Find the missing coefficients and exponents identified by question marks. Rewrite the entire equation without question marks when you have solved it.
Answers
Answer:
[tex]\dfrac{12x^{16}-18x^8-42x^6}{-6x^5}=-2x^{11}+3x^3+7x[/tex]
Step-by-step explanation:
Replace the questions marks with letters:
[tex]\dfrac{12x^{a}-18x^8+bx^6}{cx^d}=ex^{11}+3x^f+7x[/tex]
[tex]\textsf{Apply the fraction rule}\quad \dfrac{a+b+c}{d}=\dfrac{a}{d}+\dfrac{b}{d}+\dfrac{c}{d}[/tex]
[tex]\implies \dfrac{12x^{a}}{cx^d}-\dfrac{18x^8}{cx^d}+\dfrac{bx^6}{cx^d}=ex^{11}+3x^f+7x[/tex]
Taking the second term and calculating the coefficient of the denominator:
[tex]\implies -\dfrac{18x^8}{cx^d}=3x^f[/tex]
[tex]\implies \dfrac{-18}{c}=3[/tex]
[tex]\implies c=\dfrac{-18}{3}=-6[/tex]
Taking the first term, substituting the found coefficient of the denominator and calculating the coefficient e:
[tex]\implies \dfrac{12x^{a}}{cx^d}=\dfrac{12x^{a}}{-6x^d}=ex^{11}[/tex]
[tex]\implies e=\dfrac{12}{-6}=-2[/tex]
Taking the third term, substituting the found coefficient of the denominator, and calculating the coefficient of the numerator and the exponent:
[tex]\implies \dfrac{bx^6}{cx^d}=\dfrac{bx^6}{-6x^d}=7x[/tex]
[tex]\implies 6-d=1\implies d=5[/tex]
[tex]\implies \dfrac{b}{-6}=7 \implies b=-42[/tex]
Taking the first term, substituting the found coefficient and exponent of the denominator and the found coefficient e, and calculating the exponent of the numerator::
[tex]\implies \dfrac{12x^{a}}{cx^d}=ex^{11}[/tex]
[tex]\implies \dfrac{12x^{a}}{-6x^5}=-2x^{11}[/tex]
[tex]\implies a-5=11 \implies a=16[/tex]
Taking the second term, substituting the found coefficient and exponent of the denominator, and calculating the exponent f:
[tex]\implies -\dfrac{18x^8}{cx^d}=-\dfrac{18x^8}{-6x^5}=3x^f[/tex]
[tex]\implies f=8-5=3[/tex]
Substituting all found letters:
[tex]\dfrac{12x^{16}-18x^8-42x^6}{-6x^5}=-2x^{11}+3x^3+7x[/tex]
Related Questions
Suppose I have an organization that has 60 people, 35 are women and 25 are men. We need to select a committee of 11 people. How many ways can such a committee be formed
Answers
Using the combination formula, it is found that such a committee can be formed in 342,700,125,300 ways.
The order in which the people are selected is not important, hence, the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 11 people are taken from a set of 60, hence:
[tex]C_{60,11} = \frac{60!}{11!49!} = 342700125300[/tex]
More can be learned about the combination formula at https://brainly.com/question/25821700
pleaseee i need some help on these 3 questions
Answers
Answer:
a) the product is equal to 953.
b) the product is greater than 443.
c) the product is greater than 181.
Step-by-step explanation:
a) 953 × 63/63 = 953
Therefore, the product is equal to 953.
b) 443 × 86/79 = 482.25
Therefore, the product is greater than 443.
c) 181 × 30/28 = 193.93
Therefore, the product is greater than 181.
Hope this helps =)
I WILL MAKR BRAINLIEST
Answers
Answer:
Ans of No.3
C 40÷(x+4)
Step-by-step explanation:
question 40÷(4+x)
ans nothing changed but x move to front of 4 and 4 move behind of x
What is the circumference of a circle with a diameter of 10 meters? (Use 3.14 for pi.)
13.14 m
31.4 m
15.7 m
314 m
Answers
Answer:
The answer is given in the picture
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECTAnswer:
31.4 m
Step-by-step explanation:
The formula for the circumference of a circle is c=dπ, so we can substitute our diameter and 3.14 for pi.
c=(10)(3.14)
c=31.4
So the diameter is 31.4 meters.
help please it´s so hard
Answers
Answer:
9
Step-by-step explanation:
To solve this expression, we need to follow the BODMAS. The BODMAS states that to simplify the expression in the parenthesis first. Then, divide or multiply if possible. Lastly, add or subtract if possible.
The BODMAS states that:
B - BracketsO - OrderD - DivisionM - MultiplicationA - AddtionS - SubtractionExpression BODMAS
⇒ 6 ÷ 2(1 + 2) ⇒ 6 ÷ 2(3) B - Brackets (BODMAS)⇒ 6 ÷ 2 × 3⇒ 3 × 3 D - Division (BODMAS)⇒ 9 M - Multiplication (BODMAS)Therefore, the value of the expression is 9.
Learn more about BODMAS: https://brainly.com/question/23827397
What is the surface area of this right prism?
48 in²
84 in²
96 in²
120 in²
Answers
Answer:
96 in²
Step-by-step explanation:
I took the test :)
Answer:
96 in² for K12
When condensing a logarithm using the the product property, you combine the answers by dividing them.
Group of answer choices
True
False
When condensing a logarithm using the the power property, you move the front number to become the exponent on the log.
Group of answer choices
True
False
When condensing a logarithm using the the quotient property, you combine the answers by dividing them.
Group of answer choices
True
False
Answers
#1
log_a(bc)=log_a^b+log_a^cNot divide we multiply
False#2
logb^a=alogbYes
True#3
Yes it's reverse of first one
TrueAnswer:
False
True
True
Step-by-step explanation:
[tex]\textsf{Product Rule}:\quad \log_n(x)+\log_n(y)=\log_n(xy)[/tex]
When condensing a logarithm using the product rule, you combine the answers by multiplying them.
[tex]\textsf{Power Rule}:\quad a \log_n(x)=\log_n(x)^a[/tex]
When condensing a logarithm using the power rule, you move the front number to become the exponent on the log.
[tex]\textsf{Quotient Rule}:\quad \log_n(x)+\log_n(y)=\log_n\left(\dfrac{x}{y}\right)[/tex]
When condensing a logarithm using the the quotient rule, you combine the answers by dividing them.
HELP 2 FOR MY SIS no hurry
Answers
First Step:
Parentheses,
7 + 5 = 12
Divide,
12 / 3 = 4
Add,
4 + 3 = 7
Multiply,
10 x 7 = 70
Answer is 70!!
hope this helps
__
What is the length of HI to the nearest hundredth?
1.32 km
16.33 km
38.02 km
Answers
Answer:
16.33 km
Step-by-step explanation:
The square length of hypotenuse is equal to the sum of two legs' square value:
|HI|^2 + |JI|^2 = |HJ|^2
|HI|^2 + (24.28)^2 = (29.26)^2
|HI|^2 + 589,5184 = 856,1476 (these are full values and will be easier to calculate with a calculator, if not we can use the approximate values: 589,5 and 856,1)
subtract 589,5184 from both sides
|HI|^2 = 266,5636 find the root of boths sides
HI = 16.33 approximately
The base HI of the right triangle is approximately 16.26 km.
Given is a right triangle with perpendicular JI = 24.28 km and hypotenuse HJ = 29.26 km we need to find the base HI.
To find the base HI of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the base HI as x.
According to the Pythagorean theorem:
HJ² = JI² + HI²
Substituting the given values:
(29.26 km)² = (24.28 km)² + x²
Simplifying the equation:
855.4276 km² = 590.7584 km² + x²
264.6692 km² = x²
To find x, we take the square root of both sides:
x = √(264.6692 km²)
Calculating the value:
x ≈ 16.26 km
Therefore, the base HI of the right triangle is approximately 16.26 km.
Learn more about Pythagorean theorem, click;
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Say that romania puts a tariff of 6% on its exports and 21% on its imports. if romania has a trade deficit of (equivalent us dollars) $26.76 billion and gained tariff revenue of $18.9603 billion, how much are romania’s imports worth? a. $62.56 billion b. $64.29 billion c. $76.17 billion d. $97.04 billion please select the best answer from the choices provided a b c d
Answers
The amount of money that Romania’s imports are worth is equal to: C. $76.17 billion.
Given the following data:
Exports tariff = 6% = 0.06.
Imports tariff = 21% = 0.21.
Trade deficit = $26.76 billion.
Tariff revenue = $18.9603 billion.
How to calculate Romania’s imports?In order to determine how much Romania’s imports are worth, we would write a mathematical expression for the total tariff revenue and trade deficit as follows:
0.06E - 0.21I = 18.9603 .....total tariff revenue (eqn. 1).
I - E = 26.76 .....trade deficit (eqn. 2).
From eqn. 2, we have:
E = I - 26.76 ..equation 3.
Substituting eqn. 3 into eqn. 1, we have:
0.06(I - 26.76) - 0.21I = 18.9603
0.06I - 1.6056 - 0.21I = 18.9603
0.27I = 18.9603 + 1.6056
0.27I = 20.5659
I = 20.5659/0.27
I = $76.17 billion.
Read more on trade deficit here: https://brainly.com/question/20247907
According to the line plot what is the total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound
Answers
Answer:
7/8
Step-by-step explanation:
I took the test
The total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound is 7/8.
How to add two fractions?Let we have to add two fractions:
[tex]\dfrac{a_1}{b_1} + \dfrac{a_2}{b_2}[/tex]
Then we will find the Lowest Common Multiple (LCM) of b_1 and
b_2. That will help to make the denominate or same.
Once the denominators become the same, the numerators can add up directly, giving us the final result of the addition.
According to the line plot;
The total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound
= 3/8 + 3/8 + 1/8
=7/8
Learn more about fraction addition here:
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The vertical of three squares are joined to form a right triangle , what is the area of the largest square
A- 25cm^2
B- 202,500cm^2
C- 34cm^2
D- 43cm^2
Answers
Answer:
43cm²
Step-by-step explanation:
let's first consider the area of a square.
the area is L² which means all sides are equal so we take the length times the breadth which is both equal because like we said all sides are equal.
so to find the side of the square using the area, we take the square root of both of the area.
[tex] \sqrt{25} = 5[/tex]
and also
[tex] \sqrt{18} = 4.2[/tex]
so we have the height of the triangle as 5cm and the base is 4.2cm.
now, from the triangle, since we have two sides and it's a right-angled, we can use Pythagoras' formula.
[tex] \sqrt{ {5}^{2} + {4.2}^{2} } = 6.53cm[/tex]
so the side 6.53cm is also the same side as the largest triangle. Since it's a square, all sides are equal. So we find the area of the largest triangle by using the formula
Area = L²
Area = 6.53²
Area = 42.6cm
the nearest cm square
Area = 43cm²
Check the picture below.
Can someone help me please?
Answers
1 yellow heart = 4
5 yellow hearts = 20
1 pink triangle = 4
5 pink triangles = 20
hope it helps...!!!
helppppnmeeeeeee please
Answers
Answer:
? = 14.48
Step-by-step explanation:
This is a right triangle so you can use trigonometry.
since you know the opposite and hypotenuse sides, use sin.
sin(?) = opposite/hypotenuse = 4/16 = 1/4
? = arcsin(1/4)
? = 14.48
How many outcomes are created by rolling a 4-sided die, 6-sided die, and a 12-sided die at the same time?
Answers
288
Step by step explanation
4x6x12
There are 288 outcomes are created by rolling a 4-sided die, 6-sided die, and a 12-sided die at the same time.
What is the combination?A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
The outcomes are created by rolling a 4-sided die, 6-sided die, and a 12-sided die at the same time.
The number of outcomes is created by rolling a 4-sided die, 6-sided die, and a 12-sided die at the same time is;
[tex]\rm Outcome=4\times 6\times 12\\\\Outcomes =288[/tex]
Hence, there are 288 outcomes are created by rolling a 4-sided die, 6-sided die, and a 12-sided die at the same time.
Learn more about combination here;
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a+b×2%
Can someone help me
:)
Answers
Without knowing what a or b is, that is as simplified as it can get.
somebody HELP ME PLS IM TRYING TO GET MY GRADES UP FROM AN F! IF ITS CORRECT AND HELPFUL U WILL BE BRAINLIEST
Find the area of the figure.
Answers
Answer:
144
Step-by-step explanation:
A=BH
your base is 9 and your height is 16. 16 times 9= 144. Hope this helps :)
An investor buys in a company and in the twelve months after she invests the value of the stock decreases by 30% , bu what amount will the value of the stock need to go up from there in order that the price of the stock will be equal to what the investor first paid for it ?
a:30%
b:37,5%
c:42. 9
d:45
e:46. 7
Answers
Answer:
B 37.5%
Step-by-step explanation:
help please ! it’s one of the multiple choices
Answers
Answer:
Option C
Step-by-step explanation:
[tex]\boxed{Log \ \dfrac{a}{b}=log \ a - log \ b}\\\\\boxed{(log \ a)^b=b*log \ a}[/tex]
[tex]\sf log_w \ \dfrac{(x^{2}-6)^4}{\sqrt[3]{x^2+8} }=log_w \ (x^2-6)^4 - log_w(x^2+8)^{\frac{1}{3}}[/tex]
[tex]\sf = 4*log_w \ (x^2 -6) - \dfrac{1}{3}log_w \ (x^2 + 8)[/tex]
If I get paid 8 dollars a hour, and I worked 180 hours how much money will I recive
Answers
Answer:
$1440
Step-by-step explanation:
It's kind of obvious, 8 x 180 = 1440
PLSS HELP WILL GIVE BRAINLIST:DDDDDD
Use the number line to help you decide which statement is true.
1
3
<
2
6
1
3
>
2
6
1
3
=
2
6
Answers
Answer:
It's 13<26
Step-by-step explanation:
PLEASE HELP ME I NEED HELP RIGHT NOW..this is weird question...it is on a problem thingy please help
um im sorry,....wtf
Answers
Answer:
I don't think it would be called bias, it's just asking for an opinion if a state can kill a person if they break the law.
Show division using an area model. Can you show 24÷ 4 with one rectangle?
Answers
Answer:
Shown division using an area model above, Yes, shown 24 ÷ 4 with one rectangle above. Question 2. Answer: Shown division using an array as shown above, 25 ÷ 4 = Quotient = 6 and Remainder = 1, Shown division using an area model above, Yes, shown 25 ÷ 4 with one rectangle above and showed
in the given figure, prove that triangle ABC = triangle ABD
Answers
Answer:
Step-by-step explanation:
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS THANKS
Answers
Answer:
The answer is B. 1/2
Step-by-step explanation:
You want to role a number less than 4 so you want 1,2,3 at least.
A dice has 6 numbers, 1-6.
So 3/6 = 1/2 making it a 50% change of you getting either 1,2,3.
What is the purpose of constructing a confidence interval?
Answers
Using the interpretation of a confidence interval, it is found that the correct option is:
In order to find a range of values to estimate the population proportion.x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has confidence level of x%. It means that we are x% confident that the population mean is between a and b.From the above bullet point, we have that the interval is taken from a sample, and is used to estimate a population parameter.Hence, the correct option is:
In order to find a range of values to estimate the population proportion.You can learn more about the interpretation of a confidence interval at
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A dress that regularly costs $92 and has tax of
8%. How much is the tax charge for this dress?
Answers
Answer:
Tax = $7.36
Step-by-step explanation:
[tex]tax=92(\frac{8}{100} )=92(0.08)=7.36[/tex]
Hope this helps
Answer:
7.36$ tax.
When finding the whole amount of dollars to the percentage, multiply the whole number(92) by the tax percentage(0.08) which is a decimal for this case.
[tex]92 * 0.08 = 7.36\[/tex]
Optionally, find the tax plus the whole number.
[tex]92 + 7.36 = 99.36\[/tex]
__________________________________________________________
Questions or Suggestions?Ask in comments.
Pls help! It's due soon and I can't figure out the answer!
Answers
Answer:
9cm and 2cm
Step-by-step explanation:
∴ They're similar triangles.
∴ [tex]\frac{a}{3}[/tex]= [tex]\frac{6}{b}[/tex] = [tex]\frac{3}{1}[/tex]
∴ a = 9cm
∴ b = 2cm
If the ball leaves her hand 6 feet above the ground at 65 feet/second: a) what is the maximum height of the ball
Answers
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&65\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&6\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+65t+6[/tex]
Check the picture below, the maximum occurs at the vertex of the parabolic path, so
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+65}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 65}{2(-16)}~~~~ ,~~~~ 6-\cfrac{ (65)^2}{4(-16)}\right)\implies \left(\cfrac{65}{32}~~,~~6+\cfrac{4225}{32} \right) \\\\\\ \left(\cfrac{65}{32}~~,~~\cfrac{4609}{32} \right) \implies \stackrel{maximum~height}{(2.03125~~,~~\stackrel{\downarrow }{72.015625})}[/tex]
]
3 3 6
Which of the following represents the solution of
?
2 2x 5x
NI
X=-
1
5
OX=-
5
9
O all real numbers
Ono solution
Answers
Answer:
They are all real numbers.
Option (2) and (5) I think is correct. x = -5 and x = 3
Step-by-step explanation:
Answer: Option (2) and (5) is correct. ... We have to find the solution of the given equation (x + 5)(x – 3) = 0 and choose the correct option from the given·