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4 years ago

Grace thought of a number, added 7, multiplied by 3, took away 5 and divided by 4 to give an answer of 7.

Mathematics

2 answers:

zzz [600]4 years ago

7 0

Answer:

The number Grace took was 4.

Step-by-step explanation:

Let us assume that she took a number 'x'

Now she added 7 in it, $x+7$

Then multiplied by 3 , $3(x+7)$ = $3x+21$

Then took away or subtracted 5.

$3x+21-5=3x+16$

And divided by 4 to get answer 7.

$\frac{3x+16}{4}=7$

Now we will solve this to get x.

$3x+16=28$

$=> 3x=28-16$

$=> 3x=12$

x = 4

Hence, the number Grace took was 4.

Gemiola [76]4 years ago

4 0

7 * 4 = 28
28 + 5 = 33
33 / 3 = 11
11 - 7 = 4

The number she thought of is 4

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EXPLANATION

For a matrix A of order n×n, the cofactor $C_{ij}$ of element $a_{ij}$ is defined to be

$C_{ij} = (-1)^{i+j} M_{ij}$

$M_{ij}$ is the minor of element $a_{ij}$ equal to the determinant of the matrix we get by taking matrix A and deleting row i and column j.

Here, we have

$C_{11} = (-1)^{1+1} M_{11} = M_{11}$

M₁₁ is the determinant of the matrix that is matrix A with row 1 and column 1 removed. The bold entries are the row and the column we delete.

$\begin{aligned} A=\begin{bmatrix} \bf 1 & \bf -6 & \bf -4\\ \bf 7 & 0 & -3 \\ \bf -9 & 8 & -8 \end{bmatrix} \implies M_{11} &= \text{det}\left(\begin{bmatrix} 0&-3 \\ 8&-8 \end{bmatrix} \right) \end{aligned}$

Since the determinant of a 2×2 matrix is

$\det\left( \begin{bmatrix} a & b \\ c& d \end{bmatrix} \right) = ad-bc$

it follows that

so $C_{11} = M_{11} = 24$

4 0

3 years ago

Here’s a graph of a linear function. Write the equation that describes that function. (Zoom in if blurry)

Maru [420]

Answer: y = x/2 + 3

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

Looking at the graph,

y2 = 6

y1 = 4

x2 = 6

x1 = 2

Slope,m = (6 - 4)/(6 - 2) = 2/4 = 1/2

To determine the intercept, we would substitute x = 2, y = 4 and m= 1/2 into y = mx + c. It becomes

4 = 1/2 × 2 + c

4 = 1 + c

c = 4 - 1

c = 3

The equation becomes

y = x/2 + 3

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3 years ago

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