the difference quotient for the given function is 2.
How to evaluate the difference quotient?For any function f(x), we define the difference quotient as:
( f(x + h) - f(x))/h
And we take the limit as h tends to zero.
Here our function is:
f(x) = 2x + 4
Replacing it in the difference quotient we get:
(2*(x + h) + 4 - 2x - 4)/h = ( 2x + 2h + 4 - 2x - 4)/h = 2h/h = 2
So we conclude that the difference quotient for the given function is 2.
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The shadow of a building is 30m long when the angle of elevation of the sun is 56°. Calculate the:
(a) height of the building
(b) length of shadow when the sun is at an angle of 32°.
Answer:
(a) height: 44.5 m
(b) shadow: 71.2 m
Step-by-step explanation:
You want building height and shadow length for angles of elevation 56° and 32°, given the shadow is 30 m when elevation is 56°.
Trig relationThe building height and shadow length are the sides opposite and adjacent (respectively) to the elevation angle in the right triangle that models the geometry. The trig function that relates these sides to the angle is the tangent function:
Tangent = Opposite/Adjacent
Application(a) building height
Using the tangent relation, we have ...
tan(56°) = (height)/(30 m)
height = (30 m)(tan(56°)) ≈ 44.4768 m
The height of the building is about 44.5 meters.
(b) shadow length
Using the same relation with the building height known, we have ...
tan(32°) = (44.4768 m)/(shadow)
shadow = (44.4768 m)/tan(32°) ≈ 71.1778 m
The length of the shadow at an angle of 32° is about 71.2 m.
Solve the function.
f(x) = x² + 2x - 1
f(-3) = [?]
Answer:
2
Step-by-step explanation:
f(-3) represents f(x) evaluated at x=3.
[tex]f(-3)=(-3)^2+2(-3)-1 \\ \\ =9-6-1 \\ \\ =2[/tex]
10 decreased by the difference of v and u
Answer:
(V - U) - 10
Step-by-step explanation:
16.468>16.4 or < or =
Answer:
The answer is not that clear: But for 16.4 it isn't correct because you need to round it from 16.468 to 16.5. so therefore the answer is <
The volume of a cone is 405 pi inches cubed with a radius of 9 inches. What is the height of the cone?
Given the values of the volume and radius, the height of the cone is 15 inches.
What is the height of the given cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The volume of a cone is expressed as;
V = (1/3)πr²h
Given the data in the question;
Volume of the cone V = 405π in³Radius r = 9 inHeight h = ?Plug in the given values and solve for h.
V = (1/3)πr²h
h = 3V / πr²
h = ( 3 × 405π in³ )/( π × (9in)²
h = ( 3 × 405 in³ )/( 81 in² )
h = ( 1215 in³ )/( 81 in² )
h = 15 inches
Given the values of the volume and radius, the height of the cone is 15 inches.
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3 times (2x + 5) - 23 = 10
Answer:
x=3
Step-by-step explanation:
3 times (2x+5)-23=10 can be rewritten as 3(2x+5)-23=10
6x+15-23=10 ----> Use distributive Property
6x-8=10 ------------> Combine Like Terms
6x=18 -----------------> Use inverse operations; add 8 on both sides; simplify
x=3 ---------------------> Use inverse operations, divide by 3, simplify
Answer:
X=3!
Step-by-step explanation:
1) 6x - 8 = 10
2) + 8 +8
3) 6x = 18
Solution: X=3
The Evans family paid $1,800 for a new refrigerator, washer, and dryer. The
refrigerator cost $250 more than the washer. The dryer cost half as much
as the washer. How much did the washer cost?
The cost of the washer based on the total cost of $1,800 of all three items is $442.86
How do represent the cost of the washer?
If we assume that the cost of the washer is x, based on that we can determine the cost of the refrigerator and the dryer while deriving from the cost of the washer as denoted below:
cost of washer=x
The cost of the refrigerator is $250 more than the cost of washer i.e. x+250
cost of dryer=0.5*x
cost of dryer=0.5x
total cost=x+x+250+0.5x
total cost=3.5x+250
total amount spent=1800
1800=3.5x+250
1800-250=3.5x
1550=3.5x
x=1550/3.5
x=$442.86
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PLEASE HELP BEEN STUCK ON THIS FORVER! AND ITS DUE SOON!
FIND THE 100TH LINE SEGMENT
CUBE #1 HAS 4 LINES
CUBE #2 HAS 12
CUBE #3 HAS 24
WHATS THE 100TH LINE SEGMENT USING NTH TERM.
PICTURE BELOW!
The 100th line segment by using the nth term of a sequence is equal to 20200.
What is a sequence?A sequence can be defined as a series of real and natural numbers in which each term or list of elements are ordered in a particular order and repetitions are allowed.
Next, we would determine the differences between the terms in this sequence until all the differences are the same:
12 - 4 = 8
24 - 12 = 12
40 - 24 = 16
12 - 8 = 4
16 - 12 = 4
Since the differences are the same, the sequence is a quadratic function and it contains an n² term. Also, the coefficient of n² is one-half of the equal difference. This ultimately implies that, the coefficient of n² is equal to 2.
In order to determine the nth term of this sequence, we would develop a table to model increment:
n 1 2 3 4
2n² 2 8 18 32
Operation +2 +4 +6 +8
Sequence 4 12 24 40
By critically observing the table above, we can logically deduce that the nth term of this sequence is given by:
aₙ = 2n² + 2n
a₁₀₀ = 2(100)² + 2(100)
a₁₀₀ = 2(10000) + 2(100)
a₁₀₀ = 20000 + 200
a₁₀₀ = 20200.
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HELP PLS JUST LOOK AT THE PICTURE
On 50th day she needs to buy new bags of rice.
What is sequence?A sequence is defined as an arrangement of numbers in a particular order.
Sequence: 0.4, 0.8, 1.2, 1.6,......20
a=0.4, d=0.4, a_n= 20
Now,
we have to find in how many days 20 pounds rice will ends
So,
a_n= a + (n-1 )d
20 = 0.4 + (n-1) * 0.4
19.6 = (n-1)0.4
19.6/0.4= n-1
49 = n-1
n= 50
Hence, on 50th day she needs to buy new bags of rice.
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Please help me asap!!! I need 3,5,7,9,10 first correct answer gets a crown and max points!!!
Answer:
3. 7
5. 8
7. 15
9. 6
10. 1
Step-by-step explanation:
find the measure of EF
Answer:
EF = 32
Step-by-step explanation:
since the base angles D and F are congruent then the triangle is isosceles with both legs congruent , that is
EF = DE = 32
Answer:
32 units
Step-by-step explanation:
It is an isosceles triangle so two sides will be the same length opposite the equal angles EF = 32
A restaurant chef made 1 1/8 pints of mushroom soup. Each bowl of soup holds 1/8 of a pint. How many bowls of soup will the chef be able to fill?
Write your answer as a fraction or as a whole or mixed number.
Answer:
9
Step-by-step explanation:
We can determine the number of bowls that can be made by dividing the size of the bowl by the amount of soup. 1 1/8 can be expressed as 8/8 + 1/8, or 9/8. (9/8)/(1/8) = 9. The chef can fill 9 bowls of soup.
Mushroom soup sounds pretty good right now ngl
In a class of 23 learners, the girls were 7 more than the boys. How many boys were in the class
Answer:
8 boys.
Step-by-step explanation:
Lets say b is the number of boys and g is the number of girls.
We know that:
23 = b + g
g = b + 7
So then lets solve for b:
23 = b + g
23 = b + ( b + 7)
Simplify.
23 = 2b + 7
Subtract 7 from both sides to isolate the b.
16 = 2b
Divide both sides by 2.
8 = b
So there are 8 boys in the class.
We can check our work by substituting the value of b into our equation.
23 = b + ( b + 7)
23 = 8 + ( 8 + 7 )
23 = 8 + 15
23 = 23
So therefore our answer is correct.
Annalea wants to know which school has higher athletic achievements relative to budget per student
The ways to know know which school has higher athletic achievements relative to budget per student are:
% of students in sports club divided by SAT averagethe number of sports medals won divided by SAT averageHow to illustrate the information?Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
% of students in sports club divided by SAT average
the number of sports medals won divided by SAT average
To determine which school has higher athletic achievements relative to the SAT average, according to the two definitions will be that Did you get the same result for both definitions?
No. The definitions have opposite results.
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Analia wants to know which school has higher athletic achievements relative to the SAT average. 1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options. Choose 2 answers: Choose 2 answers: (Choice A) A % of students in sports club divided by SAT average (Choice B) B Graduation rate divided by SAT average (Choice C) C Number of sports medals won (Choice D) D Number of sports medals won divided by SAT average 2) Determine which school has higher athletic achievements relative to the SAT average, according to the two definitions. Did you get the same result for both definitions? Choose 1 answer: Choose 1 answer: (Choice A) A Yes. According to both definitions, School A has higher athletic achievements relative to the SAT average. (Choice B) B Yes. According to both definitions, School B has higher athletic achievements relative to the SAT average. (Choice C) C No. The definitions have opposite results.
what is the sum of product of the following
-5 +8
-2 +3
-6 +4
1 +(-7)
4 + (-9)
11 + (-8)
-8 + (-5)
-2+(3)
-6+(4)
-1+(-7)
-4+(-9)
7×(-7)
8×(-4)
-9×3
-8×(-8)
-6×(-6)
-9×(-9)
-7×(-3)
-6×(-8)
Answer:
(1). 3 (2).1 (3) -2 (4). -6 (5). -5 (6). 3 (7). -13 (8). 1 (9). -2 (10). -8 (11). -13 (12) -49 (13). -32 (14) -27 (15). 64 (16). 36 (17). 81 (18). 21 (19). 48
Step-by-step explanation:
i do not know if you still need these answers but here they are
Determine whether the equation below has one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
5(x+2)=5x+10
please factor and show work
Answer:
[tex]2a^2b*(3a^2-5ab-3b^2)[/tex]
Step-by-step explanation:
Attempt factorization by grouping
(((6•(a^4))•b)-((10•(a^3))•(b^2)))-((2•3a^2)•b^3)
(((6•(a^4))•b)-((2•5a^3)•b^2))-(2•3a^2b^3)
(((2•3a^4) • b) - (2•5a^3b^2)) - (2•3a^2b^3)
6a^4b - 10a^3b^2 - 6a^2b^3 = 2a^2b • (3a^2 - 5ab - 3b^2)
Pull out the leading term and put it with the original equation
= 2a^2b • (3a^2 - 5ab - 3b^2)
This would be one of the quicker ways to factor this equation.
Hope this helps.
Can someone help with this question?✨
Answer:
Step-by-step explanation:
well what even is the question all i see is graphs
In response to an economic downturn, a company with 1500 employees reduces the number of employees to 1230. What is the percent decrease? (If necessary, round to two decimal places.)
The number of employees decreased by 18 percent
How to calculate the percent decrease of the employees ?The formular for percent decrease is
old value-new value/old value × 100
old value= 1500
new value= 1230
1500-1230/1500 × 100
= 270/1500 × 100
= 0.18 × 100
= 18
Hence the number of employees decreased by 18 percent
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Find the area of the shaded region
Given the central angle and radius of the sector, the area of the shaded region is 28.26cm².
What is the area of the shaded region?A sector is simply a part of the area of a circle bounded by the central angle and its intercepted arc. The area of a sector is expressed as;
A = (θ/360) × πr²
Given the data in the diagram;
Central angle θ = 90°Radius r = 6cmConstant pi π = 3.14Area of the sector = ?To determine the area of the shaded region, plug the given values into the formula above and solve for A.
A = (θ/360) × πr²
A = (90/360) × 3.14 × (6cm)²
A = (1/4) × 3.14 × 36cm²
A = 3.14 × 9cm²
A = 28.26cm²
Given the central angle and radius of the sector, the area of the shaded region is 28.26cm².
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Which of the following is a factor of 2x4 + 20x3 + 50x2?
2x3
x4
x + 4
x + 5
D. (x + 5)
We have to find the factor of this expression which matches to the options.
factor please show work
Answer:The answer would be 6a(4b4 +2b3 -3b2)
Step-by-step explanation:All you have to do is take 6a out of each number and put the 6a outside of parenthesis and put the rest of the equation in parenthesis.
27.08, 27.88, 27.8, 26.78 least to greatest
Answer: 26.78 27.08 27.8 27.88
Step-by-step explanation:
1: Using a Place Value Chart, compare the whole numbers in your list of decimals.
2: Set up a table for the remaining numbers.
3: Transfer the decimals from your math problem into the table.
4: Compare the digits in the tenths column of the table
5: Compare the hundredths column (2 to the right of the decimal point).
6: Examine the digits in the thousandths column.
7: Order the numbers from least to greatest.
- 27.08 - 2nd because 0 is the least/lower number than 8 (tenths value)
- 27.88 - 4th because there are two numbers after the decimal which are greater than the others (tenths & hundredths value)
- 27.8 - 3rd because there is only one number after the decimal (tenths value)
- 26.78 - 1st because 6 is the least number than 7 (tens value)
Explanation in words (Short Form)
- Using the place value chart I can count the lowest number in the tens value that will be the first least number. I will progress my way up until I will eventually find the least to greatest numbers because of there decimal points and numbers after the decimals.
Reference: Place value chart
Answer:
26.78, 27.08, 27.8, 27.88
Hope this helps.
The height h in feet that a pole vaulter can reach can be estimated using the formula hu, where v is the velocity of the athlete in feet per
second.
If the height for a women's pole vault is about 9.8 feet, about how fast was the holder running? How far will the pole vaulter run in 2 seconds?
eet
feet per second
Using the numeric value of functions, it is found that:
The holder was running at a rate of 25 feet per second.The pole vaulter will run 50 feet in 2 seconds.How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
The formula for the velocity is given as follows:
[tex]v = 8\sqrt{h}[/tex]
In which h is the height.
For this problem, we have that the height is of h = 9.8, hence:
v = 8sqrt(9.8) = 25 feet per second.
The holder was running at a rate of 25 feet per second.
Then, in two seconds, the distance is given as follows:
d = 25 x 2 = 50 feet.
The pole vaulter will run 50 feet in 2 seconds.
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(1.64 x 104) + (7.28 x 10³) =
Write your final answer in scientific notation
7450.56 is the correct answer
QUESTION BELOW SLOVE USING NTH TERM!
I found this
im using T for tails and H for heads
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
MOVE 1# TTTT
MOVE 2#THHH
MOVE 3#HTTH
MOVE4#HHHT
MOVE5#TTTH
end up like =HHHH
HOW DO I WRITE THIS OUT FOR NTH TERM.
THE QESTION IS BELOW! WILL GET 100 POINTS! PLEASE HELP BEEN STUCK ON THIS FOREVER!
2. Company A charges $4.50 per month plus $0.25 per text. Company B charges $8.00 plus
$0.20 per text. How many texts would make the two plans cost the same amount?
Ken and Sam received their monthly salary.
Ken received four times the amount of money Sam receives plus
$790 bonus because he is the hardworking one and he has
helped his boss signing a profitable deal.
Let K be the amount of money Ken received.
Write the expression that shows the amount of money Sam
received.
Answer: S = K/4 - 790
Step-by-step explanation:
the problem tells us Ken = Sam times 4 + 790.
So you need to reverse it (or solve for Ken to find Sam).
Ken/4 = Sam + 790
Ken/4-790 = Sam
find out which of the number 5,8 and 9 divide into51768 exactly
Answer: 8 and 9
Step-by-step explanation: 51768 ÷ 9 = 5752
51768 ÷ 8 = 6471
Answer:
9
Step-by-step explanation:
The digits of 51768 add up to a multiple of 9
Elise says, “if you subtract 11 from my number and multiply the difference by -4, the result is -48” What is Elise’s number?