Answer:
Perimeter = 32.3
Area = 95.24
Step-by-step explanation:
Given:
△ABC, m∠A=60°
m∠C=45°, AB = 9
To find:
Perimeter of △ABC
Area of △ABC
Solution:
Using angle sum property in a triangle:
m∠A + m∠B + m∠C = 180°
m∠B = 180° - 45° - 60° = 75°
As per Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
[tex]a[/tex] is the side opposite to [tex]\angle A[/tex]
[tex]b[/tex] is the side opposite to [tex]\angle B[/tex]
[tex]c[/tex] is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08[/tex]
[tex]\Rightarrow \dfrac{AC}{0.96} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22[/tex]
Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = 32.3
Area of a triangle is given as:
[tex]\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)[/tex]
[tex]\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}[/tex]
Find the number for which:
75% is 4.5 cm
It’s math can you help with number 3 please?
Answer:
25
Step-by-step explanation:
16+9
Answer:
The correct should be 25.
Step-by-step explanation:
If this is incorrect let me know and I will correct it.
Compare. Select <, >, or=.
3.568 ? 3.577
Answer:
3.568 < 3.577
Step-by-step explanation:
3.568 < 3.577
So 3.577 is greater than 3.568
An 8-quart jug of water costs $6.08. What is the price per cup?
Answer:
$0.19 cents
Step-by-step explanation:
First, find how many cups are in 8 quarts.
1 quart is 4 cups, so to find the number of cups, multiply 8 by 4:
8(4)
= 32 cups
Then, to find the price per cup, divide the cost by the number of cups:
6.08/32
= 0.19
So, the price per cup is $0.19 cents
Which list shows the absolute values in order from least to greatest? Question 5 options: |−2.36|, |−5.98|, 6.1 0.2, |−0.3|, |0.1| |7.6|, 5.3, 1.3
Answer:
i dont know maybe you should search google. best of Luck
Step-by-step explanation:
if 5x+2y=20 and y=10, what is 3x?
Answer:
3x = 0
Step-by-step explanation:
Given,
y = 10
now,
5x+2y = 20
or, 5x+2×10=20
or, 5x = 20-20
or, 5x = 0
or, x = 0/5
or, x = 0
Again,
3x = 3×0 =0
answer in percent 20/80 = x/100
what’s the value of x?
Answer:
x = -11
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+50 + 72+ x+80 = 180
Combine like terms
2x + 202 = 180
Subtract 202 from each side
2x+202-202 = 180-202
2x =-22
Divide each side by 2
2x/2 = -22/2
x = -11
HELP! write y+4 =-2/3(x-9) in standard form
can someone help me with this
Answer:
31°
Step-by-step explanation:
If ∠dab=55° and ∠cab=24° and ∠cab+∠dac=∠dab then all you need to do is subtract 55° and 24° to get 31°
Solve for x in the diagram shown.
e
A)
2.67
B)
4.5
5.625
D)
34.375
E)
225
Answer:
C
Step-by-step explanation:
I just took the USATP.
Answer:
D) 34.375
Step-by-step explanation:
I literally just took usatestprep yall need to stop putting wrong answers pls
If 4/5 – 3/10 = x + 11/2, find the value of
X.
Answer:
x = 85/60 or 17/12
Step-by-step explanation:
4/5 - 3/10 = x + 11/12
=> 8/10 - 3/10 = x + 11/12
=> 5/10 = x - 11/12
=> x - 11/12 = 5/10
=> x = 5/10 + 11/12
=> x = 5 * 6 / 10 * 6 + 11 * 5 / 12 * 5
=> x = 30 / 60 + 55/60
=> x= 85/60
If my answer helped, kindly mark me as the brainleist !!
Thank You!!
Answer:
maybe -5
Step-by-step explanation:
4/5-3/10=x+11/2
1/2-11/2=x
-10=2x
x=-5
Change 10/25 to a decimal
Answer:
0.4
Step-by-step explanation:
→ Convert fraction to a denominator of 100
10 / 25 ⇔ 40 / 100
Answer:
0.4
Step-by-step explanation:
An easy way to do this is to get the fraction over 100
So, multiply the fraction by 4 (because 25*4=100)
then you get 40/100 which is 0.4 in decimal form
A quadrilateral has no pairs of parallel sides, what two shapes could it be?
Answer:
Kite
Step-by-step explanation:
Def of kite has no parallel sides
Answer:
Kite and TrapeziumStep-by-step explanation:
Each of them do not have any parallel lines or sides
Ruth's credit card has an APR of 10,91%, and it computes finance charges using the previous balance method on a
30-day billing cycle. During the April billing cycle, she made a $45.17 payment on April 10th and a $88.34 purchase on
April 17th. Her total at the start of May was $847.64. What was her balance at the beginning of April?
a $890.91
b. $797.22
C.$796.87
d. $804.47
Please select the best answer from the choices provided
Answer:
It's B trust
Step-by-step explanation:
The required balance at the beginning of April is $796.87. Option C is correct.
What is interest?Simple interest is defined as the percentage of earnings on the lending for a period of time
To determine Ruth's balance at the beginning of April, we can work backward from her total at the start of May.
Let's call Ruth's balance at the beginning of May "B".
We know that during the April billing cycle:
She made a $45.17 payment on April 10th
She made a $88.34 purchase on April 17th
The APR is 10.91%
So, B = B - $45.17 - $88.34 + (B * 0.1091 * 30 / 365)
Solving for B, we get:
B = $796.87
So, the answer is C. $796.87.
Learn more about your interest here:
https://brainly.com/question/20406888
#SPJ6
Find the present value of an annuity due that pays $4000 at the beginning of each quarter for the next 7 years. Assume that money is worth 6.2%, compounded quarterly. If $90,000 is invested in an annuity that earns 5.4%, compounded quarterly, what payments will it provide at the end of each quarter for the next 7 1/2 years?
Answer:
Step-by-step explanation:
From the first question:
We are to find PV of the annuity.
Using the formula:
Present value of Annuity = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)
Where , Annuity Amount = $4,000
n = No. of periods = 7 years × 4 quarters per year = 28 periods but since the first payment is at beginning of the quarter, Then, n = 27 when considered for PVAF
r = 6.2% / 4 quarters = 1.55%,
PVAF(n0,r) when first payment is at beginning of n i.e. n0 = 1 + { [1-(1+r)^ -n0 ]/r }
= 1 + { [1-(1+0.0155)^ {-27}]/0.0155 }
= 1 + [ (1 - 0.66015 ) ] / 0.0155]
= 1 + 21.926
= 22.926
PVAF(28,1.55%) = 22.926
Thus , Present Value of Annuity = $4,000 × 22.926 = $91704.00
2. Present value of Annuity due = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)
Present Value of Annuity = $90,000
n = No. of periods = 7.5 years × 4 quarters per year = 30 periods
r = 5.4% / 4 quarters = 1.35%,
PVAF(n,r) = [1-(1+r)^-n]/r
PVAF(n,r) = [1-(1+0.0135)^ -30]/0.0135
PVAF(30,1.35%) = (1 - 0.6688)/0.0135
PVAF(30,1.35%) = 0.3312/0.0135
PVAF(30,1.35%) = 24.53
Hence ;
$90,000 = Annuity Amount × 24.53
Annuity amount = $90,000/24.53 = $3,668.48
Finding the area, any help?
Answer:
Volume: x^6
Area: 6x^4
Step-by-step explanation:
volume: length x width x height
area: 6 sides of x^4 so 6x^4
Alice is saving her chore money in a bank account. She makes a deposit of $13 in the first month.
Then every month, she deposits $25. Alice forms a sequence of her account balance, An where n
refers to the number of months. Which of the statements are correct about this sequence?
Select all that apply.
Answer:
Option (3) and Option (5)
Step-by-step explanation:
Alice invested $13 in the first month.
Then she deposits $25 every month.
Therefore, sequence formed by the deposit will be an arithmetic sequence.
First term of the sequence will be,
[tex]A_1=13[/tex]
Since, recursive formula formula of a sequence is given by the formula,
[tex]A_n=A_{(n-1)}+d[/tex]
Where 'd' = common difference in each term of the sequence
Recursive formula for the sequence will be,
[tex]A_n=A{(n-1)}+25[/tex]
Since, explicit formula for the arithmetic sequence is represented by the formula,
[tex]A_n=A_1+(n-1)d[/tex]
where n = number of term
d = common difference
Therefore, nth term of the sequence formed will be represented by the explicit formula,
[tex]A_n=13+(n-1)25[/tex]
[tex]A_{10}=13+(10-1)25[/tex]
= 13 + 225
= 238
[tex]A_{8}=13+(8-1)25[/tex]
= 188
[tex]A_{12}=13+(12-1)25[/tex]
= 288
Therefore, Option (3) and Option (5) will be the answer.
riddle #2
I am a five digit even number.
all of my digits are factor of 24.
4/5 of my digits are even.
The digit in my thousands place equals the perimeter of a 2×2 array.
The digits in my ten thousand places is twice the value of the digits in the hundreds place, but half the value of the digits in the thousands places.
The digit in my tens places equal the number of lines of symmetry in an isosceles triangle.
Answer:
28416
Step-by-step explanation:
No digits can be repeated
"All my digits are factors of 24" This means that the possible digits are: 1, 2, 3, 4, 6, 8
"The digits in my thousands place equals the perimeter of a 2x2 array" That would be 8
"The digits in my ten thousand places is twice the value of the digits in the hundreds place, but half the value of the digits in the thousands place" That would be 4, which also means that the ten thousands place is 2
"The digits in my tens place equal the number of lines of symmetry in an isoceles triangle" There is only 1 lines of symmetry
This means that we have 2841(?)
Because this number is even and no digits can be repeated, the only possible digits from those available is 6
Therefore the number is 28416
If it takes 4 years for an animal population to double, how many years will it take until the population triples?
Answer:
6 years
Step-by-step explanation:
i used a proportional approach
2 (the double)/ 4 years (the time it takes to double)
then compared it to
3(the triple)/ x amount of years
(like this)
[tex]\frac{2}{4} \ \frac{3}{x}[/tex]
then cross multipled
4 times 3= 12
then divided the 12 by the remaining 2 above the 4
In the table, please select the product (s), by name, that has the higher percentage of being ordered.
Eighteen less than 9 times a number is the same as 14 more than the number.
Comply the equation
Answer:
x=4
Step-by-step explanation:
9x-18 = x+14
9×-× = 14+18
8× = 32
X = 4
Sam bought a video game console for $150. He later sold the video game console for 13/12 of price he originally paid. Which statement about the price sam sold the video game consol for is true?
Answer:
1/45
Step-by-step explanation:
Jordan's net income for the year ended December 31, Year 2 was $200,000.
Answer:
good for her / him but uh whats the question
Ms. Chibbaro packs 6 almonds for every 3 craisins (cranberry raisins) in her snack pack. She has 12 more almonds than craisins.
Identify the critical t. An independent random sample is selected from an approximately normal population with unknown standard deviation. Find the degrees of freedom and the critical t value t∗t∗ for the given sample size and confidence level. Round critical t values to 3 decimal places.Sample size, n Confidence level Degree of Freedom Critical value, t∗t∗5 90 13 95 22 98 15 99
Answer and Step-by-step explanation: The critical value for a desired confidence level is the distance where you must go above and below the center of distribution to obtain an area of the desired level.
Each sample has a different degree of freedom and critical value.
To determine critical value:
1) Calculate degree of freedom: df = n - 1
2) Subtract the level per 100%;
3) Divide the result by 2 tails;
4) Use calculator or table to find the critical value t*;
For n = 5 Level = 90%:
df = 4
t = [tex]\frac{1-0.9}{2}[/tex] = 0.05
Using t-table:
t* = 2.132
n = 13 Level = 95%:
df = 12
t = [tex]\frac{1-0.95}{2}[/tex] = 0.025
Then:
t* = 2.160
n = 22 Level = 98%
df = 21
t = [tex]\frac{1-0.98}{2}[/tex] = 0.01
t* = 2.819
n = 15 Level = 99%
df = 14
t = [tex]\frac{1-0.99}{2}[/tex] = 0.005
t* = 2.977
The critical values and degree of freedom are:
sample size level df critical value
5 90% 4 2.132
13 95% 12 2.160
22 98% 21 2.819
15 99% 14 2.977
A goat is tired to a pole at the center of a square of length of side 20m. If the rope is 10m long. Calculate the (I) area of the square that can't be grazed by the goat (ii) fraction of grazed portion to the whole area
Answer:
percentage = 78.54%
Step-by-step explanation:
The area of a square of side length x is:
[tex]A_s=x^2[/tex]
The area of a circle of radius r is:
[tex]A_c=\pi r^2[/tex]
The goat is tied to a pole at the center of a square of a side length of x=20 cm.
The area of the square is:
[tex]A_s=20^2[/tex]
[tex]A_s=400~m^2[/tex]
The rope is 10 m long. The goat is able to graze an area of:
[tex]A_c=\pi 10^2[/tex]
[tex]A_c=100\pi~m^2[/tex]
(i)
Since the diameter of the circle (20 m) is equal to the length of the square, the area of the circle is contained in the square and the area of the square not grazed by the goat is:
[tex]A = A_s-A_c=400~m^2-100\pi~m^2[/tex]
[tex]A=100(4-\pi)~m^2[/tex]
Calculating:
[tex]A = 85.84~m^2[/tex]
(ii)
The percentage can be calculated as:
[tex]\displaystyle \frac{A_c}{A_s}*100=\frac{100\pi}{400}*100=25\pi[/tex]
Calculating:
percentage = 78.54%
pleaseeeeeeeeeeeeeeeeeeeeee help me i'm begging you so the questions is what is the multiplicative of 5 and 10-5k
Answer:
1/5 and -k/5+2
Step-by-step explanation:
inverse of 5= 1/5
swap the variables: y=10−5k becomes k=10−5y
Now, solve the equation k=10−5y
for y
y=−k/5+2
Use the graph to answer the question.
What is the average rate of change from x = 3 to x
= 11?
0 -8
1
001-
1
8
08
Answer:
Negative 1/8 is the answer
What is the median 5,7,9,10,16,17,20
Answer:
10
Step-by-step explanation:
For an odd number of values, the median is the middle value when you write the values in ascending order.
5, 7, 9, 10, 16, 17, 20
The median is 10.