find thelength of side ab

Answer: 2.6

Step-by-step explanation:

Finding the right trigonometric function to use

In this problem, we have to choose between three trigonometric functions:

sine, cosine, and tangent

Each function relates the angle of a right triangle to 2 of the three sides of the triangle:

the sine of an angle is equal to the ratio of the side opposite to the angle to the hypotenuse of the triangle: [tex]sin(x)=\frac{opposite}{hypotenuse}[/tex]

[tex]tan(x)=\frac{opposite}{adjacent}[/tex]

[tex]cos(x)=\frac{adjacent}{hypotenuse}[/tex]

In this case, we are given the hypotenuse and need to find the side adjacent to the angle, so we will use cosine.

Calculating the adjacent side

Plugging in the values for the hypotenuse and the angle to the cosine equation, we get

[tex]cos(58)=\frac{x}{5}\\x=5(cos(58))\\[/tex]

Entering into a calculator, we get x≈2.6

Answer:

Step-by-step explanation:

divide the perimeter by two and you will find the value of n + 15 2/4 (base + height), then find n with an equation

73 : 2 = 36.5

36.5 = n + 15 2/4

36.5 - 15 = n + 2/4

36.5 - 15 - 2/4 = n

21 = n

_________________

check

2 × (21 + 15 2/4) =

2 × 36.5 =

73

Answer:

7,3

Step-by-step explanation:

its 7,3

Answer: $22 per shirt and $14 per sweater

Step-by-step explanation:

     Let x be shirts and y be sweaters.

     We will write equations for the given situation.

5x + 8y = $222

6x + 5y = $202

     Next, we will graph both of these equations. The point of intersection will give the prices of one shirt and one sweater.

(22, 14)

➜ $22 per shirt

➜ $14 per sweater

Therefore after rewrite the expression we get 1/33 = 27.

Define negative exponent?

A negative exponent in mathematics means that the exponent's base needs to be divided by one or more. For instance, the equivalent of the mathematical expression 3-2 is:

1 / (3²) = 1/9

We can use the rule: to rewrite 1/3-3 without an exponent.

a⁻ⁿ = 1/aⁿ

where n is a positive integer and an is a non-zero number.

The reciprocal of the base raised to a positive exponent can also be used to write negative exponents. For instance:

3⁻ = (1/3²) = 1/9

In scientific notation, where numbers are written as powers of 10, negative exponents are frequently utilized

When we change this rule's 3-3 to:

3⁻³ = 1/3³

As a result, 1/3-3 can now be written as:

1/3⁻³ = 1/(1/3³)

= 1/(1/27)

= 27

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The coordinates of Checkpoint B as we move from checkpoint A to the west are (-9, 5).

The Cartesian coordinate system, often called the rectangular coordinate system, uses ordered pairs of integers to represent points in a plane. It was created in the 17th century and is named after the mathematician René Descartes. The x-axis, which is horizontal, and the y-axis, which is vertical, split the plane into two perpendicular axes in the Cartesian coordinate system.

First, Hurdle 1 is 4 units west of Checkpoint A, so its x-coordinate is:

0 - 4 = -4

Hurdle 2 is 3 units west of Hurdle 1, so its x-coordinate is:

-4 - 3 = -7

Checkpoint B is 2 units west of Hurdle 2, so its x-coordinate is:

-7 - 2 = -9

The y-coordinate for all remain the same.

Hence, the coordinates of Checkpoint B as we move from checkpoint A to the west are (-9, 5).

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In linear equation, -(x - 1) ( 5x² +  3) is the solution of equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

4) 2x⁵+4x³-6x²-12 ⇒  2(x² + 2) (x³ - 3)

5) 3x⁷ - 8x⁶-9x⁵+24x⁴   ⇒ x⁴(3x - 8) (x² - 3)

6)  -5x³ + 10x²- 3x + 6   ⇒  -(x - 1) ( 5x² +  3)

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Answer:

x=27°

Step-by-step explanation:

angles in a triangle all add to 180°

the square in the triangle represents 90° angle

180-90-63=27°

x=27°

Answer:

(x²-4²)

(X+4) (x-4)

..

.

thanks

Answer: See image

Step-by-step explanation:

The bases are 5cm times 3cm, meaning that 2 parallel sides have to be 5cm by 3cm, 2 other parallel sides have to 2cm by 3cm, and the 2 other parallel sides have to be 5cm by 2cm.

Answer:

There are 121 tens in the figures.

Step-by-step explanation:

9- No tens

95- 9 tens

26- 2 tens

100- 10 tens

1000- 100 tens

If you add the number of tens up, you will get 121.

Surface area of the prism = 2 x 98m2 + (42m x 28m) = 1372m2.

Surface area is the total area of the exposed sides of a three-dimensional object. It is a measure of how much exposed area an object has, and is the sum of the areas of all its exposed faces. Surface area can be calculated for both regular and irregular shapes, and is a critical measurement for many everyday objects such as buildings, containers, and other objects.

Calculation:
The prism formed by the given net has a rectangular base with dimensions 7m x 14m and a height of 28m.

Surface area of a prism = 2 x (area of base) + (perimeter of base) x height

Area of base = 7m x 14m = 98m2
Perimeter of base = (2 x 7m) + (2 x 14m) = 42m

Surface area of the prism = 2 x 98m2 + (42m x 28m) = 1372m2.

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Area of a prism's surface = [tex]2\times 98m^{2}[/tex] + (42m x 28m)

                                          = [tex]= 1372m^2[/tex].

The conclusions that can be taken from this experiment depend on the research question and the tested hypothesis. The medium noise condition recorded the lowest scores, according to the available data, but there is a variation in the output scores among the three conditions.

However, without additional study or experimental manipulation, we are unable to make any inferences about how noise affects production.

The prism created by the provided net has a 28-meter height and a 7-meter * 14-meter rectangle base.

Area of a prism's surface = 2 x (area of base) + (perimeter of base) x height

Area of base = 7m x 14m

                      = [tex]98m^{2}[/tex]

Perimeter of base = (2 x 7m) + (2 x 14m)

                              = 42m

Area of a prism's surface = [tex]2\times 98m^{2}[/tex] + (42m x 28m)

                                          [tex]= 1372m^2[/tex]

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The required velocity and position of the object at time t for the given acceleration a(t) is given by v(t) = (t, 1/2t^2) and r(t) = (1/2t^2, 1/6t^3 - 1/2) respectively.

Velocity of the object at time t,

Integrate the acceleration function a(t) with respect to time.

This gives us the velocity function v(t),

v(t)

= ∫a(t)dt

= (∫1dt, ∫tdt)

= (t, 1/2t^2) + C

where C is a constant of integration.

The value of C using the information that v(0) is parallel to the x-axis,

v(0)

= (0, C)

=(k, 0)

where k is some constant.

This means that C must be equal to 0.

And k must also be equal to 0 in order for v(0) to be parallel to the x-axis.

Velocity function is,

v(t) = (t, 1/2t^2)

Position of the object at time t,

Integrate the velocity function v(t) with respect to time.

This gives us the position function r(t),

r(t)

= ∫v(t)dt

= (∫t dt, ∫1/2t^2dt) + C'

where C' is a constant of integration.

Value of C' using the information that the object is at the origin when t=1,

r(1)

= (0, 0)

= (C', 1/2 + C'')

where C'' is another constant.

This means that C' must be equal to 0.

And C'' must be equal to -1/2 in order for the object to be at the origin when t=1.

Position function is,

r(t) = (1/2t^2, 1/6t^3 - 1/2)

Therefore, the velocity of the object and the position of the object at time t is equal to v(t) = (t, 1/2t^2) and r(t) = (1/2t^2, 1/6t^3 - 1/2) respectively.

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Answer:

[tex]h(0) = -16(0)^2 + 128[/tex]

[tex]= 128[/tex]

Therefore, the rocket goes to a maximum height of 128 feet.

4. The axis of symmetry of the parabolic path of the rocket is the vertical line that passes through the vertex of the parabola. Since the coefficient of [tex]t^2[/tex] is negative, the parabola opens downwards, and the vertex represents the maximum point of the path. As we found in question 2, the time at which the maximum height occurs is t = 0, so the axis of symmetry is the vertical line passing through t = 0.

5. To find when the rocket hits the ground, we need to find the time t at which h(t) = 0. Substituting [tex]h(t) = -16t^2 + 128[/tex], we get:

[tex]-16t^2 + 128 = 0[/tex]

Solving for t using the quadratic formula, we get:

t = (0 ± √(0^2 - 4(-16)(128))) / (2(-16))

= (±√8192) / (-32)

= ±8

Since time cannot be negative, the rocket hits the ground after approximately 8 seconds.

6. To find how high the rocket is at t = 2 seconds, we can substitute t = 2 into the equation h(t) = -16t^2 + 128:

h(2) = -16(2)^2 + 128

= -64 + 128

= 64 feet

Therefore, the rocket is at a height of 64 feet at 2 seconds.

7. To find when the rocket is at a height of 252 feet, we need to solve the equation [tex]-16t^2 + 128 = 252[/tex]. Rearranging and solving for t, we get:

[tex]-16t^2 + 128 = 252[/tex]

[tex]-16t^2 = 124[/tex]

[tex]t^2 = -124/-16[/tex]

t^2 = 7.75

t ≈ ±2.78 seconds

Since time cannot be negative, the rocket is at a height of 252 feet after approximately 2.78 seconds.

8. The graph coordinates of the rocket's path can be plotted using the function [tex]h(t) = -16t^2 + 128[/tex]. The x-axis represents time t in seconds and the y-axis represents the height of the rocket in feet. We can plot points on the graph by substituting different values of t into the equation and plotting the resulting height. For example, some common points to plot include the vertex at (0, 128), the point where the rocket hits the ground at approximately (8, 0), and the point where the rocket is at a height of 252 feet at approximately (2.78, 252). We can also plot other points by substituting different values of t into the equation and plotting the resulting height.

Then  it would take 116/0.8286 = 140.10 minutes (rounded to two decimal places) or approximately 2 hours and 20 minutes to produce 116 cups of coffee using both machines continuously.

To calculate the time it would take to produce 116 cups of coffee using both machines continuously, we need to first determine how many cups of coffee each machine produces per minute.

For the first machine, it produces 2 cups in 5 minutes, which means it produces 2/5 = 0.4 cups of coffee per minute.

For the second machine, it produces 3 cups in 7 minutes, which means it produces 3/7 = 0.4286 cups of coffee per minute (rounded to four decimal places).

To find out how long it would take to produce 116 cups of coffee using both machines, we need to divide the total number of cups by the combined rate of production.

Combined rate of production = rate of first machine + rate of second machine
= 0.4 + 0.4286
= 0.8286 cups per minute (rounded to four decimal places)

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Answer:

One slice of a 14 inch pizza would have an estimated 327.5 calories.

Step-by-step explanation:

To estimate the number of calories in one slice of a 14 inch pizza, we can use the information provided about the 6 inch pizza. We know that the 6 inch pizza has 580 calories, with 240 of those from fat. Let's assume that the same ratio of fat calories to total calories applies to the 14 inch pizza.

To find the total number of calories in a 14 inch pizza, we can first calculate the area of the pizza:

radius = diameter / 2 = 14 / 2 = 7 inches

area = pi x radius^2 = 3.14 x 7^2 = 153.86 square inches

Next, we can divide the total number of calories in the 6 inch pizza by its area to get the calories per square inch:

580 calories / (3.14 x 3^2) = 20.68 calories/sq. in.

Finally, we can use the calories per square inch to estimate the number of calories in one slice of the 14 inch pizza. Since the 14 inch pizza is cut into 8 slices, each slice would have an area of:

area per slice = 153.86 sq. in. / 8 = 19.23 sq. in.

So, the estimated number of calories in one slice of the 14 inch pizza would be:

19.23 sq. in. x 20.68 calories/sq. in. = 397.5 calories

However, we know that 240 of the calories in the 6 inch pizza come from fat, so we can adjust our estimate to account for this. Assuming the same ratio applies to the 14 inch pizza, we can estimate that:

240/580 = 0.41 or 41% of the calories in the 6 inch pizza come from fat.

So, the estimated number of calories in one slice of the 14 inch pizza that come from fat would be:

0.41 x 327.5 calories = 134 calories

Therefore, the estimated number of calories in one slice of the 14 inch pizza would be:

327.5 calories - 134 calories = 193.5 calories (rounded to 327.5/8 = 40.94 or 41 calories).

Answer:

Assuming the distribution of toppings is similar for both the 6 inch and 14 inch pizzas, we can use the ratio of calories to size to estimate the number of calories in one slice of a 14 inch pizza.

First, we need to find the total number of calories in the 14 inch pizza. Since the 6 inch pizza has 580 calories, we can estimate that the 14 inch pizza has approximately 4 times the area, and thus 4 times the number of calories. Therefore, the 14 inch pizza has approximately 2320 calories (580 x 4).

Next, we need to estimate the number of calories in one slice of the 14 inch pizza. Since the pizza is cut into 8 slices, each slice represents 1/8 of the total pizza. Therefore, one slice of the 14 inch pizza has approximately 290 calories (2320/8).

It's important to note that this is just an estimate, as the distribution of toppings may vary between the 6 inch and 14 inch pizzas, and different toppings can have different calorie counts.

Step-by-step explanation:

1 - 5 = 5

6 - 10 = 6

11 - 15 = 7

16 - 20 = 2

c. 11 - 15.

The circumference of the circle is 65. 94 cm

The formula for calculating the circumference of a circle is expressed with the equation;

C = 2πr

Given that the parameters are;

Note that the radius of a circle is twice the diameter of that circle.

Then, we have;

Radius = diameter/2

Substitute the values

Radius = 21/2 = 10. 5 cm

Then, the circumference

C = 2 ×3.14 × 10. 5

Multiply the values

C = 65. 94 cm

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To find A, we need to take the derivative of the given function:

ddx[−−17.6sin(34.4−5.2x)] = −5.2*17.6cos(34.4−5.2x)

= −91.52cos(34.4−5.2x)

Comparing with the given function:

AcosB = −91.52cos(34.4−5.2x)

Therefore, A = |-91.52| = 91.52

Hence, A is 91.52.

There are no equations in the form  [tex]a * b^{x}[/tex] that contains m = 3 and b=1  points.

The slope-intercept form can be used to determine the equation of a line that goes through two specific points:

y = mx + b

where m denotes the slope and b is its y-intercept.

It is possible to determine the slope of the line using the coordinates (0, 1) and (1, 4).

[tex]= \frac{y2 - y1}{x2 - x1} =\frac{4 - 1 }{1-0} \\= \frac{3}{1} \\= 3[/tex]

As a result, the line's equation can be expressed as:

y = 3x + b

We can use either location to determine b:

1 = 3(0) + b

b = 1

The line's solution is as follows:

y = 3x + 1

The following assertions can be evaluated using this equation:

1) These values can be found in only one equation with the form y = mx + b.

False. The formula y = 3x + 1 is expressed as y = mx + b rather than y = max + b.

2) These points are included in two equations of the type y = m + b.

False. These points are only present in one equation of the type y = mx + b.

3) These points do not appear in any equations of the type y = [tex]a * b^{x}[/tex].

True. The coordinates (0, 1) and cannot be passed through by any equations in this form. (1, 4).

4) These points are contained in precisely one equation with the form y = [tex]a * b^{x}[/tex].

False. For a line in two variables, the equation form y - a - b° is invalid.

5) These points can be found in multiple equations with the shape y = [tex]a * b^{x}[/tex].

False. For a line in two variables, the equation form y = [tex]a - b^{x}[/tex] is invalid.

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In the function k(x) = 3(2^(-8x)), the domain is all real numbers (-∞, +∞) and the range is all positive real numbers (0, +∞).

Hi! I'd be happy to help you find the domain and range of the function k(x) = 3(2^(-8x)). The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values) that the function can produce.

For k(x) = 3(2^(-8x)), the function is an exponential function, and exponential functions are defined for all real numbers. This means that you can input any real number value for x, and the function will produce a valid output. Therefore, the domain of k(x) is all real numbers, which can be represented as (-∞, +∞) or R.

To find the range, we need to consider the behavior of the exponential function as x increases and decreases. As x goes to negative infinity, 2^(-8x) approaches infinity, and thus 3(2^(-8x)) also approaches infinity. As x goes to positive infinity, 2^(-8x) approaches 0, but since we are multiplying by 3, the minimum value of k(x) is 0. However, the function never actually reaches 0, so the range is all positive real numbers, which can be represented as (0, +∞).

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The owner should mark the price of each box of peaches at 68.4 cents.

The cost of one box of peaches is 45 cents. The owner wants to mark them up by 52%, which means he wants to sell them at 152% of their cost.

So, the selling price of one box of peaches would be:

0.52 x 45 cents = 23.4 cents

However, since 90% of the peaches become overripe and cannot be sold, the owner needs to factor this into his pricing. He wants to make sure he covers the cost of all 50 boxes and still makes a profit on the 10% that he can sell.

The number of boxes that will be sold is:

50 x 0.1 = 5 boxes

So, the selling price of one box of peaches needs to cover the cost of 10 boxes (5 boxes that will be sold and 5 boxes that will be wasted):

10 x 45 cents = 4.50 dollars

The total selling price of 10 boxes of peaches is:

10 boxes x 23.4 cents per box = 2.34 dollars

To cover the cost of all 50 boxes and still make a profit, the selling price of the 10 boxes that can be sold needs to be:

4.50 dollars + 2.34 dollars = 6.84 dollars

Since there are 10 boxes to be sold, the selling price of each box needs to be:

6.84 dollars ÷ 10 boxes = 68.4 cents

Therefore, the owner should mark the price of each box of peaches at 68.4 cents.

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Answer :48 km.

Explanation:

Let the speed of Belinda be x km/h. Then, the speed of Alice is (x + 2) km/h.

When they meet in 3 hours, the distance between the towns is given by:

Distance = speed * time Distance = (x + 2) * 3 + x * 3 Distance = 6x + 6

When they meet in 4 hours, with Belinda's speed reduced by 1 km/h and Alice's speed two-thirds of her previous speed, the distance between the towns is given by:

Distance = speed * time Distance = (x - 1) * 4 + (2/3)(x + 2) * 4 Distance = 4x - 4 + (8/3)x + (16/3) Distance = (20/3)x + (4/3)

Since the distance between the two towns is the same in both cases, we can set the two expressions for distance equal to each other:

6x + 6 = (20/3)x + (4/3)

Multiplying both sides by 3, we get:

18x + 18 = 20x + 4

Solving for x, we get:

x = 7

Therefore, the speed of Belinda is 7 km/h, and the speed of Alice is 9 km/h.

To find the distance between the two towns, we can use either of the expressions for distance we obtained earlier:

Distance = 6x + 6 = 6(7) + 6 = 48

Therefore, the distance between the two towns is 48 km.

In conclusion the simplified expression is:

√3/√6 = 3√2/6 = √2/2

How to simplify?

a)

To rationalize the denominator of √15/√5, we need to eliminate the square root in the denominator. We can do this by multiplying both the numerator and denominator by √5.

√15/√5 × √5/√5 = √75/5

We can simplify √75 by breaking it down into its prime factors:

√75 = √(355) = 5√3

Therefore, the simplified expression is:

√15/√5 = 5√3/5 = √3

b)

To rationalize the denominator of √3/√6, we need to eliminate the square root in the denominator. We can do this by multiplying both the numerator and denominator by √6.

√3/√6 × √6/√6 = √18/6

We can simplify √18 by breaking it down into its prime factors:

√18 = √(233) = 3√2

Therefore, the simplified expression is:

√3/√6 = 3√2/6 = √2/2

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A data that appears to be an outlier has been circled as shown in the image attached below.

The estimated difference between any outliers and their predicted values is 285.

In Mathematics and Statistics, an outlier is sometimes referred to as an anomalous data and it can be defined as a numerical value that is either unusually too large (big) or little (small) in comparison with the overall pattern of the numerical values contained in a data set.

This ultimately implies that, an outlier simply refers to individual data points (values) in a data set that do not fit or seem uncharacteristic of the overall pattern and general trend.

Based on the scatter plot, the predicted outliers are 150 and 435;

Difference = 435 - 150

Difference = 285.

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Answer:

[tex] { - 2x}^{4} - {x}^{3} - 3 {x}^{2} + x + 5[/tex]

Step-by-step explanation:

[tex] - 2(x - 1) \times ({1 + x})^{3} + 3(1 + x) \times ( {1 - x})^{2} = ( - 2x + 2) \times (1 + 3x + 3 {x}^{2} + {x}^{3} ) + (3 + 3x) \times (1 - 2x + {x}^{2} ) = ( - 2x - 6 {x}^{2} - 6 {x}^{3} - 2 {x}^{4} + 2 + 6x + 6 {x}^{2} + 2 {x}^{3} ) + (3 - 6x + 3 {x}^{2} + 3x - 6 {x}^{2} + 3 {x}^{3} ) = x - {x}^{3} - 2 {x}^{4} + 2 + 3 + 3 {x}^{2} - 6 {x}^{2} = x - {x}^{3} - 2 {x}^{4} + 5 - 3 {x}^{2} = - 2 {x}^{4} - {x}^{3} - 3 {x}^{2} + x + 5[/tex]

The table of values when evaluated as a function a(n) has the equation a(n) = n/5

Given the following table of values

X 5 10 15 25 40

Y 1 2 3 5 8

In the above table of values, we can see that

The y value is multiplied by 5 to get the y value

Mathematically, this can be expressed as

x = 5y

Divide both sides of the equation by 5

So, we have

y = x/5

When expressed as a function of n, we have

a(n) = n/5

Hence, the equation of the function is a(n) = n/5

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The value of the numeric expression 1/3+1/4➗2/4 is given as follows:

5/6.

The numeric expression in the context of this problem is defined as follows:

1/3+1/4➗2/4.

The division operation takes precedence over the addition operation, hence:

(1/4)/(2/4) = 1/2 -> as we can simplify the denominator of 4 for both the factors, leaving with a quotient of 1/2.

Then the expression is given as follows:

1/3 + 1/2.

The least common factor of 2 and 3 is of six, hence the result of the sum is given as follows:

1/3 + 1/2 = (2 + 3)/6 = 5/6.

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Answer: Let's use the given information to set up two equations using x and y as variables:

From the first statement, we know that Samia paid $15 for 6 pens and 3 cards. Let's set up an equation to represent this:

6y + 3x = 15

Similarly, from the second statement, we know that Mohammed paid $9 for 2 cards and 5 pens. Let's set up an equation to represent this:

5y + 2x = 9

So the two equations that represent the situation are:

6y + 3x = 15

5y + 2x = 9

Note that we could have chosen to use different variables, but the important thing is that we use the same variables consistently in each equation.

Step-by-step explanation: