Alena is packing a box that has a height of one inch more than the width and a length of three inches more than the width, as shown in the diagram below. Write a polynomial expression, In simplified form, that represents the volume of the box.
(I need help...)
Answers
Answer:
The polynomial that represent the volume of the box is [tex]V=(x^{3}+4x^{2}+3x)\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the box is equal to
[tex]V=LWH[/tex]
we have
[tex]L=(x+3)\ in[/tex]
[tex]W=x\ in[/tex]
[tex]H=(x+1)\ in[/tex]
substitute in the formula
[tex]V=(x+3)(x)(x+1)\\V=(x^{2} +3x)(x+1)\\V=x^{3}+x^{2} +3x^{2} +3x\\ V=(x^{3}+4x^{2}+3x)\ in^{3}[/tex]
Related Questions
pleasssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answers
Answer:
Volume of prism is 60 cm^3.
Step-by-step explanation:
The volume of prism can be found using formula:
V= B*h
Where B= base area and h= height.
In the question, we are given Base area B= 10cm^2 and height h= 6cm.
Putting values in the formula:
V= B8h
V= 10* 6
V = 60 cm^3
So, volume of prism is 60 cm^3.
A police car drives 108km in 1 1/2 hours what is its average speed in kilometers per hour.
Answers
ANSWER
72km/h
EXPLANATION
The average speed of the car can be calculated using the formula:
Average Speed=total distance/ total time taken.
The car covers a distance of 108km in 1½ hours.
We substitute the values into the formula to obtain,
[tex]Average \: \: Speed= \frac{108}{1.5} [/tex]
[tex]Average \: \: Speed=72 {kmh}^{ - 1} [/tex]
Therefore the average speed of the journey is 72km/h
Stewart has $26 dollars. He spent $12.81, including tax, to buy a new DVD. He needs to set aside $10.00 to pay for his lunch next week. If peanuts cost $0.42 per package including tax, describe the maximum number of packages that Stewart can buy?
A) p ≤ 8
B) p ≤ 7
C) p ≥ 8
D) p ≥ 7
Answers
Answer:
The answer is B,
26-12.81=13.19
13.19-10=3.19
3.19/0.42 is a little greater than 7
Use the formula v=u+at to find the velocity when .the initial velocity is 3m/s. •the acceleration is 1.5 m/s. •the time is 7 seconds
Answers
Final Velocity = Initial Velocity + (Acceleration * time)
Final Velocity = ?
Initial Velocity = 3
Acceleration = 1.5
Time = 7
Plug in and solve
3+(1.5*7)
3+10.5
Velocity = 13.5m/s
Square RSTU dilates by a factor of 1\2 with respect to the origin to create square R'S'T'U'. If R'S' is 2 units, what is RS?
A.
4 units
B.
2 units
C.
0.5 units
D.
1 unit
Reset
Next
Answers
Answer: A.4 units
Step-by-step explanation:
We know that if a figure is dilated by a scale factor of k , then the measure of the corresponding image (l') of a line segment having measure 'l' is given by :-
[tex]l'=kl[/tex]
Given : Square RSTU dilates by a factor of 1\2 with respect to the origin to create square R'S'T'U'.
The measure of line segment R'S' = 2 units
The scale factor : [tex]k=\dfrac{1}{2}[/tex]
Using the above equation , we have
[tex]R'S'=\dfrac{1}{2}RS\\\\\Rightarrow\ RS= 2\times R'S'\\\\\Rightarrow\ RS= 2\times2=4[/tex]
Hence, RS = 4 units.
The expression on the left side of an equation is shown below. If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?
Answers
The answer is D. -2x+5.
If we simplify the left side of the equation first given, we come to the expression -2x-10.
If we solve for D., we get the same results. Thus, because an equation with all the same variable terms and constants have infinite solutions, the answer is D.
Hope this helps!
Answer:
The correct option is D) -2(x+5)
Step-by-step explanation:
Consider the provided equation.
-5(x+2)+3x=
The above equation is linear equation having one variable.
For an linear equation ax=b
a=0, b=0 in that situation the equation is in the form of 0x=0 for all value of x. Then there are infinitely many solutions.
Now solve the expression on the left side
-5(x+2)+3x
-5x-10+3x
-2x-10
-2(x+5)
Now for 0x=0 form the expression on the right side must be same as the expression on the left side for the provided equation.
Consider the options.
Option A) -5(x-3)+2x
Solve the above expression.
-5x-15+2x
-3x-15
-2(x+5)≠-3x-15
Thus the option is not correct.
Option B) -5x-10
Solve the above expression.
-5x-10
-5(x+2)
-2(x+5)≠-5(x+2)
Thus the option is not correct.
Option C) x-2x+2+3x
Solve the above expression.
x-2x+2+3x
2x+2
2(x+1)
-2(x+5)≠2(x+1)
Thus the option is not correct.
Option D) -2(x+5)
-2(x+5)=-2(x+5)
Hence, the correct option is D) -2(x+5)
Simplify Ratios 63 to 21
Answers
[tex]63:21=3:1[/tex]
Hope this helps.
r3t40
Write a quadratic equation to represent the circle graphed on the right
Answers
Answer:
The standard form: x² + (y + 1)² = 25The general form: x² + y² + 2y - 24 = 0Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (0, -1) and the radius r = 5 (look at the picture).
Substitute:
[tex](x-0)^2+(y-(-1))^2=5^2\\\\x^2+(y+1)^2=25[/tex]
use (a + b)² = a² + 2ab + b²
[tex]x^2+y^2+2y+1=25[/tex] subtract 25 from both sides
[tex]x^2+y^2+2y-24=0[/tex]
Can you form a right triangle with the three lengths given? Why or why not?
4 mi, 5 mi, 6 mi
no; 42 + 52 ≠ 62
yes; 4 + 5 = 6
yes; 42 + 52 ≠ 62
no; 4 + 5 ≠ 6
Answers
Answer:
It's the second one:
yes; 4+5=6
Step-by-step explanation:
which value of x is in the solution set of -3X+8≥14? ) A. -3 B. -1 C. 0 D. 3
Answers
Answer:
A
Step-by-step explanation:
Solving for x:
-3x + 8 ≥ 14
-3x ≥ 6
x ≤ -2
Notice the sign gets reversed when you divide or multiply by a negative number.
The only option less than -2 is -3, A.
Here's a tip: on multiple choice questions, sometimes it's faster to try each answer instead of solving the equation. This can save time on tests like the SAT or ACT.
Let's try it:
-3(-3) + 8 = 9 + 8 = 17
-3(-1) + 8 = 3 + 8 = 11
-3(0) + 8 = 0 + 8 = 8
-3(3) + 8 = -9 + 8 = -1
So you can see the answer is A.
is 4, 16, 36, 64 a geometric sequence
Answers
ANSWER
No, there is no constant ratio.
EXPLANATION
We want to determine whether the sequence
4, 16, 36, 64
is geometric.
We need to find out if there is a common ratio between the consecutive terms.
[tex] \frac{16}{4} = 4[/tex]
[tex] \frac{36}{16} = \frac{9}{4} [/tex]
[tex] \frac{64}{36} = \frac{16}{9} [/tex]
Since the ratio is not the same for the consecutive terms, the sequence is not geometric.
4, 16, 36, 64 is a geometric sequence with a common ratio of 4.
Yes, 4, 16, 36, 64 is a geometric sequence.
To determine if a sequence is geometric, we need to check if there is a common ratio between consecutive terms. In this case, the common ratio is 4.A geometric sequence is one where each term after the first is found by multiplying the previous term by a constant, which is the common ratio.katniss divided x^3+2x^2-3x-4 by x+1. she didnt get a remainder. do you agree with her?
Answers
ANSWER
Katnis is right
EXPLANATION
We use the Remainder Theorem to check if she is right.
According to the Remainder Theorem, if the polynomial function,
[tex]p(x) = {x}^{3} + 2 {x}^{2} - 3x - 4[/tex]
is divided by x+1, then the remainder is given by
[tex]p( - 1)[/tex]
We substitute x=-1 into the function to obtain,
[tex]p( - 1) = {( - 1)}^{3} + 2 { ( - 1)}^{2} - 3( - 1) - 4[/tex]
We simplify to get:
[tex]p( - 1) = - 1+ 2 (1) + 3 - 4[/tex]
[tex]p( - 1) = 4- 4[/tex]
[tex]p( - 1) = 0[/tex]
Katnis is right because the remainder is zero
Determine whether the function f(x)=|x|+x2+0.001 is even , odd or neither. 10 points
Answers
the answer is even is the right answer
ANSWER
even
EXPLANATION
The given function is
[tex]f(x) = |x| + {x}^{2} + 0.001[/tex]
If f(x) is even then f(-x) =f(x).
[tex]f( - x) = | - x| + {( - x)}^{2} + 0.001[/tex]
[tex]f( - x) = | x| + {x}^{2} + 0.001[/tex]
We can see that:
[tex]f( - x) = f(x)[/tex]
Hence the given function is even.
Will give brainliest to the correct answer.
Based on these sets of side lengths, which triangles are right triangles?
Answers
The answer is B. I think. Hope that helps!
I need help please!!
i dont get this !!
Answers
The area of the two smaller squares are shown as 25 and 144, add them together to get 25 + 144 = 169.
The area of the larger square is shown as 169, which is the same as the sum of the two smaller ones.
The answer is Yes.
yes the sum of the smaller squares is equal to the largest one. 25 + 144 = 169
The area of the largest squares is 169, so the area of the smaller squares is equal to the largest square.
Find the height, in feet, of the ball after 3 seconds in the air.
Answers
By solving a system of equations, we determined the quadratic function h(x) = 33.5x^2 + 14x + 53.5 and found that the height of the ball after 3 seconds is 229.5 feet.
Certainly! Let's go through the step-by-step calculation to find the quadratic function representing the height of the ball and then determine the height after 3 seconds.
Given information:
h(1) = 91 feet
h(2) = 164 feet
We need to find the coefficients a, b, and c in the quadratic function h(x) = ax^2 + bx + c.
Step 1: Setting up Equations
We have two equations based on the given information:
a + b + c = 91 (since h(1) = a(1)^2 + b(1) + c = a + b + c = 91)
4a + 2b + c = 164 (since h(2) = a(2)^2 + b(2) + c = 4a + 2b + c = 164)
Step 2: Solving the System of Equations
We can solve the system of equations to find the values of a, b, and c.
Subtracting the first equation from the second gives: 3a + b = 73.
Let's multiply the first equation by 3 and subtract it from the second:
3(3a + b) - (a + b + c) = 3(73) - 91
Simplifying, we get 6a - c = 110.
Step 3: Substituting into the First Equation
Substitute 6a - c = 110 into the first equation:
6a - c + c = 110 + 91
Solving, 6a = 201, which implies a = 33.5.
Step 4: Finding b and c
Substitute a back into the first equation to find b + c = 91 - 33.5, and then b and c are determined as b = 14 and c = 53.5.
Step 5: Quadratic Function
Now, we have the quadratic function h(x) = 33.5x^2 + 14x + 53.5.
Step 6: Finding h(3)
Finally, substitute x = 3 into the quadratic function:
h(3) = 33.5(3)^2 + 14(3) + 53.5
Solving this yields h(3) = 229.5 feet.
Final Answer:
The height of the ball after 3 seconds is 229.5 feet.
Find the zeros of f(x) = x^2+5x-6.
A. {-2,3}
B. {-6,1}
c. {-2,-3}
D. {-6,-1}
Answers
Answer:
x^2+5x-6
a = 1 b = 5 and c = -6
Using the quadratic formula:
x = [-5 +- sq root (25 -4 * 1 *-6) ] / 2 * 1
x = [-5 +- sq root (49)] / 2
x = [-5 +- 7] / 2
x1 = 1
x2 = -6
Step-by-step explanation:
asdfghjkllkjhgfdsaas
Answers
Answer:
13
Step-by-step explanation:
(x + 3)^3/2 = 64
√(x + 3)^3 = 64
(x + 3)^3 = 64^2
(x + 3)^3 = (4^3)^2
(x + 3)^3 = (4^2)^3
Same exponent
So
x + 3 = 4^2
x + 3 = 16
x = 13
A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.
Which best describes why the function is nonlinear?
The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
Answers
Answer:
D:The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
hope this helps you
(ps.please make me brainlyest)
Step-by-step explanation:
i just took the test on E2020 & got 100%
d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
Number of tree purchased Total Cost ($)
1 60
2 120
3 180
4 240
5 290
For the linear function rate of change is constant.
Now, between 2 and 3 trees rate of change is given by
[tex]=\frac{180-120}{3-2} \\\\=60\\[/tex]
Now, between 3 and 5 trees rate of change is given by
[tex]=\frac{200- 180}{5-3} \\\\=55[/tex]
This is clearly that the rate of change isn't constant. Therefore, the function is non-linear.
so,
d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
Learn more about linear function here
brainly.com/question/11897796
#SPJ2
A class has 15 students; 8 females and 7 males. The teacher wants to form a group of 3
students to present the results of their class project to the Board of Education. What is the
probability that the group of three will consist of all females? You can leave your answer
as an unreduced fraction.
Answers
Answer:
8/15 chance
Step-by-step explanation:
To calculate the probability of forming an all-female group of three students from a class of 15 students, we find the total combinations of choosing three females and divide by the combinations of choosing any three students, resulting in a probability of 56/455.
The question involves calculating the probability that a group of three randomly selected students will consist of all females from a class of 15 students (8 females and 7 males). This is a problem of combinatorics and probability. We use combinations to determine the number of ways to choose three female students out of eight and divide that by the number of ways to choose any three students out of the fifteen.
First, we find the number of ways to choose three females: C(8,3) = 8! / (3! * (8-3)!) = 56. Then, we find the total number of ways to choose any three students: C(15,3) = 15! / (3! * (12!)) = 455. Therefore, the probability of choosing all females is 56/455.
4x>6x plus 3. can someone help me asap. i will mark u brainliest. show steps
Answers
Answer:
x<3/-2
Step-by-step explanation:
4x>6x+3
4x-6x>3
-2x>3
x<3/-2
Also help me with my question just click on my name and see my questions
Mr. Roberts collected data to determine how many birds were at his bird feeder during different times of the day. Identify the striking deviation in his data.
A) 8-10am
B) 10am-12pm
C) 6pm-8pm
D) no striking deviation
sorry this one isnt for points this is just for help with my homework
Answers
Consider a striking deviation as an outlier (Something that stands out in a pattern, EX: 2, 3, 4, 4, 4, 5, 5, 10 where the outlier would be 10.) Because there are no outliers (Or, Striking deviations), we can conclude that the answer would be D: No striking deviation.
Alexandra is installing edge material around her yard. She has 400 ft of edge material to surround three sides of her rectangular yard. The fourth side will be against her deck and does not need edging. What is the maximum area that can be enclosed by the edging? Enter your answer in the box.
Answers
Answer:
The maximum area is equal to [tex]20,000\ ft^{2}[/tex]
Step-by-step explanation:
Let
x ----> the length of the rectangular yard
y ----> the width of the rectangular yard
we know that
The perimeter is equal to
[tex]400=x+2y[/tex] --> remember that the fourth side will be against her deck
isolate the variable y
[tex]y=200-0.5x[/tex] -----> equation A
The area of the rectangular yard is equal to
[tex]A=xy[/tex] ----> equation B
substitute equation A in equation B
[tex]A=x(200-0.5x)\\ \\A=200x-0.5x^{2}[/tex]
The quadratic function is a vertical parabola open downward
The vertex is a maximum
The x-coordinate of the vertex represent the length of the rectangular yard for an maximum area
The y-coordinate of the vertex represent the maximum area of the rectangular yard
Using a graphing tool
The vertex is the point (200,20,000)
see the attached figure
therefore
The length of the rectangular yard is 200 ft
The width of the rectangular yard is [tex]y=200-0.5(200)=100\ ft[/tex]
The maximum area is equal to [tex]20,000\ ft^{2}[/tex]
find the number of distinguishable permutations of the letters ZEBRA
Answers
Step-by-step Answer:
Since there are no repetitions in the five letters of the word ZEBRA, the number of permutations is 5! = 120 = 5*4*3*2*1.
The sum of a number and 6 is at least 15
Answers
Answer:
x>8
Step-by-step explanation:
The number has to be bigger than 8 in order to be at least fifteen, so x is greater than 8
Consider the two functions shown below.
Answers
ANSWER
The correct answer is A
EXPLANATION
If the two functions are inverses , then
[tex]f(g(x)) = g(f(x)) = x[/tex]
Given
[tex]f(x) = 5x - 11[/tex]
and
[tex]g(x) = \frac{1}{5}x + 11[/tex]
[tex]f(g(x)) = f( \frac{1}{5} x + 11)[/tex]
This implies that,
[tex]f(g(x)) = 5(\frac{1}{5} x + 11) - 11[/tex]
Expand to get;
[tex]f(g(x)) =x + 55 - 11[/tex]
[tex]f(g(x)) =x +44[/tex]
Since
[tex]f(g(x)) \ne \: x[/tex]
The two functions are not inverses
The correct answer is A
Answer:
Correct choice is A.
Step-by-step explanation:
Given functions are [tex]f\left(x\right)=5x-11[/tex] and [tex]g\left(x\right)=\frac{1}{5}x+11[/tex].
Then [tex]f\left(g\left(x\right)\right)=f\left(\frac{1}{5}x+11\right)=5\left(\frac{1}{5}x+11\right)-11=x+55-11=x+44[/tex]
By definition of inverse we says that if f(x) and g(x) are inverse of each other then f(g(x)) must be equal to x.
But in above calculation we can see that f(g(x)) is not equal to x.
Hence correct choice is A.
WILL MARK BRAINLEST!!!
What is the difference when 5x^2 − 3x + 2 is subtracted from 4x^2 − 7x + 9?
A) x^2 − 4x + 7
B) −x^2 − 4x + 7
C) 9x^2 − 4x − 11
D) −9x^2 − 4x + 7
Answers
you answer is b) -x^2-4x+7
Answer:
B
Step-by-step explanation:
4x² - 7x + 9 - (5x² - 3x + 2) ← distribute by - 1
= 4x² - 7x + 9 - 5x² + 3x - 2 ← collect like terms
= (4x² - 5x² ) + (- 7x + 3x ) + (9 - 2)
= - x² - 4x + 7 → B
A raffle prize of 14x^2/15dollars is to be divided among 7x people. Write an expression for the amount of money that each person will receive. Show Work!
Answers
For this case we must divide the following expression:
[tex]\frac {\frac {14x ^ 2} {15}} {7x}[/tex]
And in this way we get the amount of money that each person will receive.
Then applying double C we have:
[tex]\frac {14x ^ 2} {15 * 7x} =\\\frac {14x ^ 2} {105x} =\\0.133x[/tex]
Thus, each person has 0.133x of money!
Answer:
0.133x
Flight 202's arrival time is normally distributed with a mean arrival time of 10:30 p.m. and a standard deviation of 15 minutes. Use the eight-part symmetry of the area under a normal curve to find the probability that a randomly chosen arrival time is between 10:00 p.m. and 11:00 p.m.
The probability is__
Answers
Answer:
The probability is 0.953
Step-by-step explanation:
We know that the mean [tex]\mu[/tex] is:
[tex]\mu=10:30\ p.m[/tex]
The standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=0:15\ minutes[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
We seek to find
[tex]P(10:00\ p.m.<x<11:00\ p.m.)[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{10:00-10:30}{0:15}[/tex]
[tex]Z=\frac{-0:30}{0:15}[/tex]
[tex]Z=-2[/tex]
The score of Z =-2 means that 10:00 p.m. is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%
and
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{11:00-10:30}{0:15}[/tex]
[tex]Z=\frac{0:30}{0:15}[/tex]
[tex]Z=2[/tex]
The score of Z =2 means that 11:00 p.m. is 2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%
[tex]P(10:00\ p.m.<x<11:00\ p.m.)=100\%-2.35\%-2.35\%[/tex]
[tex]P(10:00\ p.m.<x<11:00\ p.m.)=95.3\%[/tex]
[tex]P(10:00\ p.m.<x<11:00\ p.m.)=0.953[/tex]
the probability is 0.4772, or 47.72%.
To find the probability that Flight 202's arrival time is between 10:00 p.m. and 11:00 p.m., we need to standardize the times and use the properties of the normal distribution. The mean arrival time is 10:30 p.m., and the standard deviation is 15 minutes.
First, convert the times to minutes past 10:00 p.m.: 10:30 p.m. is 30 minutes past, and 11:00 p.m. is 60 minutes past. Now, standardize these times using the formula for z-scores:
For 10:30 p.m.:z = (30 - 30) / 15 = 0For 11:00 p.m.:
z = (60 - 30) / 15 = 2
Using the z-table or a standard normal distribution calculator, we find the area under the curve to the left of z = 0 is 0.5, and to the left of z = 2 is approximately 0.9772. Therefore, the probability that the arrival time is between 10:00 PM and 11:00 PM is the difference of these probabilities:
P(10:00 PM < X < 11:00 PM) = P(Z < 2) - P(Z < 0) = 0.9772 - 0.5 = 0.4772
So, the probability is 0.4772, or 47.72%.
Find the slope and y-intercept.
Answers
The slope is 7/4 and the intercept is -10