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3 years ago

Jacob used 1/7 of a liter of water to fill 1/9 of the fish aquarium. How many liters of water are needed to fill the aquarium?

1 answer:

3 0

Jacob used 1/7 of a liter of water.
He needs to fill 1/9 of the fish aquarium.
Find how many liters would Jacob need to fill the aquarium
=> Let x = liters of water need to fill the aquarium
=> x/1 = 1/7 divided by 1/9
=> x = 1/7 x 9/1
=> x = 9/7, since this is an improper fraction, let’s convert it to mixed fraction
=> x = 1 and 2/7
So, Jacob need 1 and 2/7 liter of water to fill the whole aquarium.

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1) You’re baking a circular cake for a party. Your cake can be any size you want. What will the radius of your cake be and how m

HACTEHA [7]

the correct question is
1. You’re baking a circular cake for a party. Your cake can be any size you want
2. What will the radius of your cake be and how many slices will you be able to cut?
3. List the coordinates of any point in the coordinate plane.For your original discussion post, you only need to respond to #1, #2, and #3.View posts from your classmates and choose one to which you will respond.

Answer the following questions:
1. For the cake that your classmate is baking, what would be the central angle of each slice of cake?
2. If you eat two slices of cake that are side by side, what is the measure of the arc that these two slices intercept?
3. What is the circumference of the cake?
4. A circle to represent the cake is graphed on the coordinate plane. What equation represents the cake if it is centered at the point that your classmate listed for #2?
This is what my classmate posted.
1. The radius of my cake is 6 inches and I can cut 8 pieces.
2. (2,-3)

we know that
1) the radius of the cake is r=6 in and the cake will be cut into 8 pieces
2) the coordinates of any point in the coordinate plane is (2,-3)

part 1) what would be the central angle of each slice of cake?

The central angle of each slice would be found by dividing the total central angle of a circle (360°) by the number of slices (8),
so:
360/8=45 degrees

the answer part 1) is
Each slice would have a central angle of 45°.

Part 2) If you eat two slices of cake that are side by side, what is the measure of the arc that these two slices intercept?

The degree measure of the intercepted arc would be 2*45°=90°

The length in inches of the intercepted arc could be found:
Circumference=2*pi*r-----> C=2*pi*6----> 12*pi in

if 360° (full circle) has a length of---------> 12*pi in
90°----------------------> x
x=90*12*pi/360----> x=3*pi in

the formula to calculate the arc length is
[central angle in degrees/360°]*2*pi*r

Part 3) What is the circumference of the cake?

Circumference=2*pi*r-----> C=2*pi*6----> 12*pi in----> 37.68 in

the answer part 3) is
the circumference of the cake is 12*pi in or 37.68 in

Part 4) A circle to represent the cake is graphed on the coordinate plane. What equation represents the cake if it is centered at the point that your classmate listed for #2?

we know that
the center is the point (2,-3)
the equation of a circle is
(x-h)²+(y-k)²=r²
where (h,k) is the center
and
r is the radius
so
(x-h)²+(y-k)²=r²------- (x-2)²+(y+3)²=6²----> (x-2)²+(y+3)²=36

the answer part 4) is
(x-2)²+(y+3)²=36

see the attached figure

3 0

3 years ago

I need help with all 3 please

olganol [36]

Step-by-step explanation:

x +2y = 9. .....(1)

x - 2y = 5. .....(2)

from eqn (1)

x + 2y = 9

x = 9 - 2y.

substitute x = 9 - 2y into eqn (2)

9 - 2y - 2y = 5

-4y = 5 - 9

-4y = -4

y = 1

sub y = 1 into eqn (1)

x + 2y = 9

x + 2(1) = 9

x + 2 = 9

x = 9 - 2

x = 7.

(2) x + y = 9 ....(1)

x - 2y = 0 .....(2)

from eqn (2)

x - 2y = 0

x =0 + 2y

substitute x = 2y into eqn (1)

x + y = 9

(2y) + y = 9

3y = 9

y = 3

substitute y = 3 into eqn (2)

x - 2y = 0

x - 2(3) = 0

x - 6 = 0

x = 6.

(3) 2x + 7y = 5. ....(1)

2x + 3y = 9. .....(2)

from eqn (1)

2x + 7y = 5

7y = 5 - 2x

y = (5 - 2x)/7

sub y = (5 - 2x)/7 into eqn (2)

2x + 3y = 9

2x + 3(5 - 2x)/7 = 9

2x + (15 - 6x)/7 = 9

multiply through by 7

14x + 15 - 6x = 63

14x - 6x = 63 - 15

8x = 48

x = 6

sub x = 6 into eqn (1)

2x + 7y = 5

2(6) + 7y = 5

12 + 7y = 5

7y = 5 - 12

7y = -7

y = -1

6 0

3 years ago

Which is harder linear algebra or abstract algebra?

aliina [53]

They both relatively easy depending on how much time you put into understanding but. But if I have to pick which is harder I’d say linear.

6 0

4 years ago

Read 2 more answers

What is the sum of 1 2 + 1 4 12+14? Use the fraction strip to help.

olga_2 [115]

Answer:

6/8 or in simple terms, 3/4

Step-by-step explanation:

$\frac{1}{2} + \frac{1}{4} \\ = ( \frac{1}{4} + \frac{1}{4} ) + \frac{1}{4} \\ = ( \frac{1}{8} + \frac{1}{8} ) + (\frac{1}{8} + \frac{1}{8} ) + (\frac{1}{8} + \frac{1}{8} ) \\ = ( \frac{2}{8} ) + ( \frac{2}{8} ) + ( \frac{2}{8} ) \\ = \frac{6}{8} \\ = \frac{2 \times 3}{2 \times 4} \\ = \frac{3}{4}$

4 0

3 years ago

F(x) = | 3x+1 | find the vertex of value function

PilotLPTM [1.2K]

Answer:

The vertex is the point $(-\frac{1}{3},0)$

Step-by-step explanation:

we know that

The general form of an absolute value equation is

$y=a\left|x-h\right|+k$

The variable a tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables h, and k, tell us how far the graph shifts horizontally and vertically

The vertex is the point (h,k)

we have

$f(x)=\left|3x+1\right|$