Answer:
-5x=35
Step-by-step explanation:
The product= an answer to a multiplication problem, so product means multiply
A number= a variable, an unknown integer(number)
So, therefore, a number multiplied by -5 = -5x
x= the variable, the variable being multiplied should go right after the known number.
so, -5x=35
solved= divide -5 by 35 which equals -7
a negative number and a positive number being multiplied make the product a negative number.
Please mark brainliest, I hope this helps!!
Integrate the following:
[tex]\displaystyle \int \frac{x^2}{x^2+x+3}\, dx[/tex]
Answer:
[tex]\int {\frac{x^2}{x^2+x+3} } \, dx = - \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x + C[/tex]
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Completing the SquareRearranging VariablesAlgebra II
Long DivisionCalculus
U-Substitution[Integration Trick 1] Numerator Split[Integration Trick 2] Completing the SquareIntegration Rule 1: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Integration Rule 2: [tex]\int {f(x)+g(x)} \, dx =\int {f(x)} \, dx + \int {g(x)} \, dx[/tex]Integration 1: [tex]\int {\frac{1}{u} } \, du =ln|u| + C[/tex]Integration 2: [tex]\int {\frac{du}{u^2+a^2} } = \frac{1}{a} arctan(\frac{u}{a} )+C[/tex]Integration 3: [tex]\int {x^n} \, dx = \frac{x^{n+1}}{n+1} +C[/tex]Step-by-step explanation:
Step 1: Define
[tex]\int {\frac{x^2}{x^2+x+3} } \, dx[/tex]
Step 2: Simplify Function
We do long division to simplify the function inside the function.
See Attachment for Long Division Work.
Once we do long division, our function becomes [tex]1-\frac{x+3}{x^2+x+3}[/tex]
Now we rewrite our Integral: [tex]\int ({1-\frac{x+3}{x^2+x+3} }) \, dx[/tex]
Step 3: Integrate Pt. 1
Distributive Integral [Int Rule 1]: [tex]\int {1} \, dx - \int {\frac{x+3}{x^2+x+3} } \, dx[/tex]Integrate 1st Integral [Int 3]: [tex]x - \int {\frac{x+3}{x^2+x+3} } \, dx[/tex]Step 4: Identify Variables Pt.1
Set variables for u-substitution.
u = x² + x + 3
du = (2x + 1)dx
Step 5: Integrate Pt. 2
Rewrite Integral [Int Rule 1]: [tex]x - \frac{1}{2} \int {\frac{2(x+3)}{x^2+x+3} } \, dx[/tex]Distribute 2 [Alg]: [tex]x - \frac{1}{2} \int {\frac{2x+6}{x^2+x+3} } \, dx[/tex]Rewrite Integral [Alg]: [tex]x - \frac{1}{2} \int {\frac{2x+1+5}{x^2+x+3} } \, dx[/tex]Rewrite Integral [Int Trick 1]: [tex]x - \frac{1}{2} [\int {\frac{2x+1}{x^2+x+3} } \, dx + \int {\frac{5}{x^2+x+3} } \, dx ][/tex](2nd Int) Complete the Square: [tex]x - \frac{1}{2} [\int {\frac{2x+1}{x^2+x+3} } \, dx + \int {\frac{5}{(x+\frac{1}{2})^2 + \frac{11}{4} } } \, dx ][/tex]Step 6: Identify Variables Pt. 2
Set variables for u-substitution for 2nd integral.
z = x + 1/2
dz = dx
a = √(11/4)
Step 7: Integrate Pt. 3
[Integrate] U-Substitution: [tex]x - \frac{1}{2} [\int {\frac{1}{u} } \, du + \int {\frac{5}{z^2 + (\sqrt{\frac{11}{4}})^2} } \, dz ][/tex]Rewrite Integral [Int Rule 1]: [tex]x - \frac{1}{2} [\int {\frac{1}{u} } \, du + 5\int {\frac{dz}{z^2 + (\sqrt{\frac{11}{4}})^2} } ][/tex]Integrate 1st Integral [Int 1]: [tex]x - \frac{1}{2} [ln|u| + 5\int {\frac{dz}{z^2 + (\sqrt{\frac{11}{4}})^2} } ][/tex]Integrate 2nd Integral [Int 2]: [tex]x - \frac{1}{2} [ln|u| + 5(\frac{1}{\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } ) ) ][/tex]Distribute 5 [Alg]: [tex]x - \frac{1}{2} [ln|u| + \frac{5}{\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } ) ][/tex]Distribute -1/2 [Alg]: [tex]x - \frac{1}{2}ln|u| - \frac{5}{2\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } )[/tex]Rationalize [Alg]: [tex]x - \frac{1}{2}ln|u| - \frac{5\sqrt{11} }{11}arctan(\frac{z}{\sqrt{\frac{11}{4} } } )[/tex]Resubstitute variables [Alg]: [tex]x - \frac{1}{2}ln|x^2+x+3| - \frac{5\sqrt{11} }{11}arctan(\frac{x+\frac{1}{2} }{\sqrt{\frac{11}{4} } } )[/tex]Simplify/Rationalize [Alg]: [tex]x - \frac{1}{2}ln|x^2+x+3| - \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} )[/tex]Rewrite [Alg]: [tex]- \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x[/tex]Integration Constant: [tex]- \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x + C[/tex]And we have our final answer! Hope this helped you on your Calculus Journey!
hope this will help you........
can anyone out there help me? This is due today!!
WiIl give brainliest :D
Answer:
D.
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
because it the only right one according to my research
Can somebody help please
What is the question?
Core Algebra
Englis
Solving for an Unknown Using the Distributive Property
180(n-2)
The equation a = represents the angle measuresya, in a regular n-sided polygon. When the equation is
solved for n, n is equal to a fraction with a denominator of a - 180. What is the numerator of the fraction?
Answer:
-360
Step-by-step explanation:
I got it right
can yall do the work of the answer 95 to this
9514 1404 393
Answer:
? = 95°
Step-by-step explanation:
Long arc QR is twice the measure of inscribed angle QSR, so is 2×95° = 190°. That, together with the remaining short arcs ? and RS will make up the total circle of 360°.
arc QR + arc RS + ? = 360°
190° +75° +? = 360°
? = 360° -265° . . . . . . subtract 265° from both sides
? = 95°
As more people attend the play, the
amount of money received increases.
Identify the independent variable.
A
people attending
B
money received
Answer:
A
Step-by-step explanation:
what is the slope for (-11, 1) and (-2, 6)?
Answer:
5/9
Step-by-step explanation:
You can verify me by using the y2-y1/x2-x1 formula
Pls help :((. Im really stuck and confused
Step-by-step explanation:
2. AB || CD 2. Def of parallelogram
3. <BAC is congr <DCA 3. alt int angles of parallel lines
4. seg AB is congr seg CD 4. Theorem: opp sides of parallel are congr
5. <s AEB and CED are rt <s 5. Def of perpendicular lines
6. <AEB is congr <CED 6. Theorem: all right angles are congr
7. tr. AEB is congr tr. CED 7. AAS
8. seg. AE is congr seg. CE 8. CPCTC
9. <BEC is a rt < 9. Def of perpendicular lines
10. <AEB is congr <BEC 10. Theorem: all right angles are congr
11. seg BE is congr seg. BE 11. Theorem: congr of seg's is reflexive
12. tr. AEB is congr tr. CEB 12. SAS
13. seg AB congr seg BC 13. CPCTC
P decreased by the difference of q and r
Answer:
P-(q-r) that's the answer
Step-by-step explanation:
krnrnenee
50 points.
Record the simplified expression
Answer:
-4x+5
Step-by-step explanation:
-(4x-2) change sign of each in parenthesis so they are now -4+2
now you have -4x+2+3 add like terms
now you have -4x+5
[tex]\sf \longmapsto−4x+2+3[/tex]
Combine like terms[tex]\sf \longmapsto−4x+2+3[/tex]
[tex]\sf \longmapsto(−4x)+(2+3)[/tex]
[tex]\sf \longmapsto−4x+5[/tex]
Glass melts at a temperature that is higher than 2,500 degrees and less than
3,000 degrees.
Answer:
I think A is correct answer
Answer:
a
Step-by-step explanation:
What is the circumference of a circular swimming pool with a diameter of 20
feet? (Round your answer to the nearest tenth.)
A. 62.8 ft
B. 15.7 ft
c. 125.7 ft
D. 314 ft
Answer:
A. 62.8 ft
Step-by-step explanation:
[tex]C = \pi \: d = 3.14 \times 20 = 62.8 \: ft[/tex]
Determine the area of the rectangle
6x + 3
X+5
Answer:
Step-by-step explanation:
multiply the two expressions
(6x + 3)(x + 5)
6x^2 + 30x + 3x + 15
6x^2 + 33x + 15
simplify if needed
3(2x^2 + 11x +5)
hope this helps <3
someone please help 71 points
Answer:
I am not sure what you would like me to answer but you can either message me or just make another question with either the rest of the question or a picture of your question. I am happy to help under any circumstance.
Lin’s family has completed 80% of a trip. They have traveled 40 miles. How far is the trip? *
Answer:
50 miles i believe
Step-by-step explanation:
Answer:
50 miles
Step-by-step explanation:
Laura Simplified the expression 5x[(3.14+4.16)×9+2] as shown
Step 1: 5x[7.3x9+2]
Step 2. 5x[7.3x11]
Step 3. 5x80.3
Step 4. 401.5
Questions:
A. In what step did Laura first make a mistake?
B. Explain what the mistake was using mathematical detail academic language
C. Show your step by step work using mathematical detail and academic language to simplify the expression
D. What is the correct answer to the expression
Answer and Explanation
__________________________________________________________
A. Step 2
B. Step 2 is wrong because multiplying is first before adding, and Laura added before multiplying and got 401.5 instead of 338.5
C. [tex]5\cdot\left(\left(3.14+4.16\right)\cdot9+2\right)[/tex] = [tex]?[/tex]
[tex]5\cdot\left(\left(7.3\right)\cdot9+2\right)[/tex] = [tex]?[/tex]
[tex]5\cdot\left(65.7+2\right)[/tex] = [tex]?[/tex]
[tex]5\cdot\left(67.7\right)[/tex] = [tex]?[/tex]
D. [tex]338.5[/tex]
__________________________________________________________
Hope this helps! <3
__________________________________________________________
Find the slope between the points: (3,4) and (-1,-2)
Answer:
3/2 hope this helps hqhahjajja
find the slope of the following 2 points (2,-5), (9,3)
Answer:
8/7
Step-by-step explanation:
(2,-5) (9,3)
3-(-5)=8 because you apply your keep change change
9-2= 7
so 8/7
The price of a Nintendo Switch was on sale on Black Friday for $250, the original price was $300. What percent was it marked down?
A. 20%
B. 25%
C. 50%
D. None of the above.
Answer:
A
Step-by-step explanation:
Answer:
none of the above
Step-by-step explanation:
plz mark as brainliest
Please help! I am so bad at math!
Answer:
PR=12
Step-by-step explanation:
2x+6=3x-6
6=x-6
12=x
Which expression is equivalent to 2x^2 - 2x + 7?
Answer:
(o,7) vertical intercept
minimum (1/2 , 13/2)
Ms. Guthrie spent 80% of her cash on gifts.
What fraction of her cash did she spend on gifts?
She spent type your answer...
of her cash on gift.
Answer:
She spend (8/10) or (4/5) of her cash on gift.
Step-by-step explanation:
4/5 is simplified.
but not simplified its 8/10
Daniela got 78% on her last history test. If there were 50 questions on the test , how many did she get correct
Answer:
39.
Step-by-step explanation:
78% of 50 is 39. To calculate x% of a number y, we use the following rule: x% of y = (x / 100) × y.
Simplify 13 + 4(9 - 7).
A. 34
B. 21
C. 42
D. 19
Answer:
.B. 21
Step-by-step explanation:
13+4(9-7) <----- Multiply 9 and -7 by 4 (Distribute Property)
13+36-28 <----- Combine 36 and -28
13+8 <------Combine 13 and 8
21
help please I will give brainiest
Which of the following functions is graphed below
Answer:
C: y = |x-2| + 3
Step-by-step explanation:
When dealing with transformations, the numbers in the parentheses is the horizontal translation and the numbers outside the parentheses are vertical translation. The only reason the lines are | rather than ( is that they are absolute value.
When taking the horizontal measures, you always flip the sign. So since it is going to the right 2 times, you would think it would be +2, but since it is in the parentheses it would be -2.
When taking the vertical measures, it's just standard thought. So since it is up 3 it would be +3.
Putting all of that together would give you |x-2|+3
You flip an inequality symbol when you...
The box plots below show the miles per gallon (mpg) ratings distribution for three types of cars.
5.41 + k = 9.7 what is the value of k
Explain how you know when 2 ratios are proportional.
Answer:
Ratios are proportional when they represent the same relationship.
Step-by-step explanation:
Such as: finding equivalent fractions
Answer:
Ratios are proportional if they represent the same relationship.
Step-by-step explanation
One good way to tell is to make them fractions and then reduce them. If the reduced fractions are the same, you ratio is proportional! Good luck !
