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4 years ago

How is the value of 4 in 864 related to the value of 4 in 846

1 answer:

5 0

Answer: The value of the 4 in 864 is 10 times smaller than the value of the 4 in 846.

Explanation: The 4 in 864 is in the ones place, which means its value is equal to 4. On the other hand, the value of the 4 in 846 is in the tens place; which means its value is equal to 40.

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Determine all real values of p such that the set of all linear combination of u = (3, p) and v = (1, 2) is all of R2. Justify yo

Rama09 [41]

Answer:

p ∈ IR - {6}

Step-by-step explanation:

The set of all linear combination of two vectors ''u'' and ''v'' that belong to R2

is all R2 ⇔

$u\neq 0_{R2}$

$v\neq 0_{R2}$

And also u and v must be linearly independent.

In order to achieve the final condition, we can make a matrix that belongs to $R^{2x2}$ using the vectors ''u'' and ''v'' to form its columns, and next calculate the determinant. Finally, we will need that this determinant must be different to zero.

Let's make the matrix :

$A=\left[\begin{array}{cc}3&1&p&2\end{array}\right]$

We used the first vector ''u'' as the first column of the matrix A

We used the second vector ''v'' as the second column of the matrix A

The determinant of the matrix ''A'' is

$Det(A)=6-p$

We need this determinant to be different to zero

$6-p\neq 0$

$p\neq 6$

The only restriction in order to the set of all linear combination of ''u'' and ''v'' to be R2 is that $p\neq 6$

We can write : p ∈ IR - {6}

Notice that is $p=6$ ⇒

$u=(3,6)$

$v=(1,2)$

If we write $3v=3(1,2)=(3,6)=u$ , the vectors ''u'' and ''v'' wouldn't be linearly independent and therefore the set of all linear combination of ''u'' and ''b'' wouldn't be R2.

7 0

3 years ago

Of 50 students surveyed, 19 said they had soda for breakfast. write a portion in fraction, decimal, percent

Naya [18.7K]

Answers:
___________________________
In fraction: $\frac{19}{50}$ .
___________________________
In decimal: 0.38 .
_________________
In percent: 38 % .
_________________
Explanation:
_________________
19/50 = (19*2)/(50*2) = 38/100 .

38/100 = 38 ÷ 100 = 0.38 .

38/100 = 38 % .
___________________________

7 0

3 years ago

Determine if the graph is a function then state the domain and range.

nignag [31]

<h3>Explanation</h3>

A function is a set of relation that doesn't have repetitive domain. If we want to know if a graph is function or not, we have to do the line test.

Line Test

Draw a vertical line. Make sure that a line passes through a graph.
See if a line intercepts a graph more than one point or just only one.

Result

If a line intercepts a graph more than one point, it is not a function.

However, if a line only intercepts a graph just one point, it is indeed a function.

The given graph from the question is a function because it passes line test.

Domain and Range

Domain is the set of all x-values, meaning we only focus on x-axis or x-value only.

Range is the set of all y-values. We only focus on y-value or y-axis for Range.

Determine Domain from Graph

We can simply say that the domain is from starting domain or x-coordinate point to end x-coordinate point. For example, if a graph starts at x = -4 and ends at x = 2, we can say that - 4<=x=2.

Determine Range from Graph

Similar to Domain except Range starts from the minimum value or point to the maximum point or value. For example if a graph starts at min point = 6 and max point = 9. We can say that 6<=y<=9.

From the graph, the domain starts from negative infinity to positive infinity. Meaning that x can be any numbers. Hence, the domain is set of all real numbers. For range, the minimum value is 0 and max value is positive infinity. Therefore we write y>=0.

<h3>Answer</h3>

 $\begin{cases} x \in \mathbb{R} \\ y \geqslant 0 \end{cases}$ 

Domain is set of all real numbers.

Range is greater or equal to 0.

8 0

3 years ago

A rectangle has a length of twenty one cm and a diagonal of twenty nine cm. How wide is the rectangle?

GuDViN [60]

The width of the rectangle become 20 cm.

According to the statement

we have to find the width of the rectangle.

So, For this purpose, we know that the

Rectangle is a parallelogram all of whose angles are right angles.

According to the information:

A rectangle has a length of 21 cm and a diagonal of 29 cm.

Here we use the this formula

d² = l² + w²

So, Substitute the values

29² = 21² + w²

841 = 441 + w²

Now, solve it then

w² = 400

Solve the square root then value becomes

w = 20 cm.

The width of the rectangle become 20 cm.

So, The width of the rectangle become 20 cm.

Learn more about Rectangle here

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3 0

2 years ago

Graph the function

Oksana_A [137]

Answer:

To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then ... graphing showing vertical asymptote at x = 1 ... Next, I'll find any x- or y- intercepts.

6 0

3 years ago