This equation graphed is?

Answer:

The mid-point (p + q , q + p) of AB is the same distance from the x-axis and the y-axis

Step-by-step explanation:

* Lets explain how to solve the problem

- Any point will be equidistant from the x-axis and the y-axis must have

 equal coordinates

- Ex: point (4 , 4) is the same distance from the x-axis and the y-axis

 because the distance from the x-axis to the point is 4 (y-coordinate)

 and the distance from the y-axis and the point is 4 (x-coordinate)

- If (x , y) is the mid-point of a segment its endpoints are

 [tex](x_{1},y_{1})[/tex]  and [tex](x_{2},y_{2})[/tex], then

 [tex]x=\frac{x_{1}+x_{2}}{2}[/tex] and [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]

* Lets solve the problem

∵ Point A has coordinates (p , q)

∵ Point B has coordinates (p + 2q , q + 2p)

- The mid-point of AB is (x , y)

∵ [tex]x=\frac{p+p+2q}{2}[/tex]

∴ [tex]x=\frac{2p+2q}{2}[/tex]

- Take 2 as a common factor from the terms of the numerator

∴ [tex]x=\frac{2(p+q)}{2}[/tex]

- Divide up and down by 2

∴ x = p + q

∵ [tex]y=\frac{q+q+2p}{2}[/tex]

∴ [tex]y=\frac{2q+2p}{2}[/tex]

- Take 2 as a common factor from the terms of the numerator

∴ [tex]y=\frac{2(q+p)}{2}[/tex]

- Divide up and down by 2

∴ y = q + p

∴ The mid point of AB is (p + q , q + p)

- p + q is the same with q + p

∵ The x-coordinate of the mid point of AB is p + q

∵ The y-coordinate of the mid point of AB is q + p

∵ p + q = q + p

∴ The coordinates of the mid-point of AB are equal

- According the explanation above

∴ The mid-point (p + q , q + p) of AB is the same distance from the

   x-axis and the y-axis

we know it takes 20lbs of Olive to make 3 liters of oil, we also know that the orchard for a whole year gets 3000 lbs, how much oil is there in those 3000 lbs for the year?

[tex]\bf \begin{array}{ccll} \stackrel{olive}{lbs}&\stackrel{olive~oil}{liters}\\ \cline{1-2} 20&3\\ 3000&x \end{array}\implies \cfrac{20}{3000}=\cfrac{3}{x}\implies \cfrac{1}{150}=\cfrac{3}{x}\implies x= 450[/tex]

Answer:

No.

Step-by-step explanation:

No.

16 is a perfect square because 4 times itself is 16.

9 is a perfect square because 3 times itself is 9.

So there are no whole numbers such that when yoy square it (times it by itself) gives you 15.

Whole numbers are numbers contained within the following set:

{0,1,2,3,4,5,...}

So here are the first few perfect squares:

0 because 0(0)=0

1 because 1(1)=1.

4 because 2(2)=4.

9 because 3(3)=9.

16 because 4(4)=16.

25 because 5(5)=25.

36 because 6(6)=36.

49 because 7(7)=49.

64 because 8(8)=64.

81 because 9(9)=81.

As you can see 15 isn't in that list.

Answer: [tex]6[/tex]

Step-by-step explanation:

Given the following expression:

[tex]8a-1+0.5b[/tex]

You need to substitute the given values of "a" and "b" into the expression. Notice that these values are:

[tex]a=\frac{1}{4}\\\\b=10[/tex]

Then;

 [tex]8a-1+0.5b=8(\frac{1}{4})-1+0.5(10)[/tex]

Now you must solve the multiplications:

[tex]=\frac{8}{4}-1+5=2-1+5[/tex]

The final step is to add the numbers. Therefore, you get the following answer:

[tex]=6[/tex]

The value of the expression 8a - 1 + 0.5b evaluates to 6 for a = 1/4 and b= 10.

To evaluate the expression 8a - 1 + 0.5b when a = 1/4 and b = 10, you can substitute these values into the expression and then perform the calculations:

1. Substitute the value of a:

  8 * (1/4) - 1 + 0.5 * 10

2. Simplify each term:

  - First term: 8 * (1/4) = 2

  - Second term: -1

  - Third term: 0.5 * 10 = 5

3. Add the simplified terms:

  2 - 1 + 5 = 1 + 5 = 6

So, when a = 1/4 and b = 10, the expression 8a - 1 + 0.5b evaluates to 6.

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Answer:

x= 31 degrees

Step-by-step explanation:

A triangle's angles add up to 180 degrees. Look at the 123, it's not part of the triangle. Subtract it from 180. You should get 57 degrees. Now, make an equation. You know it equals 180, so you add up all the sides like this: 57+92+x=180. After solving the equation, you should get 31 degrees.

Answer:

40000

Step-by-step explanation:

4(2)395

if it smaller than 5 round down

if its lager than 5 round up

Answer:

9

Step-by-step explanation:

Using the identity

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Subtract 2(ab + bc + ca) from both sides, then

a² + b² + c² = (a + b + c)² - 2(ab + bc + ca) = 7² - 2(20) = 49 - 40 = 9

Sophie earns $8.00 per hour. To find this, dividends of $18 by 2.25, representing the total hours worked, result in the per-hour earning.

To calculate how much Sophie earns per hour, we need to divide her total earnings by the total number of hours she worked. Sophie earns $18 over 2 1/4 hours.

First, we express the hours worked as an improper fraction or a decimal for ease of calculation. Since 1/4 hour is equivalent to 15 minutes, and 2 1/4 hours are the same as 2 + 0.25 which equals 2.25 hours. Now we divide $18 by 2.25 hours to find the hourly wage:

Hourly Wage = Total Earnings / Total Hours Worked

Hourly Wage = $18 / 2.25 hours

Hourly Wage = $8.00 per hour

So, Sophie earns $8.00 per hour.

Answer:

80%

Step-by-step explanation:

The percent increase in the price of the house is 25%. This is calculated using the formula for percent increase: (Final value - Initial value) / Initial value * 100.

The question is asking for the percent increase in the price of a house. The formula for calculating percent increase is: (Final value - Initial value) / Initial value * 100. In this case, the initial value is the original house price of $400,000 and the final value is the new house price of $500,000.

So, the calculation will be: ($500,000 - $400,000) / $400,000 * 100 = 25%.

Therefore, the price of the house increased by 25% over the year.

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Step-by-step explanation:

distribute the -2 to (x+1) you end up with -2x-2=8 (multiplication property). Add 2 to both sides to get rid of the -2 of the left (addition property). 8+2=10. -2x=10 divide the -2 to both sides. x=-5 (division property).

Answer:

We have to prove that,

-2(x+1)=8, then x= -5

L.H.S.

[tex]-2(x+1)=8[/tex]

By distributive property,

[tex]-2x-2=8[/tex]

Adding 2 both sides ( Additive property of equality )

[tex]-2x-2+2=8+2[/tex]

[tex]-2x=10[/tex]

Divide both sides by -2 ( Division property of equality ),

[tex]\frac{-2x}{-2}=\frac{10}{-2}[/tex]

[tex]x=-5[/tex]

= R. H. S

Hence, proved....

Answer:

12 pages

Step-by-step explanation:

According to the question Kendra have 120 stickers

10 stickers fill a page

So, number of pages that can be filled be 120 stickers = [tex] \frac{120}{10} = 12[/tex]

Therefore, she can fill 12 pages by 120 stickers.

The total number of pages Kendra can fill with a total number of 120 stickers is 12 pages.

Kendra has 120 stickers, and 10 stickers fill a page.

To calculate how many pages she can fill, divide the total number of stickers by the stickers per page:

120 stickers ÷ 10 stickers/page = 12 pages.

Answer:

Step-by-step explanation:

Answer:

EF =58

Step-by-step explanation:

from the illustration,

EF =DF - DE

given that DF =9x-39 , DE =47 EF=3x +10

substitute them into the formula,

3x +10=9x-39 - 47

solving for x

3x +10 =9x -86

grouping like terms

3x - 9x =-86 -10

-6x=-96

dividing through by -6

[tex] \frac{ - 6x}{ - 6} = \frac{ - 96}{ - 6} [/tex]

[tex]x = \frac{96}{6} [/tex]

[tex]x = 16[/tex]

but EF=3x+10

substitute x=16 into it to get the EF

EF= 3(16)+10

EF=48+10

EF=58

[tex]\huge\boxed{58}[/tex]

First of all, we know that [tex]DE+EF=DF[/tex], because these are two segments that make up one larger segment.

Write this as an equation.

[tex]DE+EF=DF[/tex]

[tex]47+(3x+10)=9x-39[/tex]

Remove the parentheses. [tex]47+3x+10=9x-39[/tex]

Combine the like terms. [tex]3x+57=9x-39[/tex]

Subtract [tex]9x[/tex] from both sides. [tex]-6x+57=-39[/tex]

Subtract [tex]57[/tex] from both sides. [tex]-6x=-96[/tex]

Divide both sides by [tex]-6[/tex]. [tex]x=16[/tex]

Now, find [tex]EF[/tex].

[tex]3x+10[/tex]

[tex]3(16)+10[/tex]

Multiply. [tex]48+10[/tex]

Add. [tex]\boxed{58}[/tex]

The inequality c + 1/c ≥ 2 for c > 0 is proven by using the AM-GM inequality method. By applying this method, we find that the arithmetic mean of the variables is indeed greater or equal to 2, hence confirming the inequality.

To solve the inequality c + 1/c ≥ 2 for c > 0, we can use the AM-GM (Arithmetic Mean - Geometric Mean) inequality method.

According to AM-GM inequality, for any positive numbers a, b, the arithmetic mean is always greater or equal to the geometric mean. In notation: (a + b)/2 ≥ sqrt(a * b). Applying this to our problem where a = c and b = 1/c, we get (c + 1/c) / 2 ≥ sqrt(c * 1/c). This simplifies to c + 1/c ≥ 2*1 = 2, therefore our inequality is confirmed.

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The inequality c + 1/c ≥ 2 for c > 0 is proven using the AM-GM inequality by setting a = c and b = 1/c, showing that their arithmetic mean is always greater or equal to their geometric mean.

To prove the inequality c + 1/c ≥ 2 for c > 0, we can apply the AM-GM inequality which stands for Arithmetic Mean - Geometric Mean inequality. The AM-GM inequality states that for any non-negative real numbers a and b, the arithmetic mean is always greater than or equal to the geometric mean. That is, (a + b)/2 ≥ √(ab).

In our case, we can let a = c and b = 1/c. Then, according to the AM-GM inequality, we get:

When we multiply both sides of the inequality by 2, we get:

This completes the proof for the inequality c + 1/c ≥ 2 when c > 0.

Answer:

X=79

Step-by-step explanation:

The answer can be found by finding the difference of 67 and 55 which would be 12, then adding 12 and 67 to get 79. I can do this because if 2 numbers are split equally between them, then adding an number to get one will get you the other. It may seem confusing, comment if you still need help.

Answer:

A. The pattern is you multiply by 5

B. All 6 prizes are 25,000 and 5,000 and 1,000 and 200 and 40 and 8

C. ??

Step-by-step explanation:

The cash prize values in the game show reduce by a multiple of 5 each time from $25,000 to $5,000, $1,000, $200, $40, and $8. This forms a declining sequence and can be represented in a tabular form.

Contestants on a popular game show have six containers from which to select a hidden cash prize. The pattern of the prize values seems to exist in multiples of 5, with each prize being 5 times smaller than the previous one.

a. 25,000 is the highest cash prize. The next highest prize is 5,000, which is 5 times smaller than 25,000. The third prize, 1,000, is again 5 times smaller than 5,000. Thus, there seems to be a pattern where each subsequent prize is 1/5th of the preceding one.

b. Continuing this pattern, the prize values in the remaining containers would be 200, 40, and 8. Each of these values is 1/5th of the preceding value.

c. We can represent the values in a numeric sequence as follows: 25,000, 5,000, 1,000, 200, 40, 8. Our table representation would look as follows:

ContainerPrize Value125,00025,00031,000420054068

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Answer:

4 is right yur

Step-by-step explanation:

Answer: The answer is 2 10/27

Answer:

45°

Step-by-step explanation:

Complementary angles sum to 90°, thus

90° - 45° = 45° ← is the complement of 45°

Answer:

slope = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 9, - 3) and (x₂, y₂ ) = (7, - 7)

m = [tex]\frac{-7+3}{7+9}[/tex] = [tex]\frac{-4}{16}[/tex] = - [tex]\frac{1}{4}[/tex]

Answer:

-¼

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

[tex] \frac{3 - 7}{9 + 7} = - \frac{4}{16} = -\frac{1}{4} [/tex]

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Answer:

Width of rectangle is 15 ft !

Step-by-step explanation:

Given :-

• Area of rectangle = 375 ft²

• Length of rectangle = 25 ft

• Let width of the rectangle be b ft

Formula for area of rectangle

= ( lenght ) ( width )

Substituting the value ,

375 ft² = 25ft ( b ft )

[tex] \frac{375 {ft}^{2} }{25ft} = bft[/tex]

15 = b

So, the width of rectangle is 15 ft

The required width of the rectangle is  15 feet which is 25 feet long and the area is 375 square feet.

Given that,
A rectangle is 25 feet long. Its area is 375 square feet. What is the width of the rectangle is to be determined.

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

Here,
The area of the rectangle = length * width
                                     25 =  375 * width
                                      width = 375 / 25
                                      width = 15

Thus the required width of the rectangle is  15 feet.

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Answer:

x=2

Step-by-step explanation:

isolate the variable by dividing each side by factors that dont contain the variable

Answer:

the answer is C (2)

Step-by-step explanation:

Answer:  [tex]\bold{\dfrac{7-3\sqrt5}{2}}[/tex]

Step-by-step explanation:

You did great until you expanded (3 - √5)².  You forgot the middle term

[tex]\dfrac{3-\sqrt5}{3+\sqrt5}\bigg(\dfrac{3-\sqrt5}{3-\sqrt5}\bigg)\\\\\\=\dfrac{(3-\sqrt5)(3-\sqrt5)}{(3+\sqrt5)(3-\sqrt5)}\\\\\\=\dfrac{9-3\sqrt5-3\sqrt5+5}{9-3\sqrt5+3\sqrt5-5}\\\\\\=\dfrac{14-6\sqrt5}{4}\\\\\\\text{Factor out a 2 from the numerator and denominator}\\=\dfrac{2(7-3\sqrt5)}{2(2)}\\\\\\=\large\boxed{\dfrac{7-3\sqrt5}{2}}[/tex]

Answer:

4.45

Step-by-step explanation:

4 9/20

4 + 9/20

1/20 = 0.05

so 9/20 = 9 × 0.05

9/20 = 0.45

4 9/20 = 4 + 0.45

4 9/20 = 4.45

THE Answer is 67

Step-by-step explanation:

Answer:

The Correct Answer Is 57

Step-by-step explanation:

According To Research

=113+(-56)

=113-56

=57

Answer:

2

Step-by-step explanation:

Make a list

10: 1, 2, 5, 10

42: 1, 2, 3, 6, 7, 14, 21

Answer:

-262

Step-by-step explanation:

Evaluate Subtraction & Addition from right to left [or left to right, as long as you know what you are doing]:

38 + 16 - 12 - 2 - 302

|_______||____________|

[tex]44 - 316 = -262[/tex]

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Answer:

Logical-Mathematical

Step-by-step explanation:

According to the theory of multiple intelligences, human intelligence has 8 different modalities (musical-rhythmic, visual-spatial, verbal-linguistic, logical-mathematical, bodily-kinesthetic, interpersonal, intrapersonal, naturalistic). In order to understand how formulas are used, logical-mathematical intelligence is used.

The term that corresponds to understanding how formulas are used is Logical-Mathematical. This refers to an individual's proficiency in carrying out mathematical operations and understanding complex mathematical problems, including the use of formulas.

The word from the list that best fits the definition 'Understands how formulas are used' is Logical-Mathematical. This term is one of Howard Gardner's Multiple Intelligences and it refers to the ability to calculate, quantify, consider propositions and hypotheses, and carry out complete mathematical operations. In an educational setting, people who are strong in logical-mathematical intelligence can understand complex problems, detect patterns, and excel in mathematics, with skills such as understanding formulas playing a key role.

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