The perimeter of triangle XYZ is 24 units.
What is the area of triangle XYZ? Round to the nearest
tenth of a square unit.
Trigonometric area formula: Area=1/2absin(C)
o 14.7
square units
14.9 square units
15.0 square units
15.3 square units

To express this fraction in exponential form we have to remember the following property:

Applying it to our problem we have:

So the exponential form of our fraction is

The formula for the volume of a rectangular prism is

You need to write the formula for w, note that the width is being miltiplied by "lh"

to cancel this multiplication you have to divide it by "lh" and to keep the equality valid, what is done to one side of the expression must be done to the other, so divide V by "lh" too

Given:

distance from sea level to top of hill = initial heeight = 73.5 meters

velocity = 9.8 m/s

Since we can't have t to be negative, t = 5

The cannonball will reach the sea level at 5 seconds

ANSWER

EXPLANATION

First, we have to fill in the table. To do so, we will plug the x-values into the function to find the corresponding value of y,

So, the table is,

Next, we have to graph all of these points in the coordinate plane. The last one cannot be graphed because y = -81 does not fit in the given coordinate plane. Also, the first two values won't be very accurate because of the scale of the y-axis. The graphed points are,

And finally, to graph the function we join the dots with a line.

Answer:

  (a)  ∠ACE≅∠BCD

Step-by-step explanation:

You want to know the missing statement in the proof that goes with reason "Reflexive Property."

You are proving two triangles are similar by showing two corresponding angles are congruent. Corresponding angles in the two triangles are ...

The proof already shows AEC is congruent to BDC in statement 3.

The reflexive property says an angle is congruent to itself. Looking at the list of corresponding angles, the only angle that corresponds to itself is angle C, which can be named ∠ACE or ∠BCD.

The appropriate choice is ...

  ∠ACE≅∠BCD . . . . Reflexive property

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The missing statement in step 4 should be:ZACE = ZBCD

This statement is missing from the proof and should be included to establish the congruence between the angles in the two triangles.Let's go through the proof step by step and explain each statement and reason.

Given:

AE = EC; BD = DC

AEI = EC; BD = DC

Reason: Given

ZAEC is a right angle; ZBDC is a right angle

Reason: Definition of a right angle. This statement indicates that angle ZAEC and angle ZBDC are both right angles.

ZAEC ≅ ZBDC

Reason: All right angles are congruent. This statement asserts that angle ZAEC and angle ZBDC are congruent (have the same measure) because they are both right angles.

[Missing Statement]

Reason: Reflexive property. This statement is missing in the proof and should be included. The reflexive property states that any angle is congruent to itself. In this case, it implies that angle ZAEC is congruent to angle ZAEC.

AAEC ≅ ABDC

Reason: AA similarity theorem. This statement indicates that triangle AAEC is congruent to triangle ABDC. The AA similarity theorem states that if two pairs of corresponding angles in two triangles are congruent, then the triangles are similar.

So, to complete the proof, the missing statement in step 4 should be:

ZACE = ZBCD

Reason: Reflexive property. This statement establishes that angle ZACE is congruent to angle ZBCD, based on the reflexive property.

Learn more about statement here:

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Here, we are given the following numbers:

2, -2, 3, -3, 4.........

The pattern here is that a positive integer is followed by its negative value.

We can see that the number after 2 is its negative value -2

The number after 3 is its negative vaule -3

The number after 4 will be its negative which is -4

ANSWER:

-4

Answer::

Explanation:

Given the product:

First, expand the brackets:

We then simplify:

The simplified form of the product is:

Answer:

Explanation:

Given the below exponential function;

To be able to graph the above function, we'll go ahead and choose different values for x and determine the corresponding values of f(x).

When x = 0, we'll have;

Looking at all the given four graphs, we can observe that only one of them has a y-interce

Let m denote the number of minutes.

Plan A:

The customer pays a monthly fee of $30 and then an additional 9 cents per minute of use.

Mathematically,

Plan B:

The customer pays a monthly fee of $33.60 and then an additional 8 cents per minute of use.

Mathematically,

For what amounts of monthly phone use will Plan A cost less than Plan B?

Let us solve the above inequality for m

This means that for less than 360 minutes, plan A will cost less than Plan B.

we are given the following equation:

The slope-intercept form is the following:

Therefore, we need to solve for "y" in the equation. To do that we will subtract "3x" to both sides:

Now we will divide both sides by "2":

Now we will separate the numerator:

simplifying:

And thus we get the slope-intercept form.

Answer:

Explanation:

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m = slope

c = y intercept

The given equation is

y = 2x/3 - 7

By comparing both equations,

m = 2/3

If two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. This means that the slope of the perpendicular line passing through the point (2, 6) is the negative reciprocal of 2/3. It is - 3/2

Thus, m = - 3/2

We would find the y intercept of the perpendicular line by substituting m = - 3/2, x = 2 and y = 6 into the slope intercept equation. We have

6 = - 3/2 * 2 + c

6 = - 3 + c

c = 6 + 3 = 9

By substituting m = - 3/2 and c = 9 into the slope intercept equation, the equation of the perpendicular line is

y = - 3x/2 + 9

Also,

If two lines are parallel, it means that the slope of one line is equal to the slope of the other line. This means that the slope of the parallel line passing through the point (2, 6) is 2/3

Thus, m = 2/3

We would find the y intercept of the perpendicular line by substituting m = 2/3, x = 2 and y = 6 into the slope intercept equation. We have

6 = 2/3 * 2 + c

6 = 4/3 + c

c = 6 - 4/3 = 14/3

By substituting m = 2/3 and c = 14/3 into the slope intercept equation, the equation of the parallel line is

y = 2x/3 + 14/3

the slope of the line is 0

The slope of a line is a measure of its steepness of a line , The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run:

so

Step 1

given

replace in the formula

hence, the slope of the line is 0

I hope this helps you

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

Step 01:

Data

Junior

Morning 17

Afternoon 20

Evening 3

Step 02:

Junior

probability afternoon = junior afternoon / total junior afternoon

total junior afternoon = 17 + 20 + 3 = 40

probability afternoon = 20 / (17 + 20 + 3) = 0.5

The answer is:

probability afternoon = 0.5

Considering the least common multiple of 7 and 3, it is found that:

The amount of points of each question in each part are given as follows:

Both parts have the same number of points, and this amount was the least number of points for which this was possible, hence this amount is the least common multiple of 7 and 3.

Both 3 and 7 are prime numbers, hence the least common multiple of 3 and 7 is given by their multiplication, as follows:

7 x 3 = 21.

Hence each part of the test was worth 21 points.

The number of questions of each part is given by the division of 21 and the worth of each question, hence:

More can be learned about the least common multiple at https://brainly.com/question/10749076

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Given:

To find the exponential form of the above, all we need to do is to raise the base a to the power of 4x.

That is;

To find the value of x, we need to raise the power of the right - hand side so that we can equate the exponent

That is;

4x = 1

Divide both-side by 4

Answer:

×=12+5

×=144+25

×=169

×=13

Answer:

Explanations:

The volume of any rectangular box is expressed as:

Now, for the box that will be formed from the figure shown in the question, we will have:

length = 37 - 2x

breadth = 37 - 2x

height = x

Thus, we have that:

We now simplify the above as:

Now that we have obtained the expression for the volume of the box, we now have to find the value of x that maximizes it.

This is done as follows:

Method

- Differentiate the function V(x) with respect to x, and equate to zero as follows:

Now we have to find the second derivative of V(x) in order to confirm which value of x makes the function V(x) a maximum

Thus:

Now since the second derivative is a negative number when x = 6.167, we now know for sure that it is that value of x that maximizes the function V(x), and not x = 18.5.

Thus, we can conclude that the value of x that maximizes the volume of the box is:

x = 6.17 inches (to 2 decimal places)

If we had been asked to find the value of x that minimizes the volume, the answer will have been x = 18.5, because this value of x made the second derivative of V(x) positive.

Now, the maximum volume of the box is obtained by simply substituting the value of x that maximizes the function into the original expression for V(x), as follows:

We can determine an expression of y in terms of x by isolating y on one side of the equation, we can do this by means of some algebraic operations to get:

4x + 2y = 8

1. Subtract 4x from both sides of the equation:

4x - 4x + 2y = 8 - 4x

0 + 2y = 8 - 4x

2y = 8 - 4x

2. Divide both sides by 2

2y/2 = (8 - 4x)/2

y = 4 - 2x

y = -2x + 4

Then, the equation of y in terms of x is y=-2x+4

The equation for the graph is given as

Let us rearrange the equation into its Slope-Intercept form given as

Where

m = rate of change

c = y-intercept

Therefore, we will have

Divide all terms by -4 to make y a standalone variable:

Comparing with the Slope-Intercept equation, the rate of change is given as 6.

The measure of minor arc is 84 degree

The expression for the an angle inscribed in a circle, then the measurement of the angle is equal to the half of the measure of its intercepted arc.

here we have, arc length = 84 degree

Angle = 42 degree

Answer

Option C is correct.

x ≥ -6 and x ≤ 5

Explanation

In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.

But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.

Since the beginning of the blue mark is a shaded circle, the inequality is (≤ or ≥).

And considering that the region of the answer is between -6 and 5, it is evident that x is greater than or equal to -6 and less than or equal to 5. In mathematical terms,

x ≥ -6 and x ≤ 5

-6 ≤ x ≤ 5

Hope this Helps!!!

Given the function f(x) as follows:

The function has a root at x = 3

We will use the synthetic division to find the other roots:

We will divide the coefficients by 3

As follows:

So, the given function will be written as follows:

Factor the term of the quadratic function

So, there are three zeros x = 1, 2, 3

So, the answer will be option 4) x = 1, x = 2

Okay, here we have this:

Considering the provided information, and the given function we are going to calculate R(300) and then we will interpret the result, so we obtain the following:

Considering that x corresponds to the number of hats sold, then it means that if 300 hats are sold, the total revenue will be equal to $5100.

Given:

500 Kina for 18 hours of work

To determine the amount of payment if he had worked for 6 hours, we use ratio.

So,we let x be the amount of payment for 6 hours of work:

Therefore, he would be paid 166.67 Kina if he had worked for six hours.

Answer:

12 nickels, 6 dimes

Step-by-step explanation:

0.05x + 0.1y = 1.20
x - 6 = y

0.05x + 0.1(x-6) = 1.20
0.05x + 0.1x - 0.6 = 1.20
0.15x = 1.80
x = 12

(12) - 6 = y
y = 6

Now graph y = x - 6 and y = (-1/2)x + 12

If you don't know how to graph the functions, then go to khan academy for help.

ANSWER

None of these sides represent the legs.

EXPLANATION

The legs of a triangle are the sides that form the right angle in a right triangle. The legs are always the shortest sides, while the hypotenuse is the longest side.

In this case, the hypotenuse would be 15 yards, while the legs would be 12 yards and 13 yards. For this to be a right triangle, the Pythagorean Theorem must be satisfied,

These side lengths do not satisfy the Pythagorean Theorem and, therefore, this is not a right triangle. If it is not a right triangle, then it does not have legs. Hence, none of these represent the legs.

Given the exponential expression:

The equivalent expressions are:

So, the answer will be options C, D