Answer:
50%
Step-b50%y-step explanation:
Joint relative frequency
Please help with 11!!!
Answer:
Equation 1: (500×5)+75
Equation 2: (20×5)×7
Total Revenue: $1,875
Step-by-step explanation:
For equation 1 we multiply the companys $500 an hour flat rate by the number of hours the party was (5), then add the company's $75 set up fee for a total of $2,575.
For equation 2 we multiply the company's hourly pay (20) by the number of hours worked (5), after that we multiply the number of employees (7) for a total of $700.
Finally to figure out the actual revenue from the event we subtract the amount the company paid the employees ($700) from the total paycheck for hosting the party ($2,575) for a final total of $1,875.
Group of friend decided to equally hare a package of trading card if there were 48 card in the package and each peron receive 12 how many friend were in the group
There are 4 friends in the group.
Poker: In poker, the number of each card in the deck is important. A standard deck of poker cards has 52 cards, with 13 cards in each of the four suits (hearts, diamonds, clubs, spades). Each suit has cards numbered 2-10, plus a jack, queen, king and ace. This allows for the calculation of odds and probability in the game.
If each person received 12 trading cards and 48 cards in the package, you can use division to find how many people are in the group.
We know that:
48 trading cards / 12 trading cards per person = 4 people
Therefore, there are 4 friends in the group.
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You can use division to determine the number of people in the group if each person got 12 trading cards and there were 48 total cards in the package.
12 trading cards per individual times 48 trading cards equals four people.
As a result, the company consists of 4 friends.
Lines ENF are parallel the M<9 and m<5= 55
The angle measures that are correct include:
m2 = 125°
m8 = 55°
m14 = 100°
m16 = 80°
How to illustrate the angle?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Here, the measurement of the angles are as follows;
m3 = 55°
m8 = 55°
m12 = 100°
m14 = 100°
m16 = 80°
m9 = 80°
m12 = 80° (opposite angles)
m10 = m11 = 100° ( 180° - 100°)
m13 = m16 = 80°
m14 = m15 = 100°
m14 = 100°
m16 = 80°
m5 = m8 = 55°
m2 = m3 = 125°
m2 = 180° - 55° = 125°
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Lines e and f are parallel. The m9 = 80° and m5 = 55°. Which angle measures are correct? Check all that apply. m2 = 125° m3 = 55° m8 = 55° m12 = 100° m14 = 100° m16 = 80°
Goran will run at most 27 miles this week. so far, he has run 13 miles. what are the possible numbers of additional miles he will run? Use T for the number of additional miles he will run. Write ur answers as an inequality. solved for T
Answer: Goran will run at most 27 miles this week, and he has already run 13 miles, so the number of additional miles he will run is given by the difference of 27 - 13 = T.
Therefore, T = 27 - 13 = 14 miles
We can express this as an inequality:
T <= 14
This inequality represents that T, the number of additional miles he will run, can be any number less than or equal to 14.
Another way to express this is T <= 27-13
So the possible numbers of additional miles he will run are T <= 14.
Step-by-step explanation:
I need to know the steps to solve it
The value of x that makes both triangles congruent is x = -1 and x = 5
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Two triangles are congruent if their corresponding sides are equal to each other and their angles are also equal.
Since triangle ABC is congruent to DEF, hence:
BC = EF
Substituting:
4x - 2 = x² - 7
x² - 4x - 5 = 0
x² - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
(x + 1)(x - 5) = 0
x = -1 and x = 5
The value of x is x = -1 and x = 5
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Football party favor come in package like the one hown how much it cot to buy a 56 party favor Think about how you can model with math to help olve the problem
It would cost $224 to buy 56 party favors.
A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation. It is a mathematical problem expressed entirely in words typically used as an educational tool.
Word problems are regarded as an important aspect of the basic curriculum because they require students to apply their understanding of various concepts to real-life settings.
If the packages cost $4 each then 56 packages will cost 56 * 4 dollars.
we get, 56 * 4 = $224
Thus, it would cost $224 to buy 56 party favors.
Complete question: Football party favors come in packages like the one shown. How much would it cost to buy 56 party favors? Think about how you can model with math to help solve the problem. It's $4 per package.
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Work out the value of 3/3 × 10
Give your answer as a whole number or as a
fraction in its simplest form.
Answer:
10
Step-by-step explanation:
Since 3/3 = 1, then:
3/3 × 10 = 1 × 10 = 10
Please help. I will reward brainiest.
Answer:
C
Step-by-step explanation:
It can't be a or d because 15.75x needs to be greater than 145, so in c the how many he sells would represent the x value.
How many miles of track does the crew have left to lay after 19 days
The number of miles that the crew has left to lay after 19 days is given as follows:
54 miles.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing the rate of change.b is the intercept, representing the initial value.The parameters for this problem are given as follows:
m = -6, b = 168.
Hence the function is:
y = -6x + 168.
The amount of miles left after 19 days is obtained as follows:
y = -6(19) + 168
y = 54 miles.
Missing InformationThe text of the problem is:
"A railroad crew can lay 6 miles of track each day. They need to lay 168 miles of track. "
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What is the sum of 4?.
The Sum of 4 is a concept that emphasizes the fact that there are multiple, if not infinite, ways to reach certain results, goals, dreams, or destinations.
In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.
Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.
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8t^2-14t+3 factored to (at-1) (bt+c)
The value of a is 4 , b is 2 and c = -3 after factorising 8t² - 14t + 3
What is Factorisation ?The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.
Factorization is the process of dividing a whole into components that, when multiplied together, equal the original number.
Factoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.
The subsequent stages aid in the polynomial factoring process. The steps to factorizing a polynomial are listed below.
Check to see if the polynomial's terms have a common factor.Choose the best technique for factoring polynomials. You can determine the polynomial's components by regrouping or by using algebraic identities.Polynomial should be written as the sum of its components.The function is 8t² - 14t + 3
so factorising :
8t² - 14t + 3 = 8t² - 12 t - 2t + 3 = 4t(2t - 3) - (2t - 3)
= (4t - 1)(2t -3)
The value of a is 4 , b is 2 and c = -3
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How do you find the length of the third side of an obtuse triangle?.
The law of Sines is used to find the length of the third side of an obtuse triangle. The value of a i.e., third side length is equals to 6.065 units.
In geometry, obtuse triangles are defined as the triangles with an obtuse angle, which is an angle measuring greater than 90°. According to the law of sines of triangles if a triangle has sides a, b, and c, and angles A, B, and C, where side a has opposite angle A, side b has opposite angle B, and c has opposite angle C, then
sinA/a = sinB/b = sinC/c
The sum of all interior angles of a triangle is 180°. If we have two of the sides of an obtuse triangle, and two of the angles of an obtuse triangle, then we can use the law of sines to determine the third side of the obtuse triangle. Let's consider an obtuse triangle ABC present in above figure. We want to find the length of side a. We have, AB = 8 units , AC = 5 units, BC = a units.
∠A = 32° , ∠B =40° , ∠C = obtuse angle
=>∠C = 180°-∠A - ∠B = 180°- 32°- 40° = 108°
From above formula, sinA/a = sinB/b= sinC/c
=> sin 32°/5 = sin 40°/a = sin 108°/8
=> a = 5 sin 40°/ sin 32°
=> a = 5×0.6428/0.5299
=> a = 6.06529533874
=> a ≈ 6.065
Therefore, the length of third side is 6.065 units.
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What is the probability that a randomly chosen college student exercises in the morning or afternoon? 0. 37 0. 39 0. 62 0. 76.
The probability that a randomly chosen college student exercises in the morning or afternoon is 0.76
We have given that the M be the event that the student exercises in the morning and A be the event that the student exercises in the afternoon.
To find : The probability that a randomly chosen college student exercises in the morning or afternoon
P(M) = 0.25+0.37 = 0.62
P(A) = 0.14+0.37 = 0.51
P(M and A) = 0.37
Now,
P(M or A) = P(M) + P(A) - P(M and A)
= 0.62 + 0.51 - 0.37
= 0.76
Hence, Option last 0.76 is the correct choice.
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evaluate the trigonometric function using its period as an aid
Functions y = A sin(Bx + C) and y = A cos(Bx + C) have periods of 2 /|B| radians each. A function's frequency is equal to the reciprocal of its period.
What is a period in trigonometric functions?The horizontal distance covered prior to the values repeating is the period of a trigonometric function. The period is for the two graphs, and. You may recall that these numbers are the same after the unit circle has made one full rotation.Finding the value of f(x) =... or y =... that corresponds to a given value of x is the definition of function evaluation. Simply swap out all instances of x with the value that has been allocated to x to do this.You must divide pi by the absolute value of your B if either the tangent or cotangent of your trig function is present. Since our sine function, f(x) = 3 sin(4x + 2), has a period of 2 pi divided by 4, our B value, it has a sine function.To learn more about equal refer to:
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Why are 30 60 90 and 45 45 90 triangles called special right triangles?.
30-60-90 and 45-45-90 triangles are called special right triangles because they have specific ratios of their side lengths.
A 30-60-90 triangle is a special right triangle in which the angles measure 30 degrees, 60 degrees and 90 degrees, and the side length ratio is 1: √3: 2.
where the hypotenuse is twice the length . 45-45-90 triangle is a special right triangle in which the angles measure 45 degrees, 45 degrees and 90 degrees, and the side length ratio is 1:1: √2, where the hypotenuse is the square root of 2 times the length of each leg.
These ratios are unique and special among right triangles, which makes these triangles special. They are also easy to remember and use in various mathematical calculations. Because of this property, they are widely used in trigonometry and geometry and are very useful in solving problems related to the right triangles in general.
Additionally, these triangles have certain symmetry and specific relationships between the legs and hypotenuse, which makes it easy to calculate unknown sides or angles in a triangle. This makes them very useful in real-world applications such as construction, engineering, and design.
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The table below shows the coordinates of a figure that was transformed. Which is a correct description of the transformation? Question 4 options: Rotation 180° clockwise B. Reflection over the x-axis. Translation 5 units left and 2 units down. Translation 10 units left and 4 units down.
HELP PLEASEEEE
A correct description of the transformation include the following: D. translation 10 units left and 4 units down.
What is a translation?In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.
On the other hand, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.
By translating the pre-image of triangle ABC vertically down by 4 units and horizontally left by 10 unit, the coordinates of the image of triangle A'B'C' include the following:
(x, y) → (x - 10, y - 4)
Coordinate A = (5, 2) → Coordinate A' (5 - 10, 2 - 4) = (-5, -2)
Coordinate B = (6, 1) → Coordinate B' = (6 - 10, 1 - 4) = (-4, -3)
Coordinate C = (4, 5) → Coordinate C' = (4 - 10, 5 - 4) = (-6, 1)
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Complete Question:
The table below shows the coordinates of a figure that was transformed.
Pre-Image Image
A(5,2) A'(-5,-2)
B(6,1) B'(-4,-3)
C(4,5) C'(-6, 1)
Which is a correct description of the transformation?
Question 4 options: Rotation 180° clockwise B. Reflection over the x-axis. Translation 5 units left and 2 units down. Translation 10 units left and 4 units down.
A gas station employee monitored the gas sales one day. The data showed that 80% of customers purchased regular gas. Of the customers who purchased regular gas, 10% paid in cash, whereas 40% of the customers who did not purchase regular gas paid in cash. What percentage of the customers paid in cash? 48% 20% 16% 50%
Answer: 16%
Step-by-step explanation: If 80% of customers purchased regular gas and 10% of those who purchased regular gas paid in cash, then 8% paid in cash. If 100-80=20% of customers purchased something other than regular gas and 40% of those who did paid in cash, than another 8% paid in cash. 8+8=16, so (c 16 is the answer.
BONUS: Find the value of x. Show your work ACDE - AFGH D 7x 8x - 1 E F G 9x 10x + 1 H
The value of x is 1.
Comparing similar triangles.On comparison, when two or more triangles have some common relations with respect to their sides or measure of internal angles, they are said to be similar.
To find the value of x, compare the corresponding sides of the two triangles.
To have;
7x/ 9x = (8x - 1)/ (10x + 1)
9x (8x - 1) = 7x(10x + 1)
72x^2 - 9x = 70x^2 + 7x
collect like terms
72x^2 - 70x^2 - 9x + 7x = 0
2x^2 -2x = 0
2x(x - 1) = 0
2x = 0 or x - 1 = 0
x = 0. or x = 1
Therefore,
x = 1
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Answer:
Step-by-step explanation:
ur mom ur mommy
What is Y form called?.
Y form is the slope-intercept form of a straight line.
Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.
y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.
The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.
To find the equation of the straight line, we use the slope-intercept form, y = mx + b, where m is the slope of the line, b is the y-intercept of the line.
We can find the equation of a line in the form of y = mx + b, if the coordinates of points forming the line are known to us.
Thus, Y form is the slope-intercept form of a straight line.
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While using factorization method solve the following quadratic equation
1. 2t+5t+2=0
2. Y+2y+1=25
3.9-36x=36x²
Step-by-step explanation:
1) 2t + 5t + 2 = 0
Add 2t + 5t = (2+5)t = 7t
7t + 2 = 0
Substract 2 from both sides
7t + 2 - 2 = 0 - 2
7t = -2
Divide both sides by 7
7t/7 = -2/7
[tex] \sf \: t = \frac{ - 2}{7} [/tex]
[tex] \sf --------------------------------------------[/tex]
Y+2y+1=25
3y + 1 = 25
3y = 25 - 1
3y = 24
y = 24/3
y = 8
[tex] \sf --------------------------------------------[/tex]
9−36x=36x2
Step 1: Simplify both sides of the equation.
−36x+9=36x2
Step 2: Subtract 36x^2 from both sides.
−36x+9−36x2=36x2−36x2
−36x2−36x+9=0
For this equation: a=-36, b=-36, c=9
−36x2+−36x+9=0
Step 3: Use quadratic formula with a=-36, b=-36, c=9.
x=
−b±√b2−4ac/2a
x=−(−36)±√(−36)2−4(−36)(9)/2(−36)
x=36±√2592/−72
x=−1/2 + −1/2√2 or x=−1/2 + 1/2√2
Ryan earn $5 for each mall dog he walk and $8 for each large dog he walk. Today he walked dog and made a total of $49. How many mall dog did Ryan walk?
Ryan walked _______ blank mall dog
The values of x and y in the equations are 3 and 5. Thus, Ryan walked 3 small dogs.
Let L be a giant dog and s be a tiny dog. What we do know is this:
s + L = 9 (9 dogs walked) (9 dogs walked)
(Money received from walking dogs is $51; 5s + 8L = 51)
To address a problem, we can employ substitution or elimination. I'll substitute in this situation (remove L from both sides):
s = 9 - L
5(9 - L) + 8L = 51
Distribute
45 - 5L + 8L = 51
45 + 3L = 51
Subtract 45:
3L = 6
Divide by 3:
L = 2
s = 9 - 2
s = 7
check:
5 * 7 + 8 * 2 = 51
35 + 16 = 51
51 = 51
The values of x and y in the equations are 3 and 5. Thus, Ryan walked 3 small dogs.
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What percent of the men surveyed shop online? Round your answer to the nearest whole number percent.
27.5% percent of the men surveyed shop online.
How do I calculate a percentage?When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage.
Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. (Value/Total Value)100% is the formula used to calculate percentages.
The simplest way to use percentages is to compare two numbers, with the second number being rebased to 100. Consider that we are curious about the proportion of employed women who are female.
A % is a number or ratio stated as a fraction of 100 in mathematics (from the Latin per centum, "by a hundred"). The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed.
Store = 37 women
Total women: 37/49 = 0.75%
Men: shop equals 52
Total men: 11 /40 = 27.5%
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Write 28+24 as a product of two factors using the GCF and the distributive property.
Answer:
28+24 can be written as a product of two factors using the GCF and the distributive property as: (12 x 2) + (12 x 2) = 12 x (2+2) = 12 x 4 = 48
Slices of cake were sold at a bake sale.
In total, Archie sold 33 cakes and Pam sold
7³ cakes.
How many more cakes than Archie did Pam
sell?
Give your answer as a mixed number in its
simplest form.
The point that is equally spaced from a triangle's three vertices is known as the circumcenter.Triangle ABC's equilateral circumcenter is (-5, 2) .
What is the circumcenter?The point that is equally spaced from a triangle's three vertices is known as the circumcenter.
The triangle's three vertices are all located at the center of the circle.We may insert the coordinate values for the triangle ABC's vertices A(-5,3), B(5,8), and C(-5.8) into the formulas above to determine its circumcenter.
x = (8 - 3) * (-5.8^2 + 3^2 - 5^2 - 8^2)
- (3 - 8) * (-5^2 + 3^
2 - (-5) (-5)
^2 -3^2) / 2 * (3 - (-5))
* (8 - 3) - (3 - 8) * (-5.8 - (-5))
x = (-5) (-5)
y = (3 - (-5.8))
* (-5^2 + 3^2 - (-5)^2 -3^2)
- (-5 - (-5))
* (3^2 + 3^2 - (-5.8) (-5.8)
^2 - 8^2)
/ 2 * (3 - 8) (3 - 8)
* (-5 - (-5))
- (3 - 8) * (3 - (-5.8))
y = 2
The circumcenter of triangle ABC is hence (-5, 2)
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Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Show your work.
Answer: To find the coordinates of P, we will use the part-to-whole ratio of 1 to 5. This means that the distance from A to P is 1/6 of the distance from A to B.
We can find the distance from A to B by using the distance formula:
d = √((x2-x1)² + (y2-y1)²)
where (x1, y1) and (x2, y2) are the coordinates of A and B, respectively.
So, the distance from A to B is:
d = √((1-(-9))² + (8-3)²) = √((10)² + (5)²) = √(100 + 25) = √125 = 5√5
Since P partitions AB with the ratio 1 to 5, the distance from A to P is 1/6 of the distance from A to B, which is (1/6) * (5√5) = √5
To find the coordinates of P, we will use this distance and the direction from A to B to find the coordinates of P.
The direction from A to B is:
(1 - (-9))/(8 - 3) = 10/5 = 2
So, the slope of line AB is 2. Therefore, the slope of line AP is -1/2 (perpendicular to AB)
We know that A = (-9, 3) and the slope of line AP = -1/2. We can use this to find the equation of the line AP:
y - 3 = -1/2(x + 9)
y = -1/2x - 3/2 + 3
y = -1/2x + 3/2
Since the point A is on the line, we can substitute the coordinates of A into the equation:
3 = -1/2*(-9) + 3/2
3 = 4.5
This is not true, so we can say that the equation is wrong.
To find the equation of line AP, we can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
So, the equation of line AP is:
y - 3 = -1/2(x + 9)
Now we know that the point P is on the line AP and the distance from A to P is √5.
We can use this information to find the coordinates of P by moving along the line AP by √5 units in the direction of P.
To move in the direction of P, we need to move parallel to the line, which means we need to keep the slope of the line same.
So we can move
Step-by-step explanation:
Aume that one unit i old on April 27 for "$231. " Determine the gro profit for April and ending inventory on April 30 uing the (a) firt-in, firt-out (FIFO); (b) lat-in, firt-out (LIFO); and (c) weighted average cot method
(a) FIFO: The oldest unit would be the one purchased on April 27 for $231. Therefore, the gross profit for April would be the difference between the selling price and the cost of the unit sold, which is not provided in the information given. The ending inventory on April 30 would be zero, as all units were sold.
(b) LIFO: The newest unit would be the one purchased on April 27 for $231. Therefore, the gross profit for April would be the difference between the selling price and the cost of the unit sold, which is not provided in the information given. The ending inventory on April 30 would be one unit, as one unit was not sold.
(c) Weighted Average Cost: The cost of the unit sold would be the average cost of all units purchased, which is $231. Therefore, the gross profit for April would be the difference between the selling price and the average cost of all units, which is not provided in the information given. The ending inventory on April 30 would be zero, as all units were sold.
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The newest unit would be the one purchased on April 27 for $231. Therefore, the gross profit for April would be the difference between the selling price and the cost of the unit sold, which is not provided in the information given. The ending inventory on April 30 would be one unit, as one unit was not sold.
What is the multiplication rule example?.
Examples of the rules followed while applying multiplication are :
1. 0 × 9 = 0
2. 1 × 7 = 7
3. 12 × 10 = 120 , 12 × 100 = 1200.
4. 11 ×12 = 12 ×11
As given in the question,
Examples of the multiplication rules are :
1. Multiply any number by zero result is zero.
Example : 0 × 9 = 0
2. Multiply One to any real number result is the number itself.
Example : 1 × 7 = 7
3. Multiply any real numbers with 10 , 100 you have just add number of zero present.
Example : 12× 10 =120
12× 100 =1200
4.Order of the multiplication does not affect the result.
Example : 11 × 12 = 12 × 11
Therefore, the examples of multiplication rule are :
1. 0 × 9 = 0
2. 1 × 7 = 7
3. 12 × 10 = 120 , 12 × 100 = 1200.
4. 11 ×12 = 12 ×11
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The sides of a triangle are 56, 55, and 43. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
The triangle with sides 56 , 55 and 43 is acute triangle
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ABC
Now , the base of the triangle is BC
The measure of BC = 43
The height of the triangle is AB
The measure of AB = 55
The hypotenuse of the triangle is AC
The measure of AC = 56
Now , if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
On simplifying the equation , we get
BC² + AB² > AC²
Substituting the values in the equation , we get
43² + 55² > 56²
1849 + 3025 > 3136
4874 > 3136
Hence , it is an acute triangle
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What is the solution to the system of equations?.
A collection of values for the variable that simultaneously satisfy each equation in a system of equations is referred to as the solution.
Typically, a system of linear equations consists of a pair of two-variable linear equations.
1. Examine substitution and elimination as two strategies for algebraically resolving systems of linear equations.
2. Use graphical representations of systems of linear equations to better grasp when these systems have a single solution, none at all, or an unlimited number of solutions.
3. Learn about algebraic techniques for counting the number of solutions to systems with two linear equations.
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If DE=8 and EF=3, what is DF?
If DE=8 and EF=3 then the length of DF is 8.54 units.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
DEF is a given triangle.
DE is the opposite side of the triangle.
EF is the adjacent side of the triangle.
DF is hypotenuse.
By using pythagoras theorem we find the DF.
DE²+EF²=DF²
8²+3²=DF²
64+9=DF²
73=DF²
Take square root on both sides
DF=√73=8.54
Hence, the length of DF is 8.54 units.
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