Solve by completing the square.
x² + 10x = -81
O {6+i√42, 6-i√/42}
O {12+√133, 12-√133}
O {11, 1}
O {-5+2i√/14, -5-2i√/14}

The coordinates of the point that at 7/8 from a to b are (5, -5/8)

On the segment, we have the following endpoints

A = (-2, 2)

B = (6, -1)

Also, we have the line ratio to be

Ratio, m : n = 7/8

Express the ratio as a ratio

So, we have

m : n = 7 : 8 - 7

Evaluate the difference

So, we have

m : n = 7 : 1

The coordinate of the point at the given distance is then calculated as

Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)

Evaluate the products

So, we have

Point = 1/8 * (42 -2, -7 + 2)

Evaluate the sum and the difference

So, we have

Point = 1/8 * (40, -5)

Evaluate the products

So, we have

Point = (5, -5/8)

Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)

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Explanation

to find the area of the stove that does not include the area of the burnes ( yellow area), we can subtract the area of the 4 circles from the area of the full rectangle

so

Step 1

then, Let

for circle:

diameter= 6 in

for rectangle

length= 24 in

width= 22 in

Step 2

replace,

Answer:

1:2

Step-by-step explanation:

For every triangle there are two squares.

The most appropriate choice for for linear equation will be given by -

Gain in weight of Max = 7.69 pounds

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Let the gain in weight be x pounds

Weight of Max in the month of September = 3.04 pounds

Weight of Max today = 10.73 pounds

By the problem,

                          3.04 + x = 10.73

                                     x = 10.73 - 3.04

                                     x = 7.69

Gain in weight of Max = 7.69 pounds

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iven

adiius of circle = 3 ft

ind

rea and circumference of a circle

xplnanation

Circumference of a circle is given by

Area of circle =

inal ANnswer

ircumference =

Area =

The most appropriate choice for LCM will be given by

After the year 2005, France and America will be in recession in the year 2029

What is LCM?

Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.

Here,

France has a recession every 6 years.

America has a recession every 8 years.

Florence works out when France and America will both be in recession.

It will be possible in the year which is a common multiple of 6 and 8

In the year 2005, both France and America were in recession

France and America will both be in recession again after (LCM of 6 and 8) years

Now,

6 = 2 x 3

8 = 2 x 2 x 2

LCM of 6 and 8 = 2 x 2 x 2 x3

                          = 24

France and America will both be in recession again after 24 years  

After the year 2005, France and America will be in recession in the year (2005 + 24) = 2029

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The first thing we have to know is that 1 kilogram is equal to 1000 grams

if we have 5.4 kilograms

Two or more expressions with an Equal sign is called as Equation.π=  C/d for equation C = πd

Two or more expressions with an Equal sign is called as Equation.

The given equation is  C = πd

c equal to pi times of d

We need to solve it for  π

To solve for  π we have to separate  π from d. To make this We have to divide both sides by d.

So C/d= π

Hence π=  C/d for equation C = πd

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Answer:

[tex]y+1=\frac{1}{2}(x-6)[/tex]

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line to be found is 1/2.

Substituting into point-slope form, the equation is

[tex]y+1=\frac{1}{2}(x-6)[/tex]

Answer:

First Choice:

(1.4)(0.18)²

Step-by-step explanation:

Using the negative exponent rule

[tex]\left(\dfrac{a}{b}\right)^{-1} = \dfrac{b}{a}[/tex]

we get

[tex]\left(\dfrac{5}{7}\right)^{-1} = \dfrac{7}{5}[/tex]

[tex]\dfrac{7}{5} = 1.4\\\\[/tex]

Therefore
[tex]\left(\dfrac{5}{7}\right)^{-1}\left(0.18\right)^2\\\\= (1.4)(0.18)^2[/tex]

Let:

We can find the slope m, using the following formula:

Answer:

0

Answer:

250

Step-by-step explanation:

40° is the value of the angle ∠QPR.

So, PQ ⊥ PS then, ∠QPS = 90°.

According to the given figure: ∠QPR + ∠RPS = ∠QPS

Then,

So, ∠QPR = 7x - 9°

Substitute x = 7 as:

Therefore, 40° is the value of the angle ∠QPR.

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The Confidence Interval for a Population Proportion is 0.69 ± 1.13

(-0.44 to 1.82)

Confidence Interval:

Confidence Interval means a range of values that is determined through the use of observed data, calculated at a desired confidence level that may contain the true value of the parameter being studied.

Given,

n = 130 and

p= 0.69,

construct a 99% confidence interval.

Here we need to find the confidence interval.

According to the formula, the confidence interval is,

We know that,

Sample Size: 130

Sample Mean: 0.69

Confidence Level: 99%

99% Confidence Interval: 0.69 ± 1.13

(-0.44 to 1.82)

"With 99% confidence the population mean is between -0.44 and 1.82, based on 130 samples."

Margin of Error: 1.13

(to more digits: 1.13)

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As per the long division, the value of 19 divided by 6,927 is 0.002742

Long division:

Long division is the mathematical method for dividing large numbers into multiple smaller groups or parts. The number which we divide into small groups is called the dividend, the number by which we divide is called the divisor.

Given,

Here  we have to divide the number 19 by 6927.

When we divide the number, we have to following the following steps,

1) Set up the problem with long division bracket. Put dividend inside bracket and divisor on outside left.

2) 6927 goes into 19000 (2-times). Put a 2 in the next place of quotient and multiply 6927 by 2 to get 13854. Subtract 13854 from 19000 to get remainder (19000-13854=5146).

3) Now, bring down 0 from the dividend, to make 51460

4) 6927 goes into 51460 (7-times). Put a 7 in the next place of quotient and multiply 6927 by 7 to get 48489. Subtract 48489 from 51460 to get remainder (51460-48489=2971).

5) Now, bring down 0 from the dividend, to make 29710

6) 6927 goes into 29710 (4-times). Put a 4 in the next place of quotient and multiply 6927 by 4 to get 27708. Subtract 27708 from 29710 to get remainder (29710-27708=2002).

7) Now, bring down 0 from the dividend, to make 20020

8) 6927 goes into 20020 (2-times). Put a 2 in the next place of quotient and multiply 6927 by 2 to get 13854. Subtract 13854 from 20020 to get remainder (20020-13854=6166).

This process is continued so we have to take only up to these one.

Then this can be displayed in the following figure.

Question: Divide the number 19 by 6,927 using the long division method.

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The roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.

As per the question statement, we are supposed to fill the gaps to factorize the quadratic equation given :

3x² + 16x + 5 = (3x + _)(x + _)

We need to solve the expression for finding out its factors.

y = 3x² + 16x + 5

y = 3x² + 15x + x + 5

y = 3x(x + 5) + 1(x + 5)

y = (3x + 1)(x + 5)

Therefore, the  roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.

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The value of x, so f(x)=7 is 5.

According to the graph, we have a linear function and linear functions have the same slope for all value of x, we can determine the value of  f(x) for x=7 by the means of the equation for the line:

[tex]\frac{y_{b}-y_{a} }{x_{b}-x_{a} }[/tex] = [tex]\frac{y_{c}-y_{a} }{x_{c}-x_{a} }[/tex]  ....................(1)

Where:

 [tex](x_{a},y_{a} )[/tex] = (2,0) and [tex](x_{b},y_{b} )[/tex] = (5,7) are the Known points.

[tex](x_{c},y_{c} )[/tex] is the Expected point.

The value of [tex]y_{c}[/tex] = 7

Then the value of  [tex]x_{c}[/tex] is,

[tex]x_{c}=x_{a} +\frac{ y_{c}-y_{a} }{y_{b}-y_{a} } *(x_{b} - x_{a} )[/tex]

= 2+ [(7-0) / (7-0)] * (5-2)

= 2 + (5-2)

= 2+3

= 5

Therefore, the value of x, so f(x)=7  is 5.

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The graph of the inequaity expression is added as an attachment

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The mathematical statement is given as

"2.5 greater than the product of -0.5 and a number"

Product means times

So, we have the following representation

"2.5 greater than the product of -0.5 and a number" ⇒  2.5 greater than -0.5 * a number

Let the number be x

So, we have

"2.5 greater than the product of -0.5 and a number" ⇒  2.5 greater than -0.5x

Greater than is represented by >

So, we have

"2.5 greater than the product of -0.5 and a number" ⇒  2.5 > -0.5x

Next, we plot the graph of the inequality expression

See attachment for the graph of the inequality expression

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Answer:

  13

Step-by-step explanation:

You want the sum of f^-1(-7) and f(-7) given the function definition in the table.

The inverse function f^-1(x) consists of ordered pairs that are the reverse of the ordered pairs (x, f(x)). That is ...

  (x, f^-1(x)) ≡ (f(x), x)

Another way to describe f^-1(x) is "the value of z that gives f(z) = x". This means f^-1(-7) is the value of x that gives f(x) = -7. That x-value is 6:

  f^-1(-7) = 6 . . . . . from the 4th column of the table

We can read the function value directly from the table:

  f(-7) = 7 . . . . . . the first column of the table

Then the sum of interest is ...

  f^(-1)(-7) +f(-7) = (6) +(7)

  f^(-1)(-7) +f(-7) = 13

__

Additional comment

The inverse function ordered pairs are ...

  (x, f^-1(x)) = {(7, -7), (12, 11), (8, -13), (-7, 6), (13, 5)}

The solutions to the question are

The given parameters are:

Sides = 3

Fourth side = barn wall

Perimeter = 120 m

Next, we sketch the dog pen using the above parameters (see attachment)

Here, we have

P = 120m

Also, we have

P = 2x + y

This gives

2x + y = 120

Make y the subject

y = 120 - 2x

The area is calculated as

A = xy

So, we have

A = x(120 - 2x)

Hence, the area is A = x(120 - 2x)

See attachment for the graph of A = x(120 - 2x)

We have

A = x(120 - 2x)

Expand

A = 120x - 2x^2

Differentiate

120 - 4x= 0

So, we have

4x = 120

This gives

x = 30

Hence, the value of x that gives maximum area is 30

Recall that

y = 120 - 2x

So, we have

y = 120 - 2 * 30

Evaluate

y = 60

Hence, the dimensions is 30 by 60

From the graph, we have

x = 0 to 60

Hence, the domain of the function is 0 <= x <= 60

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The difference between the freezing point of seawater and the freezing point of nitric acid is 40 °C.

As per the question, we can write

The freezing point of seawater = −2 °C.

The freezing point of nitric acid = −42 °C.

We were asked to calculate the difference between the freezing point of seawater and the freezing point of nitric acid. We can find the difference between the freezing point of seawater and the freezing point of nitric acid by following the steps mentioned below;

The difference between the freezing point of seawater and the freezing point of nitric acid = Freezing point of Seawater - Freezing point of nitric acid

The difference between the freezing point of seawater and the freezing point of nitric acid = -2 - (-42) = 40 °C.

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Calculate identity exponents using the exponent of the quotient, degree of exponent, and the law of zero exponent equations and evaluate numerical equations with integer exponents.

The following is an equivalent numeric expression with an integer exponent that uses the quotient, the quotient, zero-degree rule, and the identity exponent, and evaluates the numeric expression.

[tex]2^{5} \\[/tex] × [tex]2^{6}[/tex] = [tex]2^{11}[/tex], using the product of powers.

2² × 2³ = (2×3)² = 6², using the power of a product.

[tex](2^{2})^{6}[/tex] = [tex]2^{12}[/tex], using the power of a power.

The seven laws of exponents are the power rule, the power ratio rule, the power rule, the power rule, the power quotient rule, the power zero rule, and the negative exponent rule. Arithmetic questions, as well as how to multiply, divide and add powers.

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The outcome of the quotient between the two fractions 3/4 and 2/3 is 9/8

So let's define two fractions as:

a/b and c/d.

The quotient between the fractions a/b and c/d can be written as:

(a/b)÷(c/d).

Now, the quotient is equal to the product with the inverse, so we can rewrite this as:

(a/b)÷(c/d) = (a/b)*(d/c)

Now, in this case, we want to find 3/4 divided by 2/3, this will be:

(3/4)÷(2/3) = (3/4)*(3/2) = 9/8

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The total number of different numbers which Toby could have picked according to the task content as given is; 1,000.

It follows from the task content that the number of different numbers which Toby could have picked given the conditions is to be determined.

On this note, since the required number is to be greater than 49,999 and must be a 5-digit number, the numbers which he could pick would range from;

49,999 - 99,999.

Hence, there are 5000 numbers in between.

Additionally, since the number must be a multiple of 5, the total number of multiples of 5 from 5,000 consecutive numbers is;

= 5,000/5

= 1000 different numbers.

Therefore, Toby could pick any of 1000 different numbers.

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The base of the parallelogram is 3

The height of the parallelogram is 8

Let the base be represented as (x+2)

Let the height be represented as (x-2)

The area of the parallelogram is 24

The first step is to get two numbers that can be multiplied together to get 24

= 3 × 8

The two numbers are 3 and 8

Hence the base is 3 and the height is 8

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Answer:

Step-by-step explanation:

6x-2x-8=12  

4x-8=12    (add 6x and -2x)

4x=20         (8+12=20)

x=5   (4 divide by 20 =5)

Answer:

3

Step-by-step explanation:

1 = 1

The associative property let us associate different terms or factors in order to solve some expression.

We have to find the expression in which this property is more useful.

The only expression where the associative may be helpful is C, as we can associate this way:

(43 + 60) + 40 = 43 + (60 + 40) = 43 + 100 = 143

In the other expression there is no advantage in applying this property.

Answer: C