Solve the following matrix equations.
(a) 2X=(-4 0 8)
(b) 3 X-(1 7)=(-16 -4)

Answer:

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

Convert this to vertex form by completing the square.

Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:

Answer:

[tex](x-3)^2-11[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]x^2-6x-2[/tex]

To write the given expression in the form (x + a)² + b, complete the square.

Add and subtract the square of half the coefficient of the term in x:

[tex]\implies x^2-6x+\left(\dfrac{-6}{2}\right)^2-2-\left(\dfrac{-6}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2-6x+\left(-3\right)^2-2-\left(-3\right)^2[/tex]

[tex]\implies x^2-6x+9-2-9[/tex]

The first three terms x² - 6x + 9 form a perfect square trinomial.

A perfect square trinomial can be written as the square of a binomial.

Factor the perfect square trinomial:

[tex]\implies(x-3)^2-2-9[/tex]

Simplify:

[tex]\implies(x-3)^2-11[/tex]

Therefore, the given expression written in the form (x + a)² + b is:

[tex]\boxed{(x-3)^2-11}[/tex]

Answer:

I've solved all of the above for you :)

Step-by-step explanation:

3q² + 7 = 55

3q² = + 7 - 7 = 55 - 7

3q² = 48

3q²/3 = 48/3

q² = 12

q = 2√3

√p - 4 = - 5

p - 4 = (-5)²

p - 4 + 4 = 25 + 4

p = 29

5√a/2 = 40

5√a/2 × 2 = 40 × 2

5√a = 80

5√a/5 = 80/5

√a = 16

a = 256

c³ - 4 = 23

c³ - 4 + 4 = 23 + 4

c³ = 27

c = 3

(k + 3)² = 4

k² + 6k + 9 = 4

k² + 6k + 9 - 4 = 0

k² + 6k + 5 = 0

k² + k + 5k + 5 = 0

k(k + 1) + 5(k + 1) = 0

(k + 5) (k + 1) = 0

k = (-5) or (-1)

√s + 4 = 6

s + 4 = (6)²

s + 4 - 4 = 36 - 4

s = 32

(√f - 5) = (√7 - f)

(√f - 5)² = (√7 - f)²

f - 5 = 7 - f

f - 5 + 5 + f = 7 + 5 - f + f

2f/2 = 12/2

f = 6

∛j + 9 = 0

∛j + 9 - 9 = -9

∛j = (-9)

j = (-9)³

j = (-729)

b² - 1 = 24

b² - 1 + 1 = 24 + 1

b² = 25

√b² = √25

b = 5

13 = (w - 2)² + 5

13 = w² - 4w + 4 + 5

13 - 9 = w² - 4w

w² - 4w = 4

w² - 4w - 4 = 0

w² - 2w - 2w - 4 = 0

w(w - 2) - 2(w - 2) = 0

(w - 2) (w - 2) = 0

w = 2 or 2

12 = 4√2x + 1

12/4 = 4√2x + 1/4

3 = √2x + 1

√2x + 1 = 3

2x + 1 = 9

2x + 1 - 1 = 9 - 1

2x/2 = 8/2

x = 4

(g + 1)³ = (-8)

g³ + 1³ + 3g(g + 1) = (-8)

g³ + 1 + 3g² + 3g = (-8)

g³ + 3g² + 3g = (-8) - 1

g³ + 3g² + 3g = -9

g³ + 3g² + 3g + 9 = 0

g = (-3)

∜(5m + 1) = 4

[∜(5m + 1)]⁴ = (4)⁴

5m + 1 = 256

5m + 1 - 1 = 256 - 1

5m/5 = 255/5

m = 51

∛(y³ - 19) = 2

(y³ - 19) = (2)³

y³ - 19 = 8

y³ - 19 + 19 = 8 + 19

y³ = 27

y = 3

The maximum loan you can obtain if the rate for a 25-year mortgage is 8.65% is $298,853.76

A monthly payment can be calculated as;

Monthly payment = (Monthly income - payment)(percentage payment)

38% of your gross monthly income is

 0.38 × $6,500 = $2470

If you're already spending $525 on monthly payments, the amount the bank says you can afford for a mortgage loan;

Then

$2470-525= $1945

The amortization formula can be used to find the corresponding loan value.

A = P(r/25)/(1 -(1 +r/25)^(-25t))

where A is the monthly payment on a loan of P at interest rate of r for time t years.

Filling in the known values, we have ;

 1945= P(.0525/25)/(1 -(1 +.0525/25)^(-12·30))

≈ 0.00515636808·P

Then the maximum loan can obtain is

 P = $1945/0.00515636

P ≈ $298,853.76

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top I think he or she is right

The length of the AB in the given right triangle is √3/6

Given that, a right triangle with the base measure 6 units and an acute angle 30°,

We need to find the measure of side AB,

So, we will use the concept of trigonometric ratios,

Tan 30° = AB / AC

Tan 30° = AB / 6

1 / √3 = AB / 6

AB = √3/6

Hence the length of the AB in the given right triangle is √3/6

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The area of the triangle below 8 yards

What is triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Triangles are three-sided shapes. The many kinds of triangles go by various names. The size of the angles and the length of the sides determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.7-15=8

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Answer: It is crucial for students to look for and make use of a structure because this practice requires them to reason about the underlying mathematical structure and unity of mathematics ideas.

Answer:

450 g = 6 people

? kg = 18 people

450 x 18 = 8100

8100 = 6x

8100/6 = 6x/6

x = 3150 kg of rice is needed for 18 people.

The first three terms of a sequence are given, so the 35th term is: [tex]a_n = 69[/tex]

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts. A sequence is a list of elements that has been arranged in a certain way.

An ordered list of numbers is a sequence. The three dots indicate that the established pattern should go forward. A phrase is used to describe each number in the series. The first word in the order 1, 3, 5, 7, 9,... is 1, the second is 3, the third is 5, and so on.

The first three terms are : 205, 201, 197, .......

The general term through the pattern is:

[tex]a_n = - 4n+209[/tex]

or, [tex]a_n = - 4(35)+209[/tex]    

here, n = 35

or, [tex]a_n = 69[/tex]

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The probability of rolling an odd number or a number less than 4 is 2/3.

What is probability?

The degree to which something is likely; the probability that something will occur or will be the case.

Here, we have

Given

A single die is rolled.

Sample space = {1, 2, 3, 4, 5, 6}

Let P(A) be the probability of getting an odd number, where A = {1, 3, 5}

Let P(B) be the probability of getting a number less than 4,

where B = {1,2,3}

A ⋂ B ={1, 3}

P(A) = 3/6 = 1/2

P(B) = 3/6 = 1/2

P(A ⋂ B) = 2/6 = 1/3

Let P be the required probability of getting an odd number or a number less than 4

P = P( A ⋃ B ) = P(A) + P(B) - P(A ⋂ B)

P( A ⋃ B ) = 1/2 + 1/2 - 1/3

P( A ⋃ B ) = 1 - 1/3

P( A ⋃ B ) = 2/3

Hence, the probability of rolling an odd number or a number less than 4 is 2/3.

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Answer:

He worked 26 hours at the vegetable farm and 4 hours at the paddy field.

Step-by-step explanation:

Let us take the working hour at a vegetable farm be x and at paddy field be y

He worked for both jobs for a total of 30 hours.

So,

x + y = 30 ...(1)

He earns Rs 200/- per hour from vegetable farm and Rs 250/- per hour from paddy field, total of Rs 6900.

So,

200x + 250y = 6900

2x + 5y = 138 ...(2)

From equation 1 we get,

x = 30 - y

Put the value of x = 30 - y in equation 2 we get,

2x + 5y = 138

2(30 - y) + 5y = 138

60 - 2y + 5y = 138

60 + 3y = 138

3y = 138 - 60

3y = 78

y = 26

Now, put the value of y in equation 1 we get,

x + y = 30

x + 26 = 30

x + 26 - 26 = 30 - 26

x = 4

Thus, He worked 26 hours at the vegetable farm and 4 hours at the paddy field.

Answer:

I think that's 11,8

Step-by-step explanation:

Hope its right

Answer: x = 36;  y = 36

Step-by-step explanation:

This is an isosceles triangle, so the 2 "bottom" angles are equal:

2x = 72

x = 72/2 = 36

sum of interior angles = 180

180 - 72 - 72 = 36

The difference between 3894256 and 756533 by rounding each number to the nearest thousand is 3138000

The first number = 3894256

The second number = 756533

To find the difference between the numbers we have to use the subtraction

Difference between 3894256 and 756533 = 3894256 - 756533

Subtract the numbers

= 3137723

Rounding of a number is write the numbers to the nearest place values like tens, hundreds and thousand etc.

Here, the number is 3137723 and we have to round the number to nearest thousand

Round to nearest thousand = 3137000

Therefore, the result nearest to the thousand is 3138000

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The required length of the building is given as 32 cm.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The height of the building is 250 meters, the length of the building is 160m, and on the drawing, the height of the building is 50 cm,
Scale factor = height on drawing / original height
Scale factor = 50 / 250
Scale factor = 1/5

Now,
Length in drawing = scale factor × original length,
length in drawing = 1 / 5 × 160
                           = 31

Thus, the length of the building as of the scale factor 1/5 is given as 31 cm.

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Answer: 3702

Step-by-step explanation: from plato

The constant of proportionality for the relationship is 70.

From the given graph (2, 140), (4, 280), (6, 420), (8, 560) and (10, 700).

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

From the graph we can see it is direct proportion.

Here, y∝x

⇒ y=kx

⇒ k=y/x

⇒ k=140/2

⇒ k=70

Hence, the constant of proportionality for the relationship is 70.

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A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

a. two-tailed test

b. reject H0 if Z>1.96 or Z<-1.96

c. Z = 1.73

d. we have failed to reject the null hypothesis

e. P-value = 0.0418

We need to find our critical value:

Zα/2 = Z(0.05/2) = 0.025

The Z test will be done using the next equation:

Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2

Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73

Z<1.96, therefore we have failed to reject the null hypothesis

The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis

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The absolute maximum is 1.29, which occurs at x= 9

What is absolute extrema?

An absolute extremum  of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.

Main body:

Given =

f(x) = [tex](x^{2} -64)^{1/11[/tex]

f' (x) = derivative of function f(x)

f'(x) = 1/11[tex](x^{2} -64)^{-10/11[/tex] . 2x

     = [tex]2 \frac{x}{11}[/tex][tex](x^{2} -64)^{-10/11[/tex]

putting f'(x) = 0

2x/11 [tex](x^{2} -64)^{-10/11[/tex] = 0

         [tex](x^{2} -64)^{-10/11[/tex] = 0

                     [tex]x^{2} -64[/tex] = 0

 x² = 64

x = ±8

We are given interval [-8,9].

Hence, calculating f(x) at -8, 8, 9.

f(-8) =  0

f(8) = 0

f(9) = [tex]17^{1/11}[/tex]

      = 1.29

Hence, absolute maximum value is 1.29 at x=9.

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The expressions x - 5 and x - 5 gives the equal value for the different values of x, therefore expressions are equivalent.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expressions are,

x - 5 and x - 5

To determine the expressions are equivalent,

Since, in the both, the expression x is a variable, and 5 is an integer,

Therefore, for the values of x the value of expression should be equal.

Substitute x = 0,

x - 5 = 0 - 5 = - 5

And

x - 5 = 0 - 5 = - 5

Substitute x = 1

x - 5 = 1 - 5 = - 4

and

x - 5 = 1 - 5 = - 4

Since, for the different values of x the values of expressions are equal.

Hence, expression x - 5 and x - 5 are equivalent.

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Answer:

106

Step-by-step explanation:

The pattern goes +6, +12, +18, etc

Thus, the final term is simply +30.

76+30 = 106

Hope it helps :) and let me know if you want me to elaborate.

Answer:

Step-by-step explanation:

Clearly, it can be seen that 10/12 represents the largest fraction. Hence 5/6 (which is equivalent to 10/12) is larger than 2/3 or 3/4.

Answer: no they are equal either simplified to 5/6 or decimal 0.83 repeating decimal.

Step-by-step explanation:

The equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45  × d, so option B is correct.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.

Given:

The distance travelled = 315 miles,

The distance on the map =  7 inches,

Calculate the equation represents the actual miles traveled,

Actual distance = The distance traveled / The distance on the map × The distance on the map

m = 315 / 7 × d

m = 45  × d

Therefore, the equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45  × d.

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Answer: 15, not including the frisbees. (The answer would be 20 if the frisbees were in there)

Step-by-step explanation: 25% is equivalent to 1/4, and 5 is equal to 1/4. The simplest way to solve this is to multiply 5 by 4, and you'll get 20. Then subtract 5 (the frisbees) and you'll get 15. (Sorry if that doesn't make much sense haha) Hope this helps!!

We can determine the stream's current velocity by solving a set of equations, which gives us S is 2 mi/h.

The total speed of a motorboat traveling downstream is equal to the speed of the boat in still water plus the speed of the stream, whereas the total speed of a motorboat traveling upstream is equal to the speed of the stream minus one.

Therefore, the speed upstream is: (14 mi/h - S)

The speed downstream is (14 mph + S), where S is the stream's current flow rate.

We can construct the equations below after we know that it takes 15 minutes longer to walk 12 miles downstream:

14 mph plus speed (S) times the time (T minus 15 minutes) equals 12 miles.

In order to solve this, one of the variables in one of the equations needs to be isolated. I'll isolate T in the first equation:

T = (12 miles)/(14 miles per hour Plus S)

By substituting it in the other equation, we will obtain the following value: (14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi.

Taking only the favorable outcome, we obtain:

S = (24 - 25)/(-0.5) = 2 mph

2 mi/hr is the stream's current velocity.

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By the Definition of a Correlation Coefficient,

x and y do not have a linear relationship.

Option B is the correct answer.

The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.

The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.

According to the question, If the correlation coefficient is zero, there is no linear relationship.

If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.

By the Definition of a Correlation Coefficient,

Option B is the correct answer.

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By the Definition of a Correlation Coefficient, X and Y do not have a linear relationship. Option B is the correct answer.

The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.

The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.

According to the question, If the correlation coefficient is zero, there is no linear relationship.

If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.

By the Definition of a Correlation Coefficient,

Option B is the correct answer.

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Answer:Put a one under the five then sop he last faction and start multiplying

Step-by-step explanation:

By using the concept of discount, it can be calculated that

The bike should be marked at $440

What is discount?

Sometimes during sale, the items are sold at a reduced price from the original price of the item. The difference between the reduced price and the original price of the item is called discount.

Price paid by John for a new mountain bike = $280

Markup price = [tex]\frac{10}{100} \times 280[/tex] = $28

Price after markup = $(280 + 28) - $308

Let the marked price be $x

Rate of discount = 30%

Discount = [tex]\frac{30}{100}\times x[/tex]

Price after discount = [tex]x - \frac{30}{100}\times x[/tex]

                                 = [tex]\frac{100x - 30x}{100}[/tex]

                                 = [tex]\frac{70}{100}x[/tex]

By the problem,

[tex]\frac{70}{100}x = 308\\x = \frac{308 \times 100}{70}\\[/tex]

x = $440

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Answer:

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

Given:

Find a function g which is a horizontal shrink by a factor of 1/3 of f(x).

Horizontal shrink by a factor of k is:

Apply this to the given function:

Slope of line is 1/2.

What is slope?

In arithmetic, the slope or gradient of a line is a range that describes each the direction and therefore the gradient of the road.

Main body:

to find the slope from a graph , we need to fix two co-ordinates at slope for axis

let point at x be = (40,40)

let point y = (80,60)

Formula for slope ,

m = y₂-y₁/x₂-x₁

m = 60-40/80-40

m = 20/40

m = 1/2

hence , slope of line is 1/2.

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