Find an equation of the tangent line to the graph of
y = g(x) at x = 4 if g(4) = −3 and g'(4) = 2.
(Enter your answer as an equation in terms of y and x.)

Answer:

The distance from the boathouse to the cabin = 50 yd (nearest yard)

Step-by-step explanation:

The question is incomplete.

Question:

To find the distance from the

boathouse on shore to the cabin on the island, a surveyor measures from the boathouse to point X as shown. He then finds m∠X with an instrument called a transit. Use the surveyor’s

measurements to find the distance from the boathouse to the cabin.

Find attached the diagram of the question.

Solution:

Let the distance from the boathouse to the cabin = y

the distance from the boathouse to the point X = 30yard

Find attached the diagram for the solution.

From the diagram, the triangle is a right angled triangle

Opposite = y

Adjacent = 30yd

∠X = 59°

Using trigonometry (SohCahToa)

We would apply Toa since adjacent is given and we are looking for opposite

tan θ = opposite/adjacent

tan 59° = y/30

y = 30 tan 59

y = 30(1.6643)

y = 49.929

y = 50 yd (nearest yard)

The distance from the boathouse to the cabin = 50 yd (nearest yard)

9514 1404 393

Answer:

  C)  rotation, then translation

Step-by-step explanation:

Figure 2 is rotated 90° CCW about the origin from figure 1.

Figure 3 is translated 6 units to the right from figure 2.

The transformation is ...

  rotation, then translation

Answer:

180

Step-by-step explanation:

12x15=180

Answer:

13.31 and - 3.31

Step-by-step explanation:

(x + y)^2 = x^2 + y^2 + 2xy ; x + y = 10; x^2 + y^2 = 56

This means ;

10^2 = 56 + xy;

100-56 = XY

44 = xy---------(3)

From x + y = 10

x = 10- y

Substitute that in eqn 3;

We have: 44 = (10-y) y

44 =10y - y^2

Y^2-10y -44 = 0;

From formula method of quadratic equation;

Y =[ - (-10) +_ √ (-10)^2 + 4 × 1 x (-44)] / 2 × 1

y = [ 10 +_√ (100 + 176) ]/ 2]

y = [ 10 +_ √ 276]/ 2

y = [ 10 + √ 276]/ 2 or [ 10 _ √ 276]/ 2

y = 13.31 or - 3.31

Similarly x = 10 - 13.31 or 10 - (-3.31)

x = - 3.31 or 13.31

The required ordered pairs are (5+√3, 5-√3) and  (5-√3, 5+√3).

Given equations are:

[tex]x+y=10[/tex]......(1)

[tex]x^{2} +y^{2} =56[/tex].......(2)

An equation is a statement that equates to two statements.

On squaring equation (1) we get

[tex]x^{2} +y^{2} +2xy=100[/tex]

From equation(2) [tex]x^{2} +y^{2} =56[/tex]

So, [tex]2xy=44[/tex]

[tex]xy=22[/tex]

[tex]y=\frac{22}{x}[/tex]

Put [tex]y=\frac{22}{x}[/tex] in equation (1)

We get [tex]x+\frac{22}{x} =10[/tex]

[tex]x^{2} -10x+22=0[/tex]

[tex]x=5+\sqrt{3}[/tex]

[tex]x=5-\sqrt{3}[/tex]

If  [tex]x=5+\sqrt{3}[/tex],

[tex]y=10-x[/tex]

[tex]y=5-\sqrt{3}[/tex]

So the ordered pair is [tex](5+\sqrt{3}, 5-\sqrt{3} )[/tex]

If  [tex]x=5-\sqrt{3}[/tex],

[tex]y=10-x[/tex]

[tex]y=5+\sqrt{3}[/tex]

So the ordered pair is [tex](5-\sqrt{3}, 5+\sqrt{3} )[/tex]

Hence, the required ordered pairs are [tex](5+\sqrt{3}, 5-\sqrt{3} )[/tex] and [tex](5-\sqrt{3}, 5+\sqrt{3} )[/tex].

To get more about equations visit:

https://brainly.com/question/14323743

Answer:

135

Step-by-step explanation:

volume = width*length*height

5*9*3=135

we need 135inches³ to paint it

Answer:

  d.)  Arionna is incorrect. There are 27 cubic feet in a cubic yard because a cubic yard is a prism with dimensions 3 ft times 3 ft times 3 ft. A prism with those dimensions will take 27 cubes to fill it, if each cube is a unit cube of 1 ft³.

Step-by-step explanation:

There are (3 ft)(3 ft) = 9 ft² in one square yard. To find the volume of a cubic yard, you need to multiply that by 3 ft again: (9 ft²)(3 ft) = 27 ft³.

_____

Additional comment

For many problems involving units, I like to keep the units with the numbers. That helps ensure the math is done correctly. In this problem, simply multiplying ft by ft gives ft^2, not ft^3, so you know right away that you haven't computed volume correctly.

Answer:

ooga booga ooga booga ooga booga ooga booga ooga booga

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

In similar polygons, every side of one polygon is a certain number of times bigger than the corresponding side of the other polygon. This number is the scale factor. Since the perimeter of each polygon is the sum of the lengths of the sides of that polygon, the perimeters also have the same scale factor that the sides do.

For example, if a triangle has 3 sides measuring 5 cm each and a similar triangle has 3 sides measuring 10 cm each, you see that each side of the second triangle is 2 times the length of the corresponding side of the first triangle. The scale factor from the smaller triangle to the larger triangle is 2. Now look at the perimeters. Since 5 + 5 + 5 = 15 and 10 + 10 + 10 = 30, the perimeters are 15 cm and 30 cm, and again, the perimeter of the second triangle is the same 2 times bigger than the perimeter of the first triangle.

Now look at your problem.

The perimeter of the smaller flag to the right is 16.

We see a side on the larger flag is 15, but we don't see the same side length on the smaller flag, so 15 does not help us.

Now we see that a side of the smaller flag measures 4 and the corresponding side of the larger flag measures 12. We divide the larger side length by the corresponding smaller side length to find the scale factor.

12/4 = 3

The scale factor from the smaller flag to the larger flag is 3. The perimeters also have the same scale factor of 3.

perimeter = 3 * 16 = 48

Answer: 48

Answer:

48

Step-by-step explanation:

Similar polygons have their sides in proportion, and we call the proportion between pairs of corresponding sides on two similar polygons the scale factor between them. We want to find the perimeter of the larger flag given the smaller one, and comparing the side with length 12 on the larger one with the side of length 4 on the smaller, we get a scale factor of 12 / 4 = 3.

This tells us that all the lengths on the larger flag are 3 times longer than the corresponding lengths on the smaller flag. What happens to the perimeter when we scale all of the lengths? Well, if every side gets multiplied by three, the sum of those sides will naturally be multiplied by 3, too.

Our large flag has a perimeter 3 times bigger than the smaller one, then, and 3 × 16 = 48.

0.475

1000 milliliters is equal to 1 liter

Answer: 0.475 Liters

Step-by-step explanation: So, we know one liter is exactly 1,000 milliliters...therefore this would have to be a decimal.

Therefore, 475 milliliters to liters would be 0.475 liters.

The square root of 4 is 2. Since 3 is less than 4, the square root of 3 would be just under 2.

The first graph would be correct.

Answer:

The hat was chosen was the child.

Step-by-step explanation:

Answer:

25 meters

Step-by-step explanation:

in this case they give us the information about the lake and that length corresponds to the perimeter.

the perimeter of a circle has the following formula:

p = 2 * pi * r

then r equals:

r = p / pi * 2

replacing we have:

r = 157 / (2 * 3.14)

r = 25

which means that the radius of the lake is 25 meters

Answer:

Step-by-step explanation:

1). y + 2x < 6

  (y + 2x) - 2x < 6 - 2x

   y < -2x + 6 [Slope intercept form of the inequality]

2). y + 2x < 6

  Since there is no sign of equal to (=) in the given inequality therefore, line graphed will be dashed.

Notation of less than (<) denotes the area down the line.

Option (4) will be the answer.

3). y + 2x < 6

    x ≤ 2

Please find the graph attached.

Answer:

52+n=m

Step-by-step explanation:

Answer:

6.5 /52 m = n

Step-by-step explanation:

The rate is 6.5 miles / 52 minutes

We are going to run m miles in n minutes

m = 6.5 / 52 * n

We want to solve for n

Multiply each side by 52/ 6.5

6.5 /52 m = 6.5 / 52 * n * 6.5 / 52

6.5 /52 m = n

Answer:

Joseph- 265 coins

molly- 275 coins

Answer:

In the Garden Club the cost will be a fixed fee of $25 and $10 for each rosebush, so if he buys X rosebushes, the total cost will be:

C1(X) = $25 + $10*X

While in the local nursery there is no initial cost, and each rosebush costs $15, so if he buys X rosebushes, the total cost will be:

C2(X) = $15*X

Now, let's find the value of X where C1 and C2 are equal, this is:

$25 + $10*X = $15*X

$25 = $15*X - $10*X = $5*X

X = 25/5 = 5

This means that if he buys 5 rosebushes, he will pay the same amount in both places.

If he buys less than 5 rosebushes, he will pay less in the local nursery (as it has a bigger slope, but no initial fee)

If he buys more than 5 rosebushes, he will pay less in the Garden club (because it has a smaller slope)

Find the perimeter of the circle is the same as finding the circumference of the circle.

Circumference Formula: C = 2πr

Divide the diameter by 2 to find the radius.

7 / 2 = 3.5

Solve using the given values.

C = 2(3.14)(3.5)

C = 2(10.99)

C = 21.98

Therefore, the circumference (perimeter) of the circle is 21.98cm²

Best of Luck!

Answer:

Step-by-step explanation:

Answer:

$73.68

Step-by-step explanation:

2800 divide by 38 equals 73.68

Answer:

3 units.

Step-by-step explanation:

We can calculate the length, since it only moves on the "x" axis, since on the "y" axis, it remains the same.

We know that between -2 to 5, there are 7 units. 2 + 5 = 7.

Therefore this would be the length.

We know that the perimeter is equal to:

p = 2 * w + 2 * l

P = 20

20 = 2 * w + 2 * 7

2 * w = 20 - 14

w = 6/2

w = 3

therefore, the width value is 3 units.

Answer:

3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

pls mark me brainliest

Answer:

(a) We conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism at 5% significance level.

(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child.

Step-by-step explanation:

We are given that Autism and Maternal Antidepressant Use A recent study 41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected control children without the disorder.

Of the children with autism, 20 of the mothers had used antidepressant drugs. Of the control children, 50 of the mothers had used the drugs.

Let [tex]p_1[/tex] = proportion of mothers who had used drugs having Autism Spectrum Disorder in their children.

[tex]p_2[/tex] = proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children.

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]p_1=p_2[/tex]      {means that there is no significant association between prenatal exposure to antidepressant medicine and the risk of autism}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1\neq p_2[/tex]     {means that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism}

The test statistics that would be used here Two-sample z test for proportions;

                         T.S. =  [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]  ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of mothers who had used drugs having Autism Spectrum Disorder in their children = [tex]\frac{20}{298}[/tex] = 0.067

[tex]\hat p_2[/tex] = sample proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children = [tex]\frac{50}{1507}[/tex] = 0.033

[tex]n_1[/tex] = sample of children with Autism Spectrum Disorder = 298

[tex]n_2[/tex] = sample of children without Autism Spectrum Disorder = 1507

So, the test statistics  =  [tex]\frac{(0.067-0.033)-(0)}{\sqrt{\frac{0.067(1-0.067)}{298}+\frac{0.033(1-0.033)}{1507} } }[/tex]

                                       =  2.281

The value of z test statistics is 2.281.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism.

(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child because if we reconsider our hypothesis for one-tailed test in which the null hypothesis states that the prenatal exposure to antidepressant medicine does not increases the risk of autism in the child.

For this hypothesis also, our test statistics will be more than the critical value of z and due to which we reject our null hypothesis and conclude that prenatal exposure to antidepressant medicine increases the risk of autism.

Answer:

Step-by-step explanation:

x^-2 = (-3)^-2 = 1/(-3)^2 = 1/9

Each of the following is the previous value multiplied by -3,

x^-1 = x(x^-2) = (-3)(1/9) = -1/3

x^0 = x(x^-1) = (-3)(-1/3) = 1

x^1 = -3(1) = -3

x^2 = -3(-3) = 9

Answer:

(i) See attached image file

(ii) Option A

Step-by-step explanation:

See attached image file

Answer:

Group A (distance in miles) 1, 1.5, 3.03, 3.2, 2.8, 1.5, 1.8, 2.5, 2.2) Group B (distance in miles) 2, 2.5, 3.23, 1.3, 1.8, 2.4, 3, 1.5, 1.8)Therefore, the correct answer is A) It is equal for Group A and Group B.

Answer:

The second one.

Step-by-step explanation:

The others don't add up to that number

Given Information:

Cost price = $4

Selling price = $10

Salvage value = $1.50

Average demand = μ = 250 boxes

Standard deviation = σ = 34 boxes

Required Information:

Number of lettuce boxes = ?

Answer:

The supermarket should purchase 268 boxes  of lettuce

Step-by-step explanation:

The required number of lettuce boxes that supermarket should purchase is given by

Number of lettuce boxes = μ + (z*σ)

Where μ is the average demand of lettuce boxes, σ is the standard deviation, and z is the z-score which is given by

p = C_us/(C_us + C_os)

The z-score corresponding to probability p will be obtained.

The cost of under stocking is given by

C_us = Selling price - Cost price

C_us = $10 - $4

C_us = $6

The cost of over stocking is given by

C_os = Cost price - Salvage value

C_os = $4 - $1.50

C_os = $2.50

p = C_us/(C_us + C_os)

p = 6/(6 + 2.50)

p = 0.7058

p  = 70.58%

The z-score corresponding to 70.58% probability is approximately 0.54

Number of lettuce boxes = μ + (z*σ)

Number of lettuce boxes = 250 + (0.54*34)

Number of lettuce boxes = 250 + (18.36)

Number of lettuce boxes = 268.36

Number of lettuce boxes ≈ 268

Therefore, the supermarket should purchase 268 boxes of lettuce.

How to use z-table?

Step 1:

In the z-table, find the probability you are looking for and note down the two-digit number of the given row. (e.g 0.5, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table and note down the value in the column for the remaining decimal point in the range of 0.00 to 0.09.

Step 3:

Finally, add the numbers obtained from step 1 and step 2.

Answer:

The chord is bisected

Step-by-step explanation:

The chord of a circle is a segment whose endpoints are on the circle. when a perpendicular bisector ( the radius) of any chord passes through the center of the chord at right angle to the chord, the chord is bisected into two. This is a way or could give us a good way to find the center of any circle.

     kindly find attached a diagram for your reference

Answer:

B

Step-by-step explanation: