[tex]2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\[/tex]
[tex]\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\[/tex]
[tex]x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\[/tex]
[tex]\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right][/tex]
(a) Round off 3.612 and 29.87 to 2 significant figures.
(b) Use your answers in part (a) to estimate the value of 3.612 ÷ 29.87.
also pls show how you found the answer
A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 19 feet more than the length of the shortest side. Find the dimensions if the perimeter is 167 feet.
PLS HELP URGENTT
Answer:
Please give Brainliest!
Step-by-step explanation:
The three sides are 36ft, 72ft, and 59 ft.
Someone please help me!!
Answer:
answer attached: x = 5√2
Step-by-step explanation:
Answer:
Step-by-step explanation:
All of the right triangles are similar. This means ...
long side / short side = x/2 = 25/x
Multiplying by 2x gives ...
x² = 25·2
x = (√25)(√2)
x = 5√2
_____
Additional comment
The "geometric mean" of 'a' and 'b' is √(ab). With this in mind, you can see that x is the geometric mean of the lengths 2 and 25. This is always true for this right-triangle geometry.
There are two other geometric mean relations in this geometry, having to do with the other possible ratios of sides. In effect, the length of a segment that touches the hypotenuse (longest side) of the triangle is the geometric mean of the two segments of the hypotenuse it touches.
Left side = √(2·27) = 3√6
Bottom side = √(25·27) = 15√3
Please I really need help (50 points)
Provide the missing statements and reasons for the following proof.
Answer:
PROOF FOR THE "PROVE" SECTION:
As linear pairs, angle 2 and 3 are supplementary to each other. Angle 1 is equal to angle 2, as they are both same-side interior angles. Therefore, angle 1 and angle 3 are also supplementary.
Filling in the missing blanks:
S1. Angle 1, Angle 2, Angle 3
S2. Angle 1 and Angle 2
R3. Congruent (___)
R5. supplementary angles
S7. Angle 1 = Angle 2, so Angle 1 can be substitued in for Angle 2 in any equation, and Angle 2 can be substitued for Angle 1 in any equation as well (they can replace each other, like x=y & y=x or a=b & b=a)
Hope this helped! Have a great day (pls mark brainliest)!!
WILL GIVE BRAINLIEST IF UR RIGHTTT!
Answer:
[tex]-\sqrt{5\\}[/tex]
Step-by-step explanation:
Which expression is equal to 6 x (3 + 8)?
OA (6 + 3) < (6 + 8)
OB. (6 x 3) + (6 x 8)
O C. (
63) (6 x 8)
)
D. (6 + 3) + (6 + 8)
+
[tex]6 \times (3 + 8) \\ = (6 \times 3) + (6 \times 8)[/tex]
Answer:
(6×3)+(6×8)
Hope you could get an idea from here.
Doubt clarification - use comment section.
Ok here’s another question
Answer:
20 necklaces
Step-by-step explanation:
If Elizebeth is starting off w/10 necklaces we can find on the graph that $10 buys an additional 10 necklaces. Now knowing that information we can add 10 necklaces to our original necklaces and get 20 necklaces. We can also find that our unit rate of change is 10 dollars : 10 necklaces or 1 dollar : 1 necklace. Knowing this can help us solve future problems like how many necklaces can Elizebeth get for x dollars.
help me pliz ill give u full stars i need help quick fast pliz
Answer:
[-5, 5]
Step-by-step explanation:
Help please!! Ill give 100 points!
Answer:
B)
Step-by-step explanation:
10/5 + 4(72 - 6)
10/5 + 288 - 24 Distribute the 4 to 72 and 6
2 + 288 - 24 Divide
2 + 264 Combine the like terms
262
If 35 liters of petrol cost $21.00, what is the price per liter?
Step-by-step explanation:
if 21 dollars = 35 liters
the ? dollars = 1 litre
it will be less so more which is the 35 divides
so we have
1/ 35 ×21
21/35
0.6
There are three times as many girls as boys in the school choir. If there are 24 girls how many singers are in the chior altogether
Answer: 8
Step-by-step explanation:
Answer:
chicken
Step-by-step explanation:
nugget
8. Phil received a commission of 5% on
the sale of a house. If the amount of
his commission was $4780, what was
the selling price of the house?
What’s the answer
Answer:
$95,600
Step-by-step explanation:
the question can be rephrased as '4780 is five percent of what number'?
we can use the ratio of 'is/over' = %/100 to solve
'is' = 4780
'of' = selling price of house ('p')
4780/p = 5/100
now cross-multiply:
5p = 478000
p = 95600
please help asap!!!!
Answer:
Question 2: 2/3
Question 1: 1/3
Question 3: 20
Step-by-step explanation:
Question 2: 8/4 = 2 & 12/4 = 3.
Question 1: 6/6 = 1 & 18/6 = 3.
Question 3: 10/10 = 1 & 20/10 = 2.
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK CORRECTLY
Answer:
See image
Step-by-step explanation:
Use Pythagorean Theorem
a^2 + b^2 = c^2
See image
50 POINTS MATH HELP ASAP
Answer: 90° + 41° =131° 180°-131° =149°
X=5.5-6
Step-by-step explanation:
Step-by-step explanation:
i think it is the answer ...
Graph y=2x+5 on the plane
Answer:
Incorrect
Step-by-step explanation:
for your slope go down two to the right one
Consider the equation 1/4y=1.5x. Solve the equation for y to find the constant of proportionality.The constant of proportionality for the equation is
Find the slope of the line that passes through 9,7 and 6,15
[tex]\huge \bf༆ Answer ༄[/tex]
Let's find the slope considering the points (9 , 7) and (6 , 15)
[tex] \sf \dfrac{y2 - y1}{x2 - x1} [/tex][tex] \sf \dfrac{15 - 7}{6 - 9} [/tex][tex] \sf \dfrac{8}{ - 3} [/tex][tex] - \dfrac{8}{3} [/tex]how to solve for x (proportions)
Answer:
16/3 or 5 1/3
Step-by-step explanation:
Cross Multiply
4×4
3×x
16=3x
Divide 3 from 16
x=16/3 or 5 1/3
will mark brainliest (2 possible answers pls) ( NO LINKS OR ANSWERS WITH NO EXPLANATION)
Answer:
P = 22.22
Step-by-step explanation:
f(x) = 3x + 4 + 2 g(x) = 4 Find (f + g)(x). A. (f +g)(x) = 3x +4 +6 B. (f +g)(x) = 3x + 10 c. (f +g)(x) = 3x + 6 + 4 O D. (f +g)(x) = 3x + 10
Answer:
(f+g) (x)= -5x-4= (-3x-2)
or, -5x + 3x= -4+2
or, -2x= -2
or,x= 2/2
:. x= 1
Step-by-step explanation:
Can someone help me with this? Its fairly easy but i genuinely dont remember
I need these answers for a worksheet I have and I would appreciate it if someone would help me out.
Question 1. You can combine like terms to ________ an expression.
Question 2. All ______ are like terms and can be combined.
Question 3. Terms with the same _____ are considered like terms.
Answer choices:
Constants
variables
simplify
Help bell math math math
Answer:
54
Step-by-step explanation:
C=πd
π=3
d=18
C=3×18
Therefore C=54
Answer:
c=54
Step-by-step explanation:
1.What is the domain of this graph?____
Answer:
x=2
Step-by-step explanation:
whats 8 to the power of 6 please
Answer:
262144
Step-by-step explanation:
Hope I was able to help you with your question , have a great day :)
Answer:
Step-by-step explanation:
I think 8 to the power of 6 Is 262144
need help asap :( i don’t understand it, it’s confusing lol
Answer:
At the end of the 4th round
x=4
Step-by-step explanation:
Put in a value for x for both equations
3(4) + 50 = 62
4(2)^4 = 64
62<64
So in round 4, Zavion will have more points
Answer as a each as an algebraic expression.
Answer:
is saying the half of q is 9 so you have to find out the value of q and when you find out the value for example x=18 the half of 18 is 9 I don't know if you undertand my explication
Step-by-step explanation:
18 the half of 18 is 9 because 9+9=18
2/3x + 5/6=3 1/3 I need it in as a mixed number in it's simplest form please
Answer:
3 3/4
Step-by-step explanation:
Hi Help me with question 6b) pls
Answer:
k = 9
Step-by-step explanation:
Consider the pattern on the right side , that is
[tex]T_{k}[/tex] = k(k + 2) + 1 = k² + 2k + 1
Equating
k² + 2k + 1 = 100 ( subtract 100 from both sides )
k² + 2k - 99 = 0 ← in standard form
(k + 11)(k - 9) = 0 ← in factored form
Equate each factor to zero and solve for k
k + 11 = 0 ⇒ k = - 11
k - 9 = 0 ⇒ k = 9
But k > 0 , then k = 9