MATHEMATICS HIGH SCHOOL

Which function has the greatest y-intercept?

Answers

Answer 1

Answer:

Answer:

The function f(x) has the greatest y-intercept. Option 1 is correct.

Step-by-step explanation:

The first function is

$f(x)=4x+5$

Substitute x=0 in the given function, to find the y-intercept.

$f(0)=4(0)+5=5$

The y-intercept of f(x) is 5.

From the given graph it is clear that the y-intercept of g(x) is 2.

The third function is

$h(x)=3\sin (2x+\pi)-2$

Substitute x=0 in the given function, to find the y-intercept.

$h(x)=3\sin (2(0)+\pi)-2$

$h(x)=3\sin (\pi)-2$

$h(x)=3(0)-2$

$h(x)=-2$

The y-intercept of h(x) is -2.

$5>2>-2$

Therefore the function f(x) has the greatest y-intercept. Option 1 is correct.

Answer 2

Answer:

Final answer:

The greatest y-intercept in a function refers to the function that intersects the y-axis at the highest point. We can determine this by checking the 'b' term in the equation y = mx + b.

Explanation:

To determine which function has the greatest y-intercept, you would need to examine the 'b' term in the equation y = mx + b, which represents the y-intercept. This is the point where the function intersects the y-axis. In other words, it's the y-value where the function begins. For example, within the information provided, 'ŷ-266.8863 + 0.1656x' seems to have the largest y-intercept at 266.8863.

Now consider having graphs of multiple functions; the one that intersects the y-axis at the highest point (the largest y-value) has the greatest y-intercept.

For straight lines, their slope remains the same along the line (as demonstrated in the mention of 'Figure A1 Slope and the Algebra of Straight Lines'). It's the y-intercept that determines where on the y-axis the line begins, helping us distinguish one line from another if their slopes are identical.

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True or false. If a line L1has equation y = mx + b, where m and b are constants with m ≠ 0, then an equation of a line L2 perpendicular to L1 has the form y = -1/m x C, where C is a constant.

The formula for the volume of w sphere is v=4\3 r3 what is the formula solved for r?

Answers

V of w sphere = $(4)/(3)$ $\pi$ r³
Multiply by 3 on either sides to get rid of the fraction.
$V * 3 = (4)/(3) *3 \pi r^3$
3V = 4 $\pi$ r³
Now divide either sides by 4 $\pi$ to isolate r³
$(3V)/(4 \pi ) = (4 \pi )/(4 \pi )$ r³
4 $\pi$ and 4 $\pi$ cancels out
$(3V)/(4 \pi )$ = r³
Take the cube root to isolate r.
$\sqrt[3]{ (3V)/(4 \pi ) } = \sqrt[3]{r^3}$
the cube root cancels the cube

$\sqrt[3]{ (3V)/(4 \pi ) }$ = r

What is the elapsed time between 4:25 and 7:40?4 hours, and 5 minutes
3 hours and 15 minutes
3 hours and 45 minutes
4 hours, and 15 minutes

Answers

The elapsed time between 4:25 and 7:40 is 3 hours and 15 minutes.

Given that two times 4:25 and 7:40, we need to calculate the time elapsed between these two.

To calculate the elapsed time between 4:25 and 7:40, you need to subtract the starting time from the ending time.

First, let's calculate the difference in hours. From 4:25 to 7:40, we can see that the hours have changed from 4 to 7, which means 3 hours have passed.

Next, let's calculate the difference in minutes. From 4:25 to 7:40, the minutes have changed from 25 to 40.

This means that an additional 15 minutes have passed.

Therefore, the elapsed time between 4:25 and 7:40 is 3 hours and 15 minutes.

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It would be 3 hours, and 15 minutes

For the investment with interest compounded annually, find the final balance using the formula A = P(1 + r)t $5000 for 5 years at 3.2%

A.
$5160.00

B.
$5852.86

C.
$20,037.32

D.
$25,800.00
Question Resources

Answers

B.
$5852.86

Working;
A = P(1 + r)^t
A=5000(1+ $(3.2)/(100)$ )^5
A=5852.86

Which function has an inverse that is a function? b(x) = x2 + 3
d(x) = –9
m(x) = –7x
p(x) = |x|

Answers

On the attached diagram you can see all graphs of functions b(x), d(x), m(x) and p(x).

Finding the inverse of a function f(x):

1. First, replace f(x) with y. This is done to make the rest of the process easier.

2. Replace every x with a y and replace every y with an x.

3. Solve the equation from Step 2 for y. This is the step where mistakes are most often made so be careful with this step.

4. Replace y with $f^(-1)(x).$ In other words, you’ve managed to find the inverse.

5. Remember: the domain of f is the range of $f^(-1)$ and the range of f is the domain of $f^(-1)$ .

Using this algorithm, you can find the inverse only in case C:

for m(x)=-7x:

1. y=-7x.

2. x=-7y.

3. y=-x/7.

4. $m^(-1)(x)=-(x)/(7)$ .

5. The domain and the range of m(x) are all real numbers as well as the domain and the range of $m^(-1)(x).$

Functions b(x) and p(x) are not one-to-one functions (see attached diagram), then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.

Hello,

Answer C

y=-7x ==>x=-7y==>y=-x/7 is the inverse of m(x)
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The quadratic equation (3k-2)x^2 +12x+3(k+1) =0 has equal roots. Find the two possible values of k.

Answers

$x_1=x_2 \Rightarrow \Delta=0\n\Delta=12^2-4\cdot(3k-2)\cdot3(k+1)\n\Delta=144-(36k-24)(k+1)\n\Delta=144-36k^2-36k+24k+24\n\Delta=-36k^2-12k+168\n-36k^2-12k+168=0\n-3k^2-k+14=0\n-3k^2+6k-7k+14=0\n-3k(k-2)-7(k-2)=0\n-(3k+7)(k-2)=0\nk=-(7)/(3) \vee k=2$