Which law would you use to simplify the expression (x^⁴)⁹ ?

A. product of powers
B. power of a product
C. power of a quotient
D. power of a power

Step-by-step explanation:

The change in position or displacement of an object in the time interval is known as average velocity of the object. The value of the average velocity is 60 miles per hour.

Given-

A car travels 180 miles north in 3 hours.

Average velocity- The change in position or displacement of an object in the time interval is known as average velocity of the object. It can be positive or negative depending upon the sign of the displacement.

[tex]\overline v=\dfrac{\Delta v}{\Delta t}[/tex]

Here [tex]\Delta v[/tex] is the change in displacement and [tex]\Delta t[/tex] is the change in time.

Use this formula to find the average velocity in the given formula we have to  put the values velocity and time given in the question. Therefore,

[tex]\overline v=\dfrac{180}{3}[/tex]

[tex]\overline v=60[/tex]

Hence, the value of the average velocity is 60 miles per hour.

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Answer:

(C) Square feet

Step-by-step explanation:

In order to take the measurements, he should use the square feet unit of measure.

As, the cubic feet also known as unit of volume can be defined as the volume of the cube with sides of one foot in length. Since, the bathroom is two dimensional therefore, cubic feet can't be used.

Yards are basically a unit of length use to measure length and perimeter and square yards are used in measuring the long space and the bathroom is bit too small for it.

Therefore, square feet should be used to measure.

Answer:

Teddy avoids accidents.

Step-by-step explanation:

The fourth degree polynomial g(x) with a double zero at x=1, zeros at x=-4 and x=5, and satisfying g(0)=-6 is g(x) = 3/10(x-1)²(x+4)(x-5).

A possible formula for a fourth degree polynomial g(x) with specific characteristics. The polynomial must have a double zero at x=1, zeros at x=-4 and x=5, and must satisfy g(0)=-6.

Since the polynomial has a double zero at x=1, we can represent that part of the polynomial as (x-1)². The other two zeros at x=-4 and x=5 give us factors of (x+4) and (x-5) respectively. Multiplying these factors gives us a polynomial that satisfies the zero requirements: (x-1)²(x+4)(x-5).

Now, we need to find the constant k that will make the polynomial satisfy g(0) = -6. We set up the equation using the known factors:
k(x-1)²(x+4)(x-5) and substitute x with 0 to solve for k. This gives us k(0-1)²(0+4)(0-5) = -6. Solving for k, we find k = 3/10.

Therefore, the formula for the polynomial g(x) is g(x) = 3/10(x-1)²(x+4)(x-5).

Answer:

its C on ed

Step-by-step explanation:

Answer:

it is prime

Step-by-step explanation:

Remember:

Prime numbers have 2 factors:

1

Itself

Answer:

Statement which describes the roots is:

2 real roots

Step-by-step explanation:

If the discriminant D of a quadratic equation follows:

D=0 then there are 2 equal real roots or 1 real root

D>0 then there are 2 unequal real roots

and if D<0 then there are 2 complex roots

Here, we are given  the discriminant of a quadratic equation is 4

i.e. D=4 >0

So, it means quadratic equation has 2 real roots

Hence, statement which describes the roots is:

2 real roots

Hence, statement which describes the roots is:

2 real roots

The equation sin(-13π/4) = -5π/4 is incorrect.

The correct value for sin(-13π/4) is actually 1/√2 or √2/2, not -5π/4.

Here, we have,

To understand why, let's break down the calculation step by step:

The sine function represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

In this case, we have an angle of -13π/4.

To find the reference angle,

we can add 2π to -13π/4 to bring it into the standard range of angles:

-13π/4 + 2π = -5π/4

Now, we can find the reference angle of -5π/4 in the unit circle or trigonometric table.

The reference angle of -5π/4 is π/4.

Since sine is positive in the second quadrant,

the value of sin(-5π/4) is the same as sin(π/4), which is 1/√2 or √2/2.

Therefore, the correct exact value of sin(-13π/4) is 1/√2 or √2/2, and not -5π/4.

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Answer:

Option A is correct.

Yes, by AA similarity criterion

Step-by-step explanation:

AA(Angle-Angle) Similarity Criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

In ΔBAC and ΔCED

[tex]\angle BAC = \angle CED = 17^{\circ}[/tex]   [Angle]        [Given]

[tex]\angle C = \angle C[/tex]     [Angle]          [Common angle]

Therefore, by AA similarity criterion;

[tex]\triangle BAC \sim \triangle CED[/tex]

Therefore,  ΔBAC and ΔCED are similar by AA similarity criterion.

Answer:

less than $896.00

Step-by-step explanation:

A common rule is that housing expenses should not be more than 28% of your monthly income.

your monthly income = $3,200

so your housing expense should not be more than 28% of $3,200

= [tex]\frac{28}{100}[/tex] × 3,200

= 0.28 × 3,200 = $896.00

So you can spend less than $896.00 on housing expenses.

Answer:

The answers are,

The measure of angle Z is 45°.

The perpendicular bisector of  Line segment X Z creates two smaller isosceles triangles.

Angle Y is a right angle.

Step-by-step explanation:

I got it right on geometry test.

Triangle FBD in the given regular hexagon inscribed in a circle can be proven to be an equilateral triangle based on the equal lengths of radii and the angle of 60 degrees subtended at the center by the side of the hexagon.

To prove that triangle FBD is an equilateral triangle, we first need to understand a few properties of a regular hexagon and a circle. In a regular hexagon inscribed in a circle, every angle at the center of the circle subtended by the sides of the hexagon is 60 degrees because the total degree measure at the center of the circle is 360, and this is divided equally among the six sides of the hexagon.

Triangle FBD is formed by joining the center of the circle, O, and two consecutive vertices of the hexagon, B and F. As the hexagon is regular and inscribed in a circle, both OB and OF are radii of the circle. By definition, all radii of a given circle are equal in length. Therefore, OB = OF.

The angle BFO subtended at the center by the side BF of the hexagon is 60 degrees. Hence, triangle FBD is an equilateral triangle because it has two equal sides and the included angle is 60 degrees, which are the properties of an equilateral triangle.

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To prove that triangle FBD is equilateral, one can show that the central angles corresponding to the three sides of the hexagon (angle AOB, angle BOC, and so on) are all equal. Therefore, demonstrating that angle FOB, angle BOD, and angle DOF are each 120 degrees will establish that triangle FBD is equilateral.

In a regular hexagon inscribed in a circle, the central angles formed by connecting the center of the circle (O) to consecutive vertices of the hexagon are all equal. Since each interior angle of a regular hexagon is 120 degrees, the central angles (e.g., angle AOB, angle BOC, etc.) are also 120 degrees. To prove that triangle FBD is equilateral, one needs to focus on the central angles corresponding to its sides.

The central angles associated with triangle FBD are angle FOB, angle BOD, and angle DOF. By demonstrating that each of these angles is 120 degrees, it can be concluded that triangle FBD is equilateral. The regularity of the hexagon ensures that the central angles are equal, making this an effective and straightforward way to prove the equilaterality of triangle FBD.

In conclusion, to establish the equilaterality of triangle FBD, one should emphasize the properties of central angles within the context of a regular hexagon. Specifically, showing that angle FOB, angle BOD, and angle DOF are each 120 degrees serves as a valid proof for the equilateral nature of triangle FBD within the given geometric configuration.

The expression that completes the equation is 3(7+1).

To complete the equation "24 divided by 6 + 20,"

we need to perform the division first, and then add 20 to the result.

    6 | 24 | 4

           24

        _____

            0

Here, Divisor= 6, Remainder= 0 and Quotient= 4

So, 4 + 20 = 24

Then, the equivalent value is

3 (7+1)

= 3 x 8

= 24

Therefore, the expression that completes the equation is 3(7+1).

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The question attached here is incomplete, the complete Question is

Choose the expression that completes the equation.

24 ÷ 6 + 20 =______

2(7 + 10)

4(4 + 3)

3(7 + 1)

3(7 + 7)

The cost to rent 1 canoe from the rent made by the group of the girls and boys is $25.

Word problems are a mathematical interpretation by using variables, numbers, and arithmetic operations to solve real-life problems.

From the given information:

Now, we can have a system of equations, and we can solve for the number of canoes and the inner tubes rented.

Using Elimination method:

2c + 3t = 80    --- × (1)

c + 7t = 95       --- × (2)

2c + 3t = 80

-2c + 14t = 190          

 0  +  -11t = -110        

-11t = -110

t = -110/-11

t = 10

From equation (1)

2c + 3t = 80

2c + 3(10) = 80

2c + 30 = 80

2c = 80 - 30

2c = 50

c = 50/2

c = 25

Therefore, we can conclude that the cost of the rent of 1 canoe is $25.

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As Claudia walks away from a 264-cm lamppost, the tip of her shadow moves twice as fast as she does, so the Claudia’s height is 132 cm.

To solve this problem, we can use the concept of similar triangles.

Let's assume Claudia's height is h cm.

Since Claudia's shadow tip moves twice as fast as she does, her shadow's length must be twice her height, or 2h cm.

According to the question, as Claudia walks away from the lamppost, her shadow moves twice as fast as she does.

This means the ratio of the length of the shadow to the distance Claudia walks is the same as the ratio of the distance the shadow moves to the distance Claudia walks.

We can set up the following proportion:

(2h) / 264 = h / x

where x is the distance Claudia walks from the lamppost.

Solve for h by cross multiplying:

2h * x = 264 * h

2hx = 264h

Divide both sides by h:

2x = 264

Divide both sides by 2:

x = 132 cm

Therefore, Claudia's height is h = 132 cm.

By using the principles of similar triangles and the given information that Claudia's shadow moves at double her pace, we establish a proportion between the heights and shadow lengths, solve the equation, and find that Claudia's height is 176 cm.

To solve the problem of finding Claudia's height based on the information given about her shadow, we need to apply the principles of similar triangles. The situation describes a real-world application of similar triangles, where Claudia and her shadow form one triangle, and the lamppost and its shadow form another. These triangles are similar because the angles are the same: the angle of elevation to the sun is the same for both Claudia and the lamppost, and the ground provides the same angle for both bases.

Let's denote Claudia's height as h, the distance Claudia walks away from the lamppost as x, and therefore the length of her shadow will be 2x (since it moves twice as fast). The similar triangles give us the following proportion:

Height of Lamppost / Height of Claudia = Length of Lamppost's Shadow / Length of Claudia's Shadow

264 cm / h = (x + 2x) / 2x

This simplifies to:

264 / h = 3 / 2

Solving for h, we get:

2 * 264 = 3h
h = 2 * 264 / 3
h = 528 / 3
h = 176 cm

Therefore, Claudia's height is 176 cm.

The marginal revenue for 100 units sold is 180 dollars per unit. We cannot precisely estimate the total revenue for 100 or 101 units sold without further information.

In this problem, we're dealing with the concept of marginal revenue. The marginal revenue function gives us the change in total revenue for each additional unit sold. That is given in this case as R'(q)=240-18√q.

To find the marginal revenue at 100 units, we simply substitute q = 100 into our function: R'(100)=240-18√100 = 240 - 18*10 = 180 dollars per unit.

The total revenue given a specific quantity is typically found by integrating the marginal revenue function. However, without the constants of integration or the original revenue function, we cannot accurately compute the total revenue for 100 or 101 units sold in this case.

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