Leyla drops a penny from a height of 150 m.

How long will it take the penny to hit the ground?

Use the formula h(t)=−4.9t2+vot+h o, where vo is the initial velocity and h o is the initial height. Round to the nearest tenth of a second.

Answer:

1.78

Step-by-step explanation:

To solve for x  we need to cross multiply it

We have = sign in between the fractions so we cross multiply it

9*x = 2* 8

9x = 16

Now we divide by 9 on both sides

so x= 1.7777777778

When we round to two decimal places then

x= 1.78

Answer:  The required value of x is 2 or -12.

Step-by-step explanation:  We are given to solve for x in the following equation :

[tex]x^2+10x+12=36~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be solving the given equation by the method of factorization.

From equation (i), we have

[tex]x^2+10x+12=36\\\\\Rightarrow x^2+10x+12-36=0\\\\\Rightarrow x^2+10x-24=0\\\\\Rightarrow x^2+12x-2x-24=0\\\\\Rightarrow x(x+12)-2(x+12)=0\\\\\Rightarrow (x-2)(x+12)=0\\\\\Rightarrow x-2=0,~~~~~~x+12=0\\\\\Rightarrow x=2,~-12.[/tex]

Thus, the required value of x is 2 or -12.

Answer:

After 35 years balance in the account  = $93429.71

Explanation:

We will applying the compound interest formula.

A = [tex] P(1 +\frac{r}{n})^{nt}  [/tex]

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years

Given that,

P = $6000

r = 8% = [tex] \frac{8}{100}  [/tex] = 0.08

n = 2 (because of twice in a year)

t = 35 years

[tex] A= 6000(1 + \frac{0.08}{2}) ^{2*35}  [/tex]

A = 6000[tex] (1.04)^{70}  [/tex]

A= $93429.71    (Option D)

Answer:

I just took this quiz and the answer is B:$704.50

Step-by-step explanation:

Edg 2022

Final answer:

To find the corresponding point of a function after transformation, substitute the given point into the transformed function.

Explanation:

Given: (7, -4) is on the graph of f(x).

To find: The corresponding point for the function f(x+4).

Solution:

Substitute x+4 into the function f(x) to get the new function f(x+4).

Substitute x=3 into f(x+4) to find the corresponding point.

Therefore, the corresponding point for f(x+4) is (3, -4).

Answer:

The length of the radius must be less than [tex]2[/tex]

[tex]\frac{1}{2},1,1.5[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

where r is the radius of the circle

In this problem we have that

[tex]C > A[/tex]

Substitute

[tex]2\pi r > \pi r^{2}[/tex]

Simplify

[tex]2r > r^{2}[/tex]

[tex]2> r[/tex] ------> rewrite

[tex] r< 2\ units [/tex]

The length of the radius must be less than [tex]2[/tex]

the answer is

[tex]\frac{1}{2},1,1.5[/tex]

Roderick select the length of radius, for keeping the value of circumference of the circle greater than the value of its area, should be 1/2,1 and 1.5. Thus the option A, B and C is the correct option.

Circumference of the circle is the length of its boundary. It can given as,

[tex]P=2\pi r[/tex]

The area of the circle is the space occupied by it. It can be given as,

[tex]A=\pi r^2[/tex]

Given information-

Roderick wants to draw a circle.

The circumference of the circle must be greater than the area of the circle.

The circumference of the circle having radius equal to [tex]r[/tex] units can be given as,

[tex]P=2\pi r[/tex]

The area of the circle having radius equal to [tex]r[/tex] units can be given as,

[tex]A=\pi r^2[/tex]

Now as Roderick wants to draw a circle in which, the circumference of the circle must be greater than the area of the circle. Thus,

[tex]P>A[/tex]

Put the values as,

[tex]2\pi r>\pi r^2\\2r>r^2\\2>r[/tex]

Thus the value of the  radius of Roderick circle must be less than the number 2.

Number 1/2 , 1, and 1.5 is less than the number two.

Thus, Roderick select the length of radius, for keeping the value of circumference of the circle greater than the value of its area, should be 1/2,1 and 1.5. Thus the option A, B and C is the correct option.

Learn more about the circumference and area of the circle here;

https://brainly.com/question/402655

Answer:Yes, the products are equal because of commutativity. To find the product, use distributive law. Just simplify the below:

-2x^3(x^3-3x-4) + x(x^3-3x-4) - 5(x^3-3x-4)

Step-by-step explanation:

Diannas current age is what your being asked to find

Diannas age is the unknown in the problem

The given relatioships can be written in terms of diannas current age

Answer:

The answer would be $125.01

Step-by-step explanation:

I took the test.

Sample Response: Algebra tiles would not be a good tool to use to factor the trinomial because you would need to drag an x-squared tile, 18 x-tiles, and 80 plus tiles. That is a total of 99 tiles. It would take a lot of time to drag that many tiles on the board and there might not be enough space to hold all of them. You would also need to determine how to arrange all those tiles to make a rectangle. Since 80 is a multiple of 10, you might recognize that 10 and 8 are the factors that add to 18, which would give you the values to use in the X method.

The lengths 1.5 cm, 3 cm, and 1.5 cm cannot form a triangle because the sum of the lengths of the two shorter sides is equal to the length of the longest side, which does not satisfy the Triangle Inequality Theorem.

The question asks if lengths 1.5 cm, 3 cm, and 1.5 cm can form a triangle, and if so, what kind of triangle it would be. To determine whether these lengths can form a triangle, we use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For these lengths:

We see that when we add the lengths of the two shorter sides (1.5 cm + 1.5 cm), it equals the length of the longest side (3 cm). According to the Triangle Inequality Theorem, the lengths do not meet the condition for forming a triangle because the sum must be greater than, not equal to, the length of the third side. Therefore, these lengths cannot form a triangle.

Quiz: Area of Rectangles Assessment items A rectangle is 13 yards long and 23 yards wide. What is the area of the rectangle? Enter your answer in the box as a fraction in simplest form. $$ yd2 Assessment navigation

Length of rectangle=13yards

Width of rectangle=23yards

The formula for, Area of rectangle= length*width

So, Area=13*23[tex] yards^{2} [/tex]

As, 13 multiplied by 23 is 299

So, Area=299[tex] yards^{2} [/tex]

To represent in fractions, Area=[tex] \frac{299}{1}yards^{2} [/tex]

Area=299[tex] yd^{2} [/tex]

Answer:

Option: A is correct (congruent triangles)

Step-by-step explanation:

To prove that he diagonals of a parallelogram bisect each other we have to go through the following steps:

Hence we have to use the concept of congruent triangles in order to prove that the diagonals of a parallelogram bisect each other.

Hence, option A is correct

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

We have been given a triangle and we are asked to solve for x using angle bisector theorem.

Angle bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side of triangle into segments that are proportional to the other two sides.

Using angle bisector theorem we can set an equation as:

[tex]\frac{4x+1}{5}=\frac{15}{3}[/tex]

Let us solve for x by multiplying both sides of our equation by 5.

[tex]\frac{4x+1}{5}*5=\frac{15}{3}*5[/tex]

[tex]4x+1=5*5[/tex]

[tex]4x+1=25[/tex]

Let us subtract 1 form both sides of our equation.

[tex]4x+1-1=25-1[/tex]

[tex]4x=24[/tex]

Upon dividing both sides of our equation by 4 we will get,

[tex]\frac{4x}{4}=\frac{24}{4}[/tex]

[tex]x=6[/tex]

Therefore, the value of x is 6 units.

The total area of the blades is the area of a triangle multiplied by 4.

We have then:

[tex] A = (4) * (1/2) * (b) * (h)
[/tex]

Where,

b: base of the blades

h: height of the blades

Substituting values we have:

[tex] A = (4) * (1/2) * (7) * (4)
[/tex]

Doing the calculation we have that the area of the blades is given by:

[tex] A = 56 feet ^ 2
[/tex]

Answer:

The total area of the blades is:

[tex] A = 56 feet ^ 2 [/tex]

Each blade on a windmill is in the shape of a triangle with a base of 7 feet and a height of 4 ft if there are four blades on the windmill what is the total area of the blades

Total area of blades= Sum of areas of all blades

=Sum of areas of four blades

As, all blades have same dimension

SO, Total area of blades=4*Area of one blade

As, shape of blade is triangle, Area of triangle=[tex] \frac{1}{2} [/tex]*base*height

Total Area of blades =4* [tex] \frac{1}{2} [/tex] * base * height

Total Area of blades =4* [tex] \frac{1}{2} [/tex] * 7 * 4

Total Area of blades =4* [tex] \frac{1}{2} [/tex] * 28

Total Area of blades =4* 14

Total Area of blades =56 square feet