Answer:
135 and 315degrees
Step-by-step explanation:
Given the expression
4tan²θ+tanθ=−4tanθ−1
Equate to zero
4tan²θ+tanθ+4tanθ+1 = 0
4tan²θ+5tanθ+1 = 0
Let x = tanθ
4x²+5x+1 = 0
Factorize;
4x²+4x+x+1 = 0
4x(x+1)+1(x+1) = 0
4x+1 = 0 and x+1 = 0
4x = -1 and x = -1
x = -1/4 and -1
Since x = tanθ
-1 =tanθ
θ = arctan(-1)
θ = -45degrees
Since tan is negative in the 2nd and fourth quadrant;
In the second quadrant
θ = 180 - 45 = 135degrees
In the fourth quadrant;
θ = 360 - 45 = 315degrees
Hence the required angles are 135 and 315degrees
Find the value of x. Give a reason to justify your solution.
Answer:
x =52
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles. (Exterior Angle Property)
x+72 = 90+34
x+72 = 124
x+72-72 = 124 - 72
x =52
Can someone help me?It's urgent and thank you!
Answer:
575.71
Step-by-step explanation:
Year 1: 960 x .88 (100%-12%)=844.80
Year 2: 844.80 x .88 =743.424
Year 3: 743.424x.88=654.21
Year 4: 654.21 x .88=575.71
There were 60 7th grade students last year in CHAMPS. This year, there are 48 7th grade students. What is the percent decrease from last year to this year?
20%
Hope this helps! :)
______________
Quadrilateral MNOP is similar to quadrilateral SRUT.
Which proportion can be used to find the value of x?
Answer:
8/12 = x/14
Not sure if this is a proportion but this is how I would solve it.
2- La longueur d'un rectangle mesure 2 cm de plus que le triple de sa largeur. Si le périmètre de ce rectangle est supérieur à 12 cm, mais d'au maximum 48 cm, dans quel intervalle se situe la largeur de ce rectangle?
Answer:
5 < L < 18,5
5 < L < 18,52 < W < 5,5
Step-by-step explanation:
longeur = length = L
largeur = width = W
L = 3W +2
12 < 2L+2W < 48
———————————————
12 < 2*(3W+2)+2W < 48
12 < 6W+4 +2W < 48
12 < 8W+4 < 48
8 < 8W < 44
2 < W < 5,5
———————————————
12 < 2L+2W < 48
L = 3W +2
L - 2 = 3W
L/3 -2/3 = W
12 < 2L +2*(L/3 -2/3) < 48
12 < 2L + ⅔L -4/3 < 48
12 < 2⅔L -4/3 < 48
13⅓ < 2⅔L < 49⅓
5 < L < 18,5
hope it helps.
brainly exists in French too. brainly.fr or switch country in app
If p q is true and q is true, then p is ___ true. Answer choices are always, never, sometimes
Answer:
sometimes
Step-by-step explanation:
por favor, me urge hacerla
Answer: do you have this in english so that I can help
Step-by-step explanation:
Bob works as a carpenter and needs to buy some tools for
work. A framing hammer costs $22. A 4-foot level costs
$18. A carpenter's square costs $7. What are Bob's total
expenses for these tools?
Really stuck, please help
Answer:
Step-by-step explanation:
what do you know about the angles of a triangle? They make 180° right?
since you know that, now you can find angle Y , by using the triangle on the left, and you can find X by using the triangle on the right, then, when you know X & Y , use both of those to find Z :) got it?
Answer:
we know that a triangle's angles MUST add up to 180 degrees.
We can look at the triangle with the angles of 55, 80, and y. As the angles must add to 180, 55+80+y must be 180. Therefore, we find that y is equal to 45.
We can look at the triangle with the angles of 100, 60, and x. As the angles must add to 180, 100+60+x must be 180. Therefore, we find that x is equal to 20.
We then look at the triangle formed from x, y, and z. As the angles must add to 180, x+y+z must be 180. x is 20, y is 45, so 20+45+z = 180. Thus, z is 115.
So:
y = 45
x = 20
z = 115.
A parabola is defined by the equation x2 = 3/4 y. In which direction will the parabola open?
URGENT: Graph y = cosx for -3\pi/2 <= x <= -pi/2
What is the largest value in the range?
A. -1
B. 0
C. 1/2
D. 1
Find the distance from point P to RQ
Answer:
option A : about 2.8 units
Step-by-step explanation:
To find the distance from P to RQ , Find the distance from ( 1 , 1) to (3 , 3).
[tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]= \sqrt{(3-1)^2 + (3-1)^2}\\\\= \sqrt{2^2 + 2^2 }\\\\= \sqrt{4 + 4 }\\\\= \sqrt{8}\\\\=2\sqrt{2}[/tex]
= 2.83 units
Answer:
A
Step-by-step explanation:
Remark
The distance you want is the point P to the (3,3). Then two lines meet as these two do, the shortest distance is the right angle distance. And that is how distance is defined.
Formula
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Givens
x2 = 1
x1 = 3
y2 = 1
y1 = 3
Solution
d = sqrt( (1 - 3)^2 + (1 - 3)^2 )
d = sqrt( (-2)^2 + (-2)^2 )
d = sqrt ( 4 + 4)
d = sqrt(8)
d = 2√2
d = 2.8
The length of the triangle for the pool table is the twice the sum of 5 and a number. If the rack is equilateral, what is the perimeter, in inches, of the triangle?
Answer:
30 + 6x inches
Step-by-step explanation:
Let the required number be x
If the length of the triangle for the pool table is twice the sum of 5 and a number
L = 2(5+x)
L = 10+2x
Since the triangle is quadrilateral, this means that all sides are equal
Perimeter = 3L
Perimeter = 3(10+2x)
Perimeter = 30+6x
Hence the perimeter, in inches, of the triangle is 30 + 6x inches
Find the sale price of an $18 item after a 50% discount.
Rewrite 50% as a decimal : 0.50
Multiply the price by 0.50:
18 x 0.50 = 9
The sale price is $9
Answer:
$9
Step-by-step explanation:
price of an item=$18
discount=50%
sale price =? (be x)
sale price= original price -discount% of original price
x=$18 -50/100 * $18
x=$1800-$900/100
=$900/100
=$9
therefore sale price of an item is $9.
Simplify the expression. (–8.6)0
1
–1
–8.6
0
Answer:
(-8.6)0
= 0
explanation:
What is the solution to the system of equations ?
Y=2/3 x + 3
X= - 2
Answer:
x = -2, y = 5/3
Step-by-step explanation:
we have the value of x already (-2).
x=-2
Plug it into the first equation y = 2/3x+3
y = 2/3(-2)+3
y = -4/3+3
y = -4/3+9/3
y = 5/3
x = -2, y = 5/3
The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario. Which graph represents this wage increase for x < 12?
The solution is Option C.
The graph which represents the inequality equation is
f ( x ) = { 0.50 , if x < 3
1 , if 3 ≤ x < 6
1.50 , if 6 ≤ x < 9
2.00 , if 9 ≤ x < 12 }
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number of years be = x
Let the increment in wages be = y
Now , the equation will be
For the employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour
So , the inequality equation is x < 3 , f ( x ) = 0.50
Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00
So , the inequality equation is 3 ≤ x < 6 , f ( x ) = 1
Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour
So , the inequality equation is 6 ≤ x < 9 , f ( x ) = 1.50
Employees of at least nine years, but less than twelve years receive an increase of $2.00
So , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2
Therefore , the graph which represents the solution is Option C.
Hence , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2
To learn more about inequality equations click :
https://brainly.com/question/11897796
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A rectangular park is 260 m by 480 m. Danny usually trains by running 5 circuits around the edge of
the park. After heavy rain, two adjacent sides are too muddy to run along, so he runs a triangular path
along the other two sides and the diagonal. Danny does 5 circuits of this path for training. Show that
Danny runs about 970 metres less than his usual training session
Answer:
971 m to nearest metre
Step-by-step explanation:
training distance = 5*2*(260 + 480) m
Diagonal distance = √(2602 + 4802) m
Heavy rain training distance = 5*(260 + 480 + √(2602 + 4802)) m
Difference between these:
5 × 2 × ( 260 + 480 ) - 5 ×( 260 + 480 + √ 260 ^ 2 + 480 ^ 2 )
= 970 . 5311872087638744
difference = 971 m to nearest metre
Hope this answer helps you :)
Have a great day
Mark brainliest
A system of equations consisting of a circle and a line is graphed. Which statements about the number of possible solutions are correct? Check all that apply.
A circle and a line always intersect, so the system can have an infinite number of solutions.
A circle and a line can intersect at one point, so the system can have one solution.
A circle and a line can intersect at three points, so the system can have three solutions.
A circle and a line can intersect twice, so the system can have two solutions.
A circle and a line do not have to intersect, so the system can have no solution.
Answer:
the solution is where the two objects intersect ...
1) A line can completely miss the circle (no solutions is possible)
2) a line can "kiss" the circle at one point (one solution)
3) note that a line can not "bend"... it can touch one side of the circle pass
through the center and touch the circle in a second spot (going out) .. two solutions...
those are the three possibility that are in the question that was posted...
three check comments are true
Step-by-step explanation:
x/6 + 12 = 6
Please help me
Answer:
[tex]x=-36[/tex]
Step-by-step explanation:
[tex]\frac{x}{6} +12=6[/tex]
[tex]\frac{-36}{6} +12=6[/tex]
[tex]-6+12=6[/tex]
Hence, x = -36
Answer:
X = -36
Step-by-step explanation:
x/6 + 12 = 6
-12 = -12
x/6 = -6
(6) = (6)
x = -36
74 + -28 =[find the difference and put the sign of big number]
Answer:
It should be 74+(-28) as 2 signs can bit be put together.
74+(-28)
=74-28 (sign only changes when there is (minus) before it
=48
We are not putting a minius (-) as 74 is digger that 28 and it has plus (+) before it.
I HOPE IT HELPS
HAVE A GREAT DAY
[tex]#Liliflim✌[/tex]
Pythagoras
1.if the radius of the smaller circle is 3, find it’s area
2. Find the area of the yellow ring
3. Find the area of the white ring
Answer:
1. [tex]Area = 28.26[/tex]
2 and 3: See explanation
Step-by-step explanation:
Solving (1)
[tex]r = 3[/tex] --- radius
The area is:
[tex]Area = \pi r^2[/tex]
[tex]Area = 3.14* 3^2[/tex]
[tex]Area = 28.26[/tex]
There are no enough information to solve (2) and (3) as the radius and/or diameter are not provided.
However, the following formula will be used to calculate the required areas.
[tex]Area = \pi r^2[/tex] --- same process as (1)
write 36m÷9m in standard form
The expression (36m ÷ 9m) is equivalent to 4.
What is division in mathematics? What is a mathematical function, equation and expression?division : Division is the process of splitting a number or an amount into equal parts.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the following division as follows -
(36m ÷ 9m)
We have the following expression -
36m ÷ 9m
So, we can write -
(36m/9m)
36/9
4
Therefore, the expression (36m ÷ 9m) is equivalent to 4.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
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I need to show my work but I don’t know how to do these can someone help me??
Which equation represents a line that passes through (2, -1/2) and has a slope of
3?
Answer:
it should be d or c
Step-by-step explanation:
The volume of a cuboid, whose length and height are equal is 108 m3. If the breadth is 12 m, find the cuboid's length and surface area.
Answer:
Surface area = 162 m^2
Step-by-step explanation:
Below is the given values:
Length of cuboid = Height of cuboid
The volume of the cuboid = 108 m^3
The breadth of the cuboid = 12 m
Now use the volume formula:
Volume = area of one surface × height
Volume = (L x B) * H
(L x 12) * H = 108 (L = H)
L x 12 x L = 108
L^2 = 108/12
L = 3 m
Thus length and height is = 3m
Surface area = 2 (L x B + b x h + L x h)
Surface area = 2 (3 x 12 + 12 x 3 + 3x 3)
Surface area = 162 m^2
Solve this plz for god sake
Answer:
AB = 8.66 m
Step-by-step explanation:
Here, we want to get the length AB
What we have is a right triangle
so to get the length AB, we are going to use the appropriate trigonometric ratio
From the question, AB faces the given angle and that makes it the opposite
AC faces the right angle and that makes it the hypotenuse
The relationship between the hypotenuse and the opposite can be defined by the sine
the sine of an angle is the ratio of the length of the opposite to the hypotenuse
so, we have it that;
sine 60 = AB/10
AB = 10 * sine 60
AB = 8.66 m
What solid 3D object is produced by rotating the triangle about line m? ANSWER ASAP. TROLL AND LINK ANSWERS REPORTED. WILL AWARD BRAINLIEST.
Answer:
A cone with diameter 6 units
Step-by-step explanation:
Rotating the triangle about line m will give us a cone with radius 3
If the radius is 3, the diameter is 2*r = 2*3 = 6
Answer:
Step-by-step explanation:
a cone with a radius of 5
maths pi question. SEE ATTACHMENT
Answer:
r = 6cm
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
36 pi = pi r^2
Divide each side by pi
36 pi/pi = pi r^2/ pi
36 = r^2
Take the square root of each side
sqrt(36) = sqrt(r^2)
6 =r
The radius is 6 cm
r = 6cm
Answer:
radius, r = 6cm
Step-by-step explanation:
[tex]Area = 36 \pi \\\\\pi r^2 = 36 \pi\\r^2 = 36\\r = \sqrt{36} = 6 \ cm[/tex]
Match them BRAINLIEST IF CORRECT
Answer:
1/2 for the red card
1/52 for queen of hearts
1/4 for clubs
3/13
Step-by-step explanation:
the red card is 1/2 because the only other color is black
there is only one queen of hearts
it is one of four possible symbols
because that is the only one left
