20 ft
The ceiling of Stacy's living room is a square that is 20 ft long on each side. Stacy
knows the diagonal of the ceiling from corner to corner must be longer than 20 ft.
but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry.
Round each answer to the nearest whole number and make sure to show all your
work. (Hint: the answers should be the same!)

Answer:

a=-3

Step-by-step explanation:

5a+a=-10-8

6a=-18

a=-18/6

a=-3

Answer:

  a = -3

Step-by-step explanation:

This is a linear equation in one variable that has a constant term and a variable term on each side of the equal sign. It can be solved in 3 steps, so can be called a "3-step equation."

The three steps involve separating the variable and constant terms, then dividing by the variable's coefficient.

__

  -a -10 = 5a +8 . . . . . . given

To separate the variable and constant terms, we eliminate one of the variable terms by adding its opposite to both sides of the equation. It is generally convenient to choose the variable term with the lowest coefficient value. When we add the opposite of that to both sides of the equation, the resulting variable term will have a positive coefficient. (Dealing with positive numbers generally reduces errors.)

Here the two variable terms are -a and 5a. The coefficient -1 is less than the coefficient 5, so we choose to add the opposite of -a to both sides.

  -a +a -10 = 5a +a +8 . . . . . add a to both sides

  -10 = 6a +8 . . . . . . . . . . . simplify

Now there is only one variable term, but it has a constant added to it. We can eliminate that constant by adding its opposite.

  -10 -8 = 6a +8 -8 . . . . . add -8 to both sides

  -18 = 6a . . . . . . . . . . . simplify

This equation gives us the value of a multiple of the variable (6a). To get the variable by itself, we multiply by the reciprocal of the variable's coefficient. The product of the coefficient and its reciprocal is 1, so we will have the variable alone.

Multiplying by 1/6 is the same as dividing by 6. Often, it is easier to think in terms of division. However, when the coefficient is a fraction, it can be useful to think in terms of multiplying by the reciprocal of that fraction.

  (1/6)(-18) = (1/6)(6a) . . . . . . multiply by 1/6

  -3 = a . . . . . . . . . . . . . . . simplify

The solution to the equation is a = -3.

_____

Additional comment

When we say "add" or "multiply" the equation by some number, we mean that operation to be performed on both sides of the equation. The properties of equality say we can do whatever we like to an equation, as long as we do the same thing to both sides of the equation.

Answer:

the answer is  4.979

Step-by-step explanation:

Answer:

The answer is 4.979

Step-by-step explanation:

Answer:

I assume ur asking for x and y

Step-by-step explanation:

[tex]3x + 2y = 39 \: \: \: \: \: 1 \ \\ \ 5x - y = 13 \: \: \: \: \: \: \: \: 2 \\ y = 5x - 13 \: \: \: \: \: \: \: \: 3 \\ 3 > 1 \\ 3x+ 2(5x - 13) = 39 \\ 3x + 10x - 26 = 39 \\ 13x = 39 + 26 \: \: \: \: \: \: ( \div 13) \\ x = 5 \\ x = 5 > 3 \\ y = 5(5) - 13 \\ y = 12[/tex]

Answer:

(5, 12 )

Step-by-step explanation:

3x + 2y = 39 → (1)

5x - y = 13 → (2)

multiplying (2) by 2 and adding to (1) will eliminate y

10x - 2y = 26 → (3)

add (1) and (3) term by term to eliminate y

13x + 0 = 65

13x = 65 ( divide both sides by 13 )

x = 5

substitute x = 5 into either of the 2 equations and solve for y

substituting into (1)

3(5) + 2y = 39

15 + 2y = 39 ( subtract 15 from both sides )

2y = 24 ( divide both sides by 2 )

y = 12

solution is (5, 12 )

Answer:

9 is 15% of 60.

Step-by-step explanation:

[tex]\text{Formula}=\frac{\text{Number x 100}}{\text{Percent}} =\frac{9 \times100}{15} =60[/tex]

Following shows the steps on how to derive this formula and find out 15% of what number is 9.

Step 1: If 15% of a number is 9, then what is 100% of that number? Setup the equation.

[tex]\frac{9}{15} = \frac{Y}{100}[/tex]%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

[tex]15Y=6\times100\\15Y=600[/tex]

Y = [tex]\frac{600}{100} =60[/tex]

The requried 15% of 60 is equal to 9, as of the given percentage situation.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To find the number that 15% of is equal to 9, we can set up a proportion:

15% of x = 9

Converting 15% to a decimal:

0.15x = 9

Dividing both sides by 0.15 gives:

x = 60

Therefore, 15% of 60 is equal to 9.

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Answer:

The slope of the line y = x + 1 is equal to 1.

General Formulas and Concepts:
Algebra I

Slope-Intercept Form:
[tex]\displaystyle y = mx + b[/tex]

Step-by-step explanation:

Step 1: Define

Identify given equation.

[tex]\displaystyle y = x + 1[/tex]

Step 2: Find Slope m

Let's compare our given equation to the general equation Slope-Intercept Form to identify our values for slope m and y-intercept b:

We can see that our y-intercept b is equal to 1. Let's rewrite our given expression:

Here, we can identify our slope m to be 1.

∴ the slope of the given line is equal to 1.

___

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___

Topic: Algebra I

Answer: -7 < x < 3

Step-by-step explanation:

-21 < 3x < 9

-7 < x < 3

Answer:

m = 10

Step-by-step explanation:

Find 'n' first..... then pythag theorem for 'm'....

n is to 5    as  15 is to n

n/5   = 15/n

n^2 = 75     n = sqrt (75)

Then   m^2 =  n^2 + 5^2

            m^2 = 75  +  25       s-o-o-o-o:     m = 10

Answer:

10 degrees

Step-by-step explanation:

A straight line equals 180 degrees. We already know we have 110 degrees, so we subtract 180-110 and get 70. Now, we can set up an equation:

We have to isolate x, so divide both sides by 7

70=7x

_____  =  10=x

   7

x=10 degrees

Hope this helps!

Answer + Step-by-step explanation:

GRASS method is an acronym for Given, Required, Analysis, Solution, and Statement.

Given:

Required:

Analysis:

50 (total) = x + 1/4 + 5/8 than solve for x

how much money leftover (x)

= total - spent on gif card - spent on new wallet

x = 50 - 1 / 4 - 5 / 8

Solution:

x = 50 - 1/4 - 5/8

x = 50 - 12.5 - 5/8

x = 50 - 12.5 - 31.25

x = 6.25

Statement:

We found that the leftover amount is $6.25.

Therefore, the leftover amount of money with a starting amount of $50.00 and purchasing a gift card and new wallet is in fact $6.25.

Answer:

[tex]16x^{5} + 16x^{4}[/tex]

Answer:

$42.80

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 9.75%/100 = 0.0975 per year.

Solving our equation:

A = 39(1 + (0.0975 × 1)) = 42.8025

A = $42.80

The total amount accrued, principal plus interest, from simple interest on a principal of $39.00 at a rate of 9.75% per year for 1 years is $42.80.

Answer:

Sales tax is $3.8.  So total would be 39.00+3.8= $42.8

Step-by-step explanation:

The number of second it takes the apple to hit the ground is 4 seconds

To answer the question, we need to know what functions are

Functions are mathematical equations that show the relationship between two variables

Given that when an apple is dropped from a tower 256 feet high, the function h(t) = -16t² + 256 modelshe height of the apple, in feet, after t seconds.

The time it takes the apple hits the ground is when h(t) = 0

So, h(t) = 0

-16t² + 256 = 0

-16t² = -256

t² = -256/-16

t² = 16

t = ±√16

t = ±4

Since t ≥ 0, t = 4 seconds

So, the number of second it takes the apple to hit the ground is 4 seconds

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[tex]\large\boxed{Formula: I= \frac{PRT}{100}}[/tex]

First, we'll have to multiply, principal amount (12500), rate (10) and time period (3).

[tex]12500×10×3[/tex]

[tex]=375000[/tex]

Now, we'll have to divide the amount (375000) by 100.

[tex]\frac{375000}{100}[/tex]

I=$3750

Now, we can find the total amount paid.

[tex]\large\boxed{A=SI+P}[/tex]

Let's substitute according to the formula.

[tex]A=3750+12500[/tex]

A=$16250

Therefore, simple interest is $3750 and $16250 was paid in total.

The area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively, option (a) is correct.

It is defined as the four-sided polygon in geometry having four edges and four corners. Two pairs of congruent sides, and it has one pair of opposite congruent angles.

We know the area of the kite = pq/2

Where p and q are the length of the diagonals

p = 10+10 = 20 ft

q = 7+11 = 18 ft

Area = (20×18)/2

Area = 180 square feet

Thus, the area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively option (a) is correct.

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Answer:

a) 3x⁴-4x³-8x²-35x-10

Step-by-step explanation:

3x2(x²-3x-1)+5x(x²-3x-1)+10(x²-3x-1)

3x⁴-9x³-3x²+5x³-15x²-5x+10x²-30x-10

3x⁴-9x³+5x³-3x²-15x²+10x²-5x-30x-10

3x⁴-4x³-8x²-35x-10

The expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

An expression is combination of variables, numbers and operators.

The area (w) of Vanessa's patio can be found by multiplying the length and width expressions:

w = (3x² + 5x + 10)(x² – 3x - 1)

Expanding this expression using the distributive property, we get:

w = 3x⁴ - 4x³ - 8x² + 15x³ - 25x² - 10x + 10x² - 30x - 10

Simplifying this expression, we get:

w = 3x⁴ + 11x³ - 15x² - 40x - 10

Hence, the expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

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Answer:

360 g

Step-by-step explanation:

Amount of Salt = 2.5% x Amount of Mango

Taking 9 g as the amount of salt :

Answer:

The distribution of the ages of vice president shows that the youngest age is about 36 while the oldest age is around 72. The median age of vice president is 53. On the lower end, the common age is 48 while the age of 60 is upper median age.

50 students preferred science...

Explanation:

we can consider the numbers 5 and 4 in the ratio as units

now we need to know how much each unit represent

units = 5 + 4 = 9

my sample = 90 students

each unit = 90/9 = 10 students

so each unit represents 10 students

back to the ratio

who preferred science = 5

who preferred English = 4

Number of students choose Science = 5 * 10 = 50

Answer:

I think the answer is 1,714 tubes

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

speed  = distance/time

let the time be x

40 = 9/x

so, x = 9/40

to convert it  into minutes,

(9/40)*60 = x

(9*60)/40 = x

540/40 =x

54/4 = x

27/2  = x

13.5 = x

hope this helps :)

Answer:

27/2 is the answer

If Tyler sold his car for $9200, then the approximate percentage profit for this product is 33.3%.

Final price - initial price

Calculate the percentage $2300 is equivalent to by using the information you already have.

33.3% is the profit percentage.

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Answer:

Point C

Step-by-step explanation:

Answer: Point C

Step-by-step explanation: I hope this helped! :D

Answer:

see the attachment photo!

If the shape A is translated four squares right and two squares up, the resulting coordinate point will be at (-3, 6), (-3, 3) and (-1, 3)

Translation is a way of changing the position of an object on the xy plane

Given the coordinates of the vertices (1, 4), (1, 1), (3,1)

If the shape A is translated four squares right and two squares up, the resulting coordinate point will be at (-3, 6), (-3, 3) and (-1, 3)

Note that 4 was subtracted from the x-axis and 2 added to the y-coordinates.

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Answer:

Sasha has used the theoretical probability which assumes that all the possibilities have an equal chance of occurring but in reality, the chances of each probability happening are not going to be equally split with the chances of the bus being on time being slightly higher than being early or late. This is called the experimental probability where you actually test out the probability of the bus being on time, early or late which is much more accurate than the general, theoretical probability.