(A) find the perimeter of triangle BCF, to the nearest hundredth
(B) find the area of triangle BCF
Answers
Perimeter of triangle BCF is 19.24 units. Area of triangle BCF is 15 [tex]units^{2}[/tex].
Distance formula = [tex]\sqrt{(x1-x2)^{2}+(y1-y2)^{2} }[/tex]
Perimeter = a + b + c
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
s = [tex]\frac{a+b+c}{2}[/tex]
Given, B(3,2), C(1,-2), F(-3,5).
BC = a = [tex]\sqrt{(3-1)^{2} +(2+2)^{2} }[/tex]
= [tex]\sqrt{2^{2} +4^{2} }[/tex]
= [tex]\sqrt{4+16}[/tex]
= [tex]\sqrt{20}[/tex]
= 4.47 units
CF = b = [tex]\sqrt{(1+3)^{2} +(-2-5)^{2} }[/tex]
= [tex]\sqrt{4^{2} +7^{2} }[/tex]
= [tex]\sqrt{16+49}[/tex]
= [tex]\sqrt{65}[/tex]
= 8.06 units
BF = c = [tex]\sqrt{(3+3)^{2} +(2-5)^{2} }[/tex]
= [tex]\sqrt{6^{2} +3^{2} }[/tex]
= [tex]\sqrt{36+9}[/tex]
= [tex]\sqrt{45}[/tex]
= 6.71 units
Perimeter = a + b + c
= 4.47 + 8.06 + 6.71
= 19.24 units
s = [tex]\frac{a+b+c}{2}[/tex]
= [tex]\frac{19.24}{2}[/tex]
= 9.62
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
= [tex]\sqrt{9.62(9.62-4.47)(9.62-8.06)(9.62-6.71)}[/tex]
= [tex]\sqrt{9.62*5.15*1.56*2.91}[/tex]
= [tex]\sqrt{224.91}[/tex]
= 14.99
≈ 15 [tex]units^{2}[/tex]
Hence, perimeter is 19.24 units and area is 15 [tex]units^{2}[/tex].
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Related Questions
How do you solve -110 + 96
Answers
Answer: -14
Step-by-step explanation:
−110+96
Add −110 and 96 to get −14.
−14
Answer: -14
Step-by-step explanation:
In this case, it's best you bring out the negative
- (110 - 96)
- (14)
= -14
If T is the midpoint of RS and V lies between R and T, which statement must be true?
Answers
The statement which must be true given the premise that; T is the midpoint of RS and V lies between R and T is; Choice A; RV + VT = TS.
Which answer choice represents a true statement?It follows from the task content that the answer choice which represents a true statement regarding the given description be identified.
Since it is given that T is the midpoint of RS, it follows that;
RT = TS.
Also, it is given that point V lies between R and T; it therefore obviously follows that the equation which is true about RV and VT is;
RV + VT = RT.
Therefore, since segments RT and TS are equal;
It follows from the substitution property of equality that;
RV + VT = TS.
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Visit each of the three credit reporting agencies and find an example of a credit report. For each, describe a different portion of the credit report
and how it is evaluated for credit worthiness.
Answers
Answer:
Doesn't make a lot of sense. Can you be more specific.
Step-by-step explanation:
The Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit
What are credit reporting agencies?Credit reporting companies, also known as credit bureaus or consumer reporting agencies, are companies that compile and sell credit reports.
Given are three credit reporting agencies.
Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit. Your creditworthiness is what creditors look at before they approve any new credit to you. The 3 C's of credit worthiness are Character, Capacity and Capital. Creditworthiness is determined by several factors including your repayment history and credit score.
Therefore, the Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit.
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What are all prime factorization of 34
Answers
Explanation:
7 x 12
Find the solution set of 12x-31 + 1 = 6.
x = 1 or x=-1
x = 4 or x = -1
x = 5 orx = -2
x=4 or x = -4
Answers
hope this helps!!
Line n contains points (4, –1) and (4, 9). Point p has coordinates (1, 6).
Answers
The distance between the line containing points (4, –1) and (4, 9) and point p (1,6) is of:
3 units.
Distance of point and lineThe standard equation of a line is given by the rule presented as follows:
ax + by + c = 0.
The coordinates of the points which we want to find the distance from the line are given as follows:
(x0,y0).
Then the shortest distance is given by the equation presented as follows:
D = |a(x0) + b(y0) + c|/sqrt(a²+b²).
The two points of the line are given as follows:
(4, –1) and (4, 9).
Since the x-coordinate is constant, the line has a slope of infinite, meaning that it is a vertical line defined as follows:
x = 4.
x - 4 = 0.
The point p has these following coordinates:
p(1,6).
Hence the distance between the point and the line is:
D = |a(x0) + b(y0) + c|/sqrt(a²+b²).
D = |1(1) + 0(6) - 4|/sqrt(1² + 0²).
D = |-3|
D = 3 units.
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PLS HURRY I NEED THE ANSWER FAST!!!!!!
Paula makes purses. The materials cost $2.25 per purse. She sells them for $5.00 each. Paula wants to invest $5000 for some new equipment. Which of these could be used to determine x, the number of purses Paula must sell to pay for the new equipment?
A 5.00x - 2.25x = 5000
B 5.00x + 2.25x = 5000
C 5.00x = 5000
D 2.25x = 5000
Answers
The equation that could be used to determine x, the number of purses Paula must sell to pay for the new equipment is;
A. 5.00x - 2.25x = 5000
How to solve equation word problems?We are told the materials costs $2.25 per purse.
She sells the materials for $5 each.
If the number of materials she purchased was x, it means that;
Selling price - Cost price = 5.00x - 2.25x
Now, we are told that she wants to invest $5000 for some new equipment. This means that she must realize at least $5000 in profit from the sales she is making of the materials.
Since the formula for profit is;
Profit = Selling Price - Cost Price
Then, we will have;
5.00x - 2.25x = 5000
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Answer: 5.00x - 2.25x = 5000
Step-by-step explanation:
What is the greatest common factor (GCF)?
b^5+ 2b^4+ 3b^3+b^2
A. 2b
B. b^2
C. b^3
D. 3b^4
Answers
The Greatest Common Factor is [tex]b^{2}[/tex] Option B
What is Greatest Common Factor?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers
Find the common factors of each term in order to find the greatest common factor (GCF).
The Prime Factors of:
[tex]b^{5}[/tex] = [tex]b^{5}[/tex]
2[tex]b^{4}[/tex] = 2[tex]b^{4}[/tex]
[tex]3b^{3}[/tex] = [tex]3b^{3}[/tex]
[tex]b^{2}[/tex] = [tex]b^{2}[/tex]
From the common factors, the greatest common factors is [tex]b^{2}[/tex]
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Which expression shows the distance you would drive from the library to the grocery
store along this road?
|-5+7)
-151+171
-5+7
1-5+171
Library Home
CLEAR
Grocery
Store
CHECK
Answers
Answer:
1-5+171
Step-by-step explanation:
Which triangle is △ABC similar to and why?
Answers
Answer:
can we get a picture
Step-by-step explanation:
Maria deposits $1,400 into the Park Avenue Bank. The account pays 2.5% annual interest compounded semi-annually. What is her ending balance after 3
years? Round to the nearest cent (2 digits after the decimal point).
The ending balance is
Answers
The ending balance after 3 years is $1508.34
What is compound interest?
The interest that is paid on both the initial principal and the accumulated past interest is known as compound interest.
The compound amount and compound interest are calculated by:
Compound amount, [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Compound interest, [tex]I = A - P[/tex]
where, P is the principal amount
r is the rate of interest(in decimal)
n is the number of times the interest is compounded annually
t is the time.
Given, Principal amount, P = $1400
rate of interest, r = 2.5% = 0.025
n = 2 (compounded semi-annually)
t = 3 years
Then, the compound amount is calculated by:
[tex]A=1400(1+\frac{0.025}{2} )^{2*3}\\[/tex]
or, [tex]A=1400(1+0.0125 )^{6}\\[/tex]
or, [tex]A=1400(1.0125 )^{6}\\[/tex]
or, [tex]A=1508.34[/tex]
Therefore, the ending balance is $1508.34
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Find the distance between the points (8,–2) and (8,7)
Answers
Answer:
9 units
Step-by-step explanation:
We see that on the x-axis, everything is equal.
On the y-axis, there are -2 and 7.
So we are finding the distance between -2 and 7
|-2|+|7|=9
So the distance between the points is 9 units.
You have been gotten a job offer and the company wants you to start out at 45,000 and will give you 5% raise every year write an equation you could use to determine how much you could be making after x number of years
Answers
Answer:
$51,750
Step-by-step explanation: We are going to make x = 3 and we will use the i=prt equation meaning
Step 1: (45,000)(0.05)(3)= 6750
Step 2: 45,000+ 6750= 51,750
Solution: $ 51,750
I’ll give you brainliest if you have the answer
Answers
Answer:
BGIA
Step-by-step explanation:
B = 0,4
G =-4,3
I = 4,0
A = 0,1
On a map of Texas, the cities of Midland, Lubbock, and Odessa form a triangle.
Midland is
20 miles from Odessa, and Lubbock is 113 miles from Midland. What is the farthest,
in miles,
Odessa could possibly be from Lubbock?
Answers
If Midland is 20 miles from Odessa, and Lubbock is 113 miles from Midland. Then 111.22 miles is Odessa from Lubbock.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
The cities of Midland, Lubbock, and Odessa form a triangle.
The distance between Midland and Odessa is 20 miles.
The distance between Lubock and Odessa is unknown, we need to find this.
This can be find by using Pythagorean theorem
Odessa from Lubbock=20²+x²
113²=20²+x²
12769=400+x²
12369=x²
x=111.22
Hence, 111.22 miles, Odessa could possibly be from Lubbock.
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Help with this precalc question
Answers
The principal amount invested at the rate of 6% for 3 years, then the investment results in $717.38.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the given information in the question,
Principle, P = $600
Rate, r = 6%
Time, t = 3 years.
Compound quarterly, r = 6/4
t = 4 × 3 = 12
Use the formula,
[tex]A = P(1+\frac{r}{100} )^t[/tex]
A = 600(1 + 6/4 × 100)¹²
A = 600 × (203/200)¹²
A = $717.38
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What value is equivalent to (8+2) + (6 − 4) × 3?
Answers
Answer:
16
Step-by-step explanation:
(8+2) + (6 − 4) × 3
= 10+6
=16
Alicia deposited $400 in the bank. The bank paid her simple interest at the rate of 5 percent
she have in her account at the end of 6 months?
O $10
O $20
O $410
O $420
Answers
At the end of 6 months she will have $410 when calculated using simple interest.
What is simple interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Main Body:
Principle =$400
Rate = 5%
Time = 6 months = 1/2 years
Simple interest = P*R*T/100
S.I. = 400*5*(1/2)/100
S.I. = 10
Hence total amount is 400+ 10= $410.
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In TY’s math class, 20% of students earned an A on a test. If there were 30 students in the class, how many got the A
Answers
Answer:
Step-by-step explanation
Answer:
6 students
Step-by-step explanation:
[tex]\frac{1}{5} = \frac{x}{30}[/tex]
[tex]30 = 5x[/tex]
[tex]6=x[/tex]
A medic's bag contains individually wrapped tongue depressors (each costing 4 cents) and Band-Aids (each costing 8 cents). If the materials are worth $12.48 and there are 184 individual packages in total, how many tongue depressors and Band-Aids are there?
Answers
The total number of tongue depressors and Band-Aids are 56 and 128 respectively.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given that, a medic's bag contains individually wrapped tongue depressors (each costing 4 cents) and Band-Aids (each costing 8 cents). If the materials are worth $12.48 and there are 184 individual packages in total,
Let the number of wrapped tongue depressors be w and that of Band-Aids be b,
Therefore,
w+b= 184
0.04w+0.08b = 12.48
w+2b = 312
On solving the equation, by elimination method, we get,
b = 128
Therefore, w+128 = 184
w = 56
Hence, the total number of tongue depressors and Band-Aids are 56 and 128 respectively.
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Zoe wants to buy 6 tins of beans for the cheapest possible price. Shop A and Shop B both have a special offer. Shop A 5% off the normal price of 48p each Shop B 65p each Buy 2 get 1 free Which shop should Zoe buy the beans from? You must show how you get your answer.
Answers
If LM = 2x - 9 and KN = x + 15 in rhombus KLMN, find the value of x.
Answers
The value of x in the rhombus is 24 units.
According to the question,
We have the following information:
LM = 2x - 9 and KN = x + 15 in rhombus KLMN.
Now, we know that in a rhombus opposite sides are equal. In this case, LM and KN are opposite sides.
So, we have the following expression:
2x-9 = x+15
Adding 9 to both sides of the equation:
2x = x+15+9
2x = x+24
Subtracting x from both sides of the equation:
2x-x = 24
x = 24
Hence, the value of x for the given rhombus is 24 units.
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Yu is considering two different banks for
his $3,000 savings account:
OPTION B
2% FOR 10 YEARS
COMPOUND
INTEREST
a. What is the interest earned on option A?
OPTION A
4% FOR 10 YEARS
SIMPLE INTEREST
b. What is the total value on option A?
c. What is the interest earned on option B?
d. What is the total value on option B?
e. Which is the better option?
Answers
The simple or compound interest will be
a. $120
b. $12,000
c. $15,000
d. $18,000
e. Option B is better as it is giving us more interest.
Formula of total simple interest is
SI = (P * R * T) /100 where
P = initial principal balance
r = annual interest rate
t = time (in years)
Formula of compound interest is
C.I.= P × [tex](1 + r/n)^{nt}[/tex] - P where
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
a. By applying the formula given above we will get
SI = (3000 * 0.4 * 10) / 100
SI = $120
b. Formula to find total value is P * R * T. By applying this we will get
I = 3000 * 0.4 * 10
I = $12,000
c. By putting values in the formula we will get
CI = 3000 * [tex](1 + 0.2)^{10}[/tex] - 3000
CI = 18000 - 3000
CI = $15,000
d. formula to find total compound value is P * [tex](1 + r/n)^{nt}[/tex]. By applying this in the formula we get
A = 3000 [tex]( 1 + 0.2 )^{10}[/tex]
A = $18,000
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Sam is driving on the highway. He begins the trip with 12 gallons of gas in his car. The car uses up one gallon of gas every 35 miles.
Let G represent the number of gallons of gas he has left in his tank, and let D represent the total distance (in miles) he has
traveled. Write an equation relating G to D, and then graph your equation using the axes below.
Answers
equation and graph attached
Kurt spen $96.39 over 4(1)/(4) months on movie streaming services. If he spent the same amount of money each month, how much money in dollars, did Kurt spend per month on movie streaming services?
Answers
Kurt spent a total amount of $22.68 a month on movie streaming services.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, or operations such as multiplication and division.
These operations are used from the unit rates, as when we have an amount over some time, then the amount per unit of time is the total amount divided by the total time.
We have been given the important parameters are;
The total amount = is $96.39.
The time is a mixed number, 4 and 1/4 months, hence it will be 4.25 months,
Therefore, his monthly spending is given by the unit rate as;
96.39/4.25 = $22.68 a month.
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wht r = math please help...........
Answers
2.2=r -2/3
Simpfly-r=2.8
Answer:
r = -8.6
Step-by-step explanation:
ooooo IXL, one of my fav programs from my school days
Anyway
Multiply by -3 to get rid of that awful fraction
[tex]-3*2.2=\frac{r+2}{-3} *-3[/tex]
Solve that:
[tex]-6.6=r+2\\aka: r+2=-6.6[/tex]
Subtract 2 from both sides to isolate the r variable:
[tex]r=-8.6[/tex]
And.... We have our answer!
r = -8.6
Use I=PRT
p=12,000
r=4%
t=3year
find I
Answers
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$12000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (12000)(0.04)(3) \implies I = 1440[/tex]
It takes Abby 3 hours to drive from Ashdown to Bridgeton at an average speed of 60 mph.
She then drives 30 miles from Bridgeton to Carton at an average speed of 40 mph.
Assuming Abby doesn't stop, what is her average speed from Ashdown to Carton to 1 dp?
Answers
The average speed for the given situation is 56 mph.
Given that, Abby 3 hours to drive from Ashdown to Bridgeton at an average speed of 60 mph.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Now, distance = Speed × Time
= 60 × 3
= 180 miles
She then drives 30 miles from Bridgeton to Carton at an average speed of 40 mph.
Now, Time = 30/40
= 0.75 hours
Total time =3+0.75=3.75 and total distance =180+30=210
Then average speed = 210/3.75
= 56 mph
Therefore, the average speed for the given situation is 56 mph.
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4. Which expression represents 7 more than the quotient of 12 and 4?
A. (12+4) + 7
B.7 x (12+4)
C.7+(12-4)
D. (7+12) + 4
Answers
Answer:
C
Step-by-step explanation:
Even though quotient means divide I instead used the minus symbol since they both mean something negative or taking away. Then, the 7 goes before everything adding onto what was left from the second part.
Animal-like protists, which are heterotrophs and have the ability to move. Plant-like protists, which are autotrophs that photosynthesize.
Answers
Answer:
so the answer would be a protozoa
Step-by-step explanation:
.
