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3 years ago

5 times a number increased by 4 is at least nineteen

Mathematics

1 answer:

Anna35 [415]3 years ago

5 0

Answer:

5(x+4) ≥ 19

x ≤ -1/5

Step-by-step explanation:

5(x+4) ≥ 19

5x + 20 ≥ 19

5x ≤ -1

x ≤ -1/5

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Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated

Illusion [34]

Answer:

$x=-2,0,3$

Step-by-step explanation:

We have been given a function $f(x)=15x^3-15x^2-90x$ . We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

$15x^3-15x^2-90x=0$

Now, we will factor our equation. We can see that all terms of our equation a common factor that is $15x$ .

Upon factoring out $15x$ , we will get:

$15x(x^2-x-6)=0$

Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .

$15x(x^2-3x+2x-6)=0$

$15x((x^2-3x)+(2x-6))=0$

$15x(x(x-3)+2(x-3))=0$

$15x(x-3)(x+2)=0$

Now, we will use zero product property to find the zeros of our given function.

$15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0$

$15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0$

$\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0$

$x=0\text{ (or) }x=3\text{ (or) }x=-2$

Therefore, the zeros of our given function are $x=-2,0,3$ .

7 0

3 years ago

Which defines a circle

SIZIF [17.4K]

Circle is the locus of points equidistant from a given point, the center of the circle. The common distance from the center of the circle to its points is called radius. Thus a circle is completely defined by its center (O) and radius (R): C(O, R) = O(R) = {x: dist(O, x) = R}.
Easier explanation: A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another.

4 0

3 years ago

A number is greater than another number by 5. if their sum is 21, find the number

Flura [38]

Answer:

13.

Step-by-step explanation:

x+x+5=21

2x+5=21

2x=16

x=8

5 0