The standard matrix for the linear transformation t is
| 3 6 |
| 3 -6 |
How to determine the standard matrix for the linear transformation t?The linear transformation of matrix T is given as:
t(x, y) = (3x + 6y, 3x − 6y)
When the above linear transformation is represented as a matrix, we have the following expression
T([x]) = | 3x + 6y |
[y] | 3x - 6y |
The above linear transformation of matrix can be rewritten as the following product of matrixes
T([x]) = | 3x + 6y | = | 3 6 | | x |
[y] | 3x - 6y | | 3 -6 | | y |
From the above equation, the standard matrix for the linear transformation t is
| 3 6 |
| 3 -6 |
Hence, the standard matrix for the linear transformation t is
| 3 6 |
| 3 -6 |
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in a convex hexa
gon the sum of interior is how many times the sum of exterior angles
Answer:
Twice
Step-by-step explanation:
In a convex hexagon the sum of all interior angle is equal to twice of exterior angles.
PLEASE MARK ME AS BRAINLIST
Maria wants to take a survey to predict who will win the election for her town’s mayor. Which samples are most likely to be biased? Check all that apply.
The Biased samples that are most likely to be biased are as follows;
The residents of every other house on her street.
The people at the computer store.
At the mall every 100th person from the town’s phone registry.
Every 10th person who walks down the main street in her town.
According to the statement
we have given that the:
Maria wants to take a survey to predict who will win the election for her town’s mayor.
So, For this purpose
Biased sample In epidemiology, a sample of a group that does not equally represent the members of the group.
The above people are selected randomly with no specific characteristics, so it is less likely to be biased.
These people are selected according to specific characteristics; Subscribing to the golf magazine (who tends to be rich and biased in politics).
So, it is more likely to be biased.
The Biased samples that are most likely to be biased are as follows
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Answer:
A: The residents of every house on her street
B: The subscribers to a golf magazine
C: The people at the computer store at the mall
According to the Coase theorem, negative externalities can be internalized if Select one: a. the government takes action to solve the problem. b. property rights are assigned to the party who is being damaged. c. property rights are assigned to either party. d. property rights are assigned to the party who is doing the damage.
Answer:
B. Property right are assigned to the party who is being
Chris, nina, and iana each have a 3/4 chance of going to cafe shirley for an afternoon coffee at 1:00pm. jeffrey will only go to cafe shirley for a coffee if at least one of his friends is at the cafe. what is the probability that jeffrey goes to cafe shirley for a coffee today?
Answer:
Jeffrey has 225 % chance to go to Cafe Shirley.
Step-by-step explanation:
given,
chance of going to Cafe
Chris = 3/4
Nina =3/4
iana = 3/4
To find the total probability you should add all of them:
Total probability= 3/4 + 3/4 + 3/4
= 9/4 = 2.25
to convert to percent you should times 100
2.25 x 100 = 225%//
. What is the midpoint of a line segment connecting the points (−4,6) and (8,2)?
Solve the equation 3x² = 108.
Answer:
x = 6
Step-by-step explanation:
First we divide both sides by 3 :
x² = 108 ÷ 3
x² = 36
Now we square root both sides :
x = √36
x = 6
Hope this helped and have a good day
Answer:
x = ± 6
Step-by-step explanation:
Quick steps
[tex]3x^{2} =108[/tex]
[tex]x=\sqrt{\frac{108}{3} } =\sqrt{36}[/tex]
[tex]x=[/tex] ±6
A (positive) number has two square roots; one positive and one negative
Hope this helps
evaluate the expression: 7 - 3 + 9 x 8 ÷ 2
Answer:
40
Step-by-step explanation:
7 - 3 + 9 x 8 / 2
Multiplication and division left - right.
7 - 3 + 72 / 2
7 - 3 + 36
Add and subtract left to right.
4 + 36 = 40
I'm thinking of a number. If I add 4 to the number and then multiply the result by 3,the answer is the same as subtracting 5 from the number and then multiplying the result by 2.
(a) in terms of x?
(b) solve the equation n find the number what I'm thinking of
Answer:
x=-22
Step-by-step explanation:
Let's substitute the number you are thinking of with x
(x+4)*3=(x-5)*2
3x+12=2x-10
x+12=-10
x=-22
A diver is standing on a spring board 48 feet above the pool. She jumps from the platform with an
initial upward velocity of 8 feet /second. Use the formula d(t)= -16(2t - 3)(t+1), where d is the
height of the diver above the water and t is the time in seconds. How long will it take for her to hit
the water?
It will take the diver 1.5seconds for her to hit the water
Linear equationsLinear equations are equation that has a leading degree of 2. Given the expression that expresses the distance covered by the diver as a function of time as shown;
d(t)= -16(2t - 3)(t+1)
where;
d is the height of the diver above the water and;
t is the time in seconds.
Given the following
d = 0 (the distance on the ground)
Substitute into the formula below;
-16(2t - 3)(t+1)= 0
Divide through by -16
(2t - 3)(t+1) = 0
Determine the time
2t - 3 = 0
t = 3/2
Similarly;
t +1 = 0
t = -1
Hence it will take the diver 1.5seconds for her to hit the water
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Find the dimensions of a rectangle with area 1,728 m2 whose perimeter is as small as possible
The dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.
Let the dimension of the rectangle be x and y m.
According to the given question.
The area of the rectangle is 1728 square meter.
⇒ x × y = 1728
⇒ x = 1728/y
Since, the perimeter of the rectangle is the sum of the length of its boundary.
Therefore,
Perimeter of the recatngle with dimensions x and y is given by
Perimeter of the rectangle, P = 2(x + y)
⇒ P = 2(1728/y + y)
⇒ P = 3456/y + 2y
Differentiate the above equation with respect to y
⇒ [tex]P^{'} = -\frac{3456}{y^{2} } + 2[/tex]
For the minimum(small) perimeter equate the above equation to 0.
⇒ [tex]-\frac{3456}{y^{2} } + 2 = 0[/tex]
⇒ [tex]2y^{2} =3456[/tex]
⇒ [tex]y^{2} = \frac{3456}{2}[/tex]
⇒ y^2 = 1728
⇒ y = √1728
⇒ y = 41.56 m
Therefore,
x = 1728/41.56
⇒ x = 41.57 m
Hence, the dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.
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A rectangle is 16 cm. in length. Its width is 50% of its length. what is its perimeter?
Answer: 48 cm
Step-by-step explanation:
A perimeter(P) of a rectangle is equal to 2(L + W), or 2L + 2W, so we write the equation as:
1st way:
W = 50%(16) = 0.5 x 16 = 8
P = 2(L + W)
P = 2(16 + 8)
P = 2(24)
P = 48 cm
2nd way:
P = 2L + 2W
P = 2(16) + 2[50%(16)]
P = 2(16) + 2[0.5 X 16]
P = 32 + 2(8)
P = 32 + 16
P = 48 cm
Evaluate the integral, show all steps please!
Answer:
[tex]\dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x[/tex]
Take partial fractions of the given fraction by writing out the fraction as an identity:
[tex]\begin{aligned}\dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A}{x-4}+\dfrac{B}{x+2}\\\\\implies \dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A(x+2)}{(x-4)(x+2)}+\dfrac{B(x-4)}{(x-4)(x+2)}\\\\\implies x+5 & \equiv A(x+2)+B(x-4)\end{aligned}[/tex]
Calculate the values of A and B using substitution:
[tex]\textsf{when }x=4 \implies 9 = A(6)+B(0) \implies A=\dfrac{3}{2}[/tex]
[tex]\textsf{when }x=-2 \implies 3 = A(0)+B(-6) \implies B=-\dfrac{1}{2}[/tex]
Substitute the found values of A and B:
[tex]\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x = \int \dfrac{3}{2(x-4)}-\dfrac{1}{2(x+2)}\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}[/tex]
If the terms are multiplied by constants, take them outside the integral:
[tex]\implies \displaystyle \dfrac{3}{2} \int \dfrac{1}{x-4}- \dfrac{1}{2} \int \dfrac{1}{x+2}\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating}\\\\$\displaystyle \int \dfrac{f'(x)}{f(x)}\:\text{d}x=\ln |f(x)| \:\:(+\text{C})$\end{minipage}}[/tex]
[tex]\implies \dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}[/tex]
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For an alternative approach, expand and complete the square in the denominator to write
[tex](x-4)(x+2) = x^2 - 2x - 8 = (x - 1)^2 - 9[/tex]
In the integral, substitute [tex]x - 1 = 3 \sin(u)[/tex] and [tex]dx=3\cos(u)\,du[/tex] to transform it to
[tex]\displaystyle \int \frac{x+5}{(x - 1)^2 - 9} \, dx = \int \frac{3\sin(u) + 6}{9 \sin^2(u) - 9} 3\cos(u) \, du \\\\ ~~~~~~~~~~~~ = - \int \frac{\sin(u) + 2}{\cos(u)} \, du \\\\ ~~~~~~~~~~~~ = - \int (\tan(u) + 2 \sec(u)) \, du[/tex]
Using the known antiderivatives
[tex]\displaystyle \int \tan(x) \, dx = - \ln|\cos(x)| + C[/tex]
[tex]\displaystyle \int \sec(x) \, dx = \ln|\sec(x) + \tan(x)| + C[/tex]
we get
[tex]\displaystyle \int \frac{x+5}{(x - 1)^2 - 9} \, dx = \ln|\cos(u)| - 2 \ln|\sec(u) + \tan(u)| + C \\\\ ~~~~~~~~~~~~ = - \ln\left|\frac{(\sec(u) + \tan(u))^2}{\cos(u)}\right|[/tex]
Now, for [tex]n\in\Bbb Z[/tex],
[tex]\sin(u) = \dfrac{x-1}3 \implies u = \sin^{-1}\left(\dfrac{x-1}3\right) + 2n\pi[/tex]
so that
[tex]\cos(u) = \sqrt{1 - \dfrac{(x-1)^2}9} = \dfrac{\sqrt{-(x-4)(x+2)}}3 \implies \sec(u) = \dfrac3{\sqrt{-(x-4)(x+2)}}[/tex]
and
[tex]\tan(u) = \dfrac{\sin(u)}{\cos(u)} = -\dfrac{x-1}{\sqrt{-(x-4)(x+2)}}[/tex]
Then the antiderivative we found is equivalent to
[tex]\displaystyle - \int \frac{x+5}{(x - 1)^2 - 9} \, dx = - \ln\left|-\frac{3(x+2)}{(x-4) \sqrt{-(x-4)(x+2)}}\right| + C[/tex]
and can be expanded as
[tex]\displaystyle - \int \frac{x+5}{(x - 1)^2 - 9} \, dx = -\ln\left| \frac{3(x+2)^{1/2}}{(x-4)^{3/2}}\right| + C \\\\ ~~~~~~~~~~~~ = - \ln\left|(x+2)^{1/2}\right| + \ln\left|(x-4)^{3/2}\right| + C \\\\ ~~~~~~~~~~~~ = \boxed{\frac32 \ln|x-4| - \frac12 \ln|x+2| + C}[/tex]
Point P is on line segment \overline{OQ}
OQ
. Given PQ=x+7,PQ=x+7, OP=4x-10,OP=4x−10, and OQ=4x,OQ=4x, determine the numerical length of \overline{OQ}.
OQ
.
Answer:
Step-by-step explanation:
4x - 10 + x + 7 = 4x
5x - 3 = 4x
-3 = -x
x = 3
4(3) - 10 = 12 - 10 = 2
3 + 7 = 10
10+2 = 12
4(3)= 12
An online retail company determined that their cost for each day, x, can be determined by the function C(x) = 2x^2 – 20x + 70 and their revenue by the function R(x) = –x^2 + 5x + 18. How many days will it take for the company to earn a profit?
4
5
20
22
Answer:
4
Step-by-step explanation:
revenue has to be greater than cost for a profit
revenue minus cost = profit
2x^2 – 20x + 70 - (–x^2 + 5x + 18) =
2x^2 – 20x + 70 + x^2 - 5x - 18 =
3x^2 – 25x + 52 ≤ 0
(x - 4) (3x - 13) ≤ 0
x ≤ 4
x ≤ 13/3
since its multiple choice you can enter one of the answers where the x is to get the answer
if you don't know what the question is and are short on time this may help
again:
revenue has to be greater than cost for a profit
revenue minus cost = profit
cost is 2x^2 – 20x + 70
revenue is –x^2 + 5x + 18
cost is
2(4)^2 – 20(4) + 70 =
32-80+70 =
102-80 =
22
revenue is
–x^2 + 5x + 18
–(4)^2 + 5(4) + 18
-16+20+18
-16+38
22
--------------------------------
cost is
2(5)^2 – 20(5) + 70 =
20
revenue is
–(5)^2 + 5(5) + 18
18
-------------------------------------
cost is
2(20)^2 – 20(20) + 70 =
470
revenue is
–(20)^2 + 5(20) + 18
-282
------------------------------
cost is
2(22)^2 – 20(22) + 70 =
598
revenue is
–(22)^2 + 5(22) + 18
-356
-----------------------------------------
cost is
2(3)^2 – 20(3) + 70 =
28
revenue is
–(3)^2 + 5(3) + 18
24
-------------------------------------
cost is
2(2)^2 – 20(2) + 70 =
38
revenue is
–(2)^2 + 5(2) + 18
24
How to find ‘x’ if 8.4 % of ‘x’ is 420.
I will mark the first answerer as brainliest
This is reverse percentage
8.4% = 420
÷8.4 both side
1% is now 50
1% =50
x100
100% is 5000
Check:
8.4/100 = 0.084 our decimal multiplier
5000 x 0.084 = 420
Thus, x is 5000
Hope this helps!
Help help help help help help
Answer:
∠JKL = 98
Step-by-step explanation:
the two small vertical lines on JK & KL means that
JK & KL are the same length which means that
same length means same degrees
∠KJL & ∠KLJ are the same degrees
∠KJL & ∠KLJ are both 41 degrees
triangles are 180
41 + 41 = 82
180 - 82 = 98
10. Ali's crystal ball grants two-fifths of one-fifth of
all wishes. This is ?% of all wishes.
(A)
2
(B)
25
(C) 8
(D) 60
Answer:
C
Step-by-step explanation:
2/5 x1/5 = 2/25 If you divide 2 by 25, you get.08. To change a decimal into a percent, you move the decimal two places to the right to get 8%
Jason solved the following equation to find the value for x.
-8.5x-3.5x=-78
X=6.5
Describe how Jason can check his answer.
please help me if you can
The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:
[tex]t=5.825\sqrt[3]{w/p\\}[/tex]
Where w = weight of the car
p = power delivered by the engine in horsepower (hp)
If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.
Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer
Natasha got the power right. The power is 295 hp.
How to calculate power?t = 5.825∛w / p
where,
w = weight of the carp = power delivered by the engine in horsepowerquarter mile time = tTherefore,
t = 13.4 s
p = 3590
13.4 = 5.825∛ 3590 / p
cube both sides
13.4³ = 5.825³ × 3590 / p
2406.104 = 197.645890625 × 3590 / p
cross multiply
2406.104 p = 709548.747344
p = 709548.747344 / 2406.104
p = 294.895294361
p = 295 hp
Therefore, Natasha got the power right
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Solve the system of equations below using the substitution method. y = 3x − 1y = - 4x 6
Answer:
x = 1; y = 2
Step-by-step explanation:
y = 3x − 1
y = -4x + 6
In the first equation, y = 3x - 1.
Substitute 3x - 1 for y in the second equation.
3x - 1 = -4x + 6
7x = 7
x = 1
Substitute 1 for x in the first original equation.
y = 3x - 1
y = 3(1) - 1
y = 3 - 1
y = 2
Solution: x = 1; y = 2
if you could help with all 4 questions that would be great pls answer if you know the RIGHT answer
Step-by-step explanation:
3. B
because the figure to the left of the y-axis yields the one to the right when you reflect it across y = x.
4. C
Flip either of the figures vertically across x = -1 which is their intersection point and you'll get the other.
5. D
it can't be clockwise because the x value of the vertices would have been negative. so it is 270° counterclockwise resulting in ( -y , x )
6. A
Similar to #4 which except this time, you flip it horizontally like how you lay a book or pick it up.
Write down the equation for the following
i,Grade 7 students received a total of 88 books from world vision.they received 63 books on Monday and g books on Tuesday
ii,Solve the equation above
Lois made a dish with61/3 cups of pasta. One serving of the pasta is 0.2 cups. How many servings of pasta were in the dish Lois made?
A.
B.
C.
D.
The number of servings of pasta were in the dish Lois made is 31.67.
Unit valueNumber of cups of pasta Lois made = 6 1/3 cupsA serving of the pasta = 0.2 cupsNumber of servings of pasta were in the dish Lois made = Number of cups of pasta Lois made / A serving of the pasta
= 6 1/3 ÷ 0.2
= 19/3 ÷ 0.2
= 19/3 × 1/0.2
= (19×1) / (3 × 0.2)
= 19/0.6
= 31.6666666666666
Approximately,
Number of servings of pasta were in the dish Lois made is 31.67 servings
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convert 5.75 hours to minutes
[tex]\boldsymbol{\sf{Therefore \to \ 5.75\not{h}*\dfrac{60 \ min}{1\not{h}} =345 \ min }}[/tex]
5.75 hours is equal to 345 minutes.
Please Help its a math question i will mark brainlist !! plsss look at attached image below ...blessings
Answer:
-2
Step-by-step explanation:
Every point would flip over the y axis the same distance it is from the y axis now, but just on the other side of the y axis.
In the original equation, when y = 0, x is 2, so when we flip it over the y axis, it is now at -2 when y = 0.
What is the name of each of the two blue points in the hyperbola below?
A. Focus
B. Center
C. Vertex
D. Directrix
Calculate the perimeter of 5y + 9 (3y+15) cm (7y+3)cm
Answer:
Step-by-step explanation:
assuming that the figure is a triangle with sides (5y + 9) and (3y + 15) and (7y + 3) we find the perimeter by adding everything
5y + 9 + 3y + 15 + 7y + 3 =
15y + 27
or
3(5y+9)
next time put all the data and figures, we are doing you a pleasure, at least put ALL the data.
Translate the sentence into an equation.
15 less than Taryn's age is 20
use the variable a to represent Taryn's age.
answer choices:
a. 20-a = 15
b. 15-a = 20
c. a-15= 20
d. 20-15 = a
Answer: c. a-15= 20
Step-by-step explanation:
The answer is c because a represents her age and 15 less than that would mean that you have to subtract 15 from her age which is represented by a, and then 15 less than a would equal 20, so a-15=20
Use the diagram to answer each part of the question. The image is not drawn to scale.
will mark brainiest if corrects. try ur best!
In the afternoon, the person (who is 1.6 m tall) casts a shadow that is 8 m. The distance along the ground from the person (H) to the tree (G) is 30 m, and the distance from the tree (G) to the building (F) is 105 m. Calculate the height of the tree and the building. Round answers to the nearest tenth of a meter and show all your work.
The height of the tree and the building are 7.6 m and 28.6 m respectively.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Two triangles are similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.
Triangle BGD, CHD and AFD are similar triangles.
CH = 1.6, DH = 8, GH = 30, GF = 105
FH = GF + GH = 105 + 30 = 135
FD = FH + DH = 135 + 8 = 143; GD = 30 + 8 = 38
Hence, using similar triangles:
BG/CH = GD / DH
BG / 1.6 = 38/8
BG = 7.6 m
Also:
building/CH = DF / DH
building / 1.6 = 143/8
building = 28.6 m
The height of the tree and the building are 7.6 m and 28.6 m respectively.
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Under his cell phone plan, christopher pays a flat cost of $59 per month and $3 per gigabyte. he wants to keep his bill at $62.90 per month. how many gigabytes of data can he use while staying within his budget?
The number of gigabytes of data that Christopher can use while staying within his budget exists 1.3 gigabytes.
How many gigabytes of data can he utilize while staying within his budget?The number of gigabytes of data that Christopher can use while staying within his budget is 1.8 gigabytes.
Based on the information, we get
59 + (3 × g) = 62.90
59 + 3g = 62.90
simplifying the equation, we get
3g = 62.90 - 59
3g = 3.9
Divide both sides by 3, and we get
3g/3 = 3.9/3
g = 1.3
The number of gigabytes of data that Christopher can use while staying within his budget exists 1.3 gigabytes.
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