Wesley is raising monarch caterpillars for a school science project. Every day, he feeds 7 fresh milkweed leaves to each caterpillar. Wesley wants to find out how many caterpillars he can feed in a day with a total of 42 leaves. Write an equation that can be solved for n to find the number of caterpillars he can feed in a day?

Answer:

To prove the congruence between two triangles there are several postulates, that can be applied depending on the congruent parts of the triangles.

The postulates are:

SAS (Side-Angle-Side): This postulate states that if two triangles have two corresponding sides congruent and one corresponding angle congruent, we can conclude that those triangles are completely congruent.

ASA (Angle-Side-Angle): This postulate states that if two triangles have two corresponding angles congruent and one corresponding side congruent, then those triangles are congruent.

SSS (Side-Side-Side): This postulate states that if two triangles have all three corresponding sides congruent, then triangles are congruent.

AAS (Angle-Angle-Side): If two pairs of corresponding angles are congruent and one pair of corresponding sides is congruent, then both triangle are congruent each other.

HL (Hypothenuse-Leg): this postulate is applied when we have right angles. It states that two right triangles are congruent if they have one pair of corresponding leg congruent, and the hypothenuses are also congruent. We could conclude that those right triangles are congruent.

From these postulate, we can demonstrate the congruence between two triangles. Then, from that congruence, we deduct the congruence between each corresponding parts of those triangles. For example, if we demonstrate the congruence by AAS, we deduct that the third angle is also congruent, and the other two sides are also congruent.

Answer:

when x = 39.25, y = 2.75

when x = 2.75, x = 39.25

Step-by-step explanation:

use substitution method

x+y = 42 ------ (1)

xy = 108 ------ (2)

from (1) ,

x+y = 42

y = 42-x ------ (3)

substitute (3) into (2)

xy = 108

x( 42-x ) = 108

42x - x² = 108

-x² + 42x - 108 = 0

x² - 42x + 108 = 0

use the following formula to solve the value of x:

[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \\ ii) \: x = \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

a = 1

b = -42

c = 108

[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

[tex]x = \frac{ - ( - 42) + \sqrt{( - 42) {}^{2} - 4(1)(108)} }{2(1)} [/tex]

[tex]x = \frac{42 + \sqrt{1764 - 432} }{2} [/tex]

[tex]x = \frac{42 + \sqrt{1332} }{2} [/tex]

[tex]x = \frac{42 + 6 \sqrt{37} }{2} [/tex]

[tex]x = 21 + 3 \sqrt{37} [/tex]

[tex]x = 39.25[/tex]

[tex]ii) \: x \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

[tex]x = \frac{ - ( - 42) - \sqrt{( - 42) {}^{2} - 4(1)(108} }{2(1)} [/tex]

[tex]x = \frac{42 - \sqrt{1764 - 432} }{2} [/tex]

[tex]x = \frac{42 - \sqrt{1332} }{2} [/tex]

[tex]x = \frac{42 - 6 \sqrt{37} }{2} [/tex]

[tex]x = 21 - 3 \sqrt{37} [/tex]

[tex]x = 2.75[/tex]

the 2 values of x are x = 39.25 and x = 2.75

substitute x = 39.25 into (3)

y = 42-x

y = 42-39.25

y = 2.75

substitute x = 2.75 into (3)

y = 42-x

y = 42-2.75

y = 39.25

when x = 39.25, y = 2.75

when x = 2.75, x = 39.25

Step-by-step explanation:

the answer is steaming

Answer:

Step-by-step explanation:

Start by combining like terms like 2x, 2x, and 6x to get 10x + 12= 0. thats  a start

With negative numbers the larger the number the lower the value. For example -2 is less than -1

The order from least to greatest would be:

-12, -4.3, -1 1/2

Answer:

13 1/3 cups

Step-by-step explanation:

The ratio of flour to dozens of cookies is 4:3 or 1 1/3:1

1 1/3 x 10 = 13 1/3

Answer:

13 1/3

Step-by-step explanation:

12 cups cover the first 9 cookies and than just divide 4 by 3 and you will get 1.3 which is 1 1/3 of a cup

Answer:

$32.10

Step-by-step explanation:

If you have sales tax, you would first convert the percentage to decimal, or 0.07. Then you would take this number, and add it to one before you multiply it by the price of the sweatshirt. This makes sure that you're not just calculating the sales tax, but the overall price of the shirt. So if you multiply:

30 x 1.07 = 32.1

Add the units, and you get $32.10

Hope this helps!

Answer: The answer is $32.10

Step-by-step explanation: i forgot to put my answer in the answers not comments

Answer:

x=10

Step-by-step explanation:

[tex]9x-9=81\\9x=90\\x=10[/tex]

Answer:

10

Step-by-step explanation:

Because 1 1/4 divided by 1/8 is 10

Answer: It is the distance that -5 is form 0 on the number line

Step-by-step explanation:

We can define the absolute value of any number:

IxI as:

"The distance between the point x and the origin in the coordinate axis"

If we are in one dimension, x is just a value, and the coordinate axis will be a number line.

Then we could rewrite this as:

"is the distance between the value x and the 0 in the number line"

So:

IxI = x if x > 0

IxI = -x if x < 0.

Then:

I -5 I

Is the distance between the number -5, and the 0 in the number line, and this is:

I - 5 I = 5.

The correct option is:

"It is the distance that -5 is form 0 on the number line"

Answer:

Answer: It is the distance that -5 is form 0 on the number line

Step-by-step explanation:

Answer: here's the answers to the problems

6) 17

8) 2.5

Answer:

6.  17

8.  2.5

Step-by-step Explanation:

4 x 3 + 6+9/3          12/3 + 2+7/5-3 - 6

12 + 15/3                  4 + 9/2 - 6

12 + 5                       4 + 4.5 - 6

= 17                          8.5 - 6

                                = 2.5

Answer:

It is $3.46

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

3.) (x,y)⇒(x+9,y-5)

6.) T'= (-4,5) U'= (1,-7) V'= (2,4) W'= ( 7,2) X'=( 5,-10) Y'=( 0,2) Z'= ( 8,-3)

Step-by-step explanation:

Answer:

B. Substitute 0 for y and solve for x.

Step-by-step explanation:

Finding the zeroes means solving for x when y = 0.

Given:

Slope is undefined.

To find:

Which graph has an undefined slope?

Solution:

We know that, slope is change in y-values with respect to x-values.

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope is undefined if the denominator is 0.

[tex]x_2-x_1=0[/tex]

[tex]x_2=x_1[/tex]

It means, the x-values are same. It is possible only for a vertical line.

Therefore, the slope of vertical lines are undefined or we can say that graph of a vertical line has an undefined slope. It is of the form [tex]x=a[/tex], where, a is a constant and it can be any real number.

Step-by-step explanation:

1/8+1/4+1/8=1/8+2/8+1/8=4/8=1/2

Answer:

1,2,1, 4, 1

These numbers correspond with the boxes in order from left to right.

Answer:

the answer is 48π  in²

explanation:

i took the quiz

Answer:

1753

Step-by-step explanation:

Answer:

6 + 0.02 + 0.05

hope this helps

Answer:

$2535

Step-by-step explanation:

First, find the the pay he received for the regular hours worked.  To find this, you must multiply the hours worked by his wage.

$11 × 160 = $1760

Next find the the pay received for overtime.  Do the same process as above.

$15.50 × 50 = $775

Now that you have the pay for regular hours and overtime hours, add the two amounts together to find the amount for his total paycheck.

$1760 + $775 = $2535

Answer:

Check the answers in the tables below

Step-by-step explanation:

First I will explain the steps done in each column

Column 1: Multiply 2 numbers

Column 2: Split the terms inside the bracket in such a way that adding or subtracting those numbers we get the same number.

Column 3: Using distributive property a(b+c) = (ab)+(ac)

Column 4: Solving the expression by adding or subtracting  the terms

1)

Given: Data in Column 2 100(0.04+0.06)

Column 1     Column 2               Column 3                  Column 4         Value

100(0.1)       100(0.04+0.06)     100.0.04+100.0.06          4+6                   10

2)

Given: Data in column 3 [tex]8.\frac{1}{2}+ 8.\frac{1}{4}[/tex]

Column 1     Column 2               Column 3             Column 4         Value

[tex]8(\frac{3}{4})[/tex]                 [tex]8(\frac{1}{2}+\frac{1}{4})[/tex]                   [tex]8.\frac{1}{2}+ 8.\frac{1}{4}[/tex]                    4+2               8                    

3)

Given: Data in Column 4 9+12

Column 1     Column 2               Column 3                  Column 4         Value

3(7)                    3(3+4)                    3(3)+3(4)                   9+12                  21

4)

Given: Data in Column 4 24-16

Column 1     Column 2               Column 3                  Column 4         Value

4(2)                  4(6-4)                      4.6-4.4                      24-16                8

Answer:

73.6%

Explanation: 38 is the old value and 66 is the new value. In this case we have a positive change of 73.68... percent because the new value is greater than the old value.

Answer:

B

Step-by-step explanation:

Answer:

i think it is neither

Step-by-step explanation:

Answer:

528 cookies

Step-by-step explanation:

3 hours is 180 minutes

55 minutes - the 15 for preheating is 40 minutes

180 minutes + 40 minutes = 220 (total time she could've had cookies in the oven)

220 divided by 20 is 11 (total batches of cookies)

11 times 48 is 528

Sorry if my answer is confusing lol

The total number of cookies that Amy baked is 528 cookies.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

To solve this problem, we need to convert the total time the oven was on (3 hours and 55 minutes) into minutes.

Since there are 60 minutes in an hour, the total time the oven was on in minutes is : 3 hours x 60 minutes/hour + 55 minutes = 235 minutes.

We need to subtract the time the oven was preheating (15 minutes) from the total time the oven was on to get the time that was spent baking cookies. This gives us a total of 235 minutes - 15 minutes = 220 minutes of baking time.

Since each batch of cookies takes 20 minutes to bake, the number of batches of cookies that Amy baked is :

220 minutes / 20 minutes/batch = 11 batches.

Since each batch contains 48 cookies,

So, the total number of cookies that Amy baked is :

11 batches × 48 cookies/batch = 528 cookies.

Thus, Amy baked 528 cookies overall altogether.

Learn more about Subtraction operations here:

brainly.com/question/25834626

#SPJ12

Answer:

I would say that it's A 1/3 because it's the slope and that's what a rate of increase is

Answer:

c

Step-by-step explanation:

the top one goes inside the radical and the bottom one is the root

Answer:

she have 23.75 left

Step-by-step explanation:

Answer:

Step-by-step explanation:

32.5$ multiplied by 3 =97.5%

she received 65.78. add those together and you get 163.28$

subtract 8.75 twice and you get 145.8$