Which relationships have the same constant of proportionality between yyy and xxx as the following graph?
The constant of proportionality is 3. The relationship that will have the same constant of proportionality will also have a slope of 3
For us to determine the constant of proportionality of the given graph, we must first find the equation of the line.
The standard equation of a line is expressed as y = mx + b
m is the slopeb is the y-interceptUsing the coordinate points (0, 0) and (2, 6)
Get the slope "m"
[tex]m=\frac{6-0}{2-0}\\m=\frac{6}{2}\\m=3[/tex]
Since the line passed through the origin, the y-intercept is 0
Get the required equation:
y = mx + b
y = 3x + 0
y = 3x
From the equation, the constant of proportionality is 3. The relationship that will have the same constant of proportionality will also have a slope of 3
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PLEASE ANSWER ASAP WITH AN EXPLANATION
The eighth grade class at Seven Bridges Middle School has 93 students. Each student takes a current events class, a foreign language class, or both a current events class and a foreign language class. There are 70 eighth graders taking a current events class, and there are 54 eighth graders taking a foreign language class. How many eighth graders take only a current events class and not a foreign language class?
Answer:
39 students
Step-by-step explanation:
let x represent the number of students taking both current event and foreign language
there are : 70 eight grader taking current event and 54 taking foreign
70+54-x=93
-x=93-124
x= 31 students taking both
number of eighth graders take only a current events class and not a foreign language class: 70-31=39 students
HELP ASAP MONEY & WAGES
Answer: Annual Gross Income = $55,489.20
Annual Net Income = $46,439.72
Step-by-step explanation:
Total hours worked per week = 3(10) + 5 + 11 = 46
Regular hours worked = 3(8) + 5 + 8 = 37
Overtime hours worked = 3(2) + 0 + 3 = 9
Weekly Tips at 20% of $60 for 46 hours:
0.2(60)(46) = $552.00
Annual tips = $552.00 x 52 weeks = $28,704.00
Weekly Regular pay at $10.20 per hour for 37 hours:
10.20(37) = $377.40
Annual regular pay = $377.40 x 52 weeks = $19,624.80
Weekly Overtime pay at time and a half for 9 hours:
10.20(1.5)(9) = $137.70
Annual overtime = $137.70 x 52 weeks = $7,160.40
Total Annual Gross Income = Tips + Regular Pay + Overtime
$28,704.00 + $19,624.80 + $7,160.40 = $55,489.20
****************************************************************************************
Deductions (per question 5):
a) Pension at 5% = $55,489.20(0.05) = $2,774.46
b) Employee Insurance at 2.4% = $55,489.20(0.024) = $1,331.74
c) Income Tax at 0% for $0-$11,000 = $11,000(0) = 0
Income Tax at 8% for $11,000-$25,000 = $14,000(0.08) = $1,120.00
Income Tax at 12% for $25,000-$50,000 = $25,000(0.12) = $3,000.00
Income Tax at 15% for $50,000-$100,000 = $5,489.2(0.15) =$823.38
Total Income Tax = $4,943.28
Annual Net Income = Gross - Pension - Employee Insurance - Income Tax:
$55,489.20 - $2,774.46 - $1,331.74 - $4,943.28 = $46,439.72
There are 20 girls and 26 boys on the tennis team . What is the ratio of the number of girls to the total number of players on the team
Answer:
10:23
Step-by-step explanation:
Total number of players on the team = 20 + 26 = 46 players
Number of girls = 20
Ratio of the number of girls to the number of players on the team = 20/46 = 10/23 = 10:23
Ratio is 10:23
So the polynomial 24r squared represents the surface are of a cube a : determine the polynomial that represents the area of one face of the cube b: use this answer to determine a polynomial that represents the length of an edge of the cube c: what is the length of an edge of the cube when r = 3 cm
Answer:
a. 4r² b. 2r c. 6 cm
Step-by-step explanation:
The surface area A of the cube is A = 24r². We know that the surface area, A of a cube also equals A = 6L² where L is the length of its side.
Now, equating both expressions, 6L² = 24r²
dividing both sides by 6, we have
6L²/6 = 24r²/6
L² = 4r². Since the area of one face is L², the polynomial that determines the area of one face is A' = 4r².
b. Since L² = 4r² the rea of one face of the cube, taking square roots of both sides, we have
√L² = √4r²
L = 2r
So, the polynomial that represents the length of an edge of the cube is L = 2r
c. The length of an edge of the cube is L = 2r. When r = 3 cm.
L = 2r = 2 × 3 cm = 6 cm
So, the length of an edge of the cube is 6 cm.
the question is in the attachment...
Answer:
Rest of the part will be = x - 5x/10- x/10
solution will be 4x/10 i.e 4/10 part of the garden
Step-by-step explanation:
Let the sum total of parts of garden be x
If it is divided into 10 equal parts then
one part will be equal to x/10
Given carrots are planted on 5/10 of the garden
parts on which garden is planted = 5/10 * total part of garden = 5x/10
Given peas are planted on 1/10 of the garden
parts on which peas are is planted = 1/10 * total part of garden = x/10
On rest of the part corn is planted.
Rest of the part will be = total parts of garden - part on which carrots are planted - part on which carrots are planted
Rest of the part will be = x - 5x/10- x/10 = (10x-5x-x)/10 = 4x/10
Model will be
Rest of the part will be = x - 5x/10- x/10
solution will be 4x/10 i.e 4/10 part of the garden
Bengus the expert blacksmith forged 32 swords from copper, twice as many swords from iron, and 19 swords from mythril. Estimate how many swords Bengus forged.
Answer: 115 swords
Step-by-step explanation:
He forged 32 swords from copper, 2*32 from iron and 19 from mythril. Thus, he forged 32+(32*2)+19, or 32+64+19, or 115 swords.
Hope it helps <3
Answer:
110
Step-by-step explanation:
no need
Evaluate the expression 2x – xy for x=− 1/2 and y=8
Answer:
3
Step-by-step explanation:
2x-xy
2(-1/2)-(-1/2)(8)
-1+4
=3
i neeeed help quickkkk
Answer:
20 hours
Step-by-step explanation:
If your computer can download a movie in 5 hours, then it downloads [tex]\frac{1}{5}[/tex] of a movie in 1 hour.
The extra processor in 1 hour, reduces the time down to 5 hours, so it downloads [tex]\frac{1}{4}[/tex] of the movie in 1 hour.
The time that the extra processor will spend to download a whole movie added to [tex]\frac{1}{5}[/tex] will equal [tex]\frac{1}{4}[/tex] .
So our equation is [tex]\frac{1}{5} + \frac{1}{x} = \frac{1}{4}[/tex].
To simplify this, lets multiply all sides by 20x.
[tex](\frac{1}{5}+\frac{1}{x} \cdot 20x) = \frac{1}{4}\cdot20x\\ 4x + 20 = 5x[/tex]
Now we can simplify this equation.
[tex]20 = 5x-4x\\\\20 = x\\x = 20[/tex]
So the extra processor alone would take 20 hours to download the movie.
Hope this helped!
At the souvenir shop. Theo buys k key chains and p photo frames
where each chain and frame costs $2.49. He also buys a T-shirt for
$5.99. What is the total cost of Theo's purchases in terms of k and p?
Answer:
Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99
Step-by-step explanation:
Cost of k key chain=$2.49
Cost of p photo frames=$2.49
Cost of a T-shirt=$5.99
Total cost of all items=cost of k key chain + cost of p photo frame + cost of The shirt
=2.49k + 2.49p + 5.99
Factorise
2.49 is common to both k and p
=2.49(k + p) + 5.99
Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99
f(x)=x^2-3x-2 is shifted 4 units right. The result is g(x). What is g(x)?
Answer:
[tex]\boxed{\mathrm{C.}\:\: g(x)=(x-4)^2-3(x-4)-2}[/tex]
Step-by-step explanation:
The function is shifted 4 units right.
The value of x in the function is subtracted from 4, because this is a horizontal translation.
[tex]f(x)=x^2-3x-2[/tex]
[tex]g(x)=(x-4)^2-3(x-4)-2[/tex]
Answer:
c
Step-by-step explanation:
if you shift to the right funnily enough, you have to "compensate" for that by SUBTRACTING the number of units.
EXTRA
To check, use a simple function f(x)= x²
The top of this parabola is at (0,0).
We want to check if g(x) = (x-4)² is the right function....
Now if f(x) is shifted 4 units right than all variables with x in them, need to be compensated for. The question is do you need to add or subtract...
We know that the result is g(x), and we know that the top of g(x) would end up at (4,0).
For that to happen you need to compensate with g(x) = (x-4)²
Now check if (4,0) is on g(x) by substituting x=4. if the result turns out to be 0, then you know it is ok...
Substituting x=4 indeed results to
4-4 = 0, so (4,0) is on g(x).
Conclusion, by checking this one special value, you now know you have found the correct compensation factor!
PLEASE HELP If f(x) = 2x-1 + 3 and g(x) = 5x - 9, what is (f-g) (x)
Answer:
2^(x-1) -5x +12
Step-by-step explanation:
f(x) = 2^(x-1) + 3
g(x) = 5x - 9
(f-g) (x) = 2^(x-1) + 3 - ( 5x-9)
Distribute the minus sign
2^(x-1) + 3 - 5x+9
Combine like terms
2^(x-1) -5x +12
Where L is the length, in feet, of the pendulum, and π is approximately 22 7 . How long must the pendulum be if one complete cycle takes 8 seconds?
Answer:
Length L = 51.88 feet
Step-by-step explanation:
From the given information,
The length of the pendulum can be determined by using the Formula for the period T which is the time of one full oscillation of a simple pendulum.
[tex]T = 2 \pi \sqrt {\dfrac{L}{g}}[/tex]
where;
T = period of the time of one full oscillation = 8 seconds
L = length in feet
g = acceleration due to gravity in feet = 32 ft/s²
π = 22/7
[tex]8 = 2 \times \dfrac{22}{7} \times \sqrt {\dfrac{L}{32}}[/tex]
[tex]8 = 6.2857 \times \sqrt {\dfrac{L}{32}}[/tex]
[tex]\dfrac{8}{6.2857} =\sqrt {\dfrac{L}{32}}[/tex]
[tex]1.273=\sqrt {\dfrac{L}{32}}[/tex]
[tex]1.273= {\dfrac{\sqrt L}{ \sqrt {32}}}[/tex]
[tex]1.273 \times { \sqrt {32}}}= {\sqrt L}[/tex]
[tex]7.2012= {\sqrt L}[/tex]
L = 7.2012²
L = 51.88 feet
The measure of each exterior angle of a regular polygon is 30 degrees. How many sides does the polygon have
Answer:
12 sides
Step-by-step explanation:
To find the number of sides, use a formula.
[tex]\frac{360}{\theta }=n[/tex]
θ is the measure of each exterior angle of the regular polygon.
n is the number of sides of the regular polygon.
[tex]\frac{360}{30} =12[/tex]
Paul is a year older than his wife and they have two children who are also one year apart. Paul notices that on his birthday in 2011, the product of his age and his wife's age plus the sum of his children's ages is 2011. What would have been the result if he had done this calculation thirteen years before?
Answer:
997
Step-by-step explanation:
Well let's find the square root of 2011 because Paul and his wife are about the same age.
[tex]\sqrt{2011}[/tex]
= 44.8
Paul is 45 and his wife is 44.
44 + 45 = 1980.
2011 - 1980
= 31
So the children are 15 and 16.
45 + 44 + 15 + 16
= 997
Paul and wife - 45 and 44
Children - 15 and 16
Thus,
13 years ago they would be 997.
Hope this helps :)
If you vertically stretch the exponential function, f(x) = 2^x, by a factor of 4, what is the equation of the new function?
Answer:
f( x ) = 4( [tex]2^x[/tex] )
Step-by-step explanation:
If we vertically stretch a graph by a factor of 4, the " exponential slope " extending from the x - axis, should increase by a factor of 4 as well.
Therefore, the previous function is expressed by the following ...
f( x ) = [tex]2^x[/tex] ... then this new function should be -
f( x ) = 4( [tex]2^x[/tex] )
The equation of this new function is f( x ) = 4( [tex]2^x[/tex] )
help me really urgent
As mountain climbers know, the higher you go, the cooler the temperature gets. At noon on July 4th last summer, the temperature at the top of Mt. Washington — elevation 6288 feet — was 56◦F. The temperature at base camp in Pinkham Notch — elevation 2041 feet — was 87◦F. It was a clear, still day. At that moment, a group of hikers reached Tuckerman Junction — elevation 5376 feet. To the nearest degree, calculate the temperature the hikers were experiencing at that time and place. When you decided how to model this situation, what assumptions did you make?
Answer:
a. 63 °F
b. When i decided to model the situation, I assumed that the temperature varied inversely as the elevation and that the change in elevation or temperature was linear.
Step-by-step explanation:
a. To model this situation, we assume the temperature varies inversely as elevation decreases since at elevation 6288 ft the temperature is 56 °F and at elevation 2041 ft, the temperature is 87 °F
So, we model this as a straight line.
Let m be the gradient of the line.
Let the (6288 ft, 56 F) represent a point on the line and (2041 ft, 87 °F) represent another point on the line.
So m = (6288 ft - 2041 ft)/(56 °F - 87 °F) = 4247 ft/-31 °F = -137 ft/°F
At elevation 5376 ft, let the temperature be T and (5376 ft, T) represent another point on the line.
Since it is a straight line, any of the other two points matched with this point should also give our gradient. Since in the gradient, we took the point (6288 ft, 56 °F) first, we will also take it first in this instant.
So m = -137 ft/ °F = (6288 ft - 5376 ft)/(56 °F - T)
-137 ft/°F = 912 ft/(56 °F - T)
(56 °F - T)/912 ft = -1/(137 ft/ °F)
56 °F - T = -912 ft/(137 ft/°F)
56 °F - T = 6.66 °F
T = 56 °F + 6.66 °F
T = 62.66 °F
T ≅ 62.7 °F
T ≅ 63 °F to the nearest degree
b. When i decided to model the situation, I assumed that the temperature varied inversely as the elevation and that the change in elevation or temperature was linear.
what are two ways to solve this equation.
Answer:
x = - [tex]\frac{96}{23}[/tex] or x= 4.1739
Step-by-step explanation:
[tex]\frac{3x}{8}[/tex] - [tex]\frac{4x}{3}[/tex] = 4
I will show two methods of solving this equation
First method
We will follow the steps below:
First find the LCM of 8 and 3
The LCM of 8 and 3 is 24
Next is to multiply through by 24
Our equation becomes
24 ×[tex]\frac{3x}{8}[/tex] - 24× [tex]\frac{4x}{3}[/tex] = 24× 4
3×3x - 8×4x =24×4
9x - 32x = 96
-23x = 96
Divide both-side of the equation by - 23
-23x/-23= 96/-23
x=-[tex]\frac{96}{23}[/tex] or x=4.1739
second method
[tex]\frac{3x}{8}[/tex] - [tex]\frac{4x}{3}[/tex] = 4
[tex]\frac{9x - 32x}{24}[/tex] = 4
multiply both-side of the equation by 24 or cross multiply
9x - 32x = 96
-23x = 96
divide both-side of the equation by -23
x = - [tex]\frac{96}{23}[/tex] or x= 4.1739
I need a. Correct answer I’ll mark brainliest
Answer:
7^11 / 4^11
Step-by-step explanation:
( 7/4) ^ 11
We know that ( a/b) ^c = a^c / b^c
7^11 / 4^11
Answer: B. [tex](\frac{7}{4})^{11} = \frac{7^{11}}{4^{11}}[/tex]
Step-by-step explanation:
There is exponent rule that states [tex](\frac{a}{b})^{x} = \frac{a^x}{b^x}[/tex]
So we can apply this rule to this problem.
[tex](\frac{7}{4})^{11} = \frac{7^{11}}{4^{11}}[/tex]
Write as an algebraic expression and simplify if possible: *150% of 50% of z whoever answers the fastest gets brainliest
Answer:
3z/4
Step-by-step explanation:
Here, we start by calculating the 50% of z
mathematically, that would be 50/100 * z = 50z/100 = z/2
Now we want to calculate the 150% of this.
That would be 150/100 * z/2 = 150z/200 = 3z/4
What is the value of 13 squared?
Answer: 169
Step-by-step explanation:
13 squared = 13*13
Simply plug this into a calculator to get 169
Hope it helps <3
Answer:
169
Step-by-step explanation:
the answer is 169 because u will square the 13
Find the volume of the prism.
لا
A. 120 cm3
B. 630 cm2
C. 120 units2
D. 120 units 3
First, let's find the area of the triangle:
[tex]A=\dfrac{1}{2}bh=\dfrac{1}{2}\times3\times4=6[/tex]
Now, we multiply this area by the length of the prism, which is 20
[tex]20\times6=120[/tex]
All 3 answers have 120. However, since we're calculating volume, it will be represented by [tex]\text{units}^3[/tex]. Since no specific unit (such as cm or in) is specified, it will be left at that.
Thus, the answer is answer choice D.
Let me know if you need any clarifications, thanks!
The volume of prism is 120 unit³.
The correct option is D.
What is Volume?Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed form determines how much space it can occupy in three dimensions.
First, Area of Triangle
= 1/2 x b x h
= 1/2 x 3 x 4
= 3 x 2
= 6
So, the volume of prism is
= 6 x 20
= 120 unit³
Thus, the volume of prism is 120 unit³.
Learn more about Volume here:
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The coordinates of A, B, and C in the diagram are A (p, 4), B (6, 1 ), and C (9, q). Which equation correctly relates p and q? ↔ ↔ ↔ ↔ Hint: Since AB is perpendicular to BC, the slope of AB × the slope o BC = -1. A. -q − p = 7 B. q − p = 7 C. p − q = 7 D. p + q = 7
Answer:
D. p + q = 7
Step-by-step explanation:
The slope of AB is ...
mAB = (y2 -y1)/(x2 -x1) = (1 -4)/(6 -p) = -3/(6 -p)
The slope of BC is ...
mBC = (q -1)/(9 -6) = (q -1)/3
We want the product of these slopes to be -1:
mAB·mBC = -1 = (-3/(6 -p))·((q -1)/3)
-(q-1)/(6 -p) = -1 . . . . cancel factors of 3
q -1 = 6 -p . . . . . multiply by -(6 -p)
q + p = 7 . . . . . matches choice D
Answer:
C p+q=7
Step-by-step explanation:
I did it on plato and it was right
3. Callum rolled a single six sided die 12 times and it landed on a six, three of the times. The probability that it will land on a six on the 13th roll is?
Answer:
1/6
Step-by-step explanation:
Each roll is independent. So the probability of rolling a six is 1/6, regardless of the previous rolls.
Which choice is equivalent to the expression below?
V-64
Explanation:
By definition, i = sqrt(-1)
Which means,
sqrt(-64) = sqrt(-1*64)
sqrt(-64) = sqrt(-1)*sqrt(64)
sqrt(-64) = i*sqrt(8^2)
sqrt(-64) = i*8
sqrt(-64) = 8i
On the second line, I used the rule sqrt(x*y) = sqrt(x)*sqrt(y). The fourth line used the rule sqrt(x^2) = x when x is nonnegative.
Answer:
Click 8i for Correct Answer
Step-by-step explanation:
Please help.. tysm if you do
Answer:
the answer is option A one graph
and I think or am sure it is correct ans.
Can anyone answer this?
Answer:
Because the triangle is isosceles, the base angles are congruent. Since the sum of angles in a triangle is 180° we can write:
24 + x + x = 180
24 + 2x = 180
2x = 156
x = 78°
Answer:
[tex]\boxed{x=78}[/tex]
Step-by-step explanation:
The triangle is an isosceles triangle.
The two base angles are equal.
Angles in a triangle add up to 180 degrees.
x + x + 24 = 180
Combine like terms.
2x + 24 = 180
Subtract 24 on both sides.
2x = 156
Divide both sides by 2.
x = 78
help me pls with this complete a and B I will give you brainliest if answer is correct:-)
Answer:
a) Multiplied by 1.04
b)160(1.06)=169.6
Step-by-step explanation:
Its increasing so (1+4%) will be what it multiplied to.
Hope it helps u
160(1+6%)=169.6
What is the value of x?
Answer:
The Answer is 180
Step-by-step explanation: