Can someone explain this please.

The value of x for given equation (2x - 20) /3 = 2x is x = -5

For given question,

we have been given an equation  2x minus 20 divided by 3 = 2x

i.e., (2x - 20) /3 = 2x

This equation models temperature change, where x represents the difference in degrees in the last 24 hours.

We need to solve given equation for x.

(2x - 20) /3 = 2x

(2x - 20)  = 3(2x)                ...........(Multiply by 3 on both sides)

2x - 20 + 20 = 6x + 20      ...........(Add 20 to both sides)

2x - 6x = 6x + 20 - 6x       ..........(Subtract 6x from both sides)

-4x = 20                            

x = -5                                  ..........(Divide by - 4 on both sides)

Therefore, the value of x for given equation (2x - 20) /3 = 2x is x = -5

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The postulate that proves that the triangles are congruent is: SAS congruence postulate.

The SAS congruence postulate states that when two triangles have a pair of included congruent angles, and two pairs of corresponding sides that are congruent, then both triangles are congruent.

In the triangles given, we have:

Two pairs of corresponding sides that are congruent - BL ≅ PF and BG ≅ PX

A pair of included congruent angles - <B ≅ <P.

This means both triangles are congruent by SAS.

Therefore, the postulate that proves that the triangles are congruent is: SAS congruence postulate.

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Answer:

BC = 13

Step-by-step explanation:

x + 10 + x + 14 = 22

2x + 24 = 22

2x = -2

x = -1

BC = x + 14 = -1 + 14 = 13

Answer:

Step-by-step explanation:

x - 3y = 10

5x + y = 2

x - 3y = 10

15x + 3y = 6

16x = 16

x = 1

5 + y = 2

y = -3

(1, -3)

The distance between (-3, 6) and (5, 2) is 4√5 by using the distance formula.

Distance between two points in x y plane by distance formula is:

= √{(x₁ - x₂)² + (y₁ - y₂)²}

Substituting the values of the points:

= √{( -3 - 5 )² + ( 6 - 2 )²}

Solving it further:

= √{( -8 )² + ( 4 )²}

= √{ 64 + 16 }

= √80

= √(2× 2 × 2 × 2 ×5 )

= 2×2× √5

= 4√5

So, the distance between (-3, 6) and (5, 2) is 4√5 by using the distance formula.

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Looking at the options, the only one that is true of the function f(x) over the given intervals is; The domain is; -9 < x ≤ -2, -2 < x ≤ 1 and 1 < x < 7

We are given the function;

f(x) = {3x - 1, if -9 < x ≤ -2

        {-5, if -2 < x ≤ 1

        {x - 6, if 1 < x < 7

Now, the domain of a function is defined as the set of all possible input values that make the function to exist. Meanwhile, the range of a function is the set of all possible output values that make the function to exist.

Looking at the given intervals and combining them all, we can tell that the domain is as follows; -9 < x ≤ -2, -2 < x ≤ 1 and 1 < x < 7

Now, the range for 3x - 1 is;

3(-9) - 1 = -28 and 3(-2) - 1 = -7

Range is greater than -28 and less than or equal to -7

Range of x - 6 will be greater than -5 and less than 1

Looking at the options, the only one that is true of the function f(x) over the given intervals is; The domain is; -9 < x ≤ -2, -2 < x ≤ 1 and 1 < x < 7

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Answer:

(-3,3/2)

Step-by-step explanation:

It's easy just add the abscissa and ordinate individually and divide the obtained abscissa and ordinate by 2

Answer:

k=-13

Step-by-step explanation:

-2 = k+7/3

Multiply 3 to both sides.

-2 = k+7/3

-6=k+7

Subtract 7 from both sides.

-13=k

k equal -13.

Hope this helps!

Please mark as brainliest if correct!

Answer:

Step-by-step explanation:

−2=k+7/3

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

k+7/3=−2

k+7/3−7/3    =   −2−7/3

k=    −13/3

If 192 is 60%, then 10% would be 32.

Then you can multiply both sides by ten.

This would get you: 100% would be 320 people.

Can you please give me brainliest?

Answer:500

Step-by-step explanation:

27 years are spent sleeping; 8 years are spent watching television.

What are examples of linear equations?

Let n constitute the quantity of years looking TV.

Then sleeping equals n+19. So:

             n+n+19=35

                2n=16

                  n=8

8 years are spent watching TV; 27 years are spent sleeping.

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If Brandon works at the waterpark on the weekends. Last Saturday, he worked 7 11/12 hours. On Sunday, he worked 84% of the hours he worked on Saturday, The total hours that he would have to work on the weekend is 6.65 hours

The total numbers of hours that was worked can be solved by

7 11/12 hours * 84%

= 95 / 12 * 84 / 100

= 7980 /1200

= 6.65

Therefore we can  say that if Brandon works at the waterpark on the weekends. Last Saturday, he worked 7 11/12 hours. On Sunday, he worked 84% of the hours he worked on Saturday, The total hours that he would have to work on the weekend is 6.65 hours

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Answer:

6 hours and 39 minutes is the correct answer.

Step-by-step explanation:

So, set up your problem...

STEP 1: 84% out of 100%, or 84/100

STEP 2: 7 11/12 is a mixed number, so to make solving easier, make it an improper fraction: 95/12

- 7 11/12

- 7 × 12 = 84 + 11 = 95

- Keep the denominator (12)

- 95/12 is now an improper fraction.

STEP 3: Multiply 95/12 × 84/100 = 6.65

STEP 4: Convert to hours...

- Note that 6.65 hours and 6:65 is not the same. 6.65 hours with the decimal point is 6.65 hours in terms of hours. 6:65 with the colon is 6 hours and 65 minutes.

- Start by dividing up what is before and after the decimal point. 6 = hours, .65 = fractional hours

- To convert from 6.65 decimal hours to hours and minutes, we need to convert the .65 fractional hours to minutes.

- Since there are 60 minutes in an hour, you multiply the .65 fractional hours by 60 to get minutes. .65 × 60 = 39 minutes.

So, in conclusion, the correct answer to your question is... 6 hours and 39 minutes.

Hope this helps! Have an amazing rest of your day! Please award me Brainliest!! :)

{x, y, z} = { -16/13, -10/13, -28/13}.

the image (new coordinate) after the translation is (-2.5, 9.8)

Here we have a rule (also called a transformation or an operator) that works as:

T(x, y) = (x - 7.5, y + 6.8)

So we decrease the x-value by 7.5 and increase the y-value by 6.8. This is a translation of 7.5 units to the left and 6.8 units upwards.

Now, our point is (5, 3), if we apply that transformation we will get:

T(5, 3) = (5 - 7.5, 3 + 6.8) = (-2.5, 9.8)

That is the image after the translation.

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The length of DNA in Scientific notation (standard form) = 34[tex]e^{-8}[/tex] meters

Also, the significant figure in the measurement = 1

In this question, we have been given the length of human DNA.

The genetic information of almost every living thing is stored in a tiny strand called DNA.

Human DNA is 3.4 x 10-8 meter long.

We need to write the length in standard form.

3.4 x 10-8 meter

= 3.4 x 10 ^ (-8)

= 3.4 x 0.00000001

= 0.000000034

= 0.00000003

Here Significant Figures = 1

Decimals = 8

And the length in Scientific Notation = 34[tex]e^{-8}[/tex] meters

Therefore, the length of DNA in Scientific notation (standard form) = 34[tex]e^{-8}[/tex] meters

Also, the significant figure in the measurement = 1

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-10

By BODMAS Method

8 + 3*4 ÷ -2*3

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

8 + 3*-2*3

8 +(-18)

-10

The order of operations (BODMAS) in mathematics and computer programming refers to a set of rules that represent standards for which operations to carry out first in order to evaluate a specific mathematical expression.

For instance, since the advent of contemporary algebraic notation, multiplication has been given a higher priority than addition in mathematics and most computer languages.

As a result, 1 + (2 × 3) = 7, rather than (1 + 2) × 3 = 9. is the value assigned to the expression 1 + 2 × 3. BODMAS was first used in the 16th and 17th centuries when addition and multiplication were given priority. BODMAS could only is used as a superscript to the right of their base.

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Part A: The equation of least squares regression line is

ŷ = 0.4684X + 64.69888

Part B: The residual that we have here is - 1.382

Part C: Residual refers to the difference between the observed value and the predicted value

Sum of X = 102.5

Sum of Y = 695

Mean X = 10.25

Mean Y = 69.5

Sum of squares (SSX) = 33.625

Sum of products (SP) = 15.75

Regression Equation = ŷ = bX + a

b = SP/SSX = 15.75/33.63 = 0.4684

a = MY - bMX = 69.5 - (0.47*10.25) = 64.69888

ŷ = 0.4684X + 64.69888

Residual = observed - predicted

The observed = 68

The predicted = 0.4684 x 10 + 64.69888

= 4.684 + 64.69888

= 69.382

residual = 68 - 69.382

= -1.38

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The indicated computation of (4 x 10^4) (2 x 10^3) in decimal notation is 80000000

The expression is given as

(4x10 to the power of 4) (2x10 to the power of 3) =

Rewrite properly, as:

(4 x 10^4) (2 x 10^3) =

Evaluate the product of 4 and 2

So, we have

(4 x 10^4) (2 x 10^3) = 8 x 10^4 x 10^3

Evaluate the product of 10^4 and 10^3 using the law of indices

So, we have

(4 x 10^4) (2 x 10^3) = 8 x 10^7

Evaluate the product of 8 and 10^7

So, we have

(4 x 10^4) (2 x 10^3) = 80000000

Hence, the indicated computation of (4 x 10^4) (2 x 10^3) in decimal notation is 80000000

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Answer:

360° = 131° + 110° + 107° + 108°

360° = 456° + x

.: x = -96°

According to the given statement;

Quotient in lowest terms for 8 divided by 1 4/5  is 4.4444444

A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object. Let's use an illustration to better comprehend this idea. The pizza in the following image has been sliced into 8 equally sized pieces. Now, if we wish to refer to a single portion of the pizza, we can do so by using the notation 1/8, which indicates that we are talking about one portion out of 8 equally sized portions.

According to the given values;

8 : 1( 4/5) = 40/9

= 4 4/9

≅ 4.4444444

Hence, Quotient in lowest terms for 8 divided by 1 4/5  is 4.4444444.

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49x⁶y¹⁰ tiles are required to cover the floor;

Side length of the square floor = 7x⁵y⁶;

Side length of the square tile = x²y;

Area of the given floor is = (7x⁵y⁶)²  sq units

                                          = 7²x¹⁰y¹² sq units

                                          = 49x¹⁰y¹² sq units.

Area of a tile is = (x²y)² sq units

                         = x⁴y² sq units.

Let no. of tiles required be 'n';

Area of square floor = (No. of square tiles) × (Area of 1 square tile);

49x¹⁰y¹² = n × x⁴y²;

 n = 49x⁶y¹⁰;

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93.7 feet is the distance from the bottom of the slide to the bottom of the ladder.

Let us consider the distance from the bottom of the ladder to the bottom of the slide "x" (the unknown we want to find).

The ladder's length is 35 feet, and the slide's length is 100 feet.

According to the Pythagorean theorem:

c² = a² + b²

where c is the hypotenuse (the ladder's length), and a and b are the two other sides of the right-angled triangle (the distances we want to find).

In this case, the equation becomes:

35²= x² + 100²

Solving for x:

1225 = x² + 10000

x² = 10000 - 1225

x² = 8775

Taking the square root of both sides to find "x":

x = √8775

x = 93.7 feet

So, the distance from the bottom of the slide to the bottom of the ladder is 93.7 feet.

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Answer:

e foot

Step-by-step explanation:

Answer:

How far down the wall did

the ladder

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

The number of items that must be sold for the company to make a profit is 757.

Calulation of number of items sold:

R = 195x

C = 160x + 18000

Here R means the revenue

And, C means the cost

Now

We know that

Profit = R - C

Profit = Revenue - cost

=195x - (160x + 18000)

= 195x - 160x - 18000

= 35x -18000

Now solve the above equation

So,

35x - 18000 = 8500

x=757

Therefore,

x = 757

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If a satellite flies 114550 miles in 22.91 hours, then it will flies 34850 miles in 6.97 hours

Given,

The total distance flies by the satellite = 114550 miles

Time taken = 22.91 hours

Speed of the satellite = Distance / Time taken

[tex]\frac{114550}{22.91} =5000[/tex] miles per hour

The total distance flown by the satellite in 6.97 hours

Distance = Speed × Time

= 5000×6.97

=34850 miles

Hence, if a satellite flies 114550 miles in 22.91 hours, then it will fly 34850 miles in 6.97 hours

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If the area of the rectangle (as shown below in the reference.jpeg attached hereby for reference) is 32 sq. units, then the area of the triangle shown besides the rectangle will be 16 sq. units.

As per the question statement, area of a rectangle (as shown below in the reference.jpeg attached hereby for reference) having a length of 8 units and width of 4 units is 32.

We are required to calculate the area of the triangle (shown beside the above-mentioned rectangle in the reference.jpeg attached hereby).

From the diagram, it is clear that that base of the triangle is 4 units and since it is a right-angled triangle, it's altitude or height is 8 units.

Now the formula to calculate the area of a triangle (A) having base "b" and height "h", goes as [tex]A=(\frac{1}{2}*b*h)[/tex]

Inserting the values of our concerned triangle in the above mentioned formula, we get, Area = [tex](\frac{1}{2}*4*8)=(\frac{4*8}{2})=\frac{32}{2}=16[/tex].

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Answer: b=7.5

Step-by-step explanation:

b+5=20-b

b+b+5=20-b+b     ==> add b on both sides to put b on only one side of the equation

2b+5=20

2b=15

b=7.5

Answer:

1. Distributive property

2. Reflexive property

3. Multiplication property of equality

4. Transitive property of equality

5. Addition property of equality

6. Substitution property

Step-by-step explanation: