Answer:
See below
Step-by-step explanation:
We want to prove that
[tex]\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}[/tex]
Taking the RHS, note
[tex]\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}[/tex]
Remember that
[tex]\sin^2(x) + \cos^2(x) =1 \implies 1- \cos^2(x) =\sin^2(x)[/tex]
Therefore,
[tex]\dfrac{1-\cos^2(x)}{\cos(x)} = \dfrac{\sin^2(x)}{\cos(x)} = \dfrac{\sin(x)\sin(x)}{\cos(x)}[/tex]
Once
[tex]\dfrac{\sin(x)}{\cos(x)} = \tan(x)[/tex]
Then,
[tex]\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)[/tex]
Hence, it is proved
The perimeter of a rectangle 6 5/7 ft and 2 5/6 ft
Find the value of the missing coefficient a in the equation y = a(x - 3)(x + 5) if the graph goes through the point (1, -6)
Plz help I will mark brainliest
Answer:
3
Step-by-step explanation:
you have to solve for x then you can find the coeeffiecnt
Parallelogram ABCD had coordinates A(0,7) and C(2, 1) Which statement will prove ABCD is a Rectangle?
The midpoint of AC is (1, 4).
The length of BD is √40.
The slope of BD is 1/3
The slope of AB is 1/3.
Answer:
Option (2)
Step-by-step explanation:
ABCD is a parallelogram having vertices A(0,7) and C(2, 1).
Therefore, length of diagonal AC = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(0-2)^2+(7-1)^2}[/tex]
= [tex]\sqrt{40}[/tex]
Since, diagonals of a rectangle measure the same and bisect each other,
Length of other diagonal BD will also measure [tex]\sqrt{40}[/tex].
Therefore, Option (2) will be the correct option.
Maria is shopping at the mall. She had $73 at the beginning of the day. She bought a shirt for $22 and then a pair of jeans. Now, Maria has $38 left. How much did Maria's jeans cost?
a 60
b 16
c 13
d 51
Answer:
option C = $13
Step-by-step explanation:
Amount she had in the beginning = $73
Cost of shirt = $22
Let the cost of jeans be = x
Balance in hand = $38
Amount in hand = 38 + 22 + x
73 = 60 + x
73 - 60 = x
13 = x
Therefore, cost of a pair of jeans = $13
Answer:
The answer is C
Step-by-step explanation:
WILL MARK BRAINIEST Evaluate the 6 trigonometric functions at
Step-by-step explanation:
the Adjacent = √15²-9²=√225-81=√144=12
sin 0 = 9/15 = 3/5
cos 0 = 12/15 = 4/5
tan 0 = 9/12 = ¾
sec 0 = 15/12 = 5/4
csc 0 = 15/9 = 5/3
cot 0 = 12/9 = 4/3
Triangle A B C is cut by line segment D E. Line segment D E goes from side A C to line A B. The length of A E is 12, the length of E B is 4, and the length of A D is 9. What is the length of Line segment D C? 2 units 3 units 6 units
Answer: The length of DC is 3 units
Step-by-step explanation:
The Basic proportionality theorem states that if a line is parallel to one side of a triangle and intersects the other two at different points, then the other two sides are divided in the same ratio.
The given image is attached below.
From the BPT theorem, we can say that:
[tex]\Rightarrow \frac{AE}{EB}=\frac{AD}{DC}[/tex]
We are given:
AE = 12 units
EB = 4 units
AD = 9 units
Putting values in above equation, we get:
[tex]\Rightarrow \frac{12}{4}=\frac{9}{DC}\\\\\Rightarrow DC=\frac{9\times 4}{12}\\\\\Rightarrow DC=3 units[/tex]
Hence, the length of DC is 3 units
Answer:
The answer is 3 units
Step-by-step explanation:
Mô hình quy hồi tuyến tính và ứng dụng
Answer:
where are you from Korea or not
Hope it helps you!
-miraculousfanx-
multiply (11x+y)² what is the answer?
Answer:
121x+y²
Your Welcome
BIFFY OUT!!!
2) find an equation of the line theough the given
points. Give the final answer in slope-intercept form.
(2,-2) (-1,4)
Answer:
y = -2x + 2
Step-by-step explanation:
Given the following data;
Points on the x-axis (x1, x2) = (2, -1)
Points on the y-axis (y1, y2) = (-2, 4)
To find the equation of line in slope intercept form;
First of all, we would determine the slope of the line.
Mathematically, slope is given by the formula;
[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]
[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
Substituting into the equation, we have;
[tex] Slope, m = \frac {4 - (-2)}{-1 -2} [/tex]
[tex] Slope, m = \frac {4 + 2}{-1 -2} [/tex]
[tex] Slope, m = \frac {6}{-3} [/tex]
Slope, m = -2
Next, we would use the following formula to find the equation of the line;
y - y1 = m(x - x1)
Substituting into the formula, we have;
y - (-2) = -2(x - 2)
y + 2 = -2x + 4
y = -2x + 4 - 2
y = -2x + 2 = mx + c
Three-fourths (one-fourth x + 8) minus (one-half x + 2) = StartFraction 3 Over 8 EndFraction (4 minus x) minus one-fourth?
Answer:
if I am understood your question correctly, X would be 84/29
Step-by-step explanation:
Helpppp please ASAP
Answer:
(13, -3).
Step-by-step explanation:
Expression representing transformation has been given as,
[tex]r_{y-z}oT_{4,-5}[/tex]
First apply the rule → [tex]T_{4,-5}[/tex]
Translation of the point by 4 units along the x-axis and 5 units downwards along the y-axis,
(x, y) → (x + 4, y - 5)
(-1, -8) → (-1 + 4, -8 - 5)
→ (3, -13)
Now apply the rule of reflection over the line y = -x to the image point (3, -13),
(x, y) → (-y, -x)
(3, -13) → (13, -3)
Therefore, answer will be (13, -3).
what number must you add to complete the square? x^2+24x=50
Answer:
144
Step-by-step explanation:
Divide the b term which is 24 by 2
Gives you 12, then square it.
that's 144
formula for completing squares is [tex](b/2)^{2}[/tex]
How do I compare this ratio ;
3:4 , 5:2 and 2:3
Answer:
(a) By converting to decimal:
2:3=23=0.6¯
4:5=45=0.8
As 0.6¯<0.8,2.:3<4:5.
(b) By converting to fractions:
Ratios can be compared by converting them to like fractions.
2:3=23=2(5)3(5)=1015
4:5=45=4(3)5(3)=1215
As 1015<1215,2:3<4:5.
How to solve and answer
Answer:
option A
Step-by-step explanation:
2x*(x + 3) = 6x + 4
2x *x + 2x*3 = 6x + 4 {Distributive property}
2x² + 6x = 6x + 4
Subtract 6x from both sides {Subtraction property of equality}
2x² = 4
Divide both sides by 2 {Division property of equality}
x² = 4/2
x² = 2
x = √4 {Square root property}
x = ± 2
HELPPPPPPPP PLS!!!!!!!
Answer:
(15x + 120) ft³
Or
15(x + 8) ft³
Step-by-step explanation:
The prism can be decomposed into a rectangular prism and a triangular prism
The volume of the prism = volume of the rectangular prism + volume of the triangular prism
✔️Volume of rectangular prism = L*W*H
L = 5 ft
W = 4 ft
H = 6 ft
Volume = 5*4*6 = 120 ft³
✔️Volume of triangular prism = ½*b*h*l
b = x ft
h = 6 ft
l = 5 ft
Volume = ½*x*6*5 = 15x ft³
✔️Volume of the prism = (15x + 120) ft³
what is the simplest interest rate if $126.77 in interest is earned on a deposit of $1434.85 in one year?
Answer:
9%
Step-by-step explanation:
Principal x interest rate=yearly interest
1434.85 x interest rate =126.77
interest rate = 126.77/1434.85
interest rate=.088 or 9%
The figure to the right shows two parallel lines intersected by a transversal.
Let x = 103°. Find the measure of each of the other seven angles.
Answer:
77°
Step-by-step explanation:
103° + ∠1° = 180°
Solve for the integer x in the following. 2^x = 16
Use the following figure to answer the questions
<5 and <7 are what angles
Answer:
<5 and <7 are corresponding angles.
Step-by-step explanation:
<5 and <7 are corresponding angles. They are on the same side of the transversal and on the same position on each of the parallel lines
Express in simplest radical form.
V9
Answer:
3
Step-by-step explanation:
[tex]\sqrt{9}=\sqrt{3*3} = 3[/tex]
Graph y < 1 – 3x
Need this really fast
Answer:
Step-by-step explanation:
Hope this helps
Put the following equation of a line into slope-intercept form, simplifying all fractions. 12x+9y=18
Answer:
y = -4/3x + 2
Step-by-step explanation:
Slope intercept form is y = mx + b.
Rearrange the equation into slope intercept form by isolating y:
12x + 9y = 18
9y = -12x + 18
Divide each side by 9:
y = -4/3x + 2
So, the equation is y = -4/3x + 2
I need to find the value of x?
Answer:
x=20
Step-by-step explanation:
120=6x
120/6=6x/6
20=x
Help plz ??
This is really urgent. If anyone knows the answer plz plz help me
Answer:
A
because range is all values of Y but in negative side it is infinity but in positive side range is 4
how do i find a perimeter of a traingle? give examples
Answer:
use this formula(a+b+c) a,b,c are the 3 sides of a triangle this will help you to find the perimeter of a triangle
Kathy stood on the middle rung of a ladder. She cimbed up 3 rungs, moved down 5 rungs, and then climbed up 9 rungs. Then she climbed up the remaining 2 rungs to the top of the ladder. How many rungs are there in the whole ladder?
Answer:
18 rungs
Step-by-step explanation:
Let x = number of rungs
x/2 = middle
Climbed 3
x/2 +3
Down 5
x/2 +3 -5
Climbed 9
x/2 +3 -5+9
Then climbed 2 more
x/2 +3 -5+9 +2
Now is at the top
x/2 +3 -5+9 +2 =x
Combine like terms
x/2 +9 = x
Subtract x/2 from each side
x/2+9-x/2 = x - x/2
9 = x/2
Multiply each side by 2
18 =x
Les municipalités de Sainte-Julie,
Saint-Bruno-de-Montarville, Saint-Basile-le-Grand
et Saint-Mathieu-de-Beloeil prévoient construire
une piste cyclable qui entourera le mont Saint-Bruno.
La piste cyclable est illustrée en rouge sur la carte
ci-contre. Les distances sont en kilomètres.
a) Pour construire la piste cyclable, une entreprise
demande 12 451,50$ par kilomètre.
Si les municipalités concernées ont prévu
un budget de 300 000 $ pour l'aménagement
de la piste, respecteront-elles le budget estimé ?
Answer:
CNC app BC we can we can MN we all at can we can we do all we can we go we go we cannot GL can see VM we BM
What is an equation of the line that passes through the points (-6, 3) and (-5,2)
Answer:
y=-x-3
Step-by-step explanation:
PLEASE HELP ASAP For each expression below, select the letter that corresponds to the equivalent expression from the given list.
(4x^3 – 4 + 7x) – (2x^3- 8)
is equivalent to expression___
(-3x^2 + x^4 + x) + (2x^4 - 7 + 4x) is equivalent to expression ____
(12 – 2x)(2x + 3) is equivalent to expression___
The blanks are for the letters in the picture
BAnswer:
B-D-A
Step-by-step explanation:
-
A certain game consist of rolling a single fair die and based off as a following numbers listed in the picture
Given:
A fair die is rolled.
It pays off $10 for 6, $7 for a 5, $4 for a 4 and no payoff otherwise.
To find:
The expected winning for this game.
Solution:
If a die is rolled then the possible outcomes are 1, 2, 3, 4, 5, 6.
The probability of getting a 6 is:
[tex]P(6)=\dfrac{1}{6}[/tex]
The probability of getting a 5 is:
[tex]P(5)=\dfrac{1}{6}[/tex]
The probability of getting a 4 is:
[tex]P(4)=\dfrac{1}{6}[/tex]
The probability of getting other numbers (1,2,3) is:
[tex]P(\text{Otherwise})=\dfrac{3}{6}[/tex]
[tex]P(\text{Otherwise})=\dfrac{1}{2}[/tex]
We need to find the sum of product of payoff and their corresponding probabilities to find the expected winning for this game.
[tex]E(x)=10\times P(6)+7\times P(5)+4\times P(4)+0\times P(\text{Otherwise})[/tex]
[tex]E(x)=10\times \dfrac{1}{6}+7\times \dfrac{1}{6}+4\times \dfrac{1}{6}+0\times \dfrac{1}{2}[/tex]
[tex]E(x)=\dfrac{10}{6}+\dfrac{7}{6}+\dfrac{4}{6}+0[/tex]
[tex]E(x)=\dfrac{10+7+4}{6}[/tex]
[tex]E(x)=\dfrac{21}{6}[/tex]
[tex]E(x)=3.5[/tex]
Therefore, the expected winnings for this game are $3.50.