4x + 3y = 8 2x

Makovka662 [10]

Answer:

y = 2x² - 5x + 7

Step-by-step explanation:

For this problem, imagine the standard form, which is:

f(x) = ax² + bx + c = y

Using the table, and adding that y at the end, we can plug in and write out the following equations. (Writing it out is important):

f(-1) = a(-1)² + b(-1) + c = 14

f(0) = a(0)² + b(0) + c = 7

f(1) = a(1)² + b(1) + c = 4

f(2) = a(2)² + b(2) + c = 5

Now if this doesn't look familiar, it's actually a systems of equations using the a, b, and c elements as your three variables! If you simplify the equations:

f(-1) = a - b + c = 14

f(0) = c = 7

f(1) = a + b + c = 4

f(2) = 4a + 2b + c = 5

Something unique just happened. We have already defined what ' c ' is!

c = 7

Setting that aside, if you remove the f(x) portion of the equations, you're left with:

a - b + c = 14

a + b + c = 4

4a + 2b + c = 5

Using the two upper equations, if we add them together (you can do that as it doesn't change the values of the variables) you get:

2a + 2c = 18

Note: the ' b ' variables cancelled out in the addition [ b + (-b) ]

If you further simplify the equation:

a + c = 9

Awesome. Now we already know that c = 7, so if you plug that into the equation:

a + 7 = 9

Solve for a. So then a = 2

Now that we know the following:

a = 2

c = 7

We can then use the equation:

a + b + c = 4

And solve for b!

2 + b + 7 = 4

Simplify.

b + 9 = 4

Simplify.

b = -5

Now at this point, since you know what a, b and c are, you can write the equation!

f(x) = 2x² - 5x + 7

You can confirm your work by putting any of the x values in the table through!

4 0

3 years ago

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Write a compound inequality that the graph could represent.

Dmitry_Shevchenko [17]

A solid dot on the graph of an inequality indicates that the number is contained within the inequality, so yo should use $\leq$ or $\geq$ to represent that situation, whereas a white dot indicates that the number is not contained within the inequality.

Our graph is telling us that $x$ is greater or equal than -1, and also $x$ is less than 3. So our inequality will be:

$-1 \leq x \leq 3$

3 0

3 years ago

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-7 over -10 simplified

OLga [1]

The negatives cancel to form a positive. The answer is $\frac{7}{10}$

8 0

3 years ago

Find the measure of angle 1

Lubov Fominskaja [6]

In ∆FDH, there are two slash marks in two of its legs. This indicates that this triangle is isosceles. If a triangle is isosceles, then it will have two congruent sides and therefore have two congruent angles.

In ∆FDH, angle D is already given to us as the measure of 80°. We can find out the measure of the other angles of this triangle by using the equation:

80 + 2x = 180

Subtract 80 from both sides of the equation.

2x = 100

Divide both sides by 2.

x = 50

This means that angle F and angle H in ∆FDH both measure 50°.

Now, moving over to the next smaller triangle in the picture is ∆DHG. In this triangle, there are also two legs that are congruent which once again indicates that this triangle is isosceles.

First, we have to solve for angle DHG and we do that by using the information obtained from solving for the angles of the other triangle.

**In geometry, remember that two or more consecutive angles that form a line will always be supplementary; the angles add up to 180°.**

In this case angle DHF and angle DHG are consecutive angles which form a linear pair. So, we can use the equation:

Angle DHF + Angle DHG = 180°

50° + Angle DHG = 180°.

Angle DHG = 130°.

Now that we know the measure of one angle in ∆DHG, we can use the same method as the previous step for solving the missing angles. Use the equation:

130 + 2x = 180

2x = 50

x = 25

The other two missing angles of ∆DHG are 25°. This means that the measure of angle 1 is also 25°.

Solution: 25°

8 0

3 years ago

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The management of a restaurant with locations all over the country has developed a new hamburger that researchers believe will s

Sliva [168]

Using sampling concepts, it is found that the best way to perform a randomized experiment with the goal of determining if this new hamburger will sell better than the hamburger that is currently sold is as follows:

Randomly select 40 restaurants, let each one decide if it wants to sell the new hamburger, and compare sales in those restaurants to sales in the restaurants that chose not to sell the new hamburger.

<h3>What is sampling?</h3>

It is is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

In this problem, a sample of randomly selected restaurants should be taken to sell the new hamburger, and then be compared with the ones who sell the old hamburger to see if sales increased, hence the correct option is:

Randomly select 40 restaurants, let each one decide if it wants to sell the new hamburger, and compare sales in those restaurants to sales in the restaurants that chose not to sell the new hamburger.

More can be learned about sampling concepts at brainly.com/question/25122507

3 0

2 years ago

4x + 3y = 82x - y=9​

4x + 3y = 82x - y=9