All categories

4 years ago

What is the rule/output?

Mathematics

2 answers:

tankabanditka [31]4 years ago

7 0

Answer:

The rule is y = 4x - 5.

Step-by-step explanation:

Notice that if we start with x = 1 and increase x by 1, we get 2. Simultaneously, y starts with -1 and becomes 3. Thus, the slope is m = rise / run = 4/1, or 4.

The rule is y = 4x - 5.

Check: Suppose we pick input 4 from the table. Does this rule produce output 11? Is 11 = 4(4) - 5 true? YES.

labwork [276]4 years ago

6 0

Answer:

y = 4x - 5

Step-by-step explanation:

Have you been taught to set up 2 equations and 2 unknowns?

That is actually the only way I could do this.

y = mx + b

x = 2

y = 3

3 = 2m + b

x = 1

y = -1

-1 = m + b Multiply by 2. That means that the m term will cancel.

================

-2 =2m +2b

<u>3 = 2m + b </u> Subtract

-5 = b

==================

3 = 2m + b Substitute - 5 for b

3 = 2m - 5 Add 5 to both sides.

3+5= 2m-5+5 Combine

8 = 2m Divide by 2

8/2=2m/2

m = 4

You might be interested in

Condense the following logs into a single log:

mamaluj [8]

QUESTION 1

The given logarithm is

$8\log_g(x)+5\log_g(y)$

We apply the power rule of logarithms; $n\log_a(m)=\log_(m^n)$

$=\log_g(x^8)+\log_g(y^5)$

We now apply the product rule of logarithm;

$\log_a(m)+\log_a(n)=\log_a(mn)$

$=\log_g(x^8y^5)$

QUESTION 2

The given logarithm is

$8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)$

We apply the power rule of logarithm to get;

$=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)$

We apply the product to obtain;

$=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)$

We apply the quotient rule; $\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )$

$=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})$

$=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})$

7 0

3 years ago

5) The Barnett triplets went to the school carnival. Henry rode on 5 rides, bought 2 drinks, 1 bag of popcorn and

dusya [7]

Answer:

Step-by-step explanation:

5 0

3 years ago

Prove that if the set of vectors {u1, u2, u3} is linearly dependent and u4 is any vector, then the set {u1, u2, u3, u4} is linea

Lesechka [4]

Answer with Step-by-step explanation:

We are given that the set of vectors ${u_1,u_2,u_3}$ is lineraly dependent set .

We have to prove that the set ${u_1,u_2,u_3,u_4}$ is linearly dependent .

Linearly dependent vectors : If the vectors $u_1,u_2.u_3,u_4$

are linearly dependent therefore the linear combination

$a_1u_1+a_2u_2+a_3u_3+a_4u_4=0$

Then ,there exit a scalar which is not equal to zero .

Let $a_1\neq0$ then the vector $u_1$ will be zero and remaining other vectors are not zero.

Proof:

When $u_1,u_2,u_3$ are linearly dependent vectors therefore, linear combination of vectors of given set

$a_1u_1+a_2u_2+a_3u_3=0$

By definition of linearly dependent vector

There exist a scalar which is not equal to zero.

Suppose $a_1\neq 0$ then $u_1=0$

The linear combination of the set ${u_1,u_2,u_3,u_4}$

$a_1u_1+a_2u_2+a_3u_3+a_4u_4=0$

When $a_1\neq0\; and\; u_1=0$

Therefore,the set ${u_1,u_2,u_3,u_4}$ is linearly dependent because it contain a vector which is zero.

Hence, proved .

5 0

3 years ago

In circle R with m angle QRS= 90 and QR= 3 units find the length of arc QS round to the nearest hundredth

Advocard [28]

Answer:

4.71 units

Step-by-step explanation:

The formula for arc length =

2πr × θ/360

From the above question,

r = QR = 3 units

θ = angle QRS= 90 = 90°

The length of the arc is calculated as:

2 × π × 3 × 90/360

= 4.7123889804 units

Approximately to the nearest hundredth = 4.71 units

8 0

3 years ago

The total cost of 4 starfish was $7.20. Write and solve an equation to find how much one starfish cost.

Lyrx [107]

Answer:

$1.80

Step-by-step explanation:

4x = 7.20

x = 1.80

7 0

3 years ago