All categories

2 years ago

Which value is a solution to the inequality x <4

Mathematics

2 answers:

mezya [45]2 years ago

7 0

Answer:

any number under 4 so 3 2 1 -1 -2 -3 -4 -5 -6 -7 etc

Step-by-step explanation:

guajiro [1.7K]2 years ago

6 0

Answer: oh kay then....

You might be interested in

Find an m > 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.

Aleonysh [2.5K]

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

$x^4-(3m+2)x^2+m^2=0$

$x^4+0x^3-(3m+2)x^2+0x+m^2=0$

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

$a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}$

$=\frac{0}{1}=0$

$\implies a=0----(1)$

$(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}$

$=\frac{-3m-2}{1}$

$3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2$

$-10b^2=-3m-2$

$\implies b^2=\frac{3m+2}{10}-----(2)$

$(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2$

$9b^4=m^2$

$9(\frac{3m+2}{10})^2=m^2$

$9(\frac{9m^2+4+12m}{100})=m^2$

$81m^2+36+108m=100m^2$

$-19m^2+108m+36=0$

$19m^2-108m-36=0$

$19m^2-114m+6m-36=0$

$19m(m-6)+6(m-6)=0$

$(19m+6)(m-6)=0$

$\implies m=-\frac{6}{19}\text{ or }m=6$

But m > 0,

Hence, the value of m is 6.

4 0

2 years ago

Question 4 i need help on!!

MrMuchimi

Answer:

C 20

Step-by-step explanation:

Set up equations:

Laguna's Truck Rentals

y = 2x + 20

Where x is the number of miles driven and y is the total price

How did we get to this equation?

Well, the company charges $2 for every mile driven. Therefore, by multiplying 2 and x, you will find the price paid per mile. The 20 (which represents $20) is the one-time payment you pay for simply using the service.

Salvatori's Truck Rentals

y = 3x

Where x is the number of miles driven and y is the total price

How did we get to this equation?

For this company, you only pay for how many miles you drive. There isn't a one-time payment like there is for Laguna's Truck Rentals. Therefore, you only need to multiply the price per mile ($3) by the number of miles driven (x).

Set the equations equal to each other:

2x + 20 = 3x

Why would you do this?

We need to set the equations equal to each other because we need to find the point at which the prices are the same. When two things are the same, they are equal. Therefore, we get rid of the y variable (which represents the total price) because we want to find the value of x when the equations are equal to one another.

Solve:

2x + 20 = 3x

Subtract 2x on both sides:

2x + 20 = 3x

-2x -2x

20 = x

When x is equal to 20, or when the number of miles driven is 20, the total price of the Truck Rental services is the same.

Hope this helps :)

4 0

2 years ago

What complex number is represented by the polar coordinates (4, -pi/4)

nexus9112 [7]

Answer:

$\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

Step-by-step explanation:

A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as |z|).

Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.

Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.

$\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}$

Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.

$\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

Hence, the complex number that has polar coordinate of (4,-45°) is $\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

3 0

1 year ago

How much would $600 invested at 8% interest compounded continuously be worth after 3 years? Round your answer to the nearest cen

eduard

Answer:

yes

Step-by-step explanation:

You just do it

5 0

2 years ago

Mrs. Gomez paid $780 for a new backyard fence. A new gate cost an additional $225. The fencing was a total of 120 feet. What was

Andrews [41]

I would do it this way

$780+$225=$1005

$1005/120ft= $8.375

if you have to round up $8.38 per foot

6 0

2 years ago