Answer:
As angle B is a right triangle, the sides AB and CB are perpendicular to each other. From the property of all tangents to a circle given in the beginning it can be concluded that AB is a tangent of the circle
A triangle has sides with lengths 8, 15, and 17.
1. Verify this is a Pythagorean Triple
2. Approximate the acute angles in this triangle
Yes, the given set of the sides of a triangle follows the Pythagorean Triple and the acute angles are 61.92° and 28.08°.
What is the Pythagorean Triple?Pythagorean triples are a²+b² = c² where a, b and c are the three positive integers. These triples are represented as (a, b, c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.
Given that, A triangle has sides with lengths 8, 15, and 17.
1) Checking for Pythagorean triples;
17² = 289
8²+15² = 225+64 = 289 = 17²
∴ 17² = 8²+15²
Since, they are following the Pythagoras theorem so, they are Pythagorean triples.
2) Calculating the acute angles:- [please refer to attached figure]
Let 15 be the perpendicular, 8 be the base and 17 is the hypotenuse,
sinC = 15/17 (sine of an angle is ratio of perpendicular to hypotenuse)
∠ C = sin⁻¹(15/17)
∠ C = 61.92°
∠ A = 90°-61.92°
∠ A = 28.08°
Hence, the given set of the sides of a triangle follows the Pythagorean Triple and the acute angles are 61.92° and 28.08°.
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Choose the linear Inequality that describes the graph. The gray area represents the shaded region.
Answer:
3
Step-by-step explanation:
the y axis
What is the sum of the measures of the interior angles of a 20-sided figure?
Enter your answer in the box.
__°
The sum of the measures of the interior angles of a 20-sided figure is 3240.
What are Interior angles ?
An interior angle of a polygon is an angle that is created between two of the polygon's adjacent sides. The interior angle of a polygon is also known as the angle measured at the interior of a polygon.
the number of sides of given polygon is 20.
we know that, sum of the measures of the interior angles can be found by using formula : (n-2) × 180
where n= no. of sides of given polygon
So, sum of the measures of the interior angles of 20 sided figure :
= (n-2) × 180
= (20-2) × 180
= 18 × 180
= 3240 .
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A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest tenth. Enter your answer in the box.
A rectangular prism 60 centimeters wide, 80 centimeters long, and 100 centimeters tall.
an expression to represent ( w increased by 5 )
Answer:
W + 5
Step-by-step explanation:
Given a number, W
An increase in W by a constant 5 ; can be expressed as ;
W plus the constant value increase
Hence,
Increase in W by 5 equals ;
W + 5
explain how 7/10 and 70/100 are equivalent decimals
Step-by-step explanation:
7/10 in percentage form is 70%
70/100 in percentage form is 70%
Simple as that
It is proved that the given decimals are equivalent decimals.
What are equivalent fractions? What is a mathematical function, equation and expression?equivalent fractions : Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given are the fractions -
7/10 and 70/100
We have the following fractions -
A = (7/10) = 0.7
B = 70/100 = (7 x 10)/(10 x 10) = (7/10)
B = (7/10) = 0.7
It can be seen that fraction A equals to B.
Therefore, it is proved that the given decimals are equivalent decimals.
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A watch seller gained 20% by selling a watch for rs 1260.is) What was its cost price.ii)If he had to gain 30%,at what price should have sold it
Step-by-step explanation:
A watch seller gained 20% by selling a watch for 1260.If he had to gain 30%,at what price should have he sold it?
Dalton III
Answered December 12, 2020
I shall explain the solution to this problem using rudimentary concepts.
First, we need to determine the original price of the watch.
Convert the percentage profit to a decimal by dividing by 100. In this problem, the profit is 20%, so we would divide:
20100=0.2
Add 1 to the profit expressed as a decimal.
1+0.2=1.2
Divide the price after the profit has been added by the figure which we have calculated to find the price before the profit (we shall assume that the currency used in this problem is the pound sterling)
£12601.2=£1050
Now that we have determined the original price of the watch, we shall determine at what price should the seller sell this watch in order to obtain a 30% gain. The same formula is used for the first two steps.
Convert the intended percentage profit to a decimal by dividing by 100. In this problem, the intended profit is 30%, so we would divide:
30100=0.3
Add 1 to the intended profit expressed as a decimal.
1+0.3=1.3
Now, instead of dividing, we would want to multiply the original price with the figure 1.3
£1050⋅1.3=£1365
So, in order to gain a profit of 30%, the watch seller should sell the watch at a price of £1365
What is 27^2/3 simplified
Answer:
3^3
Step-by-step explanation:
[27]^2/3 can also be written as,
[(3)^3]^2/3
Now we know that a^m * a^n = a^m+n, therfore,
[3]^ 3*2/3
Cut 3 and 3
Therefore, you get 3^3
Let me know if you understood. If you didnt I can try to explain it to you in another way.
Also, plz mark me as the brainliest!
Mr Mazibuko monthly salary before tax is R12 700 what will be his salary after paying 11% tax
Answer:
R11 303
Step :
Find 11% of R12 700
R12 700 × 11/100
=R1 397
then substract the 11% from R12 700
R12 700 - R1 397
=R11 303
Help pls also show work if needed!
Answer:
unknown value = 800
Step-by-step explanation:
f(x) = 1333/100·x + 1/5
so if x = 60 - > (1333/100)60+1/5 = 800
Answer: 800
Step-by-step explanation: 933.3-133.3=800-133.3=666.7-133.3=533.4
The population of a city has decreased by 33% since it was last measured. If the current population is 13,400, what was the previous population?
0
Х
?
Continue
Answer:
8,978 People
Step-by-step explanation:
13,400 x 0.33 = 4,422
13,400 - 4,422 = 8,978
What is the value of x? Please help asap
Answer:
x=27
Step-by-step explanation:
It’s a ratio:
9.9/11=x/30
cross multiply
11x=297
x=27
Margie needs 7 ticket to the same soccer game.
Describe the best way to figure out Margies EXACT cost, if we know that 3 tickets cost $53.00.
Answer:
$123.66
Step-by-step explanation:
53 divided by 3 is 17.66, which is how much one ticket will cost. 17.66 multiplied by 7 is 123.66
Can I have help with number 5
Answer:
1
Step-by-step explanation:
2a-21 / b
2(4)-21/3
8-7=1
Answer:
1
Step-by-step explanation:
(FIRST THING FIRST REMEMBER PEMDAS)
First you rewrite the number sentence with the clues you got.
2 x 4 - 21 / 3
Then you do 2x4 to get 8, then you rewrite the # sentence again
8 - 21 / 3
Next you divide 21 / 3 to get 7 and rewrite the sentence again
8-7
FINALLY you subtract 8-7 to get 1
Find the coordinates of the point where the lines with equations y=x and y=-6 intersect
Answer:
(-6, -6)
Step-by-step explanation:
Find the coordinates of the point where the lines with equations y=x and y=-6 intersect.
The lines intersect at y = y
Equating the right hand side of both expressions we have;
x = -6
Since y = x, hence y = -6
The required coordinate where they intersect is at (-6, -6)
what is the area of this shape?
Answer:
D) 36 cm^2
Step-by-step explanation:
(9 x 3) + (2 x 4.5)(2)(0.5) = 36 cm^2
HELP
Find the mean, median, mode, and range of the following data set.
15, 12, 19, 15, 16, 13, 15.
Mean:
Median:
Mode:
Range
A single die is rolled once. Find the probability of rolling a number less than 7.
Answer:
1/6
Step-by-step explanation:
The die is rolled once, so it is 1 out of the total number on the die ie 6, as a die has only faces or sides so its obvious out of these 6 faces only one will show.
From which types of data display can the number of observations in a data set be determined?
A. Dot plot
2. Box plot
3. Histogram
Does anyone know what 0.4 divided by 2.4 is? I think it’s 0.6 or 6 not for sure tho!
Answer:
0.16 I think............
Answer:
0.16666666666
One month Maya rented 2 movies and 3 video games for a total of $20. The next month she rented 6 movies and 5 video games for a total of $38. Find the
rental cost for each movie and each video game.
Rental cost for each movie:
Rental cost for each video game:
Answer:
[tex]M = 1.75[/tex] --- Movies
[tex]V = 5.5[/tex] --- Video games
Step-by-step explanation:
Represent the movies with M and the video games with V.
The first month, the expression is:
[tex]2M + 3V = 20[/tex]
The next month, the expression is:
[tex]6M + 5V = 38[/tex]
Required
Find M and V
We have:
[tex]2M + 3V = 20[/tex] --- (1)
[tex]6M + 5V = 38[/tex] --- (2)
Multiply (1) by 3.
3 * [tex]2M + 3V = 20[/tex]
[tex]6M + 9V = 60[/tex] --- (3)
Subtract (1) from (3)
[tex]6M + 9V = 60[/tex]
- [tex]6M + 5V = 38[/tex]
-------------------------
[tex]6M - 6M + 9V - 5V = 60 -38[/tex]
[tex]4V = 22[/tex]
Divide by 4
[tex]V = 5.5[/tex]
Substitute 5.5 for V in (1)
[tex]2M + 3V = 20[/tex]
[tex]2M + 3 * 5,5 = 20[/tex]
[tex]2M + 16.5= 20[/tex]
Subtract 16.5 from both sides
[tex]2M = 3.5[/tex]
Divide by 2
[tex]M = 1.75[/tex]
Patrick will borrow $4300 at 11.5% APR. He will pay it back over 5 years.
What will his monthly payment be? (Use the table.)
$94.56
$96.79
$123.21
$141.81
Answer:
94.56
Step-by-step explanation:
because 94,56 x 11.5 x 5 =4300
Answer:
Step-by-step explanation:
Equal installments can be found by
I=P((r-1)/(r^n-1)+(r-1)) (note monthly rate is r/12, r is about 1.00958)
I=4300((1.00958-1)/(1.00958^60-1)+0.00958)
I=$94.56
Find the number that belongs
in the green box.
322
7
125°
[?]
Round your answer to the nearest tenth.
Answer:
2.7
Step-by-step explanation:
322/7=46
46*125=2.71739
round off
2.7
How many years in a month
Answer: There are 12 months in one 1 year
Step-by-step explanation:
Find the maximum rate of change off at the given point and the direction in which it occurs.
f(x, y) = 4y √x, (4, 1)
Answer:
Maximum rate change |[tex]\nabla[/tex]f| = √65
Direction = ( 1, 8 ) / √65
i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )
Step-by-step explanation:
Given that;
f(x, y) = 4y √x, (4, 1)
{ x=4 and y=1 }
Maximum rate of change occurs with the gradient vector;
[tex]\nabla[/tex]f = [ df/dx, df/dy ] = [ 2y/√x, 4√x ]
we substitute in our value of x and y
[tex]\nabla[/tex]f = 2(1)/√4, 4√4
[tex]\nabla[/tex]f = 2/√4, 4√4
[tex]\nabla[/tex]f = ( 1, 8 )
Maximum rate change |[tex]\nabla[/tex]f| = | ( 1, 8 ) | = √( 1² + 8² ) = √(1 + 64)
Maximum rate change |[tex]\nabla[/tex]f| = √65
Direction = [tex]\nabla[/tex]f / |[tex]\nabla[/tex]f|
we substitute
Direction = ( 1, 8 ) / √65
i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )
Does anyone know the answer?
Answer:
15°
Step-by-step explanation:
2x+5=3x
5=3x-2x
5=x
Now we can solve the angle.
<BAD=2x+5 = 2(5)+5 = 10+5 = 15°
A tree initially measures 40 1/2 feet tall. Over the next 7 1/2 years, it grew to a final height of 57 feet. During those 7 1/2 years, what was the average yearly growth rate of the height of the tree?
Answer:
OK I will dot this after getting 10 followers
Answer:
deez
Step-by-step explanation:
Which of the following equations is in standard form? O y = 2x + 3 O-3x - 2x = 6 O 2x + 3y = 6 O y - 2 = 3(x + 1)
Pleaseeee helpppp it’s due in 6 minutes helpp!! Explain
Answer:
I might be wrong but since ur in a rush: 173
Step-by-step explanation:
Answer:
287.25 miles in 5.75 hours
Step-by-step explanation:
so he was first driving at 48mph because 168/3.5=48
5 miles per hour faster than that is 53mph
53*2.25=119.25
then we add 119.25 and 168
one peach weigh 5 ounces. bella buys 8 peaches. what is the total weight of the peach
Answer:
40 ounces
Step-by-step explanation:
well if every peach weighs 5 ounces and she buys 8, just do 8 x 5 and you get 40