Find the value of q.
21
17.5
q=
33

The components of the vector in rectangular form given magnitude and angle can be found as : x= |56| cos83°, y = |56| sin 83° .

Let be a vector in rectangular form, that is, a vector of the form (x, y). The magnitude can be found by applying the square root of the dot product of the vector or the Pythagorean theorem and the direction is determined by applying inverse trigonometric functions:

here, we have,

Magnitude (linear algebra approach)

|r|=√(x,y). (x.y)     (1)

Magnitude (algebra approach)

|r|=√(x²+y²)    (2)

Direction

θ = tan⁻¹ (y/x)     (3)

And the components of the vector can be found by applying the following formulas:

|r|=xcos θ   (4)

|r|=  y sinθ (5)

The components of the vector in rectangular form given magnitude and angle can be found as: x= |56| cos83°, y = |56| sin 83° ., .

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Answer:

32 cubic [tex]cm^{3}[/tex]

Step-by-step explanation:

Since each cube is 1 by 1 we can just count blocks to get its width length and height.

Width = 2

Length = 4

Height = 4

Volume= LxWxH

Volume= 4x2x4

Volume = 32 cubic [tex]cm^{3}[/tex]

Answer:

4+0.80x

Step-by-step explanation:

The angle measures for this problem are given as follows:

Angle 3 has the same measure as angle 1, thus:

m < 3 = m < 1 = 68º.

Angles 1, 2 and 3 form a ray, adding to 180º, meaning that the measure of angle 2 is obtained as follows:

m < 2 + 2 x 68 = 180

m < 2 = 44º.

The sum of the internal angles of a triangle is of 180º, hence the measure of angle 5 is given as follows:

44 + m < 5  + 35 = 180

m < 5 = 180 - 79

m < 5 = 101º.

Each exterior angle is supplementary with it's interior angle, having their measures adding to 180º, hence the measures of angles 4 and 7 are obtained as follows:

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A scale model of a regulation-sized gymnasium that is 12 inches long would be 10 inches wide.

To determine the width of a scale model of a regulation-sized gymnasium, you need to determine the scale factor used to create the model. The scale factor is the ratio of the size of the model to the size of the actual object.

In this case, the length of the model is 12 inches, while the length of the actual gymnasium is 100 feet, or 1200 inches. So, the scale factor is: 12/1200 = 1/100.

To find the width of the model, you would multiply the width of the actual gymnasium, 80 feet, by the scale factor, 1/100. This gives you a width of:

80 × 1/100 = 0.8 feet = 10 inches.

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The equation of the line that is parallel to this line and passes through the point (6, -3) is y = x/2.

The equation of the line that is perpendicular to this line and passes through the point (6, -3) is y = -2x + 9.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ 1/2 = 1/2

At data point (6, -3), a linear equation of this line can be calculated by using the point-slope form as follows:

y - (-3) = 1/2(x - 6)

y + 3 = x/2 - 3

y = x/2 - 3 + 3

y = x/2

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

At data point (6, -3), a linear equation of this line can be calculated by using the point-slope form as follows:

y - (-3) = -2(x - 7)

y + 3 = -2(x - 6)

y = -2x + 12 - 3

y = -2x + 9.

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The value of the equation is f ( x ) = x³ + 3x² - 25x - 75 and ( x + 5 ) is a factor of the equation

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

f ( x ) = x³ + 3x² - 25x - 75   be equation (1)

Now , ( x + 5 ) is a factor of the equation ,

So , x + 5 = 0

Subtracting 5 on both sides of the equation , we get

x = -5

Substitute the value of x in equation (1) , we get

f ( -5 ) = ( -5 )³ + 3 ( -5 )² - ( 25 ) ( -5 ) - 75 = 0

-125 + 3 ( 25 ) + 125 - 75 = 0

-125 + 75 + 125 - 75 = 0

0 = 0

Hence , ( x + 5 ) is a factor of the equation

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A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels towards as it approaches infinity.

Set the denominator to zero and solve for x to discover the vertical asymptotes. Set each factor to zero and solve as this has already been factored. The asymptotes are expressed as equations of lines since they are lines. Asymptotes for the vertical line are x = 3 and x = 1.

An asymptote of a curve in analytic geometry is a line where the distance between the curve and the line gets closer to zero as one or both of the x or y coordinates tends to infinity.

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9.) The transformation performed in the function[tex]f(x) = \frac{1}{2}^{-x}[/tex] is a reflection across the x-axis.

10.) The transformations performed in the function [tex]f(x) = -log_5(x-2)+17[/tex]are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞.

What is the transformation of the function?

The term "transformation of a function" refers to the process of altering the appearance of a function, either by shifting, stretching, or reflecting it along the coordinate axes.

9.) The transformation performed in the function [tex]f(x) = \frac{1}{2}^{-x}[/tex] is a reflection across the x-axis.

10.) The transformations performed in the function[tex]f(x) = -log_5(x-2)+17[/tex]are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞. As x approaches positive infinity, the value of 4^x approaches positive infinity, making the value of the function approach positive infinity.

Hence,

9.) The transformation performed in the function[tex]f(x) = \frac{1}{2}^{-x}[/tex] is a reflection across the x-axis.

10.) The transformations performed in the function [tex]f(x) = -log_5(x-2)+17[/tex]are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞.

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So Reena has ran a distance of 5 kilometers while only covering one-sixth of the distance.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

If Reena has completed one sixth of the 30 km run,

30 km / 6 = 5 km.

So, Reena has run a distance of 5 km so far when she had run one sixth of the distance.

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The vertex of the function is (x, y) = (-4, -14), so the vertex is at (x = -4, y = -14).

The equation can be written in vertex form by completing the square:

M(x) = x^2 + 8x - 10 = (x^2 + 8x) - 10 + (8/2)^2

= (x + 4)^2 - 14

The vertex of the function is (x, y) = (-4, -14), so the vertex is at (x = -4, y = -14).

To find the vertex of a quadratic function, you can use the formula:

Vertex = (x, y) = ( -b / 2a, f( -b / 2a) )

Where "a", "b", and "c" are the coefficients of the quadratic function in the standard form:

f(x) = ax^2 + bx + c

Note that the vertex of a quadratic function is either a minimum or maximum point, depending on the sign of the coefficient "a". If "a" is positive, the vertex represents the minimum point of the parabola. If "a" is negative, the vertex represents the maximum point of the parabola.

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Answer:  a) 0.00000047 = 4.7*10 7square. b) 0.0000000738 = 73.8 * 10 9 square .

Step-by-step explanation:

Answer: [tex]4.7 x 10^{-7}[/tex]

Answer: The regular price is $9

Step-by-step explanation: We do 35/5 to find the cost of each book. You get 7,then add 2 to get 9

(35/5)+2

The cash price of the refrigerator is $408.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a new refrigerator has a price of $480.00.

The store will discount the price by 15% if the purchaser pays in cash.

Now, the discount is

15% of 480

= 15/100 ×480

= 0.15×480

= 72

Now, 480-72

= $408

Therefore, the cash price of the refrigerator is $408.

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Answer:4x−6

That's one

Answer: 3 jackets and 5 sweaters

Step-by-step explanation:

j = jeans      s = sweaters

175 = 25j + 20s  ---- this will calculate the cost

8 = j + s ----- how much she bought

j = 8 - s; plug this into the cost

175 = 25(8-s) + 20s

175 = 200 - 25 + 20s; subtract 200 on both sides

-25 = -5s divide -5 to isolate the s

s = 5 Shelly bought 5 sweaters

now plug s = 5 in how much she bought

8 = j + 5

j = 3 Shelly bought 3 jackets

You have 7 lemons, by the consideration that you have 21 cuts available to divide the lemons.

What is the division?

A division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each, and so on.

To find out how many lemons you have, you need to take into consideration that you have 21 cuts available to divide the lemons.

With each cut, you can divide one whole lemon into two pieces or divide one section of lemon into two smaller pieces.

So, with 21 cuts, you can have a maximum of 2²¹ (2097152) pieces of lemon.

Since you have 30 jugs and each jug needs to have a piece of lemon, you would need at least 30 pieces of lemon.

To get 30 pieces of lemon with the minimum number of whole lemons, you would need 7 whole lemons (7 * 2 = 14 pieces, 14 * 2 = 28 pieces, 28 * 2 = 56 pieces, 56 - 30 = 26 pieces left over).

Therefore, you have 7 lemons, by the consideration that you have 21 cuts available to divide the lemons.

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The inequality for the given data can be written as 24x + 60y ≤ 2400 pounds.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that A freight elevator can hold a maximum weight of 2,500 pounds. A 180-pound person has a load of boxes to deliver. Some of the boxes weigh 25 pounds each and some weigh 60 pounds each.

The inequality can be written as:-

24x + 60y ≤ 2400 pounds

The graph of the inequality is attached with the answer below.

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Answer:

158.29 m²

Step-by-step explanation:

A = πr²

A = 3.14 × 7.1 m × 7.1 m

A = 158.29 m²

To convert 1.05 x 10^-8 to standard form, we simply need to move the decimal point 8 places to the left, since the exponent is negative.

1.05 x 10^-8 = 0.0000000105

Therefore, 1.05 x 10^-8 in standard form is 0.0000000105.

Answer:

0.0000000105.

Step-by-step explanation:

Answer:

She has 27 quarters

Step-by-step explanation:

Let:

x = Number of nickels

y = Number of quarters

US$0.05 = 5 cents = monetary value of a nickel

US$0.25 = 25 cents = monetary value of a quarter

                      x + y = 68

                     x = 68 - y  ---- --------  (equation i)

                0.05x + 0.25y = 8.80----- (equation ii)

These two are linear simultaneous equations, which can be solved either by substitution, elimination or graphical method.

Substitution method:

Substitute (equation i) into (equation ii) to solve for y:

0.05(68 - y) + 0.25y = 8.80

Expand the brackets by applying the Distributive Law and then bring all the like terms together. y needs to be isolated and made the subject of the equation:

= 3.4 - 0.05y + 0.25y = 8.80

= 0.25y - 0.05y = 8.80 - 3.40

= 0.20y = 5.40

= y = [tex]\frac{5.40}{0.20}[/tex]

∴ y = number of quarters = 27

The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.

If the sample size is large enough (typically, n >= 30), we can assume that the sample mean is approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, if we know the population mean and standard deviation, we can calculate the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24. Let's denote the population mean as mu and the population standard deviation as sigma. Then, the standard deviation of the sample mean is sigma / sqrt(n), where n = 1000 is the sample size.

We can standardize the sample mean using the z-score formula:

z = (x - mu) / (sigma / sqrt(n))

where x is the sample mean.

For the sample mean to be greater than 3,011.76, we have:

z = (3,011.76 - mu) / (sigma / sqrt(n)) > 0

And for the sample mean to be less than 2,988.24, we have:

z = (2,988.24 - mu) / (sigma / sqrt(n)) < 0

To find the probability, we need to find the area under the standard normal curve to the right of z for the first case, and to the left of z for the second case. These probabilities can be found using a standard normal table or a statistical software package.

Unfortunately, without knowledge of the population mean and standard deviation, it is not possible to determine the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24.

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Answer: $350

Step-by-step explanation:

Answer:

3.333

Step-by-step explanation:

[tex]3x - 6 = 4[/tex]

Add 6 to both sides of the equation

[tex]3x - 6 + 6 = 4 + 6[/tex]

[tex]3x = 10[/tex]

Divide both sides by 3

3x/3= 10/3

x = 3.333

Answer:

20.199

Step-by-step explanation:

ln (3x – 6) = 4

ln(3x-6)=2^2

x=2+e^4/3    

x=20.199

Answer:

Both Jill and John are correct.

Step-by-step explanation:

Triangle A and B are both similar to the triangle in question. They all have angles of 30, 60, and 90 degrees. We can infer this because all triangles have 180 degrees and the square in the corner means that it is a right angle (90 degrees).

What will the dimensions of some cross-sections of a cuboid be when cutting depends on the viewpoint.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Suppose we have a cuboid shape of a wooden block.

The height of the wooden block is h, the width of the wooden block is w and the length of the wooden block is l.

Now if we cut the wooden block along the red line a look at it from the top it will look like a rectangle width width 'w' and length 'l'.

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Answer: A. A rectangle 4 inches by 2 inches

Step-by-step explanation:

Answer:

  x ≈ -2.803

Step-by-step explanation:

You want to use the iterative formula x = ∛(5x -8) to find a solution to x³ -5x +8 = 0, starting with x₁ = -3.

Your iterator appears to be found by solving for x:

  x³ -5x +8 = 0

  x³ = 5x -8 . . . . . . add 5x-8

  x = ∛(5x -8) . . . . take the cube root

The attached table shows some iterations using this formula. To 3 dp, the solution is x ≈ -2.803.

__

Additional comment

Using a faster-converging iteration technique, we find the solution to be about ...

  x ≈ -2.8025​887521

The solution above is accurate to 3 dp.

Chen here tried to classify shapes from least specific to most specific. But the order is incorrect. The correct order is Quadrilateral, parallelogram, rhombus, square.

A quadrilateral is a shape having four sides. Any shapes with a four side is a quadrilateral. It can be an undetermined shape or a parallelogram, rectangle, rhombus or square. Parallelogram have four sides. Opposite sides are parallel and congruent. A rhombus, rectangle, square can all be considered a parallelogram.

A rhombus have four congruent sides and opposite sides are parallel. All squares are rhombi, but not all rhombi are squares. Square is the most specific shape. All sides of the square must be equal and all angles must be 90°.

We can say all squares are rhombus, all rhombi are parallelograms, all parallelograms are quadrilaterals.

So the correct order from least to most specific according to shape is Quadrilateral, parallelogram, rhombus, square.

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Answer: y=-1/2,7

Step-by-step explanation: The y intercept is at 0,7 and th eslope is going down 1 right 2

Both teams can complete the search in a time period of 4 hours.

Distance is a measurement of how far apart two points or objects are from one another. Time is a unit used to describe how long it takes for an object to travel between two points. Speed is a unit used to describe how quickly or slowly an item or a point moves.  

Here we have

Two search-and-rescue teams leave base camp at the same time,
looking for a lost child.

The first team, on horseback, heads north at 3 mph,  

The second team, on foot, heads south at 2.5 mph.

Let both teams complete searching in 'x' mins

The distance traveled by 1st team in 'x' mins = 3 × x  

= 3x  m

The distance traveled by 2nd team in 'x' mins = 2.5 × x  

= 2.5x m    

As we know total distance = 22 miles

=> 3x + 2.5x = 22 miles

=> 5.5x = 22 miles

=> x = 4 hrs  

Therefore,

Both teams can complete the search in a time period of 4 hours.

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