At 2:00pm a car's speedometer reads 20mph, and at 2:10pm it reads 30mph.
Use the Mean Value Theorem to find an acceleration the car must achieve.
Answer( in mi/h^2):
The answer should be 30 based on what I've attempted but that was wrong.
Over this 10-minute interval, the car's average acceleration is
[tex]\dfrac{30\,\mathrm{mph}-20\,\mathrm{mph}}{10\,\mathrm{min}}=\dfrac{10\,\mathrm{mph}}{\frac16\,\mathrm h}=60\dfrac{\rm mi}{\mathrm h^2}[/tex]
The MVT says that at some point during this 10-minute interval, the car must have had an acceleration of 60 mi/h^2.
The acceleration in this lapse of time is 60 miles per hour squared.
How to get the mean acceleration?To get this, we need to use the formula:
A = (difference in velocity)/time
The change in velocity is:
30mph - 20mph = 10mph
The time is from 2:00pm to 2:10 pm, so 10 minutes, but we need this in hours so:
10 min = (10/60) hours = 1/6 hours
Then the acceleration is given by:
A = 10mph/(1/6) = 60 m/h²
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What is the correct answer for this?
Answer:
4. maximum: 22; minimum: 1
5. maximum: 24; minimum: -6.25
6. maximum: 49.7; minimum: 39.625
Step-by-step explanation:
I find a graphing calculator to be "appropriate technology" for answering questions of this sort. For the first and last questions, the extremes are the values of the function at the ends of the intervals specified.
For the second question, the parabola opens upward and the vertex is in the given interval, so the vertex is the minimum. The maximum is found at the end of the interval that is farthest from the vertex.
a specialty food store carries four popcorn flavors. the presentage of each type of flavor carried by the store is shown below All the boxes of cinnamon and cheese popcorn are displayed at the front entrance is the display has 60 boxes how many boxes of popcorn does the store have in all
kettle corn 60%
caramel popcorn 10%
cinnamon popcorn 15%
cheese popcorn 15%
(answers)
A 400
B 200
C 100
D 30
Answer:
200 Boxes of Popcorn
Step-by-step explanation:
To find the total amount of popcorn boxes there are in the store, we need to consider the amount of boxes displayed at the front of the store.
We have:
60 boxes = Cinnamon + Cheese
60 boxes = 15% + 15%
60 = 30% of the total boxes in the store.
Now we know that 60 boxes is equivalent to 30%, we can use this to find the number of kettle corn.
60 + 60 = 120
30% + 30% = 60%
This means that we have 120 Kettle Korn boxes.
We can also use the amount of 60 boxes to find what 10% will be equivalent to.
60 boxes = 30%
So if we divide the number of boxes by 3, we'll get the 10% of the total number of boxes.
60/3 = 30%/3
20 = 10%
So all in all we have:
120 Kettle Korn
60 Cinnamon + Cheese
20 Caramel
120 + 60 + 20 = 200
There are 200 popcorn boxes in the store.
PLEASE HELP!!!!!! 20 POINTS!!! (BOTH QUESTIONS) VERY EASY!!!!!
The second one is d I’m pretty sure
Answer:
#23, A
#24, D
Hope this helped!!
~A̷l̷i̷s̷h̷e̷a̷♡
What is B help pleaseeee
Answer:
59.0°
Step-by-step explanation:
Many triangle solvers are available for your phone, tablet, or browser. The attachments show the input and output of one of them.
___
You can use the law of cosines to compute the result yourself.
b^2 = a^2 + c^2 - 2ac·cos(B)
cos(B) = (a^2 +c^2 -b^2)/(2ac) = (22^2 +18^2 -20^2)/(2·22·18) = 408/792
B = arccos(408/792) ≈ 58.9924° ≈ 59.0°
What percent of 370 is 166.5
A. 0.45%
B. 22%
C. 37%
D. 45%
The answer is D. 45%
The answer would be 45%
To solve this pretend that 370 is 100
Then put (x) as the value you are looking for
So 100%=370
(x)%=166.5
Then set it up like this:
100%. 370
=
x%. 166.5
Then divide or do cross multiplication and you find out that x is 45%
Hope this helps! :3
Need help multiplying -300 to N+M&M=10 for equation (1)
Answer:
3.5 pounds of nuts; 6.5 pounds of M&Ms
Step-by-step explanation:
Let m represent the number of pounds of M&Ms to use. Then 10-m is the number of pounds of nuts, and the cost of the mix is ...
6·m + 3·(10-m) = 4.95·10 . . . . . cost = cost per pound times pounds
3m +30 = 49.5 . . . . . . simplify
3m = 19.5 . . . . . . . . . . . subtract 30
m = 6.5 . . . . . . . . . . . . . divide by 3
Then 10-m = 10-6.5 = 3.5.
The manager should use 3.5 pounds of nuts and 6.5 pounds of M&Ms in the mix.
Which fraction is NOT equivalent to
8
12
?
A)
2
3
B)
24
36
C)
4
6
D)
6
10
1/3
7/12
9/12
1/4
and more
The fraction that is not equivalent to [tex]\( \frac{8}{12} \) is \( \frac{6}{10} \), option D, as it simplifies to \( \frac{3}{5} \), while the others simplify to \( \frac{2}{3} \), which is equivalent to \( \frac{8}{12} \).[/tex]
To find the fraction that is not equivalent to [tex]\( \frac{8}{12} \), we need to simplify each option and compare it with \( \frac{8}{12} \).[/tex]
We simplify each option:
A) [tex]\( \frac{2}{3} \)[/tex]
B) [tex]\( \frac{24}{36} = \frac{2}{3} \) (Equivalent to \( \frac{8}{12} \))[/tex]
C) [tex]\( \frac{4}{6} = \frac{2}{3} \) (Equivalent to \( \frac{8}{12} \))[/tex]
D)[tex]\( \frac{6}{10} = \frac{3}{5} \)[/tex]
So, the fraction that is not equivalent to [tex]\( \frac{8}{12} \) is \( \frac{6}{10} \),[/tex]option D.
The school yearbook committee surveyed the student body for an article about colleges in which they are pursuing enrollment. The table below shows the number of students in each grade level who are pursuing one or more college.
If there are 170 students in 12th grade, what percentage of the twelfth grade students have more than one college in mind? Round your answer to the nearest percent.
Out of 170 students in 12th grade, 27+23 = 50 students have more than 1 college in mind.
So 50/170, or 29% is your answer.
Answer:
29%
Step-by-step explanation:
How many times does the quadratic function below intersect the x-axis? y=x+10x+25
The quadratic function y=x^2+10x+25 intersects the x-axis at a single point (x = -5).
Explanation:A quadratic function intersects the x-axis when the value of y is equal to 0. To find the number of times the function intersects the x-axis, we need to determine the number of solutions for y = 0. The given quadratic function is y = x^2 + 10x + 25. We can solve this equation by factoring or using the quadratic formula.
Factoring: Factoring the quadratic equation, we get (x + 5)(x + 5) = 0.
Since both factors are the same, the function intersects the x-axis at a single point (x = -5).
Quadratic formula: The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.
Plugging in the values from the given quadratic function, we get x = (-10 ± √(100 - 4(1)(25))) / 2(1).
Simplifying further, we get x = (-10 ± √(100 - 100)) / 2, which reduces to x = -5. This indicates that the quadratic function intersects the x-axis at a single point (x = -5).
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A kite is a __________. A. quadrilateral B. parallelogram C. rectangle D. trapezoid
A kite is a quadrilateral.
So the correct answer is A.
Hope this helps,
Davinia.
Final answer:
A kite is a quadrilateral, which is a shape with four sides, but with unique properties that differentiate it from parallelograms, rectangles, and trapezoids.
Explanation:
A kite in geometry is a quadrilateral. A quadrilateral is a kind of shape with four sides, which might not be as commonly discussed in early education as shapes like squares and triangles. A kite is defined by two pairs of adjacent sides that are equal in length, with one pair longer than the other. Unlike a parallelogram, the sides of a kite do not always have to be parallel to each other. In addition, a kite does not necessarily have right angles as a rectangle does, nor does it have only one pair of parallel sides as a trapezoid does. Therefore, when characterizing a kite, the correct answer is A. quadrilateral.
Evaluate the exponential expression: (2x)2−3y2=___, if x = 5 and y = 3.
-125
-73
125
73
Answer:
73
Step-by-step explanation:
Put the values of the variables where the variables are, then do the arithmetic.
(2·5)^2 -3·3^2 = 10^2 -3·9 = 100 -27 = 73
___
Or, you can let a calculator or spreadsheet evaluate the function for you.
solve
y^2 + 3y = -1
-PlushDNA
Answer:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
Step-by-step explanation:
Given: [tex]y^2+3y=-1[/tex]
To solve for [tex]y[/tex], we need to get everything on one side of the equal sign and set it to zero. We can do this by adding 1 to both sides. We then get:
[tex]y^2+3y+1=0[/tex]
We can solve for [tex]y[/tex] by using the quadratic formula:
[tex]y=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}[/tex] AND [tex]y=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]
Let's identify our values:
[tex]a: 1\\b: 3\\c: 1[/tex]
Plug in the values and simplify.
[tex]y=\frac{-3+\sqrt{(3)^2-4(1)(1)}}{2(1)}\\y=\frac{-3+\sqrt{5}}{2}\\-------------------------\\y=\frac{-3-\sqrt{(3)^2-4(1)(1)}}{2(1)}\\\\y=\frac{-3-\sqrt{5}}{2}\\[/tex]
Your final answers are:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
Hi if someone could explain the right answer that would be great i’m totally lost!!
Answer:
A. lim [x ⇒ -∞] g(x) = -5 . . . . . . written in text form, not typeset
Step-by-step explanation:
A horizontal asymptote is a line that the function approaches but never reaches. It represents the limiting value that the function can have. (The function can come as close to that value as you like for some value of x, but can never actually reach that value.)
Here, you're told the asymptote for negative x values is -5. That means g(x) gets closer and closer to -5 for values of x that are more and more negative. That is, as x approaches infinity, g(x) approaches -5. We say -5 is the limit of g(x) as x approaches negative infinity.
___
The attached graph shows a function that has characteristics like those of g(x).
___
This question is about vocabulary: what is the meaning of "asymptote" and "limit", and how do you read a description of a limit written using math language.
The solids are similar. Find the missing dimension.
Answer:
25 in
Step-by-step explanation:
The diameter is shown to be 10/4 times the height, so the diameter of the smaller solid is ...
(10/4)×(10 in) = (100/4) in = 25 in
Answer:
25 in.
Step-by-step explanation:
use the distance formula to find base and height of the triangle with points (-3, 4), (1, 4), (1, 1) Show your work.
Answer:
The base = 4 units and the height = 3 units
Step-by-step explanation:
* Lets remember the rule of the distance between 2 points
- The two points are (x1 , y1) and (x2 , y2)
∴ The distance = √[(x2 - x1)²+(y2 - y1)²]
* The vertices of the triangles are (-3 , 4) , (1 , 4) , (1 , 1)
- If two points have the same y-coordinate
∴ The line joining the to point is horizontal
∴ Its length = x2 - x1
- Because √[(x2 - x1)²+(y2 - y1)²] and y2 = y1
∴ d = √(x2 - x1)² ⇒ cancel power 2 with the radical sign
∴ d = x2 - x1
* Similar you can find the vertical distance
- If two points have the same x-coordinate
∴ The line joining the to point is vertical
- Its length = y2 - y1
∵ The points (-3 , 4) , (1 , 4) have same y-coordinate
∴ This side of the triangle is horizontal
∴ Its length = 1 - -3 = 4
∵ The points (1 , 4) , (1 , 1) have same x-coordinate
∴ This side of the triangle is vertical line
∴ Its length = 4 - 1 = 3
* The two sides of the triangle are ⊥
∴ One of them is the base of the triangle and the other is the height
* The base = 4 units and the height = 3 units
Can I also get some help with this one as well? I'll do the rest. see previous post for the question. Thanks! #8 and #10.
Answer:
8. (10/7)x^(0.7) +C
10. (x^-2)/2 -x^-1 +C
Step-by-step explanation:
The integral of x^a is x^(a+1)/(a+1).
8. a = -.3, so the integral is x^0.7/0.7
___
10. This is the difference of two integrals, one with a=-2; the other with a=-3, so ...
the integral is (x^-1)/(-1) -(x^-2)/(-2)
_____
Of course, an arbitrary constant is added to each result to complete the indefinite integral.
A party rental company has chairs and tables for rent. The total cost to rent 3
chairs and 8 tables is $55. The total cost to rent 5 chairs and 2 tables is $18. What is the cost to rent each chair and each table
Answer:
chair: $1.00table: $6.50Step-by-step explanation:
When you have a non-trivial number of sets of equations to solve, it can be useful to let a machine solve them for you. Here, suitable equations for chair cost (c) and table cost (t) can be written as ...
3c+8t = 555c+2t = 18___
I find a graphing calculator easy to use for solving such equations.
___
A spreadsheet programmed with Cramer's Rule can do it, too. The second attachment shows the spreadsheet formulas used to solve the standard-form linear equations of the kind that can be written for this problem. The third attachment shows the solution(s).
It’s the second question. 8 friends share twelve candy bars equally. How many does each friend get?
Answer:
Step-by-step explanation:
If we take 1 candy bar and split it between 8 people, each person will get 1/8 of a candy bar. 1/8 for each of those 12 candy bars will give each person 12 × 1/8 = 12/8, or 3/2 = 1 1/2 bars.
You are trying to share 12 candy bars between 8 friends.
Therefore,
12 candy bars ÷ 8 friends = 1.5 bars per person
12 ÷ 8 = 1.5 candy bars
Which is the rate of change for the interval between 3 and 6 on the x-axis?
–3
–2
2
3
Answer:
The correct answer is 2.
Step-by-step explanation:
To find this, first identify the ordered pairs at those two points. They would be (3, -2) and (6, 4). Then use the slope formula with those two points to find the rate of change.
m(slope) = (y2 - y1)/(x2 - x1)
m = (4 - - 2)/(6 - 3)
m = 6/3
m = 2
Answer:
2
Step-by-step explanation:
Rate of change on the given interval a to b is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
a=3 and b=6
f(a) and f(b) are the y values on the graph at x=3 and x=6
f(3)= -3 and f(6) is 4
Now plug in the values in the formula
[tex]rate of change =\frac{4-(-2)}{6-3} =\frac{6}{3} =2[/tex]
answer is 2
Fiona has 18 coins, consisting of quarters and dimes, in her pocket. She has 6 more dimes than quarters. How many quarters does she have?
Answer:
Fiona has 6 quarters
Step-by-step explanation:
If Fiona were to have 1 quarter and 1+6 dimes she would have 8 coins
If she were to have 2 quarters and 2+6 dimes she would have 10 coins
If she were to have 3 quarters and 3+6 dimes she would have 12 coins
If she were to have 4 quarters and 4+6 dimes she would have 14 coins
If she were to have 5 quarters and 5+6 dimes she would have 16 coins
If she were to have 6 quarters and 6+6 dimes she would have 18 coins
Therefore, she has to have 6 quarters in order to have 6 more dimes and a total of 18 coins
I hope this helps, and I'm sorry it took so long for me to write this out
How much will 12 points raise an 85.6% grade PLZZZZZZZZZZZ HELP ASAP
Answer:
It depends on the max amount you can have.
Step-by-step explanation:
For example, if 100 points was the max you'd have 97.6%.
Hope this helps!
How do I answer this question on khan academy.
If [tex]b[/tex] is Ben's age and [tex]i[/tex] is Ishaan's age, then
present day: [tex]b=4i[/tex]6 years ago: [tex]b-6=6(i-6)[/tex]Rewrite the second equation as
[tex]b-6=6(i-6)\implies b-6=6i-36\implies b+30=6i[/tex]
Substitute [tex]b=4i[/tex] into this equation to solve for [tex]i[/tex]:
[tex]b+30=6i\implies4i+30=6i\implies30=2i\implies i=15[/tex]
Then
[tex]b=4i\implies b=4\cdot15=60[/tex]
So Ben is 60 years old now.
What is the answer for #7?
Answer:
radius: 1.84 inheight: 3.68 inStep-by-step explanation:
After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...
V = πr²·h = 2πr³ = 39 in³
Then the radius is ...
r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in
h = 2r = 3.67557 in ≈ 3.68 in
_____
The total surface area of a cylinder is ...
S = 2πr² + 2πrh
For a given volume, V, this becomes ...
S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r
The derivative of this with respect to r is ...
S' = 4πr -2V/r²
Setting this to zero and multiplying by r²/2 gives ...
0 = 2πr³ -V
r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r
__
If we substitute the equation for V into the equation just above this last one, we have ...
0 = 2πr³ - πr²·h
Dividing by πr² gives ...
0 = 2r - h
h = 2r . . . . . generic solution for cylinder optimization problems
The function f(x) is shown in this graph. The function g(x)=-2x-6. Compare the slopes
Since f(x) = -3x + 2, the slope of f(x) is greater than the slope of g(x).
Hence, the answer is (D).
The slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
g(x) = -2x - 6
f(x) is shown in the graph
The slope of g(x), m = -2
From the graph:
(0, 2) and (-1, 1)
M = (1-2)/(-1) = 1
Thus, the slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.
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Carrie spent $1 for every $10 she earned. How much did she earn if she spent $7?
If f(x)=x^2-5x and g(x)=8-x^3, evaluate the following:
a. (f+g)(3)
b. (g-f)(4)
c. (f*g)(-1)
d.(g/f)(-2)
Answer:
a. -25
b. -52
c. 54
d. 8/7 = 1 1/7
Step-by-step explanation:
Evaluate each of the functions for each of the variable values and compute the composite as defined.
a. (f+g)(3) = f(3) + g(3) = 3^2 -5·3 + 8 -3^3 = -25
___
b. (g -f)(4) = g(4) -f(4) = 8 -4^3 -(4^2 -5·4) = 8 -64 -16 +20 = -52
___
c. (f*g)(-1) = f(-1) · g(-1) = ((-1)^2 -5(-1)) · (8 -(-1)^3) = 6·9 = 54
___
d. (g/f)(-2) = (8 -(-2)^3)/((-2)^2 -5(-2)) = (8+8)/(4+10) = 16/14 = 8/7
_____
Comment on approach to the problem
When there are a number of evaluations of the same function with different values of the variable, it can be convenient to let a calculator or spreadsheet do those for you.
Could someone plz help with number 4 ? Thanks
Answer:
255π (cm³).
Step-by-step explanation:
1. the initial formula for the required volume is V=V1-V2, where V1=π(r1)²h, V2=π(r2)²h;
h=20m=2000cm, r1=0.5*d1, r2=0.5*d2;
d1=1cm., d2=0.7 cm.
2. the final formula of the required volume is
[tex]V=\frac{ \pi*h}{4} (d_1^2-d_2^2);[/tex]
3. if to substitute the values of d1, d2 and h, then
[tex]V=\frac{ \pi*2000}{4} (1-0.49)=500 \pi*0.51=255 \pi \ (cm^3).[/tex]
HELP ME ASAP!!!! Will somebody please explain to me how to do this. I can't pass Freshman year without getting this done.
Answer:
cot(x) = 3
Step-by-step explanation:
The cotangent is the reciprocal of the tangent.
cot(x) = 1/tan(x) = 1/(1/3) = 3
_____
It is helpful to memorize the relationships between the trig functions: SOH CAH TOA is a mnemonic that relates triangle sides to trig function values. The remaining relationships you need to know are ...
secant = 1/cosine . . . . . . so cosine = 1/secant
cosecant = 1/sine . . . . . so sine = 1/cosecant
cotangent = 1/tangent . . . . . so tangent = 1/cotangent
It is also helpful to realize that ...
tan = sin/cos
sin² + cos² = 1 . . . the "Pythagorean" relationship between sine and cosine
sec² = 1 + tan²
csc² = 1 + cot²
Solve algebraically
y=x^2 + 2x
y=3x+20
Answer:
x = 5 and y = 35
OR
x = -4 and y = 8.
Step-by-step explanation:
Equate the right-hand side of the two equations:
x² + 2 x = y = 3 x + 20.
x² + 2 x - 3 x - 20 = 0.
x² - x - 20 = 0.
Quadratic discriminant
Δ = b² - 4 a · c
= (-1)² - 4 × 1 × (-20)
= 81.
There are two roots:
x₁ = (-b + [tex]\sqrt{\Delta}[/tex]) / (2 a)
= (- (-1) + [tex]\sqrt{81}[/tex]) / (2 × 1)
= (1 + 9) / 2
= 10 / 2
= 5
and
x₂ = (-b - [tex]\sqrt{\Delta}[/tex]) / (2 a)
= (1 - 9) / 2
= -4.
Find the value of y in both case.
y₁ = 3 × 5 + 20 = 35.
y₂ = 3 × (-4) + 20 = 8.
The solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].
To solve these equations algebraically, we'll set them equal to each other since they both represent [tex]\( y \)[/tex].
Given equations:
[tex]\[ y = x^2 + 2x \][/tex]
[tex]\[ y = 3x + 20 \][/tex]
Setting them equal to each other:
[tex]\[ x^2 + 2x = 3x + 20 \][/tex]
Now, let's rearrange this equation to solve for \( x \):
[tex]\[ x^2 + 2x = 3x + 20 \[/tex]
[tex]x^2 + 2x - 3x - 20 = 0 \[/tex]
[tex]x^2 - x - 20 = 0[/tex]
This is a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex]. We need to factorize or use the quadratic formula to solve for [tex]\( x \)[/tex]. Factoring might work here:
[tex]x^2 - x - 20 = 0[/tex]
[tex](x - 5)(x + 4) = 0[/tex]
Setting each factor equal to zero:
[tex]\[ x - 5 = 0 \] or \( x + 4 = 0 \)[/tex]
Solving for [tex]\( x \)[/tex] in each case:
[tex]\[ x = 5 \] or \( x = -4 \)[/tex]
Now that we have found the potential values of [tex]\( x \)[/tex], let's find the corresponding [tex]\( y \)[/tex] values using either of the original equations. Let's use [tex]\( y = x^2 + 2x \)[/tex]:
For [tex]\( x = 5 \)[/tex]:
[tex]y = 5^2 + 2(5)[/tex]
[tex]y = 25 + 10[/tex]
[tex]y = 35[/tex]
For [tex]\( x = -4 \)[/tex]:
[tex]y = (-4)^2 + 2(-4)[/tex]
[tex]y = 16 - 8[/tex]
[tex]y = 8[/tex]
Therefore, the solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].