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OLEGan [10]
2 years ago
9

Hey can anyone help me with this problem please and thank you

Mathematics
2 answers:
krok68 [10]2 years ago
7 0

Answer:

x=20

Step-by-step explanation:

Monica [59]2 years ago
6 0
<h2><u>Answer</u><u> </u>:—</h2>

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\sf{\longrightarrow x = 20}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

\begin{gathered}\rm{ \underline{ \underline{ \red{Given}}}}\begin{cases}\sf{m||n} & \\ \\\sf{a\:transvey\:l\:passes\: through\:m\:and\:n}& \\ \\ \sf{two \:angles = (7x-3)°\:and\:(6x+17)°}&\end{cases}\\\\\end{gathered}

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

<u>➠ </u><u> </u><u>Using</u><u> </u><u>the </u><u>property</u><u> </u><u>of </u><u>adjacent</u><u> </u><u>angles </u><u>and </u><u>vertically</u><u> </u><u>opposite</u><u> </u><u>angles</u><u> </u><u>,</u><u> </u><u>we </u><u>have </u>:

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\sf{\longrightarrow (7x-3)=(6x+17)}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\sf{\longrightarrow 7x-3-6x-17=0}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\sf{\longrightarrow 7x-6x-3-17=0}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\sf{\longrightarrow x-20=0}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\sf{\longrightarrow x=20}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

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A town has a population of 6000 and grows at 3.5% every year. To the nearest year, how long will it be until the population will
kotykmax [81]

Answer:

5 years.

Step-by-step explanation:

Every year the population increases by a factor 103.5% or  1.035.

The equation relating population and time in years is:

P = 6000(1.035)^t  (This is an example of  exponential growth)

So we have:

7100 = 6000(1.035)^t

(1.035)^t = 7100/6000

(1.035)^t = 1.1833

t ln 1.035 = ln 1.1833

t = ln 1.1833/ln 1.035

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7 0
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Jasmine borrowed $15,000 for 8 years and she paid $6,600 in interest. What was the interest rate for Jasmine's loan?
weeeeeb [17]

Answer:

5.5%

Step-by-step explanation:

To find the interest rate, use the equation:  I = prt

I = Interest = $6,600

p = principal = $15,000

r = rate = unknown

t = time = 8 years


Now plug the numbers into the equation.

6,600 = 15,000 * r * 8

6,600 = 120,000 * r


Now isolate the variable by dividing both sides of the equation by 120,000.

0.055 = r


Now change the rate to a percent by moving the decimal point 2 digits to the right.

5.5% = r   OR   r = 5.5%

4 0
2 years ago
10. There are nine golf balls numbered from 1 to 9 in a bag. Three balls are randomly selected without replacement to form a 3-d
lbvjy [14]

Answer:

a) 504

b) 56

c) 0.111

Step-by-step explanation:

Data provided in the question:

There are nine golf balls numbered from 1 to 9 in a bag

Three balls are randomly selected without replacement

a) 3-digit numbers that can be formed

= ^nP_r

n = 9

r = 3

= ⁹P₃

= \frac{9!}{9!-3!}

= 9 × 8 × 7

= 504

b)  3-digit numbers start with the digit 1

=  _ _ _

in the above 3 blanks first digit is fixed i.e 1

we and we have 8 choices left for the last 2 digits

Thus,

n = 8

r = 2

Therefore,

= 1 × ⁸P₂

= 1 × \frac{8!}{8!-2!}

= 1 × 8 × 7

= 56

c) Probability that the 3-digit number formed is less than 200

Now,

The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)

and total 3-digit numbers that can be formed is part a)

therefore,

Probability that the 3-digit number formed is less than 200

= 56 ÷ 504

= 0.111

5 0
3 years ago
A family built a house in a beach resort area. In 1990, the house was 430 ft from the water. With erosion, the house was 400 ft
neonofarm [45]

We develop an equation for the given situation by first writing the general equation for lines,

                                y = mx + b

Substituting to this given the values given above,

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The value of m from the equation in 2000 is -3. Thus, the equation of that relates the variables is,

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8 0
2 years ago
Which expression is equivalent to 4(x^3)(2x)^-4
AVprozaik [17]

Answer:

=\frac{4x^{3}}{16 x^{4}}

Step-by-step explanation:

4(x^{3} )(2x)^{-4}

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=\frac{4x^{3}}{2^{4} x^{4}}

=\frac{4x^{3}}{16 x^{4}}

3 0
3 years ago
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