Answer:
82.8
Step-by-step explanation:
In the above question, we are given the following information:
The equation for the line of best fit is given as y = -1.4x + 117.8, where
x is the "age in years"
y is the "typing speed. If you are 25 years of age, what is your typing speed?
This is calculated as:
y = -1.4x + 117.8
x = 25 years
y = -1.4(25) + 117.8
y = -35 + 117.8
y = 82.8
Hence, If you are 25 years of age, what is your typing speed is 82.8
Select the correct answer. What is[tex]\sqrt{192}[/tex] in simplest form? A.32√3 B.3√8 C.8√3 D. 2√48
Answer:
C. 8√3
Step-by-step explanation:
Please mark me as brainlest!
Thanks!
48√2 in the simplest form of the expression √192.
Option D is the correct answer.
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.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We can simplify the √192 by factoring it into its prime factors:
192 = 2 × 2 × 2 × 2 × 2 × 3 × 3
Then, we can group the prime factors into pairs of two:
192 = (2 × 2) × (2 × 2) × (2 × 3) × 3
Simplifying each pair of factors under the square root gives:
[tex]\sqrt{192} = \sqrt{(2\times2)}\sqrt{(2\times2)}\sqrt{(2\times3)}\sqrt{3}\\= 4\times4\times\sqrt{6}\sqrt{3} \\= 16\sqrt{6}\sqrt{3}[/tex]
Finally, we can simplify the expression by multiplying the coefficients and combining the square roots:
[tex]16\sqrt{6}\sqrt{3} \\= 16\sqrt{18} = 16\sqrt{2\times3\times3} \\= 16\times3\sqrt{2} \\= 48\sqrt{2}[/tex]
Therefore,
48√2 in the simplest form of the expression √192.
Learn more about expressions here:
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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........
HELPPP THIS IS TIMEDD I NEED A STEO BY STEPP
Answer:
Why do you need a step by step
Step-by-step explanation:
Help. Examine the figure below. Determine which of the following angle measures are correct PICK up 2 answers
Answer:
RPQ = 30 and QRP = 75
Step-by-step explanation:
First we need to find "x".
Since we know that all the angles of a triangle must equal 180 and we know that angles PQR and QRP are the same (Due to the fact that two of the lengths of the triangle are the same) we can set up an equation.
x + (2x + 15) + (2x + 15) = 180
1. we can drop the parentheses (when there is a + in front of an expression in parentheses, the expression remains the same)
x + 2x + 15 + 2x + 15 = 180
2. We can collect the like terms to simplify the equation. (x and 2x and 2x combine to equal 5x) (Remember that there is a hidden 1 behind an "x" without a number next to it)
(the two 15's add together to make 30)
This leaves us with this equation
5x + 30 = 180
3. Now we suptract the constant from 180 (The constant is 30)
5x = 180 - 30
5x = 150
4. Now we devide both sides by 5
x = 30
Next we can find all of the angles
PRQ = (2x + 15)
1. PRQ = (2(30) + 15)
2. PRQ = (60 + 15)
3. PRQ = 75
RQP = (2x + 15)
1. RQP = (2(30) + 15)
2. RQP = (60 + 15)
3. RQP = 75
RPQ = x
RPQ = 30
Two bottle rockets are simultaneously launched on parallel paths, from 5 feet apart on level ground. After 0.1 second, the rockets are at the same height.
Which theorem or definition can you use to show that the rockets are still 5 feet apart 0.1 second after launch?
Help asap please it's due today :)
Answer:
The definition of parallel lines are lines that have a constant minimum distance between them at any given point along the lines, such that the lines are the same distance apart all through
Therefore, given that we have;
1) The path of the two bottle rockets are parallel,
2) The initial distance between the two rocket on level ground = 5 feet = The perpendicular (shortest) distance between the two rockets
3) The shortest distance between the rockets having the same height moving on parallel path will be constant = 5 feet
4) The height of the two rockets after 0.1 second = Constant = 5 feet
5) Therefore, by the definition of parallel lines, distance between the two rockets which are at the same height after 0.1 second will still be 5 feet
Step-by-step explanation:
There were 640 gallons of water in a 1,600-gallon pool. Water is being pumped into the pool at a rate of 320 gallons per hour.
If t stands for hours and the pool is being filled using the equation: 1600=320t+640, how many hours will it take to fill the pool?
Answer:
4
Step-by-step explanation:
do 320 +320 untill you get to 1,600
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x? On a coordinate plane, a circle is centered around (0, 0).
Answer:
Where are the statements to choose from??
Answer:
The graph is a function of x because the line y = 5 does not intersect the graph
Step-by-step explanation:
3 times the sum of 4 and 9:
I’m confused can anybody help me I forgot how to do it?
Answer:
39
Step-by-step explanation:
4 + 9 = 13
13 × 3 = 39
if you need more help let me know
Answer:
39 sorry if im worng
Step-by-step explanation:
3*(4+9)
WILL MARK BRANLIEST IF RIGHT
Answer:
its 3 and 4
Step-by-step explanation:
Answer:
2 and 3
Step-by-step explanation:
You are standing at the edge of a cliff. You look down with an angle of depression of 20 degrees and see a a dog at the bottom that is 130 feet away from where you're standing. What is the height of the cliff? Round your answer to the nearest tenth, and round only once.
Answer:
47.3feet
Step-by-step explanation:
The set up will give a right angled triangle.
The distance of the dog away from the cliff = 130 feet = adjacent side
Angle of depression = 20°
Height of the cliff = Opposite = x
Using the SOH, CAH, TOA trigonometry identity;
According to TOA;
tan theta = opposite/adjacent
tan 20 = x/130
Cross multiply;
x = 130tan20
x = 130(0.3639)
x = 47.3 feet
Hence the height of the cliff to the nearest tenth is 47.3feet
please please hurry ! What is the length of side X?
Answer:
its eleven
Step-by-step explanation:
it just is....
Answer:
11
Step-by-step explanation:
They are proportional, so since side RS is 3 and MN is 6, we know that Triangle MNO is twice that size, so all of the side lengths will be twice that size. So ST being 5.5 means that the same side in Triangle MNO will be twice that amount, and 5.5 * 2 = 11.
Pllzzzz help it’s an exam !!!! A side of the triangle below has been extended to form an exterior angle of 125 . Find the value of x
Answer:
i think it is 105
Step-by-step explanation:
180-125=55
180-(55+25)=105
*second 180 is triangle's total interior angle
2. Are these two ratios equivalent? 8/5, 24/20
Answer: No
Step-by-step explanation:
I took a test and this answer was correct.
Easy points if u know it
Answer:
True
Step-by-step explanation:
5x + 2 = 17
Subtract 2 from both sides
5x = 15
Divide both sides by 5
x = 3
Plug this number into the next equation and see if it is true
10x + 4 = 34
10(3) + 4 = 34
30 + 4 = 34
34 = 34
This is a true equation, so the the answer is true.
Answer:
True
Step-by-step explanation:
⇒ This is true because the whole equation 10x + 4 = 34 is 2 times more than the other equation 5x + 2 = 17.
⇒ You can see that by multiplying the whole equation 5x + 2 = 17 by 2:
2(5x + 2 = 17)
⇒ To get:
10x + 4 = 34
So both equations are equivalent, which means that the answer is true.
Hope this helps! :)
Given f(x)= 10-2x, find f(7).
o -4
O 3
o 7
O 56
The value of f(7) is -4 for the function f(x) = 10-2x. option A is correct.-
The given function is f(x)=10-2x.
In the equation, the x represents the variable.
We have to find the value of f(7).
To find the value of f(7), we need to replace x as the value 7.
Plug in x as 7 in the function:
f(7)=10-2(7)
Solve the above equation:
f(7)=10-14
When 14 is subtracted from 10, we get -4.
f(7)=-4
Hence, the value of f(7) is -4 for the function f(x)= 10-2x.
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The mean score on a physics test was 75 points. Amy’s score was 67 points, which was 2 standard deviations below the mean. What is the variance of the data set?
Answer:
D.16
Step-by-step explanation:
took the Unit test 100%
Answer:
D
Step-by-step explanation:
What is the unit rate for meters per second if a car travels 374 meters in 17 seconds?
Answer:
22meter per second
Step-by-step explanation:
374/17=22
Answer:
Could I have branliest please and heart answer is below <>
Step-by-step explanation:
22
374meters. 17
(/). divided by (/)
17seconds 17
Equals 22 meters per second
PLEASEEEEE HELPPPPP THIS IS ALGEBRA 1
Raise m to the 5th power, then multiply 8 by the result
Answer:
8m⁵
Step-by-step explanation:
m to the 5th power = m × m × m × m × m
= m⁵
Then multiplied by 8 = 8 × m⁵
= 8m⁵
Therefore, m to the 5th power multiplied by 8 will be represented by 8m⁵.
George places $5,000 into an account that earns a simple interest of 4.3%. John places $5,500 into an account that earns 4%. Who has earned the most interest at the end of 6 years?
Answer/Step-by-step explanation:
George:
4.3% ÷ 100 = 0.043
0.043 × 5000 = 215
John:
4% ÷ 100 = 0.04
0.04 × 5500 = 220
End of 6 years:
George: 215 × 6 = 1290
John: 220 × 6 = 1320
John has earned the most interest at the end of 6yrs. $1320
Please help due IN MY CLASS TODAY
Answer:
A. 3,4. E. Origin or 0,0 D. 6,-3
C. -2,-4 B. -3, 2
Step-by-step explanation:
Just go from x to y and I did this last year :p
What is the equation of a line that its parallel to -3x+4y=4 and passes through the point (4,0)?
Enter your answer in the box.
Answer:
y=3/4x-3
Step-by-step explanation:
Okay so to be parallel to an equation of another line, the line must have the same slope but a different y-intercept. First, you need to find the slope of the equation -3x+4y=4. The equation must be in y=mx+b format, so you first move -3x to the right by adding it on both sides, leaving you with 4y=3x+4. Next, you divide 4y by 4 in order to isolate y and do that on the other side. Now, you have y=3/4x+1.
To find the equation of the new line, you must put the point and slope into point slope form: y-y1=m(x-x1). In the point (4, 0), 4 would be x1 and 0 would be y1. so, the new equation is y-0=3/4 (x-4). now, distrubute the 3/4, leaving you with y=3/4x-3. This is correct since the slope remains the same in both equations with a different y-intercept. To check deeper, you could place point (4, 0) on a graph and then rise 3, run 4 until you get the line :) hope this helps
It is given that the lengths of two sides of a triangle are both 7 and the length of the remaining side is an integer. Find the maximum possible and the minimum possible perimeters of the triangle.
Answer:
Have you tried |-7|?
Step-by-step explanation:
Each interior angle of a regular polygon with 20 sides is 2° more than each interior angle of a regular polygon with n sides. Calculate the value of n. Help me please hurry any math genius:(
Answer:
400
Step-by step explanation:
The sides of the regular polygon is 20 and more than 2 so you divide the two number up to get 10 and then also you multiply all of them up together which is 400
what’s the answer to this question ?????????????
Answer is is 2 .........
How many terms are in this expression ?-3x + 7y - 6 *
Answer:
3 terms in the expression
Two complementary angles have a difference of 22 degrees. What are the two angles?
plz its due in 20 min
Answer:
If two angles sum is equal to 90° and makes right angle called = complementary angle...☺️✌️
Above sum solution....
one angle =x
other angle =y
According to question
x+y= 90°......(1)
x-y=22°......(2)
from one and two ....by eliminating method...
2y=68
y=68/2
y=34
put y in equation 1
x+y=90°
x+34=90°
x=90°-34
x= 56...
To verify add both
sum = 90°
Hence ..verified...
Step-by-step explanation:
hope its helps u...☺️✌️✌️
Answer:
13 degrees
Step-by-step explanation:
Help!!!!!!!!!!!!!!!!!!!!
Answer:
500w + 25 = 200
Step-by-step explanation:
"He withdraws $25 per week..." <------
If f(x)= x+4/x, g(x) = x-2, and h(x)= 4x-1, what is (fohog)
Answer:The answer is d (fohog)= 4x-5/4x-9
Step-by-step explanation:
2x + 6 = 10 is an example of
A) Algebraic Inequality
B) Algebraic Expression
C) Verbal Expression
D) Algebraic Equation
2x + 6 = 10 is an example of Algebraic Equation
Answer:
D is the answer for the question
PLEASE HELP
9 increased by the product of 4 and v
Answer:
4v + 9 or 9 + 4v
Step-by-step explanation:
increased means plus
the product of is multiplication
im too tired to explain annything else
gn bro