11. The U.S. Census Bureau has a population cloc
on the Internet. On a recent day, the United
States population was listed as 310,763,136.
Write this number in word form

The factors of given equation are -3/4 and -2.

Rewriting the equation -

4x² + 11x + 6 = 0

The factors for the given expression will be calculated based on two factors -

1. The sum of factors should be equal to sum of numeral value of b (11 in this case)

2. The product of factors should be equal to product of numeral values of a and c (24 in this case)

As per the above rules, the appropriate factors should be 8 and 3.

Rewriting the given equation with possible factors -

4x² + 8x + 3x + 6 = 0

Taking common values

4x(x + 2) +3(x + 2) = 0

(x + 2) (4x + 3) = 0

x = -3/4, -2

Thus, the factors of given expression are -3/4 and -2.

To check the correctness of factors, we will keep each value of x in equation.

When x = -3/4

4x² + 11x + 6 = 0

4(-3/4) + 11(-3/4) + 6 = 0

9/4 -33/4 + 6 = 0

9/4 = 2.25 and 33/4 = 8.25

2.25 - 8.25 + 6 = 0

-6 + 6 = 0

0 = 0

When x = -2

4x² + 11x + 6 = 0

4(-2)² + 11(-2) + 6 = 0

16 - 22 + 6 = 0

22 - 22 = 0

0 = 0

Since both values of x give 0 on both sides of equation, the factors of equation are correct.

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Answer:

-60x+(-85y)

Step-by-step explanation:

Answer: 2/15

Step-by-step explanation:

I DON'T KNOW OK JUST A GUESS I JUST X THE FRACTIONS FOR YOU THE REST IS ON YOU HONEY

Step-by-step explanation:

the answer to what question ?

is the request to find (solve for) x ?

if so, we have

(-3(2x - 6) + 5x)/6 = 7 + (2(-4x + 1) - 6)/3

now, I usually remove the fractions first by multiplying both sides with both denominators :

1. multiply by 6

-3(2x - 6) + 5x = 42 + 6(2(-4x + 1) - 6)/3

2. I can skip the general multiplication by 3, because the denominator 3 goes away in interaction with the new factor 6

-3(2x - 6) + 5x = 42 + 2(2(-4x + 1) - 6)

now, we do all the multiplications and see what we get :

-6x + 18 + 5x = 42 + 2(-8x + 2 - 6) =

= 42 - 16x + 4 - 12

-x + 18 = -16x + 34

15x = 16

x = 16/15

Answer:

B,A

Step-by-step explanation:

hope that's right

The sum of all decent fractions with a denominator of 20 is 4.

Thus, option (d) is correct.

To find the sum of all decent fractions whose denominator is equal to 20, consider fractions with numerators that are coprime to 20 (i.e., the numerator and 20 have no common factors other than 1).

The decent fractions with a denominator of 20 can be written as:

1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, and 19/20.

To find the sum, add up these fractions:

Sum = 1/20 + 3/20 + 7/20 + 9/20 + 11/20 + 13/20 + 17/20 + 19/20

Sum = (1 + 3 + 7 + 9 + 11 + 13 + 17 + 19) / 20

Sum = 80 / 20

Sum = 4

Therefore, the sum of all decent fractions with a denominator of 20 is 4.

Thus, option (d) is correct.

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Answer:

reduce a fraction to its simplest form, we divide both numerator and denominator by their GCF. 48 / 60 ÷ 12 / 12 = 4 / 5.

hope it helps.....

Answer:

5:4

Step-by-step explanation:

If both are even, I usually like to divide both the numerator and the denominator by 2 until I can no longer do so (meaning, dividing either of them by 2 would result in a fraction). This is, of course, if you cannot think of the greatest common factor off the top of your head.

[tex]\frac{60}{48} \to \frac{30}{24} \to \frac{15}{12}[/tex]
We cannot divide by 2 anymore, however, it is a lot simpler to detect now that we can divide by 3.

[tex]\frac{15}{12} \to \frac{5}{4}[/tex]

The function y = 7 / 8 ( 18 ) ˣ is an exponential growth function.

An exponential function is defined as y = a ˣ where x is a variable, and a is a constant called the base of the function.

We are given a function:

y = 7 / 8 ( 18 ) ˣ

We need to tell whether is is a exponential growth or decay function.

We can see that the value of a ˣ = (18) ˣ

So, the value of a = 18.

Since, it is an integer and not a fraction, its value will increase with the increase in exponent x.

So, it will be a exponential growth function.

Therefore, we get that, the function y = 7 / 8 ( 18 ) ˣ is an exponential growth function.

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Answer:

86????

Step-by-step explanation:

I am not certain, but wouldn't it be 86?

the slope would be -8/3. you go 8 down and 3 to the right.

Answer: the common number is 8 for 151 and 152

Step-by-step explanation: hope this helps

Answer:

A

Step-by-step explanation:

1/3 x 0.5 = 1/6 which is a rational number

I think you should look up the meaning of rational number to know what is the correct answer

Hence , numerical expressions for seven more than the product of a number 2 and 6 equals to 13 .

It is given that product of a number 2 and 6.

On multiplying 2 and 6 , we get

2 × 3 = 6

It is given that seven more than the product of a number 2 and 6 which means that we have to add 7 in the product of a number 2 and 6 which is given by 7 + 6 = 13

Hence , the value of the given statement is 13 .

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The radius of a circle is determined as  27.95 units.

Now the formula for the arc length when the central angle is given in the degrees;

arc length  = (θ/360°)×(2πr)

Where, r is the radius of the circle and π = 3.14.

Write the formula for r;

r = (arc length/2π)×(360°/θ)

For the given values in question;

arc length = 82 central angle = 135 degrees.

r = (82/2×3.14)×(360°/135°)

r = (13.05)×(2.67)

r = 27.95

Therefore, the radius of the circle is found as 27.95 units.

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Answer:

9

Step-by-step explanation:

4-x = 5(16-x)

44-x = 80-5x

4x = 36

x = 9

y  = -x +2 an equation in slope-intercept form of the line that bisects the angle.

What exactly does slope intercept mean?

Given:

Angled formed by ray BA and ray BC is 90 degrees.

To find:

The equation of line that bisects the angle formed by ray BA and ray BC.

If a line bisects the angle formed by ray BA and ray BC, then it must be passes through point B and makes angles of 45 degrees with ray BA and ray BC.

It is possible if the line passes though point B(-1,3) and other point (-2,4).

Equation of line is

y - y₁  = y₂ - y₁/x₂ - x₁  ( x - x₁)

y - 3 = 4 - 3 / - 2 - ( -1)  ( x - ( -1)

y - 3 = 1/-1 ( x + 1 )

y - 3 = -x -1

Add 3 on both sides

y = -x -1 + 3

y  = -x +2

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If Annie can mow 1/6 of an acre in 50 minutes, then in an hour, she can mow 1/5 of an acre.

Given the data in the question;

Let x represent the number of acres that Annie can mow in hour.

Also convert 1 hour to minutes

1 hour = (1 × 60)min = 60min

Annie can mow 1/6 of an acre in 50 minutes

Annie can mow x of an acre in 60 minutes

Hence;

1/6 × 60 = x × 50

60/6 = 50x

50x = 60/6

50x = 10

x = 10/50

x = 1/5

If Annie can mow 1/6 of an acre in 50 minutes, then in an hour, she can mow 1/5 of an acre.

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Answer:

Monday class is 1 3 hours and the Friday class is 1 1 hours. 4 2Patrick attended both exe

Step-by-step explanation:

Answer:

6, 2, 14

Step-by-step explanation:

[tex]x=-2 \implies x<1 \implies f(-2)=2(-2)^2-2=6 \\ \\ x=1 \implies 1 \leq x<2 \implies f(1)=2 \\ \\ x=2 \implies x \geq 1 \implies f(2)=4(2)^2-2=14[/tex]

Answer:

identify my own strengths

interests and challenge

Answer:

b= -81

Step-by-step explanation:

b/27 = -3

Multiply both sides by 27 and simplify

Answer:

B

Step-by-step explanation:

Solve the exponent first and thats the only remotely close answer

Answer:

x = 12

Step-by-step explanation:

Vertical angles are congruent

50 = 4x + 2  Subtract 2 from both sides

48 = 4x  Divide both sides by 4

12 = x

Answer:

4.67

Step-by-step explanation:

a. Han wrote (1/2, 0) as x-intercept of the line instead of (2, 0).

b. The x-intercept: (2, 0)

The y-intercept: (0, 5)

The y-intercept of a line is the corresponding value of y when the value of x is equal to zero.

On the other hand, the x-intercept of a line is the corresponding value of x when the value of y is equal to zero.

Y-intercept is (0, b), while x-intercept is (b, 0), where b is the value of the point on the axis that is being intercepted.

In slope-intercept form, y = mx + b or y = b + mx, the y-intercept is represented as b, which is (0, b).

Given the equation in slope-intercept form as y = 5 - 10/4x, the y-intercept, b = 5. Therefore, is expressed as (0, 5).

To find the x-intercept, substitute y = 0 into y = 5 - 10/4x:

0 = 5 - 10/4x

Solve for x

-5 = -10/4x

-20 = -10x

-20/-10 = x

x = 2

The x-intercept is (2, 0), while the y-intercept is (0, 5).

Therefore:

a. The Han got the x-intercept wrong, it should be (2, 0), not (1/2, 0).

b. The x-intercept is (2, 0), while the y-intercept is (0, 5).

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Answer:

dot = times

Step-by-step explanation:

[(6 + 2) · 5 + 4] ÷ 2 – 3 and 6 + 2 · 5 + 4 ÷ 2 – 3

[(8) × 5 + 4] ÷ 2 – 3

[(8) x 9 ] ÷ 2 – 3

([ 72 ] ÷ 2 )– 3

36 -3

33

6 + 2 x 5 + (4 ÷ 2 )– 3

6 +( 2 × 5 )+ 2 – 3

(6 + 10) + 2 – 3

(16 + 2)- 3

18 -3

15

Answer:

[(6 + 2) * 5 + 4] / 2 - 3 = 19
6 + 2 * 5 + 4 / 2 - 3 = 15

Step-by-step explanation:

1.

[8 * 5 +4] / 2 - 3

You get the number 8 by adding 6 and 2 in the parentheses then rewriting the equation.
[40 + 4] / 2 -3
You get 40 by multiplying 8 and 5 then rewriting the equation.
44 / 2 - 3
44 by adding 40 and 4; rewrite the equation.

Divide 44 by 2, which would equal 22
The equation should look like :  22 - 3
Which equals  19

2.
6 + 10 + 4 / 2 - 3
You get 10 by multiplying 2 and 5 together; and rewriting the equation.
6 + 10 + 2 - 3
You get 2 by dividing 4 and 2; rewrite the equation.
18 - 3
You get 18 by adding 6, 10, and 2
Lastly you subtract 3 to 18
Which equals 15

Hope this helps!
--Blu

A function that gives the length of the hypotenuse of an isosceles right triangle with side length s is given by h(s)=s√2 and the length of the side of the triangle is approximately 4.24 inches.

The hypotenuse of a right angled triangle is defined as the longest side of the triangle. The hypotenuse is also located opposite the right angle.

From the Pythagorean Theorem we know that for a right angled triangle, the sum of the square of the legs of the triangle is equal to the square of the hypotenuse.

Given legs of the right triangle is s. Let us consider a function h(s) for the hypotenuse.

Therefore we can define the function h(s) as

h(s)=s√2

The inverse of the function can be written as

y=s√2

or, s=y²/2

Hence the inverse function is:

h⁻¹(s)=s²/2

Now for hypotenuse = 6 inches.

Each side can be calculated using the inverse function h⁻¹(s)=s²/2.

s=6÷√2

or, s=4.242...

Hence the length of the side of the triangle is approximately 4.24 inches.

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The required simplification of rational expression is 3(x + 5) / (x + 3).

What is a rational number?

Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.

Simplifying the rational expression:  x² + 3x - 10 / x² + 4x - 12 . 3x + 18 / x + 3

Given a rational expression,

x² + 3x - 10 / x² + 4x - 12 . 3x + 18 / x + 3

On simplifying, we get,

(x² + 3x - 10).(3x + 18) / (x² + 4x - 12).(x + 3)

For numerator, (x² + 3x - 10).(3x + 18), we have,

= 3(x + 5)(x - 2)(x + 6)

For denominator,  (x² + 4x - 12).(x + 3)

= (x + 6)(x - 2)(x + 3)

Now, (x² + 3x - 10).(3x + 18) / (x² + 4x - 12).(x + 3) = 3(x + 5)(x - 2)(x + 6) / (x + 6)(x - 2)(x + 3)

= 3(x + 5) / (x + 3)

The restrictionto the given rational expression is that the denominator,  x + 3 should not be 0.

Hence, the required simplification of rational expression is 3(x + 5) / (x + 3).

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