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Answer:

Step-by-step explanation:

Givens

Area = L * w

w = x

l = x  + 4

Area = 32

Solution

32 = x(x + 4)

32 = x^2 + 4x

x^2 + 4x - 32

(x + 8)(x - 4)

Only x - 4 is going to make any sense

x - 4 = 0

x = 4

The width is 4

The length is 4 + 4 = 8

4*8 = 32 which is the area.

Final answer:

To find the length and width of the barn wall, set the width as w and form a quadratic equation w(w + 4) = 32. Solve the equation to find that the width is 4 feet and the length is 8 feet.

Explanation:

The student is asking how to find the length and width of a rectangular barn wall when the area is given (32 square feet) and the length is 4 feet longer than the width. To solve this, let's represent the width of the wall as w feet. Thus, the length will be w + 4 feet. The area of a rectangle is found by multiplying the length by the width, which gives us the equation w(w + 4) = 32.

Let's solve this quadratic equation:

Rewrite the equation: w² + 4w = 32.

Subtract 32 from both sides to set the equation to zero: w² + 4w - 32 = 0.

Factor the quadratic equation: (w + 8)(w - 4) = 0.

Solve for w: w = -8 (reject because width can't be negative) or w = 4 (accept).

Thus, the width of the wall is 4 feet and the length is 4 + 4 = 8 feet.

Answer:

The function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2.

The vertex of the function is (-2,-1)

Domain of the function is (-∞, +∞)

Range of the function is [-1, +∞).

Step-by-step explanation:

The function has a graph in two parts.

The right side part passes through the points (-2,-1) and (0,3).

So, the equation of this part will be  

[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - 0}{0 - (- 2)}[/tex]

⇒ y - 3 = 2x

⇒ y = 2x + 3

Again, the left side part of the graph passes through the points (-2,-1) and (-4,3).

Therefore, the equation of this part will be  

[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - (- 4)}{- 4 - (- 2)}[/tex]

⇒ y - 3 = - 2(x + 4)

⇒ y - 3 = - 2x - 8

⇒ y = - 2x - 5

Therefore, the function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2. (Answer)

The vertex of the function is (-2,-1) (Answer)

Domain of the function is (-∞, +∞) (Answer)

Range of the function is [-1, +∞). (Answer)

Answer:

25

Step-by-step explanation:

60 per day 25 in sales 63.75-60=3.75

3.75÷.15=25

If Nicole's earns 15% commission of her total sales, then Nicole's total sale of Monday is 25.

Percentage is a part of the whole number. It is denoted by % sign.

1 %= 1/100.

Given that,

Total salary of Nicole's = $60.

Also,

Nicole gets 15% commission of her total sales,

Total earning on Monday = $63.75

The commission earned on Monday = 63.75 - 60 = 3.75

According to given condition,

15 % = 3.75

1 % = 3.75 / 15

100 % = 3.75 / 15 x 100

100 % = 25

Total sale of Nicole's on Monday is 25.

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Answer:

[tex]y=-\frac{5}{3}x+1[/tex]

Step-by-step explanation:

Given:

Equation of the line.

[tex]3x-5y=5[/tex]

And passes through the point (9, -14)

Solution:

Now, we have to write an equation that is perpendicular to 3x -5y = 5 and passes through the point (9, -14).

Now, we write the given equation in [tex]y=mx+b[/tex] form.

[tex]3x-5y=5[/tex]

[tex]5y=3x-5[/tex]

[tex]y=\frac{3}{5}x-\frac{5}{5}[/tex]

[tex]y=\frac{3}{5}x-1[/tex]

So, the slope of the line is [tex]m=\frac{3}{5}[/tex].

The slope of the perpendicular line is [tex]-\frac{1}{m}[/tex]

now, we substitute m value in above relation.

[tex]=-\frac{1}{\frac{3}{5}}[/tex]

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

So the equation of the perpendicular line is:

[tex]y=-\frac{5}{3}x+b[/tex]--------(1)

Lets us find  b from the given points (9, -14).

[tex]-14=-\frac{5}{3}\times 9+b[/tex]

[tex]-14=-5\times 3+b[/tex]

[tex]-14=-15+b[/tex]

[tex]b=15-14[/tex]

[tex]b=1[/tex]

Now, we substitute b value in equation 1.

[tex]y=-\frac{5}{3}x+1[/tex]

Therefore, the equation of the perpendicular line is

[tex]y=-\frac{5}{3}x+1[/tex]

The equation of the line that is perpendicular to 3x - 5y = 5 passing through the point (9, -14) is y = -5x/3 + 1.

To find the equation of a line that is perpendicular to a given line, we first need to find the slope of the given line. The equation in the question is given in standard form (Ax + By = C), so we need to convert it into slope-intercept form (y = mx + b), where m is the slope. In slope-intercept form, the given equation becomes y = 3x/5 + 1.

The slope of this line is 3/5. The slope of a line perpendicular to this one is the negative reciprocal, or -5/3. This is because the product of the slopes of two perpendicular lines is -1.

We now know that the equation of the line perpendicular to the given one has the form y = -5x/3 + b. To find b (the y-intercept), we can use the point that the line has to pass through (9, -14). We substitute these values into the equation, and solve for b. This gives: -14 = -5(9)/3 + b. Solving for b gives, b = -14 + 15 = 1.

Therefore, the equation of the line perpendicular to 3x - 5y = 5 passing through the point (9, -14) is y = -5x/3 + 1.

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Answer: D. 9

Step-by-step explanation: If BD is 18 then BE is 9

Answer:

can confirm that it is 9

Step-by-step explanation:

slay have a nice day!

Answer:

y = 2 + ((-)6/5)x

Step-by-step explanation:

-6x-5y=-10

add 6x to both sides.

-5y = -10 +6x

divide both sides by -5

y = 2 - (6/5)x

Plug in 0 for x to get the y intercept:

f(0) = 2 - (6/5) (0)

y = 2

(0, 2) is the y intercept.

Do the same for values such as -1, -2, 1, and 2, etc.

Then graph it.

To find the correct graph for -6x - 5y = -10, transform it to the slope-intercept form y = 6/5x - 2, which reveals a slope of 6/5 and a y-intercept at -2. Seek a graph with a line that increases 6 units vertically for every 5 units horizontally and intersects the y-axis at -2.

To find the graph that represents the equation -6x - 5y = -10,

we first need to manipulate the equation into slope-intercept form,

which is y = mx + b where m is the slope and b is the y-intercept. Starting with the given equation:

-6x - 5y = -10

Let's isolate y by adding 6x to both sides:

-5y = 6x - 10

Now, divide each term by -5 to solve for y:

y = -6x / -5 + 10 / -5

y = 6/5x - 2

The slope-intercept form of the equation is now y = 6/5x - 2. This tells us that the slope (m) of the line is 6/5 and the y-intercept (b) is -2. You will look for the graph with a line that rises 6 units for every 5 units it moves to the right (since the slope is positive) and crosses the y-axis at -2.

Answer:

[tex]\displaystyle x=-15[/tex]

Step-by-step explanation:

Solution Of A System Of Equations

A system of linear equations is given as

[tex]\displaystyle \left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.[/tex]

There are many methods to solve them. We will use the method of reduction

The given system is

[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ x+y=10\end{matrix}\right.[/tex]

Multiplying the second equation by -3

[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ -3x-3y=-30\end{matrix}\right.[/tex]

Adding the resulting equations

[tex]\displaystyle -x=15[/tex]

[tex]\displaystyle x=-15[/tex]

Answer:

The distance of the park from the Gary's house is 125 miles.

Step-by-step explanation:

Speed of Gary = 50 miles/hour

Time taken by Gary to reach the park from his house = 2.5 hours

Now, we know that,

Distance travelled = speed × time

So,  distance between park and Gary's house = speed × time

= 50 × 2.5

= 125 miles

So, the park is 125 miles away from the Gary's house.

Answer:

D

Step-by-step explanation:

= −8x − 2y - (−9x + 8y)

Open bracket

= -8x -2y + 9x - 8y

= x - 10y

Final answer:

Subtracting Expression 1 from Expression 2 term by term results in x - 10y, which corresponds to option D).

Explanation:

To subtract Expression 1 from Expression 2, we perform the subtraction operation term by term.

For the x-terms: (-8x) - (-9x) simplifies to x.

For the y-terms: (-2y) - (8y) simplifies to -10y.

Subtracting expression 1 from expression 2:

Expression 2 - Expression 1 = (-8x - 2y) - (-9x + 8y)

Simplify to get: (-8x - 2y) + (9x - 8y)

Combining like terms, the result is x - 10y.

Therefore, subtracting Expression 1 from Expression 2 gives us x - 10y, which matches option D).

Answer:

Part 1) The number of classes must be greater than 20

Part 2) see the explanation

Part 3) [tex]\$68.76[/tex]

Part 4) [tex]\$12\ per\ hour[/tex]

Part 5) The equation that can be used is [tex]27x=242.73[/tex]  and the cost of one print is [tex]\$8.99[/tex]

Part 6) The number of classes must be greater than 30

Step-by-step explanation:

Part 1) we know that

The linear equation in slope intercept form is equal to

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

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is [tex]m=\$10\ per\ class[/tex]

The y-intercept is [tex]b=\$100[/tex]

so

[tex]y=10x+100[/tex] ----> equation A

Non-Members

The slope is [tex]m=\$15\ per\ class[/tex]

so

[tex]y=15x[/tex] ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

[tex]10x+100 < 15x[/tex]

Solve for x

subtract 10 x both sides

[tex]100 < 15x-10x[/tex]

[tex]100 < 5x[/tex]

Divide by 5 both sides

[tex]20 < x[/tex]

Rewrite

[tex]x > 20[/tex]

therefore

The number of classes must be greater than 20

Part 2) we have

The sum of 8 and 3 times a number is 23.

Let

x ----> the number

Remember that

3 times a number is the same that multiply 3 by the number ----> 3x

so

The sum of 8 and 3 times a number is 23 is the same that

[tex]8+3x=23[/tex]

solve for x

subtract 8 both sides

[tex]3x=23-8[/tex]

[tex]3x=15[/tex]

Divide by 3 both sides

[tex]x=5[/tex]

Part 3) we know that

The linear equation in slope intercept form is equal to

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

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost of renting a car for one day

x ----> the number of miles

we have

The slope is [tex]m=\$0.42\ per\ mile[/tex]

The y-intercept is [tex]b=\$36[/tex]

so

[tex]y=0.42x+36[/tex]

For x=78 miles

substitute in the linear equation and solve for y

[tex]y=0.42(78)+36[/tex]

[tex]y=\$68.76[/tex]

Part 4) Let

x ----> Alice's normal hourly rate

we know that

40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660

so

The linear equation that represent this situation is

[tex]40x+10(1.5x)=660[/tex]

solve for x

[tex]40x+15x=660[/tex]

[tex]55x=660[/tex]

Divide by 55 both sides

[tex]x=\$12\ per\ hour[/tex]

Part 5) Let

x ----> the cost of one print

we know that

The cost of one print multiplied by 27 prints must be equal to $242.73

so

The linear equation is equal to

[tex]27x=242.73[/tex]

solve for x

Divide by 27 both sides

[tex]x=\$8.99[/tex]

Part 6) we know that

The linear equation in slope intercept form is equal to

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

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is [tex]m=\$7\ per\ class[/tex]

The y-intercept is [tex]b=\$120[/tex]

so

[tex]y=7x+120[/tex] ----> equation A

Non-Members

The slope is [tex]m=\$11\ per\ class[/tex]

so

[tex]y=11x[/tex] ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

[tex]7x+120 < 11x[/tex]

Solve for x

subtract 7x both sides

[tex]120 < 11x-7x[/tex]

[tex]120 < 4x[/tex]

Divide by 4 both sides

[tex]30 < x[/tex]

Rewrite

[tex]x > 30[/tex]

therefore

The number of classes must be greater than 30

Answer:

C

Step-by-step explanation:

Given 2 similar figures with linear ratio = a : b, then

ratio of areas = a² : b² and

ratio of volumes = a³ : b³

Here linear ratio = 42 : 56 ← divide both parts by 14

linear ratio = 3 : 4 ← in simplest form, thus

ratio of areas = 3² : 4² = 9 : 16

ratio of volumes = 3³ : 4³ = 27 : 64

Answer: D

Step-by-step explanation: I just did the quiz

Answer: D

Step-by-step explanation:

Yeah the quiz was like, dud the answers D, so I was like okay it's D

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

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

Where:

m: It's the slope

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

According to the statement data we have:

[tex]m = \frac {7} {3}[/tex]

Thus, the equation is of the form:

[tex]y = \frac {7} {3} x + b[/tex]

We substitute the given point and find the cut-off point:

[tex]- \frac {35} {3} = \frac {7} {3} (0) + b\\- \frac {35} {3} = b[/tex]

Finally, the equation is:

[tex]y = \frac {7} {3} x- \frac {35} {3}[/tex]

We manipulate algebraically to obtain the standard form:

We multiply by 3 on both sides of the equation:

[tex]3y = 7x-35\\3y-7x = -35[/tex]

We multiply by -1 on both sides:

[tex]7x-3y = 35[/tex]

Answer:

[tex]7x-3y = 35[/tex]

Answer:

y = - 7

Step-by-step explanation:

line pass (8, - 7) (- 6, -7)

y = mx + b   m: slope        b: y intercept

m = difference of y / difference of x

m = (- 7 - (- 7)) / (- 6 - 8) = 0 / (-14) = 0  ...  line parallel to x axis

b = y - mx = - 7 - 0*8 = -7

equation : y = -7

Answer:

y = - 7

Step-by-step explanation:

line pass (8, - 7) (- 6, -7)

y = mx + b   m: slope        b: y intercept

m = difference of y / difference of x

m = (- 7 - (- 7)) / (- 6 - 8) = 0 / (-14) = 0  ...  line parallel to x axis

b = y - mx = - 7 - 0*8 = -7

equation : y = -7

Answer:

1/20

Step-by-step explanation:

Answer:

wouldn't it just be [tex]\frac{10}{11} x[/tex]

Step-by-step explanation:

this is also: [tex]\frac{-10*x}{-11}[/tex]

which is why it simplifies to the answer

Answer:

y=-1/5x+1

Step-by-step explanation:

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

m=(-1-2)/(10-(-5))

m=-3/(10+5)

m=-3/15

m=-1/5

y-y1=m(x-x1)

y-2=-1/5(x-(-5))

y-2=-1/5(x+5)

y=-1/5x-5/5+2

y=-1/5x-1+2

y=-1/5x+1

Answer:

Step-by-step explanation:

-3w+9-8

=-3w+1

You got the equations correct, great job on that!

Let "s" be the variable that represents how many shirts were bought. Let "p" represent the total price/cost.

Equation for the store at Town Center mall:

p = 80 + 3.5s (80 is base cost, and cost increases 3.5 per shirt)

Equation for the store in Arlington:

p = 120 + 2.5s (120 is base cost, and cost increases 2.5 per shirt)

We want to find a point where the systems are equal; thus, we are solving for a system of linear equations, and we already have the equations we need.

p = 80 + 3.5s

p = 120 + 2.5s

We know that variable "p" is equal for both equations; thus, we can combine both equations into:

80 + 3.5s = 120 + 2.5s

Subtract both sides by 2.5s

80 + 3.5s - 2.5s = 120 + 2.5s - 2.5s

80 + s = 120

Subtract both sides by 80

s = 40

Thus, both equations are equal when 40 shirts are bought.

To find the cost, use any of the two equations (or both) to find the total cost, which should be equal.

p = 80 + 3.5(40) = 220

p = 120 + 2.5(40) = 220

Thus, the total price/cost at both stores is $220.

Let me know if you need any clarifications, thanks!

                                               Question # 1

Use the points in the diagram to name the figure?

Answer:

Option B is correct. The figure is named as a line 'CD'. The symbol '⟷' is placed UPPER on a line 'CD'.

Explanation:

Note: The symbol '⟷' is placed UPPER on a line 'CD'. Also remember, that the a line is named in alphabetical order.

                                           Question # 2

Which of the following correctly names a line shown in the figure?

Answer:

The option A is correct as the line AP carries the points A and P  and extends infinitely in two directions, and the symbol '⟷' is placed UPPER on a line 'AP' which represents the line.

Explanation:

Let us look at some definitions.

As we have to determine the correct name of a line shown in figure in question 2. So, we need to recall that a line is a set of points which tend to extend infinitely in two directions. Double arrow indicates that line is extended infinitely in both directions.

In question 2, the figure shows that:

So, option A is correct.

                                              Question 3.

Which of the following correctly names a ray shown in the figure?

Answer:

Explanation:

Keywords: ray, segment, line

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Answer:

Speed of car A = 40 mph

Speed of car B =  50 mph

Step-by-step explanation:

Given:

Distance travelled by car A  = 120 miles

Distance travelled by car B  =  120 miles

To Find:

speed of each car = ?

Solution:

Let the speed of car A be x

then  speed of car B is (x +10)

The Time taken for each car is same

Time taken for car A =  Time taken for car B

We know that time  = [tex]\frac{distance}{speed}[/tex]

Time taken for car A

=> [tex]\frac{120}{x}[/tex]---------------------------(1)

Similarly

Time taken for car B

=> [tex]\frac{150}{x+10}[/tex]-----------------------(2)

Equating (1) and (2), we get

[tex]\frac{120}{x}[/tex] =  [tex]\frac{150}{x+10}[/tex]

[tex]120 \times (x+10) = 150 \times x[/tex]

120x + 1200 = 150x

1200 = 150x-120 x

1200 = 30x

[tex]x= \frac{1200}{30}[/tex]

x= 40

Speed of car A = 40mph

Speed of car B = (x+10) = (x+40) = 50mph

The cost of one candy is 66 cents.

Step-by-step explanation:

Given,

Purchase price of box of candies = $10.54

Number of candies in the box = 16

To find the cost of each candy, we will divide the purchase price of candies with total number of candies.

Cost of each candy = [tex]\frac{10.54}{16}[/tex]

Cost of each candy = $0.658

Rounding off to nearest hundredth;

Cost of each candy = $0.66 = 0.66 * 100 = 66 cents

The cost of one candy is 66 cents.

Keywords: division, multiplication

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Just multiply the total length by the fraction:

14.3 * 1/10 = 1.43 miles

Answer:

1.43

Step-by-step explanation:

NOTE: This is the way I do it , other people may have a other/faster way to do it.

For this question you simpily have to divide 14.3 by 10:

1. Convert 14.3 into a mixed number - 14 3/10

2. Divide 14 by 10 - 1.4

3. Divide 3/10 by 10 - 3/100

4. Convert 3/100 into a decimal- 0.03

5. Add the two decimals - 0.03 + 1.4 = 1.43

The relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.

In a dilation, lines that pass through the center of dilation (the point about which the dilation occurs) remain unchanged.

This means that the line WX and its corresponding line W'X' would be collinear and have the same length if they pass through the center of dilation.

If the larger figure was dilated using a scale factor of 4, it means that every point in the larger figure is four times farther from the center of dilation than its corresponding point in the smaller figure. In this case, line WX would be four times longer than line W'X', and they would be parallel since they maintain the same direction.

So, the relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.

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Answer:

The cost of the sofa is $216

Step-by-step explanation:

The sofa was sold at cost plus 25% profit

let the cost of the sofa be                               = x

therefore                                     x + 25% of x = 270

                                                    x + .25x        =  270

                                                    1.25x            =   270

                                                    1.25x/1.25    =   270/1.25

                                                     x                  =   $216

Answer:

[tex]\displaystyle x = 8[/tex]

Step-by-step explanation:

Anything set to equal x is considered an undefined rate of change [slope], which is a vertical line. This is not a function, since it flunks the vertical line test.

I am joyous to assist you anytime.

Answer:

(1). 110 followers

(2). 463 days

(3). Days since upload                0 10 20 50 100 300 500

Number of Instagram followers 100 122 149 270 732 39158 2,000,000

(5) [tex]f(x)=100(1.03)^d[/tex]

Step-by-step explanation:

Part 1:

The function that represents the situation is:

[tex]f(x) = 100(1 .01)^{2d}[/tex]

Where [tex]d[/tex] is number of days.

Using this equation we find the number of followers after 5 days:

[tex]f(d) = 100(1 .01)^{2*5}=110[/tex] followers.

Part 2:

We solve the equation

[tex]1,000,000 = 100(1 .01)^{2d}[/tex]

for [tex]d[/tex] and get:

[tex]d=463\: days.[/tex]

It takes Alexis 463 days to reach 1,000,000 followers.

Part 3:

Days since upload                0 10 20 50 100 300 500

Number of Instagram followers 100 122 149 270 732 39158 2,000,000

This is obtained from the graph of the function f(x).

Part 4:

The number of Instagram followers increases fast because the rate of increase is 1% of the previous number of followers, and as the followers increase, this 1% takes increasingly big values, leading to increasingly fast growth rate of followers. Put simply, we would say that f(x) is an exponential function.

Par 5:

If the rate is increased to 3% every 24 hours, then the function f(x) becomes:

[tex]f(x)=100(1.03)^d[/tex]

where [tex]d[/tex] is days. and if we represent this in terms of every 12 hours then

[tex]f(x)=100(1.03)^{t/2}[/tex]

where [tex]t[/tex] is every 12 hours.

Answer:

1036 students

Step-by-step explanation:

Let the number of students at West High be "w" and the number of students at East High be "e"

West High population is 250 FEWER than TWICE of East High, we can write:

w = 2e - 250

Total students in both schools is 2858, so we can write 2nd equation as:

e + w = 2858

We can replace 1st equation in 2nd to get an equation in e, and find "e":

e + w = 2858

e + (2e - 250) = 2858

3e - 250 = 2858

3e = 2858 + 250

3e = 3108

e = 3108/3

e = 1036

Hence,

number of students attending East High School = 1036 students

Answer:

let the scone be x and the large coffees be y.

7x+4y=$25.76-----equ(I)

2x+5y=$14.92-----equ(2)

make x the subject of the formulae in equation(ii).

x=$14.92/2-5y

x=7.46-5y

2*k + 3 = 13

2*k = 13 - 3

2*k = 10

k = 10/2

k = 5

The verbal statement 'Three more than twice k is thirteen' translates into the mathematical equation 2k + 3 = 13. Solving this equation, we find that k equals 5. This is an example of forming and solving an algebraic equation from a word problem.

The question asks to translate a verbal statement involving a variable into a mathematical equation. The statement is 'Three more than twice k is thirteen.' To form an equation, we first identify the mathematical operations described in the statement. 'Twice k' means we need to multiply k by 2, so we have 2k. 'Three more than' suggests an addition of 3 to the previous result, so we add 3 to 2k to get 2k + 3. Finally, 'is thirteen' tells us that this expression is equal to 13. The equation becomes 2k + 3 = 13.

To solve for k, we subtract 3 from both sides to obtain 2k = 10, and then divide by 2, resulting in k = 5. This completes the exercise of writing and solving the equation.

Example of a similar equation:

Let's say we have 'Four less than half of x is twenty.' The equation would be (1/2)x - 4 = 20. We would solve by adding 4 to get (1/2)x = 24, and then multiply by 2 to find x = 48.