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3 years ago

7

A highschool had 740 students at the start of the year but then some students left the school after that the school had 726 stud

ents what's the mathematical sentence?

1 answer:

iris [78.8K]3 years ago

8 0

The mathematical sentance would be, 740 - 14 = 726, hope this helps.:D

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The length of a rectangle is 1 ft less than twice the width, the area of the rectangle is 21 ft squared. What’s the length

guapka [62]

Answer:

The length of the rectangle is 6 feet

Step-by-step explanation:

Given as :

The length of rectangle is 1 feet less than twice the width

So, let The width of rectangle = w feet

The length of rectangle = ( 2 w - 1 ) feet

The area of the rectangle = 21 feet²

Now,

∵ The area of the rectangle = length × width

Or, 21 feet² = ( 2 w - 1 ) feet × w feet

or, 21 = 2 w² - w

or, 2 w² - w - 21 = 0

or, 2 w² + 6 w - 7 w - 21 = 0

or , 2 w ( w + 3 ) - 7 ( w + 3 ) = 0

or, ( w + 3 ) ( 2 w - 7 ) = 0

So, w = - 3 feet , $\frac{7}{2}$ feet

here we consider only positive value of w i.e $\frac{7}{2}$ feet

∴ The length of rectangle = ( 2 w - 1 ) feet

or, The length of rectangle = 2 × $\frac{7}{2}$ - 1

Or, The length of rectangle = 7 - 1 = 6 feet

Hence The length of the rectangle is 6 feet , Answer

3 0

3 years ago

1. What are the solutions (coordinate points) to the system of equations?

Leto [7]

Question 1

The given system of equations is:

$y = {x}^{2} + 5x + 6 \\ y = 3x + 6$

Equate the two equations:

${x}^{2} + 5x + 6 = 3x + 6$

Rewrite in standard form:

${x}^{2} + 5x - 3x + 6 - 6 = 0$

${x}^{2} + 2x = 0$

$x(x + 2) = 0$

$x = 0 \: or \: x = - 2$

When we put x=0, in y=3x +6, we get:

$y = 3(0) + 6 = 6$

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

$y = 3( - 2) + 6 = 0$

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

$f(x) = {x}^{6} - {x}^{4}$

Let us put x=-x,

$f( - x) = {( - x)}^{6} - {( - x)}^{4}$

This gives:

$f( - x) = {x}^{6} - {x}^{4}$

We can observe that:

$f(x) = f( - x)$

This is the property of an even function.

Question 3:

The given function is

$f(x) = {x}^{2} + 3x - 2$

The average rate of change of f(x) from x=a to x=b is given as:

$\frac{f(b) - f(a)}{b - a}$

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

$= \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11$

The average rate of change is 11

3 0

3 years ago

Find the determinant of the following matrix. A =<br>-2 6<br>3 5

Blababa [14]

Answer:

$|A| = - 28$

Step-by-step explanation:

Given

$A = \left[\begin{array}{cc}-2&6\\3&5\end{array}\right]$

Required

Determine the determinant

For a two by two matrix, A such that:

$A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

The determinant |A| is:

$|A| = a * d - b * c$

So, in

$A = \left[\begin{array}{cc}-2&6\\3&5\end{array}\right]$

The determinant is:

$|A| = -2 * 5 - 6 * 3$

$|A| = -10 - 18$

$|A| = - 28$

6 0

3 years ago

What is the constant variation of 2x+y=-4?

jeka94

Answer:

What is the constant variation of Y =- 2 3x?

The constant of variation, k , is 23 .

What is the constant variation of Y 1 2x?

The constant of variation, k , is 12 .

Step-by-step explanation:

yeet yeet yeet

5 0

3 years ago

The ______ is the control center of the nervous system. It sends and receives signals to and from the entire body.

oee [108]

The brain is the control center of the nervous system.

8 0

3 years ago