Given points A(1, 3) and B (3, 7), which of the following represents the distance of  AB

√116
√6
√14
√20

      49 is the number to be added to both the sides of the equation to complete the square.

   The equation given in the question is

Which can be written as  [tex]x^{2} +2\times (7x)=-32[/tex]

We have to convert it into square form.

  Since the standard form of the equation in square form is

(a + b)² = a² + 2ab + b²

By comparing this standard equation with the given equation,

a = x

&

b = 7

By substituting the values of 'a' and 'x' in the standard square form,

x² + 14x + 7² = -(32) + 7²

x² + 14x + 49 = -32 + 49

(x + 7)² = 17

     Therefore, 49 should be added in both the sides of the equation in order to complete the square.

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q, and p

To solve the problem, two equations were set up based on the conditions given. After substitution and simple algebraic operations, the larger number was found to be 38 and the smaller number to be 29.

The question involves finding two numbers where the sum is 67, and the smaller number is 9 less than the larger number.

Let's define the larger number as x and the smaller number as y. According to the problem:

Substitute Equation 2 into Equation 1:

x + (x - 9) = 67

2x - 9 = 67

2x = 67 + 9

2x = 76

x = 38

Now, we can find y using Equation 2:

y = x - 9

y = 38 - 9

y = 29

Therefore, the larger number is 38 and the smaller number is 29.

original height was 5" and it was enlarged to 30"

 find the ratio by dividing 30 by 5

30 / 5 = 6

 so ratio would be 1/6 meaning for every 1 inch of the original the new one is 6 inches

now you need to multiply the original width by 6 to find the new width

7" x 6 = 42"

 new width = 42"

Answer:

750

Step-by-step explanation:

for others

750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity

We need to find how many gallons of 80%

8x, since we don't know how many gallons

mixed with 250 gall of 40%: 0.40(250)

and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:

8x+0.4(250)=0.7x+0.7*250

Multiply on both sides of the equation

0.8x+100= 0.7x+175 Subtract 100 on both sides

0.8x= 0.7x+75

Subtract 0.7 on both sides

0.1x= 75

Divide both sides by 0.1

x= 750

You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.

Hence,  750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.

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Answer:   -1.9

Step-by-step explanation:just add up the values for the weight change

(-1.8)+(0.9)+(-1.4)+(0.4)

-1.9

The mathemtical expression for the word expression  5 less than twice x "  is 2x - 5 option (A) 2x -5 is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The  word expression is:

5 less than twice x

Twice the x  = 2x

5 less than twice the x:

= 2x - 5

Thus, the mathematical expression for the word expression  5 less than twice x "  is 2x - 5 option (A) 2x -5 is correct.

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The correct answer is:

The domain contains only natural numbers.

The graphs of geometric sequences are a series of unconnected points rather than a smooth curve because:

The domain contains only natural numbers.

As the geometric sequence us given as:

[tex]a_1=a,a_2=ar,a_3=ar^2,....[/tex]

where a is the first term of the sequence and r is the common ratio of the geometric sequence.

Also [tex]a_n[/tex] denotes the nth term of the sequence where n belongs to natural numbers that is the domain of the function is natural numbers.

The reason why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve is because: B. The domain contains only natural numbers.

A geometric sequence is typically a series of real and natural numbers that are calculated by multiplying the next number by the same number each time.

Mathematically, a geometric sequence is given by the expression:

[tex]a, \;ar, \; ar^{2} ....a_n[/tex]

Where:

In a geometric sequence, the graphs of geometric sequences comprises a series of unconnected points rather than a smooth curve is because the domain is made up of only natural numbers.

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To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. Given that the side length of the tile is 12 inches, the length of the diagonal is approximately 17 inches when rounded to the nearest inch.

To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides of the right triangle are the sides of the square tile, and the hypotenuse is the diagonal. Given that the side length of the tile is 12 inches, we can calculate the length of the diagonal as follows:

Square the length of one side: 12 x 12 = 144

Multiply the result by 2: 144 x 2 = 288

Take the square root of the result: √288 ≈ 16.97 inches

Rounded to the nearest inch, the length of the diagonal of the square tile is 17 inches.

Final answer:

The length of the diagonal of the square, rounded to the nearest inch, is 17 inches.

Explanation:

The length of the diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two sides of the square are both 12 inches long. So, we have:

hypotenuse² = side1² + side2²

hypotenuse² = 12² + 12²

hypotenuse² = 144 + 144

hypotenuse² = 288

To find the length of the hypotenuse (or the diagonal), we take the square root of both sides:

hypotenuse = √(288)

hypotenuse = 16.97 inches (rounded to the nearest inch)

Answer:  The required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]

Step-by-step explanation:  We are given two functions as follows :

[tex]f(x)=\dfrac{2}{x},~~~~~~~g(x)=x^2.[/tex]

We are to find f of g, i.e., f(g(x)).

To find the required value, first we have to find the f value of the function g(x).

We have

[tex]f(g(x))=f(x^2)=\dfrac{2}{x^2}.[/tex]

Thus, the required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]

Answer:

y − 100 = -12.5 (x − 4)

Step-by-step explanation:

Pick two points on the line to calculate the slope:

m = (y₂ − y₁) / (x₂ − x₁)

m = (100 − 125) / (4 − 2)

m = -12.5

Next, use point-slope form to write the line equation.

y − y₁ = m (x − x₁)

y − 100 = -12.5 (x − 4)

Answer:  [tex]\frac{1}{3}[/tex]

Explanation:

let y = [tex]log_{8} (2)[/tex]

whenever we transfer base from  log from one side to other it will remain be base after shifting to the other side.

Change log to exponent form [tex]\log_xm=n\\m =x^{n}[/tex]

here we have n = y, m=2, x=8    by substituting the values

we will get

[tex]8^{y} = 2[/tex]          (1)

we can write 8 in power of 2 that is [tex]2^{3}[/tex]

we will rewrite the above equation (1) as

[tex]2^{3y} = 2[/tex]

we can equate the power when base is same then we will get

3y = 1

then

[tex]y=\frac{1}{3}[/tex]

The result of the logarithmic expression [tex]log _82=x[/tex] is 1/3

Let the given logarithmic function be x to have:

[tex]log _82=x[/tex]

This can be transformed into indices to have:

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

Solve the resulting indices for "x" a shown:

[tex](2^3)^x = 2^1\\2^{3x}=2^1[/tex]

Cancel the base and equate the power to have:

[tex]3x = 1\\x = \frac{1}{3}[/tex]

Hence the result of the logarithmic expression [tex]log _82=x[/tex] is 1/3

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