Answer:
x=4
Step-by-step explanation:
on edge
The extraneous solution to the logarithmic equation log₇(3x²+x)-log₇x=2 is x=16
What is logarithm?When you raise a number with an exponent, there comes a result.
Lets say you get[tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
We are given the function as;
log₇(3x²+x)-log₇x=2
Domian: 3x²+x>0
x(3x+1)>0
x∈(-∞,-1/3)U(0,∞)
Hence, x∈(0,∞), Thus x∈(0,∞)
In this problem we use the following formula:
[tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\x=16[/tex]
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please help with explanation and show work :)
In a particular lottery, 5 winning numbers are drawn from a set of 37 numbers. What is the probability of picking exactly 2 of the winning numbers in this lottery? Round your answer to the nearest
thousandth (three decimal places).
Since 5 winning numbers are draw and there are exactly 2 winning numbers, the other 3 numbers chosen have to be incorrect.
The 2 numbers picked right, there are 5C2=10 different possibilities.
The other 3 numbers are just picked from the rest of the 32 numbers. Getting there are 32C3=4960 different possibilities.
For each set of 2 correct winning numbers, you could have the 4960 different losing numbers to match up to make a unique set. This meant that there are 4690*10=46900 different total possibilities.
Now the total different outcomes of how you can choose the numbers are 37C5=435897 outcomes.
Now the way to find probabilities is want/total
The want is 46900 and the total is 435897
Doing the division you get the number rounded to the nearest thousandths as 0.107 or in percent form as
10.759% chance of picking exactly 2 winning numbers.
This seems like a competition problem of some sort therefore I assume that you already know what combinations in form nCk and permutation in form nPk means.
Trigonometry help finding the value of x
Answer:
[tex]5\sqrt{3}[/tex] or 8.66
Step-by-step explanation:
use tan:
tan = [tex]\frac{opposite}{adjacent}[/tex]
⇒ tan 60 = [tex]\frac{x}{5}[/tex]
tan of 60 is 1.73
⇒ 1.732 = [tex]\frac{x}{5}[/tex]
multiply 5 on both sides
⇒ 1.732 x 5 = [tex]\frac{x}{5}[/tex] x 5
⇒ 8.66
Answer:
[tex]\boxed {\boxed {\sf D. \ 5 \sqrt 3 \ or \ 8.66}}[/tex]
Step-by-step explanation:
Remember the 3 main trigonometric ratios:
sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacentWe are given the 60 degree angle. 5 is adjacent to the angle and x is opposite. Therefore, we must tangent.
[tex]tan \theta= \frac {opposite}{adjacent}[/tex]
[tex]tan60=\frac {x}{5}[/tex]
Since we are solving for x, we must isolate that variable. It is being divided by 5 and the inverse of division is multiplication. Multiply both sides by 5.
[tex]5(tan60)=\frac {x}{5} *5[/tex]
[tex]5(tan60)=x\\5*$$1.73205080757= x\\8.66025403784=x[/tex]
If we round to the nearest hundredth, the 0 in the thousandth place tells us to leave the 6.
[tex]8.66 \approx x[/tex]
x is about 8.66 or 5√3, which is choice D.
A shipping and handling free 35.00 is charged to all furniture over $250 if the order is $437.50 what percent is the shipping and handling free?
Answer:
8%
Step-by-step explanation:
Divide 35 and 437.50 and you get 0.8
Then multiply .8 times 100 = 8%
Write the ratio as a fraction in simplest from 2ft to 30 in
Step-by-step explanation:
Two linear functions are shown.
Which function has the greater
initial value?
Function B
y = 6x + 3
Function A
Х y
- 1 9
0 6
1 3
2 0
Function has the greater initial value because the initial value for Function A is and the initial
value for Function B is
(Type integers or decimals.)
Enter your answer in the edit fields and then click Check Answer.
All parts showing
Answer:
Function A has a greater initial value because the initial value for Function A is 6 and the initial vale for Function B is 3
Step-by-step explanation:
The data for Function A is presented here as follows;
[tex]\begin{array}{cc}x&y\\-1&9\\0&6\\1&3\\2&0\end{array}[/tex]
The slope of the function, 'm', is given using any two points as follows;
m = (9 - 3)/((-1) - 1) = -3
The slope of the function = -3
The equation of function in point and slope form is given as follows;
y - 3 = -3·(x - 1)
The equation of Function A, is therefore, given as follows;
y = 3 - 3·x + 3 = 6 - 3·x
∴ y = 6 - 3·x
The equation of Function B is given as follows;
y = 6·x + 3
The initial value of a function is given by the y-intercept of the function, where the input variable (x-variable) is zero
The initial value, (y-intercept) of Function A, f(0) is therefore found as follows;
f(x) = y = 6 - 3·x
f(0) = 6 - 3×0 = 6
The initial value of Function A, f(0) = 6
Similarly, the initial value, (y-intercept) of Function B, f(0) is found as follows;
f(x) = y = 6·x + 3
f(0) = 6×0 + 3 = 3
The initial value of the Function B, f(0) = 3
Therefore, we have that Function A has a greater initial value than Function B
a function may assign the same output value to two different input values
24 is what percent of 60
Answer: 14.4
Step-by-step explanation:
60 * (24/100) = 14.4
add my sc tregan_fought
what is the area of circle if diameter is 6feet
Answer:
Area=πr²
=3.14×(6/2)²
=28.26 ft²
Step-by-step explanation:
(2) Mai walked 1/8 of a 30-mile walking trail. How many miles did Mai walk? Explain or show your reasoning. *
Answer: 3.75 miles
Step-by-step explanation:
Divide 30 by 8. 30/8= 3.75. If she walked 1/8 then she walked 3.75 miles
find the value of x in each triangle with the given angle measures
Answer:
10 - 104
11 - 25
12 - 64
13 - 109
14 - 33
15 - 90
Step-by-step explanation:
For the first 3 triangles u must add the two angles and minus it from 180
Q number 13 do the same thing then minus the number u got by 180
Q number 14 .... 66 - 180 = 33
Q number 15 it is a right angle so it is 90
please please complete it
Answer:
1. 14
2. 11
3. 19.5
4. 16
5. 76
6. 10
7. 2.5
8. 4.5
9. Mean: 10, Median: 9, Mode: 7
10. Mean: 6, Median: 7, Mode: 8,5
11. Mean: 10, Median: 11.5, Mode: 12
Step-by-step explanation:
Jean junction is selling jeans at 12% off the regular price. The regular price is $32.00 per pair. What is the discount amount
if the temperature at the North Pole is -10º F, how many degrees would the temperature have to increase for it to be 0º?
Answer:
10 degrees
Step-by-step explanation:
:) Thank you enjoy your day kind human :)
Answer:
10.
Step-by-step explanation:
-10 + 10 = 0.
works the same for degrees as well.
In a new movie
theatre, seats will
be installed in the
unshaded area
How many square
feet are available
for seats?
Answer. 655.4
Step-by-step explanation:
what did u get?
I need help with it
Answer:
variable, variable, known, unknown
Step-by-step explanation:
A study was conducted to investigate whether the mean price of a dozen eggs was different for two different grocery stores, Store A and Store B, in a large city. A carton of one dozen eggs from each store was randomly selected for each of 35 weeks, for a total sample size of 35 cartons from each store. The mean price of the 35 cartons was recorded for each store. The difference in the mean carton price for the stores will be calculated.
Which of the following is the appropriate test for the study?
A one-sample z -test for a population proportion
A one-sample t -test for a sample mean
A matched-pairs t -test for a mean difference
A two-sample t-test for a difference between population means
A two-sample z-test for a difference between population proportions
Answer:
A two-sample t-test for a difference between population means
Step-by-step explanation:
Answer:
D) A two-sample t -test for a difference between population means
Step-by-step explanation:
Two random samples are selected on a quantitative variable, and the difference in the sample means will be calculated. The appropriate test is the two-sample t-test for a difference in population means.
Pleaseee hurry and help
Answer: 37. 7in
12*3.14= 37.68
Rounded= 37.7 inches
7/9 - something = 2/9
Answer:
5/9
Step-by-step explanation:
Answer:
5/9
Step-by-step explanation:
Da Baby has $45,000 and earns $2,500 each hour
from streams. JoJo Siwa has $62,000, earns $2,000
each hour from streams.
How
SI
Each equation represents the amount in the bank after
t hours.
Da Baby: s= 2,500t + 45,000
JoJo Siwa: s= = 2,000t + 62.000
How many hours, will it take for Da Baby and JoJo
Siwa to have the same amount in the bank?
Answer:
Step-by-step explanation:
maybe 30 vtfyubf6tyubtfcgnfgghghnvb ngvbhfhgbfvgn
Find the smallest number such that the remainder is 3 when it is divided by 16,20 or 24.
(step required,thank you)
Answer: 123
Step-by-step explanation:
Foe us to solve this, we have to find the lowest common multiple of 16, 20 and 24 first and then add 3 to the LCM. This goes thus:
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160
Multiples of 20 = 20, 40, 60, 80, 10, 120, 140, 160
Multiples of 24 = 24, 48, 72, 96, 120
Therefore, the Lowe's common multiple is 120.
We then add the remainder of 3 and this will give:
= 120 + 3
= 123
Put the following equation of a line into slope-intercept form, simplifying all fractions. x + 2y = 16
Answer:
x + 2y = 16The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Rewrite in slope-intercept form.
y= −1/2x+8
Step-by-step explanation:
Hope it is helpful...
Hey there!
The answer is y = [tex]\frac{-1}{2}[/tex]x + 8
To put it into slope-intercept form, we must get "y" by itself on one side of the equation. First, to do this, we will subtract "x" from both sides.
2y = -x + 16
Lastly, we divide both sides by 2
y = [tex]\frac{-1}{2}[/tex]x + 8
Have a super awesome day! :)
Which equation represents a line passing through the point (8, 9) with a slope of 3?
The equation of a line passing through the point (8, 9) with a slope of 3 is y = 3x - 15.
What is the equation of a line passing through two given points in 2-dimensional plane?Suppose the given points are [tex](x_1, y_1) and (x_2, y_2),[/tex]
then the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
We have been given a line passing through the point (8, 9) with a slope of 3.
then the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
Its slope would be:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
m = 3
Therefore, the equation of the straight line
[tex](y - 9) = 3 (x -8)\\\\y - 9 = 3x - 24\\\\y = 3x -15[/tex]
Hence, the equation of a line passing through the point (8, 9) with a slope of 3 is y = 3x - 15.
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Easy math question! Just need to subtract, help out ASAP!
Answer:
14,599
Step-by-step explanation:
How many terms? 7y-4+3f+6t
PLs I am doing a quiz
Answer:
B
Step-by-step explanation:
Answer:Only 1 term because the others are coefficients because they have a variable by them.
what is the volume???
Answer:
that would be 80
Step-by-step explanation:
Here it is
please help me, i'll mark you brainiest
20 points
Answer: 4! 300:75 Hope you have a great day! Good luck on any stressful school homework stuff you have today too!
Step-by-step explanation: A fraction consists of two numbers and a fraction bar:
300/75
The number above the bar is the numerator: 300
The number below the bar is the denominator: 75
Divide the numerator by the denominator to get fraction's value:
300/75 =
300 ÷ 75 =
4:1
Please help! I filled in a little circle bc i thought it was right XDD
Help!!!!!! Please I have no idea what this is!!!
Answer:
33.49 cubic units
Step-by-step explanation:
[tex]V_{sphere} = \frac{4}{3} \times \pi {r}^{3} \\ \\ V_{sphere} = \frac{4}{3} \times \pi {(2)}^{3} \\ \\ V_{sphere} = \frac{4}{3} \times \pi \times 8 \\ \\ V_{sphere} = \frac{32 \times 3.14}{3} \\ \\ V_{sphere} = \frac{100.48}{3} \\ \\ V_{sphere} = 33.4933333\\ \\ V_{sphere} \approx 33.49\: units^3 [/tex]