Answer:
y=2(x-2) +2
Step-by-step explanation:
35-40 evaluate the integral by interpreting it in terms of areas.
39. [tex]\int_{-4}^{3}\left|\frac{1}{2} x\right| d x[/tex]
The value of the definite integral corresponds to the total area of two triangles (see attached plot).
[tex]\displaystyle \int_{-4}^3 \left|\frac x2\right| \, dx = \dfrac12 \times 2 \times 4 + \dfrac12 \times 3 \times \dfrac32 = \boxed{\frac{25}4}[/tex]
19-42 evaluate the integral.
23. [tex]\int_{0}^{2}(2 x-3)\left(4 x^{2}+1\right) d x[/tex]
Expand the integrand:
[tex](2x - 3) (4x^2 + 1) = 8x^3 - 12x^2 + 2x - 3[/tex]
Then integrate using the power rule:
[tex]\displaystyle \int (8x^3-12x^2+2x-3) \, dx = 2x^4 - 4x^3 + x^2 - 3x + C[/tex]
By the fundamental theorem of calculus, the definite integral has a value of
[tex]\displaystyle \int_0^2 (2x-3)(4x^2+1) \, dx = \left(2x^4 - 4x^3 + x^2 - 3x\right)\bigg|_{x=2} - \left(2x^4 - 4x^3 + x^2 - 3x\right)\bigg|_{x=0}[/tex]
[tex]\displaystyle \int_0^2 (2x-3)(4x^2+1) \, dx = 32 - 32 + 4 - 6 = \boxed{-2}[/tex]
can someone help me here
NONSENSE=REPORT
topic: Circles and its Concept
Answer:
Step-by-step explanation:
Circumference of a circle: 2πrArea of a circle: πr²π = 3.14r (radius) = d/21. Circumference: 2(3.14)(4.2) = 26.38 in.
Area: πr² = 3.14(4.2)² = 55.39 in.²
2. Circumference: 2(3.14)(1) = 6.28 m.
Area: πr² = 3.14(1)² = 3.14 m.²
Hope this helps!
which expression is equivalent to 2^2 x 2/24
a. 2^-2
b.2^-1
c.2^6
d.2^7
Answer:
noneStep-by-step explanation:
which expression is equivalent to 2^2 x 2/24
a. 2^-2
b.2^-1
c.2^6
d.2^7
2^2 * 2/24 =
4 * 2/24 =
4 * 1/12 =
1/3
then
1/3 = 0.33
find equivalent
a) 2^-2 = 0.25
b) 2^-1 = 0.5
c) 2^6 = 64
d) 2^7 = 128
Julio says "If you subtract 16 from my number and multiply the difference by -3, the result is 69." What is Julio's number?
Julio's number is 3.
What is Algebra?
Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.
Let us consider the number is 'x'
Julio's number be,
-3(x-16)=69
x-16=-13
x= -13+16
x= 3
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The longest length of a sail on Jessica's sailboat is 12v40 feet long. Which number is equivalent to this length?
O 24140
O 4840
O 247/10
O 48V/10
Answer:48V/10
Step-by-step explanation:
I got it right from Khan Academy
You decide that you will only sell two different types of frozen treats in your
ice-cream cart. You use the following criteria to help you make your decision:
• You will purchase 550 frozen treats for your cart.
• You have a budget of $450.
• Your goal is to make a profit of at least $700.
Which two frozen treats will you sell in your ice-cream cart, and how many of
each treat will you purchase? Show that your combination of frozen treats
meets the criteria.
Based on the given scenario above, the purchase decision will be I will chose Ice cream bar fruit and frozen bar fruit.
What is Purchase decision?This is know to be the thought method or act that helps a consumer to identify a need, gather options, and choosing a given product and brand.
Note that Based on the given scenario above, the purchase decision will be I will chose Ice cream bar fruit and frozen bar fruit.
If I am to purchase 550 frozen treats, I will buy:
Ice cream bar fruit = 300
Frozen bar fruit = 250
Therefore, for Ice cream bar fruit , it will be = amount x cost price
300 x 0.85 = 255
For Frozen bar fruit = 250 x 0.50
= 125
Add up the total cost= 255 + 125
Total amount spent will be= 380
Therefore we can see that the total price spent falls within the budget allocated and so I will choose both Ice cream bar fruit and frozen bar fruit.
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What is the average rate of change of the function over the interval x = 0 to x = 4? f(x)=2x−13x 5 enter your answer, as a fraction, in the box.
The average rate of change of the function over the interval x = 0 to x = 4 is: 61/400.
What is the Average Rate of Change of a Function?Average rate of change = f(b) - f(a) / b - a
Given the function, f(x) = 2x - 1 / 3x + 5.
a = 0, f(a) = 2x - 1 / 3x + 5 = 2(0) - 1 / 3(0) + 5 = -1/5
b = 4, f(b) = 2x - 1 / 3x + 5 = 2(4) - 1 / 3(4) + 5 = 7/17
Average rate of change = 7/17 - (-1/5) / 4 - 0 = 61/400
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What is h(-8) for h(x) = x²
2
-x² +7x?
Answer:
8
Step-by-step explanation:
Re-write the equation:
h(x) = x² * 2 - x² -7x
If X is equal to -8, then we can re-write the equation as:
h(-8) = (-8)² * 2 - (-8)² - 7(-8)
Following P.E.M.D.A.S. we must first solve for the exponents:
h(-8) = (64) * 2 - (64) - 7(-8)
Then we need to solve the multiplication.
h(-8) = (128) - (64) - (-56)
Now, we solve for the addition/subraction.
h(-8) = (128) - (120)
Lastly...
128 - 120 = 8
This means that if h(-8), then H = 8
I think?
what is the absolute vale of |35|
Answer:
Absolute value of any number is positive. so the absolute value of (-35) is 35.
Step-by-step explanation:
Find the volume of this triangular prism. Be sure to include the correct unit in your answer. 7m 5m 9m? Thank u!!
These points are linear. Find the slope.
Answer:
8
Step-by-step explanation:
Concepts
The formula to find the slope of a line given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. These points represent the x- and y-coordinates of the points.
Application
To find the slope of these points, we need to take two points and use the aforementioned formula. Let's take (0, 8), and (1, 16).
Solution
[tex]\frac{(16)-(8)}{(1)-(0)}[/tex] [tex]\frac{8}{1}[/tex] [tex]8[/tex]Therefore, the slope is 8.
Answer:
slope = 8
Step-by-step explanation:
Take 2 points from the given table:
[tex]\textsf{let}\:(x_1,y_1)=(0,8)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(-1,0)[/tex]
Use the slope formula to find the slope:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-8}{-1-0}=\dfrac{-8}{-1}=8[/tex]
Which statements about the cone are true? check all that apply. the radius is double the diameter. the radius is 9 mm. the base area is calculated using the radius. the volume is one-third the volume of a cylinder with the same height and diameter. the volume of the cone is 297 pi millimeters cubed.
To solve this problem, we have to understand and establish some basic mathematical facts on a cone.
The answer to this question are option b and c only.
ConeThis is a solid figure that has the base of a circle and the top is made up round triangle.
The formula of volume of a cone is given as
[tex]v = \frac{1}{3}\pi r^2 h[/tex]
where;
r = radiush = heightIn the given question, the first fact given is if the radius doubles the diameter and that false.
[tex]diameter = 2 * radius[/tex]
If we have the value of the the radius, we can calculated the base area using area of a circle
[tex]area = \pi r^2[/tex]
The volume of a cone is actually one-third the volume of a cylinder
we can only calculate the volume of the cone is we have the value of the height of the cone.
The answer to this question are option b and c only.
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Answer:
B, C, D, E
Step-by-step explanation:
Got it wrong the first time.
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:1,024
Step-by-step explanation:
We will use the formula hint it gives:
[tex]\displaystyle {1^{st}\;term} * \text{common ratio}\,^{(\text{desired term -1})}[/tex]
[tex]-1 * -4^{6-1}[/tex]
[tex]-1 * -4^{5}[/tex]
[tex]-1*-1,024[/tex]
[tex]1,024[/tex]
The 6th term in the sequence is 1,024.
A cooler is filled with different juices. There are 6 bottles of juice:
1 orange juice, 2 apple juice, 2 cranberry juice, and 1 grape juice.
What is the probability of randomly choosing 1 orange juice and then 1 apple juice
without replacing the first juice?
Answer:
1/15
Step-by-step explanation:
Total = 6 bottles
1 orange and apple
Without replacement:
P(orange and apple) = 1/6 x 1/5 = 1/15
Answer: Probability = 1/15
Carl is wrapping present in the box shown. How much wrapping paper doe she need not including overlap
Answer:
164 [tex]in^{2}[/tex]
Step-by-step explanation:
We find the areas of all the faces
30 [tex]in^{2}[/tex]
30[tex]in^{2}[/tex]
40[tex]in^{2}[/tex]
40[tex]in^{2}[/tex]
12[tex]in^{2}[/tex]
12[tex]in^{2}[/tex]
add them all up to get 164[tex]in^{2}[/tex]
:)
what is 4x^2 -40-120 is equivalent to
Answer:
Step-by-step explanation:
4x^2-40-120
4x^2-160
4x^2=160
x^2=40
sqrt40=6.32
2. Every morning, Desiree walks around her pool to get some morning exercise. She doesn't remember
the width of the pool, but she knows that the length of the pool is three less than twice the width.
Her father tells her that when he built the border of the pool, it had a perimeter of 48 feet. What is
the width of the pool?
Determine the next two terms in the arithmetic sequence.
5, 11, 17, 23,
The sequence is add 6 so the answer is 29 and 35
Answer:
Next two will be 41, 47
Step-by-step explanation:
5+6= 11
11+6= 17
17+6= 23
23+6= 29
29+6= 35
35+6= 41
41+6= 47
Answer:
29 and 39
Step-by-step explanation:
216−−−√3 radical?? a little lost (Lol)
[tex]\sqrt[n]{3}[/tex] is 216−−−√3 radical: Yes because of the √
Meaning of RadicalA radical in mathematics can be defined as the square root of a number. It can also be said to be the opposite of exponent.
The symbol of a radical is √ also known as the square root.
Radicals are really important in mathematics as they help us find the nth term of any number.
We can conclude by saying that 216−−−√3 is a radical, because the radical sign is carried by 3.
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Pls find equation of parabola
Answer:
y = - 3x² + 6x + 9
Step-by-step explanation:
given the zeros of a parabola x = a , x = b , then the factors are
(x - a) , (x - b)
here the zeros are x = - 1 and x = 3 , then
factors are (x + 1) and (x - 3)
the equation of the parabola is then the product of the factors, that is
y = a(x + 1)(x - 3) ← a is a multiplier
to find a substitute the point (0, 9 ) into the equation
9 = a(0 + 1)(0 - 3) = a(1)(- 3) = - 3a ( divide both sides by - 3 )
- 3 = a
then equation is
y = - 3(x + 1)(x - 3) ← expand factors using FOIL
= - 3(x² - 2x - 3) ← distribute parenthesis by - 3
y = - 3x² + 6x + 9
You have a job that pays $25.00 for each day you show up, plus $19.00 per hour. Which expression shows the amount you make in one day if you work for h hours?
H E L P PLEASE ASAP
Answer:
19.00 x h + 25.00 =
What you make in a day if you work for h hours.
Step-by-step explanation:
You automatically make $25.00 when you show up.
So the equation is asking for how many hours. If you get $19 per hour
then it would be $19.00 x h (how many hours you worked) + $25.00.
Example:
If you worked for 5 hours and one day, then the equation would be
19.00 x 5= 95
95 + 25 (for showing up that day) = 120
So if you worked 5 hours for one day you would make 120
(This was just an example to further explain how the equation worked)
Hope this helped!
Have a great day!!
A person invests 8000 dollars in a bank. The bank pays 6.25% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 10800 dollars
Answer:
4.8 years
Step-by-step explanation:
10 800 = 8000 e^(i t) i = decimal interest per year t = years
10800/8000 = e^(.0625 t) ln both sides
.300 = .0625 t
t = 4.8 years
Solve for x: 2x² - 7x - 30 = 0
Answer:
x=-10
Step-by-step explanation:
2x²-7x=0+30
2x²-7x=30
4x-7x=30
-3x=30
x=-10
Answer:
Step-by-step explanation:
(2x + 5)(x - 6) = 0
2x + 5 = 0
x = -5/2
x - 6 = 0
x = 6
A recipe requires 1/4 cup of oil for every 2/3 cup of water. How much oil (in cups) is
needed per cup of water?
Answer:
3/8 cup of oil
Step-by-step explanation:
divide 1/4 by 2 to get how many are needed for 1/3 cup of water, and times 3 to find one cup of water.
A box contains 6 black crayons, 4 blue crayons, 5 red crayons,3 yellow crayons, and 2 white crayons. One crayon is chosen at random. Write each probability as a fraction, a percent, and a decimal
The probability of getting black crayons is 0.3, blue crayons 0.2, red crayons 0.25, yellow crayons 0.15, and white crayons 0.1.
What is the probability?
Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
A box contains 6 black crayons, 4 blue crayons, 5 red crayons,3 yellow crayons, and 2 white crayons.
One crayon is chosen at random.
The total number of crayons = 20
The probability of getting black crayons
= 6/20
= 0.3
The probability of getting blue crayons
= 4/20
= 0.2
The probability of getting red crayons
= 5/20
= 0.25
The probability of getting yellow crayons
= 3/20
= 0.15
The probability of getting white crayons
= 2/20
= 0.1
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José tiene una tabla de: (x² -4x + 4) cm de largo y (x+4) cm de ancho ¿Cuál es el área de la tabla?
Answer:
x³ - 12x + 16
Step-by-step explanation:
(x² -4x + 4) × (x+4) =
= x³ + 4x² - 4x² - 16x + 4x + 16
= x³ - 12x + 16
POINTS!!! Answer both 3 and 4 PLEASE
Answer:
yes not function because 1 is repeated
Which two numbers on the right will you use to calculate 3 x 9?
Answer:
3×9=27 the two numbers right to use is 2and7
Nan wrote each letter in the word ILLINOIS on a separate slip of paper. She put
the slips in a bag. What is the probability of her drawing a slip that is labeled
with a vowel?
A 1/8
B. 218
C. 3/8
D. 4/8
E. 5/8
Answer:
D. 4/8
Step-by-step explanation:
To find probability, you simply divide what you are looking for over the total. In the word, ILLINOIS, you have 4 vowels, and 8 letters total, so the probability of finding a vowel would be 4/8.