Done!
Answer:
[tex](f+g)(x)=3x^3-2x^2+10x-12[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=3x^3-2x^2+4x-5\\g(x)=6x-7 \end{cases}[/tex]
[tex]\begin{aligned}(f+g)(x) & = f(x)+g(x)\\& = (3x^3-2x^2+4x-5)+(6x-7)\\& = 3x^3-2x^2+4x-5+6x-7\\& = 3x^3-2x^2+4x+6x-5-7\\& = 3x^3-2x^2+10x-12\end{aligned}[/tex]
Which of the following statements are true?
The prime factorization of 21 is 3 x 7.
The LCM of 14 and 21 is 42.
The prime factorization of 14 is 2 x 7.
14 is a composite number.
21 is a prime number.
The GCF of 14 and 21 is 14.
Answer:
The prime factorization of 14 is 2 x 7.
Step-by-step explanation:
The prime factorization of 14 is 2 x 7.
Answer:
14 is a composite number
Step-by-step explanation:
How can you make a sum of 12
There are several ways
Let's check all
1+112+103+94+85+76+60+12NO LINKS!!
Solve the compound inequality. Write the solutions in interval notation.
x + 7 ≥ 4 and 11x - 8 ≥ 3
Answer: [1, infinity)
===========================================================
Explanation:
Let's isolate x in the first inequality mentioned.
x + 7 ≥ 4
x + 7-7 ≥ 4-7
x ≥ -3
I subtracted 7 from both sides to undo the +7.
Now isolate x in the second inequality. We first add 8 to both sides, then divide both sides by 11.
11x - 8 ≥ 3
11x - 8+8 ≥ 3+8
11x ≥ 11
11x/11 ≥ 11/11
x ≥ 1
------------------
The two solutions we found were
x ≥ -3 and x ≥ 1
Next, draw out a number line with closed circles at -3 and 1. Shade to the right of each closed circle endpoint as you see below.
Notice that the two inequalities overlap for x ≥ 1
In other words, if a number is -3 or larger AND 1 or larger, then the number is 1 or larger.
The two solutions intersect to form x ≥ 1
The inequality x ≥ 1 is the same as 1 ≤ x which is the same as 1 ≤ x < infinity
Then that turns into the interval notation of [1, infinity)
The square bracket includes the endpoint 1.
If needed, use the infinity symbol in place of the word "infinity".
Answer:
[1, ∞)
Step-by-step explanation:
To solve a compound inequality, first separate it into two inequalities and solve them separately:
Solution of Inequality 1:
x + 7 ≥ 4
⇒ x ≥ 4 - 7
⇒ x ≥ -3
Solution of Inequality 2:
11x - 8 ≥ 3
⇒ 11x ≥ 3 + 8
⇒ 11x ≥ 11
⇒ x ≥ 1
As both graphs overlap for x ≥ 1, this is the solution.
Therefore, in interval notation: [1, ∞)
Find the indefinite integral using the substitution provided.
[tex]\int\limits({\frac{14e^2^x}{e^2^x+10}) } \, dx[/tex]
[tex]u=e^2^x+10[/tex]
Answer: [tex]7\text{Ln}\left(e^{2x}+10\right)+C[/tex]
This is the same as writing 7*Ln( e^(2x) + 10) + C
=======================================================
Explanation:
Start with the equation [tex]u = e^{2x}+10[/tex]
Apply the derivative and multiply both sides by 7 like so
[tex]u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\[/tex]
The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)
This way we can do the following substitutions:
[tex]\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\[/tex]
Integrating leads to
[tex]\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\[/tex]
Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.
To verify the answer, you can apply the derivative to it and you should get back to the original integrand of [tex]\frac{14e^{2x}}{e^{2x}+10}[/tex]
Sally makes $3,000 each month. What is the most she can spend on housing?
Following the 30% rule of thumb, Sally should only spend a maximum of $900 on her rent
Numbers and percentageGiven Data
Monthly Salary = $3000Percentage spent on rent = 30%Let us find 30% of $3000
= 30/100* $3000
= 0.3*$3000
= $900
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If we changed the 3 to a 0 in the equation, what would happen to the graph?
A function assigns the values. The function will move down by 3 units.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.
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Riley took tests in science.
Each test had a different score.
The mean score of the tests was .
The median score of the tests was .
Based on this information, select the two statements that must be true.
A. At least one score was exactly 85%
B. At least one score was exactly 90%
C. More than half of the scores were 85% or greater.
D. More than half of the scores were 90% or greater.
E. There were no scores less than 90%
F. There were no scores less than 85%
Answer:c
Step-by-step explanation:heheh
Answer: C
Step-by-step explanation:
A music club has $187 to buy ice cream for a party. Each carton of ice cream costs $4. If the club buys as many cartons as possible, how much money will the club have left?
Answer:
They would have $3 dollars left over.
Step-by-step explanation:
If you divide 187 by 4, you get 46.75. But if you look again, you can see that the remainder is 3 and it can confirm that it is the left over money that the club has now after buying as many ice cream cartons as possible.
Evaluate the limit. lim x → 0 4ex/2 − 4 − 2x − 1 2 x2 x3
The limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
Limit of the function
The limit of the given expression is calculated as follows;
lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³]
= (4e⁰)/2 - 4 - 2(0) - 12(0) + (0)
= (4)/2 - 4
= 2 - 4
= - 2
Thus, the limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
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Which combined inequality has the same solution set shown in the graph of x?
Number line ranging from negative four to four, with a line beginning with an open point at negative three and ending with a closed point at negative one
–3 > x ≥ –1
–3 < x ≤ –1
–3 ≤ x < –1
–3 ≤ x > –1
Step-by-step explanation:
an open (empty) point means the point itself is not included.
a closed (filled) point means the point itself is included.
the x values going from -3 (not included) to -1 (included) means
-3 < x <= -1
so, the second answer is correct.
The polynomial 40p + 50f + 90 represents the amount of ink, in milliliters, of printing "p" poster and f flyers in
colour. The polynomial 15p+20f + 45 represents the amount of ink, in milliliters, of printing "p" poster and f flyers
in black and white.
How much ink is saved (HINT: use subtraction) if someone prints 26 posters and 45 flyers in black and white rather
than in colour?
ongle below. Then determine the area when
color : 40p + 50f + 90
b&w : 15p+20f + 45
p = 26
f = 45
[substitute the values given]
color : 40(26) + 50(45) + 90
b&w : 15(26)+20(45) + 45
[solve the equation]
color : 3380
b&w : 1335
[subtract to see how much ink is saved]
3380 - 1335 = 2045
pls help! thank you!
Using the zero product property, we can set each factor equal to zero.
First Factor [tex]x^{4}+5x^{2}-36[/tex]
[tex]x^{4}+5x^{2}-36=0\\(x^{2}+9)(x^{2}-4)=0\\x^{2}+9=0, x^{2}-4=0\\x=\pm 3i, x=\pm 2[/tex]
Second Factor [tex]2x^{2}+9x+5[/tex]
Using the quadratic formula, we get [tex]x=\frac{-9 \pm \sqrt{41}}{4}[/tex].
It’s been a while since I did Math but, in most scenarios, when you solve for an equation with only 1 x variable and you substitute it back in, it should always be true and equal the answer in the original equation(?).
For this equation, the answer was x=7, but when I substitute it back in, I was unable to get the original solution back, which means it is “no solution” after all.
Why is that?
Let's replace every copy of x with 7 and simplify.
[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5*7+1}+9 = 3\\\\\sqrt{35+1}+9 = 3\\\\\sqrt{36}+9 = 3\\\\6+9 = 3 \ \text{ .... note the 6 on the left isn't negative}\\\\15 = 3\\\\[/tex]
Which is clearly false. This is probably the set of steps you followed to get "no solution".
Why is there no solution? Well let's subtract 9 from both sides to isolate the square root
[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5x+1}+9-9 = 3-9\\\\\sqrt{5x+1} = -6\\\\[/tex]
Recall that the result of a square root operation is never negative. The range of [tex]y = \sqrt{x}[/tex] and [tex]y = \sqrt{5x+1}[/tex] is the set of nonnegative numbers. There is no way we can have the left hand side result in -6
If there was a negative sign out front the square root and we have this instead
[tex]-\sqrt{5x+1}+9 = 3\\\\[/tex]
then the answer would be x = 7
Unfortunately, there isn't such a negative sign, so we stick with "no solutions".
How is the graph of the parent function y=x² transformed to produce the graph of y=3(x+1)²?
a) It is translated 1 unit right and compressed vertically by a factor of 3.
b) It is translated 1 unit left and compressed vertically by a factor of 3.
c) It is translated 1 unit right and stretched vertically by a factor of 3.
d) It is translated 1 unit left and stretched vertically by a factor of 3.
Answer:
Step-by-step explanation:
Remark
Always the easiest way to study these questions is to get a graph. The one below shows
Red: y = x^2
Blue: y= 3(x + 1)^2
You will notice that (x+1)^2 shifts the graph Left -- the opposite to what you might think.
The 3 is a little harder. It narrows the red mother graph. Which choice says that?
The choice is between b and d. Why. Because the blue graph is to the left of the red one.
You have to learn the meaning of compressed. A better word might be narrows.
Answer
B
Two large trees, 5.5m and 6.8m tall, stand 12m apart. A bird flies directly from the top of one tree to the top of the other. How far has the bird flown?
Cost of Bikes ($) at Bike Shop
312, 352, 480, 392, 368, 352, 416, 640
b. median
The median is?
Answer:380
Step-by-step explanation:sort the list, take center value or mean of center values if even number of items in list
Is 82296 a perfect square? If not, which number is multiplied to make it a perfect square?
No, Number 82296 is not a perfect square.
And, We multiply by 82296 in the number 82296 to amke a perfect square.
What is square root of a number?A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The number is,
⇒ 82296
Now,
If the number 82296 is a perfect square number.
So, We get;
⇒ x² = 82296
⇒ x = √82296
⇒ x = 286.87
So, This number is not a perfect square number.
If we multiply by the number 82296 in the number 82296, we get;
⇒ 82296 × 82296
⇒ (82296)²
Thus, It become a perfect square number.
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Which is most needed in order for groupwork technology to succeed?
PLEASE HELP The quotient of seven more than three times a number m The number 27 less than n as an algebraic expression?
The algebraic expression is (7 + 3m)/27 < n
How to determine the number?The statement is given as:
"The quotient of seven more than three times a number m and the number 27 is less than n"
The numbers are represented as n and m
Quotient means divide
So, we have:
The quotient of seven more than three times a number m and the number 27 is represented as:
(7 + 3m)/27
The result is less than n.
So, we have:
(7 + 3m)/27 < n
Hence, the algebraic expression is (7 + 3m)/27 < n
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Solve f(-4) for f(x) = 7x - 4x
f(-4)= [?]
Enter
ternational Academy of Science. All Rights Reserved.
Answer:
-12
Step-by-step explanation:
What you have to do is plug -4 into the function as a puzzle. So, replace all x with -4.
f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12
f (-4) = 7x ( 1-4 ) - 4 (-4)
= -28 + 16
= -12
What is a equation example?
An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.
A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.
Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.
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Which of the following points is shown in the graph below?
Answer:
Step-by-step explanation:
Comment
Only the x is minus. You know this because if you rotate the x axis 90 degrees clockwise, the plus axis will be on your right and the minus part of the axis on your left.The other 2 (y and z) are positive.All answers give - 4 in their choices. You are not helped much by -4y is on your left right now. That is the plus direction so y = 5z is 6 units up, so it is positive.Answer (-4,5,6)
B
4, 5, 5, 6, 7, 8, 8,9
What is the range?
A group of 31 friends gets together to pay a sport. First, people must be divided into teams. Each team has to have exactly 3 players, and no one can be on more than one team. How many teams can they make?(It is possible that not everyone can be on a team)
Answer:
10 teams (1 remainder)
Step-by-step explanation:
if each team has 3 players and there are 30 friends, divide that and youll end up with 10 teams. you will also have 1 remaining player
Adrian's annual salary is $111,000. He is not eligible for a Roth IRA because he makes
too much money. His company offers a matching program that is 1:1 up to 3% of annual
salary. (do not include commas or dollar signs in your answers)
How much should he contribute to Roth IRAS?
If he is not eligible for Roth IRAs, then he cannot contribute to Roth IRAs. However, he can contribute $3,330 monthly under his company's Matching Program.
What is a Roth IRA?The Individual Retirement Account to which employees in the United States can contribute after-tax earnings is called the Roth IRA.
Under its governing principles, certain individuals whose annual income exceeds stipulated amounts are INELIGIBLE to contribute.
How do we arrive at $3,330?Recall that the question indicates that his company offers a matching program with a ratio 1:1 up to 3% of his annual salary.
Since his annual salary is $111, 000,
3% x 111,000 = 3,330.
This means that annually, the total matching contribution due to Adrian would be:
3,330 x 2 = 6, 660.
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Evaluate 15÷3·(-2) + |-10|
[tex]15 \div 3( - 2) + | - 10| \\ 5( - 2) + 10 \\ - 10 + 10 \\ 0[/tex]
Hope it helps
please give brainliest
Select the expressions whose value is 4.
0(-2)²
02(-2)
0-4÷2
0-41
Answer: The correct answer is A, [tex](-2)^{2}[/tex].
Step-by-step explanation:
A negative multiplied with another negative is a positive. Squaring is multiplying an integer by itself. Thus, it would look like -2×-2, which is equal to 4. I hope this helps!! :)
) Find the domain of definition
a) f(x)=3x-1/√1-5x
Answer:
(-∞, 1/5)
Step-by-step explanation:
[tex]f\left( x\right) =\frac{3x-1}{\sqrt{1-5x} }[/tex]
f is defined ,if and only if ,
1 - 5x > 0
⇔ 1 > 5x
⇔ 1/5 > x
⇔ x < 1/5
Kindly solve all the questions below .
I'll give the brainliest
(4)
1. 11.444 repeater
2. 0.58333 repeater
3. 6.7333 repeater
4. 27.5454 repeater (on both 5 and 4)
5. 1.482517482517 (482517 repeater)
6. 2.285714285714 (285714 repeater)
7. 7.5666 repeater
8. 60.60606060 (60 repeater)
(5)
1. 0.666 (repeater)
2. 0.3666 (repeater)
3. 1.1818181818 (18 repeater)
4. 0.418181818 (18 repeater)
5 more than n is the quotient of n and 4
Which of the following demonstrates how the 70 is calculated using the
combination pattem?
Answer:
A because it shows that the calculations are correct as well as combination pattem