ANSWER
It is given that ABCD is a cyclic quadrilateral
(∠B−∠D)=60
o
......(1)
(∠B+∠D)=180
o
.....(2)
By adding both the equations
∠B−∠D+∠B−∠D=60
o
+180
o
So we get
2∠B=240
o
By division
∠B=120
o
By substituting equation it in equation (1)
(∠B−∠D)=60
o
120
o
−∠D=60
o
On further calculation
∠D=120
o
−60
o
by subtraction
∠D=60
o
Therefore, the smaller of the two angles ∠D=60
o
.
Step-by-step explanation:
Forty-two people charter a bus for $788. Estimate the amount each person pays.
Your answer
Answer:
$20
Step-by-step explanation:
If 42 people equally share the bus price off 788 dollars then ech person would be expected to pay 788/42 = $18.76 (2dp) though I suppose if you needed to estimate it, you would round 788 to 800 and 42 down to 40 which would give you 800/40 = 20 dollars per person which is a pretty close estimate.
Hope this helped!
From the top of a 224-ft lighthouse, the angle of depression to a ship in the ocean is 22°. How far is the ship from the base of the lighthouse? Give your answer to the nearest foot.
Answer:
x=554.41 m
Step-by-step explanation:
It is given that,
Height of the lighthouse, OA=224 ft
The angle of depression to a ship in the ocean is 22 degrees.
We need to find the distance between ship and the base of the lighthouse. The figure is attached. We can use trigonometry to find x.
[tex]\tan22=\dfrac{OA}{AB}\\\\\tan22=\dfrac{224}{x}\\\\x=\dfrac{224}{\tan22}\\\\x=554.41\ m[/tex]
So, there is a distance of 554.41 m between the ship and the lighthouse.
A bucket has a leak that started 6 hours ago. At time 0, when the bucket just emptied, a tap was turned on for 3 hours. The amount of water in the bucket can be modeled by the function f(x) = |x| over the interval [−6, 3], where x is the time, in hours, and y is the amount of water in the bucket, in gallons. Which translation of the graph represents the last 3 hours of the leak, and the tap running for 6 hours? Group of answer choices g(x) = |x − 3| g(x) = |x| + 3 g(x) = |x| − 3 g(x) = |x + 3|
Answer:
The answer is g(x) = |x - 3|
Step-by-step explanation:
Here we have a general problem of horizontal translations, we will see that the correct option is g(x) = |x - 3|
We know that the bucket was leaking for 6 hours, and then it was filled in 3 hours.
Then in the interval [-6, 0) the bucket was leaking
In the interval [0, 3] the bucket was being filled.
Now we want a transformation that represents the last 3 hours of leaking.
Also, remember that for a general function f(x), an horizontal translation of N units is written as:
g(x) = f(x + N)
If N is positive, the translation is to the left
If N is negative, the translation is to the right.
If we want to represent the last 3 hours of leaking (which happen for negative values of x) then we need to move the whole graph to the right.
So, if we define the function as:
g(x) = f(x - 3)
when we evaluate g(x) in zero we get:
g(0) = f(-3)
So this new function, at the time zero, starts representing the last 3 hours of leaking of the bucket.
Remembering that f(x) = |x|
We can see that the correct option is:
g(x) = f(x - 3) = |x - 3|
g(x) = |x - 3|
Below you can see a graph with a comparison of f(x) and g(x), where the green one is f(x) and the blue one g(x).
If you want to learn more, you can read:
https://brainly.com/question/13435754
The Roberts family is taking a road trip. They plan to drive 1500 miles over two days, stopping for the night when they are halfway. How many hours will they drive for the first day if they average 50 mph over the course of the trip?
Explain:
Answer:
Answer:
The number of hours they would have to drive for the first day if they average 50 mph over the course of the is 15 hours
Step-by-step explanation:
The given parameters are;
The distance the Roberts family plan to drive = 1500 miles
The average speed at which they drove = 50 mph
We note that the formula for average speed = Total distance/(time)
Therefore, we have;
50 mph = 1500 miles/(time, t)
Time = 1500 miles/(50 mph) = 30 hours
Given that for the first day of the 2 days, they will cover half their total distance, which is 1500 m/2 = 750 m
The time taken = 750 miles/(50 mph) = 15 hours
The time take to cover half the distance = 15 hours
Therefore, the number of hours they would have to drive for the first day if they average 50 mph over the course of the is 15 hours.
What is the distance rounded to the nearest tenth, between the points (0, 5) and (8, 0)?
Answer:
9.4
Step-by-step explanation:
The distance formula is d=√((x₂-x₁)²+(y₂-y₁)²)
d=√((8-0)²+(0-5)²)
d=√((8²)+(-5²))
d=√(64+25)
d=√(89)
d=9.433981
d=9.4
Hope this helps :-)
Answer: 9.4 units
Step-by-step explanation:
The point (1/3,1/4) lies on the terminal said of an angle. Find the exact value of the six trig functions and explain which functions are reciprocal functions to each other
Answer:
sine and cosec are inverse of each other.
cosine and sec are inverse of each other.
tan and cot are inverse of each other.
Step-by-step explanation:
Given point on terminal side of an angle ([tex]\frac{1}{3},\frac{1}4[/tex]).
Kindly refer to the attached image for the diagram of the given point.
Let it be point A([tex]\frac{1}{3},\frac{1}4[/tex])
Let O be the origin i.e. (0,0)
Point B will be ([tex]\frac{1}{3},0[/tex])
Now, let us consider the right angled triangle [tex]\triangle OBA[/tex]:
Sides:
[tex]Base, OB = \frac{1}{3}\\Perpendicular, AB = \frac{1}{4}[/tex]
Using Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow OA^{2} = OB^{2} + AB^{2}\\\Rightarrow OA^{2} = \frac{1}{3}^{2} + \frac{1}{4}^{2}\\\Rightarrow OA = \sqrt{\frac{1}{3}^{2} + \frac{1}{4}^{2}}\\\Rightarrow OA = \sqrt{\frac{4^2+3^2}{3^{2}.4^2 }}\\\Rightarrow OA = \frac{5}{12}[/tex]
[tex]sin \angle AOB = \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\Rightarrow sin \angle AOB = \dfrac{\frac{1}{4}}{\frac{5}{12}}\\\Rightarrow sin \angle AOB = \dfrac{3}{5}[/tex]
[tex]cos\angle AOB = \dfrac{Base}{Hypotenuse}[/tex]
[tex]\Rightarrow cos \angle AOB = \dfrac{\frac{1}{3}}{\frac{5}{12}}\\\Rightarrow cos\angle AOB = \dfrac{4}{5}[/tex]
[tex]tan\angle AOB = \dfrac{Perpendicular}{Base}[/tex]
[tex]\Rightarrow tan\angle AOB = \dfrac{3}{4}[/tex]
[tex]cosec \angle AOB = \dfrac{Hypotenuse}{Perpendicular}[/tex]
[tex]\Rightarrow cosec\angle AOB = \dfrac{5}{3}[/tex]
[tex]sec\angle AOB = \dfrac{Hypotenuse}{Base}[/tex]
[tex]\Rightarrow sec\angle AOB = \dfrac{5}{4}[/tex]
[tex]cot\angle AOB = \dfrac{Base}{Perpendicular}[/tex]
[tex]\Rightarrow cot\angle AOB = \dfrac{4}{3}[/tex]
Please help me with this answer
Answer:
0.703
Step-by-step explanation:
19/70 = 70.37/100
Hope This Helps :)
Answer:
0.7037
Step-by-step explanation:
0.7037 is a decimal and 70.37/100 or 70.37% is the percentage for 19/27.
What is 3x-8=4. Solve for x. Explain.
Answer:
4
Step-by-step explanation: 3 x 4 = 12.
12 - 8 = 4.
If ƒ(x) = 2x2 + 3, then which of the following represent ƒ(-1)?
Answer:
f(-1) = 1
Step-by-step explanation
[tex]f(-1)= 2(-1)^{2} + 3\\f(-1) = -2 + 3\\f(-1) = 1[/tex]
Carson needs 3 quarts of water to make fruit punch, but has only a 1-cup measuring cup. She knows there are 2 cups in 1 pint, and 2 pints in 1 quart. How can Carson find the number of cups of water she needs to make the punch.
FAST
Answer:
12
Step-by-step explanation:
3 quarts is 6 pints
6 pints is 12 cups
if there is 4 cups in a quart then 4x3=12
9 tickets cost $54. How much do 4 tickets cost?
Let's make a proportion to solve this problem.
[tex]\frac{9}{54}=\frac{4}{x}[/tex]
[tex]9x=216[/tex]
[tex]x=24[/tex]
4 tickets cost $24
Hope this helps.
頑張って!
The product of 2 and a number x is 3/4. What is the value of x? x=5/4 x=3/8 x=1 1/4 x=3/2
Answer:
x=3/8
Step-by-step explanation:
2*x=3/4
x=3/4*2
x=3/8
Answer:
9
Step-by-step explanation:
What is the pattern as the exponents decrease
Answer:
Divide the previous value by 5
Step-by-step explanation:
2(c + 3) = c - 13
Solve
Answer:
-19
Step-by-step explanation:
2 (c + 3) = c - 13
2c + 6 = c - 13
2c + 19 = c
19 = - c
c = - 19
Given the equation ay − b = c, which expression represents y? a.) c-b/a b.) c+b/y c.) c+b/a d.) c+a/b
Answer:
Option C. y = ( c + b ) / a
Step-by-step explanation:
For this problem, we must simply isolate the y variable from the unknowns a, b, and c.
ay - b = c
ay - b + b = c + b
ay = c + b
ay * ( 1 / a ) = ( c + b ) * ( 1 / a)
y = ( c + b ) * ( 1 / a )
y = ( c + b ) / a
Thus, we will want to choose option C.
Cheers.
What are the coefficients of 12-8x+14y
Answer:
the 8 and 14 would be the coefficients
Step-by-step explanation:
coefficients are the numbers only next to the variables( like x or y) so since 8 and 14 are next to the variables they are the coefficients
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x?
The graph is not a function of x because the line x = 0 intersects the graph at two points.
The graph is a function of x because the line x = 5 does not intersect the graph.
The graph is not a function of x because the line y = 0 intersects the graph at two points.
The graph is a function of x because the line y = 5 does not intersect the graph.
Answer:
The answer is either a or c .
Step-by-step explanation:
Answer:
c yw
Step-by-step explanation:
2
3) In which quadrant of the coordinate plane will the ordered pair (-8, 7)
be found? *
Answer:
2 cuadrante
Step-by-step explanation:
4y – 2(1 – y) = –44?
Answer:
y= - 7
Step-by-step explanation:
4y-2+2y= -44
6y-2= -44
6y= -44+2
6y= -42
y= -7
Answer:
y=-7
Step-by-step explanation:
4y-2+2y=-44
6y-2=-44
6y=-44+2
6y=-42
7=-7
Find the slope of the line through each pair of points. (-17,-5), (15.-13)
Which of the following is a quantitative variable?
Temperatures in New York from January to March
Price of gas at three different gas stations
Population density of a town
Symbols of elements on the periodic table
Answers: A, B, C
These three deal with numeric values, so that is why they are quantitative variables. Think quantitative as quantity to help remember.
In contrast, choice D is a qualitative variable. Instead of dealing with numbers, it deals with symbols or labels. You could also call this a categorical variable (each label being its own category).
can you please tell me the right ans
Answer: i) 512,000 cm³ ii) 512,000 cc iii) 512 litres
Step-by-step explanation:
Volume (V) of a cube is side (s) cubed: V = s³
Given: s = 80 cm
i) V = (80 cm)³
= 512,000 cm³
ii) 512,000 cm³ = 512,000 cc
iii) 512,000 cm³ × 1 liter/1000 cm³ = 512 liters
It was 12°C one person got home from school. The weather for port show me a story moving in the world drop the temperature by 70 Celsius. What is the expected temperature?
Answer:
Expected temperature = - 58°C
Step-by-step explanation:
Given:
Current temperature = 12°C
Drop in temperature = 70°C
Find:
Expected temperature
Computation:
Expected temperature = Current temperature - Drop in temperature
Expected temperature = 12°C - 70°C
Expected temperature = - 58°C
solve this question please: x² = -169
Answer:
13i, -13i
Step-by-step explanation:
To solve this equation, we need to take the square root of both sides. The square root of 169 can be either 13 or -13, but this time, they asked for -169. Whenever we take the square root of a negative number, we put the letter i, which stands for imaginary. It is never capitalized, so we remove the negative sign from -169, and take the square root of that. We get -13 and 13 as our answers, and we multiply both numbers by i to get -13i and 13i. Any solutions with i in it are considered complex solutions
Are terms and ratios related?
Find the distance between the points (-8, -10) and (18, -10).
2014
16
12
8
4
4
-20
-16
--12
-8
-4
0
12
20
16
-4
-8
(18. -10
(-8, -10
--12
-16
-20
units
IN
Answer:
26 units
Step-by-step explanation:
(-8, -10) and (18, -10)
Since the y values are the same, we only need to worry about the x values
18 - -8
18+8
26
The distance is 26 units
Answer:
8
Step-by-step explanation:
I need help with solving this equation! ( answer is supposed to be 3.888 but I have been getting a different answer every time!) 3.24 x 1.2
Answer:
I got 3.888 because when 4×2=8 and 2×2=4 and 3×2=6 so for my first row of numbers was 648 under 0 I put a 0 then multiplied 3.24 by 1 then added 648+3240=3.888
Answer:
Step-by-step explanation:
If you can't use a calculator break it apart.
1 X 3.24 is 3.24
Now take .2 x 3.24 this is easy, just remember to move the decimal in the answer one more to the left.
3.24
x .2
.684 moved the decimal one more spot
Now we take 3.24 + .684
3.24
+ .648
3.888
A recipe that makes a dozen cookies calls for 1 1/2 cups of milk, 2.25 cups of flour, and 1 1/4 cups of other ingredients. How many cups of other ingredients, milk and flour are needed to make 36 cookies? (1 dozen is 12 cookies)
Answer:
15 cupsStep-by-step explanation:
[tex]1\frac{1}{2} \:cups \:of\:milk\\2.25\:cups \:of\:flour\\1\frac{1}{4} \:cups\:of\:other\:ingredients\\\\Total = 1\frac{1}{2} + 2.25 + 1\frac{1}{4} \\= 5\:cups\\\\1\:dozen = 5\:cups\\3 \:dozen(36\:cookies) = x \:cups\\\\Cross\:multiply\\\\x = 5\times 3\\x = 15 \:cups[/tex]
Choose the answer that makes the sentence true. rational numbers are real numbers. ALL SOME NO
PLEASE HELP
Answer: All rational numbers are real numbers
Real numbers are those which can be represented on a real number line
A rational number is a number that can be written in the form of p/q where q is not equal to zero.
All rational numbers will be real numbers.
Option A is the correct answer.
What is a rational number?A rational number is a number that can be written in the form of p/q where q is not equal to zero.
Example:
2 = 2/1 is a rational number.
1/2, 3/4, 5/6 are rational numbers.
We have,
________ rational numbers are real numbers.
We have to select from the options and fill in the blanks.
- ALL
- SOME
- NO
Real numbers can be any type of number except an imaginary number denoted by i = √-1.
So,
All rational numbers will be real numbers.
Thus,
All rational numbers will be real numbers.
Option A is the correct answer.
Learn more about rational numbers here:
https://brainly.com/question/24398433
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my assignment is about multiplication and maybe division. The one of the multiplication problems are this one : Martin has 12 times as many baseball cards as Josie. Josie has 29 more cards then Kal. How many baseball cards does Martin have? write and solve equations. Matt has 14 times as many cards as Kal. How many cards does Matt have?
Answer:
well how many cards does kal have?? thats the main key to solving the question.