Answer:
a) The horizontal asymptote is y = 0
The y-intercept is (0, 9)
b) The horizontal asymptote is y = 0
The y-intercept is (0, 5)
c) The horizontal asymptote is y = 3
The y-intercept is (0, 4)
d) The horizontal asymptote is y = 3
The y-intercept is (0, 4)
e) The horizontal asymptote is y = -1
The y-intercept is (0, 7)
The x-intercept is (-3, 0)
f) The asymptote is y = 2
The y-intercept is (0, 6)
Step-by-step explanation:
a) f(x) = [tex]3^{x + 2}[/tex]
The asymptote is given as x → -∞, f(x) = [tex]3^{x + 2}[/tex] → 0
∴ The horizontal asymptote is f(x) = y = 0
The y-intercept is given when x = 0, we get;
f(x) = [tex]3^{0 + 2}[/tex] = 9
The y-intercept is f(x) = (0, 9)
b) f(x) = [tex]5^{1 - x}[/tex]
The asymptote is fx) = 0 as x → ∞
The asymptote is y = 0
Similar to question (1) above, the y-intercept is f(x) = [tex]5^{1 - 0}[/tex] = 5
The y-intercept is (0, 5)
c) f(x) = 3ˣ + 3
The asymptote is 3ˣ → 0 and f(x) → 3 as x → ∞
The asymptote is y = 3
The y-intercept is f(x) = 3⁰ + 3= 4
The y-intercept is (0, 4)
d) f(x) = 6⁻ˣ + 3
The asymptote is 6⁻ˣ → 0 and f(x) → 3 as x → ∞
The horizontal asymptote is y = 3
The y-intercept is f(x) = 6⁻⁰ + 3 = 4
The y-intercept is (0, 4)
e) f(x) = [tex]2^{x + 3}[/tex] - 1
The asymptote is [tex]2^{x + 3}[/tex] → 0 and f(x) → -1 as x → -∞
The horizontal asymptote is y = -1
The y-intercept is f(x) = [tex]2^{0 + 3}[/tex] - 1 = 7
The y-intercept is (0, 7)
When f(x) = 0, [tex]2^{x + 3}[/tex] - 1 = 0
[tex]2^{x + 3}[/tex] = 1
x + 3 = 0, x = -3
The x-intercept is (-3, 0)
f) [tex]f(x) = \left (\dfrac{1}{2} \right)^{x - 2} + 2[/tex]
The asymptote is [tex]\left (\dfrac{1}{2} \right)^{x - 2}[/tex] → 0 and f(x) → 2 as x → ∞
The asymptote is y = 2
The y-intercept is f(x) = [tex]f(0) = \left (\dfrac{1}{2} \right)^{0 - 2} + 2 = 6[/tex]
The y-intercept is (0, 6)
Find the image of the given point
under the given translation.
P(-7,1) T(x,y) = (x + 9, y-3)
P' = ([?], []).
Answer:
P' = (2, -2)
Step-by-step explanation:
You have the x-value and the y-value of the pre-image, so all you have to do is plug that into the translation statement (x + 9 , y - 3).
Since x = -7 and y = 1 that would be (-7 + 9, 1 - 3), or (2, -2).
Three dressers are placed side by side. One dresser is 5 feet 5 inches wide, another is 5 feet 10 inches wide, and the third is 3 feet 11 inches wide. How wide are they combined?
Answer:
15 feets 2 inches
Step-by-step explanation:
Given the widths :
1st dresser = 5 feets 5 inches
2nd dresser = 5 feets 10 inches
3rd dresser = 3 feets 11 inches
Their combined width is :
5ft + 5ft + 3 ft + 5in + 10in + 11in
13 feets 26 inches
Recall :
1 foot = 12 inches
26 inches = 26/12 feets = 2 feets 2 inches
Hence,
13 feets + 2feets 2 inches
Combined width = 15 feets 2 inches
16 - 2r = 3r + 6r + 1
what is r?
[tex]\\ \sf\longmapsto 16-2r=3r+6r+1[/tex]
[tex]\\ \sf\longmapsto 16-2r=9r+1[/tex]
[tex]\\ \sf\longmapsto 16-1=9r+2r[/tex]
[tex]\\ \sf\longmapsto 11r=15[/tex]
[tex]\\ \sf\longmapsto r=\dfrac{15}{11}[/tex]
Answer: r = 15/11
Step-by-step explanation:
Given
16 - 2r = 3r + 6r + 1
Combine like terms
16 - 2r = 9r + 1
Add 2r on both sides
16 - 2r + 2r = 9r + 1 + 2r
16 = 11r + 1
Subtract 1 on both sides
16 - 1 = 11r + 1 - 1
15 = 11r
Divide 11 on both sides
15 / 11 = 11r / 11
[tex]\boxed{r=\frac{15}{11} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Can someone please help me on these 4 questions PLEASE HELP ME!!
Answer:4 ans x is -32/10
7 ans b is 6
10 ans x is 25/7
13 ans x is 9/2
Step-by-step explanation:
please mark this answer as brainlist
Solve for x.
3x + 2
2x + 6
x = [?]
Answer:
4
Step-by-step explanation:
Im assuming you mean the first and second equation equal each other:
3x+2=2x+6
x=4
If lines AB and CD are paralell, which of the following statements is true? Check All That Apply
Answer:
D and E is the answer..
Step-by-step explanation:
nothing to explain .. D has the symbol of parallel.. and all parallel lines are coplaner
The correct answers are option D and option E that is AB || CD and the lines AB and CD are coplanar.
What are parallel lines?The lines which do not intersect each other at any point they can only intersect at infinity are called parallel lines. All the parallel lines are coplanar to each other.
From the above explanation, the parallel lines are represented as AB || CD and also coplanar to each other.
Therefore the correct answers are option D and option E that is AB || CD and the lines AB and CD are coplanar.
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Convert the 7pi/5 to a degree measure
A=252
B=504
C=792
D=75
Answer:
252
Step-by-step explanation:
The conversion factor is
180/pi
7pi/5 * 180/pi = 7 *180/5 = 252 degrees
rationalise the denominator of 2sq3+3sq2/4sq3+sq2
Answer:
[tex]\frac{9+5\sqrt6}{23}[/tex]
Step-by-step explanation:
We can rewrite the fraction as
[tex]\frac{2\sqrt{3}+3\sqrt{2}}{4\sqrt{3}+\sqrt{2}}[/tex]
In order to rationalize the denominator of such a complex fraction, we must multiply the fraction by the conjugate of the denominator. In this case, the conjugate of the denominator would be [tex]4\sqrt{3}-\sqrt{2}[/tex]. Multiplying both sides of the fraction by the conjugate of the denominator would result in the fraction:
[tex]\frac{9+5\sqrt6}{23}[/tex]
if (x) and 1(x) are inverse functions of each other and S(x) = 2x+5, what is (8)?
이스 NW
8
023
Answer:
B
Step-by-step explanation:
f(x) = 2x+5
f^(-1) (x) = (x-5)/2
f^(-1) (8) = 3/2
A regular polygon has exterior angles of 60°
What is the sum of the polygon’s interior angles?
Answer:
720°
Step-by-step explanation:
The sum of the exterior angles of a polygon = 360°
Divide by 60 to find number of sides (n)
n = 360° ÷ 60° = 6
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 6 , then
sum = 180° × 4 = 720°
The sum of the exterior angles of a regular polygon is 360º
Each exterior angle of a regular polygon is 60º/n
360º/n=60º
360/60=n
6=n
A polygon with 6 sides is a hexagon.
Use the formula (n-2)×180
(6-2)*180=4*180=720º
another solution...
you have 6 interior angles (hexagon)
if an exterior angle is 60º, the corresponding interior angle is 180-60=120º
you have 6 of these 120º angles
6*120=720º
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = 4/x
g(x) = 4/x
Answer:
Hello,
Step-by-step explanation:
[tex]f(x)=\dfrac{4}{x} \\\\g(x)=\dfrac{4}{x} \\\\\\(gof)(x)=f(g(x))=f(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\\\\\(fog)(x)=g(f(x))=g(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\[/tex]
5w = 23 - 3f and 4f = 12 - 2w
Answer:
f = 1, w = 4
Step-by-step explanation:
Given the 2 equations
5w = 23 - 3f → (1)
4f = 12 - 2w (add 2w to both sides )
2w + 4f = 12 ( subtract 4f from both sides )
2w = 12 - 4f → (2)
Multiplying (1) by 4 and (2) by - 3 and adding the result will eliminate f
20w = 92 - 12f → (3)
- 6w = - 36 + 12f → (4)
Add (3) and (4) term by term to eliminate f
14w = 56 ( divide both sides by 14 )
w = 4
Substitute w = 4 into either of the 2 equations and solve for f
Substituting into (1)
5(4) = 23 - 3f
20 = 23 - 3f ( subtract 23 from both sides )
- 3 = 3f ( divide both sides by - 3 )
1 = f
Answer:
Step-by-step explanation:
Could someone please help me out?
Answer:
4.5
Step-by-step explanation:
let,
k×9²=300
k = 300/81
or, k = 100/27
as two triangles are similar,
if smaller triangle's corresponding side is x (let), then,
kx²=75
100x²/27=75
x²=75×27/100
x=√81/4
x=9/2
x=4.5
The picture attached
Answer:
Step-by-step explanation:
m1 = 300
m2= 300(1+.05) = 300(1.05)
m3 = 300(1.05)(1.05)
m4= 300(1.05)(1.05)(1.05)
each subsequent month is the previous month times "1 + .05"
the "one" preserving the running total, and the extra ".05" adding the 5%
the repeating (1.05)(1.05)(1.05) is notational simplified using exponents
(1.05)(1.05)(1.05) = [tex](1.05)^{3}[/tex]
The cost of tickets of a comedy show of 'Gaijatra' is Rs 700 for an adult and Rs 500 for a child. If a family paid Rs 3,100 for 5 tickets, how many tickets were purchased in each category?
Answer:
Step-by-step explanation:
We need to create a system of equations here, one for the NUMBER of tickets sold and one for the COST of the tickets. They are very much NOT the same thing.
We have that the total number of tickets is 5, and that that total is made up of adult tickets and child tickets. The equation for the NUMBER of tickets, then, is:
a + c = 5
Now for the money.
If a child ticket costs Rc 500, the expression that represents that that is in fact the cost of the child ticket is 500c;
likewise for the adult ticket. If the adult ticket costs Rc 700, the expression that represents that is 700a.
And we know that a total of Rs 1300 was spent on the tickets. The equation for the COST is
700a + 500c = 1300
Now go back to the first equation and solve it for either a or c, it doesn't matter which. I solved for a:
a = 5 - c and we will sub that into the second equation for a:
700(5 - c) + 500c = 1300 and
3500 - 700c + 500c = 1300 and
-200c = -400 so
c = 2 tickets. That means that there were
a = 3 tickets sold for the adults.
helphelphelphelphelphelphelp
Answer:
P = 1,-10
Q=1,-1
R=7,-1
S=7,-10
Simplify the expressions by combining like terms.
30) 4x + 3-x =
Step-by-step explanation:
the answer is -1. I have a picture, take a lot at it
Answer: 3x+3
Step-by-step explanation:
4x+3-x
= (4x-x) + 3
= 3x+3
Compare the functions shown below:
Which function has the greatest maximum y-value?
Answer:Hey I'm sorry I didn't get to answer your question it's just that I need the points because I don't have enough to get help with my question. I hope you get the answer that you need for you question. Good Luck :)
Step-by-step explanation:
which algebraic expression represents this word description the quotient of six and the sum of a number and eight
work out the area of a semicircle take pi to be 3.142 11cm
Answer:
if the diameter is 11, them the answer is 47.52275cm
carly walks 30 feet in seven seconds. At this rate, how many minutes will it take for carly to walk a mile if there are 5,280 feet in one mile?
Answer:
20.53 minutes
Step-by-step explanation:
Speed = Distance/Time = 30/7
Time = Distance / Speed
= 5280/30/7
= 1232 seconds / 60 = 20.53 minutes
Answered by Gauthmath
arrange0.2,¼,30%,10%in ascending and descending order
Answer:
Ascending- 10%, 0.2, 1/4, 30%
Descending- 30%, 1/4, 0.2, 10%
Step-by-step explanation:
0.2 = 2/10 = 4/20
1/4 = 5/20
30% = 30/100 = 6/20
10% = 10/100 = 2/20
Ascending
-2/20, 4/20, 5/20, 6/20
- 10%, 0.2, 1/4, 30%
Descending
- 6/20, 5/20, 4/20, 2/20
- 30%, 1/4, 0.2, 10%
Which is the graph of y = RootIndex 3 StartRoot x EndRoot?
Given:
The equation is:
[tex]y=\sqrt[3]{x}[/tex]
To find:
The graph of the given equation.
Solution:
We have,
[tex]y=\sqrt[3]{x}[/tex]
The table of values is:
x y
-8 -2
-1 -1
0 0
1 1
8 8
Plot these points on a coordinate plane and connect them by a free hand curve as shown in the below graph.
Answer:
D
Step-by-step explanation:
edge 2020
Solve for a.
-4a – 2a – 7 = 11
a =
[?]
Answer:
or, -4a - 2a -7 = 11
or, -4a -2a =11 +7
or, - 6a = 18
or, a= 18÷ -6
a= -3
The access code for a cars security system consists of 4 digits. The first digit cannot
be 0 and the last digit nust be even. How many different codes are available?
Answer:
4500
Step-by-step explanation:
The first digit can't be 0. so it will be a number from 1000 to 9999. That's a total of 9000 numbers (9999-1000+1=9000). Since the last digit must be an even number that is one half of the 9000 numbers which is 4500.
The probability of drawing a red candy at random from a bag of 25 candies is 2/5. After 5 candies are removed from tehe bag, what is the probability of randomly drawing a red candy from the bag?
Given:
The probability of drawing a red candy at random from a bag of 25 candies is [tex]\dfrac{2}{5}[/tex].
To find:
The probability of randomly drawing a red candy from the bag after removing 5 candies from the bag.
Solution:
Let n be the number of red candies in the bag. Then, the probability of getting a red candy is:
[tex]P(Red)=\dfrac{\text{Number of red candies}}{\text{Total candies}}[/tex]
[tex]\dfrac{2}{5}=\dfrac{n}{25}[/tex]
[tex]\dfrac{2}{5}\times 25=n[/tex]
[tex]10=n[/tex]
After removing the 5 candies from the bag, the number of remaining candies is [tex]25-5=20[/tex] and the number of remaining red candies is [tex]10-5=5[/tex].
Now, the probability of randomly drawing a red candy from the bag is:
[tex]P(Red)=\dfrac{5}{20}[/tex]
[tex]P(Red)=\dfrac{1}{4}[/tex]
Therefore, the required probability is [tex]\dfrac{1}{4}[/tex].
If you apply the changes below to the absolute value parent function, 1(x) = 1X, what is the equation of the new function? Shift 8 units left. • Shift 3 units down. O A. g(x) = (x + 81 - 3 O B. g(x) B. g(x) = (x - 3| + 8 O c. g(x) = [X - 31- 8 D. g(x) = (x - 8 - 3
Answer:
A. g(x) = |x + 8| - 3Step-by-step explanation:
If the function is f(x), then shift 8 units left and 3 units down will result in:
g(x) = f(x + 8) - 3Apply to the given function to get:
g(x) = |x + 8| - 3Correct choice is A
Select the correct answer. Consider this system of equations, where function f is quadratic and function g is linear:
y = f(x)
y = g(x)
Which statement describes the number of possible solutions to the system?
A. The system may have no, 1, 2, or infinite solutions.
B. The system may have no, 1, or infinite solutions.
C. The system may have 1 or 2 solutions.
D. The system may have no, 1, or 2 solutions
Answer:
C is the answer
Step-by-step explanation:
Quadratic equations have at most 2 solution, and linear equations only have 1 solution, and since y is equal to both of them, it can only have 1 or 2 solutions.
The correct answer is option D. The system may have no, 1, or 2 solutions
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
f(x) is a quadratic function and g(x) is linear function
y=f(x)
y=g(x)
Quadratic equations have at most 2 solution
linear equations only have 1 solution,
f(x)=g(x)=y
y is equal to both of them, it can only have 1 or 2 solutions.
A line and a parabola can intersect zero, one, or two times
Therefore, a linear and quadratic system can have zero, one, or two solutions
Hence, the correct answer is option D. The system may have no, 1, or 2 solutions
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Simplify the following, leaving your answer with a positive exponent:
x^-12/ x^-7
Answer:
[tex]\frac{1}{x^{5} }[/tex]
Step-by-step explanation:
x^-12/ x^-7
= x^(-12-(-7))
= x^-5
= 1/x^5
In a large midwestern university (the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 2001 an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. The proportion of all entering freshmen in 1999 and 2001, who graduated in the bottom third of their high school class, are p1 and p2, respectively.Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999? To determine this, you test the hypothesesH0 : p1 = p2 , Ha : p1 > p2.The P-value of your test isA. 0.976.B. 0.024.C. 0.048.D. 0.001.
Answer:
B. 0.024
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
1999:
Of 100, 20 were in the bottom thid. So
[tex]p_B = \frac{20}{100} = 0.2[/tex]
[tex]s_B = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
2001:
Of 100, 10 were in the bottom third, so:
[tex]p_A = \frac{10}{100} = 0.1[/tex]
[tex]s_A = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
To determine this, you test the hypotheses H0 : p1 = p2 , Ha : p1 > p2.
Can also be rewritten as:
[tex]H_0: p_B - p_A = 0[/tex]
[tex]H_1: p_B - p_A > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the sample:
[tex]X = p_B - p_A = 0.2 - 0.1 = 0.1[/tex]
[tex]s_A = \sqrt{s_A^2+s_B^2} = \sqrt{0.03^2+0.04^2} = 0.05[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.1 - 0}{0.05}[/tex]
[tex]z = 2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of proportions of at least 0.1, which is 1 subtracted by the p-value of z = 2.
Looking at the z-table, z = 2 has a p-value of 0.976.
1 - 0.976 = 0.024, so the p-value is given by option B.
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
