Please help me!!!
Prove that :
7.1 TS is a tangent to the cyclic quadrilateral RSPD at point S.
7.2 TW ||PS
Answers
Explanation:
The various theorems involved include ...
angle sum theorem (angles in a triangle total 180°)alternate interior angles theorem (said angles are congruent)inscribed angle theorem (and "alternate")angle addition postulateFor the purpose here, we wll use the notation D.1 to refer to the angle labeled "1" at vertex D.
The argument goes something like the following.
__
∠D.1 +∠R +∠S.1 = 180° . . . . angle sum theorem
∠S.1 +∠S.2 +∠S.3 +∠S.4 = 180° . . . . angle addition postulate (∠RSW is a straight angle, equal to 180°)
∠D.1 +∠R +∠S.1 = ∠S.1 +∠S.2 +∠S.3 +∠S.4 . . . . substitution property
∠D.1 = ∠S.2 . . . . alternate interior angles theorem
∠S.2 +∠R +∠S.1 = ∠S.1 +∠S.2 +∠S.3 +∠S.4 . . . . substitute for ∠D.1
∠R = ∠S.3 +∠S.4 . . . . subtraction property (subtract ∠S.1 +∠S.2)
∠R = ∠S.3 +∠S.2 . . . . substitute ∠S.2 for equal ∠S.4 (given)
∠R = arc DS/2 . . . . inscribed angle is half the arc measure
∠TSD = ∠S.2 +∠S.3 = arc DS/2 . . . . substitution, angle addition, angle naming
TS is tangent at S . . . . converse of "inscribed angle alternate" where the vertex of an inscribed angle is a point of tangency
_____
Additional comment
The alternate to the inscribed angle theorem says the angle is half the measure of the intercepted arc even as the vertex of the inscribed angle becomes a point of tangency (one ray of the angle is a tangent, so a zero-length chord). The converse of this says the vertex is a point of tangency if the intercepted arc is twice the measure of the angle, as in this problem.
Related Questions
I need some help on these 3 questions :)
Answers
The factor of the polynomial, the area of the pool and the simplified expression are all algebraic expressions
How to simplify the expressions?Factor of the polynomial
The polynomial is given as:
2x^3 + 6x^2 + 6x + 18
Factor out 2
2x^3 + 6x^2 + 6x + 18 = 2(x^3 + 3x^2 + 3x + 9)
Factorize
2x^3 + 6x^2 + 6x + 18 = 2(x^2(x + 3) + 3(x + 3))
Factor out x + 3
2x^3 + 6x^2 + 6x + 18 = 2(x^2 + 3)(x + 3)
Expand
2x^3 + 6x^2 + 6x + 18 = (2x^2 + 6)(x + 3)
Hence, 2x^2 + 6 is a factor of the polynomial 2x^3 + 6x^2 + 6x + 18
The length of the pool
The given parameters are:
Area = 2x^3 - 29x + 12
Width = x + 4
The length is calculated as:
Length = Area/Width
This gives
Length = 2x^2 - 29x + 12/x + 4
Factorize the numerator
Length = (2x^2 - 8x + 3)(x + 4)/x + 4
Cancel out x + 4
Length = 2x^2 - 8x + 3
Hence, the length of the pool is 2x^2 - 8x + 3
Simplify the expression
The expression is given as:
(3s^2 - 2s + 1) [tex]\div[/tex] (s^2 - s + 2)
Evaluate the quotient
3 + (s - 5)/(s^2 - 5 + 2)
Hence, the simplified expression is 3 + (s - 5)/(s^2 - 5 + 2)
Read more about algebraic expressions at:
https://brainly.com/question/2164351
Hiking club wanted to cover a different trail each day for a week. On Monday they had 2.3 miles, and Tuesday they height 1.8 miles, on Wednesday they height 3.2 miles, on Thursday they hide 1.4 miles, on Friday they hike 2.8 miles. what is the total distance they hiked
Answers
Answer:
11.5 Miles
Step-by-step explanation:
Add up all the mile times.
2.3+1.8+3.2+1.4+2.8=11.5
A rectangular sheet of metal measures 8 inches by 12 inches. The metal is worth $2.00 per square inch. How much is the sheet of metal worth?
Answers
Answer:
Step-by-step explanation:
Find the area of the sheet metal
Area = L * w
L = 12
w = 8
Area = 12 * 8
Area = 96 square inches.
Find the value of the sheet metal
1 square inch costs $2.00
96 square inches cost 2 * 96 = $192.00
Explain why 0.323232 is greater than 0.32
Answers
Answer:
0.323232 is the greater number
Step-by-step explanation:
This is because if you write the numbers the same way, there is a difference between the first 0 and the 3.
Look here: 0.323232 0.320000
You can see that there is a 3 after the first 2, therefore that shall deem the greater number.
In the scale drawing below
Answers
Answer:
47.5m
Step-by-step explanation:
convert cm to metres 1.9cm×5=9.5m
Then times the side lengths with the amount of sides 9.5m×5=47.5m
Please help I'll mark brainliest 2
Answers
Answer:
True
Step-by-step explanation:
To find the amount of observations all you need to do is just add up the dots. Adding the number of observations in each range should be true
nvm someone answered lol good luck!
(x – 5)² + (y + 11)² = 49
a. What type of conic is this?
b.What is the center?
c. What is the radils?
d. What is the area of this shape?
Help pleaseee
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A
The equation is in the form of [tex](x-h)^2+(y-k)^2=r^2[/tex], which happens to be the equation of a circle
Part B
For the equation of the circle, its center is at [tex](h,k)\rightarrow(5,-11)[/tex]
Part C
Since [tex]r^2=49[/tex], then the radius of the circle is [tex]r=7[/tex]
Part D
The area of a circle is [tex]A=\pi r^2[/tex], so the area is [tex]49\pi[/tex] square units.
A battery for an underwater drone is in the shape of a square prism is designed to draw in
searates that is then used to produce energy. The base of the battery has soe lengths of 15 centimeters and the heght of the
bertery is 10 centimeters. Find the volume of the battery.
Answers
Answer:
2250 cm^3
Step-by-step explanation:
Volume of sq prism - Base x Base x Height
15 x 15 x 10 = 2250
Help picture below problem 8
Answers
Answer:
C. never
Step-by-step explanation:
A trapezoid has exactly one pair of opposite sides parallel.
A parallelogram has exactly two pairs of opposite sides parallel.
A trapezoid is never a parallelogram.
Find the measure picture below
Answers
By the vertical angle theorem, angle K is equal to the angle of measure 28 degrees.
--> so k is 28 degrees
Def. of vertical angle theorem: states that the opposite (vertical) angles of two intersecting lines are congruent
Hope that helps!
can someone tell me the answer
Answers
Answer:
A. 9/25
Step-by-step explanation:
There are a total of 25 T-shirts, which means that the denominator of the fraction is going to be 25 (which already rules out B and C). In the information they give us, they said that there are 9 red shirts. Therefore, the numerator will be 9. Our complete fraction is 9/25, or A.
I hope this helps! Have a lovely day!! :)
5. You get a car loan for $13,000 to buy a used car. The car dealer who gives you the loan charges
8.4% interest, compounded monthly, for 4 years.
(a) What's the total amount you will have to pay back for this loan?
(b) What is your monthly payment for this loan?
Answers
Answer:
Total = $15,351.10
Monthly = $319.81
A recipe called for using 5 1/8 cups of flour before baking and another 8 7/9 cups after baking. What is the total amount of flour needed in the recipe?
Answers
Answer: 13 [tex]\frac{65}{72}[/tex]
Step-by-step explanation:
This question is asking us to find the total flour used, so we will add the two amounts together.
5 1/8 + 8 7/9
-
5 + 8 = 13
1/8 + 7/9 = 9/72 + 56/72 = 65/72
-
13 + 65/72 = 13 [tex]\frac{65}{72}[/tex]
The recipe calls for 13 [tex]\frac{65}{72}[/tex] cups of flour.
Suppose that at some future time every telephone in the
world is assigned a number that contains a country code
1 to 3 digits long, that is, of the form X, XX, or XXX,
followed by a 10-digit telephone number of the form
NXX-NXX-XXXX (as described in Example 8). How
many different telephone numbers would be available
worldwide under this numbering plan?
Answers
Using the Fundamental Counting Theorem, it is found that [tex]1.11 \times 10^{13}[/tex] different telephone numbers would be avaiable worldwide.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the code, considering that for each digit there are 10 possible outcomes, the number of options is [tex]n_1 = 10 + 10^2 + 10^3 = 1110 = 1.11 \times 10^3[/tex].For the number, there are 10 digits, each with 10 options, hence the number of options is [tex]n_2 = 10^{10}[/tex].Hence, the number of different telephone numbers that would be avaiable is given by:
[tex]N = n_1n_2 = 1.11 \times 10^3 \times 10^{10} = 1.11 \times 10^{13}[/tex]
[tex]1.11 \times 10^{13}[/tex] different telephone numbers would be avaiable worldwide.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
i need help with this
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
In the given figure, Angle y is equal to Angle adjacent to 52° and 90° by Vertical opposite angle pair
And since they for straight line, their Angle sum will be equal to 180°
that is :
[tex]\qquad \tt \dashrightarrow \:y + 52 + 90 = 180[/tex]
[tex]\qquad \tt \dashrightarrow \:y + 142 = 180[/tex]
[tex]\qquad \tt \dashrightarrow \:y = 180 - 142[/tex]
[tex]\qquad \tt \dashrightarrow \:y =38 \degree[/tex]
Answer:
y = 38°
Step-by-step explanation:
We know that the angles in a straight line are added up to 180°.
So,
90 + y + 52 = 180
142 + y = 180
y = 180 - 142
y = 38°
Three students measured the heights of the daffodils they are growing.
2/3
Sofia's daffodil is 4/6
of a foot high
Mateo's daffodil is
of a foot high.
3/8
Deshawn's daffodil is
of a foot high
Which statement correctly compares two of these fractions?
L
Answers
PLEASE HELP 50 POINTS OLUS BRAINLY
Answers
Answer: 4n-7
Step-by-step explanation:
Help with tthis photo pls T.T
Answers
Answer:
1. False
2. Not sure
3. True
Statement A
A = bh/2
34 = (10)h/2
68/10 = h
h = 6.8
FALSE The actual height of the triangle is the hypotenuse of the fake outer triangle. 6.8 is not used to calculate the area.
Statement B
A = (d1 + d2)/2
56 = (d1 + d2)/2
112 = d1 + d2
I have no idea for this one. There is no way that I know of to verify the area if I don't have at least one diagonal.
Statement C
A = (a + b)(h)/2
24 = (7 + 9)(3)/2
48 = (7 + 9)(3)
16 = 7 + 9
16 = 16
TRUE Area of the trapezoid = 24 in².
The value of (2i3)3 is
IS
Answers
Answer:
Assuming you mean (2^3)3, the answer is 24
Step-by-step explanation:
using pemdas you do 2 to the third power first
2x2=4 4x2=8
then you mutiply by the number not in parenthesis; 3
8x3 = 24
Find the measure picture attached
Answers
Answer:
30
Step-by-step explanation:
90 - 60 = 30
the average of 15 pupils in a room is 11. if a man of 27 years enter the room. what will be the new average age?
Answers
Answer:
12
Step-by-step explanation:
→ Find the total age of the children
15 × 11 = 165
→ Add the mans age
165 + 27 = 192
→ Divide by 16
192 ÷ 16 = 12
what is derivative of f=x^3 + x^2
Answers
Answer:
3x^2-2x
Step-by-step explanation:
what is probability scale to the sea will disapper
Answers
Which expression is equivalent to (x – 4)(2x2 – 3x + 7)?
A. -4x(2x2 – 3x + 7)
B. x(2x2 – 3x + 7) - 4
C. x(2x2 – 3x + 7) + 4(2x2 – 3x + 7)
D. x(2x2 – 3x + 7) - 4(2x2 – 3x + 7)
Answers
Answer:
A:
-4x(2x2 – 3x + 7)
Step-by-step explanation:
This stem and leaf plot shows the height of several trees.
Height in Feet and Inches of Several Trees
5 || 8
6|| 2,3,7,8,9,9
7 || 0,1,4,5
8 ||6,7,8,9,10
What is the number of trees that are LESS than 7 feet tall?
Question Help: Message instructor
Submit Question
Answers
Answer:
7 trees.
Step-by-step explanation:
Number < 7 ft consists of the first 2 stems:
5 || 8 - 1 tree
6|| 2,3,7,8,9,9 - 6 trees
= 1 + 6
= 7.
The number of trees that are less than 7 trees as shown in the stem-and0leaf plot is: 7 trees.
What is a Stem-and-leaf Plot?In a stem-and-leaf plot, data points are represented in leaves and stems. For example, representing height of trees as 5 || 8, means a data point representing a height of a tree measuring 5 ft and 8 inches tall.
From the stem-and-leaf plot given, the data points that are below 7 feet are 7 in number, which range from 6 ft and 9 inches down to 5 ft and 8 inches.
The answer is: 7 trees.
Learn more about stem-and-leaf plot on:
https://brainly.com/question/8649311
#SPJ6
1/3 + 1/3=
5/10-2/10=
=
4/5-2/5=
11+1=
=
Answers
Answer:
Step-by-step explanation:
1/3 + 1/3= 2/3
5/10-2/10=3/10
4/5-2/5=2/5
11+1=12
You work 44 hours at Candelaria's Tortilla Factory (CTF), You earn $15.00 per hour and you get paid 1.5 times
your base rate for hours worked over 40 hours. You pay 6.25% for Social Security, and 1.45% for Medicare.
You also pay $83.00 for your health insurance. You also put 3% of your gross pay into 401(k). How much is
your take home pay?
Answers
Answer:
$537.87
Step-by-step explanation:
First, we need to determine our total pay which will be 40 hours times our $15 per hour to be $600. For the extra hours above 40, we are payed 1.5 times as much.
$15 * 1.5 = $22.5 * (44-40) = $90 additional pay
$600 + $90 = $690 total pay
Now, we calculate all of our deductions.
Subtract social security to be
690 * (1-0.0625) = $646.875
Medicare Deduction
646.875 * 0.9855 = $637.50
Health Insurance
$637.50-83 = $554.50
401k Deduction
$554.50 * 0.97 = $537.87
which combinations hold the same amount of liquid as an 8-pint bowl
Answers
1 quart = 32 fl oz
1 pt = 16 oz
Using these conversions you will multiply the number of quarts or pints by the number of ounces in each and then add the totals together to find if they equal 128 oz.
C. 4 x 32 = 128 oz
D. 2 x 32 + 8 x 8 = 128 oz
E. 3 x 32 + 2 x 16 = 128 oz
2. 28 - 3t = 10
Work out the value of t.
Answers
Answer:
t = 6
Step-by-step explanation:
28 - 3t = 10
-3t = 10 - 28
-3t = -18
t = -18/-3
t = 6
Note: (-)/(-) = +
Answer:
t=6
Step-by-step explanation:
—3t=—18
t=6
PLEASE HELP NOW I WILL FOLLOW AND GIVE BRAINLIST
Answers
Answer:
[tex] \frac{2}{5} [/tex]
Step-by-step explanation:
[tex] \frac{4}{10} = \frac{2}{5} [/tex]
good luck
Answer/Step-by-step explanation:
At least, meaning 2 1/2 or more
Now, I'm not exactly sure how they want it written so it could be two answers.
4/10
OR
4
Hope this helps :)