Answer:
x³/3 - x² + C
Step-by-step explanation:
∫ x² - 2x + 8 dx
= x³/3 - x² + C
when finding the derivative, you need to take the power plus 1 then divide by the power x^(2+1)/(2+1) = x³/3
the same goes for 2x and the 2/2 is 1 so you would get x²
since you are finding the derivative for x and 8 is a constant it equals zero.
when integrating you always need to add C at the end and C stands for a constant. The only time you do not add C is when the integral goes from one constant to the next.
Example: [tex]\int\limits^1_0 {x^2 - 3x +9} \, dx[/tex] like this...
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
An ellipse has a vertex at (0, −7), a co-vertex at (4, 0), and a center at the origin. Which is the equation of the ellipse in standard form?
Answer:
As Per Provided Information
An ellipse has a vertex at (0, −7), a co-vertex at (4, 0), and a center at the origin (0,0) .
We have been asked to find the equation of the ellipse in standard form .
As we know the standard equation of an ellipse with centre at the origin (0,0). Since its vertex is on y-axis
[tex] \underline\purple{\boxed{\bf \: \dfrac{ {y}^{2} }{ {a}^{2} } \: + \: \dfrac{ {x}^{2} }{ {b}^{2} } = \: 1}}[/tex]
where,
a = -7 b = 4Substituting these values in the above equation and let's solve it
[tex] \qquad\sf \longrightarrow \: \dfrac{ {y}^{2} }{ {( - 7)}^{2} } \: + \dfrac{ {x}^{2} }{ {(4)}^{2} } = 1 \\ \\ \\ \qquad\sf \longrightarrow \: \dfrac{ {y}^{2} }{49} \: + \frac{ {x}^{2} }{16} = 1 \\ \\ \\ \qquad\sf \longrightarrow \: \: \dfrac{ {x}^{2} }{16} \: + \dfrac{ {y}^{2} }{49} = 1[/tex]
Therefore,
Required standard equation is x²/16 + y²/16 = 1So, your answer is 2nd Picture.
Graph the circle (x+5)^2+(y+2)^2=4
(x+5)² + (y+2)² = 4
(x - x0)² + (y - y0)² = r²
with circle center point (x0 ; y0) and r for circle radius
so you have to place the point (- 5 ; - 2) and graph the circle with r = 2
Find the vertex of this parabola:
y = -x2 + 6x – 15
[tex]y = - x {}^{2} + 6x - 15[/tex]
[tex]y {}^{ \gamma } = - 2x + 6[/tex]
[tex]y {}^{ \gamma } = 0[/tex]
[tex] - 2x + 6 = 0[/tex]
[tex] - 2x = - 6[/tex]
[tex]2x = 6[/tex]
[tex]x = 3[/tex]
Substitute x=3 in y=-x²+6x-15[tex]y = - (3) {}^{2} + 6(3) - 15[/tex]
[tex]y = - 9 + 18 - 15[/tex]
[tex]y = - 9 + 3[/tex]
[tex]y = - 6[/tex]
Vertex: (3,-6)
[tex]==============================[/tex]
In order to find the vertex of a parabola, we use the following formula:
[tex]\mathfrak{\displaystyle\frac{-b}{2a} }[/tex]
Please remember that a parabola looks like this:
[tex]\tt{y=ax^2+bx+c}[/tex]
Now you know what a and b stand for.
In this case, a = -1, and b is 6:
[tex]\mathfrak{\displaystyle\frac{-6}{2(-1)} }[/tex]
Simplify:
[tex]\mathfrak{\displaystyle\frac{-6}{-2}}[/tex]
[tex]\mathfrak{3}\\=======================================[/tex]
Notes:Hope everything is clear.Let me know if you have any questions!Enjoy your day!Always remember: Knowledge is Power :)Answered by[tex]\mathcal{DiAmOnD}\\\tt{A~Creative~Helper}}}}[/tex]
Help!!!
Rationalize the denominator of;
[tex]1) \frac{1}{ \sqrt{7} } [/tex]
[tex]2) \frac{2}{ \sqrt{3} - \sqrt{2} } [/tex]
[tex]3) \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } [/tex]
Answer:
see below for explanation:-
Step-by-step explanation:
#1
[tex] \displaystyle{ \frac{1}{ \sqrt{7} } }[/tex]
[tex]\displaystyle{ \frac{1}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{7} }{7} }[/tex]
#2
[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} }{( \sqrt{3} {)}^{2} - ( \sqrt{ 2 } {)}^{2} } }[/tex]
[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} ) }{3 - 2} }[/tex]
[tex]\displaystyle{2( \sqrt{3} + \sqrt{2} )}[/tex]
#3
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{ 9 + 2 \sqrt{9 \times 2} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 6 \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{3 \sqrt{6} - 2 \sqrt{12} + 3 \sqrt{3} - 2 \sqrt{6} }{3( {3}^{2} - (2 \sqrt{2} {)}^{2} ) } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} - 4 \sqrt{3} + 3 \sqrt{3} }{3(9 - 8)} }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} - \sqrt{3} }{3} }[/tex]
Which of the following number sentences is an example of the associative property? Select all that apply.
[tex](1\frac{2}{5}*3\frac{1}{2} )*4=1\frac{2}{5} (3\frac{1}{2} *4)[/tex]
[tex]2.5*(1.8+6.3)=(2.5*1.8)+(2.5*6.3)[/tex]
10(4.6 × 3) = (10 × 4.6) × 3
6.3 × 1 = 6.3
Associative property:-
a+(b+c)=(a+b)+cLets check one by one
#1
Here the rule is
(ab)c=a(bc)Hence Yes associative property
#2
Here the rule is
a(b+c)=ab+acHence no it's distributive property
#3
a(bc)=(ab)cYes
#4
ab=baNo
Associative property meaning rearranging the parentheses in an expression which will not change the result.
✔A)
[tex]\rightarrow \sf (1\dfrac{2}{5} \ x \ 3\dfrac{1}{2} ) \ x \ 4 = 1\dfrac{2}{5} (3\dfrac{1}{2} \ x \ 4 )[/tex]
[tex]\rightarrow \sf \dfrac{98}{5} = \dfrac{98}{5}[/tex]
This uses associate property as it is rearranged in a different way and result same.
B)
[tex]\rightarrow \sf 2.5 \ x \ (1.8 +6.3) = (2.5 \ x \ 1.8)+(2.5 \ x \ 6.3 )[/tex]
This property is called distributive property. a(b + c) = a(b) + a(c)
✔C)
[tex]\sf \rightarrow 10(4.6 \ x \ 3) = (10 \ x \ 4.6) \ x \ 3[/tex]
[tex]\sf \rightarrow 138 = 138[/tex]
associate property as the following is rearranged inside the parentheses
D)
[tex]\rightarrow \sf 6.3 \ x \ 1 = 6.3[/tex]
This does not fall under any method or else multiplicative identity property.
What is the initial value & rate of change of the table
Weeks. Dollars
0. 10
2 20
4 30
6 40
Answer:
y = 10
rate of change = 5
Step-by-step explanation:
The initial value is the beginning output value, i.e. the y-value when x = 0
Therefore, the initial value is y = 10
rate of change = change in y ÷ change in x
⇒ rate of change = (40 - 30) ÷ (6 - 4)
= 10 ÷ 2
= 5
take two points : (0, 10), (2, 20)
rate of change:
[tex]\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\rightarrow \sf \dfrac{20-10}{2-0}[/tex]
[tex]\rightarrow \sf 5[/tex]
equation :
y - 10 = 5 ( x - 0 )
y = 5(x) + 10
so initial value:
y = 5(0) + 10
y = 10
Rey and Adrian have 100 marbles altogether.Rey has 4 times as many as marbles as Adrian.How many marbles does each boy have?
Answer:
100
Step-by-step explanation:
4x of 100 is 400
Cuz Why Not Give 5 start + heart please cuz why not?
6 cm
8 cm
13 cm
5.3 cm
-
What is the surface area?
Answer:
The surface area of what
pls try to send the image.
How much will the storage container
hold?
7 ft.
5 ft.
10 ft.
10 ft.
3 ft.
1 ft.
4 ft.
4 ft.
Answer:
The container will hold 190 ft^3 of volume of substance.
if the question means it.
These points are linear.
Find the slope.
X 3 4 5 6 7
y 0 9 18 27 36
slope = [?]
Kristy bought some rolls of wrapping paper and 2 bags of bows for less then $10. Each roll of wrapping paper and each bag of bows cost $1.50. Which inequality can be used to find w, the number of rolls of wrapping paper Kristy bought?
Answer:
[tex]w < 4 \frac{2}{3}[/tex]
Step-by-step explanation:
The inequality symbol for 'less than' is '<'.
Let's relate the cost and the number of each item bought together with an equation.
Total cost
= (number of rolls)(cost of each roll) +(number of bags)(cost per bag of bows)
= w(1.50) +2(1.50)
= 1.5w +3
Now, we can form the inequality.
Since the total cost is less than $10,
1.5w +3< 10
Subtract 3 from both sides:
1.5w < 10 -3
1.5w < 7
Divide both sides by 1.5:
[tex]w < 7 \div \frac{3}{2} [/tex]
[tex]w < 7 \times \frac{2}{3} [/tex]
[tex]w < \frac{14}{3} [/tex]
[tex]\textcolor{red}{w < 4 \frac{2}{3} }[/tex]
If 35% of a number is 56 and 25% of the same number is 40 find 60% of that number
35%= 56
100%= 56÷35×100
100%= 160
25%= 40
100%= 40÷25×100
100%= 160
60%= 160÷100×60
60%= 96
Is the table a linear or exponential function?
The table represents linear because the x represent the exponential functions
R\ {0}→→ Ris defined by Jff: 1 f(x)=x³-1/x³-1then show that 2 f(x) + f(1/x)=0.
[tex]\orange\bigstar \bold{ solution}[/tex]
[tex]\bold{f(x) = x³ - \frac{1}{x³ } }[/tex]
[tex]\bold{f ( \frac{1}{x} )= \frac{1}{x³} -x³ } [/tex]
[tex]\bold{f (x) + f (\frac{1}{x}) = (x³- \frac{1}{x³} ) + ( \frac{1}{x³} -x³)}[/tex]
[tex]\bold{ = 0 }[/tex]
what is the area of the triangle
Answer:
6
Step-by-step explanation:
A=(bh)/2
a=(4*3)/2
a=12/2
a=6
Answer: 12 units 2
Step-by-step explanation:base times hight
help I'm confused like always
Answer:
negative
Step-by-step explanation:
The good part about this question is you don't have to know the actual values of b or c, otherwise, I would be stumped too.
Given:
b is within 0 -> 1 b is positive
c is within -1 -> -2, c is negative
[tex]\frac{b}{c}[/tex] = b/c. When you have a fraction and one numerator is positive while the denominator is negative (or visa-versa, numerator is negative and denominator is positive), then the answer will ALWAYS be negative
so +b/-c = negative result
A college is building a new basketball court that is 88 feet long and 40 feet wide, but the wood for the court comes only in 8-meter planks that are 10 centimeters wide. How many planks are needed to surface the court?
Answer:
2816
Step-by-step explanation:
Cm to m is divide by 100
10 / 100 = 0.1.
0.1 x 8 = 0.8
40 x 88 = 3520
3520 / 0.8 = 2816
Perform the indicated operation & simplify.
[tex](8-15i) +(11+24i) = 19+9i\\\\(8-15i)-(11+24i)=-3-39i=-3(1+13i)[/tex]
a retail owner can but a certain clock at an average price of $53 per clock and sell them for an average price of $84 per clock. his fixed costs are $8000 per month and his variable cost is $5 per clock. (A) how many clocks must he sell each month to break even? (B) how many clocks must he sell to have a profit of $3000?
Answer:
(A) 308 clocks
(B) 423 clocks
Step-by-step explanation:
The contribution margin is the amount by which the selling price of the clock exceeds the cost of the clock. The contribution margin is used to figure the break-even point, and the amount of profit from sales.
contribution margin = selling price - variable cost - purchase price
contribution margin = $84 -5 -53 = $26
__
(A)To break even, the contribution margin from 'b' clocks must equal or exceed the owner's fixed cost:
26b ≥ 8000
b ≥ 8000/26
b ≥ 307.7
The owner must sell 308 clocks each month to break even.
__
(B)To make a profit of $3000, the owner must sell enough clocks to cover the $8000 fixed cost and contribute an additional $3000. That is, the total contribution margin from selling p clocks must be about $3000+8000 = $11000.
26p ≈ 11000
p ≈ 11000/26 ≈ 423.08
The owner must sell about 423 clocks each month to earn a profit of about $3000.
__
Additional comment
Selling 423 clocks will yield a profit of $2998.
If the distance from C to C’ is 8 and the scale factor is 5. What is the distance from A to C?
A. 8/5
B. 5/8
C. 10
D. 2
The circle graph shows how Lila spent her after-school time during the month of October.
Part A
If Lila spent a total of 92 hours on these activities in the month of October. How much time did she spent at Yoga?
Using proportions, it is found that she spent 25.76 hours at Yoga.
What is a proportion?A proportion is a fraction of a total amount.
Researching the problem on the internet, it is found that the circle graph shows that she spent 28% of her time of 92 hours on yoga, hence:
h = 0.28 x 92 = 25.76.
Hence, she spent 25.76 hours at Yoga.
More can be learned about proportions at https://brainly.com/question/24372153
I THINK ITS C BUT PLSS TELL ME IF IM RIGHT
Use a number line to find the value of:
eight tenths plus one eighth equals
A. eight tenths
B. one tenth
C. nine tenths
D. seven tenths
Answer:
it is .925 which is very close to 9/10 so C would be correct
Step-by-step explanation:
Answer:
0.925 so I would pick option C.
What does 5/x = 7/x+2 equal?
Solve by cross multiplying.
(5 over x and 7 over x+2)
Answer:
I have no idea ask 567 9922 mathe teacher
Hey there!
[tex] \rm{\frac{5}{x} = \frac{7}{x + 2} }[/tex]
Solve:--
[tex] \sf\rightarrow \: (7)(x) = (5)(x + 2)[/tex]
[tex] \sf\rightarrow \: 7x = 5(x + 2)[/tex]
[tex] \sf\rightarrow \: 7x = 5x + 10[/tex]
[tex] \sf\rightarrow \: 7x - 5x= 5x + 10 - 5x[/tex]
[tex] \sf\rightarrow \: 2x= 10 [/tex]
[tex] \sf\rightarrow \: \frac{ 2x}{2}= \frac{10 }{2}[/tex]
[tex] \sf\rightarrow \: x= 5[/tex]
~Done~
416
Chapter 7 Graphing and Functions
16. 2y - 5 = 0
ху
Answer:
y=2
Step-by-step explanation:
add 5 to 0 then divide 5 with 2
find the measure of angles 2, 3, and 4. input the measures then click done. i-ready
please help i missed a day of class i cant figure this out
Answer:
m∠2 = 95°
m∠3 = 85°
m∠4 = 95°
Step-by-step explanation:
Vertical Angle Theorem:
When two straight lines intersect, the opposite vertical angles formed are always equal (congruent) to each other.
Therefore,
m∠3 = 85°
m∠2 = m∠4
Linear pair:
Two adjacent angles which, when combined, form a line, so the sum of a linear pair is 180°.
Therefore,
85° + m∠2 = 180°
m∠3 + m∠4 = 180°
If 85° + m∠2 = 180°
⇒ m∠2 = 180° - 85°
⇒ m∠2 = 95°
As m∠2 = m∠4 then m∠4 = 95°
Inez bought a shipping container at a packing store
Answer: ok? whats the question
Step-by-step explanation:
Answer:
I think u forgot to mention the question?
Step-by-step explanation:
What is the volume of a rectangular prism that is 4 ft. by 12 ft. by 6 ft.? Question 21 options: 324 ft.³ 205 ft.³ 288 ft.³ 315 ft.³
Answer:
288 ft³
Step-by-step explanation:
The formula to find the volume of a rectangular prism is :
Volume = length × width × height
Let us find it now.
Volume = 4 ft × 12 ft × 6 ft
Volume = 48 ft² × 6 ft
Volume = 288 ft³
What is the value of the
expression? 1 7/8 - 6/4
Alice is making bracelets to sell. She plans to put 12 beads on each bracelet. Beads are sold in packages of 20.
#1. What is the least number of packages she can buy to make bracelets and have no beads left over?
#2 If each package of beads costs $5.50, how much will the beads cost for her project?
Show and Explain your work
Hint: the “T” Method works well for show and explain. Make sure you have all of the details explained. If someone only read your explanation they should know… what the question is, all of the steps needed to answer the question and what your final answer is.
Answer:
question 1 is 60 beads and question 2 is 16 dollars and 50 cents.
Step-by-step explanation:
for question 1 the are asking for the lowest common denomonator (60)
for question 2 you devide 60/20 and multiply by 5.50
3 x 5.50 = 16.5$
In the United States, 40% of the population have brown eyes (based on data from Dr. P. Sorita Soni at Indiana University). If 14 people are randomly selected, find the probability that at least 12of them have brown eyes.
Answer:
0.0006087 (4 sf)
Step-by-step explanation:
Binomial distribution: X ~ B(n, p)
where n is the number of trials and p is the probability of success
Let the random variable X be the number of people with brown eyes
n = 14
p = 40% = 0.4
Therefore, X ~ B(14, 0.4)
P(X ≥ 12) = 1 - P(X ≤ 11)
= 1 - 0.9993913226...
= 0.000608677...