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Kylie has 5 quarts of orange juice to fill some empty glasses. She fills each glass with 1/4 quart of orange juice. How many gla

baherus [9]

Answer:

She fills 5/4 or 1 and 1/4 glass

Step-by-step explanation:

1/4 * 5=5/4

4 0

2 years ago

Compute the product AB by the definition of the product of matrices, where A and A are computed separately, and by the row-co

chubhunter [2.5K]

Complete Question

The complete question is shown on the first uploaded image

Answer:

First question

$Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right]$

Second question

$Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * 5 )+ (3* -2)}\\{(1 * 5)+ (4 * -2)}\\{(5 * 5) + (8*-2)}\end{array}\right] = \left[\begin{array}{ccc}{-11}\\{-3}\\{29}\end{array}\right]$

Third question

$Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right]$

Fourth question

$Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * -3 )+ (3* 4)}\\{(1 * -3)+ (4 * 4)}\\{(5 * -3) + (8*4)}\end{array}\right] = \left[\begin{array}{ccc}{15}\\{13}\\{-23}\end{array}\right]$

Fifth question

The correct option is A

Step-by-step explanation:

From the question we are told that

The matrix A is $A = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]$

The matrix B is $B = \left[\begin{array}{ccc}5&{-3}\\{-2}&4\end{array}\right]$

The first question is to set up the product $Ab_1$ , where $b_1$ is the first column of matrix B, this shown as

$Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right]$

The second question is to calculate $Ab_1$ , this is evaluated as

$Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * 5 )+ (3* -2)}\\{(1 * 5)+ (4 * -2)}\\{(5 * 5) + (8*-2)}\end{array}\right] = \left[\begin{array}{ccc}{-11}\\{-3}\\{29}\end{array}\right]$

The third question is to set up the product $Ab_2$ , where $b_2$ is the second column of matrix B, this shown as

$Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right]$

The fourth question is to calculate $Ab_2$ , this is evaluated as

$Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * -3 )+ (3* 4)}\\{(1 * -3)+ (4 * 4)}\\{(5 * -3) + (8*4)}\end{array}\right] = \left[\begin{array}{ccc}{15}\\{13}\\{-23}\end{array}\right]$

The fifth question is to determine the numerical expression for the first entry in the first column of AB using the row-column rule and from the calculation of $Ab_1$ we see that it is

${(-1 * 5 )+ (3* -2)}$

5 0

3 years ago

maw [93]

Answer:

14/1.8 = x/4

Step-by-step explanation:

Using similar triangles,

height of man/length of man's shadow = height of tree/length of tree's shadow

1.8/4 = x/14

x/14 = 1.8/4

If we cross-multiply, we have

1.8 × 14 = x × 4

dividing both sides by 4 and 1.8,we have

14/4 = x/1.8

x/1.8 = 14/4

So, the two expressions we have are

x/14 = 1.8/4 and x/1.8 = 14/4.

So, the answer is 14/1.8 = x/4 since the product 1.8 × 14 = x × 4 cannot be expressed in the given ratio.

4 0

3 years ago

Find the slope of the line going through the points (-4, 3) and (-1,-6)

Fed [463]

Answer:

-3

Step-by-step explanation:

m=y2-y1/x2-x1

m=-6-3/-1-(-4)

m=-9/3

m=-3

8 0

3 years ago

Read 2 more answers

There is no smallest positive rational number because, if there were, then it could be divided by two to get a smaller one. EXPL

Gennadij [26K]

Answer:

Since a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.

Step-by-step explanation:

Let a/b be the rational number in its simplest form. If we divide a/b by 2, we get another rational number a/2b. a/2b < a/b. If we divide a/2b we have a/2b ÷ 2 = a/4b = a/2²b. So, for a given rational number a/b divided by 2, n times, we have our new number c = a/2ⁿb where n ≥ 1

Since $\lim_{n \to \infty} \frac{a}{2^{n}b }$ = a/(2^∞)b = a/b × 1/∞ = a/b × 0 = 0, the sequence converges.

Now for each successive division by 2, a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb and

a/2⁽ⁿ ⁺ ¹⁾b/a/2ⁿb = 1/2, so the next number is always half the previous number.

So, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.

3 0

3 years ago