The support arm, AB, is
perpendicular to a line tangent to this curve on a roller coaster at the point of tangency B.

The equation of the tangent line to the curve at B is 3x + 2y = 28.

Find the equation of the support arm, AB.
B(4,8)

Lines perpendicular to tangents to curves, at
the point of tangency, are referred to as “normals.”

Answer:

The best estimate for the correlation coefficient is .85.

The most appropriate choice for slope of a line will be given by-

Slope of the line = [tex]\frac{-19}{12}[/tex]

What is slope of a line?

At first it is important to know about line.

Line is a geometrical object that has only length but no breadth and no height.

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta\\[/tex]  is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

m = [tex]tan\theta[/tex]

If the line passes through ([tex]x_1,y_1[/tex]) and ([tex]x_2, y_2[/tex]) , then

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Here,

[tex]x_1 = -3, y_1 = 9. x_2 = 9, y_2 = -10[/tex]

Slope = [tex]\frac{-10 - 9}{9 - (-3))}[/tex]

         = [tex]\frac{-19}{12}[/tex]

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it is vital that we first find the gradient/slope between the points .

⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{2-(-2)}{0-2} \\m=\frac{4}{-2} \\m=-2[/tex]

The general equation of a straight line is given by y=mx+c I will use the points (0,2) to find the value of y since the other variables are found already.

[tex]2=-2(0)+c\\\\c=2[/tex]

⇒This tells us that the equation of the line is y=-2x+2

The area of a triangle bounded by the region will be 11.95 sq. units.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that,

y = f(x) = 7- (4/5)x

Slope,m = -4/5

The slope of the perpendicular lines is,

[tex]\rm m_p = \frac{-1}{\dfrac{-4}{5}} \\\\ m_ p = \dfrc{5}{4}[/tex]

The equation of the perpendicular line passing through the origin is

[tex]\rm y = \frac{5}{4} x[/tex]

The equation can be written as,

[tex]\rm \frac{5}{4} x = 7 - \frac{4}{5} x \\\\ 25 x = 140 - 16 x \\\\ 41x = 140 \\\\ x = \dfrac{140}{41} \\\\ y = \frac{175}{41}[/tex]

As a result, the y-intercept of the line is,

[tex]\rm y =7- \dfrac{4}{5}x \\\\ y= 7[/tex]

The triangle is bounded by the points (0,0), (0,7), and (140/41, 175/41)

The area of the triangle is,

[tex]\rm A= \frac{1}{2} \times 7 \times \dfrac{140}{141} \\\\ A = 11.95 \ sq. unit[/tex]

Thus, the area of a triangle bounded by the region will be 11.95 sq. unit.

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Answer: [tex]72z^{2} +55z-7[/tex]

Step-by-step explanation:

We multiply each component with each other:

8z * 9z = 72z^2

8z * -1 = -8z

9z * 7 = 63z

7 * -1 = -7

We then add it all together, 63z + -8z = 55z and get

[tex]72z^{2} +55z-7[/tex]

Answer:

18 more tickets

Step-by-step explanation:

What we know:

We know that 65 Tickets is 1 Prize.

We know we have 1,282 tickets.

So if 65 tickets is one prize

then to figure out how many for twenty then we:

65 x 20 = 1300

Now to figure out how many more she needs at the least we:

1300 - 1282 = 18

So for 1 more prize she needs 18 more tickets.

Answer:

75%

Step-by-step explanation:

If the ratio of red:blue is 3:1, then there are 4 (some multiple of 4) in all.

The ratio of red:total is 3:4

3/4 is .75, times by 100 to convert to a percent.

.75 × 100 is 75%

a) The 90% confidence interval to estimate the percentage of yellow peas is (23.09%, 29.03%.)

b) Based on the confidence interval, the results of the experiment do not appear to contradict the expectation that 25% of the offspring peas would be yellow.

Given:

Confidence level,c = 90% = 0.90

Number of successes, x = 153

Sample size,n = 434 + 153 = 587

a) The sample proportion is the number of successes divided by the sample size is,

p = x/n

p = 153/587

p ≅ 0.2606

For confidence level 1 - α = 0.90, determine [tex]z_{\alpha /2} = z_{0.05}[/tex] utilizing the normal probability table in the appendix

[tex]z_{\alpha /2} = 1.64[/tex]

The margin of error is calculated as:

[tex]E = z_{\alpha /2} \sqrt{\frac{p(1-p)}{n} }[/tex]

[tex]E = 1.64\sqrt{\frac{0.2606(1 -0.2606)}{587} }[/tex]

E ≅ 0.0297

Therefore, the boundaries of the confidence interval are:

p - E = 0.2606 - 0.0297 = 0.2309 = 23.09%

p + E = 0.2606 + 0.0297 = 0.2903 = 29.03%

We are 90% confident that the true percentage of yellow peas is between 23.09% and 29.03%.

b) As 25% is between 23.09% and 29.03%, and 25% of the offspring are expected to be yellow peas and thus the results do not contradict expectations.

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Answer:

no

Step-by-step explanation:

Generally you can't really compare two functions with a different denomination, and you want to multiply the fractions by some fraction: [tex]\frac{a}{a}[/tex] which simplifies to one so we're not changing the value of the fraction at all but it helps so we have the same denominator.

You'll notice we can multiply 4 by 2 to get 8, which would give us the same denominator as 8.

[tex]\frac{23}{4}*\frac{2}{2}=\frac{46}{8}[/tex]

Now it's much easier to compare: [tex]\frac{47}{8}\text{ and }\frac{46}{8}[/tex] and here all we have to compare is the numerators, and obviously 47 is greater than 46 so the 47/8 is greater than the 23/4. This means 47/8 is not less than 23/4

Answer:

48[tex]units^{2}[/tex]

Step-by-step explanation:

To rotate the figure 90 degrees clockwise about a point, every point (x, y) will rotate to (y, -x):

The vertices of the triangle have the following coordinates:

Applying the transformation rule, we have the new coordinates to be:

The transformed image is shown below (the black triangle):

Answer: 950

Step-by-step explanation:

$477.50 - $240.00 = 237.50

$237.50 / $0.25 = 950

Answer:

There is a proportion of 0.94% cities with average city temperatures lower than that of Kabul

Step-by-step explanation:

In this question, we are to calculate the proportion of average city temperatures lower than that of Kabul.

Firstly, we shall calculate the z score

Mathematically;

z = (value - mean)/standard deviation = 15 - 19.7/2 = -4.7/2 = -2.35

so we are to calculate the probability of; P(z< -2.35) = 0.0094

This means there is a proportion of 0.94% cities with average city temperatures lower than that of Kabul

The answer to your question is s. sqrt (316.9) = 17.8 when you take the square root of that number. As a result, the correct response is 17.8.

This is further explained below.

Generally, Because you need to calculate the sample standard deviation to answer the question, use the following formula:

[tex]s = \sqrt {{ \sum of x - \bar x}{(n - 1} }[/tex]

There are 9 numbers, there, so n - 1 = 8

find the mean

[tex]\bar x[/tex]: 15 + 42 + 53 + . . . + 47 = 227. 227 / 9

x= 25.2

After that, deduct one from each number and then square the output, as seen here:

(15 - 25.2) = 104.0 (42 - 25.2)²

= 282.2 (53 - 25.2)²

= 772.8

After that, total up all of those values. The response to this, using this illustration as an example, is

[tex]x=\frac{ 2,535.2}{ 8}[/tex]

x= 316.9.

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The equation 8(x+2) can be expressed using the distributive property as 8x + 16.

The distributive property can be described as the as the multiplication system of solving a particular expressions easily through the process of distributing another number  within the given  brackets.

The expression that was given as  8(x+2) , if it so be solved using the distributive property the we will have 8x + 16 because this result means that it has been shared in to part,  because the multiplication operation has been performed on the given expression.

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Answer:b=6

Step-by-step explanation:

We are looking for values of x that will not make the equation undefined .Obviously the function has restrictions we have to make sure that x-7 is always ≥0 because it is under a square root

[tex]x-7\geq 0\\x\geq 7[/tex]

The domain of the function is all the real numbers greater or equal to  7 .

x≥7 ε R

Answer:

-2/3

Step-by-step explanation:

I graphed it

The correct answer is option d, output = 6 - input using coordinate geometry.

In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

From the graph, we can see that the coordinates have the values

For x = 1, y = 5

For x = 2, y = 4

For x = 3, y = 3

For x = 4, y = 2

Hence, we can conclude that the output (y) = 6 - input (x)

The correct option is (d) output = 6 - input.

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Finance charge = $93.00

The interest you'll pay on a loan is defined as a finance charge, and it's most commonly used in the context of credit card debt. A financing fee is computed by taking your annual percentage rate, or APR, the amount you owe, and the time period into account.

Given that,

Interest rate = 15.5%

Date: 1-3 (3 days)

Average daily balance = amount paid × days

                                      = $200 × 3 = $600  

Date: 4-20 (17 days)

Average daily balance = amount paid × days

                                      = $300 × 17 = $5100  

Date: 21-30 (10 days)

Average daily balance = amount paid × days

                                      = $150 × 10 = $1500  

So, total average daily balance for the month

= $(600+5100+1500)

= $7200

Now, the finance charge = $7200 × (15.5÷12)

                                         = $93.00

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Answer:

Step-by-step explanation:

13) 8 - 6 + 4 = 2 + 4 = 6

14) 16÷(4-2)-3 = 16÷2 - 3 = 8 - 3 = 5

15) 3x + 5 = 17

3x = 17 - 5

3x = 12

x = 4 ≠ 2

b. solution is incorrect

16)4y - 7 = 3y - 4

4y - 3y = -4 + 7

y = 3

a. solution is correct

17) 2m - 3 < 4

2m < 4 + 3

2m < 7

m < 3.5

2 < 2.5, so a. number is a solution

18 ) 5 + 2n ≥ 12

2n ≥ 12 - 5

2n ≥ 7

n ≥ 3.5

0 is not greater than equal to 3.5, so b. number is not a solution

The measure of angles 1, 2, and 3 in exercise 11. are 100°, 80°, and 100°.

The measure of angles 1, 2, and 3 in exercise 12. are 47°, 133°, and 47°.

The measure of angles 1, 2, and 3 in exercise 13. are 80°, 80°, and 100°.

The measure of angles 1, 2, and 3 in exercise 14. are 94°, 86°, and 94°.

For 11. part:

Considering a transversal p that cuts two parallel lines l and m,

Each pair of internal angles on the same side of a transversal that intersects two parallel lines are supplementary.

m∠1 + 80° = 180°

m∠1 = 180° - 80°

m∠1 = 100°

Similarly, m∠1 + m∠2 = 180°

⇒ 100° + m∠2 = 180°

⇒m∠2 = 180° - 100°

⇒m∠2 = 80°

and also, m∠2 + m∠3 = 180°

⇒ 80° + m∠3 = 180°

⇒m∠3 = 180° - 80°

⇒m∠3 = 100°

Therefore, m∠1 = 100°, m∠2 = 80° and m∠3 = 100°.

For 12. part:

m∠3 + 133° = 180°(interior angles are supplementary)

m∠3 =  180° - 133°

⇒m∠3 = 47°

m∠2 = 133°(alternate interior angles)

The angle vertically opposite to 133° would also be 133°.

So, 133° + m∠1 = 180°( interior angles are supplementary)

m∠1 = 47°

Therefore, m∠1 = 47°, m∠2 = 133° and m∠3 = 47°.

For 13. part:

m∠3 = 100° (vertically opposite angle)

Let's assume the angle adjacent to ∠3 is x.

m∠3 + m ∠x = 180° (Linear pair property)

100° + m ∠x = 180°

m ∠x = 180° - 100°

m ∠x = 80°

Therefore, m∠1 = m∠2 = m ∠x  = 80°(Corresponding angles are equal.)

For 14. part:

m∠1 + 86° = 180°(co-interior angles are supplementary)

m∠1 = 180°- 86° = 94°

The angle vertically opposite to m∠1 is also equal to 94°.

94° + m∠1 = 180°(co-interior angles are supplementary)

m∠2 = 86°

Similarly, the angle vertically opposite to m∠2 is also equal to 86°.

86° + m∠3 = 180°(co-interior angles are supplementary)

m∠3 = 94°

Therefore, m∠1 = 94°, m∠2 = 86° and m∠3 = 94°.

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Answer:

[tex]y=-\frac{4}{3}x+3[/tex]

Answer:

221 760 inches

Step-by-step explanation:

So, 3.5miles * 63360= 221760 inches.

Formula: multiply the value in miles by the conversation factor '63360'.

Answer:

Step-by-step explanation:

it would be 42,32 i know

f(g(x)) for the given equation f(x)=8x+1 and g(x)=4x-2 is 32x-15 using substitution method of solving the equation.

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. It is a formula that expresses the connection between two expressions on each side of a sign.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

given,

f(x)=8x+1

g(x)=4x-2

f(g(x))=8(4x-2)+1

=32x-16+1

f(g(x))=32x-15

Hence, this is required f(g(x)) for the given two equations.

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Answer:

-5

Step-by-step explanation:

Answer: -5

Step-by-step explanation: -35 divided by 7 is -5

[tex] \frac{10}{4} \times \frac{23}{6} \\ = \frac{230}{24} \\ = \frac{115}{12} \\ = 9 \frac{7}{12} [/tex]

ATTACHED IS THE SOLUTION

The lengths 8 cm, 14 cm, 15 cm can form a triangle

Given 8 cm, 14 cm, 15 cm

These can form a triangle if the sum of any two sides of the triangle is greater than the third side.

8 + 14 > 15

14 + 15 > 8

8 + 15 > 14

Since all the above are true, we conclude that they can form a triangle