When solving p^2 + 5 = 8p - 7. Kate wrote p^2 + 12 = 8p. The property she used was:
1) the associative property
2) the commutative property
3) the distributive property
4) the addition property of equality

Answer:5+5=10 5+5=10

i now it because if u draw it out then u count the sides then u count the other side then u plus that then u get ur answet

The perimeter of the rectangle is 21.2 meters

Given the parameters given for our Calculation;

Area of rectangle ;

Let ;

Hence,

Area = l * 2l = 25

2l² = 25

l² = 12.5

l = √12.5

l = 3.53 m

width = 3.53 * 2 = 7.07 m

Perimeter can be calculated thus;

Hence, the perimeter of the rectangle is 21.2 m

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1. 612.85

14.42 x 42.5 = $612.85

2. 110.313

612.85 x .18 = $110.313

3. $72.063

110.313 - 38.25 = $72.063

4. %11.75

72.063 / 612.85 = 0.11758

0.11758 x 100 = %11.75

5. 479.861

110.313 x 4.35 = 479.861

Courtney's weekly earnings before taxes are $612.85. After an 18% tax, her earnings are $502.54, which becomes $464.29 after saving $38.25. The paycheck's remaining percentage is 75.76%, and her monthly earnings after taxes average $2,186.05.

Courtney earns $14.42 per hour and works 42.5 hours a week. To calculate her weekly earnings before taxes:

Weekly earnings = Hourly wage times Hours worked per week
Weekly earnings = $14.42 times 42.5
Weekly earnings = $612.85

To find out how much she makes after an 18% tax deduction:

Taxed amount = Weekly earnings times Tax rate
Taxed amount = $612.85 times 0.18
Taxed amount = $110.31

Earnings after tax = Weekly earnings - Taxed amount
Earnings after tax = $612.85 - $110.31
Earnings after tax = $502.54

After Courtney saves $38.25, her disposable weekly income is:

Money left to spend = Earnings after tax - Savings
Money left to spend = $502.54 - $38.25
Money left to spend = $464.29

Now, to calculate the percentage of paycheck left after taxes and savings:

Percentage left = (Money left to spend / Weekly earnings) times 100
Percentage left = ($464.29 / $612.85) times 100
Percentage left = 75.76%

For her monthly earnings after taxes, considering an average of 4.35 weeks per month:

Monthly earnings after taxes = Earnings after tax times Average weeks per month
Monthly earnings after taxes = $502.54 times 4.35
Monthly earnings after taxes = $2,186.05

Answer:

[tex]\frac{2}{5},\frac{1}{4},\frac{1}{10},\frac{5}{2},\frac{5}{8},\frac{4}{1},\frac{8}{5},\frac{10}{1}[/tex]

Step-by-step explanation:

Proportions are fractions that can be created using the numbers given. Let's pair each and reduce if possible.

Starting with 2:

2/5

2/8 = 1/4

2/20 = 1/10

Then 5:

5/2

5/8

5/20 = 1/4

Then 8:

8/2 = 4/1

8/5

8/20 = 2/5

Lastly 20:

20/2 = 10/1

20/5 = 4

20/8 = 5/2

So, we can see some are repeating, hence the unique proportions are:

2/5, 1/4, 1/10, 5/2, 5/8, 4/1, 8/5, 10/1

The possible proportions using the numbers 2 5 8 and 20 are:

1. 2:5 = 8:20

2. 2:8 = 5:20

3. 5:20 = 2:8

4. 8:2 = 20:5

5. 20:5 = 8:2

6. 5:2 = 20:8

To create all possible proportions using the numbers 2, 5, 8, and 20, you can set up ratios and see how you can pair these numbers.

A proportion is essentially an equation that states two ratios are equal.

Here are some possible proportions you can create:

1. 2:5 = 8:20

  (This is a direct proportion where both ratios reduce to 2:5.)

2. 2:8 = 5:20

  (Again, this is a direct proportion where both ratios reduce to 1:4.)

3. 5:20 = 2:8

  (This is just another way to write the second proportion.)

4. 8:2 = 20:5

  (This is an inverse proportion where the first ratio is the reciprocal of the second.)

5. 20:5 = 8:2

  (This is just another way to write the fourth proportion.)

6. 5:2 = 20:8

  (This is an inverse proportion where the first ratio is the reciprocal of the second.)

7. 20:8 = 5:2

These are all the possible proportions you can create using the numbers 2, 5, 8, and 20. Note that in each proportion, you can switch the positions of the numbers (e.g., 2:5 = 8:20 is the same as 5:2 = 20:8), but the ratios remain the same.

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Answer:

7 feet and 24 feet

Step-by-step explanation:

In the right triangle, the hypotenuse is 25 feet long. The area of this triangle is 84 square feet.

Let x feet and y feet be the lengths of triangle's legs.

By the Pythagorean theorem,

[tex]x^2+y^2=25^2\\ \\x^2+y^2=625[/tex]

The area of the right triangle is half the product of its legs, thus

[tex]84=\dfrac{1}{2}xy\\ \\xy=168[/tex]

Solve the system of two equations:

[tex]\left\{\begin{array}{l}x^2+y^2=625\\ \\xy=168\end{array}\right.[/tex]

From the second equation:

[tex]x=\dfrac{168}{y}[/tex]

Substitute it into the first equation:

[tex]\left(\dfrac{168}{y}\right)^2+y^2=625\\ \\168^2+y^4=625y^2\\ \\y^4-625y^2+168^2=0\\ \\D=(-625)^2-4\cdot 168^2=(625-2\cdot 168)(625+2\cdot 168)=289\cdot 961=17^2\cdot 31\\ \\\sqrt{D}=17\cdot 31=527\\ \\y^2_{1,2}=\dfrac{-(-625)\pm 527}{2}=49,\ 576\\ \\y_1=7,\ y_2=-7,\ y_3=24,\ y_4=-24[/tex]

The length of the leg cannot be negative, so

[tex]y_1=7\Rightarrow x_1=\dfrac{168}{7}=24\\ \\y_2=24\Rightarrow x_2=\dfrac{168}{24}=7[/tex]

Answer:

(100, –100)

-y = x

D) y = -x

The equation that has (100, -100) as a solution is option D:

D. y = -x

Given is a point (100, -100) we need to determine which equation can have this point as it solution.

To determine which equation has (100, -100) as a solution, we can simply substitute the values of x and y into each equation and see which one satisfies the condition.

Let's try each option:

A. y = 0.1x - 99

When x = 100, y = 0.1 × 100 - 99

= 10 - 99

= -89 (not -100)

B. y = -x - 100

When x = 100, y = -100 - 100

= -200 (not -100)

C. y = x

When x = 100, y = 100 (not -100)

D. y = -x

When x = 100, y = -100 (matches the given solution)

So, the equation that has (100, -100) as a solution is option D:

D. y = -x

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Final answer:

To find the area of a square when given its perimeter, divide the perimeter by 4 to find the side length and then square this length. Thus, a square with a perimeter of 32 inches has an area of 64 square inches.

Explanation:

If the perimeter of a square is 32 inches, we can calculate the length of one side by dividing the perimeter by 4, because a square has 4 equal sides. So each side is 32 inches ÷ 4, which equals 8 inches.

Once we have the side length, we can calculate the area of the square. The area of a square is determined by squaring its side length (side length × side length). In this case, the area would be 8 inches × 8 inches, which equals 64 square inches.

Therefore, the area of the square with a perimeter of 32 inches is 64 square inches.

Answer:

3^0 is 1 in a simplified form

Answer:

1

Step-by-step explanation:

3^0

Apply rule a^0=1 a=0

=1

Thanks for letting me help!!

Answer:

No

Step-by-step explanation:

I hope the picture helps

No, the given equation y = 0(x-4)² + 3 is not a quadratic function.

In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.

Given function is y = 0(x-4)² + 3. Solve the functions:-

y = 0(x-4)² + 3

In the second term, the value of the whole term will become zero.

y = 0 + 3

y = 3

The value of y is 3 which is a constant term. Therefore, the given equation y = 0(x-4)² + 3 is not a quadratic function.

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Answer:

See explanation

Step-by-step explanation:

A triangle PQR has its vertices at points P(1,-1), Q(3,-2) and R(3,-4).

A counterclockwise rotation by angle of 90° about the origin has the rule

[tex](x,y)\rightarrow (-y,x)[/tex]

Hence,

The image triangle is shown in attached diagram.

The distributive property is a math concept that allows multiplication to be distributed over addition or subtraction. It does not directly apply to the expression 16 + 36, as there's no multiplication involved. However, for an expression with multiplication, such as 4(16 + 36), it would simplify to 208 using the distributive property.

The distributive property is a fundamental concept in mathematics that allows us to simplify expressions involving multiplication distributed over addition or subtraction. It states that for any numbers a, b, and c, the equation a(b + c) = ab + ac holds true. This property makes it easier to work out expressions without having to perform operations within parentheses first.

In the given expression 16 + 36, however, there's no multiplication being distributed over addition, thus the distributive property doesn't directly apply here. But if we are to apply the distributive property to a multiplication over an addition, such as 4(16 + 36), then we would use the distributive property to get 4*16 + 4*36, which simplifies further to 64 + 144 = 208.

Answer:

Scalene and obtuse

Step-by-step explanation:

obtuse cuz 132 is greater than 90

scalene cuz all three sides have different lengths

Use PEMDAS:

[(30+6) -3^2] / 9* 2

= (36 -9)/ 9* 2

= 27/9* 2

= 3*2

= 6

The final answer is 6~

Answer:

6

Step-by-step explanation:

*PEMDAS*

1st write equation

[(30+6) -3^2] / 9* 2

2nd parentheses

= (36 -9)/ 9* 2

3rd divided

= 27/9* 2

4th multiply

= 3*2

6th simplify

= 6

Answer:

[tex]\frac{3x+5}{8x-2}[/tex]

Explanation:

The reciprocal of a fraction is when you just "turn it upsidedown". Which means, you take the numerator and the denominator and swap their places. So instead of having the [tex]\frac{numerator}{denominator}  you would change it to \frac{denominator}{numerator}[/tex]

Answer:

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

Step-by-step explanation:

Just invert the fraction:

= (8x - 2) / (3x + 5).

Answer:

4x^2-5y

Step-by-step explanation:

4x^2-5y

Final answer:

The question involves using algebraic expressions to square a number by multiplying it by itself and then subtracting the product of another number multiplied by five. it could be represented as 4a2 - 5b.

Explanation:

The question involves understanding how to manipulate algebraic expressions with integers and variables. When we talk about raising a number to a power, such as squaring a number, we are multiplying that number by itself. For example, the exponent is '2' and the base is the number '5', so squaring it would give us 52 = 5x5 = 25. When we consider an equation involving the square of one number and the multiplication of another, we have to apply these rules of exponents and multiplication.

In mathematics, we often encounter expressions where we square a number by raising it to the power of '2'. This also applies to variables. For instance, (2x)2 = 4x2. Remember, whether numbers are positive or negative, squaring them will always give a positive result because multiplying two negative numbers yields a positive product.

If a question involves subtracting five times one number from four times the square of another number, it could be represented as 4a2 - 5b. Here, a is being squared while b is simply being multiplied by five.

Answer:

Alejandro received 6.51 million of votes

Laine received 58% of votes

Step-by-step explanation:

If the ratio of "Laine votes" to "Alejandro votes” was 29:21, then the number of "Laine votes" was 29x and the number of "Alejandro votes” was 21x. In total, 15.5 million votes were cast. So

29x + 21x = 15.5 million

50x = 15.5 million

x = 0.31 million

Then

the number of "Laine votes" [tex]=29\cdot 0.31=8.99[/tex] million

number of "Alejandro votes” [tex]=21\cdot 0.31=6.51[/tex] million

Laine received

[tex]\dfrac{8.99}{15.5}\cdot 100\%=58\%[/tex]

(10v + 45) = 5(2v + 9)

To factor find a number that can go flu shot into the 2 numbers given. In the question you posted, th at number was 5. 5 could go into 10v and 45.

If you need a better explanation just as in the comments.

Happy to help! Please mark as BRAINLIEST! Thanks

To solve the inequality -4.4 ≥ 1.6x - 3.6, you first add 3.6 to both sides, then divide by 1.6, resulting in -0.5 ≥ x. This means all values less than or equal to -0.5 make the inequality true and the graphed solution involves a filled circle at -0.5 and shading to the left.

To find the solution set for the inequality -4.4 ≥ 1.6x - 3.6, we first need to solve the inequality. To do this, we can start by adding 3.6 to both sides of the inequality:

-4.4 + 3.6 ≥ 1.6x

-0.8 ≥ 1.6x

Now, we divide both sides of the inequality by 1.6 to solve for x:

-0.8 / 1.6 ≥ x

-0.5 ≥ x

This tells us that x can take on any value that is less than or equal to -0.5. To graph this on a number line, we would plot a filled circle on -0.5 to indicate that it is part of the solution set (x is equal to -0.5), and shade everything to the left of -0.5 to indicate that all those values are solutions since they are less than -0.5.

The total temperature rise was 19 degrees.

Temperature express the measure of hotness and coldness, how hot matter is. It measure this thing in terms of any of several arbitrary scales like Fahrenheit temperature scale, absolute scale (kelvin) etc.    

In the question statement, the temperature at 10 A.M is 12 degrees Fahrenheit. The temperature at 6:00 A.M. was -7 degrees Fahrenheit.

Here the difference in both the temperatures is as:

12 - (-7) = 21  degrees Fahrenheit

Hence there was an increase in temperature of 21 degrees Fahrenheit.

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Answer:

91

Step-by-step explanation:

You can automatically elimate all numbers containing 0.

So, I used 1 as the ones digit.

The tens digit is 8 more than the ones digit, so it would be 8+1 which equals 9.

I'm assuming it's a 2 digit number? That must be the case because otherwise there would be multiple answers.

Hope it helped! :)

D. The y-intercept is (0,5) of the function 5*(6)ˣ

Given function is f(x) = 5*(6)ˣ

Now we have to choose correct statement from the given options.

Option A: The domain of f(x) is x>0.

Exponential functions are of the form f(x) = a*bˣ

Also the given function is in exponential function.

For any exponential function, domain is the set of real numbers not only x>0,

So this option is false.

Option B : The y-intercept is (0,1).

y-intercept means the value of x is 0.

f(0) = 5*6⁰

⇒ f(0) = 5 ≠ 1

So this option is false.

Option C :  It is always decreasing.

Exponential functions are of the form f(x) = a*bˣ

The function will be increasing, if b>1

Given function is f(x) = 5*(6)ˣ

As 6>1, we can say that the function is increasing function.

So this option is false.

Option D : The y-intercept is (0,5).

y-intercept means the value of x is 0.

f(0) = 5*6⁰

⇒ f(0) = 5

So, the y-intercept is (0, 5).

So this option is true.

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Answer:

1.78913×107

Step-by-step explanation:

312·112·512≈1.78913×107

Answer:

b

Step-by-step explanation:

6y-5=11

Move -5 to the other side. Sign changes from -5 to +5.

6y-5+5=11+5

6y=11+5

6y=16

Divide by 6 for both sides to get y by itself.

6y/6=16/6

Cross out 6 and 6, divide by 6 and then becomes 1*1*y=y

y=16/6

Reduce 16/6 by dividing by 2

16/2=8

6/2=3

Answer: y=8/3 or y=2 2/3

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-10}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-1)}}}\implies \cfrac{-10+5}{4+1}\implies \cfrac{-5}{5}\implies -1[/tex]

The volume of the given sphere is 32 cm³. Thus, the correct answer is option (A) 32 cm³.

Given that the diameter of the sphere is 4 cm, the radius is half of that or 2 cm.

The formula for the volume of a sphere is:

V = (4/3)πr³

Where r is the radius of the sphere.

Here, r = 2

Substituting these values into the formula, we get:

The volume of a sphere = (4/3) × π × (2)³

The volume of a sphere  = (4/3)π(8)

The volume of a sphere  = 32π/3

Using π = 3.14, we get:

The volume of a sphere  ≈ 33.51 cm³

Therefore, the closest option to the volume of the sphere is 32 cm³.

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The median of the given data is 118.

It is required to find the median.

The median is the middle value in a set of data .The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.

Given:

The given date are arranged in ascending order

110 112 114 116 118 120 122 124 126 °F

Total number of the data is 9 which is odd ,so the median is

n+1/2

Where n=number of values in data set

According to given question we have,

Median=n+1/2

Median=9+1/2

Median=5

The 5th term of the number is median of the given data i.e 118.

Therefore, the median of the given data is 118.

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Answer: she would make $100 after 10 hours

Step-by-step explanation:

if you divide 240 by 24 you get 10 which stands for the dollar amount per hour so 10 x 10 =100

Answer: 461,160 books will be printed.

Step-by-step explanation:

1,512×305=461,160

Answer: [tex]461,160\ books[/tex]

Step-by-step explanation:

 According to the exercise, the number of copies of a book printed in each run is:

[tex]1,512\ copies\ per\ run[/tex]

Then, let be "x" the number of the number of books that will be printed in 305 runs.

In order to calculate the value of "x", you must multiply 1,512 (which is the number of copies of a book printed in each print run) by 305.

Therefore, you get that the number of books that will printed in 305 runs is:

[tex]x=(1,512)(305)\\\\x=461,160\ books[/tex]

The order of the months from greatest to least number of visitors to the online newspaper is November, October, December. This is based on comparison of the visitor counts for each month.

To determine the order of the months from greatest to least number of visitors, you need to compare the number of visitors for each month. In October, the online newspaper had 350,080 visitors. In November, there were 350,489 visitors. Finally, in December, the visitor count was 305,939.

By observing these numbers, we can see that November had the most visitors, then October, and finally December, which had the least visitors. Therefore, the order of the months from greatest to least number of visitors is: November, October, December.

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