Problem Solving
ercises: Solve each problem.
CW ALL WORK. Use a separate sheet of paper (if necessary) and staple to this page.
The Acme Supply Store sells a security system for $2150,00 excluding tax. They
sold 12 systems. If the total profit on these sales was $4824.36, how much did
each system cost Acme Supply? Show your work.
I think the answer is $1,747.97​

The slope is [tex]-10[/tex] and the y-intercept is [tex]1[/tex].

This function is written in slope-intercept form, which is [tex]y=mx+b[/tex].  In this form, [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

In this case, [tex]m=-10[/tex] and [tex]b=1[/tex], so those are the answers to this problem.

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

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

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following equation:

[tex]y = -10x + 1[/tex]

So we have to:

[tex]m = -10\\b = 1[/tex]

Answer:

[tex]m = -10\\b = 1[/tex]

Answer:

A

Step-by-step explanation:

3y (-5)(y+2)

3y(-5y-10)

3y-5y-10

-2y-10

-2y-10

3y - 5(y +2)

Use the distributive property:

3y - 5y +10

Combine like terms:

-2y+10

The answer is B.

Final answer:

To simplify (f+g)(2) with given functions f(x)=x+1 and g(x)=x^2-x, calculate the functions' values at x=2 and sum them, resulting in (f+g)(2) = 5.

Explanation:

To find and simplify the expression (f+g)(2), you first need to determine the individual functions f(x) and g(x) at the value x = 2, and then sum them.

The function f(x) is given by f(x) = x + 1. At x = 2, f(2) = 2 + 1 = 3.

The function g(x) is given by g(x) = x2 - x. At x = 2, g(2) = 22 - 2 = 4 - 2 = 2.

Adding these two results together, we get (f+g)(2) = f(2) + g(2) = 3 + 2 = 5.

Answer:62

Step-by-step explanation:

F=c+32

C=30

F=30+32

F=62

The Fahrenheit temperature equivalent to 30°C (using the formula  F = C + 32) is  62°F.

The Fahrenheit temperature equivalent to 30°C can be found using the temperature conversion formula F = C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius.

To find the temperature in Fahrenheit, substitute 30 for C:

F = 30°C + 32 = 62°F

Answer:

See attachment

Step-by-step explanation:

The given function is:

[tex]f(x)=3^{x-1}+2[/tex]

This is an exponential function with a horizontal asymptote at  [tex]y=2[/tex]

There is a translation of the form [tex]f(x)=g(x-1)+2[/tex]

The graph of the parent function [tex]g(x)=3^{x}[/tex] is shifted to the right 1 unit and shifted up by 2 units.

See attachment for graph.

Answer:

That may be one of the answers but it is check all that apply

Step-by-step explanation:

ANSWER

(0, 1), (1,3), (2, 9), (3, 27)

EXPLANATION

For an exponential function, there is a common ratio among the terms.

Therefore we need to examine the y-values of the ordered pairs to see which one has a common ratio.

For the first option, the y-values are:

0,1,8,27

[tex] \frac{27}{8} \ne \frac{8}{1} [/tex]

For the second option, the y-values are:

1,2,5,10

[tex] \frac{10}{5} \ne \frac{5}{2} [/tex]

For the third option, the y-values are:

0,3,6,9

[tex] \frac{9}{6} \ne \frac{6}{3} [/tex]

For the last option, the y-values are:

1,3,9,27

[tex] \frac{27}{9} = \frac{9}{3} = \frac{3}{1} = 3[/tex]

Since there is a common ratio of 3, the set of ordered pairs (0, 1), (1,3), (2, 9), (3, 27) could generate an exponential sequence.

Answer:

y=5/4x-4

Step-by-step explanation:

C. y = 5/4x - 4.

One of the three ways we may express a straight line is in slope-intercept form. The other forms are known as point slope form and standard form, however in this section we will mostly use slope-intercept form. The slope-intercept form is used to write a line's equation as y = mx + c.

You may be aware that a point's coordinates on a graph are x and y.

Given two coordinates of a line from that, we can calculate the slope.

slope m = (y₂ - y₁)  /  (x₂- x₁)

m = 5/4

Put the value of m and one coordinate value in the slope-intercept equation

-4 = 5/4 * 0 + c

c = -4

therefore slope-intercept equation of given coordinates is y = 5/4x - 4.

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Answer:

C

Step-by-step explanation:

(-3,0)

I did it in the quiz and the test.

Got it correct.

Answer:

7776π  or

24,429.02 unit^3 to the nearest  hundredth.

Step-by-step explanation:

The formula for the volume of a sphere is V = 4/3 π r^3   where r is the radius.

Here V = 4/3 * π * 18^3

= 7776π unit^3.

Answer:

7776 pi

Step-by-step explanation:

In a scale model, Figure A has one side measuring 45 units and another side measuring x, while Figure B has corresponding sides of 27 and 18 units. By setting up a proportion, x is determined to be 30 units.

To find the value of x, we can set up a proportion based on the given information:

In Figure A, one side is 45, and in Figure B, it corresponds to a side of 27.

In Figure A, the other side is x, and in Figure B, it corresponds to a side of 18.

So, we can set up the following proportion:

(45 / 27) = (x / 18)

Now, cross-multiply and solve for x:

45 * 18 = 27x

810 = 27x

Now, divide by 27 to find the value of x:

x = 810 / 27

x = 30

So, the value of x is 30.

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Answer:

p - q

Step-by-step explanation:

Given the factors

(x + p)(x - q) ← expanding the factors

= x² - qx + px - pq ← collect like terms

= x² + px - qx - pq ← factor out x in each of the x- terms

= x² + (p - q)x - pq

The coefficient of the x- term is p - q

Answer:

(x, y ) → (x + 4, y - 3 )

Step-by-step explanation:

A translation of 4 units to the right is a positive shift in the x- direction, that is,

The x- coordinate of the image is the original + 4

A translation of 3 units down is a negative shift in the y- direction, that is

The y- coordinate of the image is the original - 4

Putting the 2 together

(x, y ) → (x + 4, y - 3 )

Answer:

See explanation

Step-by-step explanation:

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

[tex](x,y)\to (y,-x)[/tex]

[tex]\implies A(-3,6)\to (6,3)[/tex]

[tex]\implies B(0,4)\to (4,0)[/tex]

[tex]\implies C(2,6)\to (6,-2)[/tex]

We apply the 90 degrees clockwise rotation rule again on the resulting points:

[tex]\implies (6,3)\to A''(3,-6)[/tex]

[tex]\implies (4,0)\to B''(0,-4)[/tex]

[tex]\implies (6,-2)\to C''(-2,-6)[/tex]

Let us now apply 90 degrees counterclockwise  rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

[tex](x,y)\to (-y,x)[/tex]

[tex]\implies A(-3,6)\to (-6,-3)[/tex]

[tex]\implies B(0,4)\to (-4,0)[/tex]

[tex]\implies C(2,6)\to (-6,2)[/tex]

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

[tex]\implies (-6,-3)\to A''(3,-6)[/tex]

[tex]\implies (-4,0)\to B''(0,-4)[/tex]

[tex]\implies (-6,2)\to C''(-2,-6)[/tex]

We can see that A''(3,-6), B''(0,-4) and C''(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

(x,y) --- (y, -x)

A(-3, 6) > (6, 3)

B(0, 4) > (4, 0)

C(2, 6) > (6, -2)

We apply the 90 degrees clockwise rotation rule again on the resulting points:

(6, 3) > A'(-3, 6)

(4, 0) > B'(0, -4)

(6, -2)> C'(-2, -6)

Let us now apply 90 degrees counterclockwise  rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

(x,y) --- (-y, x)

A(-3, 6) > (-6, -3)

B(0, 4) > (-4, 0)

C(2, 6) > (-6, 2)

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

(-6, -3) > A'(3, -6)

(-4, 0) > B'(0, -4)

(-6, 2) > C'(-2, -6)

We can see that A'(3,-6), B'(0,-4) and C'(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

Ez why to copy

Answer:

[tex]\large\boxed{y=\dfrac{1}{2}x+1}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{We have:}\ m=\dfrac{1}{2}\ \text{and the point}\ (6,\ 4).\\\\\text{The equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinates of the point to the equation:}\\\\4=\dfrac{1}{2}(6)+b\\\\4=3+b\qquad\text{subtract 3 from both sides}\\\\1=b\to b=1\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x+1[/tex]

Answer:

The slope is -4.

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex]

[tex]\displaystyle \frac{(-9)-(-5)}{1-0}=\frac{-4}{1}=-4[/tex]

Therefore, the slope is -4, and the correct answer is -4.

Hope this helps!

Answer:

A) 12,14,16

B) 3x+1=16

Step-by-step explanation:

A)

They already gave you the equation to solve:

n+(n+2)+(n+4)=42

n+n+2+n+4=42

Put like terms together:

n+n+n+2+4=42

Combine the like terms:

3n+6=42

Subtract 6 on both sides:

3n=42-6

Simplify:

3n=36

Divide both sides by 3:

n=36/3

Simplify:

n=12

If n=12,

then

n+2=14 and

n+4=16.

Check the addition of those numbers: 12+14+16=26+16=42.

B)

There is a lot of equations that have a solution of 5.

It might be good start with x=5.

Then just remember whatever you do to one side, you must do to the other.

x=5

Multiply both sides by 3:

3x=15

Add 1 on both sides:

3x+1=16

An example of equation that solution 5 is 3x+1=16.

Answer:

x> 5

Step-by-step explanation:

x - 8 > -3

Add 8 to each side

x - 8+8 > -3+8

x> 5

Answer:

[tex]\huge \boxed{x>5}[/tex]

Step-by-step explanation:

First, add by 8 from both sides of equation.

[tex]\displaystyle x-8+8>-3+8[/tex]

Simplify, to find the answer.

[tex]-3+8=5[/tex]

[tex]\huge \boxed{x>5}[/tex], which is our answer.

Answer:

15.5

Step-by-step explanation:

So the formula here is the square of the tangent length is equal to the product of the exterior part of the secant line and total length of the secant.

So that means we have x^2=10(14+10).

After simplifying the right hand side we have the equation is x^2=10(24) or x^2=240.

To get rid of the square on the x, we square root both sides.

x=sqrt(240)

x=15.49193338

To the nearest tenths, the answer is x=15.5

So 15.5 inches is the length of x.

Answer:

4.54%

Step-by-step explanation:

Step 1: Write the data

Total bill = $170

Penalty = $7.72

Percentage of penalty = ?

Step 2: Write the formula to find the percentage of penalty

Percentage of penalty = Penalty/Total bill * 100

Percentage of penalty = 7.72/170 * 100

Percentage of penalty = 4.54%

Therefore, the percent of penalty is 4.54%

!!

Answer:

Area of the polygon = 59 in²

Explanation:

From the given diagram, we can note that the given polygon is composed of an upper triangle, a side triangle and a rectangle

Therefore:

Area of polygon =

area of upper triangle + area of side triangle + area of rectangle

1- getting the area of the upper triangle:

We have:

base of triangle = 7 in

height of triangle = 6 in

Therefore:

Area of upper triangle = [tex]\frac{1}{2}*base*height = \frac{1}{2}*7*6=21[/tex] in²

2- getting the area of the side triangle:

We have:

base of triangle = 4 in

height of triangle = 5 in

Therefore:

Area of upper triangle = [tex]\frac{1}{2}*base*height = \frac{1}{2}*4*5=10[/tex] in²

3- getting the area of the rectangle:

We have:

length of rectangle = 7 in

width of rectangle = 4 in

Therefore:

Area of rectangle = length x width = 7 x 4 = 28 in²

4- getting the total area of the polygon:

Area of polygon =

area of upper triangle + area of side triangle + area of rectangle

Therefore:

Area of polygon = 21 + 10 + 28 = 59 in²

Hope this helps :)

Answer: [tex]AC=10.5[/tex]

Step-by-step explanation:

Assuming that [tex]b=AC[/tex] and given the following equation:

 [tex]tan(55\°)=\frac{15}{b}[/tex]

You need to solve for "b" in order to find the lenght of AC asked in the exercise.

 Therefore, with this procedure you get that the lenght of AC is the following:

[tex]\frac{15}{tan(55\°)}=b[/tex]

[tex]b=AC=10.5[/tex]

Answer:

[tex]\large\boxed{(b)\ \dfrac{x+2}{x-3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{x+1}+\dfrac{x}{x-3}-\dfrac{-x-5}{x^2-2x-3}=(*)\\\\x^2-2x-3=x^2-3x+x-3=x(x-3)+1(x-3)=(x-3)(x+1)\\\\(*)=\dfrac{1(x-3)}{(x+1)(x-3)}+\dfrac{x(x+1)}{(x+1)(x-3)}+\dfrac{-(-x-5)}{(x+1)(x-3)}\\\\=\dfrac{x-3+x^2+x+x+5}{(x+1)(x-3)}=\dfrac{x^2+(x+x+x)+(-3+5)}{(x+1)(x-3)}\\\\=\dfrac{x^2+3x+2}{(x+1)(x-3)}=\dfrac{x^2+2x+x+2}{(x+1)(x-3)}=\dfrac{x(x+2)+1(x+2)}{(x+1)(x-3)}\\\\=\dfrac{(x+2)(x+1)}{(x+1)(x-3)}\qquad\text{cancel (x + 1)}\\\\=\dfrac{x+2}{x-3}[/tex]

Answer:

Jay needs a 94 on his next test to get an average of 93 on all of his exams.

Step-by-step explanation:

The way test averages work is you take the sum of all of your tests and divide it by the number of tests. So he got an 87 on test 1, a 98 on test 2, and an unknown score on test 3 because he hasn't taken it yet.

Let x = that unknown score. The number of tests is 3. So we set up our equation as:

(87 + 98 + x) / 3

He wants an average of 93 so we set the equation equal to just that.

(87 + 98 + x) / 3 = 93

In order to isolate the numerator equation by itself, we multiply both side by 3. That way the 3 in the denominator on the left side cancels out. You now have:

87 + 98 + x = 93(3)

Simplify:

185 + x = 279

Now to get x by itself, we subtract 185 from both sides:

x = 279 - 185

x = 94

He needs a score of 94 on the next test for the test average that he wants.

Answer:

The correct option is A

Step-by-step explanation:

Lets suppose that the third side is hypotenuse.

We will apply Pythagorean theorem:

c²= a²+b²

where,

a=12 inches

b=15 inches

Now substitute the values in the theorem:

c²=(12)²+(15)²

c²=144+225

c²=369

Take square root on both sides:

√c²=√369

c= 19.2 inches.

Now assume that the third side is a leg:

Here we will find the value of b.

a=12 inches

c= 15 inches.

b= ?

Now substitute the values in the theorem:

c²=a²+b²

(15)²=(12)²+b²

225=144+b²

Move the constant to the L.H.S

225-144=b²

81=b²

Take square root on both sides:

√81=√b²

9=b

Now we will find the difference of the third sides:

19.2-9 = 10.2

Thus the length of the third side is 10.2 inches

The correct option is A....

Answer:

A.

Step-by-step explanation:

Answer:

30√3 - 21 √6

Step-by-step explanation:

The given expression is:

3√2 (5√6 -7√3)

We cannot subtract the values inside the bracket because the values inside the radicals are not same.

So multiply 3√2 with the bracket.

=3*5√2*6 -  3*7√2*3

=15√12 - 21√6

Now break √12

=15√4*3 - 21√6

write √4*3 separately:

=15√4 *√3 - 21√6

We know that √4 = 2

=15*2*√3 - 21√6

=30√3 - 21 √6

Therefore the answer is 30√3 - 21 √6 ....

Answer:

TRUE:

When x≈2.7, the graphs of f(x) and g(x) intersect

f(x)=g(x) when x=0

Step-by-step explanation:

The graphs of two function y=f(x) and y=g(x) are shown in attached diagram.

These two graphs intersect at two points (0,-3) and about (2.7,2.3). This means that

f(0)=g(0)=-3

and

f(2.7)=g(2.7)=2.3

So, x=0, y=-3 is the solution to the system (the solution to the system is ordered pair (x,y), not only x)

Points (1.5,0) and (2,0) are not solutions, because they are not points of graphs intersection.

When x≈2.7, the graphs of f(x) and g(x) intersect (TRUE)

f(x)=g(x) when x=0 (TRUE)

Answer:

f(x)=g(x) when x=0.

x=0 is a solution to the system.

When x≈2.7, the graphs of f(x) and g(x)intersect because they are equal to each other at that value.

Answer:

The sum is [tex]9,331[/tex]

Step-by-step explanation:

we have

[tex]1,6,36,...[/tex]

we have

[tex]a1=1[/tex]

[tex]a2=6[/tex]

[tex]a3=36[/tex]

Find the common ratio r

[tex]a2/a1=6/1=6[/tex]

[tex]a3/a2=36/6=6[/tex]

The common ratio is r=6

The formula to calculate the sum in a geometric sequence is equal to

[tex]S=a1\frac{(1-r^{n})}{(1-r)}[/tex]

where

n is the number of terms

r is the common ratio

a1 is the first term

we have

[tex]n=6[/tex]

[tex]a1=1[/tex]

[tex]r=6[/tex]

substitute

[tex]S=(1)\frac{(1-(6)^{6})}{(1-6)}[/tex]

[tex]S=\frac{(1-(6)^{6})}{(-5)}[/tex]

[tex]S=9,331[/tex]

To find the exact value of cos(127.5), we can use the half angle identity for cosine. By substituting the angle into the half angle identity and simplifying, we find that cos(127.5) is approximately ±0.99992.

The cosine function is a trigonometric function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. To find the exact value of cos(127.5), we can use the half angle identity for cosine. This identity states that cos(θ/2) = ±√((1 + cos(θ))/2), where θ is the original angle.

In this case, we have θ = 255 degrees (since 127.5 is half of 255). Using the half angle identity, we can calculate cos(127.5) as follows:

Therefore, the exact value of cos(127.5) is approximately ±0.99992.

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