Answers
\( |x - \frac{1}{x} | = 18 \\ \)
So :
\(x - \frac{1}{x} = 18 \: \: \: or \: \: \: x - \frac{1}{x} = - 18 \\ \)
_____________________________________________
If\(x - \frac{1}{x} = 18 \\ \)
Multiply both sides by x
\(x \times (x - \frac{1}{x} ) = x \times 18 \\ \)
\( {x}^{2} - 1 = 18x\)
Subtract both sides 18x
\( {x}^{2} - 1 - 18x = 18x - 18x\)
\( {x}^{2} - 18x - 1 = 0\)
Thus the possible values for x from this equation are :
\(x = 9 + \sqrt{82} \)
And
\(x = 9 - \sqrt{82} \)
_____________________________________________
If\(x - \frac{1}{x} = - 18 \\ \)
Multiply both sides by x
\(x \times (x - \frac{1}{x} ) = x \times - 18 \\ \)
\( {x}^{2} - 1 = - 18x\)
Add both sides 18x
\( {x}^{2} - 1 + 18x = - 18x + 18x\)
\( {x}^{2} + 18x - 1 = 0\)
And the possible values for x from the above equation are :
\(x = - 9 + \sqrt{82} \)
And
\(x = - 9 - \sqrt{82} \)
_____________________________________________
Finally the possible answers would be :
\(x = 9 + \sqrt{82} \)
\(x = 9 - \sqrt{82} \)
\(x = - 9 + \sqrt{82} \)
\(x = - 9 - \sqrt{82} \)
There you go...
Have a great day ❤
Related Questions
Ivy collects rainwater in a large barrel that weighs 35 pounds. When there are 10 gallons of water in the barrel, the total weight of the barrel and the water is 118.4 pounds. When there are 20 gallons of water, the total weight is 201.8 pounds which equation and graph match this situation?
Answers
Answer:
y = 8.34x + 35
Step-by-step explanation:
Ivy has an empty barrel having weight = 35 pounds
Having 10 gallons of water barrel weighs = 118.4 pounds
After collecting 20 gallons of water barrel weighs = 201.8 pounds
There is a common difference in the weight of the barrel as he collects the rain water = (201.8 - 118.4) = 83.4 pounds
Therefore, its a linear process and forms a straight line when we graph the function.
Let the equation of the line is,
y = mx + b
Where m = slope of the line
b = y-intercept
Two points lying on the line will be (0, 35) and (10, 118.4)
Slope of the line 'm' = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
= \(\frac{118.4-35}{10-0}\)
= 8.34
y-intercept of the line 'b' = 35
Therefore, equation of the line is,
y = 8.34x + 35
The points in the table lie on a line. What is the slope of the line?
х
-8
-2
4
10
y
8
1
-6
-13
The slope of the line is
PLEASE HELP
Answers
The slope of the line is-7/6
Which of the following tables represents a linear relationship that is also proportional?
(A)
x −1 0 1
y 0 2 4
(B)
x −3 0 3
y −2 −1 0
(C)
x −2 0 2
y 1 0 −1
(D)
x −1 0 1
y −5 −2 1
Answers
Answer: 我不知道你好
Step-by-step explanation:
A roller coaster’s height is given by the equation h = –.067t2 7t 50, where t represents the time in seconds. how long will it take riders to pass over the hill and reach ground level? hint: set h = 0. 13.40 seconds 50.07 seconds 52.24 seconds 111.19 seconds
Answers
The time it take riders to pass over the hill and reach ground level is 111.19 seconds .
Given :
the roller coaster's height expressed by the equation below;
h = -0.067t^2 + 7t + 50
where
t is the time in seconds
The driver will hit the ground at the point where h = 0
Substitute
-0.067t^2 + 7t + 50 = 0
Multiply through by -1
0.067t^2 - 7t +-50 = 0
Factorize :
On factorizing, the positive value of "t" is 111.19 seconds
Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds
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fill in the blank. a _____ is a column chart that displays frequency of occurrence on the vertical axis. histogram flowchart pictograph run chart control chart
Answers
A histogram is a column chart that displays the frequency of occurrence on the vertical axis.
In a histogram, the horizontal axis represents the range or categories of data, and the vertical axis represents the frequency or count of data falling within each range or category. The height of each column in the histogram corresponds to the frequency or count of data in that particular range or category.
Histograms are commonly used to visualize the distribution of numerical data and provide insights into the shape, center, and spread of the data. They are particularly useful in identifying patterns, outliers, and understanding the overall distributional characteristics of a dataset.
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May someone help me ✨
Answers
Answer:
Look down!
Step-by-step explanation:
1. 1/4*1/4*1/4
2. 1/4*1/2*1/2*1/4
There are 350 calories in 1 1/2 cups of spaghetti how many calories are in 2 cup?
350
674
300
467
Answers
Answer:466.66666 or 467
Step-by-step explanation:
350/3=116.66
1/2=116.666666667
In 2 cups there are four halfs so
116.66x4=466.666666667 or around
467 calories in 2 cups
A hexagon with an area of 75 square inches is dilated by a scale factor of 3. What is the area of the new hexagon?
Answers
From the given information provided, the area of the new hexagon when dilated by scale factor is 675 square inches.
When a polygon is dilated by a scale factor of k, its area is multiplied by k².
A hexagon is a six-sided polygon. It is a flat shape with straight sides, and all six of its angles add up to 720 degrees.
In this case, the hexagon is being dilated by a scale factor of 3, so the area of the new hexagon will be:
Area of new hexagon = (scale factor)² x Area of original hexagon
Area of new hexagon = 3² x 75
Area of new hexagon = 9 x 75
Area of new hexagon = 675 square inches
Therefore, the area of the new hexagon is 675 square inches.
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What is the symbol for mean in stats?
Answers
The symbol of mean is "μ". The population mean, or average score for the population on a certain variable, equation as follows:
μ = ( Σ Xi ) / N
The term "mean" is simply the mathematical average of a set of two or more integers. The arithmetic mean technique, which utilizes the sum of the series' values, and the geometric mean method, which employs the average of a set of products, are only two of the methods available to determine the mean for a given collection of data. Nonetheless, most of the time, the outcomes of the various methods for determining a simple average are essentially the same. The arithmetic mean and the geometric mean are two different types of means that may be determined. By adding all the numbers in a set and dividing by the total number of integers in the set, the arithmetic mean is determined. The equation of mean will be:
μ = ( Σ Xi ) / N.
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The angle of elevation to a nearby tree from a point on the ground is measured to be 61 ∘ ∘ . How tall is the tree if the point on the ground is 59 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
106.44 ft
Step-by-step explanation:
tan = opp/adj
tan61 = opp/59
59*tan61 = opp
opp = 106.438817561014012
Rounded
106.44 ft
The ratio of people to animals is 40 to 15. There are 27 animals. How many people are there?
Answers
—- = —-
15 27
15x = 1080
x=72
there are 72 people!!
Answer: is 72 people to 27 animals
Step-by-step explanation:
I can find the ratio by cross multiplying
40/15 to x/27
15x = 1080
x = 72
you can also divide 40/15 for a ratio percent = 8/3
multiply 27 animals x 8/3 = 72
two ways to solve for ratios
3 (m+6) +7 (m-2)
7(6x + 5) - 8
4(3x + 5) - 13
Answers
Answer:SAME SIGNS 1. Add.
2. Sum is positive if both are positive; negative if both are negative.
5 + 8 = 13 –5 + (–8) = –13
DIFFERENT SIGNS
1. Subtract the absolute values.
2. Answer is sign of the integer with the greater absolute value.
5 + (–8) = –3 –5 + 8 = 3
Find each sum. 1. –4 + (–8)
–12
4. –16 + 11 –5
7. –49 + (–32)
–49 –81 –32 –81
2. 14 + 16 30
5. 28 +(–42) –14
8. 23 + (–23) 0
3. –43 + (–12) –55
6. 75 + (–5) 70
9. 86 + (–18)
86 68–18 68
Integers
Multiplying & Dividing
RULE
EXAMPLES
1. Multiply or divide.
2. The answer is positive if the signs are the same (both positive or both negative); negative if the signs are different (one positive and one negative).
–5 x(–8) = 40 40 4 = 10
16 x(–3) = –48 –20 10 = –2
Find each product or quotient.
1. –3 x (–8) 24
4. 0 x (–121)
0 5 –13
2. –5 x (–5) 25
3. –15 x 3 –45
5. –35 (–7)
6. –65 5
7. 240 (–4) 8. 36 12 9. (–49 7) x 8 –7 x 8
–60 3
–56
Step-by-step explanation:
. The linear regression equation for a data set is y = -2x + 10. The observed value when x = 6 is 5. What is the residual value when x = 6?
Answers
Answer:
Step-by-step explanation:
Using standard deviation method, the residual value when x is 6 is,
y = 7.
Define residual?The discrepancy between the actual value and the expected value is known as a residual. The residual would be the vertical gap between the actual value and the line of best fit in a scatter plot with a line of best fit. This is the general shape of the residual: -predicted.
As a result, residual has a value of -1.
The linear regression equation given is,
y = -2x + 10
The value when x = 6,
y' = -2 × 6 + 10
y' = -2
Now, the observed value is given as, y = 5.
Now, the residual value is,
y - y'
= 5 - (-2)
= 5+ 2
=7
Therefore, the residual value = 7.
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I know that a number in scientific notation is written as the _______ of two factors.
Answers
power of ten
Step-by-step explanation:
Rita has two coupons for a printer.
Coupon A: 15% off of a $75 printer
Coupon B: $14 rebate on a $75 printer
Choose the coupon that gives the lower price.
Then fill in the blank with the correct value.
Coupon A gives the lower price.
The price with coupon A is Sless than the price with coupon B.
O Coupon B gives the lower price.
The price with coupon B is Sless than the price with coupon A.
Answers
well, the better bargain for Rita is the bigger savings so, we know "B" gives $14 flat right off the 75 bucks, how about "A"? is the 15% more than 14 bucks?
\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 75}}{\left( \cfrac{15}{100} \right)75}\implies 11.25\)
woopsie, no dice, so she's better off taking the $14 rebate.
Lin tried to reflect triangle ABC across line t . She knows something went wrong because the image isn’t congruent to the original figure. (images included)
What is one idea that Lin probably understands about reflections?
help!!
Answers
Answer:
the image should be the same size as the reflection
The mandatory orientation and size of the triangle image did not match with the former triangle ABC.
Given that,
Lin tried to reflect triangle ABC across line t. She knows something went wrong because the image isn’t congruent with the original figure.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
The given triangle is ABC,
Lin has to form the image of the reflection of the triangle ABC across the line t. Since the observation shows that the image formed by Lin is oriented and enlarged and does not seems to be congruent with the former triangle.
Thus, the mandatory orientation and size of the triangle image did not match the former triangle ABC.
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a fair die with its faces numbered from 1 to 6 will be rolled. which of the following is the best interpretation of the probability that the number landing face up will be less than 3 ?
Answers
When a fair die with faces numbered 1 to 6, the probability that the number landing face up is less than 3 is 1/3.
The probability measures how likely an event to occur. The probability of an event A is defined as:
P(A) = number of ways that event A can occur / all possible outcomes
In the given problem, let x be any number of die's face, then
number of ways x will show up = 1
all possible outcomes = 6
Hence,
P(x) = 1/6
Numbers that are less than 3 is 1 and 3. Therefore,
P (x<3) = P(1) + P(2)
P (x<3) = 1/6 + 1/6 = 2/6 = 1/3
Therefore, we can conclude that the probability that the number landing face up is less than 3 is 1/3
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Giselle pays $2.70 for 10 pounds of apples at the farmer's market. Torrey pays $4.05 for 15 pounds of apples at the farmer's market. What is the unit cost for apples at the farmer's market?
Answers
sry Not an answer But did you ever get the answer??
Answer: 0.27
Step-by-step explanation:
If you multiply .27 by 10 $2.70 comes up. And if you multiply .27 by 15 $4.05 comes up
Anyone know how to do this?
Answers
=======================================================
Explanation:
The 85 degree angle is smaller than the 90 degree angle (aka right angle). That must mean 5x-10 is smaller than 25
At the same time, 5x-10 must be larger than 0 to avoid having a 0 length or negative length.
So overall we can say 0 < 5x-10 < 25
-------------
Let's isolate x
0 < 5x-10 < 25
0+10 < 5x-10+10 < 25+10 ...... adding 10 to all sides
10 < 5x < 35
10/5 < 5x/5 < 35/5 .... dividing all sides by 5
2 < x < 7
This says that x is between 2 and 7, but we cannot have x equal either endpoint.
The attendance at a seminar in year 1 was 500. In Year 2, the attendance changed by 100. What was the percent change in attendance?
The percent change was 0.2%.
The percent change was 0.4%.
The percent change was 20%.
The percent change was 40%.
Answers
Answer:
C.20
Step-by-step explanation:
Hence, option (C) is correct i.e., the percent change was \(20\)%.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of \(100\). It is often denoted using the percent sign, "%".
Here given that,
The attendance at a seminar in year one was \(500\). In Year two, the attendance changed by \(100\).
So,
\(\frac{100}{500}\) ×\(100=20%\) %
Hence, option (C) is correct i.e., the percent change was \(20\)%.
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Consider a simple model to estimate the effect of personal computer ownership on college grade point average for graduating seniors at a large public university: GPA=β0+β1PC+u where PC is a binary variable indicating PC ownership. (i) Does this model uncover the ceteris parabus effect of PC ownership on GPA? Why might PC ownership be correlated with the error term? Could it be resolved by including it in the model? Is there a factor that is unobserved that could be correlated with both GPA and PC? (ii) Explain why PC is likely to be related to parents' annual income. Would parental income be a good IV for PC? Why or why not? (iii) Come up with an potential IV for PC and argue that it is exogenous and relevant. (iv) Suppose that four years ago the university provided grants to students for the purpose of buying PCs. In this, roughly half of the students received it randomly (so the students information was not used in any way to determine if they receive a grant). Explain carefully how you would construct an IV for PC using this information and argue that this IV will be exogenous and relevant in this model. Suppose you want to estimate the effect of class attendance on student performance using the simple model sperf =β0+β1 attrate +u where sperf is student performance and attrate is attendance rate. (i) Is attrate endogenous in this model? Come up with an unobserved variable that is plausibly correlated with u and attrate. (ii) Let dist be the distance from a student's living quarters to campus. Explain how dist could potentially be correlated with u. (iii) Maintain that dist is uncorrelated with u despite your answer to part (ii) i.e. it is exogenous. Now, what condition must dist satisfy in order to be a valid IV for attrate? Discuss why this condition might hold.
Answers
One reason why this condition may hold is because students who live closer to campus may be more likely to attend class since they don't have to travel as far
Part (i) Yes, this model uncovers the ceteris parabus effect of PC ownership on GPA.
There is, however, a possible correlation between PC ownership and the error term, which could be resolved by including it in the model.
There may be an unobserved factor that is correlated with both GPA and PC ownership.
It's possible that individuals who own PCs are more technologically savvy than those who don't, and that this technical proficiency is linked to higher GPAs.
Part (ii) PC is likely to be linked to parental annual income because high-income families can afford computers for their children, whereas low-income families may not.
Parental income would be a reasonable IV for PC since it is associated with the student's ability to afford a PC.
Part (iii) An potential IV for PC is the grant that students received for the purpose of purchasing a computer.
Since this grant was randomly assigned, it is exogenous and relevant.
Part (iv) In this scenario, the IV for PC would be whether or not the student received a grant to purchase a computer. This is a valid IV because the students' data was not used to determine who got the grant, and it is relevant since it is related to whether or not they owned a computer.
Part (i) Attendance rate (attrate) may be endogenous in this model, since there may be an unobserved factor that affects both attendance rate and student performance.
Part (ii) Distance from a student's living quarters to campus could be linked to the error term (u) because students who live closer to campus may have an easier time attending class and may be less susceptible to factors outside of their control that could impact their performance.
Part (iii) In order for dist to be a valid IV for attrate, it must be uncorrelated with u and must be correlated with attendance rate (attrate).
One reason why this condition may hold is that students who live closer to campus may be more likely to attend class since they don't have to travel as far.
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Enter the number in two equivalent froms
Answers
The decimal equivalent is 0.60, and the percent is 60%. If you do 3/5, you get 0.60, and to get the percentage, you move the decimal two to the right, and add the percent sign. I hope you understand. :)
Percent equivalent:60%
\(5x-6=3x-8\)
Answers
Worked it out for ya :)
![[tex]5x-6=3x-8[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/DvwXYzspCMbbblhriwR5ntKmD9kv9rB4.png)
Given: Line segment N M is parallel to line segment P O. and Angle 1 is-congruent-to angle 3 Prove: Line segment N M is parallel to line segment N O. 4 lines are connected. Line segment L M connects to line segment M N to form angle 1. Line segment M N connects to line segment N O to form angle 2. Line segment N O connects to line segment O P to form angle 3. A 2-column table has 5 rows. Column 1 is labeled statements with the entries line segment N M is parallel to line segment P O, angle 2 is-congruent-to angle 3, angle 1 is-congruent-to angle 3, angle 1 is-congruent-to angle 2, line segment L M is parallel to line segment N O. What is the missing reason in the proof?
Answers
Answer:
C
Step-by-step explanation:
The proof would be the same as statement 2 as the conditions are the same.
Answer:
C
Step-by-step explanation:
this is correct on Edge 2020 :)
1/4(16w+5) we need to simplify the answer
Answers
Answer:
4w + 5 / 4
Step-by-step explanation:
1/4 × 16w + 1/4 × 5
= 4w + 5 / 4
Select ALL of the following lines that have an x-intercept of (3, 0) and a y-intercept of (0,-4)
□y=4/3x-4
□y=-4/3x-4
□y=3x-4
□ Y=4/3(x-3)
□ y+4=4/3 (x-3)
□y+4=4/3x
Answers
The lines that have an x-intercept of (3,0) and a y-intercept of (0,-4) are:
y = 4/3x - 4
y + 4 = 4/3(x - 3)
To find a line with a given x-intercept and y-intercept, we can use the slope-intercept form of a line, which is:
y = mx + b
where m is the slope of the line, and b is the y-intercept (the y-coordinate where the line intersects the y-axis).
Both of these lines pass through points (3,0) and (0,-4), so they have the desired x- and y-intercepts.
The other lines do not pass through both of these points
y = -4/3x - 4 does not pass through (3,0)
y = 3x - 4 does not pass through (0,-4)
Y=4/3(x-3) does not pass through (0,-4)
y+4=4/3x does not pass through (3,0)
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Rectangle ABCD was dilated to create rectangle A'B'C'D. Triangle A B C D is dilated to form triangle A prime B prime C prime D. Side B C is 3.8 units. Side A prime B prime is 15 units and side B prime C prime is 9.5 units. What is AB? 6 units 7.6 units 9.5 units 12 units
Answers
Answer:
\(AB = 6\)
Step-by-step explanation:
Given
\(BC = 3.8\)
\(A'B' = 15\)
\(B'C' = 9.5\)
Required
Determine the length of AB
Because A'B'C'D is a dilation of ABCD, then the following relationship must exist:
\(A'B' : AB = B'C' : BC\)
Substitute values for A'B', B'C' and BC
\(15 : AB = 9.5 : 3.8\)
Express the ratio as fractions:
\(\frac{AB}{15} = \frac{3.8}{9.5}\)
Multiply through by 14
\(15 * \frac{AB}{15} = \frac{3.8}{9.5} * 15\)
\(AB = \frac{3.8}{9.5} * 15\)
\(AB = \frac{3.8* 15}{9.5}\)
\(AB = \frac{57}{9.5}\)
\(AB = 6\)
Answer:
A. 6 units
Step-by-step explanation:
I got it right on edge.
Please help im so confused rn :( I will give out a brainlest
Nancy's grandma needs 5/8 of a yard of lace for each doll hat she makes. How many doll hats can she make with 10 yards of lace?
Answers
Answer:
16
Step-by-step explanation:
10÷5/8=16
Which expression is equivalent to 5x + 9?
A. 5(x-4)+9
B. 5(x+4)+29
C. 5(x-4) +9
D. 5x+(x+9)
Answers
Answer:
i belive it would be D
Step-by-step explanation:
how to draw the horizontal alignment for the curve on that
shap on 12D ?
Answers
To draw the horizontal alignment for the curve on that shape on 12D, follow these steps:
Step 1: First of all, we have to determine the horizontal alignment for the curve. The horizontal alignment consists of a series of tangents, curves, and spirals.
Step 2: After that, we have to select the appropriate curve radius for the design speed, the superelevation, and the allowable sight distance.
Step 3: Next, plot the vertical curves with the curve layout. A design speed of 50 mph and a curve radius of 1200 ft will be used in this example.
Step 4: Next, we have to calculate the curve length using the formula Lc = Rθ. Here, Lc is the curve length, R is the radius, and θ is the curve angle. In this case, the curve angle is 4 degrees, so the curve length will be 83.775 ft.
Step 5: Then, we will plot the curve using a tangent-tangent-radius (TTR) method. The TTR method involves drawing a tangent to the curve's point of intersection, then drawing another tangent to the next point of intersection, and finally drawing the curve's arc with the given radius. This process is repeated until the curve's entire length is completed.
Step 6: Finally, label the horizontal and vertical curves, including the stationing and curve radius.
That's how we draw the horizontal alignment for the curve on that shape on 12D.
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