m angle PQS= 3x; m angle SQR=5x-20
Find x
Let as consider the complete ques is : Ray QS bisects ∠PQR. Solve for x and find m∠PQR. m∠PQS = 3x ; m∠SQR = 5x-20.
Given:
Ray QS bisects ∠PQR.
m∠PQS = 3x
m∠SQR = 5x-20
To find:
The value of x and m∠PQR
Solution:
Ray QS bisects ∠PQR. So,
[tex]m\angle PQS=m\angle SQR[/tex]
[tex]3x=5x-20[/tex]
[tex]3x-5x=-20[/tex]
[tex]-2x=-20[/tex]
[tex]x=10[/tex]
The value of x is 10.
Now,
[tex]m\angle PQR=m\angle PQS+m\angle SQR[/tex]
[tex]m\angle PQR=3x+5x-20[/tex]
[tex]m\angle PQR=8x-20[/tex]
Put x=10,
[tex]m\angle PQR=8(10)-20[/tex]
[tex]m\angle PQR=80-20[/tex]
[tex]m\angle PQR=60[/tex]
Therefore, the m∠PQR is 60 degrees.
What is 128,073 to the nearest thousand
There are nine different positions on a baseball team. If a team has 17 players how many different line-ups can the team make? (Assume every player can play every position.) The team can make different line-ups. Baseball games consist of nine innings. A team wants to change its line-up every inning. If no game goes to extra innings, and a season consists of 147 games, how many complete seasons can the team play without repeating a line-up? The team can play complete seasons without repeating a line-up. (Your answer should be an integer.)
Answer:
A) 24310
B) 18 seasons
Step-by-step explanation:
A) We are given the team has 17 players and there are 9 different positions in the team.
This is a combination question and thus, the number of different line-ups the team can make is;
C(17, 9) = 24310
B) We are told the basketball games consists of 9 innings.
Thus,
Number of games you can fill = 24310/9 = 2701.1111
And then we are told a season consists of 147 games.
Thus;
Number of complete seasons can the team play without repeating a line-up =
2701.1111/147 ≈ 18 seasons
Answer:
a
Step-by-step explanation:
HELP QUICK
Remove grouping symbols and combine like terms.
4a2 - 3[2b - 3b(b - 1)]
Answer:
[tex]4a^{2} + 9b^{2} + 3b[/tex]
Step-by-step explanation:
Distributive Property
[tex]4a^2 - 3(2b - 3b^{2} + 3b)[/tex]
Distributive Property
[tex] {4a}^{2} - 6b + 9b^{2} + 9b[/tex]
Combine Like Terms
[tex]4a^{2} + 9b^{2} + 3b[/tex]
A spinner with 6 equally sized slices is shown below. (2 slices are yellow, 1 is blue, and 3 are red.) The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow slice?
Answer:
1/3
Step-by-step explanation:
We have 6 slices
2 are yellow
P ( yellow) = number of yellow / total
= 2/6
= 1/3
Answer:. 1/3 probability that it stops on yellow.
Step-by-step explanation:
There are 6 possible outcomes. 2 are the incidents that you are looking for.
Make a ratio 2:6 or a fraction 2/6
Then simplify or reduce the fraction. 2/6 = 1/3
"Find y". I got this wrong and want to understand why and how to do the problem. Can someone please help?
Answer:
[tex]y=\frac{15\sqrt{3} }{4}[/tex]
Step-by-step explanation:
Well what you have here are two right triangles within another right triangles created by an altitude. This results in 3 similar triangles (see attached for reference)
As a result , using the properties of similar triangles, and taking ratios of their sides of the medium triangle and the largest triangle, we can form the following relationship:
[tex]\frac{b}{z}=\frac{y}{x} = \frac{z}{a+b}[/tex] (we know that a+b = 15), hence the equation becomes:
[tex]\frac{b}{z}=\frac{y}{x} = \frac{z}{15}[/tex] ----------eq 1
If we consider the largest triangle, we will see that
cos 30° = z / 15
but from our special angles (see second attachment) we know that cos 30° = (√3)/2
hence
(√3)/2 = z / 15
z = (15√3) / 2 --------eq 2
from the same largest triangle, we will also see that
sin 30° = x / 15
similarly from our special angles, we know that sin 30° = 1/2
hence,
1/2 = x/15
x = 15/2 --------eq 3
now that we have values for x and z, we can neglect the first term of equation 1 and form an equality with x, y and z
[tex]\frac{y}{x} = \frac{z}{15}[/tex]
[tex]y = x\frac{z}{15}[/tex] (substituting the values for x and z that we found above)
y = (15/2) · [ (15√3) / 2] / 15
y = (15√3) / 4
[tex]y=\frac{15\sqrt{3} }{4}[/tex]
If 3(y + 12) = 24, find the value of 18y.
How do I isolate R?
S = (HR(Wi - Wn)) / 1000.
First, multiply both sides by 1000.
1000S = HR(Wi - Wn)
Divide bot sides by H(Wi - Wn)
(1000S) / H(Wi - Wn) = R
Subtract.(–3x2+4x4–8x)–(–6x+3x4+2)
Answer:
x⁴ - 3x² - 2x - 2
Step-by-step explanation:
Step 1: Write out expression
(-3x² + 4x⁴ - 8x) - (-6x + 3x⁴ + 2)
Step 2: Distribute negative
-3x² + 4x⁴ - 8x + 6x - 3x⁴ - 2
Step 3: Combine like terms (x⁴)
x⁴ - 3x² - 8x + 6x - 2
Step 4: Combine like terms (x)
x⁴ - 3x² - 2x - 2
The inverse of f(x) = 2x + 3 is
O True
O False
The inverse of f (×) =2× + 3 is
yes it is true
A customer at a Mexican diner placed an order for 3 burrito bowls. He also ordered 2 plates of corn tacos at $12.96 each. He was billed
a total of $45.42.
Answer:
$6.05 for each burrito bowl
Step-by-step explanation:
12.96+12.96=25.92
45.42-25.92= 19.5
19.5/3= 6.5
You have 1/8 of a box of erasers and you need to share them with 3 total people, including yourself. What fraction of the box should each person get?
Answer:
each person should get 1/24th or 0.0417
Step-by-step explanation:
X
A spinner is divided into 4 equal sections labeled with the numbers 1 through 4. The tree
diagram represents all of the possible outcomes of spinning the spinner twice. Use the drop-
down menus to complete the statements about the possible outcomes.
Answer:
Step-by-step explanation:the first one is 8
Second 3 3- 6
1) There are total 16 possible outcomes.
2) There are 6 possible outcomes for spinning two numbers that have sum greater than 5.
3) There are 4 possible outcomes for spinning the same number twice.
What is probability?" Probability is a branch of mathematics which represents the all possibilities. It is defined as the ratio of total number of favourable outcomes to the total number of outcomes of the particular event."
According to the question,
A spinner is divided into 4 equal sections that is 1 to 4.
As per the diagram,
All possible outcomes are as follow:
{ (1 ,1), ), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4),(4,1),(4,2),(4,3), (4,4) }
1) Total possible outcomes = 16
2) Possible outcomes for spinning two numbers that have sum greater than 5 are (2,4), (3,3), (3,4), (4,2), (4,3), (4,4)
Therefore,
Total Possible outcomes for spinning two numbers that have sum greater than 5 = 6
3) Possible outcomes for spinning the same number twice are (1,1), (2,2), (3,3), (4,4)
Therefore,
Total Possible outcomes for spinning the same number twice = 4
Hence,
1) There are total 16 possible outcomes.
2) There are 6 possible outcomes for spinning two numbers that have sum greater than 5.
3) There are 4 possible outcomes for spinning the same number twice.
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#SPJ2
2.4 times (-8.3) how much would it equal
it would equal -19.92
Answer:
= −19.92
Step-by-step explanation:
Can someone please help me out?
Answer:
S=46.6
Step-by-step explanation:
x is the number of years :
from 1998 to 2020 = 22 years
S-1.9x=4.8
S-(1.9)(22)=4.8
S=4.8+41.8
S=46.6
10 decreased by twice a is 23
THERE YOU GO I HAVE TO TYPE WORDS
what is 5/6 divided by 5/9
Answer:
1 and 1/2
Step-by-step explanation:
Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.
1.5 as a decimal
1 1/2 as a fraction
BRAINLIEST!!Felicia had $80 when she went to a music store that charges $18 for each CD. She needs to have no less than $20 in her wallet when she leaves the store so she has enough money to buy gas for the ride home.
Which shows a possible number of CDs she could buy? Select three options.
1
2
3
4
5
Answer:
The possible number of CDs she could buy is 1, 2, and 3.
Step-by-step explanation:
First, you have to make an equation to solve to find the answer(s):
80 - (18 · x) ≥ 2080 is how much money Felicia has; 18 is for the cost of each CD; x is for the number of CDs; ≥ is no less; and 20 is how much money Felicia needs to have left.1.) 80 - (18 · 1) ≥ 20
80 - 18 · 1 ≥ 20
80 - 18 ≥ 20
62 ≥ 20
Since 62 ≥ 20 is always true, there are infinitely many solutions.
2.) 80 - (18 · 2) ≥ 20
80 - 18 · 2 ≥ 20
80 - 36 ≥ 20
44 ≥ 20
Since 44 ≥ 20 is always true, there are infinitely many solutions.
3.) 80 - (18 · 3) ≥ 20
80 - 18 · 3 ≥ 20
80 - 54 ≥ 20
26 ≥ 20
Since 26 ≥ 20 is always true, there are infinitely many solutions.
4.) 80 - (18 · 4) ≥ 20
80 - 18 · 4 ≥ 20
80 - 72 ≥ 20
8 ≥ 20
Since 8 ≥ 20 is false, there is no solution.
5.) 80 - (18 · 5) ≥ 20
80 - 18 · 5 ≥ 20
80 - 90 ≥ 20
- 10 ≥ 20
Since - 10 ≥ 20 is false, there is no solution.
Answer:
1,2,3
Step-by-step explanation:
If h(x)=-3x^2-4 and k(x)=4x-3, find h(k(2))
Answer:
-79
Step-by-step explanation:
Set up the composite function and simplify.
find the end point m
What decimal number is illustrated?
Answer:
0.28
Step-by-step explanation:
Using 2 shapes, how many 5-place patterns can be made
Answer:
Step-by-step explanation:
3
The projected number of people aged 65 and over in the U.S. population with Alzheimer's disease (in millions) is given byP(t) = −0.0002083t 3 + 0.0157t 2 – 0.093t + 5.2 (4 ≤ t ≤ 40);Where t is measured in years and t = 4 corresponds to the year 2014. This model does not claim validity for years 2051 and beyond. Nevertheless, the model does suggest that:
The missing part of the question is;
What is the projected number of people aged 65 and over with Alzheimer's disease in 2030 and in 2050
Answer:
In 2030, P(20) = 7.9536 (in millions)
In 2050, P(40) = 13.2688 (in millions)
Step-by-step explanation:
We are given that;
Number of people aged 65 and over in the U.S. population with Alzheimer's disease (in millions) as;
P(t) = −0.0002083t³ + 0.0157t² – 0.093t + 5.2 (4 ≤ t ≤ 40);
Where t is measured in years and t = 4 corresponds to the year 2014.
Now,
Since t = 4 represents 2014,therefore;
t = 20 would represent population in 2030
Thus in year 2030;
P(20) = −0.0002083(20)³ + 0.0157(20)² – 0.093(20) + 5.2
P(20) = 7.9536 (in millions)
Also, in year 2050, t will correspond to 40 years.
Thus;
P(40) = −0.0002083(40)³ + 0.0157(40)² – 0.093(40) + 5.2
P(40) = 13.2688 (in millions)
Jane wants to determine the shortest route from her home to her workplace.
She walks only on the sidewalks indicated by dotted lines on the map. What is
the distance of the shortest route from home to work to the nearest block?
(IMPORTANT NOTE - 1) Turn radicals into decimals. 2) Do not round decimals
until the very end of the problem).
HELP PLEASE I have no idea how to do this
Answer:
did anyone figure this out
The distance between two points on a plane can be found by Pythagoras's theorem.
The shortest route from her home to her workplace is the route that passes along the block in the middle of the graph ,which is approximately 2.5 blocks shorter, than the apparently next shortest route.
Reason:
The shortest distance between two points is a straight line.
The shortest route to her workplace are the routes that approximate a straight line the most.
Following the dotted lines, there are two routes, that are approximately direct and therefore short routes to her workplace which are;
The route heading past the block close to the center of the map to her workplaceThe route to the left of the above routeTaking the route that passes close to the center of the map to her workplace ,gives;
Path 1 = √(2² + 4²) = 2·√5 (by Pythagoras's theorem)
Path 2 = √(1² + 2²) = √5
Path 3 = 1 + 1 = 2
Path 4 = √(2² + 3²) = √13
Path 5 = 3
Cumulative distance = 2·√5 + √5 + 2 + √13 + 3 ≈ 15.3
Taking the route to the left of the above route, gives;
Path 1 = √(2² + 4²) = 2·√5
Path 2 = 7 + 6 = 13
Cumulative distance = 2·√5 + 13 ≈ 17.5
Therefore, the shortest route is the route that heads to her workplace, through, close to the center of the map, which approximately 17.5 blocks - 15.3 blocks = 2.5 blocks shorter
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Someone help me solve this plz
Answer:
Slope of it is 6
Step-by-step explanation:
Slope is on the graph going up to the 6 and then to the 4
Rewrite the expression −7/8 − 2 1/4 as the sum of two numbers.
Answer:
-3 1/8.
Step-by-step explanation:
−7/8 − 2 1/4
= -7/8 + -9/4
= -7/8 - 18/8
= -25/8
= -3 1/8.
PLS HELP I DONT UNDERSTAND :( WILL GIVE BRAINLIEST !!!
the answer is c
i already done it
Answer:
1/3 would be your answer
Step-by-step explanation:
anyway have a great day
-5(5 – 2x) = -95
show work and all steps please
Answer:
x = -7
Step-by-step explanation:
See the photo attached.
If h(x) = 6 - X, what is the value of (nºn)(10)?
Answer:
(h°h)(10) = 10
Step-by-step explanation:
(h°h) = 6-(6-x) = x
h(10) = x
x = 10
The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $13 per month plus $0.04 per call.
Answer:
Is there anything else to add onto the question? What are you trying to find :)?