Unit 8 Right triangles and trigonometry Homework 3

Answer:

y = 2x + 5

The slope: 2

Y-intercept: 5

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = the slope

b = y-intercept

Our equation

-4x+2y=10

2y = 4x + 10

y = 2x + 5

The slope: 2

Y-intercept: 5

Given that the student did not pass the exam, the probability that they revised is 24%.

Probability refers to the likelihood, odds or chance of an expected outcome given many possible outcomes.

Probability is the quotient of expected outcomes over total outcomes.

The total number of students in the class = 33

The total number of students who revised = 19

The total number of students who revised and failed the exam = 8

The probability that the student revised but failed the exam = 8/33 = 24%

or (8/19 x 19/33)

Thus, the probability that a student chosen at random from the class revised but failed the exam is 24%.

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The relative minimum and the relative maximum for the attached graph over the interval [ 1, 5 ] of the function given in graph is equal to -14 and -3 respectively.

Graph is attached.

Function shown in the attached graph over the interval [ 1, 5 ] is :

Representing the parabola function.

Vertex representing lowest point of the graph in the interval [ 1, 5 ] is given by :

( 4.5 , -14 )

Vertex representing highest point of the graph in the interval [ 1, 5 ] is given by :

( 1.5 , -3)

Relative minimum and maximum is represented by the y -coordinate of the graph.

Lowest point gives relative minimum = -14

Highest point gives relative maximum = -3

Therefore, for the function in the graph the relative minimum = -14 and relative maximum= -3.

The above question is incomplete , the complete question is:

what are the relative minimum and relative maximum values over the interval [1, 5] for the function shown in the graph?

Graph is attached.

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Answer:

24

Step-by-step explanation:

4x6=24

Answer: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80…

Step-by-step explanation:

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… and so on. It is a sequence where the difference between each next number and the preceding number, i.e. two consecutive results, is 8.

Answer:x = 1/60

Step-by-step explanation:

(8^x/4+4)=(8^-19x/4)

Apply fraction cross multiply: a/b = c/d  then a*d = c*b

8^x * 4 = (4+4) * 8^-19x

simplify

8^x * 4 = 8 * 8^-19x

Apply exponet rules

xln(8) + ln(4) = (-19x +1) ln(8)

then just solve

x= 1/60

while y = -1/8

The lateral surface area of the cylinder for the given measurements is equal to 452.16 square inches.

Pipe is in form of cylinder

Diameter of the cylinder = 6 inches

Height of the cylinder 'h' = 24 inches

Radius of the cylinder 'r' = diameter / 2

                                        = 6/ 2

                                        = 3inches

lateral surface area of the cylinder = 2πrh

value of π = 3.14

Substitute the value we get,

⇒lateral surface area of the cylinder =  2 × π × 3 × 24

⇒lateral surface area of the cylinder = 144π square inches

⇒lateral surface area of the cylinder = 144 × 31.4

⇒ lateral surface area of the cylinder = 452.16 square inches

Therefore, the lateral surface area of the cylindrical pipe is equal to 452.16 square inches.

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Therefore, Nolan has 8 dollars left to spend on gift C.

Nolan spent 9 dollars and 34 cents on gift A,

and 3 dollars and 12 cents on gift B,

for a total of

9 + 3 = 12 dollars and

34 + 12 = 46 cents spent so far.

Nolan started with 20 dollars, so he has 20 - 12 = 8 dollars remaining for gift C.

By using wildcards (such as "x" and "y") that are replaced with random values when the quiz is taken, simple calculated questions provide a technique to build individual numerical questions whose response is the result of a numerical formula that contains changeable numerical values.

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The midpoint rule is an overestimate.

This is because the midpoint rule is a form of numerical integration which approximates the area under a curve by summing the areas of rectangles that are divided into equal intervals. These rectangles are centered on the midpoints of the intervals.

Because the rectangles are centered on the midpoints instead of the endpoints of each interval, the midpoint rule overestimates the area under the curve as the rectangles are wider than the intervals.

This means that the midpoint rule produces a larger area than the exact area under the curve. This is why the midpoint rule is an overestimate.

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The midpoint rule is an overestimate of the definite integral. The midpoint rule is a numerical integration method used to approximate the definite integral of a function.

It works by dividing the interval of integration into smaller subintervals and approximating the integral by summing the areas of rectangles whose heights are determined by the function evaluated at the midpoint of each subinterval.

Since the rectangles in the midpoint rule are taller at the midpoint and shorter at the endpoints, this method generally overestimates the true area under the curve. However, if the function is well-behaved and the subintervals are small enough, the error between the midpoint rule approximation and the true definite integral can be made arbitrarily small.

In conclusion, the midpoint rule is an overestimate of the definite integral, but the error can be made small by using smaller subintervals.

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The exponential function shown in the graph is f(x) = 2ˣ

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The standard form of an exponential function is:

y = abˣ

where a is the initial value and b is the multiplication factor.

The graph shown is an exponential function.

At the point (0, 1):

y = abˣ

substituting:

1 = ab⁰

a = 1

At the point (2, 4):

y = abˣ

substituting x = 2, y = 4 and a = 1:

4 = b²

b = 2

The exponential function is y = 2ˣ

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Answer: -0.26666666666

Step-by-step explanation:

Answer: y+3= 1/7 * (x+8)

Step-by-step explanation:

The value of the expression is 40.64.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

41 + (5/7)t

When t = -1/2

41 + (5/7)t

= 41 + 5/7 x (-1/2)

= 41 - 5/14

= (574 - 5) / 14

= 569/14

= 40.64

Thus,

The value is 40.64.

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Rudy's timing in the most recent race is 312 minutes.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Rudy has run many marathons and keeps track of all of his finishing times. At a race last month, he finished in 260 minutes. At his next race, he finished with a time that was 20% longer.

Rudy's timing in the most recent race can be calculated as -

{x} = 260 + 20% of 260

{x} = 260 + (20/100) x 260

{x} = 260 + 20 x 2.6

{x} = 260 + 52

{x} = 312

Therefore, Rudy's timing in the most recent race is 312 minutes.

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The proportion is 2 : 3 and the scale model is represented by the Black tabletop color

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the scale of the color tabletop be represented as a : b

Now , the proportion will be

The scale model of the tabletop is given by A : B = 4 inches by 6 inches

So , the proportion is 4/6 = 2 : 3

And , the black tabletop has an original size of 32 inches by 48 inches

Substituting the values in the equation , we get

4 inches by 6 inches is proportional to 32 inches by 48 inches

On simplifying the equation , we get

4/6 = 32/48

2/3 = 16/24

2/3 = 8/12

2/3 = 2/3

Hence , the proportion is 2 : 3

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Answer:

your profit is 400

Step-by-step explanation:

50×225

The equation of line m passing through the points (-2,-8) and (1,1) is y = 3x - 2

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Line M goes through the points (-2,-8) and (1,1). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-8)=\frac{1-(-8)}{1-(-2)} (x-(-2))\\\\y=3x-2[/tex]

The equation of line m is y = 3x - 2

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(-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is y < x+5

First, we have to find the x-intercept which occurs at y = 0

0 < x + 5

x<-5

For y-intercept,

y <  0+ 5

y <5

As a result, the obtained ordered pair is  (-5, 0 ) and (0, 5).

Hence, (-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5

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The required unit rate is [tex]\frac{3}{4}[/tex] book/ hour

When two different types of quantities with various units are being compared, the ratio of rate is applied. On the other hand, the unit rate shows how many units of one quantity are equivalent to one unit of another. A unit rate is a ratio between two separate units with 1 as the denominator.

Here we have

1/4 book/ 1/3 hour  

We can convert the given fraction into a unit rate as given below

=> 1/4 book/ 1/3 hour  

=>  [tex]\frac{1}{4} \times (\frac{3}{1})[/tex]  book/ hour

=>  [tex]\frac{3}{4}[/tex] book/ hour

Therefore,

The required unit rate is [tex]\frac{3}{4}[/tex] book/ hour

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The simplified expression is j^-4k^-12

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

j^-5k^-5 x jk^-7

Rewrite as

j^-5k^-5 x jk^-7 = j^-5 * j * k^-5k^-7

Apply the law of indices in the products

j^-5k^-5 x jk^-7 = j^-4 * k^-12

So, we have

j^-5k^-5 x jk^-7 = j^-4k^-12

Hence, the expression is j^-4k^-12

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After 10 years at 9% compound interest per annum, The amount will be £393.57.

The amount of money you will have after 10 years can be calculated using the formula for compound interest:

[tex]A = P * (1 + r/n)^{nt}[/tex]

where:

A is the final amount,

P is the initial amount (principal),

r is the interest rate as a decimal,

n is the number of times the interest is compounded per year,

t is the number of years the money is invested.

In this case:

P = £200

r = 9% = 0.09

n = 1 (because interest is compounded annually)

t = 10

So, plugging in the values, we get:

[tex]A = 200 * (1 + 0.09/1)^{1 * 10)} = 200 * (1.09)^{10}[/tex]

[tex]A = 200 * 1.96787 = 393.57[/tex]

So, after 10 years at 9% compound interest per annum, you will have £393.57.

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The value of 'x' in the linear pair of angles is 126°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know the sum of linear pair of angles is 180°.

Therefore, From the given information

(x - 6)° + 60° = 180°.

x + 54° = 180°.

x = 180° - 54°.

x = 126°.

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Answer: 1  7/24

Step-by-step explanation:

1. A function that has a V-shaped graph that opens up or down is the absolute value function.

2. The lowest or highest point on the graph of an absolute value function is the vertex.

3. The line that divides the graph of an absolute value function into two sections that are reflections of each other is the line of symmetry.

The absolute value function of vertex (h,k) is given by the equation presented as follows:

y = |x - h| + k.

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The exponential function to model the population of Valley View is [tex]y = 1800(1.012)^t[/tex].

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

An exponential function is written in the form -

[tex]y=ab^t[/tex]

Here, y is the function, a is the base value b is the rate and t is time period.

The number of people in Valley view is 1800. So, the base is a = 1800.

The function y depicts the towns population.

Each decade the population grows by 12%.

The growth rate per year is = 12 / 10

The growth rate is 1.2%

The value for b will be = 1 + r

b = 1 + 1.2/100

b = 1 + 0.012

b = 1.012

So, the exponential equation will be -

[tex]y = 1800(1.012)^t[/tex]

Therefore, the exponential equation is [tex]y = 1800(1.012)^t[/tex].

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The exact value of the trigonometric function sin (A + B) is equal to 1020 / 1189.

In this problem we must determine the exact value of the sine of the sum of two acute angles. There are acute angles in the first quadrant, thus:

sin θ > 0

cos θ > 0

tan θ = sin θ / cos θ

In addition, by trigonometric formulas:

cos θ = √(1 - sin² θ)

cos θ = 1 / √(tan² θ + 1)

Where θ is the angle, in degrees.

sin (α + β) = sin α · cos β + cos α · sin β

If we know that sin A = 40 / 41 and tan B = 20 / 21, then the exact value of sin (A + B) is:

cos A = √[1 - (40 / 41)²]

cos A = 9 / 41

cos B = 1 / √[1 + (20 / 21)²]

cos B = 21 / 29

sin B = √[1 - (21 / 29)²]

sin B = 20 / 29

sin (A + B) = (40 / 41) · (21 / 29) + (9 / 41) · (20 / 29)

sin (A + B) = 1020 / 1189

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The length of AB is [tex]2\sqrt{105}[/tex].

An altitude is a line which passes through the vertex of the triangle and meets the opposite side at the right angle. A triangle has three altitudes.

Consider the triangle ABC, with right angle at B,

Let AB = x, BC = y, BD = z.

By pythagoras theorem,

[tex]AC^{2} =AB^{2} +BC^{2}[/tex]⇒[tex]x^{2} +y^{2} = 21^{2}[/tex]----------(1)

From triangle ADB,

[tex]z^{2} +11^{2} =x^{2}[/tex]-------(2)

[tex]z^{2} +10^{2} =y^{2}[/tex]--------(3)

(2)-(3), we get, [tex]x^{2} -y^{2} =21[/tex]-----(4)

subtract (1) and (4) we get,

[tex]x^{2} =420[/tex]

⇒[tex]x=2\sqrt{105}[/tex]

Hence, the length of AB is [tex]2\sqrt{105}[/tex] in simplest radical forms.

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Answer:

5^-18

Step-by-step explanation:

here is the answer please mark me as the brainliest

Answer: To find the minimum value of c = x + 3y, you need to solve the optimization problem with a constraint or without any constraint.

Without a constraint:

The minimum value of c = x + 3y without a constraint is achieved when the partial derivatives of c with respect to x and y are equal to zero.

Let's take the partial derivative of c with respect to x:

dc/dx = 1

And with respect to y:

dc/dy = 3

Setting these equal to zero, we have:

1 = 0 and 3 = 0

Since the partial derivatives are not equal to zero, there is no minimum value of c without a constraint.

With a constraint:

If there is a constraint, such as a limit on x or y, then the minimum value of c can be found by using optimization techniques, such as the method of Lagrange multipliers.

Step-by-step explanation: