Answer:
[tex]x-2y=-12[/tex]
Step-by-step explanation:
Hi there!
1) Determine the equation of the line in slope-intercept form
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
Plug in the slope [tex]\frac{1}{2}[/tex]
[tex]y=\frac{1}{2}x+b[/tex]
Plug in the given point (6,9) and solve for b
[tex]9=\frac{1}{2}(6)+b\\9=3+b[/tex]
Subtract 3 from both sides
[tex]9-3=3+b-3\\6=b[/tex]
Plug 6 back into [tex]y=\frac{1}{2}x+b[/tex]
[tex]y=\frac{1}{2}x+6[/tex]
2) Rearrange the equation into standard form
Standard form: [tex]Ax+By=C[/tex] where A, B and C are integers and A is typically positive
[tex]y=\frac{1}{2}x+6[/tex]
Multiply both sides by 2 to remove the fraction
[tex]2y=1x+12\\2y=x+12[/tex]
Subtract x from both sides to isolate 12 as C
[tex]2y-x=x+12-x\\2y-x=12\\-x+2y=12[/tex]
Multiply both sides by -1 to make A positive
[tex]x-2y=-12[/tex]
I hope this helps!
What is the value of X
A. x=20
B. x=15
C. x=10
D. x=5
the product of 2 numbers, p and q, decreased by 3 times their sum. (as an algebraic expression)
Answer:
3 - (p*q) im not sure lol
Step-by-step explanation:
76. In the diagram below, lines land mare
parallel. Both are intersected by
transversal t.
What is the value of x?
lim x->1+( sin(1-x)-(e^(x-1))+1)/ lnx
We're given the one-sided limit,
[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}[/tex]
Evaluating the limand directly at x = 1 gives the indeterminate from
(sin(1 - 1) - exp(1 - 1) + 1) / ln(1) = 0/0
so we can potentially solve the limit by applying L'Hopital's rule. Doing so gives
[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}=\lim_{x\to1^+}\frac{-\cos(1-x)-e^{x-1}}{\frac1x}=\frac{-\cos(0)-e^0}{\frac11}=\boxed{-2}[/tex]
Triangle D E F is shown. Angle E F D is a right angle. The length of E F is 24 and the length of D F is 7.
Which trigonometric ratios are correct for triangle DEF? Select three options.
sin(D) = StartFraction 24 Over 25 EndFraction
cos(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 24 Over 7 EndFraction
sin(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 7 Over 24 EndFraction
Answer:
Sin(E) = 7/25
Sin(D) = 24/25
Tan(D)= 24/7
Step-by-step explanation:
Sin=opp/hyp
Tan=opp/adj
Cos=adj/hyp
The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
How to determine the trigonometric ratios?The given parameters are:
EF = 24
DF = 7
Start by calculating the length DE using:
DE²= EF² + DF²
So, we have:
DE²= 24² + 7²
Take the square root of both sides
DE= 25
The sine of the angles is calculated using:
sin(Ф) = opp/hyp
So, we have:
sin(E) = 7/25
sin(D) = 24/25
The tangent of the angles is calculated using:
tan(Ф) = opp/adj
So, we have:
tan(D)= 24/7
Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
Read more about trigonometric ratios at:
https://brainly.com/question/11967894
PLEASE HELP ASAP PLSSSSS !!!
Answer:
133 answer ---------------------------------------- helpful answer
ACTIVITY 1 Directions: Interpret these circle graphs
A. The pie graph below shows what a normal human body is made of.
Questions:
1. As shown in the graph,what composes the human body?
2. Which makes up the greatest part of the human body? the least?
Step-by-step explanation:
1) it is composed of 20% of fat, 17% of bone, 50% of muscle and 13% others(minerals)
2) muscle makes up the greatest part and the minerals makes up the least.
hope it heals u.
make me brain list Pls.
Simplify the given expression and enter in numerical form.6+5
Answer:
6+5=11
Step-by-step explanation:
6 is added to 5
i am sorry if i am wrong
Find the slope in each line
Ethan is 1.6 metres tall, Uzma is 154 cm tall.
Work out how much taller Ethan is than Uzma.
Answer:
1.6 metres is 160 centimetres
Ethan is 6 centimetres taller than Uzma
you toss six coins at the same time. how many possible outcomes are there?
64
36
12
6
Answer:
64 outcomes
Step-by-step explanation:
Let the number of coins be n.Let the number of outcomes per coin be X.Given the following data;
Number of coins = 6
Number of outcomes for a single coin = 2
A single coin comprises of a head (H) and a tail (T), thus, the number of outcomes for a single coin is two (2).
To find how many possible outcomes we would have from tossing six coins at the same time, we would use the following formula;
[tex] Number \; of \; outcomes = X^{n} [/tex]
Substituting the values, we have;
Number of outcomes = 2⁶
2⁶ = 2 * 2 * 2 * 2 * 2 * 2
2⁶ = 64
Number of outcomes = 64
Therefore, the number of outcomes for a single coin tossed at the same time is equal to sixty four (64). It would have a total of 32 heads (H) and a total of 32 tails (T).
Choose all of the symbols that make the following sentence true.
4 ^0 ___ 5 ^-1
=
<
≥
≤
≠
>
Answer:
≠ and >
Step-by-step explanation:
_________________
According to a government study, among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,020. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $456. Use Appendix B.3. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,600 per year on reading and entertainment
Answer:
z = x-u/s
z = 2600 - 2020/456
z = 1.27
= .897
1-.898 = .102
z > 1.27 = 10.2%
The percentage of adults spending more than $2,600 per year on reading and entertainment is 10.2%.
What is the z-score?The standard score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.
Given that according to a government study, among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,020. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $456.
The percentage will be calculated as,
z = x-u/s
z = 2600 - (2020/456)
z = 1.27
The value of z=1.27 in the table is 0.897. The percentage will be calculated as,
P = 1-.898 = .102
z > 1.27 = 10.2%
Therefore, the percentage of adults spending more than $2,600 per year on reading and entertainment is 10.2%.
To know more about z-score follow
https://brainly.com/question/25638875
#SPJ5
using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation 10.0y-4.55x=581. where x is the number of years after 2000 what is projected population in 2026?
Answer:
The projected population in 2026 is of 699.3 million.
Step-by-step explanation:
Population:
The population, in x years after 2000, is given by the follwing equation:
[tex]y - 4.55x = 581[/tex]
That is:
[tex]y(x) = 4.55x + 581[/tex]
What is projected population in 2026?
2026 - 2000 = 26, so this is y(26).
[tex]y(26) = 4.55(26) + 581 = 699.3[/tex]
The projected population in 2026 is of 699.3 million.
Please help me please please I really need help please please
A moving company charges $30 plus $0.15 per mile to rent a moving van. Another company charges $15 plus $0.20 per mile to rent the same van. For how many miles will the cost be the same for the two companies? Write and solve an equation.
Which is the graph of an even monomial function?
Answer:
The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.
Keith is looking at a cliff. He determines that the angle of elevation to the top is 70° from where he is at. 70m away from Keith, Alan estimates the angle between the base of the cliff, himself, and Keith to be 29° while Keith estimates the angle between the base of the cliff, himself, and Alan to be 48°. What is the height, h, of the cliff to the nearest tenth of a metre?
1) 78.8m
2) 83.9m
3) 89.0m
4) 95.7m
This question completely baffled me on my homework, I still haven't done it because I don't even know how to approach it (Since it's a 3D problem)
Please help me out
Also, this homework is due in an hour so I'm starting to sweat
9514 1404 393
Answer:
4) 95.7 m
Step-by-step explanation:
The angle at the cliff base between Alan and Keith is ...
B = 180° -29° -48° = 103°
The law of sines will tell you the distance KB from Keith to the cliff base is
KB/sin(A) = KA/sin(B)
KB = KA×sin(A)/sin(B) = (70 m)sin(29°)/sin(103°) ≈ 34.82935 m
The height of the cliff is found from the tangent relation ...
Tan = Opposite/Adjacent
tan(70°) = height/(34.83 m)
height = (34.83 m)tan(70°) = 95.693 m
The height of the cliff is about 95.7 m.
_____
Additional comment
These problems can usually be resolved into two 2-D problems. Here, we can work out the distance we need from Keith to the cliff by considering only the ground plan of the site. Then we can work out the height of the cliff only considering the vertical plane containing Keith and the base of the cliff.
The attachment shows the ground plan triangle KAB.
Jake wants to surprise his parents with a small anniversary party at their favorite restaurant.
It will cost $35.75 per person for dinner, including tip and tax.
His budget for the party is $600.
What is the maximum number of people Jake can have at the party without exceeding his budget?
Answer:
16 people
Step-by-step explanation:
35.75 times 16 is 572, times 17 is 607.75, he only has 600 and he cant have a fraction of a person, so he can have 16 people
if a student is selected at random, find the probability that the student is 14 year old
Answer:
If the student is selected at random the answer is if you put 14 years apart of the student selected at random means the answer are not apart.
Step-by-step explanation:
14 years selected the problem is that 14-9 is more then 9 and u add that up to get the right equation for the 14 years apart
please help step by step, please
9514 1404 393
Answer:
title: 300%payday: 650%check cashing: 214%Step-by-step explanation:
The formula for simple interest is ...
I = Prt
where P is the principal amount loaned, r is the annual rate, and t is the time in years. Solving for interest rate, we get ...
r = I/(Pt)
We assume 12 months or 52 weeks in a year.
__
Car title loan
r = 125/(500×1/12) = 3 × 100% = 300%
The APR is 300%.
__
Payday loan
r = 125/(500×2/52) = 6.5 × 100% = 650%
The APR is 650%.
__
Check cashing
r = 19.66/(478.41×1/52) ≈ 2.1369 × 100% ≈ 214%
The APR is about 214%.
Which of the following is a characteristic of a plane
Answer:
I think you meant to add a list of answers but didn't so here's the characteristics of a plane: Flat, two dimensional, extends infinitely, and is assembled about multiple points and lines.
Step-by-step explanation:
Answer:
If you are taking the FLVS test it is "Two endpoints"
Step-by-step explanation:
Just took the test
hope it helps :)
Tamara uses a coupon to save 20% off her purchase at the bookstore. The original cost of Tamara's purchase is d dollars.
Which expressions represent the cost, in dollars, of Tamara's purchase after using the coupon? Choose all that apply.
Answer:
The equation would be d - (d×0.2)
Meg makes a dot plot for the data 9, 9, 4, 5, 5, 3,
4,5, 3, 8, 8, 5. Where does a gap occur?
The gap consists of the values 6 and 7.
Check out the dot plot below to see what I mean. We have one cluster on the left from 3 to 5. Then another cluster on the right from 8 to 9.
Answer:
The gap is present around 6 & 7
Step-by-step explanation:
Since there is no evidence of dots above 6 & 7, there must have been a freeze in data around then, called a gap.
Two functions are shown in the table below f(x) equals -X squared plus 4X +12 And G(x)
equals X +2
Answer:
[tex]x = -2; x = 5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = -x^2 + 4x + 12[/tex]
[tex]g(x) = x +2[/tex]
Required
For what value of x is: [tex]f(x) = g(x)[/tex]
[tex]f(x) = g(x)[/tex] implies that
[tex]-x^2 + 4x + 12 = x + 2[/tex]
Collect like terms
[tex]-x^2 + 4x -x + 12 -2 = 0[/tex]
[tex]-x^2 + 3x + 10 = 0[/tex]
Expand
[tex]-x^2 + 5x-2x + 10 = 0[/tex]
Factorize
[tex]-x(x - 5)-2(x - 5) = 0[/tex]
Factor out x - 5
[tex](-x - 2)(x - 5) = 0[/tex]
Solve for x
[tex]-x - 2 = 0; x - 5 = 0[/tex]
So:
[tex]x = -2; x = 5[/tex]
) A desk organizer sells for $35, which includes a markup rate of 60% based on the selling price.
a. Find the markup.
b. Find the cost.
Answer: a. $21
b. $14
Step-by-step explanation:
Selling price of desk organizer = $35
Markup rate = 60%
a. The markup will be:
= Markup rate × Selling price
= 60% × $35
= 0.6 × $35
= $21
Therefore, the markup is $21
b. The cost will then be:
Cost price = Selling price - Markup
= $35 - $21
= $14
please help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
the correct answer is marked
Step-by-step explanation:
The circle with center (h, k) and radius r has equation ...
(x -h)² +(y-k)² = r²
For the given center, that is ...
(x -1)² +(y +1)² = r²
The value of r² can be found by using the given point for x and y, and seeing what value of r² makes the equation true.
(5 -1)² +(7 +1)² = 4² +8² = 16 +64 = 80
So, r² = 80 makes the equation true, and that equation is ...
(x -1)² +(y +1)² = 80
My rule is: y = 1/3x + 11/15
Find y, if x=1
Find y, if x=6
QUESTION 14 · 1 POINT
Translate the English phrase into an algebraic expression: 6x less than 81xsquared
Answer:
Step-by-step explanation:
81x² - 6x
Answer:
81x² - 6x
Step-by-step explanation:
81x² - 6x
4/8 =?/2 please answer
Answer:
? = 1
Step-by-step explanation:
4/8 = ?/2
Change the ? into a variable so it's easier to calculate:
Variable x = ?
4/8 = x/2
Cross multiply:
4 × 2 = 8 × x
8 = 8x
Divide both sides by 8 to isolate the variable:
1 = x
Check your work:
4/8 = 1/2
4 × 2 = 8 × 1
8 = 8
Correct!
4
)
5 + 15x
42x + 4
A) -2
C) -10
B) 3
D) -8
Answer:
D
Step-by-step explanation:
D
