Answer:
The constant of proportionality is k=1/4
Step-by-step explanation:
For the equation y=kx, y varies directly with x with the constant of proportionality k. Therefore, k=1/4 is the answer.
At noon, a tank contained 8 in. of water. After several hours, it contained 6 in. of water. What is the percent decrease of water in the tank?
Answer:
25%
Step-by-step explanation:
8-6=2
2/8=0.25
0.25×100=25%
I need the answer for this ASAP
Answer:
Y is cookies x is cupcakes
for the first birthday party: 20x + 40y = 61
For the second party 30x + 30y = 64.50
There aren't any other constraints
20x + 40y = 61
30x + 30y = 64.50
Step-by-step explanation:
PLEASE HELP ME WITH THIS QUESTION
Answer:It’s money so use the $ symbol. You got this
Step-by-step explanation:
7 grade math hellp me
Answer:
32
Step-by-step explanation:
180 - 148 = 32
I hope this helps!
3 to the power of -2 as a fraction
From the power rules, the power [tex]3^{-2}[/tex] is equal to the fraction [tex](\frac{1}{3})^{-2}[/tex].
Power RulesThere are different power rules one of them is the negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent. See the examples:
[tex]5^{-3}=(\frac{1}{5})^3=\frac{1}{125} \\ \\ \\ {\frac{4}{6} }^{-2}={\frac{6}{4} }^2=\frac{36}{16}[/tex]
Then, the question gives:
[tex]3^{-2}=({\frac{1}{3}})^2[/tex]
Read more about power rules here:
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how to solve 1/2(x-6) = 1/2
Answer:
x=7
Step-by-step explanation:
1/2(x-6)=1/2
(1/2)(x)+(1/2)(−6)=1/2
1/2x+−3=1/2
1/2x−3=1/2
1/2x−3+3=1/2+3
1/2x=7/2
2*(1/2x)=2*(7/2)
x=7
tada!
I’ll give brainliest!
Add 3/4 + (2^1/2) using the number line
Select the location on the number line to plot the sum
Answer: -1 3/4
Step-by-step explanation
just add the fractions together :)
(between the -2 and -1 1/2)
Complete the point-slope equation of the line through -8,1 and -6,5
Answer:
y+1=3(x+8)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-(-1))/(-6-(-8))
m=(5+1)/(-6+8)
m=6/2
m=3
y-y1=m(x-x1)
y-(-1)=3(x-(-8))
y+1=3(x+8)
6(31)+6(4)-6(15) mental math form
[tex]6(31)+6(4)-6(15)=6(31+4-15)=6(20)=120[/tex]
ok done. Thank to me :>
[tex] \frac{1.3}{7.8} \: \frac{3}{18} [/tex]
Is this equivalent?
Answer:
Yes
Explanation:
1.3/7.8 = 0.167
3/18 = 0.167
An equivalent fraction is a fraction that is the same as another fraction with a different denominator.
I hope it helps.
True or false is 6x10^5 is 20 times as much as 3x10^4
answer
TRUE
HOPE IT WILL HELP YOU
PLEASE LAST FEW SETS OF QUESTIONS FOR SEMESTER PLEASE HELP 2
Problem 1
Answer: C) 132.6--------------------
Explanation:
a1 = 1.7 = amount of concrete for the first step
a4 = x = amount of concrete for the fourth step
Sn = sum of the first n terms of an arithmetic sequence
Sn = (n/2)*(a1 + an)
S4 = (4/2)*(a1 + a4)
S4 = 2(1.7+x)
S4 = 2x+3.4
S4 = 17
2x+3.4 = 17
2x = 17-3.4
2x = 13.6
x = (13.6)/2
x = 6.8
We need 6.8 cubic feet of concrete for the fourth step. We'll use this value to help us find the common difference d
an = nth term of an arithmetic sequence
an = a1 + d(n-1)
a4 = a1 + d(4-1)
a4 = a1 + 3d
6.8 = 1.7 + 3d
6.8-1.7 = 3d
5.1 = 3d
(5.1)/3 = d
1.7 = d
d = 1.7
Coincidentally, the common difference is the same as the first term. This won't always happen.
Now we can compute the 12th term
an = a1 + d(n-1)
a12 = 1.7 + 1.7(12-1)
a12 = 20.4
which is then used to find the sum of the first 12 terms
Sn = (n/2)*(a1 + an)
S12 = (12/2)*(a1 + a12)
S12 = 6(1.7 + 20.4)
S12 = 132.6
=============================================================
Problem 2
Answer: C) [tex]x^2 + (y-10)^2 = 225\\\\[/tex]--------------------
Explanation:
The center is (h,k) = (0,10) which is where the nozzle is located.
The distance from (0,10) to (0,25) is 15 units, so r = 15.
Also, the distance from (0,10) to (0,-5) is also 15 units.
Plug those values into the equation below.
[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-0)^2 + (y-10)^2 = 15^2\\\\x^2 + (y-10)^2 = 225\\\\[/tex]
That equation represents the boundary of the circle, which is where the water can reach.
=============================================================
Problem 3
Answer: B) 2.336 ft--------------------
Explanation:
a1 = height 1st bounce = 6.7 fta2 = height 2nd bounce = 81% of a1 = 81% of 6.7 = 0.81*6.7 = 5.427a3 = height 3rd bounce = 81% of a2 = 81% of 5.427 = 0.81*5.427 = 4.39587Or note that,
a3 = 0.81*(a2) = 0.81*(0.81a1) = a1*(0.81)^2 = 6.7*(0.81)^2 = 4.39587
which must mean,
a4 = a1*(0.81)^3a5 = a1*(0.81)^4a6 = a1*(0.81)^5This is based off the idea that [tex]a_n = a(r)^{n-1}[/tex]
So,
a6 = a1*(0.81)^5
a6 = 6.7*(0.81)^5
a6 = 2.33614554867
a6 = 2.336
1. Which of the following is the remainder when the polynomial x^2-5x+3 is divided by (x -8)?
(1) 107
(3) 3
(2) 27
(4) 9
Answer:
27
Step-by-step explanation:
Use synthetic division:
8 | 1 -5 3
__8_24
1 3 | 27
Therefore, (x²-5x+3)/(x-8) = x+3 R27
HELP ME FAST PLZZ
Wendy has 5 1/3 of ribbon.
Part A: How many 2/3 -foot pieces can Wendy cut from the 5 1/3 feet of ribbon? Show your work. (5 points)
Part B: Using the information in Part A, interpret the meaning of the quotient in terms of the two fractions given. (5 points)
Answer:
Part A: 8 ribbons
Part B: see below
Step-by-step explanation:
first 5 1/3 = 16/3
[tex] \frac{16}{3} \div \frac{2}{3} \\ = \frac{16}{3} \times \frac{3}{2} \\ = \frac{48}{6} = 8[/tex]
the answer is 8 dude!
Select the equation that has a = 112 as its solution.
a−114=35
a+358=434
416+a=523
a×38=214
Answer:
none
Step-by-step explanation:
a-114=35 ⇒ a= 149
a+358=434⇒ a=76
416+a=523⇒ a=107
ax38=214⇒ a=5.63
The equation that has 112 as it's solution is not existing in the options.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given are four linear equations.
Check the solution of each equation.
a - 114 = 35
Adding both sides of the equation with 114,
⇒ a = 35 + 114 = 149
a + 358 = 434
Subtracting both sides of the equation with 358,
⇒ a = 434 - 358 = 76
416 + a = 523
Subtracting both sides of the equation with 416,
a = 523 - 416 = 107
a × 38 = 214
Dividing both sides of the equation with 38,
a = 214/38 = 5.63
Hence none of the equations have 112 as it's solution.
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The cost C to produce x number of tennis rackets is C = 190 + 18. The tennis rackets are sold wholesale for $23
each, so revenue R is given by R = 23x. Find how many tennis rackets the manufacturer needs to produce and
sell to break even.
38 tennis rackets or
43 tennis rackets or
19 tennis rackets or
33 tennis rackets
Answer:
19 tennis rackets
Step-by-step explanation:
a family buys 6 airline tickets online. the family buys travel insurance that costs 18 per ticket. the total cost is 1,044
Answer:
936
Step-by-step explanation:
Therefore you multiply 6 by 18 = 6×18= 108
1,044 - 108 = 936
So therefore the total is 936
The sum of n terms of the AP √3, √8, √18, √32,.... is
S = √2+√8+√18+√32+……………… n terms.
or, S = √2 + 2√2 +3√2 +4√2.+………………….+ n terms.
This is an A.P. in which a = √2. , d = √2.
Sn = n/2.[2.a +(n-1).d].
or, Sn = n/2.[ 2√2 +(n-1).√2].
or, Sn = (n/2).√2.[ 2 +n-1].
or, Sn = n.(n+1)/√2. Answer.
Given AP :√2,√8,√18,√32,...
First term = √2
Common difference = √8-√2
⇛ √(2×2×2)-√2
⇛ 2√2-√2
⇛√2
We know that
Sum of first n terms of an AP
⇛ Sn = (n/2)[2a+(n-1)d]
⇛ Sn = (n/2)[2√2+(n-1)(√2)]
⇛ Sn = (n/2)[2√2+√2 n -√2]
⇛ Sn = (n/2)[√2 n +√2)
⇛ Sn = (n/2)×(√2)(n+1)
⇛Sn = (n/√2)(n+1)
⇛ Sn = n(n+1)/√2
Additional comment:
nth term of an AP = a+(n-1)d
Sum of first n terms of an AP
Sn = (n/2)[2a+(n-1)d]
Sum of the first n terms = Sn =
(n/2)(a+an)
If a,b,c are the three consecutive terms in an AP then b = (a+c)/2
also read similar questions: Find the sum of last ten terms of the AP : 8, 10, 12,...., 126.
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The sum of the 8th & 4th of an Ap is 24 and sum of and sum of 6th & 10th term is 44 Find the Ap
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Tara wants to put a white fence aroung the yard including the garden. Write an
expression for the perimeter of her yard (including the garden).
Then simply the expression.
The perimeter of a rectangle is 2L + 2W, where L and W are the length and width, respectively. The dimensions of the garden are given, 6 x 12 ft.
The amount of fencing needed is 2(6) + 2(12) = 12 + 24 = 36 ft of fencing
04.03 HC)
Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
(10 points)
Part A:
To find the average rate of change, let us first write out the equation to find it.
Δy/Δx = average rate of change.
Finding average rate of change for Section A
Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5
Δx = 1- 0 = 1
Plug the numbers in: Δy/Δx = 5/1 = 5
Therefore, the average rate of change for Section A is 5.
Finding average rate of change for Section B
Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36
Δx = 3 - 2 = 1
Plug the numbers in: Δy/Δx = 36/1 = 36
Therefore, the average rate of change for Section B is 36.
Part B:
(a) How many times greater is the average rate of change of Section B than Section A?
If Section B is on the interval [2,3] and Section A is on the interval [0,1].
For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.
(b) Explain why one rate of change is greater than the other.
Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.
The sum of three consecutive even numbers is 36. What is the smallest numbers ?
Answer:
The numbers are 11,12,13
The smallest number is 11
Step-by-step explanation:
Let the first number be x
The next number is x+1
The third number is x+2
x+x+1+x+2 = 36
Combine like terms
3x+3 = 36
Subtract 3 from each side
3x+3-3 = 36-3
3x=33
Divide each side by 3
3x/3 = 33/3
x=11
The numbers are 11,12,13
The smallest number is 11
Mrs. Nisbet had 97 books in her classroom library. She received a grant to expand her classroom library. After spending the money, she had 213 books. What is the percent increase? *
Answer: 219
Step-by-step explanation:
I need help asap!! pls pls PLS help
Answer:
Step-by-step explanation:
It's the third choice. Since the triangles are given as similar and they are right triangles, points A, B, and D are all on the hypotenuses of those 2 triangles and are co-linear. The slope between all points on a single line is constant.
What is the equation of the line that passes through
(-5, 0) and (4, 3)?
Answer:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]
Step-by-step explanation:
The point-slope form of an equation for a line is y = mx + b (m is the slope; b is the y-intercept).
First, find the slope using the two given points.
[tex]m=\frac{y_2 - y_1}{x_2-x_1}=\frac{3-0}{4-(-5)}=\frac{3}{9}=\frac{1}{3}[/tex]
At this stage, you know the slope and need to find the y-intercept. Plug in one of the points (either one) into the equation. Let's use (-5, 0).
[tex]y=\frac{1}{3}x+b\\0=\frac{1}{3}(-5)+b\\0=-\frac{5}{3}+b\\\frac{5}{3}=b[/tex]
The equation for the line is [tex]y=\frac{1}{3}x+\frac{5}{3}[/tex].
You can check for errors by putting in the point you didn't use...
Check to make sure the point (4, 3) satisfies the equation.
[tex]3=\frac{1}{3}(4)+\frac{5}{3}\\3=\frac{4}{3}+\frac{5}{3}\\3=\frac{9}{3}[/tex] True!
Pls help I’ll brainlest
Complete the activities below
Answer:
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
rate of change or slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{rise}{run}[/tex]
y = mx + b
"b" is y-intercept
~~~~~~~~~~~~~~~~~~~
Find the measure of the angle marked and indicated in bold
Answer plzzz!!!!!!!!!!!
Answer:
110
Step-by-step explanation:
Know the angle for BCD which is 130.
Subtract 180 from 130 and you get angle c for the triangle which is 50
Already knowing B and C, add them both which comes up to 70
All triangle angles equal 180 so subtract 70 for 180 and you get 110
please help!! 100 points
[tex]\\ \tt\bull\rightarrowtail h(x)=1/5(x^2-6)-8[/tex]
[tex]\\ \tt\bull\rightarrowtail h(4)[/tex]
[tex]\\ \tt\bull\rightarrowtail 1/5(4^2-6)-8[/tex]
[tex]\\ \tt\bull\rightarrowtail 1/5(16-6)-8[/tex]
[tex]\\ \tt\bull\rightarrowtail 10/5-8[/tex]
[tex]\\ \tt\bull\rightarrowtail 2-8[/tex]
[tex]\\ \tt\bull\rightarrowtail -6[/tex]
Launch Problem
Melanie was training for a race. The line plot below shows the number of miles Melanie ran last week.
5. How many miles did Melanie run altogether last week?
Answer:
5 miles
Step-by-step explanation:
add the points together.
it seems like each point is how many miles they ran each day.
1/4 + 2(1/2) + 3/4 + 3(1) = 5
2/3 divided by 10
PLEASE answer
Answer:
1/15
Step-by-step explanation:
2/3 x 1/10 = 2/30 or 1/15
Answer:
1/15
Step-by-step explanation: