A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 18, 3, 0, 3, 6, 3.
Using only the values given in the table for the function f(x) = –x3 + 4x + 3, what is the largest interval of x-values where the function is increasing?
(
,
)
The largest interval of x-values where the function is increasing is (-1, 1)
How to determine the largest increasing interval?The table of values is added as an attachment
From the table, the function f(x) decreases from x = -3 to x = -1 and x = 1 and x = 2
So, we make use of the intervals
x = -1, 0 and 1
From the table,
From x = -1 to 0, the change is 3
From x = 0 to 1, the change is 3
From x = -1 to 1, the change is 6
Using the above highlights, the largest increasing interval is (-1, 1)
Hence, the largest interval of x-values where the function is increasing is (-1, 1)
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Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative three and negative four.
The equation of the graphed parabola is y=a[tex](x+3)^{2}[/tex]-4.
Given that parabola is plotted, concave up , with vertex located at coordinates (-3,-4).
We are required to find the equation of the graphed parabola.
The equation of a quadratic function of vertex (h,k) is given by:
y=a[tex](x-h)^{2}[/tex]+k
In the above equation a is the leading coefficient.
We have been given point (-3,-4).
We have to just put the value of h=-3 and k=-4 and the required equation will be as under:
y=a[tex](x+3)^{2}[/tex]-4
Hence the equation of the parabola which is plotted, concave up, with vertex located at coordinates (-3,-4) is y=a[tex](x+3)^{2}[/tex]-4.
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How do you know that ABC is similar to BDC? Explain your answer.
Answer: No
Step-by-step explanation:
There is only one pair of congruent angles that can be determined, but to prove triangles similar, there needs to be two pairs of congruent angles.
The reference angle for is, which has a terminal point of (2).
What is the terminal point of ?
(-²)
(-4/2, 4/2)
○ B. (2,-²)
(-2/²2,-4/2)
OA
A.
O C.
○ D. (22)
Answer: C
Step-by-step explanation:
[tex]\frac{5\pi}{4}[/tex] is in the third quadrant, so both x and y are negative.
Therefore, the only possible answer is C.
Surface area=
Volume =
Help me please thanks
which of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it?
A. time(length)
B.length(time)
C.cost(time)
D. time(race)
The answer choice which best fits the function described in the task content is; Choice A; time(length).
Which would be a good name for the function?It follows from the task content that the function takes the length of a race and returns the time needed to complete it.
On this note, it follows that the time taken is a function of the length of the race.
Hence, the appropriate name of the function is; Choice A.
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What is the solution to the system of equations? (–21, 9) (9, –21) (–1, 9) (9, –1)
The solution to the system of equations is the point ( -1, 9 ).
What is the solution to a system of linear equations?
If you have a system of equations that contains two equations with the same two unknown variables, then the solution to that system is the ordered pair that makes both equations true at the same time.
The system of equations
y = -3x + 6 ...................(1)
y = 9 .................(2)
Substitute equation (2) in equation
9 = -3x + 6
subtract both sides
9 - 6 = -3x + 6 - 6
3 = -3x
Divide by -3 both sides
x = -1
the solution is the point ( -1, 9 )
Therefore,the solution to the system of equations is the point ( -1, 9 ).
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The complete question is -
Y = –3x + 6 y = 9 what is the solution to the system of equations? (–21, 9) (9, –21) (–1, 9) (9, –1)
Answer:
c
Step-by-step explanation:
What is the solution to the system of equations?
(–21, 9)
(9, –21)
(–1, 9)
(9, –1)
ASSIGNMENT
Evaluate -
[tex]\sf \: \displaystyle\int_{ - 1}^{25}\sf {e}^{x - [x]} [/tex]
- Need help!
Answer:
26
Explanation:
[tex]\int\limits^{25}_{-1} {e^{x-[x]}} \, dx[/tex]
simplify
[tex]\int\limits^{25}_{-1} {e^{0} \, dx[/tex]
any variable to the power 0 is 1
[tex]\int\limits^{25}_{-1} 1 \, dx[/tex]
integrating 1 gives x
[tex]\left[ \:x \: \right]^{25}_{-1}[/tex]
apply limits
[tex]25 - (-1)[/tex]
add terms
[tex]26[/tex]
[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-[x]}dx[/tex]
[x] is x if x is a real number[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-x}dx[/tex]
[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^0dx[/tex]
e⁰=1[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}dx[/tex]
[tex]\\ \rm\hookrightarrow \left[x\right]_{-1}^{25}[/tex]
[tex]\\ \rm\hookrightarrow 25-(-1)[/tex]
[tex]\\ \rm\hookrightarrow 25+1[/tex]
[tex]\\ \rm\hookrightarrow 26[/tex]
Can someone help me? Just complete these 2 proofs (geometry), ASAP!!!!
Question 4
1) [tex]\overline{AC} \cong \overline{AE}, \overline{AB} \cong \overline{AD}[/tex] (given)
2) [tex]\angle A \cong \angle A[/tex] (reflexive property)
3) [tex]\triangle ABC \cong \triangle ADC[/tex] (SAS)
Question 5
3) [tex]\angle ABC \cong \angle DCB[/tex] (all right angles are congruent)
4) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)
5) [tex]\triangle ABC \cong \triangle DCB[/tex] (AAS)
if price of 12 eggs is rs 192 , how many eggs can be bought for rs 160
Answer:
10 eggs
Step-by-step explanation:
We need to work out the price per unit :
12 eggs = rs 192
1 egg = rs 192÷12
1 egg = rs 16
? egg = rs 160
16×? = 160
? = 160÷16
? = 10
So our final answer will be 10 eggs
Answer:
10
Step-by-step explanation:
The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of the completely inflated balloon is 784π cm2, how long will it take for the balloon to fully inflate?
Considering the surface area of the spherical ballon, it will take 7 seconds for the the balloon to fully inflate.
What is the surface area of a sphere?The surface area of a sphere of radius r is given by:
[tex]S = 4\pi r^2[/tex]
In this problem, the surface area is of [tex]784\pi[/tex] cm², hence the radius in cm is found as follows:
[tex]784\pi = 4\pi r^2[/tex]
[tex]4r^2 = 784[/tex]
[tex]r^2 = \frac{784}{4}[/tex]
[tex]r^2 = 196[/tex]
[tex]r = \sqrt{196}[/tex]
r = 14 cm.
The radius start at 0 cm, inflating at a rate of 2 cm/s, hence it will take 7 seconds for the the balloon to fully inflate, as 14 cm/(2 cm/s) = 7 s.
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6 out of 24 as a percentage
Answer:
25%
Step-by-step explanation:
When you simple 6 out of 24 you get a quarter.
A quarter us equivalent to 25%
-499" is to the __________ of "-500" on a number line
Answer: right
Step-by-step explanation:
[tex]-499 > -500[/tex], and larger numbers are to the right of numbers smaller than them on the number line.
witch is a value of a perfect square
Answer:
it depends.
Step-by-step explanation:
A perfect square is a number that can be expressed as the product of an interger by itself or as the second exponent of an interger. For example, 25 is a perfect square because it is the product of interger 5 by itself, 5 × 5 =25.
Sample response: there is a common ratio of 2/3 between the height of the ball at each bounce. so, the bounce heights form a geometric sequence: 27, 18, 12. two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet. what did you include in your response? check all that apply. there is a common ratio between bounce heights. multiply 12 by 2/3. the height on the fourth bounce is 8 feet.
Answer:
Step-by-step explanation:
A Geometric sequence can be used:
To Model this sequence you need to use this formula
A (subscript n) = Ar(n-1)
a = value of the first term
n = the # of the term you want to find (For example, if you want to find the term number 3, it is 12)
r = the common ratio, this is obtained by dividing the second term in the sequence by the first.
So the value of r is = 2/3 because 27 times 2/3 = 18 which is the second term
n = 4 since you want to find the 4th term in the sequence
Plug it in and the results are
4th term = 27(2/3)^(4-1) = 8
The answer is 8
What are the roots of the polynomial equation? –3, –2, 3 –3, 2 18, 32 18, 32, 66
The root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3
How to determine the roots of the equation?The graph that completes the question is added as an attachment
The polynomial function is given as:
x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
From the attached graph, we have the following highlight:
The curves of both equations intersect at
x = -3, x = -2 and x = 3
This means that the root of the polynomial function is -3, -2 and 3
Hence, the root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3
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Complete question
Carlos graphed the system of equations that can be used to solve x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
What are the roots of the polynomial equation?
A) –3, –2, 3
B) –3, 2
C) 18, 32
D) 18, 32, 66
Need it solved correctly for khan academy
The tiger population loses 3/5 of its size every 2.94 decades
Rate of change using differential calculus
The given equation is:
[tex]N(t)=710(\frac{8}{125} )^t[/tex]
Find the derivative of the given function
[tex]\frac{dN}{dt} =710(0.064)^tln(0.064)\\\\\frac{dN}{dt} =-1951.7(0.064)^t[/tex]
When the tiger loses 3/5 of its population
dN/dt = 3/5
Solve for t
[tex]\frac{3}{5} =-1951.7(0.064)^t\\\\-0.0003=(0.064)^t[/tex]
Take the natural logarithm of both sides
[tex]ln(-0.0003)=t(ln0.064)\\\\-8.087=-2.75t\\\\t=\frac{-8.087}{-2.75} \\\\t=2.94[/tex]
The tiger population loses 3/5 of its size every 2.94 decades
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give the volume and surface area of the sphere shown
Answer:
V≈3053.63
A≈1017.88
Step-by-step explanation:
V=[tex]\frac{4}{3}[/tex]π [tex]r^{3}[/tex]=[tex]\frac{4}{3}[/tex]·π·[tex]9^{3}[/tex] ≈3053.62806
A=4π[tex]r^{2}[/tex]=4·π·[tex]9^{2}[/tex] ≈1017.87602
what is the volume of a sphere with a radius of 6 inches
Answer:
288pi in^3 , which is 904.78 in^3 to nearest hundredth.
Step-by-step explanation:
V = 4/3 pi r^3
= 4/3 pi * 6*3
= 288pi in^3
= 904.7786842 in^3
Find the maximum of the objective
function, f, subject to the constraints
f = 4x + 3y
Maximum value = 880/3.
Maximizing the objective function in the LP model means that the value occurs in an acceptable set of decisions. Linear programming refers to selecting the best alternative from the available alternatives that can represent the objective and constraint functions as linear mathematical functions.
As mentioned above, the equation is an example of a constraint. You can use this to think about what it means to solve equations and inequalities. For example, solving 3x + 4 = 10 yields x = 2. This is an easy way to express the same constraints.
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The sum of 3 consecutive integers is 2190. what is the value of the smallest integer?
Answer:
3x+2=2190
3x=2190-2
3x=2188
x=2188÷3
x=729
The sum of a number and its reciprocal is 122/11. Find the
number.
O -11
09
O 11
Answer:
11
Step-by-step explanation:
if the some of a number is an restrocal is 122 upon 11 find the integers value of x let the number bees two values of x i e 11 and 1 upon 11 are possible hence required in future value of x is 11
please provide the answer?
Using the given table:
a) the average rate of change is 32.5 jobs/year.
b) the average rate of change is 12.5 jobs/year.
How to find the average rate of change?
For a function f(x), the average rate of change on an interval [a, b] is:
[tex]\frac{f(b) - f(a)}{b - a}[/tex]
a) The average rate of change between 1997 and 1999 is:
[tex]A = \frac{695 - 630}{1999 - 1997} = 32.5[/tex]
So the average rate of change is 32.5 jobs/year.
b) Now the interval is 1999 to 2001.
The rate this time is:
[tex]A ' = \frac{720 - 695}{2001 - 1999} = 12.5[/tex]
So the average rate of change is 12.5 jobs/year.
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If is any positive two-digit integer, what is the greatest positive integer that must be a factor of
Answer:
23
Step-by-step explanation:
small brain
Lamont is making a blue print of his shoebox. He made a drawing of how he would like to make the box. If the drawing is 4 inches long and the scale of the drawing is 1 inch = 2 feet, how long is the box?
Answer:
The box is 8 feet long.
Step-by-step explanation:
1 inch = 2 feet.
Multiply 4 by 2.
4×2=8
I multiplied 4 by 2 because 1-inch equals 2 feet, which means if we multiply both terms by 4, you will get 4 inch = 8 feet.
Hope this helps!
On a balance scale, $3$ green balls balance $6$ blue balls, $2$ yellow balls balance $5$ blue balls, and $6$ blue balls balance $4$ white balls. How many blue balls are needed to balance $4$ green, $2$ yellow and $2$ white balls
The number of blue balls that are needed to balance four green, two yellow and two white balls is 16 blue balls.
Numbers of blue balls neededGreen(g)
Blue (b)
Yellow (y)
White (w)
First step is to formula an equation
3g=6b
g=2b
2y=5b
y=5/2b
4w=6b
w=3/2b
Second step is to substitute
4g+2y+2w
=4(2b)+2(5/2b)+2(3/2b)
=8b+5b+3b
=16b
Therefore 16 blue balls are needed.
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The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds
The correct option is (c) h = 10sin(π15t)+35.
The equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds is h = 10sin(π15t)+35.
How do windmills rotate?The blades of a turbine, which resemble propellers and function much like an airplane wing, capture the wind's energy.
A pocket of low-pressure air develops on one side of the blade when the wind blows. The blade is subsequently drawn toward the low-pressure air pocket, which turns the rotor.
Calculation for the equation of the model height-
Let's now review each choice individually and select the best one.
The blade is horizontal at time t = 0. As a result, h = 35 at t = 0 is valid for all of the possibilities in this situation.
They accomplish two spins in a minute. The blades will so complete one rotation in 30 seconds. and they will complete a quarter rotation in 15/2 seconds. Because of this, the blade will be vertically up from time t = 0 to t = 15/2. Its height in this instance should be 35 + 10 = 45 ft. Let's now examine the available possibilities.
If we put t=15/2 in the options
Option (a) gives h = 25
Option (b) gives h = -10sin(15/2) + 35
Option (c) gives h = 45
Option (d) gives h = 10sin(15/2) + 35
Therefore, the correct equation is given in option c.
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The complete question is -
The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.
a) h = −10sin(π15t)+35
b) h = −10sin(πt)+35
c) h = 10sin(π15t)+35
d) h = 10sin(πt)+35
Bob and Carol are teenagers. Bob is two years older than Carol. If the digits of Carol's age are reversed, the new number would be three times as large as Bob's age. Find Bob's age.
Bob is 2 years older than Carol and the reverse of Carol's age is 3 times Bob's age, which makes Bob's to be 17 years.
How can Bob's age be calculated?Let 1B represent Bob's age and let 1C represent Carol's age, we can write the following equations;
1B = 1C + 2Reversing Carol's age gives;
C1 = 3 × 1BThe multiples of 3 that have the form X1 have 7 as the rightmost number.
Given that 1B is a teenager, we have;
When;
1B = 171C = 17 - 2 = 15The reverse of Carol's age is therefore;
C1 = 51 = 3 × 17Therefore, from the given description, Bob's age 1B = 17 years
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The ____ of two numbers is greater than or equal to the numbers
Answer:
sum
Step-by-step explanation:
example
2+3=5
This is greater than the two numbersPLEASE HELP IM STUCK
Answer:
y =- [tex]\frac{1}{4}[/tex]x - 1
Step-by-step explanation:
You are asked to give the equation of the line in slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
Y-intercept is the point where the graph intersects the y-axis at point (b, 0). The graph seems to cross the y-axis at (-1, 0), so the b value is -1.
Slope is rise over run. Looking at the graph, it goes down 1 unit every 4 units to the right, so the slope is -1/4.
Answer:
Below in bold.
Step-by-step explanation:
The slope is -1/4 and y-intercept is -1
y = -1/4x - 1