What is the equation of the line perpendicular to 2x - 3y = 13 that passes through the point (-6, 5)?
y=x+9
y=-3x-4
y=-x-13
y-x-1

The system of equation has one solution

The equations are given as:

y = -x - 4

3y -x = -7

Rewrite the first equation as:

y + x = -4

Add y + x = -4 to the second equation to eliminate x

4y = -11

Divide by 4

y = -11/4

Substitute y = -11/4 in y + x = -4

-11/4 + x = -4

Make x the subject

x = -4 + 11/4

Evaluate

x = -5/4

The above means that the system of equation has one solution

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Option A and B. The system has one solution and the system consists of parallel lines.

The slope of the lines is calculated as follows;

y = -x - 4

slope = - 1

3y - x = -7

3y = x - 7

y = x/3 - 7/3

slope = 1/3

y = -x - 4   ----(1)

3y - x = -7  ----(2)

solve (1) and (2)

3(-x - 4) - x = -7

-3x -12 - x = -7

-4x = 5

x = -5/4

y = -5/4 - 4

y = -5.25

Thus, the system has one solution and the system consists of parallel lines.

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By the property of corresponding angles  ∠3 ≅ ∠5.

In geometry, a transversal is any line that intersects two straight lines at distinct points.

If two parallel lines are cut by a transversal, then each pair of corresponding angles are equals.

That is, ∠3 = ∠5 and ∠4 = ∠6.

Therefore the given angles ∠3 and ∠5 are equal.

Hence  ∠3 ≅ ∠5 .

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If the two buses are 640 miles apart after 5 hours. Then the rate of each bus will be 57 miles per hour and 71 miles per hour.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

Two buses leave a station at the same time and travel in opposite directions.

One bus travels 14 miles faster than the other.

Let x be the speed of first bus. Then the speed of the second bus will be (x + 14).

If the two buses are 640 miles apart after 5 hours.

Then the rate of each bus will be

Then the relative speed of the buses will be

S = x + x + 14

S = 2x + 14

Then the value of x will be

2x + 14 = 640 / 5

2x + 14 = 128

      2x = 114

        x = 57 miles per hour

Then the speed of the other bus will be

⇒ 57 + 14

⇒ 71 miles per hour

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The slope for both the line is m= 1/3 and  they are parallel lines , Option B and C are correct two options

The first equation is

 y = (1/3)x-4 and not y = -x-4

(if the equation is not corrected then it will not have two true statements)

A system of equation is a set of equation which have a common solution

The given system of equation is

y = (1/3)x-4

3y -x = -7

3y = x-7

As it can seen from the standard equation of a line that

y =mx+c

so slope for both the line is m= 1/3

Therefore they are parallel lines

Thus , Option B and C are correct two options

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The final decomposition of the given partial fraction is; 7 + (-7/(x² + 3))

We are given the polynomial fraction (7x² + 14)/(x² + 3) to decompose.

Now, due to the fact that the degree of the numerator is not less than the degree of the denominator, we will perform polynomial long division to get;

(7x² + 14)/(x² + 3) = 7 + (-7/(x² + 3))

Now, the second term (-7/(x² + 3)) cannot be decomposed further and as such, we say that our final decomposition of the given partial fraction is;

7 + (-7/(x² + 3))

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Answer:

x = -14

Step-by-step explanation:

- x + 8 + 3x = x - 6

- x + 8 + 3x - x + 6 = 0

x + 14 = 0

x = -14

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.6625, 0.7388).

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

Given sample, n= 782

As, 548 were not captured.

x= 548

So, p= 548/ 782

     p = 0.7007

q= 1- 0.7007 = 0.2993

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

Now,

α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

For confidence level of 98% , z is 2.33

Now,

(0.70007 - 2.33√ (0.7007(0.2993))/782 , 0.70007 + 2.33 √(0.7007(0.2993))/782

= (0.6625, 0.7388)

Hence, 98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.6625, 0.7388).

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Answer:

1,887,436,800

Step-by-step explanation:

f(t) = a·b^t

f (t) = number of cases at year t

a = starting value = 1800 in 1983

b = growth factor = 2

t = years since 1983 = 2003 - 1983 = 20

f(t) = 1800·(2)^20 =

1,887,436,800

wyzant

philip p

Answer:

really good

Step-by-step explanation:

Answer: He have to pay $172.5 if he buys 150 such articles.

72 articles for --> $82.80
1 article for - - - > 82.80/72

150 articles for --> (82.80/72)*150
                           = $172.5

Answer:

$172.5

Step-by-step explanation:

Given:

Shopkeeper buys = 72 articles

Price = $ 82.8

To Find:

The amount he'll need to pay If he buys 150 articles.

Solution:

Amount if he buys 150 articles

[tex] \boxed{\rm \: No. \: of \: articles \: he \:will \: buy × \cfrac{Cost \: of \: that \: article \: he \: has}{Number \: of \: articles \: he \: has}} [/tex]

[tex] = \$ \bigg(\rm150 * \cfrac{82.80}{72}\bigg) [/tex]

[tex]= \$ (150* 1.15)[/tex]

[tex] = \$172.5[/tex]

So we can conclude that:

$172.5 he will have to pay if he buys 150 such articles.

Step-by-step explanation:

you mean, what is the price of a pizza, right ? and I guess it is pizza slices ...

1 hamburger = $2.50

5 hamburgers = 5×1 hamburger = 5×2.5 = $12.50

that leaves for the 11 pizzas (slices)

40 - 12.5 = $27.50

so, 1 pizza (slice) is

27.5 / 11 = $2.50

Answer:

One hamburger costs $2.50

One pizza also costs $2.50

Step-by-step explanation:

Let's say Nigel is the one purchasing lots of food for no reason.

Nigel bought 11 pizzas and 5 hamburgers for $40 (DAMMMM WHAT COUPON IS THAT??)

We can write this algebraically:

11p + 5b = 40

We know that the price of 1 Hamburger is $2.50.

Now we can plug that into out equation and find the price of one pizza:

11p + 5(2.50) = 40

11p + 12.5 = 40

11p = 27.5

p = 2.5

Now, we have the price of one pizza, $2.50

Answer:

y = 3x - 2

Step-by-step explanation:

The number beside the x is the slope. The number at the end of the equation is the y-intercept.

All the answers are in this form:

y = mx + b

m is the slope.

b is the y-intercept.

With a 3 filled in for slope and -2 filled in for the y-intercept, you get:

y = 3x + -2

is the same as,

y = 3x - 2

Answer:

[tex]\boxed {t < 15}[/tex]

Step-by-step explanation:

Given :

⇒ t - 3 < 12

Add 3 to each side :

⇒ t - 3 + 3 < 12 + 3

⇒ t < 15

Answer: t < 15

Step-by-step explanation:  

rearrange the terms                                       t - 3 < 12

calculate the sum or difference                    t < 12 + 3

answer                                                             t < 15                            

The interest rate will be equal to 24% in 2 years.

Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-

Given that:-

The interest rate will be calculated by using the following formula:-

[tex]A = P[1+\dfrac{r}{n}]^{nt}[/tex]

[tex]50=32[1+\dfrac{r}{1}]^{2}[/tex]

[tex]\dfrac{50}{32}=(1+r)^2[/tex]

1.56 = ( 1 + r )²

√1.56 = ( 1 + r )

r = 1.24 - 1

r = 0.24

r = 24%

Therefore  interest rate will be equal to 24% in 2 years.

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Answer:

I iitiriririrrifjjrjr idiocy jdkthink 179.86

The associative property of adding or multiplying can be represented by (a + b) + c = a + (b + c) and a * (b * c) = (a * b) * c

An equation is an expression that shows the relationship between two or more numbers and variables.

The associative property states that when adding or multiplying it can be represented by:

(a + b) + c = a + (b + c)

For multiplication:

a * (b * c) = (a * b) * c

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 3\sqrt3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \tan(60) = \cfrac{x}{3} [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{3} = \dfrac{x}{3} [/tex]

[tex]\qquad \tt \rightarrow \: x = 3 \sqrt{3} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The value of the probability P(x > 2) is 0.8369

The given parameters are:

n = 5

p =0.7

The probability is calculated as:

[tex]P(x) = ^nC_x *p^x * (1 - p)^x[/tex]

Using the complement rule, we have:

P(x > 2) = 1 - P(0) - P(1) - P(2)

Where:

[tex]P(0) = ^5C_0 *0.7^0 * (1 - 0.7)^5[/tex]

P(0) = 1 *1 * (1 - 0.7)^5 = 0.00243

[tex]P(1) = ^5C_1 *0.7^1 * (1 - 0.7)^4[/tex]

P(1) = 5 *0.7^1 * (1 - 0.7)^4 = 0.02835

[tex]P(2) = ^5C_2 *0.7^2 * (1 - 0.7)^3[/tex]

P(2) = 10 *0.7^2 * (1 - 0.7)^3 = 0.1323

Recall that:

P(x > 2) = 1 - P(0) - P(1) - P(2)

So, we have:

P(x > 2) = 1 - 0.00243 - 0.02835 - 0.1323

Evaluate

P(x > 2) = 0.83692

Approximate

P(x > 2) = 0.8369

Hence, the value of the probability P(x > 2) is 0.8369

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The expression that is not rational is the first one:

[tex]f(x) = \frac{6x}{4}[/tex]

A rational expression is something of the form:

[tex]f(x) = \frac{q(x)}{p(x)}[/tex]

Such that q(x) can be any polynomial, and p(x) is a polynomial of at least degree 1.

This means that we need to have the variable "x" on the denominator.

Then is easy to recognize the expression that is not rational, is the one that does not have x on the denominator, which is the first one:

[tex]f(x) = \frac{6x}{4}[/tex]

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Answer: B

Step-by-step explanation:

I took the test and this was the correct answer

Answer:

A. (2,10)

Step-by-step explanation:

5x + y = 20

y = 5x

The second equation is already solved for y, so substitute 5x for y in the first equation to find x.

5x + 5x = 20

10x = 20

x = 2

Now substitute 2 for x in the second original equation to find y.

y = 5(2)

y = 10

Answer: (2, 10) which is A.

Answer:

[tex] \frac{dy}{dy} = \frac{x - 5}{3y + 6} [/tex]

Expand cos(A - B) with the identity

cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

A is in quadrant II, so sin(A) > 0, and B is in quadrant I, so sin(B) > 0. Using the Pythagorean identity, we get

cos²(A) + sin²(A) = 1   ⇒   sin(A) = + √(1 - (-3/5)²) = 4/5

cos²(B) + sin²(B) = 1   ⇒   sin(A) = + √(1 - (8/17)²) = 15/17

Then

cos(A - B) = (-3/5) × 8/17 + 4/5 × 15/17 = 36/85

cos (A - B) is 36/85

Expand cos(A - B) with the identity

You get, cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

Since A is in quadrant II, so sin(A) > 0,

B is in quadrant I, so sin(B) > 0.

Using the Pythagorean identity, we get

cos²(A) + sin²(A) = 1  

Make sin A the subject of formula

[tex]sin(A)^{2}[/tex] =  ([tex]\sqrt{(1 - (-3/5}[/tex])²)

Find the square root of both sides, square root cancels square

[tex]sin A[/tex] = 4/5

Repeat the same for the second value

[tex]sin A^{2} = \sqrt{(1- 8/17)^2}[/tex]

[tex]sin A[/tex] = 15/17

Substitute values into cos(A - B)

cos(A - B) =  cos(A) cos(B) + sin(A) sin(B) = (-3/5) * 8/17 + 4/5 * 15/17

cos (A - B) = 36/85

Therefore, cos (A - B) is 36/85

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Answer:

subract 4 from both sides

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

yes.......................

Step-by-step explanation:

According to the compound interest model, we find the following results: I) x ≈ 11.5 yr, C' = $ 101317.36, II) r ≈ 7.4 %, x ≈ 9.8 yr, III) C = $ 7626.38, x ≈ 8.6 yr, IV) r ≈ 6.5 %, C = $ 12801.61

Compound interest describes the capital gain in term of deposited capital and the consideration that such capital is increased continuously in time. The compound interest model is shown below:

C' = C · (1 + r/100)ˣ     (1)

Where:

The doubling time (x) is the period needed for a capital to be doubled. It is described by the following expression based on (1):

x = (㏒ 2)/[㏒ (1 + r/100)]     (2)

Now we proceed to calculate each missing variable:

Case I - Doubling time

x = (㏒ 2)/[㏒ (1 + 6.2/100)]

x ≈ 11.5

Case I - Current capital

C' = 75000 · (1 + 6.2/100)⁵

C' = 101317.36

Case II - Interest rate

[tex]r = 100\cdot \left(\sqrt [5] {\frac{7130.90}{5000} }-1\right)[/tex]

r ≈ 7.4

Case II - Doubling time

x = (㏒ 2)/[㏒ (1 + 7.3/100)]

x ≈ 9.8

Case III - Initial capital

C = 11414.71/(1 + 8.4/100)⁵

C = 7626.38

Case III - Doubling time

x = (㏒ 2)/[㏒ (1 + 8.4/100)]

x ≈ 8.6

Case IV - Interest rate

[tex]r = 100\cdot \left(\sqrt [11] {2 }-1\right)[/tex]

r ≈ 6.5

Case IV - Initial capital

C = 17539.32/(1 + 6.5/100)⁵

C = 12801.61

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The critical probability, assuming a confindence level of 58% is 0.79.

From the information given, the confidence level is 58%. The alpha will be:

= 1 - (58/100)

= 1 - 0.58

= 0.42

The critical probability will be:

= 1 - (0.42/2)

= 1 - 0.21

= 0.79

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Answer: [tex]y=3x-17[/tex]

Step-by-step explanation:

use point-slope form:

[tex]y_{1} -y=m(x_{1} -x)[/tex]

[tex]y-1=3(x-6)[/tex]

[tex]y-1=3x-18[/tex]

[tex]y=3x-17[/tex]

Answer:

equation: y = 3x - 17

[image attached]

Step-by-step explanation:

we know that the equation for a line is y = mx + b

we are given a point, (6, 1)

remember that a point is (x, y)

we can plug these sample x and y values into our equation, replacing x and y

 y = mx + b

 1 = m6 + b

we know that m = 3 [this was a given], so we can plug this into our equation

1 = (3)(6) + b

1 = (18) + b

1 = 18 + b       [we can now solve for "b"]

1 = 18 + b

-18    - 18

-17 = b

so, we can re-write our equation so that we can graph it:

y = 3x - 17

we can now plug in x-values to graph this:

(you'll see these written in the table on the graph)

y = 3(0) - 17

y = -17

y= 3(1) - 17

y = 3 - 17

y = -14

y = 3(2) - 17

y = 6 - 17

y = -11

y = 3(3) - 17

y = 9 - 17

y = -8

y = 3(4) - 17

y = 12 - 17

y = -5

y = 3(-1) - 17

y = -3 - 17

y = -20

y = 3(-2) - 17

y = -6 - 17

y = -23

y = 3(-3) - 17

y = -9 - 17

y = -26

[there is an image attached of my graph]

hope this helps!! :)