write an equation of a line that passes through point T(-2,-5) and is parallel to the line y= 5x +7

Answer:

Step-by-step explanation:

SOLUTION.

We have been told that Lucas and Natalie walked the same distance, and that x is the number of feet Lucas traveled.

a. The expression for the number of feet Lucas has walked = x

b. Since Natalie walked the same distance as Lucas,

The expression for the number of feet Natalie has walked = x

c. The expression for the total number of feet Lucas and Natalie has walked

x + x = 2x

d. The expression for the distance between Natalie and Lucas is

210 - 2x

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

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

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

8

Step-by-step explanation:

Because you need to round 0.8064516129 to the nearest tenth

A diameter is a straight line that connects two points on the circumference of a circle and passes through the center. It is a fundamental concept in the study of circles and is used to calculate various properties and measurements associated with circles.

A straight line that passes through one side of a circle to the other is called a diameter.

In geometry, a circle is a closed curve consisting of all points in a plane that are equidistant from a fixed center point.

The diameter of a circle is a line segment that passes through the center of the circle and has both endpoints on the circumference.

It is the longest chord of the circle and divides the circle into two equal halves called semicircles.

The diameter plays a significant role in the properties and measurements of circles.

One important property is that the diameter is twice the length of the radius, which is the distance from the center of the circle to any point on the circumference.

In mathematical terms, if r represents the radius and d represents the diameter, then d = 2r.

The diameter of a circle has several important applications and implications.

It is used to calculate the circumference of a circle using the formula C = πd, where C represents the circumference.

Additionally, the diameter is crucial in determining the area of a circle, which is given by the formula \(A = \pi r^2,\)

where A represents the area.

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The component of the data that a data analyst is most interested in is sample size.

Given,

To prevent results from being skewed or causing incorrect conclusions, we must identify the data element on which the data analyst should concentrate;

The data analyst;

A data analyst looks at data to uncover useful consumer insights and possible applications for the knowledge. They also tell the management of the business as well as other stakeholders of this information.

Although it is advisable for data analysts to have a foundational knowledge of statistics and mathematics, many of their responsibilities can still be carried out without it. However, knowledge in statistics, linear algebra, and calculus is often required for data analysts.

Here,

A data analyst's primary interest in the data is sample size

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Answer:

D.

Step-by-step explanation:

The volume can be found by adding the volumes of a cylinder (the upper part of the figure) and a cone (the lower part of the figure).

Volume of Cylinder:  \(V=\pi r^2 h=\pi(3^2)(3)=27\pi\approx 84.823 \text{ cubic feet}\)

Volume of Cone:  The height of the cone is 3 feet (the whole figure is 6 feet tall and the cylinder uses up 3 feet of that -- 6 - 3 = 3).

\(V=\frac{1}{3}\pi r^2 h=\frac{1}{3}\pi(3^2)(3)=9\pi\approx 28.274\)

The total volume is 84.823 + 28.274, about 113.1 cubic feet

Answer:

The correct answer is:

It is a continuous random variable (B)

Step-by-step explanation:

Continuous Random Variables are variables that take on a number of possibilities of values that cannot be counted. The values have infinite possibilities. In this example, the height of a Giraffe measured in meters can be an unlimited possibility if values say, 10.5m, 15.22m 12.0m etc. The possibilities are endless.

Discrete Random variables are variables that take on a number of possibility of occurrences that can be counted. For instance, if a dice is rolled, the possibilities can either be a 1, 2, 3, 4, 5 or 6. There are six values that can be gotten, nothing in-between.

I think the answer is B.

Please check to make sure.

Answer:

uuuummmmmm go to khanacademy but i think 140

Step-by-step explanation:

The line that is perpendicular to the equation of a line given is y = -2x + 3

The equation of a perpendicular line can be found using the slope of the line first and then applying the points through which the line passes through.

For the given question, the equation of the line is y = 1/2x + 11 and the point is (6, -9).

To find an equation of a line;

The equation of the line can be modified into y - y₁ = m(x - x₁)

substituting the values into the equation above gives y = -2x + 3

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Answer:

Either 8 or one

Step-by-step explanation:

Not really enough info but if u want me to explain my answer I can

Answer:

1. b = 2A/h

2. h = 2A/b

Step-by-step explanation:

All you have to do is isolate the variable.

1.

Isolate b:

A = 1/2 x b x h

Multiply each side by 2

2A = b x h

Isolate b by dividing both sides by h

b = 2A/h

2.

Isolate h:

A = 1/2 x b x h

Multiply each side by 2

2A = b x h

Isolate h by dividing both sides by b

h = 2A/b

Answer:

Option (3)

Step-by-step explanation:

Given functions are,

f(x) = \(\frac{1}{4^x}\)

g(x) = log(2x)

By using a graphing utility we can draw the graphs of the given system of equations.

Common points of the graph will be the solutions of the equations,

From the graph attached,

Solution of the functions is → (0.937, 0.273)

                                             → (0.9, 0.3)

Option (3) will be the answer.

Answer:

Question 3

First option:
\(\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}\)

Question 4
Third option:
\(\dfrac{1}{4} \div \dfrac{2}{5}\)

Question 5

Second Option:
\(\dfrac{7}{10}\)

Step-by-step explanation:

Question 3

If  \(\dfrac{4}{5}\) inches of rain falls every  \(\dfrac{2}{3}\) hours then the unit rate in inches per hour is inches \(\div\) hours

This would be:
\(\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}\)

This is the first option in Question 3 answer choices

Question 4

\(\dfrac{\dfrac{1}{4}\;km}{\dfrac{2}{5}\;min}\)

is nothing but the numerator ÷ denominator which would be:

\(\dfrac{1}{4} \div \dfrac{2}{5}\)

This is the third option in Question 4 answer choices

Question 5

\(\dfrac{1}{2} \div \dfrac{5}{7}\\\)

Flip the divisor \(\dfrac{5}{7}\); it comes \(\dfrac{7}{5}\)

Multiply:
\(\dfrac{1}{2} \times \dfrac{7}{5}\)

The result is
\(\dfrac{7}{10}\)

This is the second option in Question 4 answer choices

Answers:

Question 3: \(\frac{\frac{4}{5}in.}{\frac{2}{3}hr.}\)

Question 4: \(\frac{1}{4}\) ÷ \(\frac{2}{5}\)

Question 5: \(\frac{7}{10}\)

Explanations:

Question 3: We're told that rain is falling at a rate of  \(\frac{4}{5} in.\) every  \(\frac{2}{3} hr.\), and the unit rate we're looking for is inches per hour (or more precisely, inches per 1 hour). Based on these parameters, we know that you have to divide the unit inches by the unit hours. So using the numbers above, the correct complex fraction to represent this situation would be \(\frac{\frac{4}{5} in.}{\frac{2}{3} hr.}\) .

Question 4: In this question, we are given a complex fraction and asked to rewrite it as a simple division problem. The complex fraction is \(\frac{\frac{1}{4} km.}{\frac{2}{5} min.}\), so in order to write this as a division expression, you simply take the numerator fraction and divide it by the denominator fraction, which will end up being \(\frac{1}{4}\) ÷ \(\frac{2}{5}\). Therefore, that will be your answer.

Question 5: Now, we have a division expression and are asked to use the Keep, Change, Flip method to solve the problem. First and foremost, the Keep, Change, Flip method is essentially telling you that when you are dividing by a fraction, you keep the dividend the same, you change the divisor - specifically switching the numerator with the denominator, which is creating the reciprocal of that fraction - and multiply by the reciprocal of the original divisor instead.

                   A good example of the Keep, Change, Flip method from above would be \(\frac{1}{2}\) ÷ \(\frac{1}{3}\). You keep the dividend, change the divisor, specifically flip the function around to create its reciprocal, and instead multiply by the divisor's reciprocal. Following those steps, \(\frac{1}{2}\) ÷ \(\frac{1}{3}\)  will become \(\frac{1}{2}\) × \(\frac{3}{1}\) or \(\frac{1}{2}\) × \(3\).

                  Now that we understand how to use the Keep, Change, Flip method, we can use it to solve the expression \(\frac{1}{2}\) ÷ \(\frac{5}{7}\). We keep \(\frac{1}{2}\) the same, flip \(\frac{5}{7}\) to make its reciprocal, and multiply \(\frac{1}{2}\) by that instead. So the final answer will be \(\frac{1}{2}\) ÷ \(\frac{5}{7}\) = \(\frac{1}{2}\) × \(\frac{7}{5}\) = \(\frac{7}{10}\).

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

12.5

Step-by-step explanation:

divide both sides by 2 leaving you with y=12.5.

Answer:

-9

Step-by-step explanation:

If you find the -6 point on the number line and move to the left three spaces, you stop at -9. You are taking away three spaces from an already negative number. So, you move to the left to show you subtracting something.

Hope this helps! :)

Answer:

-9

Step-by-step explanation:

Using absolute value (6+3) you can add -6 to -3.

An equation that describes this function in slope-intercept form is y = -6x - 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-7 - 5)/(1 + 1)

Slope (m) = -12/2

Slope (m) = -6

At data point (-1, 5) and a slope of -6, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -6(x + 1)

y - 5 = -6x - 6

y = -6x - 1

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Summary:

Dan borrowed $1549.00 and needs to repay the loan in two equal payments. The first payment is due in three months, and the second payment is due in eight months. The loan carries an annual interest rate of 7%. We need to determine the size of the equal payments.

Explanation:

To calculate the size of the equal payments, we can use the concept of present value. The present value is the current value of a future payment, taking into account the interest earned or charged.

First, we need to determine the present value of the loan amount. Since the loan is to be repaid in two equal payments, we divide the loan amount by 2 to get the present value of each payment.

Next, we need to calculate the present value of each payment considering the interest earned. We use the formula for present value:

PV = PMT / (1 + r)^n

Where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

Using the given information, we know that the interest rate is 7% per annum, which means the interest rate per period is (7% / 12) since the loan payments are made monthly. We can now calculate the present value of each payment using the formula.

Finally, we add up the present values of both payments to find the total present value. We divide the total present value by 2 to get the size of the equal payments.

By performing these calculations, we can determine the size of the equal payments.

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Answer: b

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

D.)   9 − 2x − 2x2

a typical neighborhood, which consists of two blocks east-west and three blocks north-south, covers an area of 75,000 square meters or 300,000 square meters.

The size of each street block is given as 50 meters north-south by 250 meters east-west. Therefore, the area of each block can be calculated as 50 meters * 250 meters = 12,500 square meters.To find the area covered by a typical neighborhood, which consists of two blocks east-west and three blocks north-south, we multiply the number of blocks in each direction. The neighborhood covers 2 blocks east-west * 3 blocks north-south = 6 blocks in total.

The total area covered by the neighborhood can be calculated by multiplying the number of blocks by the area of each block. Thus, 6 blocks * 12,500 square meters/block = 75,000 square meters.

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Answer: 6

Step-by-step explanation:

0, 3, 4 , 6, 6, 7, 7, 9

6+6= 12

12 ➗ 2 = 6

The value of x is 3 and solution is extraneous

Here, we have,

Solving equations

Given the equation below;

√8x+1 = 5

Square both sides to have;

8x+1 = 5^2

8x + 1 = 25

Subtract 1 from both sides

8x + 1 = 25 -1

8x = 24

x = 24/8

x = 3

Hence the value of x is 3

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Answer:

Diagonal = 9m

Step-by-step explanation:

area of a rectangle=L×W.-----------(I)

L=2W---------------(ii)

from (1)

32=2W×W

32=2W²

W²=32/2

W²=16

W=√16

W=4

from (ii)

length(L)=2W=2(4)=8m

Width(W)=4m

ii)Diagonal of a rectangle involves the use of Pythagoras theorem

Hyp²=opp²+Adj²

Hyp²=8²+4²

Hyp²=64+16

Hyp²=80

Hyp=√80

Hyp=8.94427191

Hyp=9m

:-The diagonal =9m

The length of the hypotenuse of a 45-45-90 triangle is √2x units.

To find the hypotenuse of a 45-45-90 triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

Let's denote the length of each leg of the triangle as "x". Since the triangle is isosceles, both legs are of equal length. Therefore, we can write:

Leg 1 = Leg 2 = x

To find the length of the hypotenuse (which we'll call "h"), we can use the Pythagorean theorem as follows:

x² + x² = h²

Simplifying this equation, we get:

2x² = h²

To solve for h, we need to take the square root of both sides of the equation:

√(2x²) = √(h²)

√2 * x = h

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If the series ∑an and ∑bn are both convergent series with positive terms, then the series ∑anbn is also convergent.

This can be proven using the Comparison Test for series convergence. Since an and bn are both positive terms, we can compare the series ∑anbn with the series ∑an∑bn.

If ∑an and ∑bn are both convergent, then their respective partial sums are bounded. Let's denote the partial sums of ∑an as Sn and the partial sums of ∑bn as Tn.

Then, we have:

0 ≤ Sn ≤ M1 for all n (Sn is bounded)

0 ≤ Tn ≤ M2 for all n (Tn is bounded)

Now, let's consider the partial sums of the series ∑an∑bn:

Pn = a1(T1) + a2(T2) + ... + an(Tn)

Since each term of the series ∑anbn is positive, we can see that each term of Pn is the product of a positive term from ∑an and a positive term from ∑bn.

Using the properties of the partial sums, we have:

0 ≤ Pn ≤ (M1)(Tn) ≤ (M1)(M2)

Hence, if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is also convergent.

Therefore, the given statement is True.

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Answer:

Step-by-step explanation:

bearing is the angle which a line makes with the north.