What is the value of x in the solution to this system of equations?


x = –3y + 12


6x – 2y = –48

Answer:The height of the roof in his house is 72.43 ft.

Step-by-step explanation:

The volume of square pyramid is :

B= area of the base.

h= the height.

Given that,

The roof is a square pyramid in shape. The volume of the roof is 18929.333 cubic feet.

The side length of the base of the roof is 28 feet.

Since the base of the roof is square in shape.

The area of the square is = side²

The area of the base is =(28×28) square feet

                                      =784  square feet

Assume the height of the roof be h ft.

Then, the volume of the roof is =  

                                                   square feet.

According to the problem,

ft.

The height of the roof in his roof is 72.43 ft.

Step-by-step explanation:

So to solve this question, your goal is to find out how the way it is solved is not correct.

Your answer would be: On the third line, the student adds the 8 to both sides instead of subtracting. The way the initial equation is given is

y-(-8)=-6(x-2). After distributing the six, the student should make the 8 positive because subtracting a negative makes a positive. After solving, the equation should look like: y(+8)=-6x+12, so you would subtract the 8 from both sides instead of adding it, and solve from there.

Answer:

36- degree rotation m8

Step-by-step explanation:

mark me brainliest :)

Answer:

Rational, Natural, Whole, Integer

Step-by-step explanation:

Answer:

(7, -1)

Step-by-step explanation:

3x + 7y = 14

y = x - 8

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

Add 56 to both sides.

10x = 70

Divide both sides by 10.

x = 7

3(7) + 7y = 14

21 + 7y = 14

Subtract 21 from both sides.

7y = -7

Divide both sides by 7.

y = -1

(7, -1)

Answer:

continuous, continuous

Step-by-step explanation:

The Area of triangle with the given height 10 cm and base 6 cm is calculated to be  30 square centimeters.

To calculate the area of a triangle with height 10 cm and base 6 cm, we can use the formula:

Area = (1/2) x Base x Height

Substituting the given values, we get:

Area = (1/2) x 6 cm x 10 cm

Area = 30 square cm

Therefore, the area of the triangle is 30 square centimeters.

We can see that the area of the triangle is calculated by multiplying the base and height and then dividing the result by 2. In this case, the height of the triangle is 10 cm and the base is 6 cm, so the area is 30 square cm. This formula can be used to calculate the area of any triangle, regardless of its size or shape.

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The complete question is :

Calculate the Area of triangle with the height 10 cm and base 6 cm .

52

hope it helps and give brainliest if my answer helps...

Answer:

c.44

Step-by-step explanation:

when x= 8 => f(8) = 6.8-4 =44

The length of the bar is 10.5 foot and the width of the bar is 5.7 foot .

In the question ,

it is given that

the base area of the large chocolate bar is 59.85 square foot .

let the length of the chocolate bar be "l"

and the breadth of the chocolate bar be "b"

given that the length is 0.9 foot shorter than twice its width , means

l = 2w - 0.9

we have the area of rectangle = length \(\times\) width

Substituting the values of length , width and area we get

59.85 = (2w - 0.9 ) * w

59.85 = 2w² - 0.9w

2w² -0.9w -59.85 = 0

On solving the quadratic equation ,

we get w = -5.25 and w = 5.7

width cannot be in negative , so, the width is 5.7 foot .

and l = 2(5.7) -0.9 = 11.4 - 0.9 = 10.5

Therefore , the length of the bar is 10.5 foot and the width of the bar is 5.7 foot .

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The geometric series is convergent and its sum is \(1/\sqrt{10}\)

A geometric series is a series of numbers where each term is found by multiplying the preceding term by a constant ratio. It can be represented by the formula\(a + ar + ar^2 + ar^3 + ...\) where a is the first term, r is the common ratio, and the series continues to infinity. The sum of a geometric series can be calculated using the formula \(S = a(1 - r^n) / (1 - r)\), where S is the sum of the first n terms.

The given series is a geometric series with a common ratio of \(1/\sqrt{10}\)
For a geometric series to be convergent, the absolute value of the common ratio must be less than 1. In this case,\(|1/√10|\)is less than 1, so the series is convergent.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

sum = a / (1 - r),

where a is the first term and r is the common ratio.

Plugging in the values, we get:

\(sum = 1 / (\sqrt{10}  - 1)\)

Therefore, the geometric series is convergent and its sum is 1 / (\(\sqrt{10}\) - 1).

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Answer:

x = -12

Step-by-step explanation:

−10x + 1 + 7x = 37

Combine like terms

-3x+1 = 37

Subtract 1 from each side

-3x +1-1 = 37-1

-3x = 36

Divide each side by -3

-3x/-3 = 36/-3

x = -12

Answer:

x = -12

Step-by-step explanation:

\(-10x+1+7x=37\\\\\mathrm{Group\:like\:terms}\\-10x+7x+1=37\\\\\mathrm{Add\:similar\:elements:}\:-10x+7x=-3x\\-3x+1=37\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\-3x+1-1=37-1\\\\Simplify\\-3x=36\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{36}{-3}\\\\x =-12\)

e follSOLUTION

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the general equation of an ellipse

STEP 2: Identify the parameters

the length of the major axis is 2a

the length of the minor axis is 2b

STEP 3: Get the equation of the ellipse

STEP 4: Pick the nearest equation from the options,

Hence, the equation of the ellipse in the image is given as:

OPTION A

Answer:

about 703.69

Step-by-step explanation:

To calculate the base you would use pi radius squared: 153.93

Since you have 2 bases you would multiply that by 2: 307.87

Then you need to find the circumference (2 pi radius) : 43.98

Then you multiply the circumference by the height: 395.82

Add the bases and the sides to get 703.69

Answer:

32.5cm\(^{2}\)

Step-by-step explanation:

A= (7) (9) = 63 / 2

A= 32.5cm\(^{2}\)

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

Once the bits of the binary number have been multiplied by the corresponding positional weights, the binary number can then be converted into its corresponding decimal number by adding the resulting products.

To convert a number in base 2 (binary), base 8 (octal) or base 16 (hexadecimal) to a base 10 (decimal) number, you can use the following method:

Write the number in base 2, 8, or 16 and the corresponding base 10 place values.

Multiply each digit by its corresponding place value and add the results.

For example, to convert the base 10 number 11.011 to a base 10 number:

Write the number and the corresponding base 10 place values: 11.011

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

As the number is already in base 10, it does not need to be converted. The value is 11.011

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The function S(t) = -15t^(5/3) + C which we get by integration of S'(t) and the company  will continue to manufacture this computer for approximately 5.47 months.

To find S(t), we need to integrate the given rate of decline, S'(t), with respect to time (t). We have:

S'(t) = -25t^(2/3)

Integrating both sides with respect to t, we get:

S(t) = ∫(-25t^(2/3) dt)

Using the power rule for integration, we obtain:

S(t) = (-25 * (3/5) * t^(5/3)) + C
S(t) = -15t^(5/3) + C

Now, we're given that at t = 0, S(0) = 2,050 computers. We can use this information to find the constant of integration, C:

S(0) = -15(0)^(5/3) + C
2,050 = C

Thus, the function for the monthly sales is:

S(t) = -15t^(5/3) + 2,050

The company will stop manufacturing when S(t) = 1,000 computers. To find when this occurs, we'll set S(t) equal to 1,000 and solve for t:

1,000 = -15t^(5/3) + 2,050
-1,050 = -15t^(5/3)

Now, isolate t^(5/3) and solve for t:

t^(5/3) = 1,050 / 15
t^(5/3) = 70

Take the cube root of both sides:

t^(5/3)^(3/5) = 70^(3/5)
t = 70^(3/5)

Calculating this value, we get approximately:

t ≈ 5.47

So, the company will continue to manufacture this computer for approximately 5.47 months.

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Answer:

g(x) = \(12.(\frac{3}{4})^x\)

Step-by-step explanation:

Exponential function g has been represented by the table attached,

Equation of the exponential function is,

g(x) = \(a.(b)^x\)

Now we substitute the values of x and g(x) from the table,

For a point (0, 12),

12 = \(a(b)^0\)

a = 12

For another point (1, 9),

9 = \(a.(b)^1\)

9 = a × b

9 = 12 × b

b = \(\frac{9}{12}\)

b = \(\frac{3}{4}\)

Therefore, equation of the exponential function will be,

g(x) = \(12.(\frac{3}{4})^x\)

The figure that represent the rotation and reflection of the scalene triangle is given as follows:

Figure B.

The five more known rotation rules are given as follows:

A 90º clockwise rotation means that the scalene triangle is rotated right, and thus the figure would be given by option D.

After the vertical reflection, the orientation of the triangle would be changed, meaning that it would then be given by option B.

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y = (-1/2)x + 4 is the equation for the linear function with an x-intercept of 8 and a y-intercept of 4.

We are aware that lines might have several kinds of equations; the typical form is

The equation of a line in slope-intercept form is Ax + By + c = 0, and

y = mx + b.

m is the slope, and b is the y-intercept.

The y-intercept, or (0,b), is the point where the line crosses the y-axis at x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.

Given, An x-intercept for a linear function is 8, and a y-intercept is 4.

The two points on the line are therefore (8, 0) and (0, 4).

Slope(m) is now equal to (4 - 0)/(0 - 8).

m slope = 4/8.

slope(m) equals -1/2.

With a y-intercept of 4, it represents the value of b in the equation y = mx + b.

Consequently, the equation is y = (-1/2)x + 4 is linear.

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Given data:

A particle at t1= 2 s is at x1= 30 cm

At t2 = 10 s is at x2 = 78 cm.

(a) The average velocity is given as:

vav, x = displacement/time interval

= (x2 - x1) / (t2 - t1)

Taking the values from the given data, we get:

vav, x = (78 - 30) / (10 - 2)

= 48 / 8

= 6 m/s

(b) Average speed is given as the total distance travelled divided by the time taken.

Since the displacement is given, we cannot determine the distance travelled.

Hence, we cannot determine the average speed from these data.

So, the answer to part (b) is "No".

Hence, the average velocity of the particle is 6 m/s and the average speed cannot be determined.

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Therefore, the answer is:

b. 2 and 3

Answer:

4 km -> 400,000 mm

put a decimal point at the end of 4 and move it to the left 6 times because we know that 1 km is equal to 100,000 and it has zeros.

hence, it is proven that 4 km is equal to 4000,000.

Answer:

Step-by-step explanation:

9.80 = 196

1 = 196/ 9.80

4.20 = 196/9.80 x 4.20

4.20 =

Answer:

Step-by-step explanation:

Let X be par.

Jenny made x-1 strokes

Jérôme made x+4 strokes.

So, we can use the amount of strokes made, but we have to use absolute value brackets ( | | )

|-1| + |4| = 5.

Jérôme made 5 more strokes than Jenny

Using a standard normal distribution table or a calculator, we can find the area under the curve between Z1 and Z2 is (-2,0).

This area represents the probability of observing rainfall greater than 4 inches is 2.

To sketch the graph of the distribution, we'll use a normal distribution curve. The mean (average) rainfall per day is 3.0 inches, and the standard deviation is 0.5 inches.

The graph will be centered around the mean, and we'll show up to 3 standard deviations on either side.

The mean (µ) is 3.0 inches, and the standard deviation (σ) is 0.5 inches.

One standard deviation below the mean is µ - σ = 3.0 - 0.5 = 2.5 inches.

Two standard deviations below the mean is µ - 2σ = 3.0 - (2 × 0.5) = 2.0 inches.

Three standard deviations below the mean is µ - 3σ = 3.0 - (3 × 0.5) = 1.5 inches.

Similarly, one, two, and three standard deviations above the mean are:

One standard deviation above the mean is µ + σ = 3.0 + 0.5 = 3.5 inches.

Two standard deviations above the mean is µ + 2σ = 3.0 + (2 × 0.5) = 4.0 inches.

Three standard deviations above the mean is µ + 3σ = 3.0 + (3 × 0.5) = 4.5 inches.

The graph will be bell-shaped, with the peak at the mean (3.0 inches) and tapering off as we move away from the mean.

The x-axis represents the rainfall in inches, and the y-axis represents the probability density.

To find the percentage of days with rainfall between 2 and 3 inches in May, we need to calculate the area under the normal distribution curve between these two values.

This area represents the probability of observing rainfall between 2 and 3 inches.

We can use the Z-score formula to convert the rainfall values into standard deviations from the mean:

Z = (X - µ) / σ

For 2 inches:

Z1 = (2 - 3) / 0.5 = -2

For 3 inches:

Z2 = (3 - 3) / 0.5 = 0

The corresponding probability will give us the percentage of days with rainfall between 2 and 3 inches in May.

To estimate the number of days with more than 4 inches of rain in May, we need to calculate the probability of observing rainfall greater than 4 inches.

We can use the Z-score formula again to convert the rainfall value into standard deviations from the mean.

For 4 inches:

Z = (4 - 3) / 0.5 = 2

Using the standard normal distribution table or a calculator, we can find the area under the curve to the right of Z.

Multiplying this probability by the total number of days in May (31) will give us the expected number of days with more than 4 inches of rain.

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When a die is cut horizontally and vertically, the resulting cross sections are a square and a rectangle, respectively.

A die is a cube with six faces, each having a square shape. When the die is cut horizontally, the resulting cross section will also be a square. This is because the horizontal cut passes through the cube's faces, creating a flat surface with the same shape and size as the original faces.

On the other hand, when the die is cut vertically, the resulting cross section will be a rectangle. This is because the vertical cut intersects two adjacent faces of the cube, creating a flat surface with a rectangular shape.

Therefore, cutting a die horizontally produces a square cross section, while cutting it vertically produces a rectangular cross section.

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Answer:

During that time, math symbols (like the division and multiplication sign) and numbers weren't invented yet, so they used words because that was the only choice either than verbally speaking.

Step-by-step explanation:

This is open-ended question, so you can write something similar to the answer I wrote or add on to it :-)

I searched online for the answer and found it on Brainly just to let you know because I was unsure about it loll

Credit: Edufirst

Hope it helps (●'◡'●)

The scale factor is 3/4, so the correct option is B.

To get the scale factor, we just need to take the quotient between the length of a side in the image, and the length of the correspondent side in the preimage.

Let's use the top sides for this, we can see that:

In the image: H'I' = 3 units.

In the preimage HI = 4 units.

Then the scale factor for this transformation is:

K = 3/4

The correct option is B.

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Answer:

what is the area of the trapezoid