f(x) = x2 + 3x + 2 is shifted 2 units left. The result is g(x). What is g(x)?
Answer:
[tex]g(x) = x^2+7x+12[/tex]
Step-by-step explanation:
If we are given a function f and we want to shift it a units horizontally, the resulting function will be f(x - a), where a positive a is a shift rightwards and a negative a is a shift leftwards.
We have the function:
[tex]f(x)=x^2+3x+2[/tex]
And we want to shift it two units to the left.
Since we want to shift it two units to the left, a = -2. Therefore, our new function, let's call it g, must be f(x - (-2)) or f(x + 2). Substitute:
[tex]g(x) = f(x+2)=(x+2)^2+3(x+2)+2[/tex]
Simplify. Expand:
[tex]g(x) = (x^2+4x+4)+(3x+6)+2[/tex]
Combine like terms. Hence:
[tex]g(x) = x^2+7x+12[/tex]
53:45
What is the equation of the line that is parallel to the line x=-2 and passes through the point (-5, 4)?
6 m.
O x= -5
O x = 4
O y=-5
O y = 4
Marks and rem
Save and Exit
ed
Answer:
x=-5
Step-by-step explanation:
any line parallel to x=a is x=b
line parallel to x=-2 is x=-5
The equation of the line is x = -5.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
The line x = -2 is a vertical line passing through the point (-2, y) for all y. Since we want a line parallel to this line, it must also be a vertical line.
Therefore, the equation of the line that is parallel to x = -2 and passes through the point (-5, 4) is simply x = -5.
So the answer is x = -5.
Learn more about Linear equations here:
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An experiment consists of rolling a six sided die to select a number between between 1 and 6 and drawing a card at random from a set of 10 cards numbered 1,2,3,...10. Which event definition corresponds to exactly one outcome of the experiment?
Answer:
Man this is confusing
Step-by-step explanation:
find the value of x.
Answer:
x = 116
Step-by-step explanation:
The sum of the angles of a 4 sided polygon is 360
96+x+64+84 = 360
Combine like terms
x+244=360
Subtract 244 from each side
x+244-244=360-244
x = 116
Sum of all angles of a quadrilateral = 360°
So, 96° + 84° + 64° + x° = 360°
=> 244° + x° = 360°
=> x° = 360° - 244°
=> x° = 116°
=> x = 116
Please help me out with this one!
Answer:
87 in^2
Step-by-step explanation:
24 + 18 + 15 + 30
the 30 is 2(1/2 * 5 * 6)
Help me solve this problem please
Answer:
A and D
step by step explanation:
What is the value of x that makes the given equation true?
2(x−8)=x+5x
a x=-4
b x=-16
c x=-2
d x=0
Answer:
x = -4
Step-by-step explanation:
2(x−8)=x+5x
Distribute
2x - 16 = x+5x
Combine like terms
2x-16 = 6x
Subtract 2x from each side
2x-16 = 6x-2x
-16 = 4x
Divide by 4
-16/4 = 4x/4
-4 =x
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]\sf{2(x-8)=x+5x }[/tex] [tex]\sf{2x-16=6x }[/tex] [tex]\sf{2x-6x=16 }[/tex] [tex]\sf{-4x=16 }[/tex] [tex]\sf{ x=\dfrac{16}{-4} }[/tex] [tex]\sf{x=-4 }[/tex][tex]\sf{ }[/tex]
please I really need help with this
Answer:
24
Step-by-step explanation:
(1+25) - (16)(1/8)
26 - 2
24
Cheers
Answer:
24
Step-by-step explanation:
(1+5^2) -16 ( 1/2)^3
PEMDAS
Parentheses first
Exponents in the parentheses
(1+25) -16 ( 1/2)^3
Then add in the parentheses
(26) -16 ( 1/2)^3
Then exponents
(26) -16 ( 1/8)
Then multiply
26 - 2
Then subtract
24
What is the measure of n
Answer:
n = [tex]\sqrt{32}[/tex]
Step-by-step explanation:
The 2 right triangles inside the larger right triangle are similar , so corresponding sides are in proportion
[tex]\frac{8}{n}[/tex] = [tex]\frac{n}{4}[/tex] ( cross- multiply )
n² = 32 ( take the square root of both sides )
n = [tex]\sqrt{32}[/tex]
What is the value of A when we rewrite (1/8)^x + (1/8)^x-2 as A x (1/8)^x
Answer:
-63
Step-by-step explanation:
Given the expression:
[tex](1/8)^x + (1/8)^{x-2}[/tex]
Using the law of indices, this can be written as:
[tex](\frac{1}{8})^x-(\frac{1}{8} )^x * (\frac{1}{8})^{-2}\\(\frac{1}{8})^x (1-(\frac{1}{8})^{-2})\\(\frac{1}{8})^x(1-8^2)\\(\frac{1}{8})^x(-63)\\-63(\frac{1}{8})^x\\[/tex]
This shows that the value of A is -63
Answer:
EVERYONE THE ANSWER IS …. 65
Step-by-step explanation:
I did the quiz I hate it :(
Find the slope of the line passing through the points D (10, 8) and E (-4,4)
Answer:
Slope=2/7
Step-by-step explanation:
Slope=rise/run
[tex]rise = 8 - 4 = 4 \\ run = 10 - ( - 4) = 14 \\ slope = \frac{4}{14} = \frac{2}{7} [/tex]
add 7 with the diffrence of 12 and 9 =
Answer:
7+3 = 10
Step-by-step explanation:
if I understand the problem strangeness right, and there is nothing missing in it, then this is the simple answer.
the difference of 12 and 9 is 12-9 = 3.
and then adding this 3 to 7 is 7+3 =10
Answer:
10
Step-by-step explanation:
The difference of 12 and 9 is 3.
Now,
If we add 7 to 3, the answer is 10.
Which of the following is equal to
square root symbol 9•4
Answer:
sqrt(9) sqrt(4)
Step-by-step explanation:
sqrt(9*4)
We know that sqrt(a*b) = sqrt(a) sqrt(b)
sqrt(9) sqrt(4)
Answer:
The answer would be B
Step-by-step explanation:
help me solve this percentages and prices. (show your work)
Answer:
$34.50
$1.01
Step-by-step explanation:
For these two problems, you must find a percent of a number. Since percentages can easily be turned into decimals, this is easy to do. First, turn the percent into a decimal by moving the decimal point two to the left; so, 6.25% becomes 0.0625. Then, multiply this number by the cost, 32.47. Finally add that, 2.02, to the cost to get the final answer, $34.50. For the next question do the same. Turn the percent into a decimal and then multiply that by the cost to get the total tax, $1.01.
HELP QUICK PLEASE!
Given: AC BD and AD BC
B
D
What postulate could prove DCA ACDB
O Side-Side-Side
O Side-Angle-Side
Angle-Side-Angle
Angle-Angle-Side
Answer:
Step-by-step explanation:
Side - side - side. In fact the two triangles have the side CD in common
Find the value of x.
A. 70
B. 30
C. 65
D. 40
Answer:
Option (A)
Step-by-step explanation:
From the figure attached,
By applying triangle sum theorem in ΔBCP,
m∠CBP + m∠CPB + m∠BCP = 180°
15° + 20° + m∠BCP = 180°
m∠BCP = 145°
m∠ACB + m∠BCP = 180° [Linear pair of angles are supplementary]
m∠ACB + 145° = 180°
m∠ACB = 35°
Since, ∠ACB is the inscribed angle and AB is the intercepted arc.
Therefore, m(arc AB) = 2m(∠ACB)
m(arc AB) = 2 × 35°
= 70°
Therefore, Option (A) is the correct option.
Can someone help me with this math homework please!
Answer:
The graph for a member's yearly cost for total game tokens purchased would have a y-intercept of (0, 60). However, the nonmember's yearly cost would have a different y-intercept of (0,0). This is because the member's yearly cost has a yearly initial fee of $60, while as the nonmember yearly cost doesn't include an inital fee. Also, the graph for the nonmember's yearly cost would be steeper than the member's graph because the slope 1/5 is greater than 1/10.
Hope this helps (●'◡'●)
The fractions 1/10 and 1/5 convert to 0.1 and 0.2 respectively.
So the equations y = (1/10)x+60 and y = (1/5)x are the same as y = 0.1x+60 and y = 0.2x in that order.
We see that the nonmember cost graph is steeper since the slope 0.2 is larger than 0.1; the further we move away from 0, the steeper the slope. A steeper slope means that you pay more per token. This is the unit cost.
Specifically, you would pay 0.20-0.10 = 0.10 more dollars per token if you are a nonmember compared to if you are a member.
---------------------------
Also, notice that the y intercepts of y = 0.1x+60 and y = 0.2x are 60 and 0 in that order. The members pay an up front fee of $60 before they can buy any tokens. Nonmembers don't have to pay an upfront cost.
Visually, the graph for the members will be much higher up compared to the nonmembers graph. Both lines are increasing, but the members graph is increasing less overall. At some point, the two lines intersect. After this point, it makes more sense to be a member.
aint the answer for this 10 just let me if im wrong
Answer:
Yup
Step-by-step explanation:
Rationalise the denominator as per necessary and simplify.
Answer:
[tex]8\sqrt{7}[/tex]
Step-by-step explanation:
[tex]\frac{21}{\sqrt{7} } * \frac{\sqrt{7} }{\sqrt{7} }[/tex] = [tex]\frac{21\sqrt{7} }{7}[/tex]
[tex]\frac{21\sqrt{7} }{7}[/tex] = [tex]\frac{147\sqrt{7} }{14}[/tex]
[tex]\frac{147\sqrt{7} }{14} - \frac{35\sqrt{7} }{14}[/tex]
[tex]\frac{112\sqrt{7} }{14}[/tex]
[tex]8\sqrt{7}[/tex]
Which of the following points is not a solution of the inequality y ≥ |x| + 3?
(-3, 6)
(0, 4)
(-3, 0)
========================================================
Explanation:
If we plug the coordinates of point A into the inequality, then we get
y ≥ |x| + 3
6 ≥ |-3| + 3
6 ≥ 3 + 3
6 ≥ 6
Which is true. Since we're looking for a non-solution, we rule out choice A.
You should find choice B is a similar story to choice A, so we can rule this out as well.
-----------
Choice C is the answer because
y ≥ |x| + 3
0 ≥ |-3| + 3
0 ≥ 3 + 3
0 ≥ 6
which is false.
Check out the graph below and notice how point C is not in the shaded solution region, and it's not on the boundary either. This is a visual way to quickly find the answer.
The boundary line y = |x|+3 is solid because of the "or equal to". We shade above the boundary line due to the greater than sign.
What is the volume of the cylinder below?
A. 196pi units3
B. 784pi units3
C. 98pi units 3
D. 112pi units 3
Answer:
196π units^3
Step-by-step explanation:
The volume of a cylinder is:
πr^2h
SINCE, there is no given pi, the formula will be:
r^2h
Use the formula on the given dimensions:
r^2h
= (7^2) 4
= (49) 4
= 196
So we could just leave the final answer as:
196π
The real volume will be solved once π is given.
I hope I helped!
The volume of the cylinder given is 196 π, Option A is correct.
The volume of the cylinder is given by V=πr²h
Where r is radius of cylinder and h is the height of the cylinder.
V is the volume
r=7
h=4
Now plug in these values in volume formula.
V=π(7)².4
=π.49.4
V=196π
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2. If f(x) = 2x2 – 7x -10, find the following: a) f(x-1) b) x, if f(x) = 5 Please helpppppp
Answer:
a) f(x-1) = 2x^2-11x-1
b) x = -1.5 or 5
Step-by-step explanation:
a) To get f(x-1)
We proceed to substitute x-1 for x as follows
f(x-1) = 2(x-1)^2 -7(x-1) -10
f(x-1) = 2(x^2 - 2x + 1) -7(x-1)-10
f(x-1) = 2x^2 -4x + 2 -7x + 7-10
f(x-1) = 2x^2-11x-1
b) What we have to do here is substitute 5 for f(x) and solve for x
5 = 2x^2 -7x-10
2x^2 -7x -10-5 = 0
2x^2 - 7x - 15 = 0
2x^2 -10x + 3x -15 = 0
2x(x-5) + 3(x-5) = 0
(2x + 3)(x-5) = 0
2x + 3 = 0 or x -5 = 0
2x = -3 or x = 5
x = -3/2 or x = 5
x = -1.5 or 5
What is true about angle ∠APD?
Answer:
HEY MATE FIRST OF ALL THE QUESTION IS NOT COMPLETE. TRY MAKING IT MORE CLEAR NEXT TIME !
Step-by-step explanation:
IF THE QUESTION IS THIS IN THE BELOW THEN HERE IS THE ANSWER .
What is true about angle ∠APD?
It is to angle Angle A P C.
It is to angle Angle C P B.
SOLUTION :
Answer: It is supplementary to angle Angle A P C.
It is vertical to angle Angle C P B.
I hope this help :)
which of the followingis multiplicative of -a? (-1/a a 1 1/a)
Given:
The given value is [tex]-a[/tex].
To find:
The multiplicative inverse of [tex]-a[/tex].
Solution:
We know that [tex]y[/tex] is the multiplicative interval of [tex]x[/tex] if [tex]xy=1[/tex].
Let [tex]x[/tex] be the multiplicative inverse of the given value [tex]-a[/tex]. Then,
[tex](-a)\times x=1[/tex]
Divide both sides by [tex]-a[/tex].
[tex]x=\dfrac{1}{-a}[/tex]
[tex]x=-\dfrac{1}{a}[/tex]
Therefore, the multiplicative inverse of [tex]-a[/tex] is [tex]-\dfrac{1}{a}[/tex]. Hence the correct option is A.
Avery can sweep the deck in 5 minutes and Madeline can do it in 7 minutes. How long will it take them to do it together?
Avery in 5 minutes sweeps 1 deck, so in 1 minute she sweeps 1/5 of the deck
Madeline in 7 minutes sweeps 1 deck so in 1 minute she sweeps 1/7 of the deck.
1/5 + 1/7 = 7/35 + 5/35 = 12/35
Together they will sweep 1 deck in x minutes : 1/x
12/35 = 1/x =
X = 35/12 = 2.92 minutes. ( round the answer as needed)
Someone help me with his math question
Answer:
42.94
Step-by-step explanation:
add all together then times by 13% and add it to the original sum
Answer: $89.27
Step-by-step explanation:
I added everything together than to find the tax I multiples the total amount by .13 or %13 and once I got that number and I added it to the total cost.
Find the sum of the arithmetic sequence: -94, -112, -130,...; S10
A) 1280
B)-1280
C)-130
D) -1750
Answer:
D) -1750
Step-by-step explanation:
[tex]{ \boxed{ \bf{sum = \frac{n}{2}(2a + (n - 1)d) }}}[/tex]
n is number of terms, n=10.
a is first term, a=-94
d is common diffrerence, d = -112-(-94) = -18
[tex]{ \sf{sum = \frac{10}{2} ( - 188 + (10 - 1) \times - 18)}} \\ { \sf{sum = - 1750}}[/tex]
Classify the following triangle. Check all that apply.
C=-(251x3+281)+3X251-(1-281)
Answer:
-1
Step-by-step explanation:
=-251x3+281 +251x3-1+281
=-1
The patio on the landscaping blueprint measures 2 inches wide and 5.5 inches long.If the actual patio is going to have a width of 20 feet, what would its length be?
Answer:
55 feet
Step-by-step explanation:
simple 5.5 x 10
Answer:
660 inches or 55 feet
Step-by-step explanation:
20 feet * 12 = 240 inches
2/5.5 = 240/×
2x = 240 * 5.5
2x= 1320
x=660 inches
660 inches ÷ 12 = 55 feet