Banu is 20 years older than binu. In 5 years, Banu will be twice as old as binu. Find their present age.

Answer:

[tex]x^4-5x^2-36=0[/tex]

Step-by-step explanation:

We need to find equation that has exactly two real and two non real solutions

2 real  and 2 non real solution means 4 solutions

x^3 equation has maximum of 3 solutions

So we ignore equation that has largest exponent x^3

We ignore options B  and D

Let check option A

[tex]x^4 - 36x^2=0[/tex]

factor the left hand side

Factor out x^2

[tex]x^2(x^2 - 36)=0[/tex]

WE set each factor =0  and solve for x

x^2 =0  so x=0

x^2 - 36 =0 so x= +-6

So solutions are x=0, x=6 , x=-6. Only 3 real solutions we got

LEts check with option C

[tex]x^4-5x^2-36=0[/tex]

Factor left hand side

[tex] (x^2-9)(x^2+4)=0[/tex]

set each factor =0  and solve for x

x^2 -9 =0  so x= -3, + 3

x^2 + 4 =0 , x^2 = -4, so x= +2i, -2i

So we got two real solutions (-3,+3) and two non real solutions (-2i,+2i)

Answer:

C. x^4 - 5x^2 - 36 = 0

Answer:

i got 185.4 so basically 184.

412 times 5% equals 20.6

times that by 9 for 9 months then that gives you the answer.

Answer:

1. The population increases exponentially, therefore the number of members in the team will increase by the equation modeled by :

[tex]\text{Number of members = }a_0(1+\frac{Rate}{100})^{Time}\\\\\implies\text{Number of members = }412(1+\frac{5}{100})^9\\\\\implioes\text{Number of members after 9 months = }639[/tex]

2. Total cost of the toy is calculated by multiplying the initial cost and the amount of tax charged on the toy.

Here, 15.85 represents the initial cost of the toy

Hence, 1 + x represents the amount of tax charged on the toy.

3. Rate per year is given to be 12.5%

Now, to find monthly rate, divide the yearly rate by 12

[tex]\text{Monthly Rate = }\frac{12.5}{12}=1.04\%[/tex]

4. Rate per year is given to be 20%

Now, to find monthly rate, divide the yearly rate by 12

[tex]\text{Monthly Rate = }\frac{20}{12}\approx 1.7\%[/tex]

5. The value of a truck after t years is represented by the function f(t)=22,200(0.92)t .

Here, 2200 is the initial value of the truck.

Answer:

B) simple random

The sampling method described in the scenario is "simple random sampling." Option B

With basic random sampling, every unit in the population has an equal chance of being chosen, and there is no set pattern or grouping involved in the selection process.

In this instance, the hammers are put into boxes, and a random box is chosen for quality assurance inspection. It meets the criteria for simple random sampling because each box has an equal probability of being picked.

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Hi There!

Solution + Answer:

2 gallons of milk: 3.29 * 2 = $6.58

4 gallons of ice-cream: 3.59 * 4 = $14.36

5 pounds of strawberries: 0.72 * 5 = $3.60

Total price before tax: 6.58 + 14.36 + 3.60 = $24.54

Tax: 24.54 * 0.0375 = $0.92025

Total price after tax: 24.54 + 0.92025 = $25.46025

Round: 25.46025 = $25.46

Hope This Helps :)

According to the question,

2 gallons of milk,

= [tex]3.29\times 2[/tex]

= [tex]6.58[/tex] ($)

4 gallons of ice-cream,

= [tex]3.59\times 4[/tex]

= [tex]14.36[/tex] ($)

5 pounds of strawberries,

= [tex]0.72\times 5[/tex]

= [tex]3.60[/tex] ($)

Now,

The total price before tax will be:

= [tex]6.58+14.36+3.60[/tex]

= [tex]24.54[/tex] ($)

The tax will be:

= [tex]24.54\times 0.0375[/tex]

= [tex]0.92025[/tex] ($)

hence

The total price after tax will be:

= [tex]24.54+0.92025[/tex]

= [tex]25.46025[/tex]

or,

= [tex]25.46[/tex] ($)

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Answer: 33

Step-by-step explanation:

           Today                3 years ago

Ben:   x + 20                  (x + 20) - 3    

Dan:     x                          x - 3

  3 years ago, Ben was 3 times as old as Daniel

⇒  (x + 20) - 3  = 3(x - 3)

       x + 17        = 3x - 9

             17        = 2x - 9

             26       = 2x

             13        = x

Today, Ben = x + 20

                   = 13 + 20

                   = 33

Answer:

Ben is 33 years old

Step-by-step explanation:

Let Ben’s age = B

Let Daniel’s age = x

B = x + 20  (20 years older than Daniel)

Their ages 3 years ago:

B = 3x  (also given in problem)

B = x + 20  (given in problem)

x + 20 = 3x  (Since both equations are equal to B, set them equal to each other)

20 = 2x (simplify)

x = 10

B = 10 + 20 = 30

Their ages now:

Add 3 to their "ages three years ago"

New x = Daniel’s age = old age + 3 = 10 + 3 = 13 years old

B = Ben’s age = old age + 3 = 30 + 3  = 33 years old

Answer:

x = 21.5

Step-by-step explanation:

In the given trapezoid, the angles are consecutive interior angles.

i.e, consider the parallel sides of a trapezoid as parallel lines and the common side as the transversal. So, it is parallel lines cut by a transversal make a pair of consecutive interior angles which are supplementary.

i.e,

(5x + 13)° + (3x - 5)° =180°

5x + 13 + 3x - 5 = 180

8x + 8 = 180

8x = 180 - 8 =172

x= 172/8 = 21.5

So, 5x + 13 = 5(21.5) + 13 = 120.5°

3x - 5 = 3(21.5) -5 = 59.5°

Answer:

[tex]y= 51(1.5)^x[/tex]

Step-by-step explanation:

The ordered pairs model an exponential growth function. {(−1,34), (0,51), (1,76.5), (2,114.75)}

Exponential function equation is y=ab^x

Lets plug in the ordered pairs and find our 'a'  and 'b'

(0,51)

[tex]51= ab^0[/tex]

a= 51

(−1,34)

[tex]34= 51b^{-1}[/tex]

Divide both sides by 51

[tex]\frac{34}{51} = b^{-1}[/tex]

So b = 51/34

b= 1.5

Plug in the values of 'a'  and 'b'

Equation becomes [tex]y= 51(1.5)^x[/tex]

Answer:

Correct choice is D (1,0) and (-2,-1)

Step-by-step explanation:

Triangle DBC has vertices B(-3,1), C(3,3) and D(-1,-3). By the triangle midline theorem, the midline joining the midpoints of two sides is parallel to the third side. Thus, you have to find the coordinates of the midpoints of the sides DB and DC of the triangle DBC.

Let point E be the midpoint of the side BD, then point E has coordinates [tex]\left(\dfrac{x_B+x_D}{2},\dfrac{y_B+y_D}{2}\right).[/tex] If B(-3,1) and D(-1,-3), then

[tex]E\left(\dfrac{-3+(-1)}{2},\dfrac{1+(-3)}{2}\right)\Rightarrow E(-2,-1).[/tex]

Let point F be the midpoint of the side DC, then point F has coordinates [tex]\left(\dfrac{x_C+x_D}{2},\dfrac{y_C+y_D}{2}\right).[/tex] If C(3,3) and D(-1,-3), then

[tex]F\left(\dfrac{3+(-1)}{2},\dfrac{3+(-3)}{2}\right)\Rightarrow F(1,0).[/tex]

Answer:

D: (1,0) and (-2,-1)

Step-by-step explanation:

if you where to plot all the other answers and take a straight edge (ruler) and drew a line through them you would find this is the only proper answer. and i used geogebra

Answer:

The correct answer is B) y – 2 = (x – 3)

Step-by-step explanation:

In order to find this, look at the base form of point-slope form.

y - y1 = m(x - x1)

Seeing as there is subtraction symbols after x and y, we know that we would be subtracting the x and y values. Since 2 is the y value, it would go in for y1 and 3 being the x value puts it in for x1. Once you do that, you'll get the equation above.

Answer:

-1/2

Step-by-step explanation:

The given polynomial only has one exponent, so the degree of the polynomial is the number of the exponent.

The degree is 3.

Answer: The Answer is B

Step-by-step explanation:

FIrst we see post 7 and -5 we need to cancel out seven sooooo we make sevena a neg and do -5 and -7 and we get -12 we divide this by -2 and we get post 6

x=6

-2x+7=-5

-2(-7)+7=-5(-7)

-2(-2)x=-12(-2)

x=6

Answer:

b  6

Step-by-step explanation:

-2x+7 = -5

Subtract 7 from each side

-2x +7-7 = -5 -7

-2x = -12

Divide by -2

-2x/2 = -12/-2

x=6

Answer:

D. [tex]\frac{3}{7}[/tex]

Step-by-step explanation:

We have been given that the probability of an event is 3/10.  

To find the odds of the same event we will use formula:

[tex]\text{Odds of an event}=\frac{\text{Probability of the event}}{\text{1-Probability of the event}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{1-\frac{3}{10}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{\frac{1*10}{10}-\frac{3}{10}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{\frac{10-3}{10}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{\frac{7}{10}}[/tex]

Dividing a fraction with another fraction is same as multiplying the 1st fraction by the reciprocal of second fraction.

[tex]\text{Odds of the event}=\frac{3}{10}\times \frac{10}{7}[/tex]

[tex]\text{Odds of the event}=\frac{3}{7}[/tex]

Therefore, the odds of the same event is [tex]\frac{3}{7}[/tex] and option D is the correct choice.

Answer:

see attached diagram

Step-by-step explanation:

A dilation with a scale factor of [tex]\dfrac{1}{3}[/tex] centered at the origin has a rule:

[tex](x,y)\mapsto\left(\dfrac{x}{3},\dfrac{y}{3}\right).[/tex]

Then the image of the triangle ABC is triangle DEF(see attached diagram) with coordinates

Answer:

Step-by-step explanation:

1) [tex](a^3)^{-2}  = a^{-6}\\[/tex]

2) [tex](a^{-1} * a^{-2} )^{-3} = (a^{-1 + (-2)})^{-3} }=a^{-9}[/tex]

3) [tex]((a^{2})^{-2})^{2}=(a^{-4})^{2}=(a^{-8})[/tex]

4) [tex](a*a)^{2} =  (a^{2})^{2}=a^{4}[/tex]

Lisa spends 4 minutes per call, so to spend a total of 12 minutes on the phone, she needs to route 3 calls.

Lisa spent 8 minutes on the phone routing 2 phone calls, which means she spends 4 minutes per call. This is calculated using the unit rate which is the time spent per phone call. To find out how many phone calls Lisa would have to route to spend a total of 12 minutes, we can set up a proportion where 4 minutes corresponds to 1 phone call (the unit rate), and 12 minutes corresponds to the number of phone calls we want to find (let's call it x calls).

The proportion is as follows:

4 minutes/1 call = 12 minutes/x calls

Cross-multiplying to solve for x gives us:

4 * x = 12 * 1

4x = 12

x = 12 / 4

x = 3 calls

Therefore, Lisa needs to route a total of 3 calls to spend 12 minutes on the phone.

Final answer:

A disadvantage of using credit is that it can be tempting to overspend.

Explanation:

A disadvantage of using credit is that it can be tempting to overspend.

When using credit, individuals can easily spend more than they can afford, leading to financial difficulties and debt. It is important to use credit responsibly and only borrow what can be comfortably repaid.

Answer:

true

Step-by-step explanation:

on a football feild there are 4,320 inches and on a basketball court there are 2,865 centemeters

Answer:

B on edg

Step-by-step explanation:

You got this chief.

Hello from MrBillDoesMath!

Answer:

10.2

Discussion:

Let the length of the missing side = "s" Applying the Pythagorean theorem to this right triangle gives:

4^2 + s^2 = 11^2    =>

16 + s^2 = 121        =>             ( 4*4 = 16, 11*11 = 121)

16 - 16  + s^2 = 121 - 16 =>     (subtract 16 from both sides)

s^2 = 105 =>

x = sqrt (105)

which is approximately 10.2

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

Answer: D

Step-by-step explanation:

log₂ (x - 4) = 4

        x - 4 = 2⁴

        x - 4 = 16

        x      = 20

Answer:

The slope is 2

The slope represents  how much it costs per visit the pool.

We have a positive slope when lines go  from bottom left to top right

The y intercept is where we cross the y axis which is 4.

x is the  number of visits to the pool

y is the  total cost in dollars

f(x) = 2x+4

Step-by-step explanation:

To find the slope we take two point ( 0,4) and (1,6)

and use the formula

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

  = (6-4)/(1-0)

 m= 2/1

The slope is 2

It represents  how much it costs per visit the pool.

We have a positive slope when lines go  from bottom left to top right

The y intercept is where we cross the y axis which is 4.

x is the  number of visits to the pool

y is the  total cost in dollars

f(x) = mx+b  where m is the slope and b is the y intercept

f(x) = 2x+4

Answer:

the answer is D edge 2021

Step-by-step explanation:

The empirical rule states that at 95% the measurements would be within 2 standard deviations of the mean.

You are given a mean of 68 inches and a standard deviation of 4.

2 times the standard deviation = 2 x 4 = 8

So 95% of the heights would be between 68-8 = 60 inches and 68+8 = 76 inches.

Answer:

60 -76 is the range

Step-by-step explanation:

As the graph shows, if we are in 2 standard deviations of the mean, we are in (34.1 + 13.6) *2 = 47.7*2 = 95.4 %

Our mean is 68

2  standard deviations is 2 * 4 = 8

68-8 = 60

68 * 8 = 76

We need to be between 60 and 76 to have at 95% confidence interval

Answer:

22662

Step-by-step explanation:

14000(1+3.5/100)^14

The population after 14 years is 22662.

It is given that,

Explanation:

The exponential growth model is:

[tex]P=P_0\left(1+r\right)^t[/tex]

Where, [tex]P[/tex] is population after [tex]t[/tex] years, [tex]P_0[/tex] is the initial population and [tex]r[/tex] is the growth rate.

Substituting [tex]P_0=14000,r=0.035,t=14[/tex] in the above equation.

[tex]P=14000\left(1+0.035\right)^{14}[/tex]

[tex]P=14000\left(1.035\right)^{14}[/tex]

[tex]P=22661.7233[/tex]

[tex]P\approx 22662[/tex]

Thus, the population after 14 years is 22662.

Learn more:

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Answer:

(no horizontal asymptotes found)

Step-by-step explanation:

Answer:

A polynomial needs to have either addition, subtraction or multiplication in the equation.

The 2nd, 3rd and 4th answers have subtraction and addition, so those are polynomials.

The first answer is a fraction, which is a division problem, therefore is not a polynomial.

Answer:

[tex]g(x)= 24(3)^{x-2}+6[/tex]

Step-by-step explanation:

f(x)=8(3)^x−2 +2

The graph of f(x) is stretched vertically by a factor of 3 to form the graph of g(x)

When f(x) is stretched vertically then we multiply f(x) by 3 to get g(x)

g(x) = 3f(x)

[tex]g(x)= 3(8(3)^{x-2}+2)[/tex]

Now we distribute 3 inside the parenthesis

[tex]g(x)= 24(3)^{x-2}+6[/tex]

This is our required g(x)

Answer:

Step-by-step explanation:

Problem One (left panel)

Question A

Question B

The rate of change = (56 - 52)/(3 - 1) = 4/2 = 2  miles / hour^2 (you have a slight acceleration.

Question C

The way I have done it the domain is n from 1 to 6

Question 2 (Right Panel)

Question A

The equation for the table is f(x) = 3x - 3 which was derived simply by putting all three points into y = ax + b and solving.

Part B

Hello from MrBillDoesMath!

Answer:

Choice C    (6)

Discussion:

Since it is an isosceles trapezoid the length of the two legs (i.e.  AB = 5y-10 and CD = 2y+8) are equal.  In other words,

5y - 10 = 2 y + 8

Subtract 2y from each side:

5y - 2y - 10 = 8

Now add 10 to each side

5y - 2y - 10 + 10 = 8 + 10 =>

3y + 0 = 18 =>

3y = 18 =>

y = 6

Regards,  

MrB

To find the value of y in the isosceles trapezoid ABCD, set up an equation using the given measurements for AB, BC, and CD. Solve the equation to find the value of y.

To find the value of y in the isosceles trapezoid ABCD, we can set up an equation using the given measurements for AB, BC, and CD. Since AB and CD are the legs of the trapezoid, they should be equal. Therefore, we can set AB equal to CD and solve for y:

5y - 10 = 2y + 8

Subtract 2y from both sides:

3y - 10 = 8

Add 10 to both sides:

3y = 18

Divide both sides by 3:

y = 6

Therefore, the value of y is 6. Answer choice C) 6 is correct.

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Answer:

The cost of the 40 rulers is £8 .

Step-by-step explanation:

As given in the question

15 rulers cost £3

i.e

15 rulers = £3

Cost of the one ruler.

[tex]1\ ruler = \frac{3}{15}[/tex]

1 ruler cost =  £ 0.2

Now find out the cost for 40 rulers .

Cost for 40 rulers = 40 × 0.2

                              = £8

Therefore the cost of the 40 rulers is £8 .

The question involves finding the unit price of a ruler and then finding the cost of 40 rulers. The price for one ruler is £0.2, and hence, the price for 40 rulers would be £8.

This is a mathematics question about unit price and proportionality. First, we need to find the price of one ruler by dividing the total cost by the number of rulers. So, £3 divided by 15 rulers is £0.2 per ruler. To find out how much 40 rulers costs, we multiply the price of one ruler by the quantity we desire which is 40 rulers. So, £0.2 multiplied by 40 equals to £8.

Therefore, the cost of 40 rulers would be £8.

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