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].
The smith family went out for dinner the price of the meal was $39.85 the sales tax was 8.1% of the price of the meal the tip was 17% of the meal and the sales tax how much did the smith family pay for the meal including tax and tip PLEASE HELP ILL GIVE LOTS OF POINTS
9514 1404 393
Answer:
$50.40
Step-by-step explanation:
Adding the tax multiplies the amount by 1+8.1% = 1.081.
Adding the tip multiplies the amount by 1+17% = 1.17.
Then the amount with tax and tip is ...
$39.85 × 1.081 × 1.17 = $50.40
The Smith family paid $50.40 for the meal.
Please help geometry people.
Answer:
Since QPR is an isoscelese triangle, QP and PR are congruent.
Therefore PR = 8
My guess for ST is z=1. So (5z = 5) and( 2z = 2). Then add 3 to 2 and you get 5. So ST = 5
Step-by-step explanation:
Hope this helps!!!
Please mark brainliest.
I need help with all the questions you see
Answer:
1/ -6=12+1/3a
Rewrite the equation as 12+1/3a=−6.
12+1/3a= −6
Combine 1/3 and a.
12+a/3= −6
Move all terms not containing a to the right side of the equation.
a/3= −18
Multiply both sides of the equation by 3.
3⋅a/3=3⋅ −18
Simplify both sides of the equation.
a= −54
2/ -6 =12 -1/3a
Rewrite the equation as 12−13a=−6.
12−1/3a=−6
Combine a and /13.
12−a/3=−6
Move all terms not containing a to the right side of the equation.
−a/3=−18
Multiply both sides of the equation by −3.
−3⋅(−a/3)=−3 ⋅−18
Simplify both sides of the equation.
a=54
Step-by-step explanation:
Find the missing value to the nearest hundredth.
Cos = 5/36
Answer:
Step-by-step explanation:
"cos" by itself is meaningless. It needs an argument.
cos(x°) = 5/36
x° = arccos(5/36) ≅ 82.2°
Help! Benji has 10 bills that add up to $320. Some are 50-dollar bills and the rest are 20-dollar bills. How many 50-dollar bills and 20-dollar bills are there ?
The candy of a lolipop is in the shape of a sphere with a diameter of 4 cm. The
cylindrical stick inside the candy is the same height as the sphere and has a radius of
0.5 cm. What is the composite volume of the candy? Round to the nearest tenth, if
necessary.
Find the slope-intercept form of an equation of the line perpendicular to the graph of x – 3y = 5 and passing through (0, 6).
Answer:
y=-3x+6
Step-by-step explanation:
x-3y=5
y=1/3x-5/3
slope of perpendicular line is -3 (opposite reciprocals)
y=mx+b
x=0 and y=6
6=3x+b
6=3(0)+b
6=b
y=-3x+6
Todo Binomio es polinomio falso o verdadero?
Answer:
Todo los binomios son casos especiales de polinomios.
Step-by-step explanation:
Answer:
verdadero eso puse yo :D
is 25 meters longer then 35 yards
PLEASE HURRY! I NEED HELP! THIS IS DUE TOMORROW! If you answer this I will give you brainliest!
Answer:
the answer is 3
Step-by-step explanation:
how i got this answer is........i did the round robin and i times 1 *5+4 and i got 9 so you will get 3/4 *9/5 and i got 27/9 and you will divided 9*3 and you will get 3 so that is the answer 3
i hope you did good on your test
Find the mode of the data
Answer:
9
Step-by-step explanation:
Mode: the value that occurs most frequently in a given set of data
9 has the most dots stacked up for the number of hours slept--
(in that particular data set)
Hope this made sense!
El día 12 de diciembre en Moscú se registró una temperatura de 13° bajo cero, a esa misma hora, en buenos Aires hacía una temperatura de 25 grados sobre cero. ¿Qué diferencia térmica existía en ese momento entre las dos ciudades? A.38 B.-38 C.12 D.-12
Answer:
A. [tex]38\ \text{grados}[/tex]
Step-by-step explanation:
La temperatura en Moscú es de 13 grados bajo cero. Entonces, la temperatura es de -13 grados.
La temperatura en Buenos Aires es de 25 grados bajo cero. Entonces, la temperatura es de 25 grados.
La diferencia de temperatura entre las dos ciudades es
[tex]25-(-13)=38\ \text{grados}[/tex]
La diferencia de temperatura entre las dos ciudades en un momento dado es [tex]38\ \text{grados}[/tex].
if diameter of a circle is 28cm.find radius & circumference.
Answer:
Radius = 14 cm, Circumference = 88 cm
Step-by-step explanation:
d = 28 cm
r = 1 / 2 * 28
= 14 cm
Circumference = 2πr
= 2 * 22 / 7 * 14
= 2 * 22 * 2
= 88 cm
Hope it helps :)
Please mark my answer as the brainliest
Step-by-step explanation:
Diameter (d) = 28 cmRadius (R) = d /2 = 28 / 2 = 14 cmCircumference (C) = πd= 3.14 * 28= 87.92[tex]hope \: it \: will \: help[/tex]
Will mark BRAINlIEST!!!
What is 2/7+ (−4/7)
Answer:
- 2/7
Step-by-step explanation:
+ and - becomes -
2/7 - 4/7 = - 2/7
PLEASE MARK BRAINLIEST!!! <3
Answer:
6/9 yeah that's it I looked It, up.
Step-by-step explanation:
[tex]\frac{3}{x+3} -\frac{4}{x-3}=\frac{5x}{x^{2} -9}[/tex]
Answer:
Step-by-step explanation:
[tex]\frac{3}{x+3}-\frac{4}{x-3}=\frac{3*(x-3)}{(x+3)(x-3)}-\frac{4(x+3)}{(x-3)(x+3)}\\\\=\frac{3*x-3*3}{(x+3)(x-3)}-\frac{4*x+4*3}{(x+3)(x-3)}\\\\=\frac{3x-9}{x^{2}-3^{2}}-\frac{4x+12}{x^{2}-3^{2}}\\\\=\frac{3x - 9 -(4x + 12)}{x^{2}-3^{2}}\\\\=\frac{3x-9-4x-12}{x^{2}-9}\\\\=\frac{-x-21}{x^{2}-9}\\\\[/tex]
[tex]\frac{3}{x+3}-\frac{4}{x-3}=\frac{5x}{x^{2}-9}\\\\\frac{-x-21}{x^{2}-9}=\frac{5x}{x^{2}-9}\\\\-x-21=\frac{5x}{(x^{2}-9)}*(x^{2}-9)\\[/tex]
-x - 21 = 5x
Add 'x' to both sides
-x -21 +x = 5x + x
-21 = 6x
6x = -21
x = -21/6
= -7/2
x = -3.5
Sally makes $10 per hour and a $20 bonus.
Jerry makes $9 per hour and a $50 bonus.
Which set of equations describe Sally and Jerry's income?
Any help?
Sally: 10h + 20
Jerry 9h + 50
h = hours
can i please have help? :) match each function to the correct organic compound. PROTEINS a. used for energy b, used for tissue repair and growth c. used for storing and transmitting genetic d. used for long - term storage
Answer:
b
Step-by-step explanation:
They are used for tissue repair and growth
Which of the following equations could you solve by first adding six and then dividing by negative three?
6 - 3 x = -9
+ 6 = -9
-3 x - 6 = -9
3 x - 6 = -9
Answer:
-3x - 6 = -9 (The third answer)
Step-by-step explanation:
When solving for x, you have to undo each operation. When solving -3x - 6 = -9, you have to undo the -6 first. To do this, add 6 to both sides. Then, you must undo the -3x. To do this, divide by -3 from both sides.
Quadrilateral ABCD is rotated 90° about the origin. What are the coordinates of quadrilateral A’B’C’D?
A. A (5,-5), B' (1.-5). C'(1.-2).
D'(5.-1)
B. A(-5, -5), B'(-5, -1) C'(-2,-1), D'(-1,-5)
C. A'(-5,5), B'(-1,5), C'(-1,2).
D'(-5,1)
D. A'(5, -5), B' (5. -1), C' (2-1),
D' (1.-5)
Answer:
A
Step-by-step explanation:
Answer:
A. A (5,-5), B' (1.-5). C'(1.-2).
D'(5.-1)
Step-by-step explanation:
I got right
Can someone please help me solve these?
9514 1404 393
Answer:
(c) h(x) = (3x +4)(2x +1)
Step-by-step explanation:
The answer choices differ in the values they create for the last two terms of the trinomial. The last term (+4) is created by all of the choices except the first one.
The middle term (11x) is only created by the third choice:
(3x +4)(2x +1) = (3x)(2x) +(3x)(1) +(4)(2x) +(4)(1)
= 6x^2 +3x +8x +4
= 6x^2 +11x +4 . . . . matches the given h(x)
A pattern is made from four congruent squares.
The sides of the squares are parallel to the axes.
У.
B (27, 30)
Point A has coordinates (3, 2)
Point B has coordinates (27, 30)
Point C is marked on the diagram.
Work out the coordinates of C.
Answer:
The coordinates of C are (15,16)
Step-by-step explanation:
As we can see, point C lies half the distance of AB
So we can use the midpoint formula to get the coordinates of C
we have this as:
(x,y) = (x1 + x2)/2 , (y1 + y2)/2
(x1,y1) = (3,2)
(x2,y2) = (27,30)
Thus, we have
(x,y) = (3 + 27)/2, (30 + 2)/2
(x,y) = 30/2 , 32/2
(x,y) = (15,16)
-2 +2 = -3(x-4)
what is x
Answer:
x = 4
Step-by-step explanation:
Mark brainliest
2,6,18,54 what is the 10th term of the sequence
Answer:
78
Step-by-step explanation:
I'm really good at these
Answer:
Step-by-step explanation:
This is a geometric sequence with common ratio 3.
10th term = (4th term)×3¹⁰⁻⁴ = 54×3⁶ = 39366
It takes Kyle of an hour to walk of a mile. He walks 2 miles. How many hours did it take him?
of 1/5an hour
of 2/5an hour
of 3/5 an hour
of 4/5 an hour
forgot it has answer choices
Answer:
iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
I believe the correct answer is 4/5 of an hour.
9 A rectangle of perimeter 42 cm is
pcm long and q cm broad. If the
difference between the length and
breadth is 9 cm. find
pand q
the area of the rectangle
Answer:
The correct answer is = p = 15 and q = 6.
Step-by-step explanation:
Given:
Perimeter of rectangle = 42 cm
p - q = 9 cm
length = p
width = q
we know:
Perimeter of rectangle= 2(l+w)
solution:
42 = 2(P+q)
21= p+q
Difference of p and q = 9 cm.
Then, P+q=21 .... 1
P-q=9 ....2
Adding both 1 and 2
2P = 30
P= 15cm and
q = 15-9
= 6cm
In January, Mr Tan's students read 20 books. In Febuary, they read 15 books. What is the percent increase or decrease in the number of books they read?
A. 5% decrease
B. 15% increase
C. 25% increase
D. 25% decrease
Answer:
D. 25% decrease
Step-by-step explanation:
Since it's clear that they read less books to find how much it decreased we multiply 100 with 15 then divide it by 20
100 × 15 ÷ 20 = 75 this result shows a 25% decrease.
Please help marking brainiest
Answer:
can you blow the image up or tell me what it says
Step-by-step explanation:
First answer gets brainly!
Step-by-step explanation:
Solve 4[10x + 5) = 260
Answer:
sry dont know
Step-by-step explanation:
Answe
its x=6
Step-by-step explanation:
HELP ME PLZZZZZZZZZZ
Answer:
In both cases, we have similar figures.
This means that the shape of the figures is the same, but the size is different:
PQST is similar to STNR and to NRPQ
VUYZ is similar to YZWX and to VUWX
this means that, for example, in problem 18, the ratio between ST and NR must be the same as the ratio between PQ and ST. This happens because the measure increases by the same scale factor.
With this in mind, we can solve the problem:
18)
ST = 7.5
NR = 5.5
Then the quotient ST/NR is:
ST/NR = 7.5/5.5
And, as we said above:
PQ/ST = ST/NR
PQ/7.5 = 7.5/5.5
PQ = (7.5/5.5)*7.5 = 10.23
19) Here we should have:
YZ/VU = WX/YZ
Then:
22.9/35 = WX/22.9
(22.9/35)*22.9 = WX = 14.98