Solve 4x + 6 = 20.
OA. x= 11 and x = -11
OB. x= -11 and x = -1
OC. x= -11 and x = 1
OD. x = 11 and x = -1

A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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The coordinates of the pre-image point A are (-4, 8).Hence, the correct answer is (-4, 8).

The given image point of A after a translation right 5 units and down 3 units is the point B(-3, -11).

To determine the coordinates of the pre-image point A, we need to move 5 units to the left and 3 units up.

Let the pre-image point A be (x, y).

Then, the image point B is obtained from A by translation of 5 units to the right and 3 units down.

So, we have the following equations:

y - (-11) = -3x - (-3)y + 11 = -3x + 9On

solving the above equations, we get

x = -4 and y = 8.

So, the coordinates of the pre-image point A are (-4, 8).

Hence, the correct answer is (-4, 8).

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I think the answer is 30x+330>50x

Step-by-step explanation:

for the option A it was slightly changed,

cause the $30 was deposited by helen not Vince.

so check that well

Answer:

499500

Step-by-step explanation:

Hope this helps. :)

Answer:

Calculate Grass Seed Quantity

From the table above, Sun & Shade Mix requires 6 lbs. of seed per thousand sq. ft. for a new planting.

Step-by-step explanation:

The number N(t) of people in a community exposed to an advertisement is given by the logistic equation N(t) = L / (1 + (L/N0 - 1) * e^(-kt)), where N0 = N(0), L is the limiting number of people, and k is a constant. To solve for N(t), use the given values: N0 = 500, N(1) = 600, and L = 30,000.

1. First, solve for k using the equation: 600 = 30,000 / (1 + (30,000/500 - 1) * e^(-k))
2. Simplify and solve for e^(-k): e^(-k) = (30,000/600 - 1) / (30,000/500 - 1)
3. Calculate e^(-k) ≈ 0.0654
4. Solve for k ≈ 2.7269
5. Now, find N(t) using N(t) = 30,000 / (1 + (30,000/500 - 1) * e^(-2.7269t))

N(t) is found using the logistic equation with the calculated k value and the given initial values.

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Answer:

7.5 cups of yogurt

Step-by-step explanation:

We know that for each bowl you need 1.5 cups of yogurt. Currently Themba has 6.75 cups of yogurt. We multiply 1.5 by 5 to get 7.5 cups of yogurt.

Simplified version of the given radical expression would be...

\(5x^2\sqrt{7x}\)

Hope this helps!

Answer:

it is the answer check out.

Step-by-step explanation:

I hope it can help you

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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The particular solution to the given differential equation dy/dx = sin(x^2) with the initial condition y(√π) = 4 is (B) y = -cos(x^2)/(2x) + 4 - 1/(2√π).

To find the particular solution, we integrate the given function sin(x^2) with respect to x. However, since there is no direct antiderivative for sin(x^2), we cannot find a simple closed form expression for the integral. Hence, we need to use numerical or approximative methods to evaluate the integral.

None of the given options (A), (C), or (D) provide a correct representation of the particular solution. Option (B) includes the term -cos(x^2)/(2x), which is a common approximation method for the integral of sin(x^2). The other terms in (B) account for the initial condition y(√π) = 4. Therefore, (B) y = -cos(x^2)/(2x) + 4 - 1/(2√π) is the correct particular solution to the differential equation with the given initial condition.

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Answer:

students' ratings of their professors' performance on a five-point scale ranging from poor to excellent

Step-by-step explanation:

There are four type of scales in mathematics. They include:

1. Nominal scale : they do not measure quantity. they are used to classify a population into two or more scales that are exhaustive and mutually exclusive. e.g. classifying a population based on gender, naming the different car brands seen in a school's parking lot

2. Ordinal scale : this scale measures ranks a population from best to worst or from least to most. e.g. ranking the participants of a race based on their performance

3. Interval scale : this scale has the property of order and equal intervals. Zero is not meaningful.

Interval scale is used when the difference between the numbers are meaningful. e.g. students' ratings of their professors' performance on a five-point scale ranging from poor to excellent Here a child who is scored 1, did very poorly and a child scored 5, performed excellently well.

4. Ratio scale :  this scale has the property of order, a meaningful zero and equal intervals.

The frequentist probability is objective, based on observed data, need large sample or long term frequency, and doesn't have prior knowledge.

Frequentist probability is a definition of probability that defines the probability of an event as the probability of an event being observed in a long-term or infinite experiment.

Frequentist probability is different from Bayesian probability in following points,

Thus, the statement are true for frequentist definition for the probability is doesn't have prior knowledge, need large sample, based on observed data, and objective.

Your question is incomplete, but it is general information about the frequentist definition of probability.

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So, the solution to the integral is \((-sin(2x) + 2cos(2x))e^{(-x)}/5.\)

To evaluate the integral ∫\(e^{(-x)} sin(2x) dx\), we can use integration by parts. The formula for integration by parts is ∫u dv = uv - ∫v du, where u and v are functions of x.

Let's assign u = sin(2x) and \(dv = e^{(-x)} dx\). Then, we can find du and v as follows:

Differentiating u = sin(2x) with respect to x:

du/dx = 2cos(2x)

Integrating \(dv = e^{(-x)} dx:\)

\(v = ∫e^{(-x)} dx \\= e^{(-x)}\)

Now, we can apply the integration by parts formula:

\(e^{(-x)} sin(2x) dx = -sin(2x)e^{(-x)} - (-e^{(-x)} )(2cos(2x)) dx\)

Simplifying the integral on the right-hand side:

Now, we have a new integral to evaluate. Let's use integration by parts again. This time, let's assign u = cos(2x) and dv = e^(-x) dx:

Differentiating u = cos(2x) with respect to x:

du/dx = -2sin(2x)

Integrating dv = e^(-x) dx:

v = ∫e^(-x) dx = -e^(-x)

Applying the integration by parts formula again:

∫e^(-x)cos(2x) dx = -cos(2x)e^(-x) - ∫(-e^(-x))(-2sin(2x)) dx

\(= -cos(2x)e^{(-x)} + 2∫e^{(-x)}sin(2x) dx\)

Dividing both sides by 5:

∫e^(-x) sin(2x) dx = (-sin(2x) + 2cos(2x))e^(-x)/5\(∫e^{(-x)} sin(2x) dx = (-sin(2x) + 2cos(2x))e^{(-x)}/5\)

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A DTH TV connection provides channels in English and other languages in the ratio 7:13. To find out what percentage of the channels are in English, you need to divide the number of English channels by the total number of channels and then multiply the result by 100.

Let's assume that there are a total of 100 channels available on this DTH TV connection. According to the given ratio, 7 out of every 20 channels will be in English. So, the percentage of channels in English will be:

(7/20) x 100 = 35%

Therefore, 35% of the channels on this DTH TV connection are in English.

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The constant, reveals that 8100 will be decreased by 0.2% every year.

The constant, describes how many percent a rate of change of a quantity decreases or increases.

Given the function, f(t) = 8100(0.998)^10t, thus:

0.998 (0.2%)  is less than 1

Therefore, the constant, reveals that 8100 will be decreased by 0.2% every year.

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Answer:

Is rational. The value is 0.42857.

Step-by-step explanation:

Answer:

The cost of admission to a festival was $112 for 9 children and 3 adults. The admission was $108 for 8 children and 3 adults in another festival. How much was the admission for each child and adult?

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

probability= no. of objects/no. of total number

= 3/9

=1/3

The ordered pair for the system of linear equation is; (4,4)

What is a System of Equations?

A finite collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.

Finding the values of the variables employed in a system of equations entails solving the set of equations. While keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system.

Linear Equation x - 2y = 4

We can substitute the values in the given equation and can check whether LHS is equal to RHS or not.

if LHS = RHS then it is a solution for the given equation.

x - 2y = 4  ---  Equation (1)

i) Consider (0, 2)

By Substituting x = 0 and y = 2 in the given Equation (1)

x - 2y = 4

0 - 2(2) = 4

0 - 4 = 4

- 4 ≠  4

L.H .S ≠ R.H .S

Therefore, (0, 2) is not a solution to this equation.

ii) Consider (2, 0)

By Substituting, x = 2 and y = 0 in the given Equation (1),

x - 2y = 4

2 - 2(0) = 4

2 - 0 = 4

2 ≠ 4

L.H .S ≠ R.H .S

Therefore, (2, 0) is not a solution to this equation.

iii) (4, 0)

By Substituting, x = 4 and y = 0 in the given Equation (1)

x - 2y = 4

4 - 2(0) = 4

4 - 0 = 4

4 = 4

L.H .S = R.H .S

Therefore, (4, 0) is a solution to this equation.

iv) (√2, 4√2)

By Substituting, x = √2 and y = 4√2 in the given Equation (1)

x - 2y = 4

√2 - 8√2 = 4

-7√2 ≠ 4

L.H .S ≠ R.H .S

Therefore, (√2, 4√2) is not a solution to this equation.

v) (1, 1)

By Substituting, x = 1 and y = 1 in the given Equation (1)

x - 2y = 4

1- 2 (1) = 4

1 - 2 = 4

-1 ≠ 4

L.H .S ≠ R.H .S

Therefore, (1, 1) is not a solution to this equation.

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700

Use the simple interest formula

I = P r t

where I = simple interest

P = principal

r= rate of interest

t= number of years

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

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Answer:

7/2pi

Step-by-step explanation:

Circumference is

\(2r\pi \\ 2 \times 7\pi \\ 14\pi \\ \frac{1}{4} \times 14\pi \\ \frac{7}{2} \pi\)

Answer:

Any number greater than 43.54 and less than 43.6 rounds to 43.6. So, 43.55, 43.56, 43.57, 43.58 and 43.59 all round up to 43.6.

Answer:

x = -8 + sqrt(10) and x = -8 - sqrt(10)

Step-by-step explanation:

The quadratic equation to be solved is:

2(x + 8)² + 9 = 29

First, we need to simplify the left-hand side of the equation by expanding the squared term:

2(x + 8)(x + 8) + 9 = 29

Simplifying further, we get:

2(x² + 16x + 64) + 9 = 29

Distributing the 2, we get:

2x² + 32x + 128 + 9 = 29

Combining like terms, we get:

2x² + 32x + 137 = 29

Subtracting 29 from both sides, we get:

2x² + 32x + 108 = 0

Dividing both sides by 2, we get:

x² + 16x + 54 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula :

The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).

Step-by-step explanation:

44°+53°+x°=180°

97°+x°=180°

x°=180°-97°

x°=83°

Answer:

I think the answer is -1 1/2

Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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