This table shows values that represent a quadratic function.
What is the average rate of change for this quadratic function for the interval
from x= 1 to x= 3?
Answer:
D. -4
Step-by-step explanation:
Using the general formula, [tex] m = \frac{f(b) - f(a)}{b - a} [/tex] , average rate of change for the quadratic function from x = 1 to x = 3, can be calculated as shown below:
Where,
[tex] a = 1, f(1) = -2 [/tex]
[tex] b = 3, f(3) = -10 [/tex]
Plug in the above values in the average rate of change formula:
[tex] m = \frac{-10 - (-2)}{3 - 1} [/tex]
[tex] m = \frac{-10 + 2}{2} [/tex]
[tex] m = \frac{-8}{2} [/tex]
[tex] m = -4 [/tex]
Average rate of change is D. -4
A state highway department uses a salt storage enclosure that is in the shape of a cone, as shown above. If the volume of the storage enclosure is 48π m3, then what is the diameter of the base of the cone, in meters?
Answer:
Diameter of the base of the cone = 8 meters
Step-by-step explanation:
State highway department uses a salt storage enclosure which is in the shape of a cone.
Height of the storage in conical shape = 9 meters
Volume of the storage = 48π m³
Let the radius of this conical storage = r meters
Formula to get the volume of a cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here 'r' is the radius of the base of the cone and 'h' is the height of the cone.
Therefore, Volume = [tex]\frac{1}{3}(\pi ) r^{2}(9)[/tex]
[tex]48\pi=3\pi r^{2}[/tex]
r² = [tex]\frac{48\pi }{3\pi }[/tex]
r = [tex]\sqrt{16}[/tex]
r = 4 meters
Since, diameter = 2r
= 2(4)
= 8 meters
Therefore, diameter of the base of the cone = 8 metres
Find the value of x.
Answer:
I think it is 32 hopes its right
The steepness or grade of a road is expressed as a percent. if a road rises 6feet for every 24 horizontal feet. What is the slope of the road? what percent grade is this ?
Answer:
25%
Step-by-step explanation:
The ratio of rise to run is ...
rise/run = 6 ft/24 ft = 1/4
Expressed as a percentage, this is ...
1/4 × 100% = 25%
_____
Comment on this grade
Interstate highways are limited to a 7% grade. Most local jurisdictions limit the grade of a road to somewhere between 12% and 15%.
The Varners live on a corner lot. Often, children cut across their lot to save walking distance. The children’s path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot. Hypotenuse: 32 ft , Short leg: x , Long leg: x+6
Answer:
[tex]x= \sqrt{503}-3[/tex]
Step-by-step explanation:
Hypotenuse = 32 feet
Short leg = x
Long leg = x+6
We will use Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]32^2=x^2+(x+6)^2[/tex]
[tex]1024=x^2+x^2+36+12x[/tex]
[tex]2x^2+12x-988=0[/tex]
[tex]x=-3-\sqrt{503}, \sqrt{503}-3[/tex]
Since the distance cannot be negative
So,[tex]x= \sqrt{503}-3[/tex]
Directions: Calculate the percent increase or decrease between the starting and ending
quantities below. Round your answer to one decimal place.
1. Start: 3
End: 10
2. Start: 9
End: 20
3. Start: 100
End: 85
4. Start: 45
End: 20
5. Start: 30
End: 60
I'll do the first two to get you started
===============================================
Problem 1
A = 3 = starting value
B = 10 = ending value
C = percent change
C = [ (B - A)/A ] * 100%
C = [ (10-3)/3 ] * 100%
C = (7/3) * 100%
C = 2.3333333 * 100%
C = 233.33333%
C = 233.3%
The positive C value means we have a percent increase. If C was negative, then we'd have a percent decrease.
Answer: 233.3% increase===============================================
Problem 2
A = 9 = start value
B = 20 = end value
C = percent change
C = [ (B - A)/A ] * 100%
C = [ (20-9)/9 ] * 100%
C = (11/9)*100%
C = 1.2222222222*100%
C = 122.22222222%
C = 122.2%
Answer: 122.2% increaseHelp, please show work
Answer:
132
Step-by-step explanation:
If US bisects the angle then
BUS = SUL
2x+10 = 3x-18
Subtract 2x from each side
2x+10 -2x = 3x-18-2x
10 = x-18
Add 18 to each side
10+18 =x
28 =x
We want to find BUL
BUL = BUS + SUL
2x+10 + 3x-18
5x-8
5*28 -8
140-8
132
Answer:
m<BUL=132
Step-by-step explanation:
Since US bisects <BUL, we know that <BUS ≅ <SUL
This is based on the angle bisector definition.
Hence, we can set up an equation to solve for x.
<BUS≅<SUL
2x+10=3x-18
Subtract 10 from both sides
2x+10-10=3x-18-10
2x=3x-28
Subtract 3x from both sides
2x-3x=3x-3x-28
-x=-28
Divide both sides by -1
x=28
m<BUL is the sum of m<BUS and m<SUL
m<BUL=m<BUS+m<SUL
m<BUS=2x+10
m<SUL=3x-18
Plug it in
m<BUL=2x+10+3x-18
Combine like terms
m<BUL=5x-8
Plug in 28 for x
m<BUL=5(28)-8
m<BUL=140-8
m<BUL=132
What is the area of triangle PQR to the nearest tenth of a square meter? Drawing is not to scale. A. 24.1 m2 B. 34.4 m2 C. 48.2 m2 D. 68.8 m2
Answer:
b
Step-by-step explanation:
The area of triangle PQR which is an SAS triangle, to the nearest tenth, is: A. 24.1 m²
What is the Area of an SAS Triangle?The area of an SAS triangle = ½ × bc × sin(A).
Given the following:
PQ (b) = 14 mRQ (c) = 6 mAngle Q (A) = 35°Area of triangle PQR = ½ × (14)(6) × sin(35)
Area of triangle PQR = 24.1 m²
Learn more about the area of an SAS triangle on:
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Sala earns 12 dollars each hour working part-time at a bookstore. She earns one additional dollar for each book that she sells. Let A be the amount (in dollars) that Salma earns in an hour if she sells B books. Write an equation relating A to B. Then graph your equation using the axes below.
Answer:
y=12a+b
Step-by-step explanation:
A store pays $10 for each shirt it buys. The store sells each shirt for 60%
more. What is the price of a shirt at the store?
Answer:
16$ per shirt
Step-by-step explanation:
60% of 10 is 6
10 + 6 = 16
Find the slope of this graph
Please help me with this question. I need to submit today. Question number 4. Lhakpa is a name of the person.
Answer:
Known:
width: 1/3
length: 3/5
Ask:
the area of floor?
Solution:
We need to multiply the width and length first!
width × length
= 1/3 × 3/5
= 3/15
= 1/5
Next subtract the number of floor witch has full fraction 1/1, so
= 1/1 - 1/5
= 5/5 - 1/5
= 4/5
So, the area of the floor is 4/5
hope it helps ^°^
Whats 7 over 10m plus 9 plus 3 over 1 I need help
Answer:
12.7
Step-by-step explanation:
(7/10)+((9+3)/1)
(0.7)+(12)
12.7
A. ASA
B. CPCTC
C. AAS
D. SAS
Answer:
It is ASA congruence rule as the 2 angles and the included side of the triangle are equal
To make a large poster of the bill of rights to hang on the classroom wall, a poster that is 22 inches by 46 inches is copied. In the classroom version is to be 3 1/2 times scale, what are the dimensions of the new document? PLEASE ANSWER QUICKLY WILL GIVE BRAINLIEST WHOEVER ANSWERS FIRST!! MUST BE CORRECT!!!!
Answer:
77 inches by 161 inches
Step-by-step explanation:
This is because you need to multiply 22 by 3.5(3 1/2) and the answer you get is 77 then you multiply 46 by 3 1/2 and the answer you get is 161.
So the dimensions of the new document is 77 inches by 161 inches.
Jill paid $36 for calendars marked down $5 apiece from the original price, she could have gotten 5 fewer calendars. How many cards did she buy
Answer:
she bought 7 cards
Step-by-step explanation
7x5=35 and im sure there is tax
f(x)2x/x+3,x≠-3 can somebody please explain.
Answer:
x cannot equal -3 because if -3 is plugged in for x, there will be a zero in the denominator and you cannot divide by 0
Sasha deposited $1,400 in an account that pays 1.5% simple interest. She created a graph of her
account balance equation (A = Prt + P) with a slope of 21.
true or false?
Answer:
The answer is False.
What is the median of the data represented in the box plot shown in the image? A. 15 B. 25 C. 35 D. 45 Show all work!
Answer:
35
Step-by-step explanation:
The median is the middle number in the data
The middle is the line in the middle of the box
Median is 35
In a box plot, the median can be found by looking the middle dot in the rectangle.
As we can we, the middle dot represents 35 and the median.
Best of Luck!
Mathematics, probability and chance Can somebody help me, I always thank and vote
Answer:
A. 0
Step-by-step explanation:
In order for there to be a 1 in 3 chance, there would have to be an equal number of the three chalices. Since four is the smallest number, the other two must have four left as well. That means Donavan drank 1 spoiled milk and 2 flat sodas. Therefore, he drank 0 purified water.
A building 50ft tall is on top of a hill A surveyor is at a point on the hill and observes that the angle of elevation to the top of the
building measures 48° and to the bottom of the building is 20°. How far is the surveyor from the bottom of the building?
Answer:
48-20
Step-by-step explanation:
The distance of the surveyor from the bottom of the building is 125.1 feet.
What is the angle of elevation?You look straight parallel to the ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called the angle of elevation.
Assume the distance of the surveyor from the bottom of the building is represented by x.
First, we have to know that the Tan of 48° is equal to 1.11.
The equation to get the distance will then be;
tan(48) = 50/h
h = 45.05 feet
Now, tan(20) = 45.05 /x
x = 45.05 / 0.36
x = 125.1 feet
The distance of the surveyor from the bottom of the building is 125.1 feet.
Learn more about trigonometric;
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The hanger image below represents a balanced equation. Find the value of r that makes the equation true.
Step-by-step explanation:
R is 4 times so the equation will be
32 = 4r
32/4 = r
8 = r
If you transform x2 + y2 = 25 into 4x2 + 4y2 = 25, which option below describes the effect of this transformation on the radius? A. It multiplies the radius by 2. B.It multiplies the radius by 4. C.It divides the radius by 4. D.It divides the radius by 2.
Answer:
C. It divides the radius by 4.
Step-by-step explanation:
We have x2 + y2 = 25.
If all terms were multiplied by 4, we would have 4x2 + 4y2 = 100. But, the radius is 25 units. 100 / 25 = 4. So, the radius was divided by 4.
Hope this helps!
please help real quick
Answer:
B. 945 m^3
Step-by-step explanation:
We just need to find the volume of the big box and the small box and find the difference.
To find the volume of a box, we multiply length, width, and height
Big box:
15.3x7x10=1071
1071
Small box:
4.2x3x10=126
126
1071-126=945
945 m^3
Answer:
b
Step-by-step explanation:
Graph the line with the slope 1/3 that contains the point (-4, -3)
Answer:
So, 1 point is on (-4, -3)
Other point is on (-4, -7)
Step-by-step explanation:
Slope = y/x - y1/x1
=> -3 / -4 - ? = 1/3
=> -3 / -4 - 1/3 = ?
=> -3 -1 / -4 - 3
=> -4 / -7
So, -3 / -4 - (-4 / -7)
=> -3 +4 / -4 + 7
=> 1/3
So 1 point is on (-4 , -3)
Other point is on (-4, -7)
Answer:no
Step-by-step explanation:
No
Iy
What is the domain of the function f(x) = 3|x + 4[ + 1?
ca
4+
3
-2-
1+
O all real numbers
O all real numbers less than or equal to -4
O all real numbers greater than or equal to 1
O all real numbers greater than or equal to -4
-7-5-5
3-2-11
5.6
X
2.
2Y
16
Answer:
all real numbers
Step-by-step explanation:
The function f(x) = 3|x +4| +1 is defined for all values of x. Its domain is all real numbers.
Calculate the surface area of a cube when the length of a side a = 15cm.
Surface area = 6a^2
Answer:
[tex]\boxed{ \sf 1350 \ cm^2}[/tex]
Step-by-step explanation:
Surface area of a cube = 6a²
a = side length
The side length is given 15 cm.
[tex]6(15)^2[/tex]
[tex]6(225)[/tex]
[tex]1350[/tex]
The surface area of the cube is 1350 cm².
Among Patients who did not relapse which statement was most effective and what’s its conditional relative frequency
Answer:
For those who achieve a year of sobriety, less than half will relapse. If you can make it to 5 years of sobriety, your chance of relapse is less than 15 percent.
So A
Answer:
2
Step-by-step explanation:
Two birds start from the same nest and head off in opposite directions. The speed of the first bird is 15mph more than the speed of the second.After 6 hours the two birds are 402 miles apart. Find the speed of each bird?
Answer: Speed of first bird =41 mph
Speed of second bird = 26 mph
Step-by-step explanation:
Let x be the speed of the second bird, then the speed of first bird will be x+15.
After 6 hours ,
Distance covered by first bird= (x+15)(6) [Distance = speed × time]
= 6x+90
Distance covered by second bird= (x)(6) = 6x
After 6 hours the two birds are 402 miles apart.
[tex]\Rightarrow\ 6x+90+6x=402\\\\\Rightarrrow\ 12x=402-90\\\\\Rightarrow\ 12x=312\\\\\Rightarrow\ x=\dfrac{312}{12}\\\\\Rightarrow\ x=\dfrac{312}{12}=26[/tex]
Speed of second bird = 26 mph, Speed of first bird = 26+15 = 41 mph.
The two points on the coordinate plane represent Jane's house and her friend's house. Find the distance between the houses. Question 3 options: A) units B) units C) units D) units
Answer:
8.3
Step-by-step explanation:
To do this use the distance formula
[tex]d = \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
First find the coordinates Jane (-5, -2) Friend (3, -4)
Now solve for d (8.246)
Answer:
10 units or approx. 8.25 units
Step-by-step explanation:
Jane's house is at coordinate (-5,-2) and her friend's house is at coordinate (3,-4).
You can find the answer in 2 ways.
1) Hypotenuse (the diagonal side or side across from the right angle) - approx. 8.25 units
2) Down and Side (go down 2 units and go side 8 units) - 10 units
Hope that helps and maybe earns a brainliest!
Have great day ahead! :)
