Step-by-step explanation:
[tex]6 \cos {}^{2} (x) + 4 \sin {}^{2} (x) = 5[/tex]
[tex]6(1 - sin {}^{2} x) + 4 \sin {}^{2} (x) = 5[/tex]
[tex]6 - 6 \sin {}^{2} (x) + 4 \sin {}^{2} (x) = 5[/tex]
[tex]6 - 2 \sin { }^{2} (x) = 5[/tex]
[tex] - 2 \sin {}^{2} (x) = - 1[/tex]
[tex] \sin {}^{2} (x) = \frac{1}{2} [/tex]
[tex] \sin(x) = \frac{1}{ \sqrt{2} } [/tex]
Take the arc Sine of the function
[tex]arcsin( \frac{1}{ \sqrt{2} } ) = \frac{\pi}{4} [/tex]
Finally, Sine is a periodic function so it has two answers within the interval (0, 2 pi)
Use the identity
[tex] \sin(x) = \sin(x + \pi) [/tex]
We know that
[tex] \sin( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} } [/tex]
so using the identity
[tex] \sin( \frac{\pi}{4} + \pi ) = \sin( \frac{5\pi}{4} ) [/tex]
So we have two answers.
[tex]( \frac{\pi}{4} )[/tex]
[tex]( \frac{5\pi}{4} )[/tex]
The Roman god Neptune and the Greek god Poseidon BOTH were considered to be the god ofA)war.B)time.C)the sea.D)the underworld.
Answer:
C)The sea
Step-by-step explanation:
Ares is the god of war
Hades is the god of the underworld
Cronos is the god of time
Write a general rule for finding the sign in a multiplication or division problem with more than two integers
please help brainliest
Solve. −7/8=−1/6−3/10x Enter your answer as a mixed number in simplest form in the box. x =
Answer:
X=[tex]\frac{36}{85}[/tex]
Step-by-step explanation:
-[tex]-\frac{7}{8}=-\frac{1}{6}-\frac{3}{10x}[/tex]
move the contants to the right hand side
[tex]-\frac{3}{10x}=-\frac{1}{6}+\frac{7}{8}[/tex]
Add the to terms on the right
[tex]-\frac{3}{10x}=\frac{17}{24}[/tex]
Cross multiply
72=170x
Swap sides of the equation
170x=72
Divide by 170 to both sides
x=[tex]\frac{36}{85}[/tex]
This is the simplest form.
The solution of the linear equation −7/8 = −1/6 − (3/10)x in the form of a mixed fraction number will be 2 ¹³/₃₆.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The linear equation is given below.
−7/8 = −1/6 − (3/10)x
Simplify the equation, then we have
−7/8 = −1/6 − (3/10)x
(3/10)x = −1/6 + 7/8
(3/10)x = 17/24
x = 85/36
x = 2 ¹³/₃₆
The arrangement of the direct condition −7/8 = −1/6 − (3/10)x as a blended part number will be 2 ¹³/₃₆.
More about the solution of the equation link is given below.
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Find the center of the circle that you can circumscribe about DABC.
. A(2, 8), B (0,8), and C (2,2)
The center of the circle that circumscribe about DABC is [tex](h,k) = (1, 5)[/tex].
A circle can be modelled after a expression of the form:
[tex]A\cdot x + B\cdot y + C =-x^{2}-y^{2}[/tex] (1)
We can determine all coefficients by knowing three distinct points on plane.
If we know that [tex](x_{1}, y_{1}) = (2, 8)[/tex], [tex](x_{2}, y_{2}) = (0, 8)[/tex] and [tex](x_{3}, y_{3}) = (2, 2)[/tex], then the solution of the system of linear equations is:
[tex]2\cdot A + 8\cdot B + C = -68[/tex] (2)
[tex]8\cdot B + C = -64[/tex] (3)
[tex]2\cdot A + 2\cdot B + C = -8[/tex] (4)
[tex]A = -2, B = -10, C = 16[/tex]
Now we proceed to complete squares and factor each resulting perfect square trinomial in order to determine the coordinates of the center of the circle:
[tex]x^{2}+y^{2}-2\cdot x -10\cdot y +16 = 0[/tex]
[tex](x^{2}-2\cdot x +1)-1+(y^{2}-10\cdot y +25)-25 +16 = 0[/tex]
[tex](x-1)^{2}+(y-5)^{2}= 10[/tex]
The center of the circle that circumscribe about DABC is [tex](h,k) = (1, 5)[/tex].
To learn more on circles, we kindly invite to check this verified question: https://brainly.com/question/11833983
what is the solution for x^0.5logx=0.01x^2 ?
Answer:
x1= 100 x2=99.999
Step-by-step explanation:
[tex]x^{0.5\log _{10}\left(x\right)}=0.01x^2[/tex]
[tex]0.5\log _{10}\left(x\right)\log _{10}\left(x\right)=\log _{10}\left(0.01\right)+2\log _{10}\left(x\right)[/tex]
u=log(x)
[tex]0.5uu=\log _{10}\left(0.01\right)+2u[/tex]
[tex]u=2+\sqrt{1.0E-15},\:u=2-\sqrt{1.0E-15}[/tex]
[tex]x=10^{2+\sqrt{1.0E-15}},\:x=10^{2-\sqrt{1.0E-15}}[/tex]
Which number below is an integer but not a natural number?
A) -1/2
B) Square root of 8
C) -5
D) 72
Answer:
C) -5
Step-by-step explanation:
-5 is an integer but not a whole number or a natural number.
Find the slope of 3x-y=24
Answer: slope = 3
Step-by-step explanation: 3x - y = 24
3x - 3x -y = 24 -3x
-y = -3x + 24
-y/-1 = -3x + 24/1
y = 3x - 24
Which number sentence is true?
OA) 5.6 > |-8.91
OB) |-5.6] < |-8.91
OC) -5.6 > 1-8.91
OD 15.6] > 1-8.91
The first one (when simplify) is
5.6>8.91
Which is not true if you plot it on a number line
The second one (when simplify) is
5.6<-8.91
which is not true because it is the same thing as number 1
The third one (when simplify) is
-5.6>8.91
which is obviously not true since negatives are way smaller than positives
So that leaves us the last one
Thefore the answer is OD.
I hope this helped!!
Question 2 of 5
-64
O A. - 16
O B. -4
O C. 4 or -4
OD. -8
Answer:
B.-4
Step-by-step explanation:
Hope it help!!!!!!
32-?-10+4=16 what is the missing number?
What is the value of k?
Answer:
k = 10
Step-by-step explanation:
the sum of any two interior angles is equal to the exterior angle of the unknown interior angle
4k+5 + 6k+10 = 115
10k + 15 = 115
10k = 100
k = 10
simplify this expression
Option B
If any doubt leave a comment
which of the following is would most likely negatively affect a person’s net worth
Step-by-step explanation:
Net Worth
Your assets are anything of value that you own that can be converted into cash. Examples include investments, bank and brokerage accounts, retirement funds, real estate and personal property (vehicles, jewelry, and collectibles)—and, of course, cash itself. Intangibles such as your personal network are sometimes considered assets as well. Your liabilities, on the other hand, represent your debts, such as loans, mortgages, credit card debt, medical bills, and student loans. The difference between the total value of your assets and liabilities is your net worth.
please help 25 points
Answer:
jijijija
Step-by-step explanation:
Answer:
s = -52
Step-by-step explanation:
We assume you want to find the value of s.
[tex]\dfrac{12+s}{-20}=2\\\\12+s=-40\qquad\text{multiply by -20}\\\\\boxed{s=-52}\qquad\text{subtract 12}[/tex]
Does the graph represent a function?
Answer:
no
Step-by-step explanation:
If it represented a function then it wouldn't be curved. curved lines don't represent a function
9. GIVEN: y(x + 1) = 51; y = 3 PROVE: x = 16
Answer:
see explanation
Step-by-step explanation:
y(x + 1) = 51 ← substitute y = 3 into the equation
3(x + 1) = 51 ( divide both sides by 3 )
x + 1 = 17 ( subtract 1 from both sides )
x = 16
Given:
y(x + 1) = 51y = 3What to prove: x = 16
=> y(x + 1) = 51=> 3(x + 1) = 51=> 3x + 3 = 51=> 3x = 51 - 3=> 3x = 48=> x = 16Conclusion:We have now proved that x = 16.
Hoped this helped.
[tex]BrainiacUSer1357[/tex]
If cos(θ)= -2/3 and θ lies in quadrant II, find the value of cotθ
[tex]\text{Given that,}\\\\\cos \theta = - \dfrac 23\\\\\implies \cos^2 \theta = \dfrac 49\\\\\implies 1- \sin^2 \theta = \dfrac 49\\\\\implies \sin^2 \theta =1-\dfrac 49\\\\\implies \sin^2 \theta =\dfrac 59\\\\\\\text{Now,}\\\\\cot^2 \theta = \dfrac{\cos^2 \theta}{\sin^2 \theta} \\\\\\\implies \cot^2 \theta = \dfrac{\tfrac 49}{\tfrac 59}\\\\\\\implies \cot^2 \theta = \dfrac 49 \times \dfrac 95\\\\\\\implies \cot^2 \theta = \dfrac 45\\\\\\[/tex]
[tex]\implies \cot \theta = \pm\sqrt{\dfrac 45} = \pm \dfrac 2{\sqrt 5}\\\\\\\text{Since}~ \theta ~ \text{lies in the second quadrant,} \cot \theta ~\text{will be negative.}\\\\\text{Hence,}~ \cot \theta = - \dfrac{2}{\sqrt 5}[/tex]
Answer:
yysywywyyw7e7eueuuwuwuuwueu3u3
Greg has entered a cycle race of 125 km. he rides the first 85 km in 2.5 hours. he rides the rest of the way in 2 hours. How much faster did he ride during the first part of the journey compared to the second?
Answer:
He rides 14km/hr faster
Step-by-step explanation:
Speed = distance/ time
In the first part,
Speed= 85/2.5
= 34km/hr
In the second part,
Distance= 125-85
=40km
Speed= 40/2
=20km/hr
How much faster did Greg ride ?
34-20= 14km/hr
Given m=-2/3, b=-7 give the point in slope form, slope intercept form, standard form, ;general form. HELP IS NEED ASAP PLEASE!!!
Answer:
Step-by-step explanation:
m=-2/3
b=-7
First, find the slope-intercept form.
y=mx+b
You know what the m and b values are, so simply plug them into the equation.
Slope-Intercept Form
y=-2/3x-7
From there, let's find the point-slope equation.
An easy way to find a coordinate point that the line crosses is to set one of the x or y variables equal to 0.
So let's set the x to 0.
y=-2/3x-7
y=-2/3(0)-7
y=-7
Therefore, when x is 0, y is equal to -7. We can now write our point. (0,-7)
Use the point-slope formula to write the point-slope equation.
y-y1=m(x-x1)
Point-Slope Equation
y-(-7)=-2/3(x-0)
Now, to find the standard form equation, let's find it using our slope-intercept equation. The formula to find standard form is
ax+by=c
y=-2/3x-7
Standard Form Equation
2/3x+y=-7
If the radius of a circle is ‘r’ units, which of the following is its circumference? *
Answer:
2πrExplanation:
The area of the unit circle is π (in general πr2 where r is the radius).
Round 23.4456 x 6.66 to the nearest ten (my brain isn't cooperating)
Answer:
160
Step-by-step explanation:
23.4456 x 6.66=156.147696 respectively.
156.147696 to the nearest ten is 160.
Can someone please give me the (Answers) to this? ... please ...
What is the name give to the angle pair 3 and 5?
The 2 pentagons above are similar. What is the area of the smaller pentagon?
Answer:
16^2
Step-by-step explanation:
All you have to do is do 64 *.25 and you get 16
The area of the smaller pentagon is 4 in². thus option B is correct.
How to determine the area of the smaller pentagon?The ratio of the side lengths are given:
Small : Large = 3.5 : 14
The area of the larger pentagon is given;
Area = 64 in²
By Using the given parameters, the area of the small pentagon:
Area = (Small/Large)² * Area of Large
Area = (3.5/14)² * 64
Area = 4
Hence, the area of the smaller pentagon is 4 in². thus option B is correct.
Read more about areas:
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What value(s) of x will make x2 = 25 true?
A. 5 and -5
B. 5
C. 5
D. 12.5 and -12.5
x^2 = 25
x = -5, 5
Check your work!
(-5)^2 = 25
(5)^2 = 25
Hope this helps! :)
There 7 ducklings .they sleep in 1 large nest .write and solve an equation that shows how many ducklings sleep in the nest
Answer:
7 ÷ 1 = 7
Step-by-step explanation:
Answer:
I think
Step-by-step explanation:
I think you are subtracting
8x7= something x0.1
please help me
let something = x
[tex]8 \times 7=x \times 0.1 \\ x = \frac{8 \times 7}{0.1} \\ x = \frac{8 \times 7 \times 10}{1} \\ x = 560[/tex]
therefore, something = 560
correct answer:-8x7= 560 x0.1[tex]\sqrt{3} sinx+cosx=2[/tex]
Answer:
Solution is in the photo
What is the least positive integer which when divided by 5 gives a remainder of 4, when divided by 6 gives a remainder of 5, when divided by 7 gives a remainder of 6, when divided by 8 gives a remainder of 7, when divided by 9 gives a remainder of 8, and when divided by 10 gives a remainder of 9
Answer:
2519
Step-by-step explanation:
In each case, the remainder is 1 less than the divisor. This means the number of interest will be 1 less than the least common multiple of 5, 6, 7, 8, 9, 10.
The prime factors of these numbers are ...
5 = 5
6 = 2·3
7 = 7
8 = 2³
9 = 3²
10 = 2·5
The unique factors are 2, 3, 5, 7. When they are used to their highest powers, the resulting product is ...
2³·3²·5·7 = 2520
The number of interest is 1 less than this, so is 2519.
2519 is the least positive integer that will give the required remainders.
what does 1/4 divided by 1/10 equal
Answer: 2/5
Step-by-step explanation: hope it helps