Find the equation of the line in slope-intercept form containing the two points: (−1,5) and )(4,−3) Leave equation in fractional form.

Step-by-step explanation:

[tex]\pink{\large{\underline{\underline{\sf Given:-}}}}[/tex]

[tex]\pink{\large{\underline{\underline{\sf To \: find:-}}}}[/tex]

[tex]\pink{\large{\underline{\underline{\sf Solution:-}}}}[/tex]

We know that,

[tex]\underline{\boxed{\sf (Radius)^2= (Slant height)^2-(height)^2}}[/tex]

[tex] \sf (Radius)^2 = (16)^2-(12)^2[/tex]

[tex] \sf (Radius)^2 = 256-144=112[/tex]

[tex] \longmapsto \sf Radius = \sqrt{112}≈10.6\:cm[/tex]

The system of equations of two unknowns is formulated and solved.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}[/tex]

                                                              [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28 } \end{gathered}$}[/tex]

                                                                  [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x=\dfrac{5}{7}(\pm 28)=\pm 20 } \end{gathered}$}[/tex]

The fraction that satisfies the request is [tex]\bf{\dfrac{20}{28}}[/tex] , since in [tex]\bf{\dfrac{-20}{-28}}[/tex] the negative signs are canceled and the first fraction is obtained.

Answer:

x = 3

Step-by-step explanation:

Angle S and Angle T are consecutive interior angles. Therefore, we know that T + S = 180°.

First, we need to solve for T, and since angles S and T are consecutive interior angles, we know that T + S = 180°. If we reorganize the equation to include the things we know (S = 105°), then we get 180° - 105° = 75°. So T is 75°.

Now, we use T = 75° and the information given to us in the picture to set up an equation. 75 = 24x + 3. Now, we can find x by isolating it. Do this by:

1) Subtracting 3 from both sides to give you 72 = 24x. We do this to get rid of the 3 from the "x side", but we must also do it to the other to keep the equation true. This moves the 3 from the "x side" to the other since we're trying to isolate x.

2) Divide 24 by both sides to get 3 = x. We use the same logic as we did for 3, except this time we divide since that's the opposite of multiplying.

In conclusion, x = 3.

Answer:

C)   y = -3x + 15

Step-by-step explanation:

Let's start with the hours required, 15.  For each day worked we can subtract 3 hours.  X days would mean 3x hours.  Subtract that from the goal of 15 hours:

15 - 3x

The time remaining, y, is given by the equation 15 - 3x.

Rearrange the equation to match the format in the options,

y = 15 - 3x

y = -3x + 15

Option C

When written in factored form, 4w² -11w-3 is equivalent to (4w+1)(w−3).

When an expression is written as a result of the multiplication of some terms, then that multiplication form is called the factored form of that expression.

Example:   6 = 3 x 2 is a factored way of writing 6.

Given expression as

4w² -11w-3

4w²- 12 w− 1w − 3

(4w+1)(w−3)

Thus, the factored form of 4w² -11w-3 is (4w+1)(w−3).

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The margin of error is inversely proportional to the sample size. As the sample size increases, the margin of error decreases.

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

The margin of error is given as

[tex]\rm ME = z\times \sqrt{\dfrac{p(1-p)}{n}}[/tex]

We know that margin of error is inversely proportional to the sample size.

As the sample size increases, the margin of error decreases.

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Answer: 37.9 inch the length of lead stripping .

Step-by-step explanation:

Given ,

Sides of windows are [tex]6\frac{4}{5}[/tex]  and [tex]15\frac{14}{25}[/tex]

[tex]= (6\frac{4}{5} + 15 \frac{14}{25} ) * 2\\ \\=\frac{34}{5} + \frac{389}{25} * 2\\\\ \frac{170}{25} + \frac{389}{25}* 2 \\\\= \frac{559}{25} * 2\\\\= \frac{948}{25} \\\\= 37.9 inch[/tex]

So , the answer is 37.9 inch

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For a given central angle,  the length of the arc it intersects depends on the radius of the circle and the central angle.

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

Length of an Arc = 2π×R×(θ°/360°)

where

θ is the angle, that which arc creates at the center of the circle in degree.

The measurement of the length of an arc formed by a central angle that intersects the circle at two points is given as,

[tex]\rm {Length\ of\ the\ arc} = 2\pi \times \text{Radius of the circle}\times \dfrac{\text{(Measurement of central angle)}}{360^o}[/tex]

Now, the length of the arc EF will be,

Arc EF = 2π × (AB) × (θ/360°)

Where θ is the measurement of the central angle.

Hence, For a given central angle,  the length of the arc it intersects depends on the radius of the circle and the central angle.

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Answer: Plato/edmentum sample answer  

Step-by-step explanation:

For a given central angle, the length of the arc it intersects depends only on the radius of the associated circle.

The answer is 0.75 because I took the test and that's what the answer was :)

The solution to the system of linear equations is: (−5, −11).

The solution to a system is the x and y -coordinates that satisfies the two linear equations.

Given the linear equations:

Line A: y = x − 6

Line B: y = 3x + 4

Now, equating these two equations

x - 6 = 3x + 4

2x = -10

x = -5

y = -11

Hence, the solution is: (−5, −11), because the point satisfies both equations.

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Answer:

A. Upward

B. (-2, -1)

C. X= -3, -1 ||| Y= 3

D. X=-2

Step-by-step explanation:

The probability will include:

The probability of P(A and 1) will be:

= 1/4 × 1/6

= 1/24

The probability of P(C and 2) will be:

= 1/4 × 2/6

= 1/12

The probability of P(B and 3) will be:

= 2/4 × 1/6

= 1/12

The probability of P(A and 4) will be:

= 1/4 × 2/6

= 1/12

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The weight of the last child is 36 lbs.

The average weight of the three children is 60 lbs. The total weight will be:

= 60 × 3

= 180 lbs.

When another child is added, the weight is 54lb. The total weight will be:

= 54 × 4

= 216 lbs

The weight of the last child will be:

= 216 - 180

= 36 lbs.

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The graph of the function y = x+2 is steeper than the graph y = 2x-1.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given functions are:-

The graph of the functions is attached with the answer below. In the graph, we can see that the slope of the graph y = x+2 is steeper than the graph of y = 2x - 1.

The two graphs intersect at the point ( 3,5 ) so it is the solution of the two linear equations.

Hence the graph of the function y = x+2 is steeper than the graph y = 2x-1.

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The amount each friend does pay is £9.75

We are going to find 5% of the total amount paid and divide it by the numbers of all the friends to determine the amount paid by each one of them.

From the given information:

Therefore, the cost of each friend is = [tex]\dfrac{136.5}{14}[/tex]

The cost of each friend = £9.75

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Answer:

true

Step-by-step explanation:

The statement is true because every graph associated a unique x-value for each y - value

Answer:

0.65%

Step-by-step explanation:

i took the test

Using the normal distribution and the central limit theorem, it is found that:

a) Since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.

b) There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given by, respectively:

[tex]\mu = 255, \sigma = 30[/tex]

In item a, according to the Central Limit Theorem, since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.

For item b, we have that n = 40 > 15, hence the standard error is given by:

[tex]s = \frac{30}{\sqrt{40}} = 4.74[/tex]

The probability is one subtracted by the p-value of Z when X = 260, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260 - 255}{4.74}[/tex]

Z = 1.05

Z = 1.05 has a p-value of 0.8531.

1 - 0.8531 = 0.1469.

There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.

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Using it's concept, it is found that the vertical asymptote of the function [tex]f(x) = \frac{3}{x+5}[/tex] is of x = -5.

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

In this problem, the function is fraction given by:

[tex]f(x) = \frac{3}{x + 5}[/tex]

At the denominator, we have that:

x + 5 = 0 -> x = -5

Hence the vertical asymptote of the function [tex]f(x) = \frac{3}{x+5}[/tex] is of x = -5.

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Answer: A) x= -5

Took the test and got 100% :)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{4 +3} \implies \cfrac{ -4 }{ 7 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{4}{7}}(x-\stackrel{x_1}{(-3)})\implies y-3=-\cfrac{4}{7}(x+3)[/tex]

Answer:

7 hours and 12 minutes

Step-by-step explanation:

there are 24 hours in a day, so multiply 6/20 by 24 to find the number of hours:

6*24/20 = 36/5 = 7  1/5 hours

we now know maria sleeps for 7 whole hours

next, there are 60 minutes in an hour, so multiply 1/5 by 60 to get 12 minutes

Answer:

none because i boiled them all

Step-by-step explanation:

Answer:

31 kids

Step-by-step explanation:

56-25=31

Answer:

40°, 60°, 80°

Step-by-step explanation:

sum the parts of the ratio , 2 + 3 + 4 = 9 parts

the sum of the 3 angles in a triangle = 180° , then

180° ÷ 9 = 20° ← value of 1 part of the ratio , then

2 parts = 2 × 20° - 40° = ∠ A

3 parts = 3 × 20° = 60° = ∠ B

4 parts = 4 × 20° = 80° = ∠ C

Answer:

Step-by-step explanation:

10 rolls = $30

12 rolls = ...

Because $3 for each roll of tape, so 3 x 10 = 30. All we have to do is multiply 3 by 12 to get how much for 12 rolls.

36.

The surface area of the rectangular prism with the dimensions that are stated is: 384 in.²

Surface area = perimeter of base × height of prism + 2(base area)

= (s1 + s2 + s3)L + 2(1/2bh)

Given the following:

Surface area = (6 + 8 + 10)14 + 2(1/2 × 6 × 8)

Surface area = 384 in.²

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Answer:

length = 6cm , breadth = 4cm

Step-by-step explanation:

Let's assume length = l

breadth = b

Given perimeter of a rectangle = 20 cm

2(l+b) = 20

l+b = 20/2

l+b = 10

l = 10 - b____(1)

Given area of rectangle = 24 cm²

l×b = 24____(2)

(1) in (2) => l × b = 24

(10-b) × b = 24

10b - b² = 24

10b = 24 + b²

0 = b² - 10b + 24

b² - 10b + 24 = 0

b² + 6b + 4b + 24 = 0

b(b+6) +4(b+6) = 0

(b+4)(b+6) = 0

b+4 = 0. &. b+6 = 0

b = -4. b = -6

breadth must be less than length and it should be positive

So b = 4 cm

b=4 in (1)

(1)=> l = 10 - b

l = 10 - 4

l = 6

Answer:

ab<6 units

Step-by-step explanation:

One of the basic property of any triangle is that the sum of the length of any two sides of a triangle is always greater than the length of the third side. Here we are given a triangle abc, in whicn bc=4ac= 8-abIf have to make some conclusion about ab.As per the property discussed above ab<ac+bcab<8-ab+42ab<12ab<6Hence the length of ab must be less than 6 units

Answer:

8

Step-by-step explanation:

Given algebraic expression:

5(x - 1) - 2

To:

Evaluate this expression using x = 3

Solution:

Evaluate by plugging x = 3 to this expression:

Simplify using PEMDAS.

We can conclude:

By evaluating x = 3 to the given expression,the answer will be 8.