A girl is twice as old as her sister. Five years hence, the product of their ages (in years) will be 375. Find their present ages. A girl is twice as old as her sister. Five years hence, the product of their ages (in years) will be 375. Find their present ages.

Answers

Answer 1

Answer: girls=20, sister=10

Step-by-step explanation:

Let x = the girl's sister's age (present)

Let 2x= the girl's age (present)

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

According to the question

(x+5)(2x+5)=375

Expand parentheses by FOIL (First Outer Inner Last)

2x²+5x+10x+25=375

Combine like term (5x and 10x)

2x²+15x+25=375

Subtract 375 on both sides

2x²+15x+25-375=375-375

2x²+15x-350=0

Find the factors (cross factor)

(x-10)(x+17.5)=0

x=10 or x=-17.5 (rej) ⇔ the age can't be negative

the girl's age is 20, and her sister's age is 10.


Related Questions

A post is put every 6 feet along a fence around a rectangular field that is 42 feet long and 36 feet wide. What is the total number of feet around the field? *

Answers

Answer:

26 posts

Step-by-step explanation:

find perimeter:

42+42+36+36= 156

divide by 6

156/6=26

Please, can you do this step-by-step.... 2 1/3 + 6 3/5

Answers

Answer:

8 14/15

Step-by-step explanation:

Step 1:

2 1/3 + 6 3/5

Step 2:

2 5/15 + 6 9/15

Answer:

8 14/15

Hope This Helps :)

Answer:8  14/15

Step-by-step explanation:

convert to lcd, 2  5/15 6 9/15

add them and you get that

look at the image and show work 4) translation: 6 units left K, J, I, L​

Answers

Answer:

K (-5, 2); J (-2, 3); I (-1, 1); L (-5, -3)

Step-by-step explanation:

Translating the shape 6 units to the left means that every point/vertex will be moved 6 units to the left of where it is originally drawn.

Point K is at (1, 2). Since we are only moving it left (on the x-axis), the y value will not change. To move K left 6, we have to subtract 6 from its current x-value, 1. We get -5 for the new x-value. Because the y value didn't change, the new location of K is (-5, 2).

Point J is at (4, 3). Subtracting 6 from 4 (the x value) gives us the new x value of -2. Again, the y value does not change and so our new location for J is (-2, 3).

Point I is at (5, 1). If we subtract 6 from 5, we get -1. This is our new x value for I. The new point is (-1, 1). (Once again, the y value does not change).

Point L is at (1, -3). By subtracting 6 from the original x value, 1, we get our new x value: -5. The new point for L is (-5, -3).

Is 1/2 rational or a not whole interger

Answers

Answer:

Every integer is a rational number, numbers like 1/2,and -3/7 are also rational,  It is an Rational number

Step-by-step explanation:

Here is a central angle that measures 1.5 radians. Select all true statements. Question 1 options: A) The area of the whole circle is 1.5 times the area of the slice. B) The radius is 1.5 times longer than the length of the arc defined by the angle. C) The ratio of radius to arc length is 1.5. D) The length of the arc defined by the angle is 1.5 times longer than the radius. E) The ratio of arc length to radius is 1.5. F) The circumference of the whole circle is 1.5 times the length of the arc formed by the angle.

Answers

Answer:

  D, E

Step-by-step explanation:

The applicable formula is ...

  s = rθ

so, for θ = 1.5, the arc length is 1.5 times the radius. The true statements are ...

  D) The length of the arc defined by the angle is 1.5 times longer than the radius.

  E) The ratio of arc length to radius is 1.5.

The ages of an audience at a concert were recorded as follows:
12, 14, 13, 11, 10, 16, 17, 13, 12, 10, 10, 14, 15, 15, 12, 15, 17, 15
(a) Create a frequency table with the above information.

Answers

I hope this helps!!!

Mx-y when m=2,x=7. And y= 5

Answers

(2•7)-5
14-5= 9
So the answer is 9

Answer:

9

Step-by-step explanation:

mx - y (m = 2, x = 7, y = 5)

(2*7) - 5

= 14 - 5

= 9

.8787... as a fraction

Answers

Step-by-step explanation:

Write 0.8787 as

0.8787/1

Multiply both numerator and denominator by 10 for every number after the decimal point

0.8787 × 10000

1 × 10000

=

8787/10000

Reducing the fraction gives

8787/10000

- 5у - 25 - - 40
What is y

Answers

The answer is y=-3 hope it helps

If 2.5 pounds of strawberries cost $10, how much do 8 pounds of strawberries cost? Question 17 options: $3.13 $32.00 $40.00 $2.00

Answers

Answer:

32 dollars for 8 pounds

Step-by-step explanation:

1. 2.5 times 3 = 7.5

2. 10 times 3 = 30

3. 2.5 divided by 5 = .5

4. 10 divided by 5 = 2

5. 7.5 + .5 equals 8

6. 30 + 2 = 32.

hope this helps you:)

Answer:

$32.00

Step-by-step explanation:

i took 10 divided by 2 and got its $4 a pound then take 8 times 4 and got 32

this is true or false? and why.​

Answers

true because the way I have been taught to think about it since elementary, the end of the sign (< or >) with the 2 lines is greater than the side where they connect to make one, and in both of the examples they are saying 3 is greater than x


If 9 is subtracted from a certain number and the difference is divided by 3, the result is 1 more than
1/7 of the original number. Find the original number.

Answers

Answer:

Let the number be x.

(x-9)/3= (x/7)+1

(x-9)/3= (x+7)/7

Cross multiplying

7x-63= 3x+21

4x= 84

x= 42

Hope this will help :-)

a table is on sale for 72% off. the price is $246.40. What is the regular price

Answers

Answer:

$68.99

Step-by-step explanation:

This is called percentage decrease:

(100 - 72)% = 28%

246.40 × 28/100

= $68.99

Tommy used a straightedge and a compass to construct a square inside circle C, as shown.
Which of the following steps did Tommy take to construct the inscribed square? Select all steps in the construction.
A Construct a perpendicular bisector of the diameter AB.
B. Construct a perpendicular bisector of the diameter DE.
C. Construct a bisector of ADB to find the location of point E.
D. Use the compass to draw a circle centered at point c.
O E Use the compass to draw two arcs of the same radius centered at point C.
OF Use the straightedge to draw diameter AB of the circle.
OG Use the straightedge to draw lines connecting the endpoints of the two diameters.

Answers

Answer:

The correct options are;

A. Construct a perpendicular bisector of the diameter AB

D. Use the compass to draw a circle centered at point C

E. Use the compass to draw two arcs of the same radius centered at point C

F. Use the straightedge to draw diameter AB of the circle

G. Use the straightedge to draw lines connecting the endpoints of the two diameters

Step-by-step explanation:

To draw an inscribed square of a circle, the circle is first constructed. The diameter of the circle is drawn with a straight edge to find the first two vertices of the intended inscribed square. The perpendicular bisector of the diameter is then drawn intersecting the circumference to provide the other two vertices of the square.

The straightedge is then used to draw lines that connect the endpoints of the two diameters to form the inscribed square of the circle.

Suppose f(x) = 2x-1 and g (x) = x + 1/a. Which value(s) of a would make the composite functions commutative? A. 0 B. 2 C. any value of a D. no value of a

Answers

Answer:

2

Step-by-step explanation:

A commutative function means that when you insert one function in space of x in the other function, they will equal x. The equation is f(g(x)) = g(f(x)) = x

So, 2([tex]\frac{x+1}{a}[/tex]) - 1 = [tex]\frac{(2x-1)+1}{a}[/tex]

If you multiply both sides by a, you get   2a([tex]\frac{x+1}{a}[/tex]) - a = (2x-1)+1

Simplify it                                                   2a([tex]\frac{x+1}{a}[/tex]) - a = 2x

Add a to both sides                                    2a([tex]\frac{x+1}{a}[/tex])  = 2x +a

The two as on the left cancel out                   2(x+1)=2x+a

Distribute the 2                                               2x+2=2x+a

Then subtract 2x from both sides                        2 = a

Therefore, a = 2

Hope this helps!

Answer:2

Step-by-step explanation:

Irene's grandfather arrived in Sydney from Athens at 10 pm on Friday after a 25-hour trip. The flight began at 12 noon on Thursday, Athens time. What is the time difference between Athens and Sydney?

Answers

The question is incomplete:

Irene's grandfather arrived in Sydney from Athens at 10 pm on Friday after a 25-hour trip. The flight began at 12 noon on Thursday, Athens time. What is the time difference between Athens and Sydney?

A. Athens time is 9 hours behind  Sydney time.

B. Athens time is 9 hours ahead of  Sydney time.

C. Athens time is 15 hours behind  Sydney time.

D. Athens time is 15 hours ahead of  Sydney time.

Answer:

A. Athens time is 9 hours behind  Sydney time.

Step-by-step explanation:

The statement indicates that the flight began at 12 noon on Thursday, Athens time and that it lasted 25 hours. So, you can calculate the Athens time when he arrived after 25 hours which would be 1 pm on Friday. Also, the statement says that Irene's grandfather arrived in Sydney at 10 pm on Friday and now we know that at that moment it was 1 pm on Friday, Athens time. From these, you can calculate the difference between 1 pm and 10 pm that would be 9 hours. Because of this, the answer is that the time difference between Athens and Sydney is that Athens time is 9 hours behind  Sydney time.

If segment BD is congruent to segment BC, BD=5x-26, BC=2x+1, and AC=43, find AB

Answers

Answer:Thats a tough one

Step-by-step explanation: Do you need this answer urgently?

Russell runs 9/10 miles in 5 minutes. At this rate, how many miles can he run in one minute

Answers

Answer:

9/50 miles

Step-by-step explanation:

9/10 miles in 5 minutes

= 9/50 miles in 1 min

2-55 Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. Find the probability that a call takes

Answers

The question is incomplete. Here is the complete question.

Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. find the probability that a call takes

a) 3 minutes or less

b) 4 minutes of less

c) 5 minutes of less

d) Longer than 5 minutes

e) Longer than 7 minutes

Answer: a) P(X<3) = 0.882

              b) P(X<4) = 0.908

              c) P(X<5) = 0.928

              d) P(X>5) = 0.286

              e) P(X>7) = 0.174

Step-by-step explanation: Exponential distribution is related with teh amount of time until some specific event happens.

If X is a continuous random variable, probability is calculated as:

[tex]P(X<x) = 1-me^{-mx}[/tex]

in which:

m is decay parameter, given by: [tex]m=\frac{1}{mean}[/tex]

For the Nite Time Inn calls:

[tex]m=\frac{1}{4}[/tex]

m = 0.25

(a) P(X<3)

[tex]P(X<3) = 1-0.25e^{-0.25.3}[/tex]

[tex]P(X<3) = 1-0.25e^{-0.75}[/tex]

[tex]P(X<3) = 1-0.25*0.472[/tex]

P(X < 3) = 0.882

The probability the call takes less than 3 minutes is 0.882.

(b) P(X<4)

[tex]P(X<4) = 1-0.25e^{-0.25.4}[/tex]

[tex]P(X<4) = 1-0.25e^{-1}[/tex]

P(X < 4) = 0.908

The probability the call takes less tahn 4 minutes is 0.908.

(c) P(X<5)

[tex]P(X<5) = 1-0.25e^{-0.25.5}[/tex]

[tex]P(X<5) = 1-0.25e^{-1.25}[/tex]

P(X < 5) = 0.928

The probability of calls taking less than 5 minutes is 0.928.

(d) P(X>5)

Knowing that the sum of probabilities of less than and more than has to equal 1:

P(X<x) + P(X>x) = 1

P(X>x) = 1 - P(PX<x)

[tex]P(X>x) = 1-(1-me^{-m*x})[/tex]

[tex]P(X>x)=me^{-mx}[/tex]

For P(X>5):

[tex]P(X>5) = 0.25e^{-1.25}[/tex]

P(X > 5) = 0.286

The probability of calls taking more than 5 minutes is 0.286.

(e) P(X>7)

[tex]P(X>7)=0.25e^{-0.25.7}[/tex]

[tex]P(X>7)=0.25e^{-1.75}[/tex]

P(X > 7) = 0.174

The probability of calls taking more than 7 minutes is 0.174.

Out of 340 racers who started the marathon, 302 completed the race, 26 gave up, and 12 were disqualified. What percentage did not complete the marathon?

Answers

Answer:

11.18%

Step-by-step explanation:

Total = 340

Completed = 302

Not completed = 340 - 302 = 38

Not completed% = 38/340*100% =  11.18%

Which of the expressions has a sum of 15.41? Select all that apply. A. 11 . 38 + 4 . 03 B. 10 + 5 . 41 C. 12 . 38 + 2 . 93 D. 9 . 2 + 6 . 21 E. 7 . 54 + 6 . 87

Answers

Answer: A. 11 . 38 + 4 . 03

                B. 10 + 5 . 41

                 D. 9 . 2 + 6 . 21

Step-by-step explanation:

Step 1

Compute the sum of the given options

a)  11 . 38 + 4 . 03 = 15.41

b) 10 + 5 . 41= 15.41

c) 12 . 38 + 2 . 93= 15.31

d) 9 . 2 + 6 . 21 =15.41

e) 7 . 54 + 6 . 87=14.41

Step 2

Eliminate the expressions that do not give a sum of 15.41 , we have

a)  11 . 38 + 4 . 03 = 15.41

b) 10 + 5 . 41= 15.41

d) 9 . 2 + 6 . 21 =15.41

Therefore, the expressions with sum of 15.41  are A, B  and D

Which of the following is an odd function??
O g(x) = x2
O g(x) = 5x - 1
O g(x) = 3
O g(x) = 4x

Answers

Step-by-step explanation:

An odd function is where g(x) = -g(-x).

Therefore the answer is g(x) = 4x, as it passes through the origin and g(x) is positive when x is positive, and g(x) is negative when x is negative.

The odd function will be g(x) = 4x. Then the correct option is D.

What is an odd function?

A true function f(x) is said to be an odd function if the output value of f(-x) is the same as the negative of f(x) for all values of x in the domain of f.

The equation should be stored in an odd function:

f(-x) = -f(x)

Let's check all the options.

A. The function is g(x) = x².

Substitute x = -x, then we have

g(x) = (-x)²

g(x) = x²

This is an even function.

B. The function is g(x) = 5x – 1.

Substitute x = -x, then we have

g(x) = 5(–x) – 1

g(x) = – (5x + 1)

This is a neither even nor odd.

C. The function is g(x) = 3.

Substitute x = -x, then we have

g(x) = 3

This is an even function.

D. The function is g(x) = x.

Substitute x = -x, then we have

g(x) = -x

g(x) = x

This is an odd function.

Then the correct option is D.

More about the odd function link is given below.

https://brainly.com/question/14264818

#SPJ2

Which graph is generated by this table of values? x –5 –3 –1 4 y 2 4 1 0 On a coordinate plane, points are at (negative 5, 2), (negative 3, 4), (negative 1, 1), and (4, 0). On a coordinate plane, points are at (negative 5, negative 2), (negative 3, negative 4), (negative 1, negative 1), and (4, 0). On a coordinate plane, points are at (0, 4), (1, negative 1), (2, negative 5), and (4, negative 3). On a coordinate plane, points are at (1, negative 1), (3, negative 4), (4, 0), and (5, negative 2).

Answers

Answer:

The answer is A

Step-by-step explanation:

All you must do is find the correct values in the graph.

The graph which is generated by the table of values x -5,-3,-1,4 and y=2,4,1,0 is on coordinate plane points are at (-5,2) ,(-3,4) ,(-1,1) ,(4,0).

What is function?

A function is a relationship between two or more variables having each value of x corresponding to y values. Values of x are known as domain and values of y are known as codomain.

How to graph function?

We have been given the following table as under:  

  x                           y

 -5                          -3

 -3                           4

 -1                           1

   4                           0

We have to plot the points -5 ,-3,-1,4 on x axis and corresponding-3,4,1,0 on y-axis.

Hence the graph of given table of values is that on coordinate plane points are at (-5,2) (-3,4)(-1,1)(4,0).

Learn more about function at https://brainly.com/question/10439235

#SPJ2

The width of kevin's yard is three times the width of his garage, increased by 12 feet. What expression describes the width of kevin's yard if g represents the width of his garage?

Answers

Answer:

The expression that describes the width of Kevin’s yard is (3g + 12) feet

Step-by-step explanation:

This is an expression problem.

From the question, we are made to know that the width of the yard is 3 times the width of the garage increased by 12 feet.

Now, we are told that the width of the garage is g feet and we want to find the width of the yard.

The width of the yard will be g feet * 3 + 12

Mathematically that would be 3g + 12 feet

Solve the formula for the specified variable A= P+Prt for r​

Answers

Answer:

R=a/pt-1/t

Step-by-step explanation:

r= a/pt-1/t

Step-by-step explanation:

Trevor picked 5 ⅗ pounds of cherries. He distributed them evenly into 12 containers. How many pounds of cherries were in each container?

Answers

Answer:

7/15

Step-by-step explanation:

For me, it is easier to take the 3/5 and put it in decimal form which is .6 and add the 5 to it, making 5.6, and then in a calculator put in 5.6 divided by 12 and you should get a big decimal that's pretty big but if you have a graphing calculator and convert that to a fraction and you should get 7/15, This is a pretty lazy way of me doing it but that's how I did it.

If the spread of data on one side of the median of a data set is much greater than the spread of data on the other side, then what shape does the data distribution have? Explain.

Answers

um it should be at least 12 in

Please help me solve the problem

Answers

Answer:

Probability of getting a green marble=5/15=3/5

Probability of getting a black marble=5/15=3/5

An actor gains 20 pounds for a part and then loses 15 pounds during the filming of the movie to go along with the story. How many pounds is the actor above or below his original weight?

Answers

Answer:

5 pounds above his original weight

Step-by-step explanation:

An actor gains 20 pounds for a role in a movie

He loses 15 pounds during the movie to blend with the story line of the movie

Since he gained 20 pounds and loses 15 pounds

20 pounds -15 pounds

= 5 pounds

Hence the actor is 5 pounds above his original weight

Cynthia besch wants to buy a rug for a room that is 20 ft wide and 33 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 378 ft² of carpeting. What dimensions should the rug have?​

Answers

Answer:

Length of rug = 14 ft

Width of rug = 27 ft

Step-by-step explanation:

Given:

Length of rug = 20 ft

Width of rug = 33 ft

Area she afford = 378 ft²

Find:

New sides

Computation:

Assume;

Uniform strip = x

So,

Length of rug = 20 - x ft

Width of rug = 33 - x ft

Ares = l × b

[20-x][33-x] = 378

660 - 20x - 33x + x² = 378

x² - 53x + 282

x² - 47x - 6x + 282

x(x-47) -6(x-47)

So,

x = 6 and x = 47

X = 47 not be taken, So x=6

Length of rug = 20 - 6 ft

Width of rug = 33 - 6 ft

Length of rug = 14 ft

Width of rug = 27 ft

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