Answer:
c, a, b
Step-by-step explanation:
Given
See attachment for matrices
(a)
[tex]D = \left[\begin{array}{cc}\cos\theta &\sin\theta\\ -\sin\theta& \cos\theta\\\end{array}\right][/tex]
The determinant of the matrix is:
[tex]|D |= (\cos\theta * \cos\theta - \sin\theta *- \sin\theta)[/tex]
[tex]|D | = \cos^2\theta + \sin^2\theta[/tex]
Using trigonometry ratio, we have:
[tex]|D | = 1[/tex]
(b)
[tex]\left[\begin{array}{ccc}2&0\\0&2\end{array}\right][/tex]
The determinant of the matrix is:
[tex]|D| = 2 * 2 - 0 * 0[/tex]
[tex]|D| = 4 - 0[/tex]
[tex]|D| = 4[/tex]
(c)
[tex]\left[\begin{array}{ccc}0&i\\-i&0\end{array}\right][/tex]
The determinant of the matrix is:
[tex]|D| = 0 * 0 -(-i * i)[/tex]
[tex]|D| = 0 +i^2[/tex]
[tex]|D| = i^2[/tex]
In complex numbers
[tex]i^2 = -1[/tex]
So:
[tex]|D| = -1[/tex]
So, the order of the determinants is: c, a, b
If f(y) = 8 + e-9y, find f'(y). Use exact values.
Answer:
[tex]f'(y) = -9e^{-9y}[/tex]
Step-by-step explanation:
The given function is :
[tex]f(y) = 8 + e^{-9y}[/tex]
We need to find the value of f'(y).
[tex]f'(y)=\dfrac{d}{dy}[8+e^{-9y}][/tex]
[tex]=\dfrac{d}{dy}(8)+\dfrac{d}{dy}(e^{-9y})\\\\=0+e^{-9y}\dfrac{d}{dy}(-9y)\\\\=-9e^{-9y}[/tex]
So, the value of f'(y) is equal to [tex]-9e^{-9y}[/tex].
Find the greatest common factor (GCF) of 12 and 20. Show work.
The measure of angle 1 is 39 degrees. What is the measure of the angle adjacent to angle
1?
Answer:
51
Step-by-step explanation:
90-39 = 51
A wheel of radius 10 cm is turning at a rate of 5 revolutions per minute.
Calculate : the angle subtended at the centre by the minor arc.
Complete question:
A wheel of radius 10 cm is turning at a rate of 5 revolutions per minute.
Calculate the angle subtended at the centre by the minor arc after 1 second.
Answer:
the angle subtended at the centre by the minor arc is 30⁰
Step-by-step explanation:
Given;
radius of the wheel, r = 10 cm = 0.1 m
angular speed of the when, ω = 5 rev/min
duration of the motion, t = 1 second
Determine the angular speed in radian per second,
[tex]\omega = 5\ \frac{rev}{\min} \times \frac{2\pi \ rad}{1 \ rev} \ \times \frac{1 \min}{60 \ s} = \frac{10\pi \ rad}{60 \ s} = \frac{\pi }{6} rad/s[/tex]
After 1 second, the angular distance turned by the wheel is calculated as;
[tex]\theta = \omega t\\\\\theta = \frac{\pi \ rad} {6 \ s} \times 1 \ s\\\\\theta = \frac{\pi } {6 } \ rad\\\\in \ degrees; \theta = \frac{\pi \ rad}{6} \times \frac{180^0}{\pi \ rad} = \frac{180^0}{6} = 30^0[/tex]
Therefore, the angle subtended at the centre by the minor arc is 30⁰
Match the word with the definition.
Step-by-step explanation:
practical range = 8
vertical line test = 5
range = 3
domain = 2
relation = 1
function = 4
function Notation =6
practical domain=7
Find the surface area of the rectangular prism
2km
4km
6km
Answer:
88km is your answer
Step-by-step explanation:
brainlest pls
ASAP ANSWER PLEASE
A linear function has a slope of 2 and crosses the y axis at -8. What is the equation of the line?
Answer:
y = 2x -8
Step-by-step explanation:
The slope intercept form for a line is
y = mx+b where m is the slope and b is the y intercept
y = 2x -8
If you apply the changes below to the absolute value parent function, f(x) = [X],
what is the equation of the new function?
.
Shift 4 units to the right.
• Shift 6 units up.
A. g(x) = 5x + 6 + 4
B. g(x) = x - 41 + 6
C. g(x) = 1x - 61 + 4
D. g(x) = 5x + 4 + 6
Answer:
B
Step-by-step explanation:
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Here f(x) is shifted 4 units to the right , so
g(x) = | x - 4 |
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here f(x) is shifted 6 units up , so
g(x) = | x - 4 | + 6 → B
The simplified equation for the new function is g(x) = |x - 4| + 6.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The absolute value parent function is f(x) = |x|.
To shift 4 units to the right, we replace x with (x - 4) since we want the graph to move 4 units to the right.
To shift 6 units up, we add 6 to the entire function since we want the graph to move 6 units up.
So the equation of the new function g(x) is:
g(x) = |x - 4| + 6
Thus,
The simplified equation for the new function is g(x) = |x - 4| + 6.
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What is the answer to the expression?
Use Distributive Property to solve the expression.
2(35x + 15)
A designer builds a model of a sports car. The finished model is exactly the same shape as the original, but smaller. The scale factor is 2:15
Answer:
[tex]Ratio = 2 : 15[/tex]
Step-by-step explanation:
Given
[tex]k = 2 : 15[/tex] --- scale factor
Required [missing from the question]:
The ratio of width of the model to the original
From the question, we understand that the scale factor is: 2 : 15
The ratio of the width of the model to the original equals the given scale factor i.e.
[tex]Ratio = 2 : 15[/tex]
Solve for xxx. Enter the solutions from least to greatest. (x -7)(-4x -2)=0(x−7)(−4x−2)=0left parenthesis, x, minus, 7, right parenthesis, left parenthesis, minus, 4, x, minus, 2, right parenthesis, equals, 0
Answer:
-1/2, 7
Step-by-step explanation:
Given the expression
(x -7)(-4x -2)=0
This means that;
x - 7 = 0 and -4x - 2 = 0
x = 0+7 snd -4x = 2
x = 7 and x = -2/4
x = 7 and -1/2
Hence the solution from least to greatest is -1/2, 7
If you don't do a foreign language class in middle school, in high school will one be given to you? Is it a necessity?
Answer this please, I need help.
The amount of sales is 7500$
Sammy has 21 books on his shelf. Two-thirds of the books are mysteries. How many books are mysteries?
Answer:
14 books my good sir
Step-by-step explanation:
Find each missing measure.
Answer:
Each angle is 60 degrees
Step-by-step explanation:
The sides of the triangle are equal, which means the angles are equal. Since the sum of the interior angles of a triangle are 180 degrees, each angle is 180/3 = 60 degrees.
STION 6*
What is the value of x, if x = 32?
Answer:
32 is the value
Step-by-step explanation:
find the value of x that makes m ll n.
Answer:
11. x = 6
12. x = 7
Step-by-step explanation:
11.
16x - 6 = 90
16x = 96
x = 6
12.
12x - 4 = 10x + 10
2x = 14
x = 7
A half the radius, or 1/2r
B the circumference, or 2πr
C half the circumference, or πr
D the Radius, r
The base of the parallelogram formed from the circle is half the circumference or πr .
A circumference is the length of the circle which is the perimeter of the circle.
The circumference of the circle can be given by the formula C = 2πr , where r is the radius of the circle.
If a circle is divided into equal sectors then the approximate size of the polygon formed by rearranging the sectors is a parallelogram.
The base of the parallelogram will be half of the circumference , or
base = 0.5 × 2 πr = πr
And the height will be the radius r of the circle.
Now area of a parallelogram is given by base × height
Now area = πr × r = πr²
Therefore the area of the circle is πr² .
Hence the base of the parallelogram formed from the circle is half the circumference or πr .
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Please help I don’t understand! Giving brainliest!
its A f(x) =8x+6
Put the value of x in each f(x)
for instance: put the -½ in third f(x) you will have f(x)= -2,but the first f(x) =2
Determine the scale factor.
A
6
-4
3
B
А
B
1
2.
0
8 9 X
3 4 5 6
с
D
-2
D'
C'
Your answer
Answer:
3 or 1/3 depending on going from small to large, or from large to small
Step-by-step explanation:
the same scale factor applies to all sides of the transformed shape.
when going from small to large, every unit of side length turns into 3 units.
when going from large to small, every 3 units of side length turn into 1 unit.
Solve the espresso on for a=12, b=6 and c=3
Look at the picture ! Will give Brainly
Answer:
Step-by-step explanation:
bc²-2a/b=6(3)²-2×12/6=54-4=50
HELP ILL GIVE BRAINLIEST
Answer:
1
Step-by-step explanation:
So what is slope?
Slope is the change in y over the change in x.
You find the change in y and x when you compare two points on the line.
In this case, lets chose the two points they give us:
(1, -4) and (6, 1)
What is the difference of y? That looks like 5(1+4) or (1--4).
What is the difference of x? That looks like 5(6-1=5)
So we can tell the slope is y/x, or 5/5.
This can simpfly to 1.
So 1 is your slope!
5 and 1/7 * 8
HELP ME PLZ
Answer:
41 1/7
Step-by-step explanation:
5 1/7 x 8
Convert 5 1/7 to improper fraction
5 1/7 = 36/7
Multiply.
36 x 8
---- --
7 x 1
288/7
Simplify.
41 1/7
---
hope it helps
Classify the triangle by its angle measures.
Answer:
d) Acute
Step-by-step explanation:
if all three angle measures are less than 90 degrees, the triangle is acute
If −2x + 3 = 13, then 2x =____?
Which set Doesnt describe a function??
Answer:
set c is the answer
Step-by-step explanation:
for a pair to be a function it can't have 2 different numbers for the same x value
Willl give 100 points!!
Find the exact value of sine, cosine and tangent.
Answer:
Step-by-step explanation:
c i think
Find the value of x such that the data set has the given mean.
102, 119, 107, 114, 110, x; mean 118
Answer:
a
Step-by-step explanation:
Answer:
[see below]
Step-by-step explanation:
[tex]\frac{(102+119+107+114+110+x)}{6} =118\\\\6*(\frac{(102+119+107+114+110+x)}{6}) =118*6\\\\x+552=708\\\\x+552-552=708-552\\\\\boxed{x=156}[/tex]
Hope this helps.
Help me please I need to ge tthis done so can get an a
Answer:
n>- 5/14
Step-by-step explanat
What is the size of the blue angle, and what do we call an angle with these measurements?
Answers:
The blue angle is 135 degrees
The angle is obtuse
==========================================
Explanation:
Along the inner ring of values, the left arrow points at 135 (the midpoint of 130 and 140). Therefore, the blue angle is 135 degrees. Or you could note that starting at 130, and counting 5 spaces, will get you to 135. You could start at 140, and count down 5 spaces to get to the same spot.
Another way you can get the answer is to note that the blue arrow on the left is pointing at 45 along the top ring of numbers. This adds to 90 to get 90+45 = 135
Either way, you should get to 135 degrees as the angle value.
-------------
The angle is obtuse because the angle is larger than 90 degrees. It's wider or larger than a right angle.