Jessica had 207 dollars to spend on 8 books. After

URGENT!! HELP WITH THIS MULTIPLE CHOICE MATH PROBLEM (MORE COMING...)

ch4aika [34]

Your answer would be 0,6.

- Because if you look at it correctly you see the right is at 0 and the top is at 6

6 0

2 years ago

Read 2 more answers

1 point) Are the functions f,g, and h given below linearly independent? f(x)=e3x+cos(5x), g(x)=e3x−cos(5x), h(x)=cos(5x). If the

Fynjy0 [20]

Answer:

Functions are linearly dependent (are not linearly independent.)

Step-by-step explanation:

Remember that two functions f(x), g(x) and h(x) are said linearly independent on an interval I if the <em>only solution</em> to the equation

$\alpha f(x)+\beta g(x)+\omega h(x)=0, \ \text{for all } x\in I$

is the trivial one: α = 0, β = 0, ω = 0. If they are not linearly independent, they are called linearly dependent.

Now, let f(x), g(x) and h(x) be the functions:

$f(x)=e^{3x}+\cos(5x),$

$g(x)=e^{3x}-\cos(5x),$

$h(x)=\cos(5x).$

Then, letting α = 1, β= -1 and ω = -2, we see that:

$\alpha f(x)+\beta g(x)+ \omega h(x)=e^{3x}+\cos(5x)-e^{3x}+\cos(5x)+2\cos(5x)=0.$

Hence, the functions f(x), g(x) and h(x) are not linearly independent, or equivalently, are linearly dependent.

8 0

2 years ago

Consider the problem of finding the line of symmetry and vertex of the quadratic equation f(x) =x^2-8x+15 What is the error in t

Jet001 [13]

We are given the quadratic:

$f(x)=x^2-8x+15$ , with a=1, b=-8, c=15.

We know that the x-coordinate of the vertex, which is the point where the line of symmetry passes through is

$\displaystyle{ -\frac{b}{2a}$ .

Thus, the x-coordinate of the vertex is $-\frac{b}{2a} =-\frac{-8}{2\cdot1}= \frac{8}{2}=4$ .

Thus, the line of symmetry is x=4.

Answer: <span>B. The line of symmetry should have been 4 instead of –4. </span>

6 0

2 years ago

I NEED HELP WITH THIS PLEASE !!! AND EXPLAINED PLEASE!

Ksenya-84 [330]

Answer:

Step-by-step explanation:

Find the vertex and intercepts of y = 3x2 + x – 2 and graph; remember to label the vertex and the axis of symmetry.

This is the same quadratic as in the last example. I already found the vertex when I worked the problem above. This time, I also need to find the intercepts before I do my graph. To find the y-intercept, I set x equal to zero and solve:

y = 3(0)2 + (0) – 2

= 0 + 0 – 2 = –2

Then the y-intercept is the point (0, –2). To find the x-intercept, I set y equal to zero, and solve:

0 = 3x2 + x – 2

0 = (3x – 2)(x + 1)

3x – 2 = 0 or x + 1 = 0

x = 2/3 or x = – 1

Then the x-intercepts are at the points (–1, 0) and ( 2/3, 0).

The axis of symmetry is halfway between the two x-intercepts at (–1, 0) and at ( 2/3 , 0); using this, I can confirm the answer from the previous page:

(–1 + 2/3) / 2 = (–1/3) / 2 = –1/6

The complete answer is a listing of the vertex, the axis of symmetry, and all three intercepts, along with a nice neat graph:

The vertex is at ( –1/6 , –25/12 ), the axis of symmetry is the line x = –1/6 , and the intercepts are at (0, –2), (–1, 0), and ( 2/3, 0).

graph of y = 3x^2 + x - 2 with vertex and intercepts marked.

Find the intercepts, the axis of symmetry, and vertex of y = x2 – x – 12.

To find the y-intercept, I set x equal to 0 and solve:

y = (0)2 – (0) – 12 = 0 – 0 – 12 = –12

To find the x-intercept, I set y equal to 0 and solve:

0 = x2 – x – 12

0 = (x – 4)(x + 3)

x = 4 or x = –3

To find the vertex, I look at the coefficients: a = 1 and b = –1. Plugging into the formula, I get:

h = –(–1)/2(1) = 1/2 = 0.5

To find k, I plug h = 1/2 in for x inside y = x2 – x – 12, and simplify:

k = (1/2)2 – (1/2) – 12 = 1/4 – 1/2 – 12 = –12.25

Once I have the vertex, it's easy to write down the axis of symmetry: x = 0.5. Now I'll find some additional plot points, to fill in the graph:

T-chart

graph of y = x^2 - x - 12

The vertex is at the point (0.5, –12.25),

the axis of symmetry is the line x = 0.5,

and the intercepts are at the points (0, –12), (–3, 0), and (4, 0).

4 0

3 years ago

The radius of a circle is increased from 8.008.00 to 8.038.03 m. Estimate the resulting change in area, and then express the es

Reika [66]

Answer:

Step-by-step explanation:

The area of a circle is expressed as

Area = πr^2

Where r = radius of the circle

π = constant = 3.14

The radius of a circle is increased from 8.00800 to 8.03803 m. This means that the original radius of the circle is 8.00800 and the new radius of the circle is 8.03803

Area of original circle =

3.14 × 8.00800^2 = 201.36212096

Area of new circle =

3.14 × 8.03803^2 = 202.87516852203

Increase in area = 202.87516852203 - 201.36212096

= 1.51304756203

Expressing the change as a percentage, it becomes

1.51304756203/201.36212096 ×100

Percentage change = 0.75 %

7 0

3 years ago