Answers
x = - 1
given [tex]\sqrt{(1-3x)}[/tex] = x + 3
square both sides
1 - 3x = (x + 3 )² ( expand right side using FOIL )
1 - 3x = x² + 6x + 9 ( subtract 1 - 3x from both sides )
0 = x² + 9x + 8
0 = ( x + 1)(x + 8)
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = -1
x + 8 = 0 ⇒ x = - 8
As a check
substitute these values into the equation and if both sides are equal then they are the solutions
x = - 1 : [tex]\sqrt{1+3 }[/tex] = 2 and - 1 + 3 = 2 ← true
x = - 8 : [tex]\sqrt{1+24}[/tex] = 5 and - 8 + 3 = -5 ← false
thus the only solution is x = - 1
Related Questions
PLZ HELP ME WITH GEOMETRY
Answers
B a counterclockwise rotation about the origin of 90°
under a counterclockwise rotation about the origin
a point ( x , y ) → (- y, x)
figure Q to figure Q'
( 4,2 ) → (- 2, 4 )
(7, 5 ) → (- 5, 7 )
(3, 7 ) → (- 7 , 3 )
(2, 4 ) → (- 4, 2 )
(5, 4 ) → (- 4, 5 )
the coordinates of the original points of the vertices of Q map to the corresponding points on the image Q'
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4. Work out the value of k.
Answers
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
slope = [tex]\frac{k-(-5)}{6-3}=\frac{k+5)}{3}[/tex]
We know slope =4
[tex]\frac{k+5)}{3}=4[/tex]
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
Let f(x) = cos(x). Find the x-intercepts of f(x) on [0, 2π).
Answers
the x-intercepts of cosx are
[tex]\frac{\pi }{2}[/tex] and [tex]\frac{3\pi }{2}[/tex] on [0, 2π )
The x-intercepts of the function f(x) = cos(x) on [0, 2π) are π/2 and 3π/2.
Explanation:The x-intercepts of the function f(x) = cos(x) on the interval [0, 2π) can be found by setting f(x) equal to zero and solving for x.
cos(x) = 0
To find the values of x for which cos(x) equals zero, we need to determine when the cosine function equals zero on the given interval. The cosine function equals zero at every multiple of π/2. Therefore, the x-intercepts of f(x) are π/2 and 3π/2.
Learn more about x-intercepts here:https://brainly.com/question/12791065
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Plz answer this ASAP! What is the x-coordinate of the solution for the system of equations? {y−x=910+2x=−2y Enter your answer in the box.
Answers
:) Here is your answer -7
Answer:
the answer is -7
Step-by-step explanation:
thxs person who answered before me :)
Find the angle complementary to the angle 80°.
Answers
The answer is 10 degrees since 90 - 80 = 10
the angle = 10°
Complementary angles sum to 90°
the complement of 80° is 90° - 80° = 10°
plz help asap geometry
Answers
Answer:
i think its d
Step-by-step explanation:
Answer:
I think it is C triangle ABD and triangle ADC. I hope that helped.
A window frame has a length of (5x + 3) inches and a width of (x + 6) inches. The area of the glass in the window is (4x² + 26x + 15) square inches.
What is the area of the trim around the glass in the window?
A. (x²+3x+7) square inches
B. (9x²+33x+59) square inches
C. (x²+7x+3) square inches
D. (9x²+59x+33) square inches
Answers
C
the area (A ) of the trim is the area of the window frame subtract the area of glass
area of window frame = (5x + 3)(x + 6) = 5x² + 33x + 18
A = 5x² + 33x + 18 - (4x² + 26x + 15)
= 5x^2 + 33x + 18 - 4x² - 26x - 15 = x² +7x + 3 inches²
Partial results of a survey about students who wear glasses are shown in the two-way table.
Which of the following statements are true? Check all that apply.
225 students were surveyed.
25 girls always wear glasses.
15 girls sometimes wear glasses.
52 boys never wear glasses.
75 boys were surveyed.
65 students sometimes wear glasses.
Answers
25 girls always wear glasses. false 35
15 girls sometimes wear glasses. true
52 boys never wear glasses. true
75 boys were surveyed. false 127
65 students sometimes wear glasses. true
Answer:
a. True, b. False, c. True, d. True, e. False, f. True
Step-by-step explanation:
Partial results of a survey about students who wear glasses are shown in the two-way table.
First we complete the table to understand options easily
Always Sometimes Never Total
Boys 25 50 52 127
Girls 35 15 48 98
Total 60 65 100 225
Now we can solve all the options easily.
a. 225 students were surveyed - True
b. 25 girls always wear glasses - False (35)
c. 15 girls sometimes wear glasses - True
d. 52 boys never wear glasses - True
e. 75 boys were surveyed - False (127)
f. 65 students sometimes wear glasses -True
Compare 9.36 to 9.359
Answers
9.36 is 0.001 more than 9.359
Both numbers round to the same value.
9.359 has greater precision.
half the quotient of a number and 3 is ten. find the number.
Answers
call that number x.
[tex]\frac{1}{2}\frac{x}{3}=10\\\frac{x}{3}=20\\x=60[/tex]
The table shows a linear function.
Which equation represents the function?
x f(x)
10 −1
5 2
0 5
−5 8
A)f(x)=−53x+5
B)f(x)=−35x+5
C)f(x)=53x+5
D)f(x)=53x−1
Answers
Answer:
B) f(x) = -3/5x +5
Step-by-step explanation:
There are several ways you can write the equation of a line from a list of points. When you look through the list and see that one of them is the y-intercept, then the problem can be easier. When you look through the list of answers and see that the required answer is in slope-intercept form, then you know all you need to do is find the slope to go with the intercept you've located.
The point (x, f(x)) = (0, 5) tells you the y-intercept is 5.
The slope, the change in y divided by the change in x for two points, is ...
... (-1 -2)/(10 -5) = -3/5
This is the slope and the coefficient of x in the linear equation.
Now, we know the y-intercept (b=5) and the slope (m=-3/5), so we can fill in the slope-intercept form of the equation of a line:
... y = mx + b
... y = (-3/5)x + 5
PICK MORE THAN ONE ANSWER:
Eva earned the following test scores in science:
82, 100, 96, 90, 91
Ms. Wade entered the next score as 0 because Eva was absent on test day and hadn’t had a chance to make up the test. Which statements are true based on the data? Check all that apply.
After adding the 0 test score, the mean would be the most appropriate measure of center to describe the data.
After adding the 0 test score, the mean would be affected.
After adding the 0 test score, the median would be the most appropriate measure of center to describe the data.
Before the missed test, Eva’s median score was 96.
Before the missed test, Eva’s median score was 91.
Before the missed test, Eva’s mean score was 91.8.
Answers
Answer:
The correct answers are "After adding the 0 test score, the mean would be affected.", ad "Before the missed test, Eva’s median score was 91".
Step-by-step explanation:
We know that the mean and median scores would not be helpful in determining Eva's abilities since the 0 is not a representation of how much she knows. However, it will affect the average as adding a 0 to the numerator and a 1 to the denominator will lower the average.
Finally, we can tell the median is 91 before added as when we line up the scores in ascending order, the middle number is 91.
82, 90, 91, 96, 100
Answer:
Statements that are true based on the data:
-After adding the 0 test score, the mean would be affected.
-After adding the 0 test score, the median would be the most appropriate measure of center to describe the data.
-Before the missed test, Eva’s median score was 91.
-Before the missed test, Eva’s mean score was 91.8.
Step-by-step explanation:
-After adding the 0 test score, the mean would be the most appropriate measure of center to describe the data: NO, it won't because the data now has an extreme value that shifts the mean value significantly.
-After adding the 0 test score, the mean would be affected: YES, The mean value would be greatly impacted by adding the 0, (mean=76.5 with the 0; 91.8 without the 0),
-After adding the 0 test score, the median would be the most appropriate measure of center to describe the data: YES, because the median won't be affected as much as the mean by the extreme value.
-Before the missed test, Eva’s median score was 96: NO, the median score was 91 at that point.
-Before the missed test, Eva’s median score was 91: YES, the median score was 91, the median is defined as the value where 50% of sorted values are below and 50% are above
-Before the missed test, Eva’s mean score was 91.8: YES, the mean is defined as the sum of all values divided by the total number of values
The formula for calculating the median is:
-odd number of values: [tex]$ x_m = x_\frac{n+1}{2}[/tex]
-even number of values: [tex]$ x_m = \frac{x_\frac{n}{2}+x_\frac{n+2}{2}}{2}[/tex]
MEDIAN BEFORE ADDING THE 0: 82,90,91,96,100
[tex]$ x_m = x_\frac{5+1}{2}[/tex]=3 (third value)
MEDIAN AFTER ADDING THE 0: 0,82,90,91,96,100,
[tex]$ x_m = \frac{x_\frac{6}{2}+x_\frac{6+2}{2}}{2}[/tex]=average between the 3 and 4 values
[tex]$ x_m = \frac{90+91}{2}[/tex]=90.5
The formula for calculating the mean is: [tex]mean ={\frac{1}{n} \sum_{i=1}^n (x_i) $[/tex]
MEAN BEFORE ADDING THE 0
[tex]mean ={\frac{1}{5} \sum_{i=1}^5 (x_i) $[/tex]=[tex]\frac{459}{5}[/tex]=91.8
MEAN AFTER ADDING THE 0
[tex]mean ={\frac{1}{6} \sum_{i=1}^6 (x_i) $[/tex]=[tex]\frac{459}{6}[/tex]=76.5
My friend needed help with this and I found the height through the theorem but can't figure out how to get the base of the overall triangle
Answers
You found CD from the Pythagorean theorem to be ...
... CD = √(5² -2²) = √21
Since triangle ADC ~ triangle ACB, the ratios of corresponding sides are the same:
... AC/AD = AB/AC
... AB = AC²/AD
... AB = 5²/2 = 12.5 . . . . . . . the base of the overall triangle
_____
Then the area (A) is ...
... A = (1/2)bh
... A = (1/2)(12.5)(√21) ≈ 28.64 square units
_____
As you see here, the altitude of a right triangle divides it into three similar triangles. From smallest to largest, they are ...
... ADC ~ CDB ~ ACB
You can figure this using AAA similarity, since the smallest and largest triangles listed above share an acute angle vertex (∠A). That, together with the right angle, means all angles are congruent. After that, then you know ∠ACD ≅ ∠CBD, so you can show the middle sized triangle is similar to the other two.
chest volume is 8100 cubic inches the length is 30 inches and the width is 15 inches how tall will the chest be
Answers
The volume of a cuboid is given in terms of length, width, and height by ...
... V = LWH
Filling in the given numbers, we can solve for the height.
... 8100 in³ = (30 in)(15 in)H
Dividing by the coefficient of H, we have ...
... (8100 in³)/(450 in²) = H = 18 in
The chest will be 18 inches tall.
use subtraction 14 x 25 x 4
Answers
Answer:
The correct answer would be -15
Step-by-step explanation:
Although you have the multiplication symbols here, if we were to use subtraction as your instructions indicate, we would just complete the operations from left to right.
14 - 25 - 4
-11 - 4
-15
HHELLLP IDEK HOW TO DO THIS THIS IS DUE TODAY!!!!!
Answers
The slope is 8/5 because you are increasing 8 units in the y axis and 5 units in the x direction. So the equation here would be d = 8/5t which means for every increase in t by 1, d will increase by 8/5.
if the x-intercept (–68, 0), and the y-intercept (0, –34), what is the equation?
Answers
y = - [tex]\frac{1}{2}[/tex] x - 34
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 68, 0 ) and (x₂, y₂ ) = (0, - 34 )
m = [tex]\frac{-34-0}{0+68}[/tex] = [tex]\frac{-34}{68}[/tex] = - [tex]\frac{1}{2}[/tex]
the y-intercept = (0, - 34 ) ⇒ c = - 34
y= - [tex]\frac{1}{2}[/tex] x - 34
Answer:
Y=-.5x-34
Step-by-step explanation:
this is because you can do y2-y1/x2-x1 to get slope
-34/68
Which equals one half so currently
Y=-1/2x
To get the y intercept we can look at the number when x=0 so it would be -34. So here is the equation
Y=-.5x-34
help please...........
1. y = 3 x
y = -8x
2. y = - 7x
y =-4x - 12
Answers
-11x = 0
x= 0
y= 3(0)= 0
(0, 0)
2. -7x = -4x - 12
-3x = -12
x = 4
y = -7(4)= -28
(4, -28)
(1)
both equations express y in term of x, hence equate the right sides
- 8x = 3x ( subtract 3x from both sides )
- 11x = 0 ( divide both sides by - 11 )
x = 0
substitute x = 0 into y = 3x → y = 0
solution is : (x, y ) → (0, 0)
(2)
both equations express y in terms of x, hence equate the right sides
- 4x - 12 = - 7x ( add 7x to both sides )
3x - 12 = 0 ( add 12 to both sides )
3x = 12 ( divide both sides by 3 )
x = 4
substitute x = 4 into y = - 7x → y = - 28
solution is : (x, y ) = (4, - 28 )
Please Help ASAP 20 points
Find the slope of the line through the given points.
(−1, 2) and (−5,10)
(1,3) and (0,−9)
(18, 6) and (−7, 7)
(−7, 10 ) and (1, 10)
Answers
What is the value of x?
3x−8=8x+4/2
Enter your answer in the box.
Answers
Answer:
x = -2
Step-by-step explanation:
3x -8 =8x +4/2
3x -8 =8x +2
3x -3x -8 = 8x -3x +2 (subtract 3x both sides )
-8 = 5x +2
-8-2 =5x+2 -2 (subtract 2 both sides )
-10 =5x
-10/5 = 5x/5 (divide 5 both sides)
-2 = x
Can someone help me with this question?
Answers
Try this solution:
1. m∠A=m∠L; m∠B=m∠M and m∠C=m∠N;
2. m∠B=m∠M=35° and m∠C=m∠N=95°;
3. m∠A=m∠L=180°-(m∠B+m∠C)=180-35-95=50°
answer: 50°
Genes are responsible for:
A. all inherited traits of an organism.
B. all traits of an organism.
C. no traits of an organism.
D. all preferences of an organism.
Answers
A. all inherited traits of an organism.
Genes are something you inherit from a family and are passed on. Sometimes you might skip your parents and inherit a trait from a another past relative.
All inherited traits of an organsim
What is the expanded equivalent of cos(a – b)?
Answers
cos(a-b) = cos(a)cos(b)+sin(a)sin(b)
PLZ HELP ME WITH GEOMETRY
Answers
You just need to use your test-taking skill to eliminate the wrong answers here.
There is no such thing as a "Congruent Angles Postulate," so the last two choices can be eliminated.
The AA Similarity Postulate refers to triangles, not angles, so the second choice can be eliminated.
That only leaves the (correct) first choice.
A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. Determine whether a probability distribution is given. If a probability distribution is not given, identify the requirements that are not satisfied. Probability Distribution 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 P(x)
Does the table show a probability distribution? Select all that apply.
A.
Yes, the table shows a probability distribution.
B.
No, the sum of all the probabilities is not equal to 1.
C.
No, the random variable x's number values are not associated with probabilities.
D.
No, the random variable x is categorical instead of numerical.
E.
No, not every probability is between 0 and 1 inclusive.
x P(x)
0 0.092
1 0.338
2 0.418
3 0.152
Answers
Answer:
A.
Yes, the table shows a probability distribution.
Step-by-step explanation:
Given that a sociologist randomly selects single adults for different groups of three. And the random variable x is the number in the group who say that the most fun way to flirt is in person.
Since sample size is only 3, x cannot be more than 3.
So x can take values as 0 1 2 3
Prob distribution is given as
x P(x)
0 0.092
1 0.338
2 0.418
3 0.152
We find that x values are from 0 to 3.
Each probability is positive but less than 1.
Also total probability = 1
So this is a perfect probability distribution.
A.
Yes, the table shows a probability distribution.
Given: ∠A ≅∠D, ∠B ≅∠E m∠C = x, m∠F = 2x−30° Find: m∠C
This is 2 seperate triangles
ABC is one triangle and DEF is a different triangle
Answers
Answer:
[tex]m\angle c = 30^\circ[/tex]
Step-by-step explanation:
We are given the following information in the question:
ΔABC and ΔDEF
[tex]\angle A \cong \angle D\\\angle B \cong \angle E\\m\angle c = x \\m\angle F = 2x-30[/tex]
According to angle sum property of the triangle the sum of all angles of triangle is equal to 180 degrees.
Since two corresponding angles of the two triangle are equal, therefore the third angle is also equal.
[tex]x = 2x - 30\\\Rightarrow x = 30[/tex]
Thus,
[tex]m\angle c = 30^\circ[/tex]
The measure of the angle from the given information is m∠C = 2x - 30°
How to determine the measure of the angle?Given the information, we have two separate triangles: ABC and DEF.
In triangle ABC, we are given that ∠A ≅ ∠D and ∠B ≅ ∠E.
In triangle DEF, we are given that m∠C = x and m∠F = 2x - 30°.
To find m∠C, we need to find the value of x.
Since ∠A ≅ ∠D, and ∠B ≅ ∠E, we can conclude that triangle ABC is congruent to triangle DEF by the Angle-Angle (AA) congruence criterion.
Using this congruence, we can determine that m∠C = m∠F.
Therefore, we have:
m∠C = m∠F
Since we know that m∠F = 2x - 30°, we can substitute this value into the equation:
m∠C = 2x - 30°
This gives us the measure of angle C in terms of x.
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Please see attached below. Please explain
Answers
Answer:
8 years
Step-by-step explanation:
The formula for the computation of simple interest is ...
... I = Prt
where I is the interest amount, P is the principal amount, r is the rate, and t is the number of years.
Fill in the given numbers and solve for t.
... 5704 = 15500×0.046×t
... 5704/713 = t = 8 . . . . . . divide by the coefficient of t
It takes 8 years to earn $5704 on that investment at 4.6% per year.
Perform the indicated operation and write the result in the form a+bi. -9i(-9i+4)+3(8+8i)
Answers
- 57 - 12i
distribute the parenthesis
= 81i² - 36i + 24 + 24i
[ note that i² = (√- 1 )² = - 1 ]
= - 81 - 36i + 24 + 24i ( collect like terms )
= - 57 - 12i
Answer:
D^^
Step-by-step explanation:
Edge
PLZ HELP GEOMETRY BELOW
Answers
c (16, 7 )
the transformation which maps KLMN to K'L'M'N' is a translation < 10, 3 >
Applying the same translation to STUV
T(6, 4 ) → T'(6 + 10, 4 + 3 ) = T'(16, 7 )
Suzy puts 2 slices of cheese on each sandwich. she makes 4 cheese sandwich. how many slices of cheese does Suzy use in all
Answers
If she puts 2 slices in 4 sandwiches, the answer would be 8.
(4 x 2)= 8.
Hope this helps & good luck. :)
if she has 4 sandwhiches and 2 slices of chesse on each you can multiply
4*2=8