whats the distance between the points (2, 7) and (2, 15)

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:

[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]

Answer:

Here!! Hope i helped.

[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:

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:

B

Step-by-step explanation:

answer is based on results from the Cartesian plane

Answer:

32x^10y

Explanation -

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

It should look like this

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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Answer:

C) 26

Simplify using the FOIL method--used to multiply binomials--and then combine real and imaginary parts of the problem.

5 × 5 = 25 + positive 1(i) = 26

Answer:

option c, 26

Step-by-step explanation:

(5 + i)(5 - i)

Apply complex arithmetic rule: (a + bi)(a - bi) = a^2 + b^2

a = 5, b =1

(5)^2 + (1)^2

(5)^2 = 25

(1)^2 = 1

25 + 1

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:

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

Answer:

8.382 cm

Step-by-step explanation:

1in = 2.54 cm

3.30 x 2.54 = 8.382 cm

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:

9.500+9.100+9.625+9.250=

18.600+18.875=

37.475

Hope this helps!

Answer:

  b) 70

  c) 62

Step-by-step explanation:

Numbers are relatively prime when they have no factors in common.

__

The factors of 51 are ...

  51 = 3×17

The factors of the other numbers are ...

  84 = 2²×3×7 . . . . . has a factor of 3 in common with 51

  70 = 2×5×7 . . . . . . no factors in common

  62 = 2×31 . . . . . . . no factors in common

  30 = 2×3×5 . . . . . has a factor of 3 in common with 51

The numbers 70 and 62 are relatively prime to 51.

Answer:

No, it will not

Step-by-step explanation:

as square of 2 is 4

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:

[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]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer: [tex]i\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{-5}=\sqrt{(-1)(5)}=\sqrt{-1} \sqrt{5}=\boxed{i\sqrt{5}}[/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)

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:

42 degrees

Step-by-step explanation:

48+90=138

180-138=42

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]

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:

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:

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 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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