The solutions to the equation [tex]3-k=\sqrt{3k+1}[/tex] are k = 1 and 8
The given equation is:
[tex]3-k=\sqrt{3k+1}[/tex]
Square both sides of the equation
[tex](3-k)^2=3k+1[/tex]
Expand the left side of the equation above
[tex](3-k)^2=3k+1\\\\(3-k)(3-k)=3k+1\\\\3^2-3k-3k+k^2=3k+1\\\\9-6k+k^2=3k+1[/tex]
Write the quadratic equation in standard form
[tex]k^2-6k-3k+9-1=0\\\\k^2-9k+8=0\\\\[/tex]
Factor the quadratic equation
[tex](k-8)(k-1)=0[/tex]
Use the zero product property
k - 8 = 0
k = 8
k - 1 = 0
k = 1
The solutions to the equation [tex]3-k=\sqrt{3k+1}[/tex] are k = 1 and 8
Learn more here: https://brainly.com/question/25840704
answer
first one: 8 and 1
second one: is 1
Step-by-step explanation:
slay
Select the correct answer.
Estimate the solution to the following system of equations by graphing.
3x + 5y = 14
6x - 4y=9
Answer:
Approximately (2, 1)
See image
Step-by-step explanation:
Rearrange each equation so it is ready to be graphed on an x-y-axis (see image) look for the point where the two lines cross. This is the solution for the system of equations.
Answer: 5/2, 4/3
explanation: got it from a different verified answer
2.
If you were to flip a coin 20 times, what is the probability
you would get at most 13 heads?
a) .9423
b) .1316
c) .0577
d) .0739
Answer:
A) .9423
Step-by-step explanation:
The chance of getting at most 13 heads is 0.9423
37. Briefly explain how the use of credit helped increase the average
American's standard of living in the 20th century.
Answer: If a person has a better credit, they have better chances of getting the job they had applied for. Getting the job means they get a stable income. Having a stable income helps a person to buy all essential needs.
Step-by-step explanation:
pls answer quickly
Students at a school were asked to state their preferences in music. Results of the survey are shown in the circle chart.
What percent of students preferred rock and classical music?
A) 15%
B) 26%
C) 39%
D) 57%
Answer:
B) 26%
Step-by-step explanation:
The yellow part of the graph represents Rock, which is 15%, and the red part of the graph represents Classical. So, you simply add them together.
Answer:
B) 26%.
Step-by-step explanation:
Find the Rock percentage in the chart. (15%)
Find the Classical percentage in the chart. (11%)
Add the Rock and Classical percentages together. (26%)
What is the relation between the sine and cosine values of angles in each quadrant? How would you use the 60° angle to find sine and cosine of 120°, 240°, and 300°? What angles could we find sine and cosine for using information for π/4 and π/6?
The angles, 60°, [tex]\displaystyle \frac{\pi}{4}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are special angles that have known trigonometric ratio values.
First part;
The sine and cosine gives the coordinates of the tip of the radius of a unit circle as it rotates P(cos(θ), sin(θ))Second part;
With the knowledge of the sine and cosine of 60°, we have; sin(60°) = sin(120°), sin(240°) = -sin(60°), sin(300°) = -sin(60°)cos(120°) = -cos(60°), cos(240°) = -cos(60°), cos(300°) = cos(60°)Third part;
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \frac{3 \cdot \pi}{4}[/tex], [tex]\displaystyle \frac{5 \cdot \pi}{4}[/tex], and [tex]\displaystyle \frac{7 \cdot \pi}{4}[/tex] [tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle \frac{11 \cdot \pi}{6}[/tex]Reasons:
First Part;
Considering a unit circle with the center at the origin of the graph, we have;
The sine of the angle, θ, rotated by the radius is the vertical distance of a point P on the circle which is the location of the radius, from the horizontal axis.
The cosine of the angle, θ, is the horizontal distance of P from the vertical axis, such that we have;
The coordinates of point P = (cos(θ), sin(θ))
In the four quadrant, we have;
First Quadrant; All trigonometric ratios are positive
Second Quadrant; sine is positive
Third Quadrant; Tan is positive
Fourth Quadrant; Cosine is positive
Second part;
We have; At 120°, the point P is the same elevation from the horizontal axis, therefore;
sin(60°) = sin(120°) = 0.5·√3
However, the x-coordinate of the point P is in the negative direction, therefore, we get;
cos(120°) = -cos(60°) = -0.5
Similarly from the quadrant relationship, we have;
240° is in the third quadrant, and it is 60° below the negative horizontal line, therefore;
sin(240°) = -sin(60°) = -0.5·√3
cos(240°) = -cos(60°) = -0.5
300° is in the fourth quadrant, and it is 60° below the positive x-axis, therefore;
sin(300°) is negative and cos(300°) is positive
Which gives;
sin(300°) = -sin(60°) = -0.5·√3
cos(300°) = cos(60°) = 0.5
Third part;
[tex]\displaystyle \frac{\pi}{4} =45^{\circ}[/tex]
[tex]\displaystyle \frac{\pi}{6} =30^{\circ}[/tex]
The sine and cosine of 45° can be used to find the sine and cosine of (180° + 45°) = 225°, (360° - 45°) = 315°
Also, due to the mid location of the angle 45° on the quadrant, we have;
Another angles is the sines and cosine of (90° + 45°) = 135°
Therefore, [tex]\displaystyle \frac{\pi}{4}[/tex], can be used to find the sine and cosine of 135°, 225°, and 315°
[tex]\displaystyle 135^{\circ} = \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle 225^{\circ} = \frac{5 \cdot \pi}{4}[/tex], [tex]\displaystyle 315^{\circ} = \frac{7 \cdot \pi}{4}[/tex]
Therefore,
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle \mathbf{\frac{5 \cdot \pi}{4}}[/tex], and [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{4}}[/tex]
Similarly, the sine and cosine of, [tex]\displaystyle \frac{\pi}{6}[/tex] = 30° can be used to find the sine and cosine of 150°, 210°, and 330°.
[tex]\displaystyle 150^{\circ} = \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle 210^{\circ} = \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle 330^{\circ} = \frac{11 \cdot \pi}{6}[/tex]
[tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \mathbf{ \frac{5 \cdot \pi}{6}}[/tex], [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{6}}[/tex], and [tex]\displaystyle \mathbf{\frac{11 \cdot \pi}{6}}[/tex]
Learn more about the sine and cosine of angles here:
https://brainly.com/question/4372174
Answer:
Step-by-step explanation:
The cosine value of an angle is the x coordinate of the point the angle corresponds to on the unit circle, and the sine value of an angle is the y coordinate of that point. 120, 240, and 300 all form 60 degree reference angles which in turn forms 30-60-90 triangles which help to find the sine and cosine of these corresponding angles. Pi/4 radians converts to 45 degrees which forms a 45-45-90 special triangle on the unit circle which has its own known trigonometric ratio. Pi/6 radians converts to 30 degrees which forms a 30-60-90 triangle on the unit circle which also has a known trigonometric ratio. These ratios help find the sine and cosine of the angles on the unit circle which corresponds to a point on the coordinate plane.
Question 34, the answer is C. I just need the working. Tysm
Answer:
C
Step-by-step explanation:
∠ ABC = 90° ( angle in a semicircle )
Using the cosine ratio in right triangle ABC and the exact value
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos30° = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{10}{AC}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
AC × [tex]\sqrt{3}[/tex] = 20 ( divide both sides by [tex]\sqrt{3}[/tex] )
AC = [tex]\frac{20}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ( rationalising denominator )
AC = [tex]\frac{20\sqrt{3} }{3}[/tex]
radius AO = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × [tex]\frac{20\sqrt{3} }{3}[/tex] = [tex]\frac{10\sqrt{3} }{3}[/tex] → C
Solve.
x/2=−0.73
What is the solution to the equation?
Enter your answer as a decimal in the box.
x =
x/2 = -0.73
To solve for x multiply both sides by 2:
x = -1.46
5x + 15y = 1200 models how many cars washed (x) and how many bikes sold (y) Jim has to do to save $1200. Of the four combinations of car washed and bikes sold below, which does NOT result in $1200?(3, 79)(6, 78)(8, 76)(9, 77)
Answer:
(8, 76)
Step-by-step explanation:
Correlation coefficients
PLEASE HELP I BEG IMMA FAILLLLLLLLL
A rectangular garden is 40 ft wide and 55 ft long. On a blueprint, the width is 8 in. Identify the length on the blueprint.
Answer:
11
Step-by-step explanation:
First, you set up the proportion for the garden, 40/55 (width/length). Then, right beside it, you set up the proportion for the blueprint garden, 8/x (x because this is the answer we are trying to find). You can then do a scale factor to find the answer and the scale factor is 5 ( because 40 divided by 5 is 8) so you can divide 55 by 5 to get 11!! I hope this helps bro!! :D
The soccer team provides 5 liters of water for the coaches and 1.25 liters of water for each player during practice.
Which equation represents the total number of liters of water, w, based on the number of players, p?
Answer:
y=1.25x+5
Step-by-step explanation:
please help i will give brainliest
Answer:
Step-by-step explanation:
C
If the width of the rectangle is three times the lengthAnd a perimeter is 72 feet What are the length and width of the rectangle
Answer:
Width = 27
Length = 9
*You might of switched width and length around please check*
Step-by-step explanation:
Width = 3x
Length = x
Perimeter Formula
2(3x+x) = 72
2(4x) = 72
8x = 72
x = 9
Since X was found, plug it in to find the width and length
3(9) = 27
x = 9
ALGEBRA Find x and y so that each quadrilateral is a parallelogram.
(Please do at least 2, but doing all 4 would be greatly appreciated, and i will mark u brainliest.)
PLEASE HELP ME I'M FAILING MATH-
Select the correct texts in the passage. Julian factored the expression
[tex] {2x}^{4} + {2x}^{3} - {x}^{2} - x[/tex]
His work is shown. At which step did Julian make his first mistake, and which statement describes the mistake?
[tex]julian \: should \: have \:factored \:( {2x}^{2} - 1) \: as \: a \: difference \: of \: squares \: \\ \\ julian \: incorrectly \: factored \: - 1 \: from \: the \: second \: group \: of \: terms \: \\ \\ julian \: should \: have \: factored \: 2x \: from \: all \: terms \: instead \: of \: x \: \\ \\ julian \: incorrectly \: factored \: {2x}^{2} \: from \: the \: first \: group \: of \: terms[/tex]
Julian factored the expression of 2x^4 + 2x³ - x²- x, the step 2 ( x (2x² (x + 1)) - 1(x − 1)) is wrong statement.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We have been given an expression as;
2[tex]x^{4}[/tex] + 2x³ - x²- x
Step 1;
x(2x³ + 2x²- x − 1)
Step 2;
x (2x² (x + 1)) - 1(x − 1)
Step 3;
x²(2x²-1) (x + 1)(x - 1)
Hence, Julian incorrectly factored -1 from the second group of terms.
we can write the correct factored as;
x (2x²- 1))(x + 1)
Therefore, Julian factored the expression of 2[tex]x^{4}[/tex] + 2x³ - x²- x, the step 2 ( x (2x² (x + 1)) - 1(x − 1)) is wrong statement.
To know more about an expression follow;
brainly.com/question/19876186
#SPJ5
21.6% of all registered doctors were female, if there were 45,200 females registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number
Answer:
209259
Step-by-step explanation:
45200 / 21.6 = 209259.259259
209259.259259 rounded to nearest whole number = 209259
chose the expressions that are equivalent to the expression 3 2/3
A) square root 3^6
B) ^3 square root 3•3
C) square root 3^2 3^2
D) ^3 square root 3^2
E) square root 3^3
F) ^3 square root 9
G) square root 3•3•3•3•3•3
H) square root 3•3•3
Answer:
E no is the correct answer
HELP PLEASE!!!
What is the ratio of 1713.57^2/4113.87^3.
Answer:
4.21747×10^-5
Step-by-step explanation:
Your calculator can do the division for you. The ratio is about 4.21747×10^-5.
__
This is approximately 10/237109.
The perimeter of the triangle is 20.6 centimeters. What is the unknown side length?
Answer:
OK so a triangle has 3 sides and the perimeter around it is 20.6 cm to find the unknown for the length of a side it would be 20.6 ÷3 which is = to 6.86 to 2 decimal places
Step-by-step explanation:
20.6÷3
= 6.86 cm to 2 dp
Can some one help? This is sooooooo hard
Answer:
median is a hight of a triangle
If you need 10 cups of flour for every 6 cups of sugar, how much sugar do you need if you have only one cup of flour?
Answer:
2/3
Step-by-step explanation:
1/(3/4)=4/3(4/3)2.5
10 cups/=3.333
An amusement park has two themed resorts, Stargazer Suites and Retro Retreat. The graph and table below display the cost of the stay, y, for different numbers of nights, x, for the two different resorts.
Which statement correctly compares the nightly rates at Stargazer Suites and Retro Retreat?
The nightly rate at Stargazer Suites is $15 more than the nightly rate at Retro Retreat.
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
The nightly rate at Retro Retreat is $30 more than the nightly rate at Stargazer Suites.
The nightly rate at Retro Retreat is $80 more than the nightly rate at Stargazer Suites.
The nightly rate at each resort is the same.
Answer:
to confusing
Step-by-step explanation:
Answer:
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
Step-by-step explanation:
Solve the inequality: 4(2x-11) is less than equal to -12 + 2(x-4) No "files" please and also need an explanation
[tex]4(2x-11) \leq -12 +2(x-4)\\\\\implies 8x - 44 \leq -12 + 2x -8\\\\\implies 8x -44 \leq 2x -20\\\\\implies 4x - 22 \leq x - 10~~~~~~~~~~~~~~~~~~~;[\text{Dividing both sides by 2}]\\\\\implies 4x -22 +22 \leq x -10 +22~~~~~~;[\text{Adding 22 to both sides}]\\\\\implies 4x \leq x+12\\\\\implies 4x -x \leq x+12-x~~~~~~~~~~~~~~~~;[\text{Subtracting x from both sides}]\\\\\implies 3x \leq 12\\\\\implies x \leq 4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Dividing both sides by 3}][/tex]
[tex]\text{Interval solution,} ~(-\infty, 4][/tex]
The diameters of a circle is 7m. Find its area to the nearest tenth?? Help please
Area =[tex]\pi r^{2}[/tex]
The diameter is double the length of the radius
7 ÷ 2 = 3.5
3.5 × 3.5 = 12.25
[tex]12.25\pi[/tex] = 38.4845100064751
38.4845100064751 rounded to the nearest tenth is 38.5
Answer:
A = 38.5 sq meters
Step-by-step explanation:
A = πr²
since diameter is 7, then radius is 7/2
A = π(7/2)²
A = 38.48
A = 38.5 rounded to nearest tenth
75,15,3 find the 6th term
Answer:
0.024
Step-by-step explanation:
75, 15, 3, ...
Now, let's take a look at thus pattern.
You'll notice how the numbers decrease.
Divide 75 by 5.
We get 15
Divide 15 by 5.
We get 3.
Then we have the pattern now.
3 ÷ 5 = 0.6 (4th term)
0.6 ÷ 5 = 0.12 (5th term)
0 12 ÷ 5 = 0.024 (6th term)
I hope it helps.
20(d – 4) + 4d *less than sign and a line under it* 8
Answer:
the anser od 20(d-4)+4d is5
[tex]x3 = -8[/tex] i want the answer
Answer:
x=-8/3
Step-by-step explanation:
I need help, can someone explain #4,5,6 in full detail. (I'm very visual)
Answer
4= 55 and 3/4 5= 4 2/5 6= 6 and 1/2
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
I did #4 for you:
[tex]11\frac{8}{9}+5\frac{1}{2}[/tex]
[tex]11+5+\frac{8}{9}+\frac{1}{2}[/tex]
[tex]16+\frac{16}{18}+\frac{9}{18}[/tex]
[tex]16+\frac{24}{18}[/tex]
[tex]16+\frac{4}{3}[/tex]
[tex]16+1+\frac{1}{3}[/tex]
[tex]17\frac{1}{3}[/tex]
It really helps to break up the mixed numbers into parts and change the fractions so they have the same denominator. Try to do #5 and #6 the same way I did.
How many meters are in 28% of 15 km?
Explanation Please with proportions.
I will reward the brainiest
Answer:
4200
Step-by-step explanation:
Answer: 4,200 meters
Step-by-step explanation:
[tex]\frac{28}{100} * 15 = 4.2 km = 4200 m[/tex]
Disney is hiring new employees. They currently employ 2,550 workers and want to hire
10 new workers per day. How many days will it take them to have employed 5,000
workers?
Answer:
I think it is 500
Step-by-step explanation:
5000 / 10 = 500
