MATHEMATICS HIGH SCHOOL

2. Given the following functions f(x) and g(x), solve (f + g)(5) and select the correct answer below:f(x) = 8x − 13

g(x) = x − 9

23
27
31
40

Answers

Answer 1

Answer: I chose this answer which is
A.) 23

Answer 2

Answer:

Answer:

The answer is 23.

Step-by-step explanation:

First you insert 5 into the X place in both equations.

f(5)=8(5) - 13 and g(5)=5 - 9

Then you would solve as you normally would.

F(5)=40 - 13, F(5)=27.

G(5)=-4

Then you add them together because that is what the question is asking when the say (f+g).

Your final answer is 23.

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Provide the reasons for the fol owing proof Given: JK ≅ KL, NK ≅ KM Prove ΔNKJ ≅ ΔMLK Statements Reasons 1. JK≅KL,NK≅KM 1. Given 2. 3. ΔNKJ ≅ ΔMLK 3.________ ANSWER CHOICES a. reflexive property of ≅ ; SAS b. reflexive property of ≅ ; ASA c. vertical angles are congruent; ASA d. vertical angles are congruent; SAS
John Gray bought a basic car for $32,750.00, with options that cost $375.00. There's a 6% sales tax in his state and a combined $50.00 license and registration fee. What was John's total cost?A. $35,165.50 B. $33,175.00 C. $35,140.00 D. $35,162.50

. Let A = (−2, 4) and B = (7, 6). Find the point P on the line y = 2 that makes the total distance AP + BP as small as possible.

Answers

Answer:

P(1,2)

Step-by-step explanation:

There are 2 points.

A(-2,4) and B(7,6)

the point P on the y=2 can also represented as P(x,2)

We can use the distance formula to find the distances AP and BP

$\text{dist} = √((x_1 - x_2)^2 + (y_1 - y_2)^2)$

for AP: A(-2,4) and P(x,2)

$AP = √((-2 - x)^2 + (4 - 2)^2)$

$AP = √((-2 - x)^2 + 4)$

$AP = √((-1)^2(2 + x)^2 + 4)$

$AP = √((2 + x)^2 + 4)$

for BP: B(7,6) and P(x,2)

$BP = √((7 - x)^2 + (6 - 2)^2)$

$BP = √((7 - x)^2 + 16)$

the total distance AP + BP will be

$√((2 + x)^2 + 4)+√((7 - x)^2 + 16)$ (plot is given below)

Our task is to find the value of x such that the above expression is small as possible. (we can find this either through plotting or differentiating)

If you plot the above equation, the minimum point of the curve will be clearly visible, and it will be at x = 1. Hence, the point P(1,2) is such that the total distance AP + BP is as small as possible.

Final answer:

The point P that makes the total distance AP + BP smallest on the line y=2 is given by the x-coordinate of the midpoint of A and B because the shortest distance is in a straight line. Therefore, the point P is (2.5, 2).

Explanation:

To find the point P on the line y = 2 that makes the total distance AP + BP the smallest, you need to recall that the shortest distance between two points is a straight line. So, ideally, we want to find a point P (x,2) that is on the same vertical line (or x-coordinate) that intersects the line AB at the midpoint.

Step 1: Find the midpoint of A and B. The midpoint M is obtained by averaging the x and y coordinates of A and B: M = ((-2+7)/2 , (4+6)/2) = (2.5, 5).

Step 2: Since line y = 2 is horizontal, the x-coordinate of our point P will stay the same with the midpoint x-coordinate. Therefore, P has coordinates (2.5, 2).

So, the point on the line y = 2 that makes the total distance AP + BP as small as possible is P (2.5, 2).

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Statistics that are used to draw conclusions about larger groups are called __________.

Answers

INFERENTIAL STATISTICS uses a sample data from a portion ofthe whole population in order to draw a sound result from them and assume thatthe result is based on the whole population. For example, in a population of100 only 10 of the children can be picked from the population pool and beconducted with the study. The result of the study is automatically inferred asjudgment that is probable and accurate. For example, if in a sample of 10, 3out of 10 children are malnourished, it is automatically applied that 30 out ofthe 100 children are malnourished.

TIMED PLEASE HURRYTwo hundred students were surveyed about their favorite fruit. How many more students preferred apples than cherries?

2

4

35

70

Answers

The total number of students who preferred apples than cherries are 70 if the two hundred students were surveyed about their favorite fruit option, fourth is correct.

What is the percentage?

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

From the diagram, we can see the total 35% students preferred apples.

Total number of students = 200

The number of students who preferred apples than cherries = 200×35%

= 200(35/100)

= 2(35)

= 70

Thus, the total number of students who preferred apples than cherries are 70 if the two hundred students were surveyed about their favorite fruit option fourth is correct.

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Answer:

The answer is 4.

Step-by-step explanation:

I believe that, if I'm correct, 2 students are equal to 1%. 2 x 35 = 70. 2 x 33 = 66. 70 - 66 = 4 more students. I hope this is correct.

the sales tax on a used truck is 600 dollars. If the tax rate is 6%. Find the purchase price of the truck

Answers

.06=600
.06/.06=600/.06
$10,000=original price
but we still have to add tax
therefore,
$10,000+600=sale price
sale price=$10,600

How many hydrogen atoms are there in 5 molecules of CHCl3

Answers

Step-by-step explanation:

Each molecule has ONE hydrogen atom

so FIVE molecules would have FIVE hydrogen atoms

In triangle ABC, the measure of angle B is 50 degrees. Select all possible values for the measures of A and C if ABC is an acute triangle. m\angle∠A= 58 degrees; m\angle∠C= 72 degrees m\angle∠A= 100 degrees; m\angle∠C= 30 degrees m\angle∠A= 80 degrees; m\angle∠C= 50 degrees m\angle∠A= 60 degrees; m\angle∠C= 70 degrees m\angle∠A= 90 degrees; m\angle∠C= 40 degrees m\angle∠A= 105 degrees; m\angle∠C= 25 degrees

Answers

Answer:

Step-by-step explanation:

Sum of angle in a triangle = 180°

<A+<B+<C = 180

Given <B = 50°

Substituting into the formula

<A+50+<C = 180

<A+<C = 180-50

<A+<C = 130°

Since the ∆ABC is an acute triangle, the angles <A and <C must be angles less than 90° since acute angles are angles less than 90°

The possible values of <A and <C that will be acute and give a sum of 130° are;

∠A= 58° and ∠C= 72°

∠A= 80° and ∠C= 50°

∠A= 60° and ∠C= 70°

You can see that all the Angles are less than 90° and their sum is 130°

Final answer:

Out of the options provided, for an acute triangle ABC with angle B equal to 50 degrees, angles A and C can measure 58 and 72 degrees respectively or 60 and 70 degrees.

Explanation:

In Mathematics, especially Geometry, we know that the sum of the angles in any triangle, acute or otherwise, equals 180 degrees. In the given triangle ABC, m∠B is 50 degrees. If ABC is an acute triangle, none of these angles can be equal to or more than 90 degrees as an acute angle is less than 90 degrees.

So the possible values for measures of angles A and C are:

m∠A= 58 degrees; m∠C= 72 degrees
m∠A= 60 degrees; m∠C= 70 degrees

The other options cannot be correct because either they would make the sum of the angles more than 180 degrees, or one of the angles would be equal to or greater than 90 degrees.