Answer:
[tex]\displaystyle \tan \left(\frac{7\pi}{8}\right) = -\left(2 + \sqrt{2}\right)[/tex].
Step-by-step explanation:
Assume that the following are known:
The tangent half-angle identity: [tex]\displaystyle \tan\left(\frac{\theta}{2}\right) = \frac{1 - \cos(\theta)}{\sin(\theta)}[/tex].The sine and cosine of [tex]\displaystyle \frac{\pi}{4}[/tex]: [tex]\displaystyle \sin\left(\displaystyle \frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}[/tex], [tex]\displaystyle \cos\left(\displaystyle \frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}[/tex].The trigonometric identities for the sine and cosine of supplementary angles: [tex]\sin(\theta) = -\sin(2\pi - \theta)[/tex] and [tex]\cos(\theta) = \cos(2\pi - \theta)[/tex].The angle in question [tex]\displaystyle \frac{7 \pi}{8}[/tex] isn't very well-known. However, note that:
[tex]\displaystyle \frac{7 \pi}{8}[/tex] is equal to one-half times the angle [tex]\displaystyle \frac{7\pi}{4}[/tex];[tex]\displaystyle \frac{7\pi}{4}[/tex] is equal to [tex]2\pi[/tex] minus [tex]\displaystyle \frac{\pi}{4}[/tex], which is an angle with known sine and cosine values.Since the angle [tex]\displaystyle \frac{7\pi}{4}[/tex] is equal to [tex]\displaystyle 2\pi - \frac{\pi}{4}[/tex], its sine and cosine can be found from the sine and cosine of [tex]\displaystyle \frac{\pi}{4}[/tex] using the trigonometric identities [tex]\sin(2\pi - \theta) = -\sin(\theta)[/tex] and [tex]\cos(2\pi - \theta) = \cos(\theta)[/tex]:
[tex]\displaystyle \sin\left(\frac{7\pi}{4}\right) = -\sin\left(2\pi - \frac{7\pi}{4}\right) = - \sin\left(\frac{\pi}{4}\right) = - \frac{\sqrt{2}}{2}[/tex].[tex]\displaystyle \cos\left(\frac{7\pi}{4}\right) = \cos\left(2\pi - \frac{7\pi}{4}\right) = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}[/tex].Apply the tangent half-angle identity to find the tangent of [tex]\displaystyle \frac{7 \pi}{8}[/tex]:
[tex]\begin{aligned}\tan\left(\frac{7\pi}{8}\right) &= \tan\left(\frac{7\pi/4}{2}\right) = \frac{1 - \cos(7\pi/4)}{\sin(7\pi/4)} \\ &= \frac{1 - \left(\sqrt{2}/2\right)}{\sqrt{2} / 2} = \frac{2 - \sqrt{2}}{\sqrt{2}} = \frac{\left(\sqrt{2}\right)^2 - \sqrt{2}}{\sqrt{2}} = \sqrt{2} - 1 \end{aligned}[/tex].
Without drawing the graph of the function y=1.2x−7, see if the graph passes through points: (100; 113)
Answer:
The graph of the function passes through the point (100; 113).
Step-by-step explanation:
In order to calculate if the graph of the function passes through the point or not, we need to insert the point's coordinates in the function and check if the equation is valid or not, if it is, then the graph passes through them.
[tex]y(x) = 1.2*x - 7\\y(100) = 1.2*100 - 7\\y(100) = 120 - 7 \\y(100) = 113[/tex]
Which is equal to the "y" coordinate of the point, therefore the graph of the function passes through the point (100;113).
Answer:
yes
Step-by-step explanation:
PLSSSS ANSWERRR
a−b−c+d, if a=−5; b=4; c=1; d=−3
Answer:-13
Step-by-step explanation:-5-4-1+-3
Solve for x rounded to the nearest tenth.
X
18
cos 70 =x/18
Answer:
6.2 =x
Step-by-step explanation:
cos 70 =x/18
Multiply each side by 18
18cos 70 =x/18 *18
18cos 70 =x
6.15636258 = x
To the nearest tenth
6.2 =x
Answer:
x = 1260
Step-by-step explanation:
Arithmetic or geometric
1/3, 2/3 ,1 4/3
Please help
Answer:
arithmetic
Step-by-step explanation:
Geometry is shapes ...
PLSS HELP ASAP! WILL MARK BRAINLIEST
2x-5/8 + x = 2x+5/2 + 4
collect the like terms
2x + x -2x = 5/2+4 +5/8
X = 57/8
Jamie's partner for a project has a passive-aggressive personality. What is 5 points
the best way to work with her?
A. Procrastination
B. Directness
C. Stubbornness
D. Motivation
Answer:
directness
Step-by-step explanation:
(-8x) . 3x^2 please help
Answer:
-24x³
Step By Step:
(-8x) · 3x²
-8x · 3x²
-8 · 3x · x²
-24x · x²
-24x³
The Answer would be -24x³
Hope This helps∞
Give Brainliest if you please
Which question can be represented by the equation 5/6 divided by 3/4?
Answer choices:
How many 5/6 scoop of ice-cream can fit into 3/4 pound container?
How many 3/4 pound hamburgers can be made with 5/6 pound of meat?
What is the difference between a 5/6 foot piece of ribbon and a 3/4 foot piece of ribbon?
CHOOSE ONE
Answer:
1/12
Step-by-step explanation:
Please help this is a different one!
Answer:
The first number line.
Step-by-step explanation:
In the first number line, both lines decrease, which is the same as the word problem says. Hope this helps!
lol this is my last question :)
Answer:
≈ 36.9
Step-by-step explanation:
You are given the opposite and adjacent side, leading you to use tan. However, since you're trying to find the angle measurement, you use the inverse of tan: [tex]tan^-1[/tex]
Set it up like this:
[tex]tan^-1 ( \frac{24}{32})=?[/tex]
When you solve, you get:
36.86
Round to the nearest tenth:
36.9
if A= and B=, find BA.
Answer:
Option d.
Step-by-step explanation:
The given matrices are
[tex]A=\begin{bmatrix}3&2&-4\\ \:5&-5&-3\\ \:4&1&1\end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}2&-4&1\\ \:5&-3&2\\ \:4&4&-5\end{bmatrix}[/tex]
We need to find BA.
[tex]BA=\begin{bmatrix}2&-4&1\\ \:5&-3&2\\ \:4&4&-5\end{bmatrix}\begin{bmatrix}3&2&-4\\ \:5&-5&-3\\ \:4&1&1\end{bmatrix}[/tex]
[tex]BA=\begin{bmatrix}2\cdot \:3+\left(-4\right)\cdot \:5+1\cdot \:4&2\cdot \:2+\left(-4\right)\left(-5\right)+1\cdot \:1&2\left(-4\right)+\left(-4\right)\left(-3\right)+1\cdot \:1\\ 5\cdot \:3+\left(-3\right)\cdot \:5+2\cdot \:4&5\cdot \:2+\left(-3\right)\left(-5\right)+2\cdot \:1&5\left(-4\right)+\left(-3\right)\left(-3\right)+2\cdot \:1\\ 4\cdot \:3+4\cdot \:5+\left(-5\right)\cdot \:4&4\cdot \:2+4\left(-5\right)+\left(-5\right)\cdot \:1&4\left(-4\right)+4\left(-3\right)+\left(-5\right)\cdot \:1\end{bmatrix}[/tex]
[tex]BA=\begin{bmatrix}-10&25&5\\ 8&27&-9\\ 12&-17&-33\end{bmatrix}[/tex]
Hence, option (d) is correct.
Answer CORRECTLY !!!!! Will mark brainliest !!!!
Answer:
g(q) = [tex]\frac{5q}{8}[/tex]
Step-by-step explanation:
Given
- 7q + 12r = 3q - 4r
Rearrange making r the subject
Add 7q to both sides
12r = 10q - 4r ( add 4r to both sides )
16r = 10q ( divide both sides by 16 )
r = [tex]\frac{10q}{16}[/tex] = [tex]\frac{5q}{8}[/tex] , thus
g(q) = [tex]\frac{5q}{8}[/tex]
What is the value of y?
Answer:
65 degrees
Step-by-step explanation:
First, solve for the unknown angle( not the y's).
the angle 130 is supplementary to that angle so we will use an equation to solve it. (supplementary means it adds up to 180 degrees)
x+130=180
-130 -130
x = 50 so, 50 is the measure of the interior angle
Now we have to use another equation to solve for y:
50+2y=180
-50 -50
2y = 130
/2 /2
y = 65
Thus, y is 65
So the right answer is 65 degree
Look at the attached picture
Hope it will help you
Good luck on your assignment
Can I get some help with 26 please?
Answer:
C.
Step-by-step explanation:
easiest way to find is to look at "X value", and sub. 2 then the "Y value" and add 3
hope this helps :)
Use 30-60-90 or 45-45-90 triangle relationships to find the missing variable
Answer:
Step-by-step explanation:
it is 30-60-90
triangle.
so smaller side is half the hypotenuse.
x=(10√3)/2=5√3
if hypotenuse=10√5,then x=10√5/2=5√5
5. A race course is 99 meters long. There are trees
along 38 meters of the course. How long is the part
of the course without trees?
unit
Answer:
61
Step-by-step explanation:
99 minus 38
Answer:
61 meters
Step-by-step explanation:
To find this answer, you need to subtract the length with trees from the total length of the course. With this information, you get an equation that looks something like x + 38 = 99, with x being the length of the course without trees.
Subtract 38 from both sides:
x + 38 = 99
- 38 - 38
x = 99 - 38
Simplify:
x = 61
In the talent show, 6 students plan to sing, 7 students plan to dance, and 2 students plan to
tell jokes. Rick said that the ratio of singers to joke-tellers is 6 to 2. Leah said that the ratio of
joke-tellers to singers is 1 to 3. Who is correct? Explain why.
Answer:
Rick is correct
Step-by-step explanation:
Answer:
Rick is correct because there are 6 students that plan to sing and there are only 2 students that plan to tell jokes so the ratio is 6 to 2
Step-by-step explanation:
Evaluate the algebraic
expression:
Plz answer quick
Answer:
7,-5,-11
Step-by-step explanation:
-3(-4)-5=7
-3(0)-5=-5
-3(2)-5=-11
PLEASE ANSWER THIS QUESTION ILL MARK YOU AS THE BRAINLIEST
Please help !!!!!!! Will mark brainliest for the correct answer !!!!!!!!
Answer:
Step-by-step explanation:
-2m - 5n = 7m - 3n
-9m - 5n = -3n
-9m = -2n
m = 2n/9
g(m)= 2n/9
-9/2m is the answer.
-2m-5n=7m-3n
-2n=9m
n=9m/-2
so -9/2m
hope this helps :)
Solve the equation square root of 3x+4=4
The solution of equation for x is,
⇒ x = 4
We have to given that;
The equation is,
⇒√ (3x + 4) = 4
Now, We can simplify as;
⇒ √3x + 4 = 4
Take square both side,
⇒ 3x + 4 = 4²
⇒ 3x + 4 = 16
Subtract 4 both side,
⇒ 3x = 16 - 4
⇒ 3x = 12
Divide by 3;
⇒ x = 12/3
⇒ x = 4
Thus, The solution of equation for x is,
⇒ x = 4
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Need help anyone asap xd?
Answer:
B
Step-by-step explanation:
Let's start by converting each of these into decimal form.
[tex]\pi\approx 3.1416\\\sqrt{10}\approx 3.1623\\\dfrac{22}{7}\approx 3.1428[/tex]
Therefore, the correct order is:
[tex]3.14, \pi, \dfrac{22}{7}, \sqrt{10}[/tex]
or answer choice B. Hope this helps!
Answer: B. 3.14, π, 22/7, square root of 10
Step-by-step explanation:
To order the numbers in increasing order, first solve for each to get the numbers into their simplest forms.
Pi can be estimated to 3.1415, which is already bigger than 3.14.
Knowing this, you can eliminate choice A, which lists pi as less than 3.14.
Dividing 22 by 7 gets you ~3.142, which is greater than both pi and 3.14.
Knowing this, you can eliminate choices C and D, which list 22/7 as less than 3.14 and pi.
The correct answer choice is B.
A bowl contains a total of 26 blue and red marbles. There are two more red marbles than
blue marbles. How many blue marbles are in the bowl?
Which of the following let statements should you use?
Let x = the number of red marbles. Let x + 2 = the number
of blue marbles.
Let x = the number of blue marbles. Let 2x = the number of
red marbles.
Let x = the number of blue marbles. Let x + 2 = the number
of red marbles.
Answer:
There are 26 total marbles. We will call x the number of blue
marbles. So there are x+2 red marbles. If you add them together you
get x + x + 2....and all that equals 26 (subtract 2 from each side
Step-by-step explanation:
Hope this helps
Solve the system of equations.
y = x + 3
y = x2 - 2x - 1
A.
(-1, 7) and (4, 2)
B.
(-1, 4) and (4, -1)
C.
(-1, 2) and (4, 7)
D.
(1, 4) and (-4, -1)
Answer:
The answer is ( -1, 2) and ( 4,7 )
Step-by-step explanation:
Answer:
Step-by-step explanation:
x^2 - 2x - 1 = x + 3
x^2 - 3x - 4 = 0
(x - 4)(x + 1)= 0
x - 4 = 0
x = 4
y= 4^2 - 2(4) - 1 = 16-8-1= 8-1= 7
(4, 7)
x + 1 = 0
x = -1
(-1)^2 - 2(-1)-1= 1+2-1=3-1=2
(-1,2)
answer is C
In a school, the ratio of the number of boys to the number of girls in a school is 7 : 5 - if there are 600 students in the school, how many girls are there?
How many students does each unit represent?
Answer:
350 girls.
5 unit represents 250 girls and the 7 unit represents 350 boys
Step-by-step explanation:
Add 5+7 =12
600÷12=50
RATIO OF BOYS TO GIRLS IS 7:5 SO
50x5=250 GIRLS.
7*50=350
so 5 unit represents 250 girls and the 7 unit represents 350 boys.
Answer:7
Step-by-step explanation:
Which function has a negative discriminant value?
Answer:
Step-by-step explanation:
e
Answer:
the third one
Step-by-step explanation:
A tennis supply store pays a wholesaler $90 for a tennis racquet and marks it up by 60%.
What do they charge for the tennis racquet?
Answer:
you divide 144 by 90: 144/90, and get 1.6, 160% markup, or just 1.6 markup
Step-by-step explanation:
Answer:
$144
Step-by-step explanation:
First you do .60 × 90 to get how much he added onto the original price. That was $54, then I added the original price. So I did 90 + 54 and got $144. Hope this helps! If you are still confused please comment!
Use the distributive property and combine like terms to simplify: (4y−1)−(y−2)
Answer:
3y+1
Step-by-step explanation:
(4y-1)-(y-2)
= 4y-1-y+2
=3y+1
What two-dimensional figure results from slicing the sphere with the green plane?
Answer:
a circle
since you cut a sphere in half the two faces will be circles
what is the distance between the y intercept of the function f(x)=3(2)^x and the y intercept of the function g(x) represented by the table below
A: 2 units
B: 3 units
C: 8 units
D: 9 units
The distance between the y-intercept of the function f(x)=3(2)ˣ and the y-intercept of the function g(x) for this case is given by: Option C: 8 units
What is y-intercept of a function?The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.
Assume that we've got: y = f(x)
At y-axis, we've got x = 0, so putting it will give us the y-intercept.
Thus, y-intercept of y = f(x) is y = f(0)
What is the equation of a line passing through two given points in 2 dimensional plane?Suppose the given points are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], then the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
We're given that:
[tex]f(x) = 3(2)^x[/tex]
Its y-intercept is:
[tex]y = f(0) = 3(2)^0 = 3\times 1 = 3[/tex]
Assuming y = g(x) is a linear function, from the first two points [tex](x_1, y_1) = (-5,15)[/tex] and [tex](x_2, y_2) = (-2, 3)[/tex], we get:
[tex](y - 15) = \dfrac{3 - 15}{-2 - (-5)} (x -(-5))\\\\y -15 = -\dfrac{12}{3} (x+5)\\\\y-15 = -4x - 20\\y = -4x - 5[/tex]
Checking if really y = g(x) is linear or not by evaluating it on its rest of the points:
[tex]y = g(2) = -4(2) -5 =-8-5 = -13\\\\y = g(5) = -4(5) -5 = -25[/tex]
These outputs matches with the table output, so we can take:
[tex]g(x) = -4x -5[/tex]
Its y-intercept is:
[tex]y = g(0) = -4(0) -5 = -5[/tex]
The distance between 3 and -5 on the y-axis is the absolute difference between these values of y, evaluated as:
[tex]d = |3 - (-5)| = |8| = 8[/tex] units.
Thus, the distance between the y-intercept of the function f(x)=3(2)ˣ and the y-intercept of the function g(x) for this case is given by: Option C: 8 units.
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