Main Factoring Special Case Quadratics

Answer:

The volume is approximately 13 1/8 feet.

Step-by-step explanation:

Volume of a rectangular prism is calculated by multiplying the width, length, and height together.

3.5w × 2.5l × 1.5h = 13.125

13.125 = 13 1/8. The fraction cannot be reduced any further, so this is its simplest form.

Answer:

n = 6

Step-by-step explanation:

[tex] \frac{ {5}^{n} \times {5}^{3} }{ {5}^{7} } = {5}^{2} \\ \\ \implies \: \frac{ {5}^{n + 3} }{ {5}^{7} } = {5}^{2} \\ \\ \implies \: {5}^{n + 3 - 7} = {5}^{2} \\ \\ \implies \: {5}^{n - 4} = {5}^{2} \\ \\ \implies \:n - 4 = 2 \\ \\ \implies \:n = 4 + 2 \\ \\ \implies \:n = 6[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \frac{5 {}^{n} \times {5}^{3} }{5 {}^{7} } = {5}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \frac{5 {}^{n + 3} {}^{} }{5 {}^{7} } = {5}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:5 {}^{n + 3 - 7} = {5}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:5 {}^{n - 4} = {5}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:{}{n - 4} = {2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:n = 2 + 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:n = 6[/tex]

Hence, value of n is 6

Answer:

3 cups. 15 cookies to 1 cup of flour.

Step-by-step explanation:

The answer is 3 cups. The first thing you do is find the unit rate. Divide 30 by 2 and you know that 1 cup of flour makes 15 cookies. Then divide 45 by 15 which is 3 and which tells you that 3 cups of flour makes 45 cookies.

Answer: 89

Step-by-step explanation:

60 + 31 = 91

180 - 91 = 89

If this isn’t correct then sorry :/

Answer:

Angle BFC.

Step-by-step explanation:

Because angle BFD is a right angle because angle AFE is equal to BFD because of vertical angles

Answer:

its here..........,,,

➙ a quadratic equation in which Harry lagged due to an error made by him, 2x² - x - 6= 0

➙ the given quadratic equation.

➙ We will apply the quadratic formula as given in the question. So, let's study about quadratic equation first because we are supposed to apply the formula in equation.

What is quadratic equation?

➙ A quadratic equation in the variable x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers, a ≠ 0.

Now, what is quadratic formula?

➙The roots of a quadratic equation ax + bx + c = 0 are given by [tex]\sf{\:\frac{-b \pm\: \sqrt {b ^ 2 - 4ac}}{2a}}[/tex] provided b - 4ac ≥ 0.

here as per the given quadratic equation,

a = 2, b = -1 and c = -6

putting in the formula,

[tex]\implies\sf{x=\frac{-(-1) \pm\: \sqrt {(-1)^2 - 4(2)(-6)}}{2(2)}}[/tex]

[tex]\implies\sf{x=\frac{1 \pm\: \sqrt {1+48}}{4}}[/tex]

[tex]\implies\sf{x=\frac{1 \pm\: \sqrt {49}}{4}}[/tex]

[tex]\implies\sf{x=\frac{1 \pm\: 7}{4}}[/tex]

Solving one by one,

[tex]\implies\sf{x=\frac{1 + \: 7}{4}}[/tex]

[tex]\implies\sf{x=\frac{8}{4}}[/tex]

[tex]\implies{\boxed{\bf{x=2}}}[/tex]

________________

[tex]\implies\sf{x=\frac{1 - \: 7}{4}}[/tex]

[tex]\implies\sf{x=\frac{-6}{4}}[/tex]

[tex]\implies{\boxed{\bf{x=\frac{-3}{2}}}}[/tex]

________________________________

Note - Hey dear user!! You haven't provided the solution which was solved by Harry (A.T.Q). Please go through the solution as it will help you to find the error done by Harry.

________________________________

Hope it helps!! (:

Explanation:

To go from km to meters, multiply by 1000

This is because 1 km = 1000 meters

The value of x which saisfies the equation sin(x+37)°=cos(2x+8)° is 135 or 15.

We can use the fact that:

[tex]\sin(\theta ^\circ) = \cos(90 - \theta^\circ)[/tex]

to convert the sine to cosine (but the angles won't stay same unless its 45 degrees).

For this case, we're specified the equation sin(x+37)°=cos(2x+8)°.

Converting sine to cosine, we get:

[tex]\cos(90 - x - 37)^\circ = \cos(2x + 8)^\circ\\[/tex]

Since cosine is a periodic function with period of [tex]360^\circ[/tex], thus, we get:
[tex]90 - x - 37= 2x + 8 +360 n[/tex]

where n = an integer (positive, negative, or zero).

or

[tex]90 - 37 - 8= 3x + 360 n\\\\x = \dfrac{45 - 360n}{3} = 15 - 120n[/tex]

This is the general solution of the considered equation.

Assuming that only principal values (from 0 to 360 degrees) angles are allowed, we need:

[tex]0 \leq x + 37 \leq 360\\\\and\\\\0 \leq 2x+8 \leq 360[/tex]

The first inequality gives:

[tex]-37 \leq x \leq 323[/tex]

The second inequality gives:

[tex]-4 \leq x \leq 176[/tex]

We need to satisfy both the inequalities, so the final boundaries on x are:

[tex]-4 \leq x \leq 176[/tex] (the minimum ones for which both inequalities stay true).

n < -2 gives x > 255, and n > 1 gives x < -105

So, values of n for which [tex]-4 \leq x \leq 176[/tex] is true are n = -1, or n = 0

Thus, x = either 135 or 15

sin

Thus, the value of x which saisfies the equation sin(x+37)°=cos(2x+8)° is 135 or 15

Learn more about sine to cosine conversion here:

https://brainly.com/question/1421592

Answer:

2

Step-by-step explanation:

Answer:

The answer is 8

Step-by-step explanation:

If n = 8 and m = 3, 8 - 3 = 5.

40 ÷ 5 = 8

Hope this helps

Answer: 718 in^2.

Step-by-step explanation: To find the volume of a cone, you use the following equation:

V = π x r^2 x h x 1/3, where π is approximately 3.14, r^2 is the radius of the cone squared, h is the cone's height, and V is the volume of the cone.  Since a cone's volume is one-third of a cylinder's, that's why we multiply by 1/3, in case you're confused about where the 1/3 comes from.

Now, we substitute the following so we can solve this problem:

V ≈ 3.14 x 7^2 x 14 x 1/3.

Now that we've filled in the following, we can solve it:

Therefore your answer is 718.01333333 in^2 or rounded to the nearest whole number is 718 in^2.

Let me know if this is right! :)

Answer:

4.6320447e+16

I used a calculator for this LOL.

The dropdown numbers is an illustration of combination

The smallest dropdown number is 1025

From the question, we have the following parameters:

We start counting from 1023, 1024, 1025, 1026...........

The number 1025 satisfies the given conditions

Hence, the smallest dropdown number is 1025

Read more about combination at:

https://brainly.com/question/11732255

Answer:

I am pretty sure it is 100in^3 + s^3

Answer:

12×8/2=48

10×10=100

2(48)+3(100)

96+300= 396ft²

Answer:

A dodecahedron has 12 sides

Step-by-step explanation:

Hope that helps!

Answer:

[tex]5.4 \times {10}^{ - 17} {m}^{2} [/tex]

[tex]s = \frac{1}{2} \times 3.6 \times10^{ - 9} \times 3 \times {10}^{ - 8} = 5.4 \times {10}^{ - 17} {m}^{2} [/tex]

Answer:

[tex]\frac{7\pi }{4}[/tex] radians

Step-by-step explanation:

to convert degrees to radians

radians = degrees × [tex]\frac{\pi }{180}[/tex] , then

radian measure = 315° × [tex]\frac{\pi }{180}[/tex] ( cancel 315 and 180 by 45 )

                          = 7 × [tex]\frac{\pi }{4}[/tex]

                         = [tex]\frac{7\pi }{4}[/tex]

315 degrees is equal to 5.49779 radians.

To convert degrees to radians, you need to multiply the degree measure by the conversion factor of π/180.

Let's convert 315 degrees to radians:

315 degrees × (π/180)

315×3.14 /180

= 5.49779 radians

Therefore, 315 degrees is equal to 5.49779 radians.

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Answer:

[tex] \frac{1}{ \sqrt{2} } [/tex]

Step-by-step explanation:

Given

[tex]theta = 22 \frac{1}{2} = \frac{45}{2} [/tex]

[tex]2 \times theta = \frac{45}{2} \times 2 = 45[/tex]

Sin2theta=sin45⁰=1/√2

[tex] \frac{1}{ \sqrt{2} } [/tex]

is your answer

Answer:

[tex]\sf \dfrac{\sqrt{2}}{2}[/tex]

Step-by-step explanation:

[tex]\sf If\:\theta=\left(22\dfrac12\right)^{\circ}[/tex]

[tex]\sf \implies2\theta=2\cdot\left(22\dfrac12\right)^{\circ}=45^{\circ}[/tex]

[tex]\sf Therefore\:\sin2\theta=\sin(45)^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]

Proof

If a right triangle has an interior angle of 45°, then the third interior angle will also be 45° (since the sum of the interior angles of a triangle is 180°).

This means that the two legs of the right triangle are equal in length.

Using Pythagoras' Theorem, we can state that the hypotenuse of a right triangle with two legs of equal length will be √2 times the length of a leg.

Let a = b = 1

⇒ 1² + 1² = c²

⇒ c = √2

The sine trig ratio is:

[tex]\mathsf{\sin(\theta)=\dfrac{O}{H}}[/tex]

where:

[tex]\implies \sf \sin(45^{\circ})=\dfrac{1}{\sqrt{2} }[/tex]

[tex]\implies \sf \dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}[/tex]

[tex]\implies \sf \sin(45^{\circ})=\dfrac{\sqrt{2}}{2}[/tex]

695 km/h

explanation

3475/5 = 695

hope it helps...!!!

u (-1 ; 0)

t (-3 ; 0)

Answer:

A = bh

A = 45 x 46

A = 2070 inches

Answer:

2070 squre in

Step-by-step explanation:

because the base is 46 and the height is 45 then we just multiply the two together to find the area.

so we solve it and we get

45*46=2070

Answer:

-[tex]15 {a}^{2}b[/tex]

Answer:

45n+12mm

Step-by-step explanation:

I hope this is right if it is right pls mark me as brainliest and learn well

the value of a and b will be 45 and 0 for the given expression.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, the shapes are a circle with a radius of 21mm and a quarter circle of 6mm.

Since Radius = 21 cm

the radius of the circle/ radius of the quarter circle = 7/2

Total length = Sum of the circumference of both the circle

Since the formula for the circumference of a circle:

C = 2 * pi * radius

Total length = 2* pi* r + 1/4 * (2 * pi * r')

Total length = 2 *pi * 21 + pi * 3

Total length = π(42 + 3)

total length = 45π + 0

therefore, the value of a and b will be 45 and 0 for the given expression.

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The quadratic equation that can be used to represent the thickness of the border is 4x²+18x-3258=0.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.

As it is given that the length and the width of the centre area are 72 inches and 36 inches, respectively. When the dimensions of the centre area are converted into the feets, it will be,

[tex]\rm Length = \dfrac{72\ inches}{12} = 6\ feet[/tex]

[tex]\rm Width= \dfrac{36\ inches}{12} = 3\ feet[/tex]

If we take the borders of the table into account, the length and the breadth  of the table will become,

Length = (6+x+x) = (6+2x)

Width = (3+x+x) = (3+2x)

We know that the area of a rectangle is given as the product of the length and width, and also it is mentioned that the area of the entire table is 3,276 square feet. Therefore, the area of the table can be written as,

[tex]{\rm Area=Length \times Width}\\\\3276 = (6+2x)(3+2x)\\\\3276= 18+ 12x+ 6x + 4x^2\\\\4x^2+18x+18-3276=0\\\\4x^2+18x-3258=0\\[/tex]

Thus, the quadratic equation that can be used to represent the thickness of the border is 4x²+18x-3258=0.

Learn more about Quadratic Equation:

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40° + S = 180°

- 40° + 40° + S = 180° - 40°

S = 140°

The number of tiles with a length of 0.15 meters that would be needed by Hassan to place along the edge of the counter is: 20 tiles.

The tile's length is the longer side of a tile depending on the shape of the tile.

The length of the given tile is, 0.15 meter.

Length of the edge of he counter = 3 meters.

Number of tiles Hassan needs = 3/0.15

Number of tiles Hassan needs = 20 tiles.

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Answer: 20 tiles.

Step-by-step explanation:

The number of tiles with a length of 0.15 meters that would be needed by Hassan to place along the edge of the counter is: 20 tiles.

What is a Tile's Length?

The tile's length is the longer side of a tile depending on the shape of the tile.

The length of the given tile is, 0.15 meter.

Length of the edge of he counter = 3 meters.

Number of tiles Hassan needs = 3/0.15

Number of tiles Hassan needs = 20 tiles.