What is an equation of the line that passes through the point (8, – 7) and is parallel
to the line x + 2y = 18?

Answer:

Solution in photo

Step-by-step explanation:

Based on the data provided, the amount after 2 years is #3386.7

Where:

P is principal

r = rate

n is the number of years

From the data provided:

P = 3000

n = 2

r = 6 1/4% = 0.0625

Amount = 3000 * (1 + 0.0625)²

Amount = #3386.7

Therefore, the amount after 2 years is #3386.7

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Answer:

42/3=14

14*5=70

The answer is 70

Answer:

70 push ups

Step-by-step explanation:

1. Find out the pushup per minute.

42/3 = 14

2.Multiply

14 x 5 = 70

Answer:

Each square on the travel chessboard is 0.75 inches by 0.75 inches

Step-by-step explanation:

A scale factor of 1/3 when dilating means that we divide 2.25 by 3. That equals 0.75 :)

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  =  $272,090

      A) - Calculate the Percentage of the Value Remaining After the Decrease

       B) - Calculate the NEW VALUE of the house

A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE

      100%  -  9%  =  91%

        0.91

B) - Calculate the NEW VALUE of the house:

NEW VALUE  =  OLD VALUE  *  REMAINING PERCENTAGE

NEW VALUE  =  299,000  *  0.91

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  = $272,090

I hope it helps!

The pairs of complementary angles are:

1) 36° and 54°

4) 23° and 67°

5) 5° and 85°

Two angles A and B are complementary if the sum of the measures is equal to 90°.

For the given options, the 3 correct ones are:

1) 36° and 54°

The sum gives:

36° + 54° = 90°

So these are complementary.

4) 23° + 67° = 90°

These are also complementary.

5) 5° + 85° = 90°

These are also complementary.

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Answer:

9(x² + 5y⁴) (x² - 5y⁴)

Step-by-step explanation:

9x⁴ - 225y⁸

factor out a 9

9(x⁴ - 25y⁸)

factor (x⁴ - 25y⁸)

(x⁴ - 25y⁸)

x² • x² = x⁴

5y⁴ • -5y⁴ = -25y⁸

(x² + 5y⁴) (x² - 5y⁴)

↓

9(x² + 5y⁴) (x² - 5y⁴)

Step-by-step explanation:

To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:

9^2 + 3(9) - 5 = 81 + 27 - 5 = 103

Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.

rate my answer, please.

Answer: 348in^2

Step-by-step explanation:

8 x 9 = 72

72 x 2 = 144in^2 (front and back)

8 x 6 = 48

48 x 2 = 96in^2 (sides)

9 x 6 = 54

54 x 2 = 108in^2 (top and bottom)

Total Surface area = 144 + 96 + 108 = 348in^2 (second option on picture)

Answer:

Step-by-step explanation:

Answer:

Entrada

{-x = -1, x = +61, x = 3}

Resultado

{-x = -1, x = 61, x = 3}

Alternate form

{x = 1, x = 61, x = 3}

The answer will be  \(x=-1,\:x=3,\:x=\sqrt{6}i,\:x=-\sqrt{6}i\)

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation.

Given equation:

x^7 - 11x^6 +48X^5 - 120x^4 + 225x^3 - 243x^2 - 162X + 486 = 0.

x^7 +48X^5+ 225x^3+ 486 = 11x^6+ - 120x^4 + 243x^2 + 162x

On solving

\(\left(x+1\right)\left(x-3\right)^4\left(x^2+6\right)=0\)

\(\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\)

\(x+1=0\quad \mathrm{or}\quad \:x-3=0\quad \mathrm{or}\quad \:x^2+6=0\)

Hence, the solution is \(x=-1,\:x=3,\:x=\sqrt{6}i,\:x=-\sqrt{6}i\)

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Step-by-step explanation:

6+11÷2×8=92 area of trapezoid

Answer:

\(\boxed{\sf{\green{68}}}\) square centimeters.

Step-by-step explanation:

Here's the required formula to find the area of trapezoid :

\({\longrightarrow{\pmb{\sf{A = \dfrac{b_1 + b_2}{2} \cdot \: h}}}}\)

Substituting all the given values in the formula to find the area of trapezoid :

\({\longrightarrow{\sf{Area_{(Trapezoid)} = \dfrac{b_1 + b_2}{2} \cdot \: h}}}\)

\({\longrightarrow{\sf{Area_{(Trapezoid)} = \dfrac{6 + 11}{2} \cdot \: 8}}}\)

\({\longrightarrow{\sf{Area_{(Trapezoid)} = \dfrac{17}{2} \cdot \: 8}}}\)

\({\longrightarrow{\sf{Area_{(Trapezoid)} = \dfrac{17}{2} \times 8}}}\)

\({\longrightarrow{\sf{Area_{(Trapezoid)} = \dfrac{17}{\cancel{2}} \times \cancel{8}}}}\)

\({\longrightarrow{\sf{Area_{(Trapezoid)} = 17 \times 4}}}\)

\({\longrightarrow{\sf{Area_{(Trapezoid)} = 68}}}\)

\(\star{\boxed{\sf{\pink{Area_{(Trapezoid)} = 68 \: {cm}^{2}}}}}\)

Hence, the area of trapezoid is 68 cm².

\(\rule{300}{2.5}\)

Answer:

Step-by-step explanation:

6 = a / 4 + 2

=> 6 - 2 = a / 4 + 2 - 2
=> 4  =  a / 4
=> a = 16

Answer:

a = 16

Step-by-step explanation:

\(6=a/4+2\)

\(6(-2)=a/4+2(-2)\)

\(4=a/4\)

\(4(4)=(a/4)(4)\)

\(16=a\)

\(a=16\)

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

(B) The volume of a rectangular pyramid is 1/3 the volume of a rectangular prism. The volume of the rectangular pyramid is 66 cm3.

Step-by-step explanation:

Volume of a rectangular prism:

The volume of a rectangular prism is given by:

\(V_R = A_{b}*h\)

In which \(A_b\) is the base area and h is the height.

Volume of a pyramid:

\(V_P = \frac{A_{b}*h}{3}\)

Relation:

From this, given the same base and the same height, the volume of the pyramid will be a third of the rectangular prism.

A rectangular prism has a volume of 198 cm³

So the volume of the pyramid is 1/3 of this, that is, 198/3 = 66 cubic centimers.

The correct answer is given by option B.

The measure of Angle C is approximately 26°.

A, B, C are vertices of a triangle, where AB = 8 cm, BC = 6 cm. To determine the measure of angle C, we need to use the cosine rule.

The cosine rule states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the angle between them.

Mathematically, we can represent it as follows:a² = b² + c² - 2bc cos(A)where a is the side opposite to angle A, b is the side opposite to angle B, c is the side opposite to angle C.

In this case, we have AB = c = 8 cm, BC = a = 6 cm, and AC = b. We need to find the measure of angle C, which is represented as cos(C).

Using the cosine rule, we can write the equation as follows:$$\begin{aligned} b^2 &= c^2 + a^2 - 2ca\cos(C) \\ \Right arrow b^2 &= 8^2 + 6^2 - 2 \times 8 \times 6 \cos(C) \\ \Right arrow b^2 &= 64 + 36 - 96 \cos(C) \\ \Right arrow b^2 &= 100 - 96 \cos(C) \end{aligned}$$We know that b is a positive length. Hence, b² > 0 or 100 - 96 cos(C) > 0. Solving for cos(C),  

we get: cos(C) < 100/96cos(C) < 1.0417Using a calculator, we can determine the inverse cosine of 1.0417 as:cos⁻¹(1.0417) = 0.4569 radians = 26.201° (rounded to the nearest degree)

Therefore, the measure of angle C is approximately 26°.

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Answer:

⠀

Step-by-step explanation:

⠀

We know,

\({\longrightarrow \qquad \boldsymbol{\pmb{Area_{(semicircle)} = \dfrac{1}{2}( \pi {r}^{2} ) }}}\)

⠀

Where,

⠀

Now, Substituting the values in the formula :

⠀

\({\longrightarrow \qquad \rm{{Area_{(semicircle)} = \it \dfrac{1}{2} \times 3.14 \times ({8})^{2} }}}\)

\({\longrightarrow \qquad \rm{{Area_{(semicircle)} = \it \dfrac{1}{ \cancel2} \times 3.14 \times \cancel{64} }}}\)

⠀

\({\longrightarrow \qquad \rm{{Area_{(semicircle)} = \it {1} \times 3.14 \times 32 }}}\)

⠀

\({\longrightarrow \qquad \rm{{Area_{(semicircle)} = \it {1} \times 100.48 }}}\)

⠀

\({\longrightarrow \qquad \boldsymbol{ \pmb{Area_{(semicircle)} \approx \it 100.48 }}}\)

⠀

Therefore,

Answer:

100.48 cm² ( option 2 )

Step-by-step explanation:

Given:-

To find:-

Solution:-

Area of semi-circle :-

\( \frac{1}{2} \pi \: r {}^{2} \)

1/2 × 3.14 × 8²

\(100.48 \: cm {}^{2} \)

Answer:

m<P = 50°

Step-by-step explanation:

Given:

Arc CE = 82°

Arc DF = 98°

Ratio of arc CD to Arc EF = 2:7

Thus, let,

Arc CD = 2x

Arc EF = 7x

A full circle = 360°

Therefore,

Arc CE + Arc DF + Arc CD + Arc EF = 360°

Substitute

82° + 98° + 2x + 7x = 360°

Add like terms

180° + 9x = 360°

Subtract 180° from both sides

180° + 9x - 180° = 360° - 180°

9x = 180°

Divide both sides by 9

9x/9 = 180/9

x = 20

✔️Arc CD = 2x

Plug in the value of x

Arc CD = 2(20) = 40°

Arc EF = 7x = 7(20) = 140°

✔️Find m<P:

Recall: the measure of the external angle created when two secants intersect = half the difference of the major and minor arcs that are intercepted

Thus:

m<P = ½(arc EF - arc CD)

Substitute

m<P = ½(140° - 40°)

m<P = ½(100°)

m<P = 50°

Answer:

21.6

Step-by-step explanation:

44-27.5=16.5

line segment VX-36= line segment VW we will call line segment VW C

C-36=VX we will call line segment VX H for Hypotenuse

Ratio 27.5/44 = 0.625 the ratio must be the same.

So 36/0.625=57.6 so 57.6-36= 21.6

I got three different answers. This checked out twice../

If An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. Its  possible reading on the scale if you put 500 kilograms of iron ore on it is :495, 505.

Percent error = 1%

Kilogram of iron ore = 500 kilograms

First step is to find the 1% of 500 kilograms

= .01 × 500 kilograms

= 5

Second step is to find the possible reading

Possible reading :

500 - 5

=495

500 + 5

= 505

Therefore we can conclude that  based on the above analysis the possible reading can be between 495 and 505.

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Answer:

30calories

Step-by-step explanation:

Answer:

30 calories per ounce

Step-by-step explanation:

The answer given by rachelwang2022 is correct.

I am just adding to the explanation

Since there are 150 calories in a 5-ounce container, you can determine the number of calories per ounce by simply dividing 150 by 5.

150/5 = 30 calories per ounce

Step 1: Observe the given figure state the obvious angles

Hence, arc QS=45°

Answer:

x - 9 = -1

Step-by-step explanation:

When you see less than you switch the numbers. So, for instance, it says 9 less than x means x-9

Answer:

The correct answer is :

1. Line PQ (One line PQ).

Step-by-step explanation:

The first step to solve this question is to draw the plane A with the points P and Q lying on it.

We know that given two different points there is only one line that contains this two different points.

Let's analyze each option.

''2. Lines PQ and QP''

This option is wrong because there aren't two different lines. In fact it is only one line that can be named line PQ or line QP.

''3. The 2 lines PQ and QP plus another line that does not lie in plane A.''

This option is assuming that exist three lines that contain P and Q. This option is also wrong.

''1. Line PQ''

This option is correct. It will be clarify with the drawing I will attach.

''We can't name them all!''

This option is assuming that exist infinite lines that contain P and Q. This option is wrong.

In the drawing I call the line that contains P and Q as line L.

Given that P and Q lie in plane A necessarily the line L must lie on the plane A.

Only one line contains points P and Q

The given parameters are:

There are at least two points in a line

This means that, a line can contain points P and Q, and any other points

Hence, only one line contains points P and Q

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Answer:

x < -5

Step-by-step explanation:

-2(5x + 1) > 48

Divide by -2, remembering to flip the inequality

-2/ -2(5x + 1) < 48/-2

5x +1 < -24

Subtract 1 from each side

5x+1-1 < -24-1

5x < -25

Divide by 5

5x/5 < -25/5

x < -5

Answer:

-14,950

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

Log(x²+8)=log 10+ log x

Log(x²+8)=log(10×x)

x²+8=10x

x² - 10x + 8=0

x is approximately to - 1 and - 8✅

The solutions to the given equation are x = -1 and x = 8.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

Using logarithmic properties, we can simplify the given equation:

logs(x² + 8) = 1 + log g(x)

logs(x² + 8) - log g(x) = 1

log[(x² + 8)/g(x)] = 1

(x² + 8)/g(x) = 10

x² + 8 = 10g(x)

Now we can solve for x by substituting the given answer options and solving for g(x):

For x = -2 and x = -4:

x = -2:

(-2)² + 8 = 12, which is not equal to 10 g(x) for any value of g(x).

So x = -2 is not a solution.

x = -4:

(-4)² + 8 = 24, which is also not equal to 10g(x) for any value of g(x).

So x = -4 is not a solution.

For x = -1 and x = 8:

x = -1:

(-1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = -1 is a solution.

x = 8:

(8)² + 8 = 72, which is equal to 10g(x) when g(x) = 7.2.

So x = 8 is a solution.

For x = 1 and x = -8:

x = 1:

(1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = 1 is a solution.

x = -8:

(-8)² + 8 = 56, which is not equal to 10g(x) for any value of g(x).

So x = -8 is not a solution.

Therefore,

The solutions to the given equation are x = -1 and x = 8.

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Answer:

No, he should not. He will only have $200 left over which he needs to put aside for savings and buying food and other goods and utilities. He should not buy until he has saved up more.

Step-by-step explanation:

Answer:

D. (7,5)

Step-by-step explanation:

Imagine a full parallelogram, complete the shape from there

The value of the logarithm of the number 52.66 is 1.7215.

The value of the logarithm of the number 52.66 is calculated as follows;

Using the logarithm table, we will follow the steps below;

From the logarithm table, log 52 under 6 = 7210

mean difference of 6 = 5

The total = 7210 + 5 = 7215

0.7215 (the result is called the mantissa)

Now, we will look for the characteristics part.

Since 52 is a number between 50 and 100, the characteristic is 1

Finally, we will combine both the characteristic part and the mantissa part to get the desired logarithm value as follows;

= 1 + 0.7215

= 1.7215

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Answer:

Step-by-step explanation:

The answer is, no!

Step-by-step explanation:

The reason to that answer is that some other shapes are also, having the same properties as shown. An example for that property would also mean a rectangle and not always a parallelogram.

So, here is the given information on what we need to classify a shape as a parallelogram:-

1) Parallel Sides

2)Opposite Sides are equal.

3) Adjacent sides are not equal.

4) Opposite angles are equal.

5)Adjacent angles are not equal.

Based on this, we can classify a shape as a parallelogram.

Hope, this answer helps!