Answer:
(identity has been verified)
Step-by-step explanation:
Verify the following identity:
sin(x)^4 - sin(x)^2 = cos(x)^4 - cos(x)^2
sin(x)^2 = 1 - cos(x)^2:
sin(x)^4 - 1 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2
-(1 - cos(x)^2) = cos(x)^2 - 1:
cos(x)^2 - 1 + sin(x)^4 = ^?cos(x)^4 - cos(x)^2
sin(x)^4 = (sin(x)^2)^2 = (1 - cos(x)^2)^2:
-1 + cos(x)^2 + (1 - cos(x)^2)^2 = ^?cos(x)^4 - cos(x)^2
(1 - cos(x)^2)^2 = 1 - 2 cos(x)^2 + cos(x)^4:
-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = ^?cos(x)^4 - cos(x)^2
-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = cos(x)^4 - cos(x)^2:
cos(x)^4 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2
The left hand side and right hand side are identical:
Answer: (identity has been verified)
What is the slope of the line described by the equation below?
y- 5= -3(x - 17)
O A. -3
B. 3
O c. 5
OD. -5
Hellppp
To write 11x^2+17x-10 in factored form, Diego first listed pairs of factors of -10.
(__+10)(__+-1)
(__+1)(__+-10) (fill in blanks)
(You dont need to explain just answer it)
-3x^2+6x+9=
WHY JUST WHY !!!! ?
Oh, my, goodness!!!!!! :)
You are cracking me up so much right now!!!!! :)
But, yeah, I hear ya! :)
Answer:
[tex]=-3\left(x+1\right)\left(x-3\right)[/tex]
Step-by-step explanation:
[tex]-3x^2+6x+9\\\mathrm{Factor\:out\:common\:term\:}-3:\quad -3\left(x^2-2x-3\right)\\-3x^2+6x+9\\\mathrm{Rewrite\:}9\mathrm{\:as\:}3\cdot \:3\\\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2\\=-3x^2+3\cdot \:2x+3\cdot \:3\\\mathrm{Factor\:out\:common\:term\:}-3\\=-3\left(x^2-2x-3\right)\\\mathrm{Factor}\:x^2-2x-3:\quad \left(x+1\right)\left(x-3\right)\\x^2-2x-3\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(x^2+x\right)+\left(-3x-3\right)[/tex]
[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+x\mathrm{:\quad }x\left(x+1\right)\\x^2+x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\=xx+x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(x+1\right)\\\mathrm{Factor\:out\:}-3\mathrm{\:from\:}-3x-3\mathrm{:\quad }-3\left(x+1\right)\\-3x-3\\\mathrm{Factor\:out\:common\:term\:}-3\\=-3\left(x+1\right)\\=x\left(x+1\right)-3\left(x+1\right)\\\mathrm{Factor\:out\:common\:term\:}x+1\\=\left(x+1\right)\left(x-3\right)[/tex]
[tex]=-3\left(x+1\right)\left(x-3\right)[/tex]
x+y= 2
y=-12? + 3
\right.V)
1. In two or more complete sentences, explain how to solve the system of equations algebraically.
2. Solve the system of equations. In your final answer, include all of your work.
Answer:
11
Step-by-step explanation:
11
x f(x)
--------
-3 -18
-2 -4
-1 0
0 0
1 2
2 12
3 36
What is the degree of the polynomial represented in the table?
4
5
2
3
Answer:
I think that the answer is 4
NEED HELP :(
Use the commutative or associative property to simplify the expression.
1/4(4y)
Answer:
y
Step-by-step explanation:
Associative Property a(bc)=(ab)c
1/4(4y)=(1/4(4))y
y
I really need help on these 2 questions. Please!!!!
Help please! Will give brainly! Jada noticed that the distances fallen are all multiples of 16. She wrote down:
Answer:
Look at the underlined numbers
So we have 16 = 16*1
then 64 = 16*4
the difference would be 3
then 144 = 16*9
the difference would be 5
256 = 16*16
the difference would be 7
400 = 16*25
the difference would be 9
so the next one would be 11+25=
3, 5, 7, 9, 11
ANSWER: 16*(11+25) = 36*16 = 576
Step-by-step explanation:
I explained before this
A restaurant has 75% of its tables being used. Which ratio compares the used tables with all the tables in the restaurant? A. 50:100 B. 25:75 C. 25:100 D. 15:20
Answer:
D
Step-by-step explanation:
It would 75:100
We then can simplify that by dividing by 5 so we get
15:20
Answer: 15:20
Step-by-step explanation:
75% tables are used out of 100%
The ratio will be 75:100 = 15:20
From a point P, a boy observe that the angle of elevation of the top of a pole is 45, if the height of the
pole is 15 m, find the distance of P from the foot of the pole.
Please help
Answer:
15m
Step-by-step explanation:
The pole is perpendicular to the floor and the angle of elevation is 45. Thus, it forms a right-angled, isoceles triangle. So the distance from point P to the bottom of the pole is equal to the height of the pole, which is 15m
PLEASE ANSWER ASAPPP
The scouts sold small and large boxes of cookies as a fund raiser. One scout sold 7 small boxes and 12 large boxes for $54.00. Another scout sold 5 small boxes and 10 large boxes for $60.00. The scout leader wrote a system of equations to represent the their sales.
7 x + 12 y = 54. 5 x + 10 y = 60.
Which constants can each equation be multiplied by so that one variable is eliminated when the equations are added? Check all that apply.
1. The first equation can be multiplied by 5 and the second equation by –6 to eliminate the y.
2. The first equation can be multiplied by –5 and the second equation by 6 to eliminate the y.
3. The first equation can be multiplied by –5 and the second equation by 7 to eliminate the x.
4. The first equation can be multiplied by 5 and the second equation by –7 to eliminate the x.
5. The first equation can be multiplied by –5 and the second equation by 10 to eliminate the x.
Answer:
1, 2, 3, 4
Step-by-step explanation:
1) works 60y+(-60y)=0
2) works(-60y)+60y=0
3)works (-35x)+35x=0
4) works 35x+(-35x)=0
5) doesn't work (-35x)+100x doesn't equal 0
Answer:
1,2,3,4
Step-by-step explanation:
(x⁵-9x³+7x)+(x³-x⁵-7-x)
Answer: -8x^3 - x - 7
Answer:
First open parenthesis:
x^5-9x^3+7x+x^3-x^5-7-x
-8x^3+6x-7
[tex]-8x^{3} +6x-7[/tex]Which of the following relations represents a function?
O A. {(1, 1), (1, 2), (1,3)}
O B. {(1, 1), (2, 1), (3, 1)}
O C. {(1, 1), (2, 2), (3, 3)}
O D. Both B and C.
OPTION NUMBER D IS CORRECT
D.Both B and C.
Step-by-step explanation:
function is the relation from set A to B such that every element of set A(domain) should have only 1 image in Set B(co domain).
What is the leading coefficient and constant of this problem?
(8
2/7*3/8>3/8 because 2/7>1
pls help this is due in 20 min pls help.
Answer:
32 2/5
Step-by-step explanation:
Twice of the width is 10 4/5
So 10 4/5 plus 5 2/5 is 16 1/5
Then you add it to 16 1/5 because it is the perimeter and it has the same sides
Answer:
4. [tex]32 \frac{2}{5}[/tex]
Step-by-step explanation:
so the formula for perimeter is l + l + w + w
the width is 5 2/5 and the length is 5 2/5 * 2
that means the length is 10 4/5
so back to the formula [tex]5 \frac{2}{5} + 5 \frac{2}{5} +10 \frac{4}{5} +10 \frac{4}{5}[/tex]
simplified is 10 4/5 + 20 8/5
simplified is 30 12/5
simplified is [tex]32 \frac{2}{5}[/tex]
Write a linear equation in standard form for the line that goes through
(-14,-5) and (4,7)
A. Y-5. }(x-4)
O B. -2x+ 3y = 1
C. - 2x + 3y - 13
O D. 2x - 3y = 13
Answer:
[tex]3y - 2x = 13[/tex]
Step-by-step explanation:
Given
Points (-14,-5) and (4,7)
Required
Find its linear equation in a standard form
To find the linear form, we start by calculating the slope of the line
This is calculated as thus:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where [tex](x_1,y_1) = (-14,-5)\ and\ (x_2,y_2) = (4,7)[/tex]
So, [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{7 - (-5)}{4 - (-14)}[/tex]
[tex]m = \frac{7 + 5}{4 + 14}[/tex]
[tex]m = \frac{12}{18}[/tex]
Simplify fraction to lowest term
[tex]m = \frac{6*2}{6*3}[/tex]
[tex]m = \frac{2}{3}[/tex]
The equation of the line can then be calculated using any of the given points;
Using
[tex]m = \frac{y - y_1}{x - x_1}[/tex]
[tex]Where\ (x_1,y_1) = (-14,-5)\ and\ m = \frac{2}{3}[/tex]
We have
[tex]\frac{2}{3} = \frac{y-(-5)}{x-(-14)}[/tex]
[tex]\frac{2}{3} = \frac{y+5}{x+14}[/tex]
Multiply both sides by 3
[tex]3 * \frac{2}{3} = \frac{y+5}{x+14} * 3[/tex]
[tex]2 = \frac{y+5}{x+14} * 3[/tex]
[tex]2 = \frac{3(y+5)}{x+14}[/tex]
Multiply both sides by x + 14
[tex]2 * (x + 14) = \frac{3(y+5)}{x+14} * (x + 14)[/tex]
[tex]2 * (x + 14) = 3(y+5)[/tex]
Open brackets
[tex]2 * x + 2 * 14 = 3* y+ 3 * 5[/tex]
[tex]2x + 28 = 3y+ 15[/tex]
Subtract 2x from both sides
[tex]2x - 2x + 28 = 3y+ 15 - 2x[/tex]
[tex]28 = 3y+ 15 - 2x[/tex]
Subtract 15 from both sides
[tex]28 - 15 = 3y+ 15 - 2x - 15[/tex]
[tex]28 - 15 = 3y - 2x + 15- 15[/tex]
[tex]13 = 3y - 2x[/tex]
Reorder
[tex]3y - 2x = 13[/tex]
Hence, the equation of the line in standard form is [tex]3y - 2x = 13[/tex]
how many different measurements are found in this diagram ¿
A total of 70 tickets were sold for a concert and earn the organizers $804. If the cost of each ticket is either $10 or $12, how many tickets of each type were sold.
A. 18 tickets cost and 52 cost $12
B. 52 tickets cost $10 and 18 tickets cost $12
C. 65 tickets cost $12 and 5 tickets cost $10
D. 5 tickets cost $12 and 65 tickets cost $10
Answer: A = $804 18 tickets cost $10 and 52 cost $12
Step-by-step explanation:
A = $804 18 tickets cost $10 and 52 cost $12
B = $736
C = $830
D = $170
What is the value of x?
A-14
B-15
C-16
D-17
Answer:
A
Step-by-step explanation:
The answer is a because first you need to add up 110+110+70
You would get 290
Then subtract 360-290
You would get 70
Divide 70/5
You get 14, the answer.
Answer: A
Step-by-step explanation:
14 weeks is expressed as a percentage of 50 weeks is?
Answer:
28%
Step-by-step explanation:
Fraction= 14 out of 50 weeks
To find percentage multiply the fraction by 100
14/50 * 100
= 1400/50
= 28 percent
Answer:
28%
Step-by-step explanation:
50 ws ................ 100%
14 ws ......................x%
x = 14*100/50 = 14*2 = 28%
ΔFGH, the measure of ∠H=90°, the measure of ∠F=15°, and GH = 57 feet. Find the length of FG to the nearest tenth of a foot.
Answer:
FG-220.2 feet
Step-by-step explanation:
The base of the triangle is FH
The perpendicular of the triangle GH=57 feet
The hypotenuse of the triangle is FG
We know that
sin∠F=Perpendicular/Hypotenuse
Hypotenuse= Perpendicular/sin∠F
Hypotenuse= 57/sin∠15
Hypotenuse=220.23109
Round of to nearest tenth
Hypotenuse=220.2 feet
What is the area of a rectangle that has a length of 16.17 and a width of
8.75? DO NOT ROUND. *
Answer:
A =141.4875
Step-by-step explanation:
The area of a rectangle is given by
A = l*w
A = 16.17 * 8.75
A =141.4875
Abraham currently has a balance of $3,075.21 in an account he has held for 13 years. He
opened the account with an initial deposit of $2,152. What is the simple interest rate on the
account?
2.3%
7.7%
3.3%
11.0%
Answer: 3.3%
Step-by-step explanation:
Amount = prt / 100
3075.21 = (2152 x r x 13)/100
Answer:
the answer is letter c
Step-by-step explanation:
The volume of this rectangular prism is 6x2. What does the coefficient 6
mean in terms of the problem?
height = x
width = X
length = 6x
o
A. The length of the prism is 6 units.
B. The total volume of the prism is 6 cubic units.
O
C. The length is 6 times the width.
D. The width is 6 times the height and the length.
Answer:
C
Step-by-step explanation:
The length is 6 times the width.
6 times x is 6x
You are welcome and don't for get to click THANKS
Answer: C
Step-by-step explanation:
Can someone help me with this please!!!
Answer:
first itself we should do the answer and only we can answer it
Step-by-step explanation:
How much is a penny and a quarter
Answer:
check google
Step-by-step explanation:
Answer: 26¢
Step-by-step explanation: A penny equals 1¢ and a quarter is 25¢ so together that would make 26¢
Nate asked some of his friends how many people live in their homes. The answers were: 4,3,3,6, 10, 7, 4, and 3.
What is the range of the data?
Answer:
7
Step-by-step explanation:
10-3=7
If 5 deli sandwiches cost $29.75, how much will 8 sandwiches cost?
Question 10 options:
a)
$37.75
b)
$29.75
c)
$0.16
d)
$47.60
what property is 5(8+3)=5*8+5*3?
Answer:
distributive property
Step-by-step explanation:
5(8+3)=5*8+5*3
This is an example of the distributive property
The 5 is distributed to each of the terms inside the parentheses
The heights of the sunflowers, in inches,
in Brittany's garden are shown below.
65 66 64 63 64
62. 65. 63, 64, 66
Brittany displayed the data in a dot pot
Which of the dot plots correctly displays
Brittany s dala?
Answer:
See picture attached
Step-by-step explanation:
The options are not provided, so I made my own dot plot. To did it, I ordered the set, and counted how many times each height appears, as follows:
62: once
63: twice
64: three times
65: twice
66: twice
Those are the numbers of dots you have to put over each height.
