Answers
Answer:
[tex]4\sqrt{3}[/tex]
Step-by-step explanation:
Since <PDA is right, the vertical angle, <BDC is right as well. Using sum of angles in a triangle, the angles in triangle BDC sum to 180, and for solving for <DCB, you get 30 degrees.
The line connecting the intersection of the tangents to the radius bisects the angle formed by the tangents; therefore, m<PCA is also 30 degrees.
A radius drawn to the point of tangency is perpendicular to the tangent, so <PAC is a right triangle. We can use sum of angles in a triangle for triangle PAC. Since <PCA is 30 and <PAC is right, <DPA is 60 degrees.
Now, we can look at triangle DPA, using sum of angles in a triangle, we can conclude triangle DPA is a 30-60-90 special right triangle. The leg opposite the 60 degree angle is √3 times the leg opposite the thirty degree angle. Since <DPA is 60 degrees and <PAD is 30:
[tex]DP\sqrt{3} = 6\\DP = \frac{6}{\sqrt{3} } \\DP = \frac{6}{\sqrt{3} } \times \frac{\sqrt{3} }{\sqrt{3} } \\DP = \frac{6\sqrt{3} }{3} \\DP = 2\sqrt{3}[/tex]
Also, in a 30-60-90, the hypotenuse is twice the leg opposite the 30 degree angle, so x is 2 * 2√3. or [tex]4\sqrt{3}[/tex].
Related Questions
Which is the graph of f(x)?
Answers
Answer: [tex]fx[/tex]
The slope is 0, and
the y-intercept is (0, 0)
[tex]\left[\begin{array}{ccc}x&y\\0&0\\1&0\end{array}\right][/tex]
In order to find the graph of "f(x)", we need to graph the line using the slope and y-intercept, or two points.
Solving System of Equations Using Subtraction.
X + 4y = 11
X - 6y = 11
Answers
Answer:
x=11
y=0
Step-by-step explanation:
Don't know if this is what you're looking for but this is correct if you plug it in.
X + 4y = 11 Get x by itself. x=-4y+11 and plug it into the bottom.
X - 6y = 11
simplify -4y+11-6y=11
11-10y=11
-10y=0
y=0 plug it into the original and you will get
x=11
x=11
this is due today. help please
Answers
In the triangle represented in the diagram, The value of X is: 23°
Meaning of a TriangleA triangle can be defined as a plain shape that has three sides, three edges and three angles.
A triangle is majorly defined as a shape that possesses three angles and their interior angles sum up to 180°
In conclusion, in the triangle represented in the diagram, The value of X is: 23°
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Considering the sum of the internal angles of a triangle, it is value that the value of x is of x = 23º.
What is the sum of the internal angles of a triangle?A triangle has three angles, and their sum is of 180º.
In this problem, the angles are:
x, 67º, 90º.
Hence:
x + 67º+ 90º = 180º.
x = 23º.
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Which expression is equivalent to
4^sqrt 6 / 3^sqrt2
Answers
Answer: Choice C
[tex]\frac{\sqrt[12]{55,296}}{2}[/tex]
==========================================================
Explanation:
Recall the process to rationalize the denominator is to multiply top and bottom by the denominator expression. This only works if we have a square root in the denominator.
For cube roots, we'll need to multiply two copies of the denominator to top and bottom. This will get us three copies of [tex]\sqrt[3]{2}[/tex] so that the cube root goes away.
Check out the steps below to see what I mean:
[tex]\frac{\sqrt[4]{6}}{\sqrt[3]{2}}\\\\\\\frac{\sqrt[4]{6}\sqrt[3]{2}\sqrt[3]{2}}{\sqrt[3]{2}\sqrt[3]{2}\sqrt[3]{2}}\\\\\\\frac{6^{1/4}*2^{1/3}*2^{1/3}}{\left(\sqrt[3]{2}\right)^3}\\\\\\\frac{6^{3/12}*2^{4/12}*2^{4/12}}{2}\\\\\\\frac{\left(6^3*2^4*2^4\right)^{1/12}}{2}\\\\\\\frac{\left(55,296\right)^{1/12}}{2}\\\\\\\frac{\sqrt[12]{55,296}}{2}\\\\\\[/tex]
In short,
[tex]\frac{\sqrt[4]{6}}{\sqrt[3]{2}}=\frac{\sqrt[12]{55,296}}{2}[/tex]
We have the 12th root of 55,296 all over top the integer 2. The "2" is not part of the 12th root. This shows why choice C is the final answer.
Answer:
C
Step-by-step explanation:
I need help please help me and thank you :))
Answers
Answer:
see explanation
Step-by-step explanation:
∠ CZD = 90° , then
∠ CZF = 90° - ∠ FZD = 90° - 40° = 50°
∠ FZD and ∠ AZG are vertically opposite angles and are congruent , so
∠ AZG = 40°
∠ CZF and ∠ GZE are vertically opposite angles and are congruent , so
∠ GZE = 50°
E
∠ AZB + ∠ BZC = 90° , that is
3x - 2 + 32 = 90
3x + 30 = 90 ( subtract 30 from both sides )
3x = 60 ( divide both sides by 3 )
x = 20
The measure of angle is 0 is 7pi/4. The measure of its reference angle is ___ °, and tan 0 is ____
Answers
Answer: pi/4 and -1
Step-by-step explanation:
Use the given information to determine which of the following relationships
can be proved and why.
ZL= 20
ZME P
M
Answers
Answer:
C. ∆LMN ~ ∆OPQ, because of AA
Step-by-step explanation:
All of the triangle congruence postulates require at least one pair of corresponding sides be congruent (in addition to other requirements). Triangle similarity can be proved if there are two pairs of congruent corresponding angles.
__
congruenceNo sides are given as congruent, so no congruences can be proved.
similarityTwo pairs of corresponding angles are said to be congruent, so we can say ...
∆LMN ~ ∆OPQ, because of AA
1. Which shows the factoring pattern for the sum of cubes?
1. (a+b)(a2–ab+b2)
2. (a+b)(a2–ab–b2)
3. (a–b)(a2–ab+b2)
4. (a+b)(a+b)(a+b)
2. Select all the solutions of x3+2x2−9x=18.
1. x=2
2. x=−3
3. x=3
4. x=−2
3. If x=−1 is a root of the polynomial 0=x3+2x2−5x−6, what are the other roots?
1. x=3, x=−2
2. x=−3, x=2
3. x=−1, x=−3, x=2
4. x=0, x=−3, x=2
4. Subtract: (x2–1)–(x3–2x+1)
1. –x^3 – x^2 + 2x
2. –x^3 – x^2 + 2x + 2
3. –x^3 + x^2 + 2x – 2
4. –x^3 + x^2 – 2x – 2
5. What is the largest multiplicity in the factored polynomial y=(x2−1)(x+2)(x+4)?
1. 4
2. 1
3. 0
2. 0
Answers
The solution to the questions are:
The expression that represents the factoring pattern is (a + b)(a² - ab + b²)The solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2The other roots are x = -3 and x = 2The result of subtracting the expressions is - x³ + x² + 2x - 2The largest multiplicity is 1Factoring pattern for the sum of cubesAs a general rule, the sum of cubes x³ and y³ is:
x³ + y³= (x+y)(x² - xy + y²)
Replace x with a and y with b
a³ + b³= (a + b)(a² - ab + b²)
Hence, the expression that represents the factoring pattern is (a + b)(a² - ab + b²)
The solutions of the polynomialThe equation is given as:
x³ + 2x² - 9x = 18
Subtract 18 from both sides
x³ + 2x² - 9x - 18 = 0
Factorize the expression
x²(x + 2) - 9(x + 2) = 0
Factor out x + 2
(x²- 9)(x + 2) = 0
Express x²- 9 as a difference of two squares
(x + 3)(x - 3)(x + 2) = 0
Split
(x + 3) = 0 or (x - 3) = 0 or (x + 2) = 0
Remove brackets
x + 3 = 0 or x - 3 = 0 or x + 2 = 0
Solve for x
x = -3, x = 3 and x = -2
Hence, the solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2
The other roots of the polynomialThe polynomial equation is given as:
0 = x³ + 2x² - 5x - 6
Rewrite as:
x³ + 2x² - 5x - 6 = 0
Factorize the expression on the left-hand side
(x + 3)(x + 1)(x - 2) = 0
Split
x + 3 = 0 or x + 1 = 0 or x - 2 = 0
Solve for x
x = -3 or x = -1 or x = 2
Hence, the other roots are x = -3 and x = 2
Subtract the expressionsThe expression is given as:
(x² - 1) - (x³ - 2x + 1)
Expand
x² - 1 - x³ + 2x - 1
Collect like terms
- x³ + x² + 2x - 1 - 1
Evaluate the like terms
- x³ + x² + 2x - 2
Hence, the result of subtracting the expressions is - x³ + x² + 2x - 2
The largest multiplicity of the polynomialThe polynomial is given as:
y = (x² - 1)(x + 2)(x + 4)
Express x² - 1 as a difference of two squares
y = (x - 1)(x + 1)(x + 2)(x + 4)
The power of each factor in the above expression is 1.
This means that the largest multiplicity is 1
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Solve for X
1.1x + 1.4x = 350
Answers
Answer:
X= 140
Step-by-step explanation:
I hope this helps. =D
Answer:
x=140
Step-by-step explanation:
1.1x+1.4x=350 1. combine like terms which 1.1x+1.4x
2.5x=350 2. /2.5 on both sides
x=140
50 POINTS HELP ME PLEASE ITS GEOMETRY
Answers
Answer:
x is the midpoint of a segment in the diahram
Answer:
x is mid point
Step-by-step explanation:
I hope it's helpful for
period of f(x)=cos(x)+2
Answers
Answer:
The period is 2π
Explanation:
The period is 2 times pi because 2 is the standalone-term multiplied by pi to get the period.
Andrei wants to fill a glass tank with spherical marbles and then fill the remaining space with water.
The variable "w" models the amount of water (in liters) Andrei uses if he uses n marbles.
w = 32 - 0.05n
What is the volume of each marble?
Answers
The volume of each marble is 0.05 liter
How to determine the volume?The volume function is given as:
w = 32 - 0.05n
The variable n represents the number of marbles.
This means that 0.05n represents the volume of n marbles and 32 represents the total volume of the glass tank
To get the volume of each marble, we divide 0.05n by n
i.e.
Volume = 0.05n/n = 0.05
Hence, the volume of each marble is 0.05 liter
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Please don’t lie to me and tell the right answer and if you do get it correct I will give you a shout out thanks
Answers
Answer:
Part A = 7
Part B = 1
I hope this is right, sorry if it isn't
Answer:
See below
Step-by-step explanation:
5 cups cheese / ( 2/3 cup cheese/plate ) =
5 * 3/2 = 15/2 = 7 1/2 or 7 full plates
2/3 cup cheese / plate * 9 plates =
2/3 * 9 = 6 cups cheese total
she has 5 cups to start.....she will need 1 cup more
Somebody please answer quick, will mark whoever is first Brainliest. Select the correct answer from the drop-down menu
The graphed linear equation is
A. 3x - 2y = -12
B. 2x - 3y = -12
C. 3x + 2y = 12
D. 3x + 3y = -12
Answers
Answer:
C. 3x + 2y = 12
explanation:
answer asap!!! please
Answers
Answer:
D.
Step-by-step explanation:
You can see it in the graphs after you plot it.
Allison earned a score of 95% on a test where the mean was only an 82%. How far above average was her score?
Answers
Answer:
The correct answer is 13%.
Step-by-step explanation:
We can easily put in the equation:
95 - 82 = 13
Hope this helps:) Goodluck!
which of the following is located over the center of the base of a regular pyramid
A vertex
B slant height
C face
D edge
Answers
Vertex is located over the center of the base of a regular pyramid.
What is Vertex Angle?
Vertex angle is defined as the angle formed by two lines or rays that intersect at a point. These two rays make the sides of the angle.
Here, Vertex is the point which is located over the center of the base of a regular pyramid.
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please simplify and keep the answer with exponents.
(6^7 * 6^12)/ 6^8
Answers
Answer:
6¹¹
Step-by-step explanation:
Simplifying the numerator :
When two terms with the same base are multiplied, the powers are added6⁷ x 6¹²6¹⁹Solving the expression :
When two terms with the same base are divided, the powers are subtracted6¹⁹ / 6⁸6¹¹Hey can someone help me I dont really undertstand this, (thank you ^^)
Answers
Answer:
exact area = 81π in.²
approximate area = 254.34 in.²
Step-by-step explanation:
Exact:
area = πr²
r = radius = diameter/2 = 18 in./2 = 9 in.
area = πr²
area = π × (9 in.)²
area = 81π in.²
exact area = 81π in.²
Approximate:
π = 3.14 (approximately)
area = πr²
area = 81π in²
area = 81 × 3.14 in.²
approximate area = 254.34 in.²
High school geometry. help is needed, please and thank you.
Answers
Ariana has 4 posters she wants to hang on the wall how many different ways can the posters be arranged
Answers
Answer:
4 different ways
Step-by-step explanation:
there are four different ways she can post it because there are four posters she want to hang on the wall.
What is the length of st given s (-3, 4) and t (1, 0)
Answers
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[1 - (-3)]^2 + [0 - 4]^2}\implies d=\sqrt{(1+3)^2 +(-4)^2} \\\\\\ d=\sqrt{32}\implies d\approx 5.66[/tex]
A new amusement park presold discounted tickets for the opening day as well as upon arrival at the park. the opening day ticket sales for the park, including presales, is represented by this function, where is the number of tickets sold h hours after opening at 7:00 a.m. what is the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m.? a. tickets per hour b. tickets per hour c. tickets per hour d. tickets per hour
Answers
The approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour
How to determine the rate of change?The missing part of the question is represented by the following function:
[tex]T(h) = \frac{386 + 110h}{h}[/tex]
10:00 a.m is 3 hours after 7:00 am and 1:00 p.m is 6 hours after 7:00 am.
This means that:
h = 3 at 10:00 am
h = 6 at 1:00 pm
Next, we calculate T(3) and T(6)
[tex]T(3) = \frac{386 + 110*3}{3} =238.7[/tex]
[tex]T(6) = \frac{386 + 110*6}{6} =174.3[/tex]
The average rate of change is then calculated as:
[tex]T'(h) = \frac{T(3) - T(6)}{3 - 6}[/tex]
This gives
[tex]T'(h) = \frac{238.7 - 174.3}{-3}\\[/tex]
Evaluate
T'(h) = -21
This means that the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour
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Erica buys a package of note cards costing $1.44. She gives the cashier
$5.00. The cashier gives her her change using the least number of coins and
bills possible. How many of each coin or bill does she receive?
Answers
Answer:
See below.... several options
Step-by-step explanation:
Change is $3.56
3 dollar bills one 50 c piece one nickel one penny
(though 50 cent pieces are uncommon.....this may be 2 quarters)
[For a while , there was $ 2 bills
so it could be one 1 dollar bill and one $ 2 bill instead of three dollar bills]
_____ teaspoon is equivalent to 5 ml.
Answers
Answer:
1.01 teaspoons is equal to 5 ml
Step-by-step explanation:
it goes up by ( 0.202884 )
1 ml 0.202884 tsp
2 ml 0.405768 tsp
3 ml 0.608653 tsp
4 ml 0.811537 tsp
5 ml 1.0144 tsp
6 ml 1.2173 tsp
7 ml 1.4202 tsp
Hope This Helped
Please help! This is a problem that is relatively easy but I still need help!
Answers
Answer:
Hi,
Step-by-step explanation:
The triangles CBA and DEA are equals ( 3 sides 2 to 2 equals), angles CAB and DAE are also equals:
6t-12=18-4t
10t=30
t=3(°)
angle CAB=6t-12=6*3-12=6(°)=angle(DAE)
angle BCA=(180-6)/2=87(°)=angle CBA=angle (ADE)=angle(DEA)
The graph shows a proportional relationship between the number of plants and the number of flowers on the plants. What is the constant of proportionality in terms of flowers per plant?
Answers
The constant of proportionality in terms of the number of flowers per plant is 5.
What is the proportional relationship?If two quantities varies directly to each other i.e if y varies proportional to x then
y =kx .....[1] where, k is the constant of proportionality.
Suppose, y represents the number of roses and x represents the number of plants.
Given is the graph shows a proportional relationship between the number of plants and the number of flowers on the plants. The graph attached below has the coordinates points,
(0, 0)
(1, 5)
(2, 10)
(3, 15)
(4, 20)
Substitute any coordinate points like (3, 15) in above equation to find k.
15 =k x 3
k = 5
Therefore, the constant of proportionality in terms of the number of flowers per plant is 5.
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Answer:
5
Step-by-step explanation:
Kayla drew a right triangle. Which could be the lengths of the triangle's sides?
A. 12 cm, 25 cm, 37 cm B. 9 cm, 16 cm, 25 cm
C. 8 cm, 14 cm, 17 cm D. 7 cm, 24 cm, 25 cm
Answers
Answer:
A triangle has side lengths 10 feet, V205 feet, and V105 feet
Step-by-step explanation:
find the value of x and y
Answers
Answer:
x= 131
y = 49
Step-by-step explanation:
X and 49 form a straight line so they add to 180
x+49 = 180
x = 180-49
x =131
49 and y are alternate interior angles and alternate interior angles have the same value
y = 49
Step-by-step explanation:
please mark me as brainlest
Is LMN = OPQ? If so, name the congruence postulate that applies. N Given: LM = OP PQ = MN P M = 00 O A. Congruent - SAS O B. Congruent - SSS O C. Might not be congruent O D. Congruent - ASA
Answers
Based on the sides of LMN and OPQ, the congruence postulate that applies is B. Congruent - SSS.
When is the SSS rule used?It is used when the two triangles given have three equal corresponding sides which also have equal angles.
All three sides of LMN and OPQ are equal sides and have equal angles and so the SSS rule applies.
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