What is the equation of this line

Answer:

(2.83 , 1 , 4)

Step-by-step explanation:

[tex]2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\[/tex]

Rewrite these equations in matrix form

[tex]\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\[/tex]

we can write it like this,

[tex]AX=B\\X=A^{-1}B[/tex]

so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.

We get the inverse of matrix A,

[tex]A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right] \\[/tex]

now multiply the matrix with B

[tex]X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\[/tex]

This question is incomplete, the complete question is;

Students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Their replies are summarized below.

credits earned        very           deg.of certainty           very          Row Total

                           uncertain     somewhat certain        certain                                                

under10                    24                         16                          6                  46

10 through 59          16                           8                          20               44

60 or more               2                           14                          22               38

col total                    42                         38                         48               128

Under the assumption of independence, the expected frequency in the upper left cell is:__________.

A. 12.47

B. 14.56

C. 2.00

D. 11.09

Answer:

Under the assumption of independence, the expected frequency in the upper left cell is 12.47

Option A) 12.47 is the correct Option

Step-by-step explanation:

Given the data in table in the question;

the expected frequency in the upper left cell will be;

Eij = (Ti × Tj) / N

Row total Ti = 38

Column total Tj = 42  

Total frequency N = 128

so we substitute

Eij = (38 × 42) / 128

= 1596 / 128

= 12.468 ≈ 12.47

Therefore Under the assumption of independence, the expected frequency in the upper left cell is 12.47

Option A) 12.47 is the correct Option

Answer:

-20/3

Step-by-step explanation:

here x=5 and y=2 then put the value and get answer.

Answer:

I think the answer is D  

Step-by-step explanation:

Answer:

G=13. On kahn

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

add al the numbers that are alike so xes with xes blah blah

17x+10=180

-10 both sides

17x=170

divide 17 both sides

check

5(10)=50-1=49

80+5=85

40+6=46

49+85+46=180

Answer:

Price of tne Vest + $40 - 1.40 = $38.6

Step-by-step explanation:

3.5% * n = $1.40

0.035 * n = $1.40

0.035/0.035 * n = $1.40/0.035

n = $40

The price of the vest not including the tax is, $40

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Since, Tax is a sum levied by the government or an agency of the government on goods and services. taxes increases the price of products

Now,

Let p = price of a vest

Hence, from the question, this equation can be formed,

⇒ 35% of p = $1.40

⇒ 0.035 x p = $1.4

divide both sides of the equation by 0.035;

⇒ p = $40

Thus, The price of the vest not including the tax is, $40

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Complete question is this;

Jill paid a sales tax of $1.40 when she bought a vest. What was price of vest not including tax? Sales tax = 3.5%

Answer:

Step-by-step explanation:

lets remember that 1kg=2.2 lb

if

2.2 lbs................................1 kg

120lbs...................................? kg

120/2.2=54.54 kg

Answer:

The answer is 1

Step-by-step explanation:

30 minus 24 is 6 and 6 divided by 6 is 1

A. $ 58.50

B. $ 80

C. No, it did not mark up 30%.

Step-by-step explanation:Since,

A. We have,

Mark up percentage = 30%

Actual price = $ 45,

B. We have,

SP = $ 104,

C.  We have,

AP = $ 75,

SP = $100,

Thus, mark up percentage =

= 33.33 %

Hence, store did not mark up the price by 30%.

Answer:

<

Step-by-step explanation:

Answer:

huh??

Step-by-step explanation:

Answer:

the domain is that x is a set of real numbers.

the range is y ≤ -3

Step-by-step explanation:

y = -|x + 3|

y is either positive or equal to zero.

Now, x is all real numbers because any value of x used will yield a valid value of y.

Thus, we can say that the domain is that x is a set of real numbers.

Now, for the range:

The minus sign in front of the absolute value indicates that the function has a maximum value.

Thus, the range is y ≤ -3

Answer:

I think it's A.

Step-by-step explanation:

I hope it is helpful to you

Answer:

Each person would get 1/6 of the pizza

Step-by-step explanation:

1/3 divided by 2 is 1/6. Do that again and you will get four of 1/6.

Answer:

I believe the answer is '2 solutions'.

Step-by-step explanation:

Combine each equation, solve the resulting question which comes out as two seperate variables, x = -1.197-- and y = 7.3990. I believe your answer is '2 solutions' because of this.

Answer:

1 solution

Step-by-step explanation:

(x + 3)⁵

= x⁵ + 3⁵

= x⁵ + 243

Answer:

The answer is 2.5 or 5/2 as a fraction.

Step-by-step explanation:

P.S Can I have brainliest?

Answer:

2.5

Step-by-step explanation:

[tex]\frac{5}{8}[/tex] ÷ [tex]\frac{1}{4}[/tex]

turns into

[tex]\frac{5}{8}[/tex] ×[tex]\frac{4}{1}[/tex] = [tex]\frac{20}{8}[/tex]

and 20/8 as a decimal is 2.5 :) hope this helps!

Answers:

Refer to the diagram below

========================================

Explanation:

For points D,E,F,G we will follow these steps

Let's go through an example:

Point D is located at (-3, -9). Apply the three steps mentioned above.

In short, D(-3,-9) reflects over the line x = 3 to land on D ' (9, -9)

The other points E, F, G will follow the same steps to get the answers you see at the top.

The diagram below visually summarizes everything.

-------------

Side notes:

Answer:

angle IJA is a right angle

Answer:

135.05 ; 2.762 ; (133.201, 136.899) ; (132.840, 137.260)

Step-by-step explanation:

Given the data:

Urban area Price/liter

St. John, NL 137.1

Halifax 133.6

Montreal 136.2

Regina 132.3

Saskatoon 132.2

Yellowknife 138.9

Mean = (137.1 + 133.6 + 136.2 + 132.3 + 132.2 + 138.9) / 6

= 810.3 / 6

= 135.05

Standard deviation (σ) : √Σ(X - mean)²/n-1

(137.1 - 135.05)^2 + (133.6 - 135.05)^2 + (136.2 - 135.05)^2 + (132.3 - 135.05)^2 + (132.2 - 135.05)^2+ (138.9 - 135.05)^2 = 38.135

√(38.135 / (6 - 1))

= √7.627

= 2.7617023

= 2.762

C.)

90% confidence interval of the mean :

Mean ± Zcrit * σ/√n

Zcrit at 90% = 1.64

135.05 ± 1.64 * (2.762/√6)

135.05 ± 1.64 * 1.1275817

Lower Value = (135.05 - (1.64 * 1.1275817)) = 133.201

Upper Value = (135.05 + (1.64 * 1.1275817))) = 136.899

Confidence interval = (133.201, 136.899)

D.)

95% confidence interval of the mean :

Mean ± Zcrit * σ/√n

Zcrit at 95% = 1.96

135.05 ± 1.96 * (2.762/6)

135.05 ± 1.96 * 1.1275817

Lower Value = (135.05 - (1.96 * 1.1275817)) = 132.840

Upper Value = (135.05 + (1.96 * 1.1275817)) = 137.260

Confidence interval = (132.840, 137.260)

Answer:

a,c,d

Step-by-step explanation:

Answer:

the answer is F, C, A

GIVE ME THE ANSWER!!!!!!!!!!!!!!!!!!

Recall that

cos²(x) + sin²(x) = 1

for all x, so that

sin(x) = ± √(1 - cos²(x))

Given that cos(θ) = 4/9 > 0, and

tan(θ) = sin(θ) / cos(θ) < 0

it follows that sin(θ) < 0, so

sin(θ) = - √(1 - cos²(θ)) = - √(1 - (4/9)²) = - √(65)/9

The value of sinθ is √(65)/9.

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function.

Since cos(theta) = 4/9 and tan(theta) < 0, we know that theta is in the second quadrant of the unit circle, where cosine is positive and sine is positive.

We can use the Pythagorean identity to find sin(theta):

sin²(theta) + cos²(theta) = 1

Substituting in the given value of cos(theta), we get:

sin²(theta) + (4/9)² = 1

sin²(theta) + 16/81 = 1

sin²(theta) = 1 - 16/81

sin²(theta) = 65/81

Taking the square root of both sides, we get:

sin(theta) = ± sqrt(65)/9

Since theta is in the second quadrant where sine is positive, we can take the positive root:

sin(theta) = sqrt(65)/9

Therefore, sin(theta) = sqrt(65)/9.

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Answer:

B' = 105°

C = 27°

A = 48°

Step-by-step explanation:

Given

B = 105°

C = (2x - 3)°

C' = (5x - 48)°

Rotation = 90°

Before solving the requirements of this question, it should be noted that rotation do not change the angle of shapes.

i.e. an angle retain its measurements pre and after rotation.

Solving (a): The measurement of B'

Using the analysis above.

B' = B

Recall that

B = 105°

So:

B' = 105°

Solving (b): A and C

First, I'll solve for C.

Using the same analysis above.

C = C'

Substitute values for C and C'

5x - 48 = 2x - 3

Collect like terms

5x - 2x = 48 - 3

3x = 45

Multiply both sides by ⅓

⅓*3x = ⅓*45

x = 15

Substitute 15 for x in

C = (2x - 3)°

C = 2 * 15 - 3

C = 30 - 3

C = 27°

Solving for A

The sum of angles (A, B and C) is represented as:

A + B + C = 180

Substitute values for B and C

A + 105° + 27° = 180°

A + 132° = 180°

Collect like terms

A = 180° - 132°

A = 48°

Answer:

8 beacaus the seven increased from 4

The quotient after increased by 4 is 8.

To calculate the quotient of 28 divided by 7, we perform the division and get:

28 ÷ 7

= 28/7

= (7 x 4)/ 7

= 4

Next, we are asked to increase this quotient by 4. Adding 4 to the quotient:

= 4 + 4

= 8.

Therefore, the quotient after increased by 4 is 8.

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Answer:

Step-by-step explanation:

[tex]\sin^4x-\sin^2x=\cos^4x-\cos^2x\\\\Ls=\sin^2x(\sin^2x-1)=-\sin^2x(1-\sin^2x)=-\sin^2x\cos^2x\\\\Rs=\cos^2x(\cos^2x-1)=-\cos^2x(1-\cos^2x)=-\cos^2x\sin^2x\\\\Ls=Rs\\\\\text{used}\\\\a^n\cdot a^m=a^{n+m}\\\\\text{distributive property}\ a(b+c)=ab+ac\\\\\sin^2x+\cos^2x=1\to \sin^2x=1-\cos^2x\\\\\sin^2x+\cos^2x=1\to \cos^2x=1-\sin^2x}[/tex]

Answer: D

Step-by-step explanation:

The best use of the associative and commutative properties to simplify the expression 2.4 + 13 - 5 + 3.6 + 7 would be:

D. (2.4 + 3.6) + [13 + 7 + (-5)]

By applying the associative property, we can group the numbers in a way that allows for easier computation.

Here, we group 2.4 and 3.6 together and 13, 7, and -5 together. This allows us to simplify each group separately and then add the results together.

Calculating the groups:

(2.4 + 3.6) = 6

[13 + 7 + (-5)] = 15

Now, we add the results together:

6 + 15 = 21

So, the simplified expression is 21. Therefore, option D provides the best use of the associative and commutative properties to simplify the given expression.

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