Answer:
Question 9: Variables: (smallest) s, q, r (largest)
Question 10: 5 whole numbers (7, 8, 9, 10, and 11)
Step-by-step explanation:
For question nine, there are two given statements... s=q-2 and q<r. Say we plug in 10000 (a really big #) in for q, then we would get s=9998 and r>10000. This way, we can see that s would be the smallest, then q, and r is the largest. <em>(q<r can be written as r>q)</em>
<em />
For question 10, it states
. This can be split into
and
. When x is 12 in the first equation then
and when x is 6 in the second equation
(0.5 is also
). Therefore, x must be a whole number less than 12 and greater than 6, and it cannot be either 12 or 6. Whole numbers between 6 and 12 are 7, 8, 9, 10, and 11 or 5 whole numbers.
Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.
By being congruent, the corresponding angles and sides are equal.
Therefore,
,
,
,
,
.
By using 
So, 
Therefore, the measure of angle 1 is 100 degrees.
So, Option B is the correct answer.
Answer:
The length of the flag is 730 ft and the width is 310 ft
Step-by-step explanation:
<u><em>The correct question is</em></u>
The perimeter of the flag is 2080 ft what is the flags width and length <u>if</u> the length is 420 ft greater than the width
Let
L ----> the length of the flag
W ---> the width of the flag
we know that
The perimeter of the flag (rectangle) is equal to

we have

so

----> equation A
---> equation B
Solve the system by substitution
substitute equation B in equation A
solve for W
<em>Find the value of L</em>
----> 
therefore
The length of the flag is 730 ft and the width is 310 ft
Answer:
He has 30 penguins and 10 cats.
Step-by-step explanation:
Let's define the variables:
C = number of cats.
P = number of penguins.
We know that he has a total of 40 pets, then:
C + P = 40
We also know that the total heads (40 heads, each animal has one) plus the number of wings (P*2, each penguin has 2) is equal to the number of feet of his pets (4*C + 2*P, because each cat has 4 paws, and each penguin has 2)
Then we have the equation:
40 + 2*P = 4*C + 2*P
Notice that in the second equation we have the term 2*P in both sides of the equation, then we can just subtract 2*P in both sides to get:
(40 + 2*P) - 2*P = 4*C + 2*P - 2*P
40 = 4*C
Now with this, we can find the value of C.
40/4 = C = 10
Then he has 10 cats.
Now we can replace this in the equation:
P + C = 40
to find the value of P
P + 10 = 40
P = 40 - 10 = 30
P = 30
He has 30 penguins.