2. In the xy-plane above, ABCD is a square and point E is the center of the square. The coordinates of points C and E are (7,2) and (1,0), respectively. Write an equation of the line that passes through points A, E, and C. 6 2 C X A D

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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If the recycling center gives Marry $0.40 per pound money she will earn for both days of recycling is $11.20

What information is given in the question?

Marry collected 16.2 pounds of cans for the recycling center on Monday.

On Tuesday, she collected 11.8 pounds.

The recycling center gives her $0.40 per pound.

According to the given question:

To find how much money she will earn for both days of recycling, calculate money earned on Monday and Tuesday. Then add the amount to get the amount earned on both days.

Money earned by Marry on Monday = 16.2 x 0.40 = $6.48

Similarly, money earned by Marry on Tuesday = 11.8 x 0.40 = $4.72

Therefore, Total money earned by Marry for both days

= 6.48 + 4.72

= $11.20

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Answer:

5/6

Step-by-step explanation:

i used a caculater

BRAINLIEST PLEASE

Answer:

The integer -37 represents the direction and the distance covered by Jose from Gainesville to Ocala.

Step-by-step explanation:

The direction is represented by the sign that accompanies the distance, since Jose is returning from Gainesville, then the direction must represented by a minus sign (-), since he is travelling southwards. The distance is the magnitude of the length covered by Jose during his return. Hence, distance is represented by the natural number 37.

Finally, the integer -37 represents the direction and the distance covered by Jose from Gainesville to Ocala.

Answer:

2/-3

Step-by-step explanation:

Hope this helped. And I know that you can choose more than one, but I'm pretty sure this is the only one that's equivalent to -2/3

Answer:

33.51

Step-by-step explanation:

You need to use the equation \(\frac{4}{3} \pi r\)³.

Hope this helps.

Answer:10.7π

Step-by-step explanation:

radius=r=2

volume of sphere=4/3 x π x r x r x r

Volume of sphere=4/3xπx2x2x2

Volume of sphere=(4xπx2x2x2) ➗ 3

Volume of sphere=32π ➗ 3

Volume of sphere=10.7π

g is the centroid of triangle abc, the value of x is 2/3.

The length of segment DG is (2/3) * (length of AB) ,The length of segment AG is (1/3) * (length of AB),The length of segment AD is (1/3) * (length of AB).

The centroid of a triangle is the point at which the three medians of the triangle intersect each other. In other words, it is the point of intersection of the three lines which each divide the opposite side of the triangle into two equal parts.

Let us consider a triangle ABC with vertices A (a1, b1), B (a2, b2), and C (a3, b3). The x coordinate of the centroid G (x, y) is given by:

x = (a1 + a2 + a3) / 3

The y coordinate of the centroid G (x, y) is given similarly as x

In your question, the x coordinate of the centroid G is given as x = 2/3. This means that the x coordinate of G is 2/3 of the way between A and B.

Therefore, the length of segment DG is (2/3) * (length of AB).

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Answer:

Hello! Thank you a lot! My nice thing would have to be keep going even when things get hard. We all have something unique about us and were all on a journey to figure out what that is. Don't let anyone take away what makes you unique.

Step-by-step explanation:

Answer:

Purchase Price = $150 and Total Price = $162

Step-by-step explanation:

Purchase price = Tax Amount / Tax Percentage (as decimal)

Purchase Price = $12 / .08

Purchase Price = $150

Total Price = Purchase Price + Tax

Total Price = 150 + 12 = $162

I hope this helps!

-The Business Man

Answer:

Kirsty raised £143.75 and Flo raised £28.75

Step-by-step explanation:

x = money raised by Flo

5*x = money raised by Kirsty

6*x = money raised together

6x = £172.50

Now divide each side by 6:

x = £172.50:6

x = £28.75 (money raised by Flo)

£172.50-£ 28.75 = £143.75 (money raised by Kirsty)

Kirsty raised £143.75 and Flo raised £28.75

Answer:

y=-4x+5...

Step-by-step explanation:

y=-4x+5...

Answer:

\(\bold{V=7048.48 ft^3}\)

Step-by-step explanation:

Solution Given:

radius(r)=12

In right-angled triangle

Hypotenuse = 18

base angle =60°

Note:
In a right-angled triangle, we can use the trigonometric ratios sine, cosine, and tangent to relate the angles and sides of the triangle.
Here are the trigonometric ratios for a right-angled triangle:

Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

\(\boxed{\bold{sin(A) =\frac{ opposite}{hypotenuse}}}\)

Cosine (cos): The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

\(\boxed{\bold{cos(A) = \frac{adjacent}{hypotenuse}}}\)

Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

\(\boxed{\bold{tan(A) =\frac{ opposite}{adjacent}}}\)

Now for the question:

Over here the relation between opposite or height and hypotenuse is given by Sine, So using this formula:

\(\bold{sin(60^0) =\frac{ opposite\:or\ height}{18}}\)

doing criss-cross multiplication:

Sin 60°*18=opposite or height

\(\frac{\sqrt{3}}{2}*18\) =opposite or height

opposite or height(h)=\(9\sqrt{3}\)

Again,

We have

\(\boxed{\bold{Volume\:of\:cylinder= \pi * r^2 * h}}\)

where:

π (pi) is a mathematical constant approximately equal to 3.14

r is the radius of the base of the cylinder

h is the height of the cylinder

Now Substituting value

\(Volume = \pi * r^2 * h\\Volume=3.14*12^2*9\sqrt{3}\\Volume=\bold{7048.48 ft^3}\)

Answer:

225 stickers

Step-by-step explanation:

(900+450)/2 = 1,350/2= 675

so, Carla shared with Justin :

900-675 = 225 stickers

9514 1404 393

Answer:

  91, including Mr. Jones

Step-by-step explanation:

The total cost for n people to go on the trip will be ...

  C(n) = 45n +1295

If Mr. Jones does not pay anything, this cost is divided among the remaining (n-1) persons, so the cost per person is ...

  \(c(n)=\dfrac{C(n)}{n-1}\\\\c(n)=\dfrac{45(n-1)+45+1295}{n-1}=45+\dfrac{1340}{n-1}\)

We want to find n such that c(n) < 60.

  \(45+\dfrac{1340}{n-1}<60\\\\\dfrac{1340}{n-1}<15\qquad\text{subtract 45}\\\\\dfrac{1340}{15}<n-1\qquad\text{multiply by $\dfrac{n-1}{15}$}\\\\90\dfrac{1}{3}<n\qquad\text{add 1}\)

A total of 91 people would need to attend in order for the cost per person to be less than $60.

Answer:

(fog)(x) = 2sqrt(x) + 3

Domain: {x | x ∈ R, x>=0}

Step-by-step explanation:

(fog)(x) = f(g(x))

let f(a) = f(g(x))

f(a) = 2a+3 = 2(g(x)) + 3 = 2sqrt(x) + 3

To find domain, pick most restricting domain of the functions that make up the compound function.

The value of derivative of d/dx[5f(x)-4x] at x=2 = 16.

From the table:

At x=2,

f'(x) = 4

f(x) = 4x

= d/dx(5*4x - 4x)

= d/dx(20x - 4x)

= d/dx(16x)

= 16

Therefore the value of derivative of d/dx[5f(x)-4x] at x=2 = 16.

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According to the question the total area in black around the star is 972 cm².

Area is a two-dimensional measurement of space, representing the total amount of space taken up by a shape or object. It is typically measured in units of square meters, square feet, or square miles. Area can be used to measure the size of a house, a room, a parcel of land, or any other two-dimensional shape. Calculating area requires measuring the length and width of the shape, and then multiplying these two measurements together. Area is an important concept in mathematics, as it is used in many calculations, such as the area of a circle, the area of a triangle, and the area of a trapezoid.

This is because each side of the black square is 12 cm, and the star is surrounded by 8 black squares. To calculate the total area, we need to multiply the length of each side (12 cm) by the number of squares (8). This gives us 96 cm. We then need to square this number to get the area, which is 972 cm².

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Answer: 6 3/4 I hope this helps

Step-by-step explanation:

27/4

Convert the improper fraction into a mixed number

6 3/4

Mixed number-A number written as a whole number and a fraction.

The total amount to each person end up paying $20.54.

To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.

To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.

The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.

Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.

To split this evenly among the five people, we divide by 5:

$102.72 ÷ 5 = $20.54

So each person will end up paying $20.54.

20% of $85.60 is ($85.60 * 0.20) = $17.12

Add the tip to the total bill:

$85.60 + $17.12 = $102.72

Divide the total amount by the number of people (5): $102.72 / 5 = $20.54

Therefore, the answer is B. $20.54.

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Answer:

The correct answer is A.

Step-by-step explanation:

The correct answer is A.

To find the length of one side of the square, we need to take the square root of the area. Therefore, the square root of 90 is approximately 9.49 feet. Since this value falls between 9 feet and 10 feet, but is closer to 9 feet, the statement "√90 feet is between 9 feet and 10 feet but is closer to 9 feet" is true. So, Jimmy should cut the carpet to 9.49 feet to fit the square-shaped room.

Answer:

Step-by-step explanation:

The the length of LJ is approximately 3.5.OptionD) is correct.

To find the length of LJ, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle.

Let's denote the length of JL as x. Then, we can set up the following proportion:

sin(23°) / LJ = sin(89°) / KL

where KL is given as 9.

We can simplify this proportion by using the fact that sin(89°) = cos(1°) (since the sine of the complement of an angle is equal to the cosine of the angle), and by using a calculator to find the values of sin(23°) and cos(1°):

0.3919 / LJ = 0.0175 / 9

Multiplying both sides by x and then dividing both sides by 0.0175, we get:

LJ = 0.3919*9/ 0.0175

x ≈ 3.5

Therefore, the length of LJ is approximately 3.5.OptionD) is correct.

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The cost of one small box of fruit and the cost of one large box of fruit is $11.5 and $14.5 respectively.

Let

cost of one small box of fruit = x

cost of one large box of fruit = y

15x + 15y = 390

20x + 25y = 592.50

From (1)

x + y = 26

x = 26 - y

Substitute x = 26 - y into (2)

20x + 25y = 592.50

20(26 - y) + 25y = 592.50

520 - 20y + 25y = 592.50

- 20y + 25y = 592.50 - 520

5y = 72.50

divide both sides by 5

y = 72.50/5

y = 14.5

Substitute y = 14.5 into

15x + 15y = 390

15x + 15(14.5) = 390

15x + 217.5 = 390

15x = 390 - 217.5

15x = 172.5

divide both sides by 15

x = 172.5/15

x = 11.5

Therefore, small box cost $11.5 and large box cost $14.5

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Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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Answer:

NM = 17, LY = 5, m<NLY = 53.13 degrees, m<NMY = 28.07 degrees

Step-by-step explanation:

To solve for NM, you just use the Pythagorean theorem,

\(8^{2} + 15^{2} = x^{2}\)

64 + 225 = \(x^{2}\)

289 = \(x^{2}\)

\(17 = x\)

To solve for LY, you can use geometric mean,

\(\frac{10}{y} = \frac{15+y}{10}\\\\100 = 15y + y^{2} \\y^{2} +15y - 100 = 0\\(y+20)(y-5) = 0\\y= 5\)

To solve for the other angles, use the inverse.

Sin-1, = 8/10

= 53.13

Other angle =

Tan-1 = 8/15

= 28.07

Hope this helps, I put a lot of time into this :)

The probability that a point falls in the red-shaded square is given as follows:

p = 9/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probability that a point falls in the red shared square is then given by the division of the area of the red shaded square by the division of the area of the larger square.

The area of the red-shaded square is given as follows:

3² = 9.

The area of the larger square is given as follows:

4² = 16.

Hence the probability is given as follows:

p = 9/16.

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Explanation

So for the first one

For the second one

For the last one

Therefore, the answers are options 1 and 111

Thus, option C is correct