Answer:
This is an obtuse scalene triangle with the length of E measuring around 749 cm.
<D = 54.754° ≈ 55°
<E = 114°
<F = 11.246° ≈ 11°
Side D = 670 cm
Side E = 749.46937 cm ≈ 749 cm
Side F = 160 cm
Explanation:
When given two sides, and an angle, we can use trigonometry to find the missing angles, and sides.
Given the triangle ∆DEF with side D measuring 670 cm, side F measuring 160 cm, and angle E measuring 117°, we can apply the law of sines to identify the missing information. A & a chronologically refers to the first angle, and side. B & b chronologically refers to the second angle, and side. And C & c chronologically refers to the third angle, and side.
a / Sin (A) = b / Sin (B) = c / Sin (C)
[side 1]. [side 2]. [side 3].
↓ ↓ ↓
sideD/sin(<D) SideE/sin(<E) SideF/sin(<F)
______________________________
670cm / Sin(D) = E cm / Sin(114) = 160 / sin(F).
Since we are only given two sides with an angle measure, we can refer to the law of cosines to figure this one out.
It states that A = arccos(b²+c²-a²/2bc) → cos(A) = b²+c²-a²/2bc
B = arccos(a²+c²-b²/2ac) → cos(B) = a²+c²-b²/2ac
and C = arccos(a²+b²-c²/2ab) → cos(C) = a²+b²-c²/2ab
capital A, B, and C are angles A, B, and C.
lowercase a, b, and c are sides a, b, and c.
Therefore c² = a² + b² − 2ab cos(C),
b² = a² + c² - 2ac cos (B), and a² = b²+c² - 2bc.
SOH CAH TOA.
Since we know this, we can solve for pretty much everything as long as we are given at least 3 variables. Chronologically, because we are solving for side e, we must use b² = a² + c² - 2ac cos (B), because the rest are only variables we are given, making it easy to solve. So b² = 670² + 160² - 2(670 × 160) × cos(114°) = 561704.3362754.
Now take the square root of that to get b by itself, so √561704.3362754.... = 749.4693698046.... ≈ 749
Answer:749
Step-by-step explanation:
S.A.S law or Cosines
e=561704.33628= 749.469= 749
number 10?? please help.
Answer:
∠GFM= 124°
Step-by-step explanation:
∠GFH= 180° -90° -(5x +9)° (∠ sum of △FGH)
∠GFH= 90° -5x° -9°
∠GFH= (81 -5x)°
∠GFM +∠GFH= 180° (adj. ∠s on a str. line)
25x -1 +81 -5x= 180
20x +80= 180 (simplify)
20x= 180 -80 (-80 on both sides)
20x= 100
x= 100 ÷20 (÷20 on both sides)
x= 5
∴∠GFM
= 25x -1
= 25(5) -1
= 124°
-4(-5+x)>56
??? whats the answer
Answer:
x < -9
Step-by-step explanation:
-4(-5+x)>56 (given)
20 - 4x >56 (distributive property of inequality)
-4x > 36 (subtraction property of inequality)
x < -9 (division property of inequality)
The sign flips since it was divided by a negative number.
please answer fast
but i need a correct
answer
Answer:
Step-by-step explanation:
11/20ths
Which set of ordered pairs represents a function?
A {(1, 2), (2, 3), (2, 4), (2,5)}
B {(2, 3), (3, 5), (5, 7), (7, 9)}
C {(3, 3), (3, 5), (3, 6), (4, 5)}
D {(0,1), (0, 2), (0, 3), (0,4)}
Answer:
Step-by-step explanation:
The anser would be B.
The y is allowed to repeat a number but the x cannot. If the x does repeat a number then its not a function. (X,Y)
Terry has $5.79 to go shopping Which mixed number below is the fraction equivalent to $5.79? 500 a 5 79/100 b. 5 79/1000 57 9/100 d 57 9/10
Answer:
579/100 is the same if u turned it into a decimal it would be 5.79
Step-by-step explanation:
you would do 579 divided by 100 and that will give you 5.79
Answer:
the answer is 579/100
Step-by-step explanation:
HELP!! BRAINLIEST AND 10 POINTS !!!! THANK YOU SO MUCH
Answer:
B and C
Step-by-step explanation:
BRAINLIEST PLEASE
What is 1 5/9 as a percent?
Answer:
1 and 55%
Step-by-step explanation:
Five divided by nine.
Abdul made $252 for 12 hours of work.At the same rate,how many hours would he have to work to make $105
Answer:
5 hours
Step-by-step explanation:
252 divided by 12= 21
21x5=105
I need this answer ACAP, please! (Marta likes to make soup during the winter months. No matter how much soup she makes, she always freezes 32 ounces to save for later, then serves what's left).
60 divided by 32
60 plus 32
60 times 32
60 minus 32
Which one?
Answer:
60 minus 32
Step-by-step explanation:
Since she freezes 32 ozs everytime, shes taking away 32 oz, so your bassicaly losing 32 ozs temperorily.
A logo is made of a square and a semicircle. The square has side lengths of 12 inches. One side of the square is also the diameter of the semicircle. What is the approximate total area of the logo?
Answer:
The square has side lengths of 22 inches. One side of the square is also the diameter of the semicircle
Step-by-step explanation:
Hopefully its right!
Kyle plans to make 15 hamburger patties, each weighing 14 pound, for a cookout. At the store, hamburger meat is priced at $3.66 per pound. If Kyle orders the exact amount of meat he needs, how much will it cost, rounded to the nearest cent?
Answer:
Total cost= $768.66
Step-by-step explanation:
Giving the following information:
Production= 15 units
Standard quantity= 14 pounds per unit
Standard cost= $3.66 per pound
First, we need to calculate the total pounds required to make the hamburgers:
Total pounds= 14*15
Total pounds= 210 pounds
Now, the total cost:
Total cost= 210*3.66
Total cost= $768.66
Find the area of the trapezoid.
Put the steps in order?
The ratio of the sides of two similar rectangles is 3:5. The larger rectangle has an area of 36 sq. cm. What is the area of the smaller rectangle?
Answer:
21.6 sq cm
Step-by-step explanation:
3:5
x:36
cross-multiply because they are in proportion
x*5=3*36
divide both sides by 5
x= 3*36/5=21.6
Which ordered pairs in the form (x, y) are solutions to the equation 3x−4y=21?
Select each correct answer.
(−3, 3)
(7, 0)
(−1, −6)
(11, 3)
Not long after he begins to study algebra he will likely meet with the "tank" problems, the "labor" problems and many other puzzle problems. He finds these problems carefully phrased in the language of practical mathematics. However, a study of the original problems and the fanciful way in which they were stated will reveal the fact that they were originally intended mostly for puzzles. The present-day student of algebra would doubtless work as industriously over the so-called practical problems if he were told they were puzzle problems that his predecessors had worked on for the past 1600 years.
The problems given below are selected from a collection made by Metrodorus about 310 A. D. found in The Greek Anthology. It is not known how much farther back they date. It will not be difficult for the reader to trace many of the problems found in the present-day algebras back to their original source. He may judge for himself as to whether the modern text-book writer has improved the problems by leaving off the little fanciful touches of rhetoric, found in the original.
The original problems were solved by rhetorical algebra as our symbols, +, -, ×, ÷, etc., were introduced many centuries later, about 1540.
Answer:
wow thats some good information there!
Step-by-step explanation:
Find the length of YZ.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The triangle is right-angle so we are allowed to use the Pythagorean theorem.
According to the Pythagorean theorem :
[tex] ({XZ})^{2} = ({XY})^{2} + ({YZ})^{2} [/tex]
[tex] {65}^{2} = {56}^{2} + ( {YZ})^{2} [/tex]
[tex] {65}^{2} - {56}^{2} = ({YZ})^{2} [/tex]
[tex]( {YZ})^{2} = 1089[/tex]
[tex]YZ = \sqrt{1089} [/tex]
[tex]YZ = 33[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Help please! Thanks!
Answer:
50
Step-by-step explanation:
120 +angle1 = 180 angle 1 is 60 70+60+angle2 should be equals 180 so 2 is 50 degree
1 is 60 degree 3 is 80 degree 4 is 100 degree 2 is 50 degree
60+40 +angle3 = 180 angle3 is 80
3+4 should be equal 180 3 is 80 180-80= 100 4 is 100
Graph the function . What is the missing x-coordinate for the point , to the nearest tenth?
6.1
7.3
8.4
9.5
Answer:
Your answer would be D. 9.5.
Step-by-step explanation:
Edge 2020
Answer:
The Answer is 9.5
Step-by-step explanation:
Edge 2021
Claire wants to build a patio outside her café. The rectangular space outside of Claire's café is three times as long as it is wide. The area of the space is 48 m2. Claire
would like to build a patio with dimensions 3.5 m by 12.5 m in this space. Will it fit? Explain.
pls help
Answer:
Step-by-step explanation:
It will fit in the space but it won't cover the entire space. the area is 48m2, but the patio in question will cover 43.75 of the 48m2. Also, it stated that the rectangular space is 3 times as long, and the patio is 3.57x as long as the width. So yes, it will fit, but it will not be a picture perfect fit, there will be some obscenities.
Step-by-step explanation:
Let length of space be lm and width be wm.
l = 3w --(1)
lw = 48 --(2)
sub (1) into (2):
3w(w) = 48
3w^2 = 48
w^2 = 16
w = ± 4 (rej -4 since w > 0)
when w = 4, l = 3(4) = 12
Since dimensions of the patio is 3.5m by 12.5m, and the dimensions of the space is 4m by 12m it does not fit
This is a topic known as simultaneous equations. If you would like to find out more / know when and how to use it, you can check out my Instagram page (learntionary)
Which property was used to simplify the expression?
4(b+2) = 4b+8
distributive property
commutative property
associative property
inverse property
Answer:
distributive
Step-by-step explanation:
they took the number outside of the parentheses and multiplied by the inside
Alex bought 3 tacos for $4.00. How much would she have to pay for 10 tacos at this rate?
Which statement is Irue about the given information?
+
B
с
DE
Answer:
b
Step-by-step explanation:
awnser 3
both are congrent
Correct 25.0457 to 2 significant figure
9514 1404 393
Answer:
25.
Step-by-step explanation:
The first two significant figures are 2 and 5. The next figure is 0, so we don't need to round up. The number to 2 significant figures is 25.
Jose can use the rule m(x)=10+3x to find m(x) , the amount of money he will have after a week of doing x additional hours of chores. Evaluate m(20), What does this mean?
Answer:
70
Step-by-step explanation:
Given:
m(x) = 10 + 3x
where,
m(x) = the amount of money he will have after a week of doing x additional hours of chores
x = additional hours of chores
Evaluate m(20), What does this mean?
m(x) = 10 + 3x
m(20) = 10 + 3(20)
= 10 + 60
= 70
m(20) = 70
m(20) means additional hours of chores is 20
Marco went to the cafeteria to buy chicken sandwiches, C, worth $2.00, and hamburgers, h, worth $2.50.
He bought a total of 9 items and spent a total of $20.50. How many hamburgers and chicken sandwiches
did Marco buy?
HELP
Answer:
5 Hamburgers = $12.50 4 Chicken sandwiches $8.00( $12.50 + $8.00 = $20.50
Step-by-step explanation:
Answer:
Marco bought 5 hamburgers and 4 chicken sandwiches.
Step-by-step explanation:
Set up a system of equations:
2c + 2.5h = 20.5
c + h = 9
Solve by elimination by multiplying the bottom equation by -2:
2c + 2.5h = 20.5
-2c - 2h = -18
Add the equations together and solve for h:
0.5h = 2.5
h = 5
So, he bought 5 hamburgers. Plug in 5 as h into the second equation to solve for c:
c + h = 9
c + 5 = 9
c = 4
So, Marco bought 5 hamburgers and 4 chicken sandwiches.
help plz (I give you brainlist)
Answer:
58.3825
Step-by-step explanation:
Add all 4 numbers together and divided by how many numbers are there (4)and you get your answer
please help meeeeeeeeee
Answer:
FRACTION DECIMAL PERCENT
3/100 0.03 3%
3/2 1.5 150%
13/20 0.65 65%
2/3 0.6667 66.67%
Jordan created a scale drawing of a rectangular room. The drawing is 8 inches long by 6 inches wide. He used a scale of 1 inch equals 3 ft. What is the area, in the square feet, of the room?
Answer: 432 ft^2
Step-by-step explanation:
If 1"=3', and the box is 8"x6", then we can simply multiply the 8 and 6 by three. You would get 24 by 18.
Follow this up by the equation a=w*l to get
a=24*18 = 432 ft^2.
HELP PLEASE
3. A child swims 50 yards in 50 seconds.
How many FEET can she swim per second?
Answer:
3 ft.
Step-by-step explanation:
They swim 1 yard a second and 1 yard = 3 ft.