Peter’s new salary by the given data is $36,400.
We are given that;
Salary= 35000
Percentage= 4%
Now,
To find Peter’s new salary, we need to add the amount of his raise to his old salary. The amount of his raise is 4% of his old salary, which means we need to multiply his old salary by 0.04 (or 4/100).
The amount of his raise is:
0.04 × 35000
= 1400
35000 + 1400
= 36400
Therefore, by the given percentage the answer will be $36,400.
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Peter’s new salary by the given data is $36,400.
We are given that;
Salary= 35000
Percentage= 4%
Now,
To find Peter’s new salary, we need to add the amount of his raise to his old salary. The amount of his raise is 4% of his old salary, which means we need to multiply his old salary by 0.04 (or 4/100).
The amount of his raise is:
0.04 × 35000
= 1400
35000 + 1400
= 36400
Therefore, by the given percentage the answer will be $36,400.
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For each function below, identify and enter the percent rate of change per unit, t. Round to the nearest tenth of a percent.
Then use the drop-down menus to classify each as exponential growth or decay.
The percent rate of each function given is:
[tex]f(t) = 1.18^t:16.99\%\\\\g(t) = 2^{-2t}:-9.1\%\\\\h(t) = 1.19^{\frac{t}{10} }:8.5\%\\\\k(t) = 0.13^t:-19.5\%[/tex]
What is percent rate of change?A measure known as the percent rate of change quantifies the amount of change in a quantity over time and is given as a percentage of the initial number. It is frequently used to keep tabs on population growth, shifts in the financial markets, and other occurrences.
You must first determine the amount of change in the quantity (often done by deducting the beginning value from the final value) in order to compute the percent rate of change. To calculate the percent rate of change, divide this amount of change by the starting value, multiply the result by 100, and add a percent sign.
[tex]f(t) = 1.18^t:[/tex] 16.99% is the percent rate of change per unit (t). This increase is exponential.
[tex]g(t) = 2^{-2t}:[/tex] Approximately -9.1% of a percent rate of change per unit, t. The decline is exponential.
[tex]h(t) = 1.19^{\frac{t}{10} }:[/tex] The average percent rate of change for unit t is around 8.5 percent. This increase is exponential.
[tex]k(t) = 0.13^t:[/tex] t represents the percent rate of change, which is around -19.5% per unit. The decline is exponential.
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math adjacent angles
Answer: ∠EFA and/or ∠CFB
Step-by-step explanation:
Adjacent: In order to classify adjacent the 2 angles need to have a common side and common vertex
Starting Angle: ∠CFE
Possible Adjacents: ∠ EFA and/or ∠CFB
Angles in a Triangle
Answer:
55
Step-by-step explanation:
The first we need to do is find the other angle measures. The left angle must be supplementary with 110, so it must measure 70. The right angle must be supplementary with 125, so it must measure 55. The sides of an angle add up to 180, so 180-70-55= 55
The angle of x is 55°.
There is 180° in a triangle. First, we need to calculate the angles of the other two sides. A straight line also forms 180°. Therefore the first angle will be
180 - 110= 70°
The second angle will be
180 - 125 = 55°
Angles of the triangle excluding x will be
70 + 55 = 125°
Since there is 180° in a triangle, x will be
180 - 125= 55°
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The answers are A = 46% and B = 20%.
Given that, a table of data, each cell in the table shows the number of cars in that category.
A) The probability that the car's total repair cost is less than $10000 =
86 / (86+35+67) x 100 = 86/188 x 100 = 46%
B) The probability that the car's purchase was more than $40,000 =
40 / (40+86+71) x 100 = 40/197 x 100 = 20%
Hence, the answers are A = 46% and B = 20%.
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Frank used 2 1/3 gallons of gas on Saturday and 3 2/5 gallons of gas on Sunday. How many gallons did he use on the two days combined? Write your answer as a mixed number in simplest form.
Frank used a total of 2 14/15 gallons of gas on Saturday and Sunday combined.
To find the total amount of gas Frank used on both days, we need to add the amount of gas he used on Saturday and Sunday.
First, we need to make sure that both quantities are in the same form. We can convert the mixed number 2 1/3 to an improper fraction by multiplying the whole number by the denominator and adding the numerator. This gives us:
2 1/3 = (2 x 3 + 1)/3 = 7/3
Next, we can add the two quantities by finding a common denominator. The lowest common denominator for 3 and 5 is 15. So, we can write:
7/3 gallons + 3 2/5 gallons = (35/15 + 9/15) gallons
= 44/15 gallons
To simplify the answer, we can express the mixed number as a whole number and a proper fraction by dividing the numerator by the denominator. This gives us:
44/15 = 2 14/15
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Can anyone help QUICK? Giving 10 points, and brainliest!
Answer:
1. 62
Step-by-step explanation:
f(x) = x² on [3, 3+h]
The average rate of change of the function f(x) = x² on the interval [3, 3 + h] is given as follows:
h + 6.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.
The function in this problem is given as follows:
f(x) = x².
Then the outputs are obtained as follows:
f(3) = 3² = 9.f(3 + h) = h² + 6h + 9.The change in the output is given as follows:
h² + 6h + 9 - 9 = h² + 6h.
The change in the input is given as follows:
3 + h - 3 = h.
Hence the rate is:
r = (h² + 6h)/h.
r = h(h + 6)/h
r = h + 6.
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Total Time Slept
Individual Total Time Slept
(hours)
Individual Total Time Slept
(hours)
Mike 8
1
2
Gina 10
John 10 Elisabeth 9
Susan 8
1
2
Alexis 9
1
2
Linda 8
1
2
Drake 8
1
2
Frankie 6
1
2
Vincent 8
1
2
Bob 7
1
2
Herbert 9
Kim 7
1
2
John 10
Louie 9
1
2
Chrissy 7
1
2
Pamela 8
1
2
Liam 10
Heather 8 Julian 8
1
2
© 2017 Connections Education LLC. All rights reserved. 2
1. What was the most common amount of sleep?
2. Is there an outlier in the data? If so, what is it? Explain how you know.
3. What is the difference in hours between the longest night’s sleep and the
shortest night’s sleep?
4. How many people slept longer than 8 hours?
3
Part 2
Directions: The next day, Molly asked 5 more people how long they slept the night
before. Below is a chart of their answers. Add their times to the line plot you
created in Part 1.
Total Time Slept
Name Total Time Slept
(hours)
Zaria
7
LaDajia
12
Devonte
7
Leon
8
Kylie
7
1. Describe how the new data has changed the line plot.
2. Is there an outlier in the data? If so, is it the same as the outlier before the
new data was added? Explain.
3. How many total people slept less than 8 hours? How do you know?
The most common amount of sleep: is 8 hours (6 individuals).
Outlier: Frankie (slept for 6 hours), as there is a significant difference between his sleep time and the rest of the individuals in the dataset (range of 4 hours).
The predominant resting time among the subjects is 8 hours.
Nonetheless, it's worth noting that an outlier exists within the dataset; Frankie spent a mere 6 hours sleeping - which amounts to two hours less than the sleep duration recorded by the second least rested individual (8 hours).
This information can be extracted from analyzing the figures and noticing the conspicuous discrepancy between Frankie's slumbering span and that of the other participants in the pool of data and this is the outlier.
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A triangle has two sides of length 3.2 cm and 8.5 cm.
Which value could be the length of the third side of the triangle?
Any value between 5.3 cm and 11.7 cm (exclusive) could be the length of the third side of the triangle which is 6.7cm in the given options.
What is the triangle inequality theorem?The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides a, b, and c, where c is the longest side, the following inequality holds:
a + b > c
This means that the length of any side of a triangle must be less than the sum of the lengths of the other two sides. This theorem is fundamental in geometry and is used in many proofs and applications.
According to the given informationAccording to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the length of the third side must be greater than the difference between the other two sides and less than their sum.
Let's apply this rule to the given triangle. We have two sides of length 3.2 cm and 8.5 cm.
To be a valid triangle, the length of the third side must satisfy the following inequality:
8.5 cm - 3.2 cm < third side < 8.5 cm + 3.2 cm
5.3 cm < third side < 11.7 cm
Therefore, any value between 5.3 cm and 11.7 cm (exclusive) could be the length of the third side of the triangle. So it's 6.7cm.
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The perimeter of a rectangle is 18 X +6 the width of the rectangle is 2X +5 what is an expression for the length of the rectangle
If perimeter of rectangle is denoted as "18x+6" and width is denoted as "2x+5", then the expression for length of the rectangle will be .
The "Perimeter" of a rectangle is known as the "total-distance" around the outside of rectangle.
Let length of rectangle be denoted by "L". The formula for the "peri-meter" for rectangle is : P = 2(length + width),
The "peri-meter" is = "18x + 6", and "width" is "2x + 5".
Substituting these values into the formula,
We get,
⇒ 18x + 6 = 2(L + 2x + 5),
⇒ 18x + 6 = 2L + 4x + 10,
⇒ 18x - 4x - 10 - 6 = 2L,
⇒ 14x - 16 = 2L,
⇒ 7x - 8 = L,
Therefore, the expression for the length of the rectangle is "7x - 8".
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A garden is in the shape of a square with a perimeter of 36 feet. The garden is surrounded by two
fences. One fence is around the perimeter of the garden, whereas the second fence is 2 feet from th
first fence on the outside. If the material used to build the two fences is $1.15 per foot, what was the
total cost of the fences?
The perimeter of the square garden is 36 feet, which means that each side of the square is 36/4 = 9 feet long. Therefore, the total cost of the fences is $92.
How is Perimeter calculated?The length of the outer fence, which is 2 feet away from the garden, is equal to the perimeter of a larger square with sides that are 2 feet longer than the sides of the original garden.
So, the length of the outer fence is 4(9+2) = 44 feet.
The length of the inner fence, which is around the perimeter of the garden, is equal to the perimeter of the original square garden, which is 4(9) = 36 feet.
The total length of both fences is the sum of the lengths of the inner and outer fences:
36 + 44 = 80 feet.
The cost of the fences is the total length of both fences multiplied by the cost per foot:
80 x $1.15 = $92.
Therefore, the total cost of the fences is $92.
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Find x, y, and z. If necessary, round to the tenths place. A. x = 23, y = 44.5, z = 116 B. x = 23, y = 89, z = 116 C. x = 44.5, y = 44.5, z = 116 D. x = 66, y = 89, z = 116
The measure of angle x is 23⁰.
The value of arc angle y is 45.5⁰.
The value of arc angle z is 116⁰.
What is the value of x, y and z?The measure of angle x, y and z is calculated as follows;
∠mEGF = ¹/₂ (arc EF - arc DC ) (intersecting chord theorem)
33 = ¹/₂ (89 - x )
2(33) = 89 - x
66 = 89 - x
x = 89 - 66
x = 23⁰
The value of arc angle z is calculated as follows;
89 + 132 + 23 + z = 360 (sum of angles of a circle)
244 + z = 360
z = 360 - 244
z = 116⁰
The value of angle y is calculated as follows;
∠mGEF = ¹/₂(z) (intersecting chord theorem)
∠mGEF = ¹/₂(116)
∠mGEF = 58⁰
∠mEFG = 180 - (58 + 33) = 89
y + 89 + y = 180 (sum of angles on a straight line)
2y + 89 = 180
2y = 91
y = 91/2
y = 45.5⁰
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The measure of angle x is 23⁰.
The value of arc angle y is 45.5⁰.
The value of arc angle z is 116⁰.
What is the value of x, y and z?The measure of angle x, y and z is calculated as follows;
∠mEGF = ¹/₂ (arc EF - arc DC ) (intersecting chord theorem)
33 = ¹/₂ (89 - x )
2(33) = 89 - x
66 = 89 - x
x = 89 - 66
x = 23⁰
The value of arc angle z is calculated as follows;
89 + 132 + 23 + z = 360 (sum of angles of a circle)
244 + z = 360
z = 360 - 244
z = 116⁰
The value of angle y is calculated as follows;
∠mGEF = ¹/₂(z) (intersecting chord theorem)
∠mGEF = ¹/₂(116)
∠mGEF = 58⁰
∠mEFG = 180 - (58 + 33) = 89
y + 89 + y = 180 (sum of angles on a straight line)
2y + 89 = 180
2y = 91
y = 91/2
y = 45.5⁰
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ap calculus problem
no need full detail solution
If Limₙ→∞, aₙ ≠ 0 or does not exist, then ∑^∞_{n= 1} (aₙ) diverges.
option C.
What is the solution of the limit function?
The solution of the limit function is calculated as follows;
Limₙ→∞, aₙ ≠ 0 or does not exist, then ∑^∞_{n= 1} (aₙ),
So in this type of function, we will conclude that the function diverges.
This is known as the divergence test, which states that if the limit of the nth term of a series does not approach zero, then the series diverges.
In other words, we can say that if the terms of the series do not approach zero, the series will not converge.
Thus, based on the given option, the correct answer is diverges.
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Use the given information to find the p-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject
the null hypothesis or fail to reject the null hypothesis).
The test statistic in a right-tailed test is z=0.52.
A. 0.3015; fail to reject the null hypothesis
B. 0.0195; reject the null hypothesis
C. 0.3015; reject the null hypothesis
D. 0.6030; fail to reject the null hypothesis
A. 0.3015; fail to reject the null hypothesis
The test statistic is z = 0.52 and p-value (0.3015) is greater than the significance level (0.05)
Given data ,
Under the premise that the null hypothesis is true, the p-value is the likelihood of witnessing a test statistic that is as severe as the one computed or even more extreme. The p-value of a right-tailed test is the likelihood of seeing a test statistic that is higher than or equal to the computed test statistic.
We can compare the test statistic to the critical value or use a conventional normal distribution table to calculate the p-value given that the test statistic is z = 0.52 and the significance threshold is 0.05
Looking up the p-value corresponding to z = 0.52 in a standard normal distribution table or using a calculator, we find that the p-value is approximately 0.3015.
Since the p-value (0.3015) is greater than the significance level (0.05), we fail to reject the null hypothesis.
Hence , 0.3015; fail to reject the null hypothesis
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sin(75°)= sqrt1-cos(150°)/2 true or false
[tex] \sqrt{ \frac{1 - cos(150)}{2} } = \sqrt{ \frac{1}{2} - \frac{cos(150)}{2} } = \sqrt{ \frac{1}{2} - \frac{ \frac{ - \sqrt{ 3}}{2} }{2} } = \sqrt{ \frac{2}{4} + \frac{ \sqrt{3} }{4} } = \sqrt{ \frac{2 + \sqrt{3} }{4} } [/tex]
[tex]= \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]
BTW:
[tex]sin(75) = \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]
[tex] = > sin(75) = \sqrt{ \frac{1 - cos(150)}{2} } [/tex]
Ans: True
Ok done. Thank to me >:33
What is the slope of the line 9x+3y=11
Step-by-step explanation:
Arrange this equation into y = mx + b form.....m is the slope
9x+3y =11
3y = -9x + 11
y = -9/3 x + 11/3
y = -3 x + 11/3 m = slope = - 3
Determine whether the graph of the quadratic function y = –2x^2 – 4x + 4 opens upward or downward. Explain.
The graph of the quadratic function [tex]y=-2x^2-4x+4[/tex] opens downward.
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here the given function is [tex]y=-2x^2-4x+4[/tex]
The general form of the quadratic function is y=[tex]ax^2+bx+c[/tex]
Then, a= -2
Which is negative value.
Then the graph is open downward.
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Please Help me with this math problem ASAP? x=?
The value of x in the expression is
x = -4.24How to find xTo solve for x in the the equation e^(3x+10) = 13^(x/4) we can take the natural logarithm (ln) of both sides
ln(e^(3x+10)) = ln(13^(x/4))
3x + 10 = (x/4) * ln(13)
Isolating x by collecting like terms
3x - (x/4) * ln(13) = -10
factor out x as a common factor:
x * (3 - ln(13)/4) = -10
x = -10 / (3 - ln(13)/4)
x = -4.2395
x = -4.24 to 2 decimal place
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What is the solution to 2|1-x|+1>3
Answer:
x < 0, x > 2
Step-by-step explanation:
|1-x| > 1
(x-1)^2 > 1
x^2 -2x + 1 > 1
x^2 - 2x > 0
x(x-2) > 0
Using the graph of y=x(x-2), x(x-2)> 0 when
x < 0, x > 2
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You invest $1800 in an account paying 6.3% interest compounded daily. What is the account's effective annual yield? You invest $1800 in an account paying 6.3% interest compounded daily. What is the account's effective annual yield?
The account's effective annual yield if you invest $1800 and it pays 6.3% interest compounded daily, is calculated as: 6.53%.
How to Find the Effective Annual Yield?In order to find the effective annual yield of an account, the formula to apply is expressed as:
Effective annual yield = (1 + r/n)^n - 1
where:
r represents the annual interest rate (as a decimal)
n represents the number of times the interest is compounded per year
In this case, we are given the following:
Annual interest rate = 6.3% = 0.063
The interest is compounded daily, so n = 365 (days in a year)
Plugging in the variables we have:
Effective annual yield = (1 + 0.063/365)^365 - 1
Effective annual yield = 0.0653 or 6.53%
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Draw a pie chart to show the periods of sunshine cloudiness and darkness during the day
The procedure for creating a pie chart based on a given set of data involves a number of steps such as.
Create a circular shape with a non-specific measurement for its radius. Begin by drawing radii that correspond to the values of each respective component, using the horizontal radius as a starting point and ensuring that the central angles match. Apply the same procedure to all element of the given information.What is the pie chart?The Steps to draw a pie chart for weather conditions in Kaduna:
1. Draw a circle to represent 24-hour period.
2. Divide circle into sections for sunshine, cloudiness, and darkness.
Lastly, Use the weather duration to find section size.
Sunlight: 10/24 = 42% of circle. Cloudy for 3 hours = (3/24) or 12.5% of circle. 11 hours for darkness = (11/24) or 45.8% of circle.Thus, Label pie chart sections attached as "Sunshine", "Cloudiness", and "Darkness".
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See text below
b Discuss the performance with your teach During a 24-hour period in Kaduna, the sun shone for 10 hours, it was cloudy for 3 hours and it was dark for the remainder of the time. Draw a pie chart to show the periods of sunshi cloudiness and darkness during the day.
Identify the domain and range of the function. y=3√x
A. Domain: x≥3, Range: y≥3
B. Domain: All Real Numbers, Range: All Real Numbers
C. Domain: x≥0, Range: y≥0
D. Domain: x≤0, Range: y≤0
The domain and range of the function are C. Domain: x≥0, Range: y≥0
Identifying the domain and range of the functionThe domain of the function is the set of all possible input values (x) for which the function is defined.
In this case, the function y = 3√x is defined for non-negative real numbers, because the root of a negative number is not a real number.
Therefore, the domain of the function is:
Domain: {x | x ≥ 0}
The range of the function is the set of all possible output values (y) that the function can take.
Since the root of any positive number is also positive, the function y = 3√x will always return a positive number for any positive input value.
Therefore, the range of the function is:
Range: {y | y ≥ 0} or [0, ∞) in interval notation.
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uppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1600 bacteria selected from this population reached the size of 1838 bacteria in four hours. Find the hourly growth rate parameter.
Answer:
Below.
Step-by-step explanation:
Exponential growth equation is
Nt = No e^kt where No is initial quantity , Nt is quantity after time t and k is some constant.
Here we have:
1838 = 1600 e^4k
e^4k = 1838/1600 = 1.14875
4k = ln 1.14875 = 0.138674
k = 0.034669
You have 2 bird feeders that hold 5 5/12 cups of seeds. You have a third bird feeder that holds 4 1/2 cups of seeds. One scoop of seeds holds 1 1/6 cups of seeds. How many scoops of seeds are needed to fill all three bird feeders?
The number of scoops of seeds needed to fill three bird feeders is 13 1/7 scoops of seeds .
How to find the feed ?To calculate the total seed quantity required to fill all three feeders, begin by computing the volume for the first two dispensers: each can hold 5 and five-twelfths cups of seeds.
Next, this text assumes an understanding that one scoop of seeds holds approximately 1 and one-sixth cups of product. Using this information, we determine how many scoops are needed to satisfy all three bird feeders' capacity.
By multiplying the first fraction's value with the reciprocal of the second fraction helps you divide fractions accurately:
(46 / 3) x (6 / 7) = (46 x 6) / (3 x 7) = 276 / 21
276 / 21 = 13 3/21
13 3/21 = 13 1/7 scoops
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Can you check if all these answers are correct?
Question 1: The side length c of the triangle is equal to: c 2 =a 2 +b 2 −2abcosC where a and b are the other two side lengths of the triangle, and C is the angle opposite side c. To solve for c, you can plug in the values of a, b, and C into the formula and solve for c. For example, if a=3, b=4, and C=60 ∘ , then you would plug in these values into the formula and solve for c as follows: c 2 =3 2 +4 2 −2⋅3⋅4cos60 ∘ c 2 =25 c= 25 =5 Therefore, the side length c of the triangle is equal to 5. Question 2: The angle C of the triangle is equal to: cosC= 2ab a 2 +b 2 −c 2 where a, b, and c are the other two side lengths of the triangle. To solve for C, you can plug in the values of a, b, and c into the formula and solve for C. For example, if a=3, b=4, and c=5, then you would plug these values into the formula and solve for C as follows: cosC= 2⋅3⋅4 3 2 +4 2 −5 2 =− 4 1 C=cos −1 (− 4 1 )≈109.47 ∘ Therefore, the angle C of the triangle is approximately 109.47 degrees. Question 3: The area of the triangle is equal to A= 2 1 absinC where a and b are the other two side lengths of the triangle, and C is the angle opposite side c. To solve for A, you can plug in the values of a, b, and C into the formula and solve for A. For example, if a=3, b=4, and C=60 ∘ , then you would plug in these values into the formula and solve for A as follows: A= 2 1 ⋅3⋅4sin60 ∘ =6 3 Therefore, the area of the triangle is equal to 6 3 . Question 4: The perimeter of the triangle is equal to: P=a+b+c where a, b, and c are the three side lengths of the triangle. To solve for P, you can simply add up the values of a, b, and c. For example, if a=3, b=4, and c=5, then you would add up these values to get P=12. Therefore, the perimeter of the triangle is equal to 12. Question 5: The centroid of the triangle is located at a point that is: One-third of the way from each vertex to the opposite side. Equidistant from all three vertices. On the medians of the triangle. To find the centroid of the triangle, you can use the following formula: G=( 3 a+b+c , 3 a+b+c , 3 a+b+c ) where (a,b,c) are the coordinates of the three vertices of the triangle.
Answer:
All of the answers appear to be correct based on the given formulas and values.
Karen can fit 25 vinyl records of
diameter 12 in. inside a cylindrical
carton with the same diameter.
What is the thickness of each
record if the
volume of the
carton is 100T
cubic inches?
carton
Round your
answer to the nearest hundredth
of an inch.
The value of the thickness of each record if the volume of the carton is 100π is,
⇒ 2.78 inches
We have to given that;
Karen can fit 25 vinyl records of diameter 12 in. inside a cylindrical carton with the same diameter.
We know that;
Volume of cylinder is,
⇒ V = πr²h
Hence, We get;
100π = π × (12/2)² × h
100 = 36h
h = 100 / 36
h = 50/18
h = 2.78 inches
Thus, The value of the thickness of each record if the volume of the carton is 100π is,
⇒ 2.78 inches
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Δ XYZ, shown below, is a 30° - 60° - 90° triangle.
8). Which leg is the shorter leg?
9). In a 30° - 60° - 90° triangle, the shorter leg is always opposite the _____° angle.
10). Which leg is the longer leg?
11). In a 30° - 60° - 90° triangle, the longer leg is always opposite the ____° angle.
12). If YZ = 5, then XY = ____ and XZ = _______.
13). If YZ = 6, then XY = ____ and XZ = _______.
14). If XY = 8, then YZ = _____ and XZ = _______.
15). If XY = 6, then YZ = _____ and XZ = _______.
Answer:
8). YZ
9). 30°
10). XY
11). 90°
12). XY=10 and XZ=5√3
13). XY=12 and XZ=6√3
14). YZ=4 and XZ=4√3
15). YZ=3 and XZ=3√3
Me pueden ayudar a realizar este ejercicio con método de sustitución, reducción e igualación, por favor
The solution of the system of equations is x = -5/17 and y = -16/17.
To do this, we can use a method called substitution. In this method, we solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation. This results in a new equation with only one variable, which can be solved to find the value of that variable. Once we know the value of one variable, we can substitute it into either equation to find the value of the other variable.
Let's apply this method to your system of equations:
5x - y/2 = -1 (Equation 1)
3x - 2y = 1 (Equation 2)
First, we'll solve Equation 1 for y in terms of x:
5x - y/2 = -1
y/2 = 5x + 1 (Add y/2 to both sides)
y = 10x + 2 (Multiply both sides by 2)
Now we substitute this expression for y into Equation 2:
3x - 2(10x + 2) = 1 (Substitute y = 10x + 2)
3x - 20x - 4 = 1
-17x = 5
x = -5/17
Now that we know the value of x, we can substitute it into either Equation 1 or Equation 2 to find the value of y. Let's use Equation 1:
5x - y/2 = -1
5(-5/17) - y/2 = -1
-25/17 - y/2 = -1
y/2 = -1 + 25/17
y/2 = -8/17
y = -16/17
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Complete Question:
What is the solution of the system of equations:
5x - y/2 = -1
3x - 2y = 1
Felix is purchasing a brownstone townhouse for $2,500,000. To obtain the mortgage, Felix is required to make a 18% down payment. Felix obtains a 30-year mortgage with an interest rate of 6.5%.
a) Determine the amount of the required down payment.
b) Determine the amount of the mortgage.
c) Determine the monthly payment for principal and interest.
quiz
Help me please with this question, been stuck on it for a couple days
Answer:
-4.01, -4, -7,
Step-by-step explanation:
It's as simple as substituting and solving. However, this one isnt so simple. The problem tries to trick you because each of the numbers that is provided is supposed to be substituted for x. For example, one of the numbers is 4, which means the equation would be -(4)+6[tex]\geq[/tex]10. But in this problem, the 4 would become a negative four due to the negative sign next to the x. In contrast, the negative numbers in the list provided would then become positive because negative times a negative is positive.