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Answer:

Angle B = 29.74

Step-by-step explanation:

Tan(x)=opp/adj

Tan(x)=4/7

x=[tex]Tan^{-1} (\frac{4}{7} )[/tex]

x=29.74

Answer:

The maximum number of works that he can write while staying in his time budget is 24.

21 poems and 3 short stories

Step-by-step explanation:

In order to solve this problem we must first determine what our variables are. In this case it's the number of poems and short stories he can write.

p = # of poems

s = # of short stories

Next, we must build our objective function which will represent the total number of works he can write.

N=p+s

where N is the number of works.

Next, we must write the constrains based on the information provided by the problem.

The problem tells us that it takes him 30 hours to write a poem and 70 hours to write a short story and that he has 840 hours available to write them, so that constrain will be the following:

[tex]30p+70s \leq 840[/tex]

it also tells us that he wants to write at least 4 poems and 3 short stories so there we have our other two constrains.

[tex]p \geq 4[/tex]

[tex]s \geq 3 [/tex]

once we got our constrains we can go ahead and graph them to see how they will behave. (See attached picture)

In the graph p is the horizontal axis and s is the vertical axis.

On the graph we can see a polygon that is formed by the restriction. The vertices of the polygon will represent the optimal conditions for this linear programming problem. There are three optimal solutions there, so we need to test them to see which will return the greatest number of works he can write while keeping the given conditions.

Option 1:

4 poems and 3 short stories

N=4+3

N= 7 works

Option 2:

4  poems and 10 short stories

N=4+10

N=14 works

Option 3:

21 poems and 3 short stories

N=21+3

N=24 works

So the optimal solution will be given by option 3 with 21 poems and 3 short stories.

Answer:

60

Step-by-step explanation:

All angles in a triangle equal 180

you already have Angles A (30) and C (90)

Set your formula up as

180-30-90=B

60=B

Answer:

3:1

Step-by-step explanation:

If you look at the sides, they all have the same factor of three, and dividing by three gets you to the smaller rectangular prism.

Answer:

Example 1: The PIN code is an example when order is important. The PIN code 1234 is different from the PIN code 4321. When selecting more than one item without replacement and order is important, it is called a Permutation. When order is not important, it is called a Combination.

Step-by-step explanation:

When we hear the word "combination" in our daily life, we immediately think about the collection of things in the form of a set or a group. For instance, if anyone says that my bowl has a combination of apples, carrots, and bananas, then we immediately think that the bowl has three items. We are not concerned with the order in which these three things were put in the bowl. In mathematics, the combination means the number of ways in which different objects are combined to form a set.

Answer:

so the other guy can get brainlest ur welcome

Step-by-step explanation:

Answer:

$3.47

the cost of each pen is $3.47

Step-by-step explanation:

subtract the price of notebook from total price

43.73 - 12.50

= 31.23

divide total from number of pens

31.23 / 9

= 3.47

Answer:

[tex]A = 100^o[/tex]

[tex]B = 43.0^o[/tex]

[tex]C =37.0^o[/tex]

Step-by-step explanation:

Given

[tex]A = 100^o[/tex]

[tex]b = 51[/tex]

[tex]c =45[/tex]

Required

Complete the triangle (See attachment)

First, calculate side a using cosine's equation

[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]

[tex]a^2 = 51^2 + 45^2 -2*51*45 \cos (100^o)[/tex]

[tex]a^2 = 4626 -4590 *-0.1736[/tex]

[tex]a^2 = 4626+ 796.8[/tex]

[tex]a^2 = 5422.8240[/tex]

Take square roots

[tex]a = 73.6398[/tex]

The measure of B and C can then be calculated using sine's equation

[tex]\frac{a}{\sin A} =\frac{b}{\sin B} =\frac{c}{\sin C}[/tex]

So:

[tex]\frac{73.6398}{\sin (100)} =\frac{51}{\sin B}[/tex]

[tex]\frac{73.6398}{0.9848} =\frac{51}{\sin B}[/tex]

Cross multiply

[tex]\sin B * 73.6398 = 51 * 0.9848[/tex]

[tex]\sin B * 73.6398 = 50.2248[/tex]

Solve for sin B

[tex]\sin B = \frac{50.2248}{73.6398}[/tex]

[tex]\sin B = 0.6820[/tex]

Take arc sin of both sides

[tex]B = \sin^{-1}(0.6820)[/tex]

[tex]B = 43.0^o[/tex]

To calculate C, we make use of:

[tex]A + B + C = 180^o[/tex] --- angles in a triangle

[tex]100 + 43 + C = 180[/tex]

[tex]143 + C = 180[/tex]

Collect like terms

[tex]C =180-143[/tex]

[tex]C =37.0^o[/tex]

Answer:

Your answer is -6

Step-by-step explanation:

In other words, only choice A and choice D are false.

====================================================

Explanation:

An included angle is one between two given sides. Think of the angle sandwiched in between.

For choice A, the included angle is actually angle R. This is because the "R" shows up in QR and RP. This is the overlapping or shared letter between the segments. So we can see that statement A is false.

In contrast, choice B and choice C are true. Choice B is true because of what I mentioned in the previous paragraph. Choice C is true because Q shows up in both QR and PQ. It might help to draw out the diagram to see why this works.

------------------------

For choices D through F, we'll just take this logic in reverse.

The segment RP has angles R and P involved. In other words, segment RP is between angles R and P. We can rule out choice D since choice E is true.

Choice F is true as well because segment QP involves angles Q and P. No diagrams are needed but it might help to draw out the diagram to see what's going on.

------------------------

Overall, we have four true statements and they are choices B, C, E and F.

Rotating the figure about the y-axis results in the creation of a cylindrical figure of radius 2 units and 6 units tall.

Answer:

1

Step-by-step explanation:

the degree of 3x-6 is 1

Answer:

-4 and 1

Step-by-step explanation:

-4 times 1 equals -4 and then -4 plus 1 equals 3

The two numbers that satisfy the given conditions are 4 and -1. They multiply to -4 and add up to 3.

To find two numbers that satisfy the given conditions, we can set up a system of equations.

Let's assume the two numbers are represented by 'x' and 'y'. We know that their product is -4 and their sum is 3, so we can write the following equations:

xy = -4 (Equation 1)

x + y = 3 (Equation 2)

To solve this system of equations, we can use the substitution or elimination method. Let's use the substitution method.

From Equation 2, we can express y in terms of x: y = 3 - x.

Substituting this into Equation 1, we get:

x(3 - x) = -4

Expanding and rearranging the equation, we have:

3x - x² = -4

Rearranging again, we get a quadratic equation:

x² - 3x - 4 = 0

We can factor this equation:

(x - 4)(x + 1) = 0

Setting each factor to zero, we find two possible solutions for x:

x - 4 = 0 --> x = 4

x + 1 = 0 --> x = -1

Now, we can substitute these values of x back into Equation 2 to find the corresponding values of y:

For x = 4: y = 3 - 4 = -1

For x = -1: y = 3 - (-1) = 4

Therefore, the two numbers that satisfy the given conditions are 4 and -1. They multiply to -4 and add up to 3.

To learn more about the system of equations;

brainly.com/question/13729904

#SPJ6

Taking point (0,-2) of graph one and replacing in the equation;

2x+3y=6

2(0)+3(-2)=6

-6=6

So graph isn't the required graph.

Taking point (0,2) of graph 2;

2x+3y=6

2(0)+3(2)=6

6=6

So, graph 2 is the required graph.

Answer:

nice

Step-by-step explanation:

Answer:

When x =4 y=12

Step-by-step explanation:

Inverse variation is

xy = k  where k is a constant

y =3 and x = 16

3*16 = k

48 = k

The equation is

xy = 48

Now let x = 4

4y = 48

Divide each side by 4

4y/4 = 48/4

y = 12

When x =4 y=12

Answer:

6

Step-by-step explanation:

4 x 6=24 9 x 2=18

24-18=6

Answer:

y = -2/3 x + 6

Step-by-step explanation:

Using the coordinates (1, 16/3) and (3,4)

Slope m = 4-16/3/3-1

Slope m = -4/3 * 1/2

Slope m = -2/3

For the y-intercept

Substitute (3,4) and m = -2/3 into y  =mx+b

4 = -2/3(3) + b

4 = -2 + b

b = 4 + 2

b = 6

Get the required equaton;

Recall that y = mx+b

y = -2/3 x + 6

The given triangle is a Right angled triangle,

By applying trigonometry :

[tex] \boxed{\tan( \theta) = \frac{opposite \: \: side}{adjacent \: \: side} }[/tex]

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

The answer is 1.829365

Step-by-step explanation:

3/4+6/7+2/9=1.83

Answer:

461/252

Step-by-step explanation:

See the steps below:)

Step-by-step explanation:

It helps to draw a picture but also write what you are given

The square measures 7ft on all sides

youre paying by the square foot

to get square feet, use L x W

so 7ft x 7ft = 49 ft^2

so if we are charged $7 for 1 ft^2, then you add $7, 49 times

So youd write and solve

7 + 7 + 7 + 7 +... + 7 = $7 x 49ft^2

Answer:

2 bicycles

Step-by-step explanation:

as there were 5 bicycles and tricycles

now,

total no.of wheels = 16

2x + 3(6 - x) = 16

2x + 18 - 3x= 16

2 - x = 0

2 = x

therefore, there are 2 bicycles.

Answer:

40

Step-by-step explanation:

hope this helps

Answer:

Use MATH.WAY, it will help with any math problem

Step-by-step explanation:

Answer:

D) line graph

Step-by-step explanation:

There is two lines on the graph that have points on each which makes this graph a line graph.

Hope this helped :)

Answer:

its a line graph

Step-by-step explanation:

is a graph that uses lines to connect individual data points displaying quantitative values over a specified time interval.

Answer:

x=1/4

Step-by-step explanation:

1/4+3/4=1 whole

Answer:

[tex]x = \frac{1}{4}[/tex]

Step-by-step explanation:

Step 1: Subtract [tex]\frac{3}{4}[/tex] from 1

[tex]1 - \frac{3}{4}\\\\= \frac{1}{4}[/tex]

Therefore, the point could be [tex]\frac{1}{4}[/tex]

Answer:

it's 3 by 10

just take l.c.m