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Complete the proofs for theorem 7.
Theorem 7: Supplements of congruent angles are congruent.

Answer:

(-3/2, 5/2)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

3x + y = -2

5x - y = -10

Step 2: Solve for x

Eliminate y

Step 3: Solve for y

Answer:

7 is the greatest comman factor of 28 and 49

Answer:

76

Step-by-step explanation:

Answer: L=A/W

Or you can plug in the values for Area and width.

Step-by-step explanation:

If you divide the total area by the width, you get the length

A: 400

L: ?

W: 50

400=50L

400/50=50L/50

8=L

L=400/50

L=8

Hope this helps!

Answer: a. $9.45 ; b. $135.45

Step-by-step explanation:

Since two pairs of shorts for $25 each, the total amount she'll pay for the shorts is:

= $25 × 2

= $50

Since the four shirts with an average cost of $19 per shirt. The total amount she'll pay for the shirt is:

= $19 × 4

= $76

A. Her sale tax will be calculated as:

= 7.5% × ($50 + $76)

= 0.075 × $126

= $9.45

B. Her total cost will be:

= Cost of shorts + Cost of shirts + Sales tax

= $50 + $76 + $9.45

= $135.45

Answer:

Part A- 9.45  Part B- 135.45

Step-by-step explanation:

Answer:

The answer is 144.

Step-by-step explanation:

The question said 6 gallons of water comes out every minute. So, if you multiply 6x24 you get the answer of 144.

Answer:

The answer is 13%

Step-by-step explanation:

The approximate percent increase is 13%.

Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. To calculate the percentage we need to have the initial value and the increased (new) value. In other words, we can say that percentage increase is a measure of percent change which gives the extent to which a quantity gains magnitude, intensity, or value. If the percentage increase is a negative value, then we can say that there is a percentage decrease of the same magnitude.

Following the concept of percentage increase, the percentage increase formula is derived and expressed as: Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100. It should be noted that since the percentage has to be a positive quantity, we take the absolute value of the initial value. If the percentage increase is a negative value, then it is a percentage decrease. The percentage increase is the relative change in the quantity with respect to its initial value. If the percentage change is positive, then it is the percentage increase and if the percentage change is negative, it is a percentage decrease.

Given:

initial =$900,000

Final = $900,000

% increase = $900,000- $800,000/ $800,000 * 100

% increase = 100, 000/8000

% increase = 12.5 %

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Answer:

53

Step-by-step explanation:

Do what is in the parentheses first and then outside. Multiply 3 by 6 then subtract 7. Add 11 to 42 and you get 53.

Answer: 53

Step-by-step explanation:

Step-by-step explanation:

[tex] - 2 \times \frac{1}{2} \div 3 \times \frac{1}{2 } \\ - \frac{5}{2} \div \frac{7}{2} \\ - \frac{5}{2} \times \frac{2}{7} \\ = - \frac{5}{7} [/tex]

6) The solution set of the equation x² + 8x - 15 = 5x + 13 is {-7, 4}.

7) The zeroes of the expression 2x (x - 5) (x + 7) are {-7, 0, 5}.

8) The expression (x + 5) (x + 8) + (x + 5)(2x - 3) can be written as a product of (x + 5) and (3x + 5).

9) There are 2 integer solutions on the interval 0 ≤ x ≤ 10 for the equation x³ - 5x² + 2x + 13 = 5.

We have,

6)

x² + 8x - 15 = 5x + 13

Rearranging the equation:

x² + 8x - 5x - 15 - 13 = 0

x² + 3x - 28 = 0

Now, factorize the quadratic equation:

(x + 7)(x - 4) = 0

Setting each factor equal to zero:

x + 7 = 0 or x - 4 = 0

Solving for x:

x = -7 or x = 4

7)

2x (x - 5) (x + 7) = 0

Setting each factor equal to zero:

2x = 0 or x - 5 = 0 or x + 7 = 0

Solving for x:

x = 0 or x = 5 or x = -7

8)

(x + 5) (x + 8 + 2x - 3)

Simplifying the expression inside the parentheses:

(x + 5) (3x + 5)

9)

x³ - 5x² + 2x + 13 = 5

Substitute each integer value from 0 to 10 into the equation and count the number of solutions.

Substituting each integer value,

x = 0,

x³ - 5x² + 2x + 13 = 5

0 - 0 + 0 + 13 = 5

13 = 5

Not true.

Similarly,

x = 2,

x³ - 5x² + 2x + 13 = 5

8 - 20 + 4 + 13 = 5

25 - 20 = 5

5 = 5

True.

x = 4,

x³ - 5x² + 2x + 13 = 5

64 - 80 + 8 + 13 = 5

85 - 80 = 5

5 = 5

True.

There are two integer solutions:

x = 2 and x = 4.

Therefore,

The solution set of the equation x² + 8x - 15 = 5x + 13 is {-7, 4}.

The zeroes of the expression 2x (x - 5) (x + 7) are {-7, 0, 5}.

The expression (x + 5) (x + 8) + (x + 5)(2x - 3) can be written as a product of (x + 5) and (3x + 5).

There are 2 integer solutions on the interval 0 ≤ x ≤ 10 for the equation x³ - 5x² + 2x + 13 = 5.

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Answer:

padlet        com     /vpena20241    

/sv1blyklvnvfbcdw

Step-by-step explanation:

Answer: number 3

Step-by-step explanation:

Answer:$240

Step-by-step explanation:

Answer:

The answer is option B: a < -21 1/3

Step-by-step explanation:

You can use a calculator to divide -16 by 3/4. Since it is an inequality, multiplication or division causes you to flip the sign.

Answer:

482.70

Step-by-step explanation:

First, find out how much he earned per hour last week. 576.56 divided by 43 is 13.41.

Second, multiply his hourly earnings by 1.2, 1.2*13.41=16.09 So he earns 16.09 per hour

Lastly, multiply 16.09 by 30, 16.09*30=482.7 So he earns about $482.70 each week.

Answer:

B.

Step-by-step Explanation:

The correct number line for -2.75 < x in the given options is the second diagram.

A number line is a picture of straight line that represents real numbers. These real numbers include both negative and positive numbers.

For the given expression which -2.75 < x, that is negative 2.75 is less than x or x is greater than negative 2.75.

On the number line, the arrow with unshaded circular bottom must start from -2.75 and point towards the right.

Thus, the correct number line in the given options is the second diagram or option B.

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Answer:

138/92*320 = 480 milligrams. ... If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should be given to a patient who ... If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should be given to a patient who weighs 138 pounds. 2.

Step-by-step explanation:

I hope I help :)

Answer:

Refexive I think

Step-by-step explanation:

5(3) = 3(5)

or

x(y) = y(x)

I found this

"Anything equals itself: this is the "reflexive" (reflecting onto itself) property. Also, it doesn't matter which order the equality is in; if x = y, then y = x: this is the "symmetric" (they match) property."

Answer:

D?

Step-by-step explanation:

I think so

Answer:

D.The character's transformation shows that the unlikeliest of people can be heroes.

Answer:

9

Step-by-step explanation:

Answer:

ok

Step-by-step explanation:

Answer:

83

Step-by-step explanation:

Answer:

x = 59

y = 83

Step-by-step explanation:

First, you need to solve for y in order to solve for x. Using the Triangle Sum Theorem, you will find that y is 83 degrees.

Now, using the Vertical Angles Theorem, you can figure out the third angle of the triangle in which x is, 83.

Using the Triangle Sum Theorem again, you will find that x is 59.

Answer:

11

Step-by-step explanation:

3 - (-8) = 3 + 8 = 11

Answer: 11

Step-by-step explanation:

This is because when you subtract a negative number from a positive you get a positive (here's a lil trick if you have 2 minuses In a row they become a plus sign) so the answer is 11