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Keith_Richards [23]
4 years ago
9

Theo made a donation to a charity. His grandfather agreed to add$4.00 to Theo's donation amount and then donate half of the sum.

Theo's grandfather donate b$4.25
Write and solve an equation to the amount of Theo's donation.​
Mathematics
1 answer:
lisov135 [29]4 years ago
6 0

Answer:

The needed equation is:4.25  =( \frac{p+4}{2} )

The amount of Theo's donation  =  $ (4.5)

Step-by-step explanation:

Let us assume the amount of Theo's donation  = $ p

Now, his grandfather added $4 to the donation.

So, the New amount  = Theo's amount  +  Grandfather's share

                                   = $p +  $ 4 = $ (4 +p)

Again, the half of the total amount  = (\frac{4 +p}{2})

So, the amount donated to the charity =  (\frac{4 +p}{2})

But according to the question, amount donated = $4.25

\implies 4.25  =( \frac{p+4}{2} )\\\implies 4.25 \times 2  = p+ 4\\\implies  p +  4  = 8.5\\\implies  p =  8.5 - 4  = 4.5\\\implies p = 4.5

Hence, the amount of Theo's donation  = $ p   = $ (4.5)

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pshichka [43]

The given area of the shape of 57.8·π cm², and length of the slant sides

being a factor of the radius, gives the length of the radius as <u>3.4 cm</u>.

<h3>How can the length of the radius be calculated?</h3>

Given;

Radius of the two cones are equal.

Slant height of one cone = 2 × Radius

Slant height of the other cone = 3 × Radius

Surface area of the shape = 57.8·π cm²

The curved surface area of a cone = π·r·l

Required:

The radius of the cone.

Solution;

Surface areas of the cones are therefore;

π·r × 2·r, and π·r × 3·r

The total surface area is therefore;

π·r × 2·r + π·r × 3·r = 57.8·π

5·r²·π = 57.8·π

Which gives;

r² = 57.8 ÷ 5 = 11.56

r = √(11.56) = 3.4

  • The radius of the cones, r =<u> 3.4 cm</u>

Learn more about finding the surface area of 3-D shapes here:

brainly.com/question/15635229

8 0
2 years ago
7y 12=-4(y-4)<br><br> a.-1 5/11<br> b.4/11<br> c.-11/16<br> d. 2 3/4
otez555 [7]
A. -4/11 would be the correct answer

4 0
3 years ago
Construction viable argument. is 10% of 10% of 100 the same as 20% of 100​
IgorC [24]

Answer:

no

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20% of 100 is 20.

7 0
3 years ago
You are enclosing a rectangular garden with 60 feet of ornamental fencing. the area of the garden is 200 square feet. what are t
Lilit [14]

The perimeter is equal to 60 feet and has the formula:

Perimeter = 2 l + 2 w

60 = 2 l + 2 w

 

The area is equal to 200 square feet and has the formula:

Area = l w

200 = l w

 

Rewriting area in terms of l:

l = 200 / w

 

Combining this with the perimeter formula:

60 = 2 (200 / w) + 2 w

60 = 400 / w + 2 w

Multiplying all by w:

60 w = 400 + 2 w^2

Dividing by 2 and rearranging:

w^2 – 30 w = - 200

Completing the square:

(w – 15)^2 = - 200 + (-15)^2

(w – 15)^2 = 25

w – 15 = ±5

w = 10, 20

 

Hence the dimensions of the garden is 10 feet by 20 feet

5 0
4 years ago
Please answer these two! Thank you so much!!
Gala2k [10]

Answer:

3. y = 1

4. y = 3, x = 12

Step-by-step explanation:

Like the question says, we'll be using substitution, so for the first one, we'll be substituting the value of x into the equation

x = 5

3x- 5y = 10

3 (5) - 5y = 10

15 - 5y = 10

5y = 15 - 10

5y = 5

y = 1

For the next one, it's a similar idea, except the value of x has the variable y in it, which is fine, as there is still only one value in the equation we'll be solving:

x = 4y

x + y = 5

4y + y = 5

5y = 15 (we needed to collect like terms to simplify)

y = 15/5

y = 3

we still have to find x, to this, we substitute the value of y into any of the equations:

x = 4y

x = 4 (3)

x = 12

Hope this helps,

Cate

3 0
3 years ago
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