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3 years ago

Find the quotient: (x2−5x+8)÷(x+2)

Mathematics

1 answer:

Aneli [31]3 years ago

3 0

Answer:

Quotient = x - 7

Step-by-step explanation:

We are dividing x^2 - 5x +8 by x + 2

x + 2√x^2 - 5x + 8

Starting with dividing by x

x - 7

x + 2√ x^2 - 5x + 8

Multiplying x by x + 2

x + 2√ x^2 - 5x + 8

x^2 + 2x

= -7x + 8

Step ii, pick -7 for division

-7x + 8

-7x - 14

= +8 -(-14)

= 8+14

= 22

The answer is

( x - 7) remainder 22

(x - 7) is the quointent

22 is the remainder

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Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the

maksim [4K]

Answer:

The line of symmetry is x = -3

Explanation:

Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:

$y=ax^2+bx+c$

The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:

$x_v=-\frac{b}{2a}$

In this problem, we have:

$y=-x^2-6x-13$

Then:

a = -1

b = -6

We write now:

$x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3$

Part 3:

For this part, we need to find the x-intercepts. This is, when y = 0:

$-x^2-6x-13=0$

To solve this, we can use the quadratic formula:

$x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}$

And solve:

$x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}$ $x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}$

Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.

Part 4:

To find the y intercept, we need to find the value of y when x = 0:

$y=-0^2-6\cdot0-13=-13$

The y-intercept is at (0, -13)

Part 5:

Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:

$x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20$ $x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8$

The two points are:

(1, -20)

(-1, -8)

Part 6:

Now, we can use 3 points to find the graph of the parabola.

We can locate (1, -20) and (-1, -8)

The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3

Then, y-coordinate of the vertex is:

$y=-(-3)^2-6(-3)-13=-9+18-13=-4$

The third point we can use is (-3, -4)

Now we can locate them in the cartesian plane:

And that's enough to get the full graph:

8 0

1 year ago

Grades on a standardized test are known to have a mean of 1000 for students in the United States. The test is administered to 45

krok68 [10]

Answer:

The 95% confidence interval is $1003 < \mu$

Yes there is statistically significant evidence that students in Florida perform differently from other students in the United States

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 1000$

The sample size is $n = 453$

The sample mean is $\= x = 1013$

The standard deviation is $s = 108$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

=> $\alpha = 5\%$

=> $\alpha = 0.05$

The critical value for $\frac{\alpha }{2}$ obtained from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }$

=> $E = 1.96 * \frac{108}{\sqrt{453} }$

=> $E = 9.946$

Generally the 95% confidence interval is mathematically represented as

$\= x - E < \mu < \= x + E$

=> $1013 - 9.946 < \mu < 1013 + 9.946$

=> $1003 < \mu$

Given that the population mean(1000) is not within the 95% confidence interval for l for the average test score for students in Florida, then it means that there is statistically significant evidence that students in Florida perform differently from other students in the United States

4 0

3 years ago

I need this to be specific and quick! 35 points!

g100num [7]

D) these two figures are similar they don't look similar at first because the X'Z'Y' is more upwards. But they are congruent meaning they are similar or exactly the same almost. This basically tells me that I need to use translation.

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4 years ago

The function h is defined by h(x)=4+3x over 5+x<br><br> Find h(4z)

Jobisdone [24]

Answer:

h(4z)=4+12z / 5+4z

Step-by-step explanation:

The function h is defined by h(x)=4+3x over 5+x

This can be written as

h(x)=4+3x / 5+x

The value of the function at any time depends on the value of x. x is the independent variable. The variable,x can take any value at any time.

To find h(4z), it means that x is taking the value of 4z.

We will substitute 4z in the place of x in the function. This becomes

h(4z)=4+3×4z / 5+4z

h(4z)=4+12z / 5+4z

5 0

3 years ago

Plz, help ASAP!!!!!!!!!!!!!!!

blsea [12.9K]

Answer: m∠QPR = 40

<h2>Step-by-step explanation:</h2>

Because PG is perpendicular to PS, it is safe to assume that angle QPS is 90 degrees.

(7x-9) + (4x +22) = 90

x = 7

Because we need to find the degrees of QPR, plug in the equation for that angle with the value of x we found.

7(7) - 9 = 40

m∠QPR = 40

8 0

3 years ago