Answer:
Step-by-step explanation:
The first one is in standard form;
the second one is in point-slope form;
the third one is in slope-intercept form;
the last one is in standard form
These are all lines, so as you can see, there are 3 different formats for writing the equation of a line.
What is the linear function equation represented by the graph?
Enter your answer in the box.
Picture below
find the radius of a circle that has a circumference of 16
Answer: 2.54647909 or 2.55
Step-by-step explanation:
radius=C/2π
r=16/2π
r=16/6.2831853071796
r=2.54647909
Use trigonometric identities to solve each equation within the given domain.
sec(x) cos(3x) = 0 from [– π/2 , π/2] PLEASE SHOW WORK!!!!
Recall the triple angle identity for cosine:
cos(3x) = cos³(x) - 3 sin²(x) cos(x)
… = cos³(x) - 3 (1 - cos²(x)) cos(x)
… = 4 cos³(x) - 3 cos(x)
and the definition of secant,
sec(x) = 1/cos(x)
So we have
sec(x) cos(3x) = 0
(4 cos³(x) - 3 cos(x))/cos(x) = 0
cos(x) (4 cos²(x) - 3)/cos(x) = 0
If cos(x) ≠ 0 (this happens at the endpoints of the interval [-π/2, π/2]), we can simplify this to
4 cos²(x) - 3 = 0
cos²(x) = 3/4
cos(x) = ±√3/2
But since -π/2 < x < π/2, we know cos(x) > 0, so we ignore the negative case:
cos(x) = √3/2
==> x = π/6 and x = -π/6
The solution of the given trigonometric equation by using trigonometric identities is [tex]\frac{\pi }{6} \ and \frac{-\pi }{6}[/tex].
What are trigonometry identities?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
Some trigonometric identities are[tex]cos(3x) = 4cos^{3}(x) -3cos(x)[/tex]
According to the given question.
We have an equation
[tex]sec(x)cos(3x) = 0[/tex]
Since, the above equation can be written as by using trigonometric identities
[tex]sec(x)cos(3x) = 0\\\implies \frac{1}{cos(x)} (4cos^{3} x-3cos(x))=0[/tex]
Solve the above equation for x.
[tex]\implies 4cos^{2} x -3= 0[/tex]
[tex]\implies 4cos^{2}x = 3\\ \implies cos^{2} x = \frac{3}{4} \\\implies cos x = \sqrt{\frac{3}{4} } \\\implies cos x = \pm\frac{\sqrt{3} }{2}[/tex]
In the given domain [tex][\frac{-\pi }{2}, \frac{\pi }{2} ][/tex] we know that cosx > 0. Therefore, we take only positive part
[tex]\implies cosx = \frac{\sqrt{3} }{2} \\\implies x = cos^{-1} \frac{\sqrt{3} }{2} \\\implies x = \frac{\pi }{6}, and \frac{-\pi }{6}[/tex]
Hence, the solution of the given trigonometric equation by using trigonometric identities is [tex]\frac{\pi }{6} \ and \frac{-\pi }{6}[/tex].
Find out more information about trigonometric identities here:
https://brainly.com/question/12537661
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P= 3in
a) find the length of each side of the square
b) find the area of the square
Step-by-step explanation:
what does P mean ?
I assume it is perimeter ?
what is the perimeter of a square ?
come on, there is practically nothing in math that is easier to solve.
a square has 4 equal sides.
so, to go one time around the whole square, we have to go along every one of its 4 sides (which are all of equal length).
so, when I get the perimeter number, I know this is the result of all 4 sides added together.
and how can we express having 4 times the same number ? exactly how we say it in English : 4 times the number.
therefore
P = 4 × side length
and from there we can immediately deduct
side length = P / 4 = 3/4 in
now we know how long the sides of the square are.
what is the area of the square ?
like for any rectangle the area is length×width. just that length=width, so that we end up with length×length = length².
therefore, the area is
3/4 × 3/4 = (3/4)² = 9/16 in²
this is important : a length is measured e.g. in inches (in). an area is then measured in square-inches = in²
If the squad root of 16 = x, then 2x =
Step-by-step explanation:
Mark me as the brainliest
PLEASE HELP ME! WHAT IS THE ANSWER TO THIS QUESTION? GIVE A STEP BY STEP EXPLANATION!
Step-by-step explanation:
-6(4v) + -6(9) = 42
-24v - 54 = 42
-24v = 42 + 54
-24v = 96
-v = 96/24
-v = 4
v = -4
Answer:
I think it's -33\24 V
Step-by-step explanation:
bc the equation is -6(4v+9)=42
so you would multiply -6 and 4 to get -24V +9=42
so then you would subtract 9 from both sides to cancel out the 9 and get 33
then take 33 over -24 but that isn't able to be devided so it would stay a fraction
find : (f/g)(x) pls help
Answer:
4
Step-by-step explanation:
f(x) = 16x+12
g(x) = 4x+3
f(x) / g(x) =
Factoring f(x) =4(4x+3)
f(x) /g(x) = 4(4x+3) / (4x+3) = 4
help me please to solve this 2 questions pleasee faster.. i will mark you as brainliest
Answer:
1. x=72, y=, 108
2.x=30, y=72
Step-by-step explanation:
Brainliest please~
i need help cant understand it
Answer:
105
Step-by-step explanation:
Because the lines are parallel, we know that those angles have to add up to 180. so we just do
x+75=180
or 180-75=105
x+75°=180°
x=180°-75°
x=105°
or
180°-75° = 105°
please mark this answer as brainlist
if (p+2q)/p = 7/5 , find the value of q/p , where p ≠ 0
Work Shown:
(p+2q)/p = 7/5
(p/p)+(2q/p) = 7/5
1 + 2(q/p) = 7/5
2(q/p) = 7/5 - 1
2(q/p) = 7/5 - 5/5
2(q/p) = (7-5)/5
2(q/p) = 2/5
q/p = (2/5)*(1/2)
q/p = (2*1)/(5*2)
q/p = 1/5
Answer:
q/p = 1/5
Step-by-step explanation:
(p+2q)/p = 7/5
Multiply each side by p
(p+2q)/p *p = 7/5*p
(p+2q) = 7p/5
Multiply each side by 5
(p+2q)*5 = 7p/5 *5
5p + 10q = 7p
Subtract 5p from each side
5p + 10q -5p = 7p -5p
10 q = 2p
divide each side by p
10q/p = 2p/p
10 q/p = 2
Divide each side by 10
q/p = 2/10
q/p = 1/5
Cost of bananas is increased by rupees per dozen one can get two dozen less for 840 rupees find the cost of one dozen
Answer:
Let the cost of banana per dozen be Rs. x.
Amount for which bananas are bought = Rs. 840
No. of dozens of bananas for Rs 840 = 840/x
New cost of banana per dozen = Rs. (x + 1)
New No. of dozens of bananas for Rs 840 = 840/x+1
According to given condition,
840/x – 840 / x + 1 = 2
∴ 840[1/x – 1/x+1] = 2
∴ 840 [x+1- x / x(x+1)] = 2
∴ 840 [1/ (x² + x)] = 2
∴ 840 = 2(x² + x)
∴ 2x2 + 2x – 840 = 0
Dividing by 2, we get
x² + x – 420 = 0
x² – 20x + 21x – 420 = 0
∴ x (x – 20) + 21 (x – 20) = 0
∴ x – 20 = 0 or x + 21 = 0
∴ x = 20 or x = –21
∴ The cost of bananas cannot be negative.
∴ x = 20
The original cost of one dozen banana is Rs. 20
hope it helps you
Step-by-step explanation:
Find the perimeter of this semi-circle with diameter, d = 22cm.
Give your answer as an expression in terms of t.
Answer:
=22tcm
Step-by-step explanation:
Perimeter of a circle =πD
But π=t
hence perimeter; = 22tcm
where t=π
What value from the set {6, 7, 8, 9, 10} makes the equation 5x + 2 = 47 true? Show your work. (5 points)
Answer:
trure correct
ok must of luck
Help plz ffggggggggggggggggggggggggggggg
Answer:
< EFG
< GFE
Step-by-step explanation:
The letter for the vertex must be in the middle
< EFG
< GFE
<F
PLEASE HELP ME I DONT UNDERSTAND
Answer:
no
Step-by-step explanation:
the square root of 2 is not rational
what is the answer to this?
Answer:
x is any number
y depends on x value
Find the value of m.
A. 7
B. 2
C. 42
D. 14
Answer:
A. 7
Step-by-step explanation:
3m + 21 = 6m
Move variables to one side to get:
3m + 21 = 6m
-3m -3m
21 = 3m
Then isolate variable by dividing by 3
21/3 = 3m/3
m = 7
Choice A is the correct answer
Ade thinks of a number He doubles it and then subtract 5 The result cannot be less than 100 find the range of values of x
Answer: [tex]x\in [53,\infty)[/tex]
Step-by-step explanation:
Given
Ade doubles her number and subtract 5 from it. The result cannot be less than 100
Suppose the number is [tex]x[/tex]
According to the question
[tex]\Rightarrow 2x-5\geq100\\\text{Solve the inequality}\\\Rightarrow 2x\geq105\\\Rightarrow x\geq52.5\\\text{for integer number, the range is given by }\\\Rightarrow x\in [53,\infty)[/tex]
in how many ways can alice give 12 apples to 3 children
Answer:
Step-by-step explanation:
give four apples to each child because 12/3 is 4
Answer:
91
Step-by-step explanation:
Sue has 3 cats. Each cat eats 1 4 of a tin of cat food each day. Sue buys 4 tins of cat food. Has Sue bought enough cat food to feed her cats for 5 days? You must show how you get your answer
Answer:
3 3/4 tins of food
Step-by-step explanation:
Number of cats = 3
Quantity of food for each cat per day = 1/4 of a tin
Total tins of cat food sue bought = 4 tins
Has Sue bought enough cat food to feed her cats for 5 days?
Quantity of food 3 cats eat per day = Quantity of food for each cat per day × Number of cats
= 1/4 × 3
= 3/4 of a tin
Total Quantity of food 3 cats eat for 5 days = Quantity of food 3 cats eat per day × 5 days
= 3/4 × 5
= (3 * 5) / 4
= 15/4
= 3 3/4 tins of food
Total Quantity of food 3 cats eat for 5 days = 3 3/4 tins of food
Recall,
Total tins of cat food sue bought = 4 tins
Therefore, Sue bought enough cat food to feed her cats for 5 days
Make an Inequality! Twice the difference of a number and 7 is less than -30. Use c as the variable.
Answer:
7 - 2c < - 30
*To do this equation you would have to start with -30, because of "less than"
Hope this helps.
(x + 1)(x + 3) + (x + 2)(x + 4)
Step-by-step explanation:
x²+3x+x+3+x²+4x+2x+8
2x²+10x+11....then solve quadratically
Answer:
Step-by-step explanation:
Hello!
(x + 1)(x + 3) + (x + 2)(x + 4)
x*x = x²
x*3 = 3x
1*x = x
1*3=3
x*x=x²
x*4 = 4x
2*x= 2x
2*4 = 8
x²+3x+x+3+ x² + 4x+ 2x+ 8=
2x² + 10x+ 11
Guided Practice
Use the vertical motion formula h = –16t2 + vt + c.
A child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft. Substitute the values into the vertical motion formula and let h = 0. Use the quadratic formula to solve for t. How long is the ball in the air?
A.
0.8 s
B.
0.8 s or –0.2 s
C.
0.2 s
Answer:
t = -0.22secs and 0.85secs
Step-by-step explanation:
Given the expression
h = –16t² + vt + c.
If a child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft, then;
v = 10, c = 3
Since we are to let h = 0, then the equation becomes:
0 = –16t² + 10t + 3
Multiply through by a minus sign
16t² - 10t - 3 = 0
Factorize the reulting expression:
t = -(-10)±√(-10)²-4(16)(-3)/2(16)
t = 10±√100+192/32
t = 10±√292/32
t = 10±17.09/32
t = 10-17.09/32 and 10+17.09/32
t = -7.09/32 and 27.09/32
t = -0.22secs and 0.85secs
Answer:
0.8 s
Step-by-step explanation:
I got it right in grandpoint.
SOMEONEEEE HELPPP MEEEE OUTTTT!!!!
Answer:
24°
Step-by-step explanation:
cos ? = 41/45
? = arccos 41/45
? = 24
Answered by GAUTHMATH
The length of a rectangular playing field is 5m longer than its width. If the perimeter of the field is 150m,find it's width
Answer:
35
Step-by-step explanation:
Make equations, l = w+5 and 2l + 2w = 150
Substitute w+5 into 2l + 2w = 150
Simplify to get 4w + 10 = 150
Subtract 10 from both sides to get 4w = 140
Divide both sides by 4 and you get 35 as width
Answer:
The width of the field is 35 meters.
Step-by-step explanation:
Recall that the perimeter of a rectangle is given by:
[tex]\displaystyle P = 2(w+\ell)[/tex]
Where w is the width and l is the length of the rectangle.
We know that the perimeter is 150 meters. Thus:
[tex]150=2(w+\ell)[/tex]
Divide both sides by two:
[tex]75=w+\ell[/tex]
We are given that the length is five meters longer than the width. So:
[tex]\ell = w+5[/tex]
Substitute:
[tex]75=w+(w+5)[/tex]
Combine like terms:
[tex]75=2w+5[/tex]
Subtract five from both sides:
[tex]70=2w[/tex]
And divide both sides by two. Hence:
[tex]w=35[/tex]
Thus, the width of the rectangular field is 35 meters.
The tables represent two linear functions in a system.
A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 26, 18, 10, 2. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 14, 8, 2, negative 4.
What is the solution to this system?
Answer:
how?
Step-by-step explanation:
i didnt get this question
Answer:
(8,-22)
Step-by-step explanation:
I took the quiz and did my work on paper but the paper got wet and I don't remember the steps I did
What is the value of q?
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
4
+
Submit Answer
Answer: 2 =
attempt 1 out of 2
PLS HELP
Answer:
69
Step-by-step explanation:
cuz
what is the value of i^n if the remainder of n/4 is 3?
Answer:
-i
Step-by-step explanation:
i =i
i^2=-1
i^3= -i
i^4=1
i^5=1
what is another name for this polynomial?
PLS HELP ASAP¡
A
P
E
X
Answer:
4x^4 + 6x^3 + 5x + 4 poly means many ....polynomial
x^2 + 1 ... two parts bi-nomial
ax^2 + bx + c ... three parts tri-nomial
3x^2y^3 ... one part monomial
Step-by-step explanation:
