a positive real number is 4 less than another. If the sum of the square of the two numbers is 62, find the numbers.
Answers
We have two positive numbers x and y.
We know that x is 4 less than y, so we can write:
\(x=y-4\)We know that the sum of the square of the two numbers is 62, so we can write:
\(x^2+y^2=62\)If we replace x with y we can find the value of y as:
\(\begin{gathered} x^2+y^2=62 \\ (y-4)^2+y^2=62 \\ (y^2-8y+16)+y^2=62 \\ 2y^2-8y+16-62=0 \\ 2y^2-8y-^{}46=0 \\ 2(y^2-4y-23)=0 \\ y^2-4y-23=0 \end{gathered}\)We have to calculate the roots of y:
\(\begin{gathered} y=\frac{-(-4)\pm\sqrt[]{(-4)^2-4\cdot1\cdot(-23)}}{2\cdot1} \\ y=\frac{4\pm\sqrt[]{16+92}}{2} \\ y=\frac{4\pm\sqrt[]{108}}{2} \\ y\approx\frac{4\pm10.4}{2} \\ y_1\approx\frac{4-10.4}{2}=-3.2\longrightarrow\text{Not valid (it has to be positive)} \\ y_2\approx\frac{4+10.4}{2}=\frac{14.4}{2}=7.2 \end{gathered}\)The value of y is 7.2.
Then, the value of x is 7.2 - 4 = 3.2.
We can check the squares as:
\(\begin{gathered} x^2+y^2 \\ 3.2^2+7.2^2 \\ 10.24+51.84 \\ 62.08 \end{gathered}\)The difference between 62.08 and 62 is an error of approximation when rounding the square root of 108.
Answer: the numbers are approximately 3.2 and 7.2.
Related Questions
Find x.
Do not round your answer
12 cm
6 cm
5 cm
Answers
The value of x from the given diagram is 16.6
Secant-secant theoremIn order to determine the value of x from the given figure, we will use the secant-secant theorem shown by the equation.
(6 +12) * 6 = (5 + x) * 5
Expand
36+72 = 25 + 5x
108 = 25 + 5x
5x = 108 - 25
5x = 83
x = 83/5
x = 16.6
Hence the value of x from the given diagram is 16.6
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(1 3/4 + 2 3/8) + 5 7/8=
Answers
Answer:
10
Step-by-step explanation:
help pls i'm lost plssssssssssss
Answers
James T-shirt business uses the demand function P = -Q+31 and the supply function P = Q-17. According to these functions, what will the
equilibrium point (P.Q) be for James T-shirt business?
Answers
The equilibrium point for James T-shirt business is (P, Q) = (7, 24).
To find the equilibrium point (P, Q) for James T-shirt business
we need to set the demand function equal to the supply function and solve for the values of P and Q.
Demand function: P = -Q + 31
Supply function: P = Q - 17
Setting them equal:
-Q + 31 = Q - 17
Adding Q to both sides and subtracting 31 from both sides:
2Q = 48
Dividing both sides by 2:
Q = 24
Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.
P = Q - 17
P = 24 - 17
P = 7
Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).
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3. Use the equation y = 3.2x + 5
to complete in the table.
Type the answers in the boxes below.
1
2
4
3. Is y proportional to x and y?
Select the correct choice from the drop down.
Explain why or why not.
Type your response in the space below.
Answers
Answer/Step-by-step explanation:
Plug in the value of x in each row into the equation, y = 3.2x + 5, to find their corresponding y values respectively.
When x = 1:
y = 3.2(1) + 5
y = 3.2 + 5
y = 8.2
When x = 2:
y = 3.2(2) + 5
y = 6.4 + 5
y = 11.4
When x = 4:
y = 3.2(4) + 5
y = 12.8 + 5
y = 17.5
You have the following table:
x | y
1 | 8.2
2 | 11.4
4 | 17.5
To find out if y is proportional to x, find the ratio of y to x of each pair in the table.
x | y | ratio of y to x (y/x)
1 | 8.2 | 8.2/1 = 8.2
2 | 11.4 | 11.4/2 = 5.7
4 | 17.5 | 17.5/4 = 4.375
As you can see, here is no equal ratio. Each pair has a different ratio. Therefore, the a proportional relationship does not exist between x and y.
What is another word for magnitude?
A large
B size
C small
D attract
Please help!
Answers
Answer: D ( sorry if i get it wrong but i tried)
Step-by-step explanation:
Answer:
so it's D
Step-by-step explanation:
sorry for copying i just need brainly crowns i lost all of them
Assume a recent sociological report states that university students drink 4.14 alcoholic drinks per week on average, with a standard deviation of 1.5301. Suppose Jason, a policy manager at a local university, decides to take a random sample of 150 university students to survey them about their drinking habits.
Determine the mean of the sampling distribution of the sample mean alcohol consumption. Provide your answer with precision to two decimal places
Answers
A) Sample mean = 4.14 alcoholic drinks per week
B) Sample standard deviation = 0.12
How to find the mean and standard deviationWe are given the following in the question:
Population mean, μ = 4.14Sample size, n = 150Population standard deviation, σ = 1.5301We have to estimate the following:
A) Sample mean alcohol consumption
\(\bar{\text{x}}=\mu=4.14\)
B) Standard deviation of the sampling distribution of the sample mean alcohol
\(\text{s}=\dfrac{\sigma}{\sqrt{\text{n}}} =\dfrac{1.5301}{\sqrt{150}} =0.12493\thickapprox0.12\)
Thus, the sample mean is 4.14 alcoholic drinks per week and sample standard deviation is 0.12 alcoholic drinks per week.
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A data set contains an independent and a dependent variable. Which must be true of the data set if a linear function can
be used to represent the data?
O The set must have a constant additive rate of change.
The set must have a constant multiplicative rate of change.
O The values in the set must be positive.
O The values in the set must be increasing.
Mark this and return
Save and Exit
Next
Submit
Answers
The answer choice which must be true regarding the linear function is; The set must have a constant additive rate of change.
Which is true about a linear function?Since a linear function typically takes the slope-intercept form; f(x) = mx +c.
It therefore follows that the equation must have a constant slope m, which is the described additive constant rate of change.
It therefore follows that, the answer choice which is true regarding the linear function is therefore; The set must have a constant additive rate of change.
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3 units
Which expression can be used which expression can be used to represent the
volume of this prism?
'6 units
o 8 x 9 units
8 units
o 6 1l units
o 48 x 3 units
14 x 3 units
Answers
Answer:
Expression that represents the volume of the prism in cubic units is V = A × H cubic units where A is the base area and H is the height of the prism. The volume (V) of a prism is given by the area, (A) of the base multiplied by the height, (H) of the prism. Explanation: V = B × H cubic units.
Step-by-step explanation:
Suppose y varies inversely with x, and y = 36 when x=112
What inverse variation equation relates x and y ?
Answers
The inverse variation equation that relates x and y is x = 4032 / y.
What is the equation that relates x and y?if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable
The equation that represents inverse proportion : x = b/y
where b = constant of proportionality
112 = b /36
b = 36 x 112 = 4032
The equation : x = 4032 / y
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If i purchase 25 candy bars priced at 3/$1.00,how much do I owe you
Answers
Every three candy bars cost a dollar.
Divide 25 by three.
$8.33
y=x^2-2x+7
i need help finding the axis of symmetry,the domain, the y-intercept and x intercept
Answers
The axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .
Explain about the features of parabolic function?A parabolic function is one that satisfies the formula f(x) = ax2 + bx + c and, when represented graphically in two dimensions, has the shape of a parabola. Any quadratic equation with just a second degree in x is the equation for a parabolic function.
The following characteristics define a basic parabola:
The y-axis, a symmetry axis, is where it is symmetric.At the origin, marking the minimal turning point, y has its minimum value. It is sometimes referred to as the parabola's vertex.The parabola's arms are infinitely long.Thus, from the given graph the value are obtained as:
the axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .Know more about parabolic function
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T=A3/2 with out rational exponents
Answers
After the conversion, we get T² = 1/3 A
It is given that
T = \(A^{\frac{3}{2} }\)
We have to convert the equation without rational exponents
T³ = A²
1/2 T = A³
T² = A³
T² = 1/3A
Therefore we get T² = 1/3 A without using the exponents.
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99 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Two stockpots are similar cylinders. The smaller stockpot has a height of 10 inches and a radius of 2.5 inches, the volume of larger one is 628.32 cubic inches.
We know that, to find volume:
Volume = π * \(r^2\) * h
For the smaller stockpot:
Radius (r) = 2.5 inches
Height (h) = 10 inches
Volume = π * (2.5)² * 10 ≈ 196.35 cubic inches
For the larger stockpot:
Radius (r) = 2.5 inches
Height (h) = 16 inches
Volume = π * (2.5)² * 16
≈ 628.32 cubic inches
Thus, the volume of larger one is 628.32 cubic inches.
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On a certain hot summer day, 511 people use the public swimming pool. Daily prices are $1.50 per child and $2.00 per adult. The receipt for admission totaled 854.50$ how many children and how many adults swim at the public pool that day?
Answers
Answer:
303 kids and 200 adults
Step-by-step explanation:
sue eats 3/8 of a cherry pie. Jan
eats
Answers
Answer:
If you're saying Jan ate 1/4 of what was left. How much of the pie did Jan eat?
then the answer is 5/32
Step-by-step explanation:
1. Given the following information about trig ratios, determine the value of sin 0 and cot 0. Make sure you answer
is given in simplified radical form.
sec and sin 0 <0
7
2
Answers
The solution is, sinФ = √45/7 & cotФ =2/√45.
What is trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
here, we have,
secФ = 7/2
so, cosФ = 2/7
cos^2Ф = 4/49
i.e. sin^2Ф = 1- cos^2Ф
= 1 - 4/49
= 45/49
so, sinФ = √45/7
now, we know,
cotФ = cosФ/sinФ
= 2/√45
Hence, The solution is, sinФ = √45/7 & cotФ =2/√45.
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help me with this question
Answers
Answer:
A
Step-by-step explanation:
The opposite of 6 IS -6
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeebrainliest
Answers
Answer:
1/3
Step-by-step explanation:
Divide the numerator and denominator by 6.
6/18 = 1/3
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that exactly 10 flights arrive on time.
Answers
Probability that exactly 10 flights arrive on time is 53.33%.
Given that,
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation.
Recently, Southwest Air had the best rate with 80% of its flights arriving on time.
Total number flights in sample = 15
Probability that exactly 10 flights arrive on time is,
P = 10/15 × 80%
= 0.5333
= 53.33%
Hence the required probability is 53.33%.
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Find the equation of the line through the points (9,−2) and (1,6).
You should get your answer in slope-intercept form.
Answers
Answer: y=-x+7
Step-by-step explanation:
Answer:
Your given points: (9,-2)and (1,6)
x1=9
y1=-2
x2=1
y2=6
Step-by-step explanation:
To find slope take the points you got from graph and put it into the equation y2-y1/x2-x1
6-(-2)/1-9=6+2/1-9=8/-8=-1
SLOPE IS m=-1
Then take that slope u got and plug into this equation to find equation of the line
y-y1=m(x-x1)
y-(-2)=-1(x-9)
y+2=-x+9
-2. -2
——————
y=-x+7 ANSWER CHECK
isaac invested $77,000 in an account paying interest rate of 4.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be the count after 12 years?
Answers
Answer:
$133,728 would be in the count after 12 hours.
Step-by-step explanation:
Continuous compounding:
The amount of money, in continuous compounding, after t years, is given by:
\(P(t) = P(0)e^{rt}\)
In which P(0) is the initial deposit and r is the interest rate, as a decimal.
Isaac invested $77,000 in an account paying interest rate of 4.6% compounded continuously.
This means that \(P(0) = 77000, r = 0.046\)
Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be the count after 12 years?
This is P(12). So
\(P(t) = P(0)e^{rt}\)
\(P(12) = 77000e^{0.046*12} = 133728\)
$133,728 would be in the count after 12 hours.
The population of a rural city follows the exponential growth model P(t)=3400^0.0371t where t is the number of years after 1986 . a) Use this model to approximate the population in 2030.
Answers
After answering the presented question, we can conclude that expressions Therefore, the population of the rural city in 2030 is approximately 11,014.18.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
To approximate the population in 2030, we need to find the value of P(t) when t = 44, since 2030 is 44 years after 1986.
Using the given exponential growth model, we have:
\(P(t) = 3400^(0.0371t)\\P(44) = 3400^(0.0371*44)\\P(44) = 3400^1.6334\\P(44) = 11014.18\\\)
Therefore, the population of the rural city in 2030 is approximately 11,014.18.
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Tina pet sits to earn extra money. She charges a flat service fee of $20, plus $15 per day. If one of her customers spent less than $125, which of the following inequalities could be used to solve for x, the number of days the customer paid for pet sitting?
Answers
Therefore, **x < 7** is the inequality that may be utilized to find x
What is inequality?A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).
For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".
Let x represent how many days the client paid for pet sitting.
$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.
We are aware that the customer's purchase was under $125. Consequently, we can write:
20 + 15x < 125
Putting this disparity simply:
15x < 105
x < 7
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What is the volume of this figure
a
12 cubic units
b
16 cubic units
c
28 cubic units
d
40 cubic units
Answers
Answer:
c
28 cubic units
Step-by-step explanation:
from the given graph: state it's
a) amplitude
b) period
c) function of the graph:
Answers
Step-by-step explanation:
The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.
The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).
Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).
Function of graph:
By playing around in a graphing calculator, I got the equation to be
2 (cos (x + pi/2)).
the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.
What is the value of u?
Answers
Answer:
66-26 = 40
Step-by-step explanation:
u = 40 degrees
what are the similarities and differences in linear and exponential in intercepts?
what are the similarities and differences in linear and exponential in domain and range?
what are the similarities and differences in linear and exponential in asymptotes?
what are the similarities and differences in linear and exponential in misc.?
Answers
Answer:
What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.
Graph of linear function
Graph of linear function
A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.
A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.
Examples of linear functions include:
If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.
Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.
If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.
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Exponential Functions
What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.
Graphs of exponential functions
Graphs of exponential functions
An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.
An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.
Examples of exponential functions include:
Step-by-step explanation:
What is the population standard deviation?
{5,8,8,5}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2.
Answers
5, 8, 8, 5 has a population standard deviation of 3
Given,
The population is
{5, 8, 8, 5}
The population's mean is calculated as follows:
Sum of terms / Number of terms
Calculate the values and then replace them in the equation.
Sum equals 5 + 8 + 8 + 5 = 26
Number of terms = 4
The population's average is 26 / 4 = 6.5
The population's variance is equal to (5 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (5 - 6.5)²
= (-1.5) (-1.5)² + (1.5) (1.5)² + 1.5² + (-1.5) (-1.5)²
= 2.25 + 2.25 + 2.25 + 2.25
= 9
The population's standard deviation is equal to
= 3
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how many wall are there in your room? what are the shape of the floor and ceiling in your room ? how can you find the area of each shape?prepare the answer. present the conclusion in the form of report. plz answer the question in right.
Answers
My room is made up of four walls, both the floor and the ceiling are rectangular in shape.
There are four walls in my room. The shape of the floor is a rectangle and given that the ceiling is the same form above the floor, it is also shaped as a rectangle.
To get the area of a rectangle, you use this formula since my floor and ceiling are rectangle.
Area = L * W
where
L = length
W= width
But if you have a square floor and ceiling, the area of a square is
Area = s²
given that it is side * side.
In conclusion, there are 4 walls in every room. The shape of the ceiling or floor could be a rectangle or a square. It depends on your room and its measurements. To get the area, multiply the length by the width.
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