A commercial contractor needs to clear a plot of land for a new bank. Ryan can clear the lot in 7.5 hr. Ethan can do the same job in 10.5 hr. How long will it take them, working together, to clear the land ?

Answer:

[tex]\large\boxed{x^2+y^2+4x-2y+1=0}[/tex]

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

The general form of an equation of a circle:

[tex]x^2+y^2+Dx+Ey+F=0[/tex]

We have the center (-2, 1). Substitute to the equation in the standard form:

[tex](x-(-2))^2+(y-1)^2=r^2\\\\(x+2)^2+(y-1)^2=r^2[/tex]

Put thr coordinates of the point (-4, 1) to the equation and calculate a radius:

[tex](-4+2)^2+(1-1)^2=r^2\\\\r^2=(-2)^2+0^2\\\\r^2=4[/tex]

Therefore we have the equation:

[tex](x+2)^2+(y-1)^2=4[/tex]

Convert to the general form.

Use [tex](a\pm b)^2=a^2\pm 2ab+b^2[/tex]

[tex](x+2)^2+(y-1)^2=4\\\\x^2+2(x)(2)+2^2+y^2-2(y)(1)+1^2=4\\\\x^2+4x+4+y^2-2y+1=4\qquad\text{subtract 4 from both sides}\\\\x^2+y^2+4x-2y+1=0[/tex]

The mechanical energy will be 100 Joules

Mechanical energy is the sum of kinetic and potential energy in an object that is used to do work. In other words, it is energy in an object due to its motion or position, or both.

So

Mechanical energy = 60J + 40J

Mechanical energy = 100 Joules

Answer:

The correct answer option is C. 100 Joules.

Step-by-step explanation:

We are given that Greta jumps up 2 feet into the air. Her potential energy is 60 Joules while her kinetic energy is 40 Joules.

We are to calculate her total mechanical energy which will be the sum of her potential energy and her kinetic energy.

So we simply need to add the two given values of the energies.

Total mechanical energy = 60 + 40 = 100 Joules

5/6 × 3/4

=5/2 × 1/4

=5/8

Answer

5/8 students buy orange juice

To find the fraction of students who buy orange juice, we first find the fraction of students who buy juice and then multiply it by the fraction that buy orange juice.

To find the fraction of students who buy orange juice, we first need to determine the fraction of students who buy juice. Since 5/6 of students buy juice, this means that 5/6 of the total number of students buy juice.

Next, we need to determine the fraction of students who buy orange juice out of those who buy juice. Since 3/4 of the students who buy juice buy orange juice, this means that 3/4 * 5/6 of the total number of students buy orange juice.

To find the final fraction, we multiply the two fractions:

3/4 * 5/6 = (3 * 5) / (4 * 6) = 15 / 24 = 5/8

Therefore, the fraction of students who buy orange juice is 5/8.

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I believe your answer is C). because 5% of 60,000 is 3,000, then 3,000 x 15 = 45,000.

Answer:

51 and 64

Step-by-step explanation:

The Empirical Rule states that 68% of normally distributed data lies within one standard deviation of the mean.

Hence, if the mean is 57.5, one standard dev. above that is 57.5+6.5, or 64, and one standard dev. below the mean is 57.5-6.5 = 51.

Thus,

we can conclude that 68% of the students received scores between 51 and 64.

Final answer:

Approximately 68% of the eighth-grade students received scores between 51 and 64.

Explanation:

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. So, in this case, 68% of the eighth-grade students received scores between the mean of 57.5 minus one standard deviation of 6.5 and the mean plus one standard deviation.

Calculating the range:

Therefore, we can conclude that approximately 68% of the students received scores between 51 and 64.

Answer:

All together the expression is 6n2 + 6m + 2n.

The number of terms is 3.

A coefficient is 6, 6 or 2.

A factor is 2(3n2+3m + n)

Step-by-step explanation:

Simplify the expression by combining like terms. Like terms are terms which have the same base.

-3n -2m + 5n + 8m + 6n2

These are the like terms:

-3n + 5n = 2n

-2m + 8m =6m

6n2

All together the expression is 6n2 + 6m + 2n.

The number of terms is 3.

A coefficient is 6, 6 or 2.

A factor is 2(3n2+3m + n)

[tex]You're \ asking: 90/100 \ divided \ by \ 15.\\\\Let's \ do \ this \ together \ in \ steps!\\\\Divide.\\9/10 \ divided \ by \ 15.\\\\Make \ a \ fraction.\\\\9/10 \ x \ 1/15\\\\Simplify.\\\\9x1/10x15\\\\Simplify.\\\\9/150\\\\Simplify.\\\\\fbox{3/50}\\\\\bold{Thanks \  for \ using  \ Brainly!}[/tex]

Answer:

The answer is (1, -8)

Step-by-step explanation:

The vertex of a parabola is the lowest or highest point on the parabola.

In this graph, the vertex would be the lowest point.

Visually, you can see that the lowest point on this graph is at the point (1, -8).

Answer:

see explanation

Step-by-step explanation:

Given

x² + 17x - 60 = 0

To factor the quadratic

Consider the factors of the constant term (- 60) which sum to give the coefficient of the x- term (+ 17)

The factors are + 20 and - 3, since

product = + 20 × - 3 = - 60 and sum = + 20 - 3 = + 17, thus

x² + 17x - 60 = (x + 20)(x - 3) = 0

Equate each factor to zero and solve for x

x + 20 = 0 ⇒ x = - 20

x - 3 = 0 ⇒ x = 3

Answer:

6

Step-by-step explanation:

f (x)=x^2and g(x)=x+6  (I will assume you meant x not c)

The first step if to find f(0)

f(0) = 0^2 = 0

Now we find g(f(0))= g(0)

g(0) = 0+6  = 6

g(f(0) =6

If you meant c

Then g(f(0) = c+6

Answer:

if you mean minutes the answer is 150 seconds

Step-by-step explanation:

each minute is 60 seconds so 2 minutes is 120 and the half a minute is 30 seconds so 60+60+30=150

if you ment hours then the answer is 9000 seconds

2 and a half days= 216000

Answer: Depends

Step-by-step explanation: For minutes, it's 150 seconds. Every minute is 60 seconds, and 2.5*60 = 150. If you mean hours, then it's 9000 seconds. That equation would be [tex](60*60)*2.5[/tex]. If you mean milliseconds, then it would be 0.0025 seconds.

The product of −8/5, −3/2, and −10 is −24. The calculation involves two steps: first multiplying the two negative fractions, which results in a positive product, and then multiplying that result by a negative integer, resulting in a negative final product.

To find the product of −8/5, −3/2, and −10, you multiply the three numbers together.

Remember that when you multiply two negative numbers, the result is positive, and when you multiply a negative number by a positive number, the result is negative.

Multiplying −8/5 and −3/2 first gives:

(−8/5) × (−3/2) = 24/10 = 2.4, and since both numbers are negative, the result is positive.

Now, multiply the result by −10:

2.4 × (−10) = −24. Since you are now multiplying a positive number by a negative number, the result is negative.

Therefore, −8/5 multiplied by −3/2 and then by −10 results in −24.

The product is [tex]\(-24\)[/tex].

To find the product of the given expressions, you simply multiply the numbers together.

[tex]\[\left(-\frac{8}{5}\right) \cdot \left(-\frac{3}{2}\right) \cdot \left(-10\right)\][/tex]

First, multiply the fractions:

[tex]\[\left(-\frac{8}{5}\right) \cdot \left(-\frac{3}{2}\right) = \frac{24}{10}\][/tex]

Now, multiply the result by the remaining number:

[tex]\[\frac{24}{10} \cdot (-10) = -24\][/tex]

Complete the question:

Find the product -8/5(- 3/2)(-10​)

Answer:

685 254

Step-by-step explanation:

The value of a digit increases by a factor of 10 each time you move it one place to the left.

Thus, if you move a digit two places to the left, you increase its value by a factor of 10 × 10 = 100.

Move the 5 from the tens place to the thousands place, and you increase its value from 50 to 5000 (a factor of 100).

Answer:

x = -1

Step-by-step explanation:

You can write the equation of the line by finding the slope between the points and substitute it with a point into the point slope form.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{6--5}{-1--1} =\frac{11}{0} = und[/tex]

These points have a slope which is undefined. This means it is a vertical line that crosses through the x-axis at the x-coordinate of both points -1. The equation is x = -1.

Answer:

c: 1,335 yd³

Step-by-step explanation:

The formula for volume of a cylinder is V = πr²h  where r is the radius of the base circle, and h is the height of the cylinder

We are given r = 5, and h = 17.  Plug them in and solve for V...

V = π(5²)(17)

    V = π(25)(17)

          V = 425π

              V = 425(3.14) = 1,334.5 yd³,

so 1,335 yd³ rounded to the nearest cubic yard

Answer:

311 students

Step-by-step explanation:

Let s represent the number who prefer sushi

Let p represent the number who prefer pizza

Five times the number who prefer sushi = 5s

27 fewer than (5s) = 5s - 27

P = 5s - 27

1,528 = 5s - 27

1,555 = 5s (add 27 to both sides)

311 = s (divide both sides by 5)

311 students prefer sushi to pizza.

Given that Lake Snider High School surveyed its student population about if they prefer pizza or sushi, and the students who prefer pizza represent twenty-seven fewer students than five times the number of students who prefer sushi, if 1,528 students prefer pizza, to determine how many students prefer sushi the following calculation must be performed:

Therefore, 311 students prefer sushi to pizza.

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Answer:

y=17,x=15

Step-by-step explanation:

180-112=68

68/4=y=17

180-68=112

112-7=105

105/7=x=15

The original blanket was a square with side 31 inches both in length and width. After adding 1 foot to one side, and subtracting 4 inches from the other, new dimensions are 43 inches and 27 inches, respectively. Thus, the new area of the blanket is 1161 square inches.

To solve this problem, we first need to note that the area of a rectangle (which our blanket has now become) is the product of its length and width. Since Kiara's blanket was originally a square before she added 1 foot to one side (12 inches) and subtracted 4 inches from the adjacent side, the original side length was the square root of the given area, i.e., √960 inch² = 31 inch. So, one dimension after alteration is 31 inches + 12 inches = 43 inches, and the other (after cutting) is 31 inches - 4 inches = 27 inches. Therefore, the new area of the blanket is 43 inches x 27 inches which equals 1161 square inches.

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The area​ of the original blanket is 784² square inches

Let's denote the side length of the original square blanket as 'x' inches.

After adding 1 foot (12 inches) to one side, the length of that side becomes x + 12 inches.

After cutting 4 inches off from an adjacent side, the length of that side becomes x - 4 inches.

We are given that the area of the resulting blanket is 960 square inches. This can be expressed as:

(x + 12)(x - 4) = 960

Expanding the left side of the equation, we get:

x^2 + 8x - 48 = 960

Adding 48 to both sides of the equation, we get:

x^2 + 8x = 1008

Dividing both sides of the equation by x, we get:

x + 8 = 1008/x

Solving for x using a quadratic equation solver or by trying out different values, we find that x ≈ 28.

Therefore, the area of the original square blanket is:

x^2 = 28^2 = 784 square inches

Complete question

Kiara made a square baby blanket. She decided to add 1 foot of material to one side, then cut 4 inches of material off from an adjacent side. The area of the resulting blanket is 960 square inches. Find the area of the original blanket. A) 625in^2 amazed B) 676in^2 perplexed C) 729in^2 thrilled D) 784in^2 baffled

Answer:  [tex]\bold{\dfrac{3\pi}{2}}[/tex]

Step-by-step explanation:

Coterminal means it is in the same place on the Unit Circle but one or more rotations clockwise or counterclockwise.

Note: one rotation is 2π (which is equivalent to [tex]\frac{4\pi}{2}[/tex])

[tex]-\dfrac{13\pi}{2}+\dfrac{4\pi}{2}=-\dfrac{9\pi}{2}\\\\.\qquad\qquad\quad=-\dfrac{9\pi}{2}+\dfrac{4\pi}{2}=-\dfrac{5\pi}{2}\\\\.\qquad\qquad\qquad\qquad\qquad\quad=-\dfrac{5\pi}{2}+\dfrac{4\pi}{2}=-\dfrac{\pi}{2}\\\\.\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad=-\dfrac{\pi}{2}+\dfrac{4\pi}{2}=\dfrac{3\pi}{2}\\\\\\\dfrac{3\pi}{2}\text{ is between 0 and }2\pi\text{ so this is the angle we are looking for!}[/tex]

Answer:

#1) 108.375 cubic inches

Step-by-step explanation:

For a pan of dimensions 8.5 in x 8.5 in, with height 2.25 in:

If cornbread fills to .75 in from the top, the height of cornbread is 2.25-.75 = 1.5 in

Volume = length*width*height (for rectangular prisms)

So Volume of corn bread = 1.5*8.5^2 = 108.375 cubic inches

For the second part, it is a poorly worded question. Squares are two dimensional, so it realistically cannot be cut into squares. If the question means cubes, the answer is yes to a certain extent. Since the height is exactly 1.5 in, and the pan is 8.5 in x 8.5 in, Marita can cut the cornbread into squares, but she cannot cut all of it into squares since 8.5/1.5 is not a whole number.

you need to actually add the diagram you know, save it as an image (or take a photo) and put it on here

Answer:

[tex]\large\boxed{(1,\ -2)}[/tex]

Step-by-step explanation:

[tex]|a|=a\ \text{for}\ a\geq0\\\\|a|=-a\ \text{for}\ a<0\\\\\text{Examples}\\\\|3|=3,\ |1.6|=1.6\\|-3|=-(-3)=3,\ |-1.6|=1.6\\===================[/tex]

[tex]y<-|x|\\\\\text{Put the values of x and y from the coordinates of the points and check inequality}\\\\(1,\ -2)\to x=1,\ y=-2\\-2<-|1|=-1\qquad\text{CORRECT :)}\\\\(1,\ -1)\to x=1,\ y=-1\\-1<-|1|=-1\qquad\text{FALSE :(}\\\\(1,\ 0)\to x=1,\ y=0\\0<-|1|=-1\qquad\text{FALSE :(}[/tex]

Answer:

m = 17

Step-by-step explanation:

14m - 13m =17

Combine like terms

m(14-13) = 17

m = 17

Answer:

m=17

Step-by-step explanation:

Answer:

See picture.

Step-by-step explanation:

This line is in point slope form [tex]y - y_1 = m(x-x_1)[/tex] where [tex](x_1, y_1)[/tex] is a point on the line. Begin graphing the line by first graphing the point (-3, 3) from the equation. Then move up 1 unit and over 2 units according to slope. This new point is (-1,4).

Answer mine!

Step-by-step explanation:

Answer my question to please!!

Answer:

a1 = 10

an = an-1 * -2

Answer:

48/1369

Step-by-step explanation:

We have 37 marbles all together. If we pick one red marble, the chances of that are 6/37. If we replace it and pick a blue one, the chances of that are 8/37. Once we have these numbers, we multiply 6/37 x 8/37 and you will get 48/1369

You should find that each side is 5 units long, so you have a rhombus. Also, each angle is 90 degrees so you have a rectangle. Combine the properties of a rhombus and a rectangle and you get a square as the best description.

Answer:

You are correct

Step-by-step explanation:

If you put the coordinates into a graph, you come out with a square that is slightly rotated.

Answer:

B is correct

Step-by-step explanation:

-(-x) = x, because a double negative like this equals a positive.

Therefore, you are actually saying -x+x= 0 which is true.

Equation B. is true for all values of x.

Step-by-step explanation: First, let's graph this down.

With all the points touching except (-2, -6) and (8, 18), it's safe to say that these are the coordinates that have to be removed. Also, just for an extra help, the linear line is 2x + 1 = y

The data points that need to be removed from this table for it to represent a linear function are  (-2, -6) and (8, 18).

Function is a type of relation, or rule, that maps one input to specific single output.

WE have been given the points that need to be removed from this table for it to represent a linear function.

With all the points touching except (-2, -6) and (8, 18), we can say that these are the coordinates that have to be removed.

Also, for an extra information, the linear line is 2x + 1 = y

Therefore, the data points that need to be removed from this table for it to represent a linear function are  (-2, -6) and (8, 18).

The points are attached below on the graph.

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Answer:

12/80 as a decimal equals 0.15

Step-by-step explanation:

Answer: -0.15

Step-by-step explanation:

Get both sides on 100

12 + 12 * 1/4 = 15

80 + 80 * 1/4 = 100

-15/100 = -0.15