Answer: D
Step-by-step explanation:
[tex](4x+y)^3\\\\=(4x)^3+3*(4x)^2*y+3*(4x)*y^2+y^3\\\\=64x^3+48x^2y+12xy^2+y^3\\\\Answer\ D[/tex]
Answer:
D
Step-by-step explanation:
A ball is dropped from a height of 14 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen. (a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. (Enter an exact number.)
Answer:
Hello,
742/27 (ft)
Step-by-step explanation:
[tex]h_1=14\\\\h_2=\dfrac{14}{3} \\\\h_3=\dfrac{14}{9} \\\\h_4=\dfrac{14}{27} \\\\[/tex]
[tex]d=14+2*\dfrac{14}{3} +2*\dfrac{14}{9} +2*\dfrac{14}{27} \\=14*(1+\dfrac{1}{3}+\dfrac{2}{9} +\dfrac{2}{27} )\\=14*\dfrac{53}{27} \\=\dfrac{742}{27} \\[/tex]
The total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]
What is the total distance?
Distance is a numerical measurement of how far apart objects or points are. It is the actual length of the path travelled from one point to another.
Here given that,
A ball is dropped from a height of [tex]14[/tex] ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen.
So, after striking with the ground it covers the distance [tex]14[/tex] ft. so it rebounds to the height is [tex]\frac{1}{3}(14)[/tex].
Then again it hits the ground and covers the distance [tex]\frac{1}{3}(14)[/tex] and again after rebounding it goes to the height is
[tex]\frac{1(1)}{3(3)}.(14)=\frac{(1)^2}{(3)^2}(14)[/tex]
Then it falls the same distance and goes back to the height
[tex]\frac{1}{3}[/tex] ×[tex](\frac{(1)^2}{(3)^2})[/tex] ×[tex]14[/tex] = [tex]\frac{(1)^3}{(3)^3}(14)[/tex]
So, the total distance travelled is
[tex]14+2[\frac{1}{3}(14)+(\frac{1}{3})^2(14)+(\frac{1}{3})^3(14)+...][/tex]
We take the sum is twice because it goes back to the particular height and falls to the same distance.
[tex]S=14+2(\frac{\frac{1}{3}(14)}{1-\frac{1}{3}})\\\\\\S=\frac{a}{1-r}\\\\\\S=14+2(\frac{\frac{14}{3}}{\frac{2}{3}})\\\\S=14+2(\frac{14}{2})\\\\S=14+2(7)\\\\S=14+14\\\\S=28ft[/tex]
Hence, the total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]
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Can I get help with this -5-(3^2+2)
Answer:
-16
Step-by-step explanation:
-5-(3^2+2)
Parentheses first
-5-(9+2)
-5-(11)
Subtract
-16
If ∠G measures 45°, ∠F measures 82°, and f is 7 feet, then find g using the Law of Sines. Round your answer to the nearest foot. triangle EFG with side e across from angle E, side f across from angle F, and side g across from angle g 4 feet 5 feet 6 feet 7 feet
The value of g across from angle G is 5feet
According to sine rule
[tex]\frac{e}{sinE}=\frac{f}{sinF}=\frac{g}{sinG}[/tex]
Given the following
∠G = 45°
∠F = 82°
f = 7feet
Required
side g
Substitute the given values into the formula
[tex]\frac{f}{sinF}=\frac{g}{sinG}\\ \frac{7}{sin82}=\frac{g}{sin45}\\\frac{7}{0.9903}=\frac{g}{0.7071}\\7.0686=\frac{g}{0.7071}\\g=7.0686*0.7071\\g=4.998\\g\approx5ft[/tex]
Hence the value of g across from angle G is 5feet
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The length of the line segment EF ([tex]g[/tex]) is approximately 5 feet.
Let be [tex]EFG[/tex] a Triangle, whose expression derived from the Law of Sines is described below:
[tex]\frac{e}{\sin E} = \frac{f}{\sin F} = \frac{g}{\sin G}[/tex] (1)
Where:
[tex]e[/tex] - Measure of the line segment FG, in feet.
[tex]f[/tex] - Measure of the line segment EG, in feet.
[tex]g[/tex] - Measure of the line segment EF, in feet.
[tex]E[/tex] - Angle at vertex E, in sexagesimal degrees.
[tex]F[/tex] - Angle at vertex F, in sexagesimal degrees.
[tex]G[/tex] - Angle at vertex G, in sexagesimal degrees.
We can determine a missing length, by knowing the length of a neighboring side and two consecutive angles. If we know that [tex]f = 7\,ft[/tex], [tex]G = 45^{\circ}[/tex] and [tex]F = 82^{\circ}[/tex], then the measure of the line segment EF is:
[tex]g = f\cdot \left(\frac{\sin G}{\sin F} \right)[/tex] (2)
[tex]g = (7\,ft)\cdot \left(\frac{\sin 45^{\circ}}{\sin 82^{\circ}} \right)[/tex]
[tex]g\approx 4.998\,ft[/tex]
[tex]g \approx 5\,ft[/tex]
The length of the line segment EF ([tex]g[/tex]) is approximately 5 feet.
. 15cm 11cm 5cm.
please help find the area and the perimeter of the Right triangle using formular below
P= a+h+d
A=b×h
Answer:
length =15
breadth =11
height =5
Step-by-step explanation:
p=l+ b+h
p=15+11+5
p=31is ur ans
A=b×h
a=11×5
a=55is ur ans
King
13.
а/8 = $1.25
Can someone help explain
Answer:
a= $10.00
Step-by-step explanation:
It's very simple. Move /8 to the other side of the equation. It should give you $1.25 x 8. Solve the multiplication and you should get $10.00.
If I didn't make my explanation clear enough, please comment. I sometimes don't even explain myself very well.
Answer:
a = 10
Step-by-step explanation:
a/8 = 1.25
multiply both sides by 8 to isolate a.
(8)(a/8) = 1.25(8)
which gives you
a = 1.25(8)
which simplifies to
a = 10
if point B is the midpoint of points A and C, find the value of x and AC. AB= 5x - 2, BC= 9x -10
9514 1404 393
Answer:
x = 2AC = 16Step-by-step explanation:
The midpoint divides the segment into two equal lengths:
AB = BC
5x -2 = 9x -10
8 = 4x
2 = x
AB = 5(2) -2 = 8
AC = 2AB = 2(8) = 16
HURRY plSSSSSSSSSSSSSSSSSSSSSS
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is eighty degrees and the other is unknown.
Answer:
The unknown is 100
Step-by-step explanation:
A straight line is 180 degrees
We have two angles x, and 80
x+80 = 180
x = 180-80
x= 100
16 • (14) =
-9 • (-8) =
- 13 • 7
Answer:
16×14 = -9×(-8) = -13×7
Falso
Step-by-step explanation:
62 + 7h in a algebraic expression
Step-by-step explanation:
62 + 7h is already an algebraic expression.
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? O a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. O d) She will have a hard time focusing.
Option C
Customers will think she is very busy
A messy desk indicates that the person is very busy.
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A 40-foot ladder is leaning against a building and forms a 29.32° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.
45.88 feet
34.88 feet
22.47 feet
19.59 feet
Answer:
34.88
Step-by-step explanation:
I took the test
The distance between the building and the ladder is 34.88 foot, the correct option is B.
What is a Right Triangle?A triangle in which one of the angle measure is equal to 90 degree is called a right triangle.
The ladder forms a right triangle with the building and the ground,
The length of the triangle is 40 foot
The angle made by the ladder is 29.32 degree
By using Trigonometric Ratios
cos 29.32 = Base / Hypotenuse
cos 29.32 = Base / 40
Base is the distance between the building and the ladder.
Base = 34.88 foot
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A person invests 3500 dollars in a bank. The bank pays 4.75% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 5800 dollars?
9514 1404 393
Answer:
10.7 years
Step-by-step explanation:
The formula for the balance in an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where principal P is invested at annual rate r compounded n times per year for t years. We want to solve for t.
5800 = 3500(1 +0.0475/4)^(4t)
58/35 = 1.011875^(4t) . . . divide by 3500 and simplify a bit
log(58/35) = 4t·log(1.011875) . . . . take logs
t = log(58/35)/(4·log(1.011875)) . . . . divide by the coefficient of t
t ≈ 10.6966 ≈ 10.7
The person must leave the money n the bank for about 10.7 years for it to reach $5800.
How many roots does the equation (8/(x^2 - 16) )+ 1 = 1/(x -4) have?
Plz show ALL STEPS
Answer:
Step-by-step explanation:
Which of the following algebraic equations models the English sentence, a number decreased by two is equal to
four?
A W + 2 = 4
B 2 -w = 4
C W-2 = 4
D w= 2-4
Answer:
The choose C. w–2=4
I hope I helped you^_^
Answer: C
Step-by-step explanation:
Solve for x: −7 < x − 1 < 8
6 < x < 9
−6 > x > 9
6 > x > −9
−6 < x < 9
Answer:
-6 < x < 9
Step-by-step explanation:
-7+1 < x-1+1 < 8+1
therefore:
-6 < x < 9
help! due august 12th
In the triangle shown, AB = 2x + 9 and BC = 5x – 12. Find the value of x.
Answer:
x=7
Step-by-step explanation:
AB=BC[ because two sides of isosceles triangles are equal ]
or, 2x+9=5x-12
or,9+12=5x-2x
or,21=3x
or,x= 21/3
therefore, x=3
find the missing side. round your answer to the nearest tenth
Answer:
60.6
Step-by-step explanation:
tan(theta) = P/B
tan(24) = 27/x, x=27/tan(24)=60.6
Please need help with this ASAP !!!!!
First concert mixed fractions to normal Form
[tex]\\ \sf\longmapsto 1\dfrac{1}{4}=\dfrac{5}{4}[/tex]
[tex]\\ \sf\longmapsto 1\dfrac{3}{4}=\dfrac{7}{4}[/tex]
if all are in AP then common difference will be same[tex]\\ \sf\longmapsto \dfrac{3}{4}-\dfrac{1}{4}=\dfrac{5}{4}-\dfrac{3}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{3-1}{4}=\dfrac{5-3}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{2}{4}=\dfrac{2}{4}[/tex]
Hence it's true
Answer: True
Explanation:
1/4, 3/4, 1 1/4, 1 3/4
1 1/4 = 5/4
1 3/4 = 7/4
1/4, 3/4, 5/4, 7/4
= 0.25, 0.75, 1.25 , 1.75
This is arithmetic
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solve for x in the equation:log6-2logx=1.4
9514 1404 393
Answer:
x = (√6)/10^0.7 ≈ 0.488737
Step-by-step explanation:
It can work reasonably well to take antilogs first.
[tex]\log(6)-2\log(x)=1.4\\\\\dfrac{6}{x^2}=10^{1.4}\\\\\dfrac{6}{10^{1.4}}=x^2\\\\x=\dfrac{\sqrt{6}}{10^{0.7}}\approx0.488737[/tex]
Lillie is saving up for a trip she is taking with friends during her break from school. If Lillie's current monthly net pay is $560.00 and her monthly expenses are $347.49, what percent of her net pay is left for savings? (2 points)
19%
23%
38%
Answer:
38%
Step-by-step explanation:
First determine her savings
560-347.49
212.51
Then divide by the total amount
212.51/560
.379482143
Change to percent form
37.948%
Answer:
38%
Step-by-step explanation:
[tex]560.00-347.49=212.51\\212.51\div560.00==38[/tex]
What is the volume of the sphere shown below with a radius of 6?
A. 483 Cu, units
B. 2887 cu units
C. 1627 cu units
D. 14431 Cu, units
Answer:
B
Step-by-step explanation:
Volume of the sphere = (4/3)*pi*6^3=288*pi
Answer:
288 pi units^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 pi (6)^3
V = 4/3 pi (216)
V = 288 pi units^3
44,587 plus what equals 65,000
Let the missing number be x.
=> x + 44587 = 65000
=> x = 65000 - 44587
= 20413
Ans.= The missing number will be 20413.
Hope this answer helps you..
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To make a batch of salad dressing, combine 9 tablespoons of oil with 18 tablespoons of vinegar. How many tablespoons of vinegar are needed for every tablespoon of oil?
Answer:
18 divided by nine is two. so for every one table spoon of oil there's two table spoons of vinegar. Please give brainliest
Answer:
2
Step-by-step explanation:
Make a ratio:
Oil : Vinegar
9 : 18
1 : 2
For each tablespoon of oil, 2 tablespoons of vinegar is needed.
Hope this helped.
Instructions: Find the area of the trapezoid
and round to the nearest tenth.
10.2 mi.
7 mi.
4.2 mi.
Area:
mi?
Answer:
299.88 mi. !!!!!
you just multiple all of them together to get the area!!!
If ABCD is a square where A(-4;2) B(-2;-1) C(1;1) , determine the coordinates of of D
Answer:
(4;-1)
Step-by-step explanation:
A(-4;2)
B(-2;-1)
C(1;1)
D(-4;-1)
Answer:
-1;4
Step-by-step explanation:
Which graph represents x < 15?
Answer:
B
Step-by-step explanation:
x<15
There is an open circle at 15 and the line goes to the left
Which best describes the relationship between the line that passes through the points (-6, 5) and (-
2,7) and the line that passes through the points (4, 2) and (6, 6)?
Answer:
Line that passes through the points (-6,5) and (-2,7) is,
y=x/2+8, slope is 1/2
line that passes through the points (4,2) and (6,6) is,
y=2x-6, slope is 2
so, there is no relationship between those two lines,
intersection point is (28/3,38/3)
If K = (AB)/(A+B) , then B =?
Answer:
K(A+B)/A
Step-by-step explanation:
K = (AB)/(A+B)
K(A+B)=AB
K(A+B)/A=B
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
Y=4x+3
Y=
M=
B=
Please Show your work and include a picture of the graph if you can
Answer:
y=4x+3
m=4
b=3
Step-by-step explanation:
Since the equation is already solved for y, we don't have to do that. The equation is actually in slope-intercept form, where y=mx+b. m represents the slope, and b represents y-intercept.
Therefore, we can tell m=4 and b=3.
I have also included a picture of what the graph should look like.
