Answer:
572 7s are needed to be added together
Step-by-step explanation:
Basically, what we are asked here is the multiple of 7 which is closest to but above 4,000
Then, from this multiple , the number of 7s which are added together to give it is our answer.
By multiplication; 7 * 572 = 4,004
This is the closest multiple of 7 to 4000 which is also above it.
So the fewest number of 7s which we can add together is 572
PLEASE help me solve this question! No nonsense answers please!
Answer:
[tex]\boxed{\sf Option \ 1}[/tex]
Step-by-step explanation:
The profit is revenue (R ) - costs (C ).
Subtract the expression of costs (C ) from revenue (R ).
[tex]10x-0.01x^2-(2x+100)[/tex]
Distribute negative sign.
[tex]10x-0.01x^2-2x-100[/tex]
Combine like terms.
[tex]8x-0.01x^2-100[/tex]
The first option has a positive 100, which is wrong.
The rest options are right, when we expand brackets the result is same.
to make a set for a stage, you bought a piece of lumber 9 feet long. How many 2 1/4 foot pieces can you cut from this piece of lumber? please answer ASAP
Answer:
4 pieces
Step-by-step explanation:
Total length of lumber = 9 feet
How many 2 1/4 foot pieces can you cut from this piece of lumber
To find the number of 2 1/4 foot pieces of lumber in a 9 feet of lumber, we will divide the total length of lumber by the length of each piece of lumber
9 ÷ 2 1/4
= 9 ÷ 9/4
= 9 × 4/9
= 36/9
= 4 pieces of lumber
Therefore, 4 pieces of 2 1/4 foot of lumber can be gotten from 9 feet of lumber
helpppppppppppppppp
Express the following English phrase using an algebraic expression.
The product of 12 and a number y.
Represent "The product of 12 and a number y " mathematically.
Answer:
12y
Step-by-step explanation:
product means multiplycation so twelve times y is 12y
The distance of planet Mercury from the Sun is approximately 5.8. 107 kilometers, and the distance of planet Venus from the Sun is 1.1 . 108 kilometers. About how
many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun?
O 5.2. 107 kilometers
O 4.7. 108 kilometers
O 5.2. 108 kilometers
O 5.7. 109 kilometers
please help :) Geography doesn’t simply begin and end with maps showing the location of all the countries of the world. In fact, such maps don’t necessarily tell us much. No—geography poses fascinating questions about who we are and how we got to be that way, and then provides clues to the answers. ~Kenneth Davis The speaker in the passage above is stating that a. maps are not helpful to historians. b. human geography is more important than physical geography. c. historians want to know where people settled. d. physical features and locations tell historians about the ways people lived.
Answer:
d. physical features and locations tell historians about the ways people lived.
Step-by-step explanation:
I believe this is the correct answer
Question 3 of 18
Suppose the probability of success in a binomial trial is 0.26. What is the
probability of failure?
A. 0.26
B. 0.65
O C. 0.35
O D. 0.74
Answer:
D. 0.74.
Step-by-step explanation:
It is a BINOMIAL trial, which means that there are only two outcomes: either success, or failure.
So, if the probability of success is 0.26, the probability of failure will be 1 - 0.26 = 0.74.
Hope this helps!
solve show all steps what is 7x-28≥-7
Answer:
x≥3
Step-by-step explanation:
7x-28≥-7
Add 28 to each side
7x-28+28≥-7+28
7x≥21
Divide by 7
7x/7≥21/7
x≥3
Answer:
7x-28≥-7
7x≥21
x≥3
Tim owns a clothing store where he designs pairs of shorts, s, and T-shirts, t.
He sells the shorts for $12 and the T-shirts for $8 each. Tim can work 18
hours a day, at most. It takes him 30 minutes to design a T-shirt and 45
minutes to design a pair of shorts. He must design at least 12 items each
day, but he cannot design more than 30 items in one day. Which set of
inequalities below represents this scenario?
A. s 2 12 + $ ss 30 + tiss 24-0.66t, s2; 0; t2 0
B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0
O c. s? 12-ts? 30-tss 24 -0.66t, s 2 0;t20
D. S 2 12-tss 30-ts 24 -0.66t, s 20; t 0
Answer:
The correct option is;
B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t
Step-by-step explanation:
The given parameters are;
The number of T-shirts, t, and shorts, s, Tim must design a day = 12
The maximum number of T-shirts and shorts Tim can design a day = 30
The maximum number of hours Tim can work = 18 hours
Therefore, we have;
The number of shorts Tim designs in a day is ≥ The minimum number of T-shirts and shorts Tim must design a day less the number of T-shirts Tim designs
Which gives;
s ≥ 12 - t
Also the number of shorts Tim designs in a day is ≤ The maximum number of T-shirts, and shorts, Tim can design a day less the number of T-shirts Tim designs
Which gives;
s ≤ 30 - t
The number of 45 minute period for the design of shorts in 18 hours = 18×60/45 = 24
The fraction of 36 minutes in 45 minutes = 36/45 = 0.667
Therefore we have;
The number of shorts Tim designs in a day is ≤ The number of 45 minute periods in 18 hours less the number of 36 minutes periods used to design T-shirts
Which gives;
s ≤ 24 - 0.66·t
The correct option is s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t.
Answer:
B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0
Step-by-step explanation:
Hope this helps!!
Raj correctly determined that ray LH is the bisector of AngleGLI. A line contains points K, L, M. 4 lines extend from point L. One line extends to point F, another to G, another to H, and another to I. Which information could he have used to determine this? AngleGLH Is-congruent-to AngleILM mAngleKLM = 5mAngleILM mAngleGLI = 2mAngleGLH mAngleGLI = mAngleGLH + mAngleHLI
Answer: C.) mAngleGLI = 2mAngleGLH
Step-by-step explanation:
Hope it helps!!!
For ray LH as the bisector of angle GLI, we can determine that the relation ∠GLI = 2∠GLH holds
What is an angle?An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.
∠GLI is bisected by LH, hence:
∠GLH = ∠HLI (definition of bisection)
∠GLI = ∠GLH + ∠HLI (angle addition)
∠GLI = 2∠GLH
The information that can be used to determine this is ∠GLI = 2∠GLH
Find out more on angle at: https://brainly.com/question/25770607
I need help with this question. PLZZ HELP!!!
Answer:
the 8 in the graph
Step-by-step explanation:
A wooden jewelry box has the shape of a prism with a regular hexagonal base of 85.3 in2. The sides of the hexagonal base are all 5.73 inches. If the height of the box is 18.10 inches, what is the surface area of the wood used to make the jewelry box?
Answer:
792.9 in²
Step-by-step Explanation:
Given:
Area of the base of the regular hexagonal prism box (B) = 85.3 in²
Each side length of hexagonal base (s) = 5.73 in
Height of prism box (h) = 18.10 in
Required:
Surface area of the wood used in making the hexagonal prism box
SOLUTION:
Surface area for any given regular prism can be calculated using the following formula: (Perimeter of Base × height of prism) + 2(Base Area)
Perimeter of the hexagonal base of the prism box = 6(5.73) (Note: hexagon has 6 sides.)
Perimeter of base = 34.38 in
Height = 18.10 in
Base area is already given as 85.3 in²
Surface area of the hexagonal prism box [tex] = (34.38*18.10) + 2(85.3) [/tex]
[tex] = 622.278 + 170.6 = 792.878 in^2 [/tex]
Surface area of the wood used in making the jewelry box ≈ 792.9 in²
True or false: f(x) is a function.
0
0
3
1
3
9
f(x)
Answer:
true
Step-by-step explanation:
it is true because there is one input for y output
Answer:
True
Step-by-step explanation:
This is a function. Each value of x goes to only one value of y
which has greater cenetic energy a car traveling 30.0 km/hr or one twice as heavy traveling at 15 km/hr?
Answer:
30 km/h car
Step-by-step explanation:
From analysis the car traveling at 30 km/h has greater kinetic energy
we can deduce it from the expression of kinetic energy which is
[tex]KE=\frac{1}{2} mv^2[/tex]
Assuming the mass m= 1 kg
For the 30 km/h
[tex]KE=\frac{1}{2}*1*30^2 \\\\KE=\frac{1}{2}*1*900\\\\\KE=450 J[/tex]
For the 15 km/h
[tex]KE=\frac{1}{2}*2*15^2 \\\\ KE=\frac{1}{2}*2*225 \\\\\ KE=\frac{1}{2}*450 J\\\\\ KE=225 J[/tex]
Though the kinetic energy is a function of mass and velocity, but from our analysis the faster moving object has more KE
What is the value of b if -7 +b= -8?
Answer:
-1
Step-by-step explanation:
-7 +b = -8
↦b = -8 + 7 [ Transition]
↦b = -1
.°. b = -1
Hope you understand it ✔
Find the amplitude of y = -2 sin x
Answer:
Amplitude = 2
Step-by-step explanation:
The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x). The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.
Cheers.
In a fish tank, 1/5 of the fish are guppies and 1/12 of the fish are goldfish. Which equation most closely estimates the fraction of the fish that are guppies or goldfish in the tank.suggested answers: 1/2+1/2=1 , 1/2+1/4=3/4 , 1/4+1/4=1/2, 1/4+0= 1/4
Answer: [tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}[/tex]
Step-by-step explanation:
A or B = A+B
Given: In a fish tank, [tex]\dfrac15[/tex] of the fish are guppies and [tex]\dfrac{1}{12}[/tex] of the fish are goldfish.
Then, the fraction of the fish that are guppies or goldfish in the tank=[tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{2+5}{5\times2}[/tex]
[tex]\dfrac{7}{10}[/tex]
Hence, the equation most closely estimates the fraction of the fish that are guppies or goldfish in the tank:
[tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}[/tex]
We want to factor the following expression: 16x^4-25
Answer:
(4x2 +5)⋅(4x2 −5)
A plane is on its approach to land on the runway. The jet’s height above the ground is given in feet as a function of the time in seconds. The following table tracks the plane as it lands. t (in seconds) h (in feet) 0 4000 5 3500 10 3000 15 2500 20 2000 25 1500. Determine where the graph crosses the h-axis. Then write the equation in slope-intercept form. a. (4000, 0); h = negative 100 t + 4000 b. (0, 4000); h = negative 100 t + 4000 c. (0, 4000); h = negative 4000 t + 100 d. (100, 0); h = 4000 t minus 100
Answer:
Step-by-step explanation:
This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line. If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept. If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.
Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:
h = -100t + 4000 which appears to be choice a.
Answer:
a
Step-by-step explanation:
i took the quiz and got it right :)
find six rational numbers between 3 and 4
Answer:
3.1
3.2
3.3
3.4
3.5
3.6
Hope this answer correct :)
A student says that the function f (x) = –x² – 9 has the x-intercepts (-3,0) and (3,0). Is the student correct? If not, expl.
why.
Answer:
No
Step-by-step explanation:
The student is wrong because the function has no solutions.
You cannot factor it because the x² is negative.
If it was x² - 9 instead, you could factor it into (x-3)(x+3) which would get you the x-intercepts (-3,0) and (3,0).
But instead, -x² - 9 cannot be factored at all and has no x-intercepts/solutions.
HELP ASAP YOU WILL GET BRAINLEIST AND I WILL THANK AND RATE 5 IF RIGHT
Three people are standing on a Cartesian coordinate plane. Robert is standing at point $(4,3)$, Lucy at point $(6,1)$, and Liz at point $(1,7)$. How m. any units away is the farther person from Robert? 3 minutes ago Let f and g be inverse functions. Find f(g(8)).
Answer: Liz is further away. Her distance from Robert is 5 units.
=================================================
Work Shown:
R = Robert's location = (4,3)
L = Lucy's location = (6,1)
Z = Liz's location = (1,7)
We need to find the lengths of segments RL and RZ to find out which person (Lucy or Liz) is further from Robert.
Use the distance formula to find the length of each segment. Let's start with the distance from R to L
[tex]d = \sqrt{(x_1+x_2)^2+(y_1+y_2)^2}\\\\d = \sqrt{(4-6)^2+(3-1)^2}\\\\d = \sqrt{8}\\\\d \approx 2.828427\\\\[/tex]
The distance from Robert to Lucy is approximately 2.828427 units.
--------------
Now find the distance from R to Z
[tex]d = \sqrt{(x_1+x_2)^2+(y_1+y_2)^2}\\\\d = \sqrt{(4-1)^2+(3-7)^2}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
The distance from Robert to Liz is exactly 5 units. We see that Liz is further away from Robert, compared to Lucy's distance from him.
(Will give brainliest to the most explained answer!) Can someone explain how to factor Polynomials. Please explain it like you’re teaching this to a 5 year old. :)
Step-by-step explanation:
Find the Greatest Common Factor (GCF) of a polynomial.
Factor out the GCF of a polynomial.
Factor a polynomial with four terms by grouping.
Factor a trinomial of the form .
Factor a trinomial of the form .
Indicate if a polynomial is a prime polynomial.
Factor a perfect square trinomial.
Factor a difference of squares.
Factor a sum or difference of cubes.
Apply the factoring strategy to factor a polynomial completely
Answer:
See explanation
Step-by-step explanation:
We can factor polynomials by breaking down the expression.
For instance, let's say we have the polynomial [tex]x^2 - 9x + 14[/tex].
We can start solving this because this polynomial is in standard form, meaning that the highest exponents go first. ([tex]ax^2 + bx + c[/tex].)
To factor a polynomial, we are looking for two numbers that:
A. When multiplied, get us [tex]c[/tex] (in this case, 14)
B. When added, get us [tex]b[/tex] (in this case, -9).
If we play around with numbers, looking at the factors of 14, we see that the numbers 7 and 2 might be useful here. They add up to 9 and multiply to be 14.
However, these numbers ADD to be -9, meaning that they both need to be negative.
[tex]-7 + -2 = -9\\-7\cdot-2=14[/tex]
Now that we know our numbers, -7 and -2, we can make these our factors (which are represented by [tex](x + y)[/tex], y being our factor.
So our factors turn out to be [tex](x-7)[/tex] and [tex](x-2)[/tex].
Let me know if you need anything explained more, and I hope this helped!
a/4 + 4 = 6 please helppppp!
━━━━━━━☆☆━━━━━━━
▹ Answer
a = 8
▹ Step-by-Step Explanation
a/4 + 4 = 6
Multiply both sides:
a + 16 = 24
Subtract 16 from both sides:
16 - 16 = a
24 - 16 = 8
a = 8
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
a = 8
Step-by-step explanation:
a/4 + 4 = 6
Subtract 4 from each side
a/4 + 4-4 = 6-4
a/4 = 2
Multiply each side by 4
a/4 * 4 = 2*4
a = 8
Camila and Lucíana bought the same mobile phone but in different places. Camila's had a value of 120,000 but they gave her a 30% discount, while Luciana had a value of 150,000 on which they applied a 40% discount Who paid less?
Answer:
Camila paid less
Step-by-step explanation:
In the question, we are told:
Camila's phone had a value of 120,000 but they gave her a 30% discount.
Therefore, Camila paid:
30% × 120,000
= 30/100 × 120,000
= 36,000
Luciana had a value of 150,000 on which they applied a 40% discount
Luciana paid:
40% × 150,000
40/100 × 150,000
= 60,000
From the calculation,
Camila paid 36,000 and Luciana paid 60,000, therefore, Camila paid less.
Which equation represents the line that is perpendicular to y=3/4x+1 and passes through (-5,11)
Will give brainliest!!
Answer:
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{4}[/tex] x + 1 ← is in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] , thus
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute (- 5, 11) into the partial equation
11 = [tex]\frac{20}{3}[/tex] + c ⇒ c = 11 - [tex]\frac{20}{3}[/tex] = [tex]\frac{13}{3}[/tex]
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex] ← equation of perpendicular line
The equation of the line that passes through (-5, 11) and perpendicular to y = (3/4)x + 1 is
y = -2x + 1
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
y = (2/4)x + 1 is in the form of y = m(2)x + c
So,
m(2) = 2/4 = 1/2
The equation of the line y = m(1)x + c is perpendicular to y = (2/4)x + 1.
So,
m(1) x m(2) = -1
m(1) = -1/(1/2)
m(1) = -2
Now,
y = -2x + c passes through (-5, 11).
This means,
11 = -2 x (-5) + c
11 = 10 + c
11- 10 = c
c = 1
Thus,
The equation of the line is y = -2x + 1.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ2
Cheryl earns (p+3) dollars per hour. In 8 hour she earns ___ dollars.
Answer:
8p + 24 dollars
Step-by-step explanation:
1 hour = (p+3)
8 hours = 8 (p+3)
=> 8p + 24
In 8 hours, Cheryl earns 8p + 24 dollars.
Answer:
[tex]\boxed{8p + 24}[/tex]
Step-by-step explanation:
Hey there!
Well if Cheryl earns p + 3 per hour and it is asking us to find the amount made in 8 hours, we can make the following,
8(p + 3)
8*p = 8p
8*3 = 24
Together,
8p + 24
Hope this helps :)
rationalise the following 1/√7
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]1\sqrt{7}[/tex]
[tex]= \frac{1}{7} \sqrt{7}[/tex] (Decimal: 0.377964)
OR
[tex]\frac{1}{\sqrt{7} }[/tex]
[tex]= \frac{1}{\sqrt{7} } X \frac{\sqrt{7} }{\sqrt{7} }[/tex]
[tex]= \frac{\sqrt{7} }{(\sqrt{7})^{2} }[/tex]
[tex]= \frac{\sqrt{7} }{\sqrt{7} }[/tex]
I don't really know because both of them seem right..
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
❀*May*❀
i need help. Can u help me solve for x?
Answer:
[tex] x = \sqrt {40}[/tex]
Step-by-step explanation:
Given is an isosceles triangle, dotted line is the bisector of top angle which is also perpendicular bisector of the base of the triangle. Hence, by Pythagoras theorem:
[tex] {x}^{2} = {6}^{2} + ({ \frac{4}{2} })^{2} \\ = 36 + 4 \\ = 40 \\ \therefore \: x = \sqrt{40} \\ [/tex]
Answer:
D. x = sqrt(52).
Step-by-step explanation:
Since the line measuring 6 units bisects the top angle, there are two right angles. We can use the Pythagorean Theorem to solve for x.
a^2 + b^2 = x^2
4^2 + 6^2 = x^2
16 + 36 = x^2
52 = x^2
x = sqrt(52)
x = sqrt(2 * 2 * 13)
x = 2sqrt(13)
x = 7.211102551.
Hope this helps!
the perimeter of square is 76 cm find are of square
Answer:
Given the information above, the area of the square is 361 cm²
Step-by-step explanation:
A square is a shape with four equal sides. So, in order to find the area of the square, we must find the length of each individual side. We can do this by dividing the perimeter by 4 because a square has 4 equal sides meaning they have the same lengths.
The perimeter of the square is 76. So, let's divide 76 by 4.
76 ÷ 4 = 19
So, the lengths of each sides in the square is 19cm.
In order to find the area, we must multiply the length and the width together. Since a square has equal sides, then we will multiply 19 by 19 to get the area.
19 × 19 = 361
So, the area of the square is 361 cm²
Answer:
361 cm^2
Step-by-step explanation:
The area of a square can be found by squaring the side length.
[tex]A=s^2[/tex]
A square has four equal sides. The perimeter is the sum of all four sides added together. Therefore, we can find one side length by dividing the perimeter by 4.
[tex]s=\frac{p}{4}[/tex]
The perimeter is 76 centimeters.
[tex]s=\frac{76 cm}{4}[/tex]
Divide 76 by 4.
[tex]s=19 cm[/tex]
The side length is 19 centimeters.
Now we know the side length and can plug it into the area formula.
[tex]A=s^2\\s=19cm[/tex]
[tex]A= (19 cm)^2[/tex]
Evaluate the exponent.
(19cm)^2= 19 cm* 19cm=361 cm^2
[tex]A= 361 cm^2[/tex]
The area of the square is 361 square centimeters.
help me plsssssssssssssssss
Answer:
Step-by-step explanation:
I'm assuming you are trying to solve for x. I'm not sure, but that's what I figured out for the answer, so I'm gonna go with that. : )
We are looking for the value of x to make that statement true. It's going to take some trig manipulations, but if you are at this level of precalc, these identities should definitely NOT be new to you. We will begin by squaring both sides of that equation to get:
[tex]9sin^2(x)+3cos^2(x)=3[/tex]
From here we will factor out a 3 to get:
[tex]3(3sin^2x+cos^2x)=3[/tex] and then divide both sides by 3 to get:
[tex]3sin^2x+cos^2x=1[/tex]
Knowing the Pythagorean identity for the trig ratios, we will replace the sin-squared with what it is equal to in terms of cos-squared. If:
[tex]sin^2x+cos^2x=1[/tex], then
[tex]sin^2x=1-cos^2x[/tex]. Making that replacement gives us an equation with only one trig ratio in it, namely, cos:
[tex]3(1-cos^2x)+cos^2x=1[/tex] and distributing:
[tex]3-3cos^2x+cos^2x=1[/tex] which simplifies down to:
[tex]-2cos^2x=-2[/tex]. Divide both sides by -2 to get:
[tex]cos^2x=1[/tex]. When you take the square root of both sides you get:
[tex]cos(x)=1[/tex] and [tex]cos(x)=-1[/tex]. Here is where we will use the unit circle to see where the cos is 1 and where the cos is -1. You didn't give me an interval in which to work, so I am going to use from 0 degrees to 180. Within that interval, the cos is 1 at 0 degrees; within that interval, the cos is -1 at 180.
Now we need to plug those values into the original equation to see if they work. One of them may be extraneous. Plugging in 0 first:
3sin(0) + √3cos(0) = -√3. We need to see if this is true.
The sin of 0 is 0; the cos of 0 is 1, so
0 + (√3)(1) = -√3?
The left side is √3, not -√3, so 0 doesn't work. Let's try 180 now, shall we?
3sin(180) + √3cos(180) = -√3. We need to see if this is true.
The sin of 180 is 0; the cos of 180 is -1, so
0 + (√3)(-1) = -√3?
The left side is -√3 and so is the right side, so
x = 180°
