The perimeter of a rectangular pool i 110 feet. If the pool i 17 feet wide, find the length of the pool

Answer:

y = - 3x - 28

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{3}[/tex] x + 12 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute (- 9, - 1 ) into the partial equation

- 1 = 27 + c ⇒ c = - 1 - 27 = - 28

y = - 3x - 28 ← equation of perpendicular line

Answer:

A. Can be written in a fraction.

Step-by-step explanation:

Do you need any help..

Rational number can be any number that can also be wrote as a ratio or fraction of two integers would be commonly known as a rational number…

In the series of a value of a(4)=216

What do the terms sequence and series mean?

Mathematical sequence and series formulas pertain to several kinds of sequences and series. A series is the accumulation of the elements in a sequence, which is a group of arranged elements that follow a pattern. The formulas for the nth term and the sum are typically included in the sequence and series formulas.

Given that:

a(1) = 8

a(n)= 3a(n-1)

so a(4) = 3a(3) = 72*3 = 216

a(3)= 3a(2) = 24*3 = 72

a(2)= 3a(1) = 3*8 = 24

Hence a(4) = 216

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Answer:

A

Step-by-step explanation:

Option A is the only Option with the correct domain.

Answer:

$150

Step-by-step explanation:

Let's call the cost price of the watch C. The salesperson sells the watch at 90% of the cost price, so they sell the watch for 0.9 * C dollars.

We know that 0.9 * C = 108 dollars, so C = 108 / 0.9 = <<108/0.9=120>>120 dollars.

The salesperson wants to make a profit of $30, so they need to sell the watch for 120 + 30 = <<120+30=150>>150 dollars.

Answer:

486

Step-by-step explanation:

area of a cube =6x²

length= 9

area=6×9²

=6×81

=486

Answer:91

Step-by-step explanation:

Formula for average is: (Unit 1 + Unit 2 + Unit 3) / 3

If we plug the values in we get

(91 + 88 + x) / 3 = 90

(179 + x) / 3 = 90

               *3    *3

179 + x = 270

x = 91

Answer:

4

Step-by-step explanation:

If I'm reading it correctly, x is multiplied by 6 to equal y.

So, 3(x) x 6 = 18(y)

Therefore, 24/6 = 4 OR,  4(x) x 6 = 24(y)

○ (ƒ − g)(x) = x² − 11x +4 is the correct Answer

Answer:

ƒ(x) = 4x² – 5

g(x) = 3x² + 6x − 4.

(ƒ – g)(x) = ƒ(x)–g(x)

= 4x² – 5 –(3x² + 6x − 4)

= 4x²–5x –3x²–6x+4

= 4x²–3x² –5x–6x +4

= x² − 11x +4

[tex] [/tex]

Thank you

Answer:

See below.

Step-by-step explanation:

1) Combine Like Terms

-8w + 16x + 20w – 40x

= -24x + 12w

2) Apply the distributive property to simplify

the expression

8(12x – 20)

= 96x - 160

3) Add 7w – 12 and -15w + 60

= -8w + 48

4) Subtract 2w + 4 from 3w – 6

= 3w - 6 - (2w + 4)

= 3w - 6 - 2w - 4

w - 10

5) Solve for x:

7.2 + x = 18.1

x = 10.9

6) Solve for x:

x – 25 = -3

x = 22

Answer:

Step-by-step explanation:

1. Combine Like Terms

[tex]\tt -8w + 16x + 20w - 40x[/tex]

[tex]\tt 12w+16x-40x[/tex]

[tex]\boxed{\tt 12w-24x}[/tex]

2) Apply the distributive property to simplify:-

[tex]\tt 8\left(12x-20\right)[/tex]

[tex]\tt 8\times \:12x-8\times \:20[/tex]

[tex]\boxed{\tt 96x-160}[/tex]

3. Add 7w – 12 and -15w + 60:-

[tex]\tt 7w-12+ (-15)w+60[/tex]

[tex]\tt 7w-15w-12+60[/tex]

[tex]\tt -8w-12+60[/tex]

[tex]\boxed{\tt -8w+48}[/tex]

4. Subtract 2w + 4 from 3w – 6:-

[tex]\tt 2w+4-3w-6[/tex]

[tex]\tt 2w-3w+4-6[/tex]

[tex]\tt -w+4-6[/tex]

[tex]\boxed{\tt -w-2}[/tex]

5. Solve for x:-

[tex]\tt 7.2+x=18.1[/tex]

[tex]\tt x+7.2=18.1[/tex]

[tex]\tt x+7.2-7.2=18.1-7.2[/tex]

[tex]\boxed{\tt x=10.9}[/tex]

6) Solve for x:

[tex]\tt x - 25 = -3[/tex]

[tex]\tt x=-3+25[/tex]

[tex]\boxed{\tt x=22}[/tex]

_________________

Hope this helps you!

Have a nice day!

Answer:

[tex](2x-3)(4x^2+6x+9)[/tex]

Step-by-step explanation:

Given expression:

[tex]8x^3-27[/tex]

Rewrite 8 as 2³ and 27 as 3³:

[tex]\implies 2^3 \cdot x^3-3^3[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot c^b=(ac)^b[/tex]

[tex]\implies (2x)^3-3^3[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Difference of Cubes Formula}\\\\$a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$\\\end{minipage}}[/tex]

Apply the Difference of Cubes Formula.

Therefore:

[tex]\implies (2x-3)((2x)^2+2x \cdot 3+3^2)[/tex]

[tex]\implies (2x-3)(4x^2+6x+9)[/tex]

The area of the circle with the given radius would be = 12.56m².

A circle is defined as the figure that do not posses any form of edges or corners and is known as a two dimensional figure with a center of 360°.

The area of the circle can be gotten when the radius is given.

The formula used for the calculation of the area of a circle = πr²

Where,

Pie (π) = 3.14 or 22/7

Radius (r) = 2 m

Area = 3.14 × 2²

= 3.14 ×4

= 12.56 m²

Therefore, the area of the given circle would be = 12.56m².

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Answer:220%

Step-by-step explanation:

Answer:

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

Given three consecutive terms of a GP:

The middle term is the geometric mean of the other terms. Therefore:

The matching choice is D.

The measure of angle ∠C = 35°, 2x = 50° and x = 25°.

In Euclidean geometry, an angle is made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively.

Angles can be formed by two rays in the plane where they are placed.

Additionally, when two planes overlap, angles are created.

Dihedral angles are what they are called.

So, m∠ABC:

We know that ∠C in triangle ABC = 180 - 145 = 35°

Now, the measure of  m∠ABC:

95 + 35 + 2x = 180

130 + 2x = 180

2x = 180 - 130

2x = 50°

x = 50/2

x = 25°

Therefore, the measure of angle ∠C = 35°, 2x = 50° and x = 25°.

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Answer: 160

Step-by-step explanation: If I remember correctly, the formula for finding the rate is:

r = d/t

So, rate = 640/4

When I divided it, I got 160.

I hope this helped!

Answer:

25.6

Step-by-step explanation:

while i do not know how to do this is dod use a rate calculator so hopes this help!

There is an 8.1% probability that any given distance will exceed 212.50 cm.

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

I frequently remind kids that we can express probabilities as ratios, percentages, fractions, or decimals so they are aware of the variety of ways we express odds.

So, the probability that the individual distance is greater:

z = 212.50-200/8.9 = 1.4

Looking up 1.4 in the normal distribution table:

P(z>1.4) = 1 - 0.9192 = 0.0808

= 8.1%

Therefore, there is an 8.1% probability that any given distance will exceed 212.50 cm.

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Complete question:
The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.9 cm.

a. find the probability that an individual distance is greater than 212.50 cm.

After the substitution 2(3y - 17) +3y = -7 is the answer of the system of equation.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given system of the equation,

x = 3y - 17      {equation 1}

2x + 3y = -7         {equation 2}

Substitute the value of x from the equation 1 to equation2,

2 (3y - 17) + 3y = -7

Therefore, after the substitution 2(3y - 17) +3y = -7 is the answer of the system of equation.

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Answer: A.-20

Step-by-step explanation:

Since x=4

substitute in and solve

h(4)=-5(4)

h(4)=-20

Answer:

Step-by-step explanation:

when x=4, then h(x)=-5 * 4=-20

Therefore, choose A

The required parameters of a smaller surface area and a smaller amount of metal per can are a radius of 3.05 cm and a height of 6.09 cm.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. A three-dimensional shape's surface area is the sum of all of its faces. Finding the area of each face and adding them together gives us the surface area of a form.

Here,

V=πr²h

178=πr²h

πrh=178/r

S=2πr²+2πrh

S=2πr²+2*(178/r)

S=2πr²+356/r

S'=4πr-356/r²

S'=0

4πr=356/r²

r³=356/4π

r³=28.343

r=3.05 cm

h=178/πr²

h=178/(3.14*3.05*3.05)

h=178/29.23

h=6.09 cm

The dimensions needed for less surface area so each can uses less metal is radius as 3.05 cm and height as 6.09 cm.

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The required linear function to model the amount of money in Iri's account at any time t using the simple interest formula is 185 + 5.55t.

An expense associated with borrowing money or other assets is interest.

The principal is the amount borrowed, and the interest is calculated as a percentage of the principal for a specific period of time.

If someone borrowed $1,000 at 2% interest and accumulated $100 in interest, the interest for that year would be $22.

It's because interest is paid on a total of $1100, which includes the principal ($1000) and accrued interest ($100). 2% of $1100 is $22.

So, in this situation, the checking account offers simple interest at a rate of 3% annually. Her account has $185 in it.

The total balance of the account will always be:

= 185 + (PRT/100)

P = principal

R = rate

T = time

Then,

= 185 + [(185 × 3 × t)/100]

= 185 + 5.55t

185 + 5.55t is the function.

Therefore, the required linear function to model the amount of money in Iri's account at any time t using the interest formula is 185 + 5.55t.

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Correct question:
Iris's checking account pays simple interest at 3% per year. She has $185 in

her account. Write a linear function to model the amount of money in her

checking account at any time t.

Answer:

The slope of both equations is 7.  Yes, since the slopes are the same, the lines are parallel.

Step-by-step explanation:

For both equations, as the x increased by 1, the y increased by 7.

The value of the given expression, 67π × 7, is 1473.4

From the question, we are to determine the value of the given expression.

From the given information,

The given expression is

67π × 7

To determine the value of the expression, we will evaluate the expression step-wisely.

Evaluate 67π

67π = 210.4867

Multiply by 7

210.4867 × 7

= 1473.4069

≈ 1473.4

Hence, the value is 1473.4

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The number based on the information given is 3.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

In this case, three times the difference of four times a number and two decreased by the sum of the number and five equals 22.

Let the number be x

3(4x - 2) - (x + 5) = 22

12x - 6 - x - 5 = 22

11x - 11 = 22

11x = 22 + 11

11x = 33

Divide

x = 33 / 11

x = 3.

The number is 3

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The equation of the inequality graph with dashed line

The equation of the inequality graph with solid line

Using the slope intercept form of the straight line which is of the form

y = mx + c

The slope, m is the ratio of the change in the output to the change in the input. This is given by the formula

m = (y₀ - y₁) / (x₀ - x₁)

Slope calculation using the points (0, -4) and  (2, 0)

m = (-4 - 0) / (0 - 2)

m = 2

y intercept, c from the graph

c = -4

applying inequality representations

shading above the line is greater than and dotted lines means it does not have equal to

hence y > 2x - 4

for the solid line graph

the slope, m calculating using the points on the graph (0, 4) and  (4, 0)

m = (4 - 0) / (0 - 4)

m = (4) / (-4)

m = -1

y intercept, c from the graph

c = 4

The equation of the line is y = -x + 4

Solid lines indicate an equality in the inequality, while shading over the line indicates a greater than

hence y ≥ -x + 4

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Congruence is a property between two or more shapes that proves that they are equal in all respect. The required proof in the given question is shown below:

Two or more figures are said to be congruent if and only if they have equal length of sides, or measure of interior angles.

A triangle is a plane shape bounded by three straight sides, with three interior angles. The series properties can be used to classify the types of triangles with respect to their sides and angles. Some types of triangles are; equilateral, isosceles, right angled, acute angles scalene etc.

Thus to prove that: ΔADE ≅ Δ CDF

                               ΔBDE ≅ ΔBDF

AD ≅ DC (congruent property of similar figures)

AE ≅ CF (similarity property)

DE ≅ DF (congruent property of similar figures)

Thus,

ΔADE ≅ ΔCDF (SSS congruent property)

Also,

EB ≅ FB (congruent property of similar figures)

BD (common side of congruent figures)

DE ≅ DF (congruent property of similar figures)

So that,

ΔBDE ≅ ΔBDF (SSS congruent property)

This implies that,

i ΔADE + ΔBDE = ΔABD

ii. ΔCDF + ΔBDF = CBD

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