3. Solve 2log4y - log4 (5y - 12) = 1/2
​

Answer:

D

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

=3x + 9 + 5x²

=5x² + 3x + 9

Answer:

128

Step-by-step explanation:

Answer:

Rate of Change/Slope = -20

Equation: y= -20x +100

Step-by-step explanation:

A. We know the rate of change is also known as the slope.  If we used the slope formula to find the slope we can find the Rate of Change.

[tex]\frac{y2 - y1}{x2 - x1} = \frac{100-80}{1-2} = \frac{20}{-1} = -20[/tex]

B. Since we know the slope and 1 point on the graph we can substitute them in for 'b'

(0,100)

(100)=-20(0) + b

b = 100

Since we know the slope and the b value we can write the equation:\

y = -20x +100

The rate of change refers to the slope of the line, that is the change in y-axis per unit change in the value on the x-axis. Hence, the rate of change is :

Slope = - 100 / 5 = - 20

General form of a slope - intercept relation :

The intercept, c can be calculated thus:

100 = - 20(0) + c

100 = 0 + c

c = 100

Hence, the slope - intercept equation will be y = - 20x + 100

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Answer:

Step-by-step explanation:

Convert 182 6/8 into improper fraction

[tex]182\frac{6}{8}=\frac{1462}{8}[/tex]

[tex]\frac{1462}{8}[/tex]÷ 3 =[tex]\frac{1462}{8}*\frac{1}{3}=\frac{1462}{24}[/tex]

= 60 22/24

Answer:

$13.12 per hour

Step-by-step explanation:

Take the total pay and divide by the number of hours

$282.08/21.5 hours

$13.12 per hour

Answer:

Step-by-step explanation:

21.5 hours - $282.08

1 - ?

$282.08/21.5 = $13.12

Answer:

a. 8 gallons

b. (11-0.75t) gallons

Step-by-step explanation:

a. Here in this question, we are told that the total amount of fuel in the fuel tank is 11 gallons and the car consumes 0.75 gallon per hour. We are interested in knowing the amount of fuel left in the tank after driving for four hours.

We proceed as follows;

Since 0.75 gallon is consumed in an hour, the amount of fuel consumed in 4 hours would be the amount consumed in an hour * 4 hours

Mathematically, that would be 0.75 * 4 = 3 gallon

Now, the amount of fuel left is simply the difference between the initial amount of fuel in the tank minus the amount of fuel present after 4 hours.

That would be; 11 - 3 = 8 gallons

b. Like above, we want to know the amount of fuel left after t hours.

Since 0.75 is used up per hour, the amount used up in t hours would be 0.75 * t = 0.75t

Now, the amount of fuel that would be left in the tank would be the difference between what we had initially and what was used up.

Mathematically, that would be 11- 0.75t

Answer:

THE OTHER ANSWER IS WRONG

Step-by-step explanation:

90=20+6x-2

92=20+6x

72=6x

12=x

Hope this helps!

Answer:

answer is 1

Step-by-step explanation:

y∝x

y=kx

15=3k

divide 3 both sides

k=5

so y=5x

when y is 5

5=5×x

divide 5 both sides

x=1

Answer: B and D

Step-by-step explanation: since it is $30 per student the total cost would have to be a multiple of 30

Answer:

0

Step-by-step explanation:

We can use the slope formula to find the slope

m = (y2-y1)/(x2-x1)

    = ( -2 - -2)/( 4 -1)

    = (-2+2)/( 4-1)

    = 0/3

   = 0

Answer:

Step-by-step explanation:

[tex](1, -2) , (4, -2)\\m = ?\\x_1 =1\\y_1 =-2\\x_2 =4\\y_2 =-2\\\\m = \frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{-2-(-2)}{4-1} \\m = \frac{-2+2}{3}\\ m = \frac{0}{3}\\ m = 0[/tex]

Answer:

Ava's share = $20

Charlotte's share = $16

Step-by-step explanation:

15x + 12x = 36 : multiply each girl's age by same amount and adding gives $36

27x = 36 : add x terms

x = 36 / 27 : divide both sides of equation by 27

x = 4 / 3

Ava's share = 15x = 15 * 4/3 = 20

Charlotte's share = 12x = 12 * 4/3 = 16

Answer:

4x

Step-by-step explanation:

8x-2y=5

8x=2y+5

8x-5=2y

4x-5/2=y

The slope of the parallel line would be 4x because the slope doesn't change. Hope this helps.

240

using pascals trianle

for the power 6 it is

1, 6,15,20, 15,6, 1

and for the third term (2x)^4 and (-1)^2

[tex]15 \times {(2x)}^{4} \times {( - 1)}^{2} [/tex]

[tex]240 {x}^{4} [/tex]

Since only the coefficient is needed

the answer is 240.

The required coefficient of third term is 480.

Coefficient of the third term of (2x−1)^6 to be determine.

Coefficient is defined as the integer present adjacent to the variable.

Here,  (2x−1)^6
Using binomial expansion,
Third term = P(6,2)(2x)^6-2(-1)^2
                  =   6*5*16x^4
                  = 480x^4

Thus, the required coefficient of third term is 480.

Learn more about coefficient here:

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Answer:

y+(21)=-4(x-7)

Step-by-step explanation:

the point slope equation , two point

m=y2-y1/x2-x1

m=23+21/-4-7=44/-11= -4

y+(21)=-4(x-7)

Answer:

Standard form is Ax + By = C

Step-by-step explanation:

Answer:

The standard form is Ax + Bx = C

Answer:

5/6w=2/3

5/6(4/5)=2/3

20/30=2/3

20/30=10/15=2/3=2/3

Proof:

5/6w=2/3

6/5*5/6w=2/3*6/5

30/30w=2/3*6/5

w=12/15=4/5

Hope this helps ;) ❤❤❤

Answer:

[tex]\huge\boxed{\sf \frac{a^2+b^2}{2(a^2-b^2)}}[/tex]

Step-by-step explanation:

=> [tex]\sf \frac{a}{2(a+b)} + \frac{b}{2(a-b)}[/tex]

LCM = 2(a+b)(a-b)

=> [tex]\sf \frac{a(a-b)+b(a+b)}{2(a+b)(a-b)}[/tex]

Simplifying further

=> [tex]\sf \frac{a^2-ab+ab+b^2}{2(a^2-b^2)}[/tex]

=> [tex]\sf \frac{a^2+b^2}{2(a^2-b^2)}[/tex]

[tex]\dfrac{a}{2(a+b)}+\dfrac{b}{2(a-b)}=\\\\\dfrac{a(a-b)}{2(a+b)(a-b)}+\dfrac{b(a+b)}{2(a+b)(a-b)}=\\\\\dfrac{a^2-ab}{2(a^2-b^2)}+\dfrac{ab+b^2}{2(a^2-b^2)}=\\\\\dfrac{a^2+b^2}{2(a^2-b^2)}[/tex]

Complete question is;

For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 31 beats per​ minute, the mean of the listed pulse rates is x over bar equals 71.0 beats per​ minute, and their standard deviation is s equals 12.6 beats per minute.

a. What is the difference between the pulse rate of 31 beats per minute and the mean pulse rate of the​ females?

b. How many standard deviations is that​ [the difference found in part​ (a)]?

c. Convert the pulse rate of 31 beats per minutes to a z score.

d. If we consider pulse rates that convert to z scores between minus 2 and 2 to be neither significantly low nor significantly​ high, is the pulse rate of 31 beats per minute​ significant?

Answer:

A) 40 beats per minute

B) 3.1746

C) z = -3.17

D) the pulse rate of 31 beats per minute is significantly low.

Step-by-step explanation:

A) The mean pulse rate is given as x bar = 71

Thus difference between this and pulse rate of 31 beats per minute is;

Difference = 71 - 31 = 40 beats per minute

B) number of standard deviations of the difference found in part a is given as;

number = difference/standard deviation(s)

number = 40/12.6

number = 3.1746

C) The z-score is calculated from;

z = (x - xbar)/s

z = (31 - 71)/12.6

z = -3.17

D) from the question we are told that the z scores between minus2 and 2 to be neither significantly low nor significantly​ high. However, we have a Z-score of -3.17 which doesn't fall into that range. Thus, the pulse rate of 31 beats per minute is significantly low.

Answer: 880 cm

Step-by-step explanation:

Given: Radius of the hula hoop = 35 cm

Hula hoop is  circular in shape

Then, Circumference = [tex]2\pi r[/tex] , where r = radius

Now , Circumference of hula hoop = [tex]2\times \dfrac{22}{7}\times35=220\ cm[/tex]

Now , the distance the hula hoop rolls in 4 full rotations = 4 × (Circumference of hula hoop)

[tex]= 4 \times 220=880\ cm[/tex]

Hence, the required distance = 880 cm

Answer:

880

Step-by-step explanation:

Answer:

A.) 375/1000, B) 75/200,  D.) 3/8

Step-by-step explanation:

A number can be represented in many forms depending on the situation, it can be represented in form of ratio, decimals, fraction e.t.c.

Given the number 0.375 which is in its decimal form, this number can also be represented in the form of a fraction.

[tex]a)0.375=\frac{0.375}{1} \\ \\multiplying\ by\ \frac{1000}{1000}\ gives:\\\\\frac{0.375}{1}*\frac{1000}{1000}= \frac{375}{1000}\\\\ b) 0.375=\frac{0.375}{1} \\ \\multiplying\ by\ \frac{1000}{1000}\ gives:\\\\\frac{0.375}{1}*\frac{1000}{1000}= \frac{375}{1000}=\frac{5(75)}{5(200)} =\frac{75}{200} \\\\d) 0.375=\frac{0.375}{1} \\ \\multiplying\ by\ \frac{1000}{1000}\ gives:\\\\\frac{0.375}{1}*\frac{1000}{1000}= \frac{375}{1000}=\frac{125(3)}{125(8)}=\frac{3}{8} \\[/tex]

Answer:

Step-by-step explanation:

y=2/5x-12 it is a linear equation in the form of y=mx+b

the best way to know is to graph the function

Answer:

  B)  (-2, 5)

Step-by-step explanation:

Perhaps easiest is to try the points to see what works. You can also graph the equations or solve by any of several other means.

Trying the points

  A) 3(-2)+4(-2) = -6 -8 = -14 ≠ 14

  B) 3(-2) +4(5) = -6 +20 = 14; -2 = 2(5) -12 = 10 -12 . . . . true

  C) 3(-4) +4(4) = -12 +16 = 4 ≠ 14

  D) 3(2) +4(2) = 6 +8 = 14; 2(2) -12 = -8 ≠ -2

__

Choice B ( -2, 5) is the only point that works in both equations.

Answer:

x = -2

y = 5

then:

B) (-2,5)

Step-by-step explanation:

3x + 4y = 14

x = 2y - 12

from te firs equation:

3x = 14 - 4y

x = (14-4y)/3

then:

2y - 12 = (14-4y)/3

3(2y-12) = 14 - 4y

3*2y + 3*-12 = 14 - 4y

6y - 36 = -4y + 14

6y + 4y = 14 + 36

10y = 50

y = 50/10

y = 5

from the second equation:

x = 2y - 12

x = 2*5 - 12

x = 10 - 12

x = -2

Check:

from the first equatión:

3x + 4y = 14

3*-2 + 4*5 = 14

-6 + 20 = 14

Answer:

The co-terminal angle of [tex]\frac{3\pi}{4}\ \text{radians}[/tex] is [tex]-\frac{5\pi}{4}\ \text{radians}[/tex].

Step-by-step explanation:

The angle provided is, [tex]\frac{3\pi}{4}\ \text{radians}[/tex].

Convert the angle into degrees as follows:

[tex]\frac{3\pi}{4}\ \text{radians}=\frac{3\times180^{o}}{4}=135^{o}[/tex]

Co-terminal angles are those angles that share the same terminal and initial sides.

To find the co-terminal angle of a provided angle, we just need to add or subtract 360° or 2π to it.

Determine the co-terminal angle of [tex]\frac{3\pi}{4}\ \text{radians}[/tex] as follows:

[tex]\text{Co-terminal Angle}=\frac{3\pi}{4}+2\pi[/tex]

                             [tex]=\frac{3\pi+8\pi}{4}\\\\=\frac{11\pi}{4}[/tex]

[tex]\text{Co-terminal Angle}=\frac{3\pi}{4}-2\pi[/tex]

                             [tex]=\frac{3\pi-8\pi}{4}\\\\=-\frac{5\pi}{4}[/tex]

Thus, the co-terminal angle of [tex]\frac{3\pi}{4}\ \text{radians}[/tex] is [tex]-\frac{5\pi}{4}\ \text{radians}[/tex].

Answer:

Its A

Step-by-step explanation:

edge

Answer:

Step 1: Address input parameters & values.

Input parameters & values:

The fraction number = 37/99

Step 2: Write it as a decimal

37/99 = 0.3737

0.3737 is the decimal representation for 37/99

Answer is 0.3737 repeating.

Hope this helps! Plz mark brainliest! ☜(ﾟヮﾟ☜)

Answer:

0.32 grams

Step-by-step explanation:

ratio of weight of -copper, zinc, manganese, and nickel = 177:12:7:4

let the

weight of copper = 177x

weight of zinc = 12x

weight of manganese = 7x

weight of nickel = 4x

Total weight of this alloy in terms of x =  177x + 12x+ 7x + 4x = 300x

given weight of alloy = 8 grams

thus,

weight of this alloy in terms of x =given weight of alloy

300x = 8 grams

x = 8/300 grams =

weight of zinc = 12x = 12 * 8/300 grams = 96/300 grams = 0.32 grams

Answer:

3(2x-5)(x+2)

Step-by-step explanation:

Factor out the 3.

3(2x²-x-10)

Factor the remaining.

3(2x-5)(x+2)

(I don‘t know what grid they’re talking about.)

Answer:

21 windows

Step-by-step explanation:

collen family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and collen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?

Answer: Let the number of window Collen father would paint be a while that of her mother be b. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father a = 2b

Let the number of windows that would be needed to be painted each by Colleen and her 2 brothers be c because they would paint the equal number of windows.

The total number of windows to be painted = 2b + b + c + c + c = 3b + 3c = 3(b + c).

Collen painted 7 windows as her mother and her own share which is one less than the fathers share. Therefore b + c = 7.

Also the fathers share a = 2b = 7 + 1 = 8 windows. Therefore b = 4 which is the mother share

Therefore the total number of windows = 3(b + c) = 3(7) = 21 windows

3b + 3c =  21

3(4) + 3c = 21

12 + 3c = 21

3c = 21 - 12

3c = 9

c = 3 which is collen and her brothers share

Answer:

14/9 inches, or an inch and 5/9 of an inch.

Step-by-step explanation:

If 2/3 inch is the same as 9 miles, then x inches represents 21 miles. We can then set up a proportion.

[tex]\frac{\frac{2}{3} }{9} =\frac{x}{21}[/tex]

9 * x = (2/3) * 21

9x = 2 * 7

9x = 14

x = 14/9 inches.

Hope this helps!

Answer:

1 5/9 ich represent 21 miles

Step-by-step explanation:

Proportions:

2/3  inch  ⇔   9 miles

M  inch   ⇔    21 miles

M = 21*(2/3) / 9

M = 14/9

14/9 = 9/9 + 5/9 = 1 + 5/9 = 1 5/9 inch

Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.

The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.

The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.

Answer:

Step-by-step explanation:

Answer:

Hey there!

The answer would be C. 4/15.

4/5(1/3)=4/15

Let me know if this helps :)