Help with math problems

Answer: The building is approximately 16.6 feet tall.

Step-by-step explanation:

Use Pythagorean theorem (a²+b²=c²) to solve this.

We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.

Your equation would be: 20²+x²=26²

subtract 20² from 26² --> 276=x²

then take the square root --> 16.6=x

To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:

3 miles x 5,280 feet/mile = 15,840 feet

Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.

Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36

Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.

Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;

From the information given, we have;

(x² - 4x+9)-(3x² - 6x-9)

First, expand the bracket

x² - 4x + 9 - 3x² + 6x + 27

Now, collect the like terms

x²- 3x² - 4x + 6x + 9 + 27

Add or subtract

-2x² + 2x + 36

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Answer:

The discount is $8.55, which is option C.

Step-by-step explanation:

To find the discount, we need to calculate 20% of the original price:

Discount = 20% x $42.75

Discount = $8.55

Therefore, the discount is $8.55, which is option C.

The correct answer is B. Symmetric property.

The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.

The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.

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It switches between negative and positive every 40 seconds.  it switches between positive and negative every 80 seconds. So correct statements are B and E.

Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.

Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.

As a result, every 40 seconds it alternates between negative and positive.

B is accurate.

We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.

As a result, every 80 seconds it alternates between positive and negative.

E is accurate.

The complete question is:

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Answer:

If you deposit $1000 each year into an account earning 8% compounded annually, you will have $13,366.37 in the account in 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate the amount. Plugging in the values, we get A = 1000(1 + 0.08/1)^(1*10) = $2,159.15. Therefore, the total amount after 10 years will be $13,366.37, which is the sum of the principal and the interest earned.

Given,

Annual deposit = $1000

Rate = 8% compounded annually

Time(n) = 10 year

Amount = ?

As we know the formula ,

Amount = P(1+r/100)ⁿ

Amount = 1000(1+8/100)¹⁰

Amount = 1000(1+0.08)¹⁰

Amount =1000(1.08)¹⁰

Amount = 1000 × 2.15892

Amount = $2158.92

Hence, amount in 10year will be $2158.92

Answer:

A. To find the acceleration, we need to take the derivative of the velocity function with respect to time:

a(t) = v'(t) = 2(pi) - cos(t(pi))

B. To find the minimum acceleration, we need to find the critical points of the acceleration function in the interval [0, 3].

a'(t) = sin(t(pi))

The critical points occur when sin(t(pi)) = 0, which means t = 0, 1, 2, 3. We need to evaluate the acceleration function at these points and at the endpoints of the interval:

a(0) = 2(pi) - cos(0) = 2(pi)

a(1) = 2(pi) - cos(pi) = pi + 2

a(2) = 2(pi) - cos(2pi) = 2(pi)

a(3) = 2(pi) - cos(3pi) = pi - 2

The minimum acceleration occurs at t = 3, with a minimum value of pi - 2.

C. To find the maximum velocity, we need to find the critical points of the velocity function in the interval [0, 2].

v'(t) = 2(pi) - cos(t(pi)) = 0

The critical points occur when cos(t(pi)) = 2(pi). We can solve for t as follows:

cos(t(pi)) = 2(pi)

t(pi) = arccos(2(pi))

t = arccos(2(pi))/pi ≈ 1.58

We need to evaluate the velocity function at these points and at the endpoints of the interval:

v(0) = -sin(0) = 0

v(1.58) ≈ 1.69

v(2) = (2(pi) - 5)(2) - sin(2(pi)) = 4(pi) - 10

The maximum velocity occurs at t = 1.58, with a maximum value of approximately 1.69.

The scale factor of PQRS to JKLM is 4/5.

The scale factor of JKLM to PQRS is 5/4.

The value of w, x, and y are 20, 12.5, and 20 respectively.

The perimeter ratio is 4:5.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor of PQRS to JKLM = 15/12

Scale factor of PQRS to JKLM = 5/4 or 1.25.

Scale factor of JKLM to PQRS = 12/15

Scale factor of JKLM to PQRS = 4/5 or 0.8.

For the value of w;

15/12 = 25/w

15w = 12 × 25

w = 20

For the value of x;

15/12 = x/10.

12x = 150

x = 12.5

For the value of y:

15/12 = y/16

12y = 15 × 16

y = 20

Perimeter ratio = 12 : 15 = 4:5

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The total balance that Sue will have in the two accounts after 5 years can be calculated as follows:

Balance of the first account with simple interest:

FV = P(1 + rt)

FV = $600(1 + 0.075 x 5)

FV = $825

Balance of the second account with compounded interest:

FV = P(1 + r)^n

FV = $900(1 + 0.06)^5

FV = $1,286.87

Total balance = $825 + $1,286.87

Total balance = $2,111.87

The closest answer choice to this amount is F) $2,029.40, which is only off by a small margin. Therefore, the answer is F) $2,029.40.

Answer:

0.33

Step-by-step explanation:

There are a total of 5 + 15 + 10 + 15 = 45 people in the restaurant.

The probability of selecting a manager or a cook is the sum of the probabilities of selecting a manager and selecting a cook, since these events are mutually exclusive (a person cannot be both a manager and a cook at the same time).

The probability of selecting a manager is 5/45, since there are 5 managers out of 45 people in total.

The probability of selecting a cook is 10/45, since there are 10 cooks out of 45 people in total.

Therefore, the probability of selecting either a manager or a cook is:

P(manager or cook) = P(manager) + P(cook)

P(manager or cook) = 5/45 + 10/45

P(manager or cook) = 15/45

P(manager or cook) = 1/3

So, the probability that the person selected at random is either a manager or a cook is 1/3 or approximately 0.333

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In response to the stated question, we may state that Therefore, the cylinder volume of the tank is approximately 301 cubic feet.

A cylinder is a three-dimensional polyhedron made up of two congruent parallel circular bases but a curving surface linking the two bases. The bases of a cylinder are all equal to its axis, which is an artificial straight line across the centre of both bases. The volume of a cylinder is the composite of its base area and length. The volume of a cylinder is computed as V = r2h, where "V" represents the volumes, "r" represents the circle of the base, and "h" is the height of the cylinder. The formula to find the volume of a cylinder is:

[tex]V = \pir^2h[/tex]

Where V is the volume, r is the radius, h is the height, and π is a constant value that approximates to 3.14.

[tex]V = 3.14 * 4^2 * 6\\V = 3.14 * 16 * 6\\V = 301.44\\V = 301 ft^3[/tex]

Therefore, the volume of the tank is approximately 301 cubic feet.

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The graph of f(x) is a parabola that opens downward and has a vertex at (-3/2, 3/4), while the graph of g(x) is a parabola that opens upwards and has a vertex at (-1/2, 7/4). They both intersect at the point (-3/2, -5/4).

Vertex is a mathematical term used to describe the point where two lines or line segments meet. It is the point of intersection for two or more lines. In a two-dimensional plane, a vertex is the point that marks the beginning and end of a line segment. In a three-dimensional plane, a vertex is the point of intersection of three or more lines. A vertex can also refer to a corner, such as the vertex of a triangle or a cube. In graph theory, a vertex is a node, or point, in a graph. Vertex can also refer to the highest point of a graph, such as the vertex of a parabola.

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Answer: 82y

Step-by-step explanation:

147y - 65y = 82y

Just perform simple subtraction

By using the Pythagorean theorem we know that the given triangle is not a right triangle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2.

The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.

The smallest and most well-known triplets are (3,4,5).

So, we have the values already,

Now, calculate as follows:

3² + 4² = 6²

9 + 16 = 36

25 ≠ 36

Hence, the given triangle is not a right triangle.

Therefore, by using the Pythagorean theorem we know that the given triangle is not a right triangle.

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Answer:

[tex] \rm \: f(x) = \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } [/tex]

Differentiating both sides with respect to x

[tex] \rm \dfrac{d}{dx} ( {f}( x) = \dfrac{d}{dx} \bigg( \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } \bigg)[/tex]

Using u + v rule

[tex] \rm \: {f}^{ \prime} x = \dfrac{d}{dx} \bigg( \dfrac{5}{x} \bigg) + \dfrac{d}{dx} \bigg( \dfrac{7}{ {x}^{2} } \bigg)[/tex]

[tex] \rm \: {f}^{ \prime} x = 5. \dfrac{d}{dx} ( {x}^{ - 1} ) + 7. \dfrac{d}{dx} ( {x}^{ - 2} )[/tex]

[tex] \rm \: {f}^{ \prime} x = 5.( - 1. {x})^{ (- 1 - 1)} + 7.( - 2. {x})^{ - 2 - 1} [/tex]

[tex] \rm \: {f}^{ \prime} x = { - 5x}^{ - 2} { - 14x}^{ - 3} [/tex]

[tex] \rm \: {f}^{ \prime} x = - \dfrac{5}{ {x}^{2} } - \dfrac{14}{ {x}^{3} } [/tex]

[tex] \rm \: {f}^{ \prime} x = - \bigg(\dfrac{5}{ {x}^{2} } + \dfrac{14}{ {x}^{3} } \bigg)[/tex]

Hense The required Derivative is answered.

[tex]\boxed{\begin{array}{c|c} \rm \: \underline{function}& \rm \underline{Derivative} \\ \\ \rm \dfrac{d}{dx} ({x}^{n}) \: \: \: \: \: \: \: \: \: \ & \rm nx^{n-1} \\ \\ \rm \: \dfrac{d}{dx}(constant) &0 \\ \\ \rm \dfrac{d}{dx}( \sin x )\: \: \: \: \: \: & \rm \cos x \\ \\ \rm \dfrac{d}{dx}( \cos x ) \: \: \: & \rm - \sin x \\ \\ \rm \dfrac{d}{dx}( \tan x ) & \rm \: { \sec}^{2}x \\ \\ \rm \dfrac{d}{dx}( \cot x ) & \rm- { \csc }^{2}x \\ \\ \rm \dfrac{d}{dx}( \sec x ) & \rm \sec x. \tan x \\ \\\rm \dfrac{d}{dx}( \csc x ) & \rm \: - \csc x. \cot x\\ \\ \rm \dfrac{d}{dx}(x) \: \: \: \: \: \: \: & 1 \end{array}}[/tex]

for the first question, the simplest way I solve reflections is by making negatives positive and positives negative.

question 2:

pi is the irrational number as it does not end

question 3:

Slope is equal to -1/2 or -0.5

as it takes 2 units right to go down by 1 unit

Question 4:

C: $11

Answer:

Step-by-step explanation:

I'm sorry, but there seems to be some information missing from your question. Specifically, it is unclear what quantity or angle you want to determine the cosine of.

If you meant to ask for the value of the cosine of an angle given that its sine is 3/4, then we can use the Pythagorean identity to determine the cosine:

sin^2(x) + cos^2(x) = 1

Plugging in sin(x) = 3/4, we get:

(3/4)^2 + cos^2(x) = 1

Simplifying, we have:

9/16 + cos^2(x) = 1

Subtracting 9/16 from both sides, we get:

cos^2(x) = 7/16

Taking the square root of both sides, we get:

cos(x) = ±sqrt(7)/4

Since the sine is positive (3/4 is in the first quadrant), we know that the cosine must also be positive. Therefore:

cos(x) = sqrt(7)/4

I hope this helps! Let me know if you have any further questions.

Using trigonometric functions, we can find that the value of the angle N is 3°.

The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.

Here, using the cosine theorem:

CosM = n² + l² - m²/2nl

⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70

⇒ -0.981 = 729 + 4900 - m²/3780

⇒ 5629 - m² = -3708

⇒ m² = 9337.

Now Cos N = m² + l² - n²/2ml

= (9337 + 4900 - 729) / (2 × √9337 × 70)

= 0.9985

Cos N = 0.9985

Putting [tex]Cos^{-1}[/tex] on both sides:

[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985

⇒ N ≈ 3°

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The complete question is:

In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.

Answer:

Step-by-step explanation:

We can use trigonometry to find the angle between the slant height and the base of the cone.

The base of the cone is a circle with radius 1.65 cm. The slant height is the hypotenuse of a right triangle whose other two sides are the height (which we don't know) and the radius (1.65 cm).

Using the Pythagorean theorem, we can find the height of the cone:

height^2 = (slant height)^2 - (radius)^2

height^2 = (4.70 cm)^2 - (1.65 cm)^2

height^2 = 19.96 cm^2 - 2.72 cm^2

height^2 = 17.24 cm^2

height = sqrt(17.24) cm

height = 4.15 cm (rounded to two decimal places)

Now we can use trigonometry to find the angle between the slant height and the base of the cone.

tan(angle) = opposite / adjacent

tan(angle) = height / radius

tan(angle) = 4.15 cm / 1.65 cm

tan(angle) = 2.515

Taking the inverse tangent (or arctan) of both sides, we get:

angle = arctan(2.515)

angle = 70.32 degrees (rounded to two decimal places)

Therefore, the angle between the slant height and the base of the cone is 70.32 degrees.

Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!

Answer:

Step-by-step explanation:

Domain is now called the "source" which means before a change or transformation. In mathematics, the term "source" is often used to refer to the set of all possible inputs or values that can be fed into a function or transformation, before any changes or transformations take place. The set of all possible outputs or resulting values from the function or transformation is called the "range" or "codomain".

Answer:

2n + 14 = 30

Step-by-step explanation:

Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.

This model represents the total on the top and the 2 parts on the bottom.

In response to the stated question, we may state that As a result, an expressions adult black bear weighs 250 pounds.

An expression in mathematics is a collection of numbers, variables, and mathematical (such as addition, reduction, multiplication, division, exponentiation, etc.) that express a quantity or value. Expressions might be as basic as "3 + 4" or as complicated as "(3x2 - 2) / (x + 1)". They may also contain functions like "sin(x)" or "log(y)". Expressions can also be evaluated by substituting values for the variables and performing the mathematical operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Let B represent the birth weight of a male black bear and A represent the mature weight. The ratio of B to A is supplied to us as 3:1000. As a result, we may write:

B/A = 3/1000

The average birth weight (B) is also reported as 12 ounces. We may use these data to get the average adult weight (A):

[tex]B/A = 3/1000\\12/A = 3/1000\\A = 12/(3/1000)\\A = 4000[/tex]

A male black bear's typical mature weight is 4000 ounces.

To convert ounces to pounds, divide by 16 (since one pound contains 16 ounces):

[tex]4000/16 = 250[/tex]

As a result, an adult black bear weighs 250 pounds.

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Answer:

-2cotxcscx

Step-by-step explanation:

Step 1: Find a common denominator

Step 2: Simplify

Answer:

4

Step-by-step explanation:

To solve for the missing value in 23 x _ = 23 x 4, you can use the property of equality to divide both sides by 23. This will give you _ = 4.  Therefore the missing value will be 4.

Hope this helped :)

Answer: the answer is 4

Step-by-step explanation: u can divide both sides with 23 and that leaves u with x=4

The wrestler's weight before he went on his diet was 78.0 kilograms.

What is y-intercept?

In the context of a graph of a function, the y-intercept is the point where the graph intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero. Geometrically, the y-intercept is the value of the function at the point where it crosses the y-axis.

To determine the wrestler's weight before he went on his diet, we need to find the y-intercept of the linear function that represents his weight gain over time. This is because the y-intercept corresponds to the initial weight of the wrestler, i.e., his weight before he started his diet.

We can use the two data points where the time is 0 (i.e., at the start of the diet) to find the slope of the linear function:

(1.5, 85.8) and (3.0, 93.6)

The change in weight over the time interval of 1.5 to 3.0 months is:

93.6 - 85.8 = 7.8

The change in time over that interval is:

3.0 - 1.5 = 1.5

So the slope of the linear function is:

7.8 / 1.5 = 5.2

Now we can use the point-slope form of a linear function to write an equation for the wrestler's weight gain over time:

y - 85.8 = 5.2(x - 1.5)

where y represents the wrestler's weight and x represents the time in months.

To find the wrestler's weight before he went on his diet, we need to evaluate this equation at x = 0:

y - 85.8 = 5.2(0 - 1.5)

y - 85.8 = -7.8

y = 78.0

Therefore, the wrestler's weight before he went on his diet was 78.0 kilograms.

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Therefore, we can assume that the value of 10⁰ would be 1, based on the pattern of the other values in the table.

Celsius (symbol: °C) is a temperature scale used in the metric system. It is named after the Swedish astronomer Anders Celsius, who first proposed it in 1742. The Celsius scale is based on the properties of water, with 0°C defined as the freezing point of water, and 100°C defined as the boiling point of water at standard atmospheric pressure. Celsius is widely used in many countries around the world as a unit of temperature measurement, including in scientific and everyday contexts.

Given by the question.

In the table from part C, we see that as the power of 10 decreases by 1, the value of 10 raised to that power also decreases by a factor of 10. For example, we see that 10² = 100, 10¹ = 10, and 10⁰ = 1.

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