The perimeter of the triangle is 37.86
Given,
The ratio of the measure of the angles of triangle = 1:2:3
Let the angles be taken as x, 2x, 3x.
Total angle of a triangle is 180°.
We can now find x.
x + 2x + 3x = 180°
6x = 180°
x = 180°/6 = 30°
x = 30°
2x = 2 × 30° = 60°
3x = 3 × 30° = 90°
Let the sides of the triangle be a, b, c.
The length of the shortest side is given = 8
Lets take a as 8.
We can use Trignometric Formulas here:
Trignometric Formulas:
sin θ = [tex]\frac{opposite side}{hypotenuse}[/tex]
cos θ = [tex]\frac{adjacent side}{hypotenuse}[/tex]
tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]
By using sin rule we can find other sides.
That is,
sin 30° = opposite side / hypotenuse
sin 30° = a/b
sin 30° = 8/b
b = 8 × sin 30°
b = 16
Next,
sin 60° = opposite side / hypotenuse
sin 60° = c/16
c = sin 60° × 16
c = 13.86
Now we can find the perimeter of the triangle = a + b + c
= 8 + 16 + 13.86
= 37.86
The perimeter of the triangle is 37.86
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Identify the segment bisector of JK
The length of JM is
Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.
What is the numerical value of JK and JM?Given the data in the question;
Point M bisects segment JK.Segment JM = 7x + 5Segment MK = 8xA bisector divides a line or angle into two equal halves.
Hence
Segment JM = Segment MK
7x + 5 = 8x
Solve for x
8x - 7x = 5
x = 5
Now, numerical value of segment JM will be;
Segment JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40
Segment JK = (7x + 5) + 8x = 7(5) + 5 + 8(5) = 80
Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.
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I can’t seem to figure out how to properly insert (r) and (t) after 2 and 3.
Answer:
7
Step-by-step explanation:
(2t+3r) divide 4
so if r=2 and t=11 the new equation will be :
(2times11 + 3times 2) divide 4
(22+6) divide 4
= 28 divide 4 = 7
Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 6+7.4+8.8+ . . . ; n=11
The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.
The given arithmetic series is 6+7.4+8.8+ . . .
The summation notion of given series is ∑6+1.4n , here n starts from 0.
The sum of arithmetic series can be written as,
[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]
n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.
We have, n=11, [tex]a_{1}[/tex] = 6
To calculate sum of arithmetic series, we need to find [tex]a_{11}[/tex] .
[tex]a_{11} = a_{1} + (n-1)d[/tex]
d = 1.4 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{11}[/tex] = 6 + (11-1)(1.4)
[tex]a_{11}[/tex] = 6 + 14 = 20
On substituting values in sum of arithmetic series formula, we get
[tex]S_{7}[/tex] = (11(6 + 20))/2 = 143
The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.
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Write an explicit formula for each sequence. Then generate the first five terms. a₁ =1024, r=0.5
The formula of the given geometric sequence is: a(n) = 1024 . (0.5)ⁿ⁻¹ and the first five terms are: 1024, 512, 256, 128, and 64.
The formula of the n-th term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
Where:
a₁ is the first term
r is the ratio = a(n)/a(n-1)
Parameters given in the problem:
a₁ =1024, r=0.5
Plug these parameters into the formula, then we get the explicit formula of the n-th term:
a(n) = 1024 . (0.5)ⁿ⁻¹
The first 5 terms:
a₁ = 1024
a(2) = 1024 . (0.5)²⁻¹
= 1024 . (0.5)¹ = 512
a(3) = 1024 . (0.5)³⁻¹
= 1024 . (0.5)² = 256
a(4) = 1024 . (0.5)⁴⁻¹
= 11024 . (0.5)³ = 128
a(5) = 1024 . (0.5)⁵⁻¹
= 1024 . (0.5)⁴ = 64
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Kate cut a 100-foot rope into two pieces.one piece was 5 feet longer than 4 times the length of the other. Find the length of each piece
Answer:
81 feet & 19 feet
Step-by-step explanation:
3/4 h -12= 8 5/8 pls answer with a detailed explanation
The value of h based on the information illustrated is 24 1/2.
How to calculate the value?It should be noted that the fraction given is illustrated as:
3/4h - 12 = 8 5/8
Add 12 to both sides
3/4h - 12 + 12 = 8 5/8 + 12
3/4h = 20 5/8
Multiply both side by 4/3
3/4h × 4/3 = 20 5/8 × 4/3
h = 165/8 × 4/3
h = 27 1/2
Therefore, the value of h is 24 1/2.
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Determine whether each sequence is arithmetic. If so, identify the common difference and find the 32 nd term of the sequence. 2,4,7,10, . . . . .
The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.
The sequence we are provided is 2, 4, 7, 10, …
Here, [tex] a_{1}[/tex] = 2, [tex] a_{2}[/tex] = 4 and [tex] a_{3}[/tex] = 7.
A sequence is considered as an Arithmetic sequence if their difference is equal. Represented as -
[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = [tex] a_{4}[/tex] - [tex] a_{3}[/tex] and so on
Now, in the given sequence
⇒[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 4 - 2
[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 2
⇒ [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 7 - 4
[tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 3
⇒ [tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 10 - 7
[tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 3
Since, the difference between the given sequence of terms are not same.
∴ The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.
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PLEASE HELP!!! Given the function defined by f(x)=6x-3, find f(-4.6). Simplify.
samantha is using a wooden strip 7/8 yard long to make a picture frame.If she cuts off a piece that is 3/4 long, which fraction best represents the porportion that is left lf the original strip?
The portion of wooden strip that is left from the original strip is 1/4
How to calculate the amount of the original strip left ?Samantha is using a wooden strip that measures 7/8 yard
Samantha cuts off a piece of the wood that is 3/4 long
The fraction that represents the proportion of the original strip that is left can be calculated as follows
7/8 - 3/4
The LCM of both fractions is 8
7 - 6/8
= 2/8
convert to the lowest term
1/4
Hence the proportion of the original wooden strip that remains is 1/4
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A die is rolled. If the number rolled is greater than 2 , find the probability that it is a 6 .
According to the question, when die is rolled check the number is greater than two and it should be [tex]6[/tex].
The total number of outcomes : [tex]n(E)= {1,2,3,4,5,6}[/tex]
And getting a number greater than [tex]2[/tex] [tex]= {3,4,5,6}[/tex]
Finally, getting a number as [tex]6 = {6}[/tex]
Therefore, the probability can be written as:
[tex]P(E) = \frac{1}{6}[/tex]
Hence, the calculated probability is [tex]\frac{1}{6} .[/tex]
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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what is 49/200 equal to explain
Answer:
0.245
Step-by-step explanation:
Divide both the numerator and denominator by 2.
49/200 will be 24.5/100
If you divide a number by 100, you move the decimal place 2 digits to the left. 24.5/100 will become 0.245
h(x) = -4x - 3, find h(2).
Answer:
-11.
Step-by-step explanation:
h(x) = -4x - 3, find h(2).
Replace the x by 2:
h(2) = -4(2) - 3
= -8 - 3
= -11.
Perform the indicated division and write your answers in the form P(x)/D(x) = Q(x) + R(x)/D(x) as shown in the following example;
Answer:
[tex]\textsf{1.} \quad 5x+3-\dfrac{3}{x-4}[/tex]
[tex]\textsf{2.} \quad 2x^2-4x+3[/tex]
[tex]\textsf{3.} \quad x^3+3x^2-2x+4+\dfrac{25}{2x-5}[/tex]
Step-by-step explanation:
Long Division Method of dividing polynomials
Dividend: The polynomial which has to be divided.Divisor: The expression by which the divisor is divided.Quotient: The result of the division.Remainder: The part left over.Divide the first term of the dividend by the first term of the divisor and put that in the answer.
Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.
Repeat until no more division is possible.
Write the solution as the quotient plus the remainder divided by the divisor.
Question 1[tex]\large \begin{array}{r}5x+3\phantom{)}\\x-4{\overline{\smash{\big)}\,5x^2-17x-15\phantom{)}}}\\{-~\phantom{(}\underline{(5x^2-20x)\phantom{-b)..}}\\3x-15\phantom{)}\\-~\phantom{()}\underline{(3x-12)\phantom{}}\\-3\phantom{)}\\\end{array}[/tex]
Solution
[tex](5x^2-17x-15) \div (x-4)=\dfrac{5x^2-17x-15}{x-4}=5x+3-\dfrac{3}{x-4}[/tex]
Question 2[tex]\large \begin{array}{r}2x^2-4x+3\phantom{)}\\3x-2{\overline{\smash{\big)}\,6x^3-16x^2+17x-6\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-4x^2)\phantom{-bbbbbbbb.)}}\\-12x^2+17x-6\phantom{)}\\-~\phantom{()}\underline{(-12x^2+8x)\phantom{))))).}}\\9x-6\phantom{)}\\-~\phantom{()}\underline{(9x-6)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Solution
[tex](6x^3-16x^2+17x-6) \div (3x-2)=\dfrac{6x^3-16x^2+17x-6}{3x-2}=2x^2-4x+3[/tex]
Question 3[tex]\large \begin{array}{r}x^3+3x^2-2x+4\phantom{)}\\2x-5{\overline{\smash{\big)}\,2x^4+x^3-19x^2+18x+5\phantom{)}}}\\{-~\phantom{(}\underline{(2x^4-5x^3)\phantom{-bbbbbbbbbbb.bb.)}}\\6x^3-19x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(6x^3-15x^2)\phantom{))))bbbb..).}}\\-4x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(-4x^2+10x)\phantom{)))..}}\\8x+5\phantom{)}\\-~\phantom{()}\underline{(8x-20)}\\25\phantom{)}\end{array}[/tex]
Solution
[tex]\begin{aligned}(2x^4+x^3-19x^2+18x+5) \div (2x-5) & =\dfrac{2x^4+x^3-19x^2+18x+5}{2x-5}\\ & =x^3+3x^2-2x+4+\dfrac{25}{2x-5}\end{aligned}[/tex]
Your friend gave you a free parking pass to a baseball game. Unfortunately, the parking spot number was smudged on the ticket. You know the parking spot was 7 spaces away from your friend's spot. If your friend's parking spot is number 19 in the same row, write and solve and absolute value equation to determine your possible parking spot number(s)? (use \displaystyle xx as the variable to represent the parking spot)
The possible parking spot numbers can be either 12th spot or 26th spot.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that the parking spot was smudged on the ticket.
Let's assume the possible parking spot numbers can be given by x which is represented by an inequality.
Your parking spot is 7 spaces away from your friend's spot which is number 19 in the same row. So , the possible parking spot numbers can be given by ;
19 - 7 ≤ x ≤ 19 + 7
12 ≤ x ≤ 26
Therefore , the possible parking spot numbers can be either 12th spot or 26th spot.
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Solve for X
Please Give explanation
Answer:
Step-by-step explanation:
[tex]\frac{x}{5} +1=\frac{1}{15}[/tex]
[tex]\frac{x}{5} = \frac{1}{15} -1[/tex]
[tex]\frac{x}{5} = \frac{1-15}{15}[/tex]
[tex]\frac{x}{5} = \frac{-14}{15}[/tex]
multiply both sides by 5
[tex]5*\frac{x}{5} = \frac{-14}{15} *5[/tex]
[tex]x=-\frac{14}{3}[/tex]
Which quadratic equation has solutions x=8 and x=−1? clear submit 8x2 7x−1=0 x2 7x−8=0 x2−x 8=0 x2−7x−8=0
The quadratic equation which has solutions x = 8 and x = -1 is [tex]\bold{x^2-7x-8}[/tex] = 0.
An equation of degree 2 is called a quadratic equation. That is, the highest power of x in the equation will be two. It has at most two solutions.
Given the solutions are x = 8 and x = -1.
If x = a is a solution, then (x-a) is a factor for the equation.
So here, x-8 and x+1 are factors of the required quadratic equation.
Thus, the quadratic equation will be, (x-8)(x+1) = [tex]\bold{x^2-7x-8}[/tex] = 0.
We can check if x = 8 and x = -1 are the solutions. Put x = 8 in [tex]\bold{x^2-7x-8}[/tex]
Then, 8 x 8 - 7 x 8 - 8 = 0 and -1 x -1 - 7 x -1 - 8 = 0.
So [tex]\bold{x^2-7x-8}[/tex] = 0 is the quadratic equation with solutions x = 8 and x = -1.
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Find a₁ for each arithmetic series.Evaluate S₁₅ for the series 3 x+(3 x-2 y)+(3 x-4 y)+ ......
In the given arithmetic series, the first term is a(1) = 3x and the sum of the first 15 terms is S(15) = 45x - 210y
The given series is:
3x + (3 x-2 y) + (3x-4y) + ......
Notice that this is an arithmetic series with:
the first term, a(1) = 3x
the second term, a(2) = 3x - 2y
the 3rd term, a(3) = 3x - 4y
Hence, the common difference is:
d = (3x - 2y) - 3x = -2y
Recall that the nth term of an arithmetic series is given by:
a(n) = a(1) + (n -1) . d
Substitute n = 15, a(1) = 3x, and d = -2y:
a(15) = 3x + (15 - 1) . (-2y)
a(15) = 3x - 28y
The sum of the first n terms in an arithmetic series is given by:
S(n) = n/2 [a(1) + a(n)]
Substitute n = 15
S(15) = 15/2 [a(1) + a(15)]
S(15) = 15/2 . (3x + 3x - 28y)
S(15) = 15 . (3x - 14y) = 45x - 210y
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Evaluate. Remember Order of
Operations! (PEMDAS)
-8 × 2² - (-40+ 6) = [?]
Answer:
The answer is 2
Step-by-step explanation:
HELP MEEE!!!! Anna walks 49,879 feet from her house. She rest to get something to eat, then she walked all the way back home. Since Anna walked 49,879 feet from her house, how many miles in total did she walk from her house and walk back?
Answer:24939.5 i think
Step-by-step explanation:
Arrange the numbers Least to Greatest1/2, -1/4, 7.2, 121, 1-41, -1.8, 9.1
The numbers in the order of least to greatest is :
₋1.8 , ₋1/4 , 1/2 , 1.41 , 7.2 , 9.1 , 121
Given, the numbers are in decimal and fraction form.
1/2 , -1/4 , 7.2 , 121 , 1.41 , -1.8 , 9.1
we need to convert the fractions and then arrange the numbers in the ascending order.
Writing the numbers in an ordered list according to their values means arranging them from least to greatest. The smallest number should be put on the left, followed by the next smallest number, which should be written directly to its right.
for 1/2:
1/2 = 0.5
for ₋1/4:
₋1/4 = 0.25
now arrange the numbers according to the least to greatest form.
we have numbers:
0.5 , 0.25 , 7.2 , 121 , 1.41 , ₋1.8 , 9.1
least to greatest form:
₋1.8 , 0.25 , 0.5 , 1.41 , 9.1 , 121
i.e , ₋1.8 , 1/4 , 1/2 , 1.41 , 9.1 , 121
Hence we get the required form.
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Zachary purchased a computer for $1,100 on a payment plan. Two months after he purchased the computer, his balance was $870. Six months after he purchased the computer, his balance was $410. What is an equation that models the balance y after x months?
Answer:
y = 1100 - 115x
Step-by-step explanation:
Let the monthly payment be $p
In two months Zach would have paid 2p dollars
Balance would be 1100 - 2p = y
We know after 2 months, balance y was actually 870
Substituting y = 870 we get
1100 - 2p = 870
Subtract 1100 on both sides
1100 - 1100 - 2p = 870 -1100
==> -2p = - 230
Divide by -2 on both sides
-2p/-2 = -230/-2
p = 115 which represents the monthly payment .
So the balance y after m months is given by the equation
y = 1100 - 115x
We can verify by plugging in the values for the second scenario
For 6 months
y = 1100 - 115 x 6 = 1100 - 690 = $410 which agrees with the given value so our equation is consistent
Find the next term in each sequence. 2,4,8,16, . . . . . .
Answer:2,4,8,16,32,64,128,256,512,1024,2048,4096
Step-by-step explanation:
You just mutiply the number with 2
The measure of one angle on a right triangle is 16° more than the measure of the smallest angle.
find the measures of all three angles
Answer: 37° 53° 90°
Step-by-step explanation:
Given:
ΔABC m∠C=90°
Solution:
m∠A+m∠B+m∠C=180°
m∠A+m∠B+90°=180°
m∠A+m∠B+90°-90°=180°-90°
m∠A+m∠B=90°
Let m∠A=x°
Hence,
m∠B=(x+16)°
Thus,
x°+(x+16)°=90°
(2x)°+16°=90°
(2x)°+16°-16°=90°-16°
(2)(x)°=74°
Divide both parts of the equation by 2:
x°=m∠A=37°
m∠B=37°+16°
m∠B=53°
Write two division problems that both have a quotient of -3.
Lo5(x2-9)=0 pls help me my assignments is too hard so i learned that you can help me thanks
The final answer is the combination of both solutions x = 3,− 3.
What are quadratic in math?
A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Latin word meaning square, is where the word "quadratic" originates.Use the quadratic formula to find the solutions
x = - b + √b² - 4ac / 2a
Substitute the values
a = 1, b = 0, and c = − 9 into the quadratic formula and solve for x.
x = 0 + √ 0² - 4 . ( 1 . 9 ) / 2. 1
Simplify
The final answer is the combination of both solutions.
x = 3,− 3
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Carla puts $625 into a savings account at an annual interest rate of 2.5%. If she does not withdraw or deposit any money, what is the interest that Carla will earn at the end of 6 months?
The formula is I=prt
Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.
What is the interest that Carla will earn at the end of 6 months?Simple interest is simply a method to determine the amount of interest charged on a sum at a given rate and for a given period of time.
It is expressed as;
I = prt
Given the data in the question;
Principal P = $625Annual interest r = 2.5% = 2.5/100 = 0.025Time period t = 6 months = 6/12 = 0.5 yearsInterest I = ?Plug the given values into the formula above and solve for I.
I = p × r × t
I = $625 × 0.025 × 0.5
I = $7.81
Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.
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80 percent of 42 is what percent of 16 ?
a. 240
b. 210
c. 150
d. 50
e. 30
The percent of 16, which is equal to the 80 percent of 42 is 210.
What is meant by percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.
Let x be the percent of 16, which is equal to the 80 percent of 42.
80% of 42 = x % of 16
80/100 [tex]*[/tex] 42 = x/100 [tex]*[/tex] 16
80(42)/100 = 16/100 [tex]*[/tex] x
Multiplying both sides of the equation by 16/100, then we get
80(42)/100 [tex]*[/tex] (16/100) = 16/100 [tex]*[/tex] x [tex]*[/tex] (16/100)
simplifying the above equation, we get
80(42)/100 [tex]*[/tex] (16/100) = x
80(42)/16 = x
210 = x
The value of x = 210.
Therefore, the correct answer is option b. 210.
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Answer:
210
Step-by-step explanation:
We can start by finding 80% of 42:
80% of 42 = (80/100) x 42 = 33.6
So, the question now becomes: what percent of 16 is 33.6?
Let's call the unknown percentage "x".
We can set up the following equation:
x/100 x 16 = 33.6
Multiplying both sides by 100/16, we get:
x = (33.6 x 100)/16
x = 210
Please help on geometry step by step im trying to learn
Answer:
m∠FQR = 23°
Step-by-step explanation:
Since m∠KQF = 90°, it's a complementary angle and is equal to 90°
Step 1: Write the equation. Since The whole angle equals 90° add everything together to equal 90°
(3x - 23)° + (2/3x + 3)° = 90
3x - 23 + (2/3)x + 3 = 90
Combine like terms
multiply the denominator by 3. (3 × 3) = 9 + 2 = 11
(11/3)x - 20 = 90
+ 20 +20
(11/3)x = 110
÷(11/3) ÷(11/3)
x = 30°
Step 2: Find m∠FQR
m∠FQR = ((2/3)x + 3))
(2/3)(30) + 3
20 + 3 = 23
m∠FQR = 23°
I hope this helps!
Answer:
Step-by-step explanation:
(2/3x+3) + (3x-23)=90
(2/3+3)x -20 =90
11/3x =90 + 20
x= 110 * 3/11 =30
FQR = 2/3x+3= 2/3 (30) +3 = 20 +3 =23
Every year, the number of birds in a bird sanctuary increases by 3 percent. In 1997, there were 175 birds in the sanctuary. Using this data, predict the number of birds in the sanctuary in 2020.
There are 190 more birds than expected at the refuge.
The information provided in the question indicates that there are 3 percent more birds than there were previously. The sanctuary houses 175 birds, which may be pictured as follows:
There are 175 birds in all.
According to the inquiry, it is rising by 3%.
Number of birds = (175)(3%) = 5.25 at this point.
As a result, given the data, the anticipated enhanced data is as follows:
Added birds is 175 + 5 + 5 + 5 = 190.
190 more birds are therefore expected in the refuge.
How much is a percentage?The final computed numbers should be divided by the total value and then multiplied by 100 to obtain the percentage.
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What is the simplified answer to 5.3. √2 ? 8√2 2/2 15√2
The simplified answer to 5.3. √2 will be 7.495.
How to calculate the value?It should be noted that we are to find the simplified answer to 5.3. √2 .
This means that we have to multiply them. This will be:
= 5.3 × ✓2
= 5.3 × 1.1414
= 7.495
Note that the options given aren't complete.
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