Answers
Answer:
The expression for the height of the solid is:
[tex]\displaystyle h = x^2+x-9[/tex]
Step-by-step explanation:
Recall that the volume of a rectangular solid is given by:
[tex]\displaystyle V = \ell wh[/tex]
Where l is the length, w is the width, and h is the height.
We know that the volume is given by the polynomial:
[tex]\displaystyle V = 3x^4-3x^3-33x^2+54x[/tex]
And that the length and width are given by, respectively:
[tex]\displaystyle \ell = 3x \text{ and } w =x-2[/tex]
Substitute:
[tex]\displaystyle 3x^4-3x^3-33x^2+54x=(3x)(x-2)h[/tex]
We can solve for h. First, divide both sides by 3x:
[tex]\displaystyle \frac{3x^4-3x^3-33x^2+54x}{3x}=(x-2)h[/tex]
Divide each term:
[tex]\displaystyle x^3-x^2-11x+18=(x-2)h[/tex]
To solve for h, divide both sides by (x - 2):
[tex]\displaystyle h = \frac{x^3-x^2-11x+18}{x-2}[/tex]
Since this is a polynomial divided by a binomial in the form of (x - a), we can use synthetic division, where a = 2. This is shown below. Therefore, the expression for the height of the solid is:
[tex]\displaystyle h = x^2+x-9[/tex]
Related Questions
Find the area of the triangle with one angle of 150 degrees, and one side 6 cm and the other 7cm.
(Sorry, I could not figure out how to upload the picture)
A. 10.5 cm²
B. 18.2 cm²
C. 12.1 cm²
D. 21 cm²
Answers
Step-by-step explanation:
here's the answer to your question
The Master Chief collects spiders and starfish. If his spiders have 8 legs and his starfish have 5 legs, how many starfish must he have, given that his spider/starfish collection totals 19 creatures and 116 legs
Answers
Answer:
12 starfish
Step-by-step explanation:
Create a system of equations where x is the number of starfish he has and y is the number of spiders he has:
x + y = 19
5x + 8y = 116
Solve by elimination by multiplying the top equation by -8:
-8x - 8y = -152
5x + 8y = 116
Add these together and solve for x:
-3x = -36
x = 12
So, he has 12 starfish.
The total number of starfish is 12 starfishes
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of starfish be = x
Let the number of spiders be = y
The number of legs for spiders = 8
The number of legs for starfish = 5
So , the equation will be
The total number of legs for x starfish = 5x
The total number of legs for y spiders = 8y
The total number of creatures = 19
So , x + y = 19 be equation (1)
And ,
The total number of legs = 116
So , 5x + 8y = 116 be equation (2)
Now , from equation (1) , x = 19 - y
Substituting the value of equation (1) in equation (2) , we get
5x + 8y = 116
5 ( 19 - y ) + 8y = 116
95 - 5y + 8y = 116
95 + 3y = 116
Subtracting 95 on both sides , we get
3y = 21
Divide by 3 on both sides , we get
y = 7
So , the number of spiders is 7 spiders
Substituting the value of y in equation (1) , we get
x + y = 19
x + 7 = 19
Subtract 7 on both sides , we get
x = 12
Therefore , the value of x is 12
Hence , The total number of starfish is 12 starfishes
To learn more about equations click :
https://brainly.com/question/10413253
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Amira is twice as old as her cousin Pam. Nine years ago, their combined age was 18. What are their present ages?
Answers
Answer:
Amira is currently 24 years old and Pam is currently 12 years old
Step-by-step explanation:
Let Amira's age be [tex]a[/tex] and Pam's age be [tex]p[/tex]. Currently, Amira is twice as old as Pam. Therefore, we can write the equation [tex]a=2p[/tex].
We can write a second equation using the other information given in the question. Nine years ago, Amira and Pam's combined ages was 18. If Amira and Pam are currently [tex]a[/tex] and [tex]p[/tex] years old, respectively, then their respective ages 9 years ago would ben [tex]a-9[/tex] and [tex]p-9[/tex]. Since these add up to 18, we have the equation [tex](a-9)+(p-9)=18[/tex].
Therefore, we have a system of equations:
[tex]\begin{cases}a=2p,\\a-9+p-9=18\end{cases}[/tex]
Substitute the first equation into the second one:
[tex]2p-9+p-9=18[/tex]
Combine like terms:
[tex]3p-18=18[/tex]
Add 18 to both sides:
[tex]3p=36[/tex]
Divide both sides by 3:
[tex]p=\frac{36}{3}=\boxed{12}[/tex]
Now substitute this into any of the equations (I'll choose the first):
[tex]a=2p,\\a=2(12),\\a=\boxed{24}[/tex]
Therefore, Amira is currently 24 years old and Pam is currently 12 years old.
A man drove his car a distance of 260 miles in 4 hours. If continuing at this rate how many miles will he travel in 8 miles
Answers
Answer:
520
Step-by-step explanation:
260/4=520/8
Method 1: Cross Multiply
Method 2: Find GCF
X^4+x^3-6x^2-14x-12=0 Make a list of possible rational roots. Test the possible roots until you find one that produces a remainder of 0 Write the resulting cubic function. Use synthetic division to find a second root that will reduce the cubic expression to a quadratic expression
Answers
Step-by-step explanation:
The Rational Roots Test states that for a polynomial with integer coefficients, the factors of the constant / the factors of the leading coefficient are the possible rational roots.
Here, the constant (the value without an x attached to it) is -12 and the leading coefficient (the value that the x to the highest degree is multiplied by) is 1 as x⁴ is multiplied by 1. The factors of -12 are
±(1, 2, 3, 4, 6, 12), so the possible rational roots are ±(1, 2, 3, 4, 6, 12)/1 (as 1 is the only factor of 1).
Trying out a few roots until we get one that works using synthetic division, we can try
x+1 (the root is x=-1)
-1 | 1 1 -6 -14 -12
| -1 0 6 8
__________________________
1 0 -6 -8 -4
the remainder is -4, so this does not work
x+2 (the root is x=-2)
-2 | 1 1 -6 -14 -12
| -2 2 8 12
__________________________
1 -1 -4 -6 0
Therefore, x=-2 is a root and x+2 is a factor of the polynomial. The quotient of the polynomial and x+2 is
-6 + (-4)x + (-1)* x² + 1 * x³ = x³-x²-4x-6
Using the rational roots theorem, the possible roots of x³-x²-4x-6 are
±(1,2,3,6)
Starting with
x-1 (root is x=1), we have
1 | 1 -1 -4 -6
| 1 0 -4
_____________________
1 0 -4 -10
there is a remainder, so this is not a root
next, x-2 (root is x=2)
2 | 1 -1 -4 -6
| 2 2 -4
_____________________
1 1 -2 -10
there is a remainder, so this is not a root
next, x-3 (root is x=3)
3| 1 -1 -4 -6
| 3 6 6
_____________________
1 2 2 0
x-3 is a factor and 3 is a root. the quotient of (x³-x²-4x-6)/(x-3) is x²+2x+2
16. Select the equation that has only one solution.
A. 8 x + 3 = 3 X + 8
B. 12 x = 12 x + 7
C.4 x + 11 = 11 + 4 x
D. 6 x + 20 = 6 x
Answers
Answer:
A is the answer...........
Explanation
8x+3=3x+8
8x-3x=8-3
5x=5
x=5/5
x=1
What is the value of x
(X+40) (3x)
A. 20
B. 35
C. 60
D. 70
Answers
Answer: A. 20 is the answer.
Step-by-step explanation:
x+40 = 3x
or, 40 = 3x-x
or, 2x = 40
or, x = 40/2
so, x = 20
In how many years will the interest of a sum Rs 3600 at the rate of 5.5% per year be Rs 594.8?
Answers
Answer:
in 3.04 years the will give required intrest
PLEASEEEE HELLLLP MEEEE
Answers
Answer:
c. 20/21
Step-by-step explanation:
You just multiply straight
3×7 = 21
4×5 =20
21/20 <---- and it can't be reduced farther than this.
Answer:
C. ²¹⁄₂₀
Step-by-step explanation:
OKOKOK DON'T WORRY I'M HERE :)))
--
When multiplying fractions, you multiply the numerators together and then multiply the denominators together.
The numerators here are 3 and 7. Multiply those and you get 21 (7 x 3 = 21).
The denominators here are 4 and 5. Multiply those and you get 20 (4 x 5 = 20).
Then you put the newly-multiplied numerator over the newly-multiplied denominator and you get ²¹⁄₂₀.
Hope this helped!!
Graph the function
Is it a, b, c or d?
Answers
Answer:
D
Step-by-step explanation:
(the line is a / shape, so the slope is positive)
(the line crosses the y axis at (0,-2))
(using the above information, we can conclude that the equation is y=2x-2)
or
slope = m = rise/run = 2/1 = 2
y=mx+b
y=2x+b
Choose any point on the line) (1,0)
0=2(1)+b
b=-2
y=2x-2
Simplify the following expressions:
a) (√3 +√7)^2
b) (√5 -√3)^2
c) (2√5 + 3√2)^2
Answers
1.) 10+2√21
2.) 8-2√15
3.) 38+2√10
solution to all the answers:
NUMBER 1:
=> use (a + b)^2 + 2ab + b^2 to expand the expression (√3 +√7)^2, then it should look like this: 3 + 2√21 + 7.
=> add the numbers: 10 + 2√21.
NUMBER 2:
=> use (a + b)^2 + 2ab + b^2 to expand the expression (√5 -√3)^2, then it should look like this: 5 - 2√15 + 3.
=> add the numbers: 8 - 2√15.
NUMBER 3:
=> use (a + b)^2 + 2ab + b^2 to expand the expression (2√5 + 3√2)^2, then it should look like this: 20 + 12√10 + 18.
=> add the numbers: 38 + 12√10.
I HOPE THIS HELPED!!
Find COS
out of
Instructions: Find the value of the trigonometric ratio. Make sure to
simplify the fraction if needed.
A
9
B
41
40
С
Cos A
Answers
[tex] \frac{9}{41} [/tex]
Step-by-step explanation:
The ratio cosine tell us that
In a right angled triangle, the cosine of an angle is the side adjacent to the angle divided by the hypotenuse of the triangle.In other words,
[tex] \cos(x) = \frac{adj}{hyp} [/tex]
The side adjacent to angle a is 9. The hypotenuse is 41.
So
[tex] \cos(a) = \frac{9}{41} [/tex]
A solution of alcohol and water is 90% alcohol. The solution is found to contain 63 milliliters of alcohol. How many milliliters total (both alcohol and water) are in the solution?
Answers
Answer:
70 [milliliters]
Step-by-step explanation:
Since the solution consists of 90% alcohol, the 63 milliliters of alcohol must represent 90% of the entire solution. Let the solution have [tex]x[/tex] milliliters in total. We have the following equation:
[tex]0.9x=63[/tex]
Divide both sides by 0.9:
[tex]x=\frac{63}{0.9}=\boxed{70}[/tex]
Therefore, there are 70 milliliters in the solution.
Answer:
[tex]thank \: you[/tex]
Find m so that the equation msin²x+cos²x=m-1 has a solution on the interval (0;π/4)
Answers
msin²x+cos²x=m-1
since the interval are 0 and π/4
Therefore
msin²(0)+cos²(0)=m-1
m(0)+1=m-1
1=m-1
m=2
use π/4 now
msin²(π/4)+cos²(π/4)=m-1
m(1/2)+(1/2)=m-1
m+1=2(m-1)
m+1=2m-2
-m=-3
m=3
Therefore
m=2 or 3
The recursive formula for a geometric sequence is: a = 4 an=an-1×3 What is the 3rd term of this sequence?
Answers
Answer:
36
Step-by-step explanation:
a1 = 4
an=an-1 *3
a2 = a1 *3 = 4*3 = 12
a3 = a2*3 = 12*3 = 36
I NEEEDDD HELPPP!!! someone please help me outttt
Answers
Answer:
45°
Step-by-step explanation:
Segments GJ and HK intersect at F.
That makes angles JFK and GFH vertical angles and congruent.
An arc has the same measure as its central angle.
m<GFH = 45°
m<JFK = m<GFH
m<JFK = 45°
Jeanette ice cream shop sold 10 sundaes with nuts and 7 sundaes without nuts to the total number of sundaes
Answers
(I will give brainliest!)
Solve for x using the distributive property
7(x-2)-3(x+3)=5(x-3)+x
Answers
Answer:
Step-by-step explanation:
7(x-2) -3(x+3) = 5(x-3) +x , distribute in parenthesis
7x -14 -3x -9 = 5x -15 +x , isolate like terms
7x -3x -5x -x = 14 +9 -15, combine like terms
-2x = 8, divide both sides by -2
x= -4
Hope this helps
Write an inequality to describe the region represented on the number line.
H
-4 -3 -2 - 1 0 1 2 3 4
O x>-3
O x>-3.5
O x<-3
O x<-3.5
Answers
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the required number line is not included in the question.
A general explanation is as follows:
An open circle means > or <
A closed circle means >= or <=
Take, for instance, the attached number line:
The open dot on -3 means >-3 or <-3
The arrow points to the right direction, means >-3 i.e. greater than -3
Hence, the inequality is:
[tex]x > -3[/tex]
Answer these 3 questions and show how por favor! 39-says what is his age
Answers
Answer:
I dont know. sorry sorry
Please help! For any positive numbers a, b, and, with b≠1, log b(a/d)
Answers
Answer:
B
Step-by-step explanation:
when logarithms of the same base (the base in this case is 'b') are being subtracted, divide the arguments ( 'a' and 'd')
Find the solution: | x + 1 | + 16 = 10
Answers
Answer:
[×1] +16=10
×=10-16
×=-6
Answer:
x=5 and x=-5
Step-by-step explanation:
First subtract 16 from both sides.
Then solve for x+1=6 and x+1=-6
you answer should be x=5 and x=-5
As James bought his textbooks for classes one semester, he estimated the cost to the nearest ten dollars. He knew he could cover the cost up to $315. His math book cost $68.41, biology text was $105.35, literature text cost $72.49, and the AutoCAD text was $59.91. What rounded sum did James determine
Answers
Answer:
$310
Step-by-step explanation:
The first step is to add the costs of the textbook together :
$68.41 + $105.35 + $72.49 + $59.91 = $306.16
In order to round off to the nearest ten dollars, look at the units figure, if the number is greater or equal to 5, add 1 to the ten figure. If this is not the case, add zero. Replace the unit digit with zero
The unit digit is greater than 6, so 1 is added to the tens digit. The amount becomes $310
which equations have a leading coefficient of 3 and a constant term of -2?
Answers
Answer: the answer to this is 3x-2
Step-by-step explanation:
Below is a histogram representing the test scores from Mrs. Smith's 3rd period Algebra class. Which set of scores below could be represented by this histogram?
Answers
Answer:
82,83,84,80,84,86,91,96,95,99,97,92
y= -(x+3)^2 -5
What is the leading coefficient?
How do you find the vertex?
Answers
Answer:
To find the leading coefficient, first expand the function:
[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]
The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².
To find the vertex: see image below
Vertex = (-3, -5)
Independent Practice
Find the first, fourth, and eighth terms of the sequence.
an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline
A.
0.667; 4.5; 364.5
B.
3; 0.375; 0.0234375
C.
0.5; 13.5; 1093.5
D.
0.5; 121.5; 280.5
Answers
Answer:
C.
0.5; 13.5; 1093.5
Step-by-step explanation:
You are responsible to provide tennis balls for a tournament. You know that a ball bounces like new when it is dropped and it bounces 82% of the previous height. Because of budget restriction for the tournament you need to test some used balls to make sure they bounce like new tennis balls. You drop a ball and it bounces multiple times; each bounce reaches 82% the height of the previous height. a. Is this sequence geometric or arithmetic
Answers
Answer:
arithmetic
Step-by-step explanation:
because it bounced double
-URGENT- please helppp-
Answers
Answer:
Last option. She didn't use the reciprocal.
Answer:
The second, third, and fourth
Step-by-step explanation:
When you multiply two fractions, you multiply the numerator and denominator, not add them. Also, when you divide by a fraction and want to turn it into multiplication, you multiply by the reciprocal, which she didn't do. Hope this helps!
The figure below is a parallelogram. AB = 5 cm and BC = 3 cm. Find angle ABC
Answers
Step-by-step explanation:
her it go u can see it.. have a nice Day
