Maggie wants to make a special card for Valentine’s Day. She starts with a
square piece of red paper with a side length of 12 cm. She then pastes two white
semi-circles, each with radius 3 cm, and a white triangle onto the square sheet of
red paper, as shown below. Determine the total amount of area available in the white region for Maggie’s special valentine greeting.

The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm

An equation is an expression that shows the relationship between two or more variables and numbers.

Let us assume that the pyramid has a volume of 75 cm³ and square base area of 25 cm², hence:

Volume = (1/3) * area of base * height

75 = (1/3) * 25 * height

height = 9cm

The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm

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The area and circumference of a circle are 12.56square feet and 12.56ft respectively

The formula for calculating the area and circumference of a circle is expressed as:

A = πr²

C = πd

where

r is the radius and d is the diameter

Area = 3.14 * (2)²

Area = 12.56ft²

For the circumference

C = 3.14(4)

C = 12.54ft

Hence the area and circumference of a circle are 12.56square feet and 12.56ft respectively

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Answer:

x = 3, x = 9/4

Step-by-step explanation:

8x = 24

x = 3 Divide both sides by 8.

4x = 9

x = 9/4 Divide both sides by 4.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation \#1.}[/tex]

[tex]\mathsf{8x = 24}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{8x = 24}[/tex]

[tex]\huge\textbf{Divide \boxed{8} to both sides:}[/tex]

[tex]\mathsf{\dfrac{8x}{8} = \dfrac{24}{8}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = \dfrac{24}{8}}[/tex]

[tex]\mathsf{x = 3}[/tex]

[tex]\huge\textbf{Therefore, the answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x =}\frak{\ 3}}\huge\checkmark[/tex]

[tex]\huge\textbf{Equation \#2.}[/tex]

[tex]\mathsf{4x = 9}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{4x = 9}[/tex]

[tex]\huge\textbf{Divide \boxed{9} to both sides:}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{9}{4}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = \dfrac{9}{4}}[/tex]

[tex]\mathsf{x = 2 \dfrac{1}{4}}[/tex]

[tex]\huge\textbf{Therefore, the answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = }\frak{\ \dfrac{9}{4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Step-by-step explanation:

volume = length • width • height

by making width subject

V=LWH

W=V/LH

W= 54/8×3

W=54/24

W=9/4

W=2.25

Answer:

2x - 5 < -8 or 2x - 5 > 8

Step-by-step explanation:

|2x - 5| > 8

2x - 5 < -8 or 2x - 5 > 8

The two inequalities that can be written from the |2x - 5| > 8 are:

2x - 5 > 8

-2x + 5 > 8

We have,

To split the inequality |2x - 5| > 8 into two separate inequalities, we consider both the positive and negative cases for the absolute value expression.

Positive case:

When 2x - 5 is positive, we have:

2x - 5 > 8 _____(1)

Negative case:

When 2x - 5 is negative, we have:

-(2x - 5) > 8

Simplifying the negative case:

-2x + 5 > 8 ______(2)

Now, we have two inequalities:

2x - 5 > 8

-2x + 5 > 8

These are the two inequalities resulting from the given inequality

|2x - 5| > 8.

Thus,

The two inequalities that can be written from the |2x - 5| > 8 are:

2x - 5 > 8

-2x + 5 > 8

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Probability that a card selected at random is purple = 7/25

Number of red cards, N(red) = 12

Number of blue cards, N(blue) = 17

Number of purple cards, N(purple) = 14

Number of yellow cards, N(yellow) = 7

Total number of cards, N(total) = 12 + 17 + 14 + 7

N(total) = 50

Probability that a card selected at random will be purple

P(purple) = N(purple) / N(total)

P(purple) = 14/50

Reduce to the lowest fraction

P(purple) = 7/25

Therefore, probability that a card selected at random is purple = 7/25

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Complete Question

There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat. If a card is selected at random, what is the probability that the card is purple

Answer:

p = 21.4 cm

∠P = 44°

Step-by-step explanation:

Apply the Pythagorean Theorem to solve for the length of p.

Now, take the inverse sine function to find angle P :

Answer:

  a) 21.4 cm

  b) 45.6°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and sides of a right triangle. Here, two relevant function are ...

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

The hypotenuse of the triangle, and the side adjacent to angle P are given, so we have ...

  cos(P) = (21 cm)/(30 cm)

The angle value can be found using the inverse cosine function:

  P = arccos(21/30)

  P ≈ 45.6°

Now, we know angle P and the side adjacent to it. We want to find the measure of side p, which is opposite the angle. This can be done using either the sine function or the tangent function. Here, we choose to use the tangent function.

  tan(P) = p/21

  p = 21×tan(P) = 21·tan(45.573°)

  p ≈ 21.4 . . . . cm

__

Additional comment

In the attached, part of the calculator keypad is shown so you can see that the inverse cosine function is the 2ND function of the Cos key. The calculator mode is set to DEG (lower left of display) so that angles are in units appropriate to this problem.

Of course, you can always use the Pythagorean theorem to find the length of side p. More calculations are involved, so we used trig functions instead. Note that the angle P must be found first using the approach here, and its value must be retained with enough significant digits to ensure accuracy in the 'p' calculation.

The effect that  'h' have on the graph of a parabola is Horizontal shift or translation .

A translation is the movement of  a shape up, down , this can also be movement from side to side.

Even though there is movement,   its appearance remains the same in any other way, hence, h values cause left or right movement with respect to the graph.

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The ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.

The angle of elevation of the ramp can be found using trigonometric ratios.

Therefore,  the angle of elevation must be equal to 4.8 degrees to obey the ADA guidelines .

Hence,

tan ∅ = opposite / adjacent

opposite side = 3.5 ft

adjacent side = 40 ft

Therefore,

tan ∅ = 3.5 / 40

∅ = tan ⁻¹ 0.0875

∅ = 5.00064459756

∅ = 5 degrees

Therefore, the ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.

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If the sales had dropped 23% then music store had sold 551 units in the second quarter.

Given that a music store had sold 715 units in first quarter and sales had dropped by 23%.

We are required to determine the sales in the second quarter.

Percentage is the number or ratio expressed in terms of 100. It is expressed as %.

Sales in first quarter=715 units

Decrease in sales=23%

In units ,decrease=715*23%

=715*23/100

=164.45

Sales of second  quarter=715-164.45

=550.55

After rounding we will get 551.

Hence if the music store sold 715 units in first quarter then the units sold by music store in second quarter 551 units.

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Answer:

see below

Step-by-step explanation:

90 degree clockwise will change x, y coordinates to  y, -x

point D  1,3    becomes   3,-1

point E   4, 4   becomes  4,-4

point F  4, -2  becomes   -2,-4

point G  1,-1    becomes    -1, -1

Answer:

x=1

Step-by-step explanation:

1 + 1/3 = 4/9

1/3 also equals 3/9

hope this helped :)

Answer :

Step-by-step explanation :

>> (3 × x + x / 3) = 4 / 9

>> (3x + x / 3) = 4 / 9

>> (4x / 3) = 4 / 9

>> 4x × 9 = 3 × 4

>> 36x = 12

>> x = 12 / 36

>> x = 6 / 18

>> x = 3 / 9

>> x = 1 / 3

Answer:

d. 64

Step-by-step explanation:

x^1/2 = 8

Square each side

(x^1/2 )^2=( 8)^2

x = 64

Answer:

88.5

Step-by-step explanation:

3.5 * 8 = 28, this is how much was spent on copies printed. If 800 copies cost $64 and 28 of that was on the 3.5 fee per 100, then the flat rate must be:

64-28 = 36.

Now, let's do 1500. For 1500 copies, you will get charged $3.5 15 times. This amounts to 52.5, then adding the fixed fee of 36 dollars, you get

88.5

Considering the given linear function, the inequality graphed is:

B. [tex]y \geq 2x + 2[/tex].

A linear function is modeled by:

y = mx + b

In which:

The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:

m = (4 - 2)/(2 - 1) = 2.

Thus the equation of the line is:

y = 2x + 2.

The left-side of the line is the values above the line, hence the inequality is:

B. [tex]y \geq 2x + 2[/tex].

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The length of side OA in the given rhombus is: 5 units.

A rhombus is a quadrilateral that has four sides that are all of the same length. Therefore, in the image given, the length of AB equals the length of OA.

Given the following:

Length of AB = |8 - 3}

Length of AB = 5 units.

AB = OA = 5 units.

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The value of the 4th iterate of the given function f(x) is -2.096

2nd option is correct.

A function's iterate is a function that is expressed as repetition of another (already iterated) function; this latter function may be referred to as the iterand.

Any function taken on its own is regarded as the first iteration.

A function is said to have an identity function at iteration zero.

According to the question,

f(x) = (3x-1)/[tex]x^{2}[/tex]

[tex]x_{o}[/tex] = -2

The first iterate is calculated by finding f(-2).

f(-2) = (3(-2)-1)/4

f(-2) = -1.75

Similarly, the next iterates are calculated as follows:

f(-1.75) = -2.048

f(-2.048) = -1.71

f(-1.71) = -2.096

Thus, the fourth iterate for the given function is [tex]x_{4}[/tex]= -2.096

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"The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location."

Polynomial functions are equations such as quadratic and cubic equations that take only the non-negative integer power of a variable or a positive integer exponent. For example, 2x + 5 is a polynomial with an exponent equal to 1.

A polynomial function is an expression that is a combination of variables of different degrees, non-zero coefficients, positive exponents (of variables), and constants. For example, f (b) = 4b2 – 6 is a polynomial of'b'and has a degree of 2.

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The surface area of the composite solid is 579.84 square feet

The composite solid that completes the question is added as an attachment

From the attached figure, we have the following figures:

The surface area of a rectangular prism is

A = 2(lw + lh + wh)

Using the dimensions of the prism, we have:

A = 2(6 * 11 + 6 * 8 + 8 * 11)

This gives

A = 404

The surface area of a cylinder is

A = 2πr^2 + 2πrh

Using the dimensions of the cylinder, we have:

A = 2 * 3.14 * 4^2 + 2 * 3.14 * 4 * 5

Evaluate

A = 226.08

The area of the circle between both shapes is

A = πr^2

This gives

A = 3.14 * 4^2

A = 50.24

The surface area of the composite solid is then calculated as:

Surface area = Area of rectangular prism + Area of cylinder - Area of circle

This gives

Surface area = 404 + 226.08 - 50.24

Evaluate

Surface area = 579.84

Hence, the surface area of the composite solid is 579.84 square feet

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we conclude that the sequence has 8 terms.

Here we have the geometric sequence:

2/81, 4/27, 8/9, ..., 6912

Notice that each term is equal to 6 times the previous term, such that:

2/81*6 = 4/27

4/27*6 = 8/9

Then the n-th term is equal to:

[tex]a_n = a_1*r^{n-1}[/tex]

Where in this case:

[tex]a_1 = 2/81\\\\r = 6[/tex]

Now we need to find the value of n such that:

[tex](2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616[/tex]

If we apply the natural logarithm to both sides, then:

[tex]n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8[/tex]

Then we conclude that the sequence has 8 terms.

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Answer:

1. pi.      2.49-12.25pi

Step-by-step explanation:

after 6.2 hours the dose will decay to 70% in your bloodstream.

We know that the half-life is 12 hours. Then the exponential relation for an initial dosage of A is:

[tex]D(t) = A*e^{-t*ln(2)/12h}[/tex]

If the dosage needs to decay to a 70% of the initial dosage, then we must have:

[tex]e^{-t*ln(2)/12h} = 0.7[/tex]

Now we need to solve that for t:

If we apply the natural logarithm in both sides, we get:

[tex]ln(e^{-t*ln(2)/12h}) = ln(0.7)\\\\-t*ln(2)/12h = ln(0.7)\\\\t = -ln(0.7)*12h/ln(2) = 6.2h[/tex]

So after 6.2 hours the dose will decay to 70% in your bloodstream.

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Taking 1 in the box it creates an expression equivalent to 2 - 5.

The expressions represent the distance between the two points on the

number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.

What is integers on number line?

Integers are represented using a number line. A straight line of numbers is shown visually as a number line. It is made up of positive integers like 1, 2, etc., negative integers like - 1, - 2, etc., and a zero that is neither positive nor negative.

Part A:

2 - 5 = -3

2 + 1 = 3

The distance on the number line between a number and 0 is its absolute value.

             a. That distance is never negative.

             b. The symbol for Absolute Value is “ | | ”.

Hence, by taking 1 in the box it creates an expression equivalent to 2 - 5.

Part B:

|-3 -2| = 1

This point represent distance from -3 to -2 on the number line is 1 unit.

|2-(-3)| = 5

This point represent distance from 2 to -3 on the number line is 5 units.

|-3 + (-2)| = 5

This point represent distance from -3 to -2 on the number line is 5 units.

|-3 - (-2)| = 1

This point represent distance from -3 to -2 on the number line is 1 units.

Therefore,

Taking 1 in the box it creates an expression equivalent to 2 - 5.

The expressions represent the distance between the two points on the

number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.

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At the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.

First of all, we would derive an expression for the position with respect to the angle (phase shift) under the appropriate conditions:

Asin(ωt + ø) = c₂sinωt + c₁cosωt.

At t = 0, we have:

y = c₂sin(0) + c₁cos(0).

y = 0 + c₁

y = 0 + 5

y = 5 units.

Therefore, we can logically deduce that at the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.

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Complete Question:

The angle Φ represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then Φ = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then Φ = π. If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then Φ = π/2. In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.

Answer:

(7,3)

Step-by-step explanation:

you can add the equations together to eliminate y and first solve for x

(x-3y = -2) + (x+3y=16) = (2x = 14)

x = 7

then plug x into one of the equations to solve for y

(7) - 3y = -2

9 = 3y

y = 3

the solution is (7,3)

Answer: (7, 3)

Step-by-step explanation:

x - 3y = -2

x + 3y = 16

Here we can add the two equations together to cancel out the y

2x = 14

divide by 2 on both sides to get

x = 7

Now that we have the X value, plug in x value into an equation to get the Y

x - 3y = -2

7 - 3y = -2

-3y = -9

y = 3

So the solution is (7, 3)

Answer:

b) x = 4

Explanation:

[tex]2x^2 - x + 10 = 38[/tex]

collect variables

[tex]2x^2 - x + 10 - 38 = 0[/tex]

simplify

[tex]2x^2 - x - 28 = 0[/tex]

breakdown

[tex]2x^2 -8x + 7x - 28 = 0[/tex]

factor out

[tex]2x(x - 4) + 7(x - 4) = 0[/tex]

collect into groups

[tex](2x + 7)(x - 4) = 0[/tex]

set to zero

[tex]2x + 7 = 0, x - 4 = 0[/tex]

relocate variable

[tex]2x = -7, x = 4[/tex]

final solutions

[tex]x = -3.5, x = 4[/tex]

The answer is b.

To find the value of x, we need to convert this into the form of a quadratic equation.

Subtract 38 from each side.

Solve by splitting the middle term.

The simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]

The complete question is added as an attachment

The equation is given as

[tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex]

Subtract (x - 10)^2 from both sides

[tex](y- 6)^2 = 4^2 - (x - 10)^2[/tex]

Evaluate 4^2

[tex](y- 6)^2 =16 - (x - 10)^2[/tex]

Take the square root of  both sides

[tex]y- 6= \sqrt{16 - (x - 10)^2}[/tex]

Add 6 to both sides

[tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]

Hence, the simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]

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