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What is the solution to the system? ​

Answer:   [tex](\text{x}-2)^2+(\text{y}-3)^2 = 16[/tex]

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Explanation:

The general circle template is

[tex](\text{x}-\text{h})^2+(\text{y}-\text{k})^2 = \text{r}^2[/tex]

(h,k) = center

r = radius

Assuming the center is (2,3) then we have h = 2 and k = 3. We also have a radius of r = 4.

[tex](\text{x}-\text{h})^2+(\text{y}-\text{k})^2 = \text{r}^2\\\\(\text{x}-2)^2+(\text{y}-3)^2 = 4^2\\\\(\text{x}-2)^2+(\text{y}-3)^2 = 16\\\\[/tex]

SOLUTION

Given:

The formula is given as:

Final answer:

The height of the pile increasing at the rate of  4.56 inches per minute when the pile is 10 ft high.

In given situation, the rate of change of height is equal to the rate of change of volume, divided by the base area.

First we find the base area.

base area = (π/4)d²

base area = (π/4)10²

base area = 25π ft²

base area ≈ 78.5 ft²

Then the rate of change of height would be,

(30 ft³/min)/(78.5 ft²)

≈ 0.38 ft/min

= 4.56 inches / minute

Therefore, the height of the pile increasing at the rate of  4.56 inches per minute when the pile is 10 ft high.

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[tex] \frac{3 \times 3 \times 2^{ - 4} \times 2^{0} }{(3 \times 2 ^{ - 3}) ^{2} } \\ = \frac{3^{ 1+1 } \times 2^{ - 4 + 0} }{3 \times 2 ^{ - 3 \times 2} } \\ = \frac{ {3}^{2} \times {2}^{ - 4} }{3 \times {2}^{ - 6} } \\ = 3^{2 - 1} \times 2^{ - 4 - ( - 6)} \\ = 3 \times {2}^{ - 4 + 6} \\ = 3 \times {2}^{2} \\ = 3 \times 4 \\ = 12[/tex]

I USED THE LAWS OF EXPONENTS.

IF YOU DO NOT KNOW THEM PLEASE TELL ME AS SOON AS POSSIBLE TO ARRANGE FOR YOU.

Given:

Required: Evaluation

Explanation:

Use BODMAS rule to evaluate all

71.

72.

73.

74.

75.

Final Answer:

71 - E

72 - AE

73 - A

74 - BE

75 - B

Dilations involve multiplication, so we have that the dilation with scale factor 1/2 of the point (3,4) is (1.5, 2)

and the dilation with scale factor 2 of the point (4,15) is (8, 30)

In order to find a vector multiplication by a scalar, we follow the rule:

then, if we apply it to the vector v, we need to find the dimensions of the vector, for that we subtract the initial point from the terminal point,

then, multiply by the scalar -1/2,

Answer:

Reasoning Criticism Lisa modeled 2 with a number line (3). Her logical number line is -6.

Therefore, Reasoning Criticism Lisa modeled 2 with a number line (3). Her logical number line is -6.

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The first piece = 20m

The second piece = 40m

The third pice = 8x = 160m

Given:

Total length of wire = 220m

2nd piece = 2 times the 1st piece

3rd piece = 4 times the 2nd

To find:

The length of each of the piece

The wire was cut into 3:

1st piece + 2nd piece + 3rd piece = 220m

let the first length = x

2nd length = 2 (1st length) = 2(x)

2nd length = 2x

3rd length = 4(2nd piece) = 4(2x)

3rd length = 8x

The first piece = 20m

The second piece = 2x = 2(20) = 40m

The third pice = 8x = 8(20) = 160m

-21

1) Let's calculate this product:

7 (-3) Multiply 7 by -3

-21

2) So, seven times negative three is equal to -21 that is the same as adding seven times the number -3. Remember different signs in a product turns to out to a negative result.

Given

capacity of 500 pounds.

weights of the passengers are 107 pounds, 172 pounds and 129 pounds.

you weigh 136 pounds

Find

is it safe for you to enter the elevator?

Explanation

as total pounds in the elevator = 107 + 172 + 129 = 408 pounds

total pounds included my weight = 408 + 136 = 544 pounds

capacity = 500 pounds

so , extra pounds = 544 - 500 = 44 pounds

so , no it is not safe for you to enter the elevator.

Final Answer

Therefore , No the weigh capacity would be exceeded by 44 pounds

The cost of 20 apples is such that the ratio of apples to cost maintained or each apple costs the same amount is $4.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

As per the given,

Melissa brought 6 apples for $1.20.

The ratio of cost to apple ⇒

1.20/6

Now let's suppose the cost of 20 apples is x dollars.

The ratio of cost to apple ⇒

x/20

Since the cost of each apple is the same, therefore, both ratios must be the same.

x/20 = 1.20/6

x = 20(1.20/6)

x = 4

Hence "The cost of 20 apples is such that the ratio of apples to cost maintained or each apple costs the same amount is $4".

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since

then

then it is the 100x0.66= 66%

A variable is a letter or term that represents an unknown number, value, or quantity. Variables are especially useful in algebraic expressions or algebra.

let a number be x

then "twice the sum of a number be 2x

given

"twice the sum of a number and 7 is negative fifteen"

⇒ 2x + 7 = -15

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To prove:

The given graph is a function.

The given graph is a function if and only if no x value has more than one value of y, or we can say that a graph is a function iff no vertical line intersects the graph in more than one point.

Thus, by the given graph it is clear that for x = 7 their are two values for y that is y = -6 , -7

So, the given graph is not a function

Vertical angles = angle AEC and angle DEB

Adjacent angles = GEF and angle CEG also GEF and FEB also DEB and BEF

AED and DEB, also AED and AEC

Complementary angles = angle GEF and angle FEB, and angle AEC and angle CEG

That's all. None of the angles are complementary

We have a ratio of students to faculty members is 25 to 2.

For a students population of 623, the number of faculty members will be:

50 faculty members will be needed for a student population of 623.

Answer

Draw the box to complete the table.

Next,

To get the top, multiply both the left and the right = 11 x (-3)

= -33

To get the top, add both the left and the right = 11 + (-3) = 11 - 3 = 8

Answer:

  4x² +28x +49

Step-by-step explanation:

You want a polynomial equivalent to the area of the figure shown.

The polynomial can represent the sum of three areas:

  blue area + green area + yellow area

  = 4x² +4(7x) +7²

  = 4x² +28x +49

Answer

The lateral area of the prism is 900 in squared

The surface area of the prism is 960 in squared

Explanation

Given:

The first side of the triangular base, a = 12 in

The second side of the triangular base, b = 13 in

The height of the prism, h = 30 in

What to find:

The lateral area and surface area of the prism.

Step-by-step solution:

The first step is to find the third side, c of the triangular base using Pythagoras rule.

Now, the next step is to calculate the lateral area of the prism using the formula below.

The lateral area of the prism is 900 in squared

The final step is to calculate the surface area of the prism using the formula below.

The base area is

Therefore, the Surface Area = (900 + 60) = 960 in squared

If a diver dives from a cliff that has a height of 125 feet, The dive lasted approximately 2.80 seconds

A diver dives from a cliff that has a height of 125 feet

The formula h = 16t², where t is time in seconds and h is the distance in feet traveled by a free-falling body or object

125 = 16t²

125/16 = t²

t = √(125/16)

t = √125/√16

t = 5√5 /4

t = 1.25 x 2.23

t = 2.795

t = 2.80

Therefore, if a diver dives from a cliff that has a height of 125 feet, The dive lasted approximately 2.80 seconds

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Given:

Quadratic equation

To write a quadratic equation that cannot be factored or cannot be solved by factoring, we note first that factoring is the easiest method to solve a quadratic equation as long as the equation is easily factorable. If not, we'll need alternative approaches like employing the quadratic formula.

We also note that factoring cannot always be used to solve quadratic equations.

Below is an example of an equation that can be solve by factoring:

Now, the equation that cannot be factored or cannot be solved by factoring is:

We cannot apply factoring to the above equation. Therefore, the answer is:

Answer: 2x + 3

Step-by-step explanation:

f(x) = 4x + 6

g(x) = 1/2 * f(x)

Plug f(x) into the g(x) equation.

g(x) = 1/2 * (4x + 6)

Now simplify,

g(x) = 2x + 3

Given the figure, we can deduce the following information:

Height=1/2 cm

Length=1/2 cm

Width= 1/6 cm

To determine the number of cubic blocks with a side length of 1/6 cm needed to fill the volume of the given prism, we first note that a cube has equal sides. So, the dimensions of the cube must be:

Height= 1/6 cm

Length=1/6 cm

Width=1/6 cm

Next, we get the volume of the cube by using the formula:

Then, we get the volume of the given prism using the same formula:

Now, we find the number cubic blocks by using the formula:

Therefore, the answer is 9.

Given,

The progression is 5, 12, 19, 26, 33...​

The first term of the series is, a = 5.

The common difference of the series is,

d = 12 - 5 = 7

The 10th term of the series is,

Hence, the 10th term of the series is 68.

The resulting value of the function [j(x+h)-j(x)/h] is 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

Given the function expressed as;

j(x) = 3⁽ˣ⁻¹⁾

Required value of the function  [j(x+h)-j(x)]/h

We have to determine the function j(x+h) and j(x)

j(x+h) = [tex]3^{(x+h) -1}[/tex]

Substitute the values,

[j(x+h)-j(x)]/h = [  [tex]3^{(x+h) -1}[/tex]  -  3⁽ˣ⁻¹⁾ ]/h

⇒ [  [tex]3^{(x-1) +h}[/tex]  -  3⁽ˣ⁻¹⁾ ]/h

⇒ [  [tex]3^{(x-1)} \times3^{h}[/tex]  -  3⁽ˣ⁻¹⁾ ]/h

⇒ 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h

Hence, the equivalent value of the function is 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h

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Given:

Rectangular safe hold 5184 cubic inches

Gold bar,

3 inches by 6 inches by 2 inches

Find-:

The volume of each gold bar

Explanation-:

The gold bar is in a rectangular shape

So volume is:

The dimension of the gold bar is 3 inches by 6 inches by 2 inches.

Volume of each gold bar is 36.

4) [tex]m\angle XWY=m\angle HGY[/tex] (definition of congruent angles)

5) [tex]\angle HGY \cong \angle GTU[/tex] (corresponding angles theorem)

6) [tex]m\angle HGY=m\angle GTU[/tex] (definition of congruent angles)

7) [tex]\angle GTU[/tex] and [tex]\angle UTR[/tex] are supplementary (linear pair)

8) [tex]m\angle GTU+m\angle UTR=180^{\circ}[/tex] (definition of supplementary angles)

9) [tex]m\angle HGY+m\angle UTR=180^{\circ}[/tex] (substitution)

10) [tex]m\angle RTU+m\angle XWY=180^{\circ}[/tex] (substitution)

Part A) Option c is correct answer. 6 x 9 can be used to model the area of the vegetable garden.

Part B) Total area of the garden in square feet is 62 square feet.

What do you mean by area?

Area is a unit of measurement used to describe a region's size on a flat or curved surface. While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.

To calculate the area we first individually calculate the area of the garden with flowers and vegetables,

Area of the garden where flowers are planted:

Area = length x breadth

Area = 4 x 2 = 8 square feet

Area of garden where vegetables are planted:

Area = 6 x 9 = 54 square feet

Total area of the garden = 8 + 54

Total area of the garden = 62 square feet

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The area of a trapezoid is computed as follows:

where a and b are the bases, and h is the height of the trapezoid. Replacing with a = 48, b = 36, and h = 21, we get:

The area of the entire trapezoidal rear window is 882 square inches