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3 years ago

Select "Yes" or "No" to indicate whether the ordered pair is on the graph of the function f(x)=−16x+1 .

1 answer:

8 0

To check if the pair is on the graph, plug the x value into the x in the equation, and solve. If the solution to the equation matches the y value from your ordered pair, it’s on the graph, so mark “yes”. If the solution isn’t the same, it’s not on the graph, so mark “no”.

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A typical lap around a track in the United States has length of 440 yards. How many lap would need to be complete to run a mile?

g100num [7]

4 laps because a mile is 1,760 yards and the 440 laps need to be divided into 1,760 so 1,760/440 is 4 so four laps are needed to complete a mile

3 0

2 years ago

◆ Quadratic Equations ◆ Please help !

Mila [183]

I'm sure there's an easier way of solving it than the way I did, but I'm not sure what it could be. Never dealt with a problem like this before.

Anyway, I just plugged in and tested. Chose random values for a, b, c, and d, which follow the rule 0 < a < b < c < d:

a = 1
b = 2
c = 3
d = 4

$\sf ax^2+(1-a(b+c))x+abc-d)$

$\sf 1x^2+(1-1(2+3))x+(1)(2)(3)-(4))$

Simplify into standard form:

$\sf x^2+(1-1(5))x+6-4$

$\sf x^2+(1-5)x+2$

$\sf x^2-4x+2$

Use the quadratic formula to solve:

$\sf x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

For functions in the form of $\sf ax^2+bx+c$ . So in this case:

a = 1
b = -4
c = 2

Plug them in:

$\sf x=\dfrac{4\pm\sqrt{(-4)^2-4(1)(2)}}{2(1)}$

Solve for 'x':

$\sf x=\dfrac{4\pm\sqrt{16-8}}{2}$

$\sf x=\dfrac{4\pm\sqrt{8}}{2}$

$\sf x\approx\dfrac{4\pm 2.83}{2}$

$\sf x\approx 0.59,3.41$

So the answer would be A.

3 0

3 years ago

Which pair of funtions is not a pair of inverse functions? please help!!

antiseptic1488 [7]

Answer:

$f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Step-by-step explanation:

we know that

To find the inverse of a function, exchange variables x for y and y for x. Then clear the y-variable to get the inverse function.

we will proceed to verify each case to determine the solution of the problem

case A) $f(x)=\frac{x+1}{6} , g(x)=6x-1$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y+1}{6}$

Isolate the variable y

$6x=y+1$

$y=6x-1$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=6x-1$

therefore

f(x) and g(x) are inverse functions

case B) $f(x)=\frac{x-4}{19} , g(x)=19x+4$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y-4}{19}$

Isolate the variable y

$19x=y-4$

$y=19x+4$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=19x+4$

therefore

f(x) and g(x) are inverse functions

case C) $f(x)=x^{5}, g(x)=\sqrt[5]{x}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=y^{5}$

Isolate the variable y

fifth root both members

$y=\sqrt[5]{x}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=\sqrt[5]{x}$

therefore

f(x) and g(x) are inverse functions

case D) $f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y}{y+20}$

Isolate the variable y

$x(y+20)=y$

$xy+20x=y$

$y-xy=20x$

$y(1-x)=20x$

$y=20x/(1-x)$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=20x/(1-x)$

$\frac{20x}{1-x}\neq \frac{20x}{x-1}$

therefore

f(x) and g(x) is not a pair of inverse functions

7 0

2 years ago

Read 2 more answers

Here is another one I need help with

aksik [14]

Answer:

Step-by-step explanation:

Surface area of objects with flat surfaces like this is simply the area of each surface added together, so let's get to work.

Both have 6 faces, so we will be adding six values together for each.

Container A:

Hopefully you can imagine the six different faces. It's kinda like a cereal box.

The front and back of a cereal box have the same area, as do the two sides and the top and bottom, so that makes it a little easier.

Front and Back: 28 * 36 = 1008

Sides: 36*6 = 216

Top and Bottom: 6*28 = 168

Let me know if you don't understand how I did any of that. Anyway, since there is a matching face for each we add them all together twice.

1008*2 + 216*2 + 168*2 = 2784 in^2

Container B has a similar setup, I won't write out everything like I did unless you want me to work it out with you.

2(16*12+16*22+22*12) = 1616 in^2

So since Container A has a surface area of 2784 and Container B has a surface area of 1616 it's obvious container A has a larger surface area

4 0

2 years ago

How do i figure out 9 1/6 - 8 5/6 and 10 3/4 - 6 4/4?

Westkost [7]

Answer:

1) $9\frac{1}{6}-8\frac{5}{6}=\frac{1}{3}$

2) $10\frac{3}{4}-6\frac{4}{4}=3\frac{3}{4}$

Step-by-step explanation:

You can convert he mixed numbers to improper fractions:

1. Multiply the whole number part by the denominator of the fraction.

2. Add the product obtained to the numerator.

3. The denominator does not change.

Then:

$9\frac{1}{6}=\frac{54+1}{6}=\frac{55}{6}\\\\8\frac{5}{6}=\frac{48+5}{6}=\frac{53}{6}\\\\10\frac{3}{4}=\frac{40+3}{4}=\frac{43}{4}\\\\6\frac{4}{4}=\frac{24+4}{4}=\frac{28}{4}$

Observe that, in each subtraction, the denominators are equal, then you can rewrite the denominator and subtract the numerators:

$1)\ \frac{55}{6}-\frac{53}{6}=\frac{55-53}{6}= \frac{2}{6}=\frac{1}{3} \\\\2)\ \frac{43}{4}-\frac{28}{4}=\frac{43-28}{4}= \frac{15}{4}$

Divide 15 by 4. The quotient will be 3 and the remainder 3.

Then:

$\frac{15}{4}=3\frac{3}{4}$

6 0

2 years ago