Solve This System Of Equations By Graphing. First Graph The Equations, And Then Type The Solution.y=5/2x1y=7/2x3 (2024)

ANSWER

EXPLANATION

Let the length of the rectangle be L.

Let the width of the rectangle be w.

The length of the rectangle is 3 more than twice the width.

This means that:

L = 3 + (2 * w)

L = 2w + 3

The perimeter of a rectangle is given as:

P = 2w + 2L

The perimeter of the rectangle is 96 inches. This means that:

96 = 2L + 2w

Recall that: L = 2w + 3

=> 96 = 2(w) + 2(2w + 3)

=> 2(w) + 2(2w + 3) = 96

A = 4489/(4π)

If we look at the equations for circumference and area (of a circle), we see that they both share the variable “r”. Therefore, we can solve for r in the circumference equation and insert it into area equation. Evaluate to find the answer.

See details:

Solution

For this case we have the following random variable:

X= amount spend on average for groceries by one person

And we have the following properties:

mean= 52

sd= 14

The distribution of the variable is normal

We can find the middle 50% using a graph like this one:

We can find two quantiles from the normal distribution that accumulates 25% of the area on each tail of the distribution and we have:

Z= -0.674 and 0.674

Now we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma},x=\mu\pm z\cdot\sigma[/tex]

So then we have:

Minimum= 52 - 0.674*14 = 42.56

Minimum= 52 + 0.674*14 = 61.44

MATHEMATICALLY WE SAY

BE AWARE THAT EIGHTHS IS

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

THEY ARE ASKING HOW MANY

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

ARE THERE IN

[tex] \frac{1}{4} [/tex]

[tex] = \frac{1}{4} \div \frac{1}{8} \\ = \frac{1}{4} \times \frac{8}{1} \\ = \frac{8}{4} \\ = 2[/tex]

YOU HAVE 2 .

The given function for the sales of [tex]S(t) = 7 - 6 \cdot \sqrt[3]{t} [/tex], gives the tax rate that maximizes government revenue as t = 343/512

What is a government tax rate?

The tax rate is the percentage of an amount that is paid to the government as tax.

The given function is presented as follows;

[tex]S(t) = 7 - 6 \cdot \sqrt[3]{t} [/tex]

Where;

t = The tax rate on imported shoes

S = The total sales

Taking the total sales as contributing to the government revenue, R(t), we have;

Revenue = R(t)

Which gives;

[tex]R(t) = t \times (7 - 6 \cdot {t}^{ \frac{1}{3} }) [/tex]

At the maximum total sales, we have;

[tex] \frac{dR(t)}{dt} = \frac{d t \times\left(7 - 6 \cdot {t}^{ \frac{1}{3} } \right) }{dt} = 0 [/tex]

[tex]\frac{d t \times\left(7 - 6 \cdot {t}^{ \frac{1}{3} } \right) }{dt} = 7- 8 \cdot \sqrt[3]{t} = 0[/tex]

Which gives;

At maximum revenue, t = (7/8)³

t ≈ 0.669921875

The tax rate that maximizes the government revenue is t = 343/512

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Answer:

Since one line is vertical, and one line is horizontal, the lines are perpendicular.

Step-by-step explanation:

The product of the slopes of perpendicular lines is -1.

We find the slopes of the 2 lines and multiply them together.

If the product equals -1, then the lines are perpendicular.

To find the slopes of the lines, we write each equation in the y = mx + b form, where m is the slope. In other words, we solve each equation for y.

3x + y = 7 + y

Subtract y from both sides.

3x = 7

x = 7/3

This is not the y = mx + b form since there is no y in the equation. A line with equation x = k, where k is a number, is a vertical line that passes through the point (k, 0), and the x-coordinate of all points on the line is k.

3(x + y) = 2 + 3x

3x + 3y = 2 + 3x

Subtract 3x from both sides.

3y = 2

y = 2/3

y = 0x + 2/3

Slope = m = 0

A line with 0 slope is a horizontal line.

Since one line is vertical, and one line is horizontal, the lines are perpendicular.

We are given the following function

[tex]f(t)=\frac{2t}{3}[/tex]

We are asked to find out the value of t which results in f(t) = 64

Let us substitute f(t) = 64 into the above function and solve for t

[tex]\begin{gathered} f(t)=\frac{2t}{3} \\ 64=\frac{2t}{3} \\ 3\cdot64=2t \\ 192=2t \\ \frac{192}{2}=t \\ 96=t \\ t=96 \end{gathered}[/tex]

Therefore, the value of t is 96

ANSWER

T = 4x + 25;

T = $37

EXPLANATION

Let the number of special exhibits to be visited be x.

The cost of the musuem entrance ticket is $25 and each special exhibit costs an additional $4.

This means that the cost of cisiting x additional exhibits is:

4 * x = $4x

Therefore, the total cost to enter the musuem and visit any number of special exhibits is:

T = 4x + 25

That is the expression that represents the total cost.

If a person wants to visit three exhibits, it means that:

x = 3

Therefore, the total cost, T, is:

T = 4(3) + 25

T = 12 + 25

T = $37

That is the total cost to enter and visit three exhibits.

Given:

The length of each ribbon is 25 cm.

The number of ribbon need by mother is 6.

Explanation:

Determine the length of ribbon for daughter's hair.

[tex]\begin{gathered} 25\cdot6=150\text{ cm} \\ =1.5\text{ m} \end{gathered}[/tex]

Since length is in decimal so we need to find multiple of 25 such that it is more than 150 and multiple of 100.

The multiples of 25 are 25,50, 75, 100, 125, 150, 175, 200, ...

Since 200 is more than 150 and multiple of 100 also.

Determine the length of 200 cm in terms of meters.

[tex]200\text{ cm}\cdot\frac{1\text{ m}}{100\text{ cm}}=2\text{ m}[/tex]

So mother needs to buy 2 meters of ribbon.

Answer: 2 meters

Three hundred fifty-one thousand five hundred twenty-seven and ninety-four thousandths

ok

Volume of a cilinder = pi*r^2*h

Substitution

Volume of a cilinder = 3.14*3^2* 6

Simplification

Volume of a cylinder = 170 ft^3

Approximately, there are 180 ft^3 of oil

Area of the circle is 28.3 in^2

Here, we want to find the area of the circle

Mathematically, the area is;

[tex]\begin{gathered} \text{Area of circle = }\pi\text{ }\times r^2 \\ But\text{ r = }\frac{d}{2} \\ \\ Area\text{ of circle = }\frac{\pi\text{ }\times d^2}{4} \\ \\ from\text{ the question, d = 6 inches} \\ \pi\text{ = }\frac{22}{7} \\ \\ \\ \text{Area of circle = }\frac{\frac{22}{7\text{ }}\text{ }\times6^2}{4} \\ \\ \text{Area of circle = }\frac{22\text{ }\times\text{ 36}}{28} \\ \\ \text{Area of circle = 28.2857} \\ \\ \text{Area of circle = 28.3 in\textasciicircum{}2} \end{gathered}[/tex]

Answer:

Explanation:

a) To draw the 1st , 5th and 6th figures, we need to know the count of squares

For the first figure, we would have 3 squares

The fifth figure would have 35 squares

The sixth figure will have 48 squares

The way to get this is to add 2 to the odd number difference between the last two terms

b) Here, we want to know how the pattern is changing

From the information provided, the first pattern has 8 squares, the second has

15 squares while the last has 24 squares

We can have a formula as follows:

[tex][/tex]

Given the figure of the functions f(x) and g(x)

The graph of the function is the shown lines

The equation of f(x):

As shown the line of f(x) passes through the points: (-2, 0) and (0, -1)

The slope of the line will be:

[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-0}{0-(-2)}=\frac{-1}{2}[/tex]

The y-intercept = -1

so, the equation of f(x) =

[tex]f(x)=-\frac{1}{2}x-1[/tex]

The equation of g(x):

As shown the line of g(x) passes through the points: (-2, 0) and (0, 1)

The slope of the line will be:

[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{0-(-2)}=\frac{1}{2}[/tex]

The y-intercept = 1

So, the equation of g(x) will be:

[tex]g(x)=\frac{1}{2}x+1[/tex]

Identify the reflection that transforms the graph of f(x) to the graph of g(x).

As shown, the functions are symmetric around the x-axis

And as we can see for the same value of x: g(x) = -f(x)

So, the type of transformation is: Reflection over the x-axis

Let's evaluate the given expression:

[tex]\text{ 14 - 16 + 8 + }\frac{\text{ 12}}{\text{ 3}}[/tex][tex]=\text{ 14 - 16 + 8 + 4}[/tex][tex]\text{ = -2 + 8 + 4}[/tex][tex]\text{ = -2 + 12}[/tex][tex]\text{ = 1}0[/tex]

Therefore, the answer is 10.

Teh ratio of boys to girls in JAnice's classroom is 3:5

Total number of students 32

Let the ratio constant is K

So,

The equation will be

3K + 5K=32

8K=32

K=32/8

K=4

So,

the boys will be

4 + 4 + 4 =3K =12

The number of girls will be :

4 + 4 + 4 + 4 + 4 = 5K =20

She made an initial deposit that we will call "D", as it is one of the unknowns.

We know that she made a weekly deposit (lets call this amount "w").

After 4 weeks she had $450 in the account balance and this is the sum of the initial deposit and 4 weekly deposits, so we can write:

[tex]D+4w=450[/tex]

At the ninth week she had $825, that correspond to the initial deposit and 9 weekly deposits. This can be written as:

[tex]D+9w=825[/tex]

We have a system of linear equations that we will solve by elimination: we will substract the first equation from the second and then find w.

[tex]\begin{gathered} (D+9w)-(D+4w)=825-450 \\ 5w=375 \\ w=\frac{375}{5} \\ w=75 \end{gathered}[/tex]

Now that we know "w", we can calculate D with any of the two equations:

[tex]\begin{gathered} D+4w=450 \\ D+4\cdot75=450 \\ D+300=450 \\ D=450-300 \\ D=150 \end{gathered}[/tex]

Answer: the initial deposit was $150.

When having an ordered pair, we say they are in direct variation if the quotient:

[tex]\frac{y}{x}[/tex]

is constant. For case 1 we have:

[tex]\frac{80}{32}=\frac{100}{x}[/tex]

we can solve for "x" by multiplying by "x" on both sides:

[tex]\frac{x80}{32}=100[/tex]

Now we multiply by 32/80 on both sides:

[tex]x=\frac{100\times32}{80}[/tex]

Solving the operations we get:

[tex]x=40[/tex]

For case 2 we have:

[tex]-\frac{7}{-28}=\frac{y}{20}[/tex]

Now we solve for "y" by multiplying by 20 on both sides:

[tex]\frac{-7\times20}{-28}=y[/tex]

Solving the operations:

[tex]y=5[/tex]

The probability of getting a red 7 would be; 1/26

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Given that the total number of cards is 52.

WE are asked to find the he probability of getting a red 7

Since there are 2 red 7 cards in the deck of cards.

So, the number of favourable outcomes would be 2.

n (E) = 2

The probability

P(E) = n (E) /n (S)

Therefore, the probability of getting a red 7 will be;

P(E) = n (E) /n (S)

P(E) = 2/52

P(E) = 1/26

Hence, The probability of getting a red 7 would be; 1/26

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Explanation

[tex]g-0.6\leq3.172[/tex]

Step 1

To solve the inequality means to find a range, or ranges, of values that an unknown g can take and still satisfy the inequality.

so

[tex]\begin{gathered} g-0.6\leq3.172 \\ \text{add 0.6 in both sides} \\ g-0.6+0.6\leq3.172+0.6 \\ g\leq3.772 \end{gathered}[/tex]

it means the solution is the set of values equal or smaller than 3.772,so

Part A:

[tex]g\leq3.772[/tex]

Step 2

Part B:the graph of the inequality looks like a marked line in the number line, from3.772 to negative infinite, as the symbol is smaller or equal, the number3.772 is part of the set , so we use a filled circle

Step 3

in step 1 we used the addition property of inequality to isolate x, then in step 2 we draw the set solution .

I hope this helps you

The graph given is a linear graph,

so that means that the cost of cheese is linearly related to the weight of cheese bought.

The increase in the cost of cheese increase for each ounce Milan buys is, therefore, the slope of the graph;

to find the slope of the graph, we use any two points on the line; i'll be using (4,96) and (2,48)

[tex]\text{slope}=\frac{96-48}{4-2}=\frac{48}{2}=24[/tex]

This means that the cost of cheese increases by 24 cents for each ounce Milan buys.

P = 2L + 2w

Length=

L = 2w + 6

New equation =

P = 2(2w + 6) + 2w

P = 4w + 12 + 2w

P = 12 + 6w

As stated in the question, the perimeter is 132 feet:

So,

132 = 12 + 6w

120 = 6w

W = 20

Now let’s find length using width:

L = 2w + 6

L = 2(20)+ 6

L = 40 + 6

Now we know that

W = 20
L = 46

Given the function :

[tex]h(x)=20(0.75)^x[/tex]

So, the decay percentage rate :

[tex]\frac{\triangle h}{\triangle x}=0.75[/tex]

convert the decimal to percentage: 0.75 = 75%

So, the answer is option A) 75%

Answer:

70.4

Step-by-step explanation:

c = 2[tex]\pi[/tex]r

c = 2(3.142)(11.2)

c = 70.3808 Rounded to 1 decimal place

c = 70.4

Answer:
70.4

Explanation:

Circumference = 2 (3.142) radius

Circumference = 2 x 3.142 x 11.2

Circumference = 70.3808

Round ur answer to 1 d.p:
=70.4

Answer:

2m(-4.2m)

-4.2[tex]m^{2}[/tex] + - (4.2[tex]m^{2}[/tex])

-8.4[tex]m^{2}[/tex]

Step-by-step explanation:

2m(-4.2m) = -8.4 [tex]m^{2}[/tex]

-4.2 [tex]m^{2}[/tex] + (-4.2 [tex]m^{2}[/tex]) = 8.4[tex]m^{2}[/tex]

Answer:

y = 6

Step-by-step explanation:

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

3 = [tex]\frac{1}{4}[/tex]k Solve for k by multiplying both sides by 4

12 = k

y = [tex]\frac{1}{2}[/tex](12)

y = [tex]\frac{12}{2}[/tex]

y= 6

Answer:

-96a + 84b + 32x + 24y

Step-by-step explanation:

if you simplify an answer then it is equivilent to the beggining equation

hope this helped:)

So, we are writing a function. c(x) is the manufacturing costs, and x is the amount of bikes manufactured. The y-intercept is 1908 because when no bikes are manufactured it still costs 1908 to run the factory. The slope is 75 because it costs $75 to create a bike. So, y = mx + b, where m is the slope and b is the y-intercept is:

c(x) = 75x + 1908