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3 years ago

Write down two prime numbers that have a sum of 32

Mathematics

1 answer:

maksim [4K]3 years ago

8 0

Answer:

3 and 29

13 and 19

Step-by-step explanation:

3+29=32

13+19=32

Note: Prime numbers are those that can only be divided by one or itself!

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Intersection point of Y=logx and y=1/2log(x+1)

GalinKa [24]

Answer:

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

The Problem:

What is the intersection point of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ ?

Step-by-step explanation:

To find the intersection of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ , we will need to find when they have a common point; when their $x$ and $y$ are the same.

Let's start with setting the $y$ 's equal to find those $x$ 's for which the $y$ 's are the same.

$\log(x)=\frac{1}{2}\log(x+1)$

By power rule:

$\log(x)=\log((x+1)^\frac{1}{2})$

Since $\log(u)=\log(v)$ implies $u=v$ :

$x=(x+1)^\frac{1}{2}$

Squaring both sides to get rid of the fraction exponent:

$x^2=x+1$

This is a quadratic equation.

Subtract $(x+1)$ on both sides:

$x^2-(x+1)=0$

$x^2-x-1=0$

Comparing this to $ax^2+bx+c=0$ we see the following:

$a=1$

$b=-1$

$c=-1$

Let's plug them into the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$x=\frac{1 \pm \sqrt{1+4}}{2}$

$x=\frac{1 \pm \sqrt{5}}{2}$

So we have the solutions to the quadratic equation are:

$x=\frac{1+\sqrt{5}}{2}$ or $x=\frac{1-\sqrt{5}}{2}$ .

The second solution definitely gives at least one of the logarithm equation problems.

Example: $\log(x)$ has problems when $x \le 0$ and so the second solution is a problem.

So the $x$ where the equations intersect is at $x=\frac{1+\sqrt{5}}{2}$ .

Let's find the $y$ -coordinate.

You may use either equation.

I choose $y=\log(x)$ .

$y=\log(\frac{1+\sqrt{5}}{2})$

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

6 0

2 years ago

A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and

Musya8 [376]

Answer:

Decreases by 2 degrees

Step-by-step explanation:

The expression that describes temperature as a function of latitude is:

$T=110-2(Latitude)$

This equation represents a linear relationship between latitude and temperature in a way that an increase in latitude causes a decrease in temperature. The magnitude of this decrease is quantified by the slope of the linear equation, which is -2. Therefore, the estimated temperature decreases by 2 degrees when latitude is increased by one.

8 0

3 years ago

Which statements about a square are always true?

arlik [135]

Answer:

All statements are true.

Step-by-step explanation:

In a square, we have

all sides equal

all angles equal to 90 degrees

diagonals always bisect each other and at right angles.

Only square is the quadrilateral which satisfies all the above properties.

A parallelogram has diagonals which do not cut at right angles.

A rhombus has all sides equal but not all angles. Neither diagonals are equal in a rhombus.

8 0

3 years ago

The formula for the cost of buying a car=

svet-max [94.6K]

8000-2600=5400
5400/12=450
monthly pavement =450
12x450+2600=8000

5 0

3 years ago

Mrs.Flores’ rectangular garden has a length of 20 meters and width of 15 meters. Her neighbor, Mr.Sosa, has a similar garden in

natima [27]

180 m

Step-by-step explanation:

Information given:

length of Mrs. Flores' garden= 20 m
width of Mrs. Flores' garden = 15 m
Scale factor = 3

Since scale factor is 3, to get measurements of sides Mr. Sosa's garden, sides of Mrs. Flores's have to be multiplied by 3. Hence,

length of Mr. Sosa's garden= 3×20= 60 m

width of Mr. Sosa's garden= 3×15= 45 m

Diagonal of a rectangle = √length²+width²

Let Diagonal = D,

D= √60²+45²

=√3600+2025

=√5625

=75 m

If Mr. Sosa cut his garden diagonally,

perimeter= length+width+diagonal

=60+45+75=180 m

7 0

3 years ago

Write down two prime numbers that have a sum of 32​

Write down two prime numbers that have a sum of 32