I NEED HELP PLEASE: If x and y are proportional, fill in the blank with a number in simplest form. ​

Answer: x = -5

Step-by-step explanation:

4−2(x+7)=3(x+5)4-2(x+7)=3(x+5)Simplify 4−2(x+7)4-2(x+7).Tap for more steps...−2x−10=3(x+5)-2x-10=3(x+5)Simplify 3(x+5)3(x+5).Tap for more steps...−2x−10=3x+15-2x-10=3x+15Move all terms containing xx to the left side of the equation.Tap for more steps...−5x−10=15-5x-10=15Move all terms not containing xx to the right side of the equation.Tap for more steps...−5x=25-5x=25Divide each term in −5x=25-5x=25 by −5-5 and simplify.Tap for more steps...x = −5

If 7/9 of the box is green counters, and there are 24 yellow counters in the box, then there are 84 green counters .

Let's assume that the total number of counters in the box is x.

We are given that 7/9 of the box is filled with green counters, which means that the remaining 2/9 of the box must be filled with yellow counters. We are also given that there are 24 yellow counters in the box.

We can set up an equation to represent the relationship between the number of yellow counters and the total number of counters:

2/9 x = 24

To solve for x, we can multiply both sides of the equation by the reciprocal of 2/9, which is 9/2:

(2/9) x * (9/2) = 24 * (9/2)

x = 108

This means that there are a total of 108 counters in the box. To find out how many of these are green counters, we can use the fact that 7/9 of the box is filled with green counters:

(7/9) * 108 = 84

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Answer:

-17

Step-by-step explanation:

The divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

To find the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k, you need to take the divergence operator (∇ · F).

The divergence of a vector field in Cartesian coordinates is given by the following formula:

∇ · F = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z),

where Fx, Fy, and Fz are the x, y, and z components of the vector field F, respectively.

In this case, we have:

Fx = (5x^2 + 7 - sin(xz)),

Fy = 0, and

Fz = (5x^2 + 7 - sin(xz)).

Taking the partial derivatives, we get:

∂Fx/∂x = 10x - zcos(xz),

∂Fy/∂y = 0, and

∂Fz/∂z = 10x - zcos(xz).

Now, substituting these derivatives into the divergence formula, we have:

∇ · F = (10x - zcos(xz)) + 0 + (10x - zcos(xz)).

Simplifying further, we get:

∇ · F = 20x - 2zcos(xz).

Therefore, the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

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Answer:

(x+2y)(x+2y)

x²+2xy+2xy+2y²

x²+4xy+2y²

(2x+3y)(2x+3y)

4x²+6xy+6xy+9y²

4x²+12xy+9y²

1) The solution to the initial-value problem is y(t) = 2 cos(4t) - (1/2) sin(4t).

2) The solution to the initial-value problem is y(t) = 0.

Let's solve the initial-value problems given.

Initial-Value Problem: y'' + 16y = 0, y(0) = 2, y'(0) = -2

We have a second-order linear homogeneous differential equation. To solve this, we assume a solution of the form y(t) = \(e^{rt\), where r is a constant to be determined.

Substituting this assumed solution into the differential equation, we get the characteristic equation:

\(r^2\) + 16 = 0

Solving the characteristic equation for r, we have:

r = ±4i

Since the roots are complex (r = 4i and r = -4i), the general solution will involve complex exponentials.

The general solution for the differential equation is:

y(t) = \(c_1\) cos(4t) + \(c_2\) sin(4t)

To find the particular solution that satisfies the initial conditions, we substitute the initial conditions y(0) = 2 and y'(0) = -2 into the general solution:

y(0) = \(c_1\) cos(0) + \(c_2\) sin(0) = \(c_1\) = 2

y'(0) = -4\(c_1\) sin(0) + 4\(c_2\) cos(0) = 4\(c_2\) = -2

Solving these equations, we find \(c_1\) = 2 and \(c_2\) = -1/2.

Therefore, the solution to the initial-value problem is:

y(t) = 2 cos(4t) - (1/2) sin(4t)

2) Initial-Value Problem: y'' + y' + 2y = 0, y(0) = y'(0) = 0

We have a second-order linear homogeneous differential equation. To solve this, we assume a solution of the form y(t) = \(e^{rt\), where r is a constant to be determined.

Substituting this assumed solution into the differential equation, we get the characteristic equation:

\(r^2\) + r + 2 = 0

Solving the characteristic equation for r, we have:

r = (-1 ± √(1 - 4(1)(2)))/2

= (-1 ± √(-7))/2

= (-1 ± i√7)/2

Since the roots are complex, the general solution will involve complex exponentials.

The general solution for the differential equation is:

y(t) = \(c_1\) \(e^{-t/2\) cos((√7/2)t) + \(c_2\) \(e^{-t/2\) sin((√7/2)t)

To find the particular solution that satisfies the initial conditions, we substitute the initial conditions y(0) = 0 and y'(0) = 0 into the general solution:

y(0) = \(c_1\) = 0

y'(0) = -(1/2)\(c_1\) + (√7/2)\(c_2\) = 0

Solving this equation, we find \(c_1\) = 0 and \(c_2\) = 0.

Therefore, the solution to the initial-value problem is:

y(t) = 0

In this case, the zero solution satisfies the initial conditions.

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Answer:

16

Step-by-step explanation:

3 divided into 12 =4

4x4=16

4 divided into 16 =4 so 16

The solution to the system of equations by substitution is x = 3 and y = -8.

To solve the system of equations by substitution:

Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x:

4x - y = 20

4x = y + 20

x = (y + 20)/4

Substitute this expression for x into the second equation:

-2x - 2y = 10

-2((y + 20)/4) - 2y = 10

(y + 20)/2 - 2y = 10

(y + 20) - 4y = 20

-y - 20 - 4y = 20

-5y = 40

y = -8

Substitute the value of y back into the first equation to find x:

4x - (-8) = 20

4x + 8 = 20

4x = 20 - 8

4x = 12

x = 12/4

x = 3

Therefore, the solution to the system of equations is x = 3 and y = -8.

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Answer:

that's a good question

Step-by-step explanation:

ANSWER

EXPLANATION

The first two pieces were 32 feet long pieces each. The third piece needs to be 1.95 times longer than each of the first two.

This means that the length of the third piece needs to be:

Hence, the length of board that should be bought is:

Answer:

Step-by-step explanation:

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

Answer:

60

Step-by-step explanation:

Answer:

c=13

Step-by-step explanation:

a^2+b^2=c^2

The total area of the given shape is 71cm².

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. A shape's area can be calculated by contrasting it with squares of a known dimension. The square meter (abbreviated as m²), which is the area of a square whose sides are one metre long, is the common measure of area in the International System of Units (SI). Three such squares would be the same size as a shape with a three square metre surface.

The following figure can be divided into a rectangle 7cm x 8cm and a triangle of height and base 6 cm and 5 cm respectively.

Area of rectangle= 7*8= 56 cm²

Area of triangle= 1/2* base*height= 1/2*6*5 = 15 cm²

Total area of shape = 56+15= 71 cm²

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Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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30° is the angle of elevation from the base to the top of the mountain.

Trigonometric ratios are the ratios of the length of sides of a triangle.

These ratios in trigonometry state the relation between the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.

The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.

Sin θ = Perpendicular / Hypotenuse

According to the question,

Perpendicular = Vertical height of Mountain. = 1290 m

Hypotenuse    = The distance from the top of the mountain to the base                               of the Mountain. = 2580 m

⇒ Sin θ = 1290/ 2580

⇒ Sin θ = 1/2⇒ θ = Sin⁻¹(1/2)

⇒ θ = 30°

Hence, 30° is the angle of elevation from the base to the top of the mountain.

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Answer: $0.28

Step-by-step explanation:

A gallon is equal to 8 pints, so half a gallon is equal to 4 pints. Therefore, the cost per pint of milk is $0.28. ( 1.12 / 4 = 0.28)

Answer: See below

Step-by-step explanation:

For both problems, we can use a proportion to solve.

1.

\(\frac{56 min}{4 tyres} =\frac{x}{12 tyres}\)               [cross multiply]

672=4x                         [divide both sides by 4]

x=168

It would take 168 minutes or 2 hours and 48 minutes.

2.

\(\frac{56 min}{4 tyres} =\frac{42min}{x}\)                [cross multiply]

56x=168                       [divide both sides by 56]

x=3

Liam would be able to fit 3 tyres.

The weight of 1,000,000 yds of a 2/30 count yarn is approximately 79.37 kgs

Given that:

Length of yarn = 1,000,000 yds

Count = 2/30

We know that,

Weight of 1 yard of yarn = count (in lbs) / 840 yards

Therefore, Weight of 1 yard of yarn = 2/30 lbs / 840 yards = 1/12600 lbs/yd

Now, We have to find the weight of 1,000,000 yards of yarn.

Weight of 1 yard of yarn = 1/12600 lbs/yd

So, the Weight of 1,000,000 yards of yarn = (1/12600) * (1000000) lbs

Weight of 1,000,000 yards of yarn = 79.37 lbs (Approximately)

Thus, the weight of 1,000,000 yds of a 2/30 count yarn is 79.37 kgs (Approximately).

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Two consecutive odd numbers are:

n and n+2

The sum of two consecutive odd numbers

the sum of two consecutive odd numbers is 72:

Use this equation to find the value of n:

n=35

n+2=35+2=37

Answer:ummm what do you need help w exactly

Step-by-step explanation:

You didn’t really show the whole graph and you didn’t really explain what yo7 need help with

Answer:

She has a total of 300 action figures.

Step-by-step explanation:

19 : 100 = 57 : x

x = 100/19 * 57

x = 300

Answer: You would be going 30 miles per hour if you traveled 8 miles in 16 minutes

Step-by-step explanation:

Step-by-step explanation:

the last option is your answer

Therefore, the appropriate test of significance to use in this scenario is a factorial ANOVA.

To determine if room temperature and paper color have an effect on student performance, you can use a factorial design experiment. This experiment involves manipulating multiple independent variables, in this case, room temperature (warm or cold) and paper color (white, yellow, or blue), to observe their effects on the dependent variable, student performance.

To analyze the data and test for significance, a factorial ANOVA (Analysis of Variance) should be used. This statistical test is specifically designed to analyze the effects of multiple independent variables and their interactions on a continuous dependent variable, such as student performance.

Factorial ANOVA allows you to examine the main effects of each independent variable (room temperature and paper color) as well as any interaction effects between them. By conducting this test, you can determine if there are significant differences in student performance based on room temperature, paper color, or the interaction between the two.

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Answer:

11)The unknown answer is 24

So sorry I couldn't solve the remaining ones

Answer:

1)90

2)77

3)110

4)30

Step-by-step explanation:

if you can tell its an isosceles triangle by the congruent marks on the two longer legs... then the two lower leg corner have congruent angles... therefor, subtract the sum of the two bottom corners from 180 and there's the top corner

Answer:Chi-square is a nonparametric statistical procedure for nominal data.

Step-by-step explanation:

Answer:

See details below:

Step-by-step explanation:

We can start with the biggest factors and work our way down to see how arrive at 4 * 25.

In this case, the first part of the tree would be 50 * 2.

2 is prime, but 50 is not and thus must be factored.

Two possible factors of 50 are 2 and 25.

The 25 is not a prime number and must be factored further.

Two possible factors of 25 are 5 and 5.

Thus, the prime factorization of 100 is 2*2*5*5.

Then to simplify, we can combine the similar factors:  (2*2) * (5*5) = 4*25

I hope this makes sense