A 30 inch tv has a screen that is 18 inches high. how wide is the screen

A positive number is 30 less than its square. Find the number.

Veronika [31]

x = x^2 - 30

or

x^2 - x - 30 = 0
Factors to
(x-6)(x+5) = 0

x = +6 is the positive number

8 0

4 years ago

The function LaTeX: f\left(x\right)=-x^2+4f ( x ) = − x 2 + 4 defined on the interval LaTeX: -8\le x\le8− 8 ≤ x ≤ 8 is increasin

enyata [817]

Given:

The function is

$f(x)=-x^2+4$

It defined on the interval -8 ≤ x ≤ 8.

To find:

The intervals on which the function is increasing and the interval on which decreasing.

Step-by-step explanation:

We have,

$f(x)=-x^2+4$

Differentiate with respect to x.

$f'(x)=-(2x)+(0)$

$f'(x)=-2x$

For turning point f'(x)=0.

$-2x=0$

$x=0$

Now, 0 divides the interval -8 ≤ x ≤ 8 in two parts [-8,0] and [0,8]

For interval [-8,0], f'(x)>0, it means increasing.

For interval [0,8], f'(x)<0, it means decreasing.

Therefore, the function is increasing on the interval [-8,0] and decreasing on the interval [0,8].

7 0

3 years ago

Find the arc length of a partial circle

marusya05 [52]

Answer:

12.5664 units (rounded off to four decimal values)

Step-by-step explanation:

Arc length = 2 × π × r × $\frac{central-angle}{360}$

For our partial circle;

The radius (r) = 8 units

The central angle = 90°

Arc length = 2 × π × 8 × $\frac{90}{360}$ = 12.5663706144 units

Or 12.5664 units (rounded off to four decimal values)

5 0

3 years ago

Read 2 more answers

A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of

babunello [35]

Answer: 0.345

Step-by-step explanation:

Given: The the setup for this hypothesis test:

$H_0:p=0.65\\\\H_a:p$

Since , the alternative hypothesis is left tail , so the test is left tail test.

$P_0=0.65\\\\Q_0=1-0.65=0.35\\\\p=\dfrac{126}{200}=0.63$

The test static for population proportion is given by :-

$z=\dfrac{p-P_0}{\sqrt{\dfrac{P_0Q_0}{n}}}\\\\\Rightarrow\ z=\dfrac{0.63-0.65}{\sqrt{\dfrac{0.65-0.35}{126}}}=−0.409878030638\approx-0.4$

The p-value of z = $P(z$

3 0

4 years ago

THIS IS AN EMERGENCY!! YOU GET ALL MY POINTS (AKA 15 I know I'm poor)!!

belka [17]

Answer:

9 grams

Step-by-step explanation:

We can use these equations:

y = ax

Where y is the total amount of baking soda (in mg)
Where a is the number of servings
Where x is the amount of baking soda in one single serving (in mg)

Here we know that y = 1800 and a = 2, so we will need to solve for x

Solving for x we get $x= \frac{y}{a}$ and plugging in our known values we get $x = \frac{1800}{2}$ and this simplifies to 900
This means one serving contains 900 mg of baking soda

We can now change the equation to solve for the total amount of baking soda required to serve 10 people

We know that a = 10 and x = 900
The equation is already solved for y, so plugging in our new values we have y = (10)(900) = 9000 mg
The recipe will require 9000 mg in order to serve 10 people

Now there are 1000 mg in 1 g, so converting mg to g we have 9000 mg is equivalent to 9 grams

5 0

3 years ago