All categories

3 years ago

Consider the equation (x−4)(x+3)=0.

Mathematics

1 answer:

Jlenok [28]3 years ago

6 0

Answer:

(1) x (x+ 3) - 4 (x +3) = 0

(2) x = 4 and x = -3

Step-by-step explanation:

given data

equation

(x−4)(x+3)=0

solution

given equation (x−4)(x+3) = 0

equation as a compound statement is

x (x+ 3) - 4 (x +3) = 0

and

two solutions to the equation are

so x (x+ 3) - 4 (x +3) = 0

x- 4 = 0 and x + 3 = 0

x = 4 and x = -3

You might be interested in

What is the slope of a line that is perpendicular to a line whose equation is -2y=3x+7? Help needed asap please :)

Alecsey [184]

I hope it helps you!!

6 0

2 years ago

Read 2 more answers

a trapezoid has base lengths of (6x-1) units and 3 units. Its midsegment has a length of (5x-3) units. What is the value of x?

vodka [1.7K]

1. You have that:

- The lengths of the bases are (6x-1) units and 3 units.
- The midsegment has a length of (5x-3) units.

2. To solve this exercise, you must apply the formula for calculate the length of the midsegment of a trapezoid, which is shown below:

Midsegment=Base1+Base2/2

As you can see, the midsegment is half the sum of the bases of the trapezoid.

3. When you substitute the values, you obtain:

(5x-3)=[(6x-1)+3]/2

4. Now, you can solve the problem by clearing the "x":

(5x-3)=[(6x-1)+3]/2
2(5x-3)=6x-1+3
10x-6=6x+2
10x-6x=2+6
4x=8
x=8/4
x=2

3 0

2 years ago

Find the area of the shape shown below. 10 20 4

Usimov [2.4K]

10 because it makes the most sense

4 0

3 years ago

Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two dis

skad [1K]

The definition of quadratic function is given by:

 $(1) \ f(x)=ax^{2}+bx+c \\ \\ where \ a, b, c \ are \ real \ values$ 

So the problem asks for two conditions:

1. Write the quadratic function in factored form. 
2. The vertex has an x-coordinate of 3.

Then the equation (1) must be written as follows:

 $f(x)=(x-m)(x-n) \\ \\ where \ m \ and \ n \ are \ the \ roots$ 

To satisfy the two conditions:

$\frac{m+n}{2}=3$

So we are free to choose the value of one root, say:

$m=1$

Thus:

$n=6-1=5$

Finally, the answer is:

$f(x)=(x-1)(x-5)$

The graph of this function is shown in the figure below.

4 0

2 years ago

Read 2 more answers

Suppose that NOP is isosceles with base.

NemiM [27]

Step-by-step explanation:

In isocseles triangle, base angles are equal :

base angles are angle N and angle P:

angle N=angle P

3x+17=4x+2

4x-3x=17-2

x=15

For angle N:

subtitute x in angle N

=3(15)+17

=45+17

=62

For angle P:

subtitute x in angle P:

=4(15)+2

=60+2

=62

For angle O:

sum of all angles in a triangle is 180.

angle N +angle P+angle O=180

62+62+angle O=180

angle O=180-62-62

angle O=56

Note: if you have any question let me know about it. thanks

4 0

2 years ago