Answers
Answer:
{-1, -8}
Step-by-step explanation:
Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".
Squaring both sides of the given equation, we get:
1 - 3x = x^2 + 6x + 9, or x^2 + 6x + 8 + 3x, or
x^2 + 9x + 8 = 0. Factoring, we get: (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.
Answer:
I hope the given equation is :
{-1, -8}
First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,
1 - 3x = (x + 3)²
1 - 3x = (x + 3)*(x + 3) Since a² = a * a
1 - 3x = x² + 3x + 3x + 3² By multiplication.
1 - 3x = x² + 6x + 9 Combine the like terms.
x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation
x² + 9x + 8 = 0 Combine the like terms.
Next step is to factor the trinomial to solve the above equation for x.
For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.
So, 8 = 1 * 8
Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,
x² + 1x + 8x + 8 = 0
(x² + 1x) + (8x + 8) = 0 Group the terms.
x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.
(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).
So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.
Hence, x = -1 and - 8.
Next step is to plug in -1 and -8 in the original equation to cross check the solutions.
For x = -1,
Simplify each sides separately.
2 = 2
2 = 2 is correct. So, x = -1 satisfy the equation.
Hence, x = -1 is the real solution of the given equation.
Similarly let's plug in x = -8 now. So,
Simplify each sides separately.
5 = 2
5 = 2 is not true. So, x = -8 is the extraneous solution.
Therefore, the only solution is x = -1.
Hence, the correct choice is C.
Hope this helps you!
Step-by-step explanation:
mark brainlies plssssssssss
Related Questions
Engineers want to design passenger seats in commercial aircraft so that they are wide enough to fit 95 percent of adult men. Assume that adult men have hip breadths that are normally distributed with a mean of 14.4 inches and a standard deviation of 1.1 inches. Find the 95th percentile of the hip breadth of adult men. Round your answer to one decimal place; add a trailing zero as needed. The 95th percentile of the hip breadth of adult men is [HipBreadth] inches.
Answers
Answer:
[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]
And if we solve for a we got
[tex]a=14.4 +1.64*1.1=16.204[/tex]
The 95th percentile of the hip breadth of adult men is 16.2 inches.
Step-by-step explanation:
Let X the random variable that represent the hips breadths of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(14.4,1.1)[/tex]
Where [tex]\mu=14.4[/tex] and [tex]\sigma=1.1[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.05[/tex] (a)
[tex]P(X<a)=0.95[/tex] (b)
We can find a quantile in the normal standard distribution who accumulates 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64
Using this value we can set up the following equation:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.95[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.95[/tex]
And we have:
[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]
And if we solve for a we got
[tex]a=14.4 +1.64*1.1=16.204[/tex]
The 95th percentile of the hip breadth of adult men is 16.2 inches.
Find the equation of the line.
Use exact numbers.
y=
Answers
Answer:
y = 2x+4
Step-by-step explanation:
First we need to find the slope using two points
(-2,0) and (0,4)
m = (y2-y1)/(x2-x1)
m = (4-0)/(0--2)
= 4/+2
= 2
we have the y intercept which is 4
Using the slope intercept form of the line
y = mx+b where m is the slope and b is the y intercept
y = 2x+4
The volume of a trianglular prism is 54 cubic units. What is the value of x?
3
5
7
9
Answers
Answer:
X is 3 units.
Step-by-step explanation:
Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.
Deanna's Quiz Scores
Use the dot plots to answer the question
has quiz scores that are less variable and
typically higher
80 82 84 86 88 90 92 94 96 98 100
Amy's Quiz Scores
.
.
.
..
80 82 84 86 88 90 92 94 96 98 100
Answers
Answer:
1.90.93
2.90.27
Step-by-step explanation:
Answer:
one above correct
Step-by-step explanation:
1st - 90.93
2nd-90.27
When $\frac{1}{1111}$ is expressed as a decimal, what is the sum of the first 40 digits after the decimal point?
Answers
Answer:
90
Step-by-step explanation:
1/1111= 0. (0009) cycles of 0009 after decimal point (one 9 per 4 digits)
Number of digits 9:
40/4= 1010*9= 90Answer:
90
Step-by-step explanation:
Which division sentence is related to the product of a/3 (a/3) when A is not equal to 0?
Answers
Answer:
Option 4.
Step-by-step explanation:
Reciprocal of the second fraction turns the product into the division of the two fractions, which equals to 1.
[tex]a/3(a/3)[/tex]
[tex]a/3 \div 3/a=1[/tex]
Two fractions are said to be the reciprocal or multiplicative inverse of each other, if their product is 1.
Answer:
D. a/3 divided by 3/a = 1
Step-by-step explanation:
edge
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)
Answers
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)
AC =
Round your answer to the nearest hundredth.
с
6
B
40°
А
Answers
Answer:
5.03
Step-by-step explanation:
Answer:
5.03 = AC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 40 = AC /6
6 tan 40 = AC
5.034597787 = AC
To the nearest hundredth
5.03 = AC
All math teachers are smart. Ms. Smith is your math teacher, so she is smart. What type of reasoning is this? inductive or deductive
Answers
Answer:
I believe it is Inductive Reasoning.
Step-by-step explanation:
Inductive Reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you've experienced, observations you've made, or facts you know to be true or false.
Deductive Reasoning is a basic form of valid reasoning.
4. The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Answers
Answer:
5in³Step-by-step explanation:
The question is in complete. Here is the complete question.
"The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Base of triangle = 1in
height of triangle = 5in"
Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\
B = Base area
H = Height of the pyramid
Base area B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]
b = base of the triangle
h = height of the triangle
B = [tex]\frac{1}{2} * 5 * 1\\[/tex]
[tex]B = 2.5in^{2}[/tex]
Since H = 6inches
Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]
[tex]V = 2.5*2\\V =5in^{3}[/tex]
Which is the cosine ratio of
Answers
Answer:The answer is B
Step-by-step explanation:
Answer:
Option B
Step-by-step explanation:
Cos A = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Where Adjacent = 28, Hypotenuse = 197
Cos A = [tex]\frac{28}{197}[/tex]
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 0.989 0.978 0.927 0.167 0.530
Answers
Answer:
0.989
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.
This means that [tex]p = 0.53[/tex]
6 randomly selected graduates
This means that [tex]n = 6[/tex]
Probability that at least one finds a job in his or her chosen field within a year of graduating:
Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]
Find the area of a triangle that has the base of 5 inches and a height of 3 3/4 inches
Answers
Answer:
9.375 in^2
Step-by-step explanation:
The top figure in the composite figure is called a . And What is the volume?
Answers
Answer:
Triangular Prism
volume 748
Please answer this correctly I want genius expert or ace people to answer this correctly as soon as possible as my work is due today
Answers
Answer:
25%
Step-by-step explanation:
The last percentile always contains 25% of the observations.
Solve for x. 9x-2c=k
Answers
Explanation the perfect square is 9x2+6x+k=(3x+k)2.=9x2+6x/k+k2.comparing the 2 sides
Please help me find Jebel dhanna in UAE map.
Answers
Answer:
The full name of the place is the "Danat Jebel Dhanna". The Jebel Dhanna is currently located in the Abu Dhabi. It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.
hope this helps ;)
best regards,
`FL°°F~` (floof)
What are the like terms in the algebraic expression? Negative a squared b + 6 a b minus 8 + 5 a squared b minus 6 a minus b Negative a squared b and negative 6 a Negative a squared b and 5 a squared b 6 a b and 5 a squared b 6 a b and negative 6 a
Answers
Answer:
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex]
Step-by-step explanation:
The expression is:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
Collect the like terms as follows:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
[tex]=(-a^{2}b+5a^{2}b-a^{2}b-a^{2}b+5a^{2}b+5a^{2}b)+(6ab+6ab+6ab)-(6a-6a-6a)-b-8[/tex]
[tex]=12a^{2}b+18ab+18a-b-8[/tex]
Thus, the final expression is [tex]12a^{2}b+18ab+18a-b-8[/tex]
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex].
Answer:
The CORRECT answer is B
Step-by-step explanation:
Which are true of the function f(x)=49(1/7)?select three options. A)The domain is the set of all real numbers. B) the range is the set of all real numbers. C) the domain is x >0. D)the range is y>0. E)as increases by 1, each y value is one -seventh of the previous y-value.
Answers
Answer:
A,D and E
Step-by-step explanation:
We are given that a function
[tex]f(x)=49(\frac{1}{7})^x[/tex]
The given function is exponential function .
The exponential function is defined for all real values of x.
Therefore, domain of f=Set of all real numbers
Substitute x=0
[tex]y=f(0)=49>0[/tex]
Range of f is greater than 0.
x=1
[tex]y(1)=\frac{49}{7}[/tex]
x=2
[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]
As x increases by 1, each value of y is one-seventh of the previous y-value.
Therefore, option A,D and E are true.
Answer:
A D E
Step-by-step explanation:
Edge2020 quiz
Alessandro wrote the quadratic equation -6=x2+4x-1 in standard form. What is the value of c in his new equation? c=-6
Answers
Answer:
5
Step-by-step explanation:
To put the equation in standard form, add 6 to both sides.
x^2 +4x -1 +6 = -6 +6
x^2 +4x +5 = 0
The new value of "c" (the constant) is 5.
Answer:
C or 5 for me
Step-by-step explanation:
Jiangsu divided 751.6 by 10 by the power of 2 and got a quotient of 0.7516. yesseinafhinks that the quotient should be7.516. Who is correct?
Answers
Answer:
yesseinafhinks
Step-by-step explanation:
Dividing by 10² is also the same thing as multiplying by 10^-2. In that case, we simply move the decimal places only 2 places back. That would give us 7.516, not 0.7516 (which is 3 times, not 2).
A triangular window has an area of 594 square meters. The base is 54 meters. What is the height?
Answers
Answer:
22 m
Step-by-step explanation:
Use the formula for the area of a triangle. Fill in the known values and solve for the unknown.
A = (1/2)bh
594 m^2 = (1/2)(54 m)h
h = (594 m^2)/(27 m) = 22 m
The height of the window is 22 meters.
Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm.Use function notation to complete the following tasks
a. Represent the area (in square cm) of a circle whose radius is 4 cm.
b. Represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm.
Answers
Answer:
(a)f(4) square cm.
(b)f(10.91)-f(10.9) Square centimeter.
Step-by-step explanation:
f(r)=the area of a circle (in square cm) that has a radius of r cm.
(a)Area (in square cm) of a circle whose radius is 4 cm.
Since r=4cm
Area of the circle = f(4) square cm.
(b) When the radius of the increases from 10.9 to 10.91 cm.
Area of the circle with a radius of 10.91 = f(10.91) square cm.Area of the circle with a radius of 10.9 = f(10.9) square cm.Change in the Area = f(10.91)-f(10.9) Square centimeter.
Any help would be appreciated
Answers
Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that 2 of them have blue eyes? Round answer to 4 decimal places. Answer:
Answers
Answer:
27.11% probability that 2 of them have blue eyes
Step-by-step explanation:
For each person, there are only two possible otucomes. Either they have blue eyes, or they do not. The probability of a person having blue eyes is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
8% of all people have blue eyes.
This means that [tex]p = 0.08[/tex]
Random sample of 20 people:
This means that [tex]n = 20[/tex]
What is the probability that 2 of them have blue eyes?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{20,2}.(0.08)^{2}.(0.92)^{18} = 0.2711[/tex]
27.11% probability that 2 of them have blue eyes
The probability that 2 of them have blue eyes is 27.11%.
Given that,
Approximately 8% of all people have blue eyes.
Out of a random sample of 20 people,
We have to determine,
What is the probability that 2 of them have blue eyes?
According to the question,
People having blue eyes p = 8% = 0.08
Sample of people n = 20
For each person, there are only two possible outcomes. Either they have blue eyes, or they do not.
The probability of a person having blue eyes is independent of any other person.
The probability that 2 of them have blue eyes is determined by using a binomial probability distribution.
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}[/tex]
Therefore,
The probability that 2 of them have blue eyes is,
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}\\\\ \rm P (X = x) = \dfrac{n!}{(n-x)! \times x!} \times p^x \times (1-p)^{n-x}}\\\\[/tex]
Substitute all the values in the formula,
[tex]\rm P (X = 2) = \dfrac{20!}{(20-2)! \times 2!} \times (0.08)^2 \times (1-0.08)^{20-2}}\\\\ P (X = 2) = \dfrac{20!}{(18)! \times 2!} \times (0.0064) \times (0.92)^{18}}\\\\ P (X = 2) = \dfrac{19\times 20}{ 2} \times (0.0064) \times (0.222)\\\\ P(X = 2) = {19\times 10}\times (0.00142)\\\\P(X = 2) = 0.2711\\\\P(X = 2) = 27.11 \ Percent[/tex]
Hence, The required probability that 2 of them have blue eyes is 27.11%.
For more details refer to the link given below.
https://brainly.com/question/23640563
Prove your work what is 1/12 of a dozen Branliest
Answers
Answer:
1/12 of a dozen is 1
Step-by-step explanation:
One dozen means 12. If you ask for 1/12 of 12, you multiply 12 and 1/12. You should get 1 as your answer.
A student walk 60m on a bearing
of 028 degree and then 180m
due east. How is she from her
starting point, correct to the
nearest whole number?
Answers
Answer:
d = 234.6 m
Step-by-step explanation:
You can consider a system of coordinates with its origin at the beginning of the walk of the student.
When she start to walk, she is at (0,0)m. After her first walk, her coordinates are calculated by using the information about the incline and the distance that she traveled:
[tex]x_1=60cos28\°=52.97m\\\\y_1=60sin28\°=28.16m[/tex]
she is at the coordinates (52.97 , 28.16)m.
Next, when she walks 180m to the east, her coordinates are:
(52.97+180 , 28.16)m = (232.97 , 28.16)m
To calculate the distance from the final point of the student to the starting point you use the Pythagoras generalization for the distance between two points:
[tex]d=\sqrt{(x-x_o)^2+(y-y_o)^2}\\\\x=232.97\\\\x_o=0\\\\y=28.16\\\\y_o=0\\\\d=\sqrt{(232.97-0)^2+(28.16-0)^2}m=234.6m[/tex]
The displacement of the student on her complete trajectory was of 234.6m
Find the Laplace transform F(s)=L{f(t)} of the function f(t)=sin2(wt), defined on the interval t≥0. F(s)=L{sin2(wt)}= help (formulas) Hint: Use a double-angle trigonometric identity. For what values of s does the Laplace transform exist? help (inequalities)
Answers
The Laplace transform of the function [tex]\frac{1}{2} (\frac{1}{s} - \frac{s}{s^2 + 4w^2} )[/tex] .
The Laplace transform exist when s > 0 .
Here, the given function is f(t) = sin²(wt) .
The Laplace transform of the the function f(t),
F(s) = f(t) = { [tex]{\frac{1}{2} \times 2sin^2(wt) }[/tex] }
F(s) = { [tex]\frac{1}{2} \times (1- cos2wt)[/tex] }
F(s) = { [tex]\frac{1}{2} - \frac{1}{2} \times cos(2wt)\\[/tex] }
F(s) = [tex]\frac{1}{2} (\frac{1}{s} - \frac{s}{s^2 + 4w^2} )[/tex]
Next,
The above Laplace transform exist if s > 0 .
Know more about Laplace transform,
https://brainly.com/question/31481915
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If the legs of a right triangle are 10 and 24, then the
hypotenuse is
Answers
26.
Step-by-step explanation:
To figure out the missing side of a right triangle, we will use the Pythagorean theorem. This is...
[tex]a^2+b^2=c^2[/tex]
With this Pythagorean theorem, a and b will always be the legs and the c will always be the hypotenuse, no matter what. Now knowing this, we can plug the legs into the equation.
[tex]10^2+24^2=c^2[/tex]
[tex]100+576=c^2[/tex]
Add the legs together.
[tex]676=c^2[/tex]
Now, since c is squared we will have to find the square root of 676.
[tex]\sqrt{676}[/tex]
= 26
Consider the graph of the line of best fit, y = 0.5x + 1, and the given data points. A graph shows the horizontal axis numbered negative 4 to positive 4 and the vertical axis numbered negative 4 to positive 4. Points show an upward trend. Which is the residual value when x = 2? –2 –1 1 2
Answers
Answer
its -1
Step-by-step explanation:
ED 2020 boiiiii
The residual value of the line of the best fit when x = 2 is -1
How to determine the residual value?The equation of the line is given as:
y = 0.5x + 1
When x = 2, we have:
y = 0.5 * 2 + 1
Evaluate
y = 2
The residual is the difference between the actual value and the predicted value.
From the complete graph, the actual value is 1.
So, we have:
Residual = 1 - 2
Evaluate
Residual = -1
Hence, the residual value when x = 2 is -1
Read more about residuals at:
https://brainly.com/question/1168961
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