1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Oxana [17]
3 years ago
6

1) "teacher" wants to build a rectangular dog bowl stand. The top of it will have a perimeter 55 1/2 inches. The length is twice

as long as the width. What are the dimensions (length and width) of the top of the dog bowl stand? (Note: Your answer should be in fraction form, not a decimal.) 2) During their basketball game, "teacher 1" shoots twice as many airballs as "teacher 2". "teacher 3" shoots 4 airballs less than "teacher 2". If they shot 24 airballs together, how many airballs did each teacher shoot?
Mathematics
1 answer:
Mice21 [21]3 years ago
7 0

Answer:

1)

L=18 \frac{1}{2} in

W= 9 \frac{1}{4} in

2)

T_{1}=14 balls

T_{2}=7 balls

T_{3}=3 balls

Step-by-step explanation:

In order to solve this problem, we need to build the equations we need. Since there are two values we want to figure out (length and width) we will then need two equations to solve simultaneously.

First, the problem tells us that the perimeter is 55 1/2 in, which can be rewritten as an improper fraction:

55 \frac{1}{2}= \frac{55*2+1}{2}= \frac{111}{2}

Next, we also know the perimeter of a rectangle is found by using the following formula:

P=2L+2W

where L is the length of the rectangle and W is its width.

So our first equation will look like this:

2L+2W=\frac{111}{2}

Next, the problem tells us that the width of the rectangle is twice its width, so our second equation will look like this:

L=2W

which can be substituted into our first equation:

2L+L=\frac{111}{2}

Now, we can solve this for L, so we get:

3L=\frac{111}{2}

L=\frac{111}{2*3}

L=\frac{111}{6}=18 \frac{3}{6}=18 \frac{1}{2}

so we can now use this information to find its width:

L=2W

\frac{111}{6}=2W

so

W=\frac{111}{6*2}

W=\frac{111}{12}=9\frac{3}{12}=9\frac{1}{4}

2)

When solving this problem it is a good idea to split it into little chunks of information. The first sentence says:

"... "teacher 1" shoots twice as many airballs as "teacher 2"."

This can be translated as an equation like this:

T_{1}=2T_{2}

The next sentence says:

""teacher 3" shoots 4 airballs less than "teacher 2"."

This can be written as an equation like this:

T_{3}=T_{2}-4

and finally, the problem states: "... they shot 24 airballs together,..."

This can be written as an equation like this:

T_{1}+T_{2}+T_{3}=24

so now we can do substitutions. We can take the first and second equations and write them into the third equation so we get:

2T_{2}+T_{2}+T_{2}-4=24

so now we can solve this equation for T_{2}, so we get:

2T_{2}+T_{2}+T_{2}=24+4

4T_{2}=28

T_{2}=\frac{28}{4}

T_{2}=7

and once we got this answer, we can find the remaining two answers:

T_{1}=2T_{2}

T_{1}=2(7)

T_{1}=14

and

T_{3}=T_{2}-4

so we get:

T_{3}=7-4

T_{3}=3

You might be interested in
What is the value of x
Mekhanik [1.2K]

Answer:

Depends on the domain and the graph.

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Any help would be greatly appreciated!
Aleks [24]

Answer:

the answer for that question is sqrt(49)

7 0
3 years ago
Read 2 more answers
A ladder leans against a building that angle of elevation of the latter is 70° the top of the ladder is 25 feet from the ground.
VashaNatasha [74]

Answer:

a. 20.5

Step-by-step explanation:

because this will form a right triangle we can use tan (opposite over adjacent) so an equation we could set up would be tan(70)=25/x

therefore we can just solve the equation which would give us 20.45. so if we round it the answer would be a

3 0
3 years ago
Read 2 more answers
NEED THIS DONE SOON
Sati [7]

65Answer:

we can use sin to find the missing length

Step-by-step explanation:

The ratio states that sin of an angle=opposite/hypotenuse

sin(65)=x/6 since we know the angle and the hypotenuse we need to figure out the opposite side

sin(65)=0.906307...

0.906307=x/6

Multiply 6 on both sides to isolate x

The answer is 5.4378...

Rounded to the hundredth is 5.44

5 0
3 years ago
(88÷1×2×5−9)+3×8 what does this make
cupoosta [38]

Answer: 6992

Step-by-step explanation: (88 / 1 = 88) (88 * 2 = 176) (176 * 5 = 880) (880 - 9 = 871) (871 + 3 = 874) (874 * 8 = 6992)

5 0
3 years ago
Other questions:
  • Where is the point if the point is between 0 and -1 on the number line?
    8·1 answer
  • Why does the inequality sign have to be flipped when multiplying and dividing by a negative number like in −2x > 10?
    10·1 answer
  • You are scheduled to receive $16,000 in two years. when you receive it, you will invest it for eight more years at 9.25 percent
    5·1 answer
  • What are linear simultaneous equations?
    8·1 answer
  • What fraction is greater 4/6 or 5/7
    6·2 answers
  • the price of coffee has dropped to $2.15 today Yesterday's price was $2.40 . Find the percentage decrease. Round your answer to
    11·1 answer
  • Which situation requires the use of the cube root?
    7·1 answer
  • Sasha's grandmother loves to travel. She sends Sasha postcards from all around the world. Sasha keeps the postcards in a special
    5·1 answer
  • What is the simplest form of this expression?
    15·1 answer
  • Please Please Please help me
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!