[tex]\dfrac{\sin \alpha}{\cos \alpha + \sin \alpha} - \dfrac{\cos \alpha}{\cos \alpha - \sin \alpha}\\\\\\=\dfrac{\sin \alpha(\cos \alpha - \sin \alpha) - \cos \alpha(\cos \alpha + \sin \alpha)}{(\cos \alpha + \sin \alpha)(\cos \alpha -\sin \alpha)}\\\\\\=\dfrac{\sin \alpha \cos \alpha - \sin^2 \alpha - \cos^2 \alpha - \cos \alpha \sin \alpha}{\cos^2 \alpha - \sin^2 \alpha}\\\\\\=\dfrac{-(\sin^2 \alpha + \cos^2 \alpha)}{\cos 2 \alpha}\\\\\\=-\dfrac{1}{\cos 2 \alpha}\\[/tex]
[tex]=-\left(\dfrac{1}{\tfrac{1- \tan^2 \alpha}{1 + \tan^2 \alpha}} \right)~~~~~~~~~~~~~~~~~~; \left[\cos 2\theta = \dfrac{1 - \tan^2 \theta}{1+ \tan^2 \theta} \right]\\\\\\\ = -\left(\dfrac{1+ \tan^2 \alpha}{1- \tan^2 \alpha}\right)\\\\\\= \dfrac{1+\tan^2 \alpha}{\tan^2 \alpha -1}[/tex]
A pile of newspapers in Mr. Moore’s ELA class was 17 ¾ inches high. Each consecutive week, for the next 5 weeks, the height of the pile of newspapers increases by 8 712 inches each week. What was the height, in inches , of the pile after 3 weeks? Step by step plz
Answer:
43 1/2
Step-by-step explanation:
answer will be:
original height plus 3 times 8 7/12 inches
3 times 8 7/12 can be done by converting the mixed number to an improper fraction:
[tex]\frac{3}{1}[/tex] · [tex]\frac{103}{12}[/tex] = [tex]\frac{103}{4}[/tex] = 25 3/4
25 3/4 added to 17 3/4 equals 42 6/4 which is 42 + 1 1/2 = 43 1/2
whats the x and y-intercepts? y=5x−13,
Step-by-step explanation:
So in a linear function, it follows the form of y=mx+b where m is the slope of the graph (rise/run) and b is the y-intercept.
Since b is (-13) that is the y-intercept.
This can also be confirmed by making x=0 since that is where the y-intercept occurs.
y=5x-13
y=5(0)-13
y=-13
To find the x-intercept, we need to make y equal zero since that is where x-intercepts are found.
0=5x-13
(now solve using algebra to isolate x)
(add 13 to both sides)
13=5x
(divide 5 from both sides)
13/5 = x
2.6=x
Your y-intercept is -13 and the x-intercept is 13/5.
Hope this Helps :D
Answer:
x-intercept: (2.6, 0) or [tex](\frac{13}{5},0)[/tex]
y-intercept: (0, -13)
Step-by-step explanation:
Because the equation is written in slope-intercept form using the formula
[tex]y=mx+b[/tex]
b = y-intercept
y-intercept will be (0, -13)
To find x-intercept basically substitute 0 for y and solve for x
so x-intercept will be [tex](\frac{13}{5},0)[/tex] or simplified (2.6, 0)
help please i need help
Answer:
what do you need help on with this and maybe i can help....
Step-by-step explanation:
System of equations pls help me
Answer:
(4,4)
Step-by-step explanation:
We can solve this system of equations using the elimination method.
In order to use the elimination method there must be two variables with the same coefficient. Note that the coefficients don't have to have the same sign ( eg. 6 and -6 would work ). If there are two similar variables with similar coefficients then you can add or subtract, depending on the signs of the coefficients, the two equations "eliminating" the variable. There would then be one variable left over in which you can solve for.
For this case, both equations have 7x, one negative 7 and one positive 7. When the signs are different you add the two equations. So our first step is to add the two equations
7x - 4y = -44
+ (-7x -3y = 16 )
-----------------------
Remove parenthesis
7x -4y = -44
-7x -3y = +16
------------------
0x - 7y = -28
We are left with -7y = -28.
Because there is now only one variable, we can solve for it.
-7y = -28
divide both sides by -7
y = 4
Now we want to find the value of x. We can do this by plugging in the value of y into one of the equations and then solving for x. Note that we can plug in 4 for y into either equation and solve for x and we would get the same answer.
7x - 3y = 16
y = 4
7x - 3(4) = 16
multiply 4 and -3
7x - 12 = 16
add 12 to both sides
7x = 28
divide both sides by 7
x = 4
So x = 4 and y = 4 so the solution to the system of equations is (4,4)
Why is this wrong?? Trying to do test corrections
Answer:
See answer below
Step-by-step explanation:
y = one time fee
35x = hourly rate( hours worked)
35x + y = $190
y = - 35x = 190
$35 per hours × hours work and you did not used the total cost $190
Next time rewrite the sentence and translate into an equation.
The customers service charges = one-time fee + hourly rate$ ( hours worked)
190 = y + 35(x) point slope form
- 35x + 190 = y
The graph shows which inequality? The vertex is (-4, -3)
Refer to the attachments.
It t takes a snail 10 seconds to move 1 centimeter.
How many centimeters does said snail move after 2 seconds?
2.5?
answer is 0.2 using cross multiplication.
Answer:
in 2 seconds, the snail will only move 0.2 centimeters or 2 millimeters. And after 2.5, 0.25 centimeters, or 2.5 millimeters.
Step-by-step explanation:
A line passes through the points (4, 6) and (8, 7). What is its equation in point-slope form?
Hello there! :)
First, let’s find the slope.
We can find it using this formula:
m=y2-y1/x2-x1
m=7-6/8-4
m=1/4
So the slope is 1/4.
Now, we can use the point-slope formula:
y-y1=m(x-x1)
y-6=1/4(x-1/4)
Hope it helps. :)
~MagicalNature
!20 points! Here are two expressions whose product is a new expression, A:
Answer:
Whats A?
Step-by-step explanation:
1) 6p + 12 - 2 = 8p + 4
6p + 12 - 2 = 8p + 4
6p + 10 = 8p + 4
6p - 8p = 4 - 10
-2p = -6
2p = 6
p = 3
Answer:
p = 3
Step-by-step explanation:
First, simplify. Combine like terms. Like terms are terms with the same variable as well as same amount of said variable:
6p + (12 - 2) = 8p + 4
6p + (10) = 8p + 4
Isolate the variable, p. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& roots)
Multiplications
Divisions
Addition
Subtraction
First, subtract 8p and 10 from both sides of the equation:
6p (-8p) + 10 (-10) = 8p (-8p) + 4 (-10)
6p - 8p = 4 - 10
-2p = -6
Next, isolate the variable, p, by dividing -2 from both sides of the equations:
(-2p)/-2 = (-6)/-2
p = -6/-2
p = 3
3 is your answer.
~
Find an equation of the vertical line through (4,-9)
Answer:
x = 4
Step-by-step explanation:
Whenever it asks for the equation of a vertical line all you have to do is look at the x point given to you which is 4 and make x = 4, doing this means that this certain vertical line covers all possible y values which includes -9 as well which is why the answer is x=4
Mary goes to the bakery with $35. She purchases 2 loaves of bread for $3 each and a cake for $15. She plans to spend the remainder of her money on cookies that cost $1.25 each.
What is the greatest number of cookies that Mary can buy?
HELPPPP
Answer:
The greatest number is 11
Step-by-step explanation:
It is 11 because 3+3=6+15=21
35-21=14
14/1.25=11.2
hope this helps
Valley schools have a student population of 1,608 students .if there are an equal number of students in the 6th grade levels, how many students are in each grade .
Answer:
268
Step-by-step explanation:
1608/6= 268
hope this helps!
In the diagram below, \overline{ST} ST is parallel to \overline{PQ} PQ. If STST is 55 more than QTQT, RT=10RT=10, and PQ=15PQ=15, find the length of \overline{QT} QT. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.PQRTS
The length of the [tex]\overline{QT}[/tex] can be determined using the given information and
the relationship between corresponding sides of similar triangles.
[tex]\underline{\overline{QT} = 5}[/tex]Reasons:
The given parameters are;
[tex]\overline{ST} \parallel \overline{PQ}[/tex]
ST = QT + 5
RT = 10
PQ = 15
Required: The length of [tex]\overline{QT}[/tex]
Solution:
Using the relationship between corresponding sides of similar triangles, ΔRST and ΔRPQ, we have;
[tex]\displaystyle \frac{\overline{ST}}{\overline{RT}} = \mathbf{\frac{\overline{PQ}}{\overline{RQ}}}[/tex]RQ = QT + RT
Therefore;
[tex]\displaystyle \frac{\overline{ST}}{\overline{RT}} = \mathbf{\frac{\overline{PQ}}{\overline{QT} + \overline{RT}}}[/tex]Which gives;
[tex]\displaystyle \frac{\overline{QT} + 5}{\overline{RT}} = \frac{\overline{PQ}}{\overline{QT} + \overline{RT}}[/tex]
Plugging in the known values gives;
[tex]\displaystyle \frac{\overline{QT} + 5}{10} = \mathbf{\frac{15}{\overline{QT} + 10}}[/tex]
[tex](\overline{QT} + 5) \times (\overline{QT} + 10) = 10 \times 15[/tex]
[tex]\overline{QT}^2 + 10\cdot \overline{QT} + 5\cdot \overline{QT} + 50 = 10 \times 15[/tex]
[tex]\overline{QT}^2 + 15\cdot \overline{QT} + 50 - 150= 0[/tex]
[tex]\mathbf{\overline{QT}^2 + 15\cdot \overline{QT} -100} = 0[/tex]
Factorizing with a graphing calculator gives;
[tex](\overline{QT} -5) \cdot (\overline{QT} + 20)= 0[/tex]
[tex]\mathbf{\overline{QT} = 5} \ or \ \overline{QT} = -20[/tex]
Therefore, given that [tex]\overline{QT}[/tex] is a natural number, we have;
[tex]\underline{\overline{QT} = 5}[/tex]
Learn more about similar triangles here:
https://brainly.com/question/4268470
can we represent any number on number line
Answer:
Rational numbers can be depicted on the number line. The centre of the number line is called Origin (O). Positive rational numbers are illustrated on the right side of zero (called origin), and negative on left side of origin. The representation of rational numbers on the number line depends on the type of fraction.
Step-by-step explanation:
The numbers on the number line increase as one moves from left to right and decrease on moving from right to left. Here, fractions and decimals have been represented on the number line. A number line can also be used to represent both positive and negative integers as well.
Graph the following equation: y - 3 = (x - 2)
Answer:
Step-by-step explanation:
I took pictures of what I found and I think is right
simplify the equation
What is 48,956 rounded to the nearest ten thousand?
Answer:
50,000
Step-by-step explanation:
THE ANSWER IS 50,000
5 4/6-4 2/3 ÷ 3 2/3?
Answer:
145/33
Step-by-step explanation:
Assuming what you wrote was mixed fractions, this is how to do the question.
Do the division first and then subtract that from 5 4/6/
What function represents the next graph?
[tex](x {}^{2} - 4) {}^{2} [/tex]
Brainliest me please please
Write in index form
5 x 5 x 5
Which properly illustrated in the statement (-2)(+5) = (+5)(-2)?
Answer: 7
Step-by-step explanation:
it is trust me.
) Use distributive property and solve
74×94
Answer:
6956
Step-by-step explanation:
i dont get the Question
A recent survey of 8,000 high school students found that the mean price of a prom dress was $195. 00 with a standard deviation of $12. 0. Alyssa thinks that her school is more fashion conscious and spent more than $195. 0. She collected data from 20 people in her high school and found that the average price spent on a prom dress was $208. 0. Which of the following is the correct z-statistic for this situation? 0. 24 4. 84 7. 51 96. 90.
Answer:4.84
Step-by-step explanation:
Answer: Check attached :) Right on ED22
Step-by-step explanation:
I'M GIVING BRAINLIEST!!!!!!!!!!!
Answer:
i dont know
Step-by-step explanation:
MEEEEEEEEEE please
What is "o"? will get 15 points for correct answer.
Answer:
54 Degrees
Step-by-step explanation:
We know that a triangle has to have 180 degrees in all. we also know that the bottom lines is a straight angle, so 180 degrees.
using this information, we can find n. We know that n+78 is 180, so n=102
We also know that o+102+24=180, so
o=54
Hope this helps!
A box of baseballs costs $66. 12. Which equation represents the cost, c, of n boxes?
Answer:
C
Step-by-step explanation:
cost=price of one box (number of boxes)
:))
Which statement is true about the polynomial 3x2y2 − 5xy2 − 3x2y2 + 2x2 after it has been fully simplified?
Answer: Varies
Step-by-step explanation:
There would still be some Xs and Ys.
The length of the base of an isosceles triangle is x. The length of a leg is 3x - 6. The perimeter of the triangle is 58. Find x.
Answer:
x = 10
Step-by-step explanation:
Perimeter of a triangle = the sum of the three sided of the triangle.
In an isosceles triangle, there are two equal sides and a base.
Perimeter = ( 3x - 6) + (3x - 6) + x
58 = 7x - 12
58 + 12 = 7x
70 = 7x
[tex]\frac{70}{7} = \frac{7x}{7}[/tex]
10 = x
Please help I’ll give brainylist in return
Answer:
Letter A because both of them are SSS
Step-by-step explanation: