Using decimal multipliers, the correct statement is given by:
(iii) S1 = S2.
What is a decimal multiplier?Increases of a% or decreases of a% re represented by decimal values, as follows:
The equivalent multiplier for an increase of a% is given by: [tex]\frac{100 + a}{100}[/tex]The equivalent multiplier for an decrease of a% is given by: [tex]\frac{100 - a}{100}[/tex]Hence, in the context of this problem:
An increase of 10% is represented by 1.1.A decrease of 10% is represented by 0.9.The options are given as follows:
S1 = 0.9 x 1.1 = 0.99.S2 = 1.1 x 0.9 = 0.99.They are equal, hence option (iii) is correct.
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The functions f(x) = −(x − 1)2 5 and g(x) = (x 2)2 − 3 have been rewritten using the completing-the-square method. apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.
The vertex of the function f(x) exists (1, 5), the vertex of the function g(x) exists (-2, -3), and the vertex of the function f(x) exists maximum and the vertex of the function g(x) exists minimum.
How to determine the vertex for each function is a minimum or a maximum?Given:
[tex]$\mathrm{f}(\mathrm{x})=-(\mathrm{x}-1)^{2}+5$[/tex] and
[tex]$\mathrm{g}(\mathrm{x})=(\mathrm{x}-2)^{2}-3$[/tex]
The generalized equation of a parabola in the vertex form exists
[tex]$y=a(x-h)^{2}+k[/tex]
Vertex of the function f(x) exists (1, 5).
Vertex of the function g(x) exists (-2, -3).
Now, if (a > 0) then the vertex of the function exists minimum, and if (a < 0) then the vertex of the function exists maximum.
The vertex of the function f(x) exists at a maximum and the vertex of the function g(x) exists at a minimum.
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Answer:
- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.
- For the function g(x) = x^4 - 3, the vertex is a minimum point.
Step-by-step explanation:
To determine if the vertex for each function is a minimum or a maximum, we need to analyze the leading coefficient of each function.
Let's start with the function f(x) = -(x - 1)^2/5. This function is already in vertex form, where the vertex is (1, 0).
Since the leading coefficient is negative (-1/5), the graph of f(x) opens downward. In this case, the vertex is a maximum point. You can visualize it as a peak on a graph.
Now, let's move on to the function g(x) = (x^2)^2 - 3. This function can be rewritten in vertex form as g(x) = x^4 - 3.
The leading coefficient is positive (1), so the graph of g(x) opens upward. In this case, the vertex is a minimum point. You can visualize it as a valley on a graph.
In summary:
- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.
- For the function g(x) = x^4 - 3, the vertex is a minimum point.
Remember, the sign of the leading coefficient determines whether the vertex is a minimum or maximum point.
18 1 / 2 miles of highway 1-35 Is undergoing repairs. The construction workers repairs The construction workers repair 2 1⁄4 Miles of hideaway each week Approximately How many weeks will it take for the repairs to be completed
Answer:
The exact amount of time would be 8 2/9 weeks, but if we are only counting full weeks, it would be finished in 9 weeks.
Step-by-step explanation:
y = xm
18 1/2 = 2 1/4x Change both numbers into improper fractions
18 1/2 would be 37/2 The denominator (bottom number) stays 2. To get the top number you would (2 x 18) + 1 or 37. That makes 37/2 equivalent to 18 1/2.
Now do the same thing to 2 1/4. The bottom number stays the same. We get the top number (4 x 2) + 1 or 9. That makes 9/4 equivalent to 2 1/4.
We know have
37/2 = 9/4 x We can solve for x by multiplying both sides of the equation by 4/9
37/2(4/9) = (9/4)(4/9)x
148/18 = x If we divide both the top and the bottom by 2 we would get 74/9 = x If we divide 74 by 9 we get 8 2/9
the sum of the digits of a two-digit number is 14. the first digit is 4 less than twice the second digit. what is the number
Answer:
86
Step-by-step explanation:
t = ten's digit u= one's digit
t + u = 14 t = 2u - 4
In the first equation substitute for t 2u - 4 that we find in the second equation above.
t + u = 14
2u - 4 + u = 14 Combine the u's
3u - 4 = 14 Now add 14 to both sides
3u = 18 Divide both sides by 3
u = 6. We found the unit's digit, now we will find the ten's unit by plugging in 6 for u in the first equation above.
t + u = 14
t + 6 = 14 Subtract 6 from both sides
t = 8
So, your answer is 86.
y=–6x+2
–12x – 2y=–4
How many solutions does this linear system have?
The linear equation y = -6x + 2; -12x - 2y = -4 has no solution
Linear equationy = -6x + 2
-12x - 2y = -4
Substitute y = -6x + 2 into (2)-12x - 2y = -4
-12x - 2(-6x + 2) = -4
-12x + 12x -4 = -4
-12x + 12x = - 4 + 4
0 = 0
Solve for xy = -6x + 2
y - 2 = -6x
x = (y - 2) / -6
Substitute into (2)-12x - 2y = -4
-12(y- 2)/ 6 - 2y = -4
(-12y + 24) / 6 - 2y = -4
-2y + 4 - 2y = 4
0 = 0
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10x(4-3x) pls someone help???
Answer: [tex]\Large\boxed{-30x^2+40x}[/tex]
Step-by-step explanation:
Given expression
10x (4 - 3x)
Expand the parenthesis by distributive property
= 10x · 4 - 10x · 3x
= (10 × 4)x - (10 × 3) (x × x)
[tex]\Large\boxed{=-30x^2+40x}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Hi :)
We'll use distributive property to solve this
————————[tex]\LARGE\boldsymbol{10x(\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}4-\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}{3x)}}}[/tex]
Thus
[tex]\large\boldsymbol{10x\cdot4-3x\cdot10x}[/tex]
Simplify
[tex]\Large\boldsymbol{40x-30x^2}[/tex]
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
.
Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.
The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.
What is the computation for the above solution?
Note that this is simple probability.
Hence probability of the 75% football starts selected randomly where the chance is 93% =
75% x 93%
= 69.75%
What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:
Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.
Recall that the total population is 100%.
Are these are independent or dependent events. Are they Inclusive or exclusive?From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.
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How do you construct a frequency distribution table using sturge’s approximation
The steps to use to construct a frequency distribution table using sturge’s approximation is as below.
How to construct a frequency distribution table?The steps to construct a frequency distribution table using Sturge's approximation are as follows;
Step 1: Find the range of the data: This is simply finding the difference between the largest and the smallest values.
Step 2; Take a decision on the approximate number of classes in which the given data are to be grouped. The formula for this is;
K = 1 + 3.322logN
where;
K= Number of classes
logN = Logarithm of the total number of observations.
Step 3; Determine the approximate class interval size: This is obtained by dividing the range of data by the number of classes and is denoted by h class interval size
Step 4; Locate the starting point: The lower class limit should take care of the smallest value in the raw data.
Step 5; Identify the remaining class boundaries: When you have gotten the lowest class boundary, then you can add the class interval size to the lower class boundary to get the upper class boundary.
Step 6; Distribute the data into respective classes:
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Jessica's dog weighed 91.5 pounds at the beginning of summer but lost 5.2
pounds by the end of summer. Which number sentence could be used to
determine the dog's weight at the end of the summer?
Answer:
91.5 - 5.2 = 86.3
Step-by-step explanation:
The initial weight was 91.5 pounds.
The dog lost 5.2 pounds which means subtraction.
91.5 pounds subtracted by 5.2 pounds that the dog lost equals 86.3 pounds.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}[/tex]
Step-by-step explanation:
To find y-intercept of a graph, we have to substitute x = 0 to find it - consider each functions:
First Choice
[tex]\displaystyle{f(x) = 2x(x+14)-64}\\\\\displaystyle{f(0) = 2\cdot 0(0+14)-64}\\\\\displaystyle{f(0) = 0\cdot 14-64}\\\\\displaystyle{f(0) = -64}[/tex]
Second Choice
[tex]\displaystyle{f(x) = (x+4)^2+2x}\\\\\displaystyle{f(0) = (0+4)^2 + 2(0)}\\\\\displaystyle{f(0) = 4^2}\\\\\displaystyle{f(0) = 16}[/tex]
Third Choice
[tex]\displaystyle{f(x) = (x-16)^2 + 4}\\\\\displaystyle{f(0) = (0-16)^2 + 4}\\\\\displaystyle{f(0) = (-16)^2 + 4}\\\\\displaystyle{f(0) = 256 + 4}\\\\\displaystyle{f(0) = 260}[/tex]
Fourth Choice
[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}\\\\\displaystyle{f(0) = -2(0-3)^2 + 2}\\\\\displaystyle{f(0) = -2(-3)^2 + 2}\\\\\displaystyle{f(0) = -2\cdot 9 + 2}\\\\\displaystyle{f(0) = -18+2}\\\\\displaystyle{f(0) = -16}\\[/tex]
Therefore, fourth choice is correct.
Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=−0. 599, α=0. 01, n=11
Yes, the correlation coefficient is statistically significance
The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.
Given,
Sample size, n = 11
Where ρ is the population correlation.
Then the number of degrees of freedom is, df = n-2 = 11-2 = 9
The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254
Here,
The null hypothesis, = ρ - 0 is rejected
Suppose lr> re 0.254
Because on the sample correlation provided, we know that lrl = 0.599>=0.254.
Here, it is clear that the null hypothesis is rejected.
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For an independent t-test, if the mean of group 1=10, mean of group 2=12, ss1 =5, ss2=8, there are 6 individuals per group. what is the value of t obtained?
The value of t obtained is 4.76
Given,
Mean of group 1, [tex]M_{1}[/tex] = 10
Mean of group 2, [tex]M_{2}[/tex] = 12
[tex]SS_{1}[/tex] = 5
[tex]SS_{2}[/tex] = 8
Number of individuals per group, n = 6
The degrees of freedom are calculated as:
[tex]df = (n_{1} -1)+(n_{2} -1)[/tex] = ( 8-1) + (8-1) = 7 + 7 = 14
The difference between sample means [tex]M_{d}[/tex] is:
[tex]M_{d}[/tex] = [tex]M_{1} -M_{2}[/tex] = 10 - 12 = 2
Here n is equal for both groups which is = 8
Now,
The standard deviation of sample 1 :
[tex]s_{1} =\sqrt{\frac{SS_{1} }{n_{1} -1} } = \sqrt{\frac{5}{8-1} } = \sqrt{\frac{5}{7} } = 0.85[/tex]
The standard deviation of sample 2 :
[tex]s_{2}= \sqrt{\frac{SS_{2} }{n_{2}-1 } } = \sqrt{\frac{8}{8-1} } = \sqrt{\frac{8}{7} } = 1.07[/tex]
Now, we have to calculate the standard error for the difference of the means.
MSE = [tex]\frac{(n_{1}-1)s^{2} _{1}+(n_{2}-1)s^{2} _{2} }{(n_{1}-1)+(n_{2}-1) }[/tex]
= [tex]\frac{(8-1)(0.85^{2})+(8-1)(1.07^{2}) }{(8-1)+(8-1)}[/tex]
= [tex]\frac{10.1318}{14}[/tex]
MSE = 0.7237
Then, the standard error can be calculated as:
[tex]s_{M_{d} } = \sqrt{\frac{2MSE}{n} } = \sqrt{\frac{2 * 0.7237}{8} } = 0.42[/tex]
Now we can calculate t :
[tex]t=\frac{M_{d} }{s_{M_{d} } } = \frac{2}{0.42} = 4.76[/tex]
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Building managers recently surveyed employees of three different companies regarding their method of transportation to work day. The results of the survey are shown in the two-way frequency table below.
Car Bus Walk Bike Subway Total
Tech company 10 16 14 38 20 98
Law firm 27 8 10 2 26 73
Finance group 18 22 12 8 34 94
Total 55 46 36 48 80 256
Which Conclusion can the building managers draw based on this data?
A: It is more common to find a bus rider who works at the tech company than a person on the subway who works at the law firm.
B: Walking to work is more common among employees at the finance group than employees at the law firm.
C: The percentage of walkers who are employers at the law firm is the same as the percentage of car drivers who are employees at the tech company.
D: Riding to work is more common among tech company employees than at the other modes of transportation.
The conclusion that the building managers can draw based on the given data is; D: Riding to work is more common among tech company employees than at the other modes of transportation.
How to Interpret Data Tables?The results of the survey are shown in the two-way frequency table below.
From the table we can see that;
Total Cars = 55
Total Number of Buses = 46
Total Number of Walks = 36
Total Number of Bikes = 48
Total Number of Subways = 80
Total Number of Tech company = 98
Total Number of Law Firms = 73
Total Number of Finance Groups = 94
Option A; There are 16 people who use buses from the tech company while there are 26 people who use subway from the Law firm. Thus, the statement is false.
Option B; There are 12 people who walk to work at the finance group while there are a total of 10 people who walk to work at the law firm. Thus the statement is false.
Option C; Percentage of walkers at law firm = 10/73 * 100% = 13.7%
Percentage of car drivers at the tech firm = 10/98 * 100% = 10.2%
Thus, the statement is false
Option D; This is true
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Answer:
It is more common to find a bus rider who works at the tech company than a person on the subway who works at the law firm.
Step-by-step explanation:
got it right on edmentum
Dean's father, Franco, is 5 times his age. Dean is 8 years older than his sister, Helen. The sum of their ages is 62 years. How old is each person
Answer:
dean = 10
franco = 50
helen = 2
steps
you want to get the age of one of the people first
'is' means equal
'older than' means plus
'sum' means total by adding
d
f = 5d
d = 8 + h
d + f + h = 62
make sure there is 1 letter to solve for
d = 8 + h -> h = d - 8
f = 5d
d = d
d + f + h = 62
d + (5d) + (d-8)
7d - 8 = 62
7d = 70
d = 10
f = 50
h = 2
Point D is located at 4. Point E is 6 less than Point D. Where is E located?
Answer:
-2
Step-by-step explanation:
<________|____|___-2___|___0___|____|____|____4________>
E D
The Point E is located at -2.
Given that Point D is located at 4. Point E is 6 less than Point D.
We need to find the location of the point E.
Based on the information provided, Point D is located at 4. Now, we know that Point E is 6 less than Point D.
When we say, "less than," it means we need to subtract the given value from Point D to find the location of Point E.
If Point D is located at 4, and Point E is 6 less than Point D, then the location of Point E can be calculated as follows:
E = D - 6
Since D is 4, we can substitute that value into the equation:
E = 4 - 6
E = -2
So, Point E is located at -2.
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I don’t understand what I did wrong
Step-by-step explanation:
You got your fraction messed up
It should be -3/2 or -1.5
Chestnut Hill Coffee Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 46 espressos in all, 26 of which were single-shot. What percentage of the espressos were double-shot? Round to the nearest hundredth.
Given the number of espresso sold at Chestnut Hill Coffee Cafe as either a single-shot or a double-shot, the percentage of double-shot espressos sold is 43.48%.
What percentage of the espressos were double-shot?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given the data in the question;
Total number of espressos sold or Whole = 46Number of single-shots or Part single = 26Number of double-shots or Part double = 46 - 26 = 20Percentage of double-shot = ?Percentage = ( Part / Whole ) × 100%
Percentage = ( Part double / Whole ) × 100%
Percentage = ( 20 / 46 ) × 100%
Percentage = 0.43 × 100%
Percentage = 43.48%
Given the number of espresso sold at Chestnut Hill Coffee Cafe as either a single-shot or a double-shot, the percentage of double-shot espressos sold is 43.48%.
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Testing: h 0 : p = 0. 74 h0:p=0. 74 h α : p < 0. 74 hα:p<0. 74 your sample consists of 43 subjects, with 33 successes. calculate the test statistic
Test statistic is 0.42.
Given
Testing:
h0 : p = 0.74
h1 : p < 0.74
Successes x = 33
Subject n = 43
A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.
It measures the accuracy of the predicted data distribution relating to the null hypothesis you use when analyzing data samples.
Test statistics z = [tex]\frac{p_{hat} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
Where [tex]p_{hat}[/tex] = Sample proportion = [tex]\frac{x}{n}[/tex]
p = population proportion
n = sample size
z = [tex]\frac{(\frac{33}{43})-0.74 }{\sqrt{\frac{0.74(1-0.74)}{43} } }[/tex]
z = 0.42
Hence,
Test statistics is 0.42..
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The proportional relationship between the number of hours a business operates and its total
cost of electricity is shown in the following graph.
Total cost (dollars)
1604
140-
120-
100-
80-
60-
40+
20-
A
Cr.
3 4 5
Number of hours
S
7
89
Which statements about the graph are true?
10
The total cost of electricity when the business operates for 4 hours is correct.
Slope of a lineThe slope of a line is also known as rate of change, The formula for calculating the slope of a line is expressed as:
Slope = y2-y1/x2-x1
If the proportional relationship between the number of hours a business operates and its total cost of electricity is shown in the following graph.
Using the coordinate points (1, 20) and (2, 40)
Slope = 40-20/2-1
Slope = 20/1
Slope = 20
This shows that the total cost of electricity is $20 when operating business for 1 hour.
According to the coordinate point A (4, 120), this shows that the y-coordinate of point A is represents the total cost of electricity when the business operates for 4 hours.
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workout the value of (3.5x10⁶)÷(5x10-³) and show your workout.
The value of the given expression is 7.0 × 10⁸
Simplifying an expressionFrom the question, we are to determine the value of the given expression
The given expression is
(3.5x10⁶)÷(5x10-³)
The expression can be simplified as follows
(3.5x10⁶)÷(5x10⁻³)
= (3.5 ÷ 5) × (10⁶ ÷ 10⁻³)
= (0.7) × (10⁶⁻⁽⁻³⁾)
= 0.7 × (10⁶⁺³)
= 0.7 × (10⁹)
= 7.0 × 10⁸
Hence, the value of the given expression is 7.0 × 10⁸
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A town is mapped on a coordinate grid. The library is located at point (-3, 9) and the museum is located at
point (8, 2).
Where is the midpoint of the line segment whose endpoints are the library and the museum?
O (-5.5, 5.5)
O (-5.5, 3.5)
O (2.5, 3.5)
O (2.5, 5.5)
Applying the Midpoint Formula, the midpoint of the line segment whose endpoints are the library and the museum is calculated as: D. (2.5, 5.5).
What is the Midpoint Formula?To find the coordinates of the midpoint between two endpoints on a coordinate plane, the midpoint formula that is used is expressed as: M[(x2 + x1)/2, (y2 + y1)/2].
Given the following coordinates:
The library is located at point (-3, 9)
The museum is located at point (8, 2), therefore, let:
(-3, 9) = (x1, y1)
(8, 2) = (x2, y2)
Midpoint = M(x, y)
Substitute the values into M[(x2 + x1)/2, (y2 + y1)/2]:
M(x, y) = [(8 + (-3))/2, (2 + 9)/2]
M(x, y) = (5/2, 11/2)
M(x, y) = (2.5, 5.5)
Thus, the midpoint of the line segment whose endpoints are the library and the museum is calculated as: D. (2.5, 5.5).
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Answer:
Its D (2.5, 5.5) On Edg 2022-23
Step-by-step explanation:
Hope This Helps:))
5107465
State the value of digit in figures ?
Place value of 5 in 5107465 is equal to 5,000,000.
According to the statement
we have given that the a value and we have find the place value of a digit 5 in this numbers.
So, For this purpose,
The given digit is 5107465
And we have find the value of digit 5 in it so,
we know that,
A Place value is the position or place of a digit in a given number .
As we can see that, in given number 5107465:-
5 is at one million place = 5 * 1,000,000 = 5,000,000
1 is at hundred thousand place = 1 * 100000 = 100000
0 is at ten thousand place = 0 * 10000 = 0
7 is at thousand place = 7 * 1000 = 7000
4 is at hundred place = 4 * 100 = 400
6 is at tens place = 6 * 10 = 60
5 is at unit place = 5 * 1 = 5
Therefore,
Place value of 5 in 5107465 is equal to 5,000,000.
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pls help with Trigonometric
The value of the given trigonometry function is 2√15/15
Half anglesHalf angles are trigonometric identities used to express sine, cosine and tangent of half angles.
For instance the value of cos theta is expressed as shown below;
cosФ = cos(Ф/2+Ф/2)
cosФ = cos²Ф/2-sin²Ф/2
cosФ = cos²Ф/2-(1-cos²Ф/2)
cosФ = 1 - 2cos²Ф/2
Given the following parameters
cosФ = -7/15
Substitute
cosФ = 1 - 2cos²Ф/2
-7/15 = 1 - 2cos²Ф/2
-2cos²Ф/2 = -7/15 - 1
-2cos²Ф/2 = -8/15
cos²Ф/2 = 4/15
cosФ/2 = 2/√15
Rationalize
2/√15 * √15/√15
2√15/15
Hence the value of the given trigonometry function is 2√15/15
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Identify the standard form of the equation by completing the square.
4x2 − 9y2 − 8x + 36y − 68 = 0
Answer:
[tex]\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1[/tex]
Step-by-step explanation:
Given equation:
[tex]4x^2-9y^2-8x+36y-68=0[/tex]
This is an equation for a horizontal hyperbola.
To complete the square for a hyperbola
Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.
[tex]\implies 4x^2-8x-9y^2+36y=68[/tex]
Factor out the coefficient of the x² term and the y² term.
[tex]\implies 4(x^2-2x)-9(y^2-4y)=68[/tex]
Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:
[tex]\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2[/tex]
[tex]\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36[/tex]
Factor the two perfect trinomials on the left side:
[tex]\implies 4(x-1)^2-9(y-2)^2=36[/tex]
Divide both sides by the number of the right side so the right side equals 1:
[tex]\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}[/tex]
Simplify:
[tex]\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1[/tex]
Therefore, this is the standard equation for a horizontal hyperbola with:
center = (1, 2)vertices = (-2, 2) and (4, 2)co-vertices = (1, 0) and (1, 4)[tex]\textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}[/tex][tex]\textsf{Foci}: \quad (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)[/tex]Build Your Math Skills 2C, Round decimals to the nearest hundredth (0.01): 2.364
Answer:2.36
Step-by-step explanation:
A weaver bought a bundle of grass of 50.00 dollars from which he made 8 mats if each mats was sold for 15.00 dollars find the percentage profit
The percentage profit is 140%
What is percentage?
Percentage can be described as the expression of a number in hundredth.
The formula for calculating percentage profit is
profit/cost price × 100
cost price= $50
selling price= $15
number of mats produced= 8
selling price of the mat= 15 × 8
= 120
Profit= selling price-cost price
= 120-50
$70
Therefore the percentage profit can be calculated as follows
= 70/50 × 100
= 1.4 ×100
= 140
Thus, the percentage profit is 140%
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In the circle below, if arc AB is congruent to arc CD, chord AB = 16x - 2 and chord CD = 14x + 8, find x.
Answer:
d. x = 5
Step-by-step explanation:
Chords that subtend congruent arcs are congruent.
SetupChord lengths are the same:
AB = CD
16x -2 = 14x +8
Solution2x = 10 . . . . . . add 2-14x
x = 5 . . . . . . . . divide by 2
HELP PLS WHAT IS X
Darn
Answer:
x = 55°
Step-by-step explanation:
x , 35° , 90° lie on a straight line and sum to 180° , that is
x + 35° + 90° = 180°
x + 125° = 180° ( subtract 125° from both sides )
x = 55°
Can anyone help me with this? I'm not very good at math... =.=
Last week the value of an investment changed at a rate of -$3.15 each day. After How many days was the total change in value -$12.60?
In four days,the total change in value -$12.60.
According to the statement
we have given that the value of an investment changed at a rate of -$3.15 each day. And we have to find that the after how many days the change in value reaches at the -$12.60.
So, here we use division rule to find the solution.
The given change value is :
-$3.15 each day.
The desired change value is :
-$12.60.
Number of days required = -12.60 / -3.15
Number of days required = 12.60 / 3.15
Number of days required = 4 days.
So, in four days the change in value reaches at the desired value of change.
So, In four days,the total change in value -$12.60.
Learn more about division rule here
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There are 3 red, 1 blue, and 2 yellow marbles in a bag. Once a marble is selected, it is not replaced. Find P(red and the yellow).
Answer:
5/6
Step-by-step explanation:
we add all the marbles together to get 6
then we seperate the marbles according to the question which would be yellow and red. that would make the probability of getting one of those to 5/6. Hope this helps :)
