Answer:
D is the answer
Answer:
The correct option is 4. The lengths of side SR and side S'R' are in the ratio 1:3.
Step-by-step explanation:
The vertices of polygon are P(0,-3), Q(3,-2), R(3,1), S(0,2), T(-2,0).
The vertices of image are P'(0,-9), Q'(9,-6), R'(9,3), S'(0,6), T'(-6,0).
It is given that polygon P'Q'R'S'T' is the image of polygon PQRST after dilation with a scale factor of 3. It means both polygons are similar.
The corresponding angles of similar figure and same and the corresponding sides are proportional. It means the sides of image are three times of the corresponding sides of pre-image.
SR and S'R' are corresponding sides.
[tex]S'R'=3\times SR[/tex]
[tex]\frac{S'R'}{3}=SR[/tex]
[tex]\frac{1}{3}=\frac{SR}{S'R'}[/tex]
[tex]1:3=SR:S'R'[/tex]
The lengths of side SR and side S'R' are in the ratio 1:3.
Therefore the correct option is 4.
Real estate values in a town are increasing at a rate of 14% per year. Mrs. Knoxville purchased a building for $590,000 in 2012.
How much can she expect to sell the building for in 2020, assuming this trend continues?
Enter your answer in the box. Round to the nearest whole dollar.
Answer:
$1808263
Step-by-step explanation:
We're given with the below information:-
Initial price of the building = Principal amount (P) = $590000
Rate of interest (r) = 14% = 0.14
Time in years (t) = 2020 - 2012 = 8
The formula to calculate the final amount where interest is continuously compounded each year is :-
[tex]A = Pe^{rt}[/tex] [e is the mathematical const = 2.71828]
Plugging in the values of P, e, r, and t in the above formula, we get
[tex]A = 590000*2.71828^{0.14*8}[/tex]
=> A= 1808262.6
=> A = $1808263 (rounded off to the nearest whole dollar)
So, she expect to sell the building in 2020 for an amount of $1808263
Answer:\
180000
Step-by-step explanatii took
Algebra II Please Help
Lawrence's parents pay him a base allowance of $20 per week and $3.55 per hour for extra chores he completes. Mrs. Johnson pays Lawrence $7.15 per hour to lifeguard at the city pool. Which equation models Lawrence's total weekly income? A. I = 7.15x ? 3.55y ? 20 c. I = (3.55 + 7.15)x + 20 b. I = (3.55 + 20)x + 7.15y d. I = 3.55x + 7.15y + 20
Answer:
7.15x + 3.55y + 20 = weekly income
Step-by-step explanation:
7.15x + 3.55y + 20 = weekly income
A student jog the same number of laps each week.9 students jogged 63 laps.How many laps will 13 students jog
use the given information to prove that BC=DE
2. CD = CD , Reflexive Prop.
3. BC = DE, Subtraction Prop.
given the height, h, and the volume V of a certain cylinder, alex uses the formula r=√v/πh to compute its radius, r, to be 10 meters. a second cylinder has the same volume as the first cylinder, but is 25 times taller. what is the radius of the second cylinder?
a). 2/5 meter
b). 2 meters
c). 50 meters
d). 250 meters
Write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms then use x=3 to show expressions are equivalent
Answer:
7x + 9
Yes they are equivalent
Step-by-step explanation:
The first expression given to us is
2x + 3 + 5x + 6
Let us call it equation (i)
Now we have to find equivalent expression to it
the given equation is 2x + 3 + 5x +6
similar terms are terms involving x and not involving x
so solving the equation gives
2x + 5x + 3 +6
= 7x + 9
Now we have two equations one is
2x + 3 +5x + 6 ...............(i)
Other is
7x + 9 ..............(ii)
To check they are equivalent or not
Put x = 3 in equation (i)
2(3)+3+5(3)+6= 6 + 3 + 15 + 6
=30
Now put x=3 in second equation
7(3)+9=21 + 9
=30
As the answer of both the equations are 30 so they are equivalent
To write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms, the expression can be simplified to 7x + 9. Substituting x with 3 in both expressions shows that they have the same value, which is 30.
Explanation:To write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms, we add the coefficients of the like terms. In this case, the like terms are the terms with the same variable, which is x. So, 2x + 3 + 5x + 6 simplifies to 7x + 9. To show that this expression is equivalent to the original expression, we can substitute x with 3. So, when we replace x with 3, both expressions 2x + 3 + 5x + 6 and 7x + 9 result in the same value, which is 30.
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What is the domain of f/g, given f(x)=x+8 and g(x)=x-3?
Answer: Correct Option is "C"
( - ∞ , 3) U (3, ∞ )
Step-by-step explanation:
The function f/g is defined as
( x + 8) / (x -3)
Domain of the function is the set of values which the independent variable can assume.
Clearly in the above function x cannot assume the value 3, otherwise the function would become undefined.
So domain of the function is
( - ∞ , 3) U (3, ∞ )
Hope it helps.
Thank you.
please help will give brainliest
What is the period of the function f(x) shown in the graph?
Answer:
The period is [tex]\pi[/tex].
Step-by-step explanation:
The answer is determined by finding the length of 1 cycle of the function. Trig functions sine and cosine have a wavy form. One starts and ends int he middle - sine. The other starts above and stops above- cosine. Regardless of the function, the period will be the same because the period asks "how fast does this function complete 1 wave?"
If cosine we start at one of the top points, trace the graph till we reach the same y-value again. The period is the time or difference in x-values. For instance if I started at the x-value [tex]\frac{\pi }{2}[/tex] and ended at [tex]\frac{3\pi }{2}[/tex] then I'd subtract them.
[tex]\frac{3\pi }{2}[/tex]-[tex]\frac{\pi }{2}[/tex]=[tex]\frac{2\pi }{2}[/tex]=[tex]\pi[/tex]
The period is [tex]\pi[/tex].
What is the domain and range of the function
Answer:
Option d is correct.
Domain = all real number
range = positive real numbers
Step-by-step explanation:
Given the function: [tex]y=f(x) = a^x[/tex]
Domain of the function is all real numbers except where the expression is undefined.
In this case, there is no real number that makes the expression undefined.
Domain of f(x) = [tex](-\infty , \infty)[/tex] = {a | a∈R}
Range is the set of all valid f(x) values.
[tex](0,1) \cup (1, \infty)[/tex]
[tex]\{y | y\neq 1 , y>0\}[/tex]
Therefore, Domain is all real number and the range of function is positive real number
A couch weighs approximately 100 pounds. If 40,000 couches are sent to furniture stores, what is the total weight in pounds of the couches?
A) 400,000
B) 4,000,000
C) 40,000,000
D) 400,000,000
23)
Which property explains how we get the equation shown in step 2?
Given: -5(x -4) - 20 = -15
Step 1: -5x + 20 -20 = -15 (Distributive)
Step 2: -5x = -15 (__________________)
Step 3: x = 3 (Multiplicative Inverse)
A) Associative
B) Commutative
C) Additive Inverse
D) Multiplicative Identity
24)
Simplify.
7x + 3(x - 2) - 4x + 8
A) 6x + 2
B) 6x + 14
C) 6x - 2
D) 14x + 2
25)
According to the distributive property, a(5 + b) =
A) 5a + b
B) 5a + ab
C) a(b + 5)
D) 5(a + b)
Answer:
Step-by-step explanation:
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Answer:
A
Step-by-step explanation:
Your first step is to figure out what f(x) is. You should start with x = 0. f(x) has a value of - 4. That only tells you that whatever x is or what it is coupled with, the constant term is - 4.
What you know so far is that y = x something - 4
Now go to work on some of the other numbers. It really doesn't look linear so don't try it.
What happens when x = 16? Somehow f(x) winds up being 0. What can cause that?
First of all it can't be y = ax - 4. We've already establish the constant must be - 4
What about y = ax^2 - 4
That cannot be either. y = 16^2*a - 4 ?? y = 256ax - 4. No other value will fit the bill.
By looking at g(x) you get the idea that y = a*sqrt(x) - 4 might have something to do with f(x). The most obvious value for a = 1, so try it first.
y = sqrt(x) - 4y = sqrt(16) - 4y = 4 - 4 = 0Looking good!!Now try some of the other values.
x = 9y = sqrt(9) - 4y = 3 - 4y = -1And that's what the table says.
The red graph is y = sqrt(x) - 4
The blue graph is y = 4*sqrt(x) - 8
Answer
It looks like A is the answer.
g(x) has a y intercept of - 8
f(x) has a y intercept of - 4
==============
The two intercepts are not equal. If they were they would start from the same point. B is incorrect
==============
C is wrong. the x intercepts are distinct points. One is 4 and the other is 16 I think.
0 = sqrt(x) - 4
4 = sqrt(x) Square both sides.
16 = x This is the x intercept of the red line
The other intercept = 4 (Blue line). I'll leave you to work it out. Leave a not if you can't.
========================
A and D can't both be true. Since A is true, D can't be.
Nick currently has 7,200 points in his fantasy baseball league, which is 20% points than Adam. How many points does Adam have?
Adam has 6,000 points.
Explanation:Let's use algebra to solve this problem. Let's assume that Adam's points are represented by 'x'. According to the problem, Nick has 20% more points than Adam, so Nick's points can be represented as 'x + 20% of x' or '1.2x'. Given that Nick has 7,200 points, we can set up the equation 1.2x = 7,200 and solve for 'x'. Divide both sides of the equation by 1.2 to isolate 'x' and find that Adam has 6,000 points.
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A. Green Grapes
B. Red Grapes
C. Red and Green Grapes cost the same
FInd the slope of a line
Answer:
First I'm not exactly sure what you're asking but the equation for slope is:
Y2-Y1/X2-X1=M
Step-by-step explanation:
M is your slope
X1 and Y1 represent your first point
X2 and Y2 represent your second point
To translate you are finding the rate of change (slope) between two points
Answer: Slope = ∆y/∆x = y2-y1/x2-x1
Step-by-step explanation:
The slope of a line which is also known as the gradient can be gotten by taking the ratio of the change in coordinate of y-axis to the x-axis of the line.
Change in y axis = y2-y1
Where y2 and y1 are final length and initial length respectively on the y axis
Change in x axis = x2-x1
Where x2 and x1 are final length and initial length respectively on the x axis.
The slope of the line therefore gives;
Slope = ∆y/∆x = y2-y1/x2-x1
what is the perimeter of triangle with side lengths of 29, 15, and 4xy?
Answer:
P =44 + 4xy
Step-by-step explanation:
To find the perimeter of a triangle, add up the three sides
P = 29+15+4xy
P =44 + 4xy
If y varies directly with x and y = 2 when x = 10, then what is the value of y when x = 40? A. 8 B. 45 C. 200 D. 320
Answer:
A
Step-by-step explanation:
given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the given condition y = 2 when x = 10
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]
y = [tex]\frac{1}{5}[/tex] x ← equation of variation
when x = 40, then
y = [tex]\frac{1}{5}[/tex] × 40 = 8 → A
The value of y when x = 40 with the same proportion will be 8 thus option (A) is correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
If y varies directly with x.
y ∝ x
y = kx
k = y/x
Thus, k will be the same for both conditions.
2/10 = y/40
1/5 = y/40
40/5 = y
8 = y
Hence "The value of y when x = 40 with the same proportion will be 8 ".
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Elaine has a $350 gift card to Target. Elaine spent $334.50 on a sound bar at Target. If the sales tax is 8%, what was her final bill? Does she have enough money on the gift card to pay for the sound bar?
Answer:
1) Her final bill: 334,5+ the tax
the tax = 334,5*8/100= 26,76 $
Her final bill = 334,5+ 26,76= 361,26 $
2) The gift card only has 350$ and the bill is 361,26
therefore she doesn't have enough money to pay for the sound bar
Step-by-step explanation:
Please help ASAP!!!
triangle a'b'c' is a dilation of triangle abc. which is the correct description of the dilation?
Answer: A
Step-by-step explanation:
[tex]\overline{AB}[/tex] has a length of 6
[tex]\overline{A'B'}[/tex] has a length of 6 + 12 = 18, which is 3 times the length of [tex]\overline{AB}[/tex]
B = B' so this will be the center point
⇒ center B and a scale factor of 3
Answer:
Option A is the answer.
Step-by-step explanation:
Triangle A'B'C' is a dilation of triangle ABC.
We can apply the formula to get the scale factor as
Scale factor = [tex]\frac{\text{One side of triangle A'B'C'}}{\text{Corresponding side of triangle ABC}}[/tex]
= [tex]\frac{A'B'}{AB}[/tex]
= [tex]\frac{AB'+AA'}{AB}[/tex]
= [tex]\frac{6+12}{6}[/tex]
= [tex]\frac{18}{6}[/tex]
= 3
Therefore, ΔABC has been dilated with a scale factor of 3 about the point B as the center.
Option A is the answer.
URGENT. Please help me!! 30 points :))
Answer:
<T = 83
Step-by-step explanation:
In a parallelogram <M = < P and < N = <T (opposite angles are congruent)
We also know that <M + <N = 180 ( consecutive angles are supplementary)
<M + <N = 180
6x+10 + 5x+10.5 = 180
Combine like terms
11x+20.5 = 180
Subtract 20.5 from each side
11x +20.5-20.5 = 180-20.5
11x = 159.5
Divide each side by 11
11x/11 = 159.5/11
x=14.5
We can find <N
<N = 5x+10.5
= 5(14.5)+105
=72.5 +10.5
= 83
<N = <T = 83
Question 11(Multiple Choice Worth 5 points) Perform the requested operation or operations. f(x) = 4x + 6, g(x) = 5x2 Find (f + g)(x).
Answer:
(f + g)(x) = 5x^2 + 4x + 6
Step-by-step explanation:
The given functions are f(x) = 4x + 6 and g(x) = 5x^2
(f + g)(x) = f(x) + g(x)
= 4x + 6 + 5x^2
= 5x^2 + 4x + 6
Thank you.
Help with these questions please!
Answer:
1. 16
2. -4
Step-by-step explanation:
First factor the expression
lim x→1 (x^3 + 5x^2 + 3x-9)/(x-1)
lim x→1 (x-1) (x+3)^2/(x-1)
Canceling the x-1 in the top and bottom
lim x→1 (x+3)^2
Let x=1
lim x→1 (1+3)^2 = 4^2 = 16
2. lim x→0 (x^2 -6x+8) /(x-2)
First factor the expression
lim x→0 (x-4) (x-2) /(x-2)
Canceling the x-2 in the top and bottom
lim x→0 (x-4)
Let x=0
lim x→0 (0-4) = -4
Filling in the table
x -.1 -.01 -.001 .001 .01 .1
f(x) -4.1 -4.01 -4.001 -3.999 -3.99 -3.9
I know this isn't helpful, but I REALLY need help on this question...
Given: f(x) = x^2 + 7x + 10. From the Rational Root Theorem, we know p=10 and q=1. List all potential roots using the ratio p/q.
A new mountain bike is on sale for 260.00, which is 35% off of is original price. What is the original price of the bike
Answer:g hvt
Step-by-step explanation:
What is the length of GH? ______cm
A six sided number cube is rolled 12 times. An even number is rolled 7 times. What is the experimental probability that an even number is rolled?
Answer:
The experimental probability is 7/12 or 58.3%
Step-by-step explanation:
In order to find the experimental probability, we just look at the amount of times it happened in our test. The fact that the actual probability is 50% does not matter when looking at experimental numbers.
2,008 kilograms of potatoes were packed into sacks weighing 8 kilograms each how many sacks were packed
Answer:
251
Step-by-step explanation:
2008/8
Answer:
16064
Step-by-step explanation:
2,008 x 8= 16064
In quadrilateral LMNO, LO ∥ MN. What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply. ML ∥ NO ML ⊥ LO LO ≅ MN ML ≅ LO MN ⊥ NO
Answer:
In quadrilateral LMNO, LO ∥ MN.
ML ∥ NO
LO ≅ MN
Answer:
1 & 3 is correct on edg.
The union of sets P = {1, 2, 3, 4, 5, 6} Q = {4, 5, 6, 7, 8, 9} is given by which of the following?
{1, 2, 3, 4, 5, 6, 7, 8, 9}
{1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9}
ø
{4, 5, 6}
Answer:
The first one, because the x values are not repeated in a data set.
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Juan runs an experiment. He flips a coin 20 times. It landed on Heads 13 times and Tails 7 times. Find the experimental probability.
Compare your experimental probability to the theoretical probability of flipping a coin and it landing on heads.
Which of the following statements is true?
Question 5 options:
The theoretical probability is greater than the experimental probability.
The experimental probability is greater than the theoretical probability.
The experimental probability is equal to the theoretical probability.
Can not determine which probability is greater.
C it the answer because since heads hit 14 times it haves a higher percent of hitting heads again.
Find the values of m and b that make the following function differentiable.
the piecewise function f of x equals x squared when x is less than or equal to three or mx plus b when x is greater than three
For [tex]f[/tex] to be differentiable, it must be continuous, so we need to have
[tex]\displaystyle\lim_{x\to3^-}f(x)=\lim_{x\to3^+}f(x)=f(3)[/tex]
By its definition, [tex]f(3)=3^2=9[/tex]. The one-sided limits are
[tex]\displaystyle\lim_{x\to3^-}f(x)=\lim_{x\to3}x^2=9[/tex]
[tex]\displaystyle\lim_{x\to3^+}f(x)=\lim_{x\to3}mx+b=3m+b[/tex]
so we require [tex]3m+b=9[/tex].
In order for [tex]f[/tex] to be differentiable at [tex]x=3[/tex], we also need to have [tex]f'(3)[/tex] exist, which requires that [tex]f'[/tex] also be continuous at [tex]x=3[/tex]. First, compute the derivatives of all pieces of [tex]f[/tex]:
[tex]f'(x)=\begin{cases}2x&\text{for }x<3\\?&\text{for }x=3\\m&\text{for }x>3\end{cases}[/tex]
[tex]f'[/tex] is continuous at [tex]x=3[/tex] if
[tex]\displaystyle\lim_{x\to3^-}f'(x)=\lim_{x\to3^+}f'(x)=f'(3)[/tex]
The one-side limits are
[tex]\displaystyle\lim_{x\to3^-}f'(x)=\lim_{x\to3}2x=6[/tex]
[tex]\displaystyle\lim_{x\to3^+}f'(x)=\lim_{x\to3}m=m[/tex]
so we need to have [tex]m=6[/tex], and moreover [tex]f[/tex] will be differentiable if we set [tex]f'(3)=6[/tex].
So with [tex]m=6[/tex], we must have [tex]3m+b=9\implies b=-9[/tex].
For the piecewise function f(x) = x^2 when x <= 3 and mx + b when x > 3, values m = 6 and b = -9 ensure differentiability at x = 3.
To make the piecewise function f(x) differentiable at x = 3, we need the two pieces, x^2 and mx + b, to smoothly connect at x = 3. This requires the values of m and b to ensure continuity of both function values and derivatives.
First, evaluate both pieces at x = 3:
x^2 when x <= 3 and mx + b when x > 3
For continuity, set these expressions equal to each other:
3^2 = m * 3 + b
This yields 9 = 3m + b. To ensure differentiability, the derivatives of both pieces must also match at x = 3:
f'(x) = 2x when x <= 3 and f'(x) = m when x > 3
For continuity of derivatives, set the derivatives equal to each other at x = 3:
2 * 3 = m
This gives m = 6. Substituting m = 6 into the continuity equation 9 = 3m + b gives b = -9.
Therefore, the values m = 6 and b = -9 make the piecewise function f(x) differentiable at x = 3.
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