Identify the equation that shows direct variation

Answer:

Step-by-step explanation:

The value of the common difference, d, in this arithmetic sequence is 42.

To find the value of d in an arithmetic sequence, we need to use the formula: a15 = a1 + (n-1)d, where a1 is the first term, a15 is the fifteenth term, d is the common difference, and n is the number of terms.

Plugging in the given values, we get:

609 = 21 + (15-1)d

Simplifying the equation, we get:

609 = 21 + 14d

Dividing both sides by 14, we get:

d = 42

Therefore, the value of d is 42.

Given that a1 = 21 and a15 = 609, we can use the formula for the nth term in an arithmetic sequence to find the common difference, d. We can plug the values into the formula a15 = a1 + (n-1)d and simplify it to solve for d. After doing the algebraic steps, we get that d = 42. Therefore, the common difference in this arithmetic sequence is 42.

The value of the common difference, d, in this arithmetic sequence is 42.

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Answer:

10

Step-by-step explanation:

Step 1:

3x - 2             Equation

Step 2:

3 ( 4 ) - 2       input x

Step 3:

12 - 2        Multiply

Answer:

10     Subtract

Hope This Helps :)

Answer:

0.42

Step-by-step explanation:

when your multiplying decimals that small, it usually doesnt go into the whole number range

The value of A that makes the equation true for all values of x is A = \(2x^2\). Answer (E).

To begin, consider the following equation:

\(2^(x/12) = A/12x^2\)

We must determine the value of A that makes this equation true for all x values.

To begin, we can take the natural logarithm of both sides of the equation:

\(2(x/12) = 2(A/12x2)\)

We can simplify the left side of the equation by using the logarithm property that states log(ab) = b*log(a):

(x/12)

\(ln(2) = 2ln(x) - ln(A) (12)\)

Then, on one side of the equation, we can isolate ln(A):

ln(A) = (x/12)

\(2ln(x) + ln(2) + ln (12)\)

With base e, we can now exponentiate both sides of the equation:

A is equal to \(e((x/12)ln(2) + 2ln(x) + ln(12)).\)

To simplify even further, we can use exponent properties to combine the terms with ln:

\(A = 2^(x/12) * (x^2) * 12\)

Simplifying:

\(A = 2x^2\)

Therefore, the value of A that makes the equation true for all values of x is \(A = 2x^2\). Answer (E).

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Answer:

2x +110= 180

2x=70

x=35

Step-by-step explanation:

Answer: E

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

If λ = 5 is a factor of the characteristic polynomial of matrix A, then 5 is an eigenvalue of A.

Given that λ = 5 is a factor of the characteristic polynomial of matrix A, we need to determine whether 5 is an eigenvalue of A or not. Definition of Characteristic Polynomial:

A matrix A is a linear transformation whose characteristic polynomial is given by;

p(x) = \text{det}(xI - A)

Definition of Eigenvalue:

Let A be a square matrix of order n and let λ be a scalar.

Then, λ is called an eigenvalue of A if there exists a non-zero vector x, such that

A \bold{x} = \lambda \bold{x}

For some non-zero vectors x is known as the eigenvector.

Now, let's prove if 5 is an eigenvalue of A, or not.

According to the question, λ = 5 is a factor of the characteristic polynomial of A.Therefore, p(5) = 0.

\Rightarrow \text{det}(5I - A) = 0

Consider the eigenvector x corresponding to the eigenvalue λ = 5;

\Rightarrow (A-5I)x = 0$$$$\Rightarrow A\bold{x} - 5\bold{x} = 0

\Rightarrow A\bold{x} = 5\bold{x}

Since A satisfies the equation for eigenvalue and eigenvector, 5 is an eigenvalue of matrix A.

Therefore, if λ = 5 is a factor of the characteristic polynomial of matrix A, then 5 is an eigenvalue of A.

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V = 7.67 (aproximately) mph

1) Gathering the data

Before the storm

50 miles

3 hour drive

After the storm

68 miles

Speed: 9 mph - x

2) Let's find the speed of Nancy before the storm:

Since in the storm the Speed was 9 mph less than 16.67 mph we have:

16.67 -9 =7.67 mph

3) Hence, her speed driving at the storm was 7.67 mph

Answer: A. h(x) = 1/4x - 2

Step-by-step explanation:

f(x) = 4x + 8

find the inverse...

A.

\(h(x) = \frac{1}{4} x-2\)

\(f(x) = 4(\frac{1}{4} x-2)+8\)

\(f(x)=x-8+8\)

\(f(x)=x\)  

\(h(x) = \frac{1}{4} (4x+8)-2\)

\(h(x)=x+2-2\)

\(h(x)=x\)

Since they both come out to 'x', they are inverses of each other.

f(x) = 4x + 8 and h(x) = 1/4x - 2 are inverses

The rate of change of the hypotenuse after 2 minutes is 0.505 cm/min

Let L be the length of one leg and D be the length of  the other leg of the right triangle and y its hypotenuse

Since it is a right angled triangle, we have that, using Pythagoras' theorem

y² = L² + D²

Since the length of sides are the same, L = D = 70 cm.

So, y² = L² + D²

y² = 70² + 70²

y² = 2(70²)

y = 70√2

y = 98.99 cm

Also, one side increases at a rate of 5 cm/min and the other side decreases at a rate of 5 cm/min.

The increase in length of one side after 2 min is 5cm/min × 2 min = 10 cm.

So, it new length is L' = 70 + 10 = 80 cm

The decrease in length of the other side after 2 min is -5cm/min × 2 min = -10 cm.

So, it new length is D' = 70 + (-10 cm) = 60 cm

So, the new hypotenuse length is y' = √(L'² + D'²)

= √(80² + 60²)

= √(6400 + 3600)

= √10000

= 100 cm

Now, the change in length of the hypotenuse side in 2 minutes is Δy = 100 cm - 98.99 cm = 1.01 cm

So, rate of change of the hypotenuse after 2 minutes is 1.01 cm/2 min = 0.505 cm/min

The rate of change of the hypotenuse after 2 minutes is 0.505 cm/min

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Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

Answer:

\(\frac{104}{100}\)

Step-by-step explanation:

You would multiply 104/100 to the price because it would be 100%, (basically the price), plus the 4/100, the tax.

Answer:

52.948 m²

Step-by-step explanation:

→ State the formula for the area

length × width

→ Substitute in the numbers

8.68 × 6.1 = 52.948 m²

Answer:

The viable solution is x = 2.

The non-viable solution is x = -5.

Step-by-step explanation:

Given system of equations:

\(\begin{cases}P(x) = -x^2 + 9x + 10\\Q(x) = 12x \end{cases}\)

where:

To calculate after how many days the two students will earn the same profit, first equate P(x) and Q(x), then rearrange the equation so that we have a quadratic equal to zero.

\(\begin{aligned}Q(x)&=P(x)\\12x&=-x^2+9x+10\\12x+x^2&=-x^2+9x+10+x^2\\x^2+12x&=9x+10\\x^2+12x-9x&=9x+10-9x\\x^2+3x&=10\\x^2+3x-10&=10-10\\x^2+3x-10&=0\end{aligned}\)

Factor the quadratic:

\(\begin{aligned}x^2+3x-10&=0\\x^2+5x-2x-10&=0\\x(x+5)-2(x+5)&=0\\(x+5)(x-2)&=0\\\end{aligned}\)

Apply the zero-product property to solve for x:

\(x+5=0 \implies x=-5\)

\(x-2=0 \implies x=2\)

As x represents the number of days, and the number of days cannot be negative, the only viable solution is x = 2. Therefore, the non-viable solution is x = -5.

Answer:

the answer will be B. a baker uses 4 cups of flour. she uses 1/4 cup to flour the counters and the rest to make 8 identical muffins.

Answer:

5. (x-8)(x+2)

10. (x-5)(x-5) OR (x-5)^2

The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F

from the question, we have the following parameters that can be used in our computation:

Yeast thrives between 90°F to 95°F

For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range

Using the above as a guide, we have the following:

T < 90°F or T > 95°F.

Where

T = Temperature

Hence, the inequality is T < 90°F or T > 95°F.

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a) There is not enough evidence to conclude that cars get significantly better fuel economy with premium gasoline.

In order to test the belief that premium gasoline provides better fuel economy, a study was conducted using 10 cars from a company fleet. Each car was randomly assigned either regular or premium gasoline, and the mileage for each tankful was recorded. The data was analyzed to determine if there is a significant difference in fuel economy between the two types of gasoline.

To evaluate this, a paired t-test can be used since the same cars were tested with both types of gasoline. The null hypothesis would be that there is no difference in fuel economy between regular and premium gasoline, while the alternative hypothesis would be that there is a significant difference.

The results of the study would be analyzed using the appropriate statistical test, such as a paired t-test, to determine the p-value. If the p-value is less than the chosen significance level (e.g., 0.05), then there would be evidence to reject the null hypothesis and conclude that there is a significant difference in fuel economy.

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Yes, irrational numbers such as π are included in the domain of the function f(x) = 7.

The domain of a function is the set of all possible input values (x) for which the function is defined. In the case of the function f(x) = 7, the output value (y) is always equal to 7, regardless of the input value.

Since every real number, including irrational numbers like π, can be an input value for f(x) = 7, the domain of this function is the set of all real numbers, which includes both rational and irrational numbers. Therefore, π is included in the domain of the function f(x) = 7.

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Answer:

A) Changing the measurement unit.

Step-by-step explanation:

"Changing the measurement unit" is the correct answer because when you convert from feet to inches, you are essentially changing the unit of measurement from a larger unit (feet) to a smaller unit (inches) within the same system of measurement (length or distance). It involves multiplying the value in feet by a conversion factor to obtain the equivalent value in inches. This process is commonly used in math, science, and everyday life when dealing with different units of measurement.

Recall that the opposite of 2 is

Therefore, the opposite of the opposite of 2 is

Now, recall that a horizontal number line is of the form:

Therefore, 2 is to the right of zero.

Answer:

On a horizontal number line, the opposite of the opposite of 2 is to the right of zero and is written as 2.

1. Joints and lamination weaken the strength of the rockmass, making it more prone to deformation and failure.

2. Waterfalls can form through the combined effects of physical and chemical weathering on rocks.

1. Joints or lamination influences the strength of the rockmass by causing it to become more brittle, therefore, affecting the ability of the rock to resist deformation or breakage. The presence of joints in rocks causes them to become less resistant to external stresses because joints are areas of weakness and can easily crack when subjected to force.

The spacing of joints and lamination also has a direct impact on the strength of rockmass. The closer the joints, the weaker the rock, and the further apart the joints, the stronger the rock. This is because as the joints get closer together, the rock loses its ability to support itself, and as such, it becomes more susceptible to deformation and failure.

2. Waterfall occurrence can be related to both physical and chemical weathering processes. Physical weathering occurs when rocks break down into smaller fragments through processes such as freeze-thaw, thermal expansion and contraction, and abrasion. As water flows through the cracks and crevices in the rock, it can cause these processes to occur and, as such, can contribute to the formation of waterfalls.

Chemical weathering occurs when rocks are broken down by chemical reactions with water, oxygen, and other chemicals. This can lead to the formation of new minerals that are less resistant to erosion than the original rock. As water flows over these rocks, it can dissolve the new minerals, creating new cracks and crevices in the rock. This can contribute to the formation of waterfalls as the water continues to erode the rock.

Overall, both physical and chemical weathering processes can contribute to the formation of waterfalls through the erosion of rocks over time.

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Answer:

i think its b

Step-by-step explanation:

Area: r2 Circumference: 2πr OR πd Radius: d2 Diameter:2r

1a) If the designer measures the pond and determines that the length of the pond across is 400 feet wide, what is the length of the radius? Show your work.

b) The designer wants to plant new flowers around the pond. How many feet of flowers would she need to plant in this new design? Round to the nearest hundredth. Show your work.

c) The designer wants to determine how much water is covered on the surface once the pond is filled up. She claims that the area would be 160,000 square feet. Is she correct? Justify your answer showing work

Step-by-step explanation:

we have to mark the angles in the point denoted in the graph and connect it

The illustration of the dilated triangle has been shown.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The vertices of a triangle are A(-4, 6), B(6.4), and C(6. - 2).
The scale factor of 1/2.​,

Coordinates of the vertices of the triangle with scale factor,
A' = (-4 × 1/2 , 6 × 1/ 2)
A' = (-2, 3)

Similarly,
B' = (3, 2)
C' = (3, -1)

Thus, the illustration of the dilated triangle has been shown.

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39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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Evaluate expression and Name the property used in each step.

              =   { [5/(3 times 1)] } 3/5

              =    {[5/(3.1)]} 3/5

We can write,

Multiplicate identity,      

              = [5/3] 3/5

Substitution,

            = (5/3) (3/5)

Cancel the numerator and denominator values,

So,

We can write,

            = 1 Multiplicative Inverse

Therefore,

3/5evaluate the expression and name the property used in each step. [5/(3times1)] 3/5 is = 1 Multiplicative Inverse.

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No , it is not possible to form a triangle with side lengths 3.5, 3.5, and 9 , because of the rule that sum of any two sides must be greater than other side. So, Option D is correct.

A triangle is a two-dimensional shape formed by three line segments connecting three points. In order to form a triangle, a necessary and sufficient condition is that the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.

If the sum of the lengths of any two sides is less than or equal to the length of the third side, then the three line segments will not be able to form a closed shape, and therefore cannot form a triangle.

In the case of the triangle with side lengths 3.5, 3.5, and 9, the sum of the lengths of the first two sides is 7, which is less than the length of the third side, 9. Hence, these three side lengths do not satisfy the triangle inequality theorem, and therefore cannot form a triangle.

In general, to determine the type of triangle that can be formed with three given side lengths, it is necessary to compare the lengths of the sides and check if any two sides are equal in length (isosceles), or if all three sides are equal in length (equilateral). If none of the sides are equal, then the triangle is called scalene.

In this case, since it is not possible to form a triangle with the given side lengths, it is not possible to determine the type of triangle that would be formed.

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Answer:

-6 47/20

Step-by-step explanation: