The longer leg is the one that faces the 60-degree angle.
Any triangle with a 90-degree angle is considered a right triangle. A unique variety of right triangle with a 30-degree angle and a 60-degree angle in addition to the right angle is known as a 30-60-90 triangle.
Triangle Properties 30-60-90
A triangle with sides of 30-60-90 can be recognized by how they relate to the angles.
The shorter leg is the one that faces the 30-degree angle.
The longer leg is the one that faces the 60-degree angle.
The hypotenuse is the side that faces the right angle of 90 degrees.
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A cylinder-shaped candle has a diameter of 5 inches and a height of 8 inches. what is the volume of the cylinder? use 3.14 for pi. round to the nearest tenth, if necessary. responses 62.8 in³ 62.8 in³ 125.6 in³ 125.6 in³ 157 in³ 157 in³ 628 in³
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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What are the additive inverse of 19 /- 6 and 2 3?
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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Prove that is a right triangle. Select the correct answer from each drop-down menu.
is congruent to because segment was constructed so that . is congruent to because segment was constructed so that . Since is a right triangle, by the
. We are given that . Since and , by the
. Also, by the
. Taking the square root of both sides of the equation gives . So, is congruent to by the definition of congruence. Applying the
, . By CPCTC, . Therefore is a right angle and is a right triangle.
ABC is a right-angled triangle.
What 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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what is the location of the vertex of this graph?
The location of the vertex of this graph is (-1, -18)
How to determine the vertex of the graphFrom 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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When the lengths of the All sides are diffrent that type of triangle is called *?
scalene triangle is a type of triangle in which all the three sides have different lengths.
What is Scalene triangle?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:
A scalene triangle has all side lengths of different measures. No side will be equal in length to any of the other sides in such a triangle. In a scalene triangle, all the interior angles are also different.A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures. However, the sum of all the interior angles is always equal to 180 degrees. Thus, it meets the angle sum property of the triangle.The scalene triangle (also known as the interscalene triangle) is located laterally at the root of the neck and is the space through which the roots and trunks of the brachial plexus and the third part of the subclavian artery exit the neckTo learn more about scalene triangle refers to;
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write the point-Slope form of the line passing through the point (6,9) with a slope of 5
I need answers fast please!
Answer:
y-9=5(x-6)
Step-by-step explanation:
the equation is y-y1=m(x-x1)
Answer:
The point-Slope form of the line is y - 9 = 5(x - 6)------------------------------
Point-slope form:
y - y₁ = m(x - x₁), where m - slope, (x₁, y₁) - a point on the lineSubstitute:
m = 5, (x₁, y₁) = (6, 9)The line is:
y - 9 = 5(x - 6)\Select all the correct answers. A triangular frame has two side lengths measuring 18 inches and 12 inches. Which values are possible lengths for the third side? 30 in 6 in 28 in 32 in 20 in 24 in
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.
What is a triangle?Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. The symbol for a triangle having vertices A, B, and C is ABC.In Euclidean geometry, any three points that are not collinear identify a distinct triangle and a distinct plane at the same time (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and that triangle is contained in just one plane.All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however in higher-dimensional Euclidean spaces, this is no longer the case. Except as specifically stated, this article is about triangles in the Euclidean plane and general Euclidean geometry.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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What are the slopes of lines parallel and perpendicular to the line 3x+y=9
(Select one answer per blank).
The slope that is parallel to 3x + y = 9 is -3.
Perpendicular slope is 1/3.
What are the Slopes of Parallel and Perpendicular Lines?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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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.
If Wendy arranged 16 rows, she arranged a total of
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
#5: A balloon is released from a height of 6 feet. The balloon rises at a constant rate of 3 feet per second. Which equation represents the height of the balloon (y), in feet, x seconds after it is released? A.x = 3y + 6 B. y = 3x + 6 C. x = 6y + 3 D. y = 6x + 3
When the balloon is released from a height of 6 feet, the equation x = 3y + 6 reflects the balloon's height (y).
what is equation ?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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Use the Exterior Angle Theorem to find the measure of each angle.
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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Two quantities are related, as shown in the table:
x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship? (4 points)
The equation that best represents the relationship is y = ½x + 2
What is linear equation?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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Is 84 divisible by3?
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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A 1. 0 kg ball i thrown into the air with an initial velocity if 30 m/. How much gravitational potential energy doe the ball have when it reache the top of it acent?
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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Which type of triangle has side measures of 6 cm, 7 cm, and 12 cm and one angle with a measure of 135°? A. acute isosceles B.right scalene C.obtuse equilateral. D.obtuse scalene (please answer this exact)
Answer: Obtuse scalene
Step-by-step explanation: Hope it helps, please mark brainliest and give thanks.
Answer:
obtuse scale
Step-by-step explanation:
Answer!! What is Simplified?
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
In circle E the length of FG is 5/3 pie and m
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.
what is circle ?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 .
- Seth bought 4 sandwiches. The bill was at the most $24.
a. Write and solve an inequality to represent the cost of each sandwich.
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
new bank customer with $3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.6%. a. How much interest will the customer earn in 20 years? b. What will the account balance be after 20 years?
The interest earned at 1.6% for 20 years will be $960.
What is simple interest?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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Maria plots the following points on a coordinate grid. Then, she connects each plotted point to the previous one in the order shown to form a figure. What is the area, in square units, of the enclosed figure? (1,3) (5,7) (5,5) (8,9) (8,3) (1,3)
Area of the enclosed figure is, 8√ 5 (5 + 2√5) units².
What is an expression?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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Jayla is creating a food budget. Each day, her goal is to spend no more than $2 for breakfast, $8 for lunch, and $8 for dinner. Since there are about 30 days in a month, she estimates she will spend roughly $60 a month on food. Is that a good estimate?
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.
How to estimate the food budget ?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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solve this please!!!!
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
What do you do when exponents are different bases?
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
Evelyn is donating boxes of pasta to a local food pantry. The weight limit on one cardboard box is 28 kilograms. If each box of pasta weighs kilogram,what is the greatest number of boxes of pasta Evelyn 2 5 can put into one cardboard box without going over the weight limit?
70 is the greatest weight that Evelyn can put into the cardboard without going over the weight limit
How to calculate greatest weight that can be put into the cardboard?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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Part B: Mr. Jackson randomly selects a student in Math Club. Use the normal
curve from Part A and the empirical rule to find each probability.
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
What is inequality?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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Luis works as a salesperson
Answer: Can you show the whole problem please?
Step-by-step explanation:
Jerrod had scores of 75, 82, 94 and 77 on his first four history tests. What must he score on the next test to have an average of at least 85? (Note: Remember that average is found by dividing the sum of the numbers, by the number of numbers.)
The score on his next test must be at least 97 to get an average score of at least 85.
What is Average Value?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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How do I do this I need help
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.
Find each measure.
*PLEASE HELP! WILL GIVE BRANLIEST!*
The value of the missing angle x in the triangle is; x = 29 degrees
How to find the missing angle of the triangle?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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go to the link ONG i will give brainly bc idc and i never use this so ill give anyone it OMM
Answer:
PLS GIVE IT TO ME
Step-by-step explanation: