Set up a linear equation(s) that will help you to find a solution to the following problem: One angle of a triangle is twice as large as another angle. The measure of the third angle is 20 more than the measure of the smallest angle. Find the measure of each angle of the triangle.

Answers

Answer 1

Answer: remember
all angles add to 180

x+y+z=180
one is 2 times as another
x=2y
measure of 3rd angle (z) is 20 more than smalllest
since y has to be doubled to get x, y is smallest
z is 20 more than y
z=20+y

we have
x=2y
z=20+y
sub those
x+y+z=180
2y+y+20+y=180
4y+20=180
minus 20 both sides
4y=160
divide 4
y=40
sub back
x=2y
x=2(40)
x=80
z=20+y
z=20+40
z=60

the angles are
80 degrees, 40 degrees, 60 degrees

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5.4 5.400 less greater

Answers

5.4 is equals to 5.400

I need help with all of these questions can you help pls

Answers

For 3) 6/10 times 18
6/10 times 18/1 = 108/10= 54/5 or 272.5

Alana bought 3/8pound of Swiss cheese and 1/4 pounds of American cheese.which pairs of fractions are equivalent to the amounts Alana bought?

Answers

is it any fraction? if so 6/16 and 2/8 are equivalent

Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2

Answers

Answer:

The correct prove will be:

$sin((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14))$ $= (1)/(8)$

Step-by-step explanation:

$sin((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14))$

Multiply and Divide by $2cos((\pi )/(14))$

= $(2sin((\pi )/(14))cos((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14)))/(2cos((\pi )/(14)))$

⇒ Let $(\pi )/(14)$ = Ф and 7Ф = $(\pi )/(2)$

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ ∵cos7Ф = 0

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ ∵sin7Ф = 1

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

$sin((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14))$ $= (1)/(8)$

Keywords: prove, sinФ, cosФ

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A cell phone company collected data if texting speed in words per minute according to time in minutes. explain why a scatter plot is used to represent the data, including the purpose of scatter plots

Answers

Answer:

Scatter plots resembles line graphs in that they are plotted on the x and y axis. The are used because they show how much one variable is affected by another.

Scatter diagrams are important since in statistics they can show the extent of correlation, if any, between the values of observed quantities or a behavior.

Answer:

A scatter plot is defined as a diagram which uses Cartesian coordinates to display values about two variables, one indepedent, the other one dependent.

This diagrams are used in statistics to display information about surveys to a certain sample in a population. The purpose of a scatter plot is to shows if the variables are related, that is, if they have any type of linear correlation between them. If they have linear correlation, then the data is represented by a line.

Now, in this case, the independent variable is time in minutes and the dependent variable is texting. Basically, with this data, the company will be able to stablish the relation between words written in a certain time, that is, the speed of texting actually.

With a scatter plot, they would find the relation that forms the speed of texting. It could be "the more time, more text is written", or "the less time, more text is written".

If we need to establish a possible relation, the most logical would be "the more time, more word are texted".

at a supermarket , Monica paid 3.20 for 2 pounds of apples and 2 pounds of oranges, while Sarah paid 4.40 for 2 pounds of apples and 4 pounds of oranges. At these rates, what is the cost , in dollars, for 3 pounds of oranges?

Answers

The cost , in dollars, for 3 pounds of oranges is 1.8

Solution:

Given that Monica paid 3.20 for 2 pounds of apples and 2 pounds of oranges

Sarah paid 4.40 for 2 pounds of apples and 4 pounds of oranges.

Let the cost of orange per pound = x

Let the cost of apple per pound = y

Therefore, we can frame an equation as follows for Monica and Sarah:

In Monica’s case:

2x + 2y = 3.20

Hence x + y = 1.6 ---- eqn 1

In Sarah’s case:

4x + 2y = 4.40

Hence 2x + y = 2.2

y = 2.2 -2x – eqn 2

Substitute eqn 2 in eqn 1 we get,

x + 2.2 -2x = 1.6

-x = 1.6-2.2 = -0.6

x = 0.6

Substituting the value of “x” in eqn 2 we get the value of “y” as 1

Thus the cost of orange per pound is 0.6

Therefore, cost of 3 pounds of oranges = 3 × 0.6 = 1.8

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