Six years ago Matt was four times as old as Brown, and in 3 years the sum of their
ages will be 43 years. Find their present ages.

Answer:

3x - 4 = 20

3x = 20 + 4

3x = 24

x = 24/3

x = 8

Answer:

[tex]3x - 4 = 20 \\3x = 20 + 4 \\ 3x = 24 \\ 3x \div 3 = x \\ 24 \ \div 3 = 8 \\ x = 8 [/tex]

9514 1404 393

Answer:

  1a. E = 5×1.59^t

  1b. 32 GWh

  1c. 1986

Step-by-step explanation:

1a. An exponential model looks like

  f(t) = a·b^t

where 'a' is the value when t=0, and 'b' is the growth factor in the time period associated with t.

Here, 'a' is 5 (GWh), and 'b' is 1+59% = 1.59. Then the desired model is ...

  E = 5·1.59^t . . . . . where t is years after 1980, and E is in GWh.

__

1b. For t=4, we have ...

  E = 5·1.59^4 ≈ 31.96 ≈ 32

About 32 GWh was generated in 1984.

__

1c. The value of t for a given value of E is ...

  E/5 = 1.59^t . . . . divide by 5

  log(E/5) = t·log(1.59) . . . . take logarithms

  t = log(E/5)/log(1.59) . . . . divide by the coefficient of t

For E = 80, the years after 1980 are ...

  t = log(80/5)/log(1.59) ≈ 5.98

About 80 GWh were generated in 1986.

Answer:

49°

Step-by-step explanation:

since its a right angle that just subtract from 90

90-41= 49

Answer:

49

Step-by-step explanation:

Because of the square at O, we know that angle XOZ is a right angle and is 90°.

Since angle XOZ is made up of angle XOY and angle YOZ, we can subtract the measure of angle XOZ by the measure of angle XOY to find the measure of angle YOZ, which is equal to x.

x = 90 - 41

x = 49

Answer:

i got 21/1

Step-by-step explanation:

fill the table

2x -y 2

6x 12^2 -6xy 12x

-y -2xy y^2 -2y

Answer:

2x^3  +7x^2+3x-2

Step-by-step explanation:

3x^3 +7x^2 -x

- ( x^3 -4x +2)

------------------------

The first step is to line up the variables by degree

 3x^3 +7x^2 -x

- ( x^3           -4x +2)

----------------------------

Then distribute the minus sign

 3x^3 +7x^2 -x

-  x^3           +4x -2

----------------------------

2x^3  +7x^2+3x-2

Answer:

Step-by-step explanation:

Repost with picture and I can help you

sorry I cant answer your question if all you write " is help me pls"

Answer:

c.{-2,2}

Step-by-step explanation:

6

x

2

−

24

=

0

Use the quadratic formula to find the solutions.

−

b

±

√

b

2

−

4

(

a

c

)

2

a

Substitute the values

a

=

6

,

b

=

0

, and

c

=

−

24

into the quadratic formula and solve for

x

.

0

±

√

0

2

−

4

⋅

(

6

⋅

−

24

)

2

⋅

6

Simplify.

x

=

±

2

The final answer is the combination of both solutions.

x

=

2

,

−

2

Answer:

=3(2(5)+1

=3×10+1

=30+1

=31

Answer:

(a) 33

(b) 27

(c) 1/2

Step-by-step explanation:

(a)

g(x) = 3(2x + 1)

g(5) = 3(2 * 5 + 1)

g(5) = 3(10 + 1)

g(5) = 3(11)

g(5) = 33

(b)

[tex] f(x) = \dfrac{12}{\sqrt{x}} [/tex]

[tex] f(9) = \dfrac{12}{\sqrt{9}} [/tex]

[tex] f(9) = \dfrac{12}{3} [/tex]

[tex] f(9) = 4 [/tex]

g(f(9)) = g(4) = 3(2(4) + 1)

g(f(9)) = 3(9)

g(f(9)) = 27

(c)

[tex] g(x) = 3(2x + 1) [/tex]

[tex] y = 3(2x + 1) [/tex]

[tex] x = 3(2y + 1) [/tex]

[tex] 2y + 1 = \dfrac{x}{3} [/tex]

[tex] 2y = \dfrac{x}{3} - 1 [/tex]

[tex] y = \dfrac{x}{6} - \dfrac{1}{2} [/tex]

[tex] g^{-1}(x) = \dfrac{x}{6} - \dfrac{1}{2} [/tex]

[tex] g^{-1}(6) = \dfrac{6}{6} - \dfrac{1}{2} [/tex]

[tex] g^{-1}(6) = 1 - \dfrac{1}{2} [/tex]

[tex] g^{-1}(6) = \dfrac{1}{2} [/tex]

Answer:

99.9973 %

Step-by-step explanation:

This is a binomial probability distribution.

Since the probability of satisfactory welds = 97% = 0.97 and the probability of defective welds = 3% = 0.03.

Since there are 3 welds and we require at least one being defective, our binomial probability is

P(x ≥ 1) = 1 - P(x ≤ 0) = 1 - P(0) = 1 - ³C₀(0.03)³(0.97)⁰ = 1 - 1 × ‭0.000027‬ × 1 = 1 - 0.000027 = 0.99997‬3 × 100% = 99.9973%

Answer: 2,16

Step-by-step explanation:

Answer:

17x + 56 = 0

Step-by-step explanation:

add 2x and 15x

Answer:

!

Step-by-step explanation:

here it is!!!!!!!!!!!!!!!

Answer:

Confidence Interval =  ( 5.6 < μ < 8.2 )

The interval shows that the mean attractiveness is Above average on a scale of 1 to 10

Step-by-step explanation:

Data Given  : 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9

a) construct a confidence interval at a 95% confidence level

confidence interval = x ± tcritical ( s / √ n ) ------ ( 1 )

n = 12

μ (mean) = ( 5+8+2+8+7+6+6+8+9+9+6+9 ) / 12  ≈ 6.92

std ( s ) = √ 1/11 *∑( xi- X )^2

= √ 1/11 *  ( 5 - 6.92)^2 + ( 8 - 6.92)^2 + ( 2 - 6.92)^2 + ( 8 - 6.92)^2 + ( 7-6.92)^2 + ( 6 - 6.92)^2 + (6 - 6.92 )^2 + ( 8 - 6.92 )^2 + ( 9 - 6.92)^2 + ( 9 - 6.92)^2 + ( 6 - 6.92 )^2 + ( 9 - 6.92 )^2

= √ 1/11 * 46.92 =  2.07

tcritical at ∝ 0.05 , df = 11  = 2.20

Back to equation 1

6.92 ± 2.2 ( 2.07 / √ 12 )

( 6.92 ± 1.31 )

Confidence Interval =  ( 5.6 < μ < 8.2 )    

Answer:

Step-by-step explanation:

sin 60=CB/18

[tex]\frac{\sqrt{3} }{2} =\frac{CB}{18} \\CB=9\sqrt{3}[/tex]

Answer: m = 7

Step-by-step explanation: This equation is written in slope-intercept form which is the same thing as y = mx + b form where m represents the slope of the line and b represents the y-intercept.

Now looking at this equation, we can see that m or the slope of the line is 7.

Answer:

523.6 m³

Step-by-step explanation:

The polyhedron is an oblique cone

Volume of oblique cone = ⅓πr²h

r = x = 5 m

h = y = 20 m

Volume = ⅓*π*5²*20

Volume = ⅓*π*25*20

Volume = 523.598777 ≈ 523.6 m³ (nearest tenth)

Answer:

Composite area is 400+157=557

or 400 + 50pi

Step-by-step explanation:

First find the area of the square

A=s*s A= 20*20

Area of the square portion is 400

then find the area of the semicircle- we know the diameter of the circle is 20, so the radius is 10.

[tex]A=\frac{1}{2} \pi r^{2}[/tex]

so

[tex]A=\frac{1}{2} \pi 10^{2} \\A=\frac{1}{2}\pi 100\\A=50\pi \\A= 157[/tex]

Composite area is 400+157=557

or 400 + 50pi

Answer:

85

Step-by-step explanation:

He has 170 correct answers, so 170 * 0.5 = 85 points  #0.5 points per 1 question

Answer:

$525.13

Step-by-step explanation:

cost per month = total expenses /  months in a year

total expenses = fixed cost + variable cost

$2,125.10 + $4,176.43 = $6,301.53

cost per month = $6,301.53/ 12 = $525.13

Answer:

0.03, 0.06, 0.2, 0.76, 1

Step-by-step explanation:

Answer:

The dolphin will be above the surface of the water for 2 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

The height of the dolphin after t seconds is given by:

[tex]h(t) = -16t^2 + 96t - 128[/tex]

According to Micha's model, how long will the dolphin be above the surface of the water?

It stays above the surface of the water between the first and the second root. Initially, it is below water, when the first time for which [tex]h(t) = 0[/tex] it crosses the surface upwards, and then the second time for which [tex]h(t) = 0[/tex] it crosses the surface downwards.

We have to find these roots. So

[tex]h(t) = -16t^2 + 96t - 128[/tex]

[tex]-16t^2 + 96t - 128 = 0[/tex]

Multiplying by -16

[tex]t^2 - 6t + 8 = 0[/tex]

[tex]\Delta = (-6)^{2} - 4*1*8 = 36 - 32 = 4[/tex]

[tex]t_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4[/tex]

[tex]t_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2[/tex]

4 - 2 = 2

The dolphin will be above the surface of the water for 2 seconds.

Answer:

B

Step-by-step explanation:

let's list everything out.

$35 for school supplies

$17.5 has already been used

$17.5 is left

pens only come in packs of 12

one pack of pens is $5

ok, so we know its definitely not C or D because they are less than 12

42 is not divisible by 12

since packs only come in 12's then it must be B.

good luck my friend!

Answer:

hmmm

Step-by-step explanation:

not sure man

Answer:

169.28

Step-by-step explanation:

18.4x9.2=169.28