Need help with this question

Answer:

  see attached

Step-by-step explanation:

You want the areas of the four triangles in the figure.

The area of a triangle is given by the formula ...

  A = 1/2bh

where b is the base of the triangle, and h is its height perpendicular to the base.

Triangles A, B, C are right triangles, so their areas are easy to figure. Triangle D will be the difference between the area of the square and the areas of the other triangles.

The calculations are shown in the first attachment. Confirmation is provided by a geometry program in the second attachment.

__

Additional comment

If all you have are the coordinates of the vertices of triangle D, this method of finding its area is as good as any. There are other methods that can also be used, but they can be more trouble.

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The values of x and y in the figure are 3√2 and 3, respectively.

The diagram shown is a right triangle with a 45-degree acute angle.

The values of variables x and y must be determined.

Using the trigonometry identity, we get:

opposite/hypotenuse = sin 45

sin45 = 3/x

x = 3/sin45

x = 3(1/√2)

x = 3√2

Likewise,

tan 45 = opposite/adjacent

tan 45 = 3/y

1 = 3/y

y = 3

As a result, the values of x and y in the figure are 32 and 3, respectively.

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The circumference of the circle with the measure of diameter as 28 cm is 87.92 cm.

Given a circle.

Also given that,

Diameter of the circle = 28 cm

We know that, radius of a circle is half the measure of the diameter of the circle.

Radius of the circle = 28 / 2 = 14 cm

The formula to find the circumference of the circle is,

Circumference = 2 πr

Here r is the radius of the circle.

Substituting the given,

Circumference = 2 π (14)

                         = 28π

                         = 28 × 3.14

                         = 87.92 cm

Hence the circumference is 87.92 cm.

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Answer: i believe it’s 68

Step-by-step explanation:

My knowledge

There are 125 stickers did Sally have to start.

We have to given that,

Sally had 52 more stickers than Joe after Joe gave 1/5 of his stickers to her.

Let us assume that,

Joe had x stickers to start with.

Since, After Joe gave 1/5 of his stickers to her.

He have 4/5 of his original amount left.

That is, 4/5x

Since, Sally had 52 more stickers than Joe

Hence, We get;

4/5x + 52 = 1/5x + y  .. (i)

where y is the number of stickers Sally had to start with.

Here, they both had a total of 260 stickers,

Hence,

x + y =260  .. (ii)

From (i) and (ii);

y = 125

Thus, There are 125 stickers did Sally have to start.

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The result of the expression 20 - 6 is 14.

To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.

Step 1: Start with the given expression, 20 - 6.

Step 2: Evaluate the subtraction operation: 20 - 6 = 14.

Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.

This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.

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Given statement solution is:- The coordinates of point B is (3, 50°).

In the given scenario, we have point A with polar coordinates (2, 50°) and the pole O. We need to find point B such that OA is parallel to OB and OB has a length of 3 units.

Since OA and OB are parallel, they have the same angle with the positive x-axis. Therefore, the angle between OB and the positive x-axis would also be 50°.

To find the coordinates of point B, we can use the polar coordinates system, where the distance from the pole is denoted by r and the angle with the positive x-axis is denoted by θ.

Since OB has a length of 3 units, the distance from the pole (r) would be 3. The angle between OB and the positive x-axis is also 50°. Therefore, the coordinates of point B would be (3, 50°).

So, one possible answer for the coordinates of point B is (3, 50°).

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$63 + ($63 · 0.28) = $80.64

[tex]f = p + pm[/tex] where:

[tex]f[/tex] = final price: $80.64,

[tex]p[/tex] = original price: $63,

and [tex]m[/tex] = markup percent (in decimal): 28% → 0.28.

The concentration of the mixture made by mixing 6 fl. oz. of a 20% alcohol solution and 4 fl. oz. of a 5% alcohol solution will be; 14%

Consider that x represents the concentration of the mixture, hence:

(6 x 20%) + (4 x 5%) = x (4 + 6)

1.2 + 0.2 = 10x

x = 0.14 = 14%

The concentration of the mixture is made by mixing 6 fl. oz. of a 20% alcohol solution and

Thus 4 fl. oz. of a 5% alcohol solution = 14%

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Answer:

x² - y + x = 16 is 1 real solution

3x² - y + 32 = 22x is 2 real solutions

y = -x² + 6x + 12 is 1 real solution

Step-by-step explanation:

sorry i am unsure about rest, they do not have a value. good luck :)

Answer:

Step-by-step explanation:

The domain and range of the given function y = -2x + 3 are

Domain = 0, 1, 2, ,3 , 4, 5, 6

Range = 3, 1, -1, -3, -5, -7, -15

The table is given below.

We have,

y = -2x + 3

We can have domain as:

x = 0, 1, 2, 3, 4, 5, 6

For x = 0,

y = -2 x 0 + 3 = 3

For x = 1,

y = -2 x 1 + 3 = -2 + 3 = 1

For x = 2,

y = -2 x 2 + 3 = -4 + 3 = -1

For x = 3,

y = -2 x 3 + 3 = -6 + 3 = -3

For x = 4,

y = -2 x 4 + 3 = -8 + 3 = -5

For x = 5,

y = -2 x 5 + 3 = -10 + 3 = -7

For x = 6,

y = -2 x 6 + 3 = -18 + 3 = -15

The range are 3, 1, -1, -3, -5, -7, -15.

The table can be assumed as:

x         y = -2x + 3

0        3

1         1

2        -1

3        -3

4       -5

5       -7

6       -15

Thus the domain and range of the given function y = -2x + 3 are

Domain = 0, 1, 2, ,3 , 4, 5, 6

Range = 3, 1, -1, -3, -5, -7, -15

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Answer:

Step-by-step explanation:

I'm sorry, but I cannot answer your question without a visual representation or description of the rectangular prism. Please provide more information or a picture so that I can assist you accurately.

Answer:

72 cm 2?? THERE Isn't anything bellow I am sorry?

Step-by-step explanation:

The value of y is 4.4.

Let's go through the steps to solve for y:

Distributive property:

[tex]1/5y + 2 - 4/5 = 1/2y - 1 + 1/10y[/tex]

Combine like terms:

[tex]1/5y + 2 - 4/5 = 1/2y - 1 + 1/10y[/tex]

Simplify the equation by getting rid of fractions. To do this, we can multiply every term by the least common denominator (LCD) of 10:

[tex]10 * (1/5y + 6/5) = 10 * (3/5y - 1 + 1/10y)[/tex]

Simplifying further:

[tex]2y + 12 = 6y - 10 + y[/tex]

Now, let's combine like terms again:

[tex]2y + 12 = 7y - 10[/tex]

Next, let's isolate the variable y. Subtract 2y from both sides and add 10 to both sides:

[tex]12 + 10 = 7y - 2y[/tex]

Simplifying:

22 = 5y

Finally, divide both sides by 5 to solve for y:

y = 22/5

Note: It's important to check our solution by substituting y = 4.4 back into the original equation to ensure it satisfies the equation.

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Answer:

11/2

Step-by-step explanation:

11/5 = 2/5y

11 = 2y

y = 11/2

The functions have the following

Domain: (-∞, -1) ∪ (-1, ∞)

Range: (-∞, -∞) excluding -5

Vertical Asymptote: x = -1

Horizontal Asymptote: y = -5

We have,

Domain:

The domain of a function refers to the set of all possible input values (x) for which the function is defined.

In this case, the function f(x) is defined for all real numbers except when the denominator (x + 1) is equal to zero.

The domain is all real numbers except x = -1.

So, the domain is (-∞, -1) ∪ (-1, ∞).

Range:

The range of a function refers to the set of all possible output values (y) that the function can produce.

In this case, we can observe that as x approaches -1 from either side, the function approaches negative infinity.

The range is (-∞, -∞) excluding -5.

Vertical Asymptote:

A vertical asymptote occurs when the function approaches infinity or negative infinity as x approaches a certain value.

In this case, the vertical asymptote occurs when the denominator (x + 1) is equal to zero, which is x = -1.

Horizontal Asymptote:

To determine the horizontal asymptote, we need to examine the behavior of the function as x approaches positive or negative infinity.

As x approaches positive or negative infinity, the term 1/(x + 1) becomes negligible compared to -5.

The horizontal asymptote is y = -5.

Thus,

The functions have the following

Domain: (-∞, -1) ∪ (-1, ∞)

Range: (-∞, -∞) excluding -5

Vertical Asymptote: x = -1

Horizontal Asymptote: y = -5

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The required surface area of the larger solid is approximately 147 mm². Option A is correct.

We know that,

The surface area of any form is the area of the shape that is fronted.

The surface area of a 3D object is the amount of area covering the outside.

Let's say the surface area of the bigger solid S.

Since the two solids are similar, their volumes have a ratio of (side length)³.

Let's say the ratio of the side lengths of the larger to the smaller solid as k. Then,

⇒ k³ (540 mm³) = 857.5 mm³

Simplifying the above equation, we get:

⇒ k = 7/6

So, the larger solid is about 7/6=1.183 times bigger than the smaller solid in terms of side length.

Since the surface area has a ratio of (side length)²,

we can find the surface area of the larger solid by:

⇒ (1.83²)(108 mm³)

≈ 174 mm³

Therefore, the surface area of the larger solid is approximately 147 mm².

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The equation of the parabola that models the cross section of the reflector is: y = (1/32)x².

To model a cross section of the reflector as a parabola that opens upward and has its vertex at the origin,

We can use the standard equation for a parabola in vertex form:

y = a(x - h)² + k

In this equation, (h, k) represents the coordinates of the vertex.

Since we want the vertex to be at the origin (0, 0), the equation becomes:

y = ax²

To determine the value of 'a,' we can use the given information that the bulb is located 8 inches from the vertex.

Since the bulb is located at the focus, we know that the distance from the vertex to the focus (f) is also 8 inches.

In a parabola, the distance from the vertex to the focus is given by the formula f = 1/(4a).

Plugging in the value of f (8) into the formula, we can solve for 'a':

8 = 1/(4a)

32a = 1

a = 1/32

Therefore, the equation of the parabola that models the cross section of the reflector is: y = (1/32)x²

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Answer:

[tex]\huge\boxed{\sf \angle AEB=86 \textdegree}[/tex]

Step-by-step explanation:

arc AB = 106°

arc CD = 66°

[tex]\displaystyle \angle AEB=\frac{1}{2} (arc \ AB+arc \ CD)[/tex]

Put the given data in the above formula.

[tex]\displaystyle \angle AEB=\frac{1}{2} (106 + 66)\\\\\angle AEB=\frac{1}{2} (172)\\\\\angle AEB=86 \textdegree \\\\\rule[225]{225}{2}[/tex]

The calculated total distance he drive is 372 miles

From the question, we have the following parameters that can be used in our computation:

So, we have

Total charges = 75 * days + 0.25 * miles

For 2 days and total ot 243. we have

75 * 2 + 0.25 * miles = 243

So, we have

miles = 372

Hence, the total distance he drive is 372 miles

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To determine the optimal number of matted and unmatted pictures to maximize the company's profit, we can set up a linear programming problem.

Let's denote:

- x: the number of matted pictures

- y: the number of unmatted pictures

The objective is to maximize the profit, which can be expressed as:

Profit = 40x + 35y

We need to consider the following constraints:

1) The number of pictures completed each day cannot exceed 36:

x + y ≤ 36

2) The total man-hours of labor cannot exceed 80:

4x + 2y ≤ 80

3) The number of pictures cannot be negative:

x, y ≥ 0

Now we can solve this linear programming problem to find the optimal values for x and y.

First, let's graph the feasible region defined by the constraints:

```

x + y ≤ 36

4x + 2y ≤ 80

x, y ≥ 0

```

The feasible region is the area of the graph that satisfies all the constraints.

Next, we need to evaluate the objective function (Profit = 40x + 35y) at the vertices of the feasible region to find the maximum profit.

We can use different methods such as the corner-point method or the simplex method to determine the vertices and evaluate the profit at each vertex.

Thus, once we find the vertex that yields the maximum profit, we will have the optimal values for x and y.

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The probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.

The probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).

To solve both of these probability problems, we can use the binomial probability formula:

P(X = k) = (n C k) × p^k × (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes

n is the total number of trials

k is the number of desired successes

p is the probability of success in a single trial

(1 - p) is the probability of failure in a single trial

(n C k) represents the binomial coefficient, calculated as n! / (k! x (n - k)!)

Let's solve each problem separately:

The probability that exactly four out of 19 adults say cashews are their favorite nut can be calculated as:

P(X = 4) = (19 C 4) ⁴(0.49⁴) (0.51¹⁵)

Using the binomial probability formula, we can calculate:

P(X = 4) ≈ 0.251

Therefore, the probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.

To find the probability that 12 or more stolen bikes will be returned out of 335 stolen bikes, we can use the binomial probability formula. Let's denote the probability of a stolen bike being returned as p = 0.03, the number of trials as n = 335, and the number of desired successes as k = 12 or more.

Using the complement rule, we can calculate the probability of not getting 11 or fewer successes:

P(X ≥ 12) = 1 - [P(X = 0) + P(X = 1) + ... + P(X = 11)]

To perform the calculation, summing up individual probabilities can be time-consuming. However, using statistical software or a binomial probability calculator can provide a convenient solution.

Using such a calculator, we find that the probability of 11 or fewer stolen bikes being returned is approximately 0.974. Therefore, the probability of 12 or more stolen bikes being returned is:

P(X ≥ 12) = 1 - 0.974 ≈ 0.026

Thus, the probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).

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Answer

[tex]\pink\sf{y=-1}[/tex]

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation [tex]\sf{y=0.5(6)-4}[/tex].

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

[tex]\sf{y=3-4}[/tex]

And now we just simplify the last part:

[tex]\sf{y=-1}[/tex]

∴ answer: y = -1

The probability that the first marble drawn is blue and the second marble drawn is red is 1/4 or 0.25, which can also be expressed as 25%.

To determine the probability of drawing a blue marble on the first draw and a red marble on the second draw, we need to consider the total number of marbles and the number of blue and red marbles in the bag

In this case, we have a bag with 12 blue marbles and 12 red marbles, making a total of 24 marbles.

When drawing the first marble, there is a 12/24 probability of selecting a blue marble since there are 12 blue marbles out of the total 24 marbles in the bag.

After replacing the first marble back into the bag and mixing up the marbles, the probability of drawing a red marble on the second draw is also 12/24, as there are still 12 red marbles remaining out of the total 24 marbles.

To find the overall probability, we multiply the probabilities of each event since they are independent events:

P(first marble is blue and second marble is red) = P(first marble is blue)[tex]\times[/tex]P(second marble is red)

[tex]= (12/24) \times (12/24)[/tex]

[tex]= (1/2) \times (1/2)[/tex]

= 1/4.

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Answer:

$132.54

Step-by-step explanation:

$1060.32 / 8 families = $132.54 / family

Answer: 126 feet

Step-by-step explanation: Convert yards into feet. IF we are given different units then you must convert it.

To convert yards into feet, MULTIPLY by 3

29 yards * 3= 87 feet

13 yards * 3= 39 feet

Now, key word= THROWS IN ALL= addition

87 + 39 is 126

1. The probability that the sensor will give an incorrect report is 0.03 or 3%.

2. The probability that the reactor will be shut down because of simultaneous false alarms by both sensors is 0.0004 or 0.04%.

3. The probability that excessive radiation will be missed simultaneously by both sensors is 0.0001 or 0.01%.

The probability of a false alarm is 0.02.

The probability of a miss is 0.01.

P(false alarm or miss)

= P(false alarm) + P(miss)

= 0.02 + 0.01 = 0.03

Therefore, the probability that the sensor will give an incorrect report is 0.03 or 3%.

2. Probability of simultaneous false alarms by both sensors:

P(false alarm by both sensors)

= P(false alarm by sensor 1) * P(false alarm by sensor 2)

= 0.02 * 0.02

= 0.0004

Therefore, the probability that the reactor will be shut down because of simultaneous false alarms by both sensors is 0.0004 or 0.04%.

3. Probability of missing excessive radiation by both sensors:

P(miss by both sensors)

= P(miss by sensor 1) * P(miss by sensor 2)

= 0.01 * 0.01

= 0.0001

Therefore, the probability that excessive radiation will be missed simultaneously by both sensors is 0.0001 or 0.01%.

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You will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.

If you decide to pay off the balance over one year instead of three, the payment amount will be higher, but the total interest paid will be lower due to the shorter repayment period.

First, let's calculate the total interest paid over three years. The total payment made over three years will be the monthly payment of $126.59 times 36 months, which is $4,553.24. The total interest paid is the difference between the total payment made and the initial balance of $3600, which is $953.24.

Now, let's consider paying off the balance over one year. The total payment made over one year will be the monthly payment of $126.59 times 12 months, which is $1,519.08. To calculate the interest paid, we can use the formula:

Total interest paid = Balance × Annual interest rate × Time

where the time is expressed in years. Plugging in the values, we get:

Total interest paid = $3600 × 0.16 × 1 = $576

Therefore, if you decide to pay off the balance over one year instead of three, you will pay an additional amount each month equal to the difference between the monthly payment for one year and the monthly payment for three years, which is:

Additional monthly payment = ($4,553.24/12) - ($1,519.08/12) = $261.76

This means that you will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.

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The amplitude and the period of the function f(x) = cos(5θ) are 1 and 2π/5

From the question, we have the following parameters that can be used in our computation:

f(x) = cos(5θ)

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

So, we have

A = 1

Period = 2π/5

Evaluate

A = 1

Period = 2π/5

Hence, the amplitude is 1 and the period is 2π/5

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