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]
Can someone please help me, i don't understand this work.
Answer: Check out the diagram below for the filled out table
Equation is y = 1.5x
Box for row one = 330
Box for row two = 1000
Box for row three = 1.5
===========================================================
Explanation
x = amount of fish in grams (horizontal axis)y = number of calories (vertical axis)The point (x,y) = (200,300) is on the blue diagonal line. It indicates that x = 200 grams of fish have y = 300 calories. Divide the two values to get the slope
slope = y/x = 300/200 = 1.5
This trick only works because the line is going through the origin. Otherwise, we'd have to use the slope formula.
The slope of 1.5 is the constant of proportionality. It tells us the equation is y = 1.5x. Whatever x is, multiply by 1.5 to get y.
So if x = 220, then y = 1.5x = 1.5*220 = 330
220 grams of fish have 330 calories. We'll write 330 in the box of the first row of the table.
-----------------
We can use this idea in reverse. If we know the calorie count (y), then we can divide by 1.5 to get the number of grams (x).
y = 1.5x
1500 = 1.5x
1.5x = 1500
x = 1500/(1.5)
x = 1000
Therefore, 1000 grams of fish have 1500 calories. We'll write 1000 in the box of the second row.
------------------
The third row of the table is going to follow the same steps as the first row.
y = 1.5x
y = 1.5*1
y = 1.5
One gram of fish produces 1.5 calories
The filled out table is shown below. I've merged the two screenshots you posted into one image, and filled out the boxes.
With words, describe the translation:
(x, y)—(x+2, y-4)
o Move 2 to the left and 4 up
o Move 6 diagonally
o Move 4 left and 2 up
o Move 2 to the right and 4 down
The recipe for 4 people says I need 300g of sugar. I am making for 10 people. How much sugar do I need in g?
Answer:
750g
Step-by-step explanation:
300 divided by 4, for amount of sugar per person
you'll get 75
then multiply 75 by 10 for 10 people
you get 750g
7+32−42÷2 what is it i need help pleaseee
Answer:
[tex]7+32-42\div 2 = 39 - 21 = 18[/tex]
Step-by-step explanation:
If the actual sale for the week is $525 and hector guessed $625, what i the percent error?
Answer:
19.0% (1dp)
Step-by-step explanation:
$625-$525=$100
$100/$525=4/21×100=19.0% (1dp)
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK
Answer:
√366
Step-by-step explanation:
a^2 + b^2 = c^2
5 + 361 = 366
√366
1.0835 rounded to the nearest tenth
Answer:
1.1
Step-by-step explanation:
Answer:
1.1
Step-by-step explanation:
A store sells 4 printers for every computers. Last month the store sells 56 computers, how many printers did they sell?
Answer:
224 printers
Step-by-step explanation:
56computers×4printers per computer=224 printers
Graph the line that passes through the points (-1,7) and (-3,5) and determine
the equation of the line.
Answer:
y = x + 8
Step-by-step explanation:
find slope first:
m = 7-5 / -1-(-3)
m = 2 / 2
m = 1
now find the y-intercept using either ordered pair; plug 'y', 'x', and 'm' into
y = mx + b to solve for 'b'
7 = 1(-1) + b
7 = -1 + b
8 = b
put 'm' and 'b' into slope-intercept equation of a line, y = mx + b to get:
y = x + 8
7) Sarawong spent half of his weekly allowance on candy. To earn more money his parents let him wash the dog for $6.10. What is his weekly allowance if he ended with $11.40?
Answer:
$10.60
Step-by-step explanation:
Sarawong ends with $11.40, and we need to find his weekly allowance by working backward. First, we learn that he earned $6.10 of that total amount of money by washing the dog, so we can subtract the two values:
11.4 - 6.1 = 5.3
So, before washing the dog, Sarawong had $5.30. But he only received this after spending half of his weekly allowance, so $5.30 must be half of his weekly allowance. If we multiply $5.30 by 2, we should be able to find his weekly allownce.
5.3 × 2 = 10.6
Now, we can check our work. First, he spends half of his weekly allowance on candy. Half of 10.6 is 5.3, so he now has $5.30. Then, he earns $6.10 more by washing the dog. 5.3 + 6.1 = 11.4, which is the ending value. So, our work was correct! Hopefully that's helpful. :)
Maggie's brother is 5 years younger than three times her
age. The sum of their ages IS 43.
How old is Maggie?
Answer:
Step-by-step explanation:
Let Maggie's age = x
The brother's age = 3x - 5
x + 3x - 5 = 43
4x - 5 = 43 Add 5 to both sides
4x - 5 + 5 = 43+5
4x = 48 Divide by 4
4x/4 = 48/4
x = 12
Maggie = 12
Brother = 3*12 - 5
Brother = 36 - 5
Brother = 31
For what value of x is line a parallel to line b?
Answer:
x = 22
Step-by-step explanation:
4x + 28 = 116 (corresponding angles are equal when two lines are parallel)
4x = 88
x = 22
Corresponding angles must be equal
[tex]\\ \tt\hookrightarrow 4x+28=116[/tex]
[tex]\\ \tt\hookrightarrow 4x=116-28[/tex]
[tex]\\ \tt\hookrightarrow 4x=88[/tex]
[tex]\\ \tt\hookrightarrow x=22[/tex]
Which graph is defined by the function given below?
y = (x-3)(x-3)
Answer: graph b
Step-by-step explanation:
Vertex: ( 3 ,0 )
Focus: ( 3 , 1 4 )
Axis of Symmetry: x = 3
Directrix: y = − 1 4
Adam is planning a pool party to celebrate the last day of school. He wants to give out beach towels to his guests as party favors. Adam ordered 14 beach towels from Sunshine Party Supply. Since this was a bulk order, Sunshine Party Supply reduced the price of each towel by $3.25. Adam paid $105 in all. How much does Sunshine Party Supply normally charge for a beach towel?
Answer:
10.75
Step-by-step explanation:
first step is to find how much adam paid for each towel
so, the equation used will be x/y=c
where x is total cost, y is number of products bought, and c equals individual cost (with discount)
we end up with 105/14= 7.5$ per towel.
and to close out, we add the given discount of 3.25 to the discounted price of 7.5
which brings the usual price per towel to 10.25
Answer:
Step-by-step explanation:
you travel 90 miles in 1.5 hours. find the speed you travel.
Answer:
60 mph
Step-by-step explanation:
Kieran buys a car for $8000 The following year he sells the car for $7500
Kieran membeli mobil seharga $8000 Tahun berikutnya dia menjual mobil seharga $7500
Loss :
= $ 8.000 – $7.500
= $ 500
then Loss is $500
#FromIndonesia
which statement is true?
Answer:
The slope of function A is less than the slope of function B
Explanation:
The slope for function B is 1/2, which is greaterthan 1/5, the slope of function A.
Answer:
the slope on Function A is less than Function B
Step-by-step explanation:
By doing rise over run we can get 1/2 on Function B and the Y intercept is 5 so the equation is y=1/2x+5
A number is chosen uniformly at random from among the positive integers less than $10^8$. Given that the sum of the digits of the number is 9, what is the probability that the number is prime
Answer:
If the sum of the digits of a number is divisible by 9, then that number is divisible by 9. An..... sorry if this does not help :(
Step-by-step explanation:
Can someone plz help Me?
Answer:
It’s A :D
Step-by-step explanation:
3 goes into 12 4 times
4 times 4 equals 16
so 16 can of soup
and then! 4 goes into 36 9 times
Click the picture to see inside! :3
Hope this helps :DDD
Joseph is going to paint the panels of a fence. He is going to use the same repeating pattern for the entire fence. The rule is "orange, yellow, pink, green, purple." If there are 98 panels in the fence, how many will be painted green?
Answer:
19 panels are painted green
Step-by-step explanation:
95/5=19 and because there are 3 colors before green again we don't have to worry about the other 3 panels
if I’m wrong, I’m sorry. If I’m right, mark me brainlest!
Dani spent $6,300 on a used car. She paid $630
as a down payment. What fraction of the orig-
inal cost was the down payment?
A. 1/10
B. 1/18
C. 1/20
D. 1/40
Answer:
1/10
Step-by-step explanation:
630/6300 = 0.1
0.1*100 = 10
10% a.k.a 1/10
Hope this helped!
The logarithmic expression [tex]log_{b}(\frac{1}{b^{-b}} )[/tex] where b > 0, is equal to
a) [tex]b^{-b}[/tex]
b) [tex]b^{b}[/tex]
c) [tex]-b[/tex]
d) [tex]b[/tex]
[tex]\log_b \left(\dfrac 1{b^{-b}}\right)\\\\=\log_b (b^{-b})^{-1}\\\\=\log_b b^b\\\\=b \log_b b\\\\=b \cdot 1\\\\=b[/tex]
Luke is going to reflect point R(6, 10) over the y-axis what are the coordinates for R
Answer:
R - (-6,10)
Flip the x-value when reflecting over y axis, and flip y-value when reflecting over x-axis
I need help plz
ASA
SSA
SAS
AAS
Answer:
SAS,
Step-by-step explanation:
2 sides and the included angle.
PLEASE HELP ASAP !! ALL 4 QUESTIONS IN THE PICTURE !
Answer:
#1= 5
#2= i think it's a red square
#3= 243
Step-by-step explanation:
ok so im rlly sorry but i think i can only solve 1 2 and 3:
for #1:
the pattern is subtracting 1,2,3,4 each time it goes to the next number.
29-28=1
28-26=2
26-23=3
23-19=4
19-?=5
?=14
19-14=5
so answer would be 5
for #2:
the pattern goes red triangle, red square, blue triange, blue square, red triangle, etc.
so with it continuing on, it would be red square
for #3:
the pattern looks like they're multiplying by 3 each time:
3x3=9
9x3=27
27x3=81
81x3=?
?=243
81x3=243
so the answer would be 243
hope this helped :)
If g(x) =3-2x, find g(-1) (show work)
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
i don't know but I think question 1 is 64
Write the name of a polynomial (using the degree) with the sequence of the
outputs: (5,2,-1,-4, ...}*
Type ONE word
Answer:
pentagon
Step-by-step explanation:
5 degree angle
What is the equation of the line in standard form?
(2,2)
Step-by-step explanation:
You have to add them together and minus the negatives
I need help PLEASE ILL GIVE YOU BRAINLEST
Answer:
y= 0.75x + -0.50
A or B is what im guessing