Which expression is the factorization of x2 10x 21?

➙ 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!! (:

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: Red line

Step-by-step explanation:

2y+x=0

2y=-x

y=-x/2

So we need a line with a slope of -1/2 that passes through the origin, which is the red line.

Explanation:

To go from km to meters, multiply by 1000

This is because 1 km = 1000 meters

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:

y = -3x + 5

Step-by-step explanation:

y = mx + c

gradient = -3 = m

y-intercept = 5 = c

Given the box-and-whisker plot, the number of employees that took a break that lasted between 37 - 41 minutes is: 180.

A box-and-whisker plot is a graphical representation of a data set showing how the data set is distributed into percentiles such as 25%, 50%, and 75%.

The range of the rectangular box covers 50% of the data set.

Thus, 37 - 41 minutes lies between 50% on the box-and-whisker plot, therefore:

50/100 × 360 = 180 employees.

In summary, given the box-and-whisker plot, the number of employees that took a break that lasted between 37 - 41 minutes is: 180.

Learn more about box-and-whisker plot on:

https://brainly.com/question/3473797

Answer:

The answer is 90

Step-by-step explanation:

Its not 180 I take k12 also.

Answer:

Kai suggested the best way to produce a random sample that is not biased

Step-by-step explanation:

Answer:

The answer is Kai suggested the best way to produce a random sample that is not biased

Step-by-step explanation:

Answer:

  x = -3/2

Step-by-step explanation:

To find the unknown value, substitute all known values and solve for the one remaining. After substitution, this becomes a 2-step linear equation, so is solved by the procedure for such equations.

  y = -6x +5 . . . . . given

  14 = -6x +5 . . . . substitute known value

  9 = -6x . . . . . . . subtract 5 (step 1)

  9/-6 = x = -3/2 . . . . divide by the coefficient of x (step 2);

Hello!

In order to find the value of x, we should take the value of y and plug it in and then simplify.

[tex]\bold{y=-6x+5}[/tex]

Plug in:

[tex]\bold{14=-6x+5}[/tex]

Switch places:

[tex]\bold{-6x+5=14}[/tex]

Now, subtract 5 from both sides:

[tex]\bold{-6x=14-5}[/tex]

[tex]\bold{-6x=9}[/tex]

Divide both sides by -6 in order to isolate x:

[tex]\bold{x=-\displaystyle\frac{9}{6}}[/tex]

Can this fraction be reduced? Sure, we can divide the numerator (9) and the denominator (6) by 3:

[tex]\bold{-\displaystyle\frac{3}{2}}[/tex]

As a Mixed Fraction:

[tex]\bold{1\displaystyle\frac{1}{2}}[/tex]

Hence, the value of x is:

[tex]\huge\boxed{\boxed{\mathfrak{\star{Answer:{\boxed{-\frac{3}{2} }}}}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

#NeverGiveUp

[tex]\rm{A~teen~who~never~gives~up}[/tex]

Answer:

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

Answer:

38.5 in²

Step-by-step explanation:

Area of circle= πr², where r is the radius

Substitute the value of the radius into the formula above:

Area of circle

= π(3.5)²

= 12.25π

= 38.5 in² (3 s.f.)

Answer:

4.6320447e+16

I used a calculator for this LOL.

695 km/h

explanation

3475/5 = 695

hope it helps...!!!

Answer:

6

Step-by-step explanation:

sqrt(3) x sqrt(12) = sqrt(3) x sqrt(4x3) = sqrt(3) x 2sqrt(3)

= 2 ( sqrt(3)² ) = 2 x 3 = 6

Let's see

[tex]\\ \rm\rightarrowtail \sqrt{3}\times \sqrt{12}[/tex]

[tex]\\ \rm\rightarrowtail \sqrt{3}\times \sqrt{2(2)(3)}[/tex]

[tex]\\ \rm\rightarrowtail \sqrt{3}\times 2\sqrt{3}[/tex]

[tex]\\ \rm\rightarrowtail 2(3)[/tex]

[tex]\\ \rm\rightarrowtail 6[/tex]

f(2) = 10

[tex]Substitute\ x=2\ into\ f(x)=3x+4[/tex]

[tex]f(2)=3\times 2+4[/tex]

[tex]f(2)=6+4[/tex]

[tex]f(2)=10[/tex]

I hope this helps you

:)

The polynomial 400x⁶ + 600x⁶ has a degree of 6 and is a binomial.

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Polynomials are classified based on degree as linear, cubic, quadratic, etc.

A polynomial with two terms is known as a binomial. Hence:

The polynomial 400x⁶ + 600x⁶ has a degree of 6 and is a binomial.

Find out more on polynomial at: https://brainly.com/question/2833285

Answer:

26

Step-by-step explanation:

Cellphone: 32 - 19 (students without tablet)

Tablet: 70 -57 (students without cellphone)

Both equations remain with only 13 students with both a cellphone and a tablet.

Then 13 + 13 = 26

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:

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:

I think it's a hope this helps

40° + S = 180°

- 40° + 40° + S = 180° - 40°

S = 140°

Answer:

  20

Step-by-step explanation:

The given relation can be written as the 2-step linear equation ...

  (1/3)n +2 1/3 = 9

  n +7 = 27 . . . . . . . . . step 1: multipy by 3 (makes the coefficient = 1)

  n = 20 . . . . . . . . . . . step 2: subtract 7 (separates variable from constant)

The number is 20.

_____

Additional comment

Usually it is convenient to do the two steps in the opposite order: get the variable term by itself, then make its coefficient 1. Here, we chose the order we did because it eliminated fractions from the problem, which is often a step you'd like to do first.

Answer: 86868575854984444  121213435457642222

Step-by-step explanation:

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.

To learn more on Unit of Measurement click:

https://brainly.com/question/12629581

#SPJ6

Answer:

11.7

Step-by-step explanation:

I think that is right because you have to - 35%

Answer:

true

Step-by-step explanation:

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:

A dodecahedron has 12 sides

Step-by-step explanation:

Hope that helps!

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]