Place the indicated product in the proper location on the grid.
a²b(3a² +4ab²)

The solution to the equation x + 2(7 - x) = 12 is x = 2.

Given the equation in the question:

x + 2(7 - x ) = 12

To solve the  equation, you need to use algebraic techniques to isolate the variable x on one side of the equation.

x + 2(7 - x) = 12

Apply distributive property

x + 2×7 + 2×-x = 12

x + 14 - 2x = 12

Combine like terms by subtracting 14 from both sides:

x - 2x = 12 - 14

-x = -2

Solve for x by dividing both sides by -1:

-x/-1 = -2/-1

x = 2

Therefore, the value of x is 2.

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The graphed line of the equation is attached 2x + 3y = -6

A linear equation is an expression that consists of a single power of the variable(s) in which it contains. This formulation can be impeccably illustrated in the following way:

ax + b = 0

The given equation 2x + 3y = -6 can be rearranged to get

y = -2/3x - 2

The x variables is plugged in to solve for y and used for the table of values for the graph

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Her next step in obtaining the area of the triangle is replacing the numeric values of h and y into the area formula.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the formula is:

A = 0.5yh.

Hence the actual values of y and h must be inserted into the formula to obtain the area of the triangle.

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Answer:

137 yd2

Step-by-step explanation:

The area of the triangle that has height of √6 and a base of √24 is calculated as: 6 square units.

The area of a triangle = 1/2 * b * h, where:

h is the height of the triangle, and

b is the base length of the triangle.

Given the following:

Height of triangle = √6

Base length of the triangle = √24

Plug in the values:

Area of triangle = 1/2 * √24 * √6

= (√24 * √6) / 2

= √144 / 2

= 12/2

Area of triangle = 6 square units.

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Answer:

Step-by-step explanation:

x^2 = 8

x=+-√8

The storage can hold approximately 10.94 cubic meters of grain.

Unit conversion is the process of converting a quantity expressed in one set of units to an equivalent quantity expressed in another set of units. For example, converting a length from feet to meters, or converting a temperature from Celsius to Fahrenheit.  

To convert cubic yards to cubic meters, multiply the given volume in cubic yards by this conversion factor to obtain the equivalent volume in cubic meters.  

Here we have

Adam’s family maintains storage that can hold 14.3 yd³ of grain.

Given that 1 yard is approximately equal to 0.9144 meters

To convert cubic yards (yd³) to cubic meters (m³),

Use the conversion factor:

1 yd³ = (0.9144 m)³

So, we can convert 14.3 cubic yards of grain to cubic meters as follows:

14.3 yd³ x (0.9144 m/yd)³ ≈ 10.94 m³

Rounding this answer to the nearest hundredth gives us:

10.94 m³ rounded to the nearest hundredth = 10.94 m³

Therefore,

The storage can hold approximately 10.94 cubic meters of grain.

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Answer: Directly proportional.

Step-by-step explanation:

      y = -x is directly proportional for a few reasons.

➜ The graph of this equation is a straight line, so all the ratios of points are equal.

➜ The constant of proportionality (k) is equal to -1.

➜ This line intersects the graph at the origin (0, 0).

➜ See the graph below.

The loan have a higher monthly payment Because the lease is riskier to the financing company.

To Determine the costs of buying versus leasing a motor vehicle, we need to consider the total costs associated with each option. For buying, the total cost is the sum of the down payment, loan payments, and the estimated value at the end of the loan, minus the resale value of the car.

On the other hand, for leasing, the total cost can be calculated as the sum of the security deposit, lease payments, and end-of-lease charges. We also need to consider the opportunity cost of investing the down payment and the security deposit.

We know that Melisha can pay for her vehicle with a 4-year loan or with a lease with the same down payment and same interest rate.

Therefore, the loan have a higher monthly payment Because the lease is riskier to the financing company.

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Answer:

Step-by-step explanation:

The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."

When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.

Therefore, option 1 is the correct definitation of perpendicular lines.

Answer: 1. Two lines that intersect in a way that forms right angles.

Step-by-step explanation:

Hope this helped! :)

If "function-g" defined for all real numbers as g(x) = x² + 6, then the value of g(-5) = 31, g(-2) = 10 and g(-1) = 7.

In mathematics, a function is generally denoted by a symbol such as "f" or "g", and its definition is given by an equation or formula that specifies the relationship between the input and output values.

The function "g" is given as : g(x) = x² + 6;, which is defined for all "real-numbers",

So, to find g(-5), g(-2), and g(-1), we simply substitute these values of x into the function "g" and simplify the resulting expressions:

⇒ g(-5) = (-5)² + 6 = 25 + 6 = 31,

⇒ g(-2) = (-2)² + 6 = 4 + 6 = 10,

⇒ g(-1) = (-1)² + 6 = 1 + 6 = 7.

Therefore, g(-5) = 31, g(-2) = 10, and g(-1) = 7.

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The given question is incomplete, the complete question is

Suppose that the function G is defined for all real numbers as g(x) = x² + 6. Find g(-5), g(-2) and g(-1).

The point (3,b) can lie on the circle with radius 8 and center (-2,-1) for values of b equal to -1 + √39 and -1 - √39.

We know that the circle with radius 8 and center (-2,-1) has the equation:

(x + 2)² + (y + 1)² = 8²

Substituting x = 3 and y = b, we get:

(3 + 2)² + (b + 1)² = 8²

Simplifying, we get:

25 + (b + 1)² = 64

(b + 1)² = 39

Taking the square root of both sides, we get:

b + 1 = ± √39

Therefore, the possible values of b are:

b = -1 ± √39

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The probability P (X≤2). from the probability distribution is 1/3

A continuous random variable is a type of random variable that can take on any value within a specific range, often an infinite range.

It has a probability distribution function that describes the probability of the variable taking on certain values within that range.

This means that

P (X≤2) =  the f(x) value

From the graph, we have

P (X≤2) = 1/3

Hence, teh value is 1/3

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Answer:

To find the coordinates of the point of intersection of the given equations, we need to solve the system of equations simultaneously. We can use the elimination method to do this:

11x - 6y = 2 (multiply both sides by 5)

-8x + 5y = 3 (multiply both sides by 11)

55x - 30y = 10

-88x + 55y = 33

Adding the two equations, we get:

-33x + 25y = 43

Solving for y, we get:

y = (33x + 43)/25

Substituting this expression for y into either of the original equations and simplifying, we get:

x = -1/7

Substituting this value of x into the equation for y, we get:

y = 1/35

Therefore, the coordinates of the point of intersection are (-1/7, 1/35).

The force parallel to the incline that would be required to hold the monolith on this causeway is 32, 120.52 Newtons.

The formula for finding the force parallel to the incline:

= mass of the monolith x acceleration due to gravity x sin( slope angle )

Mass in kg :

=  57 tons x 1000

= 57, 000 kg

Force parallel to the incline:

= 57, 000 kg x 9. 81 m/s² * sin ( 1.4 degrees )

= 57, 000 kg x 9.81 m/s² x sin ( 0.0244 radians )

= 32, 120.52 Newtons

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There are exactly 250 blocks with exactly one face painted red.

What is cube ?

A cube is a three-dimensional solid shape with six square faces of equal size that meet at 90-degree angles. It is a special case of a rectangular prism, where all of the edges have the same length.

When the 10 x 10 x 10 cube is painted red on all faces, it means that all of the 1000 unit cubes inside the large cube are red.

When the cube is cut into ten 10 x 10 x 1 slices, each slice will contain 100 unit cubes. When each slice is cut into twenty-five 2 x 2 x 1 blocks, each block will contain 4 unit cubes.

Therefore, each 2 x 2 x 1 block will come from 4 unit cubes, and each unit cube will contribute to 4 different blocks.

To count the number of blocks with exactly one face painted red, we can focus on the blocks that have a red face on the bottom (or top) and three unpainted faces on the other sides. Each such block will correspond to one of the 100 unit cubes in a slice, and there are 10 slices, so there are 1000 such blocks in total.

However, each of these blocks has four unit cubes, so we need to divide by 4 to get the number of blocks. Therefore, the answer is:

1000 ÷ 4 = 250

Therefore, there are exactly 250 blocks with exactly one face painted red.

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Answer:

B

Step-by-step explanation:

Notice that all y-intercepts are the same (doesn't give a clue to the answer).

The line has a downward slant as you move from left to right, so the slope is negative (eliminating A & C as answers).

Determine the actual slope by identifying the y-intercept and x-intercept, and calculate Rise over Run:

  Rise = -6 (goes from +6 to 0)

  Run = +12

  -6/12 = -1/2

The endpoints of the latus rectum of the parabola equation is : f. The endpoints of the latus rectum are (-6, 9) and (-6, -15).

Standard form of the equation of a parabola =y (x - h)² = 4p(y - k)

Where:

(h, k) = vertex

4p = distance between the vertex and focus

Comparing this with (x + 3)² = -20(y + 1) will gives us

(x + 3)² = -20(y + 1)

= (x - (-3))² = -20(y - (-1))

The vertex of the parabola is = (-3, -1)

4p = -20

p = -20/4

p = -5

The line that is perpendicular to the axis of symmetry (line y = -1) and passes through the focus (-3, -6) is known as the latus rectum of a parabola. The line y = - 6—the focus—and the directrix are separated by a distance of 4p = 20.

The vertex which is located at (-3, -1) is the latus rectum's midway. The latus rectum tend to has a length of 20 and passes through the points (-3, -1). Its endpoints must be located on the line x = -3 since it is perpendicular to the axis of symmetry.

The endpoints of the latus rectum are:

(-3, -1 - 10) = (-3, -11) and (-3, -1 + 10) = (-3, 9).

Therefore, the correct option is f.

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The height of the pyramid formed by the patio heater is 89.07 inches

An equation is an expression that shows how numbers and variables using mathematical operators.

Pythagoras theorem shows the relationship between the sides of a right angled triangle.

To find the height (h) of the pyramid. A right angled is form with base (b) = side of square / 2 = 22.8 / 2 = 11.4 in

Slant height (S) = 89.8 in

Using Pythagoras:

S² = h² + b²

89.8² = h² + 11.4²

h = 89.07 inches

The height of the pyramid is 89.07 inches

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If (-8,3) lies on the circle and its Center is (-4,3) then, the radius of the circle is 4.

We know that the center of the circle is (-4, 3). Let's call the radius of the circle "r".

The distance between the center of the circle and the point (-8, 3) on the circle is equal to the radius "r".

Using the distance formula, we can find the distance between these two points;

d =√[(x2 - x1)² + (y2 - y1)²]

d = √[(-8 - (-4))² + (3 - 3)²]

d = √[(-8 + 4)² + 0²]

d = √[4²]

d = 4

Since the distance between the center of the circle and the point on the circle is equal to the radius, we have;

r = d = 4

Therefore, the radius of the circle is 4.

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The horizontal asymptote is y = 3/2, and the slant asymptote is y = x/2.

We need to compare the degrees of the numerator and denominator.

The degree of the numerator is 2, and the degree of the denominator is also 2. Therefore, the horizontal asymptote is given by the ratio of the leading coefficients, which is 3/2. The horizontal asymptote is y = 3/2

Furthermore, f(x) = 3/2 + x/(2x² - 1)

This expression shows that the function has a slant asymptote given by the line: y = x/2

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The value of the function f/g is (x - 1) / (x + 8)

Let's start by writing out the functions we are given:

f(x) = 4 / (x + 8)

g(x) = x / (x - 1)

To find f/g, we need to divide f(x) by g(x). We can do this by multiplying f(x) by the reciprocal of g(x), which is (x - 1) / x. Multiplying f(x) by this reciprocal gives us:

f(x) * (x - 1) / x = 4 / (x + 8) * (x - 1) / x

To simplify this expression, we can first find a common denominator for the two fractions on the right-hand side:

4 / (x + 8) * (x - 1) / x = 4(x - 1) / x(x + 8)

Now we can simplify this expression by canceling out any common factors in the numerator and denominator. In this case, we can cancel out a factor of 4 and a factor of (x - 1):

4(x - 1) / x(x + 8) = (x - 1) / (x + 8)

Therefore, the quotient of f(x) and g(x), or f/g, is:

f/g = (x - 1) / (x + 8)

We can interpret this expression as a new function, h(x), where h(x) = f(x) / g(x) = (x - 1) / (x + 8). This new function takes a value of x and returns the ratio of f(x) to g(x) at that value.

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Answer:

C

Step-by-step explanation:

The equation is:

y = [tex]\frac{1}{4}[/tex]x - 8

If you plug in the x and y value from the table, you find they are solutions to the equation.

(36,1)

y = [tex]\frac{1}{4}[/tex]x - 8  Substitute in 36 for x and 1 for y

1 = [tex]\frac{1}{4}[/tex](36) - 8

1 = 9 - 8

1 = 1

You can do the same thing for all of the other points on the table.

Helping in the name of Jesus.

Answer:

13.3333333333 or 13.3

Step-by-step explanation:

yeah :3

Answer:

It's not clear what figure is being referred to. The provided numbers could be dimensions of a shape, but without additional information or context, it's impossible to determine the area of the figure. Can you please provide more details or a diagram?

Step-by-step explanation:

Answer:

it is a zero dimensional point

Step-by-step explanation:

points are an exact location represented by a dot.

points do not have dimension (length, width, or height)

The number of cups of frozen strawberries that are needed to make 3 gallons of punch is equal to 48 cups.

In this exercise, you're required to determine the number of cups of frozen strawberries that are needed to make 3 gallons of punch.

Thus, we would apply direct proportion.

Note: There are 16 cups of frozen strawberries in a gallon.

By direct proportion:

16 cups = 1 gallon

X cups = 3 gallons

Cross-multiplying, we have:

X = 16 × 3

X = 48 cups of frozen strawberries.

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The value of angle JKN is 73°.

Given that the m ∠JKM = 106 degrees, m ∠LKM = 66, and KN bisects LKM.

So we need to find the value of ∠JKN,

So, using the angles addition postulate,

∠LKM = ∠LKN + ∠MKN

Therefore,

∠LKN = 66/2 [definition of bisector]

∠LKN = 33°

Again, using the angles addition postulate,

∠JKM = ∠JKL + ∠LKM

∠JKL = 106 - 66

∠JKL = 40°

Therefore,

∠JKN = ∠JKL + ∠LKN

∠JKN = 40 + 33

∠JKN = 73°

Hence, the value of angle JKN is 73°.

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Answer: C

Step-by-step explanation:

We need to turn 50% into a fraction first to make it easier,

50% is equal to 1/2 because 50/100 is simplified to 1/2.

Now let's multiply!

24 x 1/2 = 24/2 = 12/1 = 12