A line contains the point (-3,4). If the slope of the line is -2/3, write the equation of the line using slope intercept form

Answer:

t ^3

Step-by-step explanation:

t^2.t

= t × t^2+1

= t^3

The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

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Answer:

(-5,5)

Step-by-step explanation:

The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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Answer:

2.5 km left

The midpoint is half of 5, which is 2.5, so he'll still have 2.5 km left to complete

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

Answer:

9. x = 12

10. x = 31

Step-by-step explanation:

9. Corresponding angles are equal, so technically you can move that (7x - 20) to be diagonal with the (4x + 16). Along with the corresponding angle, diagonal angles are equal to each other. Therefore you can set (7x - 20) equal to (4x + 16) to find x.

7x - 20 = 4x + 16

Solve

3x - 20 = 16

3x = 36

x = 12

Therefore x is equal to 12

Check:

4(12) + 16

= 64

7(12) - 20

= 64

10. All angles in a triangle have to add up to 180 degrees. Therefore, you can write your equation like this:

x + 2x + 25 + 2x = 180

Combine like terms

5x + 25 = 180

Solve

5x = 155

x = 31

Therefore, x = 31.

Check:

31 + 2(31) + 25 + 2(31) = 180

31 + 62 + 25 + 62 = 180

180 = 180

I hope this helps!!

- Kay :)

Answer: 180 per hour, 1080 per 6 hours

Step-by-step explanation:

Answer:

18, 6, 108

Step-by-step explanation:

The figure below is a right rectangular prism with rectangle ABCD as its base.

A rectangular prism is shown. Rectangles A B C D and W X Z Y are the bases. The length of A D is 9 centimeters and the length of C D is 2 centimeters. The height of A W is 6 centimeters.

What is the area of the base of the rectangular prism?

✔ 18

square centimeters

What is the height of the rectangular prism?

✔ 6

centimeters

What is the volume of the rectangular prism?

✔ 108

cubic centimeters

Answer:

18, 6, 108

Good Luck!

Answer:

Hope this helps lol !

Step-by-step explanation:

This is how to calculate net price. Start with the list price and add any taxes and other government-mandated charges. Then subtract any discounts, negotiated prices. The result you get will be the net price.

Answer:

-x - 12

Step-by-step explanation:

x- (-12) = x+12. The opposite of x+12 = -x-12. The answer is therefore -x -12, NOT x + 12.

Answer:

the equation's intervals are (0;+∞)

Step-by-step explanation:

Replace x with -12:

-12 - (-12) = -12 + 12 = 0

With -12 this equation is equal to zero, but since x > -12, that means we have to replace x with numbers that are greater that -12 (-11; -10; etc.)

And since there are open intervals ( > ), we do not count the zero.

Answer: 5.5555cm

Step-by-step explanation:

100 / 18 = 5.5555

Answer:

b = 30 yd is the answer.

Step-by-step explanation:

a = 40 yd

b = ?

c = 50 yd

According to the Pythagoras theorem,

a² + b² = c²

40² + b² = 50²

1600 + b² = 2500

b² = 2500 - 1600

b² = 900

b = 30 yd

∴ b = 30 yd is the length of the missing leg.

Step-by-step explanation:

for questions 5,6,7,8 you need to use formula

for questions 9.and 10 sorry I dunno how to do

Answer:

6

Step-by-step explanation:

First x-intercept is multiplicity of two.

Second is just one.

Third is one.

Fourth is two.

2+1+1+2=6

Answer:

622.08

Step-by-step explanation:

576 × (0.080 ÷ 1)

576 × 1.08

622.08

Answer:

622.08

Step-by-step explanation:

hope it helps you

Answer:

w = p/2 - l

Step-by-step explanation:

When a question asks to be solved by a variable it means to get that variable on one side.

To do this lets first divide each side by 2 making the equation now ...

(l + w) = p/2

Now all we have to do is subtract l on both sides. Now we know that

w = p/2 - l

Answer:

2.5

Step-by-step explanation:

Given expression:

\(6 \times \left(\dfrac{2}{3} \div 2\right)+0.5\)

Following the order of operations (PEDMAS), carry out the calculation inside the parentheses first.

When dividing a fraction by a whole number, first covert the whole number into a fraction:

\(\implies 6 \times \left(\dfrac{2}{3} \div \dfrac{2}{1}\right)+0.5\)

When dividing fractions, flip the second fraction (swap the numerator and denominator), then multiply:

\(\implies 6 \times \left(\dfrac{2}{3} \times \dfrac{1}{2}\right)+0.5\)

\(\implies 6 \times \left(\dfrac{2 \times 1}{3\times2}\right)+0.5\)

\(\implies 6 \times \left(\dfrac{2}{6}\right)+0.5\)

\(\implies 6 \times \dfrac{2}{6}+0.5\)

Now carry out the multiplication:

\(\implies \dfrac{6 \times2}{6}+0.5\)

\(\implies \dfrac{\diagup\!\!\!\!6 \times2}{\diagup\!\!\!\!6}+0.5\)

\(\implies 2+0.5\)

Finally carry out the addition:

\(\implies 2.5\)

2.5

6*(2/3)/2 + 0.5

6*1/3 + 0.5

2 + 0.5

=2.5

Answer:

excuse me can you speak english

Answer:

Population of the 48th generation will be 4469.

Step-by-step explanation:

Recursive formula by which the population is increasing,

\(L_{n+1}=L_n+95\)

L₀ = 4

Common difference 'd' = 95

Recursive formula represents a linear growth in the population.

Therefore, explicit formula for the given sequence will be,

\(L_n\) = L₀ + (n - 1)d [Explicit formula of an Arithmetic sequence]

Here n = Number of terms

L₄₈ = L₀ + (48 - 1)(95)

     = 4 + 4465

     = 4469

Therefore, population of the 48th generation will be 4469.

The area of sector GHJ is:

3.125π cm² (in terms of pi)

9.8 cm² (As a decimal rounded to the nearest tenth)

The formula for area of a sector when the angle is in radians is:

A = (1/2) * r²θ

Where θ is the angle subtended at the center and r is the radius of the circle.

In this case, r = 5 cm and θ = π/4

Substituting:

A = (1/2) * 5² * π/4

A = 3.125π cm² (in terms of pi)

As a decimal rounded to the nearest tenth:

A = 3.125 * 22/7

A = 9.8 cm²

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Answer:

Step-by-step explanation:

5+1+3+8+2=19

3/19 = 16%

Answer:

1/32

Step-by-step explanation:

Assuming that each question is independent, the probability of Yasmine answering a question correctly is 1/2, since each question has two possible answers (true or false) and she has a 50/50 chance of guessing correctly. Therefore, the probability of her answering all five remaining questions correctly is:

(1/2)^5 = 1/32

So the probability of Yasmine answering the five remaining questions correctly is 1/32, or approximately 0.03125, or about 3.125%.

Answer:

100%

Step-by-step explanation:

We know

She has answered 15 of her 20 questions correctly.

What is the probability that she will answer the five remaining questions correctly?

We take

15/15 = 100%

So, 100% she will answer the five remaining questions correctly.

Answer:

should have divided it directly ........ maybe or it's just messy........ maybe

Step-by-step explanation:

..........

...........

8x + 16 = 36

8x = 36 - 16

8x = 20

x = 20 / 8

x = 2.5

Answer: A) max at (14, 6) = 64,   min at (0,0) = 0

Step-by-step explanation:

Graph the lines at look for the points of intersection.

Input those points into the Constraint function (2x + 6y) and look for the maximum value and minimum value.

Points of Intersection: (0, 0), (17, 0), (0, 10), (14, 6)

Point     Constraint 2x + 6y

(0, 0):                    2(0) + 6(0) = 0              Minimum

(17, 0):                    2(17) + 6(0) = 34

(0, 10):                    2(0) + 6(10) = 60

(14, 6):                    2(14) + 6(6) = 64           Maximum

Answer:

third one down from the top

Step-by-step explanation:

You need to multiply 1000 by 1.12 so you start with the 1000 and continue getting higher based on the number of months

Answer: y=3x-7

Step-by-step explanation:

(2,2) and (-1,3) lie on the given line, so its slope is \(\frac{3-2}{-1-2}=-\frac{1}{3}\)

Since perpendicular lines have slopes that are negative reciprocals, the slope of the given line is 3.

Substituting into point slope form,

\(y+1=3(x-2)\\y+1=3x-6\\\boxed{y=3x-7}\)