Find n so that number sentence below is true and explain your answer, referencing the relevant properties of exponents

Since supplementary angles equal 180. (2x+15) = 45, which can be found by subtracting 135 from 180. This means that x = 15. And since angle 1 corresponds to the previous angle, we can deduce that angle 1 = 45.

2.  x = 15 deg; Δ=45 deg

Eight thousand one and forty seven hundredths.

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Let the Width be x cm

Then the length which is 5cm more than width must be (x+5) cm

Using the formula for the area = length* width

x(x+5) =50

[tex]x^2+5x =50[/tex]       (Distribute x on the parenthesis )

[tex]x^2+5x-50 =0[/tex]      (subtract 50 )

[tex](x+10) (x-5) =0[/tex]          (Factor)

[tex]x-5=0\\x+10=0[/tex]

we get

[tex]x=5[/tex]                      (Not x=-10 because negative side length not possible)

Width = 5 cm

Length = 5+5= 10 cm

Perimeter = 2(Length + width)

So

Perimeter = 2(10+5)

Perimeter = 2*15=30 cm

the length of a rectangle is 5 cm more than its width and the area is 50cm2 find the length, width, and the perimeter

L = W + 5 (5 cm more than its width)

Area = W * L

Substitute Area = 50 and L =  W + 5

50 = W ( W+5)

Distributive property

50 = W^2 + 5W

Subtract 50 from both sides

0 = W^2 + 5W - 50

Re-write

W^2 + 5W - 50 = 0

Factor

(W + 10)(W - 5) = 0

W + 10 = 0; W = -10

W - 5 = 0; W = 5

Dimension cannot be negative so W = 5 cm

L = 5 + 5 = 10 cm

Double check: A = 5 x 10 = 50 cm^2

Perimeter = 2(L + W)

Perimeter = 2(5 + 10)

Perimeter = 2(15)

Perimeter = 30 cm

Answer

L = 10 cm

W = 5 cm

P = 30 cm

Hope that helps

16.

4 ÷ 2 = 2

6 ÷ 3 = 3

so,

8 x 2 = 16

The correct answer is 65 degrees.

As the hint stated, the slope is -2 degrees.

So, the easiest way to make a equation is to use slope intercept.  

Y=mx+b

M is the slope, and B is the Y-intercept.

so.

Y = (-2)x+20

Y = -2x+20

Answer:

[tex]T=-2h+20[/tex]

Step-by-step explanation:

the temperature t in fish  starts at 20 degrees Fahrenheit at midnight when h=0.

So when h=0 the T=20 degree (0,20)

The equation of temperature is

[tex]T=m(H)+b[/tex]

Where m is the slope and b is the y intercept

y intercept is the initial degree , so b=20

m is the rate of change that is slope =-2

m=-2, b=20 , [tex]T=m(H)+b[/tex]

The equation becomes

[tex]T=-2h+20[/tex]

Answer:

2 6/7

Sorry if I'm wrong.

Answer:

(d) sin G = 15/17

Step-by-step explanation:

For angle G, opp = 15, adj = 8, hyp = 17.

cos G = adj/hyp = 8/17

sin G = opp/hyp = 15/17

Answer: (d) sin G = 15/17

Polygon FGHIJ is the result of the rotation of ABCDE. 

A = F ⇒ 117°

B = G ⇒ 90°

C = H ⇒ 127°

D = I ⇒ 90°

E = J ⇒ 117°

The measure of angle BCD remains the same because the rotation involves the whole polygon. Thus, it is still 127°

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Answer:

m∠ABC = 117 °

m∠BCD = 90 °

m∠DEA = 90°

m∠CDE = 127°

Step-by-step explanation:

Since this is a series of rigind transformations, the angles of the figure do not change, so:

A=F= 117°

B=G=117°

C=H=90°

D=I=127

E=J=90°

For this case we have,

3/4 of a bushel of apples -----------------------> $ 9

1 bushel of apples -------------------------------> x

From here the value of x is cleared, resulting in:

[tex]x =\frac{(1)(9)}{\frac{3}{4} } \\\\x = 12\\[/tex]

2/3 of a bushel of apples -----------------------> $ 9

1 bushel of apples -------------------------------> x

From here the value of x is cleared, resulting in:

[tex]x = \frac{(1)(9)}{\frac{2}{3} }\\\\x = 13.50 \\[/tex]

Therefore it is convenient to buy apples in store 1 because it is cheaper.

Answer:

It is convenient to buy apples in store 1 because it is cheaper. A division must be made for each case because you want to find the unit cost of a product having the total cost and the amount in fraction.

5x+7 is greater because 2(x-3)+4     =2x-2

1/4 - [-3/8]

[tex]\frac{1}{4}- (-\frac{3}{8})[/tex]

Negative times negative become positive

[tex]\frac{1}{4} + \frac{3}{8}[/tex]

Now to add fractions we make the denominator same

4  and 8 are in the denominator

Least common denominator of 4  and 8 is 8

To make denominators same , we multiply the numerator and denominator of first fraction by 2.

[tex]\frac{1*2}{4*2} + \frac{3}{8}[/tex]

[tex]\frac{2}{8} + \frac{3}{8}[/tex]

The denominators are same so we combine the numerators

[tex]\frac{2+3}{8}[/tex]

[tex]\frac{5}{8}[/tex]

No, x^2 + 20x - 100 is not a perfect square trinomial.

No, x^2 + 20x - 100 is not a perfect square trinomial.

In order for a trinomial to be a perfect square, it must be in the form (a + b)^2 or (a - b)^2.

The given trinomial can be factored as (x + 10)(x - 10), which is not in the form of a perfect square.

To find out how much water drips per day from a faucet that drips 2/3 gallons in 10 hours, we first find the hourly rate which is 1/15 gallons per hour. Then, we multiply this by 24 (the number of hours in a day) to find that the faucet drips 1.6 gallons of water per day.

The unit rate simply means how much of something you have per 1 unit of time or space. In this case, we want to know how much water drips per day from a faucet.

Firstly, we know that the faucet drips 2/3 gallons in 10 hours. We can convert it into how much it would drip in one hour by dividing 2/3 by 10 to get 2/30 or 1/15 gallons per hour. Secondly since one day contains 24 hours, you just multiply the hourly rate (1/15) by 24 to get the daily rate. So, 1/15 * 24 equals 1.6 gallons. Therefore, the faucet drips 1.6 gallons of water per day.

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The correct choice is (C) [tex]1\frac{3}{5}[/tex] gallons per day. To find the daily drip rate, first determine the hourly rate by dividing the given amount by 10 hours, then multiply this rate by 24 hours.

To find the unit rate of water dripped per day from a faucet that drips [tex]\frac{2}{3}[/tex] gallons of water in 10 hours, we first calculate how many gallons it drips in one hour. This is calculated by dividing the quantity of water by the time:

Since there are 24 hours in a day, we multiply the hourly rate by 24 to find the daily drip rate:

As a result, the daily water drip rate is [tex]1\frac{3}{5}[/tex] gallons per day.

Complete question:

a faucet drips [tex]\frac{2}{3}[/tex] gallons of water in 10 hours. what is the unit rate of water dripped per day

(A) [tex]\frac{1}{15}[/tex] gallon per day

(B) [tex]\frac{5}{18}[/tex] gallon per day

(C) [tex]1\frac{3}{5}[/tex] gallons per day

(D) [tex]6\frac{2}{3}[/tex] gallons per day

Answer:

$112.50

Step-by-step explanation:

You take 25 + 25 +25 +25 = 100

that equals 8 pizzas

half of 25 is 12.5

so for one pizza it is $12.50

100 + 12.5 = 112.50

Final answer:

The function rule for the area of a rectangle is A = W² + 7W. When the width is 7 feet, the area of the rectangle is 98 square feet.

Explanation:

To write a function rule for the area of a rectangle, we need to express the area in terms of the independent variable, which in this case is the width (W). The length is given as 7 feet more than the width, so we can write the length as W + 7. The area (A) of a rectangle is given by the formula A = length × width. Substituting the values, we get A = (W + 7) × W = W² + 7W.

To find the area of the rectangle when the width is 7 feet, we can plug in W = 7 into the function rule. A = 7² + 7 * 7 = 49 + 49 = 98 square feet. Therefore, the area of the rectangle is 98 square feet when the width is 7 feet.

2 and 1/10 of an hour

In other words, it is 2 hours and 6 minutes

Add 1/2 and 1 and 3/5 together to get 21/10

2(3 – 4a) + 5(a – 7)

Distribute 2  and 5 inside the parenthesis

Step 1:  2*3 - 2*4a + 5*a - 5*7

When we multiply it we will get

Step 2: 6 - 8a + 5a -35

Now we combine like terms. The terms that as same variables are like terms

-8a + 5a  is -3a

6 - 35 is -29

6 - 8a + 5a -35

Step 3: -3a -29

Final answer is -3a-29

Answer:

811÷77= 10.265....

Step-by-step explanation:

To find a fraction's simplest form, you need to find the GCF. The greatest common factor is the largest number that can go into the numerator and the denominator.

We know that 1 is a factor, but let's keep going to make sure. 2 is also a factor.

14/2 = 7

16/2 = 8

Since 14 and 16 are not divisible by 3, 2 is the GCF (we know not to continue dividing).

Therefore, it's simplest form is 7/8.

The fraction 14/16 in simplest form is 7/8.

To simplify the fraction 14/16,  find the greatest common divisor (GCD) of the numerator (14) and the denominator (16) and then divide both the numerator and denominator by the GCD.

Step 1: Find the Greatest Common Divisor (GCD) of 14 and 16.

The divisors of 14 are 1, 2, 7, and 14.

The divisors of 16 are 1, 2, 4, 8, and 16.

The largest number that appears in both lists is 2. Therefore, the GCD of 14 and 16 is 2.

Step 2: Divide both the numerator and denominator by the GCD (which is 2).

14 ÷ 2 = 7

16 ÷ 2 = 8

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Standard form: Ax + By = C

So  3x - 1 = 2y

     3x - 2y = 1

Answer

B. 3x - 2y = 1

The standard form of the equation is 3x-2y=1, the correct option is B.

Linear equations are the equations of degree 1. It is the equation for the straight line.

The standard form of linear equation is;

[tex]\rm ax+by=c[/tex]

Given

The linear equation is;

3x - 1 = 2y

The equation can be expressed in the standard form

[tex]\rm 3x - 1 = 2y\\\\ 3x -1 -2y=0\\\\3x-2y=0+1\\\\3x-2y=1[/tex]

Hence, the standard form of the equation is 3x-2y=1.

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We are given this

[tex]x^6 -64y^3[/tex]

write it as the difference of cubes

[tex](x^2)^3 -(4y)^3[/tex]

use the formula for the difference of cubes

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

Now use the formula for the difference of squares as [tex]4y = (2\sqrt{y} )^2[/tex]

[tex](x-2\sqrt{y}) (x+2\sqrt{y}) (x^4+4x^2y+16y^2)[/tex]

The correct answer is A. Because if you substitute the x and y you will get the same outcome.  y=8x substitute and you get 24= 8(3) and then multiply and you get 24 = 24