What is the length of the long leg of a 30 60 90 triangle?

ABC is a right-angled triangle.

A triangle in which one angle is 90 degree is called a Right Angled Triangle.

AB is congruent to DB because segment DE was constructed so that

DE = AB, BC is congruent to EF, because segment EF was constructed so that EF = BC,

Since Triangle DEF is a right-angled triangle.

Using Pythagoras Theorem,

DE² +EF²  = DF²  

We are given that AB²+BC² = AC²

Since, DE = AB and EF = BC, DE²  +EF²  = AC²

Also, DF² = AC² by the above equation.

DF = AC

So AC is congruent to DF by the definition of congruence.

Δ ABC ≅ Δ DEF by SSS rule

Therefore, ABC is a right-angled triangle.

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The score on his next test must be at least 97 to get an average score of at least 85.

Average value of a set of numbers is a single number which represents the whole numbers in the set.

Average value of a set of numbers is calculated by dividing the sum of all the numbers by the number of values in the set.

Here is is given that,

Jerrod had scores of 75, 82, 94 and 77 on his first four history tests.

We need to find the score of his next test such that the average of all is at least 85.

Let x be the score of his next test.

(75 + 82 + 94 + 77 + x) / 5 ≥ 85

75 + 82 + 94 + 77 + x ≥ 85 × 5

328 + x ≥ 425

x ≥ 97

Hence Jerrod must have at least a score of 97.

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The slope that is parallel to 3x + y = 9 is -3.

Perpendicular slope is 1/3.

The slope of two lines is considered parallel if the slopes are equal, and the slope of two lines is considered perpendicular if the product of the slopes is -1 or would be negative reciprocals of each other.

Given the equation of a line as 3x + y = 9, rewrite in slope-intercept form to find the slope.

3x + y = 9

y = -3x + 9

The slope is -3. The negative reciprocal of -3 is 1/3, because it has a product of -1.

Therefore, parallel slope to the line is: -3, while perpendicular slope is 1/3.

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The volume of the cylinder-shaped candle is 157 in³ which diameter and height are 5 inches and 8 inches.

What is cylinder ?

A cylinder is a three-dimensional geometric shape that has two parallel bases that are circular in shape and a curved lateral surface connecting the bases. The bases are located at the top and bottom of the cylinder. The distance between the bases is the height of the cylinder and the distance across the base is the diameter of the cylinder.

The volume of a cylinder is given by the formula V = [tex]\pi r^{2}h[/tex], where r is the radius and h is the height ,

To find the volume of the cylinder-shaped candle, we first need to find the radius. The diameter is given as 5 inches, so we can divide that by 2 to find the radius,

r = 5 inches / 2 = 2.5 inches

Now we can plug this value of r and the given height of 8 inches into the formula:

V = [tex]\pi r^{2}h[/tex] = π(2.5 inches)^2(8 inches) = 3.14 * 6.25 * 8 = 157 in³.

Hence , The volume of the cylinder-shaped candle is 157 in³ which diameter and height are 5 inches and 8 inches.

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The measure of each angle of triangle is,

m ∠C  = 46°

m ∠D  = 104°

m ∠DEF = 30°  

What is exterior angle theorem?

In Euclid's Elements, Proposition 1.16, known as the exterior angle theorem, states that the measure of a triangle's exterior angle is greater than either of its remote interior angles. Due to the fact that its proof is independent of the parallel postulate, this is a fundamental result in absolute geometry.

Let the triangle CDE is given.

m ∠D = (10y + 4)°,  m ∠C = (4y + 6)°,  m ∠DEF = 108°

We have to find the measure of each angle of triangle.

By using the Exterior angle theorem,

        m ∠C + m ∠D = m ∠DEF

(4y + 6)° + (10y + 4)° = 108°

                 14y + 10° = 108°

                         14y = 98°

                            y = 7°

⇒ m ∠C = 4y + 6 = 4(10) + 6 = 40 + 6 = 46°

 m ∠D = 10y + 4 = 10(10) + 4 = 100 + 4 = 104°

Since, the measure of three angle of triangle is 180°.

⇒ m ∠C + m ∠D + m ∠DEF = 180°

         46° + 104° + m ∠DEF = 180°

                  150° + m ∠DEF = 180°

                             m ∠DEF = 30°

Hence, the measure of each angle of triangle is,

m ∠C  = 46°

m ∠D  = 104°

m ∠DEF = 30°  

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Area of the enclosed figure is, 8√ 5 (5 + 2√5) units².

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Maria plots the following points on a coordinate grid.

Here, Points are,

⇒ (1, 3) (5, 7) (5, 5) (8, 9) (8, 3 ) (1, 3)

Clearly, It make pentagon.

And, Area of pentagon = 1/4 √5 (5 + 2√5) a²

Here, The side of pentagon = √ (7 - 3)² + (5 - 1)²

                                           = √4² + 4²

                                           = √32

                                           = 4√2

Thus, Area of figure = 1/4 √5 (5 + 2√5) a²

                               = 1/4 √5 (5 + 2√5) (4√2)²

                               = 8√ 5 (5 + 2√5)

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Answer:

y-9=5(x-6)

Step-by-step explanation:

the equation is y-y1=m(x-x1)

Answer:

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

Point-slope form:

Substitute:

The line is:

Answer: 24 = 4x

Step-by-step explanation:

First define a variable for the unknown quantity : in this situation we’ll let x represent the cost of one sandwich

now we know that 4 Sandwiches multiplied by x will equal 24

so 4x = 24 or 24 = 4x

Answer: Obtuse scalene

Step-by-step explanation: Hope it helps, please mark brainliest and give thanks.

Answer:

obtuse scale

Step-by-step explanation:

The equation that best represents the relationship is y = ½x + 2

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

From the values of x and y, let's check if the graph of y against x is linear

taking points x( 2,4) y(3,4)

slope =( 4-3)/4-2

slope = 1/2

therefore the graph is linear and slope is 1/2

the equation of a straight line = y − y 1 = m ( x − x 1 )

= y-3 = m( x- 2)

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

y = ½x -1+3

y = ½x +2

therefore the equation that best represents the relationship is y = ½x + 2

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Yes, 84 is divisible by 3. This can be demonstrated using the modulus operator.

The modulus operator returns the remainder of a division problem. In this case, we can divide 84 by 3 and see what the remainder is.

Calculation

84 ÷ 3 = 28

Remainder

84 % 3 = 0

Since the remainder is 0, this means that 84 is evenly divisible by 3. This can be shown mathematically as 84 = 3 × 28. In other words, 84 is a multiple of 3, meaning it is divisible by 3.

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The value of the missing angle x in the triangle is; x = 29 degrees

In a triangle, we know that the exterior angle is always equal to the sum of the interior opposite angles. This property is referred to as exterior angle property. This means that any two triangles will be similar if their corresponding angles tend to be congruent and the length of their sides will be proportional.

From the exterior angle property , when we apply it to the given triangle, we will have;

x + x = 58

2x = 58

x = 58/2

x = 29°

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70 is the greatest weight that Evelyn can put into the cardboard without going over the weight limit

From the question

Weight limit on one box = 28 kilograms

Weight of each box = ⅖ kilogram

To find the greatest number of boxes of pasta she can put into one cardboard box without exceeding the weight limit, we have:

G=28/2/5

To divide the fraction, change the division sign to multiplication and flip the fraction:

=28x5/2

=140/2

=70

Therefore, the greatest number of boxes Evelyn can put without going over the weight limit is 70 boxes

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Answer:

Step-by-step explanation:

the volume of rectangle is length * width * height

so v=(3x-4)*(3x+4)*2x=(9x^2-16)*2x=18x^3-32x

maybe the choice is D

Answer: Can you show the whole problem please?

Step-by-step explanation:

Answer:

y = [tex]\frac{3}{7}[/tex] x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (7, 6) ← 2 points on the line

m = [tex]\frac{6-3}{7-0}[/tex] = [tex]\frac{3}{7}[/tex]

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = [tex]\frac{3}{7}[/tex] x + 3 ← equation of line

Answer:

PLS GIVE IT TO ME

Step-by-step explanation:

Answer:

When the bases and exponents are both different, each needs to be evaluated separately:

   5^2 + 3^3 = 25 + 27 = 52

Step-by-step explanation:

1.  When the bases are the same, it is easy.  Just add the exponents:

   (5^2) * (5^4) = 5^6

2.  When the bases are different, but the exponents are the same, multiply the bases first and then use the same exponent:

    (5^3) * (4^3) = (20)^3

3.  When the bases and exponents are both different, each needs to be evaluated separately:

   5^2 + 3^3 = 25 + 27 = 52

Answer

192

Step-by-step explanation:

Given :Wendy is arranging books on the bookshelves in the school library. The total number of books she arranges is given by the equation b = 12r, where b is the total number of books and r is the number of rows. Each row contains the same number of books.

To Find: If Wendy arranged 16 rows, she arranged a total of ___ books.

Solution:

Since we are given an expression:

b = 12r

where b = total no. of books she arranged

r denotes the number of rows

Since we are asked  If Wendy arranged 16 rows, she arranged how many books

So, put r = 16 in equation

Thus b = 12*16

b = 192

Thus she arranged 192 books in 16 rows

Jayla's estimate for food is not a good estimate, given the number of days in a month and the amount she plans on spending.

Jayla has a food budget and does not want to spend more than $2 for breakfast, $8 for lunch, and $8 for dinner. The most spending per day therefore, is:

= 2 + 8 + 8

= $ 18

Given that there are 30 days in a month, the most spending estimate for the month is :

= Cost per day x Number of days

= 18 x 30

= $ 540

Jayla's estimate of $ 60 a month is therefore not good.

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The location of the vertex of this graph is (-1, -18)

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

The graph

The vertex of a graph is the minimum or the maximum of a graph

In this case, it is a minimum and the minimum is located at (-1, -18)

Hence , the vertex is (-1, -18)

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As per the given mass the potential energy of the ball will be equal to 450 J when it reaches the top to its ascent.

Here we have given that Mass of ball is 1.0kg

And we need to find the value of the kinetic energy  and here we also know that the velocity of the ball is 30m/s

As we all know that Kinetic energy is the energy possessed by a moving object. It is measured in joules, and then it depends on the mass (m) of the object and the velocity (v) by which it moves, then it can be written as,

=> K.E = 1/2mv²

=> KE = 1/2 x 1.0kg x (30m/s)²

when we simplify this then we get

=> KE = 0.5 x 1.0 x 900

Then the value of KE is  450J

Therefore the potential energy of the ball is 450 joules.

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A triangular frame has two edges lengths measuring 18 inches and 12 inches. The possible value of length for the third side is 32 in.

A triangular frame has two side lengths measuring 18 inches and 12 inches. as we know that the sum of any two sides of a triangle is always greater than the third side.

That is, the third side < 18 +12

third side < 30

according to the question, the option that fits perfectly is 32in.

Hence, The possible value of edges for the third side is 32 in.

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On solving the provided question, we can say that the inequality equation here will be The student is no more than 65 inches tall. P(x<  65) = 23.432

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

Mr. Jackson randomly selects a student in Math Club. Use the normal curve from Part A and the empirical rule to find each probability.

the inequality equation here will be

The student is no more than 65 inches tall. P(x<  65) = 23.432

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Step-by-step explanation:

-5° < 8°

that is all that is to it. really. you see ? an inequality, meaning that 2 terms or expressions are compared (like on a balance).

they can be totally balanced, that means they are equal, and then we have an equation.

or one can be bigger ("heavier"), and so one side is smaller and the other larger. and that is then not equal. we have an inequality.

scalene triangle is a type of triangle in which all the three sides have different lengths.

A triangle is scalene if all of its three sides are different (in which case, the three angles are also different). If two of its sides are equal, a triangle is called isosceles.

A scalene triangle is uneven in the sense that all three sides are of different lengths.

Explanation:

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The interest earned at 1.6% for 20 years will be $960.

Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used.

Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

Given that a new bank customer with ​$3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.6​%.

The interest after 20 years will be calculated as,

SI = ( P x R X T ) / 100

SI = ( 3000 x 1.6 x 20 ) / 100

SI = $960

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When the balloon is released from a height of 6 feet, the equation x = 3y + 6 reflects the balloon's height (y).

Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, the point-slope form, and the slope-intercept form are the three primary kinds of linear equations.  Algebra is used in many equations. When it comes to arithmetic, algebra is used when it's difficult to compute an exact amount.

given

When a balloon is released, it rises at a constant rate of 3 feet per second from a height of 6 feet.

When the balloon is released from a height of 6 feet, the equation x = 3y + 6 reflects the balloon's height (y).

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The additive inverse of 19 /- 6 is -19 /+ 6 and the additive inverse of 2 3 is -2 3.

Additive inverse is a mathematical term that refers to when two numbers are combined and their sum is equal to zero. To calculate the additive inverse of a fraction, you need to change the sign of the numerator and denominator. In the case of 19 /- 6, the -6 is already negative, so you just need to change the sign of the numerator from 19 to -19. Similarly, for 2 3, you need to change the sign of the numerator from 2 to -2. This would mean that the additive inverse of 19 /- 6 is -19 /+ 6 and the additive inverse of 2 3 is -2 3.

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The circle's shaded area, which has a sector angle of 50 degrees and an arc length of 5/3 pie, has a surface area of 15.67m2.

A circle is created in the plane by each point that is a specific distance from another point (center).  Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.

given

A / θ = πr² / 2π

A / θ = r² / 2

A = r² * θ / 2

A = (5/3)^2 * 25

A  = 15.67 m2

The circle's shaded area, which has a sector angle of 50 degrees and an arc length of 5/3 pie, has a surface area of 15.67m2 .

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The completed question is :-

In circle E , the length of FG = 5/3π  and ∠FEG = 50°  . Find the area shaded below. Express your answer as a fraction times .