Assume each variable has a different value. Which relations below are functions? a. {(a, b), (a, c), (a, d), (a, e)} b. {(a, b), (b, b), (c, b), (d, b)} c. {(a, b), (c, d), (e, f), (g, h)} d. {(a, a), (b, c), (c, c), (d, e)}A. choice a only

B. choices b and c only

C. choice c only

D. choices b, c, d only

Answers

Answer 1

Answer:

A function is a relation in which every input value x has at most one output value y.

Consider all options:

a. Relation {(a, b), (a, c), (a, d), (a, e)} is not a function, because input value a has four different output values b, c, d and e.

b. Relation {(a, b), (b, b), (c, b), (d, b)} is a function, because every input value a, b, c and d have at most one output value b.

c. Relation {(a, b), (c, d), (e, f), (g, h)} is a function, because every input value a, c, e and g have at most one output value b, d, f and g, respectively.

d. Relation {(a, a), (b, c), (c, c), (d, e)} is a function, because every input value a, b, c and d have at most one output value a, c, c and e, respectively.

Answer: correct choice is D

Answer 2

Answer: i think its D but im not 100% sure let me know if its right

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-(4x - 7) + 1 = 2 (5 - 2x) solve for x

Answers

Answer:

No solution

Step-by-step explanation:

-(4x - 7) + 1 = 2(5 - 2x)

-4x + 7 + 1 = 10 - 4x

-4x + 8 = 10 - 4x

-4x + 8 ≠ -4x + 10

No solution

What is decrease £20 by 15%

Answers

You multiply 20 by the multiplier
20x0.85=17

$15\%\cdot\pounds20=0.15\cdot\pounds20=\pounds3\n\pounds20-\pounds3=\pounds17$

A straight line has gradient m and passes through the points (0,-2). Find the two values for m for which the line is tangent to the curve y=x^2-2x 7. And for each value of m, find the coordinates of the points where the line touches the curve

Answers

Answer:

when m=2 or -2, the line is tangent to the curve at the points (2.7) and (0,7)

Step-by-step explanation:

Answer:

Hi,

Step-by-step explanation:

The curve is y=x^²-2x+7

The tangent has for equation: y=mx-2

Let's find the intersection of the tangent and the curve.

$mx-2=x^2-2x+7\n\nx^2+(-2-m)x+9=0\n\Delta=(-2-m)^2-4*9=m^2+4m-32\nThe\ point\ must\ be \ unique: \Delta=0\n\nm^2+4m-32=0\n\delta=4^2+4*32=144=12^2\n\nm=(-4-12)/(2) =-8\ or\ m=(-4+12)/(2) =4\n\nx^2+(-2-m)x+9=0\ and\ \Delta=0 = > x=(2+m)/(2) \n\nif\ m=-8\ then\ x=(2+(-8))/(2)=-3\ and\ y=mx-2=(-8)*(-3)-2=22\n\nif\ m=4\ then\ x=(2+4)/(2)=3\ and\ y=mx-2=4*3-2=10\n\n\nCoordinates\ of\ the\ points\ are (-3,22)\ and\ (3,10)\n$

Natalie charges $1490 per month to rent each of her three rental houses. Natalie must pay $5850 in maintenance cots per house per year. If all three houses are occupied, how much money will Natalie earn over seven years?

Answers

3(1490) = 4470 per month for rent she collects...4470(12) = 53640 per yr
3(5850) = 17550 per year she pays in maintenance cost

over 7 yrs...
53640(7) - 17550(7) = 375480 - 122850 = 252630 <== what she earned

The corner of a rectangle is cut, creating a right trapezoid. What is the value of x? 105o 115o 125o 135o

Answers

The value of x = 135 degrees.

You can figure this out easily by extending the top and bottom sides of the trapezoid, and finding supplementary / corresponding angles.

First, look at the top. We know that supplementary angles add up to 180 degrees (or form a straight line), so subtract 180 - 45 to get 135 degrees.

When you extend the short (bottom) side of the trapezoid along with the long (top) side and the diagonal line, it’s easy to see that there are corresponding angles. The 135-degree angle corresponds with angle x, so the measure of x would therefore be 135 degrees.

Answer:

135

Step-by-step explanation:

Fill in the blank to make a perfect square y^2-12y+?

Answers

$A\ perfect\ square:(a-b)^2=a^2-2ab+b^2\n\ny^2-12y+?\n\ny^2-2y\cdot6+?\n\n\boxed{y^2-2y\cdot6+6^2=y^2-12y+36}=(y-6)^2$

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