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3 years ago

What two consecutive odd integers have a sum of -28

Mathematics

1 answer:

tankabanditka [31]3 years ago

4 0

Answer:

-15 and -13

Step-by-step explanation:

Assume that x is an odd integer, if we added one to this integer it would become even and then if we added one again it would become odd again. With this said

x --> first odd integer

x + 2 --> second odd integer

We want these integers to equal -28 so:

x + (x + 2) = -28

2x + 2 = -28

2x = -30

x = -15

Then we plug in x back into (x+2) to get the second integer

-15 + 2 = -13

And to check

-15 + -13 = -28

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What properties can be used to solve 7y-15=-29. Identity property of multiplication,addition property of equality ,distributive

Sveta_85 [38]

Answer:

Addition Property of Equality.

Inverse property of multiplication.

Step-by-step explanation:

Given the equation:

$7y-15=-29$

First of all, let us use Addition Property of Equality.

According to the property, if we add a number on both sides of an equality, there is no change in the equality.

In other words, the equality will be same if we add the same number on Left Hand Side and Right Hand Side of the equality.

First of all, let us add 15 on both sides of the equality:

$7y-15+15=-29+15\\\Rightarrow 7y=-14$

Now, let us Inverse property of multiplication.

i.e. Multiplication of a number with its inverse is equal to 1.

$a\times \frac{1}{a} = 1$

So, let us multiply the given equation with $\frac{1}7$

$7y \times \dfrac{1}{7}=-14 \times \dfrac{1}{7}\\\Rightarrow 1y =-2\\\Rightarrow y=-2$

The properties used are:

Addition Property of Equality.

Inverse property of multiplication.

7 0

3 years ago

The sum of two numbers is thirteen, and the sum of<br> their squares is 89. Find the two number

Murljashka [212]

Answer:

$Suppose~that~the~two~numbers~are~x~and~y.\\According~to~question,\\Sum~of~the~numbers = 13\\or, x+y=13........(1)\\or, y = 13-x.......(2)\\Again,\\Sum~of~their~squares=89\\or, x^2+y^2=89\\or, (x+y)^2-2xy=89\\From~eq^n(1)~and~(2),\\13^2-2x(13-x)=89\\or, 169-26x+2x^2=89\\or, 2x^2-26x+169-89=0\\or, 2x^2-26x+80=0\\or, x^2-13x+40=0\\or, x^2-8x-5x+40=0\\or, x(x-8)-5(x-8)=0\\or, (x-5)(x-8)=0\\i.e. x=5~or~8\\When~x=5,~y=13-x=13-5=8\\When~x=8,~y=13-x=13-8=5\\So,~the~two~numbers~are~5~and~8.$

8 0

3 years ago

Consider the figure below to complete the statement.

Alona [7]

Answer:

the measurement of the angle is 17.6

Step-by-step explanation:

3 0

4 years ago

how much difference is there between investing $5,000 at 4% simple interest for 5 years and investing that same amount at 4% com

miskamm [114]

To find the difference between the tow investments we are going to use tow formulas. Simple interest formula for our simple interest investment, and compound interest formula for our compound interest investment.
- Simple interest formula: $A=P(1+rt)$
where
   $A$ is the final investment value
   $P$ is the initial investment
   $r$ is the interest rate in decimal form
   $t$ is the time in years
For our problem we know that $P=5000$ , $r= \frac{4}{100} =0.04$ , and $t=5$ , so lets replace those values in our simple interest formula to find $A$ :
$A=5000(1+(0.04)(5))$
$A=5000(1.2)$
$A=6000$

Now that we know the final investment value of our simple interest investment, lets use the compound interest formula to find the final investment value of the other one:
- Compound interest formula: $A=P(1+ \frac{r}{n})^{nt}$
where
   $A$ is the final investment value
   $P$ is the initial investment
   $r$ is the interest rate in decimal form
   $n$ is the number of times the interest is compounded per year
   $t$ is the time in years
For our problem we know that $P=5000$ , $r= \frac{4}{100} =0.04$ , and $t=5$ . Since we know that the interest is compounded quarterly (each 4 months), it mean that is compounded $\frac{12months}{4months} =3$ times per year, so $n=3$ . Now that we have all the vales, lets replace them in our formula:
$A=5000(1+ \frac{0.04}{3} )^{(3)(5)}$
$A=5000(1+ \frac{0.04}{3} )^{15}$
$A=6098.95$

now that we know the final amounts of our investments, lets find how much difference is between them:
$6098.95-6000=98.95$

We can conclude that the difference between invest $5000 in a compound interest investment vs a simple interest investment is $98.95.

5 0

4 years ago

Please help! a rectangle's width is 6 feet less than it's length. write a quadratic function that expresses the rectangles area

Monica [59]

Answer:

B. A( L) = L² - 6L

Step-by-step explanation:

A rectangle has 2 sides, length and width.

length = L

width = L - 6

Area = length × width

= L(L - 6)

= L² - 6L

The correct choice is B.

B. A( L) = L² - 6L

7 0

4 years ago

Read 2 more answers