What equation results from completing the square and then factoring?
x2 + 16x = 41

Answer;

-2

Step-by-step explanation;

Well take the last numbers in these points and subtract them

4 - (-8)

4+8

12

You've got the upper part of the slope fraction now subtract the first two numbers.

-4-2

-6

Put this fun together, 12/-6 = -2

hence, slope=-2 .

Answer:

Step-by-step explanation:

-2

Check the picture below.

\(\begin{cases} L^2+w^2=50^2\\ Lw = 1200\\[-0.5em] \hrulefill\\ L^2+w^2=2500\\ L=\sqrt{2500-w^2} \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{\sqrt{2500-w^2}~w=1200} \\\\\\ \stackrel{\textit{squaring both sides}}{w^2(2500-w^2) = 1200^2}\implies 2500w^2-w^4=1440000 \\\\\\ 0=w^4-2500w^2+1440000\implies 0=\stackrel{\textit{tis a quadratic}}{(w^2)^2-2500w^2+1440000}\)

\(0=(w^2-900)(w^2-1600)\implies \begin{cases} 0=w^2-900\\ 900=w^2\\ \sqrt{900}=w\\ \boxed{30=w}\\[-0.5em] \hrulefill\\ 0=w^2-1600\\ 1600=w^2\\ \sqrt{1600}=w\\ \boxed{40=w} \end{cases} \\\\\\ \stackrel{\textit{we know that}}{L = \sqrt{2500 - w^2}}\implies \begin{cases} L=\sqrt{2500-30^2}\\ \boxed{L=40}\\[-0.5em] \hrulefill\\ L=\sqrt{2500-40^2}\\ \boxed{L = 30} \end{cases}\)

The length of the given TV is 40 inches and width of the given TV is 30 inches.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

The area of rectangular shape TV is 1,200 square inches.

The TV is 50".

Now, L²+W²=50² ----------(I)

L×W=1200 ----------(II)

L²+W²=2500

⇒ L²=2500-W²

⇒ L=√(2500-W²)

Substitute L=1200/W in L=√(2500-W²), we get

1200/W=√(2500-W²)

Squaring on both the sides we get

1440000/W² =2500-W²

⇒ 1440000=2500W²-\(W^4\)

⇒ \(W^4\)-2500W²+1440000=0

⇒ (W²)²-2500W²+1440000=0

⇒ (W²)²-900W²-1600W²+1440000=0

⇒ W²(W²-900)-1600(W²-1600)=0

⇒ (W²-1600)(W²-900)=0

⇒ W²-1600=0 and W²-900=0

⇒ W²=1600 and W²=900

⇒ W=±40 and W=±30

So, W=40, -40, 30, -30

Length =1200/W =40 or 30

Therefore, the length of the TV is 40 inches and width is 30 inches.

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The correct answer is C) 54.34°.

If NP and QS are parallel lines and ∠NOM = 130° then the value of ∠POM is 50°.

Parallel lines are two or more lines in a plane that do not intersect, regardless of how far apart they are.

Despite being located at different distances from one another, parallel lines always have the same slope, which is the same steepness and direction.

Since NP and QS are parallel lines, we have:

∠NOM + ∠MOP = 180° (because NOM and MOP are on a straight line)

Also, the alternate interior angles NOM and POM are equal, so:

∠NOM = ∠POM

Substituting this into the first equation gives:

∠POM + ∠MOP = 180°

We can now solve for ∠POM by substituting the given value:

130° + ∠POM = 180°

∠POM = 50°

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Step-by-step explanation:

step 1. The x values refer to the domain of the function.

step 2. if you set y = 0 and solve the quadratic equation the x values refer to the point the graph crosses the x axis.

Answer:

8

Step-by-step explanation:

ok so this is just the first one but i think you use a variable for what you are trying to find out, and well call this x and then u subtract the variable from the product of the rate and the amount, and once you have it, you multiply it but its own conjugate so then u use the binomial that you get to create a function, and you can graph it if you want, and u can use the apothem (the formula involves cos, so you might need a calculator) of the polygon created on your graph to find the domain, which you will then get the 4th root of, which is your answer. anyway, i believe this is what it is, but i may be wrong. hope this helps!

The volume of ice cream Nathan serves in a single scoop cone is 67.32 in³.

The volume of a cone is calculated using the following formula as shown below;

V = ¹/₃πr²h

where;

The radius = d/2 = 5.5 in / 2 = 2.75 in

The volume of the cone is calculated as follows;

V = ¹/₃ x π x ( 2.75 in )² x 3

V = 23.76 in³

The /volume of the sphere is calculated as follows;

V = ⁴/₃ πr³

Since he added half of the volume of sphere, the new volume becomes;

V = ¹/₂ x ⁴/₃ πr³

V = ²/₃πr³

V = ²/₃π(2.75)³

V = 43.56 in³

The total volume = 23.76 in³ + 43.56 in³ = 67.32 in³

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Answer:

17is the truth

Step-by-step explanation:

The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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The rational equation where x = 7 is a solution is R(x) = (x + 2)(x - 7)/(x + 2).

A rational equation R(x) is P(x)/Q(x) where both P(x) and Q(x) are polynomials and Q(x) is ≠ 0.

Let P(x) is (x + 2)(x - 7) and Q(x) is (x + 2).

∴ R(x) = P(x)/Q(x).

= (x + 2)(x - 7)/(x + 2).

= (x - 7).

= x - 7 = 0.

x = 7.

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

5x^2+x-6

Step-by-step explanation:

(5x-1)(x+1)-5x+x-5+x

(5x^2+5x-x-1)-5x+x-5+x

5x^2+x-6

Answer:

The height is about 5 inches.

Step-by-step explanation:

The volume for a cone is \(\frac{1}{3}\) × π × r² × h

The radius of the cone is 1.5

12= \(\frac{1}{3}\) × π × 1.5² × h

12= \(\frac{1}{3}\) × π × 2.25 × h

12=0.75×π×h

Divide both sides by 0.75

16=π×h

Divide both sides by π

5≈h

The height is about 5 inches.

Answer:

D

Step-by-step explanation:

First consider a part of the numerator 5 + 3y2. This can be verbally described as "the sum of 5 and 3 times the square of y".

Then, the entire expression in the numerator, (5 + 3y2)3, can be written as "the cube of the sum of 5 and 3 times the square of y".

Next, consider a part of the denominator (4y), which can be verbally described as "the product of 4 and y".

Then, the entire expression in the denominator, (4y)3, can be written as "the cube of the product of 4 and y".

Dividing the two expressions yields the complete expression shown below.

So, the given expression can be interpreted as "the cube of the sum of 5 and 3 times the square of y divided by the cube of the product of 4 and y".

Answer:

G

f is 6/8=3/4 = 75%

h is 9/12=3/4 = 75%

I is 3/4 = 75%

so the answer is G

Answer:

\(2x + x + 42 = 90\degree \\ 3x = 48 \\ x = \frac{48}{3} = 16 \\ m \angle1 = 2(16) = 32\degree \\ m\angle2 = 16 + 42 = 58\degree \\ or \\ m\angle2 =90 - m\angle1 =90 - 32 = 58 \degree\)

#1

Clockwise 90° rotation rule (x,y)—»(y,-x)

#2

Dilation of scale factor 2

#3

reflection across x axis rule (x,y)—»(x,-y)

#4

Rule for given translation (x-5,y+2)

Answer:

Given points:

Part (a)

Rotate 90° clockwise (about the origin): (x, y) → (y, -x)

Part (b)

Dilation by a scale factor → multiply the points by the scale factor

scale factor = 2

Part (c)

Reflect across the x-axis:  (x, y) → (x, -y)

Part (d)

Translate 2 up and 5 to the left:  (x, y) → (x - 5, y + 2)

Answer:

Step-by-step explanation:

To find the missing side in the question, we use the cosine rule

That's

Since we are finding a we use the formula

From the question

b = 2

c = 4

A = 78°

Substitute the values into the above formula

We have

a² = 2² + 4² - 2(2)(4) cos 78

a² = 4 + 16 - 16 cos 78

a² = 20 - 16cos 78

a² = 16.67341

Find the square root of both sides

a = 4.0833

We have the final answer as

Hope this helps you

Answer:

2 reflection across the y axis

The value of x in the polygon will be 13.25 degrees.

The value of x is 10.

We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.

The sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.

Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees

Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:

Measure of one angle = 3960/24 = 165 degrees

165 = 12x + 6

159 = 12x

x = 13.25

Therefore, the value of x is 13.25 degrees.

Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.

Therefore, we have:

731x+86° = 7380°

Solving for x, we get:

731x = 7294°

x = 10

Therefore, the value of x is 10.

The equation that can be used to find the value of x is:

(9x+48)° + (15x-24)° = (n-2)*180°

24x + 24 = (n-2)*180°

Dividing both sides by 24, we get:

x + 1 = (n-2)*15°

Subtracting 1 from both sides, we get:

x = (n-2)*15° - 1

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Answer:

The greatest common factor between the numerator and denominator is 4x, thus the answer is

C. x

Step-by-step explanation:

To find the greatest common factor (GCF) of the numerator and denominator, we need to factor them and find the common factors.

The numerator:

4x+20 = 4x +4x+16 = 4x(1+5) = 4x(6) = 24x

The denominator:

x²+2x-15 = (x-3)(x+5)

Answer: 49/200, numerador= 49

Step-by-step explanation:

Answer:

1 1/12 cups

Step-by-step explanation:

2 1/4 = 9/4

9/4 - 1/3

27/12 - 4/12

23/12 = 1 1/12

The length x in the triangle below is 16 m.

Length is the distance between two points.

To calculate the length of the triangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for x

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The measure of the length EF of the triangle is; 21

We are given the the triangle BCD and we are told that;

E is the midpoint of BD.

F is the midpoint of CD

Now, since we have those midpoints, it means that by the concept of similar triangles, that;

DF/DC = EF/BC

Since F is the midpoint of DC, then it means that;

2DF = DC

We are given;

EF = 43 - 4x, and BC = 32 - 2x

Thus, we now have;

DF/(2DF) = (43 - 4x)/(32 - 2x)

1/2 = (43 - 4x)/(32 - 2x)

Cross multiply to get;

32 - 2x = 43 - 4x

4x - 2x = 43 - 32

2x = 11

x = 11/2

x = 5.5

Thus;

EF = 43 - 4(5.5)

EF = 43 - 22

EF = 21

Thus, we conclude that the side length EF is 21.

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Since:

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

the equation of the sphere is: x{power}2 + y{power}2 + z{power}2 = 49 To solve this problem, we need to first visualize the objects involved: a cylinder with radius 5 and a sphere with radius 7.

The cylinder has a height that is infinite (i.e., it extends infinitely in the vertical direction), while the sphere is centered at the origin.

To set up the equation of the cylinder, we can use the cylindrical coordinate system. The equation of a cylinder with radius r and infinite height in cylindrical coordinates is given by:

r{power}2 + z{power}2 = R{power}2

where r is the radial distance from the z-axis, z is the height, and R is the radius of the cylinder. In our case, we have R = 5, so the equation of the cylinder is:

r{power}2 + z{power}2 = 25

To set up the equation of the sphere, we can use the Cartesian coordinate system. The equation of a sphere with radius R centered at the origin in Cartesian coordinates is given by:

x{power}2 + y{power}2 + z{power}2 = R{power}2

In our case, we have R = 7, so the equation of the sphere is:

x{power}2 + y{power}2 + z{power}2 = 49

Now, we want to find the volume of the ring-shaped solid that remains when we bore a hole through the center of the sphere using the cylinder. To do this, we need to find the volume of the intersection of the cylinder and the sphere.

To find the intersection, we can substitute the equation of the cylinder into the equation of the sphere and solve for z. This gives us:

x{power}2 + y{power}2 + (r{power}2 - 25) = 49

r{power}2 = 74 - x{power}2 - y{power}2

So the intersection is defined by the set of points (x, y, z) that satisfy both equations. To find the volume of the intersection, we can integrate over the region where the cylinder and sphere intersect. In cylindrical coordinates, the region of integration is defined by:

r{power}2 + z{power}2 ≤ 49

r{power}2 + z{power}2 ≥ 25

Using the equation we derived earlier for r{power}2, we can rewrite this region as:

25 ≤ r{power}2 ≤ 74 - x{power}2 - y{power}2

-sqrt(74 - x{power}2 - y{power}2) ≤ z ≤ sqrt(74 - x{power}2 - y{power}2)

Finally, we can use a triple integral to find the volume of the intersection:

V = ∫∫∫ (r dz dr dθ)

Over the limits of the region described above.

After computing the integral, the result will be the volume of the ring-shaped solid that remains.

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