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3 years ago

Select steps that could be used to solve the equation 1 + 3x = -x + 4.

Mathematics

2 answers:

IrinaK [193]3 years ago

6 0

Answer: the correct answer is 1,4,5

Otrada [13]3 years ago

5 0

1 + 3x = -x + 4
add x
1 + 4x = 4
suntract 1
4x = 4 - 1 = 3
divide by 4
x = 3/4

The first one is a good choice.

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What shape is 80,100,100,80 degree

Neko [114]

I believe it is a parallelogram.
Reasons:
1. It is a quadrilateral. Quadrilaterals have a total amount of 360 degrees. 80+100+100+80=360
2. It has oposite sides that are equal
3. If you look at a parallelogram it has two obtuse angles and two acute.
100= obtuse angle 80= acute angle

5 0

3 years ago

Find the domain and range of f(x). Please explain your answer.<br> f(x) = √(x^2+5x+6)

timama [110]

Answer:

Domain:— [ x ≥ -2, x ≤ -3 ]

Range:— [ y ≥ 0 ]

Step-by-step explanation:

You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.

First, factor the quadratic expression in the surd:—

$\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}$

We can find the x-intercepts by letting f(x) = 0.

I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.

__________________________________________________________

Finding x-intercepts

Let f(x) = 0.

$\displaystyle \large{0=\sqrt{(x+3)(x+2)}}$

Solve for x, square both sides:—

$\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}$

Simply solve a quadratic equation:—

$\displaystyle \large{x=-3,-2}$

Therefore, x-intercepts are:—

$\displaystyle \large{\boxed{x=-3,-2}}$

__________________________________________________________

Finding y-intercept

Let x = 0.

$\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}$

Therefore, y-intercept is:—

$\displaystyle \large{\boxed{\sqrt{6}}}$

__________________________________________________________

However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.

For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.

See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.

Hence, the domain is:—

x ≥ -2, x ≤ -3

4 0

2 years ago

2. The number of nickels that Christine has is

aev [14]

Answer:

The number of nickels is 15

The number of Dimes is 3

Step-by-step explanation:

Let the number of dimes Christine has be d

The number of nickels with christine be n

Then the number of Nickels Christine has will be

n = 5d ----------------------------------(1)

Now The total value of both dimes and nickels is = $1.05

This can be represented as

5n +10d = 105 (in cents)

From eq(1)

5(5d) + 10d = 105

25d+10d = 105

35d = 105

$d = \frac{105}{35}$

d = 3----------------------------------(2)

Substituting (2) in (1), we get

n = 5(3)

n = 15

7 0

3 years ago

What is the measure of ZL?

Elodia [21]

Answer: C

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent.

7 0

2 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Rewrite the fol

never [62]

Vertex Form: y = a(x - h)^2 + k, with (h,k) as the vertex.

To convert it into vertex form, we are going to be completing the square. Firstly, subtract 56 on both sides: $y-56=2x^2-32x$

Next, factor out the GCF, or greatest common factor, of the right side. To find the GCF, list the factors of both terms and the greatest one they share is their GCF. In this case, the GCF is 2: $y-56=2(x^2-16x)$

Next, we want to make what's inside the parentheses a perfect square. To find the constant of the perfect square, divide the x term by 2 and square the quotient. In this case:

-16 ÷ 2 = -8, (-8)² = 64

So you're gonna have to add 64 to the inside of the parentheses. To cancel this out, you will need to add to the other side the product of 64 and 2 (since 64 is inside the parentheses), which is 128: $y+72=2(x^2-16x+64)$

Next, factor the polynomial inside the parentheses: $y+72=2(x-8)^2$

Next, subtract 72 on both sides and your vertex form is $y=2(x-8)^2-72$

Now looking at this vertex form, the vertex is (8,-72), which means that <u>the x-coordinate of the vertex is 8.</u>

6 0

3 years ago