Answers
Answer:
∠B = 74°
a ≈ 14.5 inches
c ≈ 11.4 inches
Step-by-step explanation:
The given parameters of triangle ΔABC are;
∠A = 62.2°, ∠C = 43.8° and side [tex]\overline{AB}[/tex] = b = 15.8 in
By sine rule, we have;
[tex]\dfrac{a}{sin(\angle A)} = \dfrac{b}{sin(\angle B)} = \dfrac{c}{sin(\angle C)}[/tex]
[tex]a = {sin(\angle A)} \times \dfrac{b}{sin(\angle B)}[/tex]
By angle sum property, we have;
∠B = 180° - (∠A + ∠C)
∴ ∠B = 180° - (62.2° + 43.8°) = 74°
∠B = 74°
[tex]\therefore {a} = {sin(62.2^{\circ})} \times \dfrac{15.8}{sin(74^{\circ})} \approx 14.5[/tex]
a ≈ 14.5 in.
[tex]c = {sin(\angle C)} \times \dfrac{b}{sin(\angle B)}[/tex]
[tex]\therefore {c} = {sin(43.8^{\circ})} \times \dfrac{15.8}{sin(74^{\circ})} \approx 11.4[/tex]
c ≈ 11.4 in.
Related Questions
answer choices
a.)36.94
b.)39.59
c.)18.41
d.)25.19
e.)19.74
f.)28.94
Answers
Answer:
x = 39.59
Step-by-step explanation:
take 43 degree as reference angle
using sin rule
sin 43 = opposite / hypotenuse
0.682 = 27 / x
x = 27 / 0.682
x = 39 . 589
x = 39. 59
Select a figure from the options which will replace the(?) as established by the problem figure
Answers
Answer:
a) is the correct answer.
helpp
Plzzz
It’s
A
Question-
Steven earns extra money babysitting. He charges $29.00 for 4 hours and $50.75 for 7
hours.
Enter an equation to represent the relationship. Let x represent the number of hours
Steven babysits and y represent the amount he charges.
Answers
$50.00÷7hours=×$
$50.00÷7hours= 7.25
7.25 he charges per hour
what is the operation of xy^2-2xy^2-5y^2x
Answers
Answer:
-6xy²
Step-by-step explanation:
xy² - 2xy² - 5y²x
use commutative property to reorder terms
xy² - 2xy² -5xy²
combine like terms
- xy² - 5xy²
- 6xy²
which expression is equivalent to 6-(-8)
Answers
which expression is equivalent to 6-(-8)
A purse regularly priced at $70 is on sale for 20% off. What is the scale price of the purse?
Answers
What is the area? Bit confused on this one.
Answers
Answer:
A = 9x² + 12x
Step-by-step explanation:
The area (A) of the rectangle is calculated as
A = height × width
= 3(3x² + 4x) ← distribute parenthesis by 3
= 9x² + 12x
Answer:
For the blue one:
A1=length*breadth
=3*3x^2
=9x^2
For pink:
A2=length*breadth
=3*4x
=12x
So the total area is:
A=A1+A2
=9x^2+12x
Determine the equation of the line that passes through A(2,-5) and B(6,-3).
Answers
Answer:
y = 1/2x - 6
Step-by-step explanation:
y2 - y1 / x2 - x1
-3 - (-5) / 6 - 2
2/4
= 1/2
y = 1/2x + b
-3 = 1/2(6) + b
-3 = 3 + b
-6 = b
The sum of Aini’s age and Wani’s age is 62 years old. Three years later, Aini’s age is three times Wani’s age. How old is Aini now?
Answers
Answer:
48 years old
Step-by-step explanation:
a + w = 62
a+3 = 3(w+3) =>a+3=3w+9
=> a-3w = 6
a+ w = 62
a- 3w= 6
________-
4w = 56
w = 14
so, the Aini's age now is 62-14 = 48 years old
semoga membantu
Sal knows the volume of a cylinder is 500 cubic units. He wants to create a cylinder with twice the volume. Which variation of the original cylinder will have a volume of exactly 1,000 cubic units?
Answers
find the area of the following shapes. Show the formula used and all work. Round to 1 decimal place .
Answers
Answer:
[tex]\text{d. }106,250\:\mathrm{cm^2},\\\text{e. }38.5\:\mathrm{cm^2},\\\text{a. }85\:\mathrm{ft^2},\\\text{b. }7.89676\:\mathrm{m^2}[/tex]
Step-by-step explanation:
Part D:
The figure shows a parallelogram with base 425 cm and height 250 cm. Its area can be found by [tex]A=bh[/tex] and therefore the area of this shape is [tex]A=425\cdot 250=\boxed{106,250\:\mathrm{cm^2}}[/tex]
Part E:
The figure shows a trapezoid. The area of a trapezoid is equal to the average of its bases multiplied by the height. Since one base is 2 cm and the other base is 9 cm, the average of these bases is [tex]\frac{2+9}{2}=\frac{11}{2}=5.5\:\mathrm{cm}[/tex]. The height is given as 7 cm, therefore the area of the trapezoid is [tex]7\cdot 5.5=\boxed{38.5\:\mathrm{cm^2}}[/tex]
Part A:
The composite figure consists of two rectangles. The area of a rectangle with base [tex]b[/tex] and height [tex]h[/tex] is given by [tex]A=bh[/tex]. The total area of the figure is equal to the sum of the areas of these two rectangles.
Area of first rectangle (rectangle on bottom): [tex]5\cdot 13=65\:\mathrm{ft^2}[/tex]
Area of second rectangle (rectangle on top):
*Since we don't know the dimensions, we must find them. Start by converting 108 inches to feet:
[tex]108\:\mathrm{in}=9\:\mathrm{ft}[/tex]. Therefore, the dimensions of this rectangle are (10-5) ft by (13-9) ft [tex]\implies5\text{ by } 4[/tex] and this rectangle's area is [tex]5\cdot 4=20\:\mathrm{ft^2}[/tex]
Thus, the area of the figure is equal to [tex]65+20=\boxed{85\:\mathrm{ft^2}}[/tex]
Part B:
We've already found the area of the figure in the previous part in square feet. To find the area in square meters, use the conversion [tex]1\text{ square foot}=0.092903\text{ square meter}[/tex].
Therefore, the area of the figure, in square meters, is [tex]85\cdot 0.092903=\boxed{7.89676\:\mathrm{m^2}}[/tex]
A city has a 20% chance of having a flood in any given decade. The table shows the results of a simulation using random numbers to find the experimental probability that there will be a flood in the city in at least 1 of the next 5 decades. In the table below, 1 represents a decade with a flood. The numbers 2 to 5 represents a decade without a flood.
Answers
Answer:
4/10=40%
Step-by-step explanation:
A scientist is studying the growth of anew species of bacteria. Looking back on his meticulous records, the scientist sees that his starting population was 50 bacteria. Five hours later, he measured 550 bacteria. What is the population of the bacteria after 10 hours, after 20 hours?
Answers
Answer:
In 10 hours, the population is 6050 bacteria. In 20 hours, the population is 732050 bacteria.
Step-by-step explanation:
Bacterial populations can be assumed to grow exponentially. In 5 hours, since the population will have multiplied by 11, in 10 hours it will have multiplied by 121 (11^2) and by 14641 (11^4).
50 * 11 * 11 = 6050
50 * 11 * 11 * 11 * 11 = 732050
Answer:
Step-by-step explanation:
550 = 50 [tex]x^{5}[/tex]
11 = [tex]x^{5}[/tex]
ln(11) = 5 ln(x)
x = [tex]e^{ln(11)/5}[/tex]
x = 1.615
10 hours ....
A= 50 ([tex]1.615^{10}[/tex] )
A= 50 ([tex]1.615^{10}[/tex] )
A=6050
20 hours ....
A= 50 ([tex]1.615^{20}[/tex] )
A= 50 ([tex]1.615^{20}[/tex] )
A=732,050
PLEASE HELP PLEASE PLEASE PLEASE PLEASE
Answers
Answer:
1: 98
2: 82
3: 98
4: 82
Step-by-step explanation:
So 2 is 82deg then the opposite is also 82 so 4 is 82deg
Then 82+82 = 164deg, and we remain with 360deg-164deg which is = 196.
Since the other two angles will be equal (they are opposite each other) we can decide 196/2 = 98
So 3 and 1 are 98deg
Answer:
Step
<2 and <4 are vertically opposite. They are equal
<2 = 82 Given
<4 = 82 Vertically opposite to a given
<3 = 180 - 82 <3 and <4 are supplementary. They are on the same straight line.
<3 = 98
<1 = 98 Vertically opposite angles are equal.
The mean of 5 numbers is 30. The median is 33. What might the numbers be?
Answers
Let a,b,c,d and e are five numbers
mean = (a +b+ c+ d+e)/5 = 30
⇒ (a +b+ c+ d+e) = 150_______(1)
now, Let the number excluded be a
then, new mean = (b+ c+ d+e)/4 = 28
⇒ (b+ c+ d+e)= 112
putting this value in (1),
⇒a + 112 = 150
⇒a = 150 -112 = 38
excluded number = 38
Solve
5x + 3 = x + 11
Answers
Step-by-step explanation:
5x + 3 = x + 11
4x=8
x=2
!!!!!
[tex]5x + 3 = x + 11 \\ 5x + 3 - x = 11 \\ 4x + 3 = 11 \\ 4x = 11 - 3 \\ 4x = 8 \\ x = \frac{8}{4} \\ x = 2[/tex]
HOPE IT HELPS!!!I NEED BRAINLIEST ✌️Tiles
4V3
332
233
375
Pairs
324
1
V48
1 1 1
354
745
Answers
Given:
The expressions are:
[tex]\sqrt[3]{24},\sqrt{48},\sqrt[3]{54},\sqrt{45}[/tex]
To find:
The simplified form of each expression.
Solution:
We have,
[tex]\sqrt[3]{24}[/tex]
It can be written as:
[tex]\sqrt[3]{24}=\sqrt[3]{2\times 2\times 2\times 3}[/tex]
[tex]\sqrt[3]{24}=2\sqrt[3]{3}[/tex]
Similarly,
[tex]\sqrt{48}=\sqrt{2\times 2\times 2\times 2\times 3}[/tex]
[tex]\sqrt{48}=(2\times 2)\sqrt{3}[/tex]
[tex]\sqrt{48}=4\sqrt{3}[/tex]
And,
[tex]\sqrt[3]{54}=\sqrt[3]{2\times 3\times 3\times 3}[/tex]
[tex]\sqrt[3]{54}=3\sqrt[3]{2}[/tex]
In the same way,
[tex]\sqrt{45}=\sqrt{3\times 3\times 5}[/tex]
[tex]\sqrt{45}=3\sqrt{5}[/tex]
Therefore, the required pairs are:
[tex]\sqrt[3]{24}\to 2\sqrt[3]{3}[/tex]
[tex]\sqrt{48}\to 4\sqrt{3}[/tex]
[tex]\sqrt[3]{54}\to 3\sqrt[3]{2}[/tex]
[tex]\sqrt{45}\to 3\sqrt{5}[/tex]
PLEASE HELP WITH THIS QUESTION
Answers
Answer:
D) X >= to -1
Step-by-step explanation:
Since the dot on -1 is filled in, -1 is included. The arrow points to the right, implying that X is greater than or equal to -1.
It's D)
Because the full circle means "equal to" and it's going towards the right which means it will be greater.
1. Write the equation that models the height of the roller coaster. Start by writing the equation of the circle. (Recall that the general form of a circle with the center at the origin is x2 + y2 = r2. (10 points)
Answers
Answer:
[tex]y = \sqrt{900 - x^2[/tex]
Step-by-step explanation:
Given
From the complete question, we have:
[tex]r=30[/tex] --- radius
Required
Expression for the height of the roller coaster
We have:
[tex]x^2 + y^2 = r^2[/tex] --- equation of circle
Substitute 30 for r
[tex]x^2 + y^2 = 30^2[/tex]
[tex]x^2 + y^2 = 900[/tex]
Since the roller coaster is half of the circle, the height is defined by y.
So: make y the subject
[tex]y^2 = 900 - x^2[/tex]
Take square roots
[tex]y = \sqrt{900 - x^2[/tex]
Hence, the height is:
[tex]\sqrt{900 - x^2[/tex]
can someone please help for brainlest
Answers
Answer:
yes it is correct
Step-by-step explanation:
option 1
Answer:
Your answer is correct! 9:1
Step-by-step explanation:
Old Area = side x side
? = 2 x 2
4cm
New Area-
Step 1: Triple the sides
2 x 3 = ?
6cm
Step 2: Find the area
6 x 6 = ?
36cm
The ratio of the new area to the old area is:
36 : 4
But wait! You can simply it!
36 / 4 = 9
4 / 4 = 1
So the new ratio would be:
9 : 1
Hope this helps!
Good Luck!
:)
Jessica's teacher asks a class to find the largest number that is smaller than 4.5. Jessica's friend Jeevan gives the answer 4.4. a Why is Jeevan not correct?
Answers
Jeevan is not correct, the answer could be 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that Jessica's teacher asks a class to find the largest number that is smaller than 4.5.
Since Jessica's friend Jeevan gives the answer 4.4.
Therefore, we can see that 4.4 is not a whole number thus, it isn’t the largest number that is also less than 4.5.
The correct answer could be 4.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ2
Are these lines parallel perpendicular or neither
Answers
Answer:
perpendicular
Step-by-step explanation:
start but putting each line into the standard line format
2x-y=-5
-y=-2x-5
y=2x+5
x+2y=-6
2y=-x-6
y=-(1/2)x-3
if lines are parallel the slopes would be the same. 2 is not equal to -1/2
if lines are perpendicular the slope of one would be the opposite inverse of the other.
negative inverse of 2 = - (1/2)
so the lines are perpendicular
What is the approximate distance between the two points (2, 4) and (5,0)?
Answers
First subtract the numbers and evaluate the power
Add the numbers together
And square root it
One of the byproducts of nuclear power generation is Uranium-233. Uranium is decaying at a constant 57% rate per
day. If 3,820 pounds are produced from a power plant, what will the amount be In 15 days?
Answers
Answer:
Approximately 0.0121 will be left after 15 days.
Step-by-step explanation:
We can write an exponential function to model the situation. The standard exponential function is given by:
[tex]y=a(b)^x[/tex]
Let x represent the amount of days. Since the initial amount is 3,820 pounds, a = 3820. It decays at a rate of 57% per day. So, after one day, it will only have 100% - 57% = 43% or 0.43 of its previous amount. So, b = 0.43.
Hence, our function is:
[tex]y=3820(0.43)^x[/tex]
After 15 days, x = 15. Substitute and evaluate:
[tex]y(15)=3820(0.43)^{15}\approx 0.0121\text{ pounds}[/tex]
Find the area of the following composite figure please
Answers
Step-by-step explanation:
answer is in photo above
the graph of y=-3x+4 is?
Answers
Answer:
B
Step-by-step explanation:
that is a linear equation, therefore it makes a line, eliminating choices C and D.
Lines can literally Any x or y. So it would be B, a set of all the solutions to the equations.
Find the slope of each side of this quadrilateral and use that information to explain why it is a rectangle
8
BI
Your answer might look like this (you can 'copy-paste' the sentences below and fill in the blanks)
The slope of the side BA is The slope of the side BC is_-
The slope of the side BA is__ The slope of the side AD is_
The slope of the side CD is
The slope of the side AD is_
The slope of the side CD is
The slope of the side BC is
Finding the slopes tell me that this quadrilateral is a rectangle because_
Answers
Step-by-step explanation:
the answer is in the above image
What is the perimeter, P, of a rectangle that has a length of x + 8 and a width of y - 1?
Op = 2x + 2y + 18
OP = 2x + 2y + 14
OP = x + y - 9
OP = x + y + 7
Answers
Answer:
P = 2x +2y + 14
Step-by-step explanation:
The perimeter of the rectangle is 2x + 2y + 14.
What is a perimeter?The perimeter of an object is calculated by adding the sides length of the objects.
Given that, the length and width of a rectangle is x+8 and y-1, we need to find the perimeter,
P = 2(length + width)
P = 2(x+8+y-1)
P = 2(x+y+7)
P = 2x+2y+14
Hence, the perimeter of the rectangle is 2x + 2y + 14.
Learn more about perimeter, click;
https://brainly.com/question/6465134
#SPJ7
Rami is solving the equation for x .
–6x – 1 = 5
–6x – 1 Empty square 1 = (5 Empty square 1)
–6x = 6
–6x Empty circle – 6 = 6 Empty circle –6
x = –1
Which operation symbols should Rami write in the Empty squareand the Empty circle?
Answers
Answer:
Empty square = +
Empty Circle = ÷
Step-by-step explanation:
In order to eliminate the extra numbers from the equation you have to do the opposite of the problem. So...
-6x-1=5
-6x -1+1 = 5+1 (eliminating the 1 from the -6x side and adding it to the other side)
-6x = 6
-6x ÷ -6 = 6 ÷ -6 ( eliminating the-6 so that one side just has x)
so... x= -1
Answer: Option B is your correct answer.
Find the surface area and the volume of the figure
Round to the nearest tenth if needed.
Answers
Answer:
See belowStep-by-step explanation:
Surface area:
S = 2(lw + lh + wh) + 2πrhS = 2(9*4 + 9*5 + 4*5) + 2*3.14*2*3 = 239.7 cm² (rounded)Volume:
V = lwh + πr²hV = 9*4*5 + 3.14*2²*3 = 217.7 cm³ (rounded)Answer:
> V = 217.68 cm³
> S = 227.14 cm²
Step-by-step explanation:
We are required to find the surface area and the volume of the given figure . This question is from Combination of solids . As we can see that this figure is made up of a cuboid and cylinder.
Firstly let's find out the volume .
> V = V_( cuboid) + V_(cylinder)
> V = 9cm × 4cm × 5cm + π × ( 2cm)²× 3cm
> V = 180 cm³ + 3.14 × 4cm² × 3cm
> V = 180 cm³ + 37.68 cm³
> V = 217.68 cm³
Lets find the surface area :-
> S = S_( cuboid) + S_( cylinder) - πr²
> S = 2( 9×4 + 4× 5 + 5×9) cm² + 2×π×2cm × 3cm - 3.14 × (2cm)²
> S = 239.7 cm² - 12.56 cm²
> S = 227.14 cm²
Note :-
Here we subtracted πr² from the total surface area of cuboid and cylinder because that much area of the cuboid was covered by the base of the cylinder .