Find the value of x in the given right triangle.

Which of the following statements is false? 1.5 > 1,4

ArbitrLikvidat [17]

Answer:

the first one

Step-by-step explanation:

5 0

3 years ago

How do you simply 2x+8=-6

photoshop1234 [79]

To simplify 2x + 8 = -6, the easiest way is to manipulate the equation one step at a time:

2x + 8 = -6
2x = -14 (subtract 8 from both sides)
x = -7 (divide both sides by 2)

3 0

3 years ago

Adding and subtracing linear wxpressions 12(−4x+8)−14(8x−12)

Delicious77 [7]

Answer:

-160x+264

Step-by-step explanation:

-48+96x-112x+168

-160+264

3 0

3 years ago

Determine the number of possible solutions for a triangle with B=37 degrees, a=32, b=27

vladimir1956 [14]

Answer:

Two possible solutions

Step-by-step explanation:

we know that

Applying the law of sines

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}=\frac{c}{Sin(C)}$

we have

$a=32\ units$

$b=27\ units$

$B=37\°$

step 1

Find the measure of angle A

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}$

substitute the values

$\frac{32}{sin(A)}=\frac{27}{Sin(37\°)}$

$sin(A)=(32)Sin(37\°)/27=0.71326$

$A=arcsin(0.71326)=45.5\°$

The measure of angle A could have two measures

the first measure-------> $A=45.5\°$

the second measure -----> $A=180\°-45.5\°=134.5\°$

step 2

Find the first measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=45.5\°$

$B=37\°$

$45.5\°+37\°+C=180\°$

$C=180\°-(45.5\°+37\°)=97.5\°$

step 3

Find the first length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(97.5\°)}$

$c=Sin(97.5\°)\frac{32}{sin(37\°)}=52.7\ units$

therefore

the measures for the first solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=97.5\°$ , $b=52.7\ units$

step 4

Find the second measure of angle C with the second measure of angle A

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=134.5\°$

$B=37\°$

$134.5\°+37\°+C=180\°$

$C=180\°-(134.5\°+37\°)=8.5\°$

step 5

Find the second length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(8.5\°)}$

$c=Sin(8.5\°)\frac{32}{sin(37\°)}=7.9\ units$

therefore

the measures for the second solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=8.5\°$ , $b=7.9\ units$

6 0

3 years ago

explain the benefits of each of the three forms of quadratic equations, standard form, vertex form, and factored form. What do t

mamaluj [8]

Answer:

Summary:

Standard form allow us to quickly find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Step-by-step explanation:

The three forms of quadratics are the standard form, vertex form, and the factored form. Each of them reveals a specific part about the quadratic.

Standard Form:

The standard form of a quadratic is:

$ax^2+bx+c$

There are only two details that can be conveyed by a quadratic in standard form immediately: (1) the leading coefficient a, and (2) the y-intercept.

The leading coefficient a will tell us if the parabola curves upwards or downwards.

And the constant c will give us the y-intercept.

Vertex Form:

The vertex form of a quadratic is:

$a(x-h)^2+k$

There are also two details that can be conveyed by a quadratic in vertex form: (1) the vertex, and (2) the leading coefficient.

The leading coefficient is given by a. Again, this tells us the orientation of the parabola.

And the vertex is given by (h, k).

Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.

Factored Form:

The factored form of a quadratic is:

$a(x-p)(x-q)$

Where p and q are the zeros/roots/solutions of the quadratic.

Again, factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros.

The zeros tells us when the parabola crosses the x-axis, which can assist in graphing.

Summary:

Therefore, each form of a quadratic equation has its own benefits.

Standard form allow us to find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Hence, depending on the question, each form can be useful in its own way.

4 0

3 years ago