Answers
Answer: y = 11
Step-by-step explanation:
first, i collected the like terms.
7y + 9 = 4y + 42
then, i moved the terms.
7y - 4y + 42 - 9
then, i collected the like terms and calculated it.
3y - 33
finally, i divided both sides.
y = 11
Answer:
y = 11
Step-by-step explanation:
-5y + 12y + 9 = 4y + 42
Add like terms on the left side, -5y + 12y.
7y + 9 = 4y + 42
Subtract 4y from both sides.
3y + 9 = 42
Subtract 9 from both sides.
3y = 33
Divide both sides by 3.
y = 11
Related Questions
5. Sand is dumped off a conveyor belt into a pile at the rate of 2 cubic feet per minute. The sand pile is shaped like a cone whose height and base diameter are always equal. At what rate is the height of the pile growing when the pile is 5 feet high? (The volume of a cone is fr2h where r is the radius of the base and h is the height:)
Answers
Answer:
[tex]\displaystyle \frac{dh}{dt} = \frac{8}{25 \pi} \ ft/min[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityGeometry
Volume of a Cone: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]
r is radiush is heightDiameter: d = 2r
Calculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{dV}{dt} = 2 \ ft^3/min\\b = h\\h = 5 \ ft[/tex]
Step 2: Rewrite Volume Formula
We need to rewrite the cone volume formula in terms of height h only.
Base b = diameter d of the circular base
Define: b = dSubstitute: b = 2rWe are given that the base of the cone is the same as the height.
Define: b = 2rSubstitute: h = 2rNow solve for height.
Divide 2 on both sides: h/2 = rRewrite expression: r = h/2Now find new volume formula.
Define [VC]: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]Substitute: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{h}{2})^2h[/tex]Exponents: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{h^2}{4})h[/tex]Multiply: [tex]\displaystyle V = \frac{1}{12} \pi h^3[/tex]We now have the same volume formula in terms of height h only.
Step 3: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dV}{dt} = \frac{1}{12} \pi \cdot 3 \cdot h^{3-1} \frac{dh}{dt}[/tex]Simplify: [tex]\displaystyle \frac{dV}{dt} = \frac{1}{4} \pi h^{2} \frac{dh}{dt}[/tex]Step 4: Solve for height rate
Substitute: [tex]\displaystyle 2 \ ft^3/min = \frac{1}{4} \pi (5 \ ft)^{2} \frac{dh}{dt}[/tex]Isolate h rate: [tex]\displaystyle \frac{2 \ ft^3/min}{\frac{1}{4} \pi (5 \ ft)^{2}} = \frac{dh}{dt}[/tex]Exponents: [tex]\displaystyle \frac{2 \ ft^3/min}{\frac{1}{4} \pi (25 \ ft^2)} = \frac{dh}{dt}[/tex]Multiply: [tex]\displaystyle \frac{2 \ ft^3/min}{\frac{25}{4} \pi \ ft^2} = \frac{dh}{dt}[/tex]Divide: [tex]\displaystyle \frac{8}{25 \pi} \ ft/min = \frac{dh}{dt}[/tex]Rewrite: [tex]\displaystyle \frac{dh}{dt} = \frac{8}{25 \pi} \ ft/min[/tex]Here this tells us that the rate at which the height is moving at a rate of 0.101859 feet per minute.
pls help
Quadrilateral ABCD is an isosceles trapezoid. What is the m∠B?
Answers
Answer:
<B=105°
Step-by-step explanation:
as it's an isosceles trapezoid. AD parallel to BC
ACCORDING TO THE QUESTION
75°+<B=180°
<B=180°-75°
<B=105°
On a standardized test, Rasi answered the fast: 22 questions in 5 minutes. There are 7]
questions on the test. If he continues to answer questions at the same rate how long will
it take him to complete the test?
Answers
Answer:
they are directly proportional
so
5/22*7=1.59
he would finish in 1.59 min
Solve the system: (MAFS.912-A-REI.3.6)
4+7=41
4
x
+
7
y
=
41
4+7=41
4
x
+
7
y
=
41
−7=−16
Answers
Step-by-step explanation:
[tex]4x + 7y = 41 \\ 4 \times ( - 7) + 7 \times ( - 16) = 41[/tex]
Write the equation in slope-intercept form.
(2,-3) and (1,3)
Answers
choose the definition for the function y={x+1 x≤2 x+2 x>2 y={x+1 x>2 x+2 x≤2 y={x+1 x
Answers
Answer:
D
Step-by-step explanation:
There are 25 students in Mrs. Murphy's math class. Of these students, 10 have brown hair, 8 have black hair, 5 have blonde hair, and 2 have red hair. What percentage of students in Mrs. Murphy's class have blonde hair?
Answers
The percentage of students in Mrs. Murphy's class who have blonde hair will be 20%.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
There are 25 students in Mrs. Murphy's math class. Of these students, 10 have brown hair, 8 have black hair, 5 have blonde hair, and 2 have red hair.
Then the percentage of students in Mrs. Murphy's class who have blonde hair will be
Total students = 25
Then we have
[tex]\rm P = \dfrac{5}{25} \times 100\\\\P = 0.20 \times 100\\\\P = 20 \%[/tex]
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ2
which translation moves the point back to its original position?
Answers
The line graph below shows the number of chocolate bars and ice lollies sold at a small shop over a year.
Pick the month below in which more ice lollies were sold than chocolate bars.
January
July
April
May
Answers
Answer:
July
Step-by-step explanation:
Month in which more ice lollies were sold than chocolate bars are: Jun, Jul, Aug
This means that from the answer options only July is valid.
The diagram shows a square based cuboid. Work out the volume of the cuboid. State the units of your answer.
Answers
Answer:
160cm³
Step-by-step explanation:
square based means equal sides
therefore 4cm×4cm=16cm²
16cm²×10cm=160cm³
You are opening a savings account with $500 that you have saved. The bank offers 3.2% interest, compounded yearly. How much money will you have in you account after 7 years?
Answers
Answer:
You will have $623.3441462 in your account after 7 years
Step-by-step explanation:
The formula of the compounded interest is A = P [tex](1+\frac{r}{n})^{nt}[/tex] , where
A is the new valueP is the initial valuer is the rate in decimaln is the number of periodst is the time in years∵ You are opening a savings account with $500
∴ P = 500
∵ The bank offers 3.2% interest, compounded yearly
∴ r = 3.2% ⇒ divide it by 100 to change it to decimal
∴ r = 3.2 ÷ 100 = 0.032
∵ The interest is compounded yearly
∴ n = 1
∵ The time is 7 years
∴ t = 7
→ Substitute these values in the rule above to find A
∵ A = 500 [tex](1+\frac{0.032}{1})^{1(7)}[/tex]
∴ A = 500 [tex](1.032)^{7}[/tex]
∴ A = 623.3441462
∴ You will have $623.3441462 in your account after 7 years
Paul's basketball coach decides that he will play only the first three quarters of every game this season. If he starts
the first 20 games, what expression can you write to model how much playing time he actually gets?
o 3.20
O = 20
o * + 20
03 - 20
Answers
Answer:
im thinking the answer is 3/4 x 20
Answer:
3.20
Step-by-step explanation:
i used math
A cabinet holds 16 plates and
12 bowls. What is the ratio of plates
to bowls written in simplest form?
Answers
Answer:
4:3
Step-by-step explanation:
Determine the value of x in the diagram.
Answers
Answer:
65
it's 65 because it is.. cool
Joe bought some CD's and DVD's at the store.
• He bought a total of 12 items.
• The CD's were $14.
• The DVD's were $22.
• He spent $200.
How many of each did he buy?
Answers
Answer: x=8 and y=4
Step-by-step explanation:
x+y=12 x=12-y x=12-4
14x+22y=200 x=8
14(12-y)+22y=200
168-14y+22y=200
-168 -168
-14y+22y=32
8y=32
8y/8=32/8
y=4
If $12000 is invested in an account in which the interest earned is continuously compounded at a rate of 2.5%
Answers
Complete Question
If $12000 is invested in an account in which the interest earned is continuously compounded at a rate of 2.5% for 3 years
Answer:
$ 12,934.61
Step-by-step explanation:
The formula for Compound Interest Compounded continuously is given as:
A = Pe^rt
A = Amount after t years
r = Interest rate = 2.5%
t = Time after t years = 3
P = Principal = Initial amount invested = $12,000
First, convert R percent to r a decimal
r = R/100
r = 2.5%/100
r = 0.025 per year,
Then, solve our equation for A
A = Pe^rt
A = 12,000 × e^(0.025 × 3)
A = $ 12,934.61
The total amount from compound interest on an original principal of $12,000.00 at a rate of 2.5% per year compounded continuously over 3 years is $ 12,934.61.
Travis scored 18 point in the first basketball game of the season. he scored 3 fewer points in the second game than in the first game. find the total number of points Travis scored in the first and second games.
Answers
Answer:
isn't it 33?
Step-by-step explanation:
because at first they said he scored 18 and the second time he scored 3 fewer points than the first one so its 18+(18-3)=33
Please help ASAP
Please I’ll mark you as brainlister
Answers
Answer: 15.
Step-by-step explanation:
You divide the degrees by the side length. You get 15. So 15 is the answer.
Using trigonometry Solve the triangle please help me
Answers
Answer:
The angle m ∠ W = 33°
The length of XZ = 9.8 units
The length of WX = 15.1 units
Step-by-step explanation:
Given
The right-angled triangle ΔWXZ
m ∠ X = 90°m ∠ Z = 57°Hypotenuse WZ = 18We know that the sum of the measure of angles in any triangle is 180°.
Therefore,
m ∠ W + m ∠ X + m ∠ Z = 180°
substiute m ∠ X = 90° and m ∠ Z = 57° in the formula
m ∠ W + 90° + 57° = 180°
m ∠ W + 147 = 180°
m ∠ W = 180° - 147
m ∠ W = 33°
Therefore, the angle m ∠ W = 33°
NOW,
Determining the lengths of WX and XZ
Length XZ
Using the trigonometric ratio
The adjacent to 57° is XZ.
so
cos 57° = adjacent / hypotenuse
substituting adjacent = XZ, and hypotenuse = 18
cos 57° = XZ / 18
XZ = 18 × cos 57°
XZ = 9.80 units
Therefore, the length of XZ = 9.8 units
Length WX
As
m ∠ W = 33°
The adjacent to m ∠ W = 33° is WX.
so
cos 33° = adjacent / hypotenuse
substituting adjacent = WX, and hypotenuse = 18
cos 33° = WX/ 18
WX = 18 × cos 33°
WX = 15.1 units
Therefore, the length of WX = 15.1 units
Summary:
The angle m ∠ W = 33°
The length of XZ = 9.8 units
The length of WX = 15.1 units
plss help me find this hcf
3a-6,a²-4
Answers
Step-by-step explanation:
1st expression = 3a - 6 = 3 ( a - 2 )
2nd expression = a² - 4 = a² - 2² = ( a + 2) (a - 2)
The HCF is (a -2).
Hope it helps :)❤
1234567791234556677889
Answers
Step-by-step explanation:
The rate of pictures per minute.
8 pictures per minute
8 pictures/ minute
Determine the constant of proportionality in each of the representations below.
Answers
Answer:
Pretty sure is 15
Step-by-step explanation:
90 divided by 6 is 15.
Answer:
The constant of proportionality, k is 15
Step-by-step explanation:
The constant of proportionality is the ratio between two directly proportional quantities.
Proportional quantities can be described by the equation y = kx, where k is a constant ratio.
Here, "x" is the number of tickets and "y" is the number of dollars.
k = 30/2 = 15/1 or 15
k = 15
k = 60/ 4 = 30/2 = 15/1 or 15
k = 15
k = 90/6 = 30/2 = 15/1 0r 15
k = 15
When we take the ratio of x and y for all the given values, we get an equal value for all the ratios.
Therefore, the constant of proportionality, k is 15
Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be
written using function notation?
O FU=-v+
Of(x) = - 3x + 4
o f(x) = -x +
Of = -3y + 4
Answers
Answer:
9x + 3y = 12
3y = -9x + 12
y = -3x + 4
f(x) = -3x + 4
Step-by-step explanation:
I hope it's help
A 24-f0ot ladder rests against a house near a second story window 20 feet from the ground. Assume that the ladder
and the house both stt on level ground.
To the nearest whole nurmber, find the following values:
A The measure of the angle formed by the base of the ladder and level ground is
B. The measure of the angle formed by the top of the ladder and the second story window is
C. The distance, on level ground, between the base of the ladder and the house is
feet
degrees.
feet.
Answers
Answer:
c
Step-by-step explanation:
Lenny has a model train layout on a large, rectangular board. The length, l, of the board is 3 times the width, w. Which equation can be used to find P, the perimeter of the board?
Answers
Answer:
8w
Step-by-step explanation:
Given that:
Length = l
Width = w
l = 3w
Perimeter of rectangular board :
Perimeter of a rectangle = 2(l + w)
Perimeter = 2(3w + w)
Perimeter = 2(4w)
Perimeter of rectangular board = 8w
I need help pls so I can get a good grade
Answers
Answer:
Step-by-step explanation:
C is the answer.
all parts please, i need this by the end of today and pls write answer in comments
Answers
Answer:
A
[tex] = \frac{78}{360} \\ = \frac{13}{60} [/tex]
B
[tex]let \: total \: number \: be \: x \\ \frac{13}{60} x = 1164 \\ x = \frac{1164 \times 60}{13} \\ x = 5372 \: movies[/tex]
C
A year has (4 × 12) weeks
= 48 weeks.
In 1 week = 9,568,000 movies
48 weeks = (48 × 9,568,000) movies
Average movies = 459.264 movies
D
Since 9.568 million movies are rented.
How about in one year ( 48 weeks )
Convert 1 year to weeks and compare with 1 week
Please helppp 21 points pleaseeeeeeee. If you don’t know the answer don’t answer please.
Answers
Answer:
f(x)=50x+20
0<x x<2
Step-by-step explanation:
hope it helps!
easy question in photo
Answers
Answer:
14
Step-by-step explanation:
always subtract the highest number from the lowest and I believe that is your range
Answer:
14
Step-by-step explanation:
Rauol measured the height of 12 different plants in his garden in April. He measured them again in June. What is the difference between the mean height in April and the mean height in June?
Answers
The question is incomplete. Here is the complete question.
Raoul measured the ehight of 12 different plants in his garden in April. He measured them again in June.
April Heights (in inches) 12 15 23 11 42 45 44 39 12 19 20 12
June Heights (in inches) 45 45 40 43 11 14 12 13 41 40 45 41
What is the difference between the mean height in April and the mean height in June?
Answer: The difference between means is 8.0
Step-by-step explanation: Mean is the average of a set of numbers.
It is calculated as:
[tex]\mu=\frac{\Sigma x}{n}[/tex]
where
x is the numbers in the set
n is how many numbers are there in the set
For heights in April, the mean is:
[tex]\mu_{1}=\frac{12+15+23+11+42+45+44+39+12+19+20+12}{12}[/tex]
μ₁ = 24.5
For heights in June, the mean os:
[tex]\mu_{2}=\frac{45+45+40+43+11+14+12+13+41+40+45+41}{12}[/tex]
μ₂ = 32.5
The difference between means:
μ₂ - μ₁ = 32.5 - 24.5 = 8.0
The difference between the mean height in April and in June is 8.0 inches.