 x 10°  is written in standard form.

The value of the given number 9.15 x 10°  written in standard form is given by:

9.15 x 10°

Here 10° = 1

Using property of number: Any number raise to zero is always equal to 1.

9.15 x 1

Using Multiplicative identity , number multiply to 1 remain number itself.

= 9.15

Therefore, the value of the number 9.15 x 10° written in standard form is equal to 9.15.

The complete question is:

What is the value of 9.15 x 10° written in standard form?​

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There is a total of 2152 yes votes

From the question, the statement is given as

The ratio of yes votes to no votes was 4 to 7

Mathematically, this can be represented as

Ratio = 4 : 7

Alternatively, we have

Yes : No = 4 : 7

Express the ratio as fraction

Yes = Yes/Yes + No

So, we have

Yes = 4/4 + 7

Evaluate the sum

Yes = 4/11

From the question, we have

Total votes = 5918

So, we have

Yes = 4/11 * 5918

Evaluate

Yes = 2152

Hence, the number of yes votes is 2152

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Answer:

765

Step-by-step explanation:

After using the property of power, the expressions as a power of the number a is [tex](a^3)^{-2} = a^{-6}[/tex] , [tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex] and [tex]((a^2)^{-2})^2=a^{-8}[/tex] .

In the given question we have to solve the given expressions as a power of the number a where a≠0.

The first given expression is [tex](a^3)^{-2}[/tex].

Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

Simplifying the expression.

[tex](a^3)^{-2} = a^{3*(-2)}[/tex]

[tex](a^3)^{-2} = a^{-6}[/tex]

The second expression is [tex](a^{-1}\cdot a^{-2})^{-3}[/tex]

Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(-1)\times(-3)}\cdot a^{(-2)\times(-3)}[/tex]

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{3}\cdot a^{6}[/tex]

Using the property of sum of power [tex]a^m\cdot a^n=a^{m+n}[/tex]

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(3+6)}[/tex]

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex]

The third expression is [tex]((a^2)^{-2})^2[/tex].

Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

[tex]((a^2)^{-2})^2=((a^2)^{(-2)\times2})[/tex]

[tex]((a^2)^{-2})^2=(a^2)^{-4}[/tex]

Again using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

[tex]((a^2)^{-2})^2=a^{2\times(-4)}[/tex]

[tex]((a^2)^{-2})^2=a^{-8}[/tex]

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1/[tex]a^{6}[/tex] is the required number.

Numbers, symbols and operators (such as and times) grouped together that show the value of something.

Given an expression (a³)^-2

(a³)^-2 = [tex]a^{-6}[/tex] = 1/[tex]a^{6}[/tex]

Hence, 1/[tex]a^{6}[/tex] is the value of the expression (a³)^-2

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Option A is the correct answer g(x) = |x+3| by using the relation with the parent function.

Explain absolute value function.

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.

The definition of the absolute value parent function, f(x)=| x |, is as follows:

f(x) = [tex]\left \{ {{x ~, ~ x > 0} \atop {0 ~ , ~x = 0}} \atop {-x ~, ~x < 0} \right.[/tex]

Given parent function is f(x) = |x|

g(x) is obtained by stretching the graph of f(x) by a factor of 3.

Use the function g(x)=f(x−h) to translate the absolute value function f(x)=| x | horizontally.

The graph of f(x) is moved h units to the right to obtain g(x) for h>0

The graph of f(x) is translated h units to the left to obtain g(x) when h>0

Therefore, g(x) = |x+3|

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