MATHEMATICS MIDDLE SCHOOL

If triangle abc, a=3, b=5 and c=7. Find the measure of angle b

Answers

Answer 1
Answer:

Answer:

b = 38.22

Step-by-step explanation:

In the given triangle ABC, a = 3, b = 5 and c = 7 is given.

We have to find the measure of angle b.

To get the measure of any angle we will apply cosine rule in the triangle.

b² = a² + c² - 2ac(cosb)

5² = 3² + 7² - 2×3×7×cosb

25 = 9 + 49 - 42×cosb

25 = 58 - 42cosb

-42cosb = 25 - 58 = -33

cosb = (33)/(42)

cosb = 0.7856

b= cos^(-1)(0.7856)

b = 38.22

b = 38.22 is the correct answer.
Answer 2
Answer:

Answer:

β = arccos((a^2 + c^2 - b^2)/(2·a·c))

β = arccos((3^2 + 7^2 - 5^2)/(2·3·7)) = 38.21°

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Determine whether each pair of triangles is similar. justify your answer​

Answers

Yes the two pairs of triangles are similar. They both have the same measurements. The only difference is that one triangle is flipped upside down

Find the value of one unit of the bar model. 96

Answers

The value one unit of the bar model is 12

Step-by-step explanation:

The bar is divided into 8 units in the diagram (not available in this question)

We need to find the value of each unit

If x is value of 1 bar,

8x = 96

x = 96/8

So, x = 12

Hence the value one unit of the bar model is 12

Explain the properties of exponents with examples of your own

Answers

This is about the properties of exponents.

The properties of exponents are explained below.

Exponents are values which are powers that show how many times we have to multiply a base number by itself.

The examples of properties of exponent are;

  • Product of powers; What this means is that when we multiply two or more bases that have same value, we will retain the bases and just add the exponents together. For Example; 4² × 4³; We will just retain the  base of 7 and add both exponents to get; 4⁵

  • Quotient of Powers; What this means is that when we divide two bases that have same value, we will retain the bases and just subtract the second exponent from the first one. For example; 7⁵ ÷ 7²; We will just retain the  base of 7 and subtract 2 from 5 to get; 7⁽⁵ ⁻ ²⁾ = 7³

  • Power to a Power; What this means is that when we have a power raised to another power, we multiply the exponents together and retain the base number. For example; 4²⁽³⁾; we multiply 3 by 2 to get; 4⁶.

  • Power of a Product; What this means is that when we have two bases multiplying each other in a bracket being raised to a power, we distribute the power to each of the bases. For example (xy)⁴ will give us; x⁴y⁴

  • Power of a quotient; What this means is that when we have two bases dividing each other in a bracket being raised to a power, we distribute the power to each of the bases. For example (x/y)⁴ will give us; x⁴/y⁴

Read more at; brainly.com/question/19204433
This is an example of the quotient of powers property and tells us that when you divide powers with the same base you just have to subtract the exponents. When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1.

How you be a very good maths improver

Answers

In order to improve in your math skills you have to study.
I know from experience.
You can get a tutor like I did. Some help some dont so choose wisely.
You should print out worksheets from online, if you dont have a printer just copy the question onto a piece of paper. 
STUDY!
Everyday when you come home from school, review what you have done during math class so if you forgot some of it you refresh your mind. Do the same thing before you go to sleep.
Hope I helped!
Study by finding online games and printing out worksheets. Ask your parents or guardian to quiz you and MAKE FLASHCARDS! It helps so much. When you have a spare 5 minutes pull them out and study. Take extra notes in class than your teacher wants you to and rewrite them and highlight them. Find workbooks around your house. Ask your parents/guardian to make a math test for you or just print one out. Don't stress yourself with math, take a 10 minute break before doing more every 30 minutes. I used to HATE MATH but now it's ok because I do these things. MATH IS FUN!!!!

Ali went to the store to buy vegetables. He bought 16 ounces of potatoes, 1.5 of onions, 4 ounces of celery, 1 pound of tomatoes , and 4 ounces of garlic. Part a. What was the total weight of the vegetables in pounds?
Part b. the items were packed in two bags. The first bag contained the potatoes and onions, and the second bag contained the remaining items. How many ounces do the first bag weigh? How many pounds did the second bag weigh ?
Part c. Which bag was heavier? By how much?

Answers

a. 2.537 pounds
b. 17.5 ounces 1.50 pounds
c. bag 1 was heavier by 0.40625 pounds

Verify 2+2cot^2x=2cotxsecxcscx

Answers

2+2\cot^2x=2\cot x\sec x\csc x\n\nL=2(1+\cot^2x)=2\left(1+(\cos^2x)/(\sin^2x)\right)=2\left((\sin^2x)/(\sin^2x)+(\cos^2x)/(\sin^2x)\right)\n\n=2\left((\sin^2x+\cos^2x)/(\sin^2x)\right)=2\left((1)/(\sin^2x)\right)=(2)/(\sin^2x)\n\nR=2\left((\cos x)/(\sin x)\right)\left((1)/(\cos x)\right)\left((1)/(\sin x)\right)=2\left((1)/(\sin x)\right)\left((1)/(1)\right)\left((1)/(\sin x)\right)\n\n=2\left((1)/(\sin^2x)\right)=(2)/(\sin^2x)

\boxed{L=R}

Used:\n\n\cot x=(\cos x)/(\sin x)\n\n\sin^2x+\cos^2x=1\n\n\sec x=(1)/(\cos x)\n\n\csc x=(1)/(\sin x)
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