1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elan Coil [88]
2 years ago
14

3(2x - 1) = 1/2 (4x - 2) + 2 What would it be?

Mathematics
1 answer:
Novay_Z [31]2 years ago
6 0

Answer:

X =  1

Step-by-step explanation:

Just distribute properly, and distribute the fraction multiplying the numerator by 4 and 2

You might be interested in
NO LINKS!!!!
statuscvo [17]

The instructions for these problems seem incomplete. I'm assuming your teacher wants you to find the equation of each parabola.

===============================================================

Problem 1

Let's place Maya at the origin (0,0) on the xy coordinate grid. We'll have her kick to the right along the positive x axis direction.

The ball lands 40 feet away from her after it sails through the air. So the ball lands at (40,0). At the halfway point is the vertex (due to symmetry of the parabola), so it occurs when x = 40/2 = 20. The ball is at a height of 18 feet here, which means the vertex location is (20,18).

The vertex being (h,k) = (20,18) leads to...

y = a(x-h)^2 + k\\y = a(x-20)^2 + 18

Let's plug in another point on this parabola, say the origin point. Then we'll solve for the variable 'a'.

y=a(x-20)^2+18\\\\0 = a(0-20)^2 + 18\\\\0 = a(-20)^2 + 18\\\\0 = 400a + 18\\\\-18 = 400a\\\\400a = -18\\\\a = -\frac{18}{400}\\\\a = -\frac{9}{200}

So we can then say,

y = a(x-h)^2 + k\\\\y = -\frac{9}{200}(x-20)^2 + 18\\\\y = -\frac{9}{200}(x^2-40x+400) + 18\\\\y = -\frac{9}{200}x^2-\frac{9}{200}*(-40x)-\frac{9}{200}*400 + 18\\\\y = -\frac{9}{200}x^2+\frac{9}{5}x-18 + 18\\\\y = -\frac{9}{200}x^2+\frac{9}{5}x\\\\

The final equation is in the form y = ax^2+bx+c where a = -\frac{9}{200}, \ b = \frac{9}{5}, \text{ and } c = 0

x = horizontal distance the ball is from Maya

y = vertical distance the ball is from Maya

Maya is placed at the origin (0,0)

The graph is shown below. Refer to the blue curve.

===============================================================

Problem 2

We could follow the same steps as problem 1, but I'll take a different approach.

Like before, the kicker is placed at the origin and will aim to the right.

Since the ball is on the ground at (0,0), this is one of the x intercepts. The other x intercept is at (60,0) because it lands 60 feet away from the kicker.

The two roots x = 0 and x = 60 lead to the factors x and x-60 respectively.

We then end up with the factorized form y = ax(x-60) where the 'a' is in the same role as before. It's the leading coefficient.

To find 'a', we'll plug in the coordinates of the vertex point (30,20). The 30 is due to it being the midpoint of x = 0 and x = 60. The 20 being the height of the ball at this peak.

y = ax(x-60)\\\\20 = a*30(30-60)\\\\20 = a*30(-30)\\\\20 = -900a\\\\a = -\frac{20}{900}\\\\a = -\frac{1}{45}

Let's use this to find the standard form of the parabola.

y = ax(x-60)\\\\y = -\frac{1}{45}x(x-60)\\\\y = -\frac{1}{45}(x^2-60x)\\\\y = -\frac{1}{45}*x^2-\frac{1}{45}*(-60x)\\\\y = -\frac{1}{45}x^2+\frac{4}{3}x\\\\

Refer to the red curve in the graph below.

===============================================================

Problem 3

We can use either method (similar to problem 1 or problem 2). The second problem's method is probably faster.

Logan is placed at (0,0) and kicks to the right. The ball lands at (30,0). Those x intercepts are x = 0 and x = 30 respectively, which lead to the factors x and x-30. This leads to y = ax(x-30)\\\\

The midpoint of (0,0) and (30,0) is (15,0). Eight feet above this midpoint is the location (15,8) which is the vertex. Plug in (x,y) = (15,8) and solve for 'a'

y = ax(x-30)\\\\8 = a*15(15-30)\\\\8 = a*15(-15)\\\\8 = -225a\\\\a = -\frac{8}{225}\\\\

So,

y = ax(x-30)\\\\y = -\frac{8}{225}x(x-30)\\\\y = -\frac{8}{225}(x^2-30x)\\\\y = -\frac{8}{225}*x^2-\frac{8}{225}*(-30x)\\\\y = -\frac{8}{225}x^2+\frac{16}{15}x\\\\

The graph is the green curve in the diagram below.

Like with the others, x and y represent the horizontal and vertical distance the ball is from the kicker. The kicker is placed at the origin (0,0).

Once we know the equation of the parabola, we can answer questions like: "how high up is the ball when it is horizontally 10 feet away?". We do this by plugging in x = 10 and computing y.

Side note: We assume that there isn't any wind. Otherwise, the wind would slow the ball down and it wouldn't be a true parabola. However, that greatly complicates the problem.

5 0
2 years ago
My daughter really docent understand this an di can't help her so if someone els could that would be great.
joja [24]

Answer:

B, D, F, and H

Step-by-step explanation:

You substitute in each of the numbers for x and see if it equals one of the values in the range. {-37, -25, -13, -1}

A)  -6(1)+11=-5 NO

B)  -6(2)+11=-1 YES

C)  -6(3)+11=-7 NO

D)  -6(4)+11=-13 YES

E)  -6(5)+11=-19 NO

F)  -6(6)+11=-25 YES

G)  -6(7)+11=-31 NO

H)  -6(8)+11=-37 YES

So the ones to select are B, D, F, and H.

5 0
2 years ago
Pls help i give brainliest ​
Troyanec [42]

Answer:

Step-by-step explanation:

672532 to nearest thousand = 673000

hope this helps

plz mark as brainliest!!!!!!!!!

4 0
3 years ago
Read 2 more answers
Convert 13/25 to a decimal
sergejj [24]
The decimal form is 0.52
3 0
3 years ago
Irrational numbers are imaginary. true or false
Vedmedyk [2.9K]

Imaginary numbers are not rational which may lead you to believe that they must be irrational. Though logical, you would still be incorrect because “irrational” also applies only to real numbers.

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • A phone company charges $0.06 per minute for local calls and $0.15 per minute for international calls. When your bill comes, it
    14·1 answer
  • HELP PLS DUE TODAY
    15·1 answer
  • Hi, could someone give me the correct answer i really need it and i'd appreciate it so much. Can anyone please help?
    9·1 answer
  • Pythagorean triples are given by the formulas x2 - y2, 2xy, and x2 + y2. Use the formulas for the Pythagorean triples to find a
    15·1 answer
  • What is the standard form of a quadratic equation
    15·1 answer
  • The diameter of a circle is 46 yards. What is the circle's circumference? d=46 yd Use 3.14 for it.
    14·1 answer
  • Find the value of X in each case:
    7·1 answer
  • The ordered pairs (0, 2) and (1,6)
    12·1 answer
  • Which box plot correctly represents the data 1,1,5,5,7,8,8,10,12
    13·1 answer
  • Hello! Can anyone please tell me the measurement of t and v ? Any help is gladly appreciated.​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!