Solve the following system of
equations:
y=47+ 3x
y=8+0.5x

Answer:

y = - 4x - 2 is the required equation of the line.

Step-by-step explanation:

Equation of two parallel lines differ only by a constant.

If the equation of a line is [tex]$ ax + by + l = 0 $[/tex] then the equation of the line parallel to it is given by [tex]$ ax + by + k = 0 $[/tex].

Note that only the constants differ in both the equations.

The given equation is: y = - 4x - 2

This is equivalent to 4x + y + 2 = 0.

Therefore, the equation of the line parallel to the given line will be:

4x + y + k = 0.

We are also given the point which passes through the line. We can substitute it to determine the value of 'k'.

Substituting (- 2, 6), we get:

4(-2) + 6 + k = 0

⇒ - 8 + 6 + k = 0

⇒ k = 2

Hence, the equation of the required line is: y = - 4x - 2

Answer:

Step-by-step explanation:

6t-2=5t

8t+6=7t+6

Answer:

the 3rd one i believe.

not sure.

hope this helps!

Answer:

You have 6 apples left.

Step-by-step explanation:

You have 10 apple and give away 4.

10 - 4 = 6 apples

You have 6 apples left.

Therefore( [tex]m^3 -6m^2-16m +63[/tex] )÷ (m-7)  [tex]= (m^2 +m-9)[/tex]

Step-by-step explanation:

[tex]m^3 -6m^2-16m +63[/tex]

[tex]=m^3 -7m^2[/tex][tex]+m^2 -7m[/tex][tex]-9m+63[/tex]

[tex]= m^2(m-7)[/tex][tex]+m(m-7)[/tex][tex]-9(m-7)[/tex]

[tex]= (m-7 ) (m^2 +m-9)[/tex]

Therefore( [tex]m^3 -6m^2-16m +63[/tex] )÷ (m-7)  [tex]= (m^2 +m-9)[/tex]

Answer:

6πr/11.

Step-by-step explanation:

The length of the arc = rC where C is the central angle of the sector in radians and r = the radius.

C = (3/11) * 2π

= 6π/11 radians.

So the measure of the arc = 6πr/11.

Answer:

Saturday

Step-by-step explanation:

Each day of the week is repeated after 7 days

So, after 19 days it would be Saturday

Answer:

2500

Step-by-step explanation:

5^3 is 125/2.5 is 50 and 50^2 is 2500

Answer:

20

Step-by-step explanation:

5x5x5= 125

2.5x2.5=6.25

125÷6.25= 20

Answer:

81

Step-by-step explanation:

Step-by-step explanation:

[tex]2.41 \times {10}^{4} \\ = 2.41 \times 10000 \\ = 24100 \\ [/tex]

Answer:

16.2

Step-by-step explanation:

45% = 0.45 (as a decimal)

36 × 0.45 = 16.2

Answer:

answer is 4

Step-by-step explanation:

look at picture

Answer:

x = 1

Step-by-step explanation:

14 x 2x = 28

2 x 1 = 2

14 x 2(1) = 28

14 x 2 = 28

Answer:

42 and 58

Step-by-step explanation:

Let the two numbers be represented by A And B

A + B = 100

A = B + 16

Substitute B + 16 in place of A in equation 1

We have,

B + 16 + B = 100

It can also be written as

B + B + 16 = 100

2B + 16 = 100

Subtract 16 from both sides

2B + 16 - 16 = 100 - 16

2B = 84

Divide both sides by 2

2B/2 = 84/2

B = 42

Now substitute 42 for B in any of the equations to get A.

Using equation 1

A + B = 100

A + 42 = 100

Subtract 42 from both sides

A + 42 - 42 = 100 - 42

A = 58

Therefore the two numbers are 42 and 58

The area of the metal frame surrounding a circular mirror can be calculated by figuring the expression 225x² - 9πx², which represents the area of the square minus the area of the circle.

The subject of this question is based in mathematics, specifically the area of geometry. The area of the metal frame surrounding the mirror can be found by calculating the difference between the area of the square frame and the area of the circular mirror.

The area of the square frame is given by the formula A = s² where 's' is the length of a side of the square. In this case, each side of the square is 15x so the area of the square frame would be (15x)² = 225x².

The area of the circular mirror is given by the formula A = πr² where 'r' is the radius of the circle. For this mirror, the radius is 3x, so the area of the mirror would be π*(3x)² = 9πx².

So, the area of the metal frame is the difference between the area of the square and the area of the circle. Thus, the area of the frame = 225x² - 9πx².

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Final answer:

To find the area of the metal frame, calculate the area of the square then subtract the area of the circle. The area of the frame is the difference between the square's area, (15x)², and the circle's area, π(3x)².

Explanation:

The question asks for the area of the metal frame surrounding a circular mirror with the mirror's radius being 3x and the frame's side length being 15x.

To find the area of the frame, first calculate the area of the square and then subtract the area of the circle (mirror). The area of the square is given by the formula A = side², so:

Next, calculate the area of the circle using the formula A = πr²:

Finally, subtract the mirror's area from the frame's area to find the area of the metal frame alone:

Answer:

1,200,000 square miles

Step-by-step explanation:

Given data:

Total land = 3 000 000

40% is covered by sand dunes

Land covered by sand dunes is 40% of the total area therefore

Land covered by sand dunes=(40/100) * 3000000

Land covered by sand dunes= 0.4 * 3000000

Land covered by sand dunes= 1 200 000

Final answer:

Approximately 1,200,000 square miles of Australia are covered by sand dunes, which is 40% of Australia's total area of about 3,000,000 square miles.

Explanation:

The student has asked how much of Australia is covered by sand dunes given that Australia's area is approximately 3,000,000 square miles and sand dunes cover 40% of the land.

To calculate the area covered by sand dunes, we apply the percentage to Australia's total area:

Convert the percentage into decimal form: 40% = 0.40.

Multiply the total area of Australia by the decimal: 3,000,000 square miles × 0.40.

The result gives us the area covered by sand dunes: 1,200,000 square miles.

Therefore, sand dunes cover about 1,200,000 square miles of Australia.

Answer:

B)

Step-by-step explanation:

All three trigonometric functions  are positive in Quadrant I

Sine only is positive in Quadrant II

Tangent only is positive in Quadrant III

Cosine only is positive in Quadrant IV

Now

tan 116°           tan 116° means that the angle 116° lies in the second quadrant.

sin is positive while cos and tan are negative in the second quadrant

tan 116° = -tan(180°-116)

= -tan(64°)

Answer:

2 3/6

Step-by-step explanation:

When reducing the fraction you see how many times the denominator of 6 can fit into to numerator of 15. It is 2 with 3 left over. So you write 2 3/6

Answer:

2 1/2

Step By Step:

15 divided by 6: 2 R3

2 3/6

GCF is 3

Divide both sides by 3, and get 2 1/2

Answer:

n or the number = 5

Step-by-step explanation:

5 * (-2 + n) = 91 + (-n + 1)

-10 + 5n = 19 - n + 1

6n = 20 + 10

6n/6 = 30/6

n = 5

Answer:

The number is 51.

Step-by-step explanation:

Let the number be x and the opposite of a number is -x.

5(-2+x) = 91 + (-x + 1)

-10 + x = 91-x+1

-10 + 2x = 92

2x = 102

x = 51

The surface area of prism is 185.815 square inches

Solution:

Given that,

[tex]Length = 2\frac{1}{3}\ inches = \frac{3 \times 2 + 1}{3} = \frac{7}{3}\ inches = 2.33\ inches[/tex]

[tex]Width = 8\frac{1}{2}\ inches = \frac{17}{2}\ inches = 8.5\ inches[/tex]

[tex]Height = 6\frac{3}{4}\ inches = \frac{27}{4}\ inches = 6.75\ inches[/tex]

The surface area of package is given as:

[tex]A=2(wl+hl+hw)[/tex]

Where,

"l" is the length

"w" is the width

"h" is the height

Substituting the values we get,

[tex]A = 2((8.5 \times 2.33) + (6.75 \times 2.33) + (6.75 \times 8.5))\\\\Simplify\ the\ above\ equation\\\\A = 2(19.805+15.7275+57.375)\\\\A = 2 \times 92.9075\\\\A = 185.815[/tex]

Thus the surface area of prism is 185.815 square inches

Answer:

The surface area of the prism is 185.815 square inches.

Hope this helps!

Answer:

[tex]SA=1.5\ cm^2[/tex]

Step-by-step explanation:

we know that

The surface area of a cube is equal to

[tex]SA=6s^2[/tex]

where

s is the length side of a cube

we have

[tex]s=\frac{1}{2}\ cm[/tex]

substitute

[tex]SA=6(\frac{1}{2})^2[/tex]

[tex]SA=(\frac{6}{4})=1.5\ cm^2[/tex]

Answer:

The probe's final position is -143m

Step-by-step explanation:

Note that the words 'lowered' and 'below' mean subtract; while the word 'raised' means add. Thus, interpreting the statement to mathematical expression is done below.

[tex] - 90m + 50m - 138m + 35m[/tex]

[tex] = - 143m[/tex]

Therefore, the probe's final position is -143m. Hence, the sensor is 143m below the sea level.

Answer:

x=-2

Step-by-step explanation:

first u subtract 7 on both sides resulting on 8x=-16. Then to isolate x u divide by 8 on both sides.

Answer:

Step-by-step explanation:

I've already solved this problem.

Answer: x=2 and y=8

Step-by-step explanation:see attachment

Answer:

Explanation:

1. Calculate the monthly interest owed during year 1

2. Calculate the monthly interest owed during year 2

3. Calculate the difference

Hence, the answer is the option c) $22.50

Answer:

C) 2x^2+7x-4

Step-by-step explanation:

(2x-1)(x+4)=2x^2-x+8x-4=2x^2+7x-4

Answer:94.5pie

Step-by-step explanation:

Final answer:

To calculate the volume of a cylindrical sugar container with a radius of 3 inches and a height of 10.5 inches, use the formula V = πr²h, which yields approximately 296.78 cubic inches.

Explanation:

The question asks for the volume of the container that has the shape of a cylinder. The given dimensions are a radius of 3 inches and a height of 10.5 inches. To find the volume of a cylinder, we use the formula:

V = πr²h

Where V is the volume, π (pi) is a constant approximately equal to 3.14159, r is the radius, and h is the height of the cylinder.

We calculate the volume as follows:

V = π × (3 inches)² × 10.5 inches

V = π × 9 in² × 10.5 in

V = π × 94.5 in³

V ≈ 296.78 in³

Thus, the volume of the cylinder is approximately 296.78 cubic inches

Answer:

r=9/2 or 4.5

Step-by-step explanation:

First of all our goal is to get R by itself

by cross multiplying we get,

(r+3)*3=5r

by distributive property we get

3r+9=5r

substracting 3r from both sides we get

9=2r

by dividing by 2 in both sides we get

r=9/2 or 4.5

The characteristic of the linear parent function that is not true is that the range is positive real numbers (y > 0).

The correct answer is B. The characteristic of the linear parent function that is not true is that the range is positive real numbers (y > 0).

A linear parent function is represented by the equation y = x and passes through the origin (0,0). Its domain is all real numbers (-∞, ∞) and its range is also all real numbers (-∞, ∞).

A linear function with a slope of 1 is represented by the equation y = x and is a straight line that passes through every point on the graph that has the same x and y value.

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Option B 'The range is positive real numbers (y>0)' is not a characteristic of the linear parent function. The function y=x, known as the linear parent function, has its range as all real numbers, not just positive.

The characteristic of the linear parent function, which is not accurate, is: 'The range is positive real numbers (y>0)'.

The linear parent function is y = x, which indeed meets the criteria of the remaining options. It goes through the origin (0,0), its domain covers all real numbers, as x can be any real number, and it has a slope of 1 throughout. However, its range is not only positive real numbers (y>0). The range of the linear parent function actually includes all real numbers because y (the output) can take any real value, both positive and negative, not just positive.

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