find the area of each triangle. round intermediate values to the nearest tenth. use the rounded values to calculate the next value.Round your final answer to the nearest 10
Answers
Sin(α)=opposite leg/hypotenuse
Sin(63°)=ya/35
ya=35xSin(63°)
ya=31.2
Area(a)= (15.9x31.2)/2
Area(a)=248.0
Now, we proceed to find the area of "b". We already have the length x=15.9, so:
Tan(α)=opposite leg/adjacent leg
yb=15.90xTan(42°)
yb=14.3
Area(b)=15.9X14.3/2
Area(b)=113.7
The total Area (At) is:
At=Area(a)+Area(b)
At=248.0+113.7
At=361.7
10) Triangle "a":
-Adjacent leg of the triangle "a":
Cos(α)=adjacent leg/hypotenuse
Cos(30°)=xa/48
xa=48xCos(30°)
xa=41.6
-Opposite leg of the triangle "a":
Sin(α)=opposite leg/hypotenuse
Sin(30°)=y/48
y=48xSin(30°)
y=24.0
-Area of the triangle "a":
Area(a)=41.6x24.0/2
Area(a)=499.2
Triangle "b":
-We have the value of i(y=24).
-Adjacent leg of the triangle "b":
Tan(α)=opposite leg/adjacent leg
Tan(45°)=24/xb
xb=24/Tan(45°)
xb=24
-Area of the triangle "b":
Area(b)= 24x24/2
Area(b)=288
-Total area of the triangle (At) is:
At=Area(a)+Area(b)
At=499.2+288
At=787.2
11) To find the area of the triangle shown in this exercise, we have to apply the same procedure as in exercise 10:
-Adjacent leg of the triangle "a":
Cos(α) = adjacent leg/hypotenuse
Cos(56°)=xa/14
xa=14xCos(56°)
xa=7.8
-Opposite leg of the triangle "a":
Sin(α)=opposite leg/hypotenuse
Sin(56°)=y/14
y=14xSin(56°)
y=11.6
-Area of the triangle "a":
Area(a)=7.8x11.6/2
Area(a)=45.2
Triangle "b":
-The value of its opposite leg is y=11.6.
-Adjacent leg of the triangle "b":
Tan(α)=opposite leg/adjacent leg
Tan(46°)=11.6/xb
xb=11.6/Tan(46°)
xb=11.2
-Area of the triangle "b":
Area(b)= 11.6x11.2/2
Area(b)=65.0
-Total area of the triangle (At) is:
At=Area(a)+Area(b)
At=45.2+65.0
At=110.2
12)-Adjacent leg of the triangle "a":
Cos(α)=adjacent leg/hypotenuse
Cos(54°)=xa/13
xa=13xCos(54°)
xa=7.6
-Opposite leg of the triangle "a":
Sin(α)=opposite leg/hypotenuse
Sin(54°)=y/13
y=13xSin(54°)
y=10.5
-Area of the triangle "a":
Area(a)=7.6x10.5/2
Area(a)=39.9
Triangle "b":
-Adjacent leg of the triangle "b":
Tan(α)=opposite leg/adjacent leg
Tan(42°)=7.6/xb
xb=7.6/Tan(42°)
xb=8.4
-Area of the triangle "b":
Area(b)=7.6x8.4/2
Area(b)=31.9
-Total area of the triangle (At) is:
At=Area(a)+Area(b)
At=39.9+31.9
At=71.8First, it is important to remember that the formula to calculate the area of a triangle is: A=bxh/2
As we can see in the exercises, all the triangles are divided in two triangles. So, let's call "a" to the triangle on the left and "b" to the triangle on the right.
9)To find the area of the triangle "a", we need the lenght of the adjacent leg (x) and the opposite leg (ya):
Cos(α)=adjacent leg/hypotenuse
Cos(63°)=x/35
x=35xCos(63°)
x=15.9
Sin(α)=opposite leg/hypotenuse
Sin(63°)=ya/35
ya=35xSin(63°)
ya=31.2
Area(a)= (15.9x31.2)/2
Area(a)=248.0
Now, we proceed to find the area of "b". We already have the length x=15.9, so:
Tan(α)=opposite leg/adjacent leg
yb=15.90xTan(42°)
yb=14.3
Area(b)=15.9X14.3/2
Area(b)=113.7
The total Area (At) is:
At=Area(a)+Area(b)
At=248.0+113.7
At=361.7
10) Triangle "a":
-Adjacent leg of the triangle "a":
Cos(α)=adjacent leg/hypotenuse
Cos(30°)=xa/48
xa=48xCos(30°)
xa=41.6
-Opposite leg of the triangle "a":
Sin(α)=opposite leg/hypotenuse
Sin(30°)=y/48
y=48xSin(30°)
y=24.0
-Area of the triangle "a":
Area(a)=41.6x24.0/2
Area(a)=499.2
Triangle "b":
-We have the value of i(y=24).
-Adjacent leg of the triangle "b":
Tan(α)=opposite leg/adjacent leg
Tan(45°)=24/xb
xb=24/Tan(45°)
xb=24
-Area of the triangle "b":
Area(b)= 24x24/2
Area(b)=288
-Total area of the triangle (At) is:
At=Area(a)+Area(b)
At=499.2+288
At=787.2
11) To find the area of the triangle shown in this exercise, we have to apply the same procedure as in exercise 10:
-Adjacent leg of the triangle "a":
Cos(α) = adjacent leg/hypotenuse
Cos(56°)=xa/14
xa=14xCos(56°)
xa=7.8
-Opposite leg of the triangle "a":
Sin(α)=opposite leg/hypotenuse
Sin(56°)=y/14
y=14xSin(56°)
y=11.6
-Area of the triangle "a":
Area(a)=7.8x11.6/2
Area(a)=45.2
Triangle "b":
-The value of its opposite leg is y=11.6.
-Adjacent leg of the triangle "b":
Tan(α)=opposite leg/adjacent leg
Tan(46°)=11.6/xb
xb=11.6/Tan(46°)
xb=11.2
-Area of the triangle "b":
Area(b)= 11.6x11.2/2
Area(b)=65.0
-Total area of the triangle (At) is:
At=Area(a)+Area(b)
At=45.2+65.0
At=110.2
12)-Adjacent leg of the triangle "a":
Cos(α)=adjacent leg/hypotenuse
Cos(54°)=xa/13
xa=13xCos(54°)
xa=7.6
-Opposite leg of the triangle "a":
Sin(α)=opposite leg/hypotenuse
Sin(54°)=y/13
y=13xSin(54°)
y=10.5
-Area of the triangle "a":
Area(a)=7.6x10.5/2
Area(a)=39.9
Triangle "b":
-Adjacent leg of the triangle "b":
Tan(α)=opposite leg/adjacent leg
Tan(42°)=7.6/xb
xb=7.6/Tan(42°)
xb=8.4
-Area of the triangle "b":
Area(b)=7.6x8.4/2
Area(b)=31.9
-Total area of the triangle (At) is:
At=Area(a)+Area(b)
At=39.9+31.9
At=71.8
Step-by-step explanation:
Related Questions
How can exponential growth be used to make predictions?
Answers
Find the x-intercept and the y-intercept of the line 2x-5y= -6
Answers
2(0)-5y=-6
-5y=-8
y is equal to 8/5
To find x intercept, make y equal zero
2x-5(0)=-6
2x=-1
x is equal to -1/2
Answer:
Step-by-step explanation:
2x - 5y = 6
5y = 2x - 6
y = 2/5x - 6/5
y-intercept is -6/5
x-intercept is when you say that y = 0
and so 6/5 = 2/5x
x = 6/2 = 3
Which expression could you simplify by multiplying exponents?
Answers
Answer:
So if I multiply those two expressions together, I will get eleven copies
what is it??,,,,,,,,,,,,
Answers
Answer:
99,000
Step-by-step explanation:
since 3 times 10 to the power of 3 is 1000 and 10 to the power of 5 is 100000 the answer is 99,000
Answer: 97000 more
Step-by-step explanation:
10*10*10*10*10=100000 10⁵
10*10*10=1000*3=3000 10³
So 100000-3000= 97000 more
Hope this helped!
Polynomials-Algebra
Let f(x) and g(x) be polynomials as shown below. (See picture)
Which of the following is true about f(x) and g(x)?
A. f(x) and g(x) are not closed under subtraction because when subtracted, the result will not be a polynomial.
B. f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial.
C. f(x) and g(x) are closed under subtraction because when subtracted, the result will be a polynomial.
D. f(x) and g(x) are closed under subtraction because when subtracted, the result will not be a polynomial.
Answers
Answer Update [PLATO]:
Answer choice updated to B, however the text and answer itself in the other persons submition (above) is still correct
as of 9:55am Daylight Central Timezone Apr.-10-2022
AndreanWarrior747
f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.
What is Closure Property?According to Closure Property, when something is closed, the output will be same as the input.
The polynomials f(x) and g(x) can be seen in the image.
On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.
To know more about Closure Property
https://brainly.com/question/19340450
#SPJ5
If tan 0 = -5, find the cot 0
Answers
Answer:
Step-by-step explanation:
cot(theta) = 1 / tan(theta)
cot(theta) = 1 / -5
cot(theta) = - 0.2
The Langleys spend 40% of their monthly income on rent. If their monthly income is $4,400, how much money do the Langleys spend on rent? Help please.
Answers
100%=$4400
40% $=?
40 ×4400/100
$1760
Find the measure of QS.
S9T 10 R 21 F 4x+5 Q
A. 35 B, 20 C. 27 D. 29
Answers
Answer:
C. 27
Step-by-step explanation:
((4x + 5) + 10)*10 = (21 + 9)*9 (two secants intersecting)
(4x + 5 + 10)*10 = (30)*9
(4x + 15)*10 = 270
40x + 150 = 270
40x = 270 - 150 (subtraction property of equality)
40x = 120
Divide both sides by 40
40x/40 = 120/40
x = 3
✔️QS = (4x + 5) + 10
Plug in the value of x
QS = 4(3) + 5 + 10
QS = 12 + 5 + 10
QS = 27
Which of the following equations is the correct representation of the graph below?
Answers
What is half of 2+2 First answer gets Brainliest
Answers
Answer:
Half is 2
Step-by-step explanation:
Find the area of the regular polygon. Round to the nearest tenth.
Answers
Answer:
A polygon is a very big catagory. For example, a triangle has three sides, while a quadrilateral has four sides.
A triangle would be, A=h*w/2 (h being hight, and w being width)
A quadrilateral would be, A=h*w
After dinner, Jackie's pitcher has 8 cups of sweet tea left in it. How many pints is this?
4 pints
O 21 pints
14 pints
1
pints
2
Answers
8 cups would be 4 pints for your problem
Solve the following system of equations:
-2x + y = 1
-4x + y = -1
A: (3, 1)
B: (-1, 3)
C: (-1, -3)
D: (1, 3)
Answers
Answer:
x=1,y=3
correct answer is (1,3)
Step-by-step explanation:
We can quickly eliminate y by subtracting one equation from the other
(-2x+y=1)-(-4x+y=-1)
2x=2
x=1
plug x=1 into equation 1
-2(1)+y=1
y=1+2=3
If the gas station is selling 5 bottles of water for $10, what is the unit price of each bottle of water?
Answers
Answer:
2
Step-by-step explanation:
5 bottles = 10 dollars
divide by 5 to get 1 bottle
now divide 10 by 5 that will be 2
2$ for 1 bottle
Which mathematical statement represents "17 more than a number is 26"?
O 17 > 26
On+17 - 26
017-26
26+n=17
Answers
Answer:
n +17 = 26
Step-by-step explanation:
Let the number be 'n'
17 more than 'n' = n + 17
n + 17 = 26
Answer:
n +17 = 26
Step-by-step explanation:
I got a 100 on the test ed2021
If (x-2,6)=(4,y+2)then the value of x=_____and y=____
Answers
x=6 , y = 4
Step-by-step explanation:
( x-2,6)=(4,Y+2)
this means; (x-2) &( 4) stands for" x "axis.
and( 6 )& (y+2) stands for y axis.
So, we can say( x-2)=X1 & (4)=X2 , (6)=Y1 & (y+2)=Y2
then; to Solve The Equation we use The Formula: X1=X2 for "X" And Y1=Y2 for "Y".
Solution: for "X" ; X1=X2
x-2= 4
x=4+2
x=6
For "Y" ; Y1=Y2
6 = y+2
y=6-2
y=4
finally check ; ( (x-2),6) = (4,(y+2) )
(6-2),6 = (4,(4+2) )
( (4),6) = (4,(6) )
(4,6) = (4,6)
so, X1 =X2 ; 4 = 4
Y1 = Y2 ; 6 = 6
Which instruments belong to the brass family?
Answers
Answer:
Baritone/Euphonium
Trumpet
Tuba
Trombone
Good luck!!
find the value of X in each of the following2x-7=13 3x+4=25
Answers
Answer:
2x-7=13 X=10
3x+4=25 X=7
2/3x=8 X=12
3/2x=6 X=4
Step-by-step explanation:
Answer:
a. x = 12
b. x = 4
Step-by-step explanation:
a. [tex]\frac{2x}{3}=8[/tex]
Multiply both sides by 3;
[tex]\frac{2x}{3} *3=8*3\\\\2x=24[/tex]
Divide both sides by 2;
x = 12
b. [tex]\frac{3x}{2}=6[/tex]
Multiply both sides by 2;
[tex]\frac{3x}{2}*2=6*2\\\\3x=12[/tex]
Divide both sides by 3;
x = 4
what is 1 7/8 + 2/8 ???
Answers
Answer:
The answer is 2.375.
Step-by-step explanation:
17 / 8 = 2.125.
2 / 8 = 0.25.
2.125 + 0.25 = 2.375.
In 1995, the population of a town was 33,500. It is decreasing at a rate of 2.5% per decade.
a. Identify whether the function is a growth or decay function.
b. Write the function, f(n), that expresses the population of the town after (n) decades.
c. What is the population in the year 2025 to the nearest hundred?
Answers
Answer:
See belowStep-by-step explanation:
Initial date = 1995Initial population = 33500Decrease rate = 2.5% per 10 yearsa. It is a decay function as number of population is decreasing over time
b. f(n) = 33500*((100 - 2.5)/100)^n = 33500*(0.975)^n
c. In year 2025, n = (2025 - 1995)/10 = 3
f(3) = 33500*(0.975)^3 = 31100 rounded up
1.Encuentra la ecuación de la circunferencia que tiene como ecuación ordinaria (x-4)² + (y+5)²= 25 2- encuentra la ecuación general de la circunferencia que tiene como ecuación ordinaria (x+1)² + (y+9)²=49
Answers
Responder:
1) x² + y²-8x + 10y + 16 = 0
2) x² + y² + x + 18y + 33 = 0
Explicación paso a paso:
A partir de la pregunta, debemos expresar la ecuación en la forma estándar de un círculo expresado como;
x² + y² + 2gx + 2fy + c = 0 donde;
(-g, -f) es el centro.
1) Para la ecuación (x-4) ² + (y + 5) ² = 25
Expande el paréntesis;
(x-4) ² + (y + 5) ² = 25
x²-8x + 16 + y² + 10x + 25 = 25
x²-8x + 16 + y² + 10y + 25-25 = 0
Recopile términos similares;
x² + y²-8x + 10y + 16 + 0 = 0
x² + y²-8x + 10y + 16 = 0
Por lo tanto, la ecuación requerida es x² + y²-8x + 10y + 16 = 0
2) Para la expresión (x + 1) ² + (y + 9) ² = 49
x² + x + 1 + y² + 18y + 81 = 49
x² + x + 1 + y² + 18y + 81-49 = 0
Recopile términos similares;
x² + y² + x + 18y + 82-49 = 0
x² + y² + x + 18y + 33 = 0
Por tanto, la ecuación requerida es x² + y² + x + 18y + 33 = 0
Which expression is equivalent to 2^2divided by 2/2^4
Answers
Answer: 32
Step-by-step explanation:
The expression that is equivalent to 2^2 divided by 2/2^4 would be calculated as:
= 2^2 ÷ 2/2^4
= 4 ÷ 2/16
= 4 ÷ 1/8
= 4 × 8
= 32
The expression would be equal to 32 based on the above calculation
The distance between two stars is 9.0 x 10 to the power of -3 light years. A light year is equal to
5.88 x 10 to the power of 12 miles. What is the distance, in miles, between the two stars
Answers
Answer:
The distance between the two stars in miles is 5.292 * 10^10 miles
Step-by-step explanation:
Here, we want to make a conversion from light year to miles
To make this conversion, we simply are going to multiply the light year by the miles
Mathematically, we have this as;
9 * 10^-3 * 5.88 * 10^12
= 52.92 * 10^9
= 5.292 * 10^10 miles
Solve the Equation
–x + 8 + 3x = x – 6
A. x = –18
B. x = –14
C. x = 2
D. x = 4
Answers
Answer:
x= -14
Step-by-step explanation:
-x+3x-x=-8-6
x= -14
-x+8+3x=x-6
the first thing we need to do is move the x's to the left and the numbers to the right
when moving a number from one side to another it's sign is changed
-x+3x-x=-6-8
x=-14
geometry question below
Answers
Answer:
MN║SU
OM║TU
ST = 2ON
Step-by-step explanation:
x/5 - g = a for x
how can i find x?
Answers
Answer:
X = 5a+5g
Step-by-step explanation:
Adding g on both sides gives:
X/5 = a+g
Now dividing 5 on both sides gives us the value of x which is:
X = 5(a+g)
Hence X=5(a+g) or X=5a+5g( multiplying by 5 gives us 5a and 5g)
Use elimination to solve the system.
2x + 3y = 1
5x – 4y = 14
help would be appreciated :)
Answers
Answer:
x = 2, y = -1
Step-by-step explanation:
To solve this with elimination, we first multiply the first equation by -2.5
Our new equations are:
-5x - 7.5y = -2.5
5x – 4y = 14
After adding these two equations together, the x cancels out and we have:
-11.5y = 11.5
Divide both sides by -11.5
y = -1
Plugging this value into y in one of the equations we have:
2x + 3y = 1
2x + 3(-1) = 1
2x - 3 = 1
Add 3 to both sides
2x = 4
Divide both sides by 2
x = 2
Isaac works as a cook at a restaurant. He started this week with 800 potatoes. On Monday, he used 380 potatoes. On Tuesday, he used 270 potatoes. How many potatoes were left at the end of Tuesday?
Answers
Answer:
The number of Potatoes remaining is = 150
Step-by-step explanation:
From the information given above,
On first day of the week (Sunday),
Total potato = 800
The number used include:
Monday = 380
Tuesday = 270
Total potato used = Monday + Tuesday
= 380 + 270 = 650
Remaining Potato = 800 - 650 = 150
PLEASE! 10 POINTS! For what number A does the equation 3Ax - 24 = 5x - 9 + x have no solutions for x?
Answers
Answer:
3Ax-6x = 15
3x(A-2)=15
If A were 2, the left side of the equation would be 0 and it wouldn't equal 15 no matter what the value of x is. So A is 2
What is the definition of equation
Answers
Source- dictionary
Answer: a definition of an equation can be defined as a mathematical statement consisting of an equal symbol between two expressions that have the same value.
Step-by-step explanation: