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aalyn [17]
3 years ago
5

There are three square gardens whose lengths of the sides are 3 ft, 7ft, and 2 ft respectively. Find the total area of the three

gardens in square feet
Mathematics
1 answer:
kipiarov [429]3 years ago
5 0

Answer:

62 sq ft

Step-by-step explanation:

3 · 3 = 9

The first garden's area is 9 square feet.

7 · 7 = 49

The second garden's area is 49 square feet.

2 · 2 = 4

The third garden's area is 4 square feet.

We add 9 + 49 + 4.

9 + 49 + 4 = 62

The total area of the three gardens is 62 square feet.

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What is an equation of a parabola with a vertex at the origin and directrix x=4.75?
patriot [66]
An equation for the parabola would be y²=-19x.

Since we have x=4.75 for the directrix, this tells us that the parabola's axis of symmetry runs parallel to the x-axis.  This means we will use the standard form

(y-k)²=4p(x-h), where (h, k) is the vertex, (h+p, k) is the focus and x=h-p is the directrix.

Beginning with the directrix:

x=h-p=4.75
h-p=4.75

Since the vertex is at (0, 0), this means h=0 and k=0:

0-p=4.75
-p=4.75
p=-4.75

Substituting this into the standard form as well as our values for h and k we have:
(y-0)²=4(-4.75)(x-0)
y²=-19x
4 0
3 years ago
2.The number of grams A of a certain radioactive substance present at time, in yearsfrom the present, t is given by the formulaA
professor190 [17]

Answer:

Given that,

The number of grams A of a certain radioactive substance present at time, in years

from the present, t is given by the formula

A=45e^{-0.0045(t)}

a) To find the initial amount of this substance

At t=0, we get

A=45e^{-0.0045(0)}A=45e^0

We know that e^0=1 ( anything to the power zero is 1)

we get,

A=45

The initial amount of the substance is 45 grams

b)To find thehalf-life of this substance

To find t when the substance becames half the amount.

A=45/2

Substitute this we get,

\frac{45}{2}=45e^{-0.0045(t)}

\frac{1}{2}=e^{-0.0045(t)}

Taking natural logarithm on both sides we get,

\ln (\frac{1}{2})=-0.0045(t)^{}(-1)\ln (\frac{1}{2})=0.0045(t)\ln (\frac{1}{2})^{-1}=0.0045(t)\ln (2)=0.0045(t)0.6931=0.0045(t)t=\frac{0.6931}{0.0045}t=154.02

Half-life of this substance is 154.02

c) To find the amount of substance will be present around in 2500 years

Put t=2500

we get,

A=45e^{-0.0045(2500)}A=45e^{-11.25}A=45\times0.000013=0.000585A=0.000585

The amount of substance will be present around in 2500 years is 0.000585 grams

4 0
9 months ago
Are these equations infinite solution, no solution, or one solution?
Karo-lina-s [1.5K]

Answer:

1) one solution

2) Infinitely many solution

3) no solution

Step-by-step explanation:

The first equation is -14-8x=-2(-3x+7)

Let us expand the right hand side to get:

-14-8x=-2*-3x+-2*7

We multiply -14-8x=6x-14

We group similar terms to get:

-8x-6x=-14+14

Combine similar terms to get:

-14x=0

Divide through by -14 to get:

x=0

2) The second equation is 3+5x=5(x+2)-7

We expand to obtain:

3+5x=5x+5*2-7

Multiply to get:

3+5x=5x+10-7

This gives us

3+5x=5x+3

5x=5x

1=1

There is infinitely many solutions

3) The third equation is: 36-7x=-7(x-5)

We expand to get:

36-7x=-7x+35

Group similar terms;

-7x+7x=35-36

0=-1

This statement is not true so there is no solution.

5 0
2 years ago
Help me solve this please
Semenov [28]

\huge\underline{ \underline{ \bf{Answer࿐} }}

parallel sides measure :

  • 10 ft -(a)
  • 12 ft. -(b)

Area :

  • 44 ft²

height (h) = x

___________________

\boxed{Area =  \frac{1}{2}  \times (a + b) \times h}

  • \dfrac{1}{2}  \times (10 + 12) \times x = 44

  • \dfrac{1}{2}  \times 22 \times x = 44

  • 11x = 44

  • \boxed{ 4 \:  \: ft}

Therefore, height of Trapezoid is 4 ft

_____________________________

\mathrm{ \#TeeNForeveR}

5 0
3 years ago
What is the square root of 248 + square root of 63​
enyata [817]

Answer:

1) √248 = ± 15.7480157

2)√63 = ± 7.93725393

 

Step-by-step explanation:

7 0
2 years ago
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