find the equation for the line that passes through the point (4,-3), and that is perpendicular to the line with the equation y= -3/4x-3​

Hello-

Here is the way that I learned to multiply decimals. First, remove the decimal points.

2.37 X 1.6

237 X 16

Then you multiply the numbers.

237 X 16 = 3792

Now, we move the decimal point three places to the left on our answer.

3.792

3.792 is our answer.

Answer:

38.81 pounds

Step-by-step explanation:

Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

Right rectangular prism

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

Volume of right rectangular prism

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

Volume of the container

In this case, you know that:

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= 258.75 ft³

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds

Finally, the total weight of the contents is 38.81 pounds.

Quantity of flour needed to make 20 pancakes =

\( = 1 \frac{2}{3} \: \)

\( = \frac{3 \times 1 + 2}{3} \)

\( = \frac{5}{3} \: cups \: of \: flour\)

Then , number of pancakes that can be made from 1 cup of floor :-

\(20 \div \frac{5}{3} \)

\(20 \times \frac{3}{5} \)

\( \frac{60}{5} \)

\( = 12 \: pancakes\) .

Therefore , 12 pancakes can be made from 1 cup of floor .

Number of pancakes that can be made with 1 cup of flour = 12 pancakes

Number of pancakes that can be made with 9 cups of flour :-

= 9 × 12

= 108 pancakes

Therefore , I can make 108 pancakes with 9 cups of flour .

Yes , I have enough flour to make 100 pancakes . I say this because :-

With one cup of flour I can make = 12 pancakes

With 9 cups of flour I can make =

= 9 × 12

= 108 pancakes

As I can make 108 pancakes with 9 cups of flour , I can conclude that I have enough flour to make 100 pancakes .

Answer: X=1/72

Step-by-step explanation:

3/8x-17=10

We move all terms to the left:

3/8x-17-(10)=0

Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R

We add all the numbers together, and all the variables

3/8x-27=0

We multiply all the terms by the denominator

-27*8x+3=0

Wy multiply elements

-216x+3=0

We move all terms containing x to the left, all other terms to the right

-216x=-3

x=-3/-216

x=1/72

Hello!☺

\(Answer:\boxed{x=72}\)

\(Explanation:\)

\(\frac{3}{8}x-17=10\)

Let's start by adding 17 to both sides:

\(\frac{3}{8}x-17+17=10+17\)

\(\frac{3}{8}x=27\)

In our second/final step, we will multiply both sides by 8/3:

\((\frac{8}{3})*(\frac{3}{8}x)=(\frac{8}{3})*27=72\\ x=72\)

Hope this helps!☺

Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).

To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)

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Answer:

$2,160 is what he need for both daughters for 1 year

Step-by-step explanation:

90 x 2 = 180

180 x 12 = 2,160

Dominic need to budget a total of 2160 for a year of gymnastics for both daughters.

Multiplication is one of the basic mathematical operations which includes a number added repeatedly to times of the other number. The final answer is called the product of the numbers.

Multiplication is usually denoted as '×' sign.

a × b indicates that a is added repeatedly upto b times.

Cost for the gymnastics per month per child = 90

In order to find the cost per month for both daughters, we need to multiply 90 with 2.

Cost for the gymnastics per month for 2 daughters = 2 × 90 = 180

To find the total cost for an year, we need to multiply 180 with 12.

Total cost for the year = 180 × 12 = 2160

Hence the total budget for Dominic to send both the daughter in a year is 260.

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Answer:

Easy .2619

Step-by-step explanation:

hope it helped

the answer is c

3.3 x10 restu power minus 3

Sorry for the rough sketches.

The answer has been shaded.

Answer:

3000

Step-by-step explanation:

2000 x .10= 200 that's interest for one year

200 x 5 = 1000 that's interest for 5 years

1000 + 2000= 3000 total amount of money in five years

Answer:3,221.02

Step-by-step explanation:

\(\dfrac{7!4!}{5!3!}=6\cdot7\cdot4=168\)

The value of AB is,

⇒ AB = 5.9

(rounded to nearest tenth)

We have to given that,

A right triangle ABC is shown.

Now, By trigonometry formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

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Answer: It is a 2:3 Ratio

Answer: yes

Step-by-step explanation:

the two sides are near the same with one smaller and i learned at sc that that makes it right

Answer:

7

Step-by-step explanation:

10+4 = 14

14/2  = 7

x = 7

Answer:

a.  sin(M)=7/25

b.  cos(M)=24/25

c.  tan(M)=7/24

d.  sin(O)=24/25

e.  cos(O)=7/25

f.  tan(O)=24/7

Step-by-step explanation:

Pythagorean Theorem

Note that for the given triangle, one side length is not given, so that will need to be solved for.  Since the triangle is a right triangle, the Pythagorean theorem applies:  \(a^2+b^2=c^2\) where c is the hypotenuse, and "a" and "b" are the two legs.

\(a^2+b^2=c^2\\(7)^2+b^2=(25)^2\\49+b^2=625\\b^2=625-49\\b^2=576\\b= \pm \sqrt{576}\\b= \pm 24\)

Since "b" is a length of a leg of the triangle, we assume it positive and reject the negative solution.

Thus, the missing side is 24 units long.

Trigonometric Definitions

For this problem, remember that trigonometric functions take in an angle, and output a ratio of sides.

So, it is then important to remember which two sides each trigonometric function uses to make its ratio of sides.  Many people remember this with SohCahToa, where the bolded letters represent one of the three trig functions, and the other two letter represent one of the sides of the right triangle

So:

       \(\sin(\theta)=\frac{opposite}{hypotenuse}\)       \(\cos(\theta)=\frac{adjacent}{hypotenuse}\)        \(\tan(\theta)=\frac{opposite}{adjacent}\)

So, for each situation, identify which angle is going into the function, then identify which sides you need and where they are.  Substitute and simplify.

Evaluating Trigonometric functions

a.  sin(M)

Note that here the input angle is angle M.  The hypotenuse is always across from the right angle, so the hypotenuse is side MO=25.  The adjacent here is MN=24 (the side touching angle M that isn't the hypotenuse), and the opposite side is ON=7 (the side not touching the angle M)

\(\sin(M)=\frac {opposite}{hypotenuse}\\\sin(M)=\frac {7}{25}\\\)

b.  cos(M)

Again, the input angle is angle M, so the side definitions are the same as in part a.

\(\cos(M)=\frac {adjacent}{hypotenuse}\\\cos(M)=\frac {24}{25}\\\)

c.  tan(M)

Again, the input angle is angle M, so the side definitions are the same as in part a & b.

\(\tan(M)=\frac {opposite}{adjacent}\\\tan(M)=\frac {7}{24}\\\)

d.  sin(O)

Here, the input angle is angle is different from the previous parts of the problem, so we need to look back at our triangle and determine which side is which.

The input angle is angle O.  The hypotenuse is always across from the right angle, so the hypotenuse is side MO=25.  The adjacent here is ON=7 (the side touching angle O that isn't the hypotenuse), and the opposite side is MN=24 (the side not touching the angle O)

\(\sin(O)=\frac {opposite}{hypotenuse}\\\sin(O)=\frac {24}{25}\\\)

e.  cos(M)

Again, the input angle is angle O, so the side definitions are the same as in part d.

\(\cos(O)=\frac {adjacent}{hypotenuse}\\\cos(O)=\frac {7}{25}\\\)

f.  tan(M)

Again, the input angle is angle O, so the side definitions are the same as in part d & e.

\(\tan(O)=\frac {opposite}{adjacent}\\\tan(O)=\frac {24}{7}\\\)

The value of x is -15

Functions are simply defined as expressions or rules showing the relationship between two variables.

These variables are listed as;

From the information given, we have that;

g(x) =x  -1, if g(x) = -16

Now, we have to equate the two functions, we get;

x - 1 = -16

collect the like terms, we get;

x =-16 + 1

add the values, we have;

x = -15

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The complete question:

Given g(x) =x  -1, if g(x) = -16, find x.

Answer:

0.44

Step-by-step explanation:

Given the estimated logistic regression model on risk of having squamous cell carcinoma

-4.84 + 4.6*(SMOKER)

SMOKER = 0 (non-smoker) ; 1 (SMOKER)

What is the predicted probability of a smoker having squamous cell carcinoma?

exp(-4.84 + 4.6*(SMOKER)) / 1 + exp(-4.84 + 4.6*(SMOKER))

SMOKER = 1

exp(-4.84 + 4.6) / 1 + exp(-4.84 + 4.6)

exp^(-0.24) / (1 + exp^(-0.24))

0.7866278 / 1.7866278

= 0.4402863

= 0.44

Let x be the cost of the small bag.

The large bag costs x + 30 more than the small bag.

So the cost of the large bag is x + (x + 30) = 2x + 30

The two-piece set of luggage cost is the sum of the cost of the small and large bag, so

122 = x + (2x + 30)

Solving this equation for x, we get:

x = 42

Therefore, the small bag costs 42 dollars and the large bag costs 2*42 +30 = 114 dollars.

Answer:

221  I am sorry if I am wrong. I tried

Step-by-step explanation:

4 ounces ate 328 calories : 1312 calories.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

The given 4 ounces ate 328 calories

and 1 pound = 16 ounces

16/4= 4

4 * 328 = 1312

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The two column proof is completed below

Statement                                                      Reason

1. line KI parallel to line MN                      Given

2. ∠ JKL ≅ ∠ JMN and ∠ JLK ≅ ∠ JNM   Corresponding angles are equal

3. Δ JKL ~ Δ JMN                                      Similar triangles

4. (JM)/(JK) = (JN)/(JL)                               Ratios of corresponding sides are                            

                                                                  equal

5. JM = JK + KM and JN = JL + LN         Segment Addition Postulate

6. (JK + KM)/(JK) = (JL + LN)/(JL)             Substitution property

7. (JK)/(JK) + (KM)/(JK) = (JL)/(JL) + (LN)/(JL)     Addition of fractions

8. 1 + (KM)/(JK) = 1 + (LN)/(JL)                             Simplify

9. (KM)/(JK) = (LN)/(JL)                                       Simplify (the required proof)

Similar triangles are triangles that have the same shape but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are proportional.

The equality of corresponding sides of similar triangles is used in the proof and it helped to state that: (JM)/(JK) = (JN)/(JL).

Further calculations were substitution and simplifying

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Answer:

She needs to descend 20 feet per descent.

Step-by-step explanation:

100/5 = 20

Answer:

(X'U'Y) + (XUY')

Step-by-step explanation:

Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:

[Xn(X'nY)]' = (Xn)' + (X'nY)'

Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:

(Xn)' + (X'nY)' = (X'U'Y) + (XUY')

where U represents the logical operator "or".

Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').

To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

Answer:

(1,-1)

Step-by-step explanation:

\( \large{ \begin{cases} y = 2x - 3 \\ y = - x \end{cases}}\)

Since both are y-isolated equation. We can combine both.

\( \large{2x - 3 = - x}\)

Since we want to solve for x-term, we need to isolate x-term.

So we move from -x which is the right side to x.

\( \large{2x - 3 + x = 0} \\ \large{3x - 3 = 0} \\ \large{3x = 3} \\ \large{x = 1}\)

But we are not done yet. Solving system of equations, you must solve for y-term as well. (Because we have to answer in ordered pairs which are (x, y))

Substitute x = 1 in any given equations but I will substitute x = 1 in y = -x

\( \large{y = - x} \\ \large{y = - 1}\)

Since we have got y-value. Therefore the answer is (1,-1)