Amanda is placing an order for running shoes and leather boots for her footwear boutique. She needs a total of 48 pairs of shoes and twice as many pairs of running shoes as leather boots.

Set up the two equations that can be used to find the number of each type of shoe that Amanda needs to order.

Let the equation that represents the total number of pairs of shoes be referred to as constraint 1.
Let constraint 2 refer to the equation that describes the ratio of the number of running shoes to leather boots.



Only constraint _ would be met if 18 pairs of leather boots and 36 pairs of running
shoes were ordered.

Only constraint _ would be met if 12 pairs of leather boots and 36 pairs of running shoes were ordered.

The graph at option 4 represents the given equation y = -4x - 3 correctly. This is obtained by calculating the slope and finding the y-intercept.

The slope of a line given by

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

The ratio of the difference between y-coordinates of two points on the line to the difference of their x coordinates.

The equation is y = -4x - 3

On comparing the equation with the slope-intercept form y = mx + c,

m = -4 and y-intercept c = -3.

Since the y-intercept is -3, the graphs at options 1 and 2 do not represent this equation. So, the remaining graphs may represent the given equation.

The graph at option 3 has a line with two points (2, 5) and (0, -3)

So, the slope is

m = [tex]\frac{-3-5}{0-2}[/tex]

   = 4

Thus, it is not the same as the slope of the given equation.

The graph at option 4 has a line with two points (-2, 5) and (0, -3)

So, the slope is

m = [tex]\frac{-3-5}{0+2}[/tex]

   = -4

Thus, the line shown in the graph at option 4 has a slope of -4 and the y-intercept is -3. These are the same as the given equation. So, option 4 is correct.

Therefore, the graph at option 4 is the correct representation of the given equation.

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Answer:

see explanation

Step-by-step explanation:

The standard form of a quadratic equation is

ax² + bx + c = 0 : a ≠ 0

Express the equations in this form and extract the coefficients

1

4 - 2x + 3x² = 0 , that is

3x² - 2x + 4 = 0 ← in standard form

with a = 3, b = - 2 and c = 4

2

x(x + 5) - 2x = 0 ← distribute parenthesis

x² + 5x - 2x = 0

x² + 3x = 0 ← in standard form

with a = 1, b = 3 and c = 0

3

x² - 2x(x - 2) + 5 = 0 ← distribute parenthesis and simplify

x² - 2x² + 4x + 5 = 0

- x² + 4x + 5 = 0 ← in standard form

with a = - 1, b = 4 and c = 5

Answer:

66

Step-by-step explanation:

We know x = -4. To solve, we just need to plug in -4 for x.

6 (-4 + 15) =

6 (11) =

66

Answer:

66

Step-by-step explanation:

x= -4  

6(x + 15)

Substitute x =-4 into the second equation

6(-4+15)

6(11)

66

Slope formula: y2-y1/x2-x1

Plug in: -15-0/-11-3 = -15/-14 = 15/14 = slope

For this case we have by definition, the slope of a line can be found by the following formula:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

Two points are needed through which the line passes.

According to the data we have:

[tex](x_ {1}, y_ {1}) :( 3,0)\\(x_ {2}, y_ {2}): (- 11, -15)[/tex]

Substituting we have:

[tex]m = \frac {-15-0} {- 11-3} = \frac {-15} {- 14} = \frac {15} {14}[/tex]

ANswer:

The slope is [tex]\frac {15} {14}[/tex]

ANSWER

The common ratio is -3.

EXPLANATION

In general, the common ratio of a Geometric Sequence is given by:

[tex] r = \frac{a_{n+1}}{a_{n}} [/tex]

We can find the common ratio using any two consecutive terms of the geometric sequence by dividing the subsequent term by the previous term.

The given sequence is -2,6,-18,54

Using the first two terms the common ratio is

[tex]r = \frac{6}{ - 2} = - 3[/tex]

We could also used the second and third terms to get

[tex]r = \frac{ - 18}{6} = - 3[/tex]

and so on and so forth.

Therefore the common ratio is -3.

His average pay was:

Answer:

£1350

----------- = £8.44/hr   based upon  160 work hours per week

160 hr

Step-by-step explanation:

We must assume that Han works a standard 40-hour week, and that there are 4 weeks in each month.  That comes to 160 hours.

Then his average hourly pay rate was

£1350

--------- = £8.44

160 hr

Answer:

[tex]{\huge \boxed{x=-2}[/tex]

Step-by-step explanation:

First you do is add and subtracting numbers from left to right.

-5+6=1

-9x+1=19

Then subtract by 1 from both sides of equation.

-9x+1-1=19-1

Simplify.

-9x=18

Divide by -9 from both sides of equation.

-9x/-9=18/-9

Simplify, to find the answer.

18÷-9=-2

x=-2 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

x=-2

Step-by-step explanation:

-9x -5+6=19

Combine like terms

-9x +1 = 19

Subtract 1 from each side

-9x +1-1 = 19-1

-9x = 18

Divide by -9

-9x/-9 = 18/-9

x = -2

Alright (so what I did was type this into desmos and it was the exact same line but it was the other way around so it is) C

Changing from y = -3x + 5 to y = 2x + 5 would make the slope steeper.

The slope of the new graph would become steeper.

When changing from y = -3x + 5 to y = 2x + 5, the original slope of -3 increases to 2, making the new graph steeper.

Therefore, the correct answer is D. The slope of the new graph would become steeper.

Answer:

umm his friends each got 1/8

Step-by-step explanation:

hernando ate 2/8 meaning 8-2=6= 6/8

6/8 / 6 = 1/8

:D

I guess this what you want

After Hernando ate  [tex]\frac{2}{8}[/tex] of the pizza, the remaining pizza when divided equally among his friend leaves each friend with  [tex]\frac{1}{8}[/tex] of the pizza

Given: Hernando ate [tex]\frac{2}{8}[/tex] of a pizza, number of friends is 6

First, let's find out what fraction of the pizza is left after Hernando ate his portion. Hernando ate  [tex]\frac{2}{8}[/tex], which reduces to [tex]\frac{1}{4}[/tex]. Therefore, the remaining fraction of the pizza is:

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

The remaining [tex]\frac{3}{4}[/tex] of the pizza is to be shared equally among his 6 friends. To find out how much pizza each friend gets, we divide the remaining fraction by the number of friends:

[tex]\frac{3}{4}[/tex] ÷ 6 [tex]=\frac{3}{4} \times \frac{1}{6} = \frac{1}{8}[/tex]

Each of Hernando's 6 friends gets [tex]\frac{1}{8}[/tex] of the pizza.

Answer:  84

Step-by-step explanation:

Set up a proportion as follows: [tex]\dfrac{\text{students that practice everyday}}{\text{total students}}[/tex]

[tex]\dfrac{7}{12}=\dfrac{x}{144}[/tex]

Cross multiply: 12x = 7 × 144

Divide by 12:         x = 7 × 12

Simplify:                x = 84

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=\stackrel{altitude}{height}\\ \cline{1-1} r=3\\ h=9 \end{cases}\implies V=\cfrac{\pi (3)^2(9)}{3}\implies V=27\pi \implies V\approx 84.8[/tex]

Answer:

6.06 x [tex]10^{9}[/tex]

Step-by-step explanation:

(5.25 x [tex]10^{5}[/tex] ) / (8.7 x [tex]10^{-5}[/tex] )

= (5.25 x [tex]10^{5}[/tex] ) x( [tex]10^{5}[/tex] )/ (8.7 )

= (5.25 x [tex]10^{5 + 5}[/tex] )/ (8.7 )

= 0.606 x [tex]10^{10}[/tex]

= 6.06 x [tex]10^{9}[/tex]

Answer:C 13/2

Step-by-step explanation: you do 13 x 0.5 equals 6.5, convert to a fratcion equals 13/2

Answer:

[tex]\frac{13}{2}[/tex]

Step-by-step explanation:

When you have a whole number, you gotta add a denominator, so just add 1 underneath:

[tex]\frac{13}{1}[/tex]

Then you have

[tex]\frac{13}{1}[/tex] ×[tex]\frac{1}{2}[/tex]

Multiply straight across and you get

[tex]\frac{13}{2}[/tex]

Answer:

(-1, 0)

Step-by-step explanation:

Jim, please use the symbol " ^ " to indicate exponentiation:

y = x^3 + 3x^2 – x – 3.  Thanks.

A "turning point" is a point on the graph of a function at which the derivative changes sign (e. g., from positive to negative or vice versa).  To identify turning points, we differentiate the given function twice, set the second derivative equal to zero and identify the x-values at which the sign of the derivative changes.

Given y = x^3 + 3x^2 – x – 3,

          dy/dx = 3x^2 + 6x - 1

           d²y

          ------ = 6x + 6            and this is zero at x = -1.

           dx²

We can easily show that the 2nd derivative changes sign at x = -1.

Thus, the only turning point here is (-1, [-1]³ + 3[-1]² - [-1] - 3), or (-1, 0).

Answer: (-2,3) and (0,-3)

Step-by-step explanation:

Answer:

y - 1/3 = 3/4(x - 4)

Step-by-step explanation:

We know that the general equation of a line is the following:

y - yo = m(x-xo), where 'm' represents the slope of the line, and (xo, yo) is any point that belongs to the line.

Then, the equation of the line that passes through (4, 1/3) and has a slope of 3/4 is: y - 1/3 = 3/4(x - 4)

For this case we have that by definition, the slope-intersection equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

They tell us as data that:

[tex]m = \frac {3} {4}[/tex]

Now the equation is:

[tex]y = \frac {3} {4} x + b[/tex]

We substitute the point to find "b":

[tex](4, \frac {1} {3})[/tex]

[tex]\frac {1} {3} = \frac {3} {4} (4) + b[/tex]

[tex]b = \frac {1} {3} -3\\b = - \frac {8} {3}[/tex]

Finally the equation is:

[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]

In point-slope form the equation is:

[tex]y- \frac {1} {3} = \frac {3} {4} (x-4)[/tex]

Answer:

[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]

Answer:

- (- 10)

Step-by-step explanation:

Point A is positioned at - 10 on the number line.

The opposite is the negative of the value

That is the opposite of - 10 is - (- 10)

1.

Cubic Polynomial--

A cubic polynomial is a polynomial of degree three.

2.

End behavior--

The end behavior of a function is it's behavior when x tends to infinity in both the directions i.e. when x tends to minus infinity and when x tends to plus infinity.

3.

Irreducible--

A polynomial is said to be irreducible if it can't be reduced i.e. it cannot be factored.

4.

Leading coefficient--

It is the coefficient of the highest degree term existing in the expression.

5.

Leading term--

It is the term with the highest degree.

6.

quartic polynomial-

A quadratic polynomial is a polynomial of degree 4.

7.

Zeros of polynomial--

The zeros of a polynomial are all the possible values of x at which the polynomial expression is equal to zero.

Answer:

A

Step-by-step explanation:

ABC to CAB, use that method to help you. You can research more on it.

Each line on the graph is one unit.

AB = 15 units long

Answer:

15 units

Step-by-step explanation:

Since A and B are along the same horizontal line, we count count the number of units to determine the distance

The horizontal distance from A to B is 15 units

To find the area of a rhombus, multiply the two diagonals together then divide by 2.

Area = 20 *15 = 300 / 2 = 150 sq. units.

Power = Current *Voltage  

You already have the current, but not the voltage.  

But you are given resistance, and you know that  

Voltage=Current*Resistance  

Therefore  

V=I*R=4*12=48V  

So you have 48V  

Now you can figure out the Power  

P=I*V=4*48=192W  

Therefore you have 192W.

hope this helps

The total power in a circuit is 192W.

Power exists at the time rate of excess or absorbing energy. The power delivered or absorbed by an element exists as the product of the current flowing through the component and the voltage across the element. Power exists estimated in watts. If the power exists positive then it exists absorbed by the component and if it exists negative then it is supplied by the element.

Power = Current [tex]*[/tex] Voltage

We have the current, but not the voltage.

But you are given resistance, and you know that

Voltage = Current [tex]*[/tex] Resistance

Therefore,

[tex]V=I*R=4*12=48V[/tex]

So you have 48V

Thus, we get the Power

[tex]P=I*V=4*48=192W[/tex]

Therefore, the total power in a circuit is 192W.

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Answer:

44.238

Step-by-step explanation:

50.441-6.203=44.238

Answer:

x^2 -2x-8

Step-by-step explanation:

f(x) = x + 2

g(x) = x – 4

(f*g) (x) = (x+2) (x-4)

    FOIL

first x*x = x^2

outer  -4*x = -4x

inner 2*x = 2x

last = -4*2 = -8

Add them together

x^2 -4x+2x -8

x^2 -2x-8

Answer:

C on ed

Step-by-step explanation:

Answer: A. It would be shifted up.

Step-by-step explanation: the only thing that is changing in the two equations is the last number. The last number is not there in the second equation because the y-intercept is 0. The y-intercept in the first equation is -2 and shifts up 2 to y-intercept if 0. Therefore, your answer would be A. It would shift up.

The graph of the new equation compared with the original graph is the new graph would be shifted up.

Option A is the correct answer.

We have,

If the equation y = 12x - 2 were changed to y = 12x, the graph of the new function would be different from the original.

The original equation y = 12x - 2 represents a linear function with a slope of 12 and a y-intercept of -2.

The graph of this equation would be a straight line that is steep (with a slope of 12) and shifted downward by 2 units (due to the y-intercept of -2).

However, if we change the equation to y = 12x, the new equation represents a linear function with the same slope of 12 but with no y-intercept (it passes through the origin).

The graph of this equation would still be a straight line, but it would be shifted up compared to the original equation since the y-intercept has been removed.

Therefore,

It would be shifted up.

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y = –16(x – 2)² + 68 is the equation which models the motion of the ball.

Two or more expressions with an Equal sign is called as Equation.

Given that Ryan throws a tennis ball straight up into the air.

The ball reaches its maximum height at 2 seconds.

The approximate height of the ball x seconds after being thrown is shown in the table.

We need to find the equation of the motion of the ball.

Let us take a point (0, 4) from the table.

The right equation is the point in which the equation satisfies.

y=-17(0)(0-4)

4=0

So y = –17(x)(x – 4) is false.

y = –16(x – 2)² + 68

4=-16(4)+68

The point (0, 4 ) satisfies the equation y = –16(x – 2)² + 68

Hence, y = –16(x – 2)² + 68 is the equation which models the motion of the ball.

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f(x) is the total number of hours overall that he has worked out.

x would be the number of weeks he works out.

You would multiply x ( number f weeks he works out) by 7 and then add that to the hours he already worked out (15) which will give you the total hours (f(x)).

Answer:

In this case, x represents "week", because they problem says that he exercises 7 hour per week, being week an unknown number because we don't how much time Luke is gonna keep exercising. Si, 7x represents the total amount of hours per week after the first 15 hours.

Similarly, f(x) represents the total amount of hour from the beginning, before the first 15 hours. The difference between x and f(x) is that the first one represents hours after the 15 hours, and the second one represents the total amount of hours, including before the 15 hours.

It's important to notice that 15 is not multiplied by a variable, it's because those 15 hours are already achieve, we don't if those where monthly or weekly, but the fact that they already happened means that they can't change, that's why the don't have a variable.

Answer:

A and D

Step-by-step explanation:

The remainder after division is 8, that is the 8 at the end of 2 - 4 8

Given f(x) divided by (x + h)

Then if (x + h) is a factor the remainder = 0

Hence (x + 7) is not a factor since remainder is 8

and f(- h) = remainder

that is f(- 7) = 8 → D

A and D are the correct statements.

In option  A f(-7) is the remainder which gives the value 8.

So, option A is correct.

When we put x = 7 in the function it is coming 99

So, option B and C are wrong.

So options D is correct

So, option E is wrong.

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