The average rate of change of the function over the interval -1≤x≤8 is -3.22.
How do you determine the average rate?The average rate of change of a function over an interval is given by the formula (f(b) - f(a)) / (b - a) where f(x) is the function, a is the starting point of the interval, and b is the ending point of the interval.
In this case, the function is h(x) = -x² + 4x + 12, the interval is -1≤x≤8.
Plugging in the values we have:
Average rate of change = (h(8) - h(-1)) / (8 - (-1)) = (h(8) - h(-1)) / 9
h(8) = -8² + 4(8) + 12 = -64 + 32 + 12 = -20
h(-1) = -1² + 4(-1) + 12 = 1 - 4 + 12 = 9
So the average rate of change = (-20 - 9) / 9 = -29/9 = -3.22
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Find the equation of the line that passes through both points (6,-5) (0,3)
Answer:
y = -4/3x + 3
Step-by-step explanation:
In 2010, the population of a city was 180,000. From 2010 to 2015, the population grew by 7%. From 2015 to 2020, it fell by 4%. How much did the population grow from 2010 to 2015, to the nearest 100 people?
Answer:
I. Exponential Growth. (1 ) t y C r. = +. Final. Amount. Initial. Amount. Rate of ... value increases by 7% each year. ... Step 1 Write the exponential growth function for this ... nearest hundredth. ... The population after 7 years will be approximately 38,783 people. ... Cesium-137 left from a 100 milligram sample after 180 year
Step-by-step explanation:
i think its right if not have a great day
Answer:
9800
Step-by-step explanation:
The coordinates of the vertices of △UVW are U(−2,−1), V(2,−1), and W(2,−8). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.
Answer:
UV = 4; VW = 7, UW ≈ 8.06
m∠V = 90°, m∠U ≈ 60°, m∠W ≈ 30°
Step-by-step explanation:
Using the distance formula, find the length of UW⎯⎯⎯⎯⎯⎯⎯.
UW=(2−(−2))2+(−8−(−1))2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
Simplify.
UW=(4)2+(−7)2‾‾‾‾‾‾‾‾‾‾‾‾√
Square.
UW=16+49‾‾‾‾‾‾‾√
Simplify.
UW=65‾‾‾√
Use a calculator to approximate.
UW≈8.06
Therefore, UW≈8.06.
Using the distance formula, find the length of UV⎯⎯⎯⎯⎯⎯.
UV=(2−(−2))2+(−1−(−1))2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
Simplify.
UV=(4)2+(0)2‾‾‾‾‾‾‾‾‾‾√
Square.
UV=16+0‾‾‾‾‾‾√
Simplify.
UV=16‾‾‾√
Simplify.
UV=4
Therefore, UV=4.
Using the distance formula, find the length of VW⎯⎯⎯⎯⎯⎯.
VW=(2−2)2+(−8−(−1))2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
Simplify.
VW=(0)2+(−7)2‾‾‾‾‾‾‾‾‾‾‾‾√
Square.
VW=0+49‾‾‾‾‾‾√
Simplify.
VW=49‾‾‾√
Simplify.
VW=7
Therefore, VW=7.
The figure shows the same triangle U V W on a Cartesian plane as in the beginning of the task. The length of segment U V is 4 units. The length of segment V W is 7 units. The length of segment U W is 8.06 units.
Notice that UW2=UV2+VW2. So, by the Converse of the Pythagorean Theorem, △UVW is a right triangle.
Since VW⎯⎯⎯⎯⎯⎯ and UV⎯⎯⎯⎯⎯⎯ are perpendicular, m∠V=90°.
Therefore, m∠V=90°.
By the definition of tangent, tan∠U=VWUV.
Take the inverse tangent of both sides.
m∠U=tan−1(VWUV)
Substitute 7 for VW and 4 for UV.
m∠U=tan−1(74)
Use a calculator to calculate the inverse tangent.
The figure shows a calculator screen on which the inverse tangent of seven fourths is calculated. The result of the calculation is 60 point 2 5 5 1 1 8 7.
m∠U≈60°
Therefore, m∠U≈60°.
The figure shows the same triangle U V W on a Cartesian plane as in the beginning of the task. Angle V is a right angle. Angle U measures 60 degrees.
The acute angles of a right triangle are complementary by the corollary of the Triangle Sum Theorem.
So, m∠U+m∠W=90°.
Substitute 60° for m∠U.
60°+m∠W≈90°
Subtract 60° from both sides.
m∠W≈90°−60°
Simplify.
m∠W≈30°
Therefore, m∠W≈30°.
A CIRCLE HAS A CIRCUMFENCE 43.96 YD FIND THE RADUIS OF THE CIRCLE
Answer:
≈ 7
Step-by-step explanation:
Answer the following question in *full sentences*
What does the equation 100+0.05p=0.25p represent?
The value of "p" will be "0.002".
Equation:According to the question,
[tex]100+0.05p=0.25p[/tex]By subtracting "0.25p" from both sides, we get
→ [tex]100+0.05p-0.25p=0.25p-0.25p[/tex]
[tex]100-0.2p=0[/tex]
[tex]100=0.2p[/tex]
[tex]p = \frac{0.2}{100}[/tex]
[tex]= 0.002[/tex]
Thus the above approach is right.
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Polar bears eat 8.4 pounds of fish a day. Penguins eat about 0.80 of that amount. How many pounds if fish do penguins eat?
316 students went on a field trip. Six buses were filled and 10 students traveled in cars. How many students
were in each bus?
Answer:
51
Step-by-step explanation:
316-10= 306
306 divided by 6 = 51
Rearrange p=r+3 to make r the subject
Answer:
r = p-3 this is correct answer of this question
The equation p=r+3 can be rearranged as r=p-3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is p=r+3
p equal to r plus r
Plus is the operator of addition and p and r are variables
Subtracting 3 from both sides, we get:
p - 3 = r + 3 - 3
Simplifying the right-hand side:
p - 3 = r
Therefore, r = p - 3.
Hence, the equation p=r+3 can be rearranged as r=p-3
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The entire digits of pie times the square root of 1
Answer:
3.1415926
Step-by-step explanation:
3.1415926 * 1 = 3.1415926
Answer:
g4 bk.58i
Step-by-step explanation:
Can someone please help me ASAP
Answer:
Look down below!
Step-by-step explanation:
Fist, make your inequality:
-x + 5y > -10
5y > x - 10
y = .2x - 2
Now, plug in any value of x to find y!
Ex: x = 5...
y = .2 (5) - 2
y = -1
Your first coordinate could be (5, -1)
Hope this helps!
Can you answer this for 20 points? With which countries was France at war in 1792 and 1793?
Answer:
They pitted France against Great Britain, the Holy Roman Empire, Prussia, Russia, and several other monarchies. They are divided in two periods: the War of the First Coalition (1792–97) and the War of the Second Coalition (1798–1802)
Step-by-step explanation:
Pedro tiene 335 en monedas de 5 y de 10, si en total tiene 52 monedas ¿cuantas monedas tiene de cada una?
ayuda por favor
Answer:
37 monedas de $5 y 15 monedas de $10
Step-by-step explanation:
37 x 5 = 185
15 x 10 = 150
185 + 150 = $335
Find the point-slope equation for the line that passes through the points (-6, 24) and (5, -31). Use the first point in your equation. y - [?] = [ ](x-[ ])
The y-intercept of the the inverse of the function f(x) = 1/4 x-9/4 is
Answer:
Since f(x) is a linear equation the graph of f(x) is a line with a slope of –3/4 and a yintercept of (0, 2). In looking at the graph, you can see that ...
Please answer this!!!
Will be Brainlist!!!
Answer:
show the question
sorry
Step-by-step explanation:
plz follow me
Answer:
1) а 2)b
вот правильный ответ
please help me with this
Answer:
D. [tex]\sqrt{250}[/tex]
Step-by-step explanation:
First, use prime factorization of 250 to get [tex]\sqrt{2*5^3}[/tex]
Then apply the exponent rule, [tex]a^{b+c} =a^{b}*a^{c}[/tex]
=[tex]\sqrt{2*5^2*5} }[/tex]
Apply radical rule: [tex]\sqrt{ab}= \sqrt{a} \sqrt{b}, a\geq 0, b\geq 0[/tex]
=[tex]\sqrt{5^{2}} \sqrt{2*5}[/tex]
Apply radical rule: [tex]\sqrt{a^{2}} =a, a\geq 0[/tex]
=5[tex]\sqrt{2*5}[/tex]
=5[tex]\sqrt{10}[/tex]
Answer:
D. I did the math on my calculator
A clothing store sells clothing for 2 times the wholesale plus $10. The store sells a pair of pants to customers for $48. How much did the store pay wholesalefor the pants?
Answer:
19$
Step-by-step explanation:
Let w represent the wholesale cost of the pants, or the price paid by the store
2w + 10 = 48 Subtract 10 from both sides.
2w = 38 Divide both sides by 2.
w = 19
pls help me with this I have to go to bed soon( I need the volume of the sphere)
Volume= 4/3πr^3
r = 18m
Volume = 4/3*3.14*18^3
Volume = 4/3*3.14*5832
Volume= 24416.639999 m^3
A rectangle has a length of (x + 6) units and a width of (x - 5) units. What is the area of the rectangle in terms of x?
Answer:
Area = x2 +x - 30
Step-by-step explanation:
area = length x width
(x+6) (x-5) = x2 +6x -5x -30 = x2 + x -30
For questions 7 and 8 find the unknown angle.
Answer:
58 degrees for Question 7, and 71 degrees for Question 8
Step-by-step explanation:
For question 7:
180 - 99 = 81
81 + 41 = 122
180 - 122 = 58
For Question 8:
142 / 2 = 71
Answer: 7) 58 degrees 8) 71 degrees
Step-by-step explanation:
7) 41 + x = 99 degrees (the two interior opposite angle is equal to the exterior angle)
subtract 41 on both sides
x = (99 - 41) degrees
x = 58 degrees
8) x + x = 142 degrees
2x = 142
divide 2 on both sides
x = 71 degrees
Angel repairs used furniture. He expects to use 48 oz of wood filler this month. There are 16 oz in 1 lb. How many pounds of wood filler does Angel expect to use this month?
Answer: 3
Step-by-step explanation:
48 divided by 16 is 3
The number of pounds expected to use this month is 3 pounds.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
16 oz = 1 lb
Multiply 3 on both sides.
48 oz = 3 lb
Thus,
3 pounds of wood is in 48 oz.
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PLEASE HELP!! WILL MAKE BRAINLIEST!! What is..... 3.064 x 1,000
PLS SHOW HOW YOU SOLVED THE PROBLEM
15. The perimeter of an isosceles triangle is 34 inches. When you add the base of the
triangle to one of the equal sides the sum is 18. What is the length of the base of the
triangle?
a)
2 inches
go to card 3
b) 14 inches
go to card 6
c) 9 inches
go to card 9
d) 16 inches
go to card 11
e) 4 inches
go to card 13
Answer:
D
Step-by-step explanation:
Give the least common denominator: 3/4, 7/8 _____
Step-by-step explanation:
step 1. LCD of 3/4 and 7/8 is 8.
- A unicycle tire has a radius of 13 inches. About how far will the unicycle travel in 20 rotations?
F.1633 inches
G.10,613 inches
H.82 inches
J.520 inches
Answer:
1061.32 you made a typo on G
Step-by-step explanation:
To find the distance travelled by the tire we need the circumference of it
The formula for circumference is 2πr we know pi is roughly 3.14 and the radius is 13
we plug the numbers in and get
2* 3.14* 13
6.28*13
81.64
81.64 is the circumference, now we simply just multiply 81.64 by 13 to get 1061.32
Im guessing number G was supposed to be 1061.32 instead of 10,613
Find the slope of a graph
I'll GIVE BRAINLESS
Answer: 5/4
Step-by-step explanation:
I NEED HELP NOW ITS DUE TODAY AND I HAVE MORE AHHHHHHHHH
Lin needs to save up $20 for a new game. How much money does she have if she has saved 25% of her goal?
Answer:
She has $5
Step-by-step explanation:
Math Teacher is giving extra credit to who ever can come up with the best theme for his kids birthday party!!!
Has to be a movie!
You can choose
A. Hunger Games
B. Men in Black
C. Classic Horror Movies
D. Jurassic Park
OR!!
Awnser With your own suggestion!!!!!!!
Answer:
C
Step-by-step explanation:
CLASSIC HORROR MOVIES
plz answer.
6-x=13.
Answer:
x=-19
Step-by-step explanation:
Answer:
6-x=13
6-13=x
x=6-13
x=-7
Which linear inequality best represents the graph shown?
Answer:
B
Step-by-step explanation: