Use substitution to solve the following system of equation



X =
y =



4x + y = 28


y = 3x

Answer:

16

Step-by-step explanation:

I had this on my test and got correct

Its speed of Rachel would be 30 meters per second.

Given that,

Stunt driver Rachel is trying to get out of a building that is going to blow up.

Here, the equation is,

[tex]d = - 38t + 220[/tex]

Where, variable d models Rachel's distance from her exit (in meters) t seconds after the cameras began recording the stunt.

Now, Velocity is the rate at which a distance changes over time.

[tex]d = - 38t + 220[/tex]

[tex]\dfrac{d(d)}{dt} = - 38[/tex]

Hence, Speed is the magnitude of velocity.

[tex]|- 38| = 38[/tex]

To learn more about Speed visit:

brainly.com/question/13943409

#SPJ12

If Jordan is taking out a 2-week payday loan for $600. He will be charged $95 interest for the 2-week loan. The APR for this loan is 412.8%.

Using this formula to find the Annual percentage rate (APR)

APR =Loan interest /loan amount ÷ Number of loan length / 365

Let plug in the formula

APR = 95/600 ÷ (2 × 7 days)/365 days

APR = 95/600 ÷ 14 days/365 days

APR = 4.1279 × 100

APR = 412.8% ( Approximately)

Therefore we can conclude that the APR is 412.8%.

Learn more about APR here:https://brainly.com/question/2772156
#SPJ1

Each of Liam, Anika, and Sai is figuring out the identical equation for x. 12x+4=20x-12 in the original equation. 12x+16=20x was the outcome of Sai's initial action.

Getting the variable on one side is the first step in solving an equation with a variable on both sides once it has been simplified. To do this, one of the words with the variable's addition or subtraction is reversed.

12 x + 4 = 20 x - 12 x 4 = 20 x - 12 x - 12 x 4 = 8x - 12

The linear term was then simply merged.

12 on each side is added. Consequently, 12 x + 16 = 20 x. 12 x + 4 + 12 = 20 x

12 x + 4 = 20 x - 12 is the analysis.

12 on each side added

Consequently, 12 x + 16 = 20 x. 12 x + 4 + 12 = 20 x

12 x from both sides 16 = 20 x - 12 x 16 = 8x x = 2.

To learn more about Anika refer to:

https://brainly.com/question/21919794

#SPJ1

Answer:

range for -1= 1 range for 3.7= -8.4

Step-by-step explanation:

you just plug in the two values to the equation to get the answer

Answer:

See below

Step-by-step explanation:

The chi-squared analysis aims to check whether observed frequencies in one or more categories match up with expected frequencies. I don't see any answer choices, but hopefully this short explanation will help!

The equation of the line that passes through these points X -2,0,2,3 and Y -17, -5, 7, 13 is given by y = 6x - 30

The slope, m of the linear function is calculated using the points on the form the table (0, -5) and  (2, 7)

m = (y₀ - y₁) / (x₀ - x₁)

m = (-5 - 7) / (0 - 2)

m = (-12) / (-2)

m = 6

equation passing through point (0, 5)

(y - y₁) = m (x - x₁)

y - 0 = 6 (x - 5)

y = 6x - 30

The equation of the line for the table is solved to be  y = 6x - 30

Learn more about  linear function at:

https://brainly.com/question/30125370

#SPJ1

The matching of the first row of expressions with the second row of expressions are;

1) 2√(3x²y) → x√(12y)

2) 2x√(6xy²) → y√(24x³)

3) 2y√(2x⁴) → x²√(8y²)

4) 3x²√(2y⁴) → xy√(18x²y²)

1) 2√(3x²y)

This can be broken down into the expression;

2x√(3y)

2) 2x√(6xy²)

This can broken down into;

2xy√(6x)

3) 2y√(2x⁴)

This can be simplified into;

2x²y√2

4) 3x²√(2y⁴)

This can be simplified into;

3x²y²√2

The second row of expressions are simplified as;

xy√(18x²y²)

= 3x²y²√2

x√(12y)

= 2x√3y

x²√(8y²)

= 2x²y√2

y√(24x³)

= 2xy√6x

Read more about Laws of Indices at; https://brainly.com/question/10339517

#SPJ1

Answer: Therefore, the value of h is -6.

Step-by-step explanation: The slope of a line is given by the formula:

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

where (x1, y1) and (x2, y2) are two points on the line.

In this case, the slope of the line is -2, and the two points on the line are (-1, -2) and (h, -8). Plugging these values into the formula gives us:

-2 = (-8 - (-2)) / (h - (-1))

Solving this equation for h gives us:

h = -6

Therefore, the value of h is -6.

Answer:

Eden planted 2 basil plants and 8 mint plants.

Step-by-step explanation:

Here's one possible way to write a system of equations to represent the information given in the problem:

Let x be the number of basil plants and y be the number of mint plants.

The first equation represents the total number of plants:

x + y = 10 (because Eden is planting a total of 10 herbs)

The second equation represents the total cost of all the plants:

x* $0.50 + y* $0.25 = $3

Elimination Method:

Multiply the first equation by $0.50

x* $0.50 + y* $0.50 = $5

subtracting this equation from the second equation

y* $0.25 = $3-$5 = -$2

y = 8

then substitute the value of y in first equation

x + 8 = 10

x = 2

Read more about Elimination Method:

https://brainly.com/question/13877817

#SPJ4

The total number of different 4-digit numerals that can be written using the 10 digits is 7.

Numbers are represented by digits, which include 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. A group of digits known as numerals is used to represent a number. 1234 2314 56111, for example, are numerals.

The number of different permutations of 4 digits can be calculated using the formula nPr = n! / (n-r)!.

2. In this case, n = 10 and r = 4, so nPr = 10! / (10-4)! = 10! / 6! = 5040 / 720 = 7!.

Since each digit can only be used once, there are no duplicate combinations. Therefore, the total number of different 4-digit numerals that can be written using the 10 digits is 7!

For more questions like Numbers click the link below:

brainly.com/question/62841

#SPJ4

The correct answer is 7.07 and 8.43 units, so option C is correct and 8.43 units. This can be calculated using trigonometry.

The two sides of the triangle are referred to as the opposite side and adjacent side. The adjacent side is the side of the triangle adjacent to the angle, and the opposite side is the side opposite to the angle. The adjacent side is calculated using the cosine of the angle multiplied by the hypotenuse, which in this case is 11.

Cos 40° multiplied by 11 gives a value of 7.07 units for the adjacent side.

Cos40×11= 7.07

The opposite side is calculated using the sine of the angle multiplied by the hypotenuse, which gives a value of 8.43 units.

Sin40×11= 8.43

Therefore, the lengths of the two sides of the right triangle are 7.07 units and 8.43 units.

Learn more about trigonometry:

https://brainly.com/question/13729598

#SPJ4

Answer:

x = 15

Step-by-step explanation:

[tex]\sqrt[3]{2x-3}[/tex] = 3 ( cube both sides to clear the radical )

( [tex]\sqrt[3]{2x-3}[/tex] )³ = 3³

2x - 3 = 27 ( add 3 to both sides )

2x = 30 ( divide both sides by 2 )

x = 15

To solve this equation, we need to get x by itself on one side of the equation. To do this, we can start by adding 8 to both sides of the equation to get:

2/3 x - 8 + 8 = 24 + 8

This simplifies to:

2/3 x = 32

Then, we can divide both sides of the equation by 2/3 to get:

(2/3) / (2/3) * x = 32 / (2/3)

This simplifies to:

x = 48

So the solution to this equation is x = 48.

Answer:

y=15

Step-by-step explanation:

10y+4=29

29-14= 15

therefore

y=15

10+15+4= 29 !!

The solution of expression is,

⇒ y = 2.5

We have to given that,

An expression to solve is,

⇒ 10y + 4 = 29

Now, We can simplify the expression for y as,

⇒ 10y + 4 = 29

Subtract 4 both side,

⇒ 10y + 4 - 4 = 29 - 4

⇒ 10y = 25

Divide by 10;

⇒ y = 25 / 10

⇒ y = 2.5

Therefore, The solution of expression is,

⇒ y = 2.5

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

It should be noted that (2,3) is not a solution to a the equation y = x + 1.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

No, (2,3) is not a solution to the equation y = x + 1. If we substitute 2 for x and 3 for y, we get 3 = 2 + 1 which is not true.

Learn more about equations on:

https://brainly.com/question/2972832

#SPJ1

Answer:

Use the Cosine Rule to find unknown sides and angles

Step-by-step explanation

The value of the variable based on the triangle given is 5.5 units.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

Add each side of the triangle.

3z + z + 1 + 4z - 3 = 8z - 2

8z - 2 is equivalent to the  perimeter.

Since you know the perimeter is 38 units, you can set 8z-2 to 38.

8z -2 = 38

Solve for z. Subtract 2 from each side.

8z = 36

Divide each side by 8.

z = 4.5

Now solve for side WX.

WX = z + 1

WX = 4.5 + 1

WX = 5.5

Learn more about perimeter on:

https://brainly.com/question/19819849

#SPJ1

Answer

[tex]\sqrt[3]{4^{2} }[/tex]

Step-by-step explanation:

Brandon ' s rate of change , give the graph on the amount of savings per period, is C. 75

The rate of change can be found by the formula :

= Rise / Run

The rise can be found by subtracting an earlier value of the amount in savings, from a later value of the amount in savings .

The run can be found by subtracting an earlier value in periods from a later value in periods . Therefore , the first step is to pick two points on the graph.

Points picked are ( 2 , 150 ) and ( 4 , 300 )

The rise is :

= 300 - 150

= 150

The run is :
= 4 - 2

= 2

The rate of change is :
= 150 / 2

= 75

Find out more on rate of change at https://brainly.com/question/25184007

#SPJ1

In order to solve problems involving triangles that require constructions, you can use a straightedge and compass.

Here are the steps you can follow:

First, identify the information that is given in the problem and what you need to find.

Draw a diagram of the triangle, including any given segments or angles.

Use the given information to construct any points or lines that are required.

Use the straightedge to draw any necessary lines, and use the compass to construct any circles or arcs that are required.

Use the properties of triangles and the given information to solve for the unknown quantity. It's important to note that not all problems involving triangles can be solved using constructions. In some cases, you may need to use other techniques, such as the Pythagorean Theorem or the Law of Sines.

Learn more about triangles on:

https://brainly.com/question/17335144

#SPJ1

Answer:

600

Step-by-step explanation:

To determine how well Daniel must score on Exam B in order to do equivalently well as he did on Exam A, we can use the concept of standard scores or z-scores. A z-score indicates how many standard deviations away from the mean a score is.

First, we need to convert Daniel's score on Exam A to a z-score:

z = (18 - 28) / 5 = -2

This tells us that Daniel's score on Exam A is 2 standard deviations below the mean.

We can then use this z-score to find Daniel's equivalent score on Exam B. To do this, we can use the formula:

x = z * σ + μ

Where x is the equivalent score on Exam B, z is the z-score from Exam A, σ is the standard deviation of Exam B, and μ is the mean of Exam B.

x = (-2) * 40 + 700

x = 600

Therefore, Daniel must score 600 on Exam B in order to do equivalently well as he did on Exam A.

Keep in mind that this calculation assumes that the scores on each exam are normally distributed, which may or may not be the case. It also assumes that the two exams are of similar difficulty, which also may not be the case.

The best unbiased estimate for μ is [tex]$\bar{x}$[/tex], the confidence interval for the population mean is (14.5044, 17,2956).

The best unbiased estimate for μ is [tex]$\bar{x}$[/tex].

 Sample standard mean [tex]$\bar{x}$[/tex] is the best unbiased estimate of population mean μ.

[tex]$$\begin{aligned}& \mathrm{SE}=\sigma / \sqrt{n} \\& =6 / \sqrt{100}=0.6 \\& \alpha=0.02\end{aligned}$$[/tex]

The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean.

From Table, critical values of [tex]$Z=\pm 2.326$[/tex]

Confidence interval:

[tex]$$\begin{aligned}& \bar{x} \pm \text { Z SE } \\& =15.9 \pm(2.326 \times 0.6) \\& =15.9 \pm 1.3956 \\& =(14.5044,17,2956)\end{aligned}$$[/tex]

Therefore, the confidence interval for the population mean is (14.5044, 17,2956).

For more such questions on standard error of a sample mean

https://brainly.com/question/14524236

#SPJ4

The tax increase from 7% to 21% is 7.98%.

The tax increase is calculated by subtracting the original rate from the new rate and then multiplying the difference by the original rate.

For example, if the original rate is 10% and the new rate is 20%, then the tax increase is 10% (20% - 10% = 10%).

Tax Increase = (New Rate - Old Rate) x Old Rate

In this question,

Step 1: Calculate the difference between the two percentages.

The difference between 7% and 21% is 14%.

Step 2: Multiply the original percentage (7%) by the difference (14%).

7% x 14% = 0.98

Step 3: Add the result from Step 2 to the original percentage (7%).

7% + 0.98 = 7.98

Step 4: The tax increase from 7% to 21% is 7.98%.

To learn more about tax increase refer to:

https://brainly.com/question/30307182

#SPJ1

Answer:

-45, -46

Step-by-step explanation:

-45 + (-46) = -91

When the linear functions of Amit and Camille's puppies are compared, the weight of Camille's puppies increases directly with age, whereas Amit's puppies are irregular.

Linear functions have a straight line as their graph. The following is the form of a linear function. a + bx = y = f(x). There is one independent variable and one dependent variable in a linear function. x is the independent variable, and y is the dependent variable.

Camille's dog:

slope: 0.5

1.5 y-intercept

Camille's puppy began at 1.5 pounds and is now gaining 0.5 pounds per week.

Olivia's dog:

slope: 1

4 is the y-intercept.

Olivia's puppy began at 4 pounds and gains one pound per week.

The slope represents the amount of weight gained by the puppy each week. The y-intercept denotes the puppy's initial weight.

To learn more about linear function refer to :

https://brainly.com/question/15602982

#SPJ1

The answer to the given equation is 240.

We can con solve the equation in the following ways:

6 f(x) dx = 6 * (4x) dx for x ≥ 4

Here, we will do the derivative and integration of the given equations as required. That will take us to the simplified statement. Note: we need to take into consideration the greater than equal  sign as it will directly affect the result of the equation.

= 24 * ∫x dx from 4 to 6

= 24 * (x^2/2)|4 to 6

= 24 * (6^2/2 - 4^2/2)

= 24 * (18 - 8)

= 24 * 10

= 240

Therefore, The answer to the given equation is 240.

To learn more about equations,

Visit; brainly.com/question/29657992

#SPJ4

Answer:

Step-by-step explanation:

A would-be correct because it matches the 3 parts and the 5 parts

Root x = 2 is an extraneous solution for radical equation √(4 · x - 7) - √(2 · x) = 1, whose roots are 2 and 8, respectively.

In this problem we find the definition of a radical equation, whose roots must be found by combining algebra properties and power properties. A root is an extraneous solution if the result lead to an absurdity. (i.e. 1 = 0).

First, write the complete expression:

√(4 · x - 7) - √(2 · x) = 1

Second, apply algebraic substitution formula u = 2 · x to simplify the model:

√(2 · u - 7) - √u = 1

Third, use algebra properties to clear square roots:

√(2 · u - 7) = 1 + √u

Fourth, square both sides of the expression:

2 · u - 7 = (1 + √u)²

2 · u - 7 = 1 + 2 · √u + u

u - 7 = 1 + 2 · √u

u - 2 · √u - 8 = 0

Fifth, use algebraic substitution k = √u and solve the quadratic-like equation by factorization:

k² - 2 · k - 8 = 0

(k - 4) · (k + 2) = 0

k₁ = 4 or k₂ = - 2

Sixth, find the values of x by reversing algebraic substitutions:

√u₁ = 4 or √u₂ = - 2

u₁ = 4² or u₂ = (- 2)²

2 · x₁ = 4² or 2 · x₂ = (- 2)²

x₁ = 8 or x₂ = 2

Seventh, look for any extraneous solution:

x₁ = 8

√(4 · 8 - 7) - √(2 · 8) = 1

√25 - √16 = 1

5 - 4 = 1

1 = 1

x₂ = 2

√(4 · 2 - 7) - √(2 · 2) = 1

√1 - √4 = 1

1 - 2 = 1

- 1 = 1 (CRASH!)

To learn more on extraneous solutions: https://brainly.com/question/28887790

#SPJ1