Answers
The perimeter of △ABC is approximately 25.93 units. The area of △ABC is approximately 28.62 square units.
Given that △ABC has m∠A=60°, m∠C=45°, and AB=9, we can use trigonometry to find the missing side lengths and then use them to calculate the perimeter and area of the triangle.
First, we can use the fact that the sum of the angles in a triangle is 180° to find m∠B:
m∠A + m∠B + m∠C = 180°
60° + m∠B + 45° = 180°
m∠B = 75°
Next, we can use the law of sines to find the length of side BC:
sin 60° / 9 = sin 75° / BC
BC = sin 75° * 9 / sin 60°
BC ≈ 8.14
Finally, we can use the fact that the sum of the side lengths of a triangle is its perimeter to find the perimeter of △ABC:
Perimeter = AB + BC + AC
Perimeter = 9 + 8.14 + AC
To find AC, we can use the fact that the angles in a triangle add up to 180°:
m∠A + m∠B + m∠C = 180°
60° + 75° + m∠C = 180°
m∠C = 45°
Now we can use the law of sines again to find AC:
sin 45° / AC = sin 60° / 9
AC = sin 45° * 9 / sin 60°
AC ≈ 7.79
Substituting this value into the equation for the perimeter, we get:
Perimeter = 9 + 8.14 + 7.79
Perimeter ≈ 25.93
Therefore, the perimeter of △ABC is approximately 25.93 units.
To find the area of △ABC, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
We can use the fact that △ABC is a right triangle (since m∠C = 45°) to find the height:
sin 45° = height / 9
height = sin 45° * 9
height ≈ 6.36
Substituting the values for the base and height into the formula for the area, we get:
Area = 1/2 * 9 * 6.36
Area ≈ 28.62
Therefore, the area of △ABC is approximately 28.62 square units.
Perimeter of △ABC: 20.67 units,
Area of △ABC: 20.11 square units.
Explanation:In △ABC, we are given that ∠A = 60°, ∠C = 45°, and AB = 9 units. To find the perimeter, we need to calculate the length of side BC. Using the angles, we can determine that ∠B = 180° - ∠A - ∠C = 75°. Now, applying the Law of Sines, we find BC ≈ 8.21 units. The perimeter, therefore, is the sum of the three sides: 9 + 8.21 + BC ≈ 20.67 units.
For the area, we can use the formula A = 0.5 * AB * BC * sin(∠C). Substituting the known values, we get A ≈ 0.5 * 9 * 8.21 * sin(45°) ≈ 20.11 square units.
Explanation:
In the main answer, we first addressed the perimeter by finding the length of side BC through the Law of Sines. The perimeter is then calculated by summing the three sides.
Moving on to the area, we employed the formula for the area of a triangle involving two sides and the sine of the included angle. Substituting the given values, we obtained the area of △ABC as approximately 20.11 square units.
These calculations showcase the application of trigonometric principles in solving geometric problems involving angles and side lengths. The Law of Sines and the area formula for triangles provide a mathematical framework for determining these essential properties.
Related Questions
The angle measurements in the diagram are represented by the following expressions.
Answers
so we must set our equation equal to 180.
8x+74+2x+56=180
which simplifies to 10x+130=180
then subtract 130 from both sides.
10x=50
x=5
So we plug in 5 to find the measure of b.
2(5)+56=b
10+56=b
66=b
the measure of angle b is 66 degrees
PAGEANT is most similar in meaning to beauty, sovereign, gallant, show?
Answers
The term 'pageant' is most similar in meaning to 'show.' Both terms refer to public exhibits or performances intended to entertain.
Explanation:The word pageant is conceptually closest in meaning to the term 'show.' A pageant typically refers to a public entertainment consisting of a procession of people in elaborate, colorful costumes, or an outdoor performance of a historical scene. This coincides with the term 'show,' which generally signifies a public display or exhibition, especially when intended to entertain. Drawing from the research conducted by anthropologist Marcia Ochoa, we commonly see pageants in the context of beauty competitions, such as Miss Venezuela, or similar contests held by specific communities, such as transformistas in Venezuela. These events focus on the public presentation of candidates, much like a show.
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The word “pageant” is most similar in meaning to “show”.
The word “pageant” is derived from the Latin word "pagina," which means a play or stage. In modern usage, a pageant is a public entertainment consisting of a procession of people in elaborate, colorful costumes, or an outdoor performance of a historical scene. It’s essentially a type of show that is often grand and celebrates a special event or anniversary.
Beauty: This term often refers to a combination of qualities, such as shape, color, or form, that pleases the aesthetic senses, especially the sight. In the context of a beauty pageant, it’s a show that judges its contestants primarily on their physical appearance. However, the term “beauty” itself doesn’t convey the aspect of a show or performance that “pageant” does.
Sovereign: This term refers to a supreme ruler, especially a monarch. A sovereign might be a figure in a pageant, but the word “sovereign” itself refers to a position of power and rule, not a show or performance.
Gallant: This term is used to describe someone brave, heroic, or chivalrous. A person might behave gallantly in a pageant, but again, the word “gallant” itself doesn’t convey the meaning of a show or performance.
So, among the options provided, “pageant” is most similar in meaning to “show”, as both involve a public display or performance.
For which equation would x = 0 be a solution?
6x = 1/6
4x = -4
(7 3/8)x = 0
1,000x = 0.001
Answers
multiplying by 0 will make the answer 0.
7 3/8(0) = 0
(7 3/8)x = 0
Answer:
The answer is 0 hope this helps
Step-by-step explanation:
Which equation represents y = x^2 + 16x + 70 in vertex form?
y = (x + 8)^2 − 16
y = (x + 8)^2 − 64
y = (x + 8)^2 + 68
y = (x + 8)^2 + 6
Answers
Answer: D
Step-by-step explanation:
y = x² + 16x + 70
-70 -70
y - 70 = x² + 16x next, complete the square by adding [tex](\frac{16}{2})^{2}[/tex] to both sides
y - 70 + 64 = x² + 16x + 64 remember that x² + 16x + 64 is a perfect square of (x - 8)²
y - 6 = (x + 8)²
+6 +6
y = (x + 8)² + 6
Which two numbers on the number line have an absolute value of 1? Select the location of both numbers on the number line.
-55 -4 -3 -2 -1 0 1 2 3 4
Answers
2. Solve the following system. Show all your work. -3x + 2y + z = -6 x + 3y + 2z = 5 4x + 4y + 3z = 13 Is there a step I'm skipping because every time I add the first 2 equations, I keep getting -2x + 5y + 3z with no variables eliminated.
Answers
-3x + 2y + z = -6
(3)x + 3y + 2z = 5(3) We want to get rid of any variable within 2 equations. The easiest one would be by multiplying both sides of eq#2 by 3 and add it to eq#1.
-3x+2y+z=-6
3x+9y+6z=15
Add them together to get 11y+7z=9
(-4)x+3y+2z=5(-4) Now,multiply the original eq#2 by -4 to cancel out x in the last equation
-4x-12y-8z=-20
4x + 4y + 3z = 13
add them together to get -8y-5z=-7
Now multiply the eq 11y+7z=9 by 5 and the equation -8y-5z=-7 by 7 to cancel out the z variable when we add them together.
Once we multiply them, we get
-56y-35z=-49
55y+35z=45
add them together to get -y=-4 and we know y=4
substitute y into any equation here that has y and any other 1 variable like -8y-5z=-7 and get z=-5
Finally, we know y=4 and z=-5, we can substitue that into any of the original eqs like -3x + 2y + z = -6 and we get x=-3
To check, just substitute these values into any of the equations above
what is the answer math will give brainliest
Answers
Hey there!!
Given :
g(x) = ax² + 24
and
g(4) = 8
g(4) = a(4)² +24
g(4) = 16a + 24
8 = 16a + 24
-16 = 16a
a = -1
The constant is -1.
g(-4) =?
g(-4) = -1(-4)² + 24
g(-4) = -16 + 24
g(-4) = 8
The answer is (A)
Hope it helps!
Kris wanted to understand whether students at her school were in favor of an extended school day. She surveyed some students and displayed the results in the table below: In favor Opposed Undecided Grade 9 6 4 8 Grade 10 10 11 9 Grade 11 12 15 11 Grade 12 15 6 14 If the principal randomly selects a student in grade 10 from this survey, what is the probability that the student is opposed to extending the school day?
Answers
the table below:
Grade In favor Opposed Undecided Total
Grade 9 6 4 8 18
Grade 10 10 11 9 30
Grade 11 12 15 11 38
Grade 12 15 6 14 35
If the principal randomly selects a student in grade 10 from this survey,
the probability that the student is opposed to extending the school day
P ( student in grade 10 is opposed)= Number of student in opposed(grade10) / total number of students in grade 10
Number of student opposed who is in grade10 = 11
total number of students in grade 10 = 30
P( student in grade 10 is opposed)= [tex]\frac{11}{30}[/tex]
= 0.37
the probability that the student is opposed to extending the school day= 0.37
Final answer:
The probability that a randomly selected grade 10 student from the survey is opposed to extending the school day is 11/30, or approximately 36.67%.
Explanation:
The student's question pertains to the probability of selecting a grade 10 student who is opposed to extending the school day based on the survey results provided.
To calculate this probability, we consider only the grade 10 students. According to the table, there are 10 students in favor, 11 opposed, and 9 undecided within grade 10, making a total of 10 + 11 + 9 = 30 students surveyed in the tenth grade.
The probability that a randomly selected grade 10 student is opposed to an extended school day is the number of grade 10 students opposed divided by the total number of grade 10 students surveyed.
Mathematically, it can be represented as P(Opposed) = Number of opposed students in Grade 10 / Total number of students in Grade 10 surveyed. By plugging in the numbers:
P(Opposed) = 11 / 30
Therefore, the probability is 11/30 or approximately 0.3667, which can be expressed as a percentage by multiplying by 100, yielding about 36.67%.
-4x+3y=21, where x is time and y is velocity in kilometers per hour. Use this function to determine when a certain particle will reach 30km/hr.
Answers
4
There are 112 students in the Hammond Middle School marching band. The band director wants students to march with 14 students in each row for the upcoming parade. How many rows will there be
Answers
Answer
Find out the how many rows will there be .
To proof
let us assume that the number of the rows will be x.
As given
There are 112 students in the Hammond Middle School marching band.
The band director wants students to march with 14 students in each row for the upcoming parade.
than the equation becomes in the form
[tex]x = \frac{112}{14}[/tex]
x = 8
Therefore the number of the rows will be 8.
Hence proved
Express 15$ for 10 gallons as a unit rate
Answers
That would be $1.50 per Gallon
PLEASE HELP!
1. The following formula relates the quantities temperature in Celsius (C) and temperature in kelvins (K). C = K − 273.15
(a) Write two other related equations.
(b) If the temperature is 23 in degrees Celsius, what is the temperature in kelvins? Show your work.
(c) Which is greater, 300 kelvins or 25 degrees Celsius? Show your work.
Answers
A: The other related equations would be:
K = °C + 273.15
K = °F + 457.87
Note: There are other equations that can be related, these are just ones that I find to be related. This is open to interpretation.
B:
23° C + 273.15 = 269.15 K
C:
300 K - 273.15 = 26.85 °C
300 Kelvins is greater than 25 degrees Celsius.
What is 28.37 rounded to nearest whole number
Answers
The number after rounded to nearest whole number is,
⇒ 28
We have to given that,
To round the number 28.37 nearest whole number.
Since, Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value.
Here, Number is,
28.37
Since, 3 < 5
Hence, The number after rounded to nearest whole number is,
⇒ 28
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Torri had $20 to buy a birthday present for her dad. She decided to buy a DVD for $18. The sales tax is 7%. Does que have enough money? Explain your reasoning.
Answers
Sales Tax = 7% of the 18$, which means we should multiply 18 by 0.07:
18 × 0.07 = 1.26
Sales tax = 1.26$
Now we have to add the sales tax to the original cost of the DVD which is 18$:
18 + 1.26 = 19.26
So the total cost is 19.26$
Since she has 20$, she then has enough money.
HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!
Which of these shows the result of using the first equation to substitute for y in the second equation, then combining like terms? y = 2x 2x + 3y = 16
A. 8x = 16
B. 4x = 16
C. 5x = 16
D. 5y = 16
Answers
This is my answer
By substituting y = 2x into the second equation and combining like terms, we get the equation 8x = 16.
Explanation:This question is from the field of Algebra. You are asked to substitute the first equation into the second equation, then simplify by combining like terms. Substituting y = 2x from the first equation into the second equation 2x + 3y = 16, we replace y with 2x, thus transforming the second equation into 2x + 3(2x) = 16. Distributing the 3 to the 2x within the parentheses gives us 2x + 6x = 16. By combining the like terms on the left side, we get 8x = 16 which is option A.
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Anita began solving the system {x+y=8, x−y=2 by writing 2x=10 .
Which property justifies this step?
Division Property of Equality
Multiplication Property of Equality
Addition Property of Equality
Substitution Property of Equality
Answers
Anita began solving the system {x+y=8, x−y=2 by writing 2x=10 .
x+y=8
x−y=2
When we add both equations , we will get 2x = 10
x+x becomes 2x
+y -y becomes 0
8 + 2 becomes 10
So by adding two equations we got 2x = 10
Hence we say Addition Property of Equality.
Addition Property of Equality means adding both sides of equations.
x terms and y terms are added . then number are added on the right side
Answer:
Option C is correct
Addition property of Equality justifies the step.
Step-by-step explanation:
Given the system of equation: x+y = 8 and x-y = 2.
Addition Property of Equality: The method of solving systems of linear equations is the addition Property, in which the two equations are added together to eliminate one of the variables.
Adding the equations states that we add the left sides of the two equations together, and we add the right sides together.
Using the addition property in equation: x+y=8 and x-y =2
then,
[tex](x+y)+(x-y)=8+2[/tex] or
[tex](x+x)+(y-y)[/tex] =10
Eliminate the y- variable; we have
2x=10
Therefore, the only property justifies the step is, Addition Property of Equality.
Bart and sam played a game in witch each player earns or loses points earned or lost.The player with the greatest score after two turns wins.Bart earned 123 and lost 180 points.Sam earned 185 points and lost 225 points.Use a problem-solving model to find which person won the game.Explain
Answers
you need a lot to explain
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
An on-line electronics store must sell at least $5000 worth of computers and printers per day. Each printer costs $350 and each computer costs $750. The store can ship a maximum of 20 items per day. Which system of inequalities models correctly the number of computers, c, and number printers, p, the store could sell per day?
Answers
D is the correct answer I think.
What is the answer > , <, or = -37/8______-4.63
Answers
the expression 9/2÷3 is the same as
Answers
Answer:
4.5 ÷ 3
Step-by-step explanation:
9/3 = 4.5
therefore this is the same as the previous expression
Final answer:
The expression 9/2 / 3 is equivalent to 9/2 * 1/3, which simplifies to 9/6 or 1.5. This multiplication by the reciprocal ensures the equality of the operation.
Explanation:
The expression 9/2 / 3 can be understood in terms of multiplication and division. When we divide by a number, it is the same as multiplying by its reciprocal. In this case, dividing by 3 is the same as multiplying by 1/3. Hence, we can rewrite the expression as 9/2 * 1/3.
To calculate this, we multiply the numerators together and the denominators together:
(9*1) / (2*3) = 9 / 6 = 1.5, or 3/2 when written as a fraction.
Performing the same operation on both sides of the equals sign maintains the equality. So, if any fraction has the same number in the numerator and the denominator, that fraction is equal to 1.
Someone help me please? giving away 35 points and brainliest (only if right)
1.Complete the similarity statement for the two triangles shown
Enter your answer in the box Δ XBR~ Δ
Answers
Triangle from angles YNJ=65cm
Answer:
that guy deserves the brainliest so this is just so you can get it to him
Step-by-step explanation:
There's 6 times as many dogs as cats.If the total number of dogs and cats is 35, how many dogs are there?
Answers
Let cats = X
Then doges = 6x ( 6 times as many cats, so multiply 6 by number of cats)
Now you have X + 6X = 35 ( number of cats plus number of doags equal 35)
X +6x = 35
Simplify:
7X = 35
Divide both sides by 7 to solve for x:
X = 35 / 7
X = 5
Cats = X, so there are 5 cats.
Dogs = 6X = 6(5) = 30 total dogs.
The second-largest state in the us is texas, covering 268,580 square miles (including water). What is the approximate radius of a sphere with the same surface area as the area of texas?
Answers
The state of texas covers approxmiately 268,581 squared mi. During a hail storm the entire state is covered in 1billion meters of hail.(average radius of 1.4292cm)assume the hail falls so that the gaps of air are limited to 26% of the volume.
Answer:
the answer is C. 146 miles
2x+5y=0 x+5y=-10 what is the answer? Solving systems of equations by elimination
Answers
x=10
Please comment if you dont understand the process. I am willing to help!
A plumber charges $55 per hour plus a $50 service charge. Kevin hired the plumber to install a new hot water heater. What are the total charges if the plumber took 4 hours to complete the installation? A. $220 B. $250 C. $255 D. $270
Answers
D. $270
Hello...
A plumber charges $55 per hour plus a $50 service charge. Kevin hired the plumber to install a new hot water heater. What are the total charges if the plumber took 4 hours to complete the installation? A. $220 B. $250 C. $255 D. $270
We Know:
$55 per hour
$50 Service Charge
Plumber took 4 hours
Find:
The total cost
Solution:
55 x 4 = 220
220 + 50 = 270
Answer:
Total Cost - $270
What is the result of dividing 2x^3+6x^2+6x+2 by x+1 ?
PLEASE HELP, WILL GIVE 5 RATING
Answers
2x² + 4x + 2
using long division to obtain the quotient
The result of dividing the polynomial 2x³ + 6x² + 6x + 2 by x + 1 is 2x² + 4x + 2, which can be obtained using synthetic division.
Explanation:The given question is about polynomial division. To divide a polynomial, we commonly use long division or synthetic division. In this case, we are dividing the polynomial 2x³ + 6x² + 6x + 2 by (x + 1).
Using synthetic division, we get:
First, write down the coefficients of the dividend polynomial (2, 6, 6, 2) and below them the divider (in this case, -1, because we have 'x + 1' and '-1' is the root of 'x + 1'). Copy down the leading coefficient (2 in this case) to the bottom line. Multiply it by the root identified earlier, and add it to the next coefficient (2*-1 = -2; 6 + -2 = 4). Repeat this process (4*-1 = -4; 6 + -4 = 2). At the end, you should see that the remainder is zero (2*-1 = -2; 2 + -2 = 0).
Therefore, the quotient is 2x² + 4x + 2.
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Help with algebra please (30 points)
Answers
[tex]Q6.\\v(x)=x^2-20\\\\v(x+4)=(x+4)^2-20=x^2+2(x)(4)+4^2-20\\=x^2+8x+16-20=x^2+8x-4[/tex]
[tex]TRUE[/tex]
[tex]Q7.\\c(x)=5x^2+12x,\ d(x)=7x+5x^2\\\\c(x)-d(x)=(5x^2+12x)-(7x+5x^2)=5x^2+12x-7x-5x^2\\\\=(5x^2-5x^2)+(12x-7x)=5x[/tex]
[tex]Q8.\\f(x)=6x+1,\ f(a)=25\\\\f(a)=6a+1\\\\\text{substitute}\\\\6a+1=25\qquad|-1\\\\6a=24\qquad|:6\\\\a=4[/tex]
The correct answer is a = 4
Gina takes out a loan totaling $5000. The loan has a 5% interest rate that is compounded monthly. What is the total due after 48 months, assuming that she has not made any payments?
Answers
where A is the investment/loan after n years, P is the original investment/loan and i% is the interest per annum.
A=5000(1+0.05)^48
A=52006.35
Which digit has the greatest value in the number 1,567
Answers
1 has the greatest value in the number 1,567.
What is Place value?A number's place value is the worth of each digit. Depending on where it sits in a number, each digit has a varied value. The position of the digit in the number determines whether two similar digits in the same number have different values.
For example, the place value of 5 in 3458 is 5 tens, or 50. However, the place value of 5 in 5781 is expressed as 5 thousands or 5,000.
Given number:
1567
Now, keep looking the place value of each digit
7 - ones ---> 7x 1
6 - tens ---> 6 x 10
5 - hundred ---> 5 x 100
1 - thousand ---> 1x 1000
As, 1 has thousand place value.
Hence, 1 has the greatest value in the number 1,567.
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-3/4x < 12
-
13c < -169
-
5b-28 > 27
3x-7> 4x + 2
-
Solve each inequality for the variable. Show your work
Answers
-3 / 4x < 12,
to get rid of the numbers attached to the variable 'x', you would divide the numbers, since, the original is multiplying with x, you would do the opposite, and the opposite of multiplication, is division.
So, now our equation is, - 3 / 4x divided by - 3 / 4, which would leave X by itself, then we have to do that same thing to the 12, which would be, 12 divided by - 3 / 4, which would equal, 16.
-3 / 4 < 12
÷ - 3 / 4 ÷ - 3 / 4
_____________
X > 16
Now, our equation is X > 16, which is the answer, to problem number one.
(Also a quick note, when you divide by a negative, the inequality symbol flips, for example, when we divided by -3 / 4, our inequality symbol changed from the less than symbol, to the more than symbol.)
___________________________________
Let's take a look at problem number two:
13c < -169,
Okay, so, again, you're trying to get C by itself. The number 13 is multiplying with C, so, you need to do the opposite, and divide, so you can get C by itself.
13c divided by 13 equals C
13c/13 = C
and
- 169 divided by 13, equals, -13,
So, the answer is, C < -13
Or,
13c < - 169
÷ 13 ÷ 13
__________
C < - 13
___________________________________
Let's take a look at problem number 3:
5B - 28 > 27,
Okay, so now, we have another number on the same side as B, so, we get rid of that first, it's subtracting, so now we do the opposite, and add it to the other side.
5B - 28 > 27
+28 +28
__________
5B > 55
Now, we divide both sides by 5:
5B > 55
÷5 ÷5
_______
B > 5
___________________________________
Now, Let's take a look at problem number 4:
3x - 7 > 4x + 2,
okay, so, we have multiple steps to take with this equation.
First, we want to get X by itself, so, we have to get rid of the -7, so, we do the opposite, and the opposite of subtracting, is adding.
3x - 7 > 4x + 2
+ 7 + 7
___________
3x > 4x + 9
Now, you only want to have one number with X, per equation, so, you need to move 4x to the other side, the way we do that, is by subtracting 4x.
3x > 4x + 9
-4x -4x
__________
-1x > 9
We can't have a negative number attached to the x, because that's like having a negative X, so, we have to divide one more time.
-1x > 9
÷-1 ÷-1
_______
Since, we are dividing by a negative, the inequality sign is going to flip, which would make the answer:
X < -9
___________________________________
I hope this helps!