If 32x+1 - 3x+5, what is the value of x?
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Just to be different we'll start with intercept intercept form which says the line through x intercept (a,0) and y intercept (0,b) is

[tex]\dfrac x a + \dfrac y b = 1[/tex]

Through (4,0) and (0,-2) that's

[tex]\dfrac{x}{4} + \dfrac{y}{-2} = 1[/tex]

Multiply through by the common denominator of 4 for standard form:

x - 2y = 4

For slope intercept form we solve for y

-2 y = -x + 4

y = (1/2) x - 2

We see our slope is (1/2) and we go through (4,0) so point slope form is

y - 0 = (1/2)(x - 4)

y = (1/2)(x-4)

The equation is y = 1/2(x - 4), and converting this to standard form results in x - 2y = 4.

To find the equation of the line that passes through the x-intercept (4,0) and y-intercept (0,-2), we need to derive its slope and then write the equation in different forms:

Step 1: Calculate the Slope

The slope (m) is given by
m = (y2 - y1) / (x2 - x1).
Using the given intercepts (4,0) and (0,-2):

m = (0 - (-2)) / (4 - 0) = 2 / 4 = 1/2

Step 2: Slope-Intercept Form

The slope-intercept form is
y = mx + b, where m is the slope and b is the y-intercept. We know that the y-intercept, b, is -2.

Thus, the equation in slope-intercept form is:

y = 1/2 x - 2

Step 3: Point-Slope Form

The point-slope form is given by
y - y1 = m(x - x1).
Using the point (4,0):

y - 0 = 1/2(x - 4)

Which simplifies to:

y = 1/2(x - 4)

Step 4: Standard Form

Standard form is
Ax + By = C. To convert our slope-intercept form (y = 1/2 x - 2) to standard form, we follow these steps:

Multiply both sides by 2 to eliminate the fraction:
2y = x - 4

Rearrange to get integer coefficients on the left side:
x - 2y = 4

Thus, the equation in standard form is: x - 2y = 4

Answer:

B

Step-by-step explanation:

(x-6)(x+6)

The -6x cancels out the other 6x

x^2 - 36

                                                    Question # 4

Answer:

Total number of cameras left to bid on = 3/5

Step-by-step Explanation:

To determine:

What fraction of the total number of cameras is left to bid on?

Solution Steps:

Total number of cameras left to bid on = 10/10 - 4/10

                                                                  = 6/10

                                                                   = 3/5   ∵ As 6/10 = 3/5

Hence, total number of cameras left to bid on = 3/5

                                               Question # 5

Answer:

The remaining portion of tickets = 17/100

Step-by-step Explanation:

To determine:

What portion of the tickets remain?

Solution Steps:

The remaining portion of tickets = 100/100 - 83/100

                                                       = 17/100

Hence, the remaining portion of tickets = 17/100

Keywords: fraction, number

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Answer: [tex]\frac{(x+4)(x+1)}{x+2}[/tex]

Step-by-step explanation:

The area of a rectangle [tex]A[/tex] is given by the multiplication of its base [tex]b[/tex] by its height [tex]h[/tex]:

[tex]A=(b)(h)=x^{2}+5x+4[/tex] (1)

In addition we are told the length of one of the sides (let's choose [tex]b[/tex]) is:

[tex]b=x+2[/tex] (2)

Substituting (2) in (1):

[tex](x+2)h=x^{2}+5x+4[/tex] (3)

Isolating [tex]h[/tex]:

[tex]h=\frac{x^{2}+5x+4}{(x+2)}[/tex]

Factoring in the numerator:

[tex]h=\frac{(x+4)(x+1)}{x+2}[/tex] This is the length of the other side of the rectangle

To complete the Venn diagram, calculate that 48 out of 60 farms grow potatoes and the remaining 16 grow sugar beets, since the potato farms number is three times the sugar beet farms.

The question asks us to complete a Venn diagram with information about how many farms grow potatoes vs sugar beets, given that 60 farms grow one or the other, not both. 4/5 of the 60 farms grow potatoes, which is 48 farms.

Since the number of farms that grow potatoes is three times the number that grow sugar beets,

we can determine the number of sugar beet farms by dividing the number of potato farms by 3, giving us 16 farms growing sugar beets.

Here's the step-by-step solution:

Answer:

The final amount in the account after 6 years at compound interest is $1568.78 .

Step-by-step explanation:

Given as :

The principal amount in account = p = $1500

The rate of compound interest = r = 0.75 %

The time period of the loan = t = 6 years

Let The Amount in account after 6 years = $A

From Compound Interest method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

I.e A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, A = $1500 × [tex](1+\dfrac{\textrm 0.75}{100})^{\textrm 6}[/tex]

Or, A = $1500 × [tex](1.0075)^{6}[/tex]

Or, A = $1500 × 1.04585

Or, A = $1568.775

So, The final amount= A = $1568.78

Hence The final amount in the account after 6 years at compound interest is $1568.78 . Answer

Answer:

The correct answer is A. 12 minutes.

Step-by-step explanation:

Let's solve for y, when x = 12, as follows:

y = 175 - 15x

y = 175 - 15 * 12

y = 175 - 180

y = - 5

This result means that after 12 minutes the fish tank would be completely drained and if it's needed 5 additional gallons of water could also be drained. It's not necessary to continue making more calculation with the the other options given because this is the right answer.

The correct answer is A. 12 minutes.

Answer:

Percent 250 of 275 is 90.9%

Step-by-step explanation:

We have to find 250 is what percent of 275.

Let X be the percentage, then

=> X =  [tex]\frac{250}{275} \times 100[/tex]

Now simplyfying the above relation we get

=> X =  [tex] 0.909\times 100[/tex]

=> => X = 90.9 %

Hence 250 is 90.9% of 275

Answer:

DF = 3 , ∠B = 28° , ∠P = 105° , QR = 11.6 , ∠M=45°,LN = 8.5

Step-by-step explanation:

As ΔABC≅ΔDEF ,

DF = AC and ∠B = ∠E because corresponding parts of congruent triangles are equal.

∴DF = 3 and ∠B= 28°

In the next part,

as ΔLMN≅ΔPQR,

∠P = ∠L , QR = MN , ∠M = ∠Q , LN = PR as corresponding parts of congruent triangles are equal.

∴∠P = 105° , QR = 11.6 , ∠M = 45° , LN = 8.5

Answer:

He worked 22 hours.

Step-by-step explanation:

285+45= 330

330 is the amount he earned in the first place.

330/ 15(amount earned per hour)= 22

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Answer:

A) The total feet needed for the fence total perimeter is 54 feet

B) The total cost of fence is $432

C) The square feet of grass needed foe the total area is 180 square feet

D) The total cost of the project is $572

Step-by-step explanation:

Given as :

The dimension of rectangular field

Length of rectangular field = L = 12 feet

width of rectangular field = w = 15 feet

The cost of grass per square foot = 50 cents = $0.5    ( ∵ 1 cents = $0.01 )

The cost of small fence = $8 per linear foot

Now, According to question

A ) Let The total feet needed for the fence total perimeter = A feet

∵ Perimeter of rectangular field = 2 × Length + 2 × width

Or, A = 2 × L + 2 × w

Or, A = 2 × 12 feet + 2 × 15 feet

Or, A = 24 feet + 30 feet

∴ A = 54 feet

So, The total feet needed for the fence total perimeter = A = 54 feet

B ) Let The total cost of fence = $B

So, The total cost of fence = The cost of small fence × perimeter of fence

i.e B = $8 × 54 feet

∴ B = $432

So,The total cost of fence = B = $432

C) Let the square feet of grass needed foe the total area = C square feet

∵The Area of rectangular fence = Length × width

Or, The square feet of grass needed foe the total area = Area of rectangular fence = L × w

i.e C = 12 feet × 15 feet

Or, C = 180 feet²

So,The square feet of grass needed foe the total area = C = 180 square feet

D) Let The total cost of grass = $D

∵ The cost of grass per square foot = $0.5

So,Total cost of grass = $0.5 × Area of fence

i.e D = $0.5 ×  180 feet²

Or, D = $90

So, The Total cost of grass = D = $90

E) Let the total cost of the project = $E

∵Mr. Jones spend additional $50 for tools

So, The total cost of the project =  money spent on tools + total cost of fence + Total cost of grass

i.e E = $50 + B + D

Or, E = $50 + $432 + $90

∴ E = $572

So, The total cost of the project = E = $572

Hence,

A) The total feet needed for the fence total perimeter is 54 feet

B) The total cost of fence is $432

C) The square feet of grass needed foe the total area is 180 square feet

D) The total cost of the project is $572  Answer

Answer:

n= (-m-13)/2

Step-by-step explanation:

look @ photo

Answer: m=-2n-13

               ↗️⬆️↖️

Answer:7 times what can give you 210 ... 30 so 181 and 7 times what gives you 140 ...20 so now 41 so 7 times 5 is 35 now you have 6

Step-by-step explanation:

The answers in the first box are 630, in the second box 9, and in the third box 2737 after multiplying 391 by 7.

Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them. Addition, subtraction, multiplication, and division are the four basic math operations.

We have given:

 391

 × 7

______

     7     7×1 one

630    7×9 tens

+2100    7×3 hundred

________

2737

After multiplying 391 by 7 we will get, 2737

Thus, the answers in the first box are 630, in the second box 9, and in the third box 2737 after multiplying 391 by 7.

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Answer:

Step-by-step explanation:

P = 2(L + W).....perimeter of a rectangle formula

P = 20

L = 2W + 1

20 = 2(2W + 1 + W)

20 = 2(3W + 1)

20 = 6W + 2

20 - 2 = 6W

18 = 6W

18/6 = W

3 = W <==== the width is 3 inches

L = 2W + 1

L = 2(3) + 1

L = 6 + 1

L = 7 <===== the length is 7 inches

Answer:

Width = 3 inches

Length = 7 inches

Step-by-step explanation:

L = 1 + 2W

P = 20 inches

P = 2L + 2W

2L + 2W = 20 inches

Fill in known value (length)

2(1 + 2W) + 2W = 20 inches

Solve

2 + 4W + 2W = 20 inches

6W = 18 inches

Simplify

W = 3 inches

Width = 3 inches

Length = 2(3) + 1 = 7 inches

:)

Answer:

A. [tex]\displaystyle 10\:units[/tex]

Step-by-step explanation:

Use the Distance Formula:

[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[-3 + 2]^2 + [-6 - 4]^2} = \sqrt{[-1]^2 + [-10]^2} = \sqrt{1 + 100} = \sqrt{101} ≈ 10,04987562 ≈ 10[/tex]

Since we are talking about distance, we ONLY want the NON-NEGATIVE root.

I am joyous to assist you anytime.

Final answer:

The approximate length of a line segment connecting points A(3, 6) and B(2, -4) is found using the distance formula and it is approximately 10 units.

Explanation:

To calculate the approximate length of a line segment connecting points A and B, we use the distance formula. The distance formula is derived from the Pythagorean theorem and is:

d = \/((x2 - x1)² + (y2 - y1)²)

Given points, A(3, 6) and B(2, -4), we can plug these coordinates into the formula:

d = \/((2 - 3)² + (-4 - 6)²)

Now, calculate the squares and sum:

d = \/((-1)² + (-10)²)

d = \/(1 + 100)

d = \/(101)

The square root of 101 is approximately 10.05, which is close to 10 units.
Therefore, the approximate length of the line segment connecting points A and B is 10 units, which corresponds to option A.

Answer:A

Step-by-step explanation:

The equation that best set up the quadratic formula is [tex]x = \frac{ -(-2) |+-| \sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex].

Hence, option A is the correct answer.

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

Using the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given that;

x² + 1 = 2x – 3

First we re-arrange the the equation.

x² + 1 = 2x - 3

x² - 2x + 1 + 3 = 0

x² - 2x + 4 = 0

Hence;

Next we input this values into the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

x = (-(-2)±√((-2)² - 4(1)(4))) / (2(1))

[tex]x = \frac{ -(-2) |+-| \sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex]

The equation that best set up the quadratic formula is [tex]x = \frac{ -(-2) |+-| \sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex].

Hence, option A is the correct answer.

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the two solutions are approximately [tex]\( x_1 \approx 2.95 \) and \( x_2 \approx -0.042 \).[/tex]

To find the value of x that satisfies the equation [tex]\( 32x^2 - 93x - 4 = 0 \)[/tex], we can use the quadratic formula:

[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

Where:

- a = 32

- b = -93

- c = -4

Now, let's plug these values into the quadratic formula:

[tex]\[ x = \frac{{-(-93) \pm \sqrt{{(-93)^2 - 4 \cdot 32 \cdot (-4)}}}}{{2 \cdot 32}} \]\[ x = \frac{{93 \pm \sqrt{{8649 + 512}}}}{{64}} \]\[ x = \frac{{93 \pm \sqrt{{9161}}}}{{64}} \]\[ x = \frac{{93 \pm 95.7}}{{64}} \][/tex]

Now, we have two possible solutions:

[tex]\[ x_1 = \frac{{93 + 95.7}}{{64}} \]\[ x_2 = \frac{{93 - 95.7}}{{64}} \]\[ x_1 \approx \frac{{188.7}}{{64}} \]\[ x_2 \approx \frac{{-2.7}}{{64}} \]\[ x_1 \approx 2.95 \]\[ x_2 \approx -0.042 \][/tex]

Therefore, the two solutions are approximately [tex]\( x_1 \approx 2.95 \) and \( x_2 \approx -0.042 \).[/tex]

The probable question maybe:

What are the solutions for x in the equation [tex]\( 32x^2 - 93x - 4 = 0 \)[/tex]?

Answer:

The word sum corresponds to addition, which means:

d + 12 = 20

:)

Answer: d + 12 = 20

Step-by-step explanation: In this problem, we are asked to write an algebraic expression that represents the sentence.

The key to understanding this problem is by looking at the keyword "sum." The word sum means addition so reading this problem from left to right, the sum of d and 12 that's d + 12 "is 20" = 20.

So, d + 12 = 20 will be our algebraic expression.

Answer:

Step-by-step explanation:

1,115.625 miles in 21 hrs and 15 min.....

15 minutes = 15/60 = 0.25 hrs......so they did it in 21.25 hrs

1,115.625 / 21.25 = 52.5 miles per hr <===

Answer:

The better one? 8 oz

Step-by-step explanation:

You might be wondering why. You divide the cost by the oz. (or like a kind of capacity measurement or like weigh) For example, 2.16/ 8 is 0.27, that means per oz it is 0.27. Then, you find it for a 10 oz that costs 2.75, that is equal to 0.275. 0.275 is more than 0.27 so a 8 oz must be better to buy.

Answer: 8 oz drink

Step-by-step explanation: In this problem, we are asked to determine which of the following drinks is a better buy.

A 8 oz drink that for $2.16 or a 10 oz drink for $2.75.

Since the drinks that we are comparing are different sizes, to determine which drink is a better buy, we first need to find the unit price of each drink which in this case is the cost per ounce of each drink.

For our first drink, since $2.16 is the cost for 8 oz, to find the cost per ounce, we divide 8 into 2.16 to get 0.27. So the 1 ounce drink has a unit price of 0.27 cents per ounce.

For our second drink, since $2.75 is the cost for 10 oz, to find the cost per ounce, we divide 10 into 2.75 to get 0.275.

Finally we want to know which drink is a better buy so we are looking for the drink with the lower unit price. Since 0.27 cents is less than 0.275 cents, the 8 oz drink has the lower unit price and is therefore the better buy.

Answer: [tex]A(t)=-8t+52[/tex]

Step-by-step explanation:

The  equation of the line in Slope-Intercept form is:

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

Where "m" is the slope and "b" is the y-intercept.

According to the data given in the exercise, you know that:

- [tex]A(t)[/tex] represents the area to paint the Hiros' romm as a function of time.

- The rate he painted the room was 8 square meters per hour.

- The area left to paint after 3 hours was 28 m².

Therefore, based on this, you can idenfity that:

1. The slope of the line is:

[tex]m=-8[/tex]

2. One of the point on the line is:

[tex](3,28)[/tex]

So you must substitute the slope and the coordinates of that point into [tex]y=mx+b[/tex] and then solve for "b" in order to find its value:

[tex]28=-8(3)+b\\\\28+24=b\\\\b=52[/tex]

Therefore, you can determine that the function [tex]A(t)[/tex] is:

[tex]A(t)=-8t+52[/tex]

Answer:

$13.50

Step-by-step explanation:

To find Lucas's profit, subtract the cost from his total gain.

Lucas bought 6 packs for $4 each.

6 * $4 = $24

His cost is $24.

In each of the 6 packs, there were 25 pens.

6 * 25 = 150 total pens

Lucas sold each pen for $0.25

150 * $0.25 = $37.50

$37.50 - $24 = $13.50

Answer:

Step-by-step explanation:

it equals -19

Answer:

The value of the given expression [tex]-16-3=-19[/tex]

Step-by-step explanation:

Given expression is [tex]-16-3[/tex]

To find the value of the given expression:

[tex]-16-3=-16-3[/tex]

Now taking the negative sign (-) outside the terms of the above equation we get,

[tex]-16-3=-(16+3)[/tex]

Now apply the algebraic sum to  the above expression we get,

[tex]=-19[/tex]

Therefore [tex]=-19[/tex]

The value of the given expression is [tex]-16-3=-19[/tex]

Answer:

you can only find an Infinite amount of solutions.

Step-by-step explanation:

Answer: do some math right now kehd you trash

Step-by-step explanation:

get a life

Answer:

1500

Step-by-step explanation:

75 ballons in one package, mulitiply 75 by 20 to get 1500 total balloons

Answer:1500

Step-by-step explanation:

Answer:

see the explanation

Step-by-step explanation:

we have the points

(4,7) and (4,-3)

we know that

The x=coordinate of both points are the same

so

the line that goes through those two points is a vertical line (parallel to the y-axis)

The slope is undefined

Because

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{7+3}{4-4}[/tex]

[tex]m=\frac{10}{0}[/tex]

Is undefined (the denominator is equal to zero)

see  the attached figure to better understand the problem

Answer:

Step-by-step explanation:

Sample Response: Since both points have the same x-coordinate, the line would be vertical. A vertical line has no slope because the run of the graph, which is the denominator, is zero and therefore an undefined fraction.

Answer:

Graph 3.

Step-by-step explanation:

Since they need to earn $240 by selling $3 candy bars, they must sell at least 80 candy bars since 240/3 = 80.

With this in mind, selling more than 80 candy bars would be acceptable, but selling less would not which is why the third graph is correct.

Answer:

c

Step-by-step explanation:

The waffle cone has a larger radius compared to the sugar cone.

The radius of a cone can be found using the formula:

radius = volume / height / pi

Both cones have the same volume of 12 ounces, so we can use this formula to compare their radii:

For the waffle cone: radius = 12 / 5 / pi = 0.766

For the sugar cone: radius = 12 / 8 / pi = 0.477

Therefore, the waffle cone has a larger radius compared to the sugar cone.

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The waffle cone has a larger radius of approximately 2.03 inches compared to the sugar cone's radius of approximately 1.61 inches.

To determine which cone has a larger radius, we need to calculate the radius of each cone using the volume formula for a cone. Since both cones hold the same volume (12 ounces), we'll convert this to cubic inches (since 1 ounce is approximately 1.8 cubic inches, 12 ounces is roughly 21.6 cubic inches).

The volume formula for a cone is:

V = (1/3)πr²h

Where V is the volume, r is the radius, and h is the height.

Waffle Cone:

Volume (V) = 21.6 cubic inches
Height (h) = 5 inches

Therefore, we have:

21.6 = (1/3)πr²(5)

Solving for r, we get:

21.6 = (5/3)πr²
r² = 21.6 / ((5/3)π)
r² = 12.97 / π
r ≈ sqrt(4.13)
r ≈ 2.03 inches

Sugar Cone:

Volume (V) = 21.6 cubic inches
Height (h) = 8 inches

Therefore, we have:

21.6 = (1/3)πr²(8)

Solving for r, we get:

21.6 = (8/3)πr²
r² = 21.6 / ((8/3)π)
r² = 8.1 / π
r ≈ sqrt(2.58)
r ≈ 1.61 inches

Comparing the two radii, the waffle cone has a larger radius of approximately 2.03 inches, while the sugar cone has a smaller radius of approximately 1.61 inches.

Final answer:

Equivalent fractions for 3/8 could be 6/16 or 12/32, and for 1/4, they could be 2/8 or 4/16, achieved by multiplying both the numerator and denominator by the same number.

Explanation:

The student asked which pairs of fractions are equivalent to 3/8 pound of Swiss cheese and 1/4 pound of American cheese. To find equivalent fractions, we multiply or divide both the numerator and the denominator of the fraction by the same number. For example, if we multiply the numerator and denominator of 3/8 by 2, we get 6/16, which is equivalent to 3/8. Likewise, if we multiply the numerator and denominator of 1/4 by 2, we get 2/8 which is equivalent to 1/4. Another pair of equivalent fractions can be found by multiplying 3/8 and 1/4 each by 4, resulting in 12/32 and 4/16 respectively.