The measures of angles B and D are 110° and 70° respectively.
What is cyclic quadrilateral?The rule of cyclic quadrilateral states that, the sum of the opposite is supplementary i.e 180°
Therefore, applying this rule, Angle B and D are supplementary
Then, B+D=180°
Given that, B=3x-4 and D= 2x-6
Thus, (3x-4)+(2x-6)=180°
3x-4+2x-6=180°
3x+2x-4-6=180°
5x-10=180°
5x=180°+10
5x=190°
Then, x =190/5
x=38°
Then solving for B and D;
B=3x-4
B=3(38)-4
B=114-4
B=110°
Also, D=2x-6
D=2(38)-6
D=76-6
D=70°
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What is the domain of f(x) = 3^x – 2?
Answer: In fact tis D. Is all real numbers
Step-by-step explanation: your welcome?
monique deposited 1800 at the beginning of each quarter for 6 years into an ira. given an interest rate of 6% compounded quarterly find the value
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Compare the following functions:
(see attachment)
Which function has the smallest minimum?
A. All three functions have the same minimum
B. f(x)
C. g(x)
D. h(x)
Answer:
Step-by-step explanation:
We are given three functions and we have to find which one has the smallest minimum.
I function is
[tex]f(x) = -5sin(2x-\pi) +2[/tex]
Since sine varies from -1 to 1, we get this function has a minimum when sine takes value 1.
Minimum of f(x) =1(-5)+2 =-3
II function is
a graph of parabola with minimum at x=3 and y =-2
III function is shown in tabular form.
From the table we find that minimum is x=1 y=3
Tabulating we have
f(x) (3pi/4, -3)
g(x) (3,-2)
h(x) (1,3)
Smallest is for f(x) with least value of -3
x plus 20% = 1980
what is x
What is the amplitude, period, and phase shift of f(x) = -3 cos (4x + pi) +6?
The amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.
Periodic functionA periodic function is a function that repeats itself after a definite time interval.
Given[tex]f(x) = -3cos(4x+\pi ) +6[/tex]
The cosine function is a periodic function that repeats itself in the interval of [tex]2\pi [/tex].
Step by step explanationFor maximun amplitude
[tex]cos(4x+\pi )=-1\\ [/tex]
Then
[tex]f(x)=3+6\\ f(x)= 9[/tex]
For time period
The cosine function repeats itself in the interval of [tex]2\pi [/tex].
[tex]\begin{aligned} \frac{2\pi }{T} &= 4 \\\\ T &=\dfrac{\pi }{2}\\ \end{aligned}[/tex]
For phase shift
Phase is [tex]\dfrac{\pi }{4} [/tex]
Thus, the amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.
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Write the first 4 terms of the sequence if a(4)=36 and a(n)=1/2a(n-1)+12.
A.
36, 30, 27, 25.5
B.
120, 72, 48, 36
C.
456, 216, 96, 36
D.
36, 48, 72, 120
What is the length of CF? look at image attached
Find the measure of each interior angle and each exterior angle of the following regular polygons. Show your work
Answer:
Step-by-step explanation:
As we know for a regular polygon sum of all interior angles is represented by n A = 180 (n-2)
and sum of all exterior angles is represented by n A' = 360°
Here n represents number of sides of the polygon.
Now we will go for each options given.
(A) Decagon : (Having 10 sides)
(1) 8A = 180 ( 8-2 )
8A = 180 × 6
A = [tex]\frac{1080}{8}[/tex] = 160° ( interior angle )
(2) n A' = 360°
8 A' = 360°
A = 45° ( exterior angle )
(B) Pentagon ( having 5 sides )
(1) 5A = 180 ( 5-2 )
5A = 180 × 3 = 540
A = 108° ( interior angle )
(2) 5A' = 360
A' = 72° (exterior angle )
(C) Dodecagon : ( having 12 sides )
(1) 12A = 180 (12-2)
12 A = 180 × 10 = 1800
A = 150° ( interior angle )
(2) 12 A' = 360
A' = 30° ( exterior angle )
(D) 16-gon ( having 16 sides )
(1) 16 A = 180 ( 16 - 2 )
16A = 180 × 14
16 A = 1520
A = 157.5° ( interior angle )
(2) 16 A' = 360
A' = 22.5°
(E) 25-gon ( having 25 sides )
(1) 25 A = 180 ( 25-2)
25A = 180 (23)
A = 165.6° ( interior angle )
(2) 25A' = 360
A = 14.4° ( exterior angle)
Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by seven.
a plane intersects a prism parallel to the base of the prism. the cross section is a polygon with eight sides. The base of the prism had how many sides
Words that came from the same ancestral language and originated from the same word are called
The words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.
What is ancestral language?In the historical linguistics tree model, a protolanguage is a hypothetical ancestral language from which several documented languages are thought to have evolved, constituting a language family. In most cases, protolanguages are unattested or, at most, only partially attested.
The languages of Norway, Sweden, Denmark, and Iceland descend from Old Norse. Numerous Indian languages, including Bengali, Hindi, Marathi, and Urdu, have their roots in Sanskrit. Each of these ancestral languages had a single common progenitor further back in time.
The term "cognates" in linguistics refers to words with the same etymological background. These are words that have the same pronunciation, spelling, and meaning in two different languages. For instance, Spanish has many words that are similar to English words.
Therefore, Words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.
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What type of transformation can be defined as turning a figure about a fixed point with no change to the size or shape of the figure?
12.38 in expanded form
(04.01 LC)
Which of the sets of ordered pairs represents a function?
A = {(2, −2), (5, −5), (−2, 2), (−5, 5)}
B = {(4, 2), (4, −2), (9, 3), (9, −3)}
Only A
Only B
Both A and B
Neither A nor B
Answer:
Only A
Step-by-step explanation:
Let's remember the definition of a function:
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
In A, each input has exactly one output so it's a function.
But in B, the inputs 4 and 9 have two different outputs, it can't represent a function.
The answer is only A.
1,226 days late to answer this question but that will not stop me!
The answer is... drumroll please ... Only A :]
Find the equation of the circle that has a diameter with endpoints located at (7, 3) and (7, –5).
The equation of the circle with a diameter between (7, 3) and (7, -5) is (x - 7)² + (y + 1)² = 2².
Explanation:To find the equation of the circle, we first need to find its center. The center of a circle is the midpoint of its diameter. To find the midpoint of (7, 3) and (7, -5), we can add the x-coordinates and divide by 2 to get 7. For the y-coordinates, we add -5 and 3 and divide by 2 to get -1. So, the center of the circle is (7, -1).
The radius of the circle is half the length of the diameter. The distance between the center of the circle and one of the endpoints of the diameter (7, 3) is the radius. Using the distance formula, the radius is √((7-7)² + (3+1)²) = 2.
Now, we can use the center and radius to write the equation of the circle, which is (x - 7)² + (y + 1)² = 2².
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Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?
helpppppppppppppppppppppppppppp
tristen is a saleman whose base pay plus commissions amounted to $59,238 last year. if his base pay was $31,050 and he made $97,200 is sales last year what was his rate of commission?
subtract base pay from what he made
59238-31050 = 28188
so he made 28188 in commissions
now divide that by 97200
28188/97200 = 0.29
so he makes 29% commision
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Help, please!
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 16°23'. When the boat stops, the angle of depression is 49°29' . The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]
Further explanation:
The Pythagorean formula can be expressed as,
[tex]\boxed{{H^2} = {P^2} + {B^2}}.[/tex]
Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.
The formula for tan of angle a can be expressed as
[tex]\boxed{\tan a = \frac{P}{B}}[/tex]
Explanation:
The perpendicular AB. The length of AB is [tex]200{\text{ feet}}.[/tex]
The angle of depression is [tex]\angle ACB = {14^ \circ }52'.[/tex]
One degree has 60 minutes.
[tex]{1^ \circ } = 60'[/tex]
[tex]\begin{aligned}\angle ACB &= 49 + \frac{{29}}{{60}}\\&= 49 + 0.48\\&= 49.48\\\end{aligned}[/tex]
The angle ADB is [tex]\angle ADB = {16^ \circ }23'.[/tex]
[tex]\begin{aligned}\angle ADB&= {16^ \circ }23' \\&= 16 + \frac{{23}}{{60}}\\&= {16.38^ \circ }\\\end{aligned}[/tex]
In triangle ABC.
[tex]\begin{aligned}\tan\left( {{{49.48}^\circ }} \right)&=\frac{{200}}{{BC}}\\1.13&= \frac{{200}}{{BC}}\\BC &= \frac{{200}}{{1.13}}\\BC &= 177{\text{ feet}}\\\end{aligned}[/tex]
In triangle ABD.
[tex]\begin{aligned}\tan \left( {{{16.38}^ \circ }} \right)&= \frac{{200}}{{BD}}\\0.30&= \frac{{200}}{{BD}}\\BD&= \frac{{200}}{{0.30}}\\BD &= 666.67{\text{ feet}}\\\end{aligned}[/tex]
The distance boat can travel can be obtained as follows,
[tex]\begin{aligned}DC& = BD - BC\\&= 666.67 - 177\\&= 489.67{\text{ feet}}\\\end{aligned}[/tex]
The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]
Kindly refer to the image attached.
Learn more:
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2. Learn more about equation of circle brainly.com/question/1506955.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Trigonometry
Keywords: perpendicular, person watching boat, top, lighthouse, angle of depression, angle of elevation, 200 feet tall, travel, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions.
The table shows the ages and weights of babies at a hospital.
What is the correlation between age and weight as shown in the table?
A.) none
B.) positive
C.) negative
D.) constant
Answer:
Option (b) is correct.
The correlation between age and weight shown in the table is positive.
Step-by-step explanation:
Given: The table shows the ages and weights of babies at a hospital.
We have to determine the correlation between age and weight as shown in the table.
We first Plot these points to obtain the graph as show in attachment below.
Since, Using correlation calculator , we find the correlation as 0.83113
Which is positive
Thus, The correlation between age and weight shown in the table is positive.
As age increases the weight increase.Hence, positive.
The correlation between age and weight as shown in the table is positive, This is further explained below, Option B is correct
What is correlation?Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.
In conclusion, Therefore we look at the table to decipher the correlation between age and weight.
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in the system shown below, what are the coordinates of the solution that lies in quadrant I? x^2-y^2=25, x+y=25
Find the number of permutations of the first 10 letters of the alphabet taking 2 letters at a time.
The course for the frog hopping race is 59 inches long. Max's frog has jumped 2 feet and 3 inches. How much further does Max's frog need to jump in order to reach the finish line?
To find the remaining distance Max's frog needs to jump in the race, convert the initial jump to inches, and subtract it from the total race length.
The frog hopping race's course is 59 inches long. Max's frog has jumped 2 feet and 3 inches. To find out how much further Max's frog needs to jump to reach the finish line, convert 2 feet and 3 inches to inches and subtract it from 59 inches.
The conversion is: 2 feet x 12 inches = 24 inches. Adding 24 + 3 inches gives 27 inches. Subtract 27 inches from 59 inches to find the remaining distance Max's frog needs to jump.
The distance Max's frog still needs to jump is 32 inches.
Choose the graph below that correctly represents the equation 15x − 5y = 30.
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PLEASE HELP!!!
Final answer:
To choose the correct graph that represents the equation 15x - 5y = 30, isolate y, find the slope and y-intercept, and compare to the given graphs.
Explanation:
In order to choose the correct graph that represents the equation 15x - 5y = 30, we need to solve the equation for y.
First, let's isolate y by subtracting 15x from both sides of the equation:
15x - 5y - 15x = 30 - 15x
-5y = -15x + 30
Next, divide both sides of the equation by -5 to find the value of y:
-5y/-5 = (-15x + 30)/-5
y = 3x - 6
Now that we have the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can determine the graph that represents the equation. The slope of the equation is 3, which means that for every 1 unit increase in x, y increases by 3 units. The y-intercept is -6, which means that the graph intersects the y-axis at the point (0, -6).
Based on this information, we can determine that the graph that correctly represents the equation 15x - 5y = 30 is the one where the slope is 3 and it intersects the y-axis at (0, -6).
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Find the value of each variable for the right triangles. Make sure all answers are in reduced radical from. Shoe your work.
the volume of a gas varies inversely as the pressure upon it. if the volume of the gas is 160 cubic centimeters at a pressure of 108 centimeters find the volume when the pressure is 87 centimeters
Answer? Multiple choice?
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A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day
Plz help!
What is the constant of variation for the quadratic variation?
A. 5
B. 10
C. 15
D. 25