The factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.
It is given that the expression [tex]\rm x^2+10x+21[/tex]
It is required to find which expression is the factorization of the given expression, the options are:
a) (x + 3)(x + 7)
b) (x + 4)(x + 6)
c) (x + 6)(x + 15)
d) (x + 7)(x + 14)
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have an expression:
[tex]\rm x^2+10x+21[/tex]
[tex]\rm x^2+7x+3x+21[/tex]
Breaking 10x into 7x and 3x because the multiplication of 7x and 3x is [tex]\rm 21x^2[/tex] and the addition is 10x.
[tex]\rm x^2+7x+3x+21\\\\\rm x(x+7)+3(x+7)\\\\\rm (x+7)(x+3)[/tex]or
[tex]\rm (x+3)(x+7)[/tex]
Thus, the factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.
Learn more about Polynomial here:
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A manager drew this box-and-whisker plot to represent the number of minutes each of the company's 360 employees took on their break.
How many employees took a break that lasted between 37 and 41 minutes?
Select from the drop-down menu to correctly complete the statement.
Given the box-and-whisker plot, the number of employees that took a break that lasted between 37 - 41 minutes is: 180.
What is a Box-and-whisker Plot?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.
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Answer:
The answer is 90
Step-by-step explanation:
Its not 180 I take k12 also.
……………………868685758584984444
Answer: 86868575854984444 121213435457642222
Step-by-step explanation:
The amount of money you have after investing $400 for 8 years and $600 for 6 years at the same interest rate is represented by 400x^6 + 600x^6. where x is the growth factor. classify the polynomial by the number of terms. what is the degree?
The polynomial 400x⁶ + 600x⁶ has a degree of 6 and is a binomial.
What is a polynomial?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.
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Find the LCM for the group of expressions.
Y2+2y-24;y2-16;and 2y
Answer:
its here..........,,,
Hello people ~
what's the product of the square root of 3 and the square root of 12
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]
Which of the following is a rational number(s)?
6
7
a.
b.
-1
10
Gold
-3
d. All of these
-15
The equation 2y+x=0 is shown on the graph below as a
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.
HELP ASAPPP
Inga, Kai, and Jason volunteer in the school library. They want to find the average number of pages of a library book. It would be unreasonable to calculate the number of pages in every book to find the average. They decide they need to find a valid sample.
Inga suggests choosing 100 books from the history section to get a sample.
Kai suggests randomly selecting 100 books from the library’s entire catalog.
Jason suggests using 100 books from the teen fiction section to get a sample.
Who suggested the best way to produce a random sample that is not biased?
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:
Given that f(x) = 3x + 4, find 2f(5).
f(2) = 10
Step-by-step explanation:Calculate
[tex]Substitute\ x=2\ into\ f(x)=3x+4[/tex]
Substitute[tex]f(2)=3\times 2+4[/tex]
Calculate the product or quotient[tex]f(2)=6+4[/tex]
Calculate the sum or difference[tex]f(2)=10[/tex]
I hope this helps you
:)
54 x 8181 x 12 x 8271 x 1301 x 812
Answer:
4.6320447e+16
I used a calculator for this LOL.
Find the area of a circle whose radius is 3 1/2(three whole number one over two)
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.)
Last question please help!
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
How many sides does a dodecahedron have?
Answer:
A dodecahedron has 12 sides
Step-by-step explanation:
Hope that helps!
Convert 315 degrees to radian
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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In parallelogram GOST, angle G has a measure of 40°
What is the measure of angle T?
40° + S = 180°
- 40° + 40° + S = 180° - 40°
S = 140°
T = 140°What’s 36 km=?m into a desmal
Explanation:
To go from km to meters, multiply by 1000
This is because 1 km = 1000 meters
All digits in a dropdown number are different and one of the digits is the average of all the digits. it has at least two digits. for example, 5021 is a dropdown number, but neither 4389 nor 6033 is a dropdown number.
The dropdown numbers is an illustration of combination
The smallest dropdown number is 1025
How to determine the smallest dropdown number?From the question, we have the following parameters:
The dropdown number is 4-digitThe digits are different.We start counting from 1023, 1024, 1025, 1026...........
The sum of digits in 1023 is 6, and the average is 1.5The sum of digits in 1024 is 7, and the average is 1.75The sum of digits in 1025 is 8, and the average is 2The number 1025 satisfies the given conditions
Hence, the smallest dropdown number is 1025
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Help me !!!! Emergency .
50 points + Brainliest
No spammers please
Leaders please answer this question
No. 8. a
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]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuse[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]
Help with the equation of a line
Answer:
y = -3x + 5
Step-by-step explanation:
y = mx + c
gradient = -3 = m
y-intercept = 5 = c
find the value of x when y=14. y= -6x+5
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]
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
A rectangular prism with the width as three and a half feet, the length as two and a half feet and the height as one and a half feet. i need help
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.
You have a coupon for 35% off any purchase over $15 at a pizza shop. If your order totals $18, how
much do you have to pay?
Answer:
11.7
Step-by-step explanation:
I think that is right because you have to - 35%
If X and Y are 2 finite sets such that n() = 9, n( XY) - 4 and n( XY) -15, then n() is
(A) 5
(B) 6
(C) 10
(D) 12
Answer:
I think it's a hope this helps
A survey asked 100 seventh graders if they have either a cell phone or a tablet. Of the 32 students that have a cell phone, 19 do not have a tablet. Of the 70 students that have a tablet, 57 do not have a cell phone. A total of 11 students stated they do not have a cell phone or a tablet. Some of this information is included in the frequency table.
help please!
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
Harry is trying to solve the equation 0 = 2x2 − x − 6 using the quadratic formula. He has made an error in one of the steps below. Find the step where Harry went wrong. (1 point)
➙ a quadratic equation in which Harry lagged due to an error made by him, 2x² - x - 6= 0
To solve -➙ the given quadratic equation.
Concept applied -➙ 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.
Solution -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!! (:
CAN SOMEONE PLEASE HELP ITS DUE TODAY
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
math makes me mad mad‼️‼️
695 km/h
explanation
3475/5 = 695
hope it helps...!!!
True or false if you took a true of them statement inserted a not in each clause and reversed the clauses the new statement would also be true
Answer:
true
Step-by-step explanation:
HELP ME PLEASE
PRETTY PLEASEEEEEEEEEEE
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:
3.14 x 7^2 ≈ 153.86.153.86 x 14 ≈ 2154.04.2154.04 x 1/3 ≈ 718.01333333.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! :)
The sum of one third of a number and 2 1/3 is 9 find number
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.