Answers
Answer:
x = 41.5
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
2x + 9 + x + 13 + x - 8 = 180 , that is
4x + 14 = 180 ( subtract 14 from both sides )
4x = 166 ( divide both sides by 4 )
x = 41.5
⇒The sum of the interior angles of a triangle is 180°
⇒Meaning (2x+9)°+(x-8)°+(x+13)°=180°
⇒Simplify the above equation to find the value of x.
⇒[tex]2x+x+x+9-8+13=180\\4x+14=180\\4x=180-14\\4x=166\\\frac{4x}{4} =\frac{166}{4} \\x=41.5[/tex]
∴ x=41.5
Related Questions
(25x^2+4-30x)-(9x^2+4-12x)
Answers
Answer:
16x² - 18x
Step-by-step explanation:
(25x² + 4 - 30x) - (9x² + 4 - 12x) ← distribute this parenthesis by - 1
= 25x² + 4 - 30x - 9x² - 4 + 12x ← collect like terms
= (25x² - 9x²) + (4 - 4) + (- 30x + 12x)
= 16x² + 0 + (- 18x)
= 16x² - 18x
25x^2+4-30x-9x^2+4(-1)-12x(-1)
Simplify:
25x^2-9x^2+4-4-30x+12x
Answer:
16x^2-18x
Jeremy has a huge display of holiday decorations outside his home. He used 6 kilowatt hours (KWH) of electricity in November and used a total of 120KWH during the holiday season until he took them down on December 30. Set up and solve an equation that can be used to calculate the amount of electricity Jeremy used per day during the month of December.
Answers
The equation that can be used to find the amount of electricity Jeremy used per day during the month of December is 3.8KWH per day and Jeremy used 3.8KWH per day electricity in the month of December.
How to write and solve an equation?Electricity Jeremy used in November = 6 kilowatt hours (KWH)
Total electricity used in the holiday season = 120KWH
He took the decorations down on December 30
Amount of electricity Jeremy used per day during the month of December =
(Total electricity used in the holiday season - Electricity Jeremy used in November) / 30 days
= (120KWH - 6KWH) / 30
= 114KWH / 30
= 3.8KWH per day
In conclusion, the amount of electricity Jeremy used per day in December is 3.8KWH per day.
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HELPP!!!1 i'm rushing like i need to summit that ASAP!!
Answers
The missing expression in step 2 should be [(6² + 2)/0.5] - 14.8 ÷ 8.
The missing expression in step 6 should be 76 - 1.85.
How to evaluate and solve the given expression?In order to evaluate this expression, we would apply the PEMDAS rule, where mathematical operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
For step 1, we have the following:
[(6² + 2)/|-0.5|] - 14.8 ÷ 8.
In step 2, we would take the absolute value of -0.5:
[(6² + 2)/0.5] - 14.8 ÷ 8.
Therefore, we would have the quantity of the sum of six squared (6²) plus two (2) divided by 0.25, minus 14.8 ÷ 8
In step 3, we would take the exponent of 6:
[(36 + 2)/0.5] - 14.8 ÷ 8.
In step 4, we would add 36 and 2 together:
[(38)/0.5] - 14.8 ÷ 8.
In step 5, we would divide 38 by 0.5:
76 - 14.8 ÷ 8.
In step 6, we would divide 14.8 by 0.5:
76 - 1.85
In step 7, we would subtract 1.85 from 76 as follows:
Solution = 76 - 1.85 = 74.15.
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What equation is graphed in this figure?
y−4=−1/3(x+2)
y−3=1/3(x+1)
y+2=−3(x−1)
y−5=3(x−1)
Answers
The equation of the graph in point slope form is y + 2 = -3(x - 1)
How to find equation of a graph?The equation of the graph in point slope form can be represented as follows;
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are variableusing two point let's find the slope
(0, 1)(-1, 4)
Hence,
m = 4 - 1 / -1 - 0
m = 3 / -1
m = -3
Therefore, the slope of the line is - 3.
Therefore, using one coordinates(1, -2) from the graph, the equation of the graph in point slope form is y + 2 = -3(x - 1)
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You work at a restaurant as a host and a server. You earn $9.45 for each hour you work as a host and $7.65 for each hour you work as a server.
a. Identify an equation in standard form that models your earnings.
Responses
7.65x+9.45y=160.657 point 6 5 x plus 9 point 4 5 y is equal to 160 point 6 5
y=17x+160.65y is equal to 17 x plus 160 point 6 5
9.45x+7.65y=160.659 point 4 5 x plus 7 point 6 5 y is equal to 160 point 6 5
9.45x−7.65y=160.659 point 4 5 x minus 7 point 6 5 y is equal to 160 point 6 5
Question 2
b. Graph the equation.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -1.4 to 22.4 with ticks spaced every 2 unit(s).
The vertical axis goes from -1.4 to 22.4 with ticks spaced every 3 unit(s).
Hours worked as hostHours worked as server
Answers
Answer:
7
Step-by-step explanation:
65x+9.45y=160.657 point 6 5 x plus 9 point 4 5 y is equal to 160 point 6 5
Plssssss Help mewith a and b
Answers
a. The relationship between time and distance is not an arithmetic sequence, as the rate of change is not constant.
b. The distance is given by: d(n) = 5n².
What is an arithmetic sequence?An arithmetic sequence happens when the change in the output is always the same when the input changes by one, that is, the rate of change is constant.
From the table, the increases when the input(time) increases by one are given as follows:
15, 15, 35, 45.
The increases are not constant, hence the relationship between time and distance is not an arithmetic sequence.
What is the distance at t = n?The equation for the distance is given as follows:
d(t) = 0.5gt².
The constant is:
g = 10.
Hence:
d(t) = 5t².
At a time of n seconds, the distance is found replacing the lone instance of t by n, hence:
d(n) = 5n².
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Review the proof. Step 1 / cos(2x) =1-2sin2x
Which step contains an error?step 2/ step 4/ step 6/ step 8
Answers
Answer:
Step 6 is wrong
Convert 42°C into °F
Answers
Answer: 107.6
(42c x 9/5) +32
You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos, and your total bill is $11.25. Your friend’s bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost? Explain and show work
Answers
The cost of a soft taco is $1.25 and the cost of a burrito is $2.50.
Let the cost of a soft taco would be t and,
The cost of a burrito would be b
As per the given question, the equations would be as
3t+3b=11.25 ...(i)
4t+2b=10 ...(ii)
With the two equations in that form, an elimination solution is probably the simplest.
Multiply each equation by a constant so that the coefficients of b are opposite so that when the two equations are joined, b is eliminated.
-6t-6b = -22.50
12t+6b = 30.00
_____________
6t = 7.50
t = 7.50/6 = 1.25
Substitute the value of t = 1.25 in equation (ii), and solve for b
4(1.25)+2b=10
5+2b=10
2b=5
b=2.50
Thus, the cost of a soft taco is $1.25 and the cost of a burrito is $2.50.
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during the course of the basketball season, shawna made 67 out of 100 free throws. when we say that her probability of making a free throw during the playoffs is 0.67, what type of probability are we starting?
Answers
The type of probability are we starting will be relative frequency probability or the empirical probability,
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Given that, Shawna made 67 out of 100 free throw attempts during the course of the basketball season. When we state that she has a 0.67 chance of making a free shot during the postseason,
The ratio of the number of times an event occurs to the total number of outcomes that occurred is known as relative frequency.
Thus, the type of probability are we starting will be relative frequency probability or the empirical probability,
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Which of these is not the net of a cube?
a)
b)
B
C
D
Only 1 attempt allowed
Answers
Answer: b)
Please give brainliest thx
solve for n. 15n<580.5 ill give 30 points. i need it fast asap
Answers
Answer: K 35
Step-by-step explanation:
We're given the inequality : 15n < 580.5
Divide both sides by 15.
-> 15n : 15 < 580.5 : 15
-> n < 38.7
Therefore, the final inequality is : n < 38.7
A rectangular mural measures 238 centimeters by 435 centimeters. raegan creates a mural that is 27 centimeters longer. what's is the perimeter of ragans new mural
Answers
The perimeter of Ragans new mural is 530cm.
Rectangle:
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Here it is given that the measure of the rectangle is 238 cm and 435cm.
The Raegan creates a mural that is 27cm.
The formula to calculate the perimeter of a rectangle:
Perimeter = 2(length + breadth)
Earlier the length is 238cm and the breadth is 435cm.
Now replace the breath 435cm to 27cm.
length = 238cm
breadth = 27cm
Therefore we get the perimeter of the rectangle:
Perimeter = 2( 238 + 27)
= 2( 265)
=530cm
Therefore the perimeter is 530cm.
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Answer:
1400
Step-by-step explanation:
A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 8 feet. The area of the logo must be less than 48 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle.
Use "b" for the base length of the triangular logo.
Answers
Answer:
Step-by-step explanation:
We know that the area of a triangle is given by :-
Let b be the base (in feet) of the triangle .
it is given that , The school wants the height of the triangle to be 6 feet.
Then, the area of triangle will be :-
(1)
The area of the logo must be at most (less than or equal to) 15 square feet.
i.e. Area ≤ 15 square feet (2)
Now, Substitute the value of A from (1) into (2) , we get
Divide both sides by 3 , we get
the graph of a lnear function passes through the point (-2, -7). When the input increses by 3 the value of the function increses by 8. what is the equation that models the function
Answers
The equation that models the function is y = 8/3(x) - 5/3.
Given:
The graph of a linear function passes through the point (-2, -7).
When the input increases by 3 the value of the function increases by 8.
(x,y) = (x+3,y+8)
(-2,-7) = (-2+3,-7+8)
= (1,1)
slope between (1,1) and (-2,-7) is m = -7-1/-2-1
= -8/-3
m = 8/3.
substitute m in y = mx + c
y = 8/3(x)+c
substitute (-2,-7)
-7 = 8/3(-2) + c
-7*3 = -16 + 3c
-21+16 = 3c
-5 = 3c
c = -5/3
y = 8/3(x) - 5/3.
Therefore the equation that models the function is y = 8/3(x) - 5/3.
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The chart shows the distances, in miles, between three places.
a)Write down the distance
from Hereford to Chester.
b) Which town is 99 miles
from Kendal?
c)If Ellen drives from Kendal to
Hereford via Chester, how
many miles will she drive?
Answers
The spreadsheet that shows the distances between the cities, indicates that the distances between the cities are as follows;
a) From Hereford to Chester, the distance is 95 miles
b) Chester is the town that is 99 miles from Kendal
c) Ellen will have driven 201 miles if she drives from Kendal to Hereford through Chester
What is a spreadsheet?A spreadsheet application is used for the storage analysis, organization, and computation of data.
The interpretation of the distances in the chart which is in the form of a spreadsheet are;
The value in the cell corresponding to the distance from Kendal to Chester that is the cell which is on the same column as Kendal and on the same row as Chester is 99
Therefore, the distance from Kendal to Chester is 99 miles
The value in the cell that directly links Chester to Hereford that is the cell which is on the same column as Chester and on the same row as Hereford is 95
Therefore, the distance from Chester to Hereford is 95 miles
The value in the cell that connects Kendal to Hereford, that is the cell which is on the same column as Kendal and which is on the same row as Hereford is 201
Therefore the distance from Kendal to Hereford is 201 miles
a) The distance from Hereford to Chester is 95 miles
b) The town that is 99 miles from Kendal is Chester
c) The distance Ellen will have driven if she drives from Kendal to Hereford via Chester is 201 miles
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an experiment consists of tossing a fair die until a 6 occurs four times. what is the probability that the process ends after exactly stack exchange
Answers
The experiment will end after 4th time.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .hence, after 4th trial experiment will stop.
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A local hamburger shop sold a combined total of 680 hamburgers and cheeseburgers on Friday. There were 70 fewer cheeseburgers sold than hamburgers. How
many hamburgers were sold on Friday?
hamburgers
Answers
Answer:
375
Step-by-step explanation:
h + c = 680
c = h - 70
h + h - 70 = 680
2h = 680 + 70
2h = 750
2/2 h = 750/2
h = 375
Can someone teach me how to do this?
Answers
sin^-1(-1/2) enter directly into a calculator and you'll find your answer
Shift+sin then Fraction
24. The height of an object varies directly with the length of its shadow. If a tree 8 feet tall casts a shadow 10 feet long, how long will be the shadow of a tree that is 12 feet tall?
Answers
Answer:
15 feet
Step-by-step explanation:
Given an 8' object casts a 10' shadow, you want to know the length of the shadow of a 12' object.
ProportionThe shadow length is proportional to the object length:
shadow/object = 10'/8' = s/12'
Multiplying by 12', we have ...
s = (12')(10/8) = 15'
The shadow of a tree 12 feet tall will be 15 feet long.
Question 1(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
One leg of a right triangle is 8 units long, and its hypotenuse is 14 units long. What is the length of the other leg? Round to the nearest whole number.
11 units
13 units
18 units
22 units
Question 2(Multiple Choice Worth 2 points)
(Interior and Exterior Angles LC)
Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 34.15°. What is the measure of ∠P?
145.85°
57.45°
34.15°
72.925°
Question 3(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the length of the line segment shown.
line segment from negative 3 comma 10 to 4 comma negative 1
13 units
12 units
7 units
3 units
Question 4(Multiple Choice Worth 2 points)
(Polygon Angle Sums MC)
A regular polygon has 25 sides. If one of its angles measures (6h − 15)°, what is the value of h?
h = 6.7
h = 16.7
h = 30.1
h = 33.8
Question 5(Multiple Choice Worth 2 points)
(Angle Relationships LC)
Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 109.6°.
250.4°
63.2°
70.4°
19.6°
Question 6(Multiple Choice Worth 2 points)
(Angle Relationships MC)
Two angles are complementary to each other. One angle measures 26°, and the other angle measures (10x − 11)°. Determine the value of x.
2.6
5.6
7.5
24.5
Question 7(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the distance between the points (−4, −5) and (8, 0).
13 units
12 units
8 units
29 units
Question 8(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In triangle EFG, m∠E = 95.2° and m∠F = 43.7°. Determine the measure of the exterior angle to ∠G.
138.9°
84.8°
51.5°
41.1°
Question 9(Multiple Choice Worth 2 points)
(Angle Relationships MC)
The following angles are supplementary to each other.
m∠A = (3x + 21)° and m∠B = (6x − 21)°
Determine x.
10
20
36
60
Question 10(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Determine which set of side measurements could be used to form a right triangle.
square root of 19 comma square root of 35 comma 54
square root of 15 comma 6 comma square root of 51
5, 8, 30
5, 6, 7
Question 11(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Determine which set of side measurements could be used to form a triangle.
2, 6, 10
3, 18, 22
7, 13, 16
8, 7, 19
Question 12(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
For triangle XYZ, m∠X = (7g + 12)° and the exterior angle to ∠X measures (2g + 60)°. Find the measure of ∠X and its exterior angle.
Interior angle = 49°; exterior angle = 131°
Interior angle = 131°; exterior angle = 49°
Interior angle = 96°; exterior angle = 84°
Interior angle = 84°; exterior angle = 96°
Question 13(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 9 feet of fence for the shortest side and 15 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
12 feet
16 feet
36 feet
38 feet
Question 14(Multiple Choice Worth 2 points)
(Polygon Angle Sums LC)
Find the sum of the interior angles of a 12-sided polygon.
1,080°
1,800°
2,100°
2,160°
Question 15(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (1 −1), and Monique's desk is located at (−4, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
square root of 7 feet
square root of 14 feet
square root of 85 feet
square root of 61 feet
Answers
Answer:
Step-by-step explanation:
This problem is solved using the Pythagorean theorem (a2+b2=c2). In this formula a and b are the legs of the right triangle while c is the hypotenuse.
Using the labels of our triangle we have:
o2+a2=h2
\dpi{100} h^{2}=(10ft)^{2} +(17ft)^{2}
h2=100ft2+289ft2
h=389ft2−−−−−√
So with this information you can see that the correct answer is 19.7ft
Determine the slope of the graph of x2 = ln(xy) at the point (1, e).
Answers
The slope of the given graph x^2 = ln (xy) at the point (1, e) is e
We have been given a graph x^2 = ln (xy) and a point (1, e)
Differentiate the given graph on both sides
d/dx x^2 = d/dx (ln (xy))
⇒ 2x = 1/xy × d/dx (xy)
⇒ 2x × xy = x.dy/dx + y.dx/dx
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y - y = x.dy/dx
⇒ (2x^2y - y)/x = dy/dx … (1)
The slope at the point (1, e)
m = dy/dx at x = 1, y = e
Substitute the values in Equation (1)
⇒ m = (2(1)^2 (e) - e)/1
⇒ m = (2e - e)/1
⇒ m = e/1
⇒ m = e
Hence, the slope of the given graph is e.
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A spinner with 9 equal sections is numbered 1 through 9. The probability of spinning a 3 is 1/9. What is the probability of not spinning a 3 is what
Answers
The probability of not spinning a 3 is 8/9
How to determine the probability that the number 3 is not spun?From the question, the given parameters are:
Number of sections = 9
Sections = Number 1 to 9
The probability of spinning a 3 = 1/9
The above probability can be represented as
P(3) = 1/3
The probability that the number 3 is not spun is the complement of the probability of spinning a 3
This is calculated as
P(3) + P(Not 3) = 1
Substitute the known values in the above equation So, we have the following equation
1/9 + P(Not 3) = 1
Evaluate the like terms
P(not 3) = 8/9
Hence, the probability is 8/9
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Which of these strategies would eliminate a variable in the system of equations?
Answers
The strategy which would eliminate a variable in the system of equations is to multiply the top equation by -5 , then add the equation and is denoted as option B.
What is Equation?This is a mathematical term which is made up of two expressions and is connected by an equal sign.
In the example given below:
x - 2y = 11
5x + 3y = -11
We can multiply the top by -5 which will result in:
-5x + 10y = -55 after which it is added to the other to give:
-5x + 5x + 10y + 3y = -55 + (-11)
13y = -66
y = -66/13.
From this we can notice that the variable x was eliminated which is why option B is the correct choice.
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a rancher plans to use 170 yards of fencing to enclose a rectangular corral and to divide it into two parts with a fence parallel to the shorter sides of the corral. find the dimensions of the corral if its area is to be 1200 square yards.
Answers
The dimensions of recangle is = 30 yrds.
What is the area of rectangle?Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area.Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangular floor's area.acc to our question-
2000 = 160x - 3x^23x^2 -160x + 2000 = 0x = [160 +- sqrt(160^2 - 4*3*2000)]/6x = [160 +- sqrt(1600)]/6Positive solution:x = [160 + 40]/6x = 200/6x = 33 1/3 yrds. (side);Learn more about area of rectangle click here:
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The area of a rectangular floor is 8x² + 6x-20. The width of the floor is 2x + 4. What is the length of the floor?
Answers
Answer:
Length = 4x - 5
Step-by-step explanation:
A = length x width
Write the first four terms of two different arithmetic sequences with a common difference of −3. The first sequence starts with −12 and the second sequence starts with 12.
Answers
Answer:
Step-by-step explanation:
The first arithmetic sequence would be -12, -15, -18, -21. The second sequence would be 12, 9, 6, 3.
Método de igualación. {x-2y=11
x+5y=−17
Answers
The value of x and y is 7 and -2 respectively.
The equations to solve are -
x - 2y = 11 ....[1]x + 5y =−17 ....[2]On adding equations 1 and 2 we get ,
3y = -6
y = -2
Putting the value of y in equation 1,
⇒ x - 2(-2) = 11
⇒ x + 4 = 11
⇒ x = 7
Hence ,the value of x and y is 7 and -2 respectively.
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The Clark's updated their living room by purchasing a new chair for $162.98. They paid 9% sales tax on their purchase. If
the Clark's paid $180.98 total, determine if they paid the correct amount.
Answers
162.98 multiplied by 1.09 which is 109 percent is equal to 177.65
Use the rules of measurement to divide
Answers
Answer:
[tex] \frac{ {m}^3{} }{25} [/tex]
Step-by-step explanation:
that is the answer
