Find the length of the third side. If necessary, write in simplest radical form.

When in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10)  degrees, then the ∠A, ∠B  and ∠C  are 109 degrees, 27 degrees and 44 degrees respectively  

The ∠A = (x-10) degrees

Angle B is one-quarter of angle A

∠B = (1/4)×(x-10)

= (1/4)x - (5/2)

= 0.25x-2.5

The angle C is two fifth of angle A

∠C = (2/5)(x-10)

= (2/5)x - 4

= 0.4x-4

We know sum of the angles in a triangle is 180 degrees

Then,

∠A + ∠B + ∠C = 180

Substitute the values in the equation

(x-10) + 0.25x-2.5 +0.4x-4 = 180

1.65x-16.5 = 180

1.65x = 196.5

x ≈ 119

∠A = (x-10)

= 119-10

= 109 degrees

∠B = 0.25x-2.5

= 0.25×119-2.5

≈ 27 degrees

∠C = 0.4x-4

= 0.4×119-4

≈ 44 degrees

Hence, when in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10)  degrees, then the ∠A, ∠B  and ∠C  are 109 degrees, 27 degrees and 44 degrees respectively  

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Answer:

n= -16/25

Step-by-step explanation:

⇒Plug in the given values of the variables in order and then simplify the expression

Given that a= 3 and b=4

⇒[tex]=(3)^{3} -(4)+7\\=27-4+7\\=23+7\\=30[/tex]

⇒The expression evaluated at the given known variables gives 30.

The function g(x) when x= - 2, 0 , 5 is -6 , 0 and 15 respectively.

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given: g(x) = 3x

To evaluate : The function x= - 2, 0, 5.

g(-2) = 3× -2 = -6

g(0) = 3×0 = 0

g(5)= 3×5 = 15

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In this problem, we are looking for the doubling time of the wage of the Toyota automobile assembly line workers. Initially, their wage is $6.70 and by the end of 15 years, their salary is now $29.59.

What we can find here first is the rate of the increase of the salary of the workers. We can use the equation

We are looking for the value of r. We have to derive an equation solving for r. We have

Now, we solve for the value of r given y = 29.59, y0 = 6.70, and t = 15 years. We get

The doubling time is computed as

Substitute the value of r on the equation above and solve, we get

Hence, the doubling time for this problem is equal to 7 years.

Answer: 7 years

The average consumption of the fruit juice would be 7.6 gallons for the year 2006.

Average consumption is derived by dividing the total measured consumption of that municipal service by that consumer during the three months before by three. It refers to the average consumption of a consumer of a municipal service during a certain time.

Utilizing the total of quantities consumed or dispersed over a period of time, typically 12 months, the average monthly consumption can be computed. The average number of units used each month is known as average monthly consumption, stock-outs corrected (CA).

Total consumption of the fruit juice in 2006=2.28x109 gallons.

Total population of the country in year 2006=3x108

Average Consumption=(2.28x109)/(3x108)

                = 7.6 gallons    

Hence the average consumption would be 7.6 gallons per person.

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Domain is number of minutes water has been added .

Range is amount in the pond

The domain and range of a relation are, respectively, the sets of all the x-coordinates and all the y-coordinates of ordered pairs. For example, if the relationship is R = (1, 2), (2, 2), (3,), (4, 3), then

Domain is the set of all x-coordinates that is all with values of 1, 2, 3, and 4.

The set of all y-coordinates in the range is equal to 2, 3.

Domain : Let y = f(x) be a function with an independent variable x and a dependent variable y.

Range :  a function represents a defined relationship between an independent variable (x) and a dependent variable (y). The formula to find the range of a function is y = f(x).

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The height of the building is 118. 89 feet

Trigonometric identities are simplify defined as arithmetic expressions or equations relating to many trigonometric functions, and is also known for holding true for all the values in the domain of the functions.

The different  types of trigonometric identities includes;

The trigonometric ratios for major identities are;

sine = opposite/hypotenuse

tangent = opposite/adjacent

cosine = adjacent/hypotenuse

From the information given;

cos 43 = x/170

cross multiply

x = cos 43(170)

expand the bracket

x = 124.33 feet

To determine the height of the building is the opposite side

sin 73 = x/ 124.33

cross multiply

x = sin 73(124.33)

expand the bracket

x = 118. 89 feet

Hence, the value is 118. 89 feet

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The addition of the fraction 1/10 + 11/20 based on the computation will be 13/20.

In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each slice is represented by ¼.

It should be noted that a fraction simply means a part of a whole number. It should be noted that it's usually expressed as a/b where a is the numerator and b is the denominator.

In this case, we want to add 1/10 + 11/20. This will be illustrated thus:

= 1/10 + 11/20

= 2/20 + 11/20

= 13/20

Therefore the addition is 13/20.

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It is important the order we write the vertices of a triangle in a congruent statement as

B. The order tells us what sides are congruent.

D. The order tells us what angles are congruent.

A vertex (plural vertices) in geometry is the intersection of two straight lines. Three line segments come together to form a triangle. The ends of a triangle's three sides meet at three separate points in a plane to form the triangle, which has three sides with two endpoints each. The vertices of a triangle are the three distinct intersecting points or corners.

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.

The vertices of a triangle in a congruent statement are important for the ordering. In conclusion, the correct options are B and D.

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The distance travelled by the unicycle is 226.08 inches.

The first step is to determine the circumference of  the wheel of the unicycle. A circle is a bounded figure which points from its center to its circumference is equidistant. The circumference of a circle is the distance round the circle.

Circumference of a circle = 2πr

Where:

3.14 x 2 x 12 = 75.36 inches

The next step is to multiply the circumference of the unicycle by the number of revolutions the tire made.

Distance travelled = 3 x  75.36 inches = 226.08 inches

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The function operation ( f + g )(x) of the functions f( x ) = 4x + 1 and g( x ) = x² - 5 is x² + 4x - 4.

A function is simply a relationship that maps one input to one output.

Each x-values must have one y-value to qualify as a function.

Given the data in the question;

First, set up the function operation

( f + g )(x) = f(x) + g(x)

Replace the function designators f(x) and g(x) with the actual functions.

( f + g )(x) = f(x) + g(x)

( f + g )(x) = ( 4x + 1 ) + ( x² - 5 )

Collect and add like terms

( f + g )(x) = 4x + 1 + x² - 5

( f + g )(x) = 4x + x² - 5 + 1

( f + g )(x) = 4x + x² - 4

Reorder the function

( f + g )(x) = x² + 4x - 4

Therefore, the function operation ( f + g )(x) is  x² + 4x - 4.

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The probability of a gorilla living less than 23.9 years is 0.84 (84%) if the lifespans of gorillas in a particular zoo are normally distributed.

A probability is also called as a numerical representation of the likelihood or chance that any kind of specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Probability refers to potential.

Any random event's occurrence is the exact subject of this area of mathematics. The range of the value varies from 0 to 1. Mathematics has been incorporated probability to forecast the likelihood of various types of events.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas.

We need to find the z-score herein of 23.9 years in the kind of standard normal distribution of the lifespans of gorillas in this particular zoo.

z score can be further be calculated using the equation

z = (X-M)/s

and it has been given that X is 23.9 years

M is also called the average gorilla life (20.8 years)

s is given as the standard deviation (3.1 years)

Thus, putting up the values, we have

Z = 1

The Empirical rule that is present here states that 68% of the total lifespans lie within 1 standard deviation from the other mean.

Then Half of it, 68/2 = 34 % lies right side of 1 standard span of the mean.

Since this lifespan is less than mean is 50%, 50%+34% =84% lies less than total z-score 1, that is the probability of a gorilla living less than 23.9 years.

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The set T can be rewritten by listing its elements as T = {-4}.

         Set A = {a, b, c, d}. These are the elements of set A: a, b, c, and d.

Given:

Set T is equal to  {x | x is an integer and -5 < x < -3}.

By examining the interval in the set, the set can also be written as something else. 

It should be noted that the interval consists of two inequalities combined so that x > -5 and x < -3.

As -4 > -5 and -4 < -3 via the number line so it is the only element listed in the required set notation.

Hence, the set can be rewritten as

T = {-4}

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The complete question is: "Rewrite the set T by listing its elements. Make sure to use the appropriate set notation.

T = {x | x is an integer and -5 < x < -3}."

Solution

Step 1:

Write the rational expression:

Step 2:

Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value).

Step 3

Step 4:

\ertical} Asymptote is =-8,\ =3,

Answer:

1(-3) = -3, 1f(-2) = -2

Step-by-step explanation:

The most appropriate choice for Arithmetic Progression will be given by-

The sum of the first sixteen terms of the Arithmetic Progression is 640

What is Arithmetic Progression?

A series of numbers are said to be in Arithmetic Progression if the difference between consecutive terms of the series are same.

If [tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the series, a be the first term and d the common difference,

[tex]a_n = a+(n-1)d[/tex]

If [tex]S_n[/tex] is the sum of first n terms of the series,

[tex]S_n = \frac{n}{2}(2a+(n-1)d)[/tex]

Here,

Let the first term be a and the common difference be d

The sum of the fourth and thirteen terms of an arithmetic progression is 80.

[tex]a_4 + a_{13} = 80[/tex]

[tex]a + (4-1)d + a + (13-1)d = 80[/tex]

[tex]a + 3d +a +12d =80\\2a+15d =80[/tex]

[tex]S_{16} = \frac{16}{2}(2 \times a + (16 -1) \times d)\\[/tex]

     [tex]= 8(2a+15d)[/tex]

     [tex]= 8 \times 80[/tex]

     [tex]= 640[/tex]

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Rewrite the given equation in slope intercept form, y=mx+c. Where the slope is m and the y-intercept is c.

Rewrite the given equation as follows:

Simplify the equation:

Compare to the equation y=mx+c, to get:

Hence, the slope is 6/9 and the y-intercept is -8/9.

You can also write the y-intercept as an ordered pair (0,-8/9) since the x-value at the y-intercept is zero.

Answer:

24

Step-by-step explanation:

divide the sides added together by the middle

Solution:

The cube is numbered from 1 to 6

The probability that any of the numbers from 1 to 6 will show will be

The expected value will be calculated below as

he standard form of a quadratic efunctionis:

Since the y-intercept is (0, -1.4), it follows that:

Substitute c = -1.4 into the equation:

Since the x-intercept is (0.905, 0), it follows that:

Since the graph passes through the third point (2, 0.6), it follows that:

Substitute equation (2) into equation (1):

Substitute a = -0.5 into equation (2), therefore,

Therfore the function is given by:

The equation of the parabola is y = -0.5x² + 2x - 1.4

.

Based on the attached graph, the y-intercept is 3

The y-intercept of the function is the point or points where the graph of the function crosses the y-axis i.e. the point where the value of x equals 0

The graph that completes the question is added as an attachment

Using the definition above, we understand that

The y-intercept for the graph of the exponential function is the point where x = 0

On the attached graph, we have

y = 3, when x = 0

This means that the y-intercept for the graph of the exponential function is 3

This is so because the graph of the function crosses the y-axis  at y = 3 when x = 0

Hence, the y-intercept of the exponential function is 3

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Answer:

1 Greatest Common Factor

We have to find out the greatest common factor, of the given polynomial to factorise it. This process is nothing but a type of reverse procedure of distributive law.

2. Grouping

This method is also said to be factoring by pairs. Here, the given polynomial is distributed in pairs or grouped in pairs to find the zeros.

3. Using Identities

The factorisation can be done also by using algebraic identities. The most common identities used in terms of the factorisation are:

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

a2 – b2= (a + b)(a – b)

4. Zero Factor Property :The Zero Factor Property (also called the Zero Product Property) says that if the product of two quantities is zero, then at least one of those quantities is zero. The only way to get a product equal to zero is to multiply by zero itself.

5. Greatest Common Factor (GCF) Method:

This is almost always the first method applied to factoring polynomials. Look at all of the terms and see if they all have something in common that can be removed.

6. Sum or Difference in Two Cubes

A cube is a term that has been multiplied by itself twice.

[tex] {3}^{3} {x}^{3} and \: \: \: {27x}^{3} [/tex]

are all cubed terms. The trick to remembering how to factor cubed terms is S.O.A.P. S = same sign, O = opposite sign A.P. = always positive.

The remaining wire (W) is just the original wire (850') minus the cut wire on Monday, Tuesday...

There is merely 1' of wire in the reel.

A.

This is not a correct choice

--------------------------

B.

This is a correct choice

---------------------------

C.

This is not a correct choice

------------------------------------------------

D.

This is a correct choice

-------------------------------------------

E.

This is a correct choice

Surface area of rectangular box is 78 inches².

The surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions. It is calculated in square units. The total area of all faces (or surfaces) on a 3D form is the surface area. The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.

Given Data

rectangular box with measurements as shown below 5 inches 3 inches 3 inches

Length = 5 inches

Width = 3 inches

Height = 3 inches

Surface area formula

2lw + 2lh+2hw

Equating values

2(5)(3) + 2(5)(3) +2(3)(3)

30 + 30 + 18

78

Surface area of rectangular box is 78 inches².

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Answer:

The answer is A, 3

Answer:

4 is the answer