What is the circumference of a circle with a diameter of 5.8 inches? Use 3.14 for π and round the answer to the nearest tenth. A) 9.1 inches B) 18.2 inches C) 36.4 inches D) 105.6 inches

The event of the machine working is [tex]A\cap B\cap C\cap D[/tex], and since the components operate independently, we have

[tex]P(A\cap B\cap C\cap D)=P(A)P(B)P(C)P(D)[/tex]

so just multiply the given probabilities together,

[tex]P(A\cap B\cap C\cap D)=0.99^2\cdot0.94\cdot0.93\approx0.8568[/tex]

Answer:

The time at which the pass each other on the road is 4:00 pm

Step-by-step explanation:

The first step is to write the equations that give us the position of Emily and Anthony, these are give by:

[tex]x_A = x_{A0}+v_At[/tex]  for Anthony

[tex]x_E=x_{E0}+v_Et[/tex]     for Emily

Since Antony drives 160 miles to Albany, we can claim that the distance from Kingstown to Albany is 160 miles.

Let us set the initial position of Antony in Kingstown and consider it as the origin of our coordinate system. In this way, [tex]x_{A0}=0[/tex].

This automatically tells us that Emily initial position, in Albany, is 160 miles from our origin, hence [tex]x_{E0} = 160 miles[/tex].

Now, we need to define where to start counting the time. In this problem, it is easier to set time zero when Emily leaves. The reason for this is that now, we can say that when Emily left, Anthony was already traveling during 15 mins (remember Emily departing time was 2:15 pm and Anthony's time was 2:00 pm) and Anthony's initial position was from Emily's point of view was different from zero. We can calculate this distance as the multiplication of the time Anthony was traveling times the speed at which he was driving. This is:

[tex]x_{A0}=v_At[/tex]

being [tex]t[/tex] the 15 mins he traveled before Emily started and [tex]v[/tex] the 45 m.p.h given by the problem. We also need to convert 15 mins to hours, which gives 0.25 hours. Thus:

[tex]x_{A0}=45*0.25\\x_{A0}=11.25[/tex] miles

and the position equations are now:

[tex]x_A= 11.25 + v_At[/tex] for Anthony

[tex]x_E=160 + v_Et[/tex]

Since we are asked the time at which the pass each other on the road we need to equals their positions, [tex]x_A=x_E[/tex]:

[tex]11.25+v_At=160-v_Et[/tex]

Notice here that Emily's position is negative since she is moving towards the origin of our system, meaning in the negative direction. Solving for [tex]t[/tex]:

[tex]11.25+v_At=160-v_Et\\v_At+v_Et=160-11.25\\t(v_A+v_E)=148.75\\t = \frac{148.75}{v_A+v_E}[/tex]

Substituting the values of [tex]v_A=45[/tex] and [tex]v_E=40[/tex]:

[tex]t = \frac{148.75}{45+40}=\frac{148.75}{85}\\t=1.75 h[/tex]

What we have calculated is the time interval from where we start counting the time and remember this was set at 2:15 pm when Emily left. Since the exercise asks for the hours of the day we need to add the time interval to 2:15 pm and:

[tex]1.75 h = 1 h+45 min[/tex]

And 2:15 pm + 1 h is 3:15 pm + 45 mins is 4:00 pm which is the time at which the pass each other on the road.

Final answer:

Anthony and Emily will cross paths at 4:00 p.m. after calculating the distance covered by Anthony and the remaining distance between them when Emily starts driving, with their combined speed taken into consideration.

Explanation:

To solve this question, we need to calculate the time when Anthony and Emily will cross paths on the road, given that they are traveling towards each other from Kingstown to Albany and vice-versa. Anthony drives at 45 mph whereas Emily drives at 40 mph

Let's first find out how far apart they are when Emily starts her journey at 2:15 p.m. Since Anthony left at 2:00 p.m. and drives for 15 minutes until Emily starts her journey, we calculate the distance he has covered as:

Now, the remaining distance between them is:

The combined speed at which they're closing the distance is:

To find the time it takes for them to meet, we use the formula:

Since 1.75 hours is 1 hour and 45 minutes, they will meet at:

Therefore, Anthony and Emily will cross paths at 4:00 p.m.

Answer:

Tax = $19.04

Step-by-step explanation:

Hourly wage = $6.8/hr

hours worked = 10

Tax = 28%

[tex]total \: earnings =6.8 \times 10 = 68 \\ amount \: of \: tax = 68 \times 28\% = 68 \times \frac{28}{100} \\ = 19.04[/tex]

Answer:

Proportion

Step-by-step explanation:

Proportion is just the division of the data that meets the description, between the total number of data present in the study.

For example, let's suppose that we have a tiger, a lion, a sheep, a cow and a horse, and we want to know the proportion of animals that eat meat, then, only 2 out of 5 of those eat meat, the tiger and the lion, meaning [tex]\frac{2}{5}[/tex], which would be the proportion, or 0.40

The coordinates of point Q are (0, 3).

Option C is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph,

Point Q is at y = 3 on the y-axis and 0 on the x-axis.

So,

The coordinates of point Q are (0, 3).

Thus,

The coordinates of point Q are (0, 3).

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Changing [tex]x\mapsto -x[/tex] "inverts" the orientation of the x axis, so the graph of f(x) is transformed by reflecting it about the y axis.

The transformation f(-x) represents a reflection of function f(x) across the y-axis. Even functions are unchanged by this transformation, while odd functions are reversed.

The transformation f(-x) in mathematical terms represents a reflection of the function f(x) across the y-axis. For instance, if you have a function that plots as a certain curve when x is positive, applying function to f(-x) would result in the same curve but flipped horizontally across the y-axis. This is because replacing x with -x inverts the sign of every x-coordinates of the original points, causing a mirror image reflection over the y-axis. Thus, while the original function may say f(x) = x², f(-x) would also form a parabola, but it would be flipped across the y-axis.

For example, if f(x) = x³ for x > 0 which increases, f(-x) = -x³. As x values are now negative, the graph flips and for x > 0, f(-x) decreases.

Note that even functions like f(x) = x², which are symmetric about the y-axis, remain unchanged when transformed to f(-x), while odd functions like f(x) = x³, which are symmetric about the origin, are reversed when f(-x) is implemented.

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Answer:

The answer to your question is below

Step-by-step explanation:

Equation 4x - 2y = 8 solve for y

First, pass 4x to the right side                -2y = -4x + 8

Pass -2 to the right side                             y = -4/-2 x  + 8 /-2

Simplify                                                        y = 2x -4 or    y = -4 + 2x

I can not see clearly the work of Charlize and Camille, but the one that has the answer shown above is correct.                                                                                    

Answer:

Step-by-step explanation:

Answer:

c.7,999,999

Step-by-step explanation:

The phone number is of the form ABC - XXXX

A can be any number from 2 - 9. This means number of possible values for A are 8.

The rest of the places B,C and X can be any digit from 0 - 9. This means there are 10 possible values for each of these.

Since, value to A can be assigned in 8 ways, and to the rest of the 6 positions in 10 ways, according to the fundamental rule of counting, the total number of possible phone numbers that can be formed will be equal to the product of all the individual ways:

Total possible phone numbers = 8 x 10 x 10 x 10 x 10 x 10 x 10

Since, 1 of the given number: 867-5309 is not used, the total possible phone numbers will be:

Total possible phone numbers = [tex]8 \times 10^{6} - 1 = 7999999[/tex]

Hence, option C: 7,999,999 give the correct answer.

Final answer:

The answer calculates the possible phone numbers in the (770) area code with given restrictions, ending up with 7,999 possible phone numbers.

Explanation:

To calculate how many phone numbers are possible in the (770) area code with the given restrictions, we first determine the possibilities for each digit:

A (restricted to 2-9): 8 optionsB, C, X (0-9 for each digit): 10 options each

So, the total number of possible phone numbers is: 8 (A) * 10 (B) * 10 (C) * 10 (X) = 8,000. However, we need to exclude the number 867-5309, so the final count is 8,000 - 1 = 7,999.

Answer:

B 10% off sale, with a total price to pay of 756

Step-by-step explanation:

Retail price (Rp) = $800

Taxes (T) = 5%

Total price A (TA) = Rp - 75 + (Rp - 75) 5%

TA = 800 - 75 + (800-75) 5%

TA = 725 + 725 5%

725 5% = 725*5/100 = 36.25

TA= 725+36.25 = $761.25

Total price B (TB) = RP - RP 10% + (RP - RP 10%) 5%

TB = 800 - 800 10% + (800 - 800 10%) 5%

800 10% = 800*10/100 = 80

TB = 800 - 80 + (800 - 80) 5%

TB = 720 + 720 5%

720 5% = 720*5/100 = 36

TB = 720 + 36 = $756

store pays sales tax means Walden's family will not need pay for taxes

Total price C (TC) = RP - RP 5%

TC = 800 - 800 5%

800 5% = 800*5/100 = 40

TC = 800 - 40 = $760

Means that Walden's family will need pay just the retail price

TD = $800

The beast deal is from the store B

Answer:

the answer is b

Step-by-step explanation:

hoped this helped

Answer:

The answer to your question is: h = 9 in

Step-by-step explanation:

Data

radius = 6 inches

V = 324 π in³

h = ?

Formula

V = πr²h

Then, we solve it

324π = πr²h          cancel π

 324 = r²h             substitution

324 = 6² h

h = 324 /6²           simplify

h = 324/36

h = 9 in              result

Utilizing the volume formula for a cylinder, we can calculate the minimum height required for a volume of 324π cubic inches. Given a radius of 6 inches, we solve the formula to find a minimum cylinder height of 9 inches.

The subject of this question is mathematics, specifically geometry focusing on the properties of cylinders. In this instance, we want to calculate the minimum height of a cylinder that can hold a specified volume. The formula to find the volume of a cylinder is V = πR²h, where 'R' is the radius and 'h' is the height.

Given that the radius is 6 inches and the desired volume is 324π cubic inches, we can insert these values into our formula. So, 324π = π*(6)²*h which simplifies to 324 = 36h. Then, we need to solve for 'h', which involves dividing 324 by 36. The result shows that the minimum height 'h' of the cylinder is 9 inches.

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Answer:

  5 meters

Step-by-step explanation:

The height of the lamppost above the person is twice the height of the person, so the distance between the lamppost and person is twice the length of the person's shadow. (A diagram can help you see this.)

The person's shadow is (10 m)/2 = 5 m long.

___

Check

The tip of the shadow is 15 m from the lamppost, 2.5 times the height of the lamp. The tip of the shadow is also 5 m from the person, 2.5 times the height of the person. The triangles involved are similar.

Final answer:

To find the length of the person's shadow, we use the properties of similar triangles defined by the person and the lamppost. By setting up a proportion between the person's and the lamppost's height to their respective shadow lengths and solving, we find the person's shadow is 5 meters long.

Explanation:

To solve the problem of determining the length of the shadow cast by the person standing 10 meters from the lamppost at night, we can use the concept of similar triangles.

Since the light source (lamppost) is above ground level, the triangle formed by the lamppost, the end of the shadow, and the top of the person's head is similar to the triangle formed by the person, their shadow, and the ground. Using the properties of similar triangles, the ratios of corresponding sides are equal.

Let's denote the length of the person's shadow as s. The triangles' corresponding sides' ratios would be:

Setting up the proportion, we have:

2 / s = 6 / (10 + s)

By cross-multiplying and solving for s, we get:

2(10 + s) = 6s

20 + 2s = 6s

4s = 20

s = 5

Hence, the length of the person's shadow is 5 meters.

Bobby's economic profit for the day is $0.60, calculated by subtracting his total cost of $3.40 from his total revenue of $4.00. Here option A is correct.

To calculate Bobby's economic profits, we first need to understand the concept of economic profit.

Economic profit is calculated as total revenue minus total cost. Total revenue (TR) is the total amount of money earned from selling a product, which is calculated by multiplying the quantity sold (Q) by the price per unit (P). Total cost (TC) is the total expense incurred in producing a product.

In this case, we have the following information:

Bobby sells 20 glasses of lemonade at $0.20 per cup, so his total revenue is:

TR = 20 cups * $0.20/cup = $4.00

Bobby's average total cost is $0.17 per cup. Since he sold 20 cups, his total cost is:

TC = 20 cups * $0.17/cup = $3.40

Now, we can calculate Bobby's economic profit:

Economic Profit (π) = Total Revenue (TR) - Total Cost (TC)

= $4.00 - $3.40

= $0.60

So, Bobby's economic profit for the day is $0.60.

The correct option is:

a. $0.60

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Answer:

b

Step-by-step explanation:

We must determine the the x value at 90% confidence interval. We find this from a table relating confidence intervals and x values. For 90%, z is 1.645.

WE must determine the mean of 19 and 23:

[tex]=(19+23)/2=21[/tex]

We must determine the standard deviation. We let n be the number of population which is 2. We need to take the numbers 19 and 23 and subtract  each by the mean and square the answer:

[tex](19-2)^2=289[/tex]

[tex](23-2)^2=441[/tex]

We then determine the mean of these two values as:

[tex](289+441)/2=365[/tex]

Now we take the square root of 365:

[tex]\sqrt{365}=19.1[/tex]

The standard deviation is 19.1

The answer is b

Answer: x=7

Step-by-step explanation:

Ok, so first put SR/ML=QR/KL (not dividing)

Then, fill in the blanks, x/5=4.2/3

Then, cross multiply leaving the equals sign there

x*3=4.2*5

Then, solve for x

3x=21

— —

3. 3

Lastly you get your answer of

X=7

Hope I helped

Answer:

The value of x is 7.

Step-by-step explanation:

Consider the provided figure.

It is given that both the pentagons are similar.

That means the ratio of the sides will be same and we need to find the value of x.

[tex]\frac{NM}{TS}=\frac{ML}{SR}[/tex]

Substitute the respective values in the above formula.

[tex]\frac{4}{5.6}=\frac{5}{x}[/tex]

[tex]4x=5\times 5.6[/tex]

[tex]x=\frac{28}{4}[/tex]

[tex]x=7[/tex]

Hence, the value of x is 7.

Answer:

This variable that is impacted by manipulating the independent variable is known as dependent variable

Step-by-step explanation:

One of the methods to test a hypothesis is the use of independent variable. The independent variable is manipulated to know if the change will be effective or not.

The variable which will be impacted by the independent variable is called dependent variable. The researcher manipulated the values for independent variable to check if the dependent variable changes or not ..

Answer:

  8 1/4 inches

Step-by-step explanation:

  (3 1/4 - 1/4) + (5 1/2 - 1/4) = 3 + 5 1/4 = 8 1/4 . . . inches

Answer:

35

Step-by-step explanation:

5 and 7 are both prime numbers, so the least common multiple of 5 and 7 is their product, 5 * 7 = 35

The least common denominator of the fractions 3/5 and 2/7 is found by determining the least common multiple of the denominators 5 and 7. Since they are prime numbers, their LCM is their product, which is 35.

To find the

least common denominator

(LCD) of the given

fractions

, 3/5 and 2/7, we must find the least common multiple (LCM) of the two

denominators

5 and 7. The LCM of any two numbers is the smallest number that both numbers can divide evenly into. Since 5 and 7 are prime numbers, the LCM is simply their product, which is 35. Therefore, the least common denominator of 3/5 and 2/7 is 35.

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Answer:

128 posibilities

Step-by-step explanation:

We have 7 colleges (A,B,C,...,H) which form a set with seven elements.

What you are asking is the number of elements (or cardinality) of the set that contains all possible sets formed by those 7 elements (or the "power set").

It is known that if n is the number of elements of a given set X, then the cardinality of the power set is [tex]2^n[/tex].

Therefore, there are [tex]2^7[/tex] or 128 possibilities (or elements) for the set of colleges that he applies to.

Final answer:

The number of possible combinations of colleges that Jose can apply to from 7 options is 128. This includes the possibility of not applying to any college as well.

Explanation:

The question asks how many different combinations of colleges Jose may apply to given 7 different options.

This is a problem related to the field of combinatorics in mathematics, specifically the concept of the power set, where each college can either be chosen or not, resulting in 2⁷ possible combinations.

Since he can like none, some, or all colleges, we include the possibility of an empty set, leading to a total of 2⁷ = 128 possibilities.

In each case, Jose has two options for every college - to apply (like) or not to apply (dislike).

Therefore, the number of combinations is calculated by raising 2 (the number of options for each item) to the power of 7 (the number of items).

Answer:

  the penny option is the much better deal

Step-by-step explanation:

The sequence of pay amounts for the "penny option" is ...

  $0.01, $0.02, $0.04, $0.08 ...

For day n, the amount of pay is $0.01·2^(n-1). For day 30, the amount of pay is ...

  $0.01·2^29 = $5,368,709.12

In case you can't tell, the "penny option" is a much better deal than $250.00. (You might need to credit check your parents before accepting this deal. I know my parents could not make good on this "penny option" offer.)

The total amount for the 30 days will be double this amount, less one cent, or ...

  $10,737,418.23

_____

Sum of a geometric sequence

The daily payments of the penny option are a geometric sequence. The sum of n terms of such a sequence is given by ...

  Sn = a1(r^n -1)/(r -1)

where a1 is the first term ($0.01) and r is the common ratio (2). In our case, the sum for n days is ...

  Sn = $0.01·(2^n -1)

On day 15, this will already be more than $250. The accumulated pay on that day will be $0.01·(2^15-1) = $327.67.

Answer:

[tex]y=58.67^{\circ}[/tex]

[tex]x=121.33^{\circ}[/tex]

Step-by-step explanation:

We are given that two angles are supplementary .

We have to write an equation that can be used to find the measures.

Let x and y are supplementary

According to question

[tex]x+y=180^{\circ}[/tex]( by definition of supplementary angles)

[tex]x=2y+4[/tex]

Substitute the value then we get

[tex]2y+4+y=180[/tex]

[tex]3y=180-4[/tex]

[tex]3y=176[/tex]

[tex]y=\frac{176}{3}[/tex]

[tex]y=58.67^{\circ}[/tex]

Substitute the value then, we get

[tex]x+58.67=180[/tex]

[tex]x=180-58.67[/tex]

[tex]x=121.33^{\circ}[/tex]

Answer:

16 in × 20 in

Step-by-step explanation:

Area of picture= length by width

                         =4*6=24 in²

Area of frame=Length by width

                      =16*20=320 in²

% of the picture in the frame will be

                        (24/320) * 100% =7.5%

     2. Finding the % of the picture that can fit in 18 × 24 frame

Area of picture=24 in²

Area of frame =Length by width

                       =18*24=432 in²

% of the picture in the frame will be;

                        (24/432)*100%=5.6%

The frame 16 by 20 in will keep 7.5% of the original picture

The frame 18 by 24 in will keep 5.6% of the original picture

Hence you should use the frame  of 16 by 20 in because it will keep more of the original picture.

Answer:

15

Step-by-step explanation:

Using the definition of n[tex]C_{r}[/tex]

n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]

where n! = n(n - 1)(n - 2) × 3 × 2 × 1

Hence

6[tex]C_{2}[/tex]

= [tex]\frac{6!}{2!(4!)}[/tex]

= [tex]\frac{6(5)(4)(3)(2)(1)}{2(1)4(3)(2)(1)}[/tex]

Cancel 4(3)(2)(1) on numerator/ denominator, leaving

= [tex]\frac{6(5)}{2(1)}[/tex] = [tex]\frac{30}{2}[/tex] = 15

Answer:

3.5 seconds

Step-by-step explanation:

h(t) is a quadratic function, it indicate that the object start with initial height (56).

If you want to know when the object hit the ground (h=0) you have to use the quadratic formula [tex](-b +- \sqrt{b^{2}-4ac } )/2a[/tex] and take the positive root (the negative shows a negative time, so we have to discard it).

In this case: a=-6, b=5 and c=56, then the solve is 7/2=3.5

Answer:

The volume of the ball with the drilled hole is:

[tex]\displaystyle\frac{8000\pi\sqrt{2}}{3}[/tex]

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

[tex]x^2+y^2=15^2\to y=\sqrt{225-x^2}[/tex]

Then we set the integral for the volume by using shell method:

[tex]\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx[/tex]

That can be solved by substitution:

[tex]u=225-x^2\to du=-2xdx[/tex]

The limits of integration also change:

For x=5: [tex]u=225-5^2=200[/tex]

For x=15: [tex]u=225-15^2=0[/tex]

So the integral becomes:

[tex]\displaystyle -\int_{200}^{0}\pi \sqrt{u}du[/tex]

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

[tex]\displaystyle \int_{0}^{200}\pi u^{1/2}du[/tex]

Then applying the basic rule we get:

[tex]\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}[/tex]

Since that is just half of the solid, we multiply by 2 to get the complete volume:

[tex]\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}[/tex]

[tex]=\displaystyle\frac{8000\pi\sqrt{2}}{3}[/tex]

To find the volume of the resulting solid, calculate the volume of the ball and subtract the volume of the hole. The volume of the resulting solid is (4/3)π(15)³ - 10πr².

To find the volume of the resulting solid, we need to calculate the volume of the ball and subtract the volume of the hole. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. So, the volume of the ball is V₁ = (4/3)π(15)³. The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is the height. The height of the cylinder formed by the hole is equal to the diameter of the ball, which is 2r. So, the volume of the hole is V₂ = π(5)²(2r) = 10πr².

Therefore, the volume of the resulting solid is V = V₁ - V₂ = (4/3)π(15)³ - 10πr².

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Answer:

w = 0.333

Step-by-step explanation:

In circular motion you have:

v = wr

replacing:

3 = 9w

0.333 = w

The angular speed of a point with r = 9 cm and v = 3 cm/sec is 0.33 rad/s

The angular speed (ω) is given by:

ω = v/r

Where v is the linear speed and r is the radius.

Given that v = 3 cm/sec = 0.03 m/s, radius = 9 cm = 0.09 m, hence:

ω = v/r = 0.03/0.09 = 0.33 rad/s

The angular speed of a point with r = 9 cm and v = 3 cm/sec is 0.33 rad/s

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Answer:

Compound interest the interest changes annually and with simple interest the interest is the same annually

The main difference between simple interest and compound interest is that simple interest is calculated only on the initial investment, whereas compound interest is calculated on the initial principal and also on the accumulated interest of previous periods.

The primary difference between simple interest and compound interest lies in the way they are calculated. Simple interest is calculated only on the initial amount (principal) that you invested. For example, if you invest $1000 at a simple interest of 5% per annum, your interest for the first year will be $50, and it will remain the same for all the years the money is deposited.

Compound interest, on the other hand, is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit. So, in a scenario where you invest $1000 at a compound interest of 5% per annum, your interest for the first year will be $50, but for the second year, the interest will be calculated on $1050 (Principal + Interest of first year), making the interest for the second year $52.5 rather than $50.

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Answer:

T = 4C.

Step-by-step explanation:

T = 4C.

Total number of eggs = 4 * number of chickens.

Answer:

x=4

Step-by-step explanation:

Because we know that PQ = RS, we can use the transitive property to replace PQ in the first equation with 29:

9x-7=29

1) Add 7 to both sides:

9x=36

2) divide by 9 on both sides:

x=4

Final answer:

To find x, set the given equations equal to each other. Simplify the equation and solve for x. The solution is x = 4.

Explanation:

To find x, we can set the given equations equal to each other:

9x - 7 = 29

Adding 7 to both sides, we get:

9x = 36

Dividing both sides by 9, we find:

x = 4

So, x is equal to 4.

Answer:

  88 m/s

Step-by-step explanation:

The appropriate formula relating initial speed v, acceleration a, and distance d is ...

  v² = 2ad

  v² = 2(8 m/s²)(484 m) = 7744 m²/s²

Taking the square root gives ...

  v = √7744 m/s = 88 m/s

Answer:

  y = (5/2)x + 6

Step-by-step explanation:

The given line has a slope (coefficient of x) of -2/5. The perpendicular line will have a slope that is the negative reciprocal of this:

  -1/(-2/5) = 5/2

Since you are given a point you want the line to go through, the point-slope form of the equation of the line is useful. That form for slope m and point (h, k) is ...

  y = m(x -h) +k

For your slope m=5/2 and point (h, k) = (-2, 1), the equation of the line is ...

  y = 5/2(x +2) +1

  y = 5/2x +6 . . . . . eliminate parentheses