Answer:
volume = L*B*H
Step-by-step explanation:
SO,
Volume of the box = L*B*H
OR, Volume of the box = 10*12*3
thus, Volume of the box =360
What is the factored form of this expression? 4x^3 - 8x^2 - 9x + 18
A. (2x + 3)(2x - 3)(x - 2)
B. (2x + 3)(2x + 3)(x - 2)
C. (2x + 3)(2x - 3)(x + 2)
D. (2x - 3)(2x - 3)(x - 2)
Answer: D
Step-by-step explanation:
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
(2x + 3)(2x - 3)(x - 2) is the factor form of the expression (2x + 3)(2x - 3)(x - 2).
Option A is the correct answer.
(2x + 3)(2x - 3)(x - 2).
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
4x³ - 8x² - 9x + 18
We will check the expression in factor form:
A.
(2x + 3)(2x - 3)(x - 2)
(2x + 3) (2x² - 4x - 3x + 6)
4x³ - 8x² - 6x² + 12x + 6x² - 12x - 9x + 18
4x³ - 8x² - 9x + 18 ____(1)
B.
(2x + 3)(2x + 3)(x - 2)
(2x + 3) (2x² - 4x + 3x - 6)
4x³ - 8x² + 6x² - 12x + 6x² - 12x + 9x - 18
4x³ + 4x² - 15x - 18 ____(2)
C.
(2x + 3)(2x - 3)(x + 2)
(2x + 3) (2x² + 4x - 3x - 6)
4x³ + 8x² - 6x² - 12x + 6x² + 12x - 9x - 18
4x³ + 14x² + 3x - 18 ____(3)
D.
(2x - 3)(2x - 3)(x - 2)
(2x - 3) ( 2x² - 4x - 3x + 6)
4x³ - 8x² - 6x² + 12x - 6x² + 12x + 9x - 18
4x³- 20x² + 33x - 18 ____(4)
From (1), (2), (3), and (4) we see that,
(2x + 3)(2x - 3)(x - 2) is the factor form of the expression (2x + 3)(2x - 3)(x - 2).
Option A is the correct answer.
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The table shows the height of water in feet at different times. The water rises and falls in a cyclical pattern.
A 2-column table with 5 rows. Column 1 is labeled x with entries 12 a m, 3 a m, 6 a m, 9 a m, 12 p m. Column 2 is labeled y with entries 6, 10, 6, 2, 6.
Which equation models the data in the table?
y = 6 sine (StartFraction pi Over 6 EndFraction x) + 2
y = 6 sine (StartFraction pi Over 6 EndFraction x) + 4
y = 4 sine (StartFraction pi Over 6 EndFraction x) + 6
y = 4 sine (StartFraction pi Over 6 EndFraction x) + 10
Answer:
c
Step-by-step explanation:
Modeling the data in the table is done via the equation y = 4 sine (pi/6x) + 6.
What is a cyclic pattern?Over a period of years, a cyclical pattern recurs with considerable regularity. Cyclical patterns are distinct from seasonal patterns in that they last across a number of years as opposed to only one year for seasonal trends.
Given, The table shows the height of water in feet at different times. The water rises and falls in a cyclical pattern.
Table:
12 AM 6
3 AM 10
6 AM 6
9 AM 2
12 PM 6
from the general formula of wave
y = A sin(bx + c)
Substituting values in the equation from the graph attached below:
6 = A sin(0*b + c)......(1)
10 = A sin3b + c...(2)
6 = A sin6b + c......(3)
2 = A sin9b +c........(4)
Since -c/b is a phase shift of the graph
Thus
-c/b = 6
c = -6b
from equations 2 and 1
2* 6 = Asin(-3b) = -Asin3b
2 * 6 = Asin(-6b) = -Asin6b
2* 6/6 =sin6b/sin3b
1 = Cos3b
Thus b = π/6
from substitution in equations 3
6 = A sin6b + c
=> 6 = Asin 6* pi/6 + c
=> c = 6
[tex]\begin{table}[]\begin{tabular}{ll}12 AM & 6 \\3 AM & 10 \\6 AM & 6 \\9 AM & 2 \\12 PM & 6 \end{tabular}\end{table}[/tex]from substitution in equations 2
10 = A sin3b + c
A = 4
therefore, The equation that models data in the table is y = 4 sine (pi/6x) + 6.
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1. (12 points) The tennis team at Taft High School has 8 players, and the tennis team at McKinley High School has 7 players. Rebecca is on the team at Taft, and her sister Leah is on the team at McKinley. The two teams are going to play a tournament with 4 rounds. In each round, one player from Taft will play a match against one player from McKinley. Each player can play in at most one match. A schedule for the tournament consists of an ordered list of the names of the players from each school who will play in each of the four rounds. The schedule does not include the results of each match. (a) How many schedules are there?
Complete Question
1. (12 points) The tennis team at Taft High School has 8 players, and the tennis team at McKinley High School has 7 players. Rebecca is on the team at Taft, and her sister Leah is on the team at McKinley. The two teams are going to play a tournament with 4 rounds. In each round, one player from Taft will play a match against one player from McKinley. Each player can play in at most one match. A schedule for the tournament consists of an ordered list of the names of the players from each school who will play in each of the four rounds. The schedule does not include the results of each match.
(a) How many schedules are there?
(b) How many schedules include neither sister?
Answer:
a
[tex]N = 1,411,200[/tex]
b
[tex]M = 302, 400[/tex]
Step-by-step explanation:
From the question we are told that
The number of players in Taft High School is t = 8
The number of players in McKinley High School is k = 7
The number of rounds is n = 4
The highest number of match each player can play is w = 1
Generally the total number of schedules is
[tex]N = ^tP_4 * ^k P_4[/tex]
[tex]N = ^8P_4 * ^7 P_4[/tex]
=> [tex]N = \frac{8!}{(8-4)!} * \frac{7!}{(7-4)!}[/tex]
=> [tex]N = \frac{8!}{4!} * \frac{7!}{3!}[/tex]
=> [tex]N = \frac{8*7 *6*5*4*3*2*1}{4*3*2*1} * \frac{7*6*5*4*3*2*1}{3*2*1}[/tex]
=> [tex]N = 1,411,200[/tex]
Generally the number of schedules that include neither of the sisters is mathematically represented as
[tex]M= \ ^{t-1}P_4 *\ ^ {k-1} P_4[/tex]
[tex]M= \ ^{8-1}P_4 *\ ^ {7-1} P_4[/tex]
=> [tex]M= \ ^{7}P_4 *\ ^ {6} P_4[/tex]
=> [tex]M = \frac{7!}{(7-4)!} * \frac{6!}{(6-4)!}[/tex]
=> [tex]M = \frac{7!}{3!} * \frac{6!}{2!}[/tex]
=> [tex]M = \frac{7 *6*5*4*3*2*1}{3*2*1} * \frac{6*5*4*3*2*1}{2*1}[/tex]
=> [tex]M = 302, 400[/tex]
M bisects QP, and QP = 27.4. Find QM.
Answer:
13.7
Step-by-step explanation:
All you need to do is divide by 2, hope this helped!
Answer:
QM = 13.7
Step-by-step explanation:
Step 1:
QP ÷ M = QM Def. of ∠ bisector
Step 2:
27.4 ÷ 2 Input Values
Answer:
13.7 Divide
Hope This Helps :)
#1.) What is the slope between point C and Point D? *Please Show All Work*
#2.) What is the equation of the line (Slope-Intercept Form: y = mx + b) that represents the climb from Point C to Point D? *Please Show All Work*
#3.) What is the domain and range the C to D part of the roller coaster?
Answer:
1. [tex] m = slope = \frac{12}{7} [/tex]
2. [tex] y = \frac{12}{7}x [/tex]
3. Domain: 0≤x≤7
Range: 0≤y≤12
Step-by-step explanation:
1. Assuming 1 unit = 1 box on the grid, therefore, coordinates of C and D would be:
C(0, 0),
D(7, 12)
[tex] Slope = m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 0}{7 - 0} = \frac{12}{7} [/tex]
2. Equation of the using the slope-intercept formula, [tex] y = mx + b [/tex], where,
[tex] m = slope = \frac{12}{7} [/tex]
b = y-intercept, which is where the line CD cuts the y-axis = 0
Plug in the values for m and b into the formula to get the equation of the line:
[tex] y = \frac{12}{7}x + 0 [/tex]
[tex] y = \frac{12}{7}x [/tex]
3. The domain for C to D part = all x-values = 0≤x≤7
The range = all y-values = 0≤y≤12
Please help its vocab matching
Answer:
1. S
2. G
3. I
4. O
5. P
6. D
7. C
8. F
9. J
10. Q
11. E
12. K
13. R
14. A
15. B
16. N
17. M
18. L
19. H
Step-by-step explanation:
4. O
→ 3 is a coefficient of 3x
5. P
→ 3 is a common factor in the expression 3x+9
6. D
→example of a constant term is 1,3,10
7. C
→ [tex]cosx=\frac{adjacent}{hypotenuse} =\frac{A}{H}[/tex]
8. F
→[tex]x^{2} -4[/tex] will be factorised as (x-2)(x+2)
9. J
→ example of an expression is [tex]2x+9[/tex]
10. Q
→ factors of 3 are 3×1.
11. E
→ example of factoring is [tex](x+2)(3x+4)[/tex]
12. K
→ example of a factored completely is [tex]2x(x+y)[/tex]
14. A
→example of a polynomial is [tex]3yx^{3} +xy^{2} -2x+9[/tex].
15. B
→ example of a quadratic expression is [tex]x^{2} +6x-9[/tex].
17. M
→ [tex]sinx=\frac{opposite}{hypotenuse} =\frac{O}{H}[/tex]
18. L
→ [tex]tanx=\frac{opposite}{adjacent} =\frac{O}{A}[/tex]
19. H
→ example of a term is 2x,3,40
Bernard a part of a small pizza he started with 11/12 of a pizza but only ate 2/3 of it which is the best estimate of the amount Bernard ate?
Answer:
Bernard ate a little less than Two-thirds of the pizza.
Step-by-step explanation:
i took the test
Answer:
c 2/3
Step-by-step explanation:Bernard ate part of a small pizza. He started with StartFraction 11 Over 12 EndFraction of a pizza but only ate Two-thirds of it. Which is the best estimate of the amount Bernard ate?as u can see it said HOW many did he eat he ate 2/3 of it your welcome friend!
Question
The force needed to break a board varies inversely with its length. Richard uses 24 pounds of pressure to break a 2-foot-
long board. How many pounds of pressure is needed to break a 5-foot-long board?
Provide your answer below:
Answer:
9.6
Step-by-step explanation:
60 pounds of pressure is needed to break a 5-foot-long board,
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Richard uses 24 pounds of pressure to break a 2-foot-long board.
How many pounds of pressure is needed to break a 5-foot-long board,
we have to find.
i.e. 24/2 * 5
=12*5
=60
hence, 60 pounds of pressure is needed to break a 5-foot-long board,
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factor the equation 25+10x+x^2
Step 1:
[tex]25+10x+x^2[/tex]
Let's split split 10x to factorise
Step 2:
[tex] = 25 + 5x + 5x + {x}^{2} [/tex]
Step 3:
[tex] = 5(5 + x) + x(5 + x)[/tex]
Step 4:
[tex] \green{= (5 + x)(5 + x)✓}[/tex]
________________________Best regards!
★Dull Star★
Answer:
(x+5)(x+5)
Step-by-step explanation:
Let's arrange it in a proper manner first of all.
x² + 10x + 25Step: Spilt 10x in order to factorize it.
x² + 10x + 25
0r, x² + 5x + 5x + 25
Step: Make two pairs from equation
x² + 5x + 5x + 25
0r, x(x+5) + 5(x+5)
Step: Take common thing from the given equation
x(x+5) + 5(x+5)
0r, (x+5)(x+5)
Hence, (x+5) and (x+5) are the factor for the given equation.
PLEASEE HELP ME I DID THE FIRST BUR NEED HELP WITH THE OTHERS JM BEING TIMED
Answer:
nejkbfjlsldfbzjhghbgjlfdbgjsb
Step-by-step explanation:
fjkngsdngjkngsknjb.kxnb vncx gbjfx,cnm cfjgjg.kfdontjdgklbvj.bzexpectbdfjskbhsljhelpdsfjlzbjbdzjwhen ndsjbdjzsbfzjsyouncsjdlafbjlcant njdfslabgahelpvmxnzkznf,anyonenjsdflfnSLelsendjzlknjidiotnjdflzngjlznloser fdsalfhjlzgbdhjlzfbglj
(x+4)(x-5)+(x+4)(x-2)
Answer:
(x+4)⋅(2x−7)
Step-by-step explanation:
Combine the like terms.
Recall from Intermediate Algebra that two non-vertical lines are perpendicular if and only if they have negative reciprocal slopes. That is to say, if one line has slopem1and the other has slopem2thenm1 · m2 = −1.Please note that a horizontal line is perpendicular to a vertical line and vice versa, so we assumem1 ≠ 0andm2 ≠ 0.Below, you are given a line and a point which is not on that line. Find the line perpendicular to the given line which passes through the given point.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The line is [tex]y = -4 x[/tex]
Step-by-step explanation:
From the question we are told that
The line is [tex]y = \frac{1}{4} x + 8[/tex]
The point is P(0,0 )
Generally the equation for a line is [tex]yn = mx + c[/tex]
Now comparing this with the given equation we see that
[tex]m =\frac{1}{4} = slope[/tex]
[tex]C =8 = intercept [/tex]
Generally the slope of the perpendicular to the given line is mathematically evaluated as
[tex]m_1 = - \frac{1}{m}[/tex]
=> [tex]m_1 = - \frac{1}{ \frac{1}{4}}[/tex]
=> [tex]m_1 = -4 [/tex]
Generally from the univesal equation of a line and the given point we have that
y = mx + c at p(0,0) and [tex]m_1 = -4[/tex] is
0 = -4 (0 ) + c
=> c = 0
Hence the equation perpendicular to the line given at the point given is
[tex]y = -4 x[/tex]
If y= 44 when x=240, what is the value of y when x=84?
What is the conjugate and modulus of 2 – 6i?
Answer:
2 + 6i
Step-by-step explanation:
It’s the same numbers with an opposite sign
The conjugate of 2 – 6i is 2 + 6i and the modulus is [tex]\sqrt{40}[/tex]
The conjugate of a complex number a + bi is a - bi. The conjugate is gotten by changing the sign of the imaginary part of the complex number.
The modulus of a complex number a + bi is:
|a + bi| = [tex]\sqrt{a^2+b^2}[/tex]
The conjugate and modulus of 2 – 6i is:
Conjugate of 2 - 6i = 2 + 6i
|2 - 6i| = [tex]\sqrt{2^2+(-6)^2}=\sqrt{40}[/tex]
The conjugate of 2 – 6i is 2 + 6i and the modulus is [tex]\sqrt{40}[/tex]
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Simplify.
6 ( to the power of 2 )+4 ( to the power of 2
12
20
52
100
Answer:
6 times 6 = 12 + 4 times 4 = 16 so 12 + 16 =28
Step-by-step explanation:
Determine the intercepts please be sure
Answer:
X= (-40, 0)
Y= ( 0, 15
Step-by-step explanation:
Goodluck :)
what is the value of n n+11=13
Answer:
n = 2
Step-by-step explanation:
[tex]n + 11 = 13[/tex]
Subtract 11 from both sides to isolate n.
[tex]n + 11 - 11 = 13 - 11[/tex]
[tex]n = 2[/tex]
Simplify.
2 ( to the power of 3)+4⋅8
40
80
96
160
Answer:
2 to the power of 3 is 8 so
8 + 4.8 = 12.8
Step-by-step explanation:
juan reads 300 pages in 5 days and jose reads 150 in 3 days are these reading rates equivalent
Answer:
60 pages per day.
Step-by-step explanation:
300 ÷ 5 = 60.
Find the distance and midpoint between the pair of points. A(-1, 0), B(2, -4)
Answer:
distance is 5
midpoint is (1/2,-2)
Step-by-step explanation:
Please help me i will give all of my points 14
Please help i need this right now
Answer:
3 7/12
Step-by-step explanation:
y2=2x2−1 is a function
Answer:
what do you need to to know 1) what kind of function its or 2) whats the answer of y and/or x
A bag contains the following marbles: 5 black , 15 blue, 20 brown , and 10 green . What is the ratio of the green marbles to bkue marbles ? Express your ratio as a fraction or with a colon
Answer: 1:3:4:2
Step-by-step explanation: Cause it is :D
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Which of the following numbers are between 2/5 and 7/8
15/16
3/4
3/8
1/3
5. A gift box is 8 inches long, 3 inches wide
and 4 inches tall. What is the approximate
length of its longest diagonal?
A. 9.4 inches
B. 10.2 inches
C. 15 inches
D. 89 inches
Suppose a university advertises that its average class size is 32 or less. A student organization is concerned that budget cuts have led to increased class sizes and would like to test this claim. A random sample of 40 classes was selected, and the average class size was found to be 34.8 students. Assume that the standard deviation for class size at the college is 99 students. Using α=0.10, complete parts a and b below.a. Does the student organization have enough evidence to refute the college's claim?Determine the null and alternative hypotheses.Upper H 0H0:μ▼Upper H 1H1:μ▼
Answer:
a
The student does have enough evidence to refute the college claim
b
The null hypothesis is [tex]H_o : \mu \le 32[/tex]
The alternative hypothesis is [tex]H_a : \mu > 32[/tex]
Step-by-step explanation:
From the question we are told that
The average class size is [tex]\mu = 32[/tex]
The sample size is [tex]n = 40[/tex]
The sample mean is [tex]\= x = 34.8[/tex]
The standard deviation is [tex]\siigma = 99[/tex]
The significance level is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \mu \le 32[/tex]
The alternative hypothesis is [tex]H_a : \mu > 32[/tex]
Generally the test statistics is mathematically represented as
[tex]z =\frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]z = \frac{34.8 - 32}{ \frac{99 }{\sqrt{99} } }[/tex]
=> [tex]z = 0.1789 [/tex]
Generally the p-value is mathematically represented as
[tex]p- value = P (Z > 0.1789)[/tex]
From the z- table
[tex] P (Z > 0.1789) =0.42901 [/tex]
So
[tex]p- value = 0.42901 [/tex]
So from the calculation we can see that [tex]p- value > \alpha[/tex] so we fail to reject the null hypothesis
This means that the student does not have enough evidence to refute the college claim
Jamal makes $12.00/hour and worked 9 hours today. What is his total pay? Don't forget to calculate overtime pay.
Answer:
He made $108 in 9 hours
Step-by-step explanation:
I first multiplied 12 by 9 and got 108
Answer:
$108
Step-by-step explanation:
12 x 9 = 108
$108/9 hours
True or False: 0/2=2/0
Answer:
it's true 0 divided by 2 is 0 and 2 divided by 0 is still 0
HELP FAST PLZ!!!!!! (07.01)
What is the value of x in the equation 8 + x = 37
O -5
O 5
O 11
O 24
Answer:
x = 29
Step-by-step explanation:
8 + x = 37
Subtract 8 from each side
8-8 + x = 37-8
x = 29
for the inequality Y
Step-by-step explanation:
Ur qsn is so confusing can you plz rewrite it