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2 months ago

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2 months ago

We know that

[surface area of the cone]=pi*r²+pi*r*l

where

r is the radius

l is the slant height

l²=h²+r²

h=43 m

r=14/2---> 7 m

l²=43²+7²----> l²=1898--------> l=43.57 m

[surface area of the cone]=pi*7²+pi*7*43.57----> 1111.53 m²----> 1112 m²

**the answer is the option **

** ****B. 1,112 square meters**

[surface area of the cone]=pi*r²+pi*r*l

where

r is the radius

l is the slant height

l²=h²+r²

h=43 m

r=14/2---> 7 m

l²=43²+7²----> l²=1898--------> l=43.57 m

[surface area of the cone]=pi*7²+pi*7*43.57----> 1111.53 m²----> 1112 m²

Question

Beatrice buys a dishwasher for her new house. The price of the dishwasher is D dollars, and she pays an additional 2% tax. Match the expressions to their correct meanings for Beatrice.

Solution 1

The total amount of $ that this person will have to pay for the dishwasher is given by 1.02D (dollars).

Question

Step-by-step solution for: (√2+√10)^2

Solution 1

Note: √a * √a = a

√a * √b = √ab

(√2 + √10)² = (√2 + √10)(√2 + √10)

= √2(√2 + √10) + √10(√2 + √10)

= √2*√2 + √2*√10 + √10*√2 + √10*√10

= 2 + √20 + √20 + 10

= (2 + 10) + (√20 + √20)

= 12 + 2√20

√20 = √(4 *5) = √4 * √5 = 2√5

= 12 + 2√20 = 12 + 2(2√5)

= 12 + 4√5

√a * √b = √ab

(√2 + √10)² = (√2 + √10)(√2 + √10)

= √2(√2 + √10) + √10(√2 + √10)

= √2*√2 + √2*√10 + √10*√2 + √10*√10

= 2 + √20 + √20 + 10

= (2 + 10) + (√20 + √20)

= 12 + 2√20

√20 = √(4 *5) = √4 * √5 = 2√5

= 12 + 2√20 = 12 + 2(2√5)

= 12 + 4√5

Question

If 2x2 – 13x + 20 = (2x – 5)(x – 4), which equation(s) should be solved to find the roots of 2x2 – 13x + 20 = 0? Check all that apply. A. 2x – 5 = 0
B. x + 4 = 0
C. 2x – 5 = x – 4
D. 2x + 5 = 0
E. x – 4 = 0

Solution 1

Hence, the correct options are:

**A. 2x-5 = 0**

**and E. x-4 = 0**

We are given a factorization of a polynomial function as:

The roots of the equation are the possible value of x such that the polynomial function is zero at that point.

i.e. we have to find x such that:

which could also be written as:

Hence, the equation that satisfy this equation is:

**Hence, the correct options are:**

**A. 2x-5 = 0**

**and E. x-4 = 0**

Solution 2

2x^2 – 13x + 20

= (2x – 5)(x – 4)

to find roots of 0 then (2x – 5)(x – 4) = 0

then (2x – 5) = 0 and (x – 4) = 0

answer

A. 2x – 5 = 0

E. x – 4 = 0

= (2x – 5)(x – 4)

to find roots of 0 then (2x – 5)(x – 4) = 0

then (2x – 5) = 0 and (x – 4) = 0

answer

A. 2x – 5 = 0

E. x – 4 = 0

Question

Find the zeros of the function by using the Quadratic Formula:
f(x) = X^2 +7x + 9

Solution 1

X= x(2)+7x+9×=

2(x)+7x+9x=

9x+9x=

×=18

2(x)+7x+9x=

9x+9x=

×=18

Question

In his new living room, Kirk installed carpeting on 1/2 of the floor and tile on another 1/4 of the floor. What fraction of the floor is now covered by either carpet or tile?

Solution 1

To find the total amount of floor covered add the amount of carpeting and tiling together. So 1/2 = 2/4, then 1/4 + 2/4 = (1 + 2) / 4 = 3/4. 3/4 of Captain Kirk's floor is covered.

Question

A holding pen for cattle must be square and have a diagonal length of 84 84 meters. a. find the length of a side of the pen.
b. find the area of the pen.

Solution 1

We know that

Applying the Pythagoras Theorem

c²=a²+b²

in a square

a=b

c is the diagonal-----> 84 m

c²=2a²--------> a²=c²/2-----> a²=84²/2-----> a²=3528-----------> a=√3528 m

the answer part a) is

√3528 m or 59.40 m

the area of the pen is a²------> 3528 m²

**the answer Part b) is **

**3528 m²**

Applying the Pythagoras Theorem

c²=a²+b²

in a square

a=b

c is the diagonal-----> 84 m

c²=2a²--------> a²=c²/2-----> a²=84²/2-----> a²=3528-----------> a=√3528 m

the answer part a) is

√3528 m or 59.40 m

the area of the pen is a²------> 3528 m²

Question

Sara loves to go hiking. This week she hiked 3 miles on Monday, 4 miles on Tuesday, and 3 miles on Thursday. Last week Sara hiked 8 miles. How many more miles did Sara hike this week than last week?*

Solution 1

This week, the total = 3 + 4 + 3 = 10 miles

Last week = 8 miles.

The number more = 10 - 8 = 2 miles.

2 miles more.

Last week = 8 miles.

The number more = 10 - 8 = 2 miles.

2 miles more.

Question

Use the intercept form to find the equation of the line with the given intercepts. the intercept form of the equation of a line with intercepts (a, 0) and (0, b.is

Solution 1

Assuming that the "given intercepts" are (a,0) and (0,b), the equation of the line thru these 2 pts. is easily found thru use of the point-slope formula:

b-0

m = -------- = -b/a

0-a

Then y-0 = (-b/a)(x-a), or y = (-b/a)(x-a) (answer)

b-0

m = -------- = -b/a

0-a

Then y-0 = (-b/a)(x-a), or y = (-b/a)(x-a) (answer)

Question

donovan bought 5 1/2 pounds of flour for $ 8.25. How much did the flour cost per pound? Give your answer in the correct dollar form.

Solution 1

Unit price per pound = $ 8.25 / 5.5 = $1.50

answer

the flour cost $ 1.50 per pound

answer

the flour cost $ 1.50 per pound

Solution 2

We want the unit rate: cost of flour per pound.

$8.25

--------- = $1.50/lb

5.5 lb

$8.25

--------- = $1.50/lb

5.5 lb

Question

A price of a new car was £12500
It was reduced to £11625
Work out the percentage reduction

Solution 1

£12500 - £11625 = £875

£875 / £12500 = 0.07 = 7%

answer

7%

£875 / £12500 = 0.07 = 7%

answer

7%

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