The mean age of 6 women in an office is 23 years old.
The mean age of 3 men in an office is 23 years old.
What is the mean age (nearest year) of all the people in the office?

Answer:

Point-slope form:

[tex]y-4=\displaystyle\frac{1}{3}(x+4)[/tex]

[tex]y-8=m(x-8)[/tex]

Slope-intercept form:

[tex]y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}[/tex]

Standard form:

[tex]-x+3y=16[/tex]

Step-by-step explanation:

Hi there!

1) Point-slope form

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and m is the slope

First, determine the slope:

[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the points (-4,4) and (8,8):

[tex]m=\displaystyle\frac{8-4}{8-(-4)}\\\\m=\displaystyle\frac{8-4}{8+4}\\\\m=\displaystyle\frac{4}{12}\\\\m=\displaystyle\frac{1}{3}[/tex]

Therefore, the slope of the line is [tex]\displaystyle\frac{1}{3}[/tex]. Plug this into  [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=\displaystyle\frac{1}{3}(x-x_1)[/tex]

Now, for [tex](x_1,y_1)[/tex], we can either plug in (-4,4) or (8,8):

[tex]y-4=\displaystyle\frac{1}{3}(x-(-4))\\\\y-4=\displaystyle\frac{1}{3}(x+4)[/tex]

or

[tex]y-8=m(x-8)[/tex]

2) Slope-intercept form

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

[tex]y=mx+b[/tex]

Plug in the slope

[tex]y=\displaystyle\frac{1}{3}x+b[/tex]

Now, to determine the y-intercept, plug in one of the points (-4,4) or (8,8) and solve for b:

[tex]8=\displaystyle\frac{1}{3}(8)+b\\\\8=\displaystyle\frac{8}{3}+b\\\\8-\displaystyle\frac{8}{3}=b\\\\b=\frac{16}{3}[/tex]

Therefore, the y-intercept is [tex]\displaystyle\frac{16}{3}[/tex]. Plug this back into [tex]y=\displaystyle\frac{1}{3}x+b[/tex]:

[tex]y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}[/tex]

3) Standard form

Standard form:

[tex]Ax+By=C[/tex] where A, B, and C are numbers which are typically integers

[tex]y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}[/tex]

Organize this into standard form:

[tex]-\displaystyle\frac{1}{3}x+y=\displaystyle\frac{16}{3}[/tex]

Multiply both sides by 3 so A, B, and C are integers:

[tex]-x+3y=16[/tex]

I hope this helps!

Answer:

It's a statistical question.

and there between 250-300 feet.

Answer:

The answer would be A

Step-by-step explanation:

Answer:

37 degees

Step-by-step explanation:

..........m.........

Answer:

x=37

Step-by-step explanation:

here,

143+x=180

x=180-143

x=37

The cube root of 27 is 3!!

Answer:

170.25

Step-by-step explanation:

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 15 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 15, so we can write it down as 100%=15.

4. We know, that x% equals 1135 of the output value, so we can write it down as x%=1135.

5. Now we have two simple equations:

1) 100%=15

2) x%=1135

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=15/1135

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 1135 is what percent of 15

100%/x%=15/1135

(100/x)*x=(15/1135)*x       - we multiply both sides of the equation by x

100=0.013215859030837*x       - we divide both sides of the equation by (0.013215859030837) to get x

100/0.013215859030837=x

7566.6666666667=x

x=7566.6666666667

now we have:  170.25

We have to find,

→ 15% of 1135

The value of the percentage is,

→ 15 ÷ 100

→ 0.15

Let's find the solution,

→ 1135 × 0.15

→ 170.25

Hence, the answer is 170.25.

Answer:

hi you said u can answer my qweshion

Step-by-step explanation:

The polynomial in standard form is as follows;

8x⁵  - 5y⁴ - 2xy⁵ + x²y

A polynomial can have constants, variables and exponents, but never division by a variable. example of a polynomial is as follows:

4xy² + 2y + 5

Polynomial can be named base on the number of terms. For example monomial, binomial and trinomial.

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

Therefore, the polynomial in standard form is as follows;

8x⁵  - 5y⁴ - 2xy⁵ + x²y

learn more on polynomial here: https://brainly.com/question/27205112

#SPJ1

Answer: its b

8xy5 -5y4 -2xy5 +x2y

Step-by-step explanation:

I got it right on edge

Answer:

Step-by-step explanation:

y=(-1/3)x + 3

Answer:

965.31sq.km

Step-by-step explanation:

Area of the triangle = 1/2 xy sina

a=52° , x=49 , y=50

area of triangle= 1/2 * 49 *50 *sin52°

area= 965.31 sq.km

2.

Simply do 166 divided by 83 and you'll have your answer

Answer:

x + x^2 = yx

not really sure if you are looking for this so comment if this is what you wanted

Answer:

A

Step-by-step explanation:

edge 2021

Answer:

It is A

Step-by-step explanation:

I got it right on the test Edge 2022.

Answer:

4 cassettes and 5 CDs

Step-by-step explanation:

Create a system of equations

c is cassettes and d is CDs

6c+10d=74

c+d=9

I will use substitution

c=9-d

6(9-d)+10d=74

54-6d+10d=74

4d=20

d=5

Plug 5 back into the equation

c+5=9

c=4

Answer:

Sqrt(-108)=6i*sqrt(3)

Step-by-step explanation:

-108=3*6*6*(-1). Sqrt(-108)=6i*sqrt(3) where i is iota

what's the question? we solving or simplify?

Answer and Step-by-step explanation:

When multiplying exponents:

- Product of Powers: When the base of the exponents are the same, and the bases are being multiplied to each other, the exponents are added together.

- Different bases Same Exponents: When the bases of the exponents are different, but the exponents are the same, the bases multiply together (within a parenthesis) with the exponent on the parenthesis.

- Quotient of Powers: When the base of the exponents are the same, and they are being divided by each other, the exponents will subtract from each other.

- Power of a Power: When a base has an exponent, and that entire term has and exponent, the exponents multiply together.

- Power of a Product: The opposite of Different bases Same Exponents. Distribute the exponent onto the different bases.

- Power of a Quotient: The opposite of Quotient of Powers. Distribute the exponent to the dividing bases.

- Zero Power: Any number raised to the 0 power equals 1.

- Negative Exponent: Any number raised by a negative number goes to the denominator of a fraction (if not already in the denominator), and vise versa (goes to the numerator if not already in the numerator).  

- Power of One: Any number raised to the power of 1 is the same number.

7.

[tex](-5y^3)^3 = -125y^6[/tex]

8.

[tex](-a^9b)^4 = -a^{13}b^4[/tex]

9.

[tex](\frac{1}{2}x^4 )^7 = \frac{1}{2^7 (=128)} x^{11}[/tex]

10.

[tex]2(3a^2)^3 = 2(27a^5) = 54a^5[/tex]

11.

[tex]\frac{1}{2} (4k^5)^2=\frac{1}{2} (16k^7) = 8k^7[/tex]

12.

[tex]-6(\frac{2}{3}p^8 )^3=-6(\frac{6}{27} p^{11}) = -6(\frac{2}{9}p^{11})=\frac{-12}{9} p^{11}=-\frac{4}{3}p^{11}[/tex]

13.

[tex](m^5n^3)^7 * m^2n = m^{12}n^{10}*m^2n=m^{14}n^{11}[/tex]

14.

[tex](2xy)^2(-3x^2)(4y^2) = (4x^2y^2)(-3x^2)(4y^2) = (-12x^4y^2)(4y^2)=-48x^6y^4[/tex]

15.

[tex](2x^3y^2z^2)^3(x^2z)^4=(8x^6y^5z^5)(x^6z^4)=8x^{12}y^5z^9[/tex]

16.

[tex](-xy)^2(2x^9y^5)^4 = (x^2y^2)(16x^{13}y^9)=16x^{15}y^{11}[/tex]

17.

[tex](-4mn)^3(-2m^2)^3 = (-64m^3n^3)(-8m^5)=512m^8n^3[/tex]

18.

[tex]-3(2x^4)(4x^5y)^2 = (-6x^4)(16x^7y^2)=-96x^{11}y^2[/tex]

19.

[tex](-18m^2n)^2(-\frac{1}{6} mn^2)=(324m^4n^2)(-\frac{1}{6} mn^2)=-54m^5n^4[/tex]

20.

[tex](3r^3s^5)^2-r^6s^{10} = 9r^5s^7-r^6s^{10} = r^5s^7(9-rs^3)[/tex]

21.

[tex](-2x^5y^7)^3+7x^{15}y^{21} = -8x^8y^{10}+7x^{15}y^{21} = x^8y^{10}(7x^7y^{11}-8)[/tex]

#teamtrees #PAW (Plant And Water)

I hope this helps!

Answer:

Step-by-step explanation:

2x=8 and 3y=9

x=8/2 and y=9/3

x=4 and y=3

Answer:

22:25   26:Yes 4900  27: 6 and 18  28: 44,100 and 48,024,900

Step-by-step explanation:

for 22-25 see answer #2. They gave a better answer in total.

Answer:

22.  30

prime factorization of 30

2 × 3 × 5

so there is no simplification needed here

23. 126

2 × 3 × 3 × 7

simplification

2 ×  × 7

24.  4900

2 ×2 × 5 × 5 × 7 ×7

simplification

25.  39204

2 × 2 × 3 × 3 × 3 × 3 × 11 × 11

simplification

26 .  

Yes 4900 is a square number it's square root is 70

you can even cross-check

70 × 70

= 4900

and even 39204 is a square number it's square root is 198

you can even cross-check

198 × 198

= 39204

Hence 2 numbers 4900 and 39204 are square numbers

27 .

i. highest common factor of 30 and 126

factors of 30 are 2 × 3 × 5  

factors of 126 are 2 × 3 × 3 × 7

now find common between them

common factors are 2 and 3

so multiply 2 and 3

2 × 3

= 6

6 is the highest common factor

ii. 126 and 39204

factors of 126 are 2 × 3 × 3 × 7

factors of 39204 are 2 × 2 × 3 × 3 × 3 × 3 × 11 × 11

now find common between them

common factors are 2 × 3 × 3

= 18

18 is the highest common factor

28 .

1 .  126 and 4900

factors of 126 are 2 × 3 × 3 × 7

factors of 4900 are 2 ×2 × 5 × 5 × 7 ×7

make the pairs of the numbers

2 ×2 × 5 × 5 × 3 × 3 × 7 ×7

= 44100   least common multiple

ii. 4900 and 39204

factors of 39204 are 2 × 2 × 3 × 3 × 3 × 3 × 11 × 11

factors of 4900 are 2 ×2 × 5 × 5 × 7 ×7

make the pairs of the numbers  

2 ×2 × 3 x 3 x 3 x 3 x 5 x 5 x 7 x 7 x 11 x 11

= 48024900 least common multiple

Answer:

[tex]\frac{25}{15}[/tex] is greater.

Step-by-step explanation:

25÷15=1.67

2÷3=0.67

1.67 is greater than 0.67, so [tex]\frac{25}{15}[/tex] is greater.

Also,  [tex]\frac{25}{15}[/tex] is an improper fraction, and  [tex]\frac{2}{3}[/tex] is a proper fraction. Improper fraction mast be greater than a proper fraction.

Answer:

S=(2,-2) ...............

Step-by-step explanation:

J(-3,9)

k(-10,9)

L(-10,4)

M(-3,4)

Answer:

the point is (1.73, 3)

Step-by-step explanation:

Given a vector on an xy plot, the magnitude is the hypotinuse of the triangle formed, and the direction is the angle with x axis. So we have a right angle triangle that must be a 30-60-90 (sum = 180).

Then from the lower angle

sin(60) = opposite/hypotinuse = y/(2*3**(1/2))

0.866 = y/(2*1.732)

0.866 = y/3.464

0.866 * 3.464 = y

3 = y

Then from the top angle

sin(30) = opposite/hypotinuse = x/(2*3**(1/2))

sin(30) = x/(2*3**(1/2))

0.5 = x/(2*3**(1/2))

0.5 = x/3.464

0.5 * 3.464 = x

1.73 = x

3(2x - 1) + 2(x + 5) = 47

6x - 3 + 2x + 10 = 47

6x + 2x = 47 + 3 - 10

8x = 40 / : 8

x = 5 ← the end

Answer:

x = 5

Step-by-step explanation:

[tex]3(2x - 1) + 2(x + 5) = 47[/tex]

[tex]6x - 3 + 2(x + 5) = 47[/tex]

[tex]6x - 3 + 2x + 10 = 47[/tex]

[tex]8x - 3 + 10 = 47[/tex]

[tex]8x + 7 = 47[/tex]

[tex]8x = 47 - 7[/tex]

[tex]8x = 40[/tex]

[tex](8x \div 8 = 40 \div 8 = x = 40 \div 8 )[/tex]

[tex]x = 5[/tex]

Answer:

equal measures:

lJP and NJR

MJP and PJR

Unequal measures:

KJL and LJM

KJR and MJP

MJK and PJR

Step-by-step explanation:

Answer:

Step-by-step explanation:

Determine whether each of the following pairs of angles have equal measures. Drag and drop each pair of angles into the correct catagory to show which pairs have equal measures.

Answer:

you subtract from the  x

Step-by-step explanation:

Answer: First Choice. 5ft

Step-by-step explanation:

Here we need to know the idea of the Pythagorean theorem.

Since a building is straight, the base angle is a right angle, thus it would be a right triangle.

Pythagorean Theorem: a² + b² = c²

**NOTE** Please refer to the attachment below for the figure. (I drew it, so if it was not clear and understandable for you, please tell me.)

Solve:

Given information

a = 12 ft

c = 13 ft

b = unknow base length

Given formula for Pythagorean Theorem

a² + b² = c²

Substitute values into the formula

12² + b² = 13²

Simplify exponents

144 + b² = 169

Subtract 144 on both sides

144 + b² - 144= 169 - 144

b² = 25

Square root both sides

√b² = √25

[tex]\boxed{b=5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

We can observe the numbers 72, 78, 84, 90 form an arithmetic sequence with common difference of 6.

It can be continued by adding 6 to the last number:

72,78,84,90..are in AP

[tex]\\ \rm\longmapsto a_5=72+4(6)=72+24=96[/tex]

[tex]\\ \rm\longmapsto a_6=72+5(6)=72+30=102[/tex]