Alex, an eighth grader, and Eric, a seventh grader, need to determine who came closer to their grade’s state record for the triple jump. Alex jumped 39.85 feet and Eric jumped 37 feet and 1 1/4 inches. Who was closer to the state record if the eighth-grade record is 42.25 feet and the seventh-grade record is 39 feet 3 inches? (2 points)

Answer:

c

Step-by-step explanation:

The function that has a vertex at (2, -9) is;

C: f(x) = (x - 5)(x + 1)

The formula for x-coordinate of a vertex is;

x = -b/2a

The correct function is Option C with f(x) = (x - 5)(x + 1).

We will expand to get;

f(x) = x² -5x + x - 5

f(x) = x² - 4x - 5

Putting 2 for x gives;

f(2) = 2² - 4(2) - 5

f(2) = -9

Also, x = -b/2a = -(-4)/(2*1) = 2

Thus, it is proved that option C has it's vertex at 2, -9

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y = 5 * (1/2)^x

Step-by-step explanation:

This is an exponential function

y =ab^x

where a is the initial value ( where x = 0)

a = 5

y = 5 * b^x

Pick a point to determine b

(1,2.5)

2.5 = 5 * b^1

2.5 = 5 *b

Divide each side by 5

2.5/5 = b

b = 1/2

y = 5 * (1/2)^x

Step-by-step explanation:

Simple

x - 7 = 0

x = 7

x + 8 = 0

x = - 8

Option no 1 is the correct answer

Answer:

Kayla can put 9 stickers in each bag.

she can distribute it into bags of 9 stickers each of the same colour.

Step-by-step explanation:

Given;

yellow stickers = 36

red stickers = 27

blue stickers = 18

For her to distribute the stickers into bags so that each bag contains only one color of stickers and every bag has the same number of stickers without remainder.

We need to find the highest common factor of the number of the three colours.

36 = 4×9

27 = 3×9

18 = 2×9

We can see that they are all divisible by 9

Therefore, she can distribute it into bags of 9 stickers each

Final answer:

The greatest common divisor of 36, 27, and 18 is 9, so Kayla can put 9 stickers of the same color in each bag.

Explanation:

Kayla wants to distribute her stickers into bags, with each bag containing the same number of stickers of only one color. To find out how many stickers she can put in each bag, we need to find the greatest common divisor (GCD) of the numbers of stickers she has for each color. Kayla has 36 yellow stickers, 27 red stickers, and 18 blue stickers. The GCD of 36, 27, and 18 is 9. Therefore, Kayla can put 9 stickers in each bag.

Step-by-Step Solution

Identify the quantity of each color of stickers: yellow (36), red (27), blue (18).

Calculate the GCD of the three quantities: GCD(36, 27, 18) = 9.

Distribute the stickers into bags with 9 stickers of the same color per bag.

Answer:

see below

Step-by-step explanation:

V = l*w*h for the rectangular  tank

V = 70* 40*40

   =112000 cm^3 = 1mL

The water is 84000

Make this a fraction

84000/112000  = 3/4

The water fills 3/4 of the tank

1-3/4 = 1/4

It is 1/4 from the top

Find the volume of the treasure chest

V = 12*10*8 =960

Tower

V = pi r^2

   3.14 * 10^2 *10

   =3140

Water + chest + tower

84000+960+3140 =88100

This is less than 112000 so the water will not overflow

Answer:

a) 10 cm

b) Will not overflow

Step-by-step explanation:

8400 = base area × height

84000 = 70 × 40 × h

h = 30

From the top: 40 - 30 = 10cm

b) Capacity of the tank:

70 × 40 × 40

112,000 cm³

Combined volume of the two vessels:

(12 × 10 × 8) + (3.14 × 10² × 10)

960 + 3140

4,100 cm³

4100 = 70 × 40 × rise

rise = 1.464285715 cm

Since 1.464285715 < 10

It will not overflow

Answer: The height of the monitor is 12 inches.

Step-by-step explanation:

First, you need to acknowledge the Pythagorean Theorum,

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

You already have the c and the b , so you just have to plug them in to find a!

This is what it looks like when you substitute:

a² + 16² = 20²

Then, simplify.

a² + 256 = 400

Now, to isolate the variable, you have to move 256 to the other side. This, of course, means it changes from a positive to a negative number.

a² = 400 - 256

a² = 144

Now, you have to remove the square root from a. But, don’t forget, what you do to one side, you have to do to the other side. So, your equation will now look like this:

√a²  = √144

The square root of a squared is obviously just a! And the square root of 144 is 12. Therefore, we now know that:

a = 12

So, the height of the monitor was 12 inches.

Answer:

382.5

Step-by-step explanation:

9x10=90

9x9=81

13.5x9=121.5

9x10=90

180+81+121.5= 382.5

There are two triangles.

Area of a triangle = 1/2 x 10 x 9 = 45 square in.

45 x 2 = 90 square inches

One side is 9 x 9 = 81 square inches.

One side ix 10 x 9  = 90 square inches.

One side = 9 x 13.5 = 121.5 square inches.

Total surface area = 90 + 81 + 90 + 121.5 = 382.5 square inches.

Final answer:

The value of 3a+4b is 87 when a=17 and b=9. Using the kinematics equation v=u+at, the final velocity is calculated as 13.5 m/s given the initial conditions provided.

Explanation:

To find the value of 3a+4b when a=17 and b=9, we substitute the given values into the expression:

3(17) + 4(9) = 51 + 36 = 87.

Thus, the value of 3a+4b is 87.

The next part of the question involves using the kinematics equation v = u + at to find the final velocity v. We are given an initial velocity u = 3 m/s, an acceleration a = 1.5 m/s2, and a time t = 7 seconds. Plugging the values into the formula gives us:

v = 3 m/s + (1.5 m/s2)(7 s) = 3 m/s + 10.5 m/s = 13.5 m/s.

The final velocity after 7 seconds is therefore 13.5 m/s.

Answer:

The answer is A on edge

Step-by-step explanation:

The number of ways the train could be made up are 4,151,347,200.

A permutation of a set is an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

Now the given cars are 6 flatcars, 7 boxcars, and 3 livestock cars.

So the total number of cars, n  = 6 + 7 + 3

                                                   = 16

Now, a train is made up of 9 cars,

Therefore, r = 9

Hence the required number of ways the train could be made is nPr

nPr = n!/(n-r)!

nPr = 16!/(16-9)!

nPr = 16!/7!

nPr = 16*15*14*13*12*11*10*9*8

nPr = 4,151,347,200

Hence,the number of ways the train could be made up are 4,151,347,200.

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Answer:

∠ f = 37°

Step-by-step explanation:

f and 37 are vertical angles and congruent, so

∠ f = 37°

The rent of the apartment during the 7th year of living in the apartment is $2414.

Given that, principal = $1200, rate of interest =10.5% and time period = 7 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

[tex]A=1200(1+\frac{10.5}{100} )^7[/tex]

[tex]A=1200(1+0.105)^7[/tex]

[tex]A=1200(1.105)^7[/tex]

[tex]A=1200\times2.0116[/tex]

[tex]A=2413.88[/tex]

A ≈ $2414

Therefore, the rent of the apartment during the 7th year of living in the apartment is $2414.

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Final answer:

To calculate the 7th year rent after a 10.5% annual increase starting from an initial rent of $1200, use the formula for compound interest. The rent amounts to approximately $2277.60 for the 7th year.

Explanation:

Calculating Future Rent Increase

To calculate the rent of the apartment during the 7th year after a consistent annual increase, we need to apply the percentage increase formula within a compound interest framework:

Rentₙ = Rent₀ × (1 + rate)ⁿ

Where Rentₙ is the rent after n years, Rent₀ is the initial rent, rate is the annual increase rate in decimal form, and n is the number of years.

For an initial rent of $1200 with a 10.5% increase per year:

Rent for the 7th year will be calculated as follows:

Rent₀ = $1200

rate = 10.5% or 0.105 in decimal form

n = 6 (since we are starting from year 1 to year 7)

Using the formula:

Rent₇ = $1200 × (1 + 0.105)⁶

Upon calculation, the rent for the 7th year is approximately:

Rent₇ = $1200 × (1.105)⁶ ≈ $1200 × 1.898 = $2277.60

Thus, the rent of the apartment during the 7th year of living there would be approximately $2277.60

Answer:

There are many different types of equations we can use to allow x to equal 19! Below are some examples :) See if you can come up with some on your own based off of these examples:

        x = 19.......................................There's one for you :)

        x - 4 = 15..................................Add 4 to both sides

         x = 19

Answer:

Enlargement transformation

Step-by-step explanation:

A dilation is a transformation which produces an image of the same shape as the original, but may/may not be of the same size. A dilation could be an enlargement, reduction or a congruence.

The following rule applies(given the scale factor k)

therefore, since k=6/5=1.2>1, there is an enlargement transformation

Final answer:

When the scale factor is 6/5, it indicates that each dimension of the original figure is increased to achieve the new figure's dimensions, marking this transformation as an enlargement because the scale factor is greater than 1.

Explanation:

If a scale factor is 6/5, this means every dimension in the original figure is multiplied by  6/5 to get the dimensions of the new figure. Since the scale factor is greater than 1, each dimension of the original figure is increased to get the dimensions of the new figure. Therefore, this type of dilation is an enlargement, not a reduction or congruence transformation. An enlargement increases the size of an object while keeping its shape the same. In contrast, a reduction would mean the scale factor is less than 1, and a congruence transformation, which includes transformations like translation, rotation, and reflection, does not change the size at all.

Answer:

133.97 cubic yard

Step-by-step explanation:

For Cone

radius (r) = 4yd

height (h) = 8yd

Volume of the Cone

= π r^2 * h/3

= 3.14 * 4*4 *8/3 yd

= 133.97 cubic yard

To find the surface area of a prism (or any other geometric solid) we open the solid like a carton box and flatten it out to find all included geometric forms. To find the volume of a prism (it doesn't matter if it is rectangular or triangular) we multiply the area of the base, called the base area B, by the height h.

This info should help you.

Answer:

94

Step-by-step explanation:

the area of the 3 x 5 face is used 4 times rather than twice

Answer:

150 degrees

Step-by-step explanation:

HOPE THIS HELPED!

The measure of an angle between 0° and 360° coterminal with 510° is 150°. The difference between coterminal angles yields 360°.

The angles that share a common terminal side are said to be coterminal angles. So, the difference between those angles is 360°.

The given coterminal angle is 510°.

So, the reference angle = 510° - 360° = 150°

Thus, the angle is required as a measure of 150°.

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Answer:

B.supplementary

Step-by-step explanation:

Angle ABC and Angle CBD are supplementary angles, which means they add up to 180 degrees

Answer:

x=3  y=2

Step-by-step explanation:

2x-y=4

7x+3y=27

Multiply the first equation by 3

3(2x-y)=4*3

6x - 3y+12

Add this to the second equation to eliminate y

6x -3y = 12

7x+3y=27

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

13x +0y = 39

Divide each side by 13

13x/13 = 39/13

x = 3

Now find y

2x-y =4

2(3) -y = 4

6-y=4

Subtract 6 from each side

6-y-6 = 4-6

-y = -2

y=2

Answer:

for the first job is $75.05 and for the second job is $126.75

The average earning of Don is obtained as 8.09.

In order to calculate average, divide the total sum of the data to the total number of data. An average is a standard number for a given data whose value can both be more or less than it.

The total value can be calculated by multiplying the average to the number of data.

The time spent on first job is 10 hours and on second is 15 hours.

Now, the average earning per hour can be calculated as below,

(Earning for first job + Earning for second job) ÷ 25

⇒ (10 × 7.55 + 15 × 8.45) ÷ 25

⇒ 8.09

Hence, the average earnings per hour is given as 8.09.

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Answer: -5

Step-by-step explanation:

Answer:

-5 is right

Step-by-step explanation:

Step-by-step explanation:

Step 1:  Convert miles to feet

1 mile = 5280 feet

1.5 * 5280

7920 feet

Answer:  7920 feet

Answer:

Like a square, a rectangle has lines that are perpendicular to two other lines. This means it also has four right angles.

Step-by-step explanation:

Answer:

a right triangle

Step-by-step explanation:

answer: 334 days  googled it

We have been given that Sandra bought a boat for $28,800. According to her insurance company the value of the boat depreciates 7% each year. We are asked to find the value of the boat x years after Sandra purchased it.

We will use exponential decay formula to solve our given problem.

An exponential decay function is in form [tex]y=a(1-r)^x[/tex], where,

y = Final amount,

a = Initial amount,

r = Decay rate in decimal form,

x = Time.

Let us convert 7% into decimal form.

[tex]7\%=\frac{7}{100}=0.07[/tex]

Initial value of car is $28,800, so our function will be:

[tex]y=$28,800(1-0.07)^x[/tex]

[tex]y=$28,800(0.93)^x[/tex]

Therefore, the value of boat after x years would be [tex]y=$28,800(0.93)^x[/tex].

Answer:

Step-by-step explanation:

Given a general quadratic formula given as ax²bx+c = 0

To generate the general formula to solve the quadratic equation, we can use the completing the square method as shown;

Step 1:

Bringing c to the other side

ax²+bx = -c

Dividing through by coefficient of x² which is 'a' will give:

x²+(b/a)x = -c/a

- Completing the square at the left hand side of the equation by adding the square of half the coefficient x i.e (b/2a)² and adding it to both sides of the equation we have:

x²+(b/a)x+(b/2a)² = -c/a+(b/2a)²

(x+b/2a)² = -c/a+(b/2a)²

(x+b/2a)² = -c/a + b²/4a²

- Taking the square root of both sides

√(x+b/2a)² = ±√-c/a + b²/√4a²

x+b/2a = ±√(-4ac+b²)/√4a²

x+b/2a =±√b²-4ac/2a

- Taking b/2a to the other side

x = -b/2a±√√b²-4ac/2a

Taking the LCM:

x = {-b±√b²-4ac}/2a

This gives the vertex form with how it is used to Solve a quadratic equation.

Final answer:

When two number cubes are rolled, the events of rolling the same number and getting an odd sum are mutually exclusive, as one excludes the possibility of the other occurring.

Explanation:

Two events are considered mutually exclusive if the occurrence of one event excludes the possibility of the other event occurring simultaneously. When examining whether the events of rolling two number cubes are mutually exclusive, we look at two particular events:

   The numbers rolled are the same.

   The sum of the numbers rolled is odd.

Two number cubes can simultaneously show the same number, which would be an even number (since the pairs would be (2,2), (4,4), or (6,6)) and not lead to an odd sum. Therefore, if we roll the dice and get two numbers that are the same, we cannot get an odd sum. This means that these two events cannot happen at the same time, so the correct answer is:

A. Yes because if one event occurs, the other can't occur.

Answer:

38.47 square units

Step-by-step explanation:

All we have to do is first find the perimeter of the square (which is equal to the circumference of the circle), then find the radius of the circle and finally the area of the circle.

The square has a side that measures 5.5 units.

The perimeter of a square is given as:

P = 4L

where L = length of side of the square

Therefore, the perimeter of the square is:

P = 4 * 5.5 = 22 units.

This means that the circumference of the circle is 22 units.

The circumference of a circle is given as:

C = 2πR

and the area of a circle is given as:

[tex]A = \pi R^2[/tex]

where R = radius

Therefore:

22 = 2πR

=> R = 22 / (2 * 3.14)

R = 22 / (6.28)

R = 3.50 units

The area is therefore:

[tex]A = \pi * 3.50^2[/tex]

A = 38.47  square units

The area of the circle is 38.47 square units.

The area of the circle is approximately 15.64 square units, calculated using the perimeter of the square and circle formulas.

To find the area of the circle with a circumference equal to the perimeter of the square, we'll first calculate the perimeter of the square using its side length. Then, we'll use the circumference formula to find the radius of the circle. Finally, we'll use the area formula for a circle to find the area.

Step 1:

Calculate the perimeter of the square.

Perimeter of square = 4 * side length = [tex]\(4 \times 5.5 = 22\)[/tex] units.

Step 2:

Set up the equation for the circumference of the circle.

Circumference of circle =[tex]\(2\pi \times\)[/tex] radius = Perimeter of square.

Step 3:

Solve for the radius.

[tex]\[2\pi \times \text{radius} = 22\][/tex]

[tex]\[\text{radius} = \frac{22}{2\pi}\][/tex]

Step 4:

Use the radius to find the area of the circle.

Area of circle = [tex]\(\pi \times \text{radius}^2\)[/tex]

Step 5:

Substitute the value of the radius and calculate.

[tex]\[Area = 3.14 \times \left(\frac{22}{2\pi}\right)^2\][/tex]

[tex]\[Area \approx 15.64\][/tex]

The area of the circle with a circumference equal to the perimeter of the square is approximately [tex]\(15.64\)[/tex] square units.

9514 1404 393

Answer:

Step-by-step explanation:

Regardless of the diameter, the radius is half the diameter. For this sphere, it is 5/2 m = 2.5 m.

__

The height of the sphere is equal to its diameter, so is 2r. The volume of a cylinder with radius r and height 2r is ...

  V = πr²h = πr²(2r) = 2πr³

The volume of a sphere with radius r is ...

  V = 4/3πr³

Then the ratio of sphere volume to cylinder volume is ...

  (4/3πr³)/(2πr³) = (4/3)/2 = 2/3

The sphere volume is 2/3 that of a cylinder with the same radius and height.

Answer:

D. 80

Step-by-step explanation:

edge 2021

The perimeter of the parallelogram LMNO is 80 cm

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, in a parallelogram LMNO, the length of L M is 22 cm and the length of M N is 18 cm.

Perimeter of a parallelogram = 2(sum of two adjacent sides)

= 2(18+22)

= 2×40

= 80

Hence, the perimeter of the parallelogram LMNO is 80 cm

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