In triangle ABC, m angle A=45 degrees. The altitude divides side AB into two parts of 20 and 21 units. Find BC

The number of shares he buy is $615.

Given that Barney just bought stock in Purple Dinosaur Industries and he paid a total of $7,380 and the price of the stock is $12 for one share.

We want to find the number of shares Barney buys.

The total amount barney should pay is $7380.

The price of the stock for one share is $12.

The total number of shares barney buy is 7380/12=615.

Hence, the number of shares barney should buy when he paid a total $7380 and the price of stock for one share is $12 is $615.

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A rhombus is a parallelogram because the opposite sides are parallel but every parallelogram is not a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.

We need to identify the properties of the given figure in order to answer why one figure can not be the other one:

A rhombus has all sides equal as well as parallel but all angles might not be right angles.

A square has all four sides equal and has 4 right angles.

A rectangle has equal opposite sides and 4 right angles.

A parallelogram has opposite parallel sides.

Hence, a rhombus can be a parallelogram because the opposite sides are parallel but every parallelogram can not be a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.

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The quotient is x²+x+1 - 14/(x-1) after divide x³-15 by x-1.

What is synthetic division?

In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

The divisor is x - 1.The dividend is (x³-15).

Step 1:Take the constant term of the divisor with the opposite sign and write it to the left.

Write the coefficients of the dividend to the right (missed terms are written with zero coefficients).

Step 2:Write down the first coefficient without changes:

Step 3:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 4:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum

Step 5:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum.

We have completed the table and have obtained the following resulting coefficients: 1,1,1,−14.

All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

The quotient is x²+x+1 and the remainder is -14.Therefore (x³-15)÷(x-1) = x²+x+1 - 14/(x-1)

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76263

Step-by-step explanation:

[tex] \: \: \: 20005[/tex]

[tex] + 56258[/tex]

___________

[tex] = 76263[/tex]

The correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.

What is property of similar triangle?

If the corresponding sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are similar.

They have parallel corresponding sides, and they have angles with the same measure.

hence, the correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.

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Answer:

A.

Step-by-step explanation:

Answer:

136-5x

Step-by-step explanation:

The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.

What is least common denominator?

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Given fractions are

2/3 and 8/11

L.C.M of 3 and 11 is 33.

We get,

2/3 ×11/11 = 22/33

and

8/11×3/3 = 24/33

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Answer:

Consider the right triangle below: State the Pythagorean Theorem as it relates to the above triangle. List the trig identities as they relate to the triangle above. Now suppose hypotenuse C represents a vector R, while sides B and A represent vector components Rx and Ry respectively. Redraw the triangle with the new labels below. Using Pythagorean Theorem, derive the equation for R.

Answer:

Step-by-step explanation: step 5
they have not proved the ASA postulate i.e. they the are missing a step to proove angle BEF = angle CED (Verticle angles)
so, correct answer is step number 5 and reason 'missing prior step'

Answer: A

Step-by-step explanation:

The values indicated trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) =  0.14 and csc(β) = 1.01

Trigonometric functions are the periodic functions that denote the relationship between angle and sides of a right-angled triangle e.g sine, cosine, tangent, etc.

Given: tan(β) = 7

Thus, β = arc tan 7 = 81.87

(a) cot(β) = 1/tan(β) = 1/7 = 0.14

(b) cos(β) = cos 81.87 = 0.14

(c)  tan(90-β) =  tan(90-81.87) = tan 8.13 = 0.14

(d) csc(β) = 1/sinβ = 1/sin(81.87) = 1.01

Therefore, the value of the trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) =  0.14 and csc(β) = 1.01

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sin 270° = sin 3π/2 = -1, the value of 0 is 270° or 3π/2.

Given,

sin 0 = -1

We have  to find the value of 0.

Lets see the trigonometric table for sin.

From the above table we get the value of sin 0

The value -1 is for sin 270° which is equal to sin 3π/2

That is,

sin 270° = sin 3π/2 = -1, the value of 0 is 270° or 3π/2.

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Answer:

Vertex: (-2, 3) Axis of symmetry: x = -2 The parabola opens downward.

Step-by-step explanation:

Answer:

6 pizzas

Step-by-step explanation:

12.99 times 3 which is the 3 pitchers of soda is 38.97

38.97 subtracted from 75 which is our total amount is 36.03

36.03 which is what we have left divided by 6 since each pizza is 6$ is 6.

Numerous other sorts of numbers exist, including natural, whole, rational, real, and integers. Positive and negative numbers, but not decimals or fractions, make up the category of integers.

Q      What are integers in mathematics?
ANS An integer is a whole number without any fraction or decimal part.

The traits of each group of numbers are as follows:

Answer: [tex]x=7[/tex]

Step-by-step explanation:

[tex]3^x=2187\\\\x=\log_{3} (2187)\\\\x=7[/tex]

Answer:

first angle =35

second angle=63

third angle=82

The fractions of sixth graders that reached their goal after each day are given as follows:

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

In which the technical terms related to x and y are as follows:

The fraction can be represented by bars, in which:

As shown by the image at the end of the answer, the fractions are given as follows:

The image is given at the end of the answer.

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The first step Charlie should use to solve the equation will be to open the bracket on the left side of the equation.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The equation Charlie wants to solve can be calculated as follows:

-1/4(x - 1) =2/3 x +2

The first step would be to open the parenthesis on the left side of the equation as follows:

-1/4(x - 1) =2/3 x +2

- 1 / 4 x + 1 / 4 = 2 / 3 x + 2

Let's subtract 1 / 4 from both sides of the equation

- 1 / 4 x + 1 / 4 = 2 / 3 x + 2

- 1 / 4 x + 1 / 4 - 1 / 4  = 2 / 3 x + 2 - 1 / 4

- 1 / 4 x = 2 / 3 x + 7  /4

subtract 2 / 3 x from both sides of the equation.

- 1 / 4 x = 2 / 3 x + 7  /4

- 1 / 4 x - 2 / 3 x = 2 / 3 x - 2 / 3 x + 7  /4

- 11 / 12 x = 7 / 4

cross multiply

-44x = 84

divide both sides by - 44

x = 84 / -44

x = - 21 / 11

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If a₁ = 9 and aₙ = 4 + (aₙ - 1) in an arithmetic sequence, then the value of fifth term a₅ is equal to 25.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

From the information provided, we know that the common difference is equal to 4.

Substituting the given parameters into the formula, we have;

a₅ =  9 + (5 - 1)4

a₅ =  9 + 4(4)

a₅ =  9 + 16

a₅ =  25

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Complete Question:

If a₁ = 9 and aₙ = 4 + (aₙ - 1), then find the value of a₅.

Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-4) and (0,4) is y=8/5x + 4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.

Being (x₁, y₁)= (-5, -4) and (x₂, y₂)= (0,4), the slope m can be calculated as:

m= (4 - (-4))÷ (0 - (-5))

m= (4 + 4)÷ (0 +5)

m= 8÷ 5

m= 8/5

Considering point 2 and the slope m, you obtain:

4= 8/5×0 + b

4= 0 +b

4= b

Finally, the equation of the line is y=8/5x + 4.

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The statements that are a result of corresponding parts of congruent triangles being congruent are:

An isosceles triangle is a type of triangle with two equal sides and angles. The other types of triangle includes;

From the figure;

Sides EFGH are congruent, that is, equal

Since Sides EFGH are congruent, it can not be a rectangle, it is a square.

Triangle FGH and FEH are both isosceles triangle.

Diagonal FH bisects triangle FGH and FEH

So therefore, the isosceles triangle FGH and FEH are congruent and bisected by diagonal FH.

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The number of revolutions taken by a wheel will be 353.68 millimeters.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

Given data as:

The radius of the wheel r = 45 millimeters

Circumference of wheel = Circumference of a circle

Circumference of wheel = 2πr =2π(45) = 282.74 millimeters

The distance traveled by wheel = 100,000 millimeters

Now, the number of revolutions taken by a wheel will be

⇒ distance traveled by wheel / Circumference of wheel

⇒ 100,000 / 282.74

⇒ 353.68

Thus, the number of revolutions taken by a wheel will be 353.68 millimeters.

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The equation for the function of the ordered pair is y =10x+2.

What is equation for the function?

 An equation that has one solution for y for each value of x is referred to be a function. For each input of a particular type, a function assigns precisely one output. The names f(x) or g(x) are frequently used in place of y when naming functions. If our function's value is f(2), then we should calculate its value when x=2. Each functional equation contains some information about a function or several functions. An illustration of a functional equation is f (x) f (y) = x y, f(x) f(y) = x y.

Here in given order pair , let us take any two points,

[tex](x_1,y_1)=(0,2)\\(x_2,y_2)=(1,12)[/tex]

Now using slope formula,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m =10/1 = 10

Now using equation formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-2 =10(x-0)

=> y-2 = 10x

=> y=10x+2.

Therefore equation of the following order pair is y = 10x+2.

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The two values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

The given expression is ,

2x²– 11x + 15 = 0

Solve the equation and find roots

2x² - 6x - 5x + 15 = 0

Take common elements out

2x(x - 3) - 5(x - 3) = 0

we get the brackets same that means we're on right way,

(2x - 5) (x - 3) = 0

split the values into two and find values,

2x - 5 = 0            and        x - 3 = 0

2x = 5                               x = 3

x = 5 / 2

Hence, the  values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)

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