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3 years ago

Consider the inequality -5(x+7)<-10 write inequality representing a solution for x

1 answer:

6 0

Perform indicated multiplication on left side first...

-5x-35<-10 add 35 to both sides

-5x<25 divide both sides by -5 (you must reverse sign because of division by a negative value too!)

x>5 or if you prefer...

x=(5, +oo)

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The vertex of the parabola below is at the point (3,2) and the point (4,6) is on the parabola. What is the equation of the parab

nata0808 [166]

Answer:

$\large\boxed{y=4(x-3)^2+2\ \bold{vertex\ form}}\\\boxed{y=4x^2-24x+38\ \bold{standard\ form}}$

Step-by-step explanation:

The vertex form of a parabola:

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

(h, k) - vertex

We have the vertex at (3, 2) → h = 3 and k = 2.

Substitute:

$y=a(x-3)^2+2$

The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:

$6=a(4-3)^2+2$ subtract 2 from both sides

$6-2=a(1)^2+2-2$

$4=a\to a=4$

Finally:

$y=4(x-3)^2+2$ vertex form

use (a - b)² = a² - 2ab + b²

$y=4(x^2-6x+9)+2$ use the distributive property

$y=4x^2-24x+36+2$

$y=4x^2-24x+38$ standard form

6 0

3 years ago

the slope of a line is 2. the y-intercept of the line is -6. which statements accurately describe how to graph the function

galben [10]

Answer: Locate the ordered pair (0, -6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line.

Step 1: Determine the ordered pair

To start off, let’s find the ordered pair. This will eliminate two of the options; two of the potential answers state that the ordered pair is (0,-6), while the other two say that it is (-6,0).

To find the ordered pair, let’s look at the y-intercept. We are told that it is -6. This means that the point on the y-axis is -6, while the x-axis will remain at 0. Let’s put this information into a point, with 0 as x and -6 as y. This will be (0, -6).

Now that we know that (0, -6) is the ordered pair, we know to eliminate options 3 and 4. This leaves us with only options 1 and 2 as potential answers.

Step 2: Determine how to find slope

The final thing we need to do is determine how to find the slope. We are told that the slope is 2, but the two answers we have left ask us to explain how to proceed. We could either move up 2 and over 1 on the right, or move up 2 and over 1 on the left.

To find this, let’s examine the slope. As you may know, points on the graph go left if the slope is negative, and points on the graph to right is the slope is positive.

Since our slope is positive. We will go up 2 and over 1. This will bring us our final answer by eliminating option 2. Option 1 is our answer!!

Step 3: Write out final answer

Now that we eliminated all the invalid options, let’s write out our final option as our answer.

Locate the ordered pair (0, -6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line.

Hope this helps! Comment below for more questions.

8 0

3 years ago

Which equation will help you solve this problem?

malfutka [58]

This question is a division question.
you can write an 16/2
The answer would be 8

4 0

3 years ago

Read 2 more answers

Find the constant of proportionality for this proportional relationship and write an equation. Use b for bags of candy and p for

Reika [66]

Omg that Persian who just like commented candy is good is so disrespectful, b > c period

4 0

3 years ago

How do you recognize if a binomial is a difference of perfect squares?

Sedbober [7]

First off, perfect squares are numbers that have factors that can be multiplied by two of the same numbers. (such as: 1,4,9,16,25,36,49,64,81, & 100). a perfect squares can also be when in is a number such as x^2 or x∧4 (as long as the exponents are multiples of two.) You might know that a binomial is two terms. So you can recognize it by those numbers I mentioned earlier being subtracted.

Hope you understood and I wasnt confusing =)

7 0

3 years ago