x + 4y = 13
x - y = 3
systems of equations I need help on a couple of these like ASAP

D because 2 has a x next to it so you divide by 2 on both sides

The correct answer is

H₀ : μh - μc = 0

H₀ : μh - μc ≠ 0

Given that,

Regarding the subsequent 3 inquiries: A study collected information on how much time 28 randomly chosen high school students and 31 randomly chosen college students spent each day on their cellphones. The researcher is interested in learning whether there is proof that students use their phones for varying amounts of time in high school and college.

Because the samples of college and high school students are independent, the independent samples t-test should be utilized.

The study's research (Claim) aims to ascertain whether students' cell phone usage patterns alter between high school and college.

For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,

H₀ : μh - μc = 0

H₀ : μh - μc ≠ 0

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The proper null and alternative hypotheses are

\(H_{0}\) : μh = μc

\(H_{A}\) : μh - μc

The study's research wants to ascertain whether difference between the time spent by high school students and college students.

The actual test begins by considering two hypothesis i.e. null hypothesis and alternative hypothesis.

Let, H= time spent on the phone by high school students;

C= Time spent on the phone by college students; and

d=H−C

For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,

\(H_{0} :\) μh = μc  (time spent by high school students is equal to college students)

\(H_{A} :\) μh - μc  (difference between the time spent by high school students and college students)

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No, it is not safe to assume that the sampling distribution of the sample means is about normal given the sample size.

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The volume of Brody's display case is 270 cubic inches.

Brody's display case is shaped like a rectangular prism with a length of 15 inches, a width of 9 inches, and a height of 2 inches.

A rectangular prism is a three-dimensional shape that has six faces that are all rectangles. It is also sometimes called a rectangular cuboid.

The volume of a rectangular prism is the amount of space inside the prism and is given by the formula:

Volume = length x width x height

where "length" refers to the longest side of the prism, "width" refers to the second longest side of the prism, and "height" refers to the shortest side of the prism.

To find the volume of a rectangular prism, you simply need to multiply the length, width, and height of the prism together. The resulting value will have cubic units, such as cubic inches, cubic centimeters, or cubic feet, depending on the units used for the length, width, and height.

To find the volume of the display case, we simply need to multiply its length, width, and height together. Using the values you provided:

Volume = length x width x height

Volume = 15 inches x 9 inches x 2 inches

Volume = 270 cubic inches

Therefore, the volume of Brody's display case is 270 cubic inches.

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y + x² - 4 is already in simplest form and the value of 6/5 ÷ 1/7 is 8.4.

A fraction with a reasonably prime numerator and denominator is the simplest form. It denotes that the fraction's numerator (upper or top portion) and denominator (lower or bottom portion) share no common component other than 1. A fraction is a value that denotes a portion of a larger whole.

A fraction's simplest form is also known as its reduced form. 3/4 is the simplest form of a fraction with a common component of one, for example. However, because 2/4 can be reduced further and expressed as 1/2, it is not the simplest form. In this case, 1/2 and 2/4 are equivalent fractions.

We have given two question

y + x² - 4 simplify and 6/5 ÷ 1/7 = ?

Lets simplify

y + x² - 4 is already in simplest form

For

6/5 ÷ 1/7

= 6/5 × 7/1

= 42/5

= 8.4

Thus, y + x² - 4 is already in simplest form and the value of 6/5 ÷ 1/7 is 8.4.

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For any value of 2, f(x + 1) is 3 times as large as f(x).

Now, let's consider the expression f(x + 1), which means that we are evaluating the same function but with a slightly different input value. In this case, the input value is x + 1 instead of x. We can calculate the value of f(x + 1) by substituting x + 1 into the original function equation and simplifying:

f(x + 1) = \(3^{x+1}\)

= 3ˣ * 3¹ (using the rule that \(a^b \times a^c = a^{b+c}\))

= 3ˣ * 3

We can see that f(x + 1) is equal to three times f(x), which means that it is three times as large as f(x).

This is because the function f(x) = 3ˣ is a tripling function, which means that it multiplies its input by three each time.

So, when we increase the input value by 1 (i.e., x + 1), we are effectively tripling the original input value (i.e., x) and then multiplying it by an additional factor of 3.

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The solution to the quadratic equations are

a) The number of seconds for the ball to reach the ground is t = 5 seconds

b) The number of seconds to reach the maximum height T = 2 seconds

c) The maximum height of the ball is h ( 2 ) = 144 feet

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as h ( t )

Now , the equation will be

h ( t ) = -16t² + 64t + 80   be equation (1)

a)

The number of seconds for the baseball to reach the ground be t

The height when the ball reaches the ground will be h = 0

Substituting the value of h ( t ) = 0 , we get

0 = -16t² + 64t + 80

On simplifying the equation , we get

16t² - 64t - 80 = 0

Divide by 16 on both sides of the equation , we get

t² - 4t - 5 = 0

On factorizing the equation , we get

t² + t -5t - 5 = 0

t ( t + 1 ) - 5 ( t + 1 ) = 0

( t - 5 ) ( t + 1 ) = 0

The value of t is time and it is not negative

So , when ( t - 5 ) = 0

Adding 5 on both sides of the equation , we get

t = 5 seconds

b)

The number of seconds the baseball to reach the maximum height be T

And graph of the function is a parabola open down because the leading coefficient is negative. Therefore, to get the maximum height we just have to find the vertex of this parabola

T = ( -b / 2a )

On simplifying the equation , we get

T = ( -64 / ( 2 ( 16 )

T = -64 / 32

T = 2 seconds

c)

The maximum height of the baseball is when T = 2

Substituting the value of t = 2 in the equation , we get

h ( t ) = -16t² + 64t + 80

h ( 2 ) = -16 ( 2 )² + 64 ( 2 ) + 80

On simplifying the equation , we get

h ( 2 ) = -64 + 128 + 80

h ( 2 ) = 64 + 80

h ( 2 ) = 144 feet

Hence , the equation is solved

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The points on the curve where the tangent line has a slope of -1 are (2/√3, -(2/√3)) and (-2/√3, 2/√3). None of the given answer choices matches this solution, so the correct option is (E) None of the above.

For the points on the curve where the tangent line has a slope equal to -1, we need to find the points where the derivative of the curve with respect to x is equal to -1. Let's find the derivative:

Differentiating both sides of the equation x^2 - xy + y^2 = 4 with respect to x:

2x - y - x(dy/dx) + 2y(dy/dx) = 0

Rearranging and factoring out dy/dx:

(2y - x)dy/dx = y - 2x

Now we can solve for dy/dx:

dy/dx = (y - 2x) / (2y - x)

We want to find the points where dy/dx = -1, so we set the equation equal to -1 and solve for the values of x and y:

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

Cross-multiplying and rearranging:

y - 2x = -2y + x

3x + 3y = 0

x + y = 0

y = -x

Substituting y = -x back into the original equation:

x^2 - x(-x) + (-x)^2 = 4

x^2 + x^2 + x^2 = 4

3x^2 = 4

x^2 = 4/3

x = ±sqrt(4/3)

x = ±(2/√3)

When we substitute these x-values back into y = -x, we get the corresponding y-values:

For x = 2/√3, y = -(2/√3)

For x = -2/√3, y = 2/√3

Therefore, the points on the curve where the tangent line has a slope of -1 are (2/√3, -(2/√3)) and (-2/√3, 2/√3).

None of the given answer choices matches this solution, so the correct option is:

E) None of the above.

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Third option in the given options is the correct option.

 y ≥ 3x -2

 x +2y ≤ 4

The mathematical expression with uneven parts is known as an inequality in mathematics. When a relationship leads to a non-equal comparison between two expressions or two numbers, it is referred to as an inequality in mathematics. In this case, the equal sign "=" is replaced with any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (). Mathematical inequalities can take many different forms, including absolute value inequality, rational inequality, and polynomial inequality.

Now in the given question,

The inequality sign must include "or equal to" since both lines are solid.

The shaded area is above the line with slope +3 y-intercept -2, so that inequality must be ...

 y ≥ 3x -2

The shaded area is below the line with slope -1/2 and y-intercept +2, so that inequality must be ...

 y ≤ -1/2x +2 . . . those on the line are y values that are solutions.

 2y ≤ -x +4 . . . . multiply by 2

 x +2y ≤ 4 . . . . add x

Hence, the system of linear inequalities are,

y ≥ 3x -2

 x +2y ≤ 4

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The average change in weight calculated by the researcher for the sample of 25 freshmen is an example of a statistic.

A statistic is a numerical summary of a sample that is used to make inferences about a population. In this case, the sample is the 25 freshmen, and the population could be all freshmen entering college.

The average change in weight is a statistic because it summarizes the data collected from the sample, and is used to make conclusions about the population.

It represents the typical or average amount of weight gained or lost by the freshmen in the sample during their first semester in college.

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Answer:

Plane X

Step-by-step explanation:

kindly find attached a rough sketch of the problem, that contains the drawing of the plane.

From the drawing we can see that the plane x contains points K and N.

It can be seen that point J is not located on any plane.

So the answer is only one plane which is plane x contain the point K and N.

Answer:

Step-by-step explanation:

Remark

2 angles are complementary means that 2 angles add up to 90°. That is the guiding princeple behind the problem.

Givens

Let the smallest angle = x

Let the largest angle = 4x + 30

Equation

4x + 30° + x = 90°                   Combine like terms on the left

Solution

5x + 30 = 90                            Subtract 30 from both sides.

5x + 30 - 30 = 90 - 30             Combine

5x = 60                                     Divide both sides by 5

5x/5 = 60/5

x = 12

Answer

The dimensions of the 48-square-foot rectangular enclosure with the least amount of fencing should be 25ft by 40ft.

The amount of fencing needed can be calculated by getting the perimeter of each choice of dimensions.

Perimeter is defined as the distance that surround any two-dimensional shape. For a rectangle, the perimeter is given by the formula

P = 2l + 2w

Solving for the perimeter of each of the following choices:

F. 8ft by 125ft

P = 2l + 2w

P = 2(8) + 2(125)

P = 16 + 250

P = 266ft

G. 10ft by 100ft

P = 2l + 2w

P = 2(10) + 2(100)

P = 20 + 200

P = 220ft

H. 20ft by 50ft

P = 2l + 2w

P = 2(20) + 2(50)

P = 40 + 100

P = 140ft

J. 25ft by 40ft

P = 2l + 2w

P = 2(25) + 2(40)

P = 50 + 80

P = 130ft

The dimensions with the least perimeter will require the least amount of fencing.

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Pythagoras' theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The measure of the other leg of the triangle is 5.1961 units.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

Let the length of the other leg can be represented by x.

Given the hypotenuse of a right triangle measures 6 cm and one of its legs measures 3 cm. Therefore, the measure of the other legs can be written as,

Hypotenuse² = 3² + x²

6² = 3² + x²

36 = 9 + x²

x² = 27

x = √27

x = 5.1961

Hence, the measure of the other leg of the triangle is 5.1961 units.

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The population is growing as the births are more than deaths in an year.

Increases in a population's or a dispersed group's membership are referred to as population growth.

Given:

To find: Is population growing or shrinking?

Finding:

Hence the population is growing as the births are more than deaths in an year.

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Remember that

The rule of a reflection over the line y=-x is equal to

(x,y) ------> (

The value of the discriminant when a quadratic equation has exactly one real number solution is zero.

If a quadratic equation has exactly one real number solution, it means that the discriminant of the quadratic equation is equal to zero. The discriminant is a value calculated from the coefficients of the quadratic equation and determines the nature of its solutions.

For a quadratic equation of the form ax^2 + bx + c = 0, the discriminant (D) is given by the formula:

D = b^2 - 4ac

When a quadratic equation has exactly one real number solution, it means that the discriminant is equal to zero:

D = 0

Setting the discriminant to zero, we can solve for the value of the discriminant:

b^2 - 4ac = 0

Therefore, the value of the discriminant when a quadratic equation has exactly one real number solution is zero.

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Answer:

A is the answer, i.e at the cost, c of $250.

Step-by-step explanation:

0.08c = 0.05c + 7.5

0.08c - 0.05c = 7.5

0.03c = 7.5

c = 7.5/0.03 = 250

x = -4 and y = 5 is the solution to the given system of equations.

The given equations are:

y = -2x - 3

4y + x = 16

To solve this system of equations, we can use either the substitution method or the elimination method. Let's use the substitution method here:

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

y = -2x - 3

Substitute the expression for that variable from Step 1 into the other equation. Substitute y = -2x - 3 into the second equation:

4y + x = 16

4(-2x - 3) + x = 16

Simplify and solve for the remaining variable. Distribute the 4:

-8x - 12 + x = 16

-7x = 28

x = -4

Substitute the value found in Step 3 into one of the original equations and solve for the other variable. Let's use the first equation:

y = -2x - 3

y = -2(-4) - 3

y = 5

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Complete Question:

Solve the system of equations:

y = -2x - 3

4y + x = 16

The maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.

What is a periodic function?

The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.

The maximum value of a periodic function with amplitude 6.5 and minimum value 7 is equal to the sum of the amplitude and the minimum value.

The amplitude of a periodic function is defined as the maximum distance that the function deviates from its centerline. In this case, the amplitude of the function is 6.5.

The minimum value of a function is the lowest value that the function takes on over a given period. In this case, the minimum value of the function is 7.

To find the maximum value of the function, we need to add the amplitude and the minimum value. The maximum value is equal to 6.5 + 7 = 13.5.

Hence, the maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.

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Answer:

x+15 dollars

Step-by-step explanation:

x could be any number, but if you add 15 to x, it would be x+15. Since you don't know what x is, you can't do anything else.

The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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Answer:

in neighbourhood q the total number of people in the nine families I higher than that in neighbourhood s because of we add up the number of people in the families in neighbourhood q we get a total of 35 yet we have a total of only 27 people in the nine families in neighbourhood s

hope that helps ❤

The values of x taken by the equation are (-1 + √65)/4 and -(1 + √65)/4.

We can simplify this equation by applying quadratic solving principles.

First, we bring the equation into quadratic form. The general form of a quadratic equation goes as follows:

ax² + bx + c = 0

where a,b, and c are constants, and 'a' can never be zero (a ≠ 0), as an equation without at least a minimum of second order term is not considered a quadratic.

Here, on simplification,

x * 4*(x + 2) - 6x = 16

4x*x + 4x*2 - 6x = 16

4x² + 8x - 6x - 16 = 0

4x² + 2x - 16 = 0

We can reduce the coefficients if they all have a common factor, like in this case, 2.

2x² + x - 8 = 0

a = 2, b = 1 and c = -8

We will use the quadratic formula, to figure out the solutions for x:

Formula:   x = [ -b ± √(b² - 4ac) ]/2a

So, x = [ -1 ± √1 + 64 ]/4

     x = (-1 ± √65)/4

Thus, the solutions of the equation are (-1 + √65)/4 and -(1 + √65)/4.

Question: Solve for x in 4x.(x + 2) - 6x = 16. Simplify your answer as much as possible.

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The total charges for a week = 2313.25

Given,

charges per oil change = 33.95

charges for a four-cylinder engine = 72.50

charges for a six-cylinder engine = 82.50

charges for a eight- cylinder engine = 92.50

No of oil changes done by Charlene = 35

price of 5 - four cylinder engines = 5 × 72.50

= 362.50                                .....(1)

price of 7 - six cylinder engines = 7 × 82.50

= 577.50                                ........(2)

price of 2 - eight cylinder engines = 2 × 92.50

= 185                                       ...........(3)

Now, adding (1), (2),(3)

= 362.50 + 577.50 + 185

= 1125                                        ...........(4)

Total charges for oil = 33.95 × 35

= 1188.25                                  ..........(5)

Adding (4) and (5)

= 1125 + 1188.25

= 2313.25

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Answer: the answer is B

Step-by-step explanation: regional managers fuel

Answer:

B. Regional manager's fuel

Step-by-step explanation:

Just did test

Answer:

choice D

a function is loosely defined as having one output for each input. in real people words, the x value can't repeat

Therefore, the monthly mortgage payment is $555.63.

A function is a mathematical relationship between two sets of numbers, where each element in the first set (called the domain) is paired with a unique element in the second set (called the range). In other words, it is a rule or mapping that assigns each input value in the domain to exactly one output value in the range. Functions are often written in the form f(x) = y, where f is the name of the function, x is the input value, and y is the output value.

Here,

1. Monthly Mortgage Payment Calculation:

Using the given values, we can calculate the monthly mortgage payment using the formula:

\(M = P * r * (1 + r)^{n} / ((1 + r)^{n-1} )\)

Where,

P = Loan amount = $150,000 - $30,000 (down payment)

= $120,000

r = Annual interest rate / 12

= 0.042 / 12

= 0.0035

n = Total number of payments

= 30 years * 12 months per year

= 360

Substituting the values in the formula, we get:

M = $120,000 * 0.0035 * (1 + 0.0035)³⁶⁰ / ((1 + 0.0035)³⁶⁰⁻¹)

M = $555.63 (rounded to the nearest cent)

2. Total Costs Calculation:

For the purchased home, the additional costs of home ownership include property taxes and home insurance. Let's assume the property taxes are $3,000 per year and home insurance is $1,500 per year.

a. After 1 year:

Rental home: $900 * 12

= $10,800

Purchased home: $30,000 (down payment) + $555.63 * 12 (mortgage payments) + $3,000 (property taxes) + $1,500 (home insurance)

= $41,966.56

b. After 5 years:

Rental home: $10,800 + ($75 * 5 / 4) * 5 = $12,562.50

Purchased home: $30,000 (down payment) + $555.63 * 60 (mortgage payments) + $15,000 (property taxes) + $7,500 (home insurance)

= $72,398.80

c. After 10 years:

Rental home: $10,800 + ($75 * 5) * 5 + ($75 * 5 / 4) * 10 = $20,287.50

Purchased home: $30,000 (down payment) + $555.63 * 120 (mortgage payments) + $30,000 (property taxes) + $15,000 (home insurance)

= $95,775.60

d. After 15 years:

Rental home: $10,800 + ($75 * 5) * 10 + ($75 * 5 / 4) * 15 = $29,012.50

Purchased home: $30,000 (down payment) + $555.63 * 180 (mortgage payments) + $45,000 (property taxes) + $22,500 (home insurance)

= $155,299.40

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