cos²(x) = 3 sin²(x)
1 - sin²(x) = 3 sin²(x)
1 = 4 sin²(x)
1/4 = sin²(x)
± √(1/4) = sin(x)
± 1/2 = sin(x)
sin(x) = 1/2 or sin(x) = -1/2
[x = arcsin(1/2) + 2nπ or x = π - arcsin(1/2) + 2nπ]
… … … or [x = arcsin(-1/2) + 2nπ or x = π - arcsin(-1/2) + 2nπ]
(where n is any integer)
[x = π/6 + 2nπ or x = 5π/6 + 2nπ]
… … … or [x = -π/6 + 2nπ or x = 7π/6 + 2nπ]
Which pair of angles shares ray A and F as a common side?
The pair of angles that share a ray as a common side in the given diagram is: ∠FAB and ∠FAD.
What are Adjacent Angles?Adjacent angles are angles that lie adjacent or next to each other sharing a common vertex and have the same ray as a common side.
In the diagram attached below, ∠FAB and ∠FAD share a common vertex, A, and a ray FA as a common side.
Therefore, the pair of angles is: ∠FAB and ∠FAD.
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Solve |5x + 30| = 10x Identify the solution and an extraneous solution
Answer:
B
Step-by-step explanation:
the absolute value function always gives a positive result
However, the value inside can be positive or negative, that is
5x + 30 = 10x or - (5x + 30) = 10x
solving both
5x + 30 = 10x (subtract 5x from both sides )
30 = 5x ( divide both sides by 5 )
6 = x
or
- (5x + 30) = 10x
- 5x - 30 = 10x ( add 5x to both sides )
- 30 = 15x ( divide both sides by 15 )
- 2 = x
As a check
substitute these values into the equation and if both sides are equal then it is a solution.
x = 6
left side = | 5(6) + 30 | = | 30 + 30 | = | 60| = 60
right side = 10(6) = 60
Then x = 6 is a solution
x = - 2
left side = | 5(- 2) + 30 | = | - 10 + 30 | = | 20 | = 20
right side = 10(- 2) = - 20 ≠ 20
Thus x = - 2 is an extraneous solution
Sarah opened new savings account on Tuesday with a deposit of $70. She made a deposit of $30 on Friday and a withdrawal of $60 on Saturday. Which of the following expression represents her new account balance.
Answer:
x=70+30-60
Step-by-step explanation:
Word to my mother
find the volume of the pyramid. round to the nearest hundredth
Answer:
A. 17.35 mm³
Step-by-step explanation:
Volume of a Pyramid
[tex]V = \frac{1}{3}Bh[/tex]
V ... volume
B ... area of base
h ... height
The base of this pyramid is a square. Area of a square is side times side.
[tex]B = 3.5 \times 3.5[/tex]
Let's substitute in the formula.
[tex]V = \frac{1}{3}Bh\\\\V = \frac{1}{3}(3.5\times 3.5)(4.25)\\\\V = \frac{1}{3}(12.25)(4.25)\\\\V \approx 17.35417 \text{ mm}^3[/tex]
Now let's round to the nearest hundredth.
V = 17.35 mm³
For item numbers 7-11, tell what relationship exists between the measures of each pair of angles.
Answer:
7-B (congruent)
8-D (supplement)
9-B (congruent)
10-B (congruent)
11-D (supplement)
Step-by-step explanation:
7- 1 and 3 are congruent using the corresponding angles theorem
8- they are supplements using the same side interior angle theorem
9- they are congruent using alternate interior angle theorem
10- they are congruent using the alternate exterior angle theorem
11- they are supplements using the same side exterior angle theorem
ur wlcm :)
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help me pleaseeeeeeeee
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ 2^3~~ = ~~8\implies \log_2(8)~~ = ~~3[/tex]
order the decimal greatest to least 8.31,8.295, 8.06,8.3
Answer:
Least 8.06, 8.295, 8.3, 8.31 Greatest
I inserted a photo please answer ASAP I will mark brainliest PLEASEEEEE
Answer:
B, C, D
Step-by-step explanation:
Square roots are not in polynomials
A quadratic function has zeros at 1 and -8. Which of the following could be the function?
Answer:(x-1)(x+8)
Step-by-step explanation: You need to set it up as (x+y)(x+z) format. To get that you need to flip the zeroes making them the opposite. So the answer in this case would be (x-1)(x+8).
Is constructed by making arcs centered at a and b without changing the compass width. which equation is not necessarily true? a. pq = ab b. ap = pb c. aq = bq d. ar = rb
The equation that is not necessarily true is that PQ = AB.
How to illustrate the equation?The perpendicular bisector of any line segment can be drawn by opening the compass more than half, by putting the nib of the compass at one end of a line segment, and by marking an arc on both sides of the line segment from both the ends of the segment.
The following Property that the perpendicular bisector PQ follows when it bisects the line segment AB include:
AP=BPAQ=BQAR=BR∠ARP=∠BRP=∠ARQ=∠BRQ=90°Therefore, PQ is Perpendicular Bisector of Line Segment AB is not true.
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How many sides do 2 nonagons and 3 decagons have in all?
Answer:
48 sides
Step-by-step explanation:
A nonagon has 9 sides
A decagon has 10 sides
10 + 10 + 10 = 30
9+9 = 18
30 + 18 = 48
48 sides in total
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What are the coordinates of the point that is 2/5 of the way from a to b
Answer:
the cords for a should be (-3,0) and the cords for b should be (7,15) sorry if im incorrect
14.Evaluate the expression 4x2+3y for x = 5 and y =6.
answer?
Step-by-step explanation:
Given: x=5 and y=6
=>4x2+3y
=> 8+3(6)
=> 8+18
=> 26
Hope it helps
The value of this expression is 58
Algebraic expression is a mathematical sentence that involves all mathematical operations.
In an algebra - a real number is always accompanied by some letter, which can represent a variable or unknown.
— To solve this expression, just: change the letters for the numbers and multiply/add.
⚘ Resolution
[tex]\large \sf 4x2+3y[/tex]
[tex]\large \sf 4 \cdot 5 \cdot 2 +3 \cdot 6[/tex]
[tex]\large \sf 40 +18[/tex]
[tex]\red{\boxed{\boxed{\green{\large \sf \ 58 \ }}}}\\[/tex]
Therefore, the value of this expression will be 58
Based on the work done in checking his solution, does it appear that x = 9/2 is the
solution? Explain why or why not
be detailed, giving out brainliest to.
Answer:
Yes x = 9/2 is the correct solution.
Step-by-step explanation:
You have substituted x = 9/2 into both sides of the equation and they have both simplified to the same value.
Find the length of side x in simplest radical form with a rational denominator.
V10
X
60°
30°
Check the picture below.
Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5). Show all steps.
!BRAINLIEST AND 5 STARS TO BEST ANSWER AND FULL EXPLANATION ONLY!
Hello, detailed answer is given below.
If you have any question(s), then feel free to ask in comments!
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.
△XYZ ~ △X'Y'Z'
AngleXZY ≅ AngleY'Z'X'
YX ≅ Y'X'
XZ = 2X'Z'
mAngleYXZ = 2mAngleY'X'Z'
The options that are true of the triangles include:
∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'How to illustrate the triangle?It should be noted that triangle XYZ is reflected over a vertical line. Then, it's dilated by 1/2 to form XYZ.
This implies that the triangles are similar, the angles are congruent and the side length of XYZ is twice that of X'Z.
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Answer:
∆XYZ ~∆X'Y'Z'
AngleXZY ≅ AngleY'Z'X'
XZ = 2X'Z'
Step-by-step explanation:
took test
Is this an example of inductive reasoning, deductive reasoning, or neither?
At the grocery store Mia saw a sign indicating that 3 grapefruit cost $2.50, so Mia bought 3 grapefruit.
A. Inductive
B. Deductive
C. Neither
Since the specific conclusion is based on a general premise, this is a case of deductive reasoning.
What is deductive reasoning?The term deductive reasoning has to do with the process of arriving at a specific conclusion based on a more general premise.
In this case, the conclusion arrived at was based on the fact that Mia saw a general sign that read that 3 grapefruit cost $2.50. Hence, this is a case of deductive reasoning.
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Calculate.
a) 130% of 220
Guys, can you please correct my answer for Question #45 of The Quadratic Relations for me, please?
Answer:
[tex]y=3(x-7)^2[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
Parent function
[tex]y=x^2[/tex]
Translated 7 units to the right
Subtract 7 from the x-value:
[tex]f(x-7) \implies y=(x-7)^2[/tex]
Vertically stretched by a factor of 3
Multiply the whole function by 3:
[tex]3f(x) \implies y=3(x-7)^2[/tex]
Streched 7 units right means change in x
So new equation
y=(x-7)²Vertically streched by 3
y=3(x-7)²What should be added to both sides of this equation to solve for the variable?
P-33 = 17
Answer:
You add 33 on both sides to solve for the variable.
Step-by-step explanation:
If f(x) =
(3 + x)
(x-3)
what is f(a + 2)?
Answer:
(a^2)+4a-5
Step-by-step explanation:
(3+a+2)(a+2-3)
(a+5)(a-1)
use FOIL or box method
5a-5+(a^2)-a simplifyes to
(a^2)+4a-5
Find the product or type
"impossible".
[2 6 -7][5 -2 4]
The value of (26 - 7) and (5 - 24) when they're multiplied will be -399.
How to multiply the values?From the information given, we are told to multiply (26 - 7) and (5 - 24). This goes thus:
= (26 - 7) × (5 - 24)
= 21 × -19
= -399
In this case, value of (26 - 7) and (5 - 24) when they're multiplied will be -399.
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Which expression is equivalent to
(5x³)(4x) ³2
Answer:
640[tex]x^{6}[/tex]
Step-by-step explanation:
(5x³)(4x) ³2
(4x) ³ is the same as
4³ * x³ = 64x³
--
(5x³)(64x³)2
5*64*2 = 640
x³ * x³ = [tex]x^{6}[/tex]
640[tex]x^{6}[/tex]
can someone please help me with this
Answer:
[tex]d = \sqrt{109}[/tex]
Step-by-step explanation:
Use the distance formula.
[tex]\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Your points are (-4, 11) and (6, 8).
[tex]d = \sqrt{(-4 - 6)^2 + (11 - 8)^2}\\\\d = \sqrt{(-10)^2 + (3)^2}\\\\d = \sqrt{100 + 9}\\\\d = \sqrt{109}[/tex]
What is the volume, in cubic centimeters, of a cylinder with a height of 5 centimeters and a base radius of 10 centimeters, to the nearest tenths place?
Answer:
The volume of the cylinder is approximately 1570.8 cm³.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightGeometry
Volume Formula [Cylinder]:
[tex]\displaystyle V = \pi r^2 h[/tex]
Step-by-step explanation:
Step 1: Define
Identify given variables.
h = 5 cm
r = 10 cm
Step 2: Find Volume
[Volume Formula - Cylinder] Substitute in variables:∴ the volume of a cylinder whose height is 5 cm and radius is 10 cm is approximately 1570.8 cm³.
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Topic: Geometry
Of all of the medium mirrors that were shipped, how many of them were broken? 68 78 164 208
Show problem set up for full credit.
Answer:
If the arcs are the same
4x+25=5x
x=25
So, QPR is 4(25)+25
QPR is 125
Decide whether quadrilateral ABCD with vertices 4(3,1), B(-1,-1) C(1,3), and D(5,5) is a rectangle, rhombus,
square, or parallelogram.
Answer: rectangle
Step-by-step explanation:
From the options, it is implied that it is a parallelogram.
From inspection, we can tell that not all the sides are congruent, so it is not a rhombus or a square.
To determine if it is a rectangle, we can use the slope formula to see if there is a pair of perpendicular sides (if this is the case, then this will be a parallelogram with a right angle, making it a rectangle)
[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC} \text{ because} \left(m_\overline{AB} \right) \left(m_{\overline{BC} \right)=1[/tex]
So, the most specific classification is a rectangle.
what's the number before 277000
The number is 276999