When the system is solved, the result is:

3x + y = -7
4x − y = -14


(3, -2).

(3, 2).

(-3, 2).

(-3, -2).

None of these choices are correct.

The slope-intercept representation of the linear function that passes through the points (-1, 10) and (5, -8) is:

y = -3x + 7.

The slope-intercept representation of a linear function is presented by the equation shown as follows:

y = mx + b

The coefficients of the function, along with their meaning, are presented as follows:

The two points that belong to the linear function are given as follows:

(-1, 10) and (5,-8).

Given two points, the slope is calculated as the change in y divided by the change in x of the points, hence:

m = (-8 - 10)/(5 - (-1)) = -18/6 = -3.

Then the format of the equation is:

y = -3x + b.

When x = -1, y = 10, hence the y-intercept of the function is obtained as follows:

10 = -3(-1) + b

10 = 3 + b

b = 10 - 3

b = 7.

Hence the equation is:

y = -3x + 7.

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The total cost of the car is 26,648.5 dollars.

The Latin word "per centum," which means by the hundred, is where the word "percent" comes from. Percentages are fractions with a denominator of 100. It is a relationship, in other words, where the value of the whole is always taken to be 100.

The cost of the car = $22300

The sales tax is given by

= 7% × 22300

= (7/100) × 22300

= 7 × 223

= 1561

The state requires a registration fee to be given by

= 12.5% × 22300

= (12.5/100) × 22300

= 12.5 × 223

= 2787.5

The total cost of the car is given by

Total cost = cost of car + sales tax + state registration fee

= 22300 + 1561 + 2787.5

= 26,648.5

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If Tina is training for a biathlon. She runs the downhill portion of the course at 10 miles per hour.

(s-5) = speed on level ground

Time = distance /speed

Level time + downhill time = 1 hr

Hence,

3/(s-5) + 4/s =1

multiply by s(s-5), resulting in

3s + 4(s-5) = s(s-5)

3s + 4s - 20 = s^2 - 5s

Arrange as a quadratic equation on the right

0 = s^2 - 5s - 7s + 20

s^2 - 12s + 20 = 0

factors to

(s-2)(s-10) = 0

s = 10 mph

Therefore the speed is 10mph.

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Using local linearity, f(1.2) = 9.46

Local linearity is the aprroximation of a curve at a point into a linear function.

For a locally linearized function f(x) about a point x'

f(x + Δx) = f(x) + f'(x)Δx

Now, since we desire to use local linearity to estimate f(1.2)

f(1.2) = f(1 + 0.2)

So, we have that comparing the with f(x + Δx) above, we have

f(1 + 0.2) = f(1) + f'(1)(0.2)

Given that

Substituting the values of the variables into the equation, we have

f(1 + 0.2) = f(1) + f'(1)(0.2)

f(1 + 0.2) = 9.4 + (0.3)(0.2)

f(1 + 0.2) = 9.4 + 0.06

f(1 + 0.2) = 9.46

f(1.2) = 9.46

So, f(1.2) = 9.46

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The pairs of equations and their responses are below

(1/5)^2 + 1 and 2 12/25 No

(1 + 1/4)^2 and 2 - 7/16 Yes

This is done by solve both sides of the equation. If they have same answer then they can form equation. If otherwise they they cannot form equation

solving the first expressions

left hand side

(1/5)^2 + 1

= 1/25 + 1

= 26/25

right hand side

2 * 12/25

= 24/25

comparing the two sides shows that  the 26/25 ≠ 24/25

solving the second expressions

left hand side

(1 + 1/4)^2

= (5/16)^2

= 25/16

right hand side

2 - 7/16

= 25/16

comparing the two sides shows that  the 25/16 = 25/16solving the first part

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The total debt-to-income ratio is: A. 43.45%.

Monthly gross income:

Employment wages: $115,000

Interest earned: $950

Dividends earned: $1,200

Monthly gross income  $117,150

Monthly debts:

Mortgage payments: $38,600

Auto loan payments: $3,300

Student loan payments: $9,000

Monthly debts  $50,900

Using this formula to find total debt-to-income ratio

Total debt-to-income ratio =Monthly debts / Monthly gross income

Total debt-to-income ratio = $50,900 /$117,150

Total debt-to-income ratio = 0.4345 × 100

Total debt-to-income ratio = 43.45%

Therefore the correct option is A.

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The quotient of [13/(5-i)] in the form of (a + bi) is (2.5 + 0.5i).

A complex number is a number of the form a + bi, where a and b are real numbers

Given,

13/5-i

Rationalize the number

Multiply numerator and denominator by 5+i

13/5-i×5+i/5+i

13(5+i)/25+1

65+13i/26

65/26+13/26i

2.5+0.5i

Hence, the quotient of [13/(5-i)] in the form of (a + bi) is (2.5 + 0.5i).

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Answer:

6x-

7y

=

-11

6x-7y=-11

Step-by-step explanation:

(x+2)³ - (x)³ = 56

(x²+4x+4) (x+2) - (x)³ = 56

x³ + 2x² +4x²+ 8x + 4x + 8 -x³ = 56

6x² + 12x + 8 = 56

6x² + 12x - 48 = 0

x² + 2x - 8 = 0

(x+4) (x-2) = 0

x = -4

x = 2

the integers are 2 and 4

The required two consecutive positive even integers are 2, and 4.

A number which is not a fraction, and it is a whole number.

For example -1,-2,-3,0,1,2 etc. are integers.

Let two consecutive even numbers are x and x+2,

According to given condition, the difference of cube of x and x+2 is 56,

Implies that,

(x+2)³ - (x)³ = 56

x³ + 8 + 3.x².2+ 3.x.2² -x³ = 56

6x² + 12x - 48 = 0

x² + 2x - 8 = 0

x² + 4x - 2x - 8 = 0

x = -4, 2

Both the integers are positive, so the value of x can't be negative.

Therefore, x=2 and x+2 = 4

So the integers are 2 and 4.

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Answer:

Step-by-step explanation:

3

Answer:

Step-by-step explanation:

Answer:

I think it 3 or 2 but mainly 2

Answer: lb=48

l(l-8)=48

l^2–8l=48

l^2–8l-48=0

l^2–12l+4l-48=0

l(l-12)+4(l-12)=0

l=12inches &

b=12–8=4inches

Step-by-step explanation:

The fire truck, a mile away, traveling at 44 miles per hour towards the the bush fire, which is also traveling towards at 3 miles per hour towards it, reaches the fire's front in 1/47 hours or approximately 76.6 seconds

There are 60 seconds in a minute and 60 minutes in an hour, which makes 60 × 60 = 3600 seconds in one hour.

The rate at which the bush fire is moving, v₁ = 3 miles per hour

The direction the bush fire moves = Towards the fire station

Distance of the bush fire from the fire station, d = 1 mile

Speed of the fire truck, v₂ = 44 miles per hour

The equation that gives the time, t, the fire truck reaches the fire front is presented as follows;

v₁·t + v₂·t = d

Which gives; 3 × t + 44 × t = 1

47 × t = 1

[tex]t = \dfrac{1}{47}[/tex]

The time it takes the fire truck to reach the bush fire is 1/47 of an hour, which is approximately 76.6 seconds

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The dimensions that minimize the cost of construction are : 10/∛3 in,     10/∛3 in, 2 × [tex]3^{2/3}[/tex] in

Let the side of the square base be 'a'

The height of the box be 'h'

Then, the volume of the box is given by :

= (area of square base) × height

= a² × h

Given, volume of the box = 200 in³

⇒ a² × h = 200

⇒ h = 200/a²

The area of base = a²

Given, the cost of base is : 6 cents/in²

⇒ cost of square base with side 'a' = 6 × a² cents

The area of front of the box, which is a rectangle with dimensions (h×a) is:

= a × h

Given, the cost of decorating the front side of the box = 11 cents/in²

⇒ cost of decorating the front side of the box = (a × h) × 11 cents

The area of the other three sides of the box, which comprises of three rectangles of dimensions (h×a) is :

= 3(a  × h)

Given, cost of remaining sides = 3 cents/in²

Cost of remaining 3 sides = 3(a × h) × 3 = 9(a  × h) cents

Total cost = Cost for base + Cost for front + Cost for other sides

= 6a² + 11ah + 9ah

= 6a² + 20ah

Substitute h in terms of a² in the total cost,

Total cost, T = 6a² + 20a(200/a²) = 6a² + 4000/a

Differentiate T w.r.t a :

dT/da = 6(2a) + 4000(-1/a²)       = 12a - 4000/a²

For minimization, dT/da = 0

⇒ 12a - 4000/a² = 0

⇒ 12a = 4000/a²

⇒ a³ = 4000/12

⇒ a³ = 4×1000/4×3

⇒ a³ = 1000/3

⇒ a = ∛(1000/3)

⇒ a = 10/∛3

Then, h = 200/a² = 200/(10/∛3)² = 2 × [tex]3^{2/3}[/tex]

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Properties used for each steps are Division property, Multiplication property, Addition property, Subtraction property and Distributive property.

Given equation is {2(2/5 x + 8)}/2 = {4(14- 1/5 x)}/2

1) Here first we used Division property

we divide both the equation by 2 then the equation become

(2/5 x + 8) = 2(14-1/5 x).

2) Now we will use Multiplication property,

2/5 x + 8 = 28 - 2/5 x

Interchanging the terms we get

2/5 x + 2/5 x = 28-8

3) By Addition property

4/5 x = 28-8

4) And by Subtraction property we get

4/5 x = 20

5) Lastly by Distributive property we find the value of x,

x = (20 × 5)/4

x = 100/4

x = 25

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Answer:

her total cost is $29.45

Step-by-step explanation:

last week - 8 1/2 gallons times $2.30 = $19.55

this week - 4 1/2 gallons times $2.20 = $9.90

$19.55 + $9.90 = $29.45

Answer:

Step-by-step explanation:

You will use Pythagoreans Theroy. which is going to give you the anwser of square root of 13.

Answer:

3.6

Step-by-step explanation:

We can use the Pythagorean Theorem for this problem which is a²+b²=c² .

So we'll make 2 "a", and 3 "b". So 2*2=4. Then 3*3=9

4+9=13

Now we need to find the square root of 13.

√13 = 3.60555127546399

Let's now round that number, which is going to be 3.6

A description of the quadrilateral VWXY that has equal length sides and equal length diagonals is that the quadrilateral is a square

A quadrilateral is a polygon that has four sides and four vertices or corners, such that a quadrilateral ABCD has sides AB, BC, CD, and AD, and interior angles ∠A, ∠B, ∠C, and ∠D

The given description of the quadrilateral VWXY are;

VW = 15, WX = 15, XY = 15, YV = 15

The lengths of the sides of the quadrilateral VWXY are the same

The length the diagonals are the same;

VX = WY = VX = WY

The properties of a square are;

The interior angles are congruent and equal to 90°

The four sides have equal length

Opposite sides of a square are congruent

The length of the diagonals are the same

The the same length diagonals of quadrilateral indicates that the quadrilateral can be either a square or a rectangle

The property of the quadrilateral of equal length sides indicate that the quadrilateral is a square.

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The inverse of the cubic function is f⁻¹(x) = ∛(x+5/6) and the inverse relationship is valid

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

f(x) = x³-5/6

y = x³-5/6

make x the subject:

x³= y+5/6

x = ∛(y+5/6)

x = f⁻¹(y) = ∛(y+5/6)

Thus, f⁻¹(x) = ∛(x+5/6)

To confirm the inverse relationship using composition.

Let g(x) = f⁻¹(x)

For valid confirmation f(g(x)) must be equal to g(f(x))

Let's confirm:

f(g(x)) = f(∛(x+5/6))

          = ( ∛(x+5/6) )³ - 5/6

         = x+5/6-5/6

        = x

g(f(x)) = g(x³-5/6)

         = ∛(x³-5/6+5/6)

         = ∛x³

         = x

Since  f(g(x)) = g(f(x)) then the inverse is valid

Therefore, the inverse of the cubic function is ∛(x+5/6) and the inverse is valid

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[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=3\\ k=-2 \end{cases}\implies y=a(x-3)^2 -2\hspace{5em}\textit{we also know that} \begin{cases} x=1\\ y=2 \end{cases} \\\\\\ 2=a(1-3)^2 -2\implies 4=a(-2)^2\implies 4=4a\implies \cfrac{4}{4}=a\implies 1=a \\\\[-0.35em] ~\dotfill\\\\ y=1(x-3)^2 -2\implies {\Large \begin{array}{llll} y=(x-3)^2 -2 \end{array}}[/tex]

a) i) P(x < 5) = 0.842

ii) P(X ≥ 7) = 0.0143

b) Given that P(X = 0) = 0.05, the value of p to 3 decimal places is; 0.221

c) Given the variances of x is 1.92 , the possible values of p are; 0.2 and 0.8

The binomial probability is the probability of exactly x successes on n repeated trials, with p probability.

The formula for binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

p = probability of "success"

n = number of trials, or the sample size

x = the number of "successes"

a) We are given;

p = 0.25

n = 12

Thus;

i)P(x < 5) using appendix tables online gives us;

P(x < 5) = 0.842

ii) P(X ≥ 7) can be expressed as;

1 – P(X ≤ 6)

Thus, using appendix tables online, we have;

P(X ≥ 7) =  1 – 0.9857

P(X ≥ 7) = 0.0143

b) We are given that  P(X = 0) = 0.05. Thus;

(1 - p)¹² = 0.05

1 - p = ¹²√0.05

p = 0.221

c) Variance is given by the formula;

Var = np(1 - p)

Var = 12p(1 - p) = 1.92

12 - 12p² = 1.92

12p² - 12 + 1.92 = 0

Using online quadratic equation calculator gives;

p = 0.2 or 0.8

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Complete question is;

a) A random variable has a Binomial distribution with n=12.

Given that p=0.25, find

(i) P(x < 5) ( From the table OF Appendix A)

(ii) P(x ≥ 7) ( From the table OF Appendix A)

b) Given that P(X = 0) = 0.05, find the value of p to 3 decimal places.

c)Given the variances of x is 1.92 , find the possible value of p

Answer:

24

Step-by-step explanation:

We have already determined that the first person is just a place holder. Therefore, there is only one choice for the first spot.

The number of ways "n" number of people can sit around a circular table will be (n - 1)! thus 5 people can sit in 24 ways.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

The number of ways that n person can sit around a table is written as,

n!/n=n(n−1)!/n=(n−1)!

As per the given n = 5

(5 - 1)! = 4! = 4 x 3 x 2 = 24 ways

Hence "The number of ways "n" number of people can sit around a circular table will be (n - 1)! thus 5 people can sit in 24 ways".

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Diagonalization is the process of converting a matrix into diagonal form. Diagonal matrices plainly depict a matrix's eigenvalues. A diagonal matrix is a square matrix in which all of the elements except the primary diagonal members are zero.

The primary goal of diagonalization is to determine the functions of a matrix. If P1AP = D, where D is a diagonal matrix, the entries of D are the eigenvalues of matrix A, and P is the matrix of A's eigenvectors.

If and only if the nilpotent component of a matrix is zero, it is diagonalizable. In other words, a matrix is diagonalizable if no nilpotent portion exists in its Jordan form.

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Answer: 5w=w^3

Step-by-step explanation:

This is because the product means multiplication and so it would be 5w and then is in math is the same as equals so you have an equal sign and then it would w to the third power.

The liters of water that the bucket hold is 5/7 liters of water.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, 4/5 of a liter of water filled 4/7 of a bucket. The liters that it can hold will be:

= 4/7 ÷ 4/5

= 4/7 × 5/4

= 20 / 28

= 5/7

It can hold 5/7 liters.

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Considering the polynomial f(x) = x^4  - 16x³ + 70x² + 48x - 219, we have that:

a) The zeros are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.

b) The linear factors are: (x + 1.995)(x - 1.995)(x - 8 + 3i)(x - 8 - 3i).

c) The solutions to f(x) = 0 are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.

The given zero of the polynomial is:

8 + 3i

Hence it's conjugate is also a zero, that is:

8 - 3i.

Thus the first two factors are given as follows:

(x - 8 - 3i)(x - 8 + 3i) = x² - 16x + 64 + 9i² = x² - 16x + 55.

Then the polynomial can be written as follows:

x^4  - 16x³ + 70x² + 48x - 219 = (ax² + bx + c)(x² - 16x + 55).

As a fourth order polynomial can be the product of two second order polynomials. Applying the distributive property to the right side of the equality, we have that:

x^4  - 16x³ + 70x² + 48x - 219 = ax^4 + x³(b - 16a) + x²(55a + c - 16b) + x(55b - 16c) + 55c.

Then the coefficients are given as follows:

Hence the other two factors are given as follows:

x² - 3.98 = 0

x = ± sqrt(3.98)

x = ± 1.995.

The linear factors are:

(x - x')(x - x'')(x - x''')(x - x'''').

In which x', x'', x''' and x'''' are the roots.

The solutions to f(x) = 0 are the roots.

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Answer: A

Step-by-step explanation: The dot is a filled-in circle, meaning it has to be A, B, or E. Then, B is saying that the arrow is going left, so that's wrong. E is saying that it is just 6 instead of -6, which leaves us with A.

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The total number of logs that are in the pile is 195.

From the information, the Logs are stacked in a pile where the bottom row has 24 logs, the next row has 23 logs, the following row has 22 logs and the pattern continues until the top row has 15 logs.

To calculate the total number, it simply means that you've to add the numbers for 15 to 24. This will be:

= 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24

=195

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Answer: $6.16

Step-by-step explanation:

Starting Amount: $30

30-6.97=23.03

23.03-11.37=11.66

11.66-5.50=6.16