Answer:
Step-by-step explanation:
Student 2 and student 1
log x = log(x + 3) - log(x - 1)
First note that log(x) is defined only for x > 0; log(x + 3) for x > -3; and log(x - 1) for x > 1. So if we find any solutions x ≤ 1, these will be extraneous.
Condense the right side:
log(x) = log((x + 3) / (x - 1))
Let b be the base of the logarithm. Then writing both sides as powers of this b simplifies the equation to
b^log(x) = b^log((x + 3) / (x - 1))
x = (x + 3) / (x - 1)
Solve for x :
x (x - 1) = x + 3
x ² - x = x + 3
x ² - 2x - 3 = 0
(x - 3) (x + 1) = 0
x - 3 = 0 or x + 1 = 0
x = 3 or x = -1
We throw out x = -1 because it's less than 1, so the only (real) solution is x = 3.
Please find attached photograph for your answer.
In the xy-plane, the line with equation
y = 4x - 28 crosses the x-axis at the point
with coordinates (a, b). What is the value
of a?
A. -28
B. -2
C. O
D. 5
E. 7
=======================================================
Explanation:
Any point on the x axis always has its y coordinate equal to 0.
Plug in y = 0 and solve for x
y = 4x-28
0 = 4x-28
4x-28 = 0
4x = 28
x = 28/4
x = 7
Therefore, the point (7, 0) is on the line y = 4x-28 and also on the x axis. This is known as an x intercept.
Comparing (7, 0) this to (a, b) shows that a = 7 and b = 0.
Sean's father decided that the number of hours Sean should study daily is equal to the equation y + 4 16. where y is the
number of study hours and z is the number of relaxation hours. Sesn's mother believes that the number of hours Sean should study
dally should be equal to the equation 2y + 5z = 32. Sean's parents have decided to use both equations to determine the number
of hours Sean should study and relax What is an equivalent equation to the addition of Sean's mother's equation and Sean's father's
equation? Select all that apply.
Answer and explanation:
We add both equations to get a simultaneous equation
y+4z=16
2y+5z=32
We solve the equations using elimination method:
Multiply equation 1 by 5 and equation 2 by 4 to cancel out z
5y+20z=80
8y+20z=160
-3y=-80
Y=26.7
Substitute y=26.7 in equation 1
26.7+4z=16
4z=16-26.7
z= -2.67
y+z=26.7+(-2.67)= 24.03
What is the median of the numbers ?
Answer:
4.5
Step-by-step explanation:
Its the middle of all of the numbers
Answer:
Its 5
Step-by-step explanation:
3 and 4 has 4 X's
6 has also 4 X's
so it leaves with 5.
A copy machine makes 126 copies in 4 minutes and 30 seconds. How many copies does it make per minute?
Answer:
it makes about 41 copies per minute
Please help! Find X:
5
31
10
60
Answer:
x=10
Step-by-step explanation:
2 3/8 x 16 pls urgent
Answer:
38x / 38
Step-by-step explanation:
2 3/8 = 19/8
19/8 x16
multiply --> a x b/c = a x b over c
= 19X x 16 over 8
= 304x over 8
divide
= 38x / 38
Sheila's class recycles a total of 6 pounds of paper in 2
weeks. After 5 weeks, how many pounds of paper will
Sheila's class have recycled?
Answer:
It should be 15 pounds
Step-by-step explanation:
If you divide 5 weeks (the amount you need) by 2 weeks (the current ratio 6:2) then you get 2.5. Lastly just multiply 6 pounds to it (the other part of the ratio/ pounds per 2 weeks)
What is the measure of angle DEC?
Answer:
95
Step-by-step explanation:
dct equals 140, dct also equal det plus edc, so 140 - 45 = 95
If cos(x) = 3/4 and tan(x) < 0, what is cos(2x)
Answer:
C. 1/8
Step-by-step explanation:
on edge
Answer:
1/8
Step-by-step explanation:
Please help! Find m
160°
260°
50°
80°
Answer:
The answer is 80°.
Step-by-step explanation:
360° - 100° = 260°
260° - 100° = 160°
160° / 2 = 80°
* the theorem is m < UTS = 1/2 (m < UTS - m < US)
* m = measure
The measure of m<UTS is 80 degree.
The correct option is D.
What is Arc?An "arc" is a smooth curve that connects two points in mathematics. In general, an arc is a section of a circle. It is essentially a portion of a circle's circumference.
A circle's arc is defined as a portion or segment of its circumference. A chord of a circle is a straight line that can be created by connecting the two ends of an arc. A semicircular arc is one whose length is exactly half that of a circle.
We have,
From the figure we can write
m < UTS = 1/2 (m < UTS - m < US)
As, m <UTS = 360 and arc US = 100
= 1/2(360° - 100° - 100)
= 160° / 2
= 80°
Thus, m< UTS is 80 degree.
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About how much should the gratuity for the restaurant server be? Round the percent of gratuity to the nearest benchmark percent to find the answer.
$ _____
The gratuity of the hotel server has to be $8.
How to solve for the gratuityThe tax of the restaurant server is 8.5 percent
We have tro find this based on salary
40 dollars x 0.85 = 34
The income 34 - 18
= 16
Half of 16 = 8
Hence the amount that is the percentage of gratuity is 8 percent.
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Find the lcm of 13 and 49
Answer:
637
Step-by-step explanation:
13 * 49 = 637
Answer:
it's 637 trust me ........
-2 (1 - 4x)=3x +8 is
Answer:
= 2
1. Rearrange terms
2.Distribute
3. add 2 to both sides of the equation
4.Simplify
5.Subtract 3 from both sides of the equation
6. Simplify again
7. Divide both sides of the equation by the same term
8. Simplify one more time
please help :( Find m
156°
78°
162°
81°
165
Is your answer
ggg do gets go t ra di
Given the relation y = 7x2 + 3, if the input is 4, what is the output?
115
116
118
120
The answer would be
155
Have a good day bye!
Answer:
ur answer would be 115!
Step-by-step explanation:
I got it right on the test!!
:--)
In triangle OPQ, p = 38 cm, q = 29 cm and Angle O=39º. Find the length of o, to the nearest
centimeter.
Answer:
The length of o is 24 centimeters
Step-by-step explanation:
In Δ OPQ
∵ Side p is opposite to ∠P
∵ Side q is opposite to ∠Q
∵ Side o is opposite to ∠O
→ To find side o we must use the cosine rule
∴ o = [tex]\sqrt{p^{2}+q^{2}-2(p)(q).cos(O) }[/tex]
∵ p = 38 cm
∵ q = 29 cm
∵ m∠O = 39°
→ Substitute them in the rule to find o
∴ o = [tex]\sqrt{(38)^{2}+(29)^{2}-2(38)(29).cos(39)}[/tex]
∴ o = 23.92008154
→ Round it to the nearest centimeter (whole number)
∴ o = 24 centimeters
∴ The length of o is 24 centimeters
Someone help asap
Enter the your answer in the box provided to fill in the black space that will make the equation true.
____(3 + 4) = 36 + 48
Answer:
12 will come in the blank
Step-by-step explanation:
Distributive property is used
a(b + c) = a*b + a*c
36 + 48 = 12*3 + 12*4
= 12(3 + 4)
Marge home is Is heated by hot water circulating in pipes recently the system developed a Smalley Inn loses 1 1/5 mm every 30 minutes uses complex fraction to find the amount of water in system per minute
Answer:
why are we stilll here
Step-by-step explanation:
what is the sulotion of 3^2-[3-4(8-2^2]^2
Answer:
70
Step-by-step explanation:
What is 160% of 40? Four students solved this problem and their work is shown below. Choose the student whose work is correct. Cam's work. 16 times 40 = 00 .00 + 640 = 640. Gitana's work. 1.6 times 40 = 00. 00 + 640 = 64.0. Naoko's work. 0.16 times 40 = 00. 00 + 640 = 6.40. Sanjay's work. 160 times 40 = 00. 00 + 6400 = 6400.
Answer:
Gitana's work is correct
Step-by-step explanation:
Divide 40 with 100 then multiply it by 160
40 ÷ 100 × 160 = 64
Answer:
Gitana is correct.
Step-by-step explanation:
Help! GHJ Café sells Medium and large coffees to locals in Downtown Dallas. If 7 medium cups and 10 large cups of coffee are sold, the café makes $68.75 in sales. If 10 medium and 15 large cups are sold, the total sales is $101.25. How much does a large cup of coffee sell for at GHJ Café?
Answer:
Large cup cost $4.25
Step-by-step explanation:
Medium: x
Large: y
Constraints:
7x + 10y = 68.75
10x + 15y = 101.25
Isolate y variable:
(7x + 10y = 68.75) * -10 ===> -70x - 100y = -687.50
(10x + 15y = 101.25) * 7 ===> 70x + 105y = 708.75
____________________
add the two equations 5y = 21.25
divide by 5 y = 4.25
Evaluate -2x + -3y if x = 10 and y = -6
Find x AND the length of each side if FGH is an equilateral triangle. (Round to the nearest tenth if needed)
Answer:
x = 3
Each side is 19
Step-by-step explanation:
HF = FG = HG cuz this is an equilateral triangle, meaning all sides are equal.
A parent is using a garden hose to fill up a small inflatable pool for her young child. The
pool has a capacity of 90 gallons. She turns the water off after 5 minutes, but leaves the
hose in the pool for another 3 minutes before putting it away.
In this situation, the relationship between the gallons of water in the pool and the 8
minutes since the parent started filling the pool can be seen as a function.
1. In that function, which variable is independent? Which one is dependent?
Answer:
The independent is the 90 gallons and the dependent is the 8 minutes.
Hope this helps!
Step-by-step explanation:
PLZZZZZZZZZZZZZZZZZZZZZZZZZ HELP!!!
FIND what was the mistake
and what is the correct answer
Answer:
Step-by-step explanation:
Instead of dividing both sides by 5, it is multiplied
5x + 3 = 6 {Subtract 3 from both sides}
5x + 3 - 3 = 6-3
5x = 3 {Divide both sides by 5}
5x/5 = 3/5
x = 3/5
Perform the indicated operations. Write answer in descending order.
Add -3x, 5x + y, and 7x - 8 - 3y
The required sum of -3x, 5x + y, and 7x - 8 - 3y in descending order is 9x - 2y - 8.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
To add -3x, 5x + y, and 7x - 8 - 3y, we can first combine like terms.
Group the x-terms together:
-3x + 5x + 7x = 9x
Group the y-terms together:
y - 3y = -2y
Group the constants together:
-8
Putting it all together, we get:
9x - 2y - 8
Therefore, the sum of -3x, 5x + y, and 7x - 8 - 3y in descending order is 9x - 2y - 8.
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If 2 more than 2/3 of a certain number is
8, then the number is
Answer:
4/3 because 2/3x2/1=4/3×2=8/6÷2=4/3
Have to find x and y . Please help!
Answer:
Step-by-step explanation:
x can be anything so let’s use 0, 1, 2, and 3 for x values
to find the y values, we just plug in the x values into the equation
when x = 0
y = 5/4(0) -2
y = 0 -2
y = -2
(0, -2) (x = 0, y = -2)
when x = 1
y = 5/4(1) -2
y = 5/4 -2
y = 5/4 -8/4
y = -3/4
(1, -3/4) (x = 1, y = -3/4)
when x = 2
y = 5/4(2) -2
y = 10/4 -2
y = 5/2 -4/2
y = 1/2
(2, 1/2) (x = 2, y = 1/2)
when x = 3
y = 5/4(3) -2
y = 15/4 -2
y = 15/4 -8/4
y = 7/4
(3, 7/4) (x = 3, y = 7/4)
Answer:
Table shown below
Step-by-step explanation:
Table of Values
We are given the function:
[tex]\displaystyle y=\frac{5}{4}x-2[/tex]
And it's required to fill the table of values for x and y with the condition that there are only integers.
Given the expression has a denominator of 4, to ensure there are no decimals in the results, we select values of x that are multiple of 4.
Select the values: {-4,0,4,8}
Now calculate the corresponding values of y.
x=-4
[tex]\displaystyle y=\frac{5}{4}(-4)-2=-5-2=-7[/tex]
y=-7
x=0
[tex]\displaystyle y=\frac{5}{4}(0)-2=0-2=-2[/tex]
y=-2
x=4
[tex]\displaystyle y=\frac{5}{4}(4)-2=5-2=3[/tex]
y=3
x=8
[tex]\displaystyle y=\frac{5}{4}(8)-2=10-2=6[/tex]
y=8
The filled table is shown in the attached image
What is the answer of the chart (picture) please help
Answer:
DARK Blue! 0.4!
Step-by-step explanation: