Cruz and erica were both getting ready for soccer. cruz ran 1 lap around the school. erica ran 3 laps around the playground. erica said, i ran more laps, so i ran farther. cruz said, 4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. my laps are much longer, so i ran farther. 1. who is right?

Work:

First it's a rectangle so its area is equal to the product (multiplication) of both sides of the rectangle (dimensions). A = a x b = ab

NOW: knowing the the circumference or perimeter is equal to 400m, we can say that P = 400 = 2(a+b) = 2a + 2b since the given polynom is rectangle. 2a + 2b = 400 <==> 2a = 400 - 2b <==> a = 200 - b.

We gave an expression of a in function of b. Now we can replace the variable a by 200 - b in the first expression of the area.

A = ab = (200-b)b = 200b-b^2 = -b^2 + 200b

A is now a quadratic equation. We note A(b) the epression -b^2 +200b so:

A(b) = -b^2 +200b

We can already see that A is a quadratic equation of the form:

ax^2 + b + c. The a coefficient is negative which will lead to closed parabola when looking from the top. Now we need to find the maximum of the function by using the derivatives:

A(b) = -b^2 +200b <==> A'(b) = -2b + 200b

and -2b + 200b = 0 <==> b = 100;

So the derivative function crosses the x-axis at (100; 0).

So is increasing over ]-∞; 100] and decreasing over [100; ∞[.

We obtain a maxima on (100; x) with A. To find it we need to replace 100 by b in the function A.

A(b) = -b^2 + 200b

<==> A(100) = -100^2 + 200 x 100 = - 10000 + 20000 = 10000

Now let's find a: if b = 100 what equals a ?

We know that ab = 10000 <==> 100a = 10000 <==> a = 100;

And we verify that ab = 100 x 100 = 10000.

The rectangle needs to be a square to reach the maximum area of 10000m^2 or also 0.01 km^2.

Q.E.D.

Answer:

D

Step-by-step explanation:

Yep, what you did there is correct!

The expression was: [tex](\frac{5^2}{4} )^4[/tex]

So let's solve this step by step.

First the numerator

[tex](5^2)^4[/tex]

Is the same thing as

[tex]5^8[/tex]

Since the exponents are multiplied.

Next is the denominator
[tex]4^4[/tex]

This can stay the same, since solving it as 4 x 4 x 4 x 4 will only make the fraction more complicated. Also, the answer choices below show that the denominator stays in exponential form.

==> [tex]\frac{5^8}{4^4}[/tex] is our final answer!

So the answer to this question is D. You got the question correct! :)

I hope that helped!!

The expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.

The air pressure at an altitude of 3,000 meters above the surface of the Earth is calculated as follows;

Po = ρgh

where;

Substitute the value of altitude into the equation;

Po = 3,000ρg

Thus, the expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.

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The measure of ∠6 is 54 degrees.

When parallel lines are cut by a transversal, angle relationship are formed. Therefore,

∠6 = 5x + 9 (vertically opposite angles)

∠6 = ∠2

Hence,

∠2 + 13x + 9 = 180

5x + 9  + 13x + 9 = 180

18x = 162

x = 162 / 18

x = 9

Hence,

∠6 = 5(9) + 9  54°

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The number of cuboids of dimension 2 cm x 3 cm x 4 cm, required to make a cube is 9.

Dimensions of the cuboid Deeksha made are given as 2 cm x 3 cm x 4 cm.

Thus, the volume of this cuboid = 2*3*4 cm³ = 24 cm³.

Using the formula for the volume of cuboid as the product of the three sides.

Deeksha wants to make a cube combining some number of these cuboids.

Assuming the side length of the cube to a, the volume of the cube = a³.

Assuming the number of cuboids required to make 1 cube to be n, we can write that a³ = n*(24 cm³).

To make this relation true, we need the right-hand side to be a perfect cube.

Prime factorizing the volume of the cuboid, we get 24 cm³ = 2³ * 3 cm³.

To make it a perfect cube, we need to multiply 3², by it.

Thus, n = 3² = 9.

Thus, the number of cuboids of dimension 2 cm x 3 cm x 4 cm, required to make a cube is 9.

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The provided question is incorrect. The correct question is:

"Deeksha made cuboid of size 2 cm x 3 cm x 4 cm. how many such

cuboids will be required to make a cube?"

Answer:

D: (-∞,∞)

R: (0,∞)

Step-by-step explanation:

This is a parabola, so the domain of this function is always:
D:(-∞,∞)
The y-values of this parabola do not go any lower than 0, and it goes upwards in the positive y-direction. So, the range for this function is:
R:(0,∞)

Answer:

the opposite sides of the parallelogram are equal.

so DR = HW mean : 2 y + 2 = 3 y - 9

3y - 2y = 9+2

y = 11

RW = y+4 = 11+4 = 15

DH = RW

so, 3 x + 6 = 15

3x = 15-6 = 9

x = 3

Answer:

Step-by-step explanation:

Solution

You want to find the probability of one certain event happening. For example, you want the die to come up 5 and you want the 6 to be drawn from the cards.

The total number of outcomes is 6 (for the die) times 10 for the cards.

One 1 outcome is possible.

So the vent probability is 1/6*10 = 1/60. You will have to translate this to the choices you have been given. 1/60 = 0.0167 is another possibility.

Answer

1/60 or 0.0167

Answer:

9

Step-by-step explanation:

See the attached image.

Answer: D and B

Step-by-step explanation:

Formula for two terms = a + b

Therefore,

D and B have two terms aka one plus sign

D. a + c

B. m^4 + 6m

Hi! ❄

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

The sum of two terms is what we get after adding these two terms.

If you add two positive terms, you put a + sign in between these terms.

[tex]\sf{Example\!\!:a+b}[/tex]

If you add two negative terms, you put a - sign in between these terms.

[tex]\sf{Example\!\!:a-b}[/tex] (this is the same as [tex]\sf{a+-b}[/tex])

Let's look at the provided choices to see which one works.

It doesn't, because [tex]\sf{xy\neq x+y}[/tex]. In this expression a number x was multiplied by a number y. So this one doesn't check.

One down, three to go.

It does, because [tex]\sf{m^4+6m\stackrel\checkmark{=}m^4+6m}[/tex]. A number m was multiplied by itself 4 times, and then the product of that samee number m and 6 was added to it.

So this one checks.

It doesn't. It is indeed a sum, but we need 2 terms, not 3

So this one doesn't work.

It does, because [tex]\sf{a+c\stackrel\checkmark{=}a+c}[/tex]. So Choice D. also works.

Hope that made sense !!

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

[tex]\star\tiny\pmb{calligraphy}\star[/tex]

For each of the following distance matrices of graph, the

This is used to refer to the fact that there would be a maximum distance that exists between the pair of vertices.

This used to refer to the minimum eccentricities of the vertices

This is used to show all of the vertices that have minimum eccentricities.

We have

e 1 = 3

e 2 = 3

e3 = 2

e4 = 3

e 5 = 3

e 6 = 3

e 7 = 3

e8 = 2

e 9 = 3

e 10 = 2

Then the the diameter = maximum eccentricity = 3

The radius = minimum eccentricity = 2

center = [3, 8,10]

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Answer:

y = -6x + 7.5

Explanation:

To find perpendicular bisector equation:

Given points: B(-2, 1), C(4, 2)

First find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\sf slope: \dfrac{2-1}{4-(-2)} } = \dfrac{1}{6}[/tex]

Then the perpendicular slope will be negatively inverse.

[tex]\sf perpendicular \ slope \ (m) : -(\dfrac{1}{6} )^{-1} = -6[/tex]

Then find the mid point coordinates between BC:

[tex](x_m, y_m)= \sf (\dfrac{x_1 + x_2}{2} , \dfrac{y_2 + y_1}{2} )[/tex]

[tex](x_m, y_m) = \sf (\dfrac{-2 + 4}{2} , \dfrac{1 + 2}{2} )[/tex]

[tex](x_m, y_m) = \sf ( 1 , 1.5 )[/tex]

Then find equation:

y - yₘ = m(x - xₘ)

y - 1.5 = -6(x - 1)

y = -6x + 6 + 1.5

y = -6x + 7.5

The answer is y = -6x + 15/2.

First, find the slope of BC.

m = Δy/Δx

m = 2 - 1 / 4 - (-2)

m = 1/6

Hence, the slope of the perpendicular bisector will be the negative reciprocal of the given line.

m' = - (1/ [1/6])

m' = -6

Now, find the midpoint of BC.

M = (-2 + 4 / 2, 2 + 1 / 2)

M = (1, 3/2)

Now, we can find the equation of the perpendicular bisector using the point slope form of equation.

y - y₁ = m (x - x₁)

y - 3/2 = -6 (x - 1)

y - 3/2 = -6x + 6

y = -6x + 15/2

Statements is TRUE

Based on the graph of the general solution to the differential equation dy over dx equals 2 times x - 2 times y = dy/dx=2x-2y.

A differential equation's solution is an expression for the dependent variable in terms of one or more independent variables that satisfy the relationship.

The statement which is true is the slopes are all positive in quadrant I.

Given the differential equation is dy/dx=2x-2y

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

Given dy/dx=2x-2y

now slope=2x-2y

Along x-axis, y=0. So, slope=2x+0.

Since it depends upon x hence the slope along the y-axis are not horizontal.

Along y-axis, x=0. So, slope -2y+0.

The slope along the x-axis are also not horizontal.

In quadrant I:

x,y≥20

So, dy/dx ≥20

Therefore, the slopes are all positive in quadrant I. In quadrant IV,

x≥0,y≤0

so, dy/dx is not always positive.

The slope are not all positive in quadrant IV:

Therefore, the slope are all positive in quadrant I for the differential equation dy/dx=2x-2y.

General solution to the differential equation =

dy/dx=2x-2y.

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Complete Question:

Based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true?

The slopes along the y-axis are horizontal.

The slopes along the x-axis are horizontal.

The slopes are all positive in Quadrant 1.

The slopes are all positive in Quadrant 4.

The purchase price of the new car if the sales tax is $3500 is $50000

Let the amount of sales tax be A and the purchase price be p

If the amount of sales tax is directly proportional to the purchase price, this is expressed as:

S = kp

If S = $1750 and p = $25000, the;

k = S/p

k = 1750/25000

k = 175/2500

If the sales tax is $3500, the purchase price will be given as:

S = kp
3500 = 175/2500 p

175p = 3500*2500
175p = 8750000

p = 8750000/175

p = 50000

Hence the purchase price of the new car if the sales tax is $3500 is $50000

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The equation that describes the number of bacteria in both the foods when they are mixed is; Option C: 35T₂ + 55T + 450

We are given the equations that describes the number of bacteria in both the foods when they are mixed.

Equation for first bacteria is;

N₁(T) = 15T₂ + 60T + 300

Equation for second Bacteria is;

N₂(T) = 20T² - 5T + 150

The equation that describes the number of bacteria in both the foods when they are mixed is;

N₁(T) + N₂(T) = 15T₂ + 60T + 300 +  20T² - 5T + 150

⇒ 35T₂ + 55T + 450

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Hello,

I think it is 9y² + 21y - 18 = 0

we have a = 9 ; b = 21 and c = -18

∆ = b² - 4ac = 21² - 4 × 9 × (-18) = 1089 > 0

x1 = (-b - √∆)/2a = (-21 - 33)/9 = 6

x2 = (-b + √∆)/2a = (-21 + 33)/9 = 12/9 = 4/3

S = {4/3 ; 6}

Answer:

The 18th term would be "-70"

Answer:

-70

Step-by-step explanation:

Using the Pythagorean theorem and the law of sines, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are: A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°

The theorem states that the square of the longest side of a right triangle equals the sum of the squares of the lengths of the other two smaller sides of the right triangle.

The points, M(3,2), E(3,−3), and R(9,−3) has been plotted on the graph which shows that angle E  is a right triangle, therefore:

m∠E = 90 degrees.

Find ME and ER:

ME = 5 units

ER = 6 units.

Using the Pythagorean theorem, find MR:

MR = √(ME² + ER²)

MR = √(5² + 6²)

MR = √(25 + 36)

MR = 7.81 units

Using the law of sines, find m∠M:

sin M/ER = sin E/MR

sin M/6 = sin 90/7.81

sin M = (sin 90 × 6)/7.81

sin M = 0.7682

M = sin^(-1)(0.7682)

m∠M ≈ 50°

m∠R = 180 - 50 - 90

m∠R = 40°

Thus, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are:

A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°

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The angles ∠1 ≅ ∠4 since the line BD bisects ∠ABC, AD║ BC, and AB ║ CD. This is obtained by using the angle bisector theorem, alternate interior angles, and the transitive property of congruence.

Transitive property:

If ∠a and ∠b are congruent and ∠b and ∠c are congruent, then ∠a and ∠c are also congruent.

I.e., If ∠a ≅ ∠b and ∠b ≅ ∠c, then ∠a ≅ ∠c.

The angles bisector theorem states that the ray or line which bisects the angle divides the angle into two equal parts.

I.e., If line BD bisects the angle ∠ABC, then ∠B = ∠B1 + ∠B2

(where ∠B1 = ∠B2)

The line BD bisects ∠ABC, AD║BC, and AB║CD

The line BD bisects ∠ABC. So,

∠B = ∠3 + ∠4

According to the angle bisector theorem, ∠3 ≅ ∠4.

Since AD║BC and AB║CD, the alternate angle are congruent.

I.e., ∠3 ≅ ∠1

Thus, by the transitive property of congruence,

∠1 ≅ ∠4

Hence proved.

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See below for the proof that the areas of the lune and the isosceles triangle are equal

The area of the isosceles triangle is:

[tex]A_1 = \frac 12r^2\sin(\theta)[/tex]

Where r represents the radius.

From the figure, we have:

[tex]\theta = 90[/tex]

So, the equation becomes

[tex]A_1 = \frac 12r^2\sin(90)[/tex]

Evaluate

[tex]A_1 = \frac 12r^2[/tex]

Next, we calculate the length (L) of the chord as follows:

[tex]\sin(45) = \frac{\frac 12L}{r}[/tex]

Multiply both sides by r

[tex]r\sin(45) = \frac 12L[/tex]

Multiply by 2

[tex]L = 2r\sin(45)[/tex]

This gives

[tex]L = 2r\times \frac{\sqrt 2}{2}[/tex]

[tex]L = r\sqrt 2[/tex]

The area of the semicircle is then calculated as:

[tex]A_2 = \frac 12 \pi (\frac{L}{2})^2[/tex]

This gives

[tex]A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2[/tex]

Evaluate the square

[tex]A_2 = \frac 12 \pi (\frac{2r^2}{4})[/tex]

Divide

[tex]A_2 = \frac{\pi r^2}{4}[/tex]

Next, calculate the area of the chord using

[tex]A_3 = \frac 12r^2(\theta - \sin(\theta))[/tex]

Recall that:

[tex]\theta = 90[/tex]

Convert to radians

[tex]\theta = \frac{\pi}{2}[/tex]

So, we have:

[tex]A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))[/tex]

This gives

[tex]A_3 = \frac 12r^2(\frac{\pi}{2} - 1)[/tex]

The area of the lune is then calculated as:

[tex]A = A_2 - A_3[/tex]

This gives

[tex]A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)[/tex]

Expand

[tex]A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2[/tex]

Evaluate the difference

[tex]A = \frac 12r^2[/tex]

Recall that the area of the isosceles triangle is

[tex]A_1 = \frac 12r^2[/tex]

By comparison, we have:

[tex]A = A_1 = \frac 12r^2[/tex]

This means that the areas of the lune and the isosceles triangle are equal

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Answer:

Step-by-step explanation:

b = a + b table chart what equation represents the relationship between a and b shown in the table .

Answer:

84.82 cm

Step-by-step explanation:

Volume of a cone: [tex]\frac{1}{3} \pi r^2h[/tex]

[tex]\frac{1}{3} \pi r^2h\\\\\\\\= \frac{1}{3}\pi (3)^2(9)\\\\= \frac{1}{3}\pi(9)(9)\\\\\\\= \frac{1}{3} \pi (81)\\\\= 27\pi \\[/tex]

≈ 84.82 cm

Answer: (2, 18)

Step-by-step explanation:

When x=2, [tex]f(2)=2(3)^{2}=18[/tex].

So, it should pass through (2, 18).

Answer:

(2, 18)

Step-by-step explanation:

i posted this at 1:19 in the morning, good day

Answer:

4ft^3

Step-by-step explanation:

1.333333*3*1^3=4

To start finding the volume of this sphere, we get the following data:

To find the volume we apply the following formula:

We substitute our data in the formula and solve:

Substituting values into the equation

Calculate exponent cubed

Multiplying

Therefore, the volume of the sphere is 32 ft³.

The mean of the data given is 13.4364 and.the standard deviation is 1.788.

It should be noted that the mean is the average of the giving set of numbers. In this situation, the mean is 3.1998.

E(X²) will be:

= (0² × 0.0408) + (1² × 0.1304) .... + (12² × 0.0001)

= 13.4364

Var(X) = 13.4364 - 3.1998²

= 3.198

The standard deviation will be:

= ✓3.198

= 1.788

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The area of the new rectangle will be 25 times that of the original

A rectangle is a 2D shape that has 4 sides and equal interior angles

If rectangle has a width of 2.45 feet and a length of 6.5 feet, then;

Width = 2.45 feet

Length = 6.5feet

A = 2.45 * 6.5

A = 15.925 square feet

If each side of the rectangle is increased by a factor of 5, hence;

W1 = 5(2.45) = 12.25feet

L1 = 5(6.5) = 32.5 feet

Determine the area of the new rectangle

A = 12.25 * 32.5

A = 398.125 square feet

Ratio of the area

A1/A = 398.125/15.925

A1 = 25A

Hence the area of the new rectangle will be 25 times that of the original

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Answer:

13500 ft²

Step-by-step explanation:

     We can find the width of the rectangle using Pythagorean theorem.

AD² + DC² = AC²

180² + DC²  = 195²

32400 + DC² = 38025

              DC² = 38025 - 32400

                     = 5625

               DC = √5625

                      = 75 ft

length = 75 ft

Width = 180 ft

[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]

                                 =  75 * 180

                                  = 13500 ft²