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50 3.5 3.9 4.4 5.0 5.9 7. 1 8.8 11.8 45 40 35 30 25 20 15 Reduce your greenhouse gas emissions by choosing a car with better gas mileage. MPG A n n u a l T o n so fG H G At Sunny Middle School, Ms. Addison’s class is investigating how greenhouse gases (GHGs) contribute to global climate change. They wrote their research on note cards: • Greenhouse gases cause climate change by trapping heat on the planet. • Greenhouse gases contribute to smog and air pollution, which can cause respiratory diseases, like asthma. • Extreme weather, disruptions to the food supply, and increased wildfires are also caused by greenhouse gases. “Where do greenhouse gases come from?” Mia asked. “One of the most common greenhouse gases is carbon dioxide, also known as CO2. People release CO2 into the atmosphere when we burn fossil fuels (like coal and natural gas) for energy and transportation,” Ms. Addison answered. The class examined the graph to the right. The source for the largest percentage of CO2 emissions for a typical household was vehicles. The students conducted some research and found: > Highway vehicles release about 1.7 billion tons of GHGs each year. > Each gallon of gasoline burned creates 20 pounds of GHG. > A typical vehicle releases 6 to 9 tons of GHG into the atmosphere each year. For their group project, Mia and Ichiro researched hybrid cars that combine gas and an electric motor. “Awesome, so it consumes less fuel and emits less CO2 into the environment,” Ichiro said. “While hybrid cars are better for the environment, I’m seeing that some people are hesitant to buy one because of the higher purchase price,” Mia noted. They found the graph to the right, which shows the miles per gallon (MPG) and the annual tons of GHG produced by 8 different types of cars. If each gallon of gasoline burned created 20 pounds of GHG, and the price of gasoline was $2.454 per gallon, how much money was saved annually on gas by the car that got 40 miles per gallon when compared to the car that got 20 miles per gallon? Provide your answer to the hundredths place. Note: 1 ton = 2,000 pounds
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Answer:
$42,110.65
Step-by-step explanation:
Let A be a given matrix below. First, find the eigenvalues and their corresponding eigenspaces for the following matrices. Then, find an invertible matrix P and a diagonal matrix such that A = PDPâ’1.
(a) [ 3 2 2 3 ]
(b) [ 1 â 1 2 â 1 ]
(c) [1 2 3 0 2 3 0 0 3]
(d) [3 1 1 1 3 1 1 1 3]
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It looks like given matrices are supposed to be
[tex]\begin{array}{ccccccc}\begin{bmatrix}3&2\\2&3\end{bmatrix} & & \begin{bmatrix}1&-1\\2&-1\end{bmatrix} & & \begin{bmatrix}1&2&3\\0&2&3\\0&0&3\end{bmatrix} & & \begin{bmatrix}3&1&1\\1&3&1\\1&1&3\end{bmatrix}\end{array}[/tex]
You can find the eigenvalues of matrix A by solving for λ in the equation det(A - λI) = 0, where I is the identity matrix. We also have the following facts about eigenvalues:
• tr(A) = trace of A = sum of diagonal entries = sum of eigenvalues
• det(A) = determinant of A = product of eigenvalues
(a) The eigenvalues are λ₁ = 1 and λ₂ = 5, since
[tex]\mathrm{tr}\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3 + 3 = 6[/tex]
[tex]\det\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3^2-2^2 = 5[/tex]
and
λ₁ + λ₂ = 6 ⇒ λ₁ λ₂ = λ₁ (6 - λ₁) = 5
⇒ 6 λ₁ - λ₁² = 5
⇒ λ₁² - 6 λ₁ + 5 = 0
⇒ (λ₁ - 5) (λ₁ - 1) = 0
⇒ λ₁ = 5 or λ₁ = 1
To find the corresponding eigenvectors, we solve for the vector v in Av = λv, or equivalently (A - λI) v = 0.
• For λ = 1, we have
[tex]\begin{bmatrix}3-1&2\\2&3-1\end{bmatrix}v = \begin{bmatrix}2&2\\2&2\end{bmatrix}v = 0[/tex]
With v = (v₁, v₂)ᵀ, this equation tells us that
2 v₁ + 2 v₂ = 0
so that if we choose v₁ = -1, then v₂ = 1. So Av = v for the eigenvector v = (-1, 1)ᵀ.
• For λ = 5, we would end up with
[tex]\begin{bmatrix}-2&2\\2&-2\end{bmatrix}v = 0[/tex]
and this tells us
-2 v₁ + 2 v₂ = 0
and it follows that v = (1, 1)ᵀ.
Then the decomposition of A into PDP⁻¹ is obtained with
[tex]P = \begin{bmatrix}-1 & 1 \\ 1 & 1\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}1 & 0 \\ 0 & 5\end{bmatrix}[/tex]
where the n-th column of P is the eigenvector associated with the eigenvalue in the n-th row/column of D.
(b) Consult part (a) for specific details. You would find that the eigenvalues are i and -i, as in i = √(-1). The corresponding eigenvectors are (1 + i, 2)ᵀ and (1 - i, 2)ᵀ, so that A = PDP⁻¹ if
[tex]P = \begin{bmatrix}1+i & 1-i\\2&2\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}i&0\\0&i\end{bmatrix}[/tex]
(c) For a 3×3 matrix, I'm not aware of any shortcuts like above, so we proceed as usual:
[tex]\det(A-\lambda I) = \det\begin{bmatrix}1-\lambda & 2 & 3 \\ 0 & 2-\lambda & 3 \\ 0 & 0 & 3-\lambda\end{bmatrix} = 0[/tex]
Since A - λI is upper-triangular, the determinant is exactly the product the entries on the diagonal:
det(A - λI) = (1 - λ) (2 - λ) (3 - λ) = 0
and it follows that the eigenvalues are λ₁ = 1, λ₂ = 2, and λ₃ = 3. Now solve for v = (v₁, v₂, v₃)ᵀ such that (A - λI) v = 0.
• For λ = 1,
[tex]\begin{bmatrix}0&2&3\\0&1&3\\0&0&2\end{bmatrix}v = 0[/tex]
tells us we can freely choose v₁ = 1, while the other components must be v₂ = v₃ = 0. Then v = (1, 0, 0)ᵀ.
• For λ = 2,
[tex]\begin{bmatrix}-1&2&3\\0&0&3\\0&0&1\end{bmatrix}v = 0[/tex]
tells us we need to fix v₃ = 0. Then -v₁ + 2 v₂ = 0, so we can choose, say, v₂ = 1 and v₁ = 2. Then v = (2, 1, 0)ᵀ.
• For λ = 3,
[tex]\begin{bmatrix}-2&2&3\\0&-1&3\\0&0&0\end{bmatrix}v = 0[/tex]
tells us if we choose v₃ = 1, then it follows that v₂ = 3 and v₁ = 9/2. To make things neater, let's scale these components by a factor of 2, so that v = (9, 6, 2)ᵀ.
Then we have A = PDP⁻¹ for
[tex]P = \begin{bmatrix}1&2&9\\0&1&6\\0&0&2\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}1&0&0\\0&2&0\\0&0&3\end{bmatrix}[/tex]
(d) Consult part (c) for all the details. Or, we can observe that λ₁ = 2 is an eigenvalue, since subtracting 2I from A gives a matrix of only 1s and det(A - 2I) = 0. Then using the eigen-facts,
• tr(A) = 3 + 3 + 3 = 9 = 2 + λ₂ + λ₃ ⇒ λ₂ + λ₃ = 7
• det(A) = 20 = 2 λ₂ λ₃ ⇒ λ₂ λ₃ = 10
and we find λ₂ = 2 and λ₃ = 5.
I'll omit the details for finding the eigenvector associated with λ = 5; I ended up with v = (1, 1, 1)ᵀ.
• For λ = 2,
[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}v = 0[/tex]
tells us that if we fix v₃ = 0, then v₁ + v₂ = 0, so that we can pick v₁ = 1 and v₂ = -1. So v = (1, -1, 0)ᵀ.
• For the repeated eigenvalue λ = 2, we find the generalized eigenvector such that (A - 2I)² v = 0.
[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}^2 v = \begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}v = 0[/tex]
This time we fix v₂ = 0, so that 3 v₁ + 3 v₃ = 0, and we can pick v₁ = 1 and v₃ = -1. So v = (1, 0, -1)ᵀ.
Then A = PDP⁻¹ if
[tex]P = \begin{bmatrix}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}5&0&0\\0&2&0\\0&2&2\end{bmatrix}[/tex]
The sizes of the angles in degrees of e triangles are.
2x+7
2x
X+18
Use this information to write down an equation in terms of x
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5x + 25 = 180
5x = 155
x = 31 °
for a brainlist please answer
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Answer:
The variable should not be Less than or equal to... it should be GREATER than or equal to [[tex]y\geq 2x-4[/tex]]
Step-by-step explanation:
Answer:
I believe her mistake is that the shaded area is on the wrong side of the line.
Step-by-step explanation:
The humerus is the bone in a person's upper arm.With this bone as a clue,an anthropologist can tell about how tall a person was.If the bone belongs to that of a female,then height of the person is about (2.75 × humerus length)+71.48 cm .Supposed that the humerus of the female.Supposed that the humerus of a female was found to be 31cm long,about how tall was she? Show your solution
Nonsense=acc in brainly will be deleted
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Answer:
156.73 cm
Step-by-step explanation:
height of the person = (2.75 × humerus length)+71.48 cm
length of the found humerus = 31cm
∴ height of the person = (2.75 × 31)+71.48 cm
= 85.25 + 71.48 cm
= 156.73 cm
I need help this question is do today pls help me
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Answer:
4.7 x [tex]10^{7}[/tex] miles
Step-by-step explanation:
You know Mars is further away from the sun
so the distance between earth and mars will be
1.4x[tex]10^{8}[/tex]-9.3x[tex]10^{7}[/tex]
14x[tex]10^{7}[/tex]-9.3x[tex]10^{7}[/tex]
4.7 x [tex]10^{7}[/tex] miles
Help me pleaseee asap !!!
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Step-by-step explanation:
5x+3x-14=180
8x-14=180
8x=180+14
8x=174
x=174/8
x= 21.75°
if x is 21.75°, then 5x is 108.75°
which means 3x-14 is 51.25°
therefore, f +108.75+51.25=180
f = 180-160
f=20°
which shows 2^-2 * 2^6 in exponential form
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Answer:
16
Step-by-step explanation:
2^-2=0.25
2^6=64
times
=16
HELP!!
Formula
Y=___x +___
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Answer:
look at the slope rise of 2 run of -1 or other way around so slope is
[tex] y = - \frac{2}{1}x + 5[/tex]
what times what equals 48 and adds to -16
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Answer:
-4 and -12
Step-by-step explanation:
For what times what equals 48:
-4(-12) = 48
-4 - 12 = -16
Answer:
x= -4 and y= -12
Step-by-step explanation:
x*y=48
x+y=-16
solve one equation for x
y=-16-x
then plug that y into the other equation
x(-16-x)=48
-16x-x^2=48
multiply by -1
x^2+16x=-48
complete the square
x^2+16x+64=-48+64
(x+8)^2=16
solve for x
x+8=sqrt(16)
x+8=4
x=4-8
x=-4
plug x back into original equation
x+y=-16
-4+y=-16
y=-16+4
y=-12
so your answers are x=-4 and y=-12
i need help
[tex]\bf 3x-5=16[/tex]
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Answer: x = 7
Step-by-step explanation:
do opposites to both sides. what is the opposite of -5? it would be plus 5.
add 5 to both sides
3x = 21
now what is the opposite of 3 times x? 3 divided by.
divide 3 to both sides
x = 7
Answer:
x = 7
Step-by-step explanation:
First add 5 on both sides to get 3x = 21, then divide 3 on both sides to get x = 7.
Hope this helps you :)
What equation is graphed in this figure?
O 2x+y=-3
O 20y=-3
O 2x+y=3
O 2x -y=3
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Answer: 2x-y=3
Step-by-step explanation:
Rewrite 2x-y=3 in standard form: y = 2x -3
The line on the graph has a y-intercept of -3, as does this equation. We can also see a slope of 2 (y goes up by 2 for every time x increase by 1).
How to calculate the surface area of a football.
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Answer:
A football is a sphere, so the formula for calculating its surface area is 4πr²
Hope it helps:)
please help mee!! For which value of x does f(x) = 2?
A) 2
B) 0
C) -4
D) None of the above.
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Answer:
The slope is zero
Step-by-step explanation:
0 | 2
1 | 2
3 | 2
After a baby was born, she began to gain weight at a rate of 1.5 pounds per month. The weight of the baby at birth was 12 pounds. Write an equation for W,W, in terms of t,t, representing weight, in pounds, of the newborn baby tt months after birth.
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What we know:
The baby gains 1.5 pounds per month.
Its weight at birth is 12 pounds.
Therefore, when looking to find the weight after t time, we have to take the constant and the rate of change and place them into the equation. This means our equation will look something like this:
W(t) = Rate of Change x number of months + weight at birth.
Or
W(t) = 1.5(t) + 12
So if in 4 months we look at the weight, the baby will be:
1.5 (4) + 12 = W(t)
6 + 12 = W(t)
18 = W(t)
After 4 months the baby is 18 pounds.
Answer: W(t) = 1.5(t) + 12
I hope this helps! :)
f(x)=-2x^2-2x+10 f(x)=−2x 2 −2x+10 \text{Find }f(2) Find f(2)
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Given that:
f(x) = -2x²-2x+10
f(2) = -2(2)²-2(2)+10
= -2(2*2) - 4 + 10
= -2(4) - 4 + 10
= -8 - 4 + 10
= -12 + 10
= -2 Ans.
Read more:
Similar Question
Given f(x) = 1/2x - 5, find f^-1(x) a. f^-1 (x) = -2x+10 b. f^-1(x) = 2x+5 c. f^-1(x) = 2x-10 d. f^-1(x) = 2x+10...
https://brainly.com/question/11148895?referrer
Write an equation in vertex form for each graph or given information: 31. Vertex (-5, 12) and through the point (-2, 15)
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Answer:
(-3,16)
Step-by-step explanation:
(-5,12)
f (x) = ( (x+5) (x+5) ) + 12
f (x) = x^2 + 10x + 37
(-2,15)
f (x) = ( (x+2) (x+2) ) + 15
f (x) = x^2 + 4x + 19
I’ll mark brainliest!! Please help:)
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A 12-in. steel cable weighs 0.428 lb. How much does 12.8 ft. weigh?
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Answer:
5.48 lb
Step-by-step explanation:
12 inches is 1 foot.
12.8 times that length will have 12.8 times that weight:
12.8 · 0.428 lb = 5.4784 lb ≈ 5.48 lb
__
The given values have 3 significant figures, so the answer needs to be rounded to 3 significant figures.
(3 questions for 50 points)PLZ HELP
Answers
Answer:
see explanation
Step-by-step explanation:
(10)
Since the triangles are congruent then corresponding sides are congruent, so
EF = BC , that is
4x - 1 = 19 ( add 1 to both sides )
4x = 20 ( divide both sides by 4 )\
x = 5
and
DE = AB , that is
y - 6 = 8 ( add 6 to both sides )
y = 14
-------------------------------------------------------
(11)
Since the triangles are congruent the corresponding angles are congruent, so
∠ K = ∠ Y , that is
3x - 37 = 41 ( add 37 to both sides )
3x = 78 ( divide both sides by 3 )
x = 26 , then
∠ K = 3x - 37 = 3(26) - 37 = 78 - 37 = 41°
The sum of the 3 angles in Δ ZMK = 180° then
∠ Z = 180° - (41 + 112)° = 180° - 153° = 27°
So
∠ A = ∠ Z
2y + 7 = 27 ( subtract 7 from both sides )
2y = 20 ( divide both sides by 2 )
y = 10
------------------------------------------------------------------------
(12)
Since the triangles are congruent the corresponding sides and angles are congruent
DG = BS
4x - 11 = 25 ( add 11 to both sides )
4x = 36 ( divide both sides by 4 )
x = 9
∠ T = 180° - (56 + 21)° = 180° - 77° = 103°
Then
∠ H = ∠ T
7y + 5 = 103 ( subtract 5 from both sides )
7y = 98 ( divide both sides by 7 )
y = 14
A package of breakfast bars has 12 breakfast bars in it. The total weight of the breakfast bars in the package is
552 grams. The mass of each breakfast bar is the same. What is the mass in grams of each breakfast bar?
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\sf 45-2x=75-3x
Free
Answers
[tex]\sf \longmapsto45 - 2x = 75 - 3x[/tex]
[tex]\sf \longmapsto45+−2x=75+−3x[/tex]
[tex]\sf \longmapsto−2x+45=−3x+75[/tex]
[tex]\sf \longmapsto \: −2x+45+3x=−3x+75+3x[/tex]
[tex]\sf \longmapsto \: x+45=75[/tex]
[tex]\sf \longmapsto \: x+45−45=75−45[/tex]
[tex]\sf \longmapsto \: x=30[/tex]
[tex] \boxed{\sf 30}[/tex]
PLS HELP!!!!!!! I AM GIVING BRAINLIEST!!!!!
Select the correct images.
Select the parent function and its graph.
Answers
Answer:
The answer in image one is f(x)=2x Left
The answer in image two is f(x)=x Center
the answer in image three where right Right
Answer:
The answer is f(x) = x. Its the second graph.
Step-by-step explanation:
Aroha is 3 years older than her brother. The sum of Aroha's age and her brother's age is 31. Write and solve and equation to find their ages
Answers
Answer:
Therefore, Aroha is 17 yrs old and her brother is 14 yrs old.
Step-by-step explanation:
Let's represent Aroha's brother's Agee with the letter "b" yrs old.
If Aroha is 3yrs older than her brother, she's : (b+3) yrs old.
The sum of their ages is 31,
b+(b+3)=31
2b+3=31
Collect like terms,
2b=31-3
2b=28
Divide both sides by 2,
b=14
b+3=17
A cheerful teen hoping this helps,
stay techy, brilliant and positive!
What is the value of the function y= 2x – 3 when x = -1?
O --5
O-1
o 2
03
Answers
Answer:
y= 2x-3
when X= -1
y= 2(-1)-3
y= -2-3
y= -5
The value of the given function y=2x-3 is -5 when x=-1
What is a function?A function is a correspondence from the two set A to set B in which each element of set A has a unique image in B. Generally we denote a function by f or y.
Here the given function is y=2x-3
Putting x= -1 in the given function y=2x-3 , we get
y= 2(-1) -3
y= -2-3
y= -5
Hence the value of the function y= 2x-3 is -5 when x=-1 .
To learn more about function click here:
https://brainly.com/question/25649287
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Solve.
315−14x=−45
Enter your answer in the box.
x =
plzzzzz helpp me
Answers
Answer:
180/7
Step-by-step explanation:
Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
y=-2x+5
Step-by-step explanation:
Use slope intercept form (y=mx+b) to plug in the values for m and b
Select the correct answer.
Which statement best describes the solution to this system of equations?
3x + y= 17
x+2y= 49
OA. It has no solution.
OB.
It has infinite solutions.
OC. It has a single solution: x= 15, y= 17.
OD. It has a single solution: x= -3, y = 26.
Reset
Next
Answers
Answer:
D. (-3, 26)
Step-by-step explanation:
The ratios of x- and y-coefficients are different in the two equations, so there will be a single solution. (Different ratios mean the slopes are different. Lines with different slopes must intersect in exactly one point.)
We can rearrange the first equation to give an expression for y:
y = 17 -3x
This can be substituted into the second equation to give ...
x +2(17 -3x) = 49
-5x +34 = 49 . . . . . . simplify
-5x = 15 . . . . . . . subtract 34
x = -3 . . . . . . divide by -5
Then the value of y is ...
y = 17 -3(-3) = 26
The single solution is (x, y) = (-3, 26).
Which number sentence is true?
Answers
Answer:
B
Step-by-step explanation:
Edge 2021.
ordered pairs on a vertical line have the same y coordinate. true, sometimes true or not true?
Answers
I’m a vertical line, they will always have the same x axis, but never the same y axis