All categories

3 years ago

The product of two positive consecutive odd integers is 2703. What are the positive numbers?

Mathematics

1 answer:

liberstina [14]3 years ago

7 0

Answer:

The positive numbers are 51 and 53

Step-by-step explanation:

Let first odd integer be x and another odd integer is (x+2).

According to the given condition,

The product of two positive consecutive odd integers is 2703 i.e.

x(x+2) = 2703

$x^2+2x-2703=0$

It is a quadratic equation. It can be solved as follows :

x = 51 and x = -53

Neglecting negative sign,

The first number = 51

Another number =(51+2) = 53

Hence, the positive numbers are 51 and 53.

You might be interested in

What is 1.83 as a mixed fraction

lora16 [44]

Answer:

$1\frac{83}{100}$

Step-by-step explanation:

First of all, the number before the decimal would be the whole number of the fraction.

So, $1\frac{?}{?}$

Then, you would put 0.83 over a fraction.

So because you cannot simplify it anymore, it would be $1\frac{83}{100}$

6 0

3 years ago

Please help me with #4 <br> (10 points )

myrzilka [38]

Answer:

40 feet

Step-by-step explanation:

We are given a right isosceles triangle having lengths of two sides 12 feet and 16 feet.

<em>Since, the triangle is an isosceles triangle i.e. two sides of the triangle are equal.</em>

That is, the three sides of the triangle are 12 feet, 12 feet and 16 feet.

We know that, Perimeter of a triangle = Sum of the sides

Thus, Perimeter of the given triangle = 12 + 12 + 16 = 24 + 16 = 40 feet.

Hence, the total length of the fencing needed is 40 feet.

8 0

3 years ago

Which expression is the factorization of x2 + 10x + 212

Montano1993 [528]

Answer:

The answer is option 1.

Step-by-step explanation:

Firstly, you have to elaborate the expression :

${x}^{2} + 10x + 21$

$= {x}^{2} + 3x + 7x + 21$

Next you have to take out the common factors and factorize it :

${x}^{2} + 3x + 7x + 21$

$= x(x + 3) + 7(x + 3)$

$= (x + 7)(x + 3)$

8 0

3 years ago

Read 2 more answers

The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding

melamori03 [73]

Answer:

We conclude that the mean wedding cost is less than $30,000 as advertised.

Step-by-step explanation:

We are given the following data set:(in thousands)

29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{236100}{8} = 29512.5$

Sum of squares of differences = 3408750

$S.D = \sqrt{\frac{3408750}{7}} = 697.82$

Population mean, μ = $30,000

Sample mean, $\bar{x}$ = $29512.5

Sample size, n = 8

Alpha, α = 0.05

Sample standard deviation, s = $ 697.82

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars}$ We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975$

Now,

$t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and reject it.

We conclude that the mean wedding cost is less than $30,000 as advertised.

8 0

3 years ago

Circle has a radius of 25 ft which of the following values is closest to the area of the circle in square feet a 80 B 160 C 310

Marina CMI [18]

To find the area that is the closest, use the formula for finding the area of a circle.

A = pi x r^2
3.14 x 25^2
A = 1962.5 square feet

This is closest to answer choice D.

4 0

3 years ago