Can someone help me with problems 3&4 please

Answer:

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Step-by-step explanation:

o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:

Differentiate both sides of the equation with respect to x:

cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx

Simplify by grouping the terms with dy/dx on one side and the rest on the other side:

cos(x+y) * (1 + dy/dx) + 4dy/dx = 4

Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):

cos(2π) * (1 + dy/dx) + 4dy/dx = 4

Simplify:

-5dy/dx = 4 - cos(2π)

dy/dx = -4/5

Use the point-slope form of the equation of a line to write the equation of the tangent line:

y - π = (-4/5)(x - π)

Simplify:

y = (-4/5)x + (8/5) + π

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

The linear function that represents the maximum number of points the assignment may receive is, f(x) = 200 - 10x for 1 ≤ x ≤20.

Linear functions are the functions over a variable (say x), where the highest power for the variable is 1.

In the question, we are informed that an assignment is worth 200 points. We are also said that the professor deducts 10 points per day, for each day the assignment is submitted late.

We are asked to write a linear function that represents the maximum number of points the assignment may receive at a given time, assuming it was turned in after it was due.

Since it is given that the assignment is submitted late, we assume the days of delay to be x.

For each day delayed, 10 points are deducted.

∴ For a delay of x days, points deducted = 10x

We know, the total worth of the assignment = 200.

Hence the points can be calculated as a linear function, f(x) = 200 - 10x.

Now, since we are asked to assume that the assignment was turned in after it was due, we can say that x ≥ 1.

Also, the maximum delay can be of days as the points of the assignment can not be negative, that is, x ≤ 20.

∴ The linear function that represents the maximum number of points the assignment may receive is, f(x) = 200 - 10x for 1 ≤ x ≤20.

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To find the surface area of square OABC, we calculate the side length using the coordinates of point B, resulting in 25/16 units.

To find the surface area of square OABC, we need to determine the length of one side of the square. Since point B lies on the line with the equation y = -4x + 5, we can use this information to find the coordinates of point B and then calculate the distance between points O and B to determine the side length.

First, we need to find the x-coordinate of point B. Since we know the equation of the line y = -4x + 5, we can substitute y = 0 (since point B lies on the x-axis) and solve for x:

0 = -4x + 5

4x = 5

x = 5/4

Therefore, the x-coordinate of point B is 5/4.

Next, we substitute this x-coordinate back into the equation y = -4x + 5 to find the y-coordinate of point B:

y = -4(5/4) + 5

y = -5 + 5

y = 0

So, the coordinates of point B are (5/4, 0).

Now, we can calculate the distance between points O and B using the distance formula:

Distance = \(\sqrt{[(x2 - x1)^2 + (y2 - y1)^2]}\)

        = \(\sqrt{[(0 - 0)^2 + (5/4 - 0)^2]}\)

        = \(\sqrt{[(5/4)^2]}\)

        =\(\sqrt{ [25/16]}\)

        = 5/4

Since OABC is a square, all sides are equal in length. Therefore, the side length of square OABC is 5/4.

To find the surface area of the square, we use the formula:

Surface Area = \(Side Length^2\)

            =\((5/4)^2\)

            = 25/16

Therefore, the surface area of square OABC is 25/16 square units.

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If a = < 1, 5> , b = < 4, -3 > and sa + tb = < 16, -35>, then the values of s and t are -4 and 5 respectively

a = < 1, 5 >

b = < 4, -3 >

There are scalars s and t

sa + tb = < 16, -35 >

The equations will become

1s + 4t = 16

5s - 3t = -35

Multiply the first equation by 5 and second equation by 1

The new equations will be

5s + 20t = 80

5s - 3t = -35

Subtract the second equation from second equation

23t = 115

t = 115 / 23

t = 5

Substitute the value of t in the second equation

5s - 3 × 5 = -35

5s - 15 = -35

5s = -35 +15

5s = -20

s = -20/5

s = -4

Therefore, the values of s and t are -4 and 5 respectively

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To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

Step-by-step explanation:

40 x 1 = 40

20 x 2 = 40

10 x 4 = 40

8 x 5 = 40

The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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Answer:

3 of each gallon

Step-by-step explanation:

It worked for me on ttm

Answer:

4 of 1/3 and 1 of 1/6

Step-by-step explanation:

5/6+2/3=9/6

9/6+4/3=17/6

17/6+1/6=18/6

18/6=3

Answer:

Sure, here is the inequality that represents the number of gigabytes of data (G) you can use to stay under your budget of $130:

```

cost_per_gb * G <= budget

```

where:

* cost_per_gb is the cost of data per gigabyte, which is $10 in this case

* G is the number of gigabytes of data

* budget is your budget, which is $130 in this case

To solve this inequality, we can first subtract cost_per_gb from both sides of the inequality. This gives us:

```

G <= budget / cost_per_gb

```

We can then plug in the values for cost_per_gb and budget to get:

```

G <= 130 / 10

```

```

G <= 13

```

This means that you can use up to 13 gigabytes of data and still stay under your budget. If you use more than 13 gigabytes of data, you will exceed your budget.

Here is a table that shows the cost of data for different amounts of data:

```

| Amount of data (G) | Cost (\$) |

|---|---|

| 1 | 10 |

| 2 | 20 |

| 3 | 30 |

| ... | ... |

| 13 | 130 |

| 14 | 140 |

| ... | ... |

```

Step-by-step explanation:

To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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Answer:

d. 9x^2 + 25x + 14

Step-by-step explanation:

Formula of area of a rectangle is L * W;

L being length

W being width

x + 2 is our W

9x + 7 is our L, thus;

(x+2)(9x+7)

[9x^2 + 25x + 14]

Answer:

15 degrees for the first one

90 degrees for the second one

Step-by-step explanation:

Answer:

y=7x

Step-by-step explanation:

slope intercept form is y=mx+b.

m is the slope (rise over run) and b is your y- intercept. you leave y as it is. if the line is going down, you have a negative slope. hope this helped :)

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer:

Step-by-step explanation:

we can have infinite similar triangles with different side lengths but if the  base length is same then two triangles on the opposite side of base.

On one side of base  only one triangle can be formed.

The subsets of the set {-3, 6}, which are proper subsets is the option;

A set is a model that represents a collection of mathematical objects such as numbers, lines, symbols, points, other sets, variables, or shapes.

In set theory, a set A is a subset of the set B if all the elements or members present in set A can be found in set B. Therefore, set B is said to contain set A or set A is contained in set B.

The above relationships can be expressed using examples as follows;

Let set A = {X, Y} and let set B = {X, Y, Z}, then set A is a subset of set B because the elements, X, Y, contained in set A, are also contained in set B,

Generally, the number of proper subsets of a set that contains n elements is \( {2}^{n} - 1\)

Given that the subset of a set which is not a proper subset is the set of itself.

The given set is; {-3, 6}

The number of elements in the set, n = 2

Therefore;

The number of proper subsets = 2² - 1 = 3

All the subsets of {-3, 6} are therefore;

∅, {-3}, {6}

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Answer:

2.325

Step-by-step explanation:

i used a calculator ,i think i did it right lol

Answer:

6\(cm^{2}\)

Step-by-step explanation:

0.5bh=0.5*3*4=6

Finn would run 18 miles after 6 track practices.

We have,

Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.

Unit rate: 6 miles / 2 practices = 3 miles per practice

To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.

Total miles: 3 miles/practice * 6 practices = 18 miles

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Answer:

2csc(2x)

Step-by-step explanation:

When simplifying the given expression, we can start by finding a common denominator for the fractions. The common denominator for sin x and cos x is cos x * sin x.

Rewriting the expression using the common denominator, we have:

(sin x * sin x)/(cos x * sin x) + (cos x * cos x)/(sin x * cos x)

Simplifying the fractions, we get:

sin^2(x)/(cos x * sin x) + cos^2(x)/(sin x * cos x)

Now, let's simplify each fraction individually:

sin^2(x)/(cos x * sin x) can be simplified to (sin x / cos x)

cos^2(x)/(sin x * cos x) simplifies to (cos x / sin x)

Now, combining the simplified fractions, we have:

(sin x / cos x) + (cos x / sin x)

To combine these fractions, we need a common denominator, which is cos x * sin x:

[(sin x * sin x) + (cos x * cos x)] / (cos x * sin x)

Using the Pythagorean identity sin^2(x) + cos^2(x) = 1, we can simplify the numerator:

(1) / (cos x * sin x)

Therefore, the simplified form of the expression is 1 / (cos x * sin x), or 2csc(2x)

Answer:

17/24

Step-by-step explanation:

⅓ and ⅜ need to have the same denominator so multiply each side top and bottom  

⅓ needs to be multiplied by 8 to get 8/24  

⅜ needs to be multiplied by 3 to get 9/24

Then add them to get 17/24

Thats the simplest form

Answer:

17/24

Step-by-step explanation:

1/3 x 8/8

3/8 x 3/3

8/24 + 9/24

8 + 9 = 17

and the bottoms are both 24 show it will = 24 so your answer is 17/24

Answer:

1.2 trains for $25.

Step-by-step explanation:

For 50 dollars, you could get 2.4 trains with the $25 dollar option.

For 90 dollars (an extra 40 dollars!) you only get 0.2 more trains.

If you add another $25 to the current $50 on the other option, you get 3.6 trains.

So, 1.2 trains for $25 must be the better option as you can get an extra 1 train for 15 dollars less!

Hope this helps!

Also, who buys 0.2 or 0.6 of a train? -_-

Answer: Yes, there is an outlier of 45, This means that one person's age was 45, which is 25 years younger than the next closest age.

Hope this helps! :)

Step-by-step explanation:

Answer:

D

GIVE HIME BRAINLIEST

Step-by-step explanation:

The measure of angle A is 86.

A kite is a flying object that is tethered to the ground by a string or a cord. It typically has a light framework of bamboo, plastic, or other materials, covered with paper or fabric, and often in the shape of a diamond or triangle.

We have,

From the figure,

We see that,

6x + 4 + ∠A = 180

Now,

∠A = 4x + 26

So,

6x + 4 + 4x + 26 = 180

10x + 30 = 180

10x = 180 - 30

10x = 150

x = 15

Now,

∠A = 4x + 26 = 4 x 15 + 26 = 60 + 26 = 86

Thus,

The measure of angle A is 86.

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The complete question:

Levi was designing a kite. he needs to determine the measure of angle A.

Answer:125

Step-by-step explanation:

5*5*5=125

Answer:

Step-by-step explanation:

5*5=25

25*5=125

Answer:

1/2 x 3/4 = 1/8

Step-by-step explanation:

if you make a box

cut it into half

shade in 1/2

cut it into fourths

shade in one because it's only 1/2

count up all the boxes

count how many have both shaded in

and you get 1/8

total number of balls = 5 + 3 = 8

The possibilities are:

RR (two red) and RB (one red and one blue)

RR and RB are mutually exclusive

P(RR) =