Fill in the missing number to complete the factorization:
x 3 + x 2 - 21x - 45 = (x + 3)(x - 5)(x +
Answers
Missing number to complete the factorization is 3.
What is factorization?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.
Given expression
[tex]x^{3}+x^{2} -21x-45=(x+3) (x-5) (x+a)[/tex]
Let a be the missing number
(x + 3) (x - 5) (x + a)
= [tex](x^{2} -5x+3x-15)(x+a)[/tex]
= [tex](x^{2} -2x-15)(x+a)[/tex]
[tex]x^{3}+x^{2} -21x-45=x^{3} +x^{2} a-2x^{2} -2xa-15x-15a[/tex]
By comparing the expressions
-2xa - 15x = -21x
⇒ -2xa = -6x
⇒ a = 3
[tex]x^{2} (a-2) = 1x^{2}[/tex]
⇒ a - 2 = 1
⇒ a = 3
-15a = -45
⇒ a = 3
Hence, missing number to complete the factorization is 3.
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Related Questions
solve for x 12x + 16y =6
a.x= 1/2 - 3/4y
b.x= 1/2 - 4/3y
c.x = 2 - 3/4y
d. x= 2+4/3y
Answers
2.6x=2 (3-8y)
6x=3-8y
x=3/6-8y/6
x=1/2-4y/3
Widget company made 3600 widgets in four hours. They made the same number of widgets in each hour. How many widgets did the company make in one hour?
Answers
Find the Solution of n/2-11=3 if the replacment set is {26, 28, 29, 30, 31}
Answers
- -11 = 3
2
wouldn't n=26? because 26 divided by 2 is 13 then subtract 11 and you get 3
The two triangles below are similar. What is the similarity ratio of ΔABC to ΔXYZ?
1:2
2:1
3:2
2:3
Answers
To find the similarity ratio of ΔABC to ΔXYZ, compare the corresponding sides of the triangles. The ratio will be one of the named proportions based on the specific measurements of the triangles, which are not provided in the question.
Explanation:The question pertains to finding the similarity ratio of two similar triangles. The similarity ratio of triangles is the ratio of any two corresponding lengths in the triangles. This question specifically asks for the ratio of triangle ΔABC to triangle ΔXYZ. Without the specific lengths provided, a general solution is to compare the corresponding sides of the triangles. For instance, if the length of side AB in ΔABC is twice the length of side XY in ΔXYZ, then the similarity ratio would be 2:1. If it was the other way around, the ratio would be 1:2. Similarly, if AB was three halves the length of XY, the ratio would be 3:2, and if AB was two thirds the length of XY, the ratio would be 2:3. The correct ratio would be one of the options given based on the specific lengths provided in the problem, which are not included in the question as stated.
Final answer:
Without specific side lengths, it's impossible to provide the similarity ratio of ΔABC to ΔXYZ. Additional measures of corresponding sides are needed for such a calculation.
Explanation:
To determine the similarity ratio of two similar triangles, you need to compare the lengths of corresponding sides. However, in the provided question, no specific measurements for the triangles are given, so it is not possible to calculate the exact similarity ratio of ΔABC to ΔXYZ. We would need additional information, such as the lengths of corresponding sides from both triangles, to be able to determine the correct ratio.
The process would involve dividing the length of a side from ΔABC by the length of the corresponding side from ΔXYZ. For instance, if side AB of ΔABC measures 6 cm and the corresponding side XY of ΔXYZ measures 3 cm, then the similarity ratio is 6:3 or simplified as 2:1.
What is the greatest common factor of the terms in the expression 21x-18x+28xy?
A.3
B.3x
C.x
D.xy
Answers
Answer:
The correct option is C.
Step-by-step explanation:
The given expression is
[tex]21x-18x+28xy[/tex]
The factors of each term are
[tex]21x=3\times 7\times x[/tex]
[tex]18x=3\times 6\times x[/tex]
[tex]28xy=2\times 2\times 7\times x\times y[/tex]
The common factor is x.
[tex]G.C.F.=x[/tex]
Therefore correct option is C.
round 0.9998 to 3 decimal places
Answers
Final answer:
To round 0.9998 to three decimal places, consider the fourth decimal digit (8). Since it's 5 or higher, the third decimal digit (9) rounds up, resulting in 1.000 after taking the carry-over into account.
Explanation:
To round the number 0.9998 to three decimal places, you need to look at the fourth decimal place to decide whether to round up the third decimal place. The fourth decimal place is 8, which is 5 or more, so we round up the third decimal place from 9 to 10. However, since the third place is already at the maximum digit (9), this causes a carry-over, changing the number to 1.000. But, rounding to three decimal places means you want three digits after the decimal point, so the rounded number is 1.000. Rounding introduces a small amount of imprecision, determined by the digits you're eliminating or adjusting. However, in this situation, it's clear that the number essentially rounds up to one.
Simplify (8x2 − 1 + 2x3) − (7x3 − 3x2 + 1). I don't understand what I'm doing wrong.
Answers
Did you distribute the negative 1 across the second term?
8x^2-1+2x^3-7x^3+3x^2-1
The answer should be -5x^3 + 11x^2
Write 6% as a decimal.
Answers
The owner of ProPhone has charted the company's marginal revenue and marginal cost for its latest line of smartphones, the Blazer. Use the chart to calculate the company's profit.
How many phones will ProPhone need to sell to maximize profit?
a) FOUR
b) SIX
c) NINE
d) TWELVE
Answers
Answer:
6
Step-by-step explanation:
briefly explain the process by which you would determine whether or not x-6 a factor of 3x^3-16x^2-72
Answers
put x=6 in the given eq. [tex]3 x^{3} -16 x^{2} -72=3( 6^{3} )-16( 6^{2} )-72 =3(216)-16(36)-72 [/tex]
=648-576-72
=648-648
=0
hence x-6 is a factor of the given polynomial
I need help really bad I'm gonna give 25 points who helps me
Answers
Ans
Step-by-step explanation:
Round 24.99 to the nearest tenth
Answers
24.99 rounded to the nearest tenth is 25.0.
To round 24.99 to the nearest tenth, we need to look at the digit in the hundredths place. The number 24.99 has a 9 in the tenths place and a 9 in the hundredths place.
If the hundredths place is 5 or higher, we round up the tenths place by 1.If the hundredths place is less than 5, we leave the tenths place as is.Since the hundredths place in 24.99 is 9 (which is higher than 5), we round up the tenths place from 9 to the next whole number which is 10, and it causes the digit in the ones place to increase by 1.
Therefore, 24.99 rounded to the nearest tenth is 25.0.
find the value of k so given line has slope of m 3x-ky-4=2;m=-1/2
Answers
Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.5x^2 -1.3x+9.972, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle? ...?
Answers
0 = x -1.3
x= = 1.3
0.3 cycles cannot be built, so the company should make 1 bicycle to minimize cost.
a soccer player has made 3 of his last 24 shots on goal, or 12.5%. How many consecutive goals does he need to raise his shots-on-goal average to at least 20%?
Answers
The player needs to score at least 3 consecutive goals to raise his shots-on-goal percentage to at least 20%.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's first calculate how many total shots-on-goal the player has attempted so far:
Total shots-on-goal attempted = 24
Total goals scored = 3
Shots-on-goal percentage.
= (Total goals scored / Total shots-on-goal attempted) x 100%
Shots-on-goal percentage = (3 / 24) x 100% = 12.5%
Now, let's assume that the player scores x consecutive goals in his next x consecutive shots-on-goal.
Therefore, his new total goals scored will be:
New total goals scored = 3 + x
His new shots-on-goal percentage will be at least 20%:
New shots-on-goal percentage.
= (New total goals scored / New total shots-on-goal attempted) x 100%
≥20%
Substituting the values, we get:
(New total goals scored / (24 + x)) x 100% ≥ 20%
Simplifying and solving for x:
(New total goals scored / (24 + x)) ≥ 0.2
New total goals scored ≥ 0.2 (24 + x)
3 + x ≥ 4.8 + 0.2x
0.8x ≥ 1.8
x ≥ 2.25
Therefore,
The player needs to score at least 3 consecutive goals to raise his shots-on-goal percentage to at least 20%.
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henry collects shells from the beach every day he is on vacation. each day he collects shells, he always collects three times as many white shells as black shells. which of these ratio statements could compare the number of white shells to black shells henry collects in one day?
Answers
Answer:
HFKHP[;U7P
Step-by-step explanation:
what is 14.9 divided by 0.02
Answers
Solve 2(3a² - 1) - 6a = 5a
Answers
There are 13 fish in an aquarium. Seven of the fish are guppies. How many non-guppies are in the aquarium? A. The number of guppies. B. The number of non-guppies. C. The total number of fish.
Answers
Final answer:
To find the number of non-guppies in the aquarium, subtract the number of guppies (7) from the total number of fish (13), which equals 6 non-guppy fish.
Explanation:
The student's question requires basic arithmetic to solve a subtraction problem within a real-world context of counting fish in an aquarium. Given that there are 13 fish in an aquarium and 7 are guppies, we need to find the number of non-guppies. The total number of non-guppies can be found by subtracting the number of guppies from the total number of fish.
Let's perform the calculation:
Total number of fish in the aquarium = 13
Number of guppy fish = 7
Subtract the number of guppy fish from the total number of fish to find the number of non-guppy fish. 13 (total number of fish) - 7 (number of guppies) = 6
Therefore, there are 6 non-guppie fish in the aquarium.
prove from mathematical induction,
(7^n-3^n) is divisible by 4.
...?
Answers
It is true for n = 1 since 71 - 31 = 4 which is divisible by 4.
We also need to show that it is true for n = 2 (which makes this proof a little different from most induction proofs as we will see.)
It is true for n = 2 since 72 - 32 = 49 - 9 = 40 which is divisible by 4.
Assume for some k ≧ 2 , that both 7k - 3k and 7k-1 - 3k-1 are divisible by 4. Therefore there exist integers p,q such that
(A) 7k - 3k = 4p and
(B) 7k-1 - 3k-1 = 4q
Multiply the left side of (A) by (7 + 3) and the right side by 10
(7 + 3)(7k - 3k) = 40p
FOIL the left side
7k+1 - 7·3k + 3·7k - 3k+1 = 40p
Factor 7·3 out of the two middle terms on the left:
7k+1 + 7·3(-3k-1 + 7k-1) - 3k+1 = 40p
Reverse the terms inside the parentheses:
7k+1 + 7·3(7k-1 - 3k-1) - 3k+1 = 40p
By (B) above we can replace the parentheses by 4q
7k+1 + 7·3(4q) - 3k+1 = 40p 7k+1 + 84q - 3k+1 = 40p
Rearrange the equation:
7k+1 - 3k+1 = 40p - 84q 7k+1 - 3k+1 = 4(10p - 21)q
The right side is divisible by 4, and therefore so is the left side.
Kylie has $70 to spend on clothes. She wants to buy a pair of jeans for $30 and spend the rest on t-shirts. Each t-shirt costs $8. Which inequality represents the number of t-shirts she can purchase?
x ≥ 5
x ≤ 5
x ≤ 11
x ≥ 11
Answers
Answer: The correct option is (B) [tex]x\leq 5.[/tex]
Step-by-step explanation: Given that Kylie has $70 to spend on clothes. She wants to buy a pair of jeans for $30 and spend the rest on t-shirts where each t-shirt costs $8.
We are to select the inequality that represents the number of t-shirts she can purchase.
Let x denote the number of t-shirts that she can buy.
Then, according to the given information, we have
[tex]30+x\times 8\leq 70\\\\\Rightarrow 30+8x\leq 70\\\\\Rightarrow 8x\leq 70-30\\\\\Rightarrow 8x\leq 40\\\\\Rightarrow x\leq \dfrac{40}{8}\\\\\Rightarrow x\leq5.[/tex]
Thus, the required inequality that represents the number of t-shirts she can purchase is [tex]x\leq 5.[/tex]
Option (B) is CORRECT.
The price of an item has been reduced by 70% . The original price was $60 . What is the price of the item now?
Answers
60*0.70 = 42
So, after discount, it would be: $60 - $42 = $18
So, your final answer is $18
Hope this helps!
Final answer:
The original price of the item was $60, and after a 70% reduction, the new price is $18.
Explanation:
The original price of an item was $60. After being reduced by 70%, we need to calculate what the new price will be. We can calculate the amount of discount by multiplying 70% with the original price, which is $60.
To find the discount amount: $60 × 0.70 = $42
Now, subtract the discount amount from the original price to find the new price: $60 - $42 = $18.
Therefore, after a 70% reduction, the new price of the item is $18.
P=2L+2W Solve the formula for L
Answers
Take 2 as a common on RHS.,
P = 2(L + W)
P/2 = L + W
L = P/2 - W
Hope this helps!
Which property states that any element is equivalent to itself?
A. Reflexive
B. Transitive
C. Symmetric
D. Addition property ...?
Answers
A. Reflexive
Symmetric is the property states that any element is equivalent to itself.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
The latest demand equation for your Yoda vs. Alien T-shirts is given by: q = −40x + 800 where q is the number of shirts you can sell in one week if you charge $x per shirt. The Student Council charges you $400 per week for use of their facilities, and the T-shirts cost you $4 each. Find the weekly cost as a function of the unit price x. ...?
Answers
The weekly cost as a function of the unit price x can be calculated by subtracting the revenue from the total cost. The revenue is given by the demand equation q = -40x + 800, and the total cost is the sum of the fixed cost and the variable cost. Therefore, the weekly cost as a function of the unit price x is -160x + 3600.
The weekly cost as a function of the unit price x can be calculated by subtracting the revenue from the total cost.
Revenue is given by the demand equation q = -40x + 800, where q is the number of shirts sold at price x.
Total cost is the sum of the fixed cost and the variable cost. The fixed cost is $400 per week for use of the facilities, and the variable cost is $4 per shirt.
Therefore, the weekly cost as a function of the unit price x is given by:
Cost(x) = 400 + 4q = 400 + 4(-40x + 800) = 400 - 160x + 3200 = -160x + 3600
So, the weekly cost as a function of the unit price x is -160x + 3600.
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From 1980 through 1990, the population of Country X increased by 100 percent. From 1990 to 2000, The population increased by 50 percent. What was the combined increase for the period 1980-2000
A. 150%
B. 166 2/3%
C.175%
D.200%
Answers
In 1990 the value of population is 200% (100% + 100%), therefore the 50% increase is 100%, meaning the total is 200%
Answer:200 %
Step-by-step explanation:
From 1980 to 1990 population increased by 100%
Let us Say initial population be x
therefore 100 % increase means it increases to 2x
From 1990 to 2000 population increased by 50%
i.e.[tex]2x \times 1.5=3x[/tex]
Total increase from 1980 to 2000
[tex]\frac{3x-x}{x}\times 100=200\%[/tex]
What is 0.0703 written in scientific notation?
Answers
0.0703 written in scientific notation is 7.03 × [tex]10^{-2[/tex], representing the original number more compactly with the mantissa (7.03) and exponent (-2).
To express 0.0703 in scientific notation, we first need to move the decimal point to the right until only one digit is to its left. Count the number of places you moved the decimal point, which gives us the exponent of 10. In this case, we move the decimal point three places to the right to obtain 7.03. Thus, we have 7.03 × [tex]10^{-2[/tex]. Since we moved the decimal point three places to the right, the exponent of 10 is -3.
Therefore, 0.0703 in scientific notation is 7.03 × [tex]10^{-2[/tex]. This notation represents the original number in a more compact form, where the mantissa (7.03) indicates the significant digits and the exponent (-2) denotes the power of 10 by which the mantissa is multiplied.
Which of the following represents the graph of f(x) = 2x + 2?
Answers
Answer with explanation:
The given function is :
[tex]y= f(x)=2^x+2[/tex]
To plot the graph of this function , we find x, for different integral values of y and x for different integral values of y and plot these points in x y plane.
x 0 1 2 3
y 3 4 6 10
Join these points to get required curve.
algebra help?
write a function rule for the area of a triangle with a base of 3 cm greater than 5 times its height. what is the area of a triangle when its height is 6 cm?
Answers
The area (A) of the triangle with base a and height h is:
A = a * h / 2
A base is 3 cm greater than 5 times its height: a = 5h + 3
So, the function is:
A = a * h / 2 = (5h +3) * h / 2
If the height is 6 cm:
h = 6
A = (5h +3) * h / 2
A = (5 * 6 + 3) * 6 /2
A = 33 * 3
A = 99 cm²
which ordered pair is the solution of the equation y=7x-3
Answers
To find a solution to the linear equation y=7x-3, select a value for x, substitute it into the equation, and solve for y. The resulting ordered pair (x, y) is a solution. For instance, (1, 4) is a solution when x=1.
Explanation:The question is asking for the solution to the linear equation y=7x-3. To find an ordered pair that satisfies this equation, we need to choose a value for x and then calculate the corresponding value of y using the equation. For example, if we choose x=1, we then substitute it into the equation to get y=7(1)-3, which simplifies to y=4. Therefore, the ordered pair (1, 4) is a solution to the equation y=7x-3.
In general, to find more solutions, we could select different values of x and calculate y each time. All the resulting ordered pairs would be solutions to the given equation and would lie on the line represented by this equation when plotted on a graph.