The average rate of change over an interval is the same as the slope between those two values. The formulate for slope is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
You are given the x values: x2=3 and x1=-9. Plug in these x values to g(x) find the y values:
g(3)=3^2+5(3)-2=9+15-2=22
g(-9)=(-9)^2+5(-9)-2=81-45-2=34
Now, you can solve for m:
m=(22-34)/(3--9)
m=-12/12
m=1
Hope this helps!!
the average rate of change of the function over the interval -9 ≤ x ≤ 3 is -1
The average rate is the change of expression with respect to time.
Given the expression g(x)=x^2+5x-2 within the interval -9 ≤ x ≤ 3
At the lower interval x = -9
g(-9) = (-9)²+5(-9)-2
g(-9)= 81-45-2
g(-9) = 34
At the upper interval x = 3
g(3) = (3)²+5(3)-2
g(3)= 9+15-2
g(3) = 22
The average change of the function will be expressed as:
[tex]\frac{\triangle y}{\triangle x} =\dfrac{g(b)-g(a)}{b-a}\\ \frac{\triangle y}{\triangle x} =\dfrac{g(3)-g(-9)}{3-(-9)}\\\frac{\triangle y}{\triangle x} =\dfrac{22-34}{12}\\\\\frac{\triangle y}{\triangle x} =\dfrac{-12}{12} \\\frac{\triangle y}{\triangle x} =-1[/tex]
Hence the average rate of change of the function over the interval -9 ≤ x ≤ 3 is -1
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FIRST CORRECT ANSWER GETS BRAINLEST!!!
Gregg has q quarters and p pennies. His brother has 4 times as many quarters and 8 times as many pennies as Gregg has. Write the sum of the number of coins they have, and then combine like terms.
ANSWER ASAP FOR BRAINLIESTT
Answer:
Y= 1/7x + 2/7
Step-by-step explanation:
2/7 equals to b
Hope this helps.. :)
Started at 10° and rose 1° each minute
Answer:
1, -2, 2, [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Mila reads at a rate of 3 paragraphs per minute.
After reading for 4 minutes, she had read a total of 12 paragraphs.
This situation can be represented with a linear equation written in point-slope form, where x represents the number of minutes and y represents the number of paragraphs.
Use this information to complete each statement about the linear equation.
Answer:
y= 3x
Step-by-step explanation:
This is honestly your basic times tables if we are being honest. We know that she read 3 paragraphs per minute. We also know that in 4 minutes, she read 12 paragraphs. 4 times 3 = 12. So the answer is y=3x.
Answer:
slope of the linear equation is 3
a point on the graph of a linear equation is (4,12)
linear equation can be written as y-12 = 3 (x-4)
Step-by-step explanation:
Cuz it is
Juan runs in place for 256 minutes on Monday. He runs in place for 112 times as long on Tuesday.
Juan draws this model to represent the number of minutes he runs in place on Tuesday.
How many minutes does Juan run in place on Tuesday?
Answer:
the answer is 4.25 or 4 1/4
Step-by-step explanation:
Laundry detergent is priced at 20 ounces for $3.40 or 14 ounces for $2.10.what is the the unit rate of the laundry detergent that is better value?
Answer:
0.17 cents per ounce, which is the 20 ounce
Step-by-step explanation:
3.40 / 20 = 0.17 cents per ounce
2.10/14 = 0.15 cents per ounce
Answer:
14 Ounces for $2.10
Step-by-step explanation:
To find the answer you need to find the cost per ounce by dividing the cost by the ounces
3.40/20 = 0.17. So $0.17 per ounce
2.10/14 = 0.15. So $0.15 per ounce
Orchestra Tonight is selling tickets for its local performance. Orchestra fans can buy tickets to sit in the balcony or on the top floor of the concert hall. Tickets for balcony seats are $83 each. Tickets for seating on the floor are 60% of the price of the balcony tickets. Which inequality represents all possible combinations of f, the number of tickets for floor seats and b, the number of tickets for balcony seats, that a person can buy and spend no more than $560. a 83b+138.33f>560 b 83b+49.8f>560 c 83b+49.8f\le560 d 83b+138.33f\le560
Answer:
c
Step-by-step explanation:
Given that:
Cost of balcony seat = $83
Cost of seating on floor = 60% of balcony seat = 0.6 * $83 = $49.8
Number of tickets for floor seat = f
Number of tickets for balcony seat = b
Total amount to spend should not exceed $560;
[(Cost of balcony ticket * number of balcony tickets) + ( cost of floor tickets * number of floor tickets)] ≤ 560
83b + 49.8f ≤ 560
The closest from the options given is :
83b + 49.8 < 560
How can I solve (-2)+(-2)
A person standing close to the edge on top of a 144-foot building throws a ball vertically upward. The quadratic function h ( t ) = − 16 t 2 + 128 t + 144 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown. What is the maximum height of the ball?
Answer:
400mStep-by-step explanation:
Given the quadratic equation that models the height of the ball above the ground as;
h ( t ) = − 16 t^2 + 128 t + 144
t is in seconds
To get the maximum height of the ball, first we must know the time taken by the ball to reach the maximum height.
Note that the ball has a velocity of zero at its maximum height.
v(t) = dh/dt
v(t) = -32t+ 128
at max height, v(t) = 0
0 = -32t + 128
32t = 128
t = 128/32
t = 4secs
To get the maximum height of the ball, you will substitute t = 4 into the modeled function as shown;
h ( t ) = − 16 t^2 + 128 t + 144
h ( 4 ) = − 16 (4)^2 + 128 (4) + 144
h ( 4 ) = − 256 + 512 + 144
h(4) = 400m
Hence the maximum height of the ball is 400m
2. Find the roots of the following quadratic equations by factorisation:
100x2 - 20x + 1 = 0
Answer:
x = [tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Given
100x² - 20x + 1 = 0 ← this is a perfect square
(10x - 1)² = 0, thus
10x - 1 = 0 ( add 1 to both sides )
10x = 1 ( divide both sides by 10 )
x = [tex]\frac{1}{10}[/tex]
Answer:
Step-by-step explanation:
100x^2-20x+1=0
100x^2-(10+10)X+1=0
100x^2-10x-10x+1=0
10x(10x-1)-1(10x-1)=0
(10x-1)(10x-1)=0
So roots are X=1/10,1/10
can't figure this out
Answer:
2.55%
Step-by-step explanation:
You have 11 years to make $500, To do this, take the 11 and multiply it by the percentage, after that, do $2000 divided by 11 x (percentage) answer. Then you will have the difference, which should roughly equal $556, which is slightly over $500 but you can't have it under so this is the best answer.
Bob is hiking down a 15-mile country trail. He could hike at 5 mph for the first 2 hours and then go the rest of the way at 3 mph or he could just go the whole way at 4 mph. How long would each of these options take?
Answer:
1) 11/3 hours or about 3.67 hours.
2) 3.75 hours.
Step-by-step explanation:
Let’s determine the time it will take for Bob to hike for each of the options.
Option 1) Hiking 5mph for 2 hours, then 3mph.
The total distance is 15 miles.
If Bob hiked 5mph for 2 hours, then after two hours, Bob would’ve covered 5(2)=10 miles out of 15.
Therefore, 15-10 or 5 miles still needs to be covered.
To find how long that will take, we can simply divide the distance by the rate.
We are now going at a rate of 3mph. So, 5/3 is about 1.67 hours.
So, it will take another 1.67 hours to complete the hike.
So, the total time it will take is 2+1.67 or abou 3.67 hours. More specifically, it will be 2+5/3 or 11/3 hours.
Option 2) Hiking 4mph the entire way.
The total distance is 15 miles.
If Bob hiked 4mph the entire way, to find how long it will take, we can simply divide the total distance by the rate.
So: 15/4=3.75.
Therefore, it will take 3.75 hours to hike the entire distance going 4mph.
Answer:
1) 11/3 hours or about 3.67 hours.
2) 3.75 hours.
Step-by-step explanation:
Let’s determine the time it will take for Bob to hike for each of the options.
Option 1) Hiking 5mph for 2 hours, then 3mph.
The total distance is 15 miles.
If Bob hiked 5mph for 2 hours, then after two hours, Bob would’ve covered 5(2)=10 miles out of 15.
Therefore, 15-10 or 5 miles still needs to be covered.
To find how long that will take, we can simply divide the distance by the rate.
We are now going at a rate of 3mph. So, 5/3 is about 1.67 hours.
So, it will take another 1.67 hours to complete the hike.
So, the total time it will take is 2+1.67 or abou 3.67 hours. More specifically, it will be 2+5/3 or 11/3 hours.
Option 2) Hiking 4mph the entire way.
The total distance is 15 miles.
If Bob hiked 4mph the entire way, to find how long it will take, we can simply divide the total distance by the rate.
So: 15/4=3.75.
Therefore, it will take 3.75 hours to hike the entire distance going 4mph.
Step-by-step explanation:
the shopkeeper buys 100 oranges for $ 25, 50 kg of apples for $ 80 and 20 melons for $ 15. he sells all of these oranges, apples and melons at the prices shown in the table. calculate his percentage profit
Answer:
Table?
Step-by-step explanation:
Given that sin θ = 3/4 and θ is in Quadrant II:
Find cos θ.
this is for the Sin
*Remember that sin = opposite / hypotenuse*
a² + b² = c² (where a and b are legs and c is the hypotenuse)
From the picture, you can see:
a = 3
c = 4
Plug these into the equation and solve for b.
* a² + b² = c² *
step 1: 3² + b² = 4²
step 2: 9 + b² = 16
step 3: b² = 16 - 9
step 4: b² = 7
step 5: √(b²) = √7
step 6: b = ± √7
FOR COS:
From the picture, you can see that if θ is in quadrant II, b has to be negative.
b = -√7 = adjacent
Remember that cos θ = adjacent / hypotenuse.
cos θ = adjacent / hypotenuse
cos θ = (-√7 / 4)
i need help please asap
Answer:
[tex]1.94[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
[tex]\frac{8.6 \cdot 0.082}{0.363}[/tex]
Step 2: Evaluate
Multiply: [tex]\frac{0.7052}{0.363}[/tex]Divide: [tex]1.9427[/tex]Round: [tex]1.94[/tex]Answer:
1.94
Step-by-step explanation:
First we multpiy the top
8.6 x 0.082 = 0.7052
0.7052/0.363= 1.942
=1.94
6w-19+k when w=8 and k=2
Answer:
f
Step-by-step explanation:
f
Bryan’s monthly electric bill is determined by adding a flat administration fee to the product of the number of kilowatt hours of electricity used and the cost per kilowatt hour. When he uses 1,100 kilowatt hours of electricity, his bill is $113. When he uses 1,500 kilowatt hours of electricity, his bill is $153. What is the monthly administration fee? $
Answer:
3
Step-by-step explanation:
what is the value of x
Umm there is no numbers
What is 7x=5y x 6. Plllllssss heeelllp meh. Im stupid and don't know what this is.
Answer:
x=0
Step-by-step explanation:
"x6" was replaced by "x^6".
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :7x-(5y*x^6)=0
7x - 5x6y = 0
7x - 5x6y = -x • (5x5y - 7)
-x • (5x5y - 7) = 0 Hope this helps and you are not stupid everybody has at least something that they dont understand :)))
100 points
there's a runner on 1st base and the batter hits a line drive out to right field, where does the right fielder throw the ball?
this is a "real" question
Answer:
2nd Base (I think)
Step-by-step explanation:
The right fielder is closer to the 2nd base.
Which ratio is less than 15 Over 24
A. 1/2
B. 7/8
C. 19/24
D. 6/8
Answer:
A
Step-by-step explanation:
Sarafina had 34 out of 99 hits when she was at bat during the soft ball season. What was her batting average? (use bar notation if needed)
WILL GIVE BRAINLY
SHOW WORK
Answer:
34%
Step-by-step explanation:
34/99÷1/100=
34/99×1/100=
17/99×1/50=
17/4959=34%
2 Simplify: 2 (5+ 3x) + (x + 10)
Answer:
7x+20
Step-by-step explanation:
multiply (5+3x) by 2 and combine like terms
DUE AT TWELVE.Help it's savvas math pleaseeeeeee
Answer:
65%
Step-by-step explanation:
What I did was 2900/2 is 1450 which is half and than I subtract 1450 by 1,885 giving me 435 more people. I honestly, guess 65% but I also checked it on the calculator 2900 - 65% give 1,885. So, 65% is the correct answer.
BONUS! What is the slope of the line that passes through (-3, 5) and (-1, 8)?
Answer:
The slope is 3/2
Step-by-step explanation:
Slope formula y2 - y1
x2 - x1
8-5/-1+3
3/2
The slope is 3/2
~PumpkinSpice1
Answer:
The slope is 3/2
Step-by-step explanation:
Use slope intercept form. [tex]\frac{y_2-y_1}{x2-x_1}[/tex]
[tex]\frac{8-5}{-1-(-3)}[/tex] = [tex]\frac{3}{2}[/tex]
A biker cycles 9 miles in 2 3 of an hour.
a
Make a chart and fill it in to show how far he will bike if he maintains the same pace for 2 hours, 3 hours, 3.5 hours
Answer:
2 hours: 27 miles, 3 hours: 40.5 miles, 3.5 hours: 47.25 miles
Step-by-step explanation:
1.) If a hiker hikes 9 miles in 2/3 of an hour, he will hike 4.5 (Half of 2/3 is 1/3 and half of 9 is 4.5) miles in 1/3 of an hour and 13.5 miles per hour. (1/3 times 3 gives us a whole and 4.5 times 3 is 13.5)
2.) 2 hours: 13.5 * 2 = 27 miles
3.) 3 hours: 13.5 * 3 = 40.5 miles
4.) 3.5 hours: 13.5 * 3.5 = 47.25 miles
2 hours: 27 miles, 3 hours: 40.5 miles, 3.5 hours: 47.25 miles
Step-by-step explanation:
1.) If a hiker hikes 9 miles in 2/3 of an hour, he will hike 4.5 (Half of 2/3 is 1/3 and half of 9 is 4.5) miles in 1/3 of an hour and 13.5 miles per hour. (1/3 times 3 gives us a whole and 4.5 times 3 is 13.5)
2.) 2 hours: 13.5 * 2 = 27 miles
3.) 3 hours: 13.5 * 3 = 40.5 miles
4.) 3.5 hours: 13.5 * 3.5 = 47.25 miles
this is the guys above i just need points
To plot the point (5, -3) you would move up 5, then left 3.
1. False
2. True
Answer:
False
Step-by-step explanation:
Positive in the X-axis is always to the right and negative is left and in the Y-axis positive is up and negative is down
Help me solve this problem please
Answer:
sorry im just answering this cuz need points
Step-by-step explanation:
Зу +6 - 4(х - 9) Standard Form
Answer:
3y + 42 -4x
Step-by-step explanation:
3y +6 -4(x-9) distribute -4 through the ( )
3y + 6 -4x + 36 calculate add the numbers
3y + 42 -4x
What does the area of any shape tell us??
The area of a shape tells you the amount of space inside. The perimeter tells you how long the outline is. This is what the area and perimeter tell you.
Hope this helps you!