Given:
'a' and 'b' are the intercepts made by a straight-line with the co- ordinate axes.
3a = b and the line pass through the point (1, 3).
To find:
The equation of the line.
Solution:
The intercept form of a line is
[tex]\dfrac{x}{a}+\dfrac{y}{b}=1[/tex] ...(i)
where, a is x-intercept and b is y-intercept.
We have, 3a=b.
[tex]\dfrac{x}{a}+\dfrac{y}{3a}=1[/tex] ...(ii)
The line pass through the point (1, 3). So, putting x=1 and y=3, we get
[tex]\dfrac{1}{a}+\dfrac{3}{3a}=1[/tex]
[tex]\dfrac{1}{a}+\dfrac{1}{a}=1[/tex]
[tex]\dfrac{2}{a}=1[/tex]
Multiply both sides by a.
[tex]2=a[/tex]
The value of a is 2. So, x-intercept is 2.
Putting a=2 in [tex]b=3a[/tex], we get
[tex]b=3(2)[/tex]
[tex]b=6[/tex]
The value of b is 6. So, y-intercept is 6.
Putting a=2 and b=6 in (i), we get
[tex]\dfrac{x}{2}+\dfrac{y}{6}=1[/tex]
Therefore, the equation of the required line in intercept form is [tex]\dfrac{x}{2}+\dfrac{y}{6}=1[/tex].
help please !! it's asking "find the measure of the missing angle" yet there's nothing ??
Answer:
60 degrees
Step-by-step explanation:
All the angles are the same so 180 divided by 3 is 60
Bruce overdrew his checking account by $19, for which his bank charged him a $35 overdraft fee. If he deposits $60, what will his balance be?
$
what is the answer please ?
Answer:
10
Step-by-step explanation:
i think
3. Which point has the coordinates (4, -3)?
Answer:
Step-by-step explanation:
B
I need to find the value of X if someone could help that’ll be great thank you!
What is the equation of the line with slope 3 through the point (5, 1) in point-slope form?
y-5=3(x-1)
y-1=3(x-5)
y=3x-14
y=3x+2
Help please asap!! I will mark you as brainliest :)
Answer:
k=4
Step-by-step explanation:
cross multiply so it would be:
8k+24=56
subtract 24 from 56
8k+24-24=56-24
8k=32
divde
8k/8=32/8
k=4
21 = 4x - 9 - x
what is x?
Answer:
x = 10
Step-by-step explanation:
21 = 4x - 9 - x
21 = 3x - 9
30 = 3x
10 = x
Answer:
x = 10
Step-by-step explanation:
Given
21 = 4x - 9 - x, that is
21 = 3x - 9 ( add 9 to both sides )
30 = 3x ( divide both sides by 3 )
10 = x
What is the probability that the same result (heads or tails) shows twice in a row exactly once in the ten tosses?
Answer:
1/512
Step-by-step explanation:
The probability is 2 out of 2^10 , because there are only two sequences when same result (heads or tails) shows twice in a row exactly once in the ten tosses (HTHTHTHTHT and THTHTHTHTH) out of 2^10 possible sequences.
2/2^10 = 2/1024 =1/512
12___24
1. >
2.=
3.<
I don’t know which one to pick
Answer:
<
I hope it will be useful.
NEED HELP ASAP PLZZZ
Answer:
The answer is the 1st option, so 6x+1
The price of gold rose from $790 per ounce to $860 per ounce what percent increase does this amount represent round to the nearest 10th of a percent
I dont know the answers to this and its SUPER important I get it right.
Answer:
all of dem
Step-by-step explanation:
P L E A S E H E L L P P P P P P P P !! WILL MARK BRAINLIEST
Answer:
D or the last one
Step-by-step explanation:
Answer: its the last one
Step-by-step explanation:
its the last one
i hope i helped
if i did pls mark BRAINLIEST!!
k
A salesman gets a basic wage of £160 per week plus a commision of 30%
of the sales he makes that week.
In one week his total wage was £640
Work out the value of the sales he made that week.
Answer:
The value of the sales that week was £1,600
Step-by-step explanation:
The wage of a salesman is made of two parts: A fixed-wage of £160 per week plus a commission of 30% (0.3) of the sales he makes that week.
The wage can be modeled by the function:
W = 160 + 0.3x
Where x is the amount of sales per week.
If he had a total wage of £640, then we can find the values of the sales by solving for x the equation
160 + 0.3x = 640
Subtracting 160:
0.3x = 640 - 160
0.3x = 480
Dividing by 0.3:
x = 480/0.3
x = 1,600
The value of the sales that week was £1,600
Your friend spends $20 on dinner and wants to leave a 15% tip. How much do they need to pay in tip?
6y - 26 and 2(3 - 13) Are they equivalent?
Answer:
٢٤٦ ٤٧ ٥١٩+٣٦
Step-by-step explanation:
)اتييمثتنث)٢-ثعه1غميصك
The function c(x) = 18x -10 represents the cost in dollars. How many tickets can you buy?
Note: It seems you may have unintentionally missed writing the complete question. As total cost is missing.
So, I am assuming how many tickets Mr. XYZ can buy if he/she pays 170 dollars.
The solution would still clear your concept though.
Answer:
Please check the explanation.
Step-by-step explanation:
Given the function
[tex]c(x) = 18x -10[/tex]
The slope-intercept form of the line equation
We know that the slope-intercept form of the line equation
y=mx+b
where m is the slope and b is the y-intercept
so
[tex]c(x) = 18x - 10[/tex]
comparing with the slope-intercept form of the line equation
here:
rate of change = 18c(x) or y represents the costand
'x' represents the number of tickets
Assuming the total cost i.e. c(x) = $170
In order to determine the value of x, set c(x) = 170
i.e.
170 = 18x -10
switch sides
18x - 10 = 170
add 10 to both sides
18x - 10 + 10 = 170 + 10
18x = 180
Divide 18 to both sides
18x/18 = 180/18
x = 10
Therefore, if you can buy x = 10 tickets if you pay 170 dollars.
In football A field goal counts three points and extra point after touchdowns Count as one point a kicker score 30 points on 16 kicks how many of the Kicks are field goals
Answer:
2
Step-by-step explanation:
3x30=90
15x3=45
90/45=2
Answer:
He makes 14 field goals and 7 extra point kicks
Step-by-step explanation:
f=#of field goals
e=extra kick points
f+e=21
3f+1e=49
subtract top from bottom
2f=28
f=14
Good luck!
solve for x. Enter your answer in interval notation using grouping symbols. x^2+9x<-20
Step-by-step explanation:
x^2+9x<-20
x^2+9x+20<0
( x+5)(x+4)<0
x+5<0,x+4<0
x<-4 (because x<-5 is extraneous solution)
Can some help me with number 2 please
The number line that represents opposite numbers is (a) number line 1
How to determine the number line?From the question, we understand that:
The numbers are opposite numbers
Take for instance, we have a number x.
The opposite of the number x is -x
So, the number line that represents opposite numbers must have points at x and -x
Let x = 10.
So, we have:
Opposite numbers = 10 and -10
So, the number line that represents opposite numbers must have points at 10 and -10
Hence, the number line that represents opposite numbers is (a) number line 1
Read more about number lines at:
https://brainly.com/question/4727909
#SPJ1
Help me fast ASAP pls
Answer:
C
Step-by-step explanation:
I got it right
To be labeled as a jumbo egg, the egg is supposed to weigh 2.5 oz. Mia buys a carton of jumbo eggs and measures one of the eggs as 2.4 oz. What is the percent error? *
Answer: 4.17%
Step-by-step explanation:
Formula for percentage error = [tex]\dfrac{|\text{Estimated weight - Actual weight}|}{\text{Actual weight}}\times100[/tex]
Given: Estimated weight = 2.5 oz
Actual weight = 2.4 oz
Percentage error = [tex]\dfrac{2.5-2.4}{2.4}\times100\%[/tex]
[tex]=\dfrac{0.1}{2.4}\times100\%\\\\=\dfrac{100}{24}\%=4.17\%[/tex]
Hence, the percent error = 4.17%
Describe the lines below as parallel, perpendicular,or neither.
3x+6y=42 and y=2x-1
Answer:
They are neither perpendicular nor parallel.
Step-by-step explanation:
Find the gradient of 2x + 6y = 42 by rearranging it in the form y = mx + c:
6y = -2x + 42
y = -(1/3)x + 7
The gradient is the co-efficient of x
Therefore the gradient is -(1/3)
The gradient of y = 2x - 1 is 2.
If they were parallel they would have the same gradient.
If they were perpendicular then the gradient of one would be the negative reciprocal of the other, e.g: if one was 2, the other would be -(1/2).
Neither of these are true, so they are neither perpendicular nor parallel.
The lines 3x+6y=42 and y=2x-1 are perpendicular
Two lines are parallel if they have equal slope
Two lines are perpendicular if the product of their slopes equals -1
The given lines are:
3x+6y=42 and y=2x-1
Rewrite each of the equations in the form y = mx + c
For line 3x + 6y = 42:
[tex]6y = -3x + 42\\\\y=\frac{-3}{6} x+\frac{42}{6}\\\\y=-0.5x+7[/tex]
The slope, m₁ = -0.5
For line y = 2x - 1
The slope, m₂ = 2
Since m₁ ≠ m₂, lines 3x+6y=42 and y=2x-1 are not parallel
m₁ m₂ = -0.5(2)
m₁ m₂ = -1
Since the product of the slopes equals -1, the lines 3x+6y=42 and y=2x-1 are perpendicular
Learn more here: https://brainly.com/question/20093063
Can I get some help plz?
Answer:
X=20 degree
Step-by-step explanation:
∆A+∆D+∆O=180
2x+10+2x+90=180
collect like terms
2x+2x=180-100
4x=80
(4x)/4=(80)/4
x=20 degree
Answer:
[tex]angles \: of \: triangle \: add \: up \: to \: {180}^{0} \\ {(2x + 10})^{0} + {(2x)}^{0} + {90}^{0} = {180}^{0} \\ 4x = {(180 - 90 - 10)}^{0} \\ 4x = {80}^{0} \\ x = {20}^{0} [/tex]
Dannon has $10.80 in dimes and quarters. If dannon has 32 more quarters than dimes, how many dimes does he have?
Answer:
he should have 28 dimes
Step-by-step explanation:
Answer:
0.34
Step-by-step explanation:
10.80 DIVIDED BY 32 IS 0.3375 IF YOU ROUND THAT IT WOULD BE 0.34
find the value of x
Answer:
x= 64
Step-by-step explanation:
by Z rule
x= 180-116 = 64
14. The figure shows a slice of an apple pie in the shape of a sector of a circle with centre O and radius 8cm. A cut is made along AB to remove some of the crust
Given that AB = 7 cm find:
(i) AOB in radians
(ii) the maximum number of slices that can be obtained from one full pie.
(iii) the area of the shaded segment that has been removed
Step-by-step explanation:
(i) Using the law of cosines, we can find that
[tex]cos(O) = \frac{8^{2}+8^{2} - 7^{2}}{8*8*2}[/tex] ≈ 0.62, so O ≈ 0.9
(ii) Since the whole pie has 2π radians (or 360 degrees), we can divide 0.9 by 2π to get around 6.9 slices from the pie
(iii) The area of the shaded segment can be found by finding sector OAB and subtracting triangle OAB from that. Sector OAB can be found by finding the area of the pie (π*8², since 8 is the radius) and dividing that by 6.9, so we get 64π/6.9 ≈ 29. Then, the area of the triangle is √p(p-a)(p-b)(p-c), with p being the perimeter and a, b, and c being the sides. Plugging 7, 8, and 8 in, we get 25.1781 as our area, so the difference is around 3.8
Emiliana pays 6% sales tax on a cupcake that costs 3 dollars. How much does the sales tax add to the purchase price? Please tell me how you got the answer. (answer choices: $0.018, $18, $0.18, $3.18)
Answer:
$0.18 sales tax will be added to the purchase price.
Step-by-step explanation:
Given that:
Cost of cupcake = $3
Sales tax applied = 6%
Amount of sales tax = 6% of cost of cupcake
Amount of sales tax = [tex]\frac{6}{100}*3[/tex]
Amount of sales tax = 0.06 * 3 = $0.18
Hence,
$0.18 sales tax will be added to the purchase price.
here are 5 number cards
Answer:
im doind the same question on mahswatch what is it
Step-by-step explanation: