A physical therapy facility is building a new pool that is 60 feet long and 7 feet deep. They have ordered enough tile for a
140-foot-long border around the edge. How wide should the pool be to ensure that all tiles are used?

Answer:

x = 12

Step-by-step explanation:

Given that AB = 2, AD = x, BC = 2, CD = -16 + 2x, since A, B, C, D are said to be collinear, therefore:

AB + BC + CD = AD

2 + 2 + (-16 + 2x) = x

Use this equation to solve for x

2 + 2 - 16 + 2x = x

-12 + 2x = x

Subtract 2x from both sides

-12 + 2x - 2x = x - 2x

-12 = -x

Divide both sides by -1

[tex] \frac{-12}{-1} = \frac{-x}{-1} [/tex]

12 = x (negative cancels negative)

x = 12

The side of a square is the square root of the area.

Side = sqrt(155)

Side = 12.45 inches. (Round answer as needed)

Answer:

no

Step-by-step explanation:

You will have more time to do it, but no, try extra credit

Sorry mate hope this helps<3

Answer:

3.78x10^5

Step-by-step explanation:

Answer:

  10 ft

Step-by-step explanation:

The formula for the area of a triangle can be used. Put the known values into the formula and solve for the unknown.

  A = (1/2)bh

  15 = (1/2)(3)h

  h = 15/1.5 = 10

The triangle's height is 10 feet.

Answer:

10

Step-by-step explanation:

A=1/2*b*h

15=1/2*3*h

15=3/2*h

15=3/2h

h=15/(3/2)

h=(15/1)(2/3)

h=30/3

simplify

h=10

Answer:

a). y = 0.25x + 15

b). x = 480 cups

Step-by-step explanation:

(a). Let the equation of the linear function passing through a point (x', y') is,

y - y' = m(x - x')

'm' = slope of the line

b = y-intercept

Two points lying on the linear function will be (200, 65) and (250, 77.5).

Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{77.5-65}{250-200}[/tex]

   = [tex]\frac{12.5}{50}[/tex]

   = 0.25

Therefore, equation of the line passing through (200, 65) and slope 0.25 will be,

y - 65 = 0.25(x - 200)

y - 65 = 0.25x - 50

y = 0.25x + 15

(b). For y = $135 we have to calculate the number of cups of coffee produced.

135 = 0.25x + 15

0.25x = 135 - 15

0.25x = 120

x = 480 cups

Therefore, 480 cups of coffee will be produced.

Answer:

move the decimal to the end and add a zero to 814 i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(x) = x²

h(x) = x - 3

To find (g ∘ h)(x) substitute h(x) into g(x) that's for every x in g(x) replace it with h(x)

That's

(g ∘ h)(x) = ( x - 3)²

= x² - 3x - 3x + 9

We have the final answer as

Hope this helps you

I believe the answer is A

Answer:

you just times the number buy 9 and 3 then divid by 3

Step-by-step explanation:

it is true because 14 is 1/14

Answer:

Step-by-step explanation: I have no clue

Answer:

-8.

Step-by-step explanation:

Substitute BC with the -4 and 2, as you were given those values to substitute with B and C. Multiply those two values. You get -8.

Answer: 24°

Step-by-step explanation:

Given the following :

supplement of an angle is 42 degrees less than 3 times the complement of the angle

Let the angle = θ

Supplement of angle = 180° - θ

Complement of angle = 90° - θ

Supplement of angle is also said to be:

(3 × complement) - 42° = 3(90° - θ) - 42°

= 270° - 3θ - 42° = 228° - 3θ

Hence,

180° - θ = 228° - 3θ

Solve for θ

-θ + 3θ = 228° - 180°

2θ = 48°

θ = 48°/2

θ = 24°

answer: 1.13622

Step by step explanation:

n:

0=(3x-4)/5

0=3x/5-4/5

x=1.3.....

Answer:

Length  is 4 less than 3

Step-by-step explanation:

Answer:

D. (5,1)

Step-by-step explanation:

Because it is an isosceles triangle, the next point we choose must result in two sides with the same length. This means that either the two new sides are equal, or that one of the new sides is equal to the original side. If we wanted both of the new sides to be equal, they would have to be equal distance from the new point and one of the points of the original line. However, none of the options result in both new lines being the same length.

(2,1) would result in one new length being 1 unit long (2-1 x-coordinates) and the other being square root 5 (distance from point 2,1 to point 3,3 minus both coordinates and use Pythagoras). Points 3,2 and 4,1 yield the same result: Length 1=1 unit length 2=square root 5. Length 1 = 3 unit, length 2 = square root 5.

Therefore we are looking for a point which instead yields one length which is the same length as the original. The original length was 2^2 + 2^2 = c^2 = square root 8.

If we try the point 5,1 then we get two lengths of 4 and square root 8, it forms a isosceles triangle whose base line is parallel to the x-axis.

Sorry is my explanation was confusing, it's much easier to try and draw it on a grid and visualize it. Basically the overall idea is to test the side values you get by finding the distance between the points and going with the option which results in two sides with the same length.

Hope this helped!

Answer:

D. (5,1)

Step-by-step explanation: Because it is an isosceles triangle, the next point we choose must result in two sides with the same length. This means that either the two new sides are equal, or that one of the new sides is equal to the original side. If we wanted both of the new sides to be equal, they would have to be equal distance from the new point and one of the points of the original line. However, none of the options result in both new lines being the same length.

(2,1) would result in one new length being 1 unit long (2-1 x-coordinates) and the other being square root 5 (distance from point 2,1 to point 3,3 minus both coordinates and use Pythagoras). Points 3,2 and 4,1 yield the same result: Length 1=1 unit length 2=square root 5. Length 1 = 3 unit, length 2 = square root 5.

Therefore we are looking for a point which instead yields one length which is the same length as the original. The original length was 2^2 + 2^2 = c^2 = square root 8.

If we try the point 5,1 then we get two lengths of 4 and square root 8, it forms a isosceles triangle whose base line is parallel to the x-axis.

Sorry is my explanation was confusing, it's much easier to try and draw it on a grid and visualize it. Basically the overall idea is to test the side values you get by finding the distance between the points and going with the option which results in two sides with the same length.

Answer:

5 inches

Step-by-step explanation:

Given

Length of a cube = 1 inch

Required

Determine the edge length of the cube

If the container can take 125 cubes, then that's the volume

So:

[tex]Volume = 125in^3[/tex]

Volume of a cube is calculated as thus;

[tex]Volume = Length^3[/tex]

This gives;

[tex]Length^3 = 125[/tex]

Take cube root of both sides

[tex]Length = \sqrt[3]{125}[/tex]

[tex]Length = 5[/tex]

Hence, the length is 5 inches

Answer:

distance =

[tex] \sqrt{ \frac{10}{3} } [/tex]

Step-by-step explanation:

Without going through and deriving this (my blackboard doesn't have space and a textbook, teacher, or online tutorial is probably better for that), the equation for the distance from some point on the plane to some point in space is as follows:

[tex]distance = \frac{ax + by + cz - d }{ \sqrt{ {a}^{2} + {b}^{2} + {c}^{2} } } [/tex]

•Note that the d in the equation should actually be D but Brainly doesn't allow me to do uppercase letters on mobile it seems... Anyway, d in the equation represents the value which the equation of the plane is equal to. You only gave the plane equation so I assumed d=0 in my calculations.

•x, y, and z all come from the point which you want to find the distance to. So (x,y,z)=(0,4,3) here.

•a, b, and c all come from the components of the vector normal to the surface. For planes, it simply somes to be the coefficients in front of each part. So (a,b,c)=(5,1,2) here.

With that you just need to plug the information in and simplify for your answer. My work is in the attachment, comment with questions or if anything seems off.

Steps to solve:

40 + 5x > 95 - 4x

~Subtract 40 to both sides

5x > 55 - 4x

~Add 4x to both sides

9x > 55

~Divide 9 to both sides

x > 55/9

Best of Luck!

Answer:

[tex]f(-3)=-3[/tex]

Step-by-step explanation:

[tex]f(x)=2x+3[/tex]

[tex]f(-3)=2(-3)+3[/tex]

[tex]f(-3)=-6+3[/tex]

[tex]f(-3)=-3[/tex]

Hope this helps!

(Please mark Brainliest!)

Answer:

Step-by-step explanation:

this problem is on vector

given the vectors

a = 5i + j, and

b = i − 2j

1. summation of vector a + b

[tex]= (5i+j)+(i-2j)\\\\=5i+j+i-2j\\\\[/tex]

collect like terms

[tex]=5i+i+j-2j\\\\=6i-j\\\\[/tex]

2. 2a + 3b

[tex]= 2(5i+j)+3(i-2j)\\\\=10i+2j+3i-6j\\\\[/tex]

collecting like terms we have

[tex]=10i+2j+3i-6j\\\\=10i+3i+2j-6j\\\\=13i-4j[/tex]

(3) |a|, and |a − b|.

|a|= |5i+j|

[tex]=\sqrt{5^2+1^2} \\\\=\sqrt{25+1} \\\\=\sqrt{26} \\\\= 5.1[/tex]

also,

[tex]|a - b|= |(5i+j) -(i-2j)| \\\\ a-b= 5i+j -i+2j \\\\ a-b=5i-i+j+2j \\\\a-b= 4i+3j\\\\[/tex]

[tex]|a -b|=\sqrt{4^2+3^2} \\\\|a -b|=\sqrt{16+9} \\\\|a -b|=\sqrt{25} \\\\|a -b|=25[/tex]

Answer:

= 3

Step-by-step explanation:

0

Step-by-step explanation:

im only saying this because im assuming it is on the line of the axis

Answer:

0

both x and y are zero so the y axis  is 0 then the x axis is 0

Answer:

a) [tex]c=\frac{-1+\sqrt{13}}{2}[/tex] and [tex]c=\frac{-1-\sqrt{13}}{2}[/tex]

Step-by-step explanation:

The idea for the solution of this equation is to find the value of c where both parts of the piecewise-defined function are the same. So we need to take the parts of the function and set them equal to each other, so we get:

[tex]3-x^{2}=x[/tex]

and then solve for x. We move everything to one side of the equation so we get:

[tex]x^{2}+x-3=0[/tex]

and we use the quadratic formula:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

and we substitute:

[tex]x=\frac{-1\pm \sqrt{(1)^2-4(1)(-3)}}{2(1)}[/tex]

and solve

[tex]x=\frac{-1\pm \sqrt{1+12}}{2}[/tex]

[tex]x=\frac{-1\pm \sqrt{13}}{2}[/tex]

so our two answers are:

a) [tex]c=\frac{-1+\sqrt{13}}{2}[/tex] and [tex]c=\frac{-1-\sqrt{13}}{2}[/tex]

Answer:

The number -34 belongs to:

✔️Integers and

✔️Rational numbers

Step-by-step explanation:

-34 is an integer because it can written without a fractional or decimal part.

Rational numbers are said to numbers that can actually be expressed as a fraction with integers. They have no fractional part.

For example,  −34 is a rational number because it can be written as - 34/1.

-34 can be expressed as -34/17, given an integer.

-34 is NOT a whole number because whole numbers are positive numbers.

Answer:

(0,-3) and (1,1)

Step-by-step explanation:

In order to have a slope of 4, the y coordinates need to differ by 4, and the x coordinates by 1. This is because slope is equal to rise/run. Rise being difference in y value and run difference in x.

In this pair of coordinates, the y coordinates differ in +4 (-3 and 1) and the x coordinate differs by 1 (0 and 1).

Therefore this is the pair of points with a slope of 4.

Hope this helped!

The pair of points that has a slope of 4 is the coordinate points (0, –3), (1, 1)

The formula for calculating the slope of a line passing through two points is expressed as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We need to get which of the coordinates will result in a slope of 4.

Using the coordinate points (0, –3), (1, 1)

[tex]m=\frac{1-(-3)}{1-0}\\m=\frac{1+3}{1}\\m=\frac{4}{1}\\m=4[/tex]

Hence the pair of points that has a slope of 4 is the coordinate points (0, –3), (1, 1)

Learn mroe here: https://brainly.com/question/23935638

Answer:

i think the answer would be 150. sorry if its wrong

Step-by-step explanation:

90/3*5=

30*5=

150