Hannah is 2 times her sister’s age. The sum of their ages is no more than 18 years.

1) Write an inequality that can be used to represent this situation.
2) Using the inequality you just found, solve it to find the oldest age Hannah's sister can be.

Answers

Answer 1

Answer:

1) [tex]2s+s\leq18[/tex]

2) 6 years old


Step-by-step explanation:

Let Hannah's age be [tex]h[/tex] and her sister's age be [tex]s[/tex]

Hannah is 2 times her sister’s age:

It means [tex]h=2s[/tex]

The sum of their ages is no more than 18 years:

It means the sum is LESS THAN or EQUAL TO 18. So we can write:

[tex]h+s\leq18[/tex]


1. We can substitute first equation into second equation to get our desired inequality of the situation. Thus,

[tex]h+s\leq18\\2s+s\leq18[/tex]

2. To find MAXIMUM age of Hannah's sister, let's further simplify the inequality from number 1. So,

[tex]2s+s\leq18\\3s\leq18\\s\leq\frac{18}{3}\\s\leq6[/tex]

Hence, Hannah's sister's age is LESS THAN OR EQUAL TO 6. So maximum age of her sister is 6.


Related Questions

Write 4/9, 5/9, and 6/9 as decimals. What pattern do you see? Use the pattern to predict the decimal form of 7/9 and 8/9

Answers

0.444444 , 0.555556 , 0.666667 , They each have a repeating decimal and so you can predict : 0.777778 , 0.888889

So the correct answer Is A, but can you explain how you get that answer?

Answers

The first thing to notice is that the smaller triangle on the left is equilateral, because of the same single tickmarks on each of the three sides. For any equilateral triangle, each interior angle is 60 degrees as you have marked it on the drawing.

Once you determine that, you would solve for the 120 degree angle (60+120 = 180). Afterward, solve the equation 120+x+x = 180 to find that x = 30. The equation 120+x+x = 180 refers to adding up the three angles of the smaller triangle on the right side (with angles 120, x, x). The two missing angles are both x due to the fact that this triangle is isosceles.

Answer:


Step-by-step explanation:

Since ∆ABC is equilateral, all of its angles would be the same (60°). Since a line is 180°, the other part of ∠C is 120°. Since we also know that △BCD is isosceles, we know that angles ∠B and ∠D are equal. If a triangle is 180°, and we already know that ∠C is 120°, we can do 180-120, which is 60°. If angles ∠B and ∠D are equal, we can do 60/2=30. Therefore, ∠D is 30°.

Can someone help me with these 2 problems plz

Answers

For the first one I believe that the numbers are both odd and I am not sure about the second one sorry
For the second one is yes

Find the fifth roots of 243(cos 260° + i sin 260°).

Answers

Answer:

z1=3 cos (52 + i sin 52)

z2 =3 cos (124 + i sin 124)

z3 = 3 cos (196 + i sin 196)

z4 =3 cos (268 + i sin 268)

z5= 3 cos (340 + i sin 340)

Step-by-step explanation:

To find the fifth roots of 243 (cos 260° + i sin 260°).

z ^ 1/5 = r^1/5 ( cis ( theta + 360 *k)/5)  where k=0,1,2,3,4


So the first root of 243 (cos 260° + i sin 260°)  

is z1 =  243^1/5 ( cis ( 260 + 360 *0)/5)  

          3 cis ( 260/5)

        = 3 cis (52)

        = 3 cos (52 + i sin 52)


The second root of  243 (cos 260° + i sin 260°)  

is z2 =  243^1/5 ( cis ( 260 + 360 *1)/5)  

          3 cis ( 620/5)

        = 3 cis (124)

        = 3 cos (124 + i sin 124)


The third root of  243 (cos 260° + i sin 260°)  

is z3 =  243^1/5 ( cis ( 260 + 360 *2)/5)  

          3 cis ( 980/5)

        = 3 cis (196)

        = 3 cos (196 + i sin 196)


The fourth root of  243 (cos 260° + i sin 260°)  

is z4 =  243^1/5 ( cis ( 260 + 360 *3)/5)  

          3 cis ( 1340/5)

        = 3 cis (268)

        = 3 cos (268 + i sin 268)


The fifth root of  243 (cos 260° + i sin 260°)  

is z5 =  243^1/5 ( cis ( 260 + 360 *4)/5)  

          3 cis ( 1700/5)

        = 3 cis (340)

        = 3 cos (340 + i sin 340)

A cube has a volume of 1/8. If the cube holds 24 of these sugar cubes, what is the total volume of the box?

Answers


[tex] \frac{1}{8} \div 24 = 3[/tex]

Answer:

the answer is 3 in.3

Step-by-step explanation:

PLEASE NEED HELP!
:"3

Answers

Answer:

Option 2

Step-by-step explanation:

When completing a proof, the statements and reasons should be directly connected. Since the reason listed next to the missing statement is Def of Complimentary Angles, the statement must be about angles adding to 90 degrees. The definition of Complimentary Angles is that two angles add to 90. This means option 2 is the answer.

Jenna bought a bike for $200. The value of the bike decreases by 5% each year. Write an equation to model the situation.

Answers

This is an exponential function. Since each year the value of the bike decreases by 5%, each year, the value of the bike is 100%-5%=95% of it's original value. So after x years, the value of the bike would be 200(0.95)^x.


Answer:

(200 - (200 x 5 / 100))^Y

Step-by-step explanation:

As the initial value of the bike is $200, that would be a fixed number in our equation. Each year, this will lose 5% of its value, therefore, it would be another fixed value in it. Then, we have to exponentiate it by the number of years that have passed since the initial value (Y). As a result, the equation to model the situation would be this one:

(200 - (200 x 5 / 100))^Y

If Nelson invests $5,000 for 4 years and earns $600, what is the simple interest rate?

Answers

Simple interest rate = 3%.

Since the given invested amount = $5000, number of years of investment = 4 years, interest earned = $600. 600 = 5000 × R × 4, 600 = 20000R, Dividing both sides by 20000, we get 0.003 which is 3%.

Answer:

3


Step-by-step explanation:


Jon is looking into a $4250 vacation package that is offered for 25% off. There is a 9% resort fee added on to the total. How much will the vacation cost Jon?

Answers

Answer:

3187.59

Step-by-step explanation:

Add 4250 - 25% + 9% and u should have this exact answer

- The one guy who has a F in math

As a part of a contest, a store is giving a special prize if a contestant can roll 3 standard six-sided number cubes, and get the same number on each. What is the probability a contestant will be successful?

Answers

Answer: [tex]\bold{\dfrac{1}{36}}[/tex]

Step-by-step explanation:

The first die can be any number:  [tex]P = (\dfrac{6}{6}) = 1[/tex]

The second die must match the first die: [tex]P = \dfrac{1}{6}[/tex]

The third die must also match the first die: [tex]P = \dfrac{1}{6}[/tex]

1st die   and   2nd die   and    3rd die  =  Probability of success

   1          x          [tex]\dfrac{1}{6}[/tex]             x          [tex]\dfrac{1}{6}[/tex]         =               [tex]\dfrac{1}{36}[/tex]

What is m∠C?

Enter your answer in the box.

Answers

Answer:

angle C is 60 degrees

Step-by-step explanation:

First you would solve for X

once you have that plug it in angle C

2(30)=60

Answer:

60°

Step-by-step explanation:

∠B is a right angle and all right angles are 90°, so if ∠B = 3*x then to find x you divid 3 by 90 to get x because 3*x = 90 once you do that you get 30 so x=30 then to find ∠C you just multiply 2 by 30 which gives you 60 which means the measure of ∠C = 60°

hope this helps :D

On mars,your weigh is about 1/3 of your weigh on earth. If a fifth grader weighs 96 pounds on earth,about how much would they weigh on mars

Answers

Answer:

32

Step-by-step explanation:

You just have to find out whats 1/3 of 96

just divided 96 by 3 to get 32

In the figure below, if BE is the perpendicular bisector of AD , what is the value of x?

Answers

Answer:

x = 10

Step-by-step explanation:

Since BE is perpendicular bisector AE=EDSubstituting we have:3x + 5 = x + 25 solving for x x = 10

Give the equation of the line in slope-intercept form that has the slope of 5 and goes through the point (0, -3).

Answers

Answer:

y=-3x+5

-3 is y ntercept




Given the position function s(t)=(t^3/3)-(12t^2/2)+36t between t=0 and t=15, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right.

Answers

Answer: [0, 6) ∪ (6, 15]

Step-by-step explanation:

The particle is moving to the right when the velocity is positive.

[tex]s(t)=\dfrac{t^3}{3} -\dfrac{12t^2}{2}+36t[/tex]

v(t) = s'(t)

     = t² - 12t + 36

First, find the zeros of v(t):v(t) = 0

  0 = t² - 12t + 36

     = (t - 6)²

0 = t - 6

6 = t

The zero occurs when t = 6

Next, find when v(t) > 0

Choose a test point between 0 and 6:

v(5) = (5 - 6)²

     =     (-²)

     =      (+)

Since velocity is positive between 0 and 6, the particle is moving to the right during that interval.

Choose a test point between 6 and 15:

v(7) = (7 - 6)²

     =    (+)²  

     =    (+)

Since velocity is positive when t > 6, the particle is moving to the right.

How many ways can the letters be arranged?

TJKL

A) 10 ways
B) 16 ways
C) 18 ways
D) 24 ways

Answers


The answer is D.

4 x 3 x 2 x 1 = 24 ways

This can be quickly worked out on your calculator using the ' ! ' button after inputting the number of letters/numbers.

You can always check as well, by simply working out every single way.

TJKL - different letters

for the first place you have 4 letters to choose from

for the second place you have 3 letters to choose from

for the third place you have 2 letters to choose from

for the last place you have only one letter

Therefore your answer is:

[tex]\boxed{4}\cdot\boxed{3}\cdot\boxed{2}\cdot\boxed{1}=24\to\boxed{D)}[/tex]

*Help ASAP Please! Studying for finals and I'm stuck on this question!*

5. Find the measure, to the nearest tenth, of the diagonal of a rectangle with dimensions 14 cm by 6 cm.

A) 16.3 cm
B) 12.6 cm
C) 15.2 cm
D) 4.5 cm

Answers

Answer: C

Step-by-step explanation:

A rectangle has 90° angles.  So, the diagonal cuts the rectangle into two right triangles where the length (base) and the width (side) are the legs of the right triangle and the diagonal is the hypotenuse. Thus, the Pythagorean Theorem can be used: (leg a)² + (leg b)² = (hypotenuse)²

14² + 6² = hypotenuse²

196 + 36 = hypotenuse²

232 = hypotenuse²

√232 = √hypotenuse²

15.23 = hypotenuse

Could someone help I can’t get this one

Answers

      Statement                      Reason

1. AB = CD, AD = CB           1. Given

2. AC = AC                          2. Reflexive Property

3. ΔADC ≅ ΔCBA                3. SSS

4. ∠1 = ∠4                             4. CPCTC

5. DC || AB                            5. Alternate Interior Angles Converse Thm

A student bought a truck with a down payment of 4000 and monthly payments of $250 for four years. What was the total cost of the truck

Answers

4000+250(12)(4)

Down Payment plus the price per month, multiplied by the years. The total cost should be $16000.

Find the value of x to the nearest tenth.
a. 11.3
b. 12.5
c. 12.9
d. 13.1

Answers

Answer:

B

Step-by-step explanation:

We have perpendicular bisector through a chord of the circle. We know the length, so either side of the chord is 11 due to the bisector cutting it directly in half. Since the radius is a fixed distance from the center to any point on the edge of the circle, we can draw the radius x from the circle to the end of the chord to form a right triangle.

We can use Pythagorean Theorem [tex]a^{2} +b^{2} =c^{2}[/tex] to find the missing side length x. a=6, b=11 and c=x.

[tex](6)^{2} +(11)^{2} =x^{2}[/tex]

[tex]36+121=x^2\\157=x^2\\\sqrt{157}=x\\ 12.5=x[/tex]

Jenna has some chocolate tat she wants to give to her friends. She wants to give 1/5 of a pound of chocolate to each friend. If jenna has 7pounds of chocolate, to how many friends can she give chocolate

Answers

25 friends because 7*5=35

Triangle STU is dilated to form new triangle VWX. If angle S is congruent to angle V, what other information will prove that the two triangles are similar? Side ST is congruent to side VW. Angle T is congruent to angle V. Side US is congruent to side XV. Angle U is congruent to angle X.

Answers

Answer:

(D)

Step-by-step explanation:

Two triangles are similar if it satisfies the following properties:

1) Corresponding angles are congruent.

2) Corresponding sides are all in same proportion.

Here, ΔSTU and ΔVWX are given, where ∠S is congruent to ∠V.

To prove these two triangles similar, we need one more corresponding angle to be congruent.

And from all the options, (d) Angle U is congruent to angle X. will help in proving ΔSTU and ΔVWX similar triangles.

Therefore, (d) is correct.  

Answer:

d)Angle U is congruent to angle X.

Step-by-step explanation:

Joel has 7 pounds of clay. He splits the clay into groups of 1/3 pound. How many groups does he have

Answers

The answer is 21 groups.

7/1 ÷ 1/3 flip the signs on 1/3

now just multiply across...

7/1 × 3/1


21/1

21

can someone help me please and thank you

Answers

Find the ratio of the two similar sides that both dimensions are given.

The smaller triangle aide that is 4 units is the similar side of the larger triangle given as 8 units.

8 / 4 =2, this means the larger triangle is 2 times the size of the smaller triangle, which also means the smaller triangle is 1/2 the size of the larger triangle.


X on the smaller triangle is 1/2 11 units which equals 5.5 units.

Y is 2 times 3, which equals 6 units.

x = 5.5

y = 6

Use the table below to answer this question:

x y
−3 −3
0 3
1 5
Find the average rate of change for the given function from x = −3 to x = 1.


2

−3

−1

−2

Answers

Answer:

2

Step-by-step explanation:

We can find the average rate of change by using the formula

rate of change = (y2-y1) /(x2-x1)

                         = (5-3)/(1-0)

                         = 2/1

                            =2

Answer:

A. 2

Step-by-step explanation:

average rate of change from x1 to x2 is

[f(x2) - f(x1)]/(x2 - x1)

Here we have x1 = -3; f(x1) = -3; x2 = 1; f(x2) = 5

average rate of change from x1 to x2 =

= [f(x2) - f(x1)]/(x2 - x1)

= [5 - (-3)]/(1 - (-3))

= 8/4

= 2

What is the domain restriction of this expression?
(m-7)/(4m-20)

Answer:

m ≠ ____.

Answers

Answer:

m ≠5

Step-by-step explanation:

We cannot divide by zero, so the denominator cannot equal zero.  That is the only restriction on the domain.

4m-20 ≠ 0

Add 20 to each side

4m-20+20 ≠20

4m ≠20

Divide each side by 4

4m/4 ≠20/4

m ≠5

Answer:

m ≠ 5

——

Step-by-step explanation:

Make the equation equal to zero.

4m - 20 = 0

Solve for the restriction.

4m - 20 = 0

Add 20 to both sides.

4m = 20

Divide both sides by 4.

m = 5

Answer:

m ≠ 5

How many soccer players that are getting paid around the world are there???
Answer for 15 points! PLZ be correct info!!!

Answers

265million players both male n female

What are examples of self-reliant and how are you self-reliant?
I need to hear from other peers, thank you:)

Answers

Here is an example of children being self reliant.
Most children have parents. Children are self reliant on parents until age eighteen or even later, because they rely on their parents to cook, maintain the house, pay for their food, etc.
I am self reliant sometimes on my friends because I rely on them to give me the answers for math class or to teach me.

Function g is transformed to obtain function h as shown.
(x)=4g(x+5)
A.
The graph of h is the graph of g vertically stretched by a factor of 4 and shifted 5 units to the left.
B.
The graph of h is the graph of g vertically shrunk by a factor of 4 and shifted 5 units to the right.
C.
The graph of h is the graph of g vertically stretched by a factor of 4 and shifted 5 units to the right.
D.
The graph of h is the graph of g vertically shrunk by a factor of 4 and shifted 5 units to the left.

Answers

Answer:

A

Step-by-step explanation:

The transformation is [tex]h(x)=4*g(x+5)[/tex].

4*g(x+5) means g(x) is vertically shifted by a factor if 4 by multiplying the entire function by 4. The values increase and are stretched (not shrunk to smaller).g(x+5) means the input x is increased by 5 each time. This results in a horizontal shift left on the graph

The answer is A.  The graph of h is the graph of g vertically stretched by a factor of 4 and shifted 5 units to the left.


Answer: A for plato users

The commission Gary earns is proportional to the cost of the shoes he sellis. Gary earns $15 in commission for every S150 worth of shoes that he sells. Which equation gives the total commission, C Gary will earn based on the cost, s, of the shoes he sels?

Answers

Answer:

15x + 150

Step-by-step explanation:


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