Plot the four points on the number line below -1/3 1 2/3 2/3 1 1/3

Doss [256]

$\text{Apply Pythagorean theorem,}\\\\~~~~x^2 = 6^2 +8^2\\\\\implies x = \sqrt{6^2 +8^2}\\\\\implies x = \sqrt{36 +64}\\\\\implies x =\sqrt{100}\\\\\implies x = 10~~ \text{units.}$

3 0

2 years ago

Make q subject in formula t=q/2 + 5

shusha [124]

Answer:

$q = 2(t - 5)$

Step-by-step explanation:

$t = \frac{q}{2} + 5 \\ \\ t - 5 = \frac{q}{2} \\ 2(t - 5) = q$

hope this helps you.

Have a nice day!

6 0

3 years ago

Read 2 more answers

Explain how the equation A = l × w is a formula.

devlian [24]

A formula helps you or tells you what to do to find the are, perimeter, volume of any shape. A = 1 x w is a formula to find an area of a 2-d figure. it is a formula becuase it tells you what to do to find the area.

8 0

3 years ago

JUST ANSWER PLEASE!!! QUICK

jeka57 [31]

Answer:

Options 1 and 3

Step-by-step explanation:

We should know that, the system of linear equations can be treated as matrices, i.e: we can modify or make any operations provide that we must apply the same operation for all terms of each equation.

Given: the solution for the following system is (2,9)

Px + Qy = R ⇒(1)

Tx + Uy = V ⇒(2)

We will check which system of equation has the same solution.

System A) Px + Qy = R

(P+T)x + (Q+U)y = R+V ⇒(3)

So, By summing (1) and (2) we will get the equation (3)

So, system A has the same solution (2,9)

System B) Px + Qy = R

(P+2T)x + (Q+2U)y = R-2V ⇒(4)

By multiplying equation (2) by 2 and add with equation (1), we will get:

(P+2T)x + (Q+2U)y = R+2V

Which is not the same as equation (4)

So, system B has not the same solution (2,9)

System C) (T-P)x + (U-Q)y = V-R ⇒(5)

Tx + Uy = V

By multiplying equation (1) by -1 and add with equation (2), we will get the equation (5)

So, system C has the same solution of (2,9)

System D) (T-P)x + (Q+U)y = V-R ⇒(6)

Tx + Uy = V

We cannot get equation (6) by the same operation over equation (1)

Note the coefficient of x and y⇒ (T-P) and (Q+U)

They must be (T+P) and (Q+U) OR (T-P) and (Q-U)

So, system D has not the same solution of (2,9)

System E) (5T-P)x + (5U-Q)y = V-5R ⇒ (6)

Tx + Uy = V

By subtract equation (1) from 5 times equation (2), we will get:

(5T-P)x + (5U-Q)y = 5V-R

Which is not the same as equation (6)

So, system E has not the same solution (2,9)

As a conclusion, the systems which have the same solution are:

Options 1 and 3

5 0

3 years ago

Katrina buys a 42-ft roll of fencing to make a rectangular play area for her dogs.

vekshin1

Answer:

(a) $l = -w + 21$

(b) Domain: $0$ (See attachment for graph)

(c) $f(w) = -w + 21$

Step-by-step explanation:

Given

$2(l + w) = 42$

$l = length$

$w = width$

Solving (a): A function; l in terms of w

All we need to do is make l the subject in $2(l + w) = 42$

Divide through by 2

$l + w = 21$

Subtract w from both sides

$l + w - w = 21 - w$

$l = 21 - w$

Reorder

$l = -w + 21$

Solving (b): The graph

In (a), we have:

$l = -w + 21$

Since l and w are the dimensions of the fence, they can't be less than 1

So, the domain of the function can be $0$

--------------------------------------------------------------------------------------------------

To check this

When $w = 1$

$l = -1 + 21$

$l = 20$

$(w,l) = (1,20)$

When $w = 20$

$l = -20 + 21$

$l = 1$

$(w,l)= (20,1)$

--------------------------------------------------------------------------------------------------

See attachment for graph

Solving (c): Write l as a function $f(w)$

In (a), we have:

$l = -w + 21$

Writing l as a function, we have:

$l = f(w)$

Substitute $f(w)$ for l in $l = -w + 21$

$l = -w + 21$ becomes

$f(w) = -w + 21$

5 0

3 years ago