Georgia will use the pattern shown to make a square pyramid out of cardboard. The square pyramid will not have a bottom. How much cardboard will she need if a = 14 in. and b = 9 in.? PLEASE HELP

First find the gradient of the perpendicular line. You do this by taking the negative reciprocal of the gradient of the first line (y= 1/4x +3):

Perpendicular gradient = negative reciprocal of [tex]\frac{1}{4}[/tex] = -4

Next, you substitute the x and y values into the following equation and solve:

y = -4x +c

-2 = -4(-4) +c

-2 = 16 + c

-18 = c

Substitute c back into the equation above to get the final answer:

y = -4x -18

-------------------------------------------------

Answer

y = -4x - 18

Step-by-step explanation:

Look at the picture.

A' - The complement of a set is the set of all elements in the given universal set U that are not in A.

B - A - The set difference of sets A and B is the set of all elements in A that are not in B.

A ∩ B - The intersection of sets A and B is the set of all distinct elements that are in both A and B.

The value of 'b' in the quadratic equation [tex]4x^2+bx+9=0[/tex] must result in a negative discriminant, which means [tex]b^2[/tex] must be less than 144 for the equation to have no real number solutions.

For a quadratic equation [tex]ax^2+bx+c=0[/tex] to have no real number solutions, its discriminant must be negative. The discriminant is given by the formula [tex]b^2-4ac[/tex]. In the case of the equation [tex]4x^2+bx+9=0[/tex], a is 4 and c is 9. For this equation to have no real solutions, the value of b must be such that [tex]b^2-4(4)(9)[/tex] is less than 0. This simplifies to [tex]b^2-144 < 0[/tex]. Therefore, for the student's equation to have no real number solutions, the value of b must satisfy [tex]b^2 < 144.[/tex]

For the quadratic equation 4x² + bx + 9 = 0 to have no real roots, the discriminant must be negative, which leads to the requirement that b² < 144.

To determine what must be true about b in the quadratic equation 4x² + bx + 9 = 0 with no real number solutions, we consider the discriminant of a quadratic equation, which is given by the formula Discriminant = b² - 4ac. For the given equation, a equals 4 and c equals 9. In order for a quadratic equation to have no real roots, the discriminant must be negative. Therefore, our inequality becomes b² - 4(4)(9) < 0, which simplifies to b² < 144. Therefore, the requirement for the quadratic equation to have no real solutions is that the square of b must be less than 144, elucidating the crucial role of discriminants in determining the nature of solutions in quadratic equations.

x2 - 12x - 12 = 0

(x - 6)2 - 48 = 0

(x - 6)2 = 48

Hence, the answer is (B).

Answer:

B

Step-by-step explanation:

given

x² - 12x - 5 = 7 ( add 5 to both sides )

x² - 12x = 12

To complete the square

add (half the coefficient of the x- term )² to both sides

x² + 2(- 6)x + (- 6)² = 12 + (- 6)²

x² + 2(- 6)x + 36 = 12 + 36 ← complete the square on the left side

(x - 6)² = 48 → B

16. The first attachment shows a table of the given values and the function evaluated at those points.

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17. The cost function for this problem is an expression of the total cost as a function of number of days open:

  c(x, y) = 40x + 50y

The system of inequalities expresses the constraints on delivery of glass and aluminum in terms of the number of days open:

To minimize costs, Center 1 should be open 6 15/16 days; Center 2 should be open 5 11/16 days. The cost function is minimized when it goes through the vertex of the feasible region that puts it closest to the origin.

___

18. (a) Jane can use the revenue function ...

  r(x, y) = 120x +70y

(b) The constraints on hours and numbers of visits are ...

(c) For the given vertices, Jane's best choice is (4, 7), which will produce $970 in revenue for the office.

As is sometimes the case, the integer vertex closest to the corner of the feasible region is not the one that maximizes revenue. Jane's best choice is not on the problem's list. It is (5, 6), which will produce $1020 in revenue.

See the second attachment for the graph related to the problem.

_____

Apology

The graphs are out of order because my first attempt at 17 had an error. The corrected graph was added as the last attachment.

_____

Steps

In all of these linear programming problems, the "objective function" is the function of the problem variables that you want to maximize or minimize. In order to write it, you need to understand what the problem variables are and how they relate to the objective. In each of these problems, you are told what x and y stand for and their relation to the objective.

When considering the constraints, you must consider how the problem variables relate to any limits imposed. As in problem 17, sometimes the limits are minima (must deliver at least ...). In problem 18, the limits are maxima (8 hours in a day; no more than 7 follow-ups).

So, first read and understand the problem statement and the relationships it is telling you. Then, do what the problem asks you to do. Sometimes that will involve finding a solution; sometimes not.

Often, you can use logic to help you understand whether your solution is reasonable. In the doctor problem (18), the doctor makes more money per hour doing follow-ups, so would probably want to maximize those (4, 7). However, doing that leaves a half-hour with zero revenue. That last hour is better spent seeing a new patient ($120) than seeing only one follow-up patient ($70).

Answer:

none of the above

Step-by-step explanation:

The plot has a generally downward trend, so the correlation coefficient will be negative. However, it is not scattered enough for r = -0.36 and not linear enough for r = -0.95.

My estimate of point values lets my graphing calculator give the correlation coefficient as -0.80. This is closer to -0.95 than to -0.36, but is significantly different from both of them.

Answer:

  a. add the areas of both bases to the rectangular area around the cylinder

Step-by-step explanation:

None of the other choices has anything to do with the surface area of a cylinder.

_____

Use your sense of what the question is asking about.

ANSWER:

A.  is the only answer choice talking about surface area....

distance formula

The distance formula is really just the Pythagorean Theorem in disguise. To calculate the distance AB between point A(x1,y1) and B(x2,y2) , first draw a right triangle which has the segment ¯AB as its hypotenuse. Since AC is a horizontal distance, it is just the difference between the x -coordinates: (x2−x1)

slope formula

To calculate the slope of a line you need only two points from that line, (x1, y1) and (x2, y2). The equation used to calculate the slope from two points is: On a graph, this can be represented as: There are three steps in calculating the slope of a straight line when you are not given its equation.

midpoint formula

The midpoint is halfway between the two end points: Its x value is halfway between the two x values. Its y value is halfway between the two y values.

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│Hope this helped  _____________________│

│~Xxxtentaction ^̮^ _____________________│

╩___________________________________╩    

The distance formula is d=√(x2 - x1)² + (y2 - y1)² and it's similar to the pythagorean theorem; finding the ditance between one point and another. The slope formula is y2 - y1 / x2 - x1 or rise/run. It also finds the distance between two points but slope measures whether the line is increasing or decreasing, and by what rate. The midpoint formula is (x1 + x2 /2 , y1 + y2 / 2) which is a set of coordinates. It finds the middle or midpoint of the line connecting two points.

Hope this helps!

The truck cannot drive under the archway since it is taller than the highest point of the archway.

To determine if a truck can drive under the semielliptic archway without going into the other lane, we need to compare the height and width of the truck to the height and width of the archway. The truck has a height of 12 feet and a width of 14 feet. The highest point of the archway is at its center, which is 15 feet high. So, the truck will not fit under the archway since it is taller than the highest point of the archway.

Answer:

Price of advance ticket: 15$

Price of same-day ticket: $40

Step-by-step explanation:

Let [tex]y[/tex] be the price of one advance ticket and [tex]x[/tex] the cost of one same day ticket.  

We know that the combined cost of one advance ticket and one same-day ticket is $55, so

[tex]y+x=55[/tex] equation (1)

We also know that 20 advance tickets and 35 same-day tickets cost $1700, so

[tex]20y+35x=1700[/tex] equation (2)

Now, let's solve our system of equations step-by-step:

step 1. Solve for [tex]x[/tex] in equation (1)

[tex]y+x=55[/tex]

[tex]x=55-y[/tex] equation (3)

step 2. Replace equation (3) in equation (2)

[tex]20y+35x=1700[/tex]

[tex]20y+35(55-y)=1700[/tex]

[tex]20y+1925-35y=1700[/tex]

[tex]-15y=-225[/tex]

[tex]y=\frac{-255}{-15}[/tex]

[tex]y=15[/tex] equation (4)

step 3. Replace equation (4) in equation (3)

[tex]x=55-y[/tex]

[tex]x=55-15[/tex]

[tex]x=40[/tex]

We can conclude that the price of one advance ticket is $15 and the price of one same-day ticket is $40.

Answer:

  56 photos per page

Step-by-step explanation:

1344 photos/(24 pages) = 1344/24 photos/page = 56 photos per page

Answer:

i need points to ask my question

Step-by-step explanation:

The formula to calculate the perimeter of a regular hexagon is P = 6s, where 'P' is the perimeter and 's' is the length of one side. It's crucial to use consistent units when measuring and calculating.

In mathematics, the perimeter of a shape is the distance around its borders. For a regular hexagon, which is a six-sided polygon with all sides of equal length, the perimeter is calculated by simply multiplying the length of one side by the number of sides. Therefore, if you know the length of a side, you can calculate the perimeter of the regular hexagon using the formula:

P = 6s

Where 'P' is the perimeter and 's' is the length of a side of the hexagon. It's important to use consistent units when making these measurements and calculations to ensure accuracy.

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The perimeter of a regular hexagon can be calculated using the formula: P = 6 * S, where P represents the perimeter and S represents the length of a side.

In mathematics, the perimeter of a shape is the distance around its borders. For a regular hexagon, which is a six-sided polygon with all sides of equal length, the perimeter is calculated by simply multiplying the length of one side by the number of sides.  The formula that describes the perimeter of a regular hexagon as a function of the length of its side is:

P = 6 * S

Where P represents the perimeter and S represents the length of a side.

Since a regular hexagon has six equal sides, you can multiply the length of a side by 6 to find the total perimeter.

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Answer:

Part 1) [tex]m<OAD=60\°[/tex]

Part 2) [tex]m<DBA=30\°[/tex]

Step-by-step explanation:

Part 1) Find the measure of angle OAD

we know that

OA=OD=radius of the circle

If line AD≅ line AO

then

The triangle AOD is an equilateral triangle

Remember that

An equilateral triangle has the three equal sides and the three internal angles equal (60 degrees each one)

so

[tex]m<OAD=60\°[/tex]

Part 2) Find the measure of angle DBA

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<DBA=\frac{1}{2}(arc\ AD)[/tex]

[tex]arc\ AD=m<AOD=60\°[/tex] ----> by central angle

substitute the value

[tex]m<DBA=\frac{1}{2}(60\°)=30\°[/tex]

The initial yield of potatoes per acre was 14 tons and after the introduction of the new technology, the yield increased to 18 tons. Therefore, 5600 tons were collected before the technological advances and 7200 tons were collected after.

This problem involves understanding linear equations. Let's denote the initial yield of potatoes per acre as 'x' tons and the yield after the introduction of the new technology as 'y' tons.

It's given that technological advances increase the yield by 4 tons, so we have the equation: y = x + 4. The problem also states that from a 320 acre field 640 more tons were collected than before from a 400-acre field. So, we can write it as: 320y = 400x + 640.

Solve these two equations to find the values of x and y. The initial yield of potatoes per acre (x) was 14 tons while the yield after the introduction of the new technology (y) was 18 tons. Therefore, 5600 tons of potatoes were collected before the technological advances and 7200 tons were collected after.

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Before the new methods were introduced, 640 tons of potatoes were collected. After the introduction of the new technology, 0 tons were collected.

To solve this problem, let's assume x is the number of tons of potatoes collected before the new methods were introduced, and y is the number of tons collected after the introduction of the new technology.

According to the given information, the new technology increased the crop of potatoes from 1 acre by 4 tons, so the increase in yield per acre is 4 tons.

From a field of 320 acres, 640 tons more were collected than before from a field of 400 acres. This means that the increase in yield from the reduced field of 320 acres is twice the increase in yield from the initial field of 400 acres.

Setting up the equation, we have:

(y - x) = 2(4)(320 - 400)

(y - x) = 2(4)(-80)

(y - x) = -640

We also know that the total increase in yield is 640 tons, so we have:

x + y = 640

To solve these equations, we can use substitution or elimination method. Solving for x in the second equation, we get:

x = 640 - y

Substituting x in the first equation, we have:

(y - (640 - y)) = -640

2y - 640 = -640

2y = 0

y = 0

Substituting y in the equation x + y = 640, we get:

x + 0 = 640

x = 640

Therefore, before the new methods were introduced, 640 tons of potatoes were collected, and after the introduction of the new technology, 0 tons were collected.

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Answer:

Step-by-step explanation:

1. Any linear equation that describes a line with non-zero slope through the vertex of the parabola will intersect the parabola at two points (the vertex being one of them). A simple equation for such a line is y=x.

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2. Differentiating the equation, you find that the slope of the curve y = x^2 is 2x, so if we choose a line with a slope of 1, it will go through the point on the curve with x-value equal to 1/2. The y-value at that point is y = (1/2)^2 = 1/4, so the y-intercept of the line must be -1/4.

The line that intersects the curve at one point (1/2, 1/4) is tangent at that point. It has equation y = x -1/4.

__

3. Any line with the same slope as the tangent line, but a more negative y-intercept, will not intersect the parabola at all. Such a line is y = x -1/2.

_____

Truth be told, I found the line y = x -1/2 did not intersect the parabola at all when I thought I was writing the equation for the tangent line. It was an answer to part of your question, just not the part I originally intended.

Answer:

A linear equation that intersects at two points would be y = 1x. A linear equation that only has one intersect point would be y=0. finally, a linear equation that has no intersect point would be y = x - 4. I could these by plotting them on a graph and finding out that these will work.

Step-by-step explanation:

Answer:

how many cups are needed for the recipe

Step-by-step explanation:

Answer:

y =  [4(x-3)]/3

Step-by-step explanation:

4x = 12+3y

3y = 4x-12

y =  [4(x-3)]/3

Best regards

Answer:

1

Step-by-step explanation:

Add the square of half the x coefficient: (-2/2)^2 = 1.

Answer:

a. number of periods over which interest is calculated on the loan

Step-by-step explanation:

A formula should always be accompanied by an explanation of what it calculates and the meaning of each of its variables. This formula calculates P, the periodic payment on a loan of n periods at interest rate i (compounded) per period. The principal amount of the loan is PV.

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The same formula can also be used to calculate an annuity from which payment P is received at the end of each of n periods. The amount invested is PV and the interest rate per period (compounded per period) is i.

'n' typically represents the number of periods over which interest is calculated in a loan. However, symbols' intended meanings can change depending upon the context.

In most financial and mathematical formulas, the symbol 'n' typically represents the number of periods over which interest is calculated on a loan. It's relevant to note that these periods could be months, years, or any other agreed-upon timeframe. Hence, the correct answer to your question is (a).

However, it's important to state that the representation of variables can change with different contexts. In some scenarios, 'n' could be used to denote the number of years it will take to pay the loan back, but that is not as common as using 'n' for the number of periods.

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Answer:

  (x^(11/4))(y^(5/9))

Step-by-step explanation:

The applicable rules of exponents are ...

  (x^a)(x^b) = x^(a+b)

  (x^a)/(x^b) = x^(a-b) . . . . . no surprise, since 1/x^b = x^-b

_____

Your expression simplifies to ...

  x^((5/4) -(-5/4) -(-1/4)) · y^((1/18) -(-1/2))

  = x^(5/4 +5/4 +1/4) · y^(1/18 +1/2)

  = x^(11/4) · y^(1/18 +9/18)

  = x^(11/4) · y^(5/9)

The surface area of a cylinder is given by

[tex]A_A = 2\pi rh[/tex]

which is the surface area of cylinder A.

To compute the surface area of cylinder B, we have to map [tex](r,h)\mapsto (2r, 2h)[/tex] and we have the following formula

[tex]A_B = 2\pi(2r)(2h)[/tex]

If we manipulate the second expression, we have

[tex] A_B = 8\pi rh[/tex]

Which implies

[tex]\dfrac{A_B}{A_A} = \dfrac{8\pi rh}{2\pi rh} = 4 [/tex]

Answer:

m∠LTE = 110

Step-by-step explanation:

1. add up all of the arcs.

2x+3x+4x-8+x-12

2. all of the arcs equal 360

2x+3x+4x-8+x-12=360

3. Find x

10x-20=360, x=38

4. angle LTE is equal to half of the sum of the intercepted arcs.

0.5(arc LE +GF)

5. plug in LE +GF with x

.5(76+144)

Answer:

m∠LTE = 110°

Step-by-step explanation:

We know that sum of all arcs of a circle is 360°

Therefore [tex]m(arcAL)+m(arcLG)+m(arcGF)+(mFE)=360[/tex]

Now we put the values of each arc

[tex](2x)+(3x)+(4x-8)+(x-12)=2x+3x+4x+x-8-12=10x-20=360[/tex]

10x = 360 + 20

10x = 380

[tex]x=\frac{380}{10}[/tex]

x = 38

Now from the theorem of intersecting chords in a circle

Measure of ∠LTE = [tex]\frac{1}{2}[m(arcEL)+m(arcGF)][/tex]

m(arc EL) = 2x = 2×38 = 76°

m(arc GF) = (4x - 8) = (4×38 - 8) = (152 - 8) = 144°

Now we can get the measure of ∠LTE

m∠LTE = [tex]\frac{1}{2}(76 + 144)=\frac{220}{2}=110[/tex]

Therefore m∠LTE = 110° is the answer.

Answer:

it is an identity

Step-by-step explanation:

Answer:

230

Step-by-step explanation:

Let number of downloads of standard version be x,

and

number of downloads of high quality version be y

We can write 2 equations and solve simultaneously.

"the high-quality version was downloaded three times as often as the standard version.":

[tex]y=3x[/tex]

"The size of the standard version is 2.3 megabytes (MB). The size of the high-quality version is 4.2 MB ... The total size downloaded for the two versions was 3427 MB":

[tex]2.3x+4.2y=3427[/tex]

Now, plugging in equation 1 into equation 2, we can solve for x (hence standard version downloads number):

[tex]2.3x+4.2y=3427\\2.3x+4.2(3x)=3427\\2.3x+12.6x=3427\\14.9x=3427\\x=230[/tex]

There were 230 downloads of the standard version

Answer:

270

Step-by-step explanation:

aleks answer

To finding the valu of <a and <b

<a + 120 =180 [supplementary angle]

<a= 180-120

<a= 60

Again

<a+<b+60=180 [sum of interior angle of triangle is 180]

<b=180-60-<a

<b=180-120

<b=60

hope its helps u

Answer:

The solution in the attached figure

Step-by-step explanation:

Let

x------> the numbers of boxes of popcorn sold

y-----> the number of boxes of pretzels sold

we know that

[tex]2x+5y\geq 500[/tex] ----> inequality that represent the situation

using a graphing tool

The solution is the shaded area above the solid line [tex]2x+5y=500[/tex] between the positive values of x and the positive values of y

see the attached figure

We aim to earn $500+, selling popcorn at $2/box and pretzels at $5/box. Equation: [tex]\( y \geq \frac{500 - 2x}{5} \)[/tex], where ( x ) is the number of popcorn boxes.

let's break down the problem step by step:

1. Let's define our variables:

  - ( x ): Number of boxes of popcorn sold

  - ( y ): Number of boxes of pretzels sold

2. We are given the following information:

  - The team earns $2 for every box of popcorn sold.

  - The team earns $5 for every box of pretzels sold.

  - The team wants to earn at least $500 from all sales.

3. We can express the total earnings from selling popcorn and pretzels using the given information:

  - Total earnings from popcorn sales: ( 2x )

  - Total earnings from pretzel sales: ( 5y )

4. Since the team wants to earn at least $500, we can write this as an inequality:

[tex]\[ 2x + 5y \geq 500 \][/tex]

Now, let's solve this inequality for \( y \):

[tex]\[ 2x + 5y \geq 500 \][/tex]

[tex]\[ 5y \geq 500 - 2x \][/tex]

[tex]\[ y \geq \frac{500 - 2x}{5} \][/tex]

So, the number of boxes of pretzels sold, ( y ), should be greater than or equal to[tex]\( \frac{500 - 2x}{5} \).[/tex]

Now, let's plot this inequality on a graph.

- Choose a few values of ( x ) and find the corresponding values of ( y ) using the inequality.

- Plot these points on the graph.

- Draw a line that passes through these points, and it should be a solid line because of the "greater than or equal to" sign.

- Shade the area above the line because ( y ) should be greater than or equal to[tex]\( \frac{500 - 2x}{5} \).[/tex]

Let's choose a few values of ( x ) to plot:

1. When ( x = 0):

[tex]\( y = \frac{500 - 2(0)}{5} = \frac{500}{5} = 100 \)[/tex]

2. When ( x = 100 ):

 [tex]\( y = \frac{500 - 2(100)}{5} = \frac{500 - 200}{5} = \frac{300}{5} = 60 \)[/tex]

3. When ( x = 200 ):

[tex]\( y = \frac{500 - 2(200)}{5} = \frac{500 - 400}{5} = \frac{100}{5} = 20 \)[/tex]

The average rate of change of the log function f(x) = log x from 2 to 3 is approximately 0.18, calculated using the formula for average rate of change.

In mathematics, the average rate of change of a function between two points is defined as the change in the function's output divided by the change in its input. In this case, we want to find the average rate of change of f(x) = log x from 2 to 3.

The formula for this calculation is: (f(b) - f(a)) / (b - a). In this case, a = 2 and b = 3.

Step 1: Plug the values of a and b into the function log(x): f(2) = log(2) and f(3) = log(3).

Step 2: Subtract f(2) from f(3) and then divide by the difference between 2 and 3: (log(3) - log(2)) / (3 - 2) = (0.4771 - 0.3010) / 1 = 0.1761.

So, the average rate of change of the function f(x) = log x from 2 to 3 is approximately 0.18 when rounded to the nearest hundredth.

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To find the average rate of change of f(x) = log x from 2 to 3, calculate the difference in the values of f(x) and divide it by the difference in the values of x. The average rate of change is approximately 0.41.

To find the average rate of change of f(x) = log x from 2 to 3, we need to calculate the difference in the values of f(x) at x=2 and x=3 and divide it by the difference in the values of x.

Finding the values of f(2) and f(3) we have: f(2) = log 2 ≈ 0.69 and f(3) = log 3 ≈ 1.10.

The average rate of change is calculated as:

Substituting the values, we get:

Therefore, the average rate of change of f(x) from 2 to 3 is approximately 0.41.

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Answer:

Step-by-step explanation:

There are a few ways you can write the equivalent of this.

1) Distribute the minus sign. The starting numerator is -(u-6). After you distribute the minus sign, you get -u+6. You can leave it like that, so that your equivalent form is ...

  (-u+6)/(u+2)

Or, you can rearrange the terms so the leading coefficient is positive:

  (6 -u)/(u +2)

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2) You can perform the division and express the result as a quotient and a remainder. Once again, you can choose to make the leading coefficient positive or not.

  -(u -6)/(u +2) = (-(u +2)-8)/(u +2) = -(u+2)/(u+2) +8/(u+2) = -1 + 8/(u+2)

or

  8/(u+2) -1

Of course, anywhere along the chain of equal signs the expressions are equivalent.

__

3) You can separate the numerator terms, expressing each over the denominator:

(-u +6)/(u+2) = -u/(u+2) +6/(u+2)

__

4) You can also multiply numerator and denominator by some constant, say 3:

  -(3u -18)/(3u +6)

You could do the same thing with a variable, as long as you restrict the variable to be non-zero. Or, you could use a non-zero expression, such as 1+x^2:

  (1+x^2)(6 -u)/((1+x^2)(u+2))

Answer:

  -57

Step-by-step explanation:

Put the value of x where x is and do the arithmetic.

  -7·9 +6 = -63 +6 = -57

Answer:

So, marta will sprint 225 yards.

Step-by-step explanation:

Area of parallelogram= b*h

Given: Area = 776.5 square yards

Base = 34.5 yards

Area = b* h

776.5 = 34.5 * h

776.5/34.5 =h

=> h = 22.5

Since sprint is the same distance as of height of park so,

Distance of  1 sprint = 22.5 yards

Distance of  10 sprints = 10 * 22.5 = 225 yards

Answer:

hi

Step-by-step explanation: