The standard form of a line:
[tex]Ax+By=C[/tex]
We have the equation of a line in the slope-point form:
[tex]y-3=\dfrac{1}{2}(x+6)[/tex] use distributive property
[tex]y-3=\dfrac{1}{2}x+3[/tex] add 3 to both sides
[tex]y=\dfrac{1}{2}x+6[/tex] multiply both sides by 2
[tex]2y=x+12[/tex] subtract x from both sides
[tex]-x+2y=12[/tex] change the signs
[tex]x-2y=-12[/tex]
find m ∠RPS
(Image below)
∠RPS=___
RPS is 90 degrees because of the vertical line theorem... opposite angles are always congruent.
Answer: RPS is 90 degrees
Step-by-step explanation:
Jeff has a rain gauge that shows 1 3/4 inches of rain. After it rains, the gauge shows 5 1/4 inches of rain. How much rain fell between the two readings?
A) 4 1/2 in.
B) 3 1/2 in.
C) 2 1/2 in.
D) 2 1/4 in.
That is 5 1/4 - 1 3/4
= 21/4 - 7/4
=14/4
= 3 1/2 inches
Jim drove 436 miles using 16 gallons of gas. At this rate, how many limes would he drive using 14 gallons of gas?
Bank card is charging 1.4% monthly interest on credit card charges. If you charged a $175 pair of running shoes on the card and did not pay it off this month, what would be the interest for the shoe charge? $2.45 $245 $4.90 $24.50
Answer:
Option A : the interest for the shoe charge is $2.45.
Step-by-step explanation:
As given, Bank card is charging 1.4% monthly interest on credit card charges.
This amount is charged on $175.
We have the interest value as :
[tex]0.014\times175=2.45[/tex] dollars
Hence, the interest for the shoe charge is $2.45.
the ratio of boys to girls at the beach cleanup was 7:8. If there were 43 boys, how many girls were there?
Plz Answer ASAP...thx! (20 points)
Two airplanes left the same airport and arrived at the same destination at the same time. The first airplane left at 8:00 a.m. and traveled at an average rate of 496 miles per hour. The second airplane left at 8:30 a.m. and traveled at an average rate of 558 miles per hour. Let x represent the number of hours that the first plane traveled.
How many hours did it take the first plane to travel to the destination?
(Write an equation)
Use the following information for problems 1 – 3. Suppose you sign a contract for an annual salary of $50,000 with a guaranteed raise of 5% each year.
1. Write your salary for the next n years as a geometric sequence in explicit form.
2. What will your salary be in year 5?
3. How much will you have earned in total salary by the end of your 10th year?
Initial salary = $50,000 .
Rate of raise = 5% each year.
Therefore, each next year salary would be 105% that is 1.05 times.
5% of 50,000 = 0.05 × 50000 = 2500.
Therefore raise is $2500 each year.
According to geometric sequence first term 50000 and common ratio 1.05.
Applying geometric sequence formula
[tex]a_n = ar^{n-1}[/tex]
1) [tex]a_n = 50000(1.05)^{n-1}[/tex]
2) In order to find salary in 5 years we need to plug n=5, we get
[tex]a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4[/tex]
= 50000(1.21550625)
=$60775.3125.3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.
[tex]S_n = \frac{a(1-r^n}{1-r}[/tex]
Plugging n=10, a = 50000 and r= 1.05.
[tex]S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}[/tex]
[tex]S_10 = \frac{50000(0.050)^{10}}{0.05}[/tex]
= 628894.62678.
Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.On a recent day 8 euros were worth $9 and 24 euros were worth $27 write an equation of the form y equals kx to show the relationship between the number of euros and the value in dollars.
Answer:
y=8x/9
Step-by-step explanation:
Given that 8 euros were worth $9 and
24 euros were worth $27.
Let y represent the number of Euros and x no of dollars.
Given that the relation is of the form y = kx+C
When x=0 y =0,
i.e. C =0
Hence equation is of the form y = kx
Substitute x=8 and y =9
We get 9 = 8k
Or k =8/9
Hence relation is y=8x/9 is the relation between x and y.
WE can verify this for 27 dollars worth 24 euros.
24 =8/9(27) is true.
Thus equation is verified.
What conclusion can you draw about the relative frequency of these results?
A) If you are a boy in this group, you are more likely not to eat cereal for breakfast than to eat cereal.
B) If you are a girl in this group, you are more likely to eat cereal for breakfast than not.
C) If you eat cereal for breakfast, you are a boy.
D) Knowing if a person eats cereal will help determin gender.
B) If you are a girl in this group, you are more likely to eat cereal for breakfast than not.
What is the value of x, given that Line of PQ║line BC?
A. 26
B. 15
C. 13
D. 11
The value of x is option C. 13.
What is Triangle Proportionality Theorem?The triangle proportionality theorem states that if a line is drawn inside the triangle which is parallel to any side of the given triangle, then the line intersects other two sides at two different points. Then the division of the other two sides of the triangle will be in the same ratio.
Given is a triangle ABC.
A line PQ is drawn which is parallel to the line BC.
We have to find the value of x, which is the length of AQ.
Using the triangle Proportionality theorem,
AP / PB = AQ / QC
Substituting the values,
6 / 12 = x / 26
Cross multiplying,
12x = 6 × 26
x = 156 / 12
x = 13
Hence the value of x is 13.
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Does This Table Represent a function? Why Or Why Not?
Yes, this table represents a function.
Step-by-step explanation:Function--
It is a set of ordered pair of the type: (x,y) in which each input variable i.e. x is mapped to a single output i.e. y.
i.e. each of the value of x is mapped to a single y.
Here after looking the table we observe that each of the value of the independent variable i.e. Hours of training is mapped to a single value of the dependent variable i.e. monthly pay.
Amina used the quadratic formula to solve an equation. Her result shows two solutions that are complex numbers with imaginary parts. Which expression could be Amina's result?
The expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]
Which expression could be Amina's result?
From the question, we have the following parameters that can be used in our computation:
The list of options
Also, we have that
Her result shows two solutions that are complex numbers with imaginary parts
This can be expressed as
[tex]x = \dfrac{a \pm i\sqrt{b}}{c}[/tex]
From the list of options, the expresion that are of the above form are
[tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]
hence, the expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]
Question
Amina used the quadratic formula to solve an equation. Her result shows two solutions that are complex numbers with imaginary parts. Which expression could be Amina's result?
The graph shows a car's value as a function of its age.
What was the value of the car in Year 2?
Enter your answer in the box. Do NOT enter a dollar sign or a comma in your answer.
You wish to have $3000 in 2 years to buy a fancy new stereo system. How much should you deposit each quarter into an account paying 8% compounded quarterly?
Answer:
Deposit each quarter = $342.68
Step-by-step explanation:
Formula use in this problem:
[tex] FV=C\times \left [ \frac{(1+i)^n-1}{i} \right ]\times (1+i) [/tex]
Where,
FV is future value, FV=$3000
C is cash flow quarterly( need to find),C=?
I is rate of interest ( divide by 4), i=[tex] \frac{0.08}{4}=0.02 [/tex]
N number of cash flow, n=8
Substitute all these values into formula to solve for C
[tex] 3000=C\times \left [ \frac{(1+0.02)^8-1}{0.02} \right ]\times (1+0.02) [/tex]
[tex] C=\frac{3000\times 0.02}{[(1+0.02)^8-1]\times (1+0.02)}[/tex]
So, C=$342.68
Final answer:
To achieve $3000 in 2 years in an account with 8% interest compounded quarterly, you should deposit $364.11 each quarter.
Explanation:
To find out how much you need to deposit each quarter to have $3000 in 2 years in an account that pays 8% interest compounded quarterly, you would use the future value of a series formula given by:
S = R [((1 + i)^n - 1) / i]
Where:
S = the future value of the series (in this case, $3000)
R = the regular deposit amount per period (what we're solving for)
i = the interest rate per period (8% per year or 0.08 divided by 4 for quarterly = 0.02)
n = the total number of compounds over the period (2 years * 4 quarters/year = 8 compounds)
Plugging in our values:
$3000 = R [((1 + 0.02)^8 - 1) / 0.02]
$3000 = R * [((1.02)^8 - 1) / 0.02]
$3000 = R * 8.2432
So, solving for R, we get:
R = $3000 / 8.2432 = $364.11
Therefore, to have $3000 in 2 years with an account that pays 8% interest compounded quarterly, you need to deposit $364.11 at the start of each quarter.
In a factory, a certain machine needs 10 min to warm up. it takes 15 min for the machine to run a cycle. the machine can operate for as long as 6 h per day including warm up time. Draw a graph showing the total time the machine operates during 1 day as a function of the number of cycles it runs.
-What domain and range are reasonable?
-Is the function a linear function?
Answer:
[tex]y =\frac{1}{6} + 0.25x[/tex]
[tex]0 \leq x \leq23.33[/tex]
[tex]0 \leq y \leq 6[/tex]
Step-by-step explanation:
The machine always takes 10 minutes (or 1/6 hours) to warm up and performs each cycle in 15 minutes, or 0.25 hours.
The maximum amount of daily hours that the machine can work is 6 hours.
Therefore we can represent this situation by means of an equation of the form:
[tex]y =\frac{1}{6} + 0.25x[/tex]
Where
y = daily amount of hours the machine works.
x = number of daily cycles performed.
This equation is a linear function. Because it has the form y = ax where a is a real number
The graph of this equation is shown in the attached image, where the gray shaded area represents the domain of the function.
The domain of the function is:
[tex]x\geq 0[/tex] (because you can not perform less than zero cycles a day)
[tex]x \leq23.33[/tex]. Because the machine can not exceed 6 hours per day, then it can not do more than 23.33 cycles.
So:
[tex]0 \leq x \leq23.33[/tex]
The range of the function is:
[tex]y \geq 0[/tex] (because you can not work less than 0 hours a day)
[tex]y \leq 6[/tex] (because the machine can not work more than 6 hours a day)
So
[tex]0 \leq y \leq 6[/tex]
larry is flying at an altitude of 3,000 feet above ground level. Ground level is 188 feet above sea level. If he descends 567 feet and then climbs 120 feet, how far above sea level is larry? A) 2,692 feet b) 2,741 feet c) 3,041 feet d) 3,259 feet
Larry is 2365 feet above sea level. Hope this helps :o
Answer: the answer is b 2,741 sorry im late
What’s the answer? (SOMEONE PLEASE HELP ME)
x = - [tex]\frac{7}{4}[/tex] or x = 0
take out a common factor 2x
2x(4x + 7 ) = 0
equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
4x + 7 = 0 ⇒ x = - [tex]\frac{7}{4}[/tex]
a company is planning to hire 12 new employees a simulation is run to determine 12 random birthdays using numbers to represent the days of the year (january 1 = 1 through december 31 = 365) based on the simulation what is the probability that a randomly selected employee will have a birthday in the first 100 days of the year?
344 180 274 358 64 121 32 96 151 275 93 49
(Please help and tell me how I do this)
Answers are
0.417
0.583
0.333
0.120
344 180 274 358 64 121 32 96 151 275 93 49
Out of the 12 numbers above, 5 (in bold type) are 100 or less.
5/12 = 0.41666...
Answer: 0.417
The probability that an employee selected randomly has a birthday in the first 100 days is 0.417
Recall :
Probability = required outcome / Total possible outcomes
Total possible outcomes :
344 180 274 358 64 121 32 96 151 275 93 49 = 12Required outcomes :
Values less Than or equal to 100 : 64, 96, 32, 93, 49 = 5Therefore,
P(first 100 days) = 5 / 12 = 0.41666Therefore, the selection probability is 0.417
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Which equation has the solution x = 3?
1 point
−4x + 6 − 3x = 12 − 2x − 3x
4x + 6 + 3x = 12 + 2x + 3x
4x + 6 − 3x = 12 − 2x − 3x
4x + 6 − 3x = 12x + 2x + 3x
The regular nonagon has rotational symmetry of which angle measures? Check all that apply. 40° 45° 120° 240° 260° 320°
Answer:
The correct answers are 40, 120, 240, and 320
Step-by-step explanation:
.
Answer:
1 ,3 , 4, 6
Step-by-step explanation:
The perimeter of the triangle is 70cm the area of the triangle is a squared what is a squared
Sue wants to buy a video that costs $24.95. She has $3 in her pocket and a piggy bank full of quarters,x. Which inequality can be used to represent the number of quarters sue needs to buy the game?
Given
Sue wants to buy a video that costs $24.95.
She has $3 in her pocket
a piggy bank full of quarters x
Find out the inequality can be used to represent the number of quarters sue needs to buy the game.
To proof
As given in the question
Sue wants to buy a video that costs = $24.95.
She has $3
The value of quaters in the piggy bank = x
1 $ = 4 quaters
First convert $24.95 in the quaters form
= 4 × 24.95
= 99.8 quaters
convert $3 in the quaters form
= 3 × 4
= 12 quaters
The equation become in the form
[tex]12 + x \geq 99.8[/tex]
x = 87.8 quaters
quarters sue needs to buy the game is 87.8 quaters.
Hence proved
If John ran a 5 km marathon how long What is that in meters
1750932 x 2355435 x Y= ? 50pts
Simplify as much as possible
1,750,932 x 2,355,435 = 4,124,206,515,420
4,124,206,515,420 x Y cannot be simplified anymore, therefore,
4,124,206,515,420 x Y is your answer
~Rise Above the Ordinary, Senpai
All we need to do here is simplify, since there is no given answer to y. The numbers you've provided are quite large, so I'd suggest just using a calculator, unless they're supposed to be decimals. The simplified answer to this is 412,320,615,420y.
Please help me
10 points
1. 4x = 7(x - 3) 1.Given
4x = (7)(x) + (7)(-3)
2. 4x = 7x - 21 2.Distributive property
4x - 7x = 7x - 7x - 21
3. -3x = -21 3.Subtraction property of equality
-3x : (-3) = -21 : (-3)
4. x = 7 4.Division property of equality
please help asap 25 pts
your answer is A
hope this helps :)
A = [tex]\frac{1}{2}[/tex]bh
[tex]\frac{1}{2}[/tex] × (bh) = A
[tex]\frac{bh}{2}[/tex] = A
bh = A × 2
bh = 2A
b = [tex]\frac{2A}{h}[/tex]
The answer is a: b= [tex]\frac{2A}{h}[/tex]
For which situation is the use of approximate numbers most appropriate?
A) preparing your yearly taxes
B) ordering programs for a high school musical
C) paying a cashier for a meal at a fast food restaurant
D) the maximum number of basketball players allowed on the court at a time
Which transformation shows a translation of 3 units to the right?
It is the transformation shown in (B)
(look at one point of the letter P and how it moves precisely 3 units. Also there is only the move, no flipping of the figure)
Answer is B.
B shows a translation of 3 units to the right
please help me with this problem. image attached.
The answer is D, (3, -4)
the second longest bridge in the world, the tianjin grand bridge, is 373,000 feet long. Its length is 167,700 feet less than the length of the longest bridge in the world. What is the length of the longest bridge? Show your work.
The length of the longest bridge in the world is found by adding the length of the second longest bridge namely the Tianjin Grand Bridge, and the stated difference between the two bridges' lengths. After calculation, the length of the longest bridge in the world is found to be 540,700 feet.
Explanation:To find the length of the longest bridge in the world, we should add the length of the Tianjin Grand Bridge (the second longest in the world) and the difference between the two bridges. In this case, the length of the Tianjin Grand Bridge is 373,000 feet and it's stated that this is 167,700 less than the length of the longest bridge.
So, we have to do the following calculation: 373,000 feet (length of the Tianjin Grand Bridge) + 167,700 feet (difference in length) = 540,700 feet.
So, the length of the longest bridge in the world is 540,700 feet.
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