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Romashka-Z-Leto [24]
3 years ago
14

Caitlin divides a bag of fruit snacks with 4 friends. She divides the 89 snacks equally. How many fruit snacks does each person

receive? How many fruit snacks will be left over?
Mathematics
2 answers:
viva [34]3 years ago
3 0
Each person gets 22 snacks with one left over
Karolina [17]3 years ago
3 0

Answer:

Step-by-step explanation:

Caitlin divides a bag of fruit snacks with 4 friends.

She divides the snacks equally. The number of snacks are = 89

To find how many fruit snacks will each person receive

= \frac{\text{total number of snacks}}{\text{total number of friends}}

= \frac{89}{4}

= 22 snacks and 1 remainder

Each person will receive 22 snacks and 1 fruit snack will be left over.

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Match the circle equations in general form with their corresponding equations in standard form. Not all will be used. 
Xelga [282]
<span>The standard form of the equation of a circumference is given by the following expression:

</span>(x-h)^{2}+(y-k)^{2}=r^{2} \\ \\ where \ (h, k) \ is \ the \ center \ of \ the \ circumference \ and \ r \ the \ radius
<span>
On the other hand, the general form is given as follows:

</span>x^{2}+y^{2}+Dx+Ey+F=0 \\ \\ where: \\ D=-2h, \ E=-2k, \ F=h^{2}+k^{2}-r^{2}<span>

In this way, we can order the mentioned equations as follows:

Equations in Standard Form:

</span>\bold{a)} \ (x-6)^{2}+(y-4)^{2}=56 \\ \bold{b)} \ (x-2)^{2} + (y+6)^{2}=60 \\ \bold{c)} \ (x+2)^{2}+(y+3)^{2}=18 \\ \bold{d)} \ (x+1)^{2}+(y-6)^{2}=46

Equations in General Form:

\bold{1)} \ x^{2}+y^{2}-4x+12y-20=0 \\ \bold{2)} \ x^{2}+y^{2}+6x-8y-10=0 \\ \bold{3)} \ 3x^{2}+3y^{2}+12x+18y-15=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 3, \ the \ equation \ becomes: \\ x^{2}+y^{2}+4x+6y-5=0 \\ \\ \bold{4)} \ 5x^{2}+5y^{2}-10x+20y-30=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 5, \ the \ equation \ becomes: \\ x^{2}+y^{2}-2x+4y-6=0 \\ \\ \bold{5)} \ 2x^{2}+2y^{2}-24x-16y-8=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 2, \ the \ equation \ becomes: \\ x^{2}+y^{2}-12x-8y-4=0

\bold{6)} \ x^{2}+y^{2}+2x-12y

So let's match each equation:

\bold{From \ a)} \\ \\ (h,k)=(6,4),\ r=2\sqrt{14} \\ D=-12, \ E=-8 \\ F=-4

Then, its general form is:

x^{2}+y^{2}-12x-8y-4=0

<em><u>First. a) matches 5) </u></em>

\bold{From \ b)} \\ \\ (h,k)=(2,-6),\ r=2\sqrt{15} \\ D=-4, \ E=12 \\ F=-20

Then, its general form is:

x^{2}+y^{2}-4x+12y-20=0

<em><u>Second. b) matches 1) </u></em>

\bold{From \ c)} \\ \\ (h,k)=(-2,-3),\ r=3\sqrt{2} \\ D=4, \ E=6 \\ F=-5

Then, its general form is:

x^{2}+y^{2}+4x+6y-5=0

<em><u>Third. c) matches 3)</u></em>

\bold{From \ d)} \\ \\ (h,k)=(-1,6),\ r=\sqrt{46} \\ D=2, \ E=-12, \ F=-9

Then, its general form is: x^{2}+y^{2}+2x-12y-9=0

<em><u>Fourth. d) matches 6)</u></em>
6 0
3 years ago
Read 2 more answers
Which polynomials are in standard form?
Ksivusya [100]

b

b/c when it's rearranged large to small

4 0
3 years ago
Can someone help me pls
CaHeK987 [17]

Answer:

yes

Step-by-step explanation:

7 0
3 years ago
Which series of transformations will not map figure H onto itself?
chubhunter [2.5K]

Answer:

(x + 0, y − 2), reflection over y = 1

Step-by-step explanation:

H will be shifted down 2 units and then reflected over y = 1, which maps H into itself

3 0
3 years ago
Find the radius of a circle that has an area of 6.76 cm². Use it for pi.
Inessa05 [86]

Answer:

<h2>radius = 1.47 cm</h2>

Step-by-step explanation:

Area of a circle = πr²

where

r is the radius

From the question

Area = 6.76 cm²

To find the radius substitute the value of the area into the above formula and solve for the radius

That's

6.76 = \pi \:  {r}^{2}

Divide both sides by π

We have

{r}^{2}  =  \frac{6.76}{\pi}  \\ r =  \sqrt{ \frac{6.76}{\pi} }

r = 1.46689291

We have the final answer as

radius = 1.47 cm

Hope this helps you

8 0
3 years ago
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