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**Answer:**

**Circumference = 69.14cm****Area = 380.29cm²**

**Step-by-step explanation:**

**Circumference. **

Circumference of a circle is calculated by the formula:

= Pie * diameter

= π * diameter

= 22/7 * 22

**= 69.14 cm **

**Area **

Area of circle:

= Pie * radius ²

Radius = diameter/2

= 22/2

= 11 cm

Area = 22/7 * 11²

= 22/7 * 121

**= 380.29 cm²**

Question

Which problem situation can be represented by the equation below? 150 – 3x = 60

Solution 1

X is 30 because we can minus 60on both sides and add 3x on both sides to find the answer

Solution 2

**Answer:**

C, and x=30

Karen had a gift card for $150. She bought 3 gifts for her sisters. The gifts cost the same amount, x. After paying for the gifts, her gift card had a balance of $60.

**Step-by-step explanation:**

Question

What is a ratio that compares two quantities measured in different units called

Solution 1

**Answer:**

**Rate**

**Step-by-step explanation:**

The rate is the ratio that makes the comparision between two quantities that are different to each and contains diffeent kind of measuring units

It also provide the information like feet per second, miles per hour, etc

So the ratio that makes the comparision between the different kind of units is known as rate

Question

Joseph finished his homework at 3:47pm. Round the time to the nearest ten minutes.

Solution 1

It would be 3:5 because 47 round up to 3:50

Question

Which algebraic expression is equivalent to the expression below? (6x + 13) + 6

Solution 1

**Answer:**

6x+19

**Step-by-step explanation:**

The parentheses do nothing here to stop you from adding - since every term in here is only being added, there is no reason to worry about the parentheses. Simply combine like terms (13 + 6) to achieve 6x + 19.

Question

In which number does the 9 represent 1/10 of the value that it represents in 92300

Solution 1

923000 is the **number **in which 9 **represents **1/10th of its **value **in 92300.

If an **event** can occur in m **different **ways and if following it, a **second event **can occur in n **different **ways, then the two **events **in **succession **can occur in m × n **different **ways.

we need to find the **number **in which 9 **represents **1/10th of its **value **in 92300.

here, this **number **would be 10 times **larger**.

**Multiply **92300 by 10

= 92300 x 10

= 923000.

Learn more about **multiplications**;

#SPJ2

Solution 2

**Answer:**

923000.

**Step-by-step explanation:**

You want to find the number in which 9 represents 1/10th of its value in 92300. Naturally, this number would be 10 times larger. Multiply 92300 by 10 to get 923000.

Question

Graph y−5=−2/3(x+9).
plot two different points. please show work i am very lost. thank you

Solution 1

Y -:5 = 2/3x + 6 because 6 is 2/3 of 9

add 5 to both sides

y - 5 +:5 = 2/3x + 6 + 5

y = 2/3x + 11

the y intersept is 11 or (0 , 11) when x is 0

when x is 3

y = 2/3 (3) + 11 or 2 + 11 = 13

so a 2nd point could be (3 , 13)

add 5 to both sides

y - 5 +:5 = 2/3x + 6 + 5

y = 2/3x + 11

the y intersept is 11 or (0 , 11) when x is 0

when x is 3

y = 2/3 (3) + 11 or 2 + 11 = 13

so a 2nd point could be (3 , 13)

Question

Verify the trig identity: tan^2 theta + cot^2 theta / csc^2 theta = sec^2 theta

Solution 1

**Answer:**

See proof below

Step-by-step explanation:

In trigonometry identity

tan^2 theta = sin^2 theta /cos^2 theta

cot^2 theta = cos^2 theta/sin^2 theta

csc^2 theta = 1/sin^2 theta

Substitute into the expression

(sin^2 theta /cos^2 theta )+ (cos^2 theta/sin^2 theta)/1/sin^2 theta

= [sin^4theta + cos^4theta/cos^2 theta sin^2 theta]÷(1/sin^2 theta)

= 1/cos^2 theta sin^2 theta÷(1/sin^2 theta)

= 1/cos^2 theta sin^2 theta * sin^2 theta/1

= 1/cos^2theta

= sec^2theta (Proved!)

Question

A color printer prints 26 pages in 11 minutes how many pages does it print per minute

Solution 1

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Question

What equation describes the circle that is centered at (8, 3) and has a radius of 9

Solution 1

**Answer:**

**Step-by-step explanation:**

The general equation of a circle is expressed as;

(x-a)²+(y-b)² = r² where;

(a, b) is the centre of the circle

r is the radius

Given the centre (8, 3) and the radius of 9, the equation of the circle will be;

(x-a)²+(y-b)² = r²

(x-8)²+(y-3)² = 9²

(x-8)²+(y-3)² = 81

**hence the required equation is (x-8)²+(y-3)² = 81**

Question

What is the final elevation if a butterfly starts at 20 m and changes negative 16 m

Solution 1

Answer:

4 meters

Step-by-step explanation:

Given that :

Initial elevation of butterfly = 20 meter

Change in elevation from initial height = negative 16 m = - 16 meter

Final elevation can be obtained by taking the sum of initial elevation and the change in elevation

(20 m + (- 16 m))

(20 m - 16 m)

= 4 meters

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