Joy and Willa left $3 each for a tip on a $44 restaurant bill. They are sharing the bill. How much does each person owe??
The average value of a function f over the interval [−1,2] is −4, and the average value of f over the interval [2,7] is 8. What is the average value of f over the interval [−1,7] ?
The average value of a continuous function f(x) over an interval [a, b] is
[tex]\displaystyle f_{\mathrm{ave}[a,b]} = \frac1{b-a}\int_a^b f(x)\,dx[/tex]
We're given that
[tex]\displaystyle f_{\rm ave[-1,2]} = \frac13 \int_{-1}^2 f(x) \, dx = -4[/tex]
[tex]\displaystyle f_{\rm ave[2,7]} = \frac15 \int_2^7 f(x) \, dx = 8[/tex]
and we want to determine
[tex]\displaystyle f_{\rm ave[-1,7]} = \frac18 \int_{-1}^7 f(x) \, dx[/tex]
By the additive property of definite integration, we have
[tex]\displaystyle \int_{-1}^7 f(x) \, dx = \int_{-1}^2 f(x)\,dx + \int_2^7 f(x)\,dx[/tex]
so it follows that
[tex]\displaystyle f_{\rm ave[-1,7]} = \frac18 \left(\int_{-1}^2 f(x)\,dx + \int_2^7 f(x)\,dx\right)[/tex]
[tex]\displaystyle f_{\rm ave[-1,7]} = \frac18 \left(3\times(-4) + 5\times8\right)[/tex]
[tex]\displaystyle f_{\rm ave[-1,7]} = \boxed{\frac72}[/tex]
Solve for m
bm + h = 93
Answer:
m = 93 - h / b
Step-by-step explanation:
bm + h = 93
bm = 93 - h
m = 93 - h / b
Hope it helps ⚜
Answer:
[tex]bm + h = 93 \\ add \: h \: to \: both \: sides \\ bm + h + - h = 93 + - h \\ bm = - h + 93 \\step2 \: \: divide \: both \: sides \: by \: b \\ \frac{bm}{b } = \frac{ - h + 93}{b} \\ m = \frac{ - h + 93}{b} [/tex]
A $290 suit is marked down by 30%. Find the sale price.
Answer:
I believe the new price is 203.
Step-by-step explanation:
Describe the transformation for g(x) = -f(x) - 5.
A. reflection over the x-axis and a vertical translation down by 5 units
B. reflection over the y-axis and a vertical translation up by 5 units
C. reflection over the x-axis and a horizontal translation to the right by 5 units
D. reflection over the y-axis and a horizontal translation to the left by 5 units
Answer:
A) reflection over the x-axis and a vertical translation down by 5 units
Step-by-step explanation:
Making the output negative reflects the graph over the x-axissubtracting or adding a constant from/to the function translates it down/up (along the y-axis) by that many unitsWill mark brainlist please help
Answer:
Step-by-step explanation:
If a woman making $31,000 a year receives a cost-of-living increase of 2.6%, what will her new salary be?
HELPP 100 points
What is the value of the function y = 3x – 1 when x = 12
0 -8
0-4
O 2
o 6
Answer:
The answer is B -4
Step-by-step explanation:
Answer:
y=
Step-by-step explanation:
y = 3x - 1
y = 3(12) - 1
y = 36 - 1
y = 35
In the figure below, AD and EC intersect at point G, mAGB= 31°, and mAGE equal 71°
Answer: A
Step-by-step explanation:
Because angle EGC is as straight angel, angle BGC = 180 - 31 - 71 = 78
Help me find the equation of the line. Whoever answers will get Brainliest. (SERIOUS ANSWERS ONLY)
Answer:
Y= 9/10x - 1.2 (or 1.3)
Or - 1. 2 is 6/5
Thus, Y= 9/10x - 6/5
Hope this helps!
Evaluate 2( s + t )^3 - 6 when s = 3 and t = 2 The value of the expression is
Answer:
244
Step-by-step explanation:
Over the last three evenings, Ann received a total of 70 phone calls at the call center. The first evening, she received 6 more calls than the third evening. The second evening, she received 2 times as many calls as the third evening. How many phone calls did she receive each evening? Number of phone calls the first evening: Number of phone calls the second evening: Number of phone calls the third evening:
Let x represent the number of calls received on the second evening.
The number of calls received on the first evening is x - 10.
The number of calls received on the third evening is 2x.
The sum of calls received on the three evenings is (x - 10) + x + 2x, and this is equal to 50:
(x - 10) + x + 2x = 50
4x - 10 = 50
4x = 50 + 10
4x = 60
x = 60/4
x = 15
The number of calls received on each evening is then:
First evening: x - 10 = 15 - 10 = 5
Second evening: x = 15
Third evening: 2x = 2(15) = 30
Check: 5 + 15 + 30 = 60
differentiate between factors and prime factors use relavant examples in your explanations?
Answer:
The factors of a number are all of the numbers that will divide into that number with no remainder. The prime factors of a number are the prime numbers that must be multiplied together to give the number. For example: The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The prime factors of 30 are 2, 3, and 5.
brainliest for best answer
Answer:
Slope = -5/8
Step-by-step explanation:
Take 2 points from the graph where the line is. Point 1: (1 , 6). Point 2: (9 , 1).
We are going to use the formula for finding the slope of a line now.
y2 - y1/x2 - x1 = 1 - 6/9 - 1 = -5/8
Slope = -5/8
5 x 4\9 can you tell me the way to get the answer
Answer:
[tex]\frac{20}{9}[/tex] as an improper fraction or [tex]1\frac{2}{9}[/tex] as a mixed number
Step-by-step explanation:
[tex]5*\frac{4}{9}\\ \\\frac{5}{1}*\frac{4}{9}\\ \\\frac{5*4}{1*9}\\\\\frac{20}{9}\\ \\1\frac{2}{9}[/tex]
Find the volume of this cylinder
Please help solve these two equations
Answer:
5. (x,y) = (2.3)
Step-by-step explanation:
1/2x + 2 = x+1
x = 2
y = 2+1
y = 3
(x,y) + (2,3)
{3 = 1/2 x 2 + 2
{3 = 2 + 1
{3 = 3
{3 = 3
Answer:
3. no solution
5. (x, y) = (2, 3)
Step-by-step explanation:
3.-5x +y = 1
-10x +2y = -2
Multiply the first equation by -2 and add the second equation:
-2(-5x +y) +(-10x +2y) = -2(1) +(-2)
10x -2y -10x +2y = -2 -2 . . . . eliminate parentheses
0 = -4 . . . . . . . . . no variable values will make this true: NO SOLUTION
(The lines graph as parallel lines.)
__
5.y = 1/2x +2
y = x +1
Subtract the first equation from the second:
(y) -(y) = (x +1) -(1/2x +2)
0 = 1/2x -1
0 = x -2
2 = x
y = x +1 = 2 +1 = 3 . . . . use the second equation to find y
The solution is (x, y) = (2, 3).
What is the area of this trapezoid?
Enter your answer in the box.
units2
A rectangle with a length of 3 and a height of 8 has two right triangles on each side of it with short leg lengths of 7.
Answer:
80 squared units.
Step-by-step explanation:
7 × 8 = 56 u squared for the triangles
you don't need to divide by two because there are two triangles.
3 × 8 = 24 u squared for the rectangle
56 + 24 = 80 squared u
Brainliest Appreciated!
True or false analysis only involves identifying meaning and subject and predicate terms
Answer:
i would say the answer is true but I'm not completely sure this is the answer.
Answer:
TRUE
Step-by-step explanation:
Major League Baseball requires baseball to pass a test to measure their resiliency. Baseballs approved for use in Major League Baseball must have a COR or coefficient of restitution of 0.546+_ 0.032
Answer:
0.578
Step-by-step explanation:
0.578
Answer:
0.578
Step-by-step explanation:
I'm sorry if this is wrong
Find the first four terms of the sequence given by the following.
aₙ=43-3(n-1) n=1,2,3. . .
Given :-
The general term of a sequence is given by aₙ=43-3(n-1) .To Find :-
The first four terms of the sequence.Solution :-
The given expression is [tex] /[/tex]
→ aₙ=43-3(n-1)
where n > 0
Finding the first term :
Substituting n = 1 , we have ,
→ T1 = 43 - 3(1-1)
→ T1 = 43 - 3*0
→ T1 = 43 - 0 = 43
Finding the second term :
Substituting n = 2 , we have,
→ T2 = 43 -3(2-1)
→ T2 = 43 -3*1
→ T2 = 43 -3 = 40
Finding the third term :
Substituting n = 3 , we have,
→ T3 = 43 -3(3-1)
→ T3 = 43 -3*2
→ T3 = 43 -6 = 37
Finding the fourth term :
→ T4 = 43 -3(4-1)
→ T4 = 43 -3*3
→ T4 = 43-9 = 34
Hence the first four terms of the sequence are 43 , 40 , 37 and 34 .
I hope this helps . Let me know if you need further clarification .
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
4, 9, 14, ...
Answer:
Step-by-step explanation:
As we can see 4+5=9, 9+5=14
Help me plssssssssssss
Answer:
A. 23.1
B. 0.3
Step-by-step explanation:
When rounding to one decimal place, look at the next number, (in this case, in the hundredths column) if the number is 5 or above, round up and if it’s four or below, round down
Find the surface area of this rectangular prism. Be sure
2 cm
2 cm
9 cm
Answer: 80 cm^3
Step-by-step explanation:
I assume you mean that the sides of the rectangular prism are of lengths 2cm, 2cm, and 9 cm.
Surface area of a rectangular prism: 2(wl+hl+hw)
2((2*2)+(9*2)+(9*2))
=2(4+18+18)
=2(40)
=80cm^3
Hope this helped.
Point A (-5, -3) and point B (1,5) are located on a coordinate grid. Which measurement is closest to the distance between point J and point K in units?
Answer:
-2 ,1
Step-by-step explanation:
I think its -2, 1 because its in the middle
Please Factor -5x²+13x+6
Answer:
[tex](x-3)(-5x-2)[/tex]
or [tex]-(x-3)(5x+2)[/tex]
Step-by-step explanation:
quadratic equation format: [tex]a^2+b^2+c[/tex]
Therefore, for [tex]-5x^2+13x+6[/tex], a = -5, b = 13 and c = 6
Multiply the coefficient of [tex]x^2[/tex] ([tex]a[/tex]) by the constant term ([tex]c[/tex])
[tex]\implies -5 \times 6 = -30[/tex]
Find two numbers which have a product of -30 and a sum of [tex]b[/tex] (13)
Factors of 30: 1 and 30, 2 and 15, 3 and 10, 5 and 6
So -2 and 15 have a product of -30 and sum of 13.
Rewrite [tex]13x[/tex] as [tex]15x-2x[/tex] and substitute into the equation:
[tex]\implies -5x^2+15x-2x+6[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies-5x(x-3)-2(x-3)[/tex]
The bracket created should always be the same.
The two brackets have now been found. The first bracket is the common factor of (x - 3). The second bracket is the factorized terms outside of each bracket (-5x - 2).
[tex]\implies (x-3)(-5x-2)[/tex]
Additionally, we can write (-5x - 2) as -(5x + 2)
[tex]\implies -(x-3)(5x+2)[/tex]
Match the following to their correct classification
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
4x+20
4x+20>40
4x+20=40
The option " Inequality " (3 of 3) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
An expression can either be an equation or an inequality.
The correct classification of the terms are:
Expression; 4x+20Inequality: 4x+20>40Equation: 4x+20=40How to determine the correct classificationTo determine the correct classification, we make use of the following highlights
When an expression has the "=", then the expression is an equation.When an expression has any of the following sign ">, <, >=, <= or != ", then the expression is an inequality.When the expression is neither an equation nor an inequality, then it is just an expression.Hence, the correct classifications are:
Expression; 4x+20Inequality: 4x+20>40Equation: 4x+20=40Read more about equations and inequalities at:
https://brainly.com/question/22406619
Answer: the answer is Expression; 4x+20
Inequality: 4x+20>40
Equation: 4x+20=40
Step-by-step explanation:
took the test
Use the four-step definition of the derivative to find f'(x) if f(x) = −4x^3 −1.
f(x+h) =
f(x+h)-f(x) =
f(x+h)-f(x)/h =
f'(x) =
[tex]\stackrel{de finition \textit{ of a derivative as a limit}}{\lim\limits_{h\to 0}~\cfrac{f(x+h)-f(x)}{h}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[-4(x+h)^3-1]~~ - ~~[-4x^3-1]}{h} \\\\\\ \cfrac{[-4(x^3+3x^2h+3xh^2+h^3)-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{[-4x^3-12x^2h-12xh^2-4h^3-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{-4x^3-12x^2h-12xh^2-4h^3-1+4x^3+1}{h}\implies \cfrac{-12x^2h-12xh^2-4h^3}{h}[/tex]
[tex]\cfrac{h(-12x^2-12xh-4h^2)}{h}\implies -12x^2-12xh-4h^2 \\\\\\ \lim\limits_{h\to 0}~-12x^2-12xh-4h^2\implies \lim\limits_{h\to 0}~-12x^2-12x(0)-4(0)^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \lim\limits_{h\to 0}~-12x^2~\hfill[/tex]
Becky's brother forgot about the fees that his investment account was charging him! He is charged 2% off the annual rate of return as an account management fee. Including the fee, about how much longer will it take him to double his money?
The number of years it would take to double his money is 34.7 years.
How long would it take to double his money?
The formula that can be used to determine time is:
Number of years = In(FV/PV) / r
Where:
FV = future valuePV = present valuer = interest rateFV / PV = 2In2 / 0.02 = 34.7 years
To learn more about doubling time, please check: https://brainly.com/question/25770999
what is the area of the shaded triangle?
steps please
Answer:
area of shaded: 30 m²
Explanation:
Here triangle is inscribed in a rectangle.Rectangle area: Length * WidthTriangle area: (1/2) * base * heightThe triangle here is shaded.Steps:
Rectangle area: 6 * 10 = 60 m²
Triangle area: (1/2) * 6 * 10 = 30 m² .......this is the area of shaded.
Answer:
30m²
Step-by-step explanation:
Let's derive the area of a triangle
We know the formula for the area of a rectangle:
[tex]\text{A = l * w}[/tex]Here, we can see that the area of the triangle is the rectangle's are divided by 2, or half of the rectangle's area.
Here's the formula for the area of a triangle:
[tex]\text{A} = \frac{1}{2}\text{b * h}[/tex]B is the base, the same as the length
H is the height, the same as the width
Solve:
[tex]\text{A} = \frac{1}{2}\text{b * h}[/tex][tex]\text{A} = \frac{1}{2}(10 * 6)[/tex][tex]\text{A} = \frac12(60)[/tex][tex]\text{A} = 30\\[/tex]The units is m * m, or m²
Area = 30m²
-Chetan K