Two lines in a plane can intersect,overlap or be parallel.When two lines intersect they have a common point which lies on both line.This is called solution of the two simultaneous equation which when graphed represent straight lines. Adding the two equations uses Elimination method to solve for x and y. The x and y value obtained is the common point lying on both the lines.
2x - 3y = 1
+ 2x + 3y = 2
4x =3 Or x=3/4
Substituting x value in any of the two-equation we can find the corresponding y value .
2x-3y=1
2(3/4) - 3y =1
Solving for y
y= 1/6
The point of intersection of the two lines is ( 3/4, 1/6)
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Write the equation of the line that passes through the points (8, 14) and (-2,-16) in slope-intercept form.
Answer:
y = 3x - 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 14) and (x₂, y₂ ) = (- 2, - 16)
m = [tex]\frac{-16-14}{-2-8}[/tex] = [tex]\frac{-30}{-10}[/tex] = 3 , then
y = 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 14 ) , then
14 = 24 + c ⇒ c = 14 - 24 = - 10
y = 3x - 10 ← equation of line
What is the area of cross-section ADGF of this right rectangular prism?
A.
20 square units
B.
48 square units
C.
52 square units
D.
65 square units
Answer:
C.52 square units
Step-by-step explanation:
We are given that
Length of cross-section ADGF,l=13units
Length of cross-section ADGF, b=4 units
We have to find the area of cross-section ADGF of this right rectangular prism.
We know that
Area of rectangle=[tex]l\times b[/tex]
Using the formula
Area of cross-section ADGF of this right rectangular prism
=[tex]13\times 4[/tex]
Area of cross-section ADGF of this right rectangular prism=52square units
Option C is correct.
C.52 square units
Answer:
i hope this helps
Step-by-step explanation:
Answer the photo below thanks
find the value of a and b of a+root5 is (root5+root3)(root5-root3)
Given:
Consider the value of [tex]a+b\sqrt{5}[/tex] is [tex](\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex].
To find:
The values of a and b.
Solution:
According to the given information,
[tex]a+b\sqrt{5}=(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex]
[tex]a+b\sqrt{5}=(\sqrt{5})^2-(\sqrt{3})^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]a+b\sqrt{5}=5-3[/tex]
[tex]a+b\sqrt{5}=2[/tex]
It can be written as
[tex]a+b\sqrt{5}=2+0\sqrt{5}[/tex]
On comparing both sides, we get
[tex]a=2,b=0[/tex]
Therefore, the value of a is 2 and the value of b is equal to 0.
Estimate the answer by rounding each fraction to the nearest whole number and then adding. 13 7/10 + 10 1/8
9514 1404 393
Answer:
24
Step-by-step explanation:
The rounded numbers are ...
13 7/10 = 13.7 ⇒ 14
10 1/8 = 10.125 ⇒ 10
The sum of the rounded numbers is 14 +10 = 24.
The estimate of the sum is 24.
If the sales tax rate is 7.5% in New York State, then how much sales tax would you pay in Albany for a $34 pair of pants? What is the final cost?
Answer:
Sales Tax $2.55
Final Cost $36.55
Step-by-step explanation:
Finding sales tax
34 * 7.5%= 2.55
Multiply the tax with the original cost, that will be your sales tax
Finding final cost
34 + 2.55= 36.55
Add your sales tax with the original cost, now you have the final total
Complete the following proofs.
Given: Points R, S, T, Q on circle O
Prove: m Arc RS + m Arc ST + m Arc TQ = m Arc RQ
Answer:
Points R, S, T, Q on circle O is given
and points are central arc
Step-by-step explanation:
Help please! Thank youuuuuy
Step-by-step explanation:
can an.y gi.rl message me. i have no power to inbox
if f(x)=3x-4 and g(x)=x^2 -1
what is f(g(-3))?
a) -34
b) 8
c) 20
d) 168
The sales tax in one state is 5%. Write a function rule for finding the total cost of an item with selling price x. Then find the total cost of CD player with a selling price of $110
Answer:
Total Cost = 1.05x
CD Player cost = 110*1.05 = $115.50
Step-by-step explanation:
Helen plays basketball. For free throws, she makes the shot 75% of the time. Helen must now attempt two free throws. The probability that Helen makes the second free throw given that she made the first is 0.85. What is the probability that she makes both free throws?
Answer: 0.6375
Step-by-step explanation:
Let's assume that the event that she'll make the first shot is given as P(A) while making the second shot is P(B). Therefore, P(A/B) = 0.85
Therefore, the probability that she makes both free throws will be denoted as:
= 0.75 × 0.85
= 0.6375
Short Answer
Note: Your teacher will grade your response to ensure you receive proper credit for your answer
Describe how you would estimate the square root of a number that is not a perfect square without using a calculator
Answer:
The square root must be between the square roots of the perfect squares just above and just below your number.
For example the square root of 89 must be between 9 and 10.
Step-by-step explanation:
1/6(x + 6) = 11 What is x
Answer:
x = 60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
[tex]\frac{1}{6}[/tex](x+6)=11
[tex]\frac{1}{6}[/tex]x + 1 = 11
[tex]\frac{1}{6}[/tex]x +1 -1 = 11 -1
[tex]\frac{1}{6}[/tex]x * 6 = 10 *6
x = 60
To double check
[tex]\frac{1}{6}[/tex](60+6)=11
10+1 = 11
11 = 11
is 8 x 2/8 less than 8 or greater than 8
Answer: yes if is
Step-by-step explanation:
Write the equation 9 = -5x + 4 in the form ax + b = c, where c = 9.
What are the values of a and b?
Answer:
a = - 5x and b= 4
Step-by-step explanation:
So it becomes - 5x +4=9
Hope this helps pls tell if any mistakes
Answer:
dil bende ingilizce göründüğü için anlamıyoruuumm
What is the exact length of each side?
Answer:
[tex]6a^{2} \sqrt{ab}[/tex]
Step-by-step explanation:
area of square = side x side
thus, each side = square root of area
[tex]\sqrt{36a^5b}[/tex] = 6[tex]\sqrt{a^{4} ab}[/tex] = 6[tex]a^{2}[/tex][tex]\sqrt{ab}[/tex]
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First okay and second umm my what?! Lol
The answer is : - 112
We add 14 to both side
-16x - 14 = -126
+ 14 +14
-16x = - 112. <- that’s the answer
Then we divide both sides by 16
X = 7
Ta -Da!!
Also I’ll leave this.....
Solve for xxx.
Your answer must be simplified.
15 < -5 x
Answer:
x < - 3
Step-by-step explanation:
Given
15 < - 5x
Divide both sides by - 5, reversing the symbol as a result of dividing by a negative quantity
- 3 > x , that is
x < - 3
The simplified expression is x < -3.
What is an inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is the condition of being unequal. It is used most often to compare two numbers on the number line by their size.
For the given situation,
The expression is 15 < -5x
⇒ [tex]15 < -5 x[/tex]
Divide both sides by -5,
⇒ [tex]\frac{15}{-5} < \frac{-5}{-5} x[/tex]
When we divide an inequality with negative number, we need to change the sign,
⇒ [tex]-3 > x[/tex]
⇒ [tex]x < -3[/tex]
Hence we can conclude that the simplified expression is x < -3.
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PLEASE ANSWER!!!!!
An eagle is flying at an altitude of 280 feet. The angle of depression from the eagle to a mouse on the ground is 15º. What is the direct line distance from the eagle to the mouse? Round answer to the nearest thousandth.
[tex] \sin = \frac{opp}{hyp} [/tex]
[tex] \sin(15) = \frac{280}{hyp} [/tex]
[tex]hyp = \frac{280}{ \sin(15) } [/tex]
[tex]hyp = 1081.836925 \: feet[/tex]
The direct line distance from the eagle to the mouse is 1081.837 feet
Condense to a single logarithm : log 12 18+3 log 12 2
Answer:
2 or [tex] \log_{12} 144 [/tex]
Step-by-step explanation:
I assume 12 is the base.
[tex] \log_{12} 18 + 3 \log_{12} 2 = [/tex]
[tex] = \log_{12} 18 + \log_{12} 2^3 [/tex]
[tex] = \log_{12} (18 \times 8) [/tex]
[tex] = \log_{12} 144 [/tex]
[tex] = \log_{12} 12^2 [/tex]
[tex] = 2\log_{12} 12 [/tex]
[tex] = 2 [/tex]
The entire expression simplifies to 2, but if you need the simplest log expression, then you can use
[tex] \log_{12} 144 [/tex]
Carlos tiene un terreno cuadrado que mide 8 m por lado. ¿Cuál es el área del terreno?¿Qué operación permite obtenerla?
Answer:
32 ,multiplica 8 por 2 en cuanto lo vi lo resolví
Your parents are building a pool that is 7 ft wide and 12 ft long. They want to put a walkway around the pool that is x ft wide on all sides. Write a polynomial that represents the combined area of the pool and walkway. Answer needs to be in standard form and use x as your variable.
Answer:
Combined area = 4[tex]x^{2}[/tex] + 38x + 84
Step-by-step explanation:
The rectangle formed by the pool and walkway is 12 + 2x long and 7 + 2x wide.
Area of the rectangle = lw = (2x + 12)(2x + 7) = 4[tex]x^{2}[/tex] + 38x + 84
A
walking path across a park is represented by the equation y = -3x - 6. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 3). Identify the equation that represents the new path.
Answer:
We are given the path, y=-3x-6
The general form of the straight line is 'y=mx+b', where 'm' is the slope and 'b' is the y-intercept.
Thus, the slope of the given line is -3.
As, we have that the incipient path is perpendicular to the given path.
And, we ken that, 'Product of slopes of perpendicular lines is -1'.
Since, the incipient path passes through the point (-3,3). Superseding the values in the general form, we get,
b= 3+1
b= 4.
Step-by-step explanation:
the cost of contructing a 63mcube wall is rs 84000. find the volume of each brick if the cost of a bric is rs 13
Answer:
0.00975 m^3 each
Step-by-step explanation:
rs 84000 / rs 13 = 6461.539 bricks
63 m^3 / 6461.539 = 0.00975 m^3 each
Please put all these in order. Will give brainleast if answered correctly.
Answer: I can’t see the pic it’s blank
Step-by-step explanation:
Step-by-step explanation:
The answer is two because when you have one pen and buy another one it becomes two pens
anyone think they could help me with this question???
Answer:
61
Step-by-step explanation:
As we can see the triangles are congruent so
< F = < C ( being corresponding angles of congruent triangle)
< C = 29
Now
<A +<B + <C = 180° { being sum of angles of triangle }
5x + 1 + 90 + 29 = 180°
5x = 180° - 120°
5x = 60°
x = 12°
<A = 5 * 12° + 1 = 61°
Hope it will help :)
Pleaseeee help I need a answer fast
Answer:
300
Step-by-step explanation:
im smart
someone who can actually give the answer please answer this please! do not put nothing crazy or get reported!!
Find the zeros of this polynomial.
Answer:you’ll find the answer just by understanding and looking at the photo
Step-by-step explanation:
1 + 7x
The sum of two numbersis 23. The greater number
is b. Select the expression that represents the lesser
number.
Answer:
Step-by-step explanation:
a+b = 23
a<b
a = 23-b
el área de un mosaico es de 900cm2 ¿cuánto mide por lado cada mosaico
Answer:
El lado de cada mosaico tiene una longitud de 30 cm.
Step-by-step explanation:
El area de un mosaico cuadrado es:
[tex]A=l^{2}[/tex]
Donde l es el lado del mosaico.
Entonces, si sabes que el area es 900 cm², el lado valdra:
[tex]900=l^{2}[/tex]
[tex]l=\sqrt{900}[/tex]
[tex]l=30\: cm[/tex]
Por lo tanto el lado de cada mosaico tiene una longitud de 30 cm.
Espero te haya servido!