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kkurt [141]
2 years ago
7

Find the value of x.

Mathematics
1 answer:
marysya [2.9K]2 years ago
8 0

Answer:

x = 115

Step-by-step explanation:

x = 115 because of alternate exterior angles

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Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 29% each week. The following function represents
Dmitry [639]

Answer:

Option A. f(x)=86[1.04]^{x} ; grows approximately at a rate of 0.4% daily

Step-by-step explanation:

we have

f(x)=86(1.29)^{x}

where

f(x) the number of weeds in the garden

x ----> the number of weeks

Calculate how quickly the weeds grow each day

Remember that a week is equal to seven days

so

f(x)=86(1.29)^{\frac{x}{7}}

Using the law of exponents

b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x

so

f(x)=86[(1.29)^{\frac{1}{7}}]^{x}

f(x)=86[1.04]^{x}

therefore

The rate is approximately

1.04=1+r

r=1.04-1=0.04=4% daily

8 0
3 years ago
A rectangular parcel of land has an area of 6,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than o
Drupady [299]

Answer:

50ft by 120ft

Step-by-step explanation:

Area of a rectangle = L × W

6000ft² = L × W

L = 6000/W

When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.

The formula for a right angle triangle =

a² + b² = c²( c = hypotenuse)

We are told in the question that:

A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel

Let us assume the side that the hypotenuse is longer than = Width

Hence, the Diagonal = (W + 10)²

Therefore

L² + W² = (W + 10)²

Since L = 6000/W

W² + (6000/W)² = (W + 10)²

W² + (6000/W)² = (W + 10) (W + 10)

W² + (6000/W)² = W² + 10W + 10W + 100

W² + (6000/W)² = W² + 20W + 100

W² - W² + (6000/W)² = 20W+ 100

6000²/W² = 20W + 100

6000² = W²( 20W + 100)

6000² = 20W³ + 100W²

20W³ + 100W² - 6000² = 0

20W³ + 100W² - 36000000 = 0

20(W³ + 5W² - 1800000) = 0

Factorising the quadratic equation,

20(W − 120)(W² + 125W + 15000) = 0

W - 120 = 0

W = 120

Therefore,

W(Width) = 120feet

Since the Width = 120 feet

We can find the length

6000ft² = L × W

L = 6000/W

L = 6000/120

L = 50 feet

The dimensions of the land, correct to the nearest foot is 50ft by 120ft

3 0
3 years ago
6.45 and 10.2 how does the estimate compare to the exact product
MrMuchimi
While estimating you would round the decimals and you would think in terms of how would the answer look like when you multiply 64 with 10...  640ish..and then you think about the decimals a little,,, soyou will put decimal after 64... and that will give you 64.0 or something ...While the exact answer id 65.79... Close enough.
Hope I helped..
Please mark the brainliest if I did help!
5 0
3 years ago
What equation is equivalent to 1/3 (9x+12) + 4x + 6
Irina-Kira [14]
The answer is b, 7x+10
3 0
2 years ago
Read 2 more answers
Expanding Logarithmic Expressions In Exercise, use the properties of logarithms to rewrite the expression as a sum, difference,
aev [14]

Answer:

The simplified expression is:

\ln{x} + \frac{\ln{(x-1)}}{2}

Step-by-step explanation:

We have those following logarithmic properties:

\ln{\frac{a}{b}} = \ln{a} - \ln{b}

\ln{a*b} = \ln{a} + \ln{b}

\ln{a^{n}} = n\ln{a}

In this problem, we have that:

\ln{x^{2}(x-1)}^{1/2}

Applying these properties

\frac{1}{2}*(\ln{x^{2} + \ln{(x-1)})

\ln{x} + \frac{\ln{(x-1)}}{2}

6 0
3 years ago
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