Step-by-step explanation:
Since [tex]cos(\theta) = -\frac{3}{4}[/tex] we can get some information from this. First of all [tex]cos(\theta)[/tex] is defined as [tex]\frac{adjacent}{hypotenuse}[/tex]. So the adjacent side is 3 and the hypotenuse is 4. Using this we can find the opposite side to find [tex]sin(\theta)[/tex] to calculate csc and cot of theta. So using the Pythagorean Theorem we can solve for the missing side. Also I forget to mention we have to calculate the sign of the adjacent side and the hypotenuse. Since you're given that the angle is in quadrant 2, that means the x-value is going to be negative, and the y-value is going to be negative. And the x really represents the adjacent side and the y represents the opposite. So the adjacent side is what's negative. and the opposite is positive
Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
[tex](-3)^2 + b^2 = 4^2[/tex]
[tex]9 + b^2 = 16[/tex]
[tex]b^2 = 7[/tex]
[tex]b = \sqrt{7}[/tex]
So now we can calculate [tex]sin(\theta)[/tex].
[tex]sin(\theta) = \frac{\sqrt{7}}{4}[/tex]
Now to calculate the exact value of csc you simply take the inverse. This gives you [tex]csc(\theta)=\frac{4}{\sqrt{7}}[/tex]. Multiplying both sides by sqrt(7) to rational the denominator gives you [tex]\frac{4\sqrt7}{7}[/tex].
Now to calculate cot(theta) you find the inverse of tan. Tan is defined as [tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)}[/tex]. So all you do is take the inverse which is [tex]cot(\theta) = \frac{cos(\theta)}{sin(\theta)}[/tex].
Plug values in
[tex]cot(\theta) = \frac{-\frac{3}{4}}{\frac{4\sqrt{7}}{7}}[/tex]
Keep, change, flip
[tex]-\frac{3}{4} * \frac{7}{4\sqrt7}[/tex]
Multiply:
[tex]-\frac{21}{16\sqrt7}[/tex]
Multiply both sides by sqrt(7)
[tex]-\frac{21\sqrt7}{112}[/tex]
This is the value of cot(theta)
Jillian had 2/9m of a cloth. she used 1/9m of it for sewing a blanket. how much of the cloth does she have remaining?
Hello,
2/9 - 1/9 = (2 - 1)/9 = 1/9
Select the correct answer.
Which statement best defines perpendicular lines?
A.
lines that lie in the same plane
B.
lines that intersect and form right angles
C.
lines that lie in the same plane and do not intersect
D.
lines that share a point
Answer:
c or b
Step-by-step explanation:
Answer:
Answer:B
Step-by-step explanation:
I did the test and got it right the person above help thx
Need help with Matrices!!
For f(x)=4x+1 and g(x) = x^2 - 5, find (f+g)(x).
Answer:
(f + g)(x) = x² + 4x - 4
Step-by-step explanation:
The statement (f + g)(x) is the same as f(x) + g(x). In other words, the question simply wants you to add the two functions together.
f(x) = 4x + 1
g(x) = x² - 5
(f + g)(x) <----- Original statement
f(x) + g(x) <----- Rewrite
(4x + 1) + (x² - 5) <----- Substitute the equations in f(x) and g(x)
4x + x² - 4 <----- Add 1 and -5
x² + 4x - 4 <----- Rearrange the terms
Triangles A B C and X Y Z are shown. Sides A C and Z X are congruent. Angles B A C and Z X Y are 35 degrees. Angle X Z Y is 47 degrees. Angle A B C is 98 degrees.
Determine the rigid transformations that will map ΔABC to ΔXYZ.
Translate vertex B to vertex Z; reflect ΔABC across side AB.
Translate vertex X to vertex C; rotate ΔXYZ to align the sides and angles.
Reflect ΔABC across side AB; translate vertex C to vertex X.
Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
We know that the sum of angles of a triangle is always. In ΔXYZ,
What is the sum angle of the triangle?
[tex]\angle A + \angle B + \angle C=180^0[/tex]
[tex]35^0+\angle Y+47^0=180^0[/tex]
[tex]\angle y=98^0[/tex]
In both triangles, it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A=\angle X=35^0[/tex]and.[tex]\angle B = \angle Y =98^0[/tex]
By the AAS rule of congruence, ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having the same angle and rotate the triangle to align the sides and angles.
Since vertex X and vertex A have the same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.
Hence the correct option is d.
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Answer:
D: Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Step-by-step explanation:
edge 2022
The function f(x) = 5* is reflected over the y-axis. Which equations represent the reflected function? Select two
options.
f(x) = -(5)-*
0x==3(2)
Of(x) = 5(2)
f(x) = 5(5)
f(x) = 5(5)-*
Step-by-step explanation:
To reflect a function about the vertical axis, just negate the variable.
For example, if we want to reflect this function
[tex] y = log(x) [/tex]
about the y axis or vertical axis, we just make the x negative
[tex]y = log( - x) [/tex]
Another example,
[tex]y = |x| [/tex]
To reflect about y axis or vertical axis,
[tex]y = | - x| [/tex]
So here l,the answer with negative variables are function that are reflected about the y axis.
The options are the first and the fifth option.
Given the function h of x equals three times the square root x plus 1 end root minus 2, which statement is true about h(x)? The function is increasing on the interval (–∞, –2). The function is decreasing on the interval (–3, ∞). The function is decreasing on the interval (–∞, –3). The function is increasing on the interval (–2, ∞).
The function is decreasing on the interval (–3, ∞). Therefore, the correct option is B.
How to illustrate the function?A linear function can be represented by a line. The standard form for this equation is: ax+b where,
a= the slope
b= the constant term that represents the y-intercept.
The domain of a function is the set of input values for which the function is real and defined.
Here, the function is decreasing on the interval (–3, ∞).
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cos 0 = 8/17. Find tan 0.
tan is 15/8
How to determine the identitySince cos = adjacent/ hypotenuse
Adjacent = 8
Hypotenuse = 17
Let's find opposite
Using the Pythagoras theorem
Opposite ^2 = Hypotenuse^2 - adjacent^2
Opposite = [tex]\sqrt{17^2 - 8^2}[/tex]
Opposite = [tex]\sqrt{289 - 64}[/tex]
Opposite = [tex]\sqrt{225}[/tex]
Opposite = 15
Tan = opposite/ adjacent
Tan = 15/ 8
Thus, tan is 15/8
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Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
The expression square root of 25/49 can be given as 5/7
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality is the non equal comparison of two or more numbers and variables.
The solution to the system of inequalities x – 4y < 4 and y < x + 1 is shown in the graph.
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Answer:
its c
Step-by-step explanation:
Rounded to the nearest hundredth what is a positivite solution to the quadratic equation 0=2x^(2)+3x-8
OPTIONS
1.39
2.00
2.89
3.50
Step-by-step explanation:
the equation is
2x² + 3x - 8 = 0
the generic solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 2
b = 3
c = -8
x = (-3 ± sqrt(9 - 4×2×-8))/(2×2) =
= (-3 ± sqrt(9 + 64))/4 = (-3 ± sqrt(73))/4
x1 = (-3 + sqrt(73))/4 = (-3 + 8.544003745)/4 =
= 1.386000936... ≈ 1.39
x2 = (-3 - sqrt(73))/4
but that would negative, and therefore not a wanted solution.
x ≈ 1.39
is the targeted solution.
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 + x + 4 x g(x) –2 1 –1 3 0 5 1 7 2 9
The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is
[tex](\sqrt{2},\sqrt{-2} )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]
We have given that,
f(x) = 2x^2 + x + 4
x g(x)
-2 1
-1 3
0 5
1 7
2 9
What is a polynomial function?A polynomial function is a relation where a dependent variable is equal to a polynomial expression.
A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.
The general form of a polynomial expression is:
a₀ + a₁x + a₂x² + a₃x³ + ... + anxⁿ.
The highest power to a variable is the degree of the polynomial expression. When degree = 2, the function is a quadratic function.
When degree = 1, the function is a linear function.
How do we solve the given question?
The quadratic function is given to us:f(x) = 2x^2 + x + 4.
We need to determine the linear equation g(x).
Since it's a linear equation we use the two-point method to determine the equation.
What is the two-point?y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)
We take the points g(-2) =1, g(-1) = 3
g(x) - g(1) = ((g(-2)-g(-1))/(-2+1))*(x-1)or,
g(x) - 1 = ((-2-(-1))/(-2+1))*(x-1)or, g(x) - 1 = -1(-x+1)or,
g(x) = x - 1 + 1 = x
∴ g(x) = x , is the linear function g(x)
We are asked to find the solution to the system of equations f(x) and g(x).To find the solution we need to check what is the common solution to both f(x) and g(x).
For that, we equate f(x) and g(x).2x^2 + x + 4 = x or, 2x² - x +x- 4 = 0or, 2x^2 - 4 = 02(x^2-2)=0x^2-2=0[tex]x^2-\sqrt{2}=0[/tex][tex](x-\sqrt{2}) (x+\sqrt{2})=0[/tex][tex](x-\sqrt{2})=0 \\x=\sqrt{2} or x=-\sqrt{2}[/tex]g(-1) = 3(from the table)[tex]g(\sqrt{2})=\sqrt{2} \ and \ g(\sqrt{-2}) =-\sqrt{2}[/tex][tex]f(\sqrt{2}) = 2(\sqrt{2} )^2 + (\sqrt{2} ) + 3\\=2(2)+\sqrt{2} +3\\=7+\sqrt{2}[/tex][tex]g(-\sqrt{2} )= 2(\sqrt{-2} )^2 + (\sqrt{-2} ) + 3\\=2(2)+\sqrt{-2} +3\\=7+\sqrt{-2}[/tex]
The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is [tex](\sqrt{2},\sqrt{-2} )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]
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please help its confusing me
Answer:
x=−9 and y=8
Step-by-step explanation:
Let's solve your system by elimination.
2x+3y=6;4x−y=−44
Multiply the first equation by -2,and multiply the second equation by 1.
−2(2x+3y=6)
1(4x−y=−44)
Becomes:
−4x−6y=−12
4x−y=−44
Add these equations to eliminate x:
−7y=−56
Then solve−7y=−56for y:
−7y=−56
-7y/-7 = = -56/-7
(Divide both sides by -7)
y=8
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
2x+3y=6
Substitute8 for y in 2x+3y=6:
2x+(3)(8)=6
2x+24=6(Simplify both sides of the equation)
2x+24+−24=6+−24(Add -24 to both sides)
2x=−18
2x/2 = -18/2 (Divide both sides by 2)
x=−9
Answer:
x=−9 and y=8
Answer:
x = -9
y = 8
Step-by-step explanation:
(using substitution)
4x-y = -44
4x + 44 = y
substitute (4x+44) as y in the other equation
2x + 3(4x+44) = 6
2x+12x+132 = 6
14x = -126
x = -9
then plug -9 as x into one of the equations to find y
4(-9) - y = -44
-36-y=-44
-y=-8
y=8
then check the answer by plugging in the values of x and y (-9 and 8) for x and y in one of the equations
4(-9) - (8) = -44
you get: -44 = -44, which is true, so the x and y values are correct
How many heartbeats is 4800 in a day? Put your answer in scientific notation
Answer:
Step-by-step explanation:
4.8 x 10^3 heartbeats/day
Answer: A humans heart average per minute is 80 then you got one hour 60 x 80 equals 4800
which would be 4.8x 10 over 3 which is your answer
Step-by-step explanation:
1/2+3/2=2^x
What is the solution to the equation?
Answer: x=1
Step-by-step explanation:
1/2+3/2=2^x
4/2=2^x
2=2^x
x=1
CAN SOMEONE HELP PLEASE
m4A=42°, b=10, c= 12. What is the length of a to the nearest tenth?
Answer:
a = 8.1
Step-by-step explanation:
Use the cosine rule:
[tex]a = \sqrt{b^2 + c^2 -2 bc \space\ cosA }[/tex]
Substituting the values:
[tex]a = \sqrt{10^2 + 12^2 -2(10)(12) \space\ cos 42 \textdegree\ }[/tex]
⇒ [tex]a = \sqrt{4 \space\ cos 42\textdegree\ }[/tex]
⇒ [tex]a = 8.1[/tex]
1. Complete the table to identify habits that you have that both increase and
decrease your risk of being a victim of fraud or identity theft. Write at least three
habits in each column. (6 points)
Some habits that you can engage in that would increase your risk of being victim of fraud or identity theft are:
Using the same simple password for several online accounts. Not checking your banking and credit card statements regularly. Posting too much of your life on social media.You can be less at risk of fraud or identity theft if you:
Use multiple passwords for separate accounts. Keep an eye on your credit card and bank statement reports. Update your security and app software often.How can you avoid being a victim of fraud or identity theft?When you use the same password for various accounts, all those accounts are at risk if the password is stolen. So using multiple passwords is best.
You should also regularly monitor your credit card statements and bank reports to check for unfamiliar expenses which can be flagged immediately.
Also update your apps regularly as they come with security patches to protect your data. Avoid sharing too much information on social media as these can be used to predict your passwords.
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How to work out this linear stimultaneous equations
Step-by-step explanation:
extract the third equation from one of the given equation by making at most one variable with 1 as the coefficient the subject of the equation.[tex] x = 2 - y...........(3)[/tex]now substitute the third equation to the other equation *Not the one you extracted the new equation from*[tex]y = 2 ({2 - y})^{2} + (2 -y ) - 2[/tex]After substituting simplify[tex]y = 2(2 - y)(2 - y) + 2 - y - 2 \\ y = 2(4 - 2y - 2y + {y}^{2} ) + 2 - y - 2 \\ y = 2(4 - 4y + {y}^{2} ) - y \\ y = 8 - 8y + 2 {y }^{2} - y[/tex]Therfore group the terms in the form of a general Quadratic equation.Drag each ratio to the correct location on the image. Not all ratios will be used.
Match each ratio of the volumes of two solids to the pair of solids it represents.
3:1
2r: 3h
h: 4r
4r: h
4r: 3h
4:1
Answer:
cylinder to cone = 3:1
sphere to cylinder = 4r:3h
cone to sphere = h:4r
hemisphere to cylinder = 2r:3h
Step-by-step explanation:
1. Nasim thinks of a number.
When he multiplies his number by 5 and subtracts 16 from the result, he gets the same
answer as when ads 10 to his number and multiplies that result by 3.
Find the number Nasim is thinking of.
Step-by-step explanation:
5x-16 = 3 (10+x)
=> x= 23
Help quick! pleaseeeeeee
A) The function ƒ(x) has a steeper slope than g(x).
B) The functions ƒ(x) and g(x) have the same slope.
C) The function g(x) has a steeper slope than ƒ(x).
D) There isn't enough information to determine which function has a steeper slope.
The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x). The correct option is C.
What is a Straight Line Equation?A straight line equation is represented by y = mx+c, where m is the slope and c is the y-intercept.
m is given by (y₂-y₁)/(x₂-x₁)
From the graph , the y-intercept is 4 and the two points on the line are ( 0,4) and ( 1,1).
m = -3
c =4
The equation of the function g(x) is g(x) = -3x+4
The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x).
Therefore, the correct option is C.
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Pls I will get spanked if you don't help me.
How many meters are equal to 3 kilometers? Use the pattern in the number of zeros of the product when multiplying by a power of 10 to help you.
Answers:
30 meters
300 meters
3,000 meters
30,000 meters
1KM = 1000metres
3KM =3000metres
rewrite each expression without using absolute value notation |x-y| if x>y
The expression |x - y| without using absolute value notation is x - y
How to rewrite the expression?The expression is given as:
|x - y|
Also, we have:
x > y
This means that:
|x - y| > 0
Remove the absolute notation
x - y
Hence, the expression |x - y| without using absolute value notation is x - y
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Find an equation of a line with slope -3/4 and that passes through P(-4,6) in standard, form.
Answer:
[tex]y = - \frac{3}{4}x + 3[/tex]
Step-by-step explanation:
the standard form of any straight line is:
y = m × x + c
where: y is the y value of the point
x is the x value of the point
m is the gradient/slope
SOLUTION
[tex]y = mx + c \\ 6 = - \frac{3}{4} ( - 4) + c \\ c = 3[/tex]
cos(x)=2cos^2(x)-1 0≤x≤2π
Answer:
[tex]x=0,~x=\frac{2\pi }{3},\:x=\frac{4\pi }{3},~x=2\pi[/tex]
Step-by-step explanation:
The given equation:
[tex]\cos(x)=2\cos^2(x)-1[/tex]
Let [tex]\cos(x)[/tex] be [tex]y[/tex]:
[tex]y=2y^2-1[/tex]
Rewrite as:
[tex]2y^2-y-1=0[/tex]
After solving quadratic equation, the solutions are:
[tex]y=1~~~~y=-\frac{1}{2}[/tex]
Substitute back [tex]\cos(x)[/tex], it follows:
[tex]\cos(x)=1~~~~\cos(x)=-\frac12[/tex]
For the first equation, the solution is [tex]x=0[/tex] and [tex]x=2\pi[/tex].
For the second equation, general solution is:
[tex]x=\frac{2\pi }{3}+2\pi n,\:x=\frac{4\pi }{3}+2\pi n[/tex]
But for the given interval, we must substitute n=0 into the equations so that the values of x must be within interval. Therefore:
[tex]x=\frac{2\pi }{3},\:x=\frac{4\pi }{3}[/tex]
So, the answers are:
[tex]x=0,~x=\frac{2\pi }{3},\:x=\frac{4\pi }{3},~x=2\pi[/tex]
I’m confused on this
Answer:
x = 25
Step-by-step explanation:
The mistake here is the squaring. When you square one side, you have to do the same on the other side:
[tex]\sqrt{3x+6}[/tex] = 9
[tex](\sqrt{3x+6}) ^{2}[/tex] = [tex]9^{2}[/tex]
3x + 6 = 81
3x = 75
x = 25
[tex]\huge\boxed{x=25}[/tex]
The mistake is in Step 1. The solver should have also squared [tex]9[/tex] when squaring the other side of the equation.
Correctly solving[tex]\begin{aligned}\sqrt{3x+6}&=9\\(\sqrt{3x+6})^2&=9^2\\3x+6&=81\\3x+6-6&=81-6\\3x&=75\\\frac{3x}{3}&=\frac{75}{3}\\x&=25\end{aligned}[/tex]
Write the equation of an ellipse with center (-2,-3), vertical major axis of length 14, and minor axis of
length 8.
Step-by-step explanation:
Since we have a vertical major axis, our ellipse is vertical.
The equation of a vertical ellipse is
[tex] \frac{(y - k) {}^{2} }{ {a}^{2} } + \frac{(x - h) {}^{2} }{ {b}^{2} } = 1[/tex]
where
(h,k) is the center
a is the semi major axis,
b is the semi minor axis
First, let plug in our center
[tex] \frac{(y + 3) {}^{2} }{ {a}^{2} } + \frac{(x + 2) {}^{2} }{ {b}^{2} } = 1[/tex]
Semi means half, so
a is half of 14 which is 7
B is half of 8, which is 4.
[tex] \frac{(y + 3) {}^{2} }{49} + \frac{(x + 2) {}^{2} }{16} = 1[/tex]
If you have a cube with the volume of 73.560059, what is the length of the cube?
What are the restrictions for y
X=10/5+y
Answer:
[tex]y\ne-5[/tex]
Step-by-step explanation:
So you have the equation:
[tex]x=\frac{10}{5+y}[/tex]. As you may know, you cannot divide by 0, so y has to be restricted in a way that the denominator is never equal to 0. So to find when y makes the denominator 0, simply set the denominator equal to 0, and solve for y. This gives you the equation: 5+y = 0, y=-5. So the y value CANNOT be equal to -5. Because it makes the denominator 0. so [tex]y\ne-5[/tex] would be the restriction.
Find the length of CD shown in red below. Show all work.
By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.
How to calculate the length of an arc
The figure presents a circle, the arc of a circle (s), in inches, is equal to the product of the central angle (θ), in radians, and the radius (r), in inches. Please notice that a complete circle has a central angle of 360°.
If we know that θ = 52π/180 and r = 6 inches, then the length of the arc CD is:
s = [(360π/180) - (52π/180)] · (6 in)
s ≈ 32.254 in
By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.
RemarkThe statement has typing mistakes, correct form is shown below:
Find the length of the arc EF shown in red below. Show all the work.
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A grab bag contains 12 packages worth $.70 each, 15 packages $.40 cents each, and 25 packages worth $.30 each. what is the expected value if you have to pay $.50 to pick one package at random?
group of answer choices
$0.47
-$0.08
$0.00
$0.01
The expected value of the discrete distribution, if you have to pay $.50 to pick one package at random, is of -$0.08.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
For this problem, considering the cost of $0.5, the distribution is given as follows:
P(X = 0.2) = 12/(12 + 15 + 23) = 12/50 = 0.24.P(X = -0.1) = 15/(12 + 15 + 23) = 15/50 = 0.3.P(X = -0.2) = 23/(12 + 15 + 23) = 23/50 = 0.46.Hence the expected value is given by:
E(X) = 0.2 x 0.24 - 0.3 x 0.1 - 0.2 x 0.46 = -$0.08.
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