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.
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What is the AREA of the figure
Is this equation an identity? (2x+1)^2-(x+1)^2=3(x+1)^2-1
Answer:
See below, please
Step-by-step explanation:
Left side
[tex] {(2x + 1)}^{2} - {(x + 1)}^{2} [/tex]
[tex] = (4 {x}^{2} + 4x + 1) - ( {x}^{2} + 2x + 1)[/tex]
[tex] = (4 {x}^{2} - {x}^{2} ) + (4x - 2x) + (1 -1 )[/tex]
[tex] = 3 {x}^{2} + 2x[/tex]
Right side
[tex]3 \times {(x + 1)}^{2} - 1[/tex]
[tex] = 3 \times ( {x}^{2} + 2x + 1) - 1[/tex]
[tex] = 3 {x}^{2} + 6x + 3 - 1[/tex]
[tex] = 3 {x}^{2} + 6x + 2[/tex]
After compared with both sides, we can make a conclusion that
This equation isn't an identity.
please answer these quickly i need this
Answer:
A
Step-by-step explanation:
-7i x -1
I just need to multiply these 2 numbers but i forgot how to
3
14) There are seven million, eight hundred and fifty-four thousand,
three hundred and eight people in a country. i lleda
Round this number to the nearest ten thousand people.
Answer:
7,854,000
because the 308 people would have to be at least 500 to round up to 7,855,000
Omar owns a small business selling ice-cream. He knows that in the last week 32
customers paid cash, 2 customers used a debit card, and 26 customers used a credit
card.
a
a
If next week, he is expecting 1500 customers, about how many would you expect to
pay with a debit card? Round your answer to the nearest whole number.
a
The number of customers who will pay by debit card will be 50.
What are fractions?The fraction is defined as the division of the whole part into an equal number of parts.
Last week there were
32 + 2 + 26 = 60 customers.
That means that the fraction of the customers, who paid by debit card, was
2/60 = 1/30
In situations like that, when we use historical data and try to predict future behaviour, we use that past experience and extrapolate to a predicted result.
we simply say that we expect the same fraction, 1/30 if customers use credit cards.
for the absolute number of predicted debit card customers we multiply the predicted number of customers by the expected fraction
1500 × 1 / 30 = 1500 / 30 = 50
Therefore the number of customers who will pay by debit card will be 50.
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What is the area of this figure?
Answer:
Step-by-step explanation:
Answer:
140.5 square yards
Step-by-step explanation:
split the triangle from the shape: 8+7=15yd
area of triangle = 1/2 x base x height
= 1/2 x 5 x 15
=37.5 square yards
split the rectangle from the shape: 7+2=9yd
area of rectangle = length x width
= 11 x 9
= 99 square yards
split the square from the shape
area of square = n squared
= 2^2
= 4 square yards
add them all up: 37.5+99+4
= 140.5 square yards is the final answer
my bad if you can't read the working out in the picture
Write an equation in point-slope form of the line that passes through the point (5,6) with slope 3/5
point-slope form:
y - y₁ = m(x-x₁)slope intercept form:
y = mx + bEquation:
[tex]\sf \hookrightarrow y-6 = \dfrac{3}{5} (x-5)[/tex] [tex]\sf [ \ this \ is \ point \ slope \ form \ equation \ ][/tex]
[tex]\sf \hookrightarrow y-6 = \dfrac{3}{5} x-3[/tex] ----------------
[tex]\sf \hookrightarrow y= \dfrac{3}{5} x-3+6[/tex] -------------------
[tex]\sf \hookrightarrow y= \dfrac{3}{5} x+3[/tex] [tex]\sf [ \ this \ is \ slope \ intercept \ form \ equation \ ][/tex]
Answer:
[tex]\boxed{y - 6 = \dfrac{3}{5} (x - 5)}[/tex]
Step-by-step explanation:
Given:
Line passes through: (5,6)Slope = 3/5 = 0.6Formula:
[tex]y - y_{1} = m(x - x_{1} ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{m = Slope}; \ (x_1},y_{1}) = \text{Coordinates of point}][/tex]Substitute the values into point slope form to determine the equation of the line in point slope form.
[tex]\implies y - y_{1} = m(x - x_{1} )[/tex]
[tex]\implies \boxed{y - 6 = \dfrac{3}{5} (x - 5)}[/tex]
Find the domain over which the function y = x^2 +6x is mono tonic increasing. Please help
Answer:
x > -3
Step-by-step explanation:
The function will be increasing where its derivative is positive.
__
y = x^2 +6x . . . . . given function
y' = 2x +6 . . . . . . . derivative
The derivative is positive for ...
2x +6 > 0
2x > -6
x > -3 . . . . . domain where the function is increasing
Find the total amount
$17,600 at 16% compounded
quarterly for 2 years
Answer:
57,700.10
Step-by-step explanation:
To solve, we use the equation [tex]17,600(1.16)^8[/tex]
we set it to the power of 8, since it is compounding quarterly this means it compounds 4 times a year, and since there is 2 years, we get 8 compounds.
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To solve this equation for x, we must get x by itself. How would we do this?
X + 4 = 7
A. Add 4 to both sides.
B.Subtract 4 from both sides.
Answer:
B
Step-by-step explanation:
If you were to add 4 to both sides, you would have X + 8 = 11
But when you subract, you get X = 7-4, X = 3.
calculate the value of s and t
Answer:
s = 4, t = 1.2.
Step-by-step explanation:
y = k/x (Inverse variation, k is some constant)
Substituting:
2 = k/3
k = 2*3 = 6
So the relation is y = 6/x.
So 1.5 = 6/s
s = 6/1.5 = 4.
t = 6/5 = 1.2.
Given h(r) = 5r-5,find h(2)
[tex]===================================[/tex]
let's find the value of h(2)
we know that
h(r)=5r-5
which means
h of r is 5 times r minus 5
hence
h of 2 is 5 times 2 minus 5
simplify:
h(2)=5(2)-5
h(2)=10-5
h(2)=5
[tex]==================================[/tex]
note:-Hope everything is clear; if you need any more explanation/clarification, kindly ask me, and I will comment and/or edit my answer :)Answer:
5
Step-by-step explanation:
h(2)=5r-5
=5×2-5
=10-5
=5
What are the two conditions that an asset of a business needs to fulfill?
Answer:
✒️Answer:Two conditions must be satisfied. First, the revenue must be earned, which typically means that the customer has received the good or service. Second, the revenue must have been realized or realizable, implying that the customer has paid or is expected to pay for the merchandise.
Step-by-step explanation:
#CarryOnLearning[tex]watch.some.anime[/tex]
Help for question 1 and 2
Answer:
(1). [tex]5^{4}[/tex] × [tex]13^{7}[/tex] ; (2). 3 - 5x
Step-by-step explanation:
1). [( - 5 )³ · ( - 5 )] ( [tex]13^{-2}[/tex] · [tex]13^{9}[/tex] ) = [tex](-5)^{3+1}[/tex] × [tex](13)^{-2+9}[/tex] = [tex](-5)^{4}[/tex] × [tex]13^{7}[/tex] = [tex]5^{4}[/tex] × [tex]13^{7}[/tex]
2). - 25x² ÷ 5x + 15x ÷ 5x = 3 - 5x
Find the area OR cicumference of the semi-circle below. You must show all work to get full credit. Don't forget to label your answer.
Answer:
28.274 cm^2
Step-by-step explanation:
A = pi * r^2
A = pi * 3^2
A = pi * 9
28.2743338823
or
28.274
find the total surface area of the net below.
Answer:
78,4 cm^2
Step-by-step explanation:
I did this in my head so i could be wrong but im pretty certain this is right
Write a real-world problem that can be solved using the equation:
7.5 + x = 16
PLEASE HELP ME
Answer:
8.5
Step-by-step explanation:
7.5 + 8.5 = 16
Suppose $a(x) = 3x - 7$ and $b(x) = 2 - x^3$. What is the value of $a(b(3)) - b(a(3))$?
Answer:
-76
Step-by-step explanation:
b(3)=2-3^3 = -25.
So a(b(3))=a(-25)=3(-25)-7=-82.
a(3)=3(3)-7=2.
So b(a(3))=2-2^3 = -6.
Therefore, the value of the desired expression is -82-(-6)=-76
The value of the required function [tex]a(b(3)) - b(a(3))[/tex] is (-88).
What is a function?
"A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math. f = {(a,b)| for all a ∈ A, b ∈ B}
A relation is said to be a function if every element of set A has one and only one image in set B.
A function is a relation from a non-empty set B such that the domain of a function is A and no two distinct ordered pairs in f have the same first element."
Given two functions are:
[tex]a(x) = 3x - 7\\b(x) = 2 - x^{3}[/tex]
When the value of 'x' is 3, then the values of the given two functions are:
[tex]a(3) \\= 3x - 7\\= 3(3)-7\\= 9-7\\= 2[/tex]
[tex]b(3)\\= 2 - x^{3}\\= 2-(3)^{3}\\= 2-27\\= -25[/tex]
Now the value of the required function is:
[tex]a(b(3)) - b(a(3))\\= a(-25)-b(2)\\= [3(-25)-7]-[2-2^{3}]\\= (-75-7)-(2-8)\\= -82-6\\= -88[/tex]
Therefore, the value of the required function is (-88).
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This i-ready lesson is hurting my brain, anyway I need help on this one
Answer:
I am pretty sure it is 100in^3 + s^3
What is the volume of this figure?
Enter your answer in the box.
ft³
Answer:
96
Step-by-step explanation:
L=6
W=2
H=8
LxWxH=8x6x2=96
8x6=48
48x2=96
Answer:
76
Step-by-step explanation:
the answer is 76 because I took the test
3 3/5 + 1 1/6 answer as a fraction
[tex]3 \frac{3}{5} + 1 \frac{1}{6} = \\ [/tex]
[tex] \frac{(3 \times 5) + 3}{5} + \frac{(1 \times 6) + 1}{6} = \\ [/tex]
[tex] \frac{15 + 3}{5} + \frac{6 + 1}{6} = \\ [/tex]
[tex] \frac{18}{5} + \frac{7}{6} = \\ [/tex]
[tex] \frac{18 \times 6}{5 \times 6} + \frac{7 \times 5}{6 \times 5} = \\ [/tex]
[tex] \frac{108}{30} + \frac{35}{30} = \\ [/tex]
[tex] \frac{108 + 35}{ 30} = \\ [/tex]
[tex] \frac{143}{30} \\ [/tex]
You are given two offers for a monthly wage. Option A is to be paid one cent on the first day of the month, with your wages doubling each day (2 cents on day 2, 4 cents on day 3, 8 cents on day 4, etc.) for the rest of this 30 day month. Option B is to be paid $1 on the first day of the month, with your wages increasing $100 each day ($101 on day 2, $201 on day 3, $301 on day 4, etc.). Which option will give you more money by the end of the month? Make sure to support your answer. Also remember to find the equations for the exponential function and the linear function. Substitute 30 in for x and simplify.
Answer:
Step-by-step explanation:
Option B
Because if you start with one dollar and by day 3 you get 301 dollars and option A only gives you 8 cents on day 3 you get more money by the end of the month if you choose option B.
Answer: A is the correct answer
Step-by-step explanation:
Its a because the amount keeps doubling so you will start with =
.1 then go too .2 (which is double .1)
then after .2 you will get .4( which is double .2 i will show you the graph.
.1, .2, .4, .8, 1.6, 3.2, 6.4 etc. Then when you get to day 30 you will have
53.687 million dollars, buy the end of them month, you'd be a millionaire.
What are the solution(s) for the quadratic equation?
Y=x^2-2x+1
[tex]\\ \rm\rightarrowtail x^2-2x+1=0[/tex]
[tex]\\ \rm\rightarrowtail x^2-x-x+1=0[/tex]
[tex]\\ \rm\rightarrowtail x(x-1)-1(x-1)=0[/tex]
[tex]\\ \rm\rightarrowtail (x-1)(x-1)=0[/tex]
[tex]\\ \rm\rightarrowtail x=1[/tex]
can someone help me with this please
Answer:
40 ft^2
Step-by-step explanation:
Composite shapes make a square and rectangle
4 x 4 = 16
6 x 4 = 24
24 + 16 = 40
Answer:
24 unless my mind died
Step-by-step explanation:
8+16 :D
Which value should she use as the common ratio?
0.05
0.5
1.05
5.0
Answer:
0.5
Step-by-step explanation:
0.5
I guess i am 70% sure
Complete the square to transform the expression x2 4x 2 into the form a(x − h)2 k. (x 2)2 − 2 (x 2)2 2 (x 4)2 − 2 (x 4)2 2.
The square transforms the expression [tex]\rm x^{2} +4x + 2^{2}[/tex] into the form [tex](x+2)^2-2[/tex].
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
write in the form of [tex](x+y)^{2}[/tex]
[tex]\rm x^{2} +2xy + y^{2}[/tex]
2y = 4
y = 2
so, [tex]\rm x^{2} +4x + 2^{2}[/tex]
we will now convert it into the form
[tex]\rm x^{2} +2xy + y^{2}[/tex] = [tex]\rm (x+y)^{2}[/tex]
substitute the values
[tex]\rm x^{2} +4x + 2^{2} = (x+2)^{2}[/tex]
[tex](x+2)^2-2+2^2[/tex]
[tex](x+2)^2-2[/tex]
Thus, [tex](x+2)^2-2[/tex] is the correct form.
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What would you drink to survive a extra 30 years?
A. Lean
B. Orange Juice
C. Mug
Please help me!!! I don't know!
txcfygvubhjnlkm
Answer:
See explanation
Step-by-step explanation:
look photo
Write 1.5 as an improper fraction and mixed number in simplest form.
Answer:
1 1/2 (mixed)
3/2 (improper)
Step-by-step explanation:
When the one is put to the side, you get 5/10 if you turn "0.5" into a frsaction. if you simplify 5/10, you get 1/2. Therefore, 1 1/2 is your answer. Your not done yet! After, you need to change 1 1/2 into a improper fraction which is 3/2.
good luck :)
3/2
is the answer to this question