Mathematics Middle School

Given: a = 640, A = 70°, B = 52° in triangle ABC ; find b. Round answers to the nearest whole number

Answers

Answer 1

Answer: 537

Step-by-step explanation:

Given: a = 640 A =70° B =52°

Whenever two angles and one side of a triangle is given, we can always use the sine formular to find the other side

Using the sine formula;

sin A / a = sin B /b

sin70° / 640 = sin 52° / b

cross multiply

bsin70° = 640sin52°

To get b, we divide bothside by

sin 70°

b = 640sin52° / sin 70°

b = 504. 327 / sin70°

b = 536. 693

b = 537 to the nearest whole number

Related Questions

1. You have 60 in. of molding to use as a frame around a picture you are painting. The area of the painting is giving by the function y = 30x - x^2 where x is the width in inches. What width gives the maximum area for the painting? What is the maximum area?

2. You are trying to dunk a basketball. You need to jump 2.5 ft in the air in order to dunk the ball. The height that your feet are above the ground is given by the function h = -16t^2 + 12t. What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball?

I need a lot of help with these problems. Please answer them to the best of your capabilities. I'M GOING INSANE!!! Thanks so much!

Answers

1) [tex]y = 30x - x^2 y = -x^2+30x (y = ax^2+b)[/tex]

[tex]x = -b/2a = -30/2(-1) = 15[/tex]

[tex]y = -(15)^2+20(15) y = -225+450 y = 225[/tex]

So, 15 as the width would give us the maximum area for the painting.
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2) The maximum height your feet will be above the ground is 2.25 ft.
No, you wouldn't be able to dunk the ball because the maximum height you can jump is 2.25, but you need to jump 2.5 ft to dunk.

solve the equation 30t - 4 = 1 for t

Answers

[tex]30t - 4 = 1 \\ 30t = 5 \\ t = \frac{5}{30} \\ t = \frac{1}{6} [/tex]

Answer : t = 1/6, or in decimal form, 0.17

Hope this helps. - M

Answer:

A) 1/6

Step-by-step explanation:

Is how many countries are in North America a statistical question

Answers

yes, because you could collect data to answer the question.

The question, "How many countries are in North America" is not a statistical question.

What are statistical Questions?

Statistical questions are defined as the questions which are answered by collecting data from many which will probably vary.

The given question is,

How many countries are in North America"How many countries are in North America.

Although the answers to this from the students may vary because they don't know, the answer to this question is a constant.

This is not something which varies.

Hence this is not a statistical question.

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Name the point with the given coordinates (4 -2)

Answers

The point with the given coordinates (4 -2) is h.

What are the coordinates of midpoint of the line segment AB?

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2}[/tex]

and

[tex]y = \dfrac{q+n}{2}[/tex]

We are given that;

The graph of four points

Now,

One point is k with (-4,2)

One point is g with (2,4)

One point is h with (4,-2)

One point is j with (-2,-4)

Therefore, by the midpoint the answer will be h(4,-2).

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What is the weight ( in grams) of a liquid that exactly fills a 163.5 millimeter container if the density of the liquid is 0.492 grams/millimeter?

Answers

Comment
The formula for density is [tex] \text{density} = \frac{m}{V} [/tex]

Givens
V = 163.5 mL
d = 0.492 grams / mL

Solution
m = d * V The formula has been rearranged.
m = 0.492 * 163.5
m = 80.442 grams. <<<<< Answer

Could someone please help me on this

Answers

The dependent variable would be b (affected by the change of n) and the independent variable would be n (affects b). The equation would be
b = 12n.

What is 4x-2x answer asap

Answers

4x - 2x is 2x. If we have 4 x's, and we take away 2 x's, we have 2 x's left. I hope this helps!

Here is an explanation:
[tex]4x-2x = 4(x) - 2(x) = (4-2)(x) = 2(x) = 2x. [/tex]
You could also think of this as:
( x + x + x + x ) - ( x + x ) = x + x + x + x - x - x

Dakota built a wall with bricks like this one:

Look at Dakota’s wall:

What is the length of the side of the brick labeled a? ____________

What is the length of the side of the brick labeled b? _____________

What is the total height of the wall? ____________

What is the total length of the wall? __________

Answers

I don't know if i'm right but I think the first question is 5 inches, the second question is 8 inches, the third question is 24 inches because there are three blocks and each are 8 inches so 8 x 3 = 24, and the last question is 45 inches because there are 9 bricks each 5 inches on the top so 9 x 5 = 45. (again I am not sure if this is correct but it is what I think)

Please help me.I need this answered

Answers

For the first one each side would be 2.05. Because 2.05 x4 = 8.2. I hope this helps.

1. 8.2•8.2= 67.24.
2. 0.5(9•11)= 49.5.
3. pi•(17/12)^2= about 289/144pi.
4. 3.75•7.6= 28.5.
5. (42•20)+(10•22)= 840+220= 1,060.
6. 0.5(10.667•3.2)+(10.667•15)= 170.667+160= 330 and two thirds.

Which group of numbers is ordered from least to greatest

Answers

A the answer is A yes it is A

Use unit multipliers to convert 123 pounds per mile to ounces per centimeter. There are 5,280 feet in 1 mile. There are 16 ounces in 1 pound. There are approximately 2.54 cm in 1 inch. Enter your answer as a decimal rounded to the nearest hundredth. Just enter the number.

Answers

A unit multiplier is a conversion factor of value 1 that we can use to convert quantities.
We want to convert 123 pounds per mile to ounces per centimeter.
First, we are going to express the quantity to convert as a fraction:
123 pounds per mile=[tex]123 \frac{pounds}{mile} [/tex]

Next, we are going to find our multipliers:
- We know for our problem that there are 5,280 feet in 1 mile, so our first multiplier will be: [tex] \frac{1mile}{5280ft} [/tex]
- We also know that there are 16 ounces in 1 pound, so our second multiplier will be: [tex] \frac{16ounces}{1pound} [/tex]
- We know that there are 12 inches in 1 foot, so our third multiplier will be: [tex] \frac{1ft}{12in} [/tex]
- We know that there are approximately 2.54 cm in 1 inch, so our fourth multiplier will be: [tex] \frac{1in}{2.54cm} [/tex]

Now we can put all our multipliers together:
[tex]123 \frac{pounds}{mile} * \frac{1mile}{5280ft}*\frac{16ounces}{1pound}* \frac{1ft}{12in}*\frac{1in}{2.54cm}=0.01 \frac{ounces}{cm} [/tex]

We can conclude that the answer is 0.01

graph
[tex]y = |x| - 1[/tex]

Answers

Graph y = x (black)

(0; 0); (2; 2)

Symmetry about the x-axis (green)

Translation down 1 unit (red)

i need alot of help in math

Answers

Plug in the dimensions to the formula given using a handy dandy calculator for both problems.

1. The diameter of the bottom of the cone is 4 so the radius (half that) is 2. Volume = 1/3 * pi * (2)² * 6
= 1/3 * pi * 4 * 6
= 1/3 * pi * 24
= 8 * pi
≈ 25.1327 cm³

2. They give you all you need, the radius.
Volume = 4/3 * pi * (6)³
= 4/3 * pi * 216
= 288 * pi
≈ 904.7787 in³

use the integer values of x from -3 to 13 to graph the equation y= -x

Answers

y = -x

This is an equation of the straight line, therefore we need only two points to the graph.

for x = -3 we have y = -(-3) = 3 → (-3; 3)

for x = 0 we h→ve y = -0 = 0 → (0; 0)

The graph in the attachment

a local parts shop buys a machine that costs $500,000. its value depreciates exponentially each year by 10%. what is the machines value after 5 years? round to nearest integer

Answers

Hello!

Answer:

$295.295

Explanation:

Of the statement, we have that the price of the machine decreased 10% every year exponentially, so in the first year it real value drops to 90% of the costs. For 5 years, It can be expressed and simplified by the following equation:

We can't use that the percent drop as a percent itself, so we are going to divide 90% by 100%, and it will give us an entire number.

[tex]\frac{90}{100}=0,9 \\ \\ Value=Costs.(0.9)^{years}[/tex]

By substituting we have:

[tex]Value=500000.(0.9)^{5}[/tex]

Value: $295.245

Have a nice day!

Write an algebraic expression for the word expression

The sum of 15 and the product of 5 and v

use parentheses

Answers

5(v) + 15

Hope this helps!

Help please........................

Answers

Dilation means multiply. (I don't know why they just don't say it).

You have the right answer. 2.5 * 2.5 = 6.25 Can't beat being right.

Jack or three protein bars for a total of $4.26. Which equation could be used to find the cost c in dollars of each protein bar?

Answers

Jack bought 3 protein bars for $4.26. The individual cost of the protein bars can be determined by the following:

(total cost / quantity bought) = c

$4.26 / 3 = $1.42

The cost of an individual protein bar is $1.42.

Jack bought 3 protein bars for a total of $4.26?

First, set up your equation. I'll let "b" represent the value of each individual bar:

3b = 4.26

Now, divide the total value by the number of bars for the answer:

b = $1.42

Help please! Don’t understand!

Answers

[tex]6+2-(-1)+(-8)=8+1-8=1[/tex]

Hi there! The answer is 1.

[tex]6 + 2 - ( - 1) + ( - 8) = [/tex]
Keep in mind that the sum of a plus and a minus ends up in a minus. So
+ - = -

Keep in mind that the sum of a minus and a minus ends up in a plus.
- - = +

[tex]6 + 2 + 1 - 8 = [/tex]
Now add from left to right.

[tex]8 + 1 - 8 = [/tex]
Add once more

[tex]9 - 8 = [/tex]
Subtract

[tex]1[/tex]
Hence, the answer is 1.
~ Hope this helps you!

one number is 2 larger than another number. the sum of their squares is 100. find the numbers

Answers

x= first number
x+2= second number

x^2 + (x + 2)^2= 100
square the parentheses

x^2 + [(x + 2)(x + 2)]= 100
x^2 + x^2 + 2x + 2x + 4= 100
combine like terms

2x^2 + 4x + 4= 100
subtract 100 from both sides

2x^2 + 4x - 96= 0
factor

2(x−6)(x+8)=0
set each parentheses equal to 0

x-6= 0
x= 6

OR

x+8= 0
x= -8

CHECK:
x^2 + (x + 2)^2= 100
(6)^2 + (6 + 2)^2= 100
36 + (8)^2= 100
36 + 64= 100
100= 100

x^2 + (x + 2)^2= 100
(-8)^2 + (-8 + 2)^2= 100
64 + (-6)^2= 100
64 + 36= 100
100= 100

ANSWER: x= 6 or x= -8

Hope this helps! :)

The numbers are 6 and -8

let

the first number = x

One of the number is 2 larger than another number .Therefore, the second number will be as follows;

x + 2

Sum of there squares will be as follows:

x² + (x + 2)² = 100

Therefore,

x² + x² + 4x + 4 = 100

2x² + 4x + 4 - 100 = 0

2x² + 4x - 96 = 0

x + 2x - 48 = 0

let's find x

x - 6x + 8x - 48 = 0

x(x - 6) + 8(x - 6) = 0

(x - 6)(x + 8) = 0

x -6 = 0 and x + 8 = 0

x = 6 and x = -8

The numbers are 6 and -8.

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A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f x( ) = 20x + 4. What is the range of the function for this situation? Please explain.

Answers

The range of the function would be from 0 to 244.

The range of the function is the possible output values for the function. In this case, it is from zero to the highest possible weight. Since there are 6 pairs of weight plates, we can input 12 for x to get the maximum.

20(12) + 4 = 244

Angle P measures 112 degrees, what are the measures of angle N and O?

Answers

the inside angles of a triangle need to equal 180 degrees
in this triangle the lines NP and OP are identical so the 2 unknown angles would be equal
so the 2 unknown angles would be 180 - 112 = 68 / 2 = 34 each
angle N & O are 34 degrees

The measures of angle N and O are: 34°

How to find the angle of the Isosceles triangle?

We know that Isosceles triangle has two equal sides and we also know that the sum of angles in a triangle is equal to 180 degrees.

Since an Isosceles triangle has two equal sides, we know that the base angles are equal.

We are given the apex angle as 112 degrees. Thus:

2x + 112 = 180

2x = 180 - 112

2x = 68

x = 34

Thus:

The measures of angle N and O are 34°

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The function f(x) is given by the set of ordered pairs.
{(1,0), (-10,2), (0,6), (3,17), (-2,-1)}
which equation is true?
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10

Answers

Answer: f(0) = 6.

Explanation:

Ther ordered pairs are: (x,y) or (x, f(x) )

So, (1,0) means that f(1) = 0 which denies the fourth choice.

(-10,2) means that f(-10) = 2 which denies the first choice

(0,6) means that f(0) = 6, which is the third choice. So, that is the true equation.

Answer: the correct option is (C) f(0) = 6.

Step-by-step explanation: We are given the function f(x) by the following set of ordered pairs :

{(1,0), (-10,2), (0,6), (3,17), (-2,-1)} .

We are to select the TRUE equation.

We know that

in the ordered pairs, the first element stands for the independent variable x and the second element stands for the dependent variable f(x).

So, the equations that comes from the given ordered pairs are

[tex]f(1)=0,~~f(-10)=2,~~f(0)=6,~~f(3)=17,~~f(-2)=-1.[/tex]

Thus, the only true equation is f(0) = 6.

Option (C) is CORRECT.

50 PIONTS AND BRANLIEST PWEASE HELP
The product of two rational numbers is positive. What can you conclude about the factors? Express your answer in two or more complete sentences.

Answers

If the product of two rational numbers is positive, then the two factors are either both positive rational numbers or both negative rational numbers. A positive times a positive makes a positive and a negative times a negative makes a negative.

plz make ,....................

Answers

we know that
the length of rectangle is 5*(x+6) cm
the breadth of rectangle is (2x+6) cm
perimeter=192 cm
perimeter of a rectangle=2*[length+breadth]
so
192=2*[5*(x+6)+(2x+6)]----> 192/2=[5x+30+2x+6]---> 96=7x+36
7x=96-36-----> 7x=60--------> x=60/7 cm

the answer is
x=60/7 cm or 8.57 cm

harry buys a sofa set that costs$2,000.he pays for it with 12 month installments. how much will he pay each month? if he has to pay5%in interest how much will he pay in all for the sofa set?

Answers

Harry's monthly payment for the sofa set is approximately $175, which includes principal and simple interest. The estimated total payment amount after 12 months is $2100.

Harry buys a sofa set that costs $2000 and chooses to pay for it in 12 monthly installments. First, to find out the monthly payment without interest, we divide the total cost by the number of installments. So, $2000 divided by 12 months equals to $166.67.

However, there is an interest of 5% on the outstanding amount. To calculate the total interest on an installment plan, we typically would need to calculate the interest on the reducing balance each month; however, for simplicity, let's assume it's 5% of 2000 for the year, which is $100 (5/100 * $2000). Divided by 12 months, that's about $8.33 in interest per month, giving a total monthly payment of $175 ($166.67 + $8.33).

This simplistic approach gives us a rough estimate, and the actual amount could be slightly different due to the reducing balance method used by most financing options. Assuming the simple interest calculation, Harry will pay $175 per month, and in all, he will pay an estimated total of $2100 ($175 * 12) for the sofa set.

write the function for the graph below

Answers

This is a function y=√x that was moved 2 units to the right.
y=√(x-2)

Find the product of two numbers whose sum is 11 and difference is 3.

Answers

The two numbers are 7 and 4

Let the first number = x

let the second number = y

The sum of the numbers is 11, in algebra form x + y = 11

The difference of the two numbers is 3, in algebra form, x - y = 3

To obtain the two unknown numbers, we solve the two equations;

from the first equation, x = 11 - y

substitute the value of x into the last equation;

(11 - y) - y = 3

11 - y - y = 3

11 - 2y = 3

2y = 11 - 3

2y = 8

y = 4

The value of x = 11 - 4 = 7

Thus, the two numbers are 7 and 4

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Final answer:

To find the product of two numbers with a sum of 11 and a difference of 3, solve the system of equations to find the numbers (7 and 4) and multiply them to get the product, which is 28.

Explanation:

To find the product of two numbers whose sum is 11 and whose difference is 3, we can let the two numbers be x and y, with x being the larger number. Therefore, we have two equations from the given information: x + y = 11 and x - y = 3.

Adding these two equations, we get:

2x = 14x = 7

Using x = 7 in the first equation, we have:

7 + y = 11y = 4

Now that we have both numbers, we can find their product:

Product = x * yProduct = 7 * 4Product = 28

The product of the two numbers is 28.

Two constructors working together finished building a room in 6 days. How long would it take for each constructor to build the room by himself, if it is known that one of them would require 5 more days than the other?

Answers

If the first constructor works alone for one day he will do (1/x) part of work.
If the second constructor works alone for one day he will do (1/(x+5)) part of work.
If they work together, they will do for one day

[tex] \frac{1}{x} + \frac{1}{x+5} part of work. Also, if they work together, for one day they will do 1/6 part of work. So, [/tex]
[tex] \frac{1}{x} + \frac{1}{x+5} = \frac{1}{6} , \frac{x+5+x}{x(x+5)} = \frac{1}{6} , \frac{2x+5}{ x^{2} +5x} = \frac{1}{6} , 6(2x+5)=x^{2} + 5x 12x+30 =x^{2}+5x x^{2} -7x-30=0 (x-10)(x+3)=0 x_{1}= 10, x_{2}=-3 For our problem we can use only positive value, x=10 days will work the first worker. The second worker will work x+5=10+5= 15 days. First worker alone will work 10 days, second worker alone will work 15 days. Check, (1/10)+(1/15)=(1/6) (3+2)/30=(1/6) 1/6=1/6 True [/tex]

A can build the room by himself in 10 days, and B can build the room by himself in 15 days.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's call the faster constructor "A" and the slower constructor "B".

We know that B takes 5 more days than A to complete the job.

Let's call the number of days it takes A to build the room "x".

Then the number of days it takes B to build the room is "x+5".

Now,

We also know that if they work together, they can finish the room in 6 days.

Let's call the fraction of the job that A can do in one day "a"

(which means that B can do "a - 1/6" of the job in one day).

We can use the following equation to solve for "a":

1 = (a + a - 1/6) x 6

Simplifying this equation, we get:

1 = (2a - 1/6) x 6

1 = 12a - 1

12a = 2

a = 1/6

So A can do 1/6 of the job in one day.

We can use this information to solve for "x" and "x+5":

1/x + (1/(x+5)) = 1/6

Multiplying both sides by the least common multiple of the denominators (6x (x+5) ), we get:

6 (x+5) + 6x = x (x+5)

Expanding and simplifying, we get:

x² - 7x - 30 = 0

Solving for x using the quadratic formula, we get:

x = 10 or x = -3

Since x has to be a positive number (because it represents the number of days it takes A to build the room), we can ignore the negative solution.

Now,

It takes A 10 days to build the room, and it takes B 15 days to build the room (since B takes 5 more days than A).

Therefore,

A can build the room by himself in 10 days, and B can build the room by himself in 15 days.

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A company says that the probability of finding an all-star card in a game pack is 12.5%. A student wants to determine the probability that, if he buys 6 game packs, 2 or more will have an all-star card.

To do this, he uses a random number table to pick 6 numbers from 1 to 8. He lets 1 represent a pack with an all-star card and 2 through 8 represent a pack without an all-star card. He repeats this for a total of 15 trials. The results are shown in the table.

561673 366468 314255 361362 838443 126285 257231 768551 652585 468113 123711 322764 487626 783134 384664

Select from the drop-down menus to correctly complete each statement.

To estimate the probability that 2 or more out of 6 packs will have an all-star card, the student must count the number of trials with BOX RIGHT HERE and divide by the number of trials.

This gives an estimated probability of about . BOX RIGHT HERE

PLEASE I NEED THIS ANSWERED I HOPE ITS CLEAR ENOUGH.

Answers

Answer:

the first box is "two or more 1s"

the second box is "0.13"

Step-by-step explanation: Im a K12 Student

The probability that 2 or more out of 6 packs will have an all-star card is given by the equation P = 0.1333

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that 2 or more out of 6 packs will have an all-star card be P

The probability of finding an all-star card in a game pack is 12.5 %

The student has pointed that 1 represent a pack with an all-star card and 2 through 8 represent a pack without an all-star card

The test results are given in set A = { 561673, 366468, 314255, 361362, 838443, 126285, 257231, 768551, 652585, 468113, 123711, 322764, 487626, 783134, 384664 }

The number of trials that represent that 2 or more out of 6 packs have an all-star are = { 468113 , 123711 }

Therefore , the probability is given as

Probability that 2 or more out of 6 packs will have an all-star card P = 2/15

On simplifying the equation , we get

Probability that 2 or more out of 6 packs will have an all-star card P = 0.133

Hence , the probability is 13.33 %

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