Answers
[tex] \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Volume of a rectangular prism is ~
[tex] \sf{Volume_{cuboid}= Length × Width × Height} [/tex]
[tex]\qquad \sf \dashrightarrow \: v = (4x + 2) \times (3x - 5) \times (7x + 4)[/tex]
[tex]\qquad \sf \dashrightarrow \: v = (12 {x}^{2} - 20x + 6x - 10) \times (7x + 4) [/tex]
[tex]\qquad \sf \dashrightarrow \: v = (12 {x}^{2} - 14x- 10) \times (7x + 4)[/tex]
[tex]\qquad \sf \dashrightarrow \: v = 84 {x}^{3} + 48 {x}^{2} - 98x {}^{2} - 56x - 70x - 40[/tex]
[tex]\qquad \sf \dashrightarrow \: v = 84 {x}^{3} - 50 {x}^{2} - 126x - 40[/tex]
So, the correct choice is B
Related Questions
8. Given the following function, (a) find the vertex; (b) determine whether there is a maximum or a minimum value, and find the value; (c) find the range; and (d) find the intervals on which the function is increasing and the intervals on which the function is decreasing.
Answers
Answer:
Step-by-step explanation:
Parabola:
[tex]\sf f(x) =\dfrac{-1}{2}x^2+7x - 5\\\\a = \dfrac{-1}{2} \ ; b = 7 \ ; \ c = -5[/tex]
[tex]\sf x = \dfrac{-b}{2a}\\\\x =\dfrac{-7}{2*\dfrac{-1}{2}}\\\\ = \dfrac{-7}{-1}[/tex]
x = 7
Now, to find the y-value substitute this in the equation
[tex]\sf f(x) = \dfrac{-1}{2}*7^2+7*7-5\\\\ =\dfrac{-49}{2}+49-5\\\\ = \dfrac{-49}{2}+44\\\\ = \dfrac{-49}{2}+\dfrac{88}{2}\\\\= \dfrac{39}{2}[/tex]
[tex]\boxed{Vertex(7 ,\dfrac{39}{2})}[/tex]
b) The value of a is negative. So, the parabola is open down words and the maximum value is given by the y-coordinate of the Vertex.
[tex]\sf \boxed{Maximum \ value= \dfrac{39}{2}}[/tex]
[tex]\sf c) Range = [\dfrac{39}{2}, -infinity)[/tex]
Answer:
(a) (7,39/2)
(b) Maximum, 39/2
(c) y ≤ 39/2
(d) Increase when x < 7 and decrease when x > 7
Step-by-step explanation:
Given the parabola:
[tex]\displaystyle \large{f(x)=-\dfrac{1}{2}x^2+7x-5}[/tex]
( A ) Find the vertex
In order to find the vertex, let’s use calculus for this one. Recall the power rules for differentiation:
Power Rules
[tex]\displaystyle \large{f(x)=x^n \to f'(x)=nx^{n-1}}\\\\\displaystyle \large{f(x)=kx^n \to f'(x)=knx^{n-1} \quad \tt{(k \ \ is \ \ constant)}}\\\\\displaystyle \large{f(x)=k \to f'(x)=0 \quad \tt{(k \ \ is \ \ constant)}}[/tex]
Derivative Definition
Derivative f'(x) is a slope itself or rate of changes.Derive the parabola:
[tex]\displaystyle \large{f'(x)=-\dfrac{1}{2}(2)x^{2-1} + 7(1)x^{1-1} -0}\\\\\displaystyle \large{f'(x)=-x+7}[/tex]
Since vertex has slope = 0 —> e.g f'(x) = 0:
[tex]\displaystyle \large{0=-x+7}\\\\\displaystyle \large{-x=-7}\\\\\displaystyle \large{x=7}[/tex]
Substitute x = 7 in f(x):
[tex]\displaystyle \large{f(7)=-\dfrac{1}{2}(7)^2+7(7)-5}\\\\\displaystyle \large{f(7)=-\dfrac{1}{2}(49)+49-5}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+44}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+\dfrac{88}{2}}\\\\\displaystyle \large{f(7)=\dfrac{39}{2}}[/tex]
Therefore, the vertex is at (7,39/2)
( B ) Determine if max or min then find the value
Since the parabola opens downward then there only exists maximum value. The maximum value is the y-value of vertex at x-value of vertex. Henceforth:
There is maximum value but no minimum value and the maximum value is 39/2 at x = 7.( C ) Find range
For parabola, range is minimum value </≤ y </≤ maximum value. We know that parabola has maximum value of 39/2 but no minimum value so we can just ignore it then we’d have:
y ≤ 39/2 is our range[Note: < and > are for open-dot meaning the value will not be included —> e.g x > 4 means 4 isn’t included in.]
( D ) Find the interval when function is increasing and when it’s decreasing
For parabola, the function will increase only if f'(x) or slope > 0 and will decrease only f'(x) < 0.
We know, from part A that the derivative is:
[tex]\displaystyle \large{f'(x)=-x+7}[/tex]
Therefore, when f'(x) > 0 —> e.g -x + 7 > 0:
[tex]\displaystyle \large{-x+7 > 0}\\\\\displaystyle \large{-x > -7}\\\\\displaystyle \large{x < 7}[/tex]
When f'(x) < 0 —> e.g -x + 7 < 0:
[tex]\displaystyle \large{-x+7 < 0}\\\\\displaystyle \large{-x < -7}\\\\\displaystyle \large{x > 7}[/tex]
Therefore, the function will increase when x < 7 and will decrease when x > 7.
find the value of H in this angle. check the attachment on top.
Answers
Answer:
133
Step-by-step explanation:
Line PYF is straight. Therefore, its angle measures 180°. One of the angles is 95°. The other angle measures (h-48)°.
Based on this info, we can form an equation:
95°+h°-48° = 180°
h°-48° = 180°-95°
h = 85°+48°
h = 133°
Hence, the value of h is 133°.
Hope this helps!!!
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(4a^3 - 36a^2 + 60a^2 + 72) \ (a - 6)
Answers
Answer:
4a^2+48a+288+(fraction)1800/a-6
Step-by-step explanation:
area of a circle radius 12
Answers
Answer: 3.14 x 12^2 = 452.16
Answer: 144π
Decimal Form: 452.389 (Not Rounded)
What is the value of x in the equation : sin 40 = cos (x)
Answers
Since sin x= cos (90- x)
Sin40=cos(90-40)
Sin 40=cos 50
X=50
The volume of this cube is 27 cubic meters. What is the value of m?
Answers
Hey ! there
Answer:
n is equal to 3 metersStep-by-step explanation:
In this question we are provided with a cube having volume 27 cubic meters . And we are asked to find the value of n that is basically its edge .
For finding the value of n we need to know the volume of cube. So ,
[tex] \: \qquad \: \qquad \: \underline{ \boxed{ \frak{Volume_{(Cube)} = a {}^{3} }}}[/tex]
Where ,
a refers to edge of cubeSOLUTION : -
Substituting given volume that is 27 m³ and value of a as n in formula :
[tex] \quad \longrightarrow \qquad \: n {}^{3} = 27[/tex]
Applying cube root on both sides :
[tex] \quad \longrightarrow \qquad \: \sqrt[3]{n {}^{3} } = \sqrt[3]{27} [/tex]
We get ,
[tex] \quad \longrightarrow \qquad \:n= \sqrt[3]{27} [/tex]
We know that 3 × 3 × 3 is equal to 27 that means cube root of 27 is 3 . So ,
[tex] \quad \longrightarrow \qquad \: \blue{\underline{\boxed{\frak{ n = 3 \: m}}}} \quad \bigstar[/tex]
Henceforth , value of n is ❝ 3 meters ❞Verifying : -
Now we are checking our answer whether it is wrong or right by substituting value of n and equating it with given volume that is 27 cubic meters . So ,
a³ = 27 ( where a is equal to n )Substituting values :
( 3 )³ = 273 × 3 × 3 = 279 × 3 = 2727 = 27L.H.S = R.H.SHence, Verified .Therefore, our answer is correct .
#Keep LearningAnswer:
3
Step-by-step explanation:
Formula for volume of cube :
V = n³Here, V is given to be 27 m³.
Substitute the value of V in the formula.
Solving : Take the cubic root on each side.
27 m³ = n³n = ∛27 m³n = 3 metersEvaluate
4! - (11-2)!
8!
Answers
Answer:
Step-by-step explanation:
The expanded value of n! is (n) * (n - 1) * (n - 2) until we reach one.
Given:
4! - ((11-2)!) / 8!)
Rewrite:
[tex]\displaystyle 4! - \frac{(11-2)!}{8!}[/tex]
Subtract:
[tex]\displaystyle 4! - \frac{9!}{8!}[/tex]
Expand:
[tex]\displaystyle 4*3*2*1 - \frac{9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1}[/tex]
Cancel out values that equal one in the fraction:
[tex]\displaystyle 4*3*2*1 - \frac{9}{1}[/tex]
Multiply:
[tex]\displaystyle 24 - \frac{9}{1}[/tex]
Simplify:
24 - 9
Subtract:
15
Solve the math:
Elsa is 2 years older than Bella. Emma is twice as old as Elsa. So, what will be the sum of their ages in 1 years time. And then also find out what was the summation of their ages before 5 years from now.
Answers
Answer:
Step-by-step explanation:
Let Emma's age be 2x years, then:
Elsa's age is x years, also:
Bella's age is x - 2 years.
In one years time the sum of their ages
= 2x + 1 + x + 1 + x - 2 + 1
= 4x + 1 where x = Elsa's age now.
5 years before now
Sum of their ages
= 2x -5 + x - 5 + x - 2 - 5
= 4x - 17 where x = Elsa's age now,
y=1/2x+1
how do i graph this?
Answers
Answer: Heyaa! ~
Graph the line using the slope and y-intercept, or two points.
Slope:
1/2
y-intercept: (0,1)
x ↓ y
0 ↓ 1
2 ↓ 2
Step-by-step explanation:
Hopefully this helps you! ~
Answer:
Use the Desmos graphing calculator. Look up "graphing calculator" and hit the Desmos option, then type in your equation. It works.
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a basket contains a supply of marbles of 4 different colors. marbles with the same color are assumed to be identical. in how many ways can you choose 6 marbles from the basket
Answers
For the basket with 4 different types of marbles, there are 4,096 combinations in which we can select 6 marbles (in order).
in how many ways can you choose 6 marbles from the basket?Here we need to identify the number of selections. We have 6 selections (assuming that order matters).
Marble 1:Marble 2:Marble 3:Marble 4:Marble 5:Marble 6:Now we need to find the number of options for each of these. We know that there are 4 different colors of marbles, then for each selection, we have 4 options:
Marble 1: 4 optionsMarble 2: 4 optionsMarble 3: 4 optionsMarble 4: 4 optionsMarble 5: 4 optionsMarble 6: 4 optionsThe total number of combinations is given by the product between the numbers of options, so we have:
C = 4*4*4*4*4*4 = 4,096 combinations.
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Tim tried to use Cavalieri's principle to show that the two figures have the same volume.
"The base areas are the same. Therefore, corresponding cross-sections have the same area. So the volumes must be the same."
What is the first mistake Tim made?
Answers
Answer:
The base areas aren't same
Step-by-step explanation:
The base areas arent same
Answer:
He did not establish that heights are the same.
For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio $1:2:3:4:5:6$. What is the probability of rolling a total of 7 on the two dice
Answers
Step-by-step explanation:
$ 1: 2: 3: 4: 5: 6: 7: 7: in ratio
probability on two dice
1, 2, 3, 4, 5, 6, 7, 7.
The probability of rolling a total of 7 on the two dice is 8/63 if in the particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Let x be the probability of rolling a 1.
Ratios are 1:2:3:4:5:6
Then,
x + 2x + 3x + 4x +5x + 6x = 1
21x = 1
x = 1/21
The possible combinations of two rolls that total 7 are:
{(1,6) ; (2,5) ; (3,4) ; (4,3) ; (5,2) ; (6,1)}
The probability P of rolling a total of $7$ on the two dice is equal to the sum of the probabilities of rolling each combination.
[tex]\rm P = \dfrac{1}{21}\cdot\dfrac{6}{21}+\dfrac{2}{21}\cdot\dfrac{5}{21}+\dfrac{3}{21}\cdot\dfrac{4}{21}+\dfrac{4}{21}\cdot\dfrac{3}{21}+\dfrac{5}{21}\cdot\dfrac{2}{21}+\dfrac{6}{21}\cdot\dfrac{1}{21}\\\\=\dfrac{8}{63}[/tex]
Thus, the probability of rolling a total of 7 on the two dice is 8/63 if in the particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.
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The graph of a sinusoidal function intersects its midline at (0, -3) and then has a maximum point at
(2,-1.5).
Write the formula of the function, where x is entered in radians
Answers
The formula of the function when the graph is analyzed will be y =1.5sin[(pi/4)x] - 3.
How to explain the function?From the graph, the mid line is y = -3 and the amplitude will be:
= -1.5 - (-3)
= 1.5
From the mean line to the max is ¼ of a cycle. Therefore, the period will be:
= 4 × 2 = 8
Number of cycles in 2pi will be:
= 2pi/8
= pi/4
Hence, the formula of the function will be y= 1.5sin[(pi/4)x] - 3.
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Answer:
f(x)=1.5sin (pie/4 x)-3
Step-by-step explanation:
Kahn academy aproved
This dot plot shows the number of runs scored by the Yellow
Jackets in their last 12 baseball games.
Answers
julie buys a bike for $2700 and sells it a year later, making a 15% profit
How much profit did Julie make?
Answers
Answer:
$405.
Step-by-step explanation:
That would be 15% of $2700
= 2700 * 0.15
= $405
cant solve x+4y=0
3x+2y=20
Answers
Answer:
The answer to this question is -2.
Step-by-step explanation:
First, multiply one of the equations by something that can cancel out the other variable.
3x+2y=20
3(x+4y=0)
3x+2y=20
3x+12y=0
Now, subtract both equations.
-10y=20
Now, divide both sides by -10.
y=-2
Hope this helps!
23/2 as a mixed number
Answers
Answer:
11 1/2.
Step-by-step explanation:
23 / 2 = 11 remainder 1.
So it is 11 1/2.
If 15% of the length of rope is 75cm what is half of the length of rope
Answers
Answer:
250 cm.
Step-by-step explanation:
Half = 50% so by proportion:
Half length of the rope = 75 *50/15
= 250
Answer:
250 cm
Step-by-step explanation:
15% to decimal:
15% = 15/100 = 0.15
Then, half of the lenght of rope is:
[tex](\frac{75}{0.15}) /2=500/2 = 250[/tex]
Hope this helps
PLEASE HELP!!!!
y = 1.4 (1.02)
a =
b=
r(as a percentage)
Answers
Answer:
a = 1.4 then b = (1+0.02) and r = 2%
What is the volume of a sphere with a diameter of 9.1 m, rounded to the nearest tenth of a cubic meter?
Answers
a produce company is packaging tomatoes into boxes containing 8 tomatoes each. how many boxes do they need to package 416 tomatoes?
Answers
Answer:
5.75
Step-by-step explanation:
If
1 box = 8 tomatoes
x boxes = 46 tomatoes
1 = 8
x = 46
You cross multiply giving you
8x = 46×1
8x = 46
8x/8 = 46/8
x = 5.75
I need an answer to this:
Answers
Answer:
It will decrease cause there will be more deer. Deer eat blackberry bushes
Step-by-step explanation:
Answer:
It will decrease because there will be more deer
Step-by-step explanation:
Because of the lack of wolves, the deer population would increase. Since it would increase the amount of deer there would be less of the deer's food sources.
What is the equation for an arithmetic sequence with a first term of 7 and a second term of 3? (5 points)
an = 7 − 4(n − 1)
an = 7 + 4(n − 1)
an = 7 − 3(n − 1)
an = 7 + 3(n − 1)
Answers
Answer:
1st option
Step-by-step explanation:
the equation for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 7 and d = a₂ - a₁ = 3 - 7 = - 4 , then
[tex]a_{n}[/tex] = 7 - 4(n - 1)
Answer:
The answer is option A
Step-by-step explanation:
The solution is in the image
Out of all 252 twelfth graders, how many rode in a car to school? 11 74 111 114
Answers
Out of all 252 twelfth graders, 114 rode in a car to school
How to determine the number of students?The proportion of students that rode in a car is given as:
p = 45.24%
So, the number of students that rode in a car is:
Students = 45.24% * 252
Evaluate the product
Students = 114.008
Approximate
Student = 114
Hence, 114 rode in a car to school
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complete the table of values for y=2xsquared+x
Answers
The solution of y= [tex]2x^{2} +x[/tex] given as:
x: 0 1 2 3
y: 0 3 10 21
What is Linear Equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given function is:
y= [tex]2x^{2} +x[/tex]
For finding the solution of above expression, take value of x and solve for y.
If x=0y= 2(0)+0
y=0
If x=1,y= [tex]2(1)^{2} +1= 3[/tex]
If x=2y=[tex]2(2)^{2} +2=10[/tex]
If x=3y= [tex]2(3)^{2} +3=21[/tex]
The required table is:
x: 0 1 2 3
y: 0 3 10 21
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Ms. brown is planting a rectangular garden. the garden is 90
feet long and 50 feet wide. what is the area of her garden?
a 140 ft?
b 4,000 ft?
c 280 ft?
d 4,500 ft
Answers
1/2 + 1/4 = how many quarters
Answers
Answer:
3
Step-by-step explanation:
1/2 = 0.5
1/4 = 0.25
1/2 + 1/4
= 0.5 + 0.25
= 0.75
= 75/100
= 3/4
Quarter is 1/4.
3/4 can be written as 3 x 1/4
Hence,
1/2 + 1/4 is 3 times 1/4
1/2 + 1/4 = 3 quarters.
Answer:
3/4
Step-by-step explanation:
1*(1/2)= (2/2)*(1/2)= (2*1)/(2*2)=2/4
1/2+1/4=2/4+1/4=3/4
Evaluate 2(5a – 2) a=3
Please solve
Answers
Answer:
26
Step-by-step explanation:
a=3
2(5x3-2)
5x3=15
15-2=13
2x13=26
Type the correct answer in the box. if necessary, use / for the fraction bar. you toss five fair coins. the probability that all five coins land heads is .
Answers
If all five coins land heads, the expected will 1. The probability that all five coins land heads is 1/32
What is probability?This is the likelihood or chance that an event will occur. Mathematically;
Probability = expected/total
If you toss five fair coins, the total outcome will be:
T = 2^5
T = 32
If all five coins land heads, the expected will 1. The probability that all five coins land heads is 1/32
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Calculate the values
Answers
Answer:
a=108;b=36;c=72
Step-by-step explanation:
Answer:
a = 108°
b = 36°
c = 72°
Step-by-step explanation:
Note : the sum of the interior angles of a regular pentagon = 540°
Then
The measure of one interior angle of a reg pentagon =540/5 = 108°
Therefore a = 108°
c = 180 - 108 = 72°
SRT is a new isosceles triangle then :
[tex]b=\frac{180-108}{2} = \frac{72}{2} =36[/tex]