Isabelle is designing a sandbox for her backyard. the sandbox will be a regular pentagon 3 ft each side. how much wood does she need to enclose the entire sandbox? how many square ft will the sandbox take up?

The given numbers are

5.78 x 10^5 and 8.04 x 10^-2​

We would simplify the exponents by applying one of the laws of exponents which states that

a^b x a^c = a^(b + c)

By applying this law, the expression becomes

5.78 x 8.04 x 10^(5 + - 2)

46.4712 x 10^(5 - 2)

46.4712 x 10^3

The product in scientific notation is

46.4712 x 10^3

Find the slope of the line that passes through these two points

P1 = (0, -2)

P2 = (5, 3)

The slope would be 1

Given:

Let's simplify using exponential notation.

To simplify, multiply the the base, then use law of indicies to add the exponents

We have:

3.8 x[tex]10^3[/tex] is 169 times smaller than 6.422x [tex]10^5[/tex].

The number is written in the form  [tex]a \times 10^b[/tex] where we have  [tex]1 \leq[/tex] a < 10. Scientific notations have some of the profits as:

Better readability due to compact representation Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

We need to find out how many times 3.8 x 10^5 is greater than 3.8 x 10^-7.

To do that, we have to divide 3.8 x 10^5 by 3.8 x 10^-7 and then find the answer.

Let us do that:

[tex]\begin{gathered} \frac{3.8\cdot10^3}{6.422\cdot10^{5}}\text{ = }\frac{3.8}{6.422}\cdot\text{ }\frac{10^3}{10^{5}} \end{gathered}[/tex]

= 169

According to the division law of indices states that if a numerator and a denominator have the same base (e.g. 10), then the power of the numerator can subtract of the denominator.

Therefore, 3.8 x[tex]10^3[/tex] is 169 times smaller than 6.422x [tex]10^5[/tex].

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Answer:

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Step-by-step explanation:

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Okay, here we have this:

Considering that a composite number is a number that is not prime, the only number one of the units that tells us that a two-digit number is composed is 5, since every number ending in 5 is a multiple of 5.

We have, From the graph it can be seen that when x tends to zero on the right, y

ANSWER AND EXPLANATION:

Given:

To be able to determine the distance between the moon and the sun, we'll need to divide the length of side y by the sine of angle x using the below formula;

in a cave a stalactites gets 4 millimeters longer each year.this year it is 72 centimeters long

how many years until it is 1 meter long​

we have that

the linear equation that represent this situation is equal to

y=4x+720

where

y ------> length in mm

x ----> number of years

Remember that

72 cm=720 mm

so

For y=1 m ------> y=1,000 mm

substitute in the equation

1,000=4x+720

4x=1,000-720

4x=280

x=70 years

therefore

From the diagram

Ratio of model A car to model B car = 4:6

Ratio of model A to model B = 4:6

Ratio of model B to model A = 6:4

Ratio of model A to total = 4:10

Ratio of model B to total = 6:10

If 40 model A cars sold

I know that 60 model B cars was sold.

The missing sides, x, and y can be obtained using the sine rule

Step 1: Get the angle at A

The angle at A is obtained below:

Step 2: Use the sine rule

To get y

cross multiply

To get x

Therefore, the answer is option C

The relationship of the angles are:

1. ∠5 and ∠6 are linear pairs.

2. ∠3 and ∠2 are vertically opposite angles.

3. ∠4 and ∠8 are corresponding angles.

Given that,

In the picture there are parallel lines with a transversal.

We have to find the relation between,

1. ∠5 and ∠6?

2. ∠3 and ∠2?

3. ∠4 and ∠8?

Take the 1st angles.

∠5 and ∠6 are linear pairs.

A linear pair of angles is formed when two lines intersect at a single point. If the angles follow the spot where the two lines come together in a straight line, they are said to be linear. In a pair of linear equations, the sum of the angles is always 180°.

Take the 2nd angles.

∠3 and ∠2 are vertically opposite angles.

When two straight lines collide at a particular vertex, they create angles that are perpendicular to one another vertically. Angles that are perpendicular to one another vertically are equal. These are occasionally referred to as vertical angles.

Take the 3rd angles.

∠4 and ∠8 are corresponding angles.

The angles that meet two other straight lines in the same vicinity. If the two lines are parallel, the comparable angles are also equal.

Therefore, The relationship of the angles are:

1. ∠5 and ∠6 are linear pairs.

2. ∠3 and ∠2 are vertically opposite angles.

3. ∠4 and ∠8 are corresponding angles.

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Pythagoras Theorem:

In a right angle triangle, the sum of square of base and perpendicular is equal to the square of Hypotenuse .

Hypotenuse² = Perpendicular² + base²

In the given figure, we have:

Base = k

Hypotenuse = 10

Perpendicular = 6

Substitute the valus and solve for k,

The missing side is 8

Answer: 8

To determine the factor of the given polynomial, first, we rewrite it as follows:

Now, notice that:

Factoring out the 4x+1, we get:

The 1,500 calories in the combination meal and the amount of calories per mozzarella stick and per each slider gives an equation with the following solution;

There are 11 mozzarella sticks and 2 sliders in the combination meal.

An equation in mathematics is a statement that two mathematical expressions are equal.

The number of calories in each mozzarella stick = 100

Number of calories in each slider = 200

Number of calories in the combination meal = 1,500

Number of mozzarella sticks in the combination meal = 9 + The number of sliders

Let s represent the number of sliders in the combination meal, we have;

Number of mozzarella in the combination meal = s + 9

The equation that gives the amount of calories in the meal is therefore;

200·s + 100·(s + 9) = 1,500

200·s + 100·s + 900 = 1,500

300·s = 1,500 - 900 = 600

s = 600 ÷ 300 = 2

The number of sliders in the combination meal, s = 2

The number of mozzarella in the meal = 2 + 9 = 11

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the Part a. Compute f(0). We have to evaluate the function for x = 0.

Therefore, f(0) = -7.

Part b. Solve f(x) = 0.

To solve the equation 2x - 7 = 0, we have to add 7 to both sides of the equation, and then dividing the equation by 2:

So, x = 7/2.

Part c.

Part a tells us that the graph of the function is evaluated in zero, the value for the function is -7. When x = 0, the value for y = -7. This is the intercept of the linear function.

Part b tells us that when y = 0, the value for x = 7/2.

The line passes through points (0, -7) and (7/2, 0). These are the points on y-axis and x-axis, respectively.

Answer:

The amount of money Kitty would have is;

Explanation:

Given that Kitty invested $4000 into an account that earns 8% interest compounded monthly for 10 years;

Applying the formula for compound interest;

Substituting the given values;

Therefore, the amount of money Kitty would have is;

[tex]\sf \Large \boxed{\sf +}\\ \sf \Large \boxed{\sf +}\\\\ \sf \Large \boxed{\sf 11x+-11y=-22}\\\\ 2x+9x-3y-8y=4-26\\Combine\\11x-11y=-22\\Simplify\\x-y=-2\\x=y-2\\Plug\ the\ value\ in\ the\ equation\\2(y-2)-3y=4\\2y-4-3y=4\\-y-4=4\\-y=8\\y=-8\\Solve\ for\ x\\9x-8(-8)=-26\\9x+64=-26\\9x=-90\\x=-10[/tex]

For the given table:

We will find the necessary score on the final exam for a student to earn an A (90%) in the class.

so,

The equation will be:

now, solve the equation to find x:

So, the answer will be:

The student needs a score of 85% on the final exam to earn a 90%

You have the following opeartion between sets:

(x + 2 < 5) U (x - 7 > 6)

In order to find the solution to the previoues expression, you first find the solutionof each inequality, just as follow:

x + 2 < 5 subtract 2 both sides

x < 5 - 2

x < 3

The solution interval is (-∞,3)

x - 7 > - 6 add 7 both sides

x > - 6 + 7

x > 1

The solution interval is (1, ∞)

Then, you have:

(-∞,3) U (1,∞)

which is the same that:

{x| x<3 or x>1}

The first statement is about the diameter of the circle.

The diameter of a circle is always the double of its radius.

So if circle A ras a radius of 4 inches, its diameter is:

So the first statement is true (YES)

The second statement is about the area of the circle. The area of a circle is given by the following equation:

If the radius of the circle is 4 inches, we have:

So the second statement is also true (YES)

The third statement is about the volume of a cylinder with a height of 6 inches and the circle A as the base. The volume of a cylinder is given by the equation:

Using the radius = 4 inches and the height = 6 inches, we have:

The volume is not 64pi, so this statement is false (NO).

We are given a question about factory plants making TV panels. The following information holds.

Plant A produces twice as many panels as plant B. This can be expressed mathematically as:

Also, 2% and 3% of the TV panels from Plant A and Plant B are defective, and both plants produced a total of 490 defective panels. This can be expressed mathematically as:

We can clearly see that we have derived two equations. We will substitute the first equation in the second equation to get the number of panels Plant B produced.

Therefore, the number of panels that plant B produced is:

ANSWER: 7000

.Since the old number of patients is 960

Since it is increasing by 25%, then

We will find the amount of 25% of 960, then add it to 960

Add it to 960 to find the new number of patients

Dr Wells saw 1200 patients

To find the maximum profit we need to maximize the function.

First we need to find the critical points, to do this we need to find the derivative of the function:

now we equate it to zero and solve for x:

hence the critical point of the function is x=105/4.

The next step is to determine if the critical point is a maximum or a minimum, to do this we find the second derivative:

Since the second derivative is negative for all values of x (and specially for x=105/4) we conclude that the critical point is a maximum.

Hence the function has a maximum at x=105/4. To find the value of the maximum we plug the value of x to find y:

Therefore the maximum profit is $605

We have the equation:

We can factorize this equation as:

In this case, we have 2 rational solutions.

If the solution implies the square root of -1, then we would have 2 complex solutions.

If the solution implies a square root that does not have a rational solution, then we have 2 irrational solutions.

We can see it when we apply the quadratic formula:

The term with the square root defines what type of solution we have:

If b^2-4ac<0, then we have complex solutions.

If the square root of b^2-4ac does not have a rational solution (b^2-4ac is not a perfect square), then we have irrational solutions.

If b^2-4ac is a perfect square (its square root have a rational solution), we will have rational solutions.

Answer:

• Amplitude = 2

• Period = π/4

Explanation:

Given the function:

In order to sketch the graph of y, we need to find its amplitude and period.

Comparing the function with the general sine function:

We have that:

Next, using these values, we sketch one cycle of the graph below:

Area of triangle = 105 mm²

Area of triangle = 1/2 × base × height

base = 14 mm

height = 15 mm

Area of triangle = 1/2 × 14mm × 15mm

Area of triangle = 105 mm²

Its corner points (0, 0), (2, 1), (0, 2), (1, 0)

From the question, we have

All the points should be positive, as we can see after carefully examining the equation.

There are two approaches to approach this problem. The first is to solve the equations, create a graph, and make a decision.

The alternative is to just plug the points into the equations and check to see if the conditions are met; this method is quicker for tests with MCQs.

As a result, option B is correct.

Inequalities:

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. The different inequality symbols, properties, and methods for resolving linear inequalities in one variable and two variables will all be covered in this article along with examples.

Complete question: A shaded region is described by the following inequalities: x 20, y 20, x + 2y s 4, X y sl. What are its corner points? a. (0, 0), (1, 0), (0; 1), (0, 2) b. (0, 0), (2, 1), (0, 2), (1, 0) c. (0, 0), (4, 0), (0, 2), (2, 1) d. (0, 0), (1, 0), (2, 1), (0, 1) e. (0, -1), (2, 1), (0, 2)

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We are given the following complex numbers

To perform the addition of the complex numbers, simply add the like terms together.

Similarly,

Therefore, the result of the complex addition is