Answer:
larger = 11
Step-by-step explanation:
We will consider x = bigger, y = smaller
This means x - y = 7 (The difference of two numbers is 7)
This also means that x = 7 + y
And
y + x^2 = 125 (The sum of the smaller number and the square of the larger number is 125)
If we sustitute x = 7 + y in the second equation we get
y + (7+y)^2 = 125
We can do the square of the binomial and get
y + 49 + 14y + y^2 = 125 (We substract 125 on both sides of the equation)
y + 49 + 14y + y^2 - 125 = 125 - 125
We get
y^2 + 15y - 76 = 0
We can make a factorization
(y+19)(y-4)= 0
y+19 = 0 y-4 = 0
y = -19 y=4
This means y=4 is the smaller number and x= 7+ y = 7 + 4 = 11
So x= 11 is the bigger number
Answer: 79
Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
<u>Given information</u>
10x² - 7x + 10
x = 3
<u>Substitute the value into the expression</u>
= 10 (3)² - 7 (3) + 10
<u>Simplify by multiplication</u>
= 10 (9) - 21 + 10
= 90 - 21 + 10
<u>Simplify by subtraction</u>
= 69 + 10
<u>Simplify by addition</u>
= 79
Hope this helps!! :)
Please let me know if you have any questions
3.2 I think I'm not sure but I did try...
Hi there! I can help you!
43. To solve this, we can find the unit rate by dividing the amount traveled by the amount of time. 84/1.5 is 56. You are traveling at 56 mph. 3 1/4 is equivalent to 3.25. We can multiply that by 56 to find the amount traveled in 3 1/4 hours. 56 * 3.25 is 182. There. You would cover 182 miles in 3 1/4 hours.
44. To find the amount of heart beats in 50 seconds, we can set up a proportion like this: 130/12 = x/50. You set this up, because we’re looking for the amount of heartbeats, but we know the time frame. Cross multiply the values to get 6,500 = 12x. Now, divide each side by 12 to isolate the “x”. 6,500/12 is 541.6666 (541 2/3) or 542 when rounded to the nearest whole number. The heart beats about 542 times in 50 seconds.
45. Okay. Gas costs $1.85 per gallon and there is 18 miles per gallon. To find the cost per mile, we can divide the price for a gallon of gas by 18. 1.85/18 is 0.102777 and 7’s repeating or 0.10 when rounded to the nearest hundredth. The cost for gas per miles is approx. 10 cents.
Note: You didn’t ask for question #44 to be answered, but I solved it for you anyway to help you out.