Which of the following can be used to explain a statement in a geometric proof ?
Check all that apply

• Definition
• Conjecture
• Postulate
• Corollary
• Theorem

Answer:

2.25 meters

Step-by-step explanation:

all you have to do is divide the volume of the container (43.875) by 5 (length) and 3.9 (width) because the formula for the volume of a rectangular prism is V=lwh. So the answer/height of the storage container is 2.25 meters.

The value of [tex]$\left(5^4\right)^4$[/tex] simplified to [tex]$5^{16}$[/tex], meaning x = 16.

To simplify [tex]$\left(5^4\right)^4$[/tex], we first expand it as [tex]$5^4 \cdot 5^4 \cdot 5^4 \cdot 5^4$[/tex], using four factors of [tex]$5^4$[/tex].

Applying the product of powers rule, we add the exponents together: [tex]$5^{4+4+4+4}$[/tex]. This simplifies to [tex]$5^{16}$[/tex].

In essence, raising a power to another power involves multiplying the exponents.

In this case, we have four factors of [tex]$5^4$[/tex], which means we multiply 4 by 4, resulting in [tex]$5^{16}$[/tex].

So, the value of x in the simplified power [tex]$5^x$[/tex] is 16.

Complete Question:

Simplify this power raised to a power: [tex]$\left(5^4\right)^4$[/tex]

1. Expand using four factors of [tex]$5^4$[/tex] : [tex]5^4 \cdot 5^4 \cdot 5^4 \cdot 5^4[/tex]

2. Apply the product of powers rule: [tex]5^{4+4+4+4}[/tex]

3. Simplify: [tex]5^x[/tex]

What is the value of x in the simplified power?

Answer:

B . $ 884.56

Step-by-step explanation:

Since, monthly payment formula of a loan,

[tex]P=\frac{PV(\frac{r}{12})}{1-(1+\frac{r}{12})^{-12t}}[/tex]

Where,

PV = principal value,

r = annual rate of interest,

t = number of years,

Here,

PV = $ 162,000,

r = 5.15% = 0.0515,

t = 30,

Hence, the monthly payment would be,

[tex]P=\frac{162000(\frac{0.0515}{12})}{1-(1+\frac{0.0515}{12})^{-360}}[/tex]

[tex]=\$ 884.562485827[/tex]

[tex]\approx \$ 884.56[/tex]

OPTION B is correct.

To find out how many weeks have passed, we subtract the remaining amount from the initial amount, and then divide by the amount saved each week. In this case, 6 weeks have passed.

To find out how many weeks have passed, we need to subtract the remaining amount from the initial amount, and then divide by the amount saved each week.

Initial amount saved = $440

Amount saved each week = $55

Remaining amount = $110

Weeks passed = (Initial amount saved - Remaining amount) / Amount saved each week

= ($440 - $110) / $55

= $330 / $55

= 6 weeks

Therefore, 6 weeks have passed.

Final answer:

To solve the equation 5/8 m = 25, Gabriel needs to multiply both sides of the equation by the reciprocal of 5/8, which is 8/5, to isolate m on one side. The result after simplification is m = 40.

Explanation:

To solve the equation 5/8 m = 25, Gabriel needs to isolate the variable m on one side of the equation. He should start by multiplying both sides of the equation by the reciprocal of the fraction that is multiplied by m, which is 8/5. Here's the step-by-step process:

Multiply both sides of the equation by 8/5 to cancel out the 5/8 on the left side:

(8/5) × (5/8) m = (8/5) × 25

Simplify the left side by canceling out the common factors in the fraction:

1 m = (8/5) × 25

Next, multiply the number 25 by 8/5 to find the value of m:

m = 25 × (8/5) = 40

Thus, the solution to the equation is m = 40.

Answer:

Option d) [tex](4-x^5)(16+x^{10}+4x^5)[/tex]  

Step-by-step explanation:

We are given the following in the question.

[tex]64-x^{15}[/tex]

We have to factorize the given expression.

Using the algebraic identity:

[tex]a^3 - b^3 = (a-b)(a^2+b^2+ab) = (a-b)^3 +3ab(a-b)[/tex]

[tex]64-x^{15}\\\\(4)^3 - (x^5)^3\\\\(4 - x^5)(4^2 + (x^5)^2 + 4x^5)\\\\(4-x^5)(16+x^{10}+4x^5)[/tex]

Hence, the factors of given expression is given by option d) [tex](4-x^5)(16+x^{10}+4x^5)[/tex]

The answer is B, a square. I don't know about the area though.

Jim is just as likely to get a head as Jane is to get an even number since the chance or probability of getting a head for Jim and getting a even number for Jane are equal i.e. 1/2=0.5

In a quarter there are just two outcomes-- Head and Tail

The probability of getting a head is: 1/2

Similarly in a number cube that has six possible outcomes i.e. {1,2,3,4,5,6}

The number of outcomes that represents a even number are: 3  

(Since outcomes are: 2,4 and 6)

Hence, the probability of getting a even number is: 3/6=1/2

Hence, we see that the probability of getting a head and a even number is same.

Answer:

Step-by-step explanation:

The attachment shows different types of polygons.

Now depending on these we have following five possibilities:

Case 1: Triangle and hexagon

If first polygon is triangle with three angles, the second will have 6 angles and the second polygon will be hexagon.

Case 2: Quadrilateral and heptagon

If first polygon is quadrilateral with 4 angles, the second will have 4+3 =7 angles and the second polygon will be heptagon.

Case 3: Pentagon and Octagon

If first polygon is pentagon with 5 angles, the second will have 5+3=8 angles and the second polygon will be octagon.

Case 4: Hexagon and Nonagon

If first polygon is hexagon with 6 angles, the second will have 6+3=9 angles and the second polygon will be nonagon.

Case 5: Heptagon and Decagon

If first polygon is Heptagon with 7 angles, the second will have 7+3=10 angles and the second polygon will be decagon.

Depend on the possibilities, which figure Ellen is drawing.

A closed, two-dimensional form with straight line segments is called a polygon. It does not have three dimensions. A polygon has flat surfaces throughout. A polygon must have three sides at a minimum. Only at its terminal must each side of a line segment cross another line segment. Depending on a polygon's number of sides.

Given Ellen is drawing two polygons one of the polygons has 3 more angles than the other,

Now, based on these, there are the five options listed below:

Case 1: Hexagon and triangle

If the first polygon is a triangle with three angles, the second polygon will be a hexagon with six angles.

Case 2: Heptagon and quadrilateral

If the first polygon has a quadrilateral shape and four angles, the second polygon will have four plus three more angles, making it a heptagon.

Pentagon and Octagon in Case 3

If the first polygon has a pentagon shape with five angles, the second will have an octagon shape with five plus three equals eight angles.

Hexagon and Nonagon in Case 4

If the first polygon has a hexagon shape and 6 angles, the second will have 6 + 3 = 9 angles and be a nonagon.

Heptagon and Decagon in Case 5

if the initial polygon is a hexagon, then The first polygon has 7 angles, the second has 7+3=10 angles, and the third is a decagon.

Hence the shape of polygon depend on these possibilities.

Learn more about polygon;

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They are called inverse operations:

The average rate of change over the entire slide is -0.05.

The average rate of change from x = 0 to x = 15 is calculated by finding the slope of the secant line that intersects the graph of the function at x = 0 and x = 15.

The slope of the secant line is:

m = ([tex]y_2[/tex] - [tex]y_1[/tex])/([tex]x_2[/tex] - [tex]x_1[/tex])

= (-2 - 15)/(15 - 0)

= -17/15

= -1.133

The average rate of change from x = 0 to x = 20 is calculated by finding the slope of the secant line that intersects the graph of the function at x = 0 and x = 20.

The slope of the secant line is:

m = ([tex]y_2[/tex] - [tex]y_1[/tex])/([tex]x_2[/tex] - [tex]x_1[/tex])

= (2 - 15)/(20 - 0)

= -13/20

= -0.65

The average rate of change from x = 0 to x = 20 is smaller than the average rate of change from x = 0 to x = 15.

This is because the slope of the secant line is getting closer to 0 as the interval gets larger.

If the height of the slide is 2 feet when x = 20, then the average rate of change over the entire slide is:

m = ([tex]y_2[/tex] - [tex]y_1[/tex])/([tex]x_2[/tex] - [tex]x_1[/tex])

= (2 - 1)/(20 - 0)

= -1/20

= -0.05

The average rate of change over the entire slide is also negative, but it is much smaller than the average rate of change from x = 0 to x = 15.

This is because the slope of the secant line is getting closer to 0 as the interval gets larger.

To learn more about average here:

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If a system has exactly one or infinite number of solutions then it will be a consistent system.

So, we can solve the given system of equation to get the answer.

y=4x−4 ................(1)

y=−4x+4...............(2)

After equating both the equations we will get,

4x-4= -4x+4

4x-4+4x=4 (Adding 4x to each sides).

8x-4=4

8x=4+4 (Adding 4 to each sides).

8x=8

8x/8=8/8 ( Dividing each sides by 8).

x=1

Now pluging x=1 in equation (1). So,

y=4x−4

=4(1)-4

=4-4

=0

Hence the solution of the given system is (1, 0) which also means that the two equations is intersecting at a point(1,0).

So, the given system is consistent and coincident.

Answer:

The answer is " Consistent And Independent"

Why? :

When 2 Lines intersect at one point it means it Consistent and Independent

and When the Lines are the same exact thing its Consistent and Dependent

But, when 2 lines don't intersect at all its inconsistent.   :)

I also Took The 5.11 Unit Test :)

Answer:

c) Kasimir should have divided by 100,000.

Step-by-step explanation:

Given that Kasimir rode his bike 34,478 centimeters.

We have the table

10 mm=1 cm

10 cm =1dm

10dm = 1 m

...

Hence we have 100 cm = 1 m

100x1000 cm = 1 km

1 km = 34478/100000 = 0.34478

Hence C) is right

Kasimir should have divided by 100,000.

A car maintains a speed of 23 mi/h for 5 seconds. It then accelerates to a speed of 46 mi/h in 5 seconds. It maintains that speed for the next 5 seconds. Which graph shows the car’s speed over time?

Solution:

The graph is Time versus Speed.

In figure (a), the graph has a speed or y-axis=23mi/h for time or x-axis=5seconds.

The car maintains a speed of 23mi/h for 5 seconds.

For next 5 seconds, in figure a the graph increases linearly or we have a acceleration and reaches to 46mi/h.

It accelerates to a speed of 46 mi/h in 5 seconds.

It maintains that speed for the next 5 seconds. In figure (a), after we reach speed=46mi/h, there is a straight line for 5 seconds at speed=46mi/h.

So, Answer Graph a

An oblique prism can be thought of as a leaning prism where the altitude or height of the prism is not the same as the lateral edge of the prims.

Answer:

Option A is the correct choice.

Step-by-step explanation:

We have been given that Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50.

The inequality [tex]10+2.5x\leq 40[/tex] represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.

Let us solve for x by subtracting 10 from both sides of our inequality.

[tex]10-10+2.5x\leq 40-10[/tex]

[tex]2.5x\leq 30[/tex]  

Now we will divide both sides of our inequality by 2.5.

[tex]\frac{2.5x}{2.5}\leq \frac{30}{2.5}[/tex]

[tex]x\leq 12[/tex]

Therefore, Ling can buy from 0 to 12 bags, but no more and option A is the correct choice.