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3 years ago

A triangle has two sides of length 9 and 14 what is the smallest possible whole number length for the third side

Mathematics

1 answer:

melisa1 [442]3 years ago

6 0

Let the third side = x.

The sum of any two sides must be greater than the third side

14 + 9 > x

23 > x

14 + x > 9

x > -5

9 + x > 14

x > 5

So 5 < x < 23

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Write 2 expressions that represent the areas of 4 triangles

arsen [322]

2-9x and 17x - 8x +2

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3 years ago

Find the midpoint of (0, 4) and (2, -2)

lidiya [134]

Answer:

$\text{Midpoint} = (1, \; 1)$

Step-by-step explanation:

$M = (x_M, \; y_M)$

$M = \left(\dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2}\right)$

$M = \left(\dfrac{0 + 2}{2}, \; \dfrac{4 + -2}{2}\right)$

$M = \left(\dfrac{2}{2}, \; \dfrac{2}{2}\right)$

$M = (1, \; 1)$

5 0

2 years ago

Read 2 more answers

If a club charges dues of $200 a year, it will have 50 members. For each $5 it raises its dues, it loses a member. USE AN EQUATI

Vikentia [17]

Answer:

The value is $y = \$ 225$

Step-by-step explanation:

From the question we are told that

The amount charge per year is $k = \$ 200$

The number of members it will have at this amount is $n = 50$

The amount amount increase that will lead to the loss of a single member is $z = \$ 5$

Generally the total amount the club would obtain from its members is mathematically represented as

$I = Amount \ due\ paid * Number \ of members$

Now let x denote the number of member lost

Hence

$I = (k + zx) (n-x )$

=> $I = (200 + 5x) (50-x )$

=> $I = 10000+50x-5x^2$

Thus the number of members that be removed to give the maximum income from dues is obtained by differentiating the above equation and equating it to zero

$\frac{dI}{dx} = 50-10x$

=> $x = 5$

So from $I = (200 + 5x) (50-x )$ we have

$I = (200 + 5 (5)) (50-5 )$

$I = \$ 10125$

So the amount the club should charge is

$y = \frac{10125}{50 - 5}$

$y = \$ 225$

7 0

3 years ago

What sample size is needed to give a margin of error within plus-or-minus 5% in estimating a population proportion with 90% conf

VARVARA [1.3K]

Answer: 271.

Step-by-step explanation:

When the prior population proportion of success is not available, then the formula to find the sample size is given by :-

$n=00.25(\dfrac{z_{\alpha/2}}{E})^2$

Given : Significance level : $\alpha: 1-0.90=0.1$

By using the standard normal distribution table ,

Critical value : $z_{\alpha/2}=1.645$

Margin of error : $E=0.05$

Then , the required minimum sample size will be :-

$n=0.25(\dfrac{(1.645)}{0.05})^2=270.6025\approx271$

Hence, the required minimum sample size is 271.

4 0

3 years ago

Please help me out with this please

Natali [406]

Answer:

Step-by-step explanation:

We have 2 equations represented by the lines on the graph

5x + 4y = 20

2x - 6y = 12

To plot the first equation on the graph, we a assume different points

4y = 20 - 5x

y = (20-5x)/4

y = 5 - 5x/4

If x =0, y = 5

If x = 2, y = 2.5

If x = 4, y = 0,

These points corresponds to the first line that cuts the positive y axis.

The first line that cuts the positive y axis is represented by the equation,

5x + 4y = 20

Since the left region of the line representing equation is shaded, the unshaded side represents

5x + 4y lesser than 20

To plot the second equation on the graph, we a assume different points

-6y = 12-2x

y = (2x-12)/6 = x/3 - 2

if x= 0, y = -2

If x = 3,y = 1

These points corresponds to the second line that cuts the negative y axis.

The second line that cuts the negative y axis is represented by the equation,

2x -6y = 12

Since the downward region of the line representing the equation is shaded, the unshaded side represents

2x -6y greater than 12

8 0

3 years ago