Answer:
5
Step-by-step explanation:
2 × 2 = 4
3× 3 = 9
4 × 4 =16
5 × 5 =25
16 is the only number and closest number to 21 to subtract from
A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
It will take the roller coaster 171.652 seconds to pass over the hill and reach ground level
How to determine the time to hit the ground?The function is given as:
h = –.025t^2 + 4t + 50
Set h = 0.
So, we have:
–.025t^2 + 4t + 50 = 0
Using a graphing calculator, we have:
t = -11.652 and t = 171.652
Time cannot be negative.
So, we have:
t = 171.652
Hence, it will take the roller coaster 171.652 seconds to pass over the hill and reach ground level
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help on this question please
Answer:
no because 1 x value cannot have 2 y values , i hope the helps
Choose C.
On the number line, if P points to a number 1/4 of the distance from 0.02 to 0.03, what is this number?
A 0.0021
B 0.0024
C 0.0225
D 0.025
E 0.25
Answer: C. 0.0225
Step-by-step explanation:
The distance is 0.03 - 0.02 = 0.01.
1/4 of this is 0.0025.
Adding this to 0.02, we get 0.00225.
is 66 a perfect cube with prime factorization
Answer:
no
Step-by-step explanation:
Prime factorization of 66
[tex]66=[/tex][tex]2[/tex] × [tex]3[/tex] × [tex]11[/tex]
the perfect cubes are the numbers that possess exact cubic roots
[tex]\sqrt[3]{66}[/tex] ≈ [tex]4.04[/tex]
66 is not a perfect cube
Hope this helps
Write an equation for the nth term of the arithmetic sequence 8, 3, -2, -7,... Find the 9th term of the sequence.
Answer:
The answer is ninth term is -32
Identifying Cross Sections of Solids
Which solids can have vertical cross sections that are circles? Check all that apply.
cones
O prisms
cylinders
O pyramids
spheres
Intro
Done
Answer:1,3,5
Step-by-step explanation:
Which of the following equations have complex roots?
Answer:
D
Step-by-step explanation:
Subtracting 2 from both sides and then dividing both sides by 3 gives that x² = -2/3, which indicates the roots are complex.
For F(x)=2x+1 and G(x)=c^2-7 find (FxG)(x)
The value of F(G(x)) is 2x^2 - 13
How to solve the composite functions?The functions are given as:
F(x)=2x+1
G(x)=x^2-7
To find (FxG)(x), we make use of
(FxG)(x) = F(G(x))
So, we have:
F(G(x))=2G(x)+1
Substitute G(x)=x^2-7
F(G(x))=2(x^2-7)+1
Expand
F(G(x))=2x^2 - 14 + 1
Evaluate the like terms
F(G(x))=2x^2 - 13
Hence, the value of F(G(x)) is 2x^2 - 13
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Please help I want clear answers for example
AB: X = ___ Y =___
Answer:
AB: y=2x+2
CB: y=-2x+6
CD: y=1/2x-1.5
DA: y=-3x+2
Step-by-step explanation:
Answer:
AB: [tex]y=2x+2[/tex]
CB: [tex]y=-2x+6[/tex]
CD: [tex]y=\frac{1}{2}x -1.5[/tex]
DA: [tex]y=-3x+2[/tex]
Step-by-step explanation:
So when it's saying y = __ x + __ it's asking for the slope-intercept form. This is given as y=mx+b where m is the slope and b is the y-intercept. m is the slope because as x increases by 1, the y-value will increase by m, which is by definition what the slope is [tex]\frac{rise}{run}[/tex] how much the function "rises" as x "runs".
AB: See how it "rises" by 2 and only "runs by 1", thus the slope is 2/1 or 2. the last part is the y-intercept, which is the value of y when the line crosses the y-axis. If you look at the graph when it "crosses" the y-axis it's y-value is 2. So you have the equation: [tex]y=2x+2[/tex]
CB: See how it "goes down" by 4 and "runs" by 2, thus the slope is -4/2 or -2. The y-intercept isn't shown on the graph but you can calculate that by substituting known values into the slope-intercept form. So we know so far y=-2x+b since the slope was calculated, and we can take any point on the line to calculate b, for this example I'll take the point C which is (3, 0) which is (x, y) and I'll plug that in
Plug values in:
0 = -2(3) + b
0 = -6 + b
6 = b
This gives you the complete equation: [tex]y=-2x+6[/tex]
CD: see how it only "rises" by 1 but "runs" by 2, thus the slope is 1/2. The y-intercept isn't shown on the graph but you can calculate it by substituting a point into the equation For this example I'll use point C (3, 0)
0 = 3(1/2) + b
0 = 1.5 + b
-1.5 = b
This gives you the complete equation: [tex]y=\frac{1}{2}x - 1.5[/tex]
DA: see how it "decreases" by 3 but "runs" by 1, thus the slope is -3/1 or -3. The y-intercept is known and is at (0, 2) so now we plug these values in to get the equation: [tex]y=-3x+2[/tex]
Answer two questions about Systems A and B:
A
4x+16y=12
x+2y=−9
B
4x+16y=12
x+4y=3
1) How can we get System B from System A?
Choose 1 answer:
(Choice A, Checked, Correct)
CORRECT (SELECTED)
Replace one equation with a multiple of the other equation
For the given systems the answers are:
1) "Replace one equation with a multiple of the other equation".
2) The systems are not equivalent.
How can we get System B from System A?Here we have the systems of equations:
A:
4x + 16y = 12
x +2y = -9
B:
4x + 16y = 12
x + 4y = 3
Notice that the first equation is the same in both systems, but the second is different.
In A we have:
x + 2y = -9
In B we have:
x + 4y = 3
So we need to add 2y on the left side of A, and 12 on the right side of A to get the equation in B.
Or we can just take the other equation in A, divide it by 4, and replace it.
So we need to replace the second equation in A for other equation, then the correct option is:
"Replace one equation with a multiple of the other equation".
Because we are replacing an equation in A by other to get system B, we conclude that systems are not equivalent.
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Answer:
khan
Step-by-step explanation:
Which expression is equivalent to 16^3?
Answer:
2¹²
Step-by-step explanation:
one expression equivalent to 16³ is 2¹²
think about it like this: we know that 2 to the power of 4 is 16
(2 x 2 = 4, x 2 = 8, x 2 = 16)
So for every "16" we already have 2⁴; meaning that 16³ is the same thing as 3 groups of 2⁴ -- which is 2¹²
hope this helps! have a lovely day :)
a simple pendulum of amplitude completes 24 oscillations in one minute. find the length of the string the pendulum bob is attached
[tex]frequency = \frac{24 \: osc}{60 \: sec} = 0.4 \: osc \: per \: sec[/tex]
[tex]period = \frac{1}{frequency} = \frac{1}{0.4} = 2.5 \: sec \: per \: osc[/tex]
[tex]t = 2\pi \sqrt{ \frac{l}{g} } \\ 2.5 = 2\pi \sqrt{ \frac{l}{9.8} } \\ \frac{2.5}{2\pi} = \sqrt{ \frac{l}{9.8} } \\ ( \frac{2.5}{2\pi} ) {}^{2} = \frac{l}{9.8}[/tex]
[tex]l = ( \frac{2.5}{2\pi} ) {}^{2} \times 9.8 = 1.55148 \: meters[/tex]
Pls help!! Geometry
Find the perimeter of the figure.
In circle M. Diameters JL and HK each measure 16 centimeters.
The length of the arc in the image given is approximately: A. 3.5 cm
What is the Length of Arc?Length of arc = ∅/360 × 2πr
The missing parts of the question is shown in the image below, where we are asked to find arc length of JH.
Thus, we would have the following:
∅ = 25°
Radius (r) = 16/2 = 8 cm
Substitute the values into the formula:
Arc length JH = 25/360 × 2π(8)
Arc length JH ≈ 3.5 cm
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Problem
(a) Let [tex]a_1, a_2, a_3,...[/tex] be an arithmetic progression of non-zero numbers with common difference [tex]d[/tex].
(i) Show that [tex]\frac{1}{a_na_{n+1}}=\frac{1}{da_n}-\frac{1}{da_{n+1}}[/tex] for any [tex]n\geq1[/tex].
(ii) Hence show that [tex]\frac{1}{a_1a_2}+\frac{1}{a_2a_3}+\frac{1}{a_3a_4}+...+\frac{1}{a_{99}a_{100}}=\frac{99}{a_1a_{100}}[/tex].
(b) For what value of [tex]k[/tex] does [tex]\frac{1}{3\times7}+\frac{1}{7\times11}+\frac{1}{11\times15}+...+\frac{1}{k(k+4)}+\frac{2}{25}[/tex]?
(a.i) If [tex]a_1,a_2,a_3,\ldots[/tex] are in arithmetic progression, then there is a constant [tex]d[/tex] such that
[tex]a_{n+1} - a_n = d[/tex]
for all [tex]n\ge1[/tex]. In other words, the difference [tex]d[/tex] between any two consecutive terms in the sequence is always the same.
[tex]a_2-a_1 = a_3-a_2 = a_4-a_3 = \cdots = d[/tex]
Now, we can expand the target expression into partial fractions.
[tex]\dfrac1{a_na_{n+1}} = \dfrac{\alpha}{a_n} + \dfrac{\beta}{a_{n+1}}[/tex]
Combining the fractions on the right and using the recursive equation above, we have
[tex]\dfrac1{a_na_{n+1}} = \dfrac{\alpha (a_n + d) + \beta a_n}{a_n(a_n+d)} = \dfrac{(\alpha+\beta) a_n + \alpha d}{a_n a_{n+d}} \\\\ \implies \begin{cases}\alpha + \beta = 0 \\ \alpha d = 1 \end{cases} \implies \alpha = \dfrac1d, \beta = -\dfrac1d[/tex]
and hence
[tex]\dfrac1{a_n a_{n+1}} = \dfrac1{da_n} - \dfrac1{da_{n+1}}[/tex]
as required.
(a.ii) Using the previous result, the [tex]n[/tex]-th term [tex](n\ge1)[/tex] in the sum on the left is
[tex]\dfrac1{a_n a_{n+1}} = \dfrac1d \left(\dfrac1{a_n} - \dfrac1{a_{n+1}}\right)[/tex]
Expand each term in this way to reveal a telescoping sum:
[tex]\dfrac1{a_1a_2} + \dfrac1{a_2a_3} + \dfrac1{a_3a_4} + \cdots + \dfrac1{a_{99}a_{100}} \\\\ ~~~~~~~~ = \dfrac1d \left(\left(\dfrac1{a_1} - \dfrac1{a_2}\right) + \left(\dfrac1{a_2} - \dfrac1{a_3}\right) + \left(\dfrac1{a_3} - \dfrac1{a_4}\right) + \cdots + \left(\dfrac1{a_{99}} - \dfrac1{a_{100}}\right)\right) \\\\ ~~~~~~~~ = \dfrac1d \left(\dfrac1{a_1} - \dfrac1{a_{100}}\right) = \dfrac{a_{100} - a_1}{d a_1 a_{100}}[/tex]
By substitution, we can show
[tex]a_n = a_{n-1} + d = a_{n-2} + 2d = \cdots = a_1 + (n-1)d \\\\ \implies a_{100} = a_1 + 99d[/tex]
so that the last expression reduces to
[tex]\dfrac{(a_1 + 99d) - a_1}{d a_1 a_{100}} = \dfrac{99d}{d a_1 a_{100}} = \dfrac{99}{a_1 a_{100}}[/tex]
as required. More generally, it's easy to see that
[tex]\dfrac1{a_1a_2} + \dfrac1{a_2a_3} + \dfrac1{a_3a_4} + \cdots + \dfrac1{a_na_{n+1}} = \dfrac{n}{a_1a_{n+1}}[/tex]
(b) I assume you mean the equation
[tex]\dfrac1{3\times7} + \dfrac1{7\times11} + \dfrac1{11\times15} + \cdots + \dfrac1{k(k+4)} = \dfrac2{25}[/tex]
Note that the distinct factors of each denominator on the left form an arithmetic sequence.
[tex]a_1 = 3[/tex]
[tex]a_2 = 3 + 4 = 7[/tex]
[tex]a_3 = 7 + 4 = 11[/tex]
and so on, with [tex]n[/tex]-th term
[tex]a_n = 3 + (n-1)\times4 = 4n - 1[/tex]
Let [tex]a_n=k[/tex]. Using the previous general result, the left side reduces to
[tex]\dfrac1{3\times7} + \dfrac1{7\times11} + \dfrac1{11\times15} + \cdots + \dfrac1{a_na_{n+1}} = \dfrac n{3a_{n+1}} \\\\ \implies \dfrac{\frac{k+1}4}{3(k+4)} = \dfrac2{25}[/tex]
Solve for [tex]k[/tex].
[tex]\dfrac{k+1}{12k+48} = \dfrac2{25} \implies 25(k+1) = 2(12k+48) \\\\ \implies 25k + 25 = 24k + 96 \implies \boxed{k=71}[/tex]
Find the perimeter P of ABCD with vertices A(3,1), B(6,2), C(6,-2), and D(3,-3). Round your answer to the nearest tenth, if necessary.
Step-by-step explanation:
the distance between 2 points is per Pythagoras
c² = a² + b²
with c being the Hypotenuse (the baseline opposite of the 90° angle, which is the direct distance between the points). a and b are the legs (the x and y coordinate differences).
so,
AB² = (3-6)² + (1-2)² = 9+1 = 10
AB = sqrt(10) = 3.16227766...
BC² = (6-6)² + (2 - -2)² = 0² + 4² = 16
BC = sqrt(16) = 4
CD² = (6-3)² + (-2 - -3)² = 3² + 1² = 10
CD = sqrt(10) = 3.16227766...
DA² = (3-3)² + (-3 - 1)² = 0² + 4² = 16
DA = sqrt(16) = 4
so, the perimeter is
2×4 + 2×sqrt(10) = 8 + 6.32455532... = 14.32455532... ≈
≈ 14.3
please help asap!!?!!?!
Volume is a three-dimensional scalar quantity. The length of the square base side is 5 meters.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the square pyramid is one-third of the product of the base area and the height. Therefore, the area of the base of the pyramid will be,
The volume of pyramid = (1/3) × Height × (Base length)²
75 m³ = (1/3) × 9 × (Base length)²
Base length)² = 25 m²
Base length = 5 m
Hence, the length of the square base side is 5 meters.
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Identity all obtuse angles in the drawing below
A triangle is formed between boats a and b and a submarine. the length between a and b is 1,425 feet. the angle at point a is 59 degrees and the angle at point b is 47 degrees. ships a and b are 1,425 feet apart and detect a submarine below them. the angle of depression from ship a to the submarine is 59°, and the angle of depression from ship b to the submarine is 47°. how far away is the submarine from the two ships? round to the nearest hundredth of a foot. the distance from ship a to the submarine is about feet. the distance from ship b to the submarine is about feet.
The distance from ships to the submarine is AX=1084.20
BX=1270.69
Let X be the submarine position.
GivenThe length between a and b is AB=1425
and the angle point a is at 59 degrees
the angle point b is at 47 degrees
The calculating angle at X:
∠X+∠A+∠B = 180
∠X+59°+47°=180°
∠X=180°-59°-47°
∠X=74°
Then the distance between boat A and the submarine will be found using sine law
What is sine law?Sine law is the ratio of each side of a plane triangle to the sine of the opposite angle is the same for all three sides and angles.
[tex]\frac{a}{sinA}=\frac{b}{sin B} = \frac{c}{sin C}[/tex]
so for Boat A and submarine, we use
[tex]\frac{AB}{sin X}=\frac{AX}{sin B}[/tex]
[tex]\frac{1425}{sin (74)} = \frac{AX}{sin (47)}[/tex]
When AX is the subject
AX=[tex]\frac{1425}{sin(74)}*sin(47)[/tex]
=[tex]\frac{1425}{0.9613}*0.7314[/tex]
AX=1042.245/0.9613
AX=1084.20
The distance between ship B and the submarine
The sine formula we use is
[tex]\frac{AB}{sin X}=\frac{BX}{sin A}[/tex]
Substituting[tex]\frac{1425}{sin 74}=\frac{BX}{sin 59}[/tex]
When BX is the subject
BX=[tex]\frac{1425}{sin 74}*sin(59)[/tex]
= 1425/0.9613 * 0.8572
=1221.51/0.9613
=1270.69
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Answer:
Ships A and B are 1,425 feet apart and detect a submarine below them. The angle of depression from ship A to the submarine is 59°, and the angle of depression from ship B to the submarine is 47°.
How far away is the submarine from the two ships? Round to the nearest hundredth of a foot.
The distance from ship A to the submarine is about
✔ 1,084.18
feet.
The distance from ship B to the submarine is about
✔ 1,270.69
feet.
Step-by-step explanation:
A school buys 1000 white-board markers. Below is the price per
marker for two brands. How much did the school save by buying
Brand A instead of Brand B?
Brand A: $0.27 each
Brand B: $0.36 each
A. $0.09
B. $0.90
C. $9.00
D. $90.00
Calculus help, I am trying to do this questions.. someone teach me please 10 points
Answer:
Step-by-step explanation:
A bit late, but better than never.
24. For [tex]x\neq1[/tex], we have
[tex]\dfrac{9x^2 - x - 8}{x - 1} = \dfrac{(x-1)(9x+8)}{x-1} = 9x+8[/tex]
Then as [tex]x[/tex] approaches 1, we have
[tex]\displaystyle \lim_{x\to1} f(x) = \lim_{x\to1} (9x+8) = 17 \neq 0[/tex]
so the function is not continuous at [tex]x=1[/tex]. It is thus continuous on the interval union [tex](-\infty,0)\cup(0,\infty)[/tex]. You can also write this as "[tex]x<0[/tex] or [tex]x>0[/tex]".
25. When [tex]x[/tex] approaches 2 from the left (when [tex]x<2[/tex]), we have
[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} (5-x) = 3[/tex]
When [tex]x[/tex] approaches 2 from the right [tex](x>2)[/tex], we have
[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (2x-3) = 1[/tex]
so the function is not continuous at [tex]x=2[/tex]. Thus it's continuous on [tex](-\infty,2)\cup(2,\infty)[/tex], or "[tex]x<2[/tex] or [tex]x>2[/tex]".
Lydia has half of her investments in stock paying an 11% dividend and the other half in a stock paying 14% interest. If her total annual interest is $440, how much does she have invested?
Answer
The amount that Lydia has earned on her investment is $198 on the stock paying the 11% dividend and $252 on the stock paying 14% interest for a total earned of $450 on her $3600 investment.
Calculations and ParametersLet x represent half of her total investment.
The total annual interest earned is $450.
This is represented by the following equation:
0.11x + 0.14x= 450
Collect the like terms together
0.25x = 450
x= 1800
Therefore, half of her total investment is $1800 so her total investment is $3600.
Check the solution:
0.11∗1800 + 0.14 ∗ 1800 = 450
198 + 252 = 450
Therefore, she earned $198 on the stock paying the 11% dividend, and $252 on the stock paying 14% interest for a total earned of $450 on her $3600 investment.
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Drag the tiles to the boxes to form correct pairs.
What are the unknown measurements of the triangle? Round your answers to the nearest hundredth as needed.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The measure of ∠C is 28°. And the value of b and c is 7.06 and 3.76, respectively.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.
The sum of all the angles can be written as,
∠A + ∠B + ∠C = 180°
90° + 62° + ∠C = 180°
∠C = 28°
Sin(∠B) = AC/BC
Sin(∠B) = b/8
b = 8 × Sin(62°)
b = 7.06
Cos(∠B) = AB/BC
Cos(∠B) = c/8
c = 8 × Cos(62°)
c = 3.76
Hence, the measure of ∠C is 28°. And the value of b and c is 7.06 and 3.76, respectively.
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First answer gets brainliest
Answer:
[tex]2.20b + 3.60m = 44.20\\2.50b + 3.40m = 44.70[/tex]
Step-by-step explanation:
So in this systems of equations, we know the prices of the items, so the coefficients will represent how many Mary is getting of that item. So you can represent amount of bread as the variable b and the amount of milk as the variable m. On the right will be the total amount spent, since multiplying the price by how much you buy should get you the price
So since at store A, she spends 44.20 and bread costs 2.20 and milk costs 3.60 you get
[tex]2.20b + 3.60m = 44.20[/tex]
Since at store B, she spends 44.70 and bread costs 2.50 and milk costs 3.40 you get the equation:
[tex]2.50b + 3.40m = 44.70[/tex]
Answer:
Option A
2.20b + 3.6m = 44.20
2.5b + 3.4m = 44.70
Explanation:
For store A, bread costs $2.20 and milk costs $3.60 and she pays $44.20
Equation created: 2.20b + 3.6m = 44.20
For store B, bread costs $2.50 and milk costs $3.40 and she pays $44.70
Equation created: 2.5b + 3.4m = 44.70
2 4/15-z= 1 2/3
pls solve
The value of z in the equation evaluation as given in the task content is; 3/5.
What is the value of z in the equation?It follows from the task content that the value of z as in the task content can be evaluated as follows;
2 4/15-z= 1 2/3
34/15 - z = 5/3
Hence, z = 34/15 - 5/3
z = (34-25)/15 = 9/15
z = 3/5
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Question 8 of 25
Which of the following is the quotient of the rational expressions shown here?
Answer:
B. (5x+5)/(x²-2x)
Step-by-step explanation:
As with numerical fractions, division by a rational expression is equivalent to multiplication by its reciprocal.
As a multiplication problem[tex]\dfrac{5}{x-2}\div\dfrac{x}{x+1}=\dfrac{5}{x-2}\times\dfrac{x+1}{x}[/tex]
Product of rational expressionsAs with numerical fractions, the product is the product of numerators, divided by the product of denominators.
[tex]=\dfrac{5(x+1)}{x(x-2)}=\boxed{\dfrac{5x+5}{x^2-2x}}[/tex]
The quadrilaterals ABCD and JKLM are similar.
Find the length x of LM.
D
5
4
A
3
B
2
C
M
6
X
J
3.6
M
2.4
7
Answer: 4.8
Step-by-step explanation:
Corresponding sides of similar figures are proportional, so
[tex]\frac{x}[4}=\frac{6}[5}\\\\x=4\left(\frac{6}{5} \right)=\boxed{4.8}[/tex]
A truck can travel 550 miles on a tank of gasoline. If the truck’s tank holds 26 gallons of gas then how many miles can the truck travel on one gallon?
Answer:
Twenty - one miles per gallon
Step-by-step explanation:
If a truck can travel 550 miles on a tank of gasoline holding 26 gallon of gas then to find out how many miles the truck can travel on one gallon we divide 550 by 26⇒ 550/26 = Amount per gallon which is one
⇒21.15384615384615
[tex] \approx [/tex] 21.2 miles per gallon
The distance travelled by truck in one gallon of fuel is 21.2 miles per gallon.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a truck can travel 550 miles on a tank of gasoline. The distance travelled by truck will be calculated as,
550 miles = 26 gallons
1 gallon = 550 / 26
1 gallon = 21.2 miles per gallon
Therefore, the distance travelled by truck in one gallon of fuel is 21.2 miles per gallon.
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please help! no explanation needed
Answer: C
Step-by-step explanation:
The line is dotted, so eliminate B and D.
Also, the line has a y-intercept of 1, so this eliminates A.
This means the answer must be C.
If f(x) = x2 - 1, and
g(x) = x + 2, then
f(g(x)) = [? ]x2+[?]x+[?]
Step-by-step explanation:
f.g(x) = f(x+2)
=(x+2)2 -1
=(x2+2*x*2+4)-1
=x2+4x+4-1
=x2+4x+3