Domain of f(x) is {x | x ≠ 6} and Domain of g(x) is {x | x ≠ +7 and x ≠ +7}.
How to find the domain of a function?The domain of a function is the set of all input values that make the function possible.
Now, for f(x) = (x + 6)/(x² - 12x + 36)
To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;
x² - 12x + 36 = 0
Solving this using quadratic formula gives; x = 6. Thus, domain of f(x) is;
Domain = {x | x ≠ 6}
Now, for g(x) = (x + 7)/(x² - 49)
To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;
x² - 49 = 0
Solving this using quadratic formula gives; x = +7 or -7. Thus, domain of g(x) is; Domain = {x | x ≠ +7 and x ≠ +7}
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Find the lateral area of the prism. 8cm 6cm, I 1 13cm I 10cm Lateral Area = [?]cm² 2008-2012 International Academy of Science, All Rights Reserved. Aid Enter
The lateral area of the prism is 270cm²
What is the lateral area of a prism?
The lateral area of a prism is defined as the sum of the areas of its lateral faces.
How to determine the lateral area of a prismUsing the formula;
Lateral area = (a+ b+ c) h
Where a, b, c, are all the lateral faces and h is the height
Lateral area = (8 + 6 + 13) × 10 = 27 × 10 = 270cm²
Therefore, the lateral area of the prism is 270cm²
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Simplify (2^5/3^2)^4 I need help asap within 10 min
Answer:
[tex]\frac{2^{20} }{3^{8} }[/tex]
Step-by-step explanation:
Exponent Multiplication Rule :
[tex](\frac{x^{a} }{y^{b} } )^{c} = \frac{x^{ac} }{y^{bc} }[/tex]
=============================================================
Solving :
⇒ [tex](\frac{2^{5} }{3^{2} } )^{4}[/tex]
⇒ [tex]\frac{2^{5(4)} }{3^{2(4)} }[/tex]
⇒ [tex]\frac{2^{20} }{3^{8} }[/tex]
Make the following conversion.
60 dkm =
km
Answer:
60 dkm = 6km
Step-by-step explanation:
10 dkm = 1 km
60 dkm = 60/10 km = 6 km
Find the distance between the two points
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~4 - (-2)~~)^2 + (~~1 - (-4)~~)^2} \implies d=\sqrt{(4 +2)^2 + (1 +4)^2} \\\\\\ d=\sqrt{( 6 )^2 + ( 5 )^2} \implies d=\sqrt{ 36 + 25 } \implies d=\sqrt{ 61 }[/tex]
Describe a situation in your life when what you know about probability may have helped you make a decision. How could you have used probability to help you with your decision? Generally, in what types of situations would knowledge of probability prove useful? Why?
Answer:
Knowledge > Probability
Step-by-step explanation:
In the moment knowledge would be useful because you are thinking about the decision you are making but after days, months or years probability would be in your mind. Also probability is just another word for chance so there would be no confirmation of said thing happening but when you have knowledge your brain knows that said thing is 100% going to happen, so for me personally knowledge is more useful than probability
f(x) = x². What is g(x)?
Answer:
Which class is this
I can't believe the question
WILL MARK BRAINLIEDT If the length of an arc of a circle of radius 7 is approximately 10.99 cm. What is the measure of the central angle associated with the arc? Use 3.14 for π. Give your answer in degrees and radians (approximate to two decimals and exact).
The angle that defines the arc is 1.57 radians or 90°.
How to get the angle of the arc?For a circle of radius R, the length of an arc defined by an angle θ in radians is given by:
L = θ*R.
Here we know that the radius is R = 7cm, and the length of the arc is 10.99 cm. Replacing these in the above equation:
10.99 cm = θ*7cm
θ = (10.99 cm/7 cm) = 1.57
Then the angle is 1.57 radians. Remember that:
3.14 radians = 180°
Then:
θ = (1.57/3.14)*180° = 90°
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[tex]\\ \rm\Rrightarrow \ell=\dfrac{\Theta}{180}\pi r[/tex]
[tex]\\ \rm\Rrightarrow \Theta=\dfrac{180\ell}{r\pi}[/tex]
[tex]\\ \rm\Rrightarrow \Theta=\dfrac{180(10.99}{7(3.14)}[/tex]
[tex]\\ \rm\Rrightarrow \Theta=\dfrac{1978.2}{7\pi}[/tex]
[tex]\\ \rm\Rrightarrow \Theta=90^{\circ}[/tex]
Suppose a high school student is selected at random.Let event A = junior and event B = earbuds. Are events A and B independent
Answer:
yes
Step-by-step explanation:
independence means the object or so are completely unreliant of eachother or does not have order.
for example a dependent situation would be sports players getting picked because there is order.
simplify:
x² - 25
x²-3x -15
Answer:
x² - 25=(x-5)(X+5)
x²-3x -15=5.6 or. -2.6
What is the surface area of the solid that this net can form?
13 cm
5cm
13cm
5 cm
13 cm
106 square centimeters
150 square centimeters
210 square centimeters
270 square centimeters
O 210
12 cm
12cm
13cm
5cm
5cm
5cm
5 cm
Answer:C Or 210 Sc
Step-by-step explanation:
On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions. The test is worth a total of
100 points. There are twice as many 2-point questions as 5-point questions on the test. How many 2-point questions
are on the test?
04
0 8
0 12
O 16
Which of the following steps were applied to ABCD to obtain A'B'C'D'?
A. shifted 4 units left and 3 units up
B. shifted 3 units left and 3 units up
C. shifted 4 units left and 4 units up
D. shifted 3 units left and 4 units up
Answer:
A
Step-by-step explanation:
To find the transformation, we need to take a point and the point to which it has been translated.
Let's take A and A'.
⇒ A = (2, -2)
⇒ A' = (-2, 1)
Change in x : -4 (shifted 4 units left)
Change in y : 3 (shifted 3 units up)
This means to obtain A'B'C'D' from ABCD, the graph has to be :
shifted 4 units left and 3 units up
The weight of a bag of Brand A cookies is labeled as 3 ounces on the bag. However, the actual weights of the bags vary by a small amount. According to the packaging specifications, the weights are approximately normally distributed with a mean of 3.05 ounces and a standard deviation of 0.06 ounce. Select the number to complete the sentence. According to the specifications, approximately percent of the bags weigh 3.00 ounces or more
Using the normal distribution, it is found that approximately 79.67% of the bags weigh 3.00 ounces or more.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 3.05, \sigma = 0.06[/tex]
The proportion of the bags that weigh 3.00 ounces or more is one subtracted by the p-value of Z when X = 3, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3 - 3.05}{0.06}[/tex]
Z = -0.83
Z = -0.83 has a p-value of 0.2033.
1 - 0.2033 = 0.7967 = 79.67%.
79.67% of the bags weigh 3.00 ounces or more.
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Simon is riding a bike at 12 km/h away from his friend Keesha. He throws a ball at 5 km/h back to Keesha, who is standing still on a sidewalk.
How fast would Keesha say the ball is traveling?
5 km/h
7 km/h
12 km/h
17 km/h
Keesha would say the ball is traveling at 7 km/h. The correct option is the second option 7 km/h
What is relative velocity?Relative velocity is defined as the velocity of an object with respect to another observer.
From the question, we are to determine how fast Keesha would say the ball is traveling. That is, the relative velocity
Relative velocity of the ball = 12 km/h - 5 km/h
Relative velocity of the ball = 7 km/h
Hence, Keesha would say the ball is traveling at 7 km/h. The correct option is the second option 7 km/h
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Answer:
7 km/h
Step-by-step explanation:
Suppose you have $600 to invest in a savings plan,Find the balance after one year if you deposit all the money into an account that pays 5% APR with monthly compounding.
Answer:
P(1+[tex]\frac{r}{100}[/tex])ⁿ
600(1+[tex]\frac{5}{100}[/tex])¹
600(1+0.05)¹
600(1.05)
630
Note:
P= participle
R= rate
N= years
The area of Louisiana is approximately 4 x
104 square miles. The area of the United
States is approximately 225 times greater
than the area of Louisiana. What is the
approximate area of the United States?
Answer:
93,600
Step-by-step explanation:
4x104= 416
416x225 = 93,600
Solve the inequality.
-3(4n+1) < -6(2n-6)
Answer:
no solution
Step-by-step explanation:
Given :
-3(4n+1) < -6(2n-6)
Divide by -3 on each side (and remember to change the sign) :
-1/3 x -3(4n+1) < -1/3 x -6(2n-6)
4n + 1 > 2(2n - 6)
Expand the RHS :
4n + 1 > 2(2n) - 2(6)
4n + 1 > 4n - 12
Solution :
As the coefficient of x is the same on both sides, and the constants are different, this inequality has no solution
Answer:
Given inequality:
-3(4n + 1) < -6(2n - 6)
Expand the brackets:
⇒ -12n - 3 < -12n + 36
Add 12n to both sides:
⇒ -12n - 3 + 12n < -12n + 36 + 12n
⇒ -3 < 36
Solution: True for all n
Interval Notation: (-∞, ∞)
What is Logically equivalent? Yeah
answer:
c
step by step explanation:
I did it on edge.
please help me.............
I apologize for the handwriting it's not the best :)
If there are 26 successful outcomes in a sample with a size of 50, what is the
sample proportion?
Answer:
the sample proportion is 26:50then if it simplyfy answer is13:25
ABCD is a parallelogram. Determine the length of AD.
Answer:
D) 10 units
Step-by-step explanation:
Opposite sides of a parallelogram are congruent.
__
setupThe relation between opposite sides tells you ...
BC = AD
2x = x +5
solutionx = 5 . . . . . . . subtract x from both sides of the equation
We want the length of AD, which is ...
AD = x +5 = 5 +5
AD = 10
_____
Additional comment
Often, it seems like the question is answered once the value of x is found. Here, finding the value of x is an intermediate step. The value of x is needed in order to be able to answer the question about the value of an expression involving x.
Answer:
10
Step-by-step explanation:
→ Equate both sides of the parallelogram as they are equal
2x = x + 5
→ Solve
x = 5
→ Resubstitute for the length AD
5 + 5 = 10
Find and solve a system of linear equations to answer the question below.
Joanne buys one kilogram of French Roast and one kilogram of Boxer Blend
from the Java Hut. Jacob buys two kilograms of French Roast and three
kilograms of Boxer Blend. If Joanne spends $14 for her purchase, and Jacob
spends $36 for his, what is the price of one kilogram of Boxer Blend coffee? Please help!!
Answer:
$8
Step-by-step explanation:
Let f = 1 kg of French Roast coffee
Let b = 1 kg of Boxer Blend coffee
Given:
Joanne buys 1 kg of French Roast and 1 kg of Boxer Blend. Joanne spends $14 for her purchase.⇒ f + b = 14
Given:
Jacob buys 2 kg of French Roast and 3 kg of Boxer Blend. Jacob spends $36 for his purchase.⇒ 2f + 3b = 36
Rewrite the first equation to make f the subject:
⇒ f + b = 14
⇒ f = 14 - b
Substitute this into the second equation and solve for b:
⇒ 2f + 3b = 36
⇒ 2(14 - b) + 3b = 36
⇒ 28 - 2b + 3b = 36
⇒ 28 + b = 36
⇒ 28 + b - 28 = 36 - 28
⇒ b = 8
Therefore, the price of 1 kg of Boxer Blend coffee is $8
A pair of trainers cost £60.
In a sale they are reduced by 40%. What is the new price?
Answer:
36
Step-by-step explanation:
40 % of 60 = 24
60-24=36
What is the y-intercept for this function?
a
(0, −3)
b
(3, 0)
c
(−9, 0)
d
(0, −9)
Answer:
d
Step-by-step explanation:
the y- intercept is the point on the y- axis where the graph crosses
the graph crosses the y- axis at point (0, - 9 )
then y- intercept = (0, - 9 )
If you had 36 cookies and gave 1/2 to one friend and 1/4 to another, how many could you have left?
Step-by-step explanation:
[tex] \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} [/tex]
[tex] \frac{3}{4} 36 = 27[/tex]
What is the angle of rotation of the figure?
300
Answer:
The angle of the figure is 90°
Triangle DEF is shown on the xy-coordinate plane. The triangle will be rotated 180° clockwise around point (4, 8) to create AD'E'F'. Which
characteristic of AD'E'F' will NOT be the same for the corresponding characteristic of ADEF?
O the coordinates of D'
O the coordinates of F
O the area of AD'E'F'
O the perimeter of AD'E'F'
Answer: the coordinates of D'
Step-by-step explanation:
Reflections are rigid motions, so area and perimeter are preserved.
However, the preimage of a point is only the same as the image of that same point if that point is the center of rotation. Since point D is not the center of rotation, the coordinates of D' will not be the same as those of D.
Chandler wants to buy a bike
that costs $345. He has a job that
pays an hourly wage of $6. He
needs to pay back $35 that he
borrowed from his mom. How
many hours does Chandler need to
work to have enough money to
purchase the bike?
which expression is equivalent to sin(2x) cosx
Answer:
[tex]2sin(x)cos^2(x)[/tex]
Step-by-step explanation:
To solve the problem, you must expand the trigonometric expression using the information given.
[tex]sin(2x)cosx\\sin(2x)\\=2sin(x)\\=2sin(x)cos^2(x)[/tex]
Solve. Be sure to eliminate any extraneous solutions. X= square -2x+48
Answer: X = 6
Step-by-step explanation:
Substitute the x’s in the equation for the answer options that are provided.
Solutions of quadratic equation x = √(-2x + 48) are x = -8 and x = 6.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given, quadratic equation;
x = √(-2x + 48)
Squaring on both sides,
x² = -2x + 48
x² + 2x - 48 = 0
Now, we have to solve for x.
Simplifying,
x² + 8x - 6x - 48 = 0
(x + 8)(x -6) = 0
(x + 8) = 0 and (x -6) = 0
x = -8 and x = 6
After eliminating the extraneous solutions;
we have,
x = -8 and x = 6.
Therefore, the solutions are x = -8 and x = 6.
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