Rewrite 3x + 4y = 10 using function notation.

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.

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Answer:

A. It is linear because it has a constant rate of change.

Step-by-step explanation:

A straight line graph is possible between two variables x and y only if there is a constant rate of change

y = mx+b is the equation of a straight line in general and here we find rate of change of y with respect to x is constant m which does not depend on x or y.

In other words, throughout the domain a straight line has constant slope.

Here we find that the graph given is a straight line.

Hence option A is suitable answer

A. It is linear because it has a constant rate of change.

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.

Answer: [tex]m= 8(20)+10[/tex]

Step-by-step explanation:

Given : The number of markers in each of 8 pack = 20

Then, the number of markers in 8 packs = 8 x 20 = 8(20)

Also, You already had 10 markers.

Then, the total markers you have now =  Number of markers in 8 packs+ 10

= 8(20)+10

If we denote the total number of markers be 'm'.

Then, the required equation will be :-

[tex]m= 8(20)+10[/tex]

Hence, the equation shows how to calculate the total number of markers, m, you have : [tex]m= 8(20)+10[/tex]

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 :)

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:

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.

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]

Answer:

The record number was 275 tires.

165/x=60/100

165 times 100=16500

16500/60=275

x=275

Step-by-step explanation:

Answer:

Right

Step-by-step explanation:

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.

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.

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The surface area of the given three-dimensional figure is 210 square units.

Option A will be the correct answer.

A cuboid is a three-dimensional figure having length, width and height. The surface area of a cuboid can be calculated by adding together the areas of the six faces.

For the given cuboid, length l = 8 , width w = 5 and height h = 5.

Area of Cuboid  =  2 lw + 2 lh + 2 wh

[tex]A = 2\times l\times w + 2 \times l\times h + 2\times w\times h[/tex]

Substituting the values in the above formula, the area will be,

[tex]A = 2 \times 8 \times 5 + 2 \times 8 \times 5 + 2\times 5\times 5[/tex]

[tex]A = 210 \;\rm {units}^2[/tex]

Hence, the surface area of the cuboid is 210 square units.

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