If f(x) = 2x2 + 3x and g(x) = x – 2, what is (f + g)(2)?

prove “if two angles of one triangle are congruent to two angles of a second triangle, the the third angles of the triangles are

arsen [322]

Assume that,

The two angles of one triangle are congruent to two angles of a second triangle.

To prove: The third angles of the triangles are congruent.

Since, two angles of one triangle are congruent to two angles of a second triangle.

Therefore,

$\begin{gathered} \angle C=\angle F \\ \angle A=\angle D \end{gathered}$

Adding these two we get,

$\begin{gathered} \angle C+\angle A=\angle F+\angle D \\ 180-\angle B=180-\angle E\text{ (Using angle sum property of a triangle)} \end{gathered}$

Cancelling 180 on both sides, we get

$\begin{gathered} \angle B=\angle E \\ \therefore\angle B\cong\angle E \end{gathered}$

Hence, if two angles of one triangle are congruent to two angles of a second triangle, the the third angles of the triangles are congruent.

3 0

2 years ago

Tim is now earning $500 per week after receiving an increase of $45 per week. What was Tim's previous weekly salary

Mars2501 [29]

Now Tim gets $500 after it $45 was added to what he had last week

That means that
"What Tim earned last week" + $45 = $500

Subtract $45 from $500
$500-$45= $455

If you're not sure check your work
If I make $455 now and next week I get $45 more next week
$455+$45=$500
Next week I make $500

8 0

4 years ago

Write a quadratic function in standard form with zeros 5 and 6

N76 [4]

Answer:

${x}^{2} - 11x +30$

Step-by-step explanation:

Zeros = 5 & 6

Let the variable of the quadratic function be x

Therefore, (x - 5) & (x-6) are factors

$(x - 5)(x - 6) \\ \\ = {x}^{2} - (5 + 6)x + ( - 5)( - 6) \\ \\ = {x}^{2} - 11x +30 \\ is \: the \: required \: quadratic \: \\function.$

6 0

3 years ago

If the equation of a circle is (x + 5)2 + (y - 7)2 = 36, its center point is (5, 7) (-5, 7) (5, -7)

Gnoma [55]

(-5,7) it’s always the opposite of what is being squared with x and y

4 0

3 years ago

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The hourly wages earned by 20 employees are shown in the first box and whisker plot below. The person earning $15 per hour quits

serg [7]

I added the plots in the attachments.

Answer:

The mean will decrease

The median will remain the same

Explanation:

1- checking the mean:

Mean of the salaries is calculated as follows:

$Mean = \frac{sum-of-salaries}{number-of-employees}$

Now, we can note that two parameters affect the mean, let's consider each:

a. Number of employees:

We are given that one employee is replaced with another. This means that the number of employees did not change

b. Sum of salaries:

We are given that a person earning $15 left and the new person earns $7. This means that:

New sum of salaries = old sum of salaries - 15 + 7 = old sum of salaries - 8

This means that the sum of salaries decreased by 8

Now, for the mean:

We can conclude that since the numerator decreased while the denominator stayed the same, the mean will decrease

2- checking the median:

In the whisker plots, the median is represented by the vertical line inside the plot.

In the first plot, we can note that the vertical line is nearly half the distance between 9 and 10. This means that, for the first plot, the median is approximately 9.5

In the second plot, the place of the median is unchanged. It is still approximately midway between 9 and 10 which means that the median in the second plot is approximately 9.5

Therefore, the median of the data remains unchanged.

Hope this helps :)

5 0

3 years ago

Read 2 more answers