Answer:
False
Step-by-step explanation:
A reflection image is always congruent to the original figure. Hope this helps!
Answer:
Runner 1
Step-by-step explanation:
Runner 1's speed is the slope of the line = (20-0)/(2-0) = 10
Runner 2's speed is the slope of the line = 8.5 (the coefficient of t)
Runner 3's speed is slope = (36-18)/(4-2) = 9
The fastest pace, therefore is of runner 1, because 10>9 AND 10>8.5
Hey there! Welcome to Brainly! I'm happy to help you!
Let's quickly write our equation below.
4(1-x)+2x=-3(x+1)
To solve this, we want to get the x by itself on one side of the equation so we can see what it equals on the other side. First, we need to get it out of the parentheses. To do this, we will use the <em><u>distributive property </u></em>and multiply the number before the parentheses by both terms inside of it as seen below! :)
4(1)-4(x)+2x=-3(x)-3(1)
4-4x+2x=-3x-3
Now, we need to combine our like terms.
4-2x=-3x-3
Now, we want to get all of our constants (numbers without variables) onto the right side. First, we will subtract four from both sides.
-2x=-3x-7
Now, we will add 3x to both sides.
x= -7
I hope that this helps! Have a wonderful day!
Answer:
1) 5/6 miles
2) 2 7/24 cups
Step-by-step explanation:
1) Convert each mixed number into an improper fraction.
1 ½ = (2×1+1)/2 = 3/2
2 ⅓ = (3×2+1)/3 = 7/3
To add or subtract, find the common denominator.
3/2 = 9/6
7/3 = 14/6
The difference is:
14/6 − 9/6 = 5/6
2) To add the fractions, first find the common denominator (least common multiple of the denominators). To do that, write the prime factorizations:
3 = 3
8 = 2³
4 = 2²
LCM = 2³ × 3 = 24
2/3 = 16/24
7/8 = 21/24
3/4 = 18/24
The sum is:
(16 + 21 + 18) / 24
55/24
To convert to a mixed number, divide the numerator by the denominator. 24 goes into 55 two times with a remainder of 7.
55/24 = 2 7/24
Complete question :
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700√t + 11,000 The population before construction is 67,000. Determine the projected population 16 yr after the construction of the park has begun. people
Answer:
486,200
Step-by-step explanation:
Given that the rate of change in population is represented by the function:
f(t) = 5,700√t + 11,000
To get the original function, we take the integral of the rate function because the rate of change is obtained by taking the derivate of the original equation
f(t) = 5,700t^1/2 + 11,000
Taking the integral of f with respect to t:
∫(5,700t^1/2 + 11,000)
[5700t^(1/2 + 1)] / (1/2 + 1) + 11000t + C
[(5700t^3/2)/ 3/2] + 11000t + C
Where C = constant
If population before construction = 67000
Then C = 67000
t = time = 16 years
Substitute values into the original change equation:
[(5700(16)^3/2)/ 3/2] + 11000t + 67000
[(5700 * 64) / 1.5] + 11000(16) + 67000
243200 + 176000 + 67000
= 486,200