Answer:
4(4x - 2) = x + 4
16x - 8 = x + 4
15x = 12
x = 12/15 = 4/5
Answer:
x = 0.8
Step-by-step explanation:
4(4x - 2) = x + 4
16x - 8 = x + 4
16x - x = 4 + 8
15x = 12
x = 0.8
Marty’s parents paid $1,800 in electric bills last year. What was their average electric rate per month?
Answer: 150
Step-by-step explanation:
How many months are in a year? 12.
The average rate per month is therefore 1800/12 = 150.
Hope that helped,
-sirswagger21
Kaya figured out that she will need $47,592 to attend college. What is the amount rounded to the nearest ten thousand? Help meeee
Answer:
50,000
Step-by-step explanation:
ten thousand thousand hundreds tens ones
4 7 5 9 2
When rounding to the ten thousands, we look at the thousands place
If it is 5 or higher we round the ten thousands place up
7 is five or higher so we round the 4 up one place 4 becomes 5 and the rest becomes 0
5 0 0 0 0
Answer:
$50,000
Step-by-step explanation:
=> $47,592
While rounding off to the nearest thousand, we check the thousands place. If the digit in the thousands place is greater than 5, 1 will be added to the T. Th. place while if its less than 5, there will be no change and The digits except the ten thousands place will all become zero.
So,
=> $50,000
Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. AIB Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance policy holders is
A. (76.87, 80.33)
B. (72.5, 82.9)
C. (77.1, 78.3)
D. (74.1, 81.3)
E. (74.5, 80)
Answer:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.102[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Step-by-step explanation:
Information given
[tex]\bar X=77.7[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.6 represent the sample standard deviation
n=100 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=100-1=99[/tex]
Since the Confidence is 0.90 or 90%, the significance would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value for this case would be [tex]t_{\alpha/2}=1.66[/tex]
And replacing we got:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.10[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Can someone please help
Use the In key on your calculator to estimate
the logarithm.
In 44
Round your answer to the nearest thousandth.
Answer:
3.784
Step-by-step explanation:
A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 3 categories and the second of which is classified into 4 categories. The chi-square statistic for this test would have df equal to ______.
Answer:
Degrees of freedom for independence in chi-square statistic
ν = ( r-1) (s-1) =6
Step-by-step explanation:
Explanation:-
Given data chi-square test for independence is being used to evaluate the relationship between two variables
Given "A" is classified into 3 categories
Second 'B' is classified into 4 categories
In this chi-square test, we test if two attributes A and B under consideration are independent or not
We will assume that
Null Hypothesis : H₀: The two variables are independent
Degrees of freedom in chi-square test for independence
ν = ( r-1) (s-1)
Given data 'r' = 3 and 's' = 4
Degrees of freedom for independence
ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6
Test statistic
χ ² = ∑ [tex]\frac{(O-E)^{2} }{E}[/tex]
This question is based on Chi-square test. Therefore, the chi-square statistic for this test would have df equal to [tex]X^{2} = \sum \dfrac{(O-E)^2}{E}[/tex].
Given:
Chi-square test for independence is being used to evaluate the relationship between two variables . Given "A" is classified into 3 categories . Second 'B' is classified into 4 categories
According to the question,
In this chi-square test, we would be test if two attributes A and B under consideration are independent or not.
Let assumed that, null Hypothesis : H₀: The two variables are independent
Now, degrees of freedom in chi-square test for independence is,
⇒ ν = ( r-1) (s-1)
It is given that, 'r' = 3 and 's' = 4.
Thus, degrees of freedom for independence is,
ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6
Therefore, test statistic be,
[tex]X^{2} = \sum \dfrac{(O-E)^2}{E}[/tex]
Therefore, the chi-square statistic for this test would have df equal to [tex]X^{2} = \sum \dfrac{(O-E)^2}{E}[/tex].
For more details, prefer this link:
https://brainly.com/question/23879950
A study of women’s weights found that a randomly selected sample of 234 women had a mean weight of 157.3 lb. Assuming that the population standard deviation is 15.6 lb., construct a 95% confidence interval estimate of the mean weight of all women.
A. (145.3, 160.5)
B. (155.3, 159,3)
C. (165.5, 173.5)
D. (185.7, 199.3)
Answer:
[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]
[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]
So on this case the 95% confidence interval would be given by (155.301;159.299)
And the best option would be:
B. (155.3, 159,3)
Step-by-step explanation:
Information given
[tex]\bar X=157.3[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma =15.6[/tex] represent the population standard deviation
n=234 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence level is is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]
[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]
So on this case the 95% confidence interval would be given by (155.301;159.299)
And the best option would be:
B. (155.3, 159,3)
Write an expression to represent: Four less than the quotient of a number x and 5.
Answer:
[tex]\frac{x}{5} - 4[/tex]
Step-by-step explanation:
You are dividing x by 5 and then subtracting 4.
Answer:
x/5 - 4
Step-by-step explanation:
The quotient of a number x and 5 refers to division of both terms.
x/5
Four less than the quotient refers to subtraction.
x/5 - 4
A homogeneous second-order linear differential equation, two functions y 1y1 and y 2y2, and a pair of initial conditions are given. First verify that y 1y1 and y 2y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x.
y'' + 49y = 0; y1 = cos(7x) y2 = sin(7x); y(0) = 10 y(0)=-4
1.Why is the function y, = e * a solution to the differential equation?
A. The function y1 =e 4X is a solution because when the function and its indefinite integral, , are substituted into the equation, the result is a true statement.
B. The function y1 = e 4X is a solution because when the function and its second derivative, y1" = 16 e 4x, are substituted into the equation, the result is a true statement.
2. Why is the function y2 solution the differential equation?
A. The function y2 = e 4x is a solution because when the function and its indefinite integral, are substituted into the equation, the result a true statement. The function y2 = e 4X is a solution because when the function and its second derivative, y2" = 16 e -4x are substituted into the equation, the result is a true statement. The particular solution of the form y = c, y, +c,y2 that satisfies the initial conditions y(0) 2 and y'(0) = 9 is y =.
Answer:
[tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex]
B.
B.
[tex]y = \frac{17}{8}e^4^x - \frac{1}{8}e^-^4^x[/tex]
Step-by-step explanation:
Question 1:
- We are given a homogeneous second order linear ODE as follows:
[tex]y'' + 49y = 0[/tex]
- A pair of independent functions are given as ( y1 ) and ( y2 ):
[tex]y_1 = cos ( 7x )\\\\y_2 = sin ( 7x )[/tex]
- The given ODE is subjected to following initial conditions as follows:
[tex]y ( 0 ) = 10\\\\y ' ( 0 ) = -4[/tex]
- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:
[tex]y = c_1y_1 + c_2y_2[/tex]
Solution:-
- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.
- Formulate the second derivatives of both functions y1 and y2 as follows:
[tex]y'_1 = -7sin(7x) , y''_1 = -49cos(7x)\\\\y'_2 = -7cos(7x) , y''_2 = -49sin(7x)\[/tex]
- Now plug the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.
[tex]y''_1 + 49y_1 = 0\\\\-49cos(7x) + 49cos ( 7x ) = 0\\0 = 0\\\\y''_2 + 49y_2 = 0\\\\-49sin(7x) + 49sin ( 7x ) = 0\\0 = 0\\\\[/tex]
- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.
- The complete solution to a homogeneous ODE is given in the form as follows:
[tex]y = c_1y_1 + c_2y_2\\\\y = c_1*cos(7x) + c_2*sin(7x)\\[/tex]
- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,
[tex]y (0) = c_1cos ( 0 ) + c_2sin ( 0 ) = 10\\\\y'(0) = -7c_1*sin(0) + 7c_2*cos(0) = -4\\\\c_1 ( 1 ) + c_2 ( 0 ) = 10, c_1 = 10\\\\-7c_1(0) + 7c_2( 1 ) = -4 , c_2 = -\frac{4}{7}[/tex]
- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:
[tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex] .... Answer
Question 2
- We are given a homogeneous second order linear ODE as follows:
[tex]y'' -16y =0[/tex]
- A pair of independent functions are given as ( y1 ) and ( y2 ):
[tex]y_1 = e^4^x\\\\y_2 = e^-^4^x[/tex]
- The given ODE is subjected to following initial conditions as follows:
[tex]y( 0 ) = 2\\y'( 0 ) = 9[/tex]
- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:
[tex]y = c_1y_1 + c_2y_2[/tex]
Solution:-
- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.
- Formulate the second derivatives of both functions y1 and y2 as follows:
[tex]y'_1 = 4e^4^x , y''_1 = 16e^4^x\\\\y'_2 = -4e^-^4^x , y''_2 = 16e^-^4^x[/tex]
- Now substitute the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.
[tex]y''_1 - 16y_1 = 0\\\\16e^4^x - 16e^4^x = 0\\\\0 = 0\\\\y''_2 - 16y_2 = 0\\\\16e^-^4^x - 16e^-^4^x = 0\\\\0 = 0[/tex]
- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.
- The complete solution to a homogeneous ODE is given in the form as follows:
[tex]y = c_1y_1 + c_2y_2\\\\y = c_1*e^4^x + c_2*e^-^4^x[/tex]
- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,
[tex]y ( 0 ) = c_1 * e^0 + c_2 * e^0 = 2\\\\y' ( 0 ) = 4 c_1 * e^0 - 4c_2 * e^0 = 9\\\\c_1 + c_2 = 2 , 4c_1 - 4c_2 = 9\\\\c_1 = \frac{17}{8} , c_2 = -\frac{1}{8}[/tex]
- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:
[tex]y = \frac{17}{8} e^4^x - \frac{1}{8}e^-^4^x[/tex] .... Answer
In a certainâ state, the recent average critical reading standardized test score was 514. Assume that the standard deviation is 50 and that standardized test scores are Normally distributed. Complete partsâ (a) andâ (b) below. Include a Normal curve for each part.
Required:
a. What percentage of standardized test takers scored 550 or less?
b. What percentage of standardized test takers scored 524?
Answer:
a) Percentage of standardized test takers that scored 550 or less = 76.4%
b) Percentage of standardized test takers that scored 524 = 0.782%
Step-by-step explanation:
This is a normal distribution problem with
Mean = μ = 514
Standard deviation = σ = 50
a) Percentage of standardized test takers scored 550 or less = P(x ≤ 550)
We first normalize or standardize 550
The standardized score for any is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (550 - 514)/50 = 0.72
To determine the required probability
P(x ≤ 550) = P(z ≤ 0.72)
We'll use data from the normal distribution table for these probabilities
P(x ≤ 550) = P(z ≤ 0.72) = 0.76424 = 76.424%
The normal curve for this question and the b part are sketched in the first attached image to this solution.
b) Percentage of standardized test takers that scored 524 = P(x = 524)
On standardizing,
z = (x - μ)/σ = (524 - 514)/50 = 0.20
For this part, since it's an exact probability, we will use the normal distribution formula
P(z = Z) = [1/(σ√2π)] × e^(-z²/2)
Since z = (x - μ)/σ
It can be written properly as presented in the second attached image to this question.
Putting x = 524 or z = 0.20 in this expression, we get
P(x = 524) = P(z = 0.20) = 0.0078208539 = 0.782%
Hope this Helps!!!
Find the LCM of the set of algebraic expressions.
28x2,49xy, 28y
Answer
Answer:
196x^2y
Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
i need help on this. anyone ?
Answer:
Read below
Step-by-step explanation:
To copy a segment, you have to open your compass to the length of the given segment. The instructions say to have an endpoint at R, so, with the compass open to the length of the given line segment, place one end of the compass at R and draw an arc that intersects the line that R lies on. This new segment is congruent to the given segment.
I hope this helps!
Please answer this correctly
Answer:
13 students
Step-by-step explanation:
At least 30 and fewer than 67 makes it 30-66
So,
30-66 => 13 students
Answer:
16
Step-by-step explanation:
There are two columns in the diagram.
The column headed stem represents tens while the column headed leaf represents units. e.g. 2 3 = 23
So we just have to count how many of the numbers are less than 8 in the 6th Stem column and all the numbers below it, which are:
20, 23, 28, 31, 31, 34, 38, 40, 44, 50, 51, 53, 54, 65, 65, 66
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down,drag into the correct position in the answer box.Release your mouse button when the item is place. If you change your mind,drag the item to the trash can,click the trash and to clear all your answers. Divide the following polynomials,then place the answer in the proper location on the grid. Write the answer in descending powers of x. 9x^2-18x-7 divided by (3x+1)
Answer:
[tex]\boxed{\sf \ \ 9x^2-18x-7 \ \ divided \ by \ (3x+1) \ is \ (3x-7) \ }[/tex]
Step-by-step explanation:
Hello,
let's find a and b reals so that
[tex]9x^2-18x-7=(3x+1)(ax+b)[/tex]
[tex](3x+1)(ax+b)=3ax^2+(3b+a)x+b[/tex]
we identify the terms in [tex]x^2[/tex]
9 = 3a
we identify the terms in x
-18 = 3b + a
we identify the constant terms
-7 = b
so ti goes with a = 9/3 = 3, b = -7
so we can write
[tex]9x^2-18x-7=(3x+1)(3x-7)[/tex]
so [tex]9x^2-18x-7 \ divided \ by \ (3x+1) \ is \ (3x-7)[/tex]
hope this helps
1/5divided by (-5/7)
Answer:
-0.28
Step-by-step explanation:
(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28
Answer:
[tex]-7/25[/tex]
Step-by-step explanation:
[tex]1/5 \div -5/7[/tex]
Do the reciprocal of the second fraction.
[tex]1/5 \times 7/-5[/tex]
Multiply the first fraction by the reciprocal of the second fraction.
[tex]7/-25=-0.28[/tex]
The answer in decimal form is -0.28.
The average lifetime of a set of tires is 3.4 years. The manufacturer will replace any set of tires failing within three years of the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that the tires will fail within three years of the date of purchase?
Answer: the probability that the tires will fail within three years of the date of purchase is 0.12
Step-by-step explanation:
The average lifetime of a set of tires is 3.4 years. It means that μ = 3.4
Decay parameter, m = 1/3.4 = 0.294
The probability density function is
f(x) = me^-mx
Where x is a continuous random variable representing the time interval of interest(the reliability period that we are testing)
Since x = 3 years,
Therefore, the probability that the tires will fail within three years of the date of purchase is
f(3) = 0.294e^-(0.294 × 3)
f(3) = 0.294e^- 0.882
f(3) = 0.12
Elsa is framing some photos. If she has three frames and put two photos each frame, what fraction shows one photo
Answer:
1/6Step-by-step explanation:
Number of frames =3 frames
If each frames contain 2 photos, the total number of photos in all the 3 frames will be 3*2 = 6photos
Since we have 6 photos in total, the fraction that shows one photo will be ratio of one out of the six photos and this is represented as 1/6
Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Develop the least squares estimated regression equation. What is the coefficient of determination? x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2
Answer:
Step-by-step explanation:
Hello!
Given the independent variable X and the dependent variable Y (see data in attachment)
The regression equation is
^Y= b₀ + bX
Where
b₀= estimation of the y-intercept
b= estimation of the slope
The formulas to manually calculate both estimations are:
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]
[tex]b_0= \frac{}{y} - b*\frac{}{x}[/tex]
n=7
∑X= 42
∑X²= 292
∑Y= 49
∑Y²= 403
∑XY= 249
[tex]\frac{}{y} = \frac{sumY}{n} = \frac{49}{7} = 7[/tex]
[tex]\frac{}{x} = \frac{sumX}{n} = \frac{42}{7} = 6[/tex]
[tex]b= \frac{249-\frac{42*49}{7} }{292-\frac{42^2}{7} }= -1.13[/tex]
[tex]b_0= 7- (-1.13)*6= 13.75[/tex]
^Y= 13.75 - 1.13X
Using the raw data you can calculate the coefficient of determination as:
[tex]R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]}[/tex]
[tex]R^2= \frac{(-1.13)^2[292-\frac{(42)^2}{7} ]}{[403-\frac{(49)^2}{7} ]}= 0.84[/tex]
This means that 84% of the variability of the dependent variable Y is explained by the response variable X under the model ^Y= 13.75 - 1.13X
I hope this helps!
Which lists the ratios in order from least to greatest 2:9,1:6,7:36
Answer:
1:6, 7:36, 2:9
Step-by-step explanation:
2 : 9 → 8 : 36
1 : 6 → 6 : 36
7 : 36
Least → Greatest
1:6, 7:36, 2:9
Please answer this correctly
Answer:
50
Step-by-step explanation:
The probability of it landing on yellow or blue is 5 out of 7 total possibilities.
5/7
Multiply by 70.
5/7 × 70
350/7
= 50
Answer:
50 times
Step-by-step explanation:
Yellow or blue is 5/7 of the spinner
Multiply 70 by 5/7 to find the prediction of the number of times it will land there
70(5/7) = 50
Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2? (6 points) Question 7 options: 1) x3 − 2x2 − 3x + 6 2) x3 − 3x2 − 5x + 15 3) x3 + 2x2 − 3x − 6 4) x3 + 3x2 − 5x − 15
Answer:
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
Step-by-step explanation:
A nth order polynomial f(x) has roots [tex]x_{1}, x_{2}, ..., x_{n}[/tex] such that [tex]f(x) = (x - x_{1})*(x - x_{2})*...*(x - x_{n}}[/tex],
Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2?
So
[tex]x_{1} = x_{2} = \sqrt{3}[/tex]
[tex]x_{3} = -2[/tex]
Then
[tex](x - \sqrt{3})^{2}*(x - (-2)) = (x - \sqrt{3})^{2}*(x + 2) = (x^{2} -2x\sqrt{3} + 3)*(x + 2) = x^{3} + 2x^{2} - 2x^{2}\sqrt{3} - 4x\sqrt{3} + 3x + 6[/tex]
Since [tex]\sqrt{3} = 1.73[/tex]
[tex]x^{3} + 2x^{2} - 3.46x^{2} - 6.93x + 3x + 6 = x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
[tex]solve for "m" t=\frac{ms}{m+n}[/tex]
Answer:
[tex]\boxed{\sf \ \ \ m = -\dfrac{tn}{t-s} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let s assume that m+n is different from 0
we have this equation and we need to find m as a function of t, s, and n
[tex]t=\dfrac{ms}{m+n}[/tex]
<=>
[tex](m+n)*t=ms\\\\<=> tm+tn=sm\\<=> (t-s)m = -tn\\<=> m = -\dfrac{tn}{t-s}[/tex]
for t-s different from 0, so t different from s
hope this helps
someone pls help me! ❤️❤️❤️
Answer:
(x-1) ( x -i) (x+i)
Step-by-step explanation:
x^3 -2x^2 +x-2
Factor by grouping
x^3 -2x^2 +x-2
x^2(x-2) +1(x-2)
Factor out (x-2)
(x-2) (x^2+1)
Rewriting
(x-1) ( x^2 - (-1)^2)
(x-1) ( x -i) (x+i)
Answer:
Should be b
Step-by-step explanation:
Since it's a multiple choice question you know that -2 or 2 has to be a root for the cubic.
You can test both -2 and 2 and see that replacing x for 2 has the expression evaluate to 0.
Then, since you know the imaginary roots have to be conjugates, you get B.
Find the solutions to x^2 = 8
Answer:
x=2√2 is the answer
Step-by-step explanation:
x²=8
TAKING SQUARE ROOT ON BOTH SIDES
√x²=√8
x=√2×2×2
x=√2²×√2
x=2√2
i hope this will help you
Answer:
The value of x is -2.828 or 2.828
Step-by-step explanation:
In order to eliminate of square of x, you have to square root both sides :
[tex] {x}^{2} = 8[/tex]
[tex] \sqrt{ {x}^{2} } = ± \sqrt{8} [/tex]
[tex]x = \sqrt{8} \\ x = 2 \sqrt{2} \: or \: 2.828[/tex]
[tex]x = - \sqrt{8} \\ x = - 2 \sqrt{2} \: or \: - 2.828[/tex]
What is the slope of a line that is perpendicular to the line 2y – 3x = 8?
Answer:
[tex] = \frac{3}{2} [/tex]
Step-by-step explanation:
[tex]y = mx + c[/tex]
Here,
m => slopec => interceptIn this equation ,
[tex]2y - 3x = 8[/tex]
to find the value of m or the value of slope we have to solve for y
Let's solve,
[tex]2y - 3x = 8 \\ 2y = 8 + 3x \\ \frac{2y}{2} = \frac{8 + 3x}{2} \\ y = 4 + \frac{3x}{2} \\ y = \frac{3x}{2} + 4[/tex]
So, the slope is,
[tex] = \frac{3}{2}[/tex]
2x^2+8x = x^2-16
Solve for x
Answer:
x=-4
Step-by-step explanation:
[tex]2x^2+8x=x^2-16[/tex]
Move everything to one side:
[tex]x^2+8x+16=0[/tex]
Factor:
[tex](x+4)^2=0[/tex]
By the zero product rule, x=-4. Hope this helps!
Answer:
x=-4
Step-by-step explanation:
Move everything to one side and combine like-terms
x²+8x+16
Factor
(x+4)²
x=-4
$5.60 is what perecentage of $17.50?
Answer:
To find it's percentage divide $5.60 by
$17.50 and multiply it by 100%
That is
5.60/ 17.50 × 100%
= 32%
Hope this helps you
Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation Can the method of undetermined coefficients together with superposition be applied to find a particular solution of the given equation?
A. No, because the right side of the given equation is not the correct type of function
B, Yes °
C. No, because the differential equation is not linear.
D. No, because the differential equation does not have constant coefficients.
Answer:
D. No, because the differential equation does not have constant coefficients.
Step-by-step explanation:
The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.
Find the diagonal of a square whose sides measure 3x square root of 2
Answer:
that means each side equals 8
Step-by-step explanation:
Let x1 = 12, y1 = 15, and y2 = 3. Let y vary inversely with x. Find x2.
Answer:
x2 = 60
Step-by-step explanation:
If the variables x and y are inversely proportional, the product x * y is a constant.
So using x1 and y1 we can find the value of this constant:
[tex]x1 * y1 = k[/tex]
[tex]12 * 15 = k[/tex]
[tex]k = 180[/tex]
Now, we can use the same constant to find x2:
[tex]x2 * y2 = k[/tex]
[tex]x2 * 3 = 180[/tex]
[tex]x2 = 180 / 3 = 60[/tex]
So the value of x2 is 60.
A robotic machine fills containers with an acid solution at the rate of 50 + 5 t milliliters (mL) per second, where t is in seconds and 0 ≤ t ≤ 60 . How many mL are put into a container in 60 seconds? Evaluate your answer to a whole number.
Answer:
12,000
Step-by-step explanation:
The machine fills the containers at a rate of 50+5t milliliters (mL) per second.
Therefore, the rate of change of the number of containers, N is:
[tex]\dfrac{dN}{dt}=50+5t, 0\leq t\leq 60[/tex]
[tex]dN=(50+5t)dt\\$Taking integrals of both sides\\\int dN=\int (50+5t)dt\\N(t)=50t+\frac{5t^2}{2}+C $(C a constant of integration)\\\\When t=0, , No containers are filled, therefore:$ N(t)=0\\0=50(0)+\frac{5(0)^2}{2}+C\\C=0\\$Therefore, N(t)=50t+2.5t^2[/tex]
When t=60 seconds
[tex]N(60)=50(60)+2.5(60)^2\\N(60)=12000$ mL[/tex]
Therefore, 12,000 milliliters of acid solution are put into a container in 60 seconds.