Answer:
(a) Proof explained below
(b) The two lines are parallel
Step-by-step explanation:
(a) In the second equation express [tex]x[/tex] in terms of [tex]y[/tex] to get:
[tex]x=2y-8[/tex]
Then, substitute [tex]x[/tex] for [tex]2y-8[/tex] in the first equation to get:
[tex]3(2y-8)-6y=-12[/tex]
Open parentheses using the distributive property ([tex]a(b-c)=ab-ac[/tex]) which results in:
[tex]6y-24-6y=-12[/tex]
Combine like terms to reach:
[tex]-24=-12[/tex], which is not true. Therefore, for any values of [tex]x[/tex] and [tex]y[/tex], the systems of equations will have no solutions.
Since the two lines have no solutions, that means that they are parallel.
Hope this helps :)
Problem 1. Consider first order equations and determine if they are linear homogeneous, linear inhomogeneous, or nonlinear (u is an unknown function);.
Answer:
I have to see them
Step-by-step explanation:
show them to me
find the equation of the tangent to the circle x²+y²-2x-y-15=0
Answer:
x−2y+5=0
Step-by-step explanation:
x2+y2−2x+4y=15
differentiating both sides with respect to x
2x+2yy′−2+4y′=0
2x−2+(2y+4)y′=0
y′=2−2x2y+4
y′(−1,2)=2+24+4=12
slope of tangent at (- 1, 2)=12
Equation of the tangent is
y−2=12(x+1)
x−2y+5=0
What is the range of the function {(0, 15), (4, 6), (6, 4), (8, 0)}?
The range of a function is the set of output values of the function
The range of the function is: {15, 6, 4, 0}
How to determine the rangeThe function is defined as:
(x,y) = {(0, 15), (4, 6), (6, 4), (8, 0)}
The range is the y-values.
So, we have:
y = {15, 6, 4, 0}
Hence, the range of the function is: {15, 6, 4, 0}
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help
What should be added to –7mn+2m2+3n2
to obtain 5m2+2mn-9n2
The polynomial to be added to –7mn + 2m² + 3n² to obtain 5m² + 2mn - 9n² is: 3m² - 11n² + 9mn.
Addition of PolynomialsLike terms should be combined together when adding polynomials.
Let x represent the polynomial expression that would be added to –7mn + 2m² + 3n² to obtain 5m² + 2mn - 9n².
Therefore:
–7mn + 2m² + 3n² + x = 5m² + 2mn - 9n².
x = 5m² + 2mn - 9n² - (-7mn + 2m² + 3n²)
x = 5m² + 2mn - 9n² + 7mn - 2m² - 3n²
Combine like terms together.
x = 3m² - 11n² + 9mn
Therefore, the polynomial to be added to –7mn + 2m² + 3n² to obtain 5m² + 2mn - 9n² is: 3m² - 11n² + 9mn.
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What is the measure of AngleP to the nearest whole degree? 35° 52° 57° 72°.
You can use the law of cosine to find the measure of angle P.
The measure of angle P is given by
Option C : 57°
What is law of cosine?Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
[tex]c^2 = a^2 + b^2 - 2ab\cos(\theta)}[/tex]
(c is opposite side to angle A)
Using the law of sines to find the measure of angle P in the given contextRefer to the attached figure below.
Using the cosine law, we get
|PQ| = a = 17 units, |QR| =length of opposite side to P = c = 15 units, |PQ| = b = 14 units.
Thus, let angle QPR be of θ degrees, then
[tex]cos(\theta) =\dfrac{a^2 + b^2 - c^2}{2ab} = 0.546\\\\\theta = arccos(0.546) = 56.9^\circ, -56.9^\circ[/tex]
triangle's angles are measured positive, thus, measure of angle P came out as 56.9 degrees or approx 57°
Thus,
The measure of angle P is given by
Option C : 57°
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Answer:
The answer is 57
Step-by-step explanation:
What is the factored form of 6x2 11x – 10? (2x )( x – ).
Answer:
[tex](2x+5)(3x-2)[/tex]
Step-by-step explanation:
Use slide-and-divide method
[tex]6x^2+11x-10\\\\x^2+11x-60\\\\(x+15)(x-4)\\\\(2x+5)(3x-2)[/tex]
Fiona is drawing polygons on a computer. She wants to map a regular 9-sided polygon back onto itself using a reflection. Which set of lines can fiona choose from for her line of reflection?.
any perpendicular bisector of one of the sides".
We can define a line of reflection as the line in which a shape is reflected, or we can say that it is the mirror in which the shape is reflected. The line of reflection is the perpendicular bisector of any pair of corresponding points. If you want to join sets of corresponding points on the object and image, then
Step-by-step explanation:
Which set of numbers are equivalent?
es )
A)
10
50%, 0.5,
20
B)
65
65%, 0.65,
1000
C)
7
70%, 0.7,
100
D)
95
95%, 0.95,
1000
Answer:
uhhhhhh
Step-by-step explanation: uh
1
• Write an expression that is equivalent to
4X+1+
3
4
2 1
- -2.
3 29
1
3
2
1
х
2
=
4x +1+1x
xt
?
4
3
WILL GIVE BRAINLIEST IF CORRECTT
Matt and Adam each improved their yards by planting hostas and shrubs. They bought their
supplies from the same store. Matt spent $192 on 10 hostas and 8 shrubs. Adam spent $96 on 2
hostas and 8 shrubs. What is the cost of one hosta and the cost of one shrub
Tanner has a round tablecloth with a diameter of 10 feet. What is the tablecloth’s radius?
Answer:
the radius is 5
Step-by-step explanation:
radius is half the diameter
Answer:The radius of the tablecloth is 5
Step-by-step explanation: because to find the radius when u know the diameter u divide the diameter with is 10 by 2
What is the difference between 35-(-8)
Answer:
43
Step-by-step explanation:
add 8 because --=+
Answer:
43
Step-by-step explanation:
35-(-8) is basically doing 35+8. The 2 negatives make a positive.
What is the y-intercept of y = -32?
A) (-3,-3)
B) (-3,0)
C) (0,-3)
D) (0,0)
Hi I need help with this question
The population of a city has been increasing by 2% annually. The sign shown is from the year 2000.
Write an exponential growth function that represents the population t years after 2000.
What will the population be in 2020? Round your answer to the nearest thousand. The population will be about:
We have that the exponential growth function and population be in 2020 is mathematically given as
y=325000e^{0.002t}y=469925From the question we are told
The population of a city has been increasing by 2% annually. The sign shown is from the year 2000.Write an exponential growth function that represents the population t years after 2000.What will the population be in 2020? Round your answer to the nearest thousand. The population will be about:Populationa)
Generally the equation for the standard form of exponential function is mathematically given as
y=325000e^{0.002t}
b)
With T =20
Hence
y=325000e^{0.002(20)}
y=469925For more on Population visit
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If the focus is (2, 5) and the directrix is y=3, find the equation of the parabola.
Answer:
(x-2)^{2}=4(y-4)
Answer:
y = 1/4 (x - 2)^2 + 4
Step-by-step explanation:
The equation of a parabola is
y = a(x - h)^2 + k
This is for a parabola that opens in the y direction (up or down) If you make a sketch of the focus and directrix you'll be able to see what direction it opens. See image. The parabola kind of curls around the focus and opens away from the directrix. Also, this sketch can help you find the vertex which we need, which is actually a point on the curve and which is exactly half way between the focus and directrix.
The vertex is (h, k) for this problem it is (2, 4). h is 2 and k is 4. You will fill in the 2 and 4 in the parabola formula. Then the last thing you need is the a infront of the paranthesis on the right side of the equation.
Use the formula
a = 1/4p (the p is in the denominator).
p is the distance from the vertex to the focus, so for this question, it is 1. see image.
a = 1/4(1)
a = 1/4
Fill it in the parabola formula.
y = a (x - h)^2 + k
y = 1/4 (x - 2)^2 + 4
What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)? A. X2 y2 − 4x 2y 1 = 0 B. X2 y2 4x − 2y 1 = 0 C. X2 y2 4x − 2y 9 = 0 D. X2 − y2 2x y 1 = 0.
well, we know it's centered at (-2 , 1) and it passes through (-4 , 1), if it passes through there, that means that the distance from the center to (-4 , 1) must be its radius.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-4 - (-2)]^2 + [1 - 1]^2}\implies d=\sqrt{(-4+2)^2+0^2}\implies d=2[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-2}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{2}{ r} \\\\\\\ [x-(-2)]^2+[y-1]^2=2^2\implies (x+2)^2+(y-1)^2=4[/tex]
make x the subject of the formula
a=bx+c
Answer:
(a-c)/b = x
Step-by-step explanation:
a = bx + c
subtract 'c' from each side to get:
(a-c) = bx
divide each side by 'b' to get:
(a-c)/b = x
Which of the following is the length of the
altitude a of the equilateral triangle below?
Answer:
A) [tex]\sqrt{3}[/tex]
Step-by-step explanation:
in a 30-60-90 triangle the sides, respectively, are in the ratio of 1 : [tex]\sqrt{3}[/tex] : 2
8 + 8a - 2a - 4
Pls help
Answer:
that would 6a+4
Step-by-step explanation:
8a - 2a , 8 - 4
Answer:
6a + 4
Step-by-step explanation:
8 + 8a - 2a - 4
Combine Like Terms
(8a - 2a) + (8 - 4)
6a + 4
Orlando's class needs 1,000 tree leaves for a project.
They collected 497 leaves last week and 409 leaves this week.
What is the best estimate for the number of leaves they have collected so far?
Answer:
The total is 906 but. The estimated would be 900. Or 910.
List the terms in the trinomial below: 3 + 7a - 2x
Answer:
Terms=3, 7a, 2x
Step-by-step explanation:
A plane traveled 600 miles each way to Rome and back. The trip there was with the wind. It took 6 hours. The trip back was into the wind. The trip back took 12 hours. What is the speed of the plane in still air? What is the speed of the wind?
Answer:
I am like 95% sure that the answer is
The speed of the wind is 24mph
If this is wrong sorry
Step-by-step explanation:
Diego has a skateboard, scooter, bike, and go-cart. He wants to know which vehicle is the fastest. A friend
records how far Diego travels on each vehicle in 5 seconds. For each vehicle, Diego travels as fast as he can
along a straight level path.
100 inches equal 254 centimeters. What is the distance each vehicle traveled in centimeters?
Answer:
To solve, I need more data...
Step-by-step explanation:
Answer: For the go kart it's 4800
Step-by-step explanation:
Here are the first four terms of an arithmetic sequence. 3,10,17,24. Is 150 a term in this sequence?
Answer:
1046
Step-by-step explanation:
formula for arithmetic sequence is:
aₙ = a₁ + (n-1)d
a₁ = first value in sequence
n = term value
d = common difference
a(150) = 3 + (150-1)7
= 3+1043
= 1046
150 is a term in this sequence, its 22nd of the sequence
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n-1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_{n+1} - T_n
for all positive integer values of n
Given;
The arithmetic sequence; 3,10,17,24
D= 10-3=7, a=3
150=3+(n-1)7
150=3+7n-7
150=7n-4
150+4=7n
7n=154
n=154/7
n=22
Therefore, 150 is 22nd term of the sequence.
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You're going to the store to pick up some milk and cereal and want to know how much cash to bring. You remember last time you went to the store, milk cost $3 and cereal cost $4. Should you estimate or find an exact amount of money to bring to the store?
Answer:
I would estimate the amount of cash to bring. I say this because when you think about it you have to pay taxes which would add more to the cost. So I would probably bring around $10
8 × 0.09
0.8 × 0.09
80 × 0.9
8 × 0.9
Answer:
8x0.09=0.72
0.8x0.09=0.072
80x0.9=72
8x0.9=7.2
Step-by-step explanation:
Answer:
1. = 0.72
2. = 0.072
3. = 72
4. = 7.2
Step-by-step explanation:
8 times 9 is 72. Each answer is some factor of 72. The 1st is one hundredth. The 2nd is one thousandth. The 3rd is just 72. And the last is one tenth.
help me answer this question im struggling
Answer:
A=12
B=2
C=11
Step-by-step explanation:
use M4th W4y to use it
enna has 10 3/4 yards of fabric. She uses 6 2/3 yards to make a banner.
How much fabric is left?
Enter your answer in the box as a mixed number in simplest form.
Answer:
4 1/12
Step-by-step explanation:
Answer:
first of all we will subtract 10 from 6 which is 4 the whole number is 4
second we will subtract 2 from 3 which is 1 so the numerator is 1
third we will multiply 4 with 3 that is 12 so the denominator is 12
Explain your answer fully
