Find the area of the given triangle. Round the answer to the nearest tenth.
A.
7.9 square units
B.
149.4 square units
C.
2,055.6 square units
D.
2,071.8 square units
Answers
A = √(p(p-a)(p-b)(p-c)) where a,b,c are the sides of the triangle and p is half the perimeter.
The answer is B. 149.4 square units.
Answer:
B) Area of triangle = 149.4 square units.
Step-by-step explanation:
Given : A triangle with sides 16 , 19, 27 .
To find : Area of a triangle.
Solution : We have given that triangle with sides 16 , 19, 27 .
Using heron's formula :
Area of triangle: [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex].
Where, s = [tex]\frac{a+b+c}{2}[/tex] and a,b,c are sides of triangle.
Then s = [tex]\frac{16+19+27}{2}[/tex].
s = 31 units.
Area of triangle = [tex]\sqrt{31(31-16)(31-19)(31-27)}[/tex].
Area of triangle = [tex]\sqrt{31(15)(12)(4)}[/tex].
Area of triangle = [tex]\sqrt{22320)}[/tex].
Area of triangle = 149.39 square units.
Area of triangle = 149.4 square units. ( nearest tenth)
Therefore, B) Area of triangle = 149.4 square units.
Related Questions
what does this mean:
πr
(π with an r next to it)
Answers
The mathematical expression πr means pi times the radius.
π means pi or 3.14
r means radius which is half of a diameter
When these two symbols are put right next to each other like so πr it means you are multiplying them.
(π)(r)
π·r
(3.14)r
Final answer:
πr typically represents an expression involving the mathematical constant π and the radius of a circle (r). In mathematics, this is commonly part of formulas to calculate properties of circles, such as area or circumference.
Explanation:
When you see πr in mathematics, it typically represents the expression involving the mathematical constant π (pi), which is the ratio of a circle's circumference to its diameter, and r, which stands for the radius of the circle.
The actual value of π is approximately 3.14, but it is an irrational number, meaning it extends to infinity without repeating. In many equations and formulas, πr could be part of a larger expression to calculate properties related to circles, such as the area or circumference.
For example, the formula for the circumference of a circle is 2πr, and the formula for the area of a circle is πr2. Without additional context, πr could be part of these or other mathematical expressions related to circles. It is not to be confused with the Greek letter rho, which can also be represented as p and is used in different ways in physics and other sciences.
Elise is entering a team into a 5-kilometer race. The cost for entry is $15 for a team and an additional $2 per member. The total cost can be modeled by the equation -2x + y = 15, where x is the number of members on the team and y is the total cost. What is the total cost if Elise has 5 members on her team?
Answers
After substituting the number of members into the equation and solving for the total cost, Elise's 5-member team's entry fee into the race is $25.
Explanation:The total cost of entering a team into a 5-kilometer race can be modeled by the linear equation -2x + y = 15, where x is the number of members on the team and y is the total cost. To calculate the total cost for Elise's 5-member team, we need to substitute x = 5 into the equation and solve for y.
First, we multiply the number of members by the additional cost per member: 5 members × $2/member = $10. Then, we add the team entry fee to get the total cost: $15 (team entry) + $10 (members) = $25. Therefore, the total cost for Elise's team is $25.
Final answer:
To find the total cost for Elise's team of 5 members, substitute x=5 into the equation -2x + y = 15 and solve for y to get the total cost of $25.
Explanation:
The student's question involves finding out the total cost of entering a team in a 5-kilometer race with a given equation that models the costs based on the number of team members. The equation provided is: -2x + y = 15, where x is the number of members on the team, and y is the total cost. To find the total cost for Elise's team that has 5 members, we replace the variable x with the number 5 in the equation and solve for y:
-2(5) + y = 15
-10 + y = 15
y = 25
The total cost for Elise to enter a team with 5 members in the race is $25.
A rental agency charges 6% of a month's rent for finding an apartment. Nikolai is looking at apartments with monthly rents of $880, $960, nad $1050. What is the lowest fee he might pay?
Answers
%6 of $960 is:57.6
%6 of $1050 is:64.8
A coordinate plane is placed over an empty lot. You and a friend stand back-to-back at the origin. You face the positive y-axis and your friend faces the negative y-axis. You run 20 feet forward, then 15 feet to your right. At the same time, your friend runs 16 feet forward, then 12 feet to her right. She stops and hits you with a snowball.
Answers
We have a coordinate plane that is placed over
an empty lot. So you and your friend are set at that coordinate system, so I'll
give you the representation of each statement and the distance that
the snowball travels from your friend's hand to you.
1. You face the
positive y-axis and your friend faces the negative y-axis.
This statement is represented in Figure 1. So you are the Red
square and your friend is the Blue
one. The arrows upon the squares mean that you are facing the positive y-axis
and your friend the negative one.
2. You run 20
feet forward, then 15 feet to your right. At the same time, your friend runs 16
feet forward, then 12
feet to her right.
This is shown in Figure 2. So, at the coordinate
system, you move 20 feet upward and 15 feet to your right, that is, you
walk from the origin to the point [tex]P_{1}(15,20)[/tex] first moving through
the positive y-axis and next through the positive x-axis. On the
other hand, your friend moves 16 feet downward and 12 feet to her right,
that is, she walks from the origin to the point [tex]P_{2}(-12,-16)[/tex] first
moving through the negative y-axis and next through the
negative x-axis.
3. She stops and
hits you with a snowball.
This statement is represented in Figure 3. So the snowball
has been drawn in gray. The line from your friend to you is the distance the
snowball runs.
4. Distance the ball
runs.
We can get this answer by using the Distance
Formula, that is:
[tex]d=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^2} \\
d=\sqrt{[15-(-12)]^{2}+[20-(-16)]^2} \\ \boxed{d=45ft}[/tex]
Naoya read a book cover to cover in a single session, at a rate of 555555 pages per hour. After 444 hours, he had 350350350 pages left to read.
Answers
The question involves a mathematical reading rate scenario where Naoya calculates how much of a book he has left to read. Since the numbers provided are unrealistic, an example with plausible figures is used to illustrate the process of determining total reading time and daily reading goals.
The question deals with a reading rate calculation problem involving Naoya, who has read part of a book and wants to figure out how much more he needs to read. We can figure out the total number of pages in the book by considering the pages he has read at the rate of 555,555 pages per hour over 444 hours, and adding the remaining 350,350,350 pages he has left to read. However, it appears there are typographical errors in the question with the repetition of numbers, which should likely be simplified to realistic figures before we can calculate the total number of pages in the book.To apply the concept efficiently, let's take an example with realistic numbers similar to the approach mentioned for Marta. Suppose Marta reads at a rate of 48 pages per hour and she needs to finish a 497-page novel. We divide the total page count (497) by her hourly rate (48 pages/hour) to find the total hours needed, which is approximately 10.35 hours or roughly 10 to 11 hours.
If Marta wishes to finish the novel over two weeks, she would divide her total reading time by the number of days she plans to read, ensuring she allocates enough time each day to reach her goal. Similar reading strategies can be applied whether balancing act, early bird, or taking the approach of reading a certain number of pages each day to make a larger task more doable.
Which polynomial is a quintic binomial?
x^(4)+2x^(3)-x^(2)+7x+11
x^2+4x
3x^5+2
5x^2-2x+1
Answers
binomial means the expression has two terms.
the third choice is the answer.
The correct answer is x^(4)+2x^(3)-x^(2)+7x+11
Which of the following is not good advice for reducing sibling rivalry?
Avoid comparing yourself to a sibling.
Focus on your own achievements.
Try to reduce conflicts fairly.
Have daily debates.
Answers
Answer: Have daily debates.
Step-by-step explanation:
Any one know the next number
Answers
0.20+0.38+0.24+a+2a = 1
3a+0.82 = 1
3a = 1-0.82
3a = 0.18
a = 0.18/3
a = 0.06
. Ms. Johnson, a circus ringleader, made a cake in the shape of a circus tent to use as the centerpiece at a celebration. As shown in the illustration, the cake consists of a cylinder and a cone. The height of the cone is one-half the height of the cylinder. The volume of the cylinder is 3 1470 in . The diameter of the cylinder is 12 in. What is the volume of the circus tent cake? Use 3.14 for . Round to the nearest hundredth.
Ms. Johnson wants all the circus employees to have miniature cakes in the shape of either a circus ball or a
clown hat. She wants the clown hat dessert and the circus ball dessert to have equal volumes. The radius of
both cake pieces will be 3 in. What must the height of the clown hat cake be for the two cakes to be equal in
volume? Round to the nearest hundredth if necessary. Explain or show your work.
Answers
1470=113.04h
Divide both sides by 113.04:
1470/113.04 = 113.04h/113.04
13 ≈ h
The height of the cylinder is 13 inches. We know that the height of the cone is 1/2 the height of the cylinder; 1/2(13) = 6.5 inches. The formula for the volume of a cone is:
V=1/3πr²h
The cone and the cylinder have the same radius, and we now know that the height of the cone is 6.5. Substituting this information in we have:
V=1/3(3.14)(6²)(6.5) = 244.92 in³
The total volume of the cake would be the volume of the cylinder added to the volume of the cone:
1470+244.92 = 1714.92 in³.
The formula for the volume of a sphere, for the ball cake, is
V=4/3πr³. Using the radius of 3 we have:
V=4/3(3.14)(3³)=113.04 for the volume of the circus ball cake.
The formula for the area of the cone-shaped hat cake is V=1/3πr²h. We want it to have the same volume as the circus ball cake, and we know the radius is still 3:
113.04=1/3(3.14)(3²)h
This simplifies to
113.04=9.42h
Divide both sides by 9.42:
113.04/9.42 = 9.42h/9.42
The hat cake would have to have a height of 12 inches to have the same volume.
Answer:
bce
Step-by-step explanation:
The ratio of two sides of a parallelogram is 3:4 and the perimeter is 28 in. Find the lengths of the sides of the parallelogram.
Answers
Then, w = 3h/4;
2x(3h/4) + 2h = 28;
3h/2 + 2h = 28;
3h + 4h = 56;
7h = 56;
h = 8 in;
w = 24/4;
w = 6 in.
Sides of a parallelogram are equal to [tex]\boldsymbol{6}[/tex] inches and [tex]\boldsymbol{8}[/tex] inches if ratio of sides is [tex]3:4[/tex] and perimeter is equal to [tex]28[/tex] inches.
ParallelogramA basic quadrilateral with two pairs of parallel sides is known as a parallelogram.
Ratio of two sides of a parallelogram [tex]=\boldsymbol{3:4}[/tex]
Let the sides be [tex]3x,4x[/tex].
Perimeter of a parallelogram [tex]=\boldsymbol{28}[/tex] in.
Perimeter of a parallelogram is equal to sum of all the sides.
[tex]3x+4x+3x+4x=28[/tex] in.
[tex]14x=28[/tex] in.
[tex]x=2[/tex] in.
So, sides are equal to [tex]3(2),4(2)[/tex] that is sides are equal to [tex]\boldsymbol{6}[/tex] inches and [tex]\boldsymbol{8}[/tex] inches.
Find out more information about parallelogram here:
https://brainly.com/question/1563728?referrer=searchResults
What are the solutions of the equation?
15+IXI=26
Choose all answers that are correct.
–41
–11
11
41
Answers
Please help with this one math question?
Answers
An expression is shown below:
3x3y + 15xy − 9x2y − 45y
Part A: Rewrite the expression so that the GCF is factored completely. Show the steps of your work.
Part B: Rewrite the expression completely factored. Show the steps of your work.
Answers
I imagine that the expression you are asked to work with is:
[tex]3 x^{3}y+15xy-9 x^{2} y-45y [/tex]
When you use a keyboard it is customary to use "^" to denote an exponent is coming so you could have written: 3x^3y+15xy-9x^2y-45y just to be clear.
PART A
To factor out the GCF we are looking for the greatest factor among the terms. Looking at the coefficients (the numbers) the largest number they can all be divided by is 3 so we will pull out a 3. Notice also that each term has a y in it so we can pull out that.
This gives us: [tex] 3 x^{3}y+15xy-9 x^{2} y-45y=3y( x^{3}+5x-3 x^{2} -15)[/tex]
To factor is to write as a product (something times something else). It undoes multiplication so in this case if you take what we got and multiplied it back you should get the expression we started with.
PART B
Start with the answer in part A. Namely, [tex]3y( x^{3}+5x-3 x^{2} -15)[/tex]. For now let's focus only on what is in the parenthesis. We have four terms so let's take them two at a time. I am separating the expression in two using square brackets. [tex][( x^{3}+5x)]-[3 x^{2} -15][/tex]
Let's next factor what is in each bracket:
[tex][( x^{3}+5x)]-[3 x^{2} -15] = [x( x^{2} +5)]-[3( x^{2} +5)][/tex]
Notice that both brackets have the same expression in them so now we factor that out: [tex] [x( x^{2} +5)]-[3( x^{2} +5)] = (x-3)( x^{2} +5)[/tex]
Our original expression (the one we started the problem with) had a 3y we already pulled out. We need to include that in the completely factored expression. Doing so we get: [tex]3 x^{3}y+15xy-9 x^{2} y-45y =(3y) (x-3)( x^{2} +5)[/tex]
which number is prime
A.) 49
B.) 27
C.) 14
D.) 97
Answers
Final answer:
Among the options provided, only D.) 97 is a prime number because it only has two divisors: 1 and itself. All other options have more than two divisors and thus are not prime.
Explanation:
To determine which number is prime, we must recall that a prime number is a number that has only two distinct positive divisors: 1 and itself. Now, let's evaluate the options given:
A.) 49 is 7 times 7, so this is not a prime number.
B.) 27 is 3 times 9, hence this is not a prime number either.
C.) 14 is 2 times 7, which means it is not a prime number.
D.) 97 does not have any divisors other than 1 and itself, so it is a prime number.
So, the correct answer is D.) 97, since it fulfills the conditions for being a prime number.
Trevor is analyzing a circle, y2 + x2 = 49, and a linear function g(x). Will they intersect?
Answers
[tex]x^{2}+y^{2}=49[/tex]
We can write this equation in its standard form as follows:
[tex]x^{2}+y^{2}=7^{2} \\ where \ the \ radius \ r=7[/tex]
On the other hand, the linear function is given as the following table:
[tex]x \ \ \ \ \ \ \ \ g(x) \\ -1 \ \ -9.2 \\ 0 \ \ \ \ \ -9 \\ 1 \ \ \ \ \ -8.8[/tex]
To check if the circle and the line intersects, let's substitute the equation of the line into the equation of the circle to see if there is a real solution, so:
[tex]x^{2}+(0.2x-9)^{2}=49 \\ \\ \therefore x^{2}+0.04x^{2}-3.6x+81=49 \\ \\ \therefore 1.04x^{2}-36x+32=0 \\ \\ Solving \ for \ x: \\ x_{1}=33.70 \\ x_{2}=0.91 \\ \\ Solving \ for \ y: \\ y_{1}=0.2(33.70)-9=-2.26 \\ y_{2}=0.2(0.91)-9=-8.18[/tex]
Finally the intersects are:
[tex]P_{1}(33.70, -2.26) \ and \ P_{2}(0.91, -8.18)[/tex]
Given that f(x) = 5x2 − 100, find x.
Answers
To find x, we need to solve the quadratic equation 5x^2 - 100 = 0 using the quadratic formula.
Explanation:To find x, we need to solve the quadratic equation 5x^2 - 100 = 0 using the quadratic formula. The formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 5, b = 0, and c = -100. Plugging these values into the quadratic formula, we get:
x = (-0 ± √(0^2 - 4 * 5 * -100)) / (2 * 5)
Simplifying further, we have:
x = (√2000) / 10
Therefore, x equals approximately ±14.14.
f(x)=tan(x)
Find the limit as x approaches pi/2 from the negative and positive sides then find the limit as x approaches 0.
Help please!! :(
Answers
Cody filled a container with 8 1/4 quarts of iced tea. How many 1/4-quart glasses can be served from the container?
A. 2 1/16
B. 16 1/2
C. 4 1/8
D. 33
Answers
Tell me if you want to know how it's done :)
To the nearest tenth, what is the area of a circle whose diameter is 9 feet? Use 3.14 for π . Enter your answer in the box. ft2
Answers
Area of a circle = 3.14 * r^2
D = 2r
D = 9
r = 4.5
Area = 3.14 * (4.5)^2
Area = 63.6 ft^2
help needed
An unlabeled hierarchical diagram of various astronomical bodies is shown. The labels A, B, C and D can be used to represent the galaxy, Mars, universe, moon, and solar system.
Part 1: Which four astronomical bodies would you choose to represent the four labels in the diagram?
Part 2: Explain why the hierarchical level D is different from the rest.
Answers
Cant help you for number 2 though. Hope this helps :)
4. The distance covered by the cook in Triangle A equals _______________ eighteen-inch steps.
6,480
540
360
347
5. The distance covered by the cook in Triangle B equals _______________ eighteen-inch steps.
480
500
5,760
320
6. The distance covered by the cook in Triangle C equals__________eighteen-inch steps.
347
520
6,240
9,360
Answers
to convert feet to inches we must multiply by 12
4. The distance covered by the cook in Triangle A equals
a) fridge and stove-----------> 5*16*12=960 in
b) fridge and sink-------------> 10*22*12=2640 in
c) sink and stove--------------> 15*16*12=2880 in
then add, 960 + 2640 + 2880 = 6480 in
the answer asks for the distance in 18 in lengths
so divide 6480 by 18 -------------> 6480/18=360
the answer part N 4) is 360 eighteen-inch steps
5. The distance covered by the cook in Triangle B equals
a) fridge and stove-----------> 5*16*12=960 in
b) fridge and sink-------------> 10*16*12=1920 in
c) sink and stove--------------> 15*16*12=2880 in
then add, 960 + 1920 + 2880 = 5760 in
the answer asks for the distance in 18 in lengths
so divide 5760 by 18 -------------> 5760/18=320
the answer part N 5) is 320 eighteen-inch steps
6. The distance covered by the cook in Triangle A equals
a) fridge and stove-----------> 5*15*12=900 in
b) fridge and sink-------------> 10*22*12=2640 in
c) sink and stove--------------> 15*15*12=2700 in
then add, 900 + 2640 + 2700 = 6240 in
the answer asks for the distance in 18 in lengths
so divide 6240 by 18 -------------> 6240/18=346.67------> 347
the answer part N 6) is 347 eighteen-inch steps
Select the point that satisfies y ≤ x2 - 3x + 2. A. (3, 3) B. (4, 4) C. (2, 2) D. (1, 1)
Answers
Answer:
the answer is (4,4)
Step-by-step explanation:
Length of a rectangle is 4 inches less than twice it’s width of the perimeter is 70 inches what’s the dimensions?
Answers
L= length= 2W-4
Perimeter= 70
FIND WIDTH:
P= 2(L + W)
P= 2L + 2W
substitute 2W-4 for L
70= 2(2W-4) + 2W
multiply 2 by all in parentheses
70= (2*2W) + (2*-4) + 2W
70= 4W - 8 + 2W
combine like terms
70= 6W - 8
add 8 to both sides
78= 6W
divide both sides by 6
13= W
FIND LENGTH:
substitute w=13 to find width
L= 2W-4
L= 2(13)-4
L= 26-4
L= 22
CHECK:
P= 2(L + W)
70= 2(22 + 13)
70= (2*22) + 2(13)
70= 44 + 26
70= 70
ANSWER:
length= 22 inches
width= 13 inches
Hope this helps! :)
what is the store policy at pastic mart
Answers
Hope this helped!
Help!right answer and best explanation gets brainliest
Answers
Please help! Really need help!
Answers
The graph below shows a system of equations:
The x-coordinate of the solution to the system of equations is _______________
PLEASE HELP!! :) :)
Answers
2x+3y= 2
-2x + 2y = 8
2x + 3y = 2
5y = 10
y= 2
-x + 2 = 4
-x = 2
x = -2
IMAGE ATTACHED
If A(1, 1), B(5, 4), C(10, 3), and D(6, 0) are the vertices of a quadrilateral, do the points form a parallelogram? Justify your answer.
Yes, it is a parallelogram because the slope of segment AB equals the slope of segment DC, which equals negative start fraction three over four end fraction comma and AD = BC = 5 units.
Yes, it is a parallelogram because the slope of segment AB equals the slope of segment DC, which equals start fraction three over four end fraction comma and AB = CD = 5 units.
Yes, it is a parallelogram because the midpoint of the diagonals segment AC and segment BD is (5.5, 2).
No, it is not a parallelogram because the slope of segment AB = 1 and the slope of segment DC equals negative start fraction three over four end fraction full stop
Answers
The slope of AB = (4-1)/(5-1)= 3/4
The slope of DC = (0-3)/(6-10) = 3/4
Thus, the two segments have equal slope,
Both segments are also equal in magnitude 5 units
Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 5 want an ice cream party, 7 want a movie party, 10 want a costume party, and the rest are undecided. If 20% , percent want an ice cream party, how many students are in the class?
Answers
5 x 5 = 25
There are 25 students in the class, 3 are undecided.
The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measures 120 ft by 80 ft, and the expansion will increase its area by 4,400 ft2. By how many feet should the length of the parking lot be increased? A = lw 1.2 f
Answers
Answer: The length of the parking lot should be increased 20 ft.
Please, see the attached files.
Thanks.
Answer:
b on edge
Step-by-step explanation: