2x-y=15 over 4x+3y=-5. What's is the solution to the system

Answers

Answer 1

Answer: Equation at the end of step 1 : 15 (2x - y) - ((—— • x) + 3y) = 0 4 Step 2 :Rewriting the whole as an Equivalent Fraction :

2.1 Adding a whole to a fraction

Rewrite the whole as a fraction using 4 as the denominator :

3y 3y • 4 3y = —— = —————— 1 4

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

15x + 3y • 4 15x + 12y ———————————— = ————————— 4 4 Equation at the end of step 2 : (15x + 12y) (2x - y) - ——————————— = 0 4 Step 3 :Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 4 as the denominator :

2x - y (2x - y) • 4 2x - y = —————— = ———————————— 1 4 Step 4 :Pulling out like terms :

4.1 Pull out like factors :

15x + 12y = 3 • (5x + 4y)

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

(2x-y) • 4 - (3 • (5x+4y)) -7x - 16y —————————————————————————— = ————————— 4 4 Step 5 :Pulling out like terms :

5.1 Pull out like factors :

-7x - 16y = -1 • (7x + 16y)

Equation at the end of step 5 : -7x - 16y ————————— = 0 4 Step 6 :When a fraction equals zero : 6.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

-7x-16y ——————— • 4 = 0 • 4 4

Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
-7x-16y = 0

Equation of a Straight Line

6.2 Solve -7x-16y = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -7x-16y = 0 and calculate its properties

Graph of a Straight Line :Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 0/-16 so this line "cuts" the y axis at y=-0.00000

y-intercept = 0/-16 = -0.00000 Calculate the X-Intercept :

When y = 0 the value of x is 0/-7 Our line therefore "cuts" the x axis at x=-0.00000

x-intercept = 0/-7 = -0.00000 Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.000 and for x=2.000, the value of y is -0.875. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.875 - 0.000 = -0.875 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -0.875/2.000 = -0.438 Geometric figure: Straight Line Slope = -0.875/2.000 = -0.438 x-intercept = 0/-7 = -0.00000 y-intercept = 0/-16 = -0.00000

hope this helps hope i am brainliest i need one more

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You are using a math software program to make a pattern for a plastic part. You draw the pattern on a coordinate plane with units in millimeters and the bottom left corner as the origin. Write an equation for the circular hole.Someone plz help me >_<

Answers

Answer:

(x - 48)² + (y - 24)² = 64

Step-by-step explanation:

From the graph we see that

The diameter of the circle is: d = 16 mm
Then its radius is: r = 16 mm/ 2 = 8 mm

The center has x-coordinate: h = 40 + 8 = 48
Y-coordinate: k = 32 - 8 = 24

Use circle formula:

(x - h)² + (y - k)² = r²

Substitute values to get required equation:

(x - 48)² + (y - 24)² = 8²
(x - 48)² + (y - 24)² = 64

Answer: (x - 2) ^2 + (y - 6) ^2 = 25

What digit appears in the units place in the number obtained when 2^320 is multiplied out?

Answers

Let's start with 2^x and see if we can find a recurring pattern to help us find the answer

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = (1)6
2^5 = (3)2
2^6 = (6)4
2^7 = (12)8
2^8 = (25)6

If you notice, the pattern is 2,4,8,6 in the units place. Every four consecutive x's, the cycle repeats. So at 2^4, 2^8, 2^12 (4096), and 2^16(65336), the units place will all be 6, since x is always divisible by 4 here. When x= 320, we know that 320 is divisible by 4. This means that for 2^320, the units place will also be 6.

Hope this helps, even though it's rather vague!

Given f(x)=x+5 all over 3, solve for f^-1(3) (A. -1; B. 14; C. 18; D. 21)

Answers

f^-1 means finverse
find finverse then subsitute 3 for x
to solve

replace f(x) with y
solve for x
switch x with y
replace y with finverse or f^-1

f(x)=(x+5)/3
y=(x+5)/3
3y=x+5
3y-5=x
3x-5=y
finvers=3x-5

fiinverse(3)=3(3)-5
finverse(3)=9-5
finverse(3)=4
why is it not listed again

Use the zeros of the following quadratic to find the x-value of the vertex.y = x2 – 4x – 5
A.5
B.2
C.–2
D.–5

Answers

1. y = x^2 - 4x - 5
= x^2 - 4x + 4 - 4 - 5
= (x^2 - 4x + 4) -4 - 5
y = (x-2)^2 - 9 Here, the vertex is at (2, -9)

2. x = 2 (the vertical line that goes through the vertex)
3. The graph of this function is called a parabola. To graph a parabola, use
its vertex (in this case, (2, -9) ) and y-intercept (y = -5). The y-intercept is the constant in the given equation. Use the fact that the vertical line through the vertex is a line of symmetry. Plot the point corresponding to the y-intercept that lies on the other side of the vertical line x = 2.

4. The graph is translated 2 units to the right and 9 units down.

Answer:

The answer is B.) 2

(on e2020)

What is the volume of the oblique cone? Round to the nearest tenth. 142.4 cubic units 142.4 square units 196.0 cubic units 196.0 square units