What is the difference in elevation between 3 feet above the sea and 20 feet below the sea

Answer:

4.9 in

Step-by-step explanation:

6/11 = x/9

6/11 times 9 = x

x = 4.9

Answer:

50 degrees

Step-by-step explanation:

Triangle = 180

180 - 90 = 90

? = 50 degrees

The three steps that Sergey could use to solve the quadratic equation by completing the square are:

\(5(x^2 + 4x + 4) = -4 + 7 x^2 + 4x = 7/5\s(x + 2)^2 = 27/5\)

Sergey can use the procedures below to solve the quadratic equation \(5x2 + 20x - 7 = 0\) by completing the square:

\(5x2 + 20x = 7\); move the constant word to the right.

For the coefficient of the quadratic term to be 1, divide both sides by the leading coefficient as follows:\(x2 + 4x = 7/5.\)

On the left side of the equation, multiply and divide by the square of half the x-coefficient: term's

\(x^2 + 4x + 4 - 4 = 7/5\)

Factor the perfect square trinomial after simplifying the left half of the equation:

\((x + 2)^2 = 27/5\)

Take the square root of both sides, adding the plus/minus sign as necessary:

\(x + 2 = +/- sqrt(27/5)\)

Subtracting 2 from both sides, find x, and then:

\(x = -2 +/- sqrt(27/5)\)

The three methods that Sergey could employ to solve the quadratic problem by completing the square are as follows:

\(x^2 + 4x = 7/5(x + 2)^2 = 27/5\)

\(5(x^2 + 4x + 4) = -4 + 7\)

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Answer

5^5=25

Step-by-step explanation

The correct proof of the equation is cos3θ =cos(2θ + θ) =  cos²θ - 3cosθsin²θ (Proved)

Given the trigonometry identity below:

cos3∅=cos²∅-3cos∅sin²∅

We are to prove that both sides of the equation are equal.

cos 3θ = cos(2θ + θ)

Using the double angle formula for cosine, we can expand the first term:

cos(2θ + θ) = cos2θ cos θ - sin2θ sinθ

Since cos2θ = cos²θ - sin²θ

cos(2θ + θ) =  cos²θ - sin²θ - 2cosθsinθsinθ

cos(2θ + θ) = cos²θ - sin²θ - 2cosθsin²θ

On simplifying, we can see that;

cos3θ =cos(2θ + θ) =  cos²θ - 3cosθsin²θ (Proved)

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Answer:

True

False

True

Step-by-step explanation:

Use log laws to simplify the left side of each equation.

\(\boxed{\begin{minipage}{8cm}\underline{Log laws}\\\\Product law:\quad\:$\log_axy=\log_ax + \log_ay$\\\\Quotient law:\;\;\;$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\Power law:\quad\;\;\;\:$\log_ax^n=n\log_ax$\\\end{minipage}}\)

Given logarithmic statement:

\(\log_3v-\log_3w-\log_3x=\log\left(\dfrac{v}{wx}\right)\)

Apply the quotient law for logarithms:

\(\begin{aligned}\log_3v-\log_3w-\log_3x&=\log_3\left(\dfrac{v}{w}\right)-\log_3x\\\\&=\log_3\left(\dfrac{\frac{v}{w}}{x}\right)\\\\&=\log\left(\dfrac{v}{wx}\right)\end{aligned}\)

Therefore, the given statement is true.

\(\hrulefill\)

Given logarithmic statement:

\(3\log_4n+\log_4m=\log_4(nm)^3\)

Apply the power law and the product law for logarithms:

\(\begin{aligned}3\log_4n+\log_4m&=\log_4n^3+\log_4m\\\\&=\log_4(n^3 \cdot m)\\\\&=\log_4n^3m\end{aligned}\)

Therefore, the given statement is false.

\(\hrulefill\)

Given logarithmic statement:

\(\log_2\left(\dfrac{c\sqrt[3]{d}}{e^4}\right)=\log_2c+\dfrac{1}{3}\log_2d-4\log_2e\)

Apply the quotient law, the product law, and the power law for logarithms:

\(\begin{aligned}\log_2\left(\dfrac{c\sqrt[3]{d}}{e^4}\right)&=\log_2\left(c\sqrt[3]{d}\right) - \log _2\left(e^4\right)\\\\&=\log_2\left(c\right)+\log_2\left(\sqrt[3]{d}\right)-\log _2(e^4)\\\\&=\log_2\left(c\right)+\log_2\left(d^{\frac{1}{3}}\right)- \log _2(e^4)\\\\&=\log_2c+\dfrac{1}{3}\log_2d-4\log_2e\end{aligned}\)

Therefore, the given statement is true.

Answer:

-√26, 5.15, 5.2, 16/3

Step-by-step explanation:

-√26 = -5.09

16/3 = 5.33

For Serenity's lemonade recipe, the lemons being used per cup of lemonade is 0.8

Ratio is a comparison of two quantities that are expressed in relation to each other. Ratios are typically expressed in the form of a fraction, with the numerator representing one quantity and the denominator representing the other quantity.

To find the rate at which lemons are being used in lemons per cup of lemonade, we need to calculate the ratio of lemons used to cups of lemonade.

According to the recipe, 4 lemons are required to make 5 cups of lemonade. So the rate of lemons used is:

4 lemons / 5 cups = 0.8 lemons per cup of lemonade

This means that for every cup of lemonade, 0.8 lemons are used.

Alternatively, we can also express this rate as a fraction, which gives us:

0.8 lemons / 1 cup of lemonade

Either way, the rate of lemons used is 0.8 lemons per cup of lemonade.

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Answer:

Point a tells us at 9 degrees Celsius mikoto cat lost 2 g

Step-by-step explanation:

Thank you hope this helps❤

Answer: A

Step-by-step explanation: I got it right on khan Academy

Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:

1.) 3.075 gallons.

To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.

We have that:

Hence the remaining amount is:

15 - 11.925 = 3.075 gallons.

Which means that option 1 is correct.

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Answer: 3.075 gallons

Step-by-step explanation:

Answer:its obviously 128

Step-by-step explanation:

a) If the minimum payment is 15% on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,291.99.

b)  If the minimum payment is $75 on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,293.99.

The credit card balance refers to the difference between the beginning balance, payments, and interests.

a) Current balance on a credit card = $1,500

Interest rate = 15.99%

Minimum payment = 15%

= $225 ($1,500 x 15%)

Interest = $16.99 ($1,500 - $225 x 15.99% x 1/12)

Ending Balance = $1,291.99 ($1,500 +$16.99 - $225)

b) Current balance on a credit card = $1,500

Interest rate = 15.99%

Minimum payment = $75

Interest = $18.99 ($1,500 - $75 x 15.99% x 1/12)

Ending Balance = $1,293.99 ($1,500 +$18.99 - $225)

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Hey there! :)

Answer:

(x - 9)(x - 3)

Step-by-step explanation:

We are given the polynomial:

x² - 12x + 27

Factor the equation by finding two numbers that sum up to -12 and multiply into 27. The numbers -9 and -3 satisfy these conditions:

Therefore, the equation in factored form would be:

(x - 9)(x - 3)

(x - 9)(x-3)

multiply the first and last numbers of the equation to get 27

find two numbers that multiply to 27 and add to  - 12 [the middle number]

- 9 and -3 multiply to 27 and add to  - 12

because there is no coefficient on the x2, thats your answer. (x - 9)(x-3)

hope that makes some sense :)

Answer:

circumference = 2πr

diameter = 3ft, so radius =3/2 =1.5

                       =2π ×1.5=3π= 9.42ft

Answer:

here diameter =3 ft

radius=diameter/2

=3/2

=1.5 ft

now use formula 2 pie r where pie =3.14

=2*3.14*1.5 ft

=9.42 ft

Step-by-step explanation:

Hope this helps u!!

Answer:

12.87, 12.5  is closer to 13

12.08, 12.13  is closer to 12

Step-by-step explanation:

Least to Greatest:

12

13

Answer:

VIII or 8

Step-by-step explanation:

XLII converts to 42

XXXIV converts to 34

42-34 = 8 or VIII

Answer:

Choice A

Step-by-step explanation:

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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Answer: 207

Step-by-step explanation:

Let's start by converting 4 3/5 to an improper fraction. We do this by multiplying 4 * 5 and adding it to 3. This full equation is (4 * 5) + 3 = 23. We then have 23/5. We multiplying this by 45 to get our answer. This is done by multiplying 23 * 45 and then dividing that by 5. This full equation is (23 * 45) / 5 = 207. Therefore, our answer is 207.

Answer:

huh ;-; all ik is dat

Step-by-step explanation:

8 = 4

10 = 5 so dat would be 4/5

Answer:

  d = 23 1/3

Step-by-step explanation:

You want to solve the proportion (0.3d -1)/(3 1/3) = (0.84)/(7/15).

  \(\dfrac{0.3d-1}{3\dfrac{1}{3}}=\dfrac{0.84}{\dfrac{7}{15}}\qquad\text{given}\\\\\\\dfrac{3(0.3d-1)}{10}=\dfrac{15(0.84)}{7}\qquad\text{invert and multiply}\\\\0.09d -0.3=1.8\qquad\text{simplify}\\\\0.09d = 2.1\qquad\text{add 0.1}\\\\d=\dfrac{2.10}{0.09}=\dfrac{70}{3}\qquad\text{divide by 0.09}\\\\\boxed{d=23\dfrac{1}{3}}\)

__

Check

  (0.3·(70/3) -1)/(3 1/3) = 0.84/(7/15)

  (7 -1)/(10/3) = 1.8

  6(3/10) = 1.8 . . . . . . true

Answer: 23 1/3

Step-by-step explanation:

Since the fraction 9/14 is already in simplest form, the probability of the computer picking an animal character is 9/14.

To find the probability of the computer picking an animal character, we need to determine the total number of characters and the number of animal characters.

Given:

Number of animal characters: 9

Number of human characters: 5

The total number of characters is the sum of the animal and human characters:

Total number of characters = Number of animal characters + Number of human characters

Total number of characters = 9 + 5

Total number of characters = 14

Now, to calculate the probability, we divide the number of animal characters by the total number of characters:

Probability of picking an animal character = Number of animal characters / Total number of characters

Probability of picking an animal character = 9 / 14

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a.) The area of the floor = 246.5ft²

b.) The amount that it will cost to put down the new floor would be = $2,711.5

C.) The new dimensions of the area rug would be= Length= 21ft, width = 18.5 ft.

d.) The area of the area rug would be = 388.5ft²

For question a.)

The floor has a rectangular shape. The area of a rectangle = length×width

area of the floor= 17×14.5

= 246.5ft²

For question b.)

For a square foot(1ft²) = $11

246.5ft² = 246.5×11 = $2,711.5

For question c.)

Since the rug will be extended by 2ft at each side, the new dimensions would be:

length = 2+2+17 = 21ft

width = 2+2+14.5 = 18.5ft

For question d.)

The area of the floor with the new dimensions = 21×18.5 = 388.5ft²

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<CAB= 56°

(DC= 78°

(DB= 78+56=134°

<DAB=134°

(BED=360-134= 226°

(BEC=226+78=304°

(CED= 360-78=282°

hey:) I hope this was correct and helpful

The measure of ∠STW is 119° which is an exterior angle of ΔRST.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles in a triangle is 180°.

We also know that the measure of an exterior angle in a triangle is the sum of the two opposite interior angles.

∴ In ΔRST,

14x + 7 = 9x + 3 + 44.

14x - 9x = 47 - 7.

5x = 40.

x = 8.

So, the measure of ∠STW is 14(8) + 7.

= 119°.

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Answer:

$22

Step-by-step explanation:

17.99 round up so 18

a second large pizza is 14 dollars off of the original price of 18 so 4

18+4 is 22

so 2 large pizzas would cost $22

Answer:

For every 4 votes Natalie received, Phil received 3 votes.

Step-by-step explanation: