Answer:
0.33 and 6.07
Step-by-step explanation:
what are the discontinuities of the function f(x)= (x^2 - 36)/(4x - 24)
The function f(x) = (x² - 36)/(4x - 24) has a removable discontinuity at x = 6, due to the fact that at this value the original function's denominator becomes zero.
The function given is f(x) = (x² - 36)/(4x - 24). To find the discontinuities of this function, we must identify values of x that cause the denominator to be zero, as the function would be undefined at those points. Factor the numerator and the denominator to simplify the expression. (x² - 36) can be factored as (x + 6)(x - 6), and (4x - 24) can be factored as 4(x - 6). So, the simplified function is f(x) = (x + 6)/4, but we must exclude the value x = 6 from the domain due to it making the original denominator zero. Therefore, the function is discontinuous at x = 6, which is also known as a point of removable discontinuity because the factor (x - 6) is canceled out in the simplification.
Simplify the expression
9−8b+6b
9−8b+6b
.
9−8b+6b=??
haha last one XD
factor the trinominal below please
you have 15 x and 56
so you need two numbers when added equal 15 and when multiplied equal 56
and since they are both positive, the answer also needs to be positive
so B is the correct answer
How does the volume of an oblique cone change if the height is reduced to 2/5 of its original size and the radius is doubled?
Answer:
Option (D) is correct.
Step-by-step explanation:
Let the initial original height of the cone is h and radius is r.
The volume of original cone is given by
[tex]V=\frac{1}{3}\times \pi r^{2}\times h[/tex]
Now the new height be h' = 2/5 h and radius r' = 2r
So, the new volume be
[tex]V'=\frac{1}{3}\times \pi r'^{2}\times h'[/tex]
[tex]V'=\frac{1}{3}\times \pi\times 2r^{2}\times \frac{2}{5}h[/tex]
[tex]V=\frac{8}{15}\times \pi \times r^{2}h[/tex]
One of the roots of the equation x^2 + kx -6 = 0 is 3, and k is constant
CAN SOMEONE WHO KNOWS HPW TO DO THIS EXPLAIN ME THESE
In the diagram, AC=BD=17 and BC=3. The length of segment AD is
5x2−320 factored completely?
a truck is going to a village and stops to see four trucks. how many trucks are going to the village?
The truck going to the village remains one.
This question appears to be an example of logical reasoning. If a truck is going to a village and stops to see four trucks, the number of trucks going to the village is still one. The fact that the truck stops to see four other trucks does not change its own path or destination.
Express log2 6 + log2 7 as a single logarithm.
Answer: The correct option is (C) [tex]\log_242.[/tex]
Step-by-step explanation: We are given to express the following logarithmic expression as a single logarithm :
[tex]E=\log_26+\log_27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(I)[/tex]
We will be using the following logarithmic property :
[tex]\log_ab+\log_ac=\log_a(bc)[/tex]
So, from expression (i), we get
[tex]E=\log_26+\log_7=\log_2(6\times 7)=\log_242.[/tex]
Thus, the required single logarithm is [tex]\log_242.[/tex]
Option (C) is CORRECT.
the expression equivalent to sin 3x−sin x is what
Answer:
The required equivalent form of given expression is
[tex]\sin 3x-\sin x=2\cos 2x\sin x[/tex]
Step-by-step explanation:
Given : Expression [tex]\sin 3x-\sin x[/tex]
To find : The expression is equivalent to ?
Solution :
Applying trigonometric formula,
[tex]\sin a - \sin b = 2\cos(\frac{a+b}{2})\sin(\frac{a-b}{2})[/tex]
where, a=3x and b=x
[tex]\sin 3x-\sin x=2\cos(\frac{3x+x}{2})\sin(\frac{3x-x}{2})[/tex]
[tex]\sin 3x-\sin x=2\cos(\frac{4x}{2})\sin(\frac{2x}{2})[/tex]
[tex]\sin 3x-\sin x=2\cos 2x\sin x[/tex]
Therefore, The required equivalent form of given expression is
[tex]\sin 3x-\sin x=2\cos 2x\sin x[/tex]
The expression equivalent to (sin 3x-sin x) is 2cos(2x)sin(x) and this can be determined by using the trigonometric properties.
Given :
Expression -- (sin 3x - sin x)
The following steps can be used in order to determine the expression equivalent to (sin 3x - sin x):
Step 1 - The trigonometric properties can be used in order to determine the expression equivalent to (sin 3x - sin x).
Step 2 - Below are the properties that help to evaluate the given expression.
[tex]\rm sin \;A - sin\;B = 2cos\left(\dfrac{A+B}{2}\right) sin\left(\dfrac{A-B}{2}\right)[/tex]
Step 3 - Use the above-mentioned property in the given expression.
[tex]\rm sin \;3x - sin \; x = 2 cos\left(\dfrac{3x+x}{2}\right) sin\left(\dfrac{3x-x}{2}\right)[/tex]
[tex]\rm sin \;3x - sin \; x = 2 cos\left(\dfrac{4x}{2}\right) sin\left(\dfrac{2x}{2}\right)[/tex]
[tex]\rm sin \;3x - sin \; x = 2 cos\left(2x\right) sin\left(x\right)[/tex]
So, the expression equivalent to (sin 3x-sin x) is 2cos(2x)sin(x).
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What value is a discontinuity of x squared plus 7 x plus 1, all over x squared plus 2 x minus 15?
Answer:
x = -5 is your answer
Step-by-step explanation:
option c
On a particular day, the wind added 4 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 4 miles per hour from her rate on her return trip. Jaime found that in the same amount of time she could row 57 miles with the wind, she could go only 33 miles against the wind.What is her normal rowing speed with no wind?
Answer:
15 mph
Step-by-step explanation:
Speed of wind = [tex]V_w[/tex] = 4 mph
Speed of Jaime rowing = [tex]V_r[/tex]
Speed of boat against wind = [tex]V_r-4[/tex].
Speed of boat with wind = [tex]V_r+4[/tex]
Time taken with and against wind is same = t
Distance travelled with wind = 57 mph
Distance travelled against wind = 33 mph
[tex]time=\frac{\text{Distance}}{\text{Speed}}[/tex]
Time taken to go with wind
[tex]t=\frac{57}{V_r+4}[/tex]
Time taken to go against wind
[tex]t=\frac{33}{V_r-4}[/tex]
So,
[tex]t=\frac{57}{V_r+4}=\frac{33}{V_r-4}\\\Rightarrow \frac{57}{33}=\frac{V_r+4}{V_r-4}\\\Rightarrow 57V_r-33V_r-228-132=0\\\Rightarrow V_r=\frac{360}{24}\\\Rightarrow V_r=15\ mph[/tex]
∴ Her normal rowing speed with no wind is 15 mph
Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkbook shows a balance of $487.38 as of January 29. The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28. How much did Eliza deposit in her account between January 18 and January 29?
Use the given line(s) from a random number table to select numbers to use in each problem. Select 2 contestants for a game show out of a pool of 50 46547 17395 25765 11325 14071 61688
A. 39, 25 B. 46, 47 C. 4, 6 D. 46, 25
The solution would be like this for this specific problem:
Given:
46547 17395 25765 11325 14071 61688
You want two-digit numbers between 01 and 50, so break it up into chunks of two and eliminate any string that is not between 01 and 50.
So, the numbers from the string are:
46 54 71 73 95 25 76 51 13 25 14 07 16 16 88
Eliminated numbers:
54 71 73 95 25 76 51 88
Numbers remaining:
46 25 13 14 07 16
So, the 2 contestants from a game show out of a pool of 50 would be 46 and 25 (since these are the possible contestants based from the given).
Write the expression as either the sine, cosine, or tangent of a single angle.
sine of pi divided by two times cosine of pi divided by seven plus cosine of pi divided by two times sine of pi divided by seven.
Help. Solve for x. Show your work.
a. picture one show your work
b. picture 2 show your work
Secants from the same point have the same product of length to the near intersection times length to the far intersection from the point.
1) 5(5+x) = 6(6+4)
... 25 + 5x = 60 . . . . eliminate parentheses using the distributive property
... 5x = 35 . . . . . . . . subtract 25
... x = 7 . . . . . . . . . . . divide by 5
2) The same rule applies.
... 3(3+5) = 4(4+x)
... 24 = 16 + 4x . . . . . eliminate parentheses
... 8 = 4x . . . . . . . . . . . subtract 16
... 2 = x . . . . . . . . . . . . divide by 4
Mr. Scrubs got some money for his birthday he spent 1/5 of it on dog treats then he divided the remainder equally among his 3 favorite charities what fraction of his money did each charity receive ? If he donated 60 to each charity , how much money did he received for his birthday
Find the product. (7 - 10x)2
Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which Ben agreed to pay $215 per month. Which of the following statements best gives the reasons that Ben’s rent payment is an essential (fixed) expense? a. It cannot be eliminated in a later budget, in order to save money. b. Living expenses have a higher priority than any other type of expense. c. The spender controls the amount of the rent by choice of apartment. d. He agreed to pay the same amount every month.
Solution:
Cost of apartment(Ben + Housemates) = $ 563 per month
Amount paid by Ben per month = $ 215
Yes, Accommodation provided by someone for fixed amount is an essential Expense.
All the three statements regarding Ben who pays $ 215 per month are true.
a. It cannot be eliminated in a later budget, in order to save money.
b. Living expenses have a higher priority than any other type of expense.
c. The spender controls the amount of the rent by choice of apartment.
Sarah drove 3 hours more than michael on their trip to texas. if the trip took 37 hours, how long did sarah and michael each drive?
37-3 = 34
34/2 = 17
Michael drove 17 hours
Sarah drove 20 hours (17+3)
3x + 3 − x + (−7) > 6 what is x
3x+3-x+(-7)>6
combine like terms on left side
2x-4>6
add 4 to both sides 2x>10
x=10/2 = 5
x>5
The table shows the mean daily temperature in North Dakota during a week in February. Which statement about the data is true?
A.The Lowest mean temperature was on wednesday
B.The lowest temperature was on friday
C.The highest mean temperature was on friday
D.The highest mean temperature was on monday
The correct option is 2nd option i.e., the lowest mean temperature is on Friday.
The mean temperature in North Dakota during a week in February.
We have to find which statement is true.
What is the method to find mean ?
The mean can be calculated by adding all the given numbers and then dividing by the total no. of numbers.
As per the question ;
Mean daily temperature is given in a table.
Let's arrange these temperatures day wise from highest mean temperature to lowest mean temperature.
i.e.,
Tuesday - 1.3°F > Monday - 1°F > Wednesday - 0°F > Thursday > -1.2°F > Sunday - -1.4°F > Saturday > - 1.5°F > Friday - -1.7°F
So ;
The highest mean temperature is on Tuesday of 1.3°F.
The lowest mean temperature is on Friday of -1.7°F.
Thus , the correct option is 2nd option i.e., the lowest mean temperature is on Friday.
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An airplane is flying at 180mph. A jet flying at 330 mph leaves 1 hour later traveling in the same direction. How long will it take for the jet to catch up to the airplane?
To determine how long it will take for the jet to catch up to the airplane, calculate the time by dividing the distance the airplane covers before the jet starts (180 miles) by the relative speed of the jet to the airplane (150 mph), resulting in 1.2 hours or 72 minutes.
Explanation:The subject of the question is related to the topic of relative velocity in Mathematics, specifically regarding two objects moving in the same direction. To find out how long it will take for the jet to catch up to the airplane, we need to calculate the relative speed of the two vehicles and the time it takes for one to overtake the other.
The airplane is moving at 180 mph, and the jet is flying at 330 mph. Since the jet leaves one hour later, the airplane would have traveled 180 miles by that time. The relative speed of the jet to the airplane is the difference between their speeds, which is 330 mph - 180 mph, resulting in 150 mph.
To catch up, the jet needs to cover the 180 miles separation distance at a relative speed of 150 mph. We can find the time it takes to catch up by dividing the distance by the relative speed:
Time = Distance ∗ Relative Speed = 180 miles ∗ 150 mph = 1.2 hours.
Therefore, it will take 1.2 hours or 72 minutes for the jet to catch up to the airplane after it starts its pursuit.
Help please! I will give Brainliest to most detailed answer:)
The figure shows three right triangles. Triangles JKM, KLM, and JLK are similar.
Theorem: If two triangles are similar, the corresponding sides are in proportion.
Using the given theorem, which two statements help to prove that if segment JL is x, then x^2 = 100?
1.) Segment JL • segment JM = 64
Segment JL • segment LM = 48
2.)Segment JL • segment JM = 48
Segment JL • segment LM = 36
3.)Segment JL • segment JM = 64
Segment JL • segment LM = 36
4.)Segment JL • segment JM = 36
Segment JL • segment LM = 64
*If you can, could you please give an explanation? Thanks.
Which answer represents the range of the logarithmic function given below? F(x) = log7 x
A. x>=0
B. x<0
C. x>0
D. All real numbers
Range of the logarithmic function F(x) = log7 x is C. x > 0.
What is a logarithm?The logarithm is exponentiation's opposite function in mathematics.
This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 100 = 10², the logarithm of 100 in base 10 is 2, or log10 = 2.
In the given question, F(x) = log7 x.
Assuming log7 x = y.
Therefore, x is the value equal to [tex]7^y[/tex], hence it can not be zero and negative.
Even if y is equal to zero [tex]7^y[/tex] would be 1.
∴ The range of the logarithmic function F(x) = log7 x is x > 0.
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The measures of an exterior angle and the adjacent interior angle add up to 360 because they form a linear pair
A.True
B.False
Answer: false
Step-by-step explanation:
The equation y = ax describes the graph of a line. If the value of a is negative, the line
The equation y = ax represents a straight line with slope a. If a is negative, the line slopes downward to the right, not down and to the left.
The equation y = ax describes the graph of a line. The & in the equation appears to be a typo and should likely refer to a. The constant a represents the slope of the line. When the slope a is negative, the line slopes downward as it moves to the right on a coordinate plane. This is because a negative slope indicates that as the independent variable (usually the x-axis) increases, the dependent variable (y-axis) decreases. A line with a negative slope is straight, and its steepness depends on the absolute value of the slope a. Thus, the line goes down and to the left.
Line AB has endpoints A(-4,5) and B(3,5). What is the x-coordinate of a point C such that B is the midpoint of line AC
Given the function f(x) = 0.5(3)x, what is the value of f−1(7)? 1) 0.565 2) 1.140 3) 1.771 4) 2.402
Answer:7=0.5 |x-4| -3
+3 +3
10=0.5 |x-4|
10/0.5=0.5/0.5 |x-4|
20=|x-4|
^
-20=x-4 20=x-4
+4 +4 +4 +4
-16=x 24=x
The answers are -16=x and 24=x
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Step-by-step explanation: