Domain and range from the graph of a quadratic function

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

8x - 3x + 4x = -36

x = ?

Step 02:

We must apply the algebraic rules to find the solution.

8x - 3x + 4x = -36

12x - 3x = - 36

9x = - 36

x = - 36 / 9

x = - 4

The answer is:

x = - 4

EXPLANATION

The intercept-form of a quadratic function is as follows:

y = a(x - p)(x - q)

Now, as the roots are (-5,0)

Since the parabola passes through the point (−5,0), then 0=25a−5b+c

Since the parabola passes through the point (−1,0), then 0=a−b+c.

Since the parabola passes through the point (−7,−24), then −24=49a−7b+c.

Thus, we have obtained the following system:

Solving it we get that a=−2, b=−12, c=−10.

Thus, the equation of the parabola is y=(−2x−10)(x+1)

Answer:

A, C, E

Step-by-step explanation:

4^10 = 1048576

A: (4^5)^2 = 1048576

C: 4^20 / 4^10 = 1048576

E: (4^2 x 4^3)^2 = 1048576

The percentage increase is 50%

Here, we want to calculate the percentage increase or decrease

To know if it is a decrease or an increase, we use the following simple logic.

If new amount is greater than original amount, then it is an increase.

If new amout is less than original amount, then it is a decrease

For the first question, we can see that the new amount is greater than the old amount

This indicates an increase

Mathematically;

According to the first question, new amount = 45 while old amount = 30

so;

percentage increase = (45-30)/30 * 100%

= 15/30 * 100% = 100%/2 = 50%

Answer:

3.34

Step-by-step explanation:

625 is 5^4

Using the log rule [tex]log_b(x^a)=alog_b(x)[/tex],

log_b(5^4) = 4*log_b(5)

4*0.835 = 3.34

Given:

Resolving it to its radical form can be gotten based on the general laws of indices.

We have:

I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.

Thus:

Now, we have our value in the square root form as:

Answer:

1. 1.6475.

2. 9.963.

3. 0.231

4. $1.69

5.  0.473 cm.

6. x = $200,000

Step-by-step explanation:

1.$6.59 ÷ 4 = 1.6475.

2. 10-0.037 = 9.963

3. 231 divided by 1000.

4. $0.50 + $0.80 + $0.30 + $0.09 = $1.69

5. 0.008 + 0.125 + 0.15 + 0.185 + 0.005

6. x =$10,000,000(0.02) where x is the amount of money each person will receive.  x=$200,000 (multiply)

Answer:

[tex]y=x+5[/tex]

Step-by-step explanation:

[tex]3y-3x=15 \\ \\ y-x=5 \\ \\ y=x+5[/tex]

The graph of the given line is attached below.

We are given the line:-

y = (3/5)x - 4

We will find the x and y intercepts of the line to plot in the graph.

As the equation is already in the slope intercept form, we can write,

The y-intercept of the line is -4.

Hence, the coordinates of the point will be (0,-4).

To find the x - intercept of the line we will put y = 0 in the given line.

0 = (3/5)x - 4

4 = 3x/5

x = 20/3

The coordinates of the point will be (20/3,0).

We can plot these points to get the desired graph.

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ANSWER

Quadrant III

STEP-BY-STEP EXPLANATION:

Firstly, we need to draw the cardinal points and label each quadrant on it

Looking at the ordered pair (-x, -y), you will see that the x and y-values both fall on the negative side of the x-ais and y-axis

Hence, it falls on the quadrant III

Answer:

60 degrees

Step-by-step explanation:

Total of angles of a triangle is 180

180-76-44= 60

we know that

4 lb or less ------> is less than 20 lb ------> 120

5-9 lb------------> is less than 20 lb -------> 222

10-14 lb -------> is less than 20 lb ------->378

15-19 lb ------> is less than 20 lb-------> 256

Adds the number of passenger

120+222+378+256=976

Notice that both fractions have the same denominator, therefore, we can simply add the numerators:

Adding like terms, we get:

The equation to show how many of each nut this nut bread contains is w = 2p and there are 4 walnuts.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The number of walnuts is double the number of pecans. This can be illustrated as:

w = 2p

Therefore, the number of buts will be:

w = 2p

w = 2(2)

w = 4

Therefore, ther are 4 walnuts

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Our equation

is a quadratic equation. In simple words, it's a parabola, whose graph (red curve) is the following:

The axis of symmetry of a parabola is just the line dividing the parabola into its two arms. In the graph, the axis of symmetry is the blue vertical line. It's usually represented algebraically by

The axis of symmetry of our quadratic equation is

Problem

Solution

5. E-D

Procedure

-3-2 =-5

-4-1=-5

0-7=-7

1-5=-4

2-3=-1

6- (-4)=10

And the answer would be:

-5 -5

-7 -4

-1 10

6. 3F

Procedure

3* -2=-6

3 *5 = 15

3* 1= 3

3*3 = 9

3*14=12

3 * -6= -18

And the answer would be:

-6 15 3

9 12 -18

1) In this question let's calculate the sin(θ) and cos(θ)

Given that

2) In this question, we're calculating the value of the sine and the cosine in radians.

We must remember that 5π/4 ⇒ to 225º, and that it's in the Quadrant III

If we subtract

225 -180 =45 So the sine of 5π/4 is -√2/2 and the cosine (5π/4 ) = -√2/2

2.3) The sign of the Quadrant

Since 225º is in Quadrant III both results are negative ones.

To perform a two column proof, we should give a statement and give a reason of it.

So we start with the initial statement.

1. Statement: x-4 =(1/2)(8x+6)+4x. Reason: Given

Next, we distribute the multiplication (1/2) with(8x+6). If we do so, we get the following statement.

2. Statement x-4 = (4x+3) + 4x. Reason: Distributive property of addition and multiplication.

Now, on the right we can add 4x with 4x, due to the associative property of additon, we get

3. Statement: x-4 = (4x+4x)+3 = 8x+3. Reason: Associative property of addition.

Now, we can subtract x on both sides, so we get

4. Statement: -4 = 7x+3. Reason: Subtraction property of equality.

By the same reason, we should subtract 3 on both sides. We get

5. Statement: -7 = 7x. Reason: Subtraction property of equality.

Finally, we divide by 7 on both sides, so we get

6. Statement: -1=x. Reason: Division property of equality.

7. Statement: x=-1. Reason: Symmetric property of equality.

Given the following systems of linear equations,

6x + 20y = -62 (Equation 1)

3x - 9y = -12 (Equation 2)

Step 1 : Solve 6x+20y=−62 for x:

6x + 20y + (−20y) = −62 + (−20y) (Add -20y to both sides)

6x = −20y −62

6x/6 = (−20y −62)/6 (Divide both sides by 6)

x = (-10y/3) + (-31/3)

Substitute to Equation 2:

3x−9y=−12

3[(-10y/3) + (-31/3)] - 9y = -12

−19y−31=−12 (Simplify both sides of the equation)

−19y−31+31=−12+31 (Add 31 to both sides)

−19y=19

-19y/-19 = 19/-19 (Divide both sides by -19)

y= −1

Step 2: Substitute −1 for y in x =(-10y/3) + (-31/3)

x =(-10(-1)/3) + (-31/3)

x = -7

Answer:

x=−7 and y=−1

To prove :

every differentiable function is continuous.

thus, every differentiable function is continuous.

In graph A, you can see that:

• The height of Frozen Field is 50 meters

• The height of Winter Hill is 15 meters

• The height of Blizzard Run is 35 meters

Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.

In graph B, you can see that:

• The height of Frozen Field is 45 meters

• The height of Winter Hill is 10 meters

• The height of Blizzard Run is 55 meters

Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.

Therefore, the graph where the height difference between Winter Hill and Frozen Field is equal to the height of Blizzard Run is graph A.

part A. We are given that a hiker will increase the distance covered by 10% each day. Let "S" be the distance, then on the first day the distance is:

On the second day, we must add 10% of the first day, we get:

Simplifying we get:

On the third day, we add 10% of the second day, we get:

On the fourth day, we add 10% of the third day, we get:

If we continue this pattern and we set "n" as the number of days, then a formula for the distance after "n" days is:

Now, we are given that for n = 7 the distance is 75897, therefore, we substitute n = 7 in the formula:

Substituting the value of the distance:

Now we can solve for S1, we do that by dividing both sides by 1.1 together with its

exponent:

Now we solve the operations:

Solving the operations:

Therefore, the distance the first day was 42842 miles.

part B. The formula for Sn is the given previously but we replace the known value of S1:

Part C. To determine the distance after 10 days, we substitute the value n = 10 in the formula, we get:

Solving the operations we get:

Therefore, the distance after 10 days is 101019.19 miles.

When a, b, c changes from -1 to +1, the parabolas opens and widens.

Given,

The quadratic function, f(x) = ax² + bx + c

We have to find the change in graph when a, b, c changes from -1 to 1.

First lets consider:

a and b as constants and c is varying.

That is,

x² + x + c

Then,  the parabola will move up and down.

Now, lets consider:

a and c as constants and b is varying.

That is,

x² + bx + 1

Then, the vertex will move but  all parabolas passes through the points (0, c)

Now, we can move to the question.

What happens to graph when +1 changes to -1.

So,

b and c should keep constant and a is varying.

Then,

ax² + x + 1

Here, the parabolas opens and widens.

That is,

When a, b, c changes from -1 to +1, the parabolas opens and widens.

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Answer:

B(2) = -1

Step-by-step explanation:

Assuming each division on the grid is 1 unit

Locate 2 on the x-axis. That is two divisions to the right of the origin. The y value corresponding to this is -1

Trigonometric Ratios

The figure is a triangle with hypotenuse of h = 25 feet. The angle of elevation is 35°.

The wheel is rotating 600 times per minute, find how many times rotate in 1 second:

1 minute = 60 seconds

Then, if in 1 second it rotates 10 times in 1/2 seconds it rotates:

Multiply the number of times it rotates (5 times) by 360 (a wheel has 360º)

Answer:

Explanation:

Here, we want to get the number that could be inserted into the parentheses to make it true

From the logical operator given, we can see that we need a number greater than -10

From the options given, only -3 is greater than -10, which makes it the correct answer choice

We have the following:

The first thing is to find the slope of the line, like this:

replacing:

now, the equation has the following form:

for b,

m = -1/2

y = 2

x = 0

replacing:

Therefore, the equation in standard form is:

The standard form of a linear equation in two variables is given by the expresssion:

So, rewriting the equation:

y-10=2x-16

y-2x=-16+10

y-2x=-6

2x-y=6