solve for x in the equation x^2+10x+12=36

Answer:

Step 1: a = 1, b = -4

Step 2: x = 2, f(2) = -9

Step 4: (5,0) and (-1,0)

Step 6: f(0) = -5

On the graph the points plotted are (-1,0) , (0,-5) , (2,-9) , and (5,0)

Answer:

It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6

Step-by-step explanation:

i guessed it and it was right so ye.

Answer:

y = 0.0027*x^2 + 0.0111*x + 2.8574

Step-by-step explanation:

Using Excel the procedure is:

First, insert x and y values in a table format, as can be seen in the figure

Then, select data

Next, go to insert tab and inside charts options select scatter plot without any lines

Finally, select a point in the plot, right-click, add trend line, polynomial order 2 and check display equation option

By substituting each value of the domain of x in the function and solving it we will get the range of the function for respective domain

The given function is :

f(x) = -2x - 5

For x = -2 , f(x) is:

f(-2) = (-2*-2) - 5 = 4 - 5 = -1

For x = -1, f(x) is :

f(-1) = (-2*-1) - 5 = 2 - 5 = -3

For x = 1 , f(x) is

f(1) = (-2*1) - 5 = -2 -5 = -7

For x = 2, f(x) is

f(2) = (-2*2) - 5 = -4 -5 = -9

The range is -1 , -3 , -7 , -9

Hope this helps ..!!

Thank you :)

Final answer:

A sine function with an amplitude of 4, period of 12, midline of y = 1, and y-intercept of (0, 1) would oscillate between 5 and -3, with a wave repeating every 12 units along the x-axis and starting upward from the y-intercept.

Explanation:

The graph of the sine function with the given properties will have the following characteristics:

The amplitude is 4, which means the function will oscillate 4 units above and below the midline.

The period is 12, indicating that it takes 12 units along the x-axis for the function to repeat its pattern.

The midline is y = 1, so the center of oscillation is not at the x-axis but is shifted upwards by 1 unit.

The y-intercept is (0, 1), which means the function starts at the midline.

Since the function is not a reflection over the x-axis, it means that it starts off going upwards from the midline.

Mapping these points, we can sketch the sine graph starting from the point (0, 1), curving up to a maximum of 5 (midline + amplitude), then down through the midline, reaching a minimum of -3 (midline - amplitude), and back to the midline at (12, 1), completing one full cycle.

Final answer:

To find the principal amount that would earn $500 in simple interest over 3 years at an 8% annual rate, divide the interest by the product of the rate and period. The principal amount is $2083.33.

Explanation:

Calculating the Principal Amount from Simple Interest

To calculate the principal amount that earns $500 in simple interest over 3 years at a rate of 8% per annum, we can utilize the simple interest formula:
Interest = Principal × rate × time. Plugging in the known values, we get $500 = Principal × 0.08 × 3. This yields the equation $500 = Principal  × 0.24.

To find the Principal, we divide $500 by 0.24, which gives us approximately $2083.33. Therefore, the initial principal amount is $2083.33.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y\leq x-2[/tex]

The solution of the inequality is the shaded area below the solid line

The equation of the line is [tex]y= x-2[/tex]

The slope of the line is positive [tex]m=1[/tex]

The y-intercept of the line is the point [tex](0,-2)[/tex]

The x-intercept of the line is the point [tex](2,0)[/tex]

therefore

the graph in the attached figure

Answer:

a and c

Step-by-step explanation:

We are given the quadratic equation :

[tex] x^{2} -14x-32=0 [/tex]

Now let us use AC method to factorise it.

Step 1:

Find product of A and C

A=1 and C =-32

A*C =-32

Step 2:

Find factors of -32 such that they add up to give -14.

Factors of -32 that add up to give -14 are -16 and 2.

Step 3:

Rewrite the equation using factors found in step 2.

[tex] x^{2} -16x +2x -32 =0 [/tex]

Step 4:

Factoring by grouping.

[tex] x(x-16) +2(x -16) =0 [/tex]

[tex] (x-16) (x+2) =0 [/tex]

Step 5:

Find roots.

x-16=0 gives x=16

x+2=0 gives x=-2

Answer : Roots of the given Polynomial equation are 16 and -2.

We are given the quadratic equation :

[tex] x^{2} -14x-32=0 [/tex]

Now let us use AC method to factorise it.

Step 1:

Find product of A and C

A=1 and C =-32

A*C =-32

Step 2:

Find factors of -32 such that they add up to give -14.

Factors of -32 that add up to give -14 are -16 and 2.

Step 3:

Rewrite the equation using factors found in step 2.

[tex] x^{2} -16x +2x -32 =0 [/tex]

Step 4:

Factoring by grouping.

[tex] x(x-16) +2(x -16) =0 [/tex]

[tex] (x-16) (x+2) =0 [/tex]

Step 5:

Find roots.

x-16=0 gives x=16

x+2=0 gives x=-2

Answer : Roots of the given Polynomial equation are 16 and -2.

Answer:

The initial value of the graph is 2. Third option is correct.

Step-by-step explanation:

It is given that A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.

The line is passing through the points (0,2) and (7,5).

The point (0,2) is the y-intercept and graph labeled from 0 to 7, therefore 2 is the initial value.

Slope of line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{7-0}=\frac{3}{7}[/tex]

The equation of line is

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept. So the equation of given line is

[tex]y=\frac{3}{7}x+2[/tex]

At initial condition the value of x is 0. So, put x=0.

[tex]y=\frac{3}{7}(0)+2=2[/tex]

Therefore the initial value of the graph is 2. Option 3 is correct.

Answer:

Option 3 rd is correct

Initial value = 2

Step-by-step explanation:

A equation of line is given by:

[tex]y =mx+b[/tex]          ....[1]

where

m is the slope of the line and b is the y-intercept or the initial value

As per the statement:

A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.

It is also given that:

A straight line joins the ordered pair (0, 2) with the ordered pair (7, 5)

Calculate slope:

using formula:

[tex]\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given ordered pairs we have;

[tex]\text{Slope (m)} = \frac{5-2}{7-0}=\frac{3}{7}[/tex]

y-intercept states that the graph which cut y-axis.

Substitute x =0 and solve for x:

we have given with the ordered pair (0, 2)

⇒y-intercept(b) = 2

Substitute the given values of m and b in [1]

[tex]y = \frac{3}{7}x+2[/tex]

The equation of straight line  joins the ordered pair (0, 2) with the ordered pair (7, 5) is:

[tex]y = \frac{3}{7}x+2[/tex]

The initial value of the function represented by the given graph as shown below is: 2

Using the completing-the-square method the vertex form of the function

f(x)  =  x²  +  10x  +  7 is f(x)  =  (x  +  5)²  -  18

The given function is:

f(x)  =  x²  +  10x  +  7

Comparing f(x)  =  x²  +  10x  +  7 with f(x) = ax² + bx + c

a  = 1,  b = 10,  c  = 7

(b/2)²  =  (10/2)²  =  5²

Add and subtract 5² to the right hand side of the equation

f(x)  =  x²  +  10x + 5² +  7 - 5²

f(x)   =  x²  +  10x  +  5²  +  7 - 25

f(x)   =  x²   +  10x  +  5²  - 18

f(x)  =  (x  +  5)²  -  18

f(x)  =  (x  +  5)²  -  18 is of the form f(x) = a(x - h)² + k which is the vertex form of a quadratic equation

Therefore, the vertex form of the function f(x)  =  x²  +  10x +  7 is

f(x)  =  (x  +  5)²  -  18

Learn more here: https://brainly.com/question/19105786

Answer:

Step-by-step explanation:

i did the test

To find the percentage of students who prefer walking, divide the number of students who prefer walking by the total number of students and multiply by 100. In this case, 65 students prefer walking out of a total of 300 students.

To find the percentage of students who prefer walking, you divide the number of students who prefer walking by the total number of students and then multiply by 100. In this case, 65 students prefer walking out of a total of 300 students.

So, you divide 65 by 300 and multiply by 100 to get the percentage.

Percentage of students who prefer walking = (65/300) * 100 = 21.67%

https://brainly.com/question/32197511

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Answer:

Step-by-step explanation:

Alright, lets get started.

We are asked to find arithmetic mean of two terms given.

For finding arithmetic mean, we add up the values and divide the sum by the number of values.

Here we have given two numbers , below

[tex]a_{n-1}=3.9[/tex]

[tex]a_{n+1}=7.1[/tex]

So, mean of these two numbers will be = [tex]\frac{3.9+7.1}{2}[/tex]

So, mean of these two numbers will be = [tex]\frac{11}{2}=5.5[/tex]

So, arithmetic mean for given two numbers are 5.5  :  Answer (b)

Hope it will help :)

b.  5.5

FOR LEARNING ONLY.. not necessary to read, but I hope it helps!

you start with:

[tex]a_{n-1}=3.9\\a_{n-1}=7.1[/tex]

arithmetic questions like this are like finding an average.

so you add the values while dividing by the total of values there are.

in this case:

[tex]\frac{7.1+3.9}{2}[/tex]

which is simplified to:

[tex]\frac{11}{2}[/tex]

then decimal:

[tex]5.5[/tex]