Answer:
9108
Step-by-step explanation:
23^3+(-12)^3+(-11)^3 remove parentheses
= 23^3-12^3-11^3 group difference of two cubes
= (23-12)(23^2+23*12+12^2) + 11^3 factor difference of two cubes
= 11 (23^2+23*12+12^2-11^2) factor ou 11
= 11(23(23+12) + (12+11)(12-11)) apply difference of two squares
= 11 (23*35+23*1) factor out 23
= 11(23*(35+1)) simplify
= 11*23*36 convert 11*23 into difference of 2 squares
= (17^2-6^2)*6^2 expand parentheses
= 102^2-36^2 evaluate squares
= 10404 - 1296 subtraction
= 9108
(no calculator required)
What are the zeros of the polynomial function? f(x)=x^3+x^2−9x−9
Answer:
1: x = -1
2: x = 3
3: x = -3
Step-by-step explanation:
f(x)=x^3+x^2−9x−9
f(x)=x^2(x+1) −9x−9
f(x) = x^2(x+1) - 9(x+1)
f(x)= (x+1)(x^2-9)
f(x) =(x+1)(x-3)(x+3)
Answer:
[tex]\boxed{x=-1, \ x=-3, \ x=3}[/tex]
Step-by-step explanation:
The zeros of a function are the values of x when f(x) = 0.
[tex]x^3 +x^2-9x-9=0[/tex]
Factor left side of the equation.
[tex]x^2(x +1)-9(x+1)=0[/tex]
Take (x+1) common.
[tex](x^2-9)(x+1)=0[/tex]
Set factors equal to 0.
First possibility:
[tex]x^2 -9=0[/tex]
[tex]x^2 =9[/tex]
[tex]x=\± \sqrt{9}[/tex]
[tex]x=\± 3[/tex]
[tex]x=-3 \ \mathrm{or} \ x=3[/tex]
Second possibility:
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
When solving (x + 35) = −7, what is the correct sequence of operations?
Answer:
x= -42
Step-by-step explanation:
put the liketerms together
x+35= -7
x=-35-7
note*the operation sign changes after crossing the equal sign
x= -42
expand (x-4)^4 with binomial theorem or pascal's triangle
Answer:
(x-4)^4=x⁴+4x³(-4)¹+6x²(-4)²+4x¹(-4)³+(-4)⁴
=x⁴-16x³+96x²-256x+256
Given that ΔABC is a right triangle with a right angle at C, if tan A = [tex]\frac{5}{4}[/tex], find the value for tan B.
A. tanB = [tex]\frac{3}{4}[/tex]
B. tanB = [tex]-\frac{4}{5}[/tex]
C. tanB = [tex]\frac{4}{5}[/tex]
D. tanB = [tex]-\frac{5}{4}[/tex]
Answer:
C
Step-by-step explanation:
tan A = [tex]\frac{5}{4}[/tex] = [tex]\frac{opposite}{adjacent}[/tex] , thus
The opposite side is the adjacent side for B and the adjacent side is the opposite side for B, thus
tan B = [tex]\frac{4}{5}[/tex]
need help...!! plzzz
Let n be the number of five-digit positive integers which are divisible by 36 and have their tens digit and unit digit equal. Find n/100
Answer:
1.) 10044
2.) 100.44
Step-by-step explanation:
Since n is a number of five-digit positive integers which are divisible by 36, start multiplying 36 by number. Starting from 278.
Five digits numbers start from multiplying 36 by 278. Any multiplication below 278 by 36 will give four digits numbers.
36 × 278 = 10,008
36 × 279 = 10,044
10,044 tens digit and unit digit equal. Therefore n = 10044
To find n/100, divide 10044 by 100
10044 / 100 = 100.44
Special right triangles
Answer: please find the attached files
Step-by-step explanation:
A unit circle formula and special triangle of 45, 30 and 60 degrees can be used to solve the problem.
Please find the attached files for the solution
2e - 3f = 4
2e - 5f = 8
solve this linear equation by the elimination method
please show your working ✨✨THANK YOU
Answer:
The value of e is -1 and f is -2.
Step-by-step explanation:
The steps are :
[tex]2e - 3f = 4 - - - (1)[/tex]
[tex]2e - 5f = 8 - - - (2)[/tex]
[tex]2e - 3f - 2e - ( - 5f) = 4 - 8[/tex]
[tex]2f = - 4[/tex]
[tex]f = - 4 \div 2[/tex]
[tex]f = - 2[/tex]
[tex]substitute \: f = - 2 \: into \: (1)[/tex]
[tex]2e - 3( - 2) = 4[/tex]
[tex]2e + 6 = 4[/tex]
[tex]2e = 4 - 6[/tex]
[tex]2e = - 2[/tex]
[tex]e = - 2 \div 2[/tex]
[tex]e = - 1[/tex]
To solve this system of equations by addition, our first goal is to cancel
out one of the variables by adding the two equations together.
However, before we add, we need to cancel out a variable.
I would choose to cancel out the e's.
To do this, we need a 2e and a -2e and
here we have a 2e in both equations.
If we multiply the second equation by -1 however,
that will give us the -2e we are looking for.
So we have (-1)(2e - 3f) = (4)(-1).
So rewriting both equations, our first equation stays the same
but our second equation becomes -2e + 3f = -4.
Notice that every term in the second
equation has been multiplied by -1.
2e - 3f = 4
-2e + 5f = -8
Now when we add the equations together,
the e's cancel and we have 2f = -4 so f = -2.
To find e, plug -2 back in for f in the
first equation to get 2e - 3(-2) = 4.
Solving from here, e = -1.
Note that e comes before f in our final answer, (-1, -2).
To determine which variable should go first
in your answer, use alphabetical order.
Given that T{X: 2<x ≤ 9} where x is an integer. what is n(T)
Answer:
n(T) = 7Step-by-step explanation:
Given the set T{X: 2<x ≤ 9} where x is an integer, the element of the set T will be {3, 4, 5, 6, 7, 8, 9}. note that from the inequality set 2<x ≤ 9, x is not equal to 2 but greater than 2. The inequality can be divided into two as shown;
If 2<x ≤ 9 then 2<x and x≤9
If 2<x, this means x>2 but not equal to 2. This is the reason why 2 is not contained in the set T.
Similarly if x≤9, this shows that x can not be greater than 9 but less than or equal to 9.
Since the set T = {3, 4, 5, 6, 7, 8, 9}, we are to find n(T). n(T) means cardinality of the set T and cardinality of a set is defined as the total number of element in a set.
Hence n()n(T) = 7 (since there are 7 elements in the set T)
A cube whose edge is 20 cm 1 point
long, has circles on each of its
faces painted black. What is the
total area of the unpainted
surface of the cube if the
circles are of the largest
possible areas?(a) 90.72 cm2 (b)
256.72 cm² (c) 330.3 cm² (d)
514.28 cm?
Answer:
Unpainted surface area = 514.28 cm²
Step-by-step explanation:
Given:
Side of cube = 20 Cm
Radius of circle = 20 / 2 = 10 Cm
Find:
Unpainted surface area
Computation:
Unpainted surface area = Surface area of cube - 6(Area of circle)
Unpainted surface area = 6a² - 6[πr²]
Unpainted surface area = 6[a² - πr²]
Unpainted surface area = 6[20² - π10²]
Unpainted surface area = 6[400 - 314.285714]
Unpainted surface area = 514.28 cm²
The probability that it rains is about 20%.
The probability that the bus is late is about 8%.
The probability that it rains and the bus is late is about 3%.
The probability that the train is late is about 5%.
The probability that it rains and the train is late is about 1%.
6. To decide whether the rain and the train running late are dependent or independent events, first define the two events and then write their probabilities as decimals. (3 points) Let event A = ________________________. P(A) = ______. Let event B = ________________________. P(B) = ______. A and B = ________________________. P(A and B) = ______. 7. Use the probabilities from question 6 to decide whether the rain and the train running late are independent or dependent events. (2 points: 1 point for the correct math, 1 point for the conclusion)
Answer:
Step-by-step explanation:
Let A= probability it rains
P(A)=0.2
Let B be the probability that the train is late = 0.05
P(B)=0.05
A and B is A∩B= the probability it rains and the bus is late =0.01
probability pf (A and B)=0.01
7) independent events are related by expression:
A∩B=P(A)*P(B)
=0.2*0.05=0.01
check :
p(A|B)=P(A∩B)÷P(B)=0.01/0.05= 0.2
the two event are independent
Answer:
The two are independent.
Step-by-step explanation:
All the edges of a cube have the same length. Tony claims that the formula SA = 6s, where s is the length of
each side of the cube, can be used to calculate the surface area of a cube.
a. Draw the net of a cube to determine if Tony's formula is correct.
b. Why does this formula work for cubes?
Frances believes this formula can be applied to calculate the surface area of any rectangular prism. Is
she correct? Why or why not?
d. Using the dimensions of Length, Width and Height, create a formula that could be used to calculate the
surface area of any rectangular prism, and prove your formula by calculating the surface area of a
rectangular prism with dimensions L = 5m, W = 6m and H=8m.
Answer:
Here's what I get
Step-by-step explanation:
a. Net of a cube
Fig. 1 is the net of a cube
b. Does the formula work?
Tony's formula works if you ignore dimensions.
There are six squares in the net of a cube.
If each side has a unit length s, the total area of the cube is 6s.
c. Will the formula work for any rectangular prism?
No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.
d. Area of a rectangular prism
A rectangular prism has six faces.
A top (T) and a bottom (b) — A = 2×l×w
A left (L) and a right (R) — A = 2×l×h
A front (F) and a back (B) — A = 2×w×h
Total area = 2lw + 2lh + 2wh
If l = 5 m, w = 6 m and h = 8 m,
[tex]\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}[/tex]
Can you please help me on add and subtract fractions level 1 9/8-11/8
Answer:
7/8
Step-by-step explanation:
1. Make 1 9/8 into an improper fraction
1 = 8/8
8/8 + 9/8 = 17/8
2. Subtract
17/8 - 11/8 = 7/8
Score for Question 3: of 5 points)
. What is the area of triangle BCD to the nearest tenth of a square centimeter? Use special right triangles to
help find the height. Show your work.
Answer:
[tex] \frac{25 \sqrt{3} }{2} [/tex]
Step-by-step explanation:
Height = 5 * tan 60°
[tex]height \: = 5 \sqrt{3} [/tex]
[tex]area = \frac{1}{2} \times 5 \times 5 \sqrt{3 } = \frac{25 \sqrt{3} }{2} [/tex]
What is the probability of rolling a number greater than 6 on a number cube
Answer:
0
Step-by-step explanation:
It is not possible to roll a number greater than 6 on a number cube
A probability of 0 means "impossible". This is because a standard number cube (aka a die) has sides labeled 1 through 6. There is no way to roll something larger than 6 on a single die.
A customer owes a balance of $400 on their lease. They have a $75 payment due each month. What will be their remaining balance after their next 2 monthly payments are made?
Answer:
Step-by-step explanation:
2(75)=150 that's the amount due in total for two months so
400-150= 250 they will owe $250 after two months payment
The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 36°.Calcule the height of the pole
===================================================
Work Shown:
x = starting length of the shadow
y = height of the pole
tan(angle) = opposite/adjacent
tan(58) = y/x
1.6003345 = y/x
1.6003345x = y
x = y/1.6003345
x = (1/1.6003345)y
x = 0.62486936y
-------------------------
When the angle changes, the adjacent side gets 90 meters longer
tan(angle) = opposite/adjacent
tan(36) = y/(x+90)
0.72654253 = y/(0.62486936y+90)
0.72654253(0.62486936y+90) = y
0.453994166y + 65.3888277 = y
65.3888277 = y-0.453994166y
65.3888277 = 0.546005834y
0.546005834y = 65.3888277
y = 65.3888277/0.546005834
y = 119.758478075162
y = 119.76
The height of the pole is about 119.76 meters.
To determine the relative effectiveness of different study strategies for the SAT, suppose three groups of students are randomly selected: One group took the SAT without any prior studying; the second group took the SAT after studying on their own from a common study booklet available in the bookstore; and the third group took the SAT after completing a paid summer study session from a private test-prep company. The means and standard deviations of the resulting SAT scores from this hypothetical study are summarized below:
Using the following output:
we can conclude that:
(a) the data provide strong evidence that SAT scores are related to learning strategy.
(b) the data provide strong evidence that SAT scores are related to learning strategy in the following way: The mean SAT score for students who pay for coaching is higher than the mean SAT score for students who study themselves, which in turn is higher than that of students who do not study for the test.
(c) the data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal.
(d) the data do not provide sufficient evidence that SAT scores are related to learning strategy.
(e) Both (a) and (c) are correct.
Answer:
(b) the data provide strong evidence that SAT scores are related to learning strategy in the following way: The mean SAT score for students who pay for coaching is higher than mean SAT score for students who study themselves, which in turn is higher than those students who do not study for test.
(c) The data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal.
Step-by-step explanation:
Relative effectiveness is to study the extent to which an intervention of a thing does more good than harming it when two or more alternative interventions are observed. In the given question the SAT mean score for students who are paying higher for coaching than those student who believe in self study.
The focus of a parabola is (3,-7) and the directrix is y = -4.
What is an equation of the parabola?
Answer:
(a) (x -3)^2 = -6(y +5.5)
Step-by-step explanation:
The equation of a parabola can be written as ...
(x -h)^2 = 4p(y -k)
where (h, k) is the vertex, and p is the distance from the focus to the vertex.
The vertex is half-way between the focus and directrix, so is ...
(h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)
The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...
-7 -(-5.5) = -1.5
Then the equation for the parabola is ...
(x -3)^2 = 4(-1.5)(y -(-5.5))
(x -3)^2 = -6(y +5.5) . . . . matches the first choice
Please answer this question now
Answer:
V = 60 m³
Step-by-step explanation:
Volume of Triangular Pyramid: V = 1/3bh
Area of Triangle: A = 1/2bh
b = area of bottom triangle (base)
h = height of triangular pyramid
Step 1: Find area of base triangle
A = 1/2(8)(5)
A = 4(5)
A = 20
Step 2: Plug in known variables into volume formula
V = 1/3(20)(9)
V = 1/3(180)
V = 60
what is the value of x ?
Answer:
65dg.
Step-by-step explanation:
Triangles are 180dg.
So 68dg + 47dg = 115dg.
-180dg - 115dg = 65dg.
So the missing length is 65 degrees.
Answer: 65
Step-by-step explanation:
Add both of the numbers on there. Then do 180- that number.
68+47=115
180+115=65
This is because in a triangle all the angles together equal 180.
A ladder (line segment AC in the diagram) is leaning against a wall. The distance between the foot of the ladder and the wall (BC) is 7 meters less than the distance between the top of the ladder and the ground (AB). A-Create an equation that models the length of the ladder (l) in terms of x, which is the length in meters of AB. B-If the length of the ladder is 13 meters, use the equation you wrote to find the distance between the ground and the top of the ladder (AB).
Greetings from Brasil...
a)
Let's just use Pythagoras
L² = X² + (X - 7)²
L = √(2X² - 14X + 49)b)
If L = 13, then what is the value of X ???
L² = 2X² - 14X + 49
2X² - 14X - 120 = 0
X = 12 or X = - 5
(The distance cannot be negative, so X = 12)
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. The height (in feet) of a rocket launched from the ground is given by the function f(t) = -16t2 + 160t. Match each value of time elapsed (in seconds) after the rocket’s launch to the rocket's corresponding instantaneous velocity (in feet/second).
Answer:
The pairs are;
t, v
2, 96
4, 32
5, 0
6, -32
7, -64
9, -128
Step-by-step explanation:
The given equation is f(t) = -16·t² + 160·t
We have, the velocity, v = d(f(t))/dt = d(-16·t² + 160·t)/dt = -32·t + 160
Which gives;
t, v
0, -32×(0) + 160 = 160
1, -32×(1) + 160 = 128
2, -32×(2) + 160 = 96
3, -32×(3) + 160 = 64
4, -32×(4) + 160 = 32
5, -32×(5) + 160 = 0
6, -32×(6) + 160 = -32
7, -32×(7) + 160 = -64
8, -32×(8) + 160 = -96
9, -32×(9) + 160 = -128
The given velocity values are;
96, -64, 32, 0, -128, -32 which correspond to 2, 7, 4, 5, 9, 6
The pairs are;
t, v
2, 96
4, 32
5, 0
6, -32
7, -64
9, -128
My computer can download a movie in 5 hours. If I install an extra processor it can download the movie in 4 hours. How long, working alone, would it have taken the new extra processor to download the movie?
Answer:
20 hours
Step-by-step explanation:
Computer download=5 hours
Computer + Extra processor=4 hours
Computer's rate =1/5 per hour
Computer + extra processor rate=1/4 per hour
Extras processor rate=1/x
Where,
x=how long it takes extra processor to get the job done on its own.
To find x, we have to solve the equation
1/5 + 1/x = 1/4
Subtract 1/5 from both sides
1/5 + 1/x -1/5 = 1/4-1/5
1/x=1/4-1/5
1/x = 5-4/20
1/x = 1/20
Cross product
1(20)=x(1)
20=x
x=20 hours
It would have taken the new extra processor alone 20 hours to download the movie
A restaurant wanted to track how much of a quart of soda customers drank at a meal. The line plot displays the data collected by the restaurant. How much more soda did the customers who drank 3/4 of a quart drink than the customers who drank 1/4 of a quart?
Answer:
C
Step-by-step explanation:
13/4 simplified---->3and 1/4
Christine's gross monthly salary at her job
is $5,250. She has the following
deductions from her paycheck.
What is Christine's net take-home pay per
month?
Answer:
$2587.87 per month
Step-by-step explanation:
The listed deductions are ...
25% withheld for federal income tax9.3% withheld for California state income tax6.2% withheld for Social Security tax1.45% withheld for Medicare Tax0.9% withheld for SDI- Disability Insurance5% goes into her retirement 401K account$150 goes to health insurance/ dental for her familyThe percentages have a total of ...
25 +9.3 +6.2 +1.45 +0.9 +5 = 47.85 . . . percent
So, Christine's take-home pay is ...
$5250(1 -0.4785) -150 = $2587.87 . . . per month
Find the rate of change for the situation. A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.
Demerol 45mg and atropine 400mcg/ml give how much per ml to total volume to inject demerol contains 50mg/ml, atropine contains 400mcg/ml how much volume to inject
Answer:
Volume injected = 1.65 ml
Step-by-step explanation:
mass of Demerol =45 mg.
density of pre-filled in syringe = 50 mg/ml
Volume = 45/50 = 0.9 ml
For atropine mass = 0.3 mg
density= 400 mcg/ml [ Note : 1 mcg = 0.001 mg]
volume filled = 0.3/400(0.001) = 0.75 ml
So, the total volume filled = 0.75+0.9 = 1.65 ml
Determine the minimum rotation (in degrees) which will carry the following figures onto itself (where all sides and verticles will match up). Assume this is a regular polygon. Round to the nearest tenth if necessary.
Answer:
60°
Step-by-step explanation:
A full rotation is 360°. The figure has six sides.
1. Divide
360 ÷ 6 = 60
Each angle of the polygon is 60°. Therefore, the polygon must be rotated at least 60° for the figure to match all sides and vertices.
Juan works as a tutor for $12 an hour and as a waiter for $7 an hour. This month, he worked a combined total of 110 hours at his two jobs.
Let t be the number of hours Juan worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.
Answer:
12t+7w=D
t+w=110
Step-by-step explanation:
12t= $12 made every tutor hour
7w= $7 made every waiter hour
D= total dollars made
t+w=110 is the tutor hour and the waiter hour adding together
Answer:
12t + 7y = x
or
5t + 770 = x
Step-by-step explanation:
12t + 7y = x
t = number of hours he worked as a tutor
y = number of hours he worked as a waiter
x = the total amount of money he earned
t + y = 110
=> y = 110 - t
=> 12t + 7(110 - t) = x
=> 12t + 770 - 7t = x
=> 5t + 770 = x
