◈ LHS :
[tex]:\implies\tt\:sin60\degree[/tex]
[tex]:\implies\bf\:\dfrac{\sqrt{3}}{2}[/tex]
◈ RHS :
[tex]:\implies\tt\:\dfrac{2tan30\degree}{1+tan^230\degree}[/tex]
[tex]:\implies\tt\:\dfrac{2\times \dfrac{1}{\sqrt{3}}}{1+{\large(}\dfrac{1}{{\sqrt{3}}}{\large)}^2}[/tex]
[tex]:\implies\tt\:\dfrac{2}{\sqrt{3}}\times \dfrac{3}{3+1}[/tex]
[tex]:\implies\tt\:\dfrac{2}{\sqrt{3}}\times \dfrac{3}{4}[/tex]
[tex]:\implies\bf\:\dfrac{\sqrt{3}}{2}[/tex]
Hence Proved !!
Find the standard equation of the circle defined by the equation x^2 + y^2 +8x - 12y + 43 = 0. ANSWERS ATTACHED, due in 2 HOURS, will give Brainliest!
Answer:
Solution: Option C
Step-by-step explanation:
Our goal here is to factor the expression such that it is converted into the circle equation (x - a)² + (y - b)² = r² where r = radius centered at point (a,b).
[tex]x^2\:+\:y^2\:+8x\:-\:12y\:+\:43\:=\:0[/tex] (Factor the expression "x² + 8x")
[tex]x^2+8x = x\left(x+8\right)[/tex] (Factor the expression "y² - 12y")
[tex]\:y^2-12y =y\left(y-12\right)[/tex]
That leaves us with the expression [tex]\left(x-\left(-4\right)\right)^2+\left(y-6\right)^2=3^2[/tex], or in other words [tex](x+4)^2 +(y-6)^2 = 9[/tex]. As you can see our solution is option c.
Answer ASAP, will give brainliest
Answer:
cge
Step-by-step explanation:
a statement that can be proven is called
Answer:
Theorem is a statement that can be proven .
Hope it helps.
Can somebody help me with this ?? :)
Answer:
Your answer would be D, the equation is a function because it is a polynomial and all polynomials are functions.
Step-by-step explanation:
I like to remember that polynomials have no negative , fraction exponents and no division. In this case everything is positive so I knew it was a polynomial , and like the answer says all polynomials are functions !
Hope this helped
a rectangle has a height of w^2+3w+9 and a width of w^2+2 express the area of the entire rectangle
Answer:
w⁴ + 3w³ + 11w² + 6w + 18
Step-by-step explanation:
Rectanle area = height * width
area = (w²+3w+9)(w² + 2)
= w²*w² + w²*2 + 3w*w² + 3w*2 + 9*w² + 9*2
= w⁴ + 2w² + 3w³ + 6w + 9w² + 18
= w⁴+ 3w³ + (9w²+2w²) + 6w + 18
= w⁴ + 3w³ + 11w² + 6w + 18
Answer:
w^4 + 3w^3 + 11w^2 + 6w + 18.
Step-by-step explanation:
Area = height * width
= (w^2 + 2)(w^2 + 3w + 9)
= w^2(w^2 + 3w + 9) + 2(w^2 + 3w + 9)
= w^4 + 3w^3 + 9w^2 + 2w^2 + 6w + 18
= w^4 + 3w^3 + 11w^2 + 6w + 18.
1
Parallel lines s and t are intersected by transversal lines fand g, as shown in the figure below. What is the measure of angle 1?
g
st
OA. 46°
ОВ.
136°
OC.
44°
OD. 134
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Next Question
I need the answer ASAP
Combine like terms to create an equivalent expression. 2/5m - 4/5 - 3/5m.
Answer:
Step-by-step explanation:
2/5 m and -3/5 are like terms
[tex]\frac{2}{5}m-\frac{4}{5}-\frac{3}{5}m= \frac{2}{5}m-\frac{3}{5}m-\frac{4}{5}\\\\\\=\frac{(2-3)}{5}m-\frac{4}{5}\\\\\\=-\frac{1}{5}m-\frac{4}{5}[/tex]
Marvin walks at a speed of 7 feet per second. How many feet per hour is this?
Answer:
7 x 60 = 420
420 x 60 = 25,200
25,200 feet per hour
Step-by-step explanation:
pls make me as brainleist
State the amplitude and period of f(t) = -0.3sin t/3
Answer:
Amplitude is 0.3; period is 6π
Step-by-step explanation:
The amplitude is |-0.3| = 0.3.
The period and frequency are related through
2π
period = ----------
b
where b is the coefficient of the independent variable; here that coefficient is 1/3.
Thus, the period here is found using b = 1/3:
period = 2π/b, or 2π/(1/3), or 6π
Please help its due in a hour
Answer:
160
Step-by-step explanation:
because 360 is the total and 50 plus 50 is 100 subtract that by 360 and it's 160
I WILL GIVE BRAINLIEST a scale on a map shows that 2 inches = 25 miles Part A: How many inches on the map = 60 miles? ------------------------------------------------------------------------ Part B: How many miles are represented by 1/4 inch on the map?
Answer:
4.8 in, 3.125 mi
Step-by-step explanation:
This situation models direct proportionality, hence, if one variable increases, the other goes increases as well and vice versa. In this case, the variables are inches and miles.
Part A: Since you multiply 60/25 by 25 to get 60 miles, we know that the value in inches will be 2 * 60/25 = 4.8 inches.
Part B: Since you divide 2 by 8 to get 1/4 inches, we know that the value in miles will be 25 / 8 = 3.125 miles.
what is the vertex of y = - | x + 3 | + 5
Answer:
vertex = (- 3, 5 )
Step-by-step explanation:
The general form of the absolute value function is
y = a | x - h | + k
where (h, k) are the coordinates of the vertex
Given
y = - | x + 3 | + 5 ← in general form, then
vertex = (- 3, 5 )
17. The District of Columbia has a very high population density.
There are 646,449 people in 68.3 square miles.
a. Calculate the unit rate in terms of people per square mile for the District of Columbia.
Make sure the precision of your answer is reasonable.
Answer:
9465 people/square mile.
Step-by-step explanation:
If there are 646,449 people in 68.3 square miles for the district of columbia, the unit rate in terms of people per square mile for the District of Columbia will be expressed as shown;
646,449 people = 68.3 square miles
x people = 1 square mile
Cross multiply
646,449 people * 1 square mile = 68.3 square miles * x people
x = 646,449 people * 1 square mile/68.3 square miles
x = 646,449/68.3 square miles
x = 9464.8463 square miles
x ≈ 9465 people/square mile.
Hence the unit rate in terms of people per square mile for the District of Columbia is approximately 9465 people.
Please help Faaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaast 2x ≤ − 2/7 (8x + 8)
Answer:
[tex]x\leq - \frac{8}{15} [/tex]Step-by-step explanation:
[tex]2x \leq - \frac{2}{7} (8x + 8)[/tex]First of all multiply through by 7
We have
[tex]14x\leq - 2(8x + 8)[/tex]Expand the terms in the bracket
That's
[tex]14x\leq - 16x - 16[/tex]Add 16x to both sides
That's
[tex]14x + 16x\leq16x - 16x - 16 \\30x\leq - 16[/tex]Divide both sides by 30
We have the final answer as
[tex]x\leq - \frac{8}{15} [/tex]Hope this helps you
You are choosing between two different cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $39.95 plus 12 cents per minute. Let t be the number of minutes you talk and C1 and C2 be the costs (in dollars) of the first and second plans. Give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans (Round your answer to one decimal place). C1= C2= If you talk for minutes the two plans will have the same cost.
Answer:
285.28571429 minutes
Step-by-step explanation:
Let us represent
The number of minutes you talk = t
C1 = Cost in dollars of the first plan
C2 = Cost in dollars of the second plan
First plan
The first plan charges a rate of 26 cents per minute
Converting cents to dollars
100 cents = 1 dollars
26 cents =
26/100 cents
=$ 0.26
C1 = $0.26 × t
C1 = 0.26t .......... Equation 1
Second Plan
The second plan charges a monthly fee of $39.95 plus 12 cents per minute
Converting 12 cents to dollars
100 cents = 1 dollars
12 cents =
12/100
= $0.12
C2 = $39.95 + 0.12t........Equation 2
Find the number of talk minutes that would produce the same cost for both plans
We would Equate C1 to C2
C1 = C2
0.26t = $39.95 + 0.12t
Collect like terms
0.26t - 0.12t = $39.95
= 0.14t = $39.95
Divide both sides by 0.14
= t = $34.95/0.14
t = 285.28571429 minutes
Therefore, the number of talk minutes that would produce the same cost for both plans is 285.28571429 minutes.
You get paid $6.80 per hour and worked 4 hours of overtime last week .How much overtime pay will you receive for last week ?
Which ordered pair would form a proportional relationship with the point graphed below?
ТУ
40
30
20
10
-40-30-20-1904 10 20 30 40 x
2
Bo
(-10,-40)
440
O (40, 10)
(-5, -10)
(5, 20)
O (-10.-20)
Answer:
(10, -20)
Step-by-step explanation:
i took the test plz put me as brainist
Write an equivalent expression by distributing the "-−" sign outside the parentheses: -(3.4p-6q+6) −(3.4p−6q+6)
Answer:
[tex]-(3.4p-6q+6)[/tex] = [tex]-3.4p+6q-6[/tex]
Step-by-step explanation:
Given
[tex]-(3.4p-6q+6)[/tex]
Required
Simplify
[tex]-(3.4p-6q+6)[/tex]
Rewrite as
[tex]-1(3.4p-6q+6)[/tex]
[tex]-1 * (3.4p-6q+6)[/tex]
Open the bracket
[tex]-3.4p+6q-6[/tex]
What is the slope againnn ?
Answer:
-1/2
Step-by-step explanation:
To find the slope, pick two points on the line, and use the slope formula
( 1,9) and (5,7)
m = (7-9 )/(5-1)
-2/4
-1/2
Answer:
slope = -1/2
Step-by-step explanation:
Find two points on the line that are easy to read. The easiest points to read are points that lie on grid intersections.
For example, use point (1, 9) and point (3, 8).
slope = rise/run
Rise is the vertical distance between points. Up is positive. Down is negative.
Run is the horizontal distance between points. Right is positive. Left is negative.
You need to go from one point to the other points and note the rise and run.
Start at (1, 9).
Go 1 unit down. That is a rise of -1 since you went down 1 unit.
Now go 2 units right. That is a run of +2 since you went 2 units to the right.
slope = rise/run = -1/2
Answer: slope = -1/2
The life expectancy of a monkey is 15 years, an African elephant 35 years, a beaver 5 years, and a grizzly bear 25 years. Write a relation that describes this information. Determine its domain and range.
Answer:
The domain = 1, 3, 5, 7 and the range = 5, 15, 25, and 35
Step-by-step explanation:
The given parameters are;
The life expectancy of a monkey = 15 years
The life expectancy of an African elephant = 35 years
The life expectancy of a beaver = 5 years
The life expectancy of a grizzly bear = 25 years
Therefore, if the life expectancy of a beaver = X, we have;
The life expectancy of a monkey = 3 × The life expectancy of a beaver = 3·X
The life expectancy of a beaver = X
The life expectancy of an African elephant = 7 × The life expectancy of a beaver = 7·X
The life expectancy of a grizzly bear = 5 × The life expectancy of a beaver = 5·X
Therefore;
The domain = 1, 3, 5, 7 and the range = 5, 15, 25, and 35.
Answer:
Relation = {(Monkey, 15), (African elephant, 35), (Beaver, 5), (Grizzly bear, 25)}
Domain = {Monkey, African elephant, Beaver, Grizzly bear}
Range = {5, 15, 25, 35}
Step-by-step explanation:
1. RelationRelation is just (x,y).
{(Monkey, 15), (African elephant, 35), (Beaver, 5), (Grizzly bear, 25)}
2. DomainI like to put domain as least ---> greatest, but in this case, it's just the names
{Monkey, African elephant, Beaver, Grizzly bear}
3. RangeThe numbers.
{5, 15, 25, 35}
Hope this helped! Please mark brainliest :)
~~ SUMMER ~~
Is -3 a natural number a whole number a integer a rational number or irrational number
Answer:
-3 is a rational integer.
Step-by-step explanation:
An integer is a superset of the whole numbers that includes the negated values as well as 0.
A rational number is simply anything that can be expressed as a fraction.
-3 is by these definitions, a negated 3, and any non fractional number can be expressed as a fraction.
-3 is not a natural number, as that is the set of numbers {1, 2, 3, 4, 5, ... etc} and -3 is not a whole number, as that is the set of numbers {0, 1, 2, 3, 4, ... etc}.
And -3 is also not an irrational number since it can be expressed as a fraction.
Thus, -3 is a rational integer.
Cheers.
on Tuesday at low tide the water was 17 ft below sea level. Then it rained for three days and the water level rose 20 feet. On Saturday it the water level dropped 5 ft and by Sunday it dropped another 3 feet. what was the water level by the end of the day on Sunday?
36=6u+30 PLEASE HELPPPP!!!
Answer: u = 1
36 = 6(1)+30
Step-by-step explanation:
Answer:
1=u
Step-by-step explanation:
36-30=6u+30-30
6=6u
6÷6=6u÷6
1=u
PLS HELP I NEED ASAP DUE TODAY 1.Which variable expression is a translation of the word phrase "three less than the product of a number and six"? 3−6n 6n−3 6(3−n) 6(n−3) 2.Fatima is three times the age of her younger sister Melody. Which expresses both ages in terms of Melody’s age m? Melody: m3 Fatima: m Melody: 3m Fatima: m Melody: m Fatima: 3m Melody: m Fatima: m + 3 Assessment navigation 3.A triangle has sides of length 10, 8, and y inches. Which is an expression for the perimeter of the triangle, and what is the perimeter when y = 7? y(10+8) The perimeter is 126 inches when y = 7. 10(y+8) The perimeter is150 inches when y = 7. 8(10+y) The perimeter is 136 inches when y = 7. y + 10 + 8 The perimeter is 25 inches when y = 7.
Answer:
1. 3 − 6n
2. Melody: m Fatima: 3m
3. i. Perimeter = y + 10 + 8
ii. The perimeter is 25 inches when y = 7
Step-by-step explanation:
1. Let the number be represented by n, thus the product of the number and 6 is 6n. Since 3 is less than 6n, therefore: 3 - 6n is the appropriate expression.
2. Let Melody's age be represented by m, Fatima is three times Melody's age implies 3m. So that Melody's age is m, while Fatima's age is 3m.
3. Length of the sides of the triangle in inches are 10, 8 and y.
Perimeter = addition of the length of sides of the triangle
= 10 + 8 + y
When y = 7,
Perimeter = 10 + 8 + 7
= 25 inches
Answer:
3-6n
Step-by-step explanation:
if f(x)=3(x+5) +4/x, what is f(a+2)
Answer:
f(a+2)=3(a+7)+4/(a+2)
Step-by-step explanation:
To determinef(a+2) you need to substitute a+2 for each occurrence of x in the given function. See below for full explanation.
Explanation:
If
f(x)=3(x+5)+4/x
Then
f(a+2)=3(a+2+5)+4/a+2
Simplifying gives:
f(a+2)=3(a+7)+4/(a+2)
A bakery sold a total of 500 cupcakes in a day, and 200 of them were mocha flavored. What percentage of cupcakes sold that day were mocha flavored?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{40\% \: }}}}}[/tex]
Step-by-step explanation:
Total number of cupcakes = 500
Total number of mocha flavored cupcakes = 200
To find : percentage of mocha flavored cupcakes sold that day
[tex] \boxed{ \sf{ \frac{total \: number \: of \: mocha \: flavored \: cupcakes}{total \: number \: of \: cupcakes} \times 100 \: \% \: }}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{200}{500} \times 100\%}}[/tex]
[tex] \dashrightarrow{ \sf{40 \: \% \: }}[/tex]
Hope I helped!
Best regards ! :D
Answer:
40% were mocha flavored cupcakes.
Step-by-step explanation:
200/500 = 2/5
2/5 = 40%
Hope it helped you!
Suppose A has a coordinate of 8 and AB = 3. What are the possible midpoints of AB?
Answer:
The possible midpoints of AB are 6.5 and 9.5
Step-by-step explanation:
Given that the coordinates of A is 8
The length of AB = 3
When A is the maximum coordinates of the two coordinates, A and B, we have;
The midpoint of AB = Coordinates of A - 1/2 × Length of AB
The midpoint of AB = 8 - 1/2 × 3 = 8 - 1.5 = 6.5
The midpoint of AB = 6.5
When A is the minimum coordinates of the two coordinates, A and B, we have;
The midpoint of AB = Coordinates of A + 1/2 × Length of AB
The midpoint of AB = 8 + 1/2 × 3 = 8 + 1.5 = 9.5
The midpoint of AB = 9.5
Therefore, the possible midpoints of AB are 6.5 and 9.5.
Solve the system using the elimination method.
3x + 2y-z= 8
-3x + 4y + 5z = -14
X- 3y + 4z=-14
Answer:
Step-by-step explanation:
3x + 2y - z = 8
-3x + 4y + 5z = -14
6y + 4z = -6
3x + 2y - z = 8
-3x + 9y - 12z = 42
11y - 13z = 50
6y + 4z = -6
66y - 78z = 300
-66y - 44z = 66
-122z = 366
z = -3
3x + 2y + 3 = 8
3x + 2y = 5
-3x + 4y -15 = -14
-3x + 4y = 1
3x + 2y = 5
-3x + 4y = 1
6y = 6
y = 1
3x + 2 + 3 = 8
3x + 5 = 8
3x = 3
x = 1
x=1, y = 1, z = -3
PLEASE HELP!!! Find the length of AB. Leave
your answer in terms of T.
А
20° AB = [?]
27
B
Enter
Answer:
3π
Step-by-step explanation:
Arc length is given in terms of central angle θ in radians as ...
s = rθ
For r = 27 and θ = (20/180)π, the arc length is ...
s = (27)(20/180)π = 3π
The arc length is 3π units.
Find the remainder when (2x^2 +2x+1) is divided by ( x+1)
Use the remainder theorem, which says the remainder upon dividing a polynomial [tex]p(x)[/tex] by [tex]x-c[/tex] is exactly [tex]p(c)[/tex]. In this case,
[tex]p(x)=2x^2+2x+1[/tex]
[tex]c=-1[/tex]
[tex]\implies p(c)=2(-1)^2+2(-1)+1=\boxed{1}[/tex]