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[tex]x + 5 - \cfrac{1}{3} = 12[/tex]
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[tex] \frac{1}{x} + \frac{3}{x} = 16 \\ [/tex]

[tex] \frac{4}{x} = 16 \\ [/tex]

[tex]16x = 4[/tex]

[tex]x = \frac{4}{16} \\ [/tex]

[tex]x = \frac{1}{4} \\ [/tex]

[tex] \begin{gathered}\\ \large\implies\sf{ \frac{1}{x} + \frac{3}{x} = 16} \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\implies\sf{ \frac{4}{x } = 16 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\implies\sf{ x = 16 \times 4 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \implies \orange{\underline{\boxed{\large\frak \pink{x = 64 }}}} \\ \end{gathered}[/tex]

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The length of AD in triangle ABC in which ∠1 = ∠2 is 3.75.

The (interior) bisector of an angle, also called the internal angle bisector, is the line or line segment that divides the angle into two equal parts.

Here, Let the lenght of AD be x

         AB = 10 , AC = 6 and BC = 6

by Angle-Bisector theorem which states that

if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.

So, CD/BD =AC/AB

      CD/(BC-CD) = 6/10

       10. CD = 6.BC - 6.CD

        16 CD = 6 X 6

         16 CD = 36

          CD = 36/16

         CD  = 2.25

Now, AD = AC - CD

         AD = 6 - 2.25

         AD = 3.75

Thus, the length of AD in triangle ABC in which ∠1 = ∠2 is 3.75.

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1/5 = 60/100 * x

1/5 * 100/60 = x

100/300 = x

1/3 = x

Answer:

[tex] \frac{1}{3} [/tex]

Step-by-step explanation:

According to what we know, one-fifth is 60% of a number. Let us call that unknown number x. Since

[tex] \frac{1}{5} = 60\% \: \\ then \\ x = 100\%[/tex]

60% as a fraction is 6/10 or 3/5, in that case 100% as a fraction would be 5/5.

Recall: 60% = 3/5 and 100% = 5/5

therefore:

1/5 = 3/5

x = 5/5

note in order to find the value of x we cross multiply*

[tex] \frac{1}{5} ( \frac{5}{5}) = \frac{3}{5} x[/tex]

[tex] \frac{1}{5} = \frac{3}{5} x \\ \\ \frac{ \frac{1}{5} }{ \frac{3}{5} } = \frac{ \frac{3}{5} }{ \frac{3}{5} } x \\ \\ \frac{1}{5} \times \frac{5}{3} = x[/tex]

[tex] \frac{1}{3} = x[/tex]

Answer:

4/5

Step-by-step explanation:

Answer:

=4/5 or 0.8 as decimal

Step-by-step explanation:

8/10

Factor the number: 8=2· 4

2x4

Factor the number: 10 = 2· 5

2x4/2×5

Cancel the common factor: 2

=4/5

or (decimal 0.8)

The amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.

Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.

The formula for calculating compound interest is expressed as;

A = P(1 + r/k)^(k*t)

Where A is final amount, P is initial principal balance, r is interest rate, k is  number of times interest applied per time period and t is number of time periods elapsed.

Given that;

A = P(1 + r/k)^(k*t)

A = 40500(1 + 0.038/1)¹ˣ²⁰

A = 40500 × (1.038)²⁰

A = 40500 × 2.10837

A = $85389

Therefore, the amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.

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Answer: 128°

Step-by-step explanation:

   There are 360° in a trapezoid. Since this is a right trapezoid, two of those angles will be equal to 90°. We will set up the following equation, and solve.

360° = 90° + 90° + 52° + x°

360° = 90° + 90° + 52° + x°

360° = 232° + x°

128° = x

x = 128°

   The obtuse angle has a measure of 128°.

Answer:

9) Vincent will not get the correct answer because the + 484 is unneccesary, as he already subtracted it.

10a) 310,000 + x = 465,000; so x = 155,000

10b) 930,000/310,000 = 3 times more

Step-by-step explanation:

Answer:

Here!! Hope i helped.

Answer:

11

Step-by-step explanation:

2 dozen = 24

24-10=14

14-3=11

Answer:

11

Step-by-step explanation:

two dozens is 24 because one dozen is 12. 24-10=14-3=11

Answer:

B

Step-by-step explanation:

answer is based on results from the Cartesian plane

Answer:

8.382 cm

Step-by-step explanation:

1in = 2.54 cm

3.30 x 2.54 = 8.382 cm

Answer:

[tex]x(3x-7)=3x^2-7x[/tex]

Step-by-step explanation:

[tex]\Large \begin{array}{| c | c | c |}\cline{1-3} \textsf{x} & 3x & -7\\\cline{1-3} x & 3x^2 & -7x\\\cline{1-3}\end{array}[/tex]

[tex]\textsf{Therefore,}\quad x(3x-7)=3x^2-7x[/tex]

Step-by-step explanation:

Given:
40 houses,

500 liters of waters everyday for common utilities

Unknown amount of water per house which we will call x.

4500 max liters for the gated community

Solve:

4500=40x+500

subtract 500 from both sides

4000=40x

divide by 40

100=x

Check:

40(100)+500=4500

4000+500=450

correct

Answer:

100 liters of water can be used by each house.

Answer:

32x^10y

Explanation -

You want to use distributive property. Take 2x^5 and the Exponent 2y^5

It should look like this

Answer:

x = 27.19

Step-by-step explanation:

Sin(54) =22/x

0.81=22/x

x0.81= 22

x = 27.19

Answer:

m∠A = 49°

Step-by-step explanation:

According to Angle Sum Property,

m∠A

The slope of the cubic polynomial and it's y-intercept are respectively; f(1) = -4 and f(0) = -6

We are given the equation;

f(x) = 2x³ - 6

Now, because the highest power of x is 3, it means that this is a cubic polynomial and not linear because it has a degree of 3

Thus, let us differentiate to get the slope;

f'(x) = 6x² - 6

At f'(x) = 0; x = 1

Thus, slope is;

f(1) = 2(1)³ - 6

f(1) = -4

y-intercept is f(x) at x = 0. Thus;

f(0) = 2(0³) - 6

f(0) = -6

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Answer:

9.500+9.100+9.625+9.250=

18.600+18.875=

37.475

Hope this helps!

[tex]~~~~~37^x = 12\\\\\implies \ln\left( 37^x \right) = \ln(12)\\\\\implies x \ln (37) = \ln(12)\\\\\implies x = \dfrac{\ln(12)}{\ln(37)}\\\\\implies x \approx 0.689[/tex]

Answer:

4.19

Step-by-step explanation:

Find the mean:

[tex]\text{Mean}=\frac{12+19+9}{3}=\frac{40}{3}[/tex]

Find the standard deviation:

[tex]\text{Standard Deviation}=\sqrt{\frac{(12-\frac{40}{3})^2+(19-\frac{40}{3})^2+(9-\frac{40}{3})^2}{3}}=\sqrt{\frac{158}{9}}\approx4.19[/tex]

Answer:

Step-by-step explanation:

Equation

-6(1-4v) = 3v-8(-6-6v)                  Use the distributive property to get rid of the brackets.

Solution

-6 + 24v = 3v +48 +48v              Combine

-6 + 24v = 51v + 48                     Subtract 24v from both sides

-6 +24v-24v =51v-24v +48         Combine.

-6 = 27v + 48                              Subtract 48 from both sides.

-6-48 = 27v+48-48                     Combine

-54 = 27v                                    Divide by 27

-54/27=27v/27

-2 = v

Answer

v=-2

Let's start with the given arc and its angle.

The angle YWX is going to be half the arc length.

YWX = 1/2 (226) = 113

Angles VWX and YWX form a linear pair (or are supplementary angles), which means that their sum is 180 degrees.

(15x - 8) + 113 = 180

15x + 105 = 180

15x = 75

x = 5

Hope this helps!

Answer:

Discus, Hurdles, Long jump, and 100m

Step-by-step explanation:

See

x is decreased by 3 .

and y is increased by 5

So translation is

Hence

So

x will go 3 units right

y will go 5units up

Graph attached

Answer:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:

[tex]f(x)=\left(\dfrac{1}{4}\right)^x[/tex]

Translated 3 units to the right:

[tex]f(x-3)=\left(\dfrac{1}{4}\right)^{x-3}[/tex]

Translated 5 units up:

[tex]f(x-3)+5=\left(\dfrac{1}{4}\right)^{x-3}+5[/tex]

[tex]\implies g(x)=f(x-3)+5[/tex]

Therefore:

[tex]\textsf{g(x) is a translation of f(x) by }\left(\begin{array}{c}3\\5\\\end{array}\right)[/tex]

Answer:

Step-by-step explanation:

[tex]sin^2({ \theta})+cos^2({ \theta})=1\\cos({ \theta})=-/+\sqrt{1-sin^2({ \theta})} \\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} \\ --- > sin({ \theta})=\frac{1}{3} (known)\\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} =-\sqrt{1-(-\frac{1}{3})} =-\sqrt{\frac{9-1}{9}} =-\frac{2x^{2} }{3}[/tex]

Answer:

No, it will not

Step-by-step explanation:

as square of 2 is 4

Answer:

500 km

Step-by-step explanation:

300 plus 200 is 500km this is how far it is

The distance between City A & City C is approximately 171.3km

Given that, city A is 300 km due east of city B.

City C is 200 km on a bearing of 123° from city B.

We need to find the distance between the cities A and C,

Here we will use the concept of Cosine rule,

{Refer to the figure attached}

From ∆ABC, to find |AC|,

The cosine rule will be used.

|AC|² = |BC|² + |AB|² - 2(|BC|)(|AB|)cosB

Let |AC| = x

x² = 200² + 300² - 2(200)(300)cos33

x² = 40000 + 90000 - 120000cos33

x² = 130000-100644

x² = 29356

x = √29356

x = 171.3359

x ≈ 171.3km

Therefore, the distance between City A & City C is approximately 171.3km

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Answer:

A) 400 + 72

Step-by-step explanation:

Let the certain number be denoted by x.

⇒ 5x = 40 [Equation 1]

⇒ 9x = 72 [Equation 2]

Multiply Equation 1 by 10 :

⇒ 10(5x) = 40(10)

⇒ 50x = 400 [Equation 3]

Finding the sum of Equation 2 and Equation 3 :

⇒ 50x + 9x = 400 + 72

⇒ 59x = 400 + 72

Hence, 59 times a certain number is represented by : 400 + 72