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2 years ago

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The table and the graph show the relationship between the edge length, x, of a cube and its surface area, y. Is the relation a f

unction?
Also weirdgamergirl7 if your watching this, ty for the answers <3

1 answer:

d1i1m1o1n [39]2 years ago

4 0

Answer:

Yes, the relationship between x and y is a non-linear function.

Step-by-step explanation:

Given the table

Edge Length, x Surface Area, y

1 6

2 24

3 54

4 96

The table values clearly represent a function, because each input value has one and only one output value. i.e. there is no repetition of x values.

Also from the table values and the graph, it is clear that the function is not a linear function, because the graph is not a straight line. Also, In a cubic function, the highest power over the x variable(s) is 3. So, it is not a linear function.

Hence, we conclude that Yes, the relationship between x and y is a non-linear function.

Therefore, the 'last option' is correct.

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Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 10x2+4xâ1, 3xâ4x2+3, and

lord [1]

I suppose

$H=\mathrm{span}\{10x^2+4x-1,3x-4x^2+3,5x^2+x-1\}$

The vectors that span $H$ form a basis for $P_2$ if they are (1) linearly independent and (2) any vector in $P_2$ can be expressed as a linear combination of those vectors (i.e. they span $P_2$ ).

Independence:

Compute the Wronskian determinant:

$\begin{vmatrix}10x^2+4x-1&3x-4x^2+3&5x^2+x-1\\20x+4&3-8x&10x+1\\20&-8&10\end{vmatrix}=-6\neq0$

The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of $H$ is 3.

Span:

Write an arbitrary vector in $P_2$ as $ax^2+bx+c$ . Then the given vectors span $P_2$ if there is always a choice of scalars $k_1,k_2,k_3$ such that

$k_1(10x^2+4x-1)+k_2(3x-4x^2+3)+k_3(5x^2+x-1)=ax^2+bx+c$

which is equivalent to the system

$\begin{bmatrix}10&-4&5\\4&3&1\\-1&3&-1\end{bmatrix}\begin{bmatrix}k_1\\k_2\\k_3\end{bmatrix}=\begin{bmatrix}a\\b\\c\end{bmatrix}$

The coefficient matrix is non-singular, so it has an inverse. Multiplying both sides by that inverse gives

$\begin{bmatrix}k_1\\k_2\\k_3\end{bmatrix}=\begin{bmatrix}-\dfrac{6a-11b+19c}3\\\dfrac{3a-5b+2c}3\\\dfrac{15a-26b+46c}3\end{bmatrix}$

so the vectors do span $P_2$ .

The vectors comprising $H$ form a basis for it because they are linearly independent.

4 0

2 years ago

Some of the steps in the derivation of the quadratic formula are shown. Step 4: Step 5: Step 6: Step 7: Which best explains why

Otrada [13]

Answer:

The square root of terms separated by addition and subtraction cannot be calculated individually.

Step-by-step explanation:

In order to calculate the square root, we would need a monomial or a factored expression. We do not have that, so we cannot take the square root.

6 0

2 years ago

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Joseph received a $20 gift card for downloading music. Each downloaded song costs $1.29. Explain how to write and solve an inequ

poizon [28]

<span>Let x be the number of songs downloaded.
Each song is $1.29; the total cost would be found by multiplying the cost by the number of songs, or 1.29x.
This cannot be more than 20, so we set this less than or equal to 20:
1.29x ≤ 20.

<u>To solve this, we divide both sides by 1.29: </u>
</span> $\frac{1.29x}{1.29}$ <span> ≤ </span> $\frac{20}{1.29}$ <span>;
x ≤15.5.

We <u>cannot download half of a song</u>, so we round this down to 15 (although the number rounds up mathematically, he would not have enough money to download 16 songs). This means he can download at most 15 songs.</span>

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2 years ago

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The aquarium at Sea Critters Depot contains 140 fish. Eighty of these fish are green swordtails (44 female and 36 male) and 60 a

maxonik [38]

Given that:

Total number of fish = 140

Fish are green swordtails female = 44

Fish are green swordtails male = 36

Fish are orange swordtails female = 36

Fish are orange swordtails male = 24

Solution:

A. We have to find the probability that the selected fish is a green swordtail.

$\text{P(green swordtail)}=\dfrac{\text{Total green swordtail fish}}{\text{Total fish}}$

$\text{P(green swordtail)}=\dfrac{80}{140}$

$\text{P(green swordtail)}=\dfrac{4}{7}$

Therefore, the probability that the selected fish is a green swordtail is $\dfrac{4}{7}.$

B. We have to find the probability that the selected fish is male.

$\text{P(Male fish)}=\dfrac{\text{Total male fish}}{\text{Total fish}}$

$\text{P(Male fish)}=\dfrac{36+24}{140}$

$\text{P(Male fish)}=\dfrac{60}{140}$

$\text{P(Male fish)}=\dfrac{3}{7}$

Therefore, the probability that the selected fish is a male, is $\dfrac{3}{7}.$

C. We have to find the probability that the selected fish is a male green swordtail.

$\text{P(Male green swordtail)}=\dfrac{\text{Total male green swordtail fish}}{\text{Total fish}}$

$\text{P(Male green swordtail)}=\dfrac{36}{140}$

$\text{P(Male green swordtail)}=\dfrac{9}{35}$

Therefore, probability that the selected fish is a male green swordtail is $\dfrac{9}{35}.$

D.

We have to find the probability that the selected fish is either a male or a green swordtail.

$\text{P(Male or green swordtail)}=\dfrac{\text{Total male or green swordtail fish}}{\text{Total fish}}$

$\text{P(Male or green swordtail)}=\dfrac{44+36+24}{140}$

$\text{P(Male or green swordtail)}=\dfrac{96}{140}$

$\text{P(Male or green swordtail)}=\dfrac{24}{35}$

Therefore, the probability the selected fish is either a male or a green swordtail is $\dfrac{24}{35}.$

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2 years ago

Which equation accurately represents this statement? Select three options.

atroni [7]

Complete question:

Which equation accurately represents this statement? Check all that apply.

Negative 3 less than 4.9 times a number, x, is the same as 12.8

A: -3-4.9x=12.8

B: 4.9x-(-3)=12.8

C: 3+4.9x=12.8

D: (4.9-3)x=12.8

E: 12.8=4.9x+3

Answer:

B: 4.9x-(-3)=12.8

C: 3+4.9x=12.8

E: 12.8=4.9x+3

Step-by-step explanation:

The word equation can be expressed mathematically as follows

negative 3 → -3

less than 4.9 times a number , x → 4.9 x - (-3)

is same as 12.8 → 4.9 x - (-3) = 12.8

The equation can be expressed as

4.9 x - (-3) = 12.8

when you open the bracket, you multiply -3 time - 1 . MInus times minus is equals to plus. so you get

4.9 x + 3 = 12.8

12.8 = 4.9x+3

3 0

2 years ago

Read 2 more answers