The value of x is 22.5528.
Let ABC be the triangle , <A = 70, <B = 30 ,<C = 80.
Sum of angles in a triangle is 180.
70 + 30 + <C = 180
<C = 180 - 100
<C = 80.
Let sides be a = x , b = 12 and c = ?
According to sines law,
a/sin A = b/sin B = c/sin C
substitute a ,b,A,B values
a/sin A = b/sin B
x/sin 70 = 12/sin 30
x = 0.9397*12/1/2
= 11.2764*2/1
x = 22.5528.
Therefore the value of x is 22.5528.
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A carpet installer measures three rectangular bedrooms for new carpeting how much carpet is needed for the three bedrooms bedroom a 3.1 m x 3.1 m bedroom be 2.9 m x 3.2 m bedroom c2.5 m x 3.4 m
The 27.4 m² of carpet is needed for three bedrooms.
Firstly we will calculate the area of each room.
Area of bedroom a = 3.1 × 3.1
Area of bedroom a = 9.61 m²
Area of bedroom b = 2.9 × 3.2
Performing multiplication on Right Hand Side of the equation
Area of bedroom b = 9.29 m²
Area of bedroom c = 2.5 × 3.4
Area of bedroom c = 8.5 m²
Total area of all the rooms = 9.61 + 9.29 + 8.5
Performing addition on Right Hand Side of the equation
Total area of all the rooms = 27.4 m²
Hence, 27.4 m² carpet is required for three bedrooms.
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Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer: 0.86 pounds of fruit
Step-by-step explanation:
8.3-7.44=0.86
how do u solve these simultaneous equations
y=3x+5
y=4x^2+x
The solutions to the given simultaneous equations as required in the task content are; (1.4, 9.2) and (-0.9, 2.3).
What is the solution to the simultaneous equations?It follows from the task content that the solution to the simultaneous equations as given in the task content is to be determined.
Given: y = 3x + 5 and y = 4x² + x.
Therefore, since y = y; it follows that the equation which holds true is;
3x + 5 = 4x² + x
4x² - 2x - 5 = 0.
Therefore, the quadratic equation above can be solved for the values of x so that by approximation, we have;
x = 1.4 OR x = -0.9.
Therefore, the corresponding values of y are;
y = 3(1.4) + 5 = 9.2
OR
y = 3(-0.9) + 5 = 2.3
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determine whether the lines are parallel, intersect, coincide y = x-7, y = -x + 3
The given two equations are Perpendicular to each other .
What is intersection of lines ?
It is known as an intersection of lines when two lines have exactly one point in common. A point is shared by the connecting lines. The point of intersection is the same place that may be found at the intersection of all intersecting lines. When two or more straight lines cross each other in a plane, they are said to be intersecting lines. An intersection point will be present for the two non-parallel straight lines that are coplanar. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.
Here the equation of line is y=mx+b .
Where m = slope . then,
=> y = x-7 where here slope m1= 1 and
=> y = -x+3 where here slope m2 = -1 .
Here the m1= -m2
Hence the given two equations are Perpendicular to each other .
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Round to the nearest hundredth. 44.242
Answer:
44.24
Step-by-step explanation:
The 2 in the thousandths place is lower than 5 therefore it does not round the 4 to a 5
Answer:
44.24
Step-by-step explanation:
hopes this helps please mark brainliest
1. A typical Chinese restaurant will often feature a Special Dinner, in which the customer has the choice of ordering one appetizer and one entree.
a. If there are 8 appetizers and 11 entrees, how many different Special Dinners
are there?
b. If there are 12 appetizers and 7 entrees, how many different Special Dinners
are there?
a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
Given that,
In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.
We have to find
a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.
b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.
We solve
a) We just multiply
8×11=88
b) 12×7=84
Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
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Please help, I am timed and I have no clue what to do here!
Answer:
Step-by-step explanation:
Re-order terms so constants are on the left
Then divide both sides by the same factor its -2
then Simplify answer is 1
What is the answer to this problem?
Answer:
$22,000 at 5%, $10,000 at 11%
Step-by-step explanation:
Let x be the amount invested at 5%.
[tex].05x = .11(32000 - x)[/tex]
[tex].05x = 3520 - .11x[/tex]
[tex].16x = 3520[/tex]
[tex]x = 22000[/tex]
$22,000 at 5%, $10,000 at 11%
Please help me with this question
Consider the line y=-3/4x-9.
Find the equation of the line that is perpendicular to this line and passes through the point (-4, 2).
Find the equation of the line that is parallel to this line and passes through the point (-4, 2).
Equation of perpendicular line:
Equation of parallel line:
Answer:
Equation of Perpendicular Line: 4x-3y=22
Equation of parallel line:3x+4y+4=
Give the domain and range of the relationship. List items from least to greatest. Do not include duplicates. Determine whether or not the relationship is a function.
Answer:
Domain: {2, 3, 4, 5} Range: {12, 13, 14}
Step-by-step explanation:
The relationship is a function even though two different inputs have the same output.
3409.1 in exponential form
3409.1 In exponential form is 3.4091 * 10^3
What is exponential form?Writing a number in exponential form is a way of writing numbers using base and exponents
Scientific notations is among the ways numbers appears in exponential forms
using scientific notation we have
= 3409.1
converting to fractions
= 34091 / 10
applying the scientific notation
= 3.4091 / 10 * 10000
eliminating the fraction by dividing by 10
= 3.4091 * 1000
applying exponential notation
= 3.4091 * 10^3
rewriting gives
= 3.4091 E+3
In scientific notation 10^3 is E+3 and it is called kilo and can be represented as k
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20-foot extension ladder set base six feet from house How far up will ladder reach?
The top of the 20-foot ladder used for painting will be 19 feet up from the base of the house
How to determine how high up the house the ladder will goinformation given in the question
Brian borrowed a 20-foot extension ladder: hypotenuse = 20-foot ladder
he sets the base of the ladder six feet from the house
adjacent = 6 feet from the house
opposite = how far up will the top of the ladder reach = ?
The problem is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = adjacent² + opposite²
substituting the values into the equation
let x be thow far up will the top of the ladder reach
20² = 6² + x²
400 = 36 + x²
400 - 36 = x²
x² = 364
x = √364
x = 19.08
The ladder Brain borrowed will go 19 feet high
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complete question
Brian borrowed a 20-foot extension ladder to use to paint his house. If he sets the base of the ladder six feet from the house how far up will the top of the ladder reach?
One-third of a number decreased by six equals eight. What is the number?
Answer:
42
Step-by-step explanation:
6+8=14x3=42
42/3=14-6=8
solve the inequality 2b + 5 <_ 30
The solution of the inequality 2b + 5 ≤ 30 is b ≤ 12.5
What are inequalities?Inequalities refers to some type of equations where the relationship between the left hand side and the right hand side of an equation is expressed in terms of symbols other than equal to
The symbols include
less thangreater thanless than or equal to greater than or equal toIn the problem given the symbol used is less than or equal to and the equation is solved by
2b + 5 ≤ 30
2b + 5 - 5 ≤ 30 - 5
2b ≤ 25
dividing through by 2
2b / 2 ≤ 30 / 2
b ≤ 12.5
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A triangle with two sides that measure 5 cm and
8 cm with an included angle of 39º.
Answer:
the other 2 sides equal 70.5 ...but I am not for sure because you did not give me enough information (like a picture)
48) in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people, if a) the bride must be in the picture?
The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
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y= 3x + a / 2x -5
express x in terms of a and y
The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)
Given equation y = 3x + a / 2x - 5
= y(2x - 5) = 3x + a
= 2xy - 5y = 3x + a
= 2xy - 3x = a - 5y
= x(2y-3) = a - 5y
Hence, x = (a - 5y) / (2y - 3)
First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).
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a concert venue is determining the ticket price for concerts in a particular series. the sales team finds that at a price of $38 per ticket, attendance averages 1,000 people per concert. each decrease in price of $5 adds 50 people to the average attendance. find an equation for revenue, r, as a function of p, the price of tickets. what is r(25)?
An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
Given that;
The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,
Let 'T' be the number of times the price is decreased.
So, price;
p = 38 – 5x
x = (38 - p) / 5
And as per the given condition attendance;
a = 1000 + 50x
So, the Revenue is;
To develop an equation for revenue (r) as a function of p, the price of tickets;
R = p * a
R= p * (1000 + 50x)
But, x = (38 - p) / 5
Then,
R = P * (1000 + 50(38 - p)/5)
= p * (1000 + 380 - 10p)
= p * (1380 – 10p)
= 1380p - 10p² → (I)
To get R(25) from (I);
R(25) = 1380(25) - 10(25)²
= 34500 - 6250
= 28250
Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
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-12a + -5b - 12c + 6a - 8b - (-4)
Answer:
-6a -13b - 12c + 4
Step-by-step explanation:
-12a + -5b - 12c + 6a - 8b - (-4)
-12a + -5b - 12c + 6a - 8b + 4 [a "- -" = +]
(-12a + 6a) -(5b -8b) - 12c + 4 [Group like terms.]
-6a -13b - 12c + 4
need halp with the ques answer pls
The value of A rounded to the nearest hundredth is 0 and the value of A rounded to the nearest tenth is 10
From the given number line
The value of A = 7.51
The number line is defined as the straight line that consist of integers in equal intervals. We can also says that the number line is the pictorial representation of numbers on a horizontal line.
The rounding of a number is defined as a number is make it simple by keeping its value intact but closer to the next number. The closer to tenth, hundredth, thousand etc.
The value of A = 7.51
Rounding the rounder to nearest tenth = 10
Rounding the number to nearest hundredth = 0
Hence, the value of A rounded to the nearest hundredth is 0 and the value of A rounded to the nearest tenth is 10.
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5(x+2)-3(x-2)+7x
PLEASE HELP ME RMS IS KILLING ME HOLY COW
Answer:
9x + 16
Step-by-step explanation:
Let's simplify step-by-step.
5(x+2)−3(x−2)+7x
Distribute:
=(5)(x)+(5)(2)+(−3)(x)+(−3)(−2)+7x
=5x+10+−3x+6+7x
Combine Like Terms:
=5x+10+−3x+6+7x
=(5x+−3x+7x)+(10+6)
=9x+16
Please give me brainiest!
olumide plays the piano and guitar.for every 5 min of piano practice,he spends 8 min practicing guitar.how many minutes will olumide practice piano if he spends 64 minutes practicing guitar?
Answer:
Olumide will practice 40 minutes of playing the piano
Step-by-step explanation:
Olumide practices piano and guitar in the ratio of 5:8
64 minutes of guitar playing means that Olumide has had 8 individual practicing sessions of guitar (64 / 8 = 8), so he has also had 8 practicing sessions of piano.
5 x 8 = 40 minutes of piano practice
What is the y-intercept for x^3+8x^2+11x-20? How many zeros are their in the graph?
Y+2=1/4 x in standard form
Answer:
-[tex]\frac{1}{4}x[/tex] + y = -2
Step-by-step explanation:
Standard form: Ax + By = C
y + 2 = [tex]\frac{1}{4} x[/tex]
Rearrange terms:
1. Subtract 2 from both sides
y = [tex]\frac{1}{4} x[/tex] - 2
2. Subtract [tex]\frac{1}{4} x[/tex] from both sides
-[tex]\frac{1}{4}x[/tex] + y = -2
Line ℓ has equation y=
–
x+5. Find the distance between ℓ and the point G(6,4).
Answer:
2.5√2 units
Step-by-step explanation:
The shortest distance between a point and a line is the length of the line segment perpendicular to the line and passes through the given point.
~~~~~~~~~~~~~~~~~~~~~
y = - x + 5 , slope m = - 1
Slope of perpendicular line is opposite reciprocal. In our case is 1 .
G ( 6 , 4 )
y - 4 = 1 × ( x - 6 )
y = x - 2
x - 2 = - x + 5 , x = 3.5
y = 1.5
Perpendicular line intersect the given line at the point O ( 3.5 , 1.5 )
OG = [tex]\sqrt{(6-3.5)^2 +(4-1.5)^2 }[/tex] = 2.5√2 units
very stuck please help
The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
In the question ,
it is given that
the required line is perpendicular to the line passing through (6, -2) and (-8 ,5) .
the slope is = (5 -(-2))/(-8 -6)
= 7/(-14)
= -1/2
so , the slope of the required line is = 2 .
The equation of the line passing through the point (3,1) with slope 2 is
(y - 1) = 2*(x-3)
y -1 = 2x - 6
y = 2x - 6 + 1
y = 2x - 5
the equation of line is y [tex]=[/tex] 2x - 5
the perpendicular slope is = 2
the y intercept is -5 .
Therefore , The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
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a hamburger regularly cost $6.00 each additional topping cost $0.59. on Monday the cost of hamburger only is half off
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A burger consistently cost $6.00 each extra fixing cost $0.59.
Let 'c' be the cost and 't' be the cost of topping. Then the equation is given as,
c = 0.59t + 6
On Monday the expense of the burger just is half off. Then the equation is given as,
c = 0.50(0.59t + 6)
c = 0.295t + 3
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
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Tim and Jessica plan to rent a camper van for a vacation. The van costs $183 per day.
The rental includes 120 miles for free and then charges $0.39 per mile.
The total price Tim and Jessica paid to rent the camper van is $598.74. Write an
equation that models the cost of the van rental in terms of miles traveled, m.
Create an equation
The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .
What is the equation that represents the cost?The equation that would model the cost of the van rental is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one.
The general form of linear equations is: y = a + bx
Where:
a = intercept
b = slope
The form of the equation that models the cost is:
Total cost = cost of renting the van + [cost per mile x (m - 120 miles)
$598.74 = $183 + [$0.39 x (m - 120)
$598.74 = $183 + $0.39m - 46.80
$598.74 = 136.20 + $0.39m
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a cashier cannot tell the difference between cilantro and parsley. customers would only buy either cilantro or parsley. he knows that 20% of his customers prefer parsley. these customers will buy parsley 40% of the time when shopping. otherwise, they wouldn't buy either herb. 40% of his customers prefer cilantro and will buy cilantro 15% of the time when shopping. otherwise, they wouldn't buy either herb. the other 40% of his customers don't prefer, and thus don't buy, either herb. given the next customer buys one of the two herbs, what is the probability it is parsley?
Probability that customer buy parsley given buy any of two herb
= 0.5714
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Parsley ( 0.4 , 0.6 )
buy = B ∩ P = 0.08
Don't buy = DB ∩ P = 0.12
Cilantro = ( 0.15 , 0.85 )
buy = B ∩ C = 0.06
Don't buy = DB ∩ C = 0.34
Don't buy anything = DB = 0.4
P( Buy anything ) = P(B∩P) + P( B ∩ C )
= 0.08 + 0.06 = 0.14
Now, P( P/B) = P( P ∩ B)/P(B)
= 0.08/0.14 = 4/7 = 0.5714
Hence, probability that customer buy parsley given buy any of two herb
= 0.5714
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