Find equation of the line shown

Answer:

a) Infinitely many solutions

Step-by-step explanation:

3(4x-8) = -24+12x

12x - 24 = -24 + 12x

0 = 0

infinitely many solutions

:] hope this helps

The volume of cone is gotten by dividing the volume of cylinder by 3.

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The volume of a solid figure is the amount of space it occupies in three dimension.

The volume of a cylinder = π * radius² * height

The volume of a cone = (1/3) * π * radius² * height

Hence:

If the cone and cylinder have the same radius and height:

Volume of cone = (1/3) * volume of cylinder.

The volume of cone is one-third volume of cylinder.

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Answer:

A perfect square can always be expressed as a product of pairs of equal factors

if we resolve 15x 375(which equals 5625)

225x25 = 9x25x25 = 3x3x5x5x5x5 = 3x5x5x3x5x5 or 3 to the power of 2 x 5 to the power of 4  which can also equal to 75 squared

which means that 75 is the number whose square is 5265

Answer: 1st friend = 13333 x 6

2nd friend = 13333 x 2

3rd friend = 13333

(this is rounded off the actual amount of 1 unit is 13333.3333333)

Step-by-step explanation:

1st friend = 6 units

2nd friend =2 units

3rd friend =1 unit

6+2+1 = 9

120000 divided 9 = 13333

1st friend = 13333 x 6

2nd friend = 13333 x 2

3rd friend = 13333

Answer:An equilateral triangle with sides of length 48 inches can be divided into two right triangles by drawing a line from one vertex to the midpoint of the opposite side. The height of the equilateral triangle, or the length of the line segment from the vertex to the midpoint of the opposite side, is equal to the height of each of these right triangles.

Using the Pythagorean theorem, the length of the altitude of each right triangle can be found:

sqrt(48^2 - 24^2) = sqrt(2304) = 48 inches.

The area of each right triangle is 1/2 base * height, or 1/2 * 24 * 48 = 576 square inches.

Since the equilateral triangle is made up of two of these right triangles, the total area of the equilateral triangle is 2 * 576 = 1152 square inches.

Step-by-step explanation:

An equilateral triangle with sides of length 48 inches can be divided into two right triangles by drawing a line from one vertex to the midpoint of the opposite side. The height of the equilateral triangle, or the length of the line segment from the vertex to the midpoint of the opposite side, is equal to the height of each of these right triangles.

Using the Pythagorean theorem, the length of the altitude of each right triangle can be found:

sqrt(48^2 - 24^2) = sqrt(2304) = 48 inches.

The area of each right triangle is 1/2 base * height, or 1/2 * 24 * 48 = 576 square inches.

Since the equilateral triangle is made up of two of these right triangles, the total area of the equilateral triangle is 2 * 576 = 1152 square inches.

a) The maximum number of bags is 9.

b) 2 per bag.

c) 3 per bag.

To find that, we need to find the maximum common factor between the numbers of snackbags and juice boxes.

We can rewrite these as:

18 = 2*3*3

27 = 3*3*3

Then the maximum common factor is 3*3 = 9

So that is the maximum number of bags.

b) It is given by the quotient between the number of juice boxes and the number of bags:

18/9 = 2

c) Exactly the same computation than above, this time with the number of boxes:

27/9 = 3

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The amounts of each investment are given as follows:

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

The interest accrued is given as follows:

I(t) = Prt.

An amount of x was invested at 3% during one year with a return of R, hence:

R = 0.03x.

An amount of 4000 - x was invested at 4% during one year with a return of 155 - R, hence:

155 - R = 0.04x.

From the first equation, we have that:

x = R/0.03.

x = 33.3R.

Replacing into the second equation, the value of R is obtained as follows:

155 - R = 0.04(33.3R)

1.332R = 155

R = 155/1.332

R = $116.37.

Hence the value of x, representing the amount invested at 3%, is given as follows:

x = 33.3 x 116.37

x = $3875.

The value invested at 4% is given as follows:

4000 - 3875 = $125.

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The percent of people satisfied with the survey is 55%

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, in a survey of 1,600 people who owned a certain type of​ car, 880 said they would buy that type of car again, we need to find what percent of the people surveyed were satisfied with the​ car,

The percent of people satisfied with the survey = 880 / 1600 × 100

= 55%

Hence, the percent of people satisfied with the survey is 55%

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3lb is more than 32oz

3lb=48oz

Answer:

more

Step-by-step explanation:

There are 16 ounces to a pound

3 pounds would be 48 ounces

so 3 pounds is more than 32 ounces

The cost of the hot dog and hamburger meals, given the amount bought by Mrs. Garcia and Mr. Clayton, are :

From Mrs. Garcia's purchase, we have:

2x + y = 18

And from Mr. Clayton's purchase, we have:

3x + 3y = 42

Use the substitution method to come up with the formula:

3x + 3(18 - 2x) = 42

-3x + 54 = 42

x = $ 4

Hamburgers would then cost:

2x + y = 18

2 ( 4 ) + y = 18

y = $ 10

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f(x)=-5/3x-14/3 is the formula for the function.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The function has a maximum point at (-4,2) and a minimum point at (-1,-3)

We have to find the formula for f(x).

Let the slope m=-3-2/-1+4

m=-5/3

Now let us find the y intercept

2=-5/3(-4)+b

2=20/3+b

2-20/3=b

-14/3=b

f(x)=-5/3x-14/3 is the formula for the function.

Hence, f(x)=-5/3x-14/3 is the formula for the function.

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1) Maeve needs to earn $140 each weekend to get at least $1,250, using a linear inequality.

2) The graph on a number line that solves her problem is number line D, showing Maaeve's earnings per weekend.

A linear inequality is a first-order term inequality that compares two values by the inequality symbols such as, '<', '>', '≤', '≠' or '≥'

In a linear inequality, m is the slope and b is the y-intercept with the x-intercept.

The amount Maeve currently has = $130

The number of weekends for the summer = 8

The least amount she wants to earn ≥ $1,250

130 + 8x ≥ 1,250

8x ≥ 1,250 130

8x ≥ 1,120

x ≥ 140

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Answer:

8.73in³

Step-by-step explanation:

volume =⅓πrh

⅓×3.142×2×4=

8.37 in³

Answer:

2

Step-by-step explanation:

3.6 / 1.8 = 2.

Answer:

The answer is 2

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

f(8) - f(4) = 12

f(4) =17

so f(8) = 17+12 =29

Answer:

Either [tex]c = 12[/tex] or [tex]c = (-12)[/tex].

Step-by-step explanation:

Find the [tex]x[/tex]-coordinate of the intersection of the two curves by equating their [tex]y[/tex]-values and solving for [tex]x[/tex]:

[tex]x^{2} - c^{2} = c^{2} - x^{2}[/tex].

[tex]x^{2} = c^{2}[/tex].

[tex]x = c[/tex] or [tex]x = (-c)[/tex].

In other words, the two curves intersect both when [tex]x = c[/tex] and when [tex]x = (-c)[/tex].

Assume that [tex]c \ge 0[/tex]. The area enclosed would be over the range [tex](-c) < x < c[/tex]. Note that over this range, [tex]x^{2} \le c^{2}[/tex], so [tex]x^{2} - c^{2} \le 0 \le c^{2} - x^{2}[/tex]. The curve [tex]y = c^{2} - x^{2}[/tex] would be above [tex]y = x^{2} - c^{2}[/tex].

Integrate the upper curve minus the lower curve [tex](c^{2} - x^{2}) - (x^{2} - c^{2})[/tex] over this interval to find the area enclosed:

[tex]\begin{aligned}& \int\limits_{-c}^{c} \left((c^{2} - x^{2}) - (x^{2} - c^{2})\right)\, dx \\ =\; & \int\limits_{-c}^{c} \left(2\, c^{2} - 2\, x^{2}\right)\, dx \\ =\; & {\left[2\, c^{2}\, x - \frac{2}{3}\, x^{3}\right]}_{-c}^{c} && (\text{power rule}) \\ =\; & \left(2\, c^{2}\, c -\frac{2}{3}\, c^{3}\right) - \left(2\, c^{2}\, (-c) - \frac{2}{3}\, (-c)^{3}\right) \\ =\; & \frac{8}{3}\, c^{3} \end{aligned}[/tex].

In other words, assuming that [tex]c \ge 0[/tex], area enclosed between these two curves would be [tex](8/3)\, c^{3}[/tex]. Since this area is given, the value of [tex]c[/tex] can be found as:

[tex]\begin{aligned}c &= \sqrt[3]{\frac{3}{8}\, (\text{Area})} = 12\end{aligned}[/tex].

However, note that if [tex]c < 0[/tex], the order of limits of the integral would need to be reversed:

[tex]\begin{aligned}& \int\limits_{c}^{-c} \left((c^{2} - x^{2}) - (x^{2} - c^{2})\right)\, dx \\ =\; & \cdots \\ =\; & {\left[2\, c^{2}\, x - \frac{2}{3}\, x^{3}\right]}_{c}^{-c} \\ =\; & \left(2\, c^{2}\, (-c) - \frac{2}{3}\, (-c)^{3}\right) - \left(2\, c^{2}\, c -\frac{2}{3}\, c^{3}\right) \\ =\; & \left(-\frac{8}{3}\, c^{3}\right) \end{aligned}[/tex].

Hence, [tex]c = (-12)[/tex] would also be a solution to this question.

The child's position after 90 seconds would be (0, -1).

The carousel revolves 360 degrees in one minute, which means it revolves 360/60 = 6 degrees per second.

After 90 seconds, the carousel would have revolved 90 * 6 = 540 degrees.

When the carousel revolves counterclockwise, the point (0, 1) would rotate to a new position by 540 degrees.

To find the new position, we can use the transformation:

540 - 360 = 180

hence the transformation is 180 degrees which is reflection across x axis

The rule for a reflection over the x -axis is (x, y) → (x, −y)

point (0, 1) → (0, −1)

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The differentiation of the equation will be (dy/dx) = - x² / y². Then the correct option is D.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The equation is given below.

x³ + y³ = 1

Differentiate the equation with respect to 'x'. Then we have

(d/dx) (x³ + y³) = d/dx (1)

3x² + 3y² (dy/dx) = 0

x² + y² (dy/dx) = 0

y² (dy/dx) = - x²

(dy/dx) = - x² / y²

The differentiation of the equation will be (dy/dx) = - x² / y². Then the correct option is D.

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The height of the tree given the ratio of the hikers shadow to the tree's shadow is 21.85 meters

Tree's shadow = 25.3 meters

Hikers shadow= 2.2 meters

Tree's height= x

Hiker's height= 1.9 meters

Equate the ratio of tree's to hikers

25.3 : 2.2 = x : 1.9

25.3/2.2 = x / 1.9

cross product

25.3 × 1.9 = x × 2.2

48.07 = 2.2x

divide both sides by 2.2

x = 48.07 / 2.2

x = 21.85 meters

Ultimately, the tree's height is given by 21.85 meters

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a. [tex]7[/tex]

b. [tex]2[/tex] and [tex]4x+1[/tex]; [tex]4[/tex] and [tex]x[/tex]

c. [tex]-3m+17[/tex]

d. Coefficient: [tex]4[/tex], [tex]11[/tex]; Term: [tex]4x^2, 11y, -37[/tex]; Constant: [tex]-37[/tex]; Variables: [tex]x, y[/tex]; Expression: [tex]4x^2 +11y-37[/tex]

e. Factors: [tex]-8, (m+n)[/tex]; Quotient: [tex]\frac{5-m}{n}[/tex]; Sum: [tex]m+n[/tex]; Product: [tex]8(m+n)[/tex]

A constant in the expression 3x²+7-2(4x + 1) is 7. The factors in 2(4x + 1) are 2 and (4x + 1), and the factors in 4x are 4 and x. An expression with a variable m, a coefficient -3, and a constant of 17 can be written as -3m + 17. In the expression 4x² + 11y - 37, the coefficient is 4, the term, expression, and the variables are defined, but there are no factors. In the expression m-2-8(m+n), m is a factor, 2 and 8 are factors, the quotient is (m + n), and the sum is (m - 2 - 8(m + n)).

a. A constant is a term that does not contain any variables. In the given expression, 7 is a constant.

b. The two factors in 2(4x + 1) are 2 and (4x + 1). In the expression 4x, the two factors are 4 and x.

c. An expression with a variable m, a coefficient -3, and a constant of 17 can be written as -3m + 17.

d. In the expression 4x² + 11y - 37, the coefficient is 4, the terms are 4x², 11y, and -37, there are two variables (x and y), and there are no factors.

e. In the expression m - 2 - 8(m + n), m is a factor, 2 and 8 are factors, the quotient is (m + n), and the sum is (m - 2 - 8(m + n)).

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Answer:

1-2x

Step-by-step explanation:

[tex](7+2x)-(4x+6)=7+2x-4x-6=1-2x[/tex]

The perimeter of parallelogram MBKR is 18x + 26.6.

The perimeter of the parallelogram is equal to the sum of the lengths of its sides. Given RM = 3x + 11.2, MB = 7x - 3.8 and KR = 5x + 7, we can find the perimeter by adding the lengths of RM, MB, KR and KB (the length of the fourth side). To find KB, we can use the property of a parallelogram that opposite sides are equal in length.

RM + MB + KR + KB = (3x + 11.2) + (7x - 3.8) + (5x + 7) + KB

= 15x + 15.4 + KB

= 15x + 15.4 + RM

= 15x + 15.4 + (3x + 11.2)

= 18x + 26.6

So, the perimeter of parallelogram MBKR is 18x + 26.6.

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The student spent $2.5 each day at the coffee shop.

The student spent $2.5 each day at the coffee shop because -2.5 is the coefficient of the variable "n" in the function f(n) = -2.5n + 75. The coefficient represents the rate of change or how much the value of the function changes for each unit increase in the variable. In this case, for each increase of 1 day, the value of the gift card decreases by $2.5, meaning the student spent $2.5 each day.

The function is solved and the amount of money the student spent each day on the coffee shop is A = $ 2.50

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = -2.5n + 75

We know that the function is f(n) = -2.5n + 75, where n is the number of days.

The coefficient of n (-2.5) represents the rate at which the value of the gift card is decreasing per day.

Hence , the student spent $2.5 each day at the coffee shop

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The probability of passing if the minimum passing grade is 70 %

is  0.3074.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

A quiz consists of 20 multiple-choice questions, each with 4 possible answers.

now,

n = 20, the number of questions

p = 1/4= 0.25, the probability of making a correct guess

q = 1 - p = 0.75, the probability of making an incorrect guess.

Expected success  = 70% or 7 of 10.

From the binomial distribution,

P(7of 10) = ₁₀C7 p^7q^3

               =120×0.000061×0.42

               =0.3074

Hence, the Answer: 0.3074.

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The Stafford loan will have a higher balance of $114.84 at the time of repayment.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded monthly is

A = P(1 + (r/12)/100)¹²ⁿ.

So, For Unsubsidized Stafford Loan,

A = 4980(1 + (6.25)/12/100)¹⁸.     (12 times 1.5 years two semesters and 6  

                                                                                                           months)                                                                                                                    

A = 4980(1 + 0.0052)¹⁸.

A = 4980(1.0052)¹⁸.

A = $5467.

So, Unsubsidized Stafford Loan will give a higher balance.

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Answer: The Stafford loan will have a higher balance by $114.84 at the time of repayment.

Step-by-step explanation:

The correct statement regarding the solution to the equation 1/6(3x - 6) = 1/8(4x + 8) is given as follows:

Solving results in the statement -1 = 1, which is false. There is no solution.

The equation for this problem is given as follows:

1/6(3x - 6) = 1/8(4x + 8)

Applying the distributive property to each side of the equality, we have that:

0.5x - 1 = 0.5x + 1

Isolating the variable x, we have that:

0.5x - 0.5x = 1 + 1

0x = 2.

x = 2/0.

A division by zero is a false statement, hence the equation has no solution.

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The  x = -1, 0, 1 and y = 1, 3, 5 represents a linear relationship that is also proportional.

Linear relationship is a statistical term used to describe a straight-line relationship between two variables.

A relationship is proportional if there is a constant of proportionality (k) such that for any x and y in the relationship, y = kx.

The table x = -1, 0, 1 and y = 1, 3, 5 represents a linear relationship that is proportional because we can see that for every increase in x by 1 unit, y increases by 2 units (the constant of proportionality).

This is a linear relationship because the values of x and y change in a consistent straight-line pattern.

Therefore, x = -1, 0, 1 and y = 1, 3, 5 represents a linear relationship that is also proportional.

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Answer:

A is the answer

Step-by-step explanation:

Answer:

15/24

Step-by-step explanation:

(3a-3/4)

where a is 3/8,

we substitute the value of a;

(3(3/8)-3/4)

(9/8-3/4) =15/8

15/8 times 1/3 =15/24.

Answer: 3.42x10^11

Step-by-step explanation:

The number 0.0000000000342 is equivalent to 3.42 × 10^-11. Hence, option B is the correct answer.

This type of conversion is called scientific notation.

Firstly we have to place a decimal between the two non-zero numbers which is 3.42.

And then, count the number of decimals that were moved. That is 11.

And then, determine whether the decimal point is to be moved to the left or right to return to the original number. If the decimal is moved right then the exponent is negative. If the decimal is moved left then the exponent is positive.

Here, the exponent is moved right and the decimal will be negative.

In this case, it is written as 3.42 × 10^-11.

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