What are the points on y-axis which are at a distance of 4 units from 4x+3y=12
Given:
The equation of line is
[tex]4x+3y=12[/tex]
To find:
The points on y-axis which are at a distance of 4 units from the given line.
Solution:
The point lie on the y-axis. So, their x-coordinate must be zero.
Let the points are in the form of (0,k).
The distance between a point [tex](x_0,y_0)[/tex] and a line [tex]ax+by+c=0[/tex] is
[tex]d=\dfrac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}[/tex]
The given equation can be written as
[tex]4x+3y-12=0[/tex]
The distance between (0,k) and [tex]4x+3y-12=0[/tex] is 4 units.
[tex]4=\dfrac{|4(0)+3(k)-12|}{\sqrt{4^2+3^2}}[/tex]
[tex]4=\dfrac{|0+3k-12|}{\sqrt{16+9}}[/tex]
[tex]4=\dfrac{|3k-12|}{\sqrt{25}}[/tex]
[tex]4=\dfrac{|3k-12|}{5}[/tex]
Multiply both sides by 5.
[tex]20=|3k-12|[/tex]
[tex]\pm 20=3k-12[/tex]
[tex]12\pm 20=3k[/tex]
[tex]\dfrac{12\pm 20}{3}=k[/tex]
Now,
[tex]k=\dfrac{12-20}{3}\text{ and }k=\dfrac{12+20}{3}[/tex]
[tex]k=\dfrac{-8}{3}\text{ and }k=\dfrac{32}{3}[/tex]
Therefore, the two points are [tex]\left(0,\dfrac{-8}{3}\right)\text{ and }\left(0,\dfrac{32}{3}\right)[/tex].
Six friends share 3/4 of a pound of roasted almonds. What fraction of a pound does each friend receive
Answer: 1/8 pounds of roasted almonds
Step-by-step explanation:
There are six friends and each of them are to receive and equal piece out of a 3/4 pound of roasted almonds.
The almonds each friend will get will therefore be the 3/4 pack divided by 6:
= 3/4 ÷ 6
= 3/4 * 1/6
= 3/24
= 1/8 pounds of roasted almonds
When dividing by a number, you can instead multiply by the inverse of that number.
Charlie runs laps around a track. The table shows how long it takes him to run different numbers of laps. How long would it take Charlie to run 9 laps?
Number of laps 2, 4, 6, 8, 10
Time (min) 16, 32, 48, 64, 80
Answer:
72
Step-by-step explanation:
It would take Charlie 72 minutes to run 9 laps. To solve the question find how long it takes to run 1 lap. Do this by dividing the number of minutes by the number of laps ran. For example, 16/2 equals 8, which means it took him 8 minutes to run one lap. To check you can divide the other values, like 32/4= 8 and 48/6 = 8. Then, multiply 8*9 it see how long it takes for him to run 9 laps. Therefore, the answer is 72 because 8*9=72.
Add the polynomials.
(3x² - 7x+2) + (7x2 - 6x)
Answer:
If by the 7x2 you mean 7x² it will be
10x²-13x+2
help please this is due tonight
Answer:
x = 5
Step-by-step explanation:
Since the triangles have to be congruent (through SSS), we know that:
2x + 3 = 4x - 7
We simplify this to: 2x = 10
And then: x = 5
La probabilidad de que al tirar un dado, salga 1, es de 1/6. La probabilidad de que salga 3, es de 1/6. Calcular la probabilidad de que al tirar un dado, salga 1 o 3.
Respuesta. La probabilidad de sacar um 3 seria de 16.66% osea un sexto ,de sacar un numero par es de tres sexto osea del 50% y de sacar un numero impar es de tres sexto osea 50% igual ke los pares y de sacar un numero menor k 7 es de 6 sobre 6 osea 100%.
El valor uno corresponde al suceso seguro: lanzamos un dado al aire y la probabilidad de que salga cualquier número del 1 al 6 es igual a uno (100%). El resto de sucesos tendrá probabilidades entre cero y uno: que será tanto mayor cuanto más probable sea que dicho suceso tenga lugar.
A new phone costs $230 and the sales tax rate is 7%. What is the total cost of the camera after tax?
That's a question about percentage.
One way to represent percentage is using decimal number. In this way, 1 is equivalent to 100% and the other less percentages using numbers between 0 and 1.
Examples:
90% is equivalent to 0,90.5% is equivalent to 0.05. It's not 0.5 because 0.5 is equivalent to 50%.13.17% is equivalent to 0.1317.245% is equivalent to 2.45.If we want to know the percentage of a number, we should multiplacate the number by the porcentage in the decimal number form.
Examples:
55.90% of 200 is equal to: [tex]200 \times 0.5590 = 111.8[/tex]360% of 88 is equal to: [tex]88\times 3.6 = 316.8[/tex]In our problem, we have a phone with a increase of 7%. To solve that, it's important to perceive that $230 is equal to 100% and with a increase of 7%, we will pay 107%.
107% in the decimal number form is 1.07. With that information, we should multiplicate 1.07 by the original value and we will find the answer.
We know that [tex]230\times 1.07 = 246.1[/tex], therefore, the total cost of the phone after tax is $246.1.
I hope I've helped. :D
Enjoy your studies. \o/
what shape/figure has reflectional symmetry and point symmetry?
8. The double box plot shows the costs of MP3 players at two different stores. Which one of the following inferences is NOT true based on the dot plots shown below:
A. 75% of the prices at Electronics World are lower then $75.
B. 75% of the prices at Bargain Basement are lower than $65.
C. The median price at Electronics World is $10 more than at Bargain Basement.
D. MP3 players are more expensive at Bargain Basement.
2007 Federal Income Tax Table
Single:
Over But not over The tax is
$0 $7,825 10% of the amount over $0
$7,825 $31,850 $788 + 15% of the amount over $7,825
$31,850 $77,100 $4,386 + 25% of the amount over $31,850
$77,100 $160,850 $15,699 + 28% of the amount over $77,100
$160,850 $349,700 $39,149 + 33% of the amount over $160,850
$349,700 And Over $101,469 + 35% of the amount over $349,700
Maria Contrerras earned $53,000 in taxable income. She figured her tax from the single taxpayer table above.
1. Find her earned income level.
2. Entered the base amount. = $
3. Found the amount over $ = $
4. Multiplied line 3 by 25% = $
5. Added Lines 2 and 4 = $
Tax= $ 7,173.5
Step-by-step explanation:
Her taxable income is $ 43,000 which lies in the tax category $ 31,850 to
$ 77,100.
Tax for $ 31,850 is $ 4,386
Plus 25% of the amount = ( $ 43,000- $ 31,850 )= $ 11,150 over
25 % of $ 11,150= $ 2,787.5
Total Tax= $ 4386 + $ 2787.5= $ 7,173.5
Omar has a new credit card. He earns
300
300300 reward points for every
100
100100 dollars he spends.
If Omar earned
1800
18001800 reward points, how much money did he spend?
dollars
Answer:
$600
Step-by-step explanation:
Omar spent $600.
Essentially, we divide his total number of points:
1800
by the amount earned
300
=
6
we take that and multiply by 100 (our amount needed to be spent to earn points) and boom, problem solved.
Which expression is equivalent to x 2 - 17x - 60?
Answer:
(x-20)(x+3)
Step-by-step explanation:
Answer:
( x − 20)( x + 3)
Step-by-step explanation:
i did the test
isabella earned $44.00 for 4 hours of work how much was earned per hour
Answer:
$11
Step-by-step explanation:
44/4 = 11
Answer:
11 was earned per hour
Step-by-step explanation:
44 divided by 4 is 11
A teacher puts 119 students into teams of 12 for a car wash fundraiser extra students work as coumunity  Volunteers how many students work as Community volunteers pls help
Answer:
Step-by-step explanation:
119/12
108car wash
11 students as community volunteers
3.01 greater or less than 4?
Answer:
Less
Step-by-step it is greater by 1.01
Answer:
Less than
Step-by-step explanation:
3 itself is already less than 4. How can 3.01 be greater than 4? When comparing positive numbers, compare from left to right. If the place of the first number is larger (for example comparing 10 with 100), than the one with the larger place is greater (tenth place will always be smaller than hundreds place).
If the first digit of both numbers are the same place (for example 10 and 20), than look at the value, which one is greater? Since 2 is greater than 1, we know 20 is bigger than 10. This holds true regardless of what follows the 2 or 1. For example, 20 is still bigger than 19.987
The only exception is when we are comparing 20 and 19.999 (where 9 is repeated). I will not be proving it here, but 0.999 (9 repeated) is said to be equal to one. Which means that 20 and 19.999 (9 repeated) are equal.
30 POINTS PLEASE HELP!!!
The ratio of two sides of a parallelogram is 3:4 and the perimeter is 28 in. Find the lengths of the sides of the parallelogram.
Answer:
the lengths of sides are 8 and 6.
Step-by-step explanation:
Let us denote side lengths of the parallelogram as x and y.
Then first condition can be written as x/y=3/4.
Second condition can be written as 2x+2y=28.
We can multiply both sides of the first equation by y and get x=(3y)/4.
Now we have x expressed in terms of y. It is convenient because we can substitute x in the second equation:
2(3y/4)+2y=28
And we can solve it for y.
1.5y+2y=28
3.5y=28
y=8
What is left is to find x. We may use the expression for x again: x=(3*8)/4=6
Ans: the lengths of sides are 8 and 6.
Find the sum of the linear expressions
(8x - 16) + (-12x - 2)
Answer:
-4x-18
Step-by-step explanation:
pickle
Answer: -4x-18
Step-by-step explanation:
8x-16-12x-2=8x+-16+-12x+-2
Then you combine like terms.
8x+-16+-12x+-2= (8x+-12x)+(-6+-2)
Your answer will be -4x-18
I hope this helps
Leah bought two pounds of strawberries for $9.60. What is the price, in dollars per ounce of strawberries?
Answer:
i dunno man like 20x2853-3835734= close to 1 ish maybe
Step-by-step explanation:
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gIB BRAIN SMARTER
help>>>>>>!!!!!!!!!!!
Please help me out please
Answer:
x = -0.8
<CAD = -8
Step-by-step explanation:
10x + 4 = 5x - 4 (Clean up)
10x = -8 (Divide each side by 10)
x = -0.8
<CAD = 5x - 4
<CAD = 5(-0.8) - 4
<CAD = -4 - 4
<CAD = -8
Solve for x: x + 16 = -18
Answer:
Step-by-step explanation:
Let's solve your equation step-by-step.
x+16=−18
Step 1: Subtract 16 from both sides.
x+16−16=−18−16
x=−34
Answer:
x=−34
Question 3
For the triangle shown, calculate the perimeter
2.5 km
51.8°
62.1
Answer: The perimeter is 9.31km
Step-by-step explanation:
We have two triangle rectangles, and the perimeter of the complete triangle will be equal to the sum between the hypotenuses (of both triangles) and the bottom cathetus (of both triangles)
For a triangle rectangle and a given angle A (that is not the right angle)
Remember the relationships:
Sin(A) = (opposite cathetus)/(hypotenuse)
Cos(A) = (adjacent cathetus)/(hypotenuse)
Tan(A) = (opposite cathetus)/(adjacent cathetus)
With this, we can find the measures of each triangle in the imae.
The left triangle rectangle.
We have a cathetus (opposite) with length of 2.5km and A = 51.8°
Then the hypotenuse can be found by:
Sin(51.8°) = (2.5km)/(hypotenuse)
then:
hypotenuse = (2.5km)/sin(51.8°) = 3.18 km
And the bottom cathetus can be found with:
Tan(51.8°) = (2.5km)/(adjacent cathetus)
adjacent cathetus = (2.5km)/(Tan(51.8°)) = 1.98 km
For the other triangle, we have A = 62.1°, and the opposite cathetus is 2.5 km
We can use the same relationships than before:
Sin(62.1°) = (2.5km)/(hypotenuse)
then:
hypotenuse = (2.5km)/sin(62.1°) = 2.83 km
And the bottom cathetus can be found with:
Tan(62.1°) = (2.5km)/(adjacent cathetus)
adjacent cathetus = (2.5km)/(Tan(62.1°)) = 1.32 km
Then the perimeter of the complete triangle is:
Perimeter = 3.18 km + 1.98 km + 2.83km + 1.32 km = 9.31 km
Follow the steps and finish the solution.
7(x-3) = 28
7x-21 = 28
Distributive property
7X=49
Addition property of equality
Division property of equality
X= -
What is the value of x?
O 7
O 9
O 42
056
Answer:
7 because 7x = 49 is 7 because 7 goes to itself 1 and to 49 7
Amelia's water bottle holds 4 pints, 2 cups. How many cups does Amelia's water bottle hold? Note: 1 pint = 2 cups
Answer:
10 cups
Step-by-step explanation:
4x2=8. 8+ the 2 cups in the beginning would be 10 cups.
1. The equation y = 2x + 6 represents a function.
a. Complete the x and y table:
х
y
2
10
15
21.5
Answer:
Step-by-step explanation:
x | y
2 | 10
15| 15
21.5 | 17.5
There is 3/4 of a pizza. 1/3 of the pizza has pepperoni on it. How much
of the pizzas has pepperoni on it?
Answer:
4/12
Step-by-step explanation:
There are 5 candy canes for every 9 presents. How many candy canes are there when there are 108 presents
Answer:
When there are 108 presents, there are 60 candy canes
Step-by-step explanation:
candy canes : presents = 5:9
5/9 = x/108
cross multiply:
(5) (108) = 9x
540 = 9x, divide both sides by 9
x = 60
Find the value of x.
Answer
x=7
Step-by-step explanation:
I honestly forgot how to explain but my logic is that 43+137+137+43=360
so, x would equal 7
0.4 / 17= what i need help this is ilx
Answer:
.0235294117647
Step-by-step explanation:
Answer:
0.02352941176
Step-by-step explanation:
WRITE AN EQUATION which describes the line that contains (9,4) and has an undefined slope.
Answer:
x = 9
Step-by-step explanation:
A line with an undefined slope will be a vertical line.
This means the equation of the line will be in x = form, because the line will only go through one x value.
Since the given point has the x value of 9, this means the line will only go through that value.
So, the equation of the line will be x = 9