Answer:
.5 of a minute
Step-by-step explanation:
rationalise the denominator and simplify
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Step-by-step explanation:
[tex] \bf \underline{Given-} \\ [/tex]
[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ [/tex]
[tex] \bf \underline{What\: to\: do-} \\ [/tex]
To rationalise the denominator
[tex] \bf \underline{Solution-} \\ [/tex]
[tex]\textsf{We have,}[/tex]
[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ [/tex]
[tex]\textsf{The denominator is 5+2√3. Multiplying the numerator and denominator by 7-4√3,}\\[/tex]
[tex]\textsf{we get,}\\[/tex]
[tex] ⟹\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ [/tex]
[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3}) } \\ \\ [/tex]
[tex]\textsf{⬤ Applying Algebraic Identity
(a+b)(a-b) = a² - b² to the denominator}\\[/tex]
[tex]\textsf{We get,}\\[/tex]
[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 {)}^{2} - (4 \sqrt{3} {)}^{2} } \\ \\ [/tex]
[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 8 \sqrt{3 \times 3} }{49 - 48} \\ \\ [/tex]
[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 24 }{1} \\ \\ [/tex]
[tex]⟹(35 - 24) - 6 \sqrt{3} \\ \\ [/tex]
[tex]⟹11 - 6 \sqrt{3} \: \: \: \tt \red{ Ans}. \\ \\ [/tex]
[tex] \bf \underline{Hence \:the \:denominator\: is\: rationalised.}\\[/tex]
what is the percent increase im 13 to 14, round to the nearest percent
please hurry
Answer:
20 percent
Step-by-step explanation:
lupita and kevin walk to school.lupita walks 3/5 mi.kevin walks 0.65 mi.who walks a greater distance to school?how much greater?
Answer:
0.05
Step-by-step explana
Find the Lcm of 9,12 and 24
Answer:
144
Step-by-step explanation:
6x⁴+5x³-10x+4 how to factorize this polynomial
Yes, this is polynomial, and your answer will be:
(2x − 1) (3x − 2) (x^2 + 2x + 2)
Edit:
Factor 6x^4 + 5x^3 − 10x + 4 using the rational roots test.
(2x − 1) (3x^3 + 4x^2 + 2x − 4)
Factor 3x^3 + 4x^2 + 2x − 4 using the rational roots test.
(2x − 1) (3x − 2) (x2 + 2x + 2)
The factorized form of the given polynomial is (2x − 1)(3x − 2)(x² + 2x + 2).
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The polynomial is given in the question, as follows:
6x⁴ + 5x³ − 10x + 4
We have to factor using the rational roots test,
⇒ (2x − 1)(3x³ + 4x² + 2x − 4)
Similarly, factor 3x³ + 4x² + 2x − 4 operates the rational roots test.
⇒ (2x − 1)(3x − 2)(x² + 2x + 2)
Thus, the factorized form is (2x − 1)(3x − 2)(x² + 2x + 2).
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Rosa purchaded a sofa that was on sale for 20% off. The sofa cost $ 1850. How much does the Sofa cost?
Answer:
Step-by-step explanation:
370
621000 in scientific notation
Answer:
the correct answer is 6.21×10^5
Answer:
6.21 x 10^5
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
estimate the solution to the system of equations
omg, I just said the answer was B.
Johnny took a math test with 25 questions He answered 22 questions correctly in order to get an a he had to get 90% of them right. On the same exam Johnny's friend Jessie answered 4 times more questions correct than incorrect. Who got a higher percentage on the test. Johnny or Jessie?
Answer:
Jessie
Step-by-step explanation:
Jessie answered 4 more times correct that Johnny so she will get a better grade.
Determine the remaining sides and angles of the triangle ABC
what is the measure of angle B
what is the length of side a
what is the length of side b
Answer:
The measure of angle B is 41.5°
The length of side a is 30.6 feet ⇒ to the nearest tenth
The length of side b is 32.9 feet ⇒ to the nearest tenth
Step-by-step explanation:
The sum of the measures of the interior angles in a triangle is 180°In the given Δ ABC
∵ m∠A = 38.1°
∵ m∠C = 100.4°
→ By using the fact above
∵ m∠A + m∠B + m∠C = 180°
∴ 38.1 + m∠B + 100.4 = 180
→ Add the like terms in the left side
∴ 138.5 + m∠B = 180
→ Subtract 138.5 from both sides
∴ m∠B = 41.5°
∴ The measure of angle B is 41.5°
∵ a is the opposite side of ∠A
∵ b is the opposite side of ∠B
∵ c is the opposite side of ∠C
→ By using the sine rule
∴ [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
∵ c = 48.4 ft, m∠A = 38.1°, m∠B = 41.5°, and m∠C = 100.4
→ Substitute them in the sine rule above
∴ [tex]\frac{a}{sin38.1}[/tex] = [tex]\frac{b}{sin41.5}[/tex] = [tex]\frac{48.4}{sin100.4}[/tex]
→ By using cross multiplication between the 1st and the 3rd fractions
∴ a × sin 100.4 = 48.8 × sin 38.1
→ Divide both sides by sin 100.4
∴ a = 30.61429861
∴ The length of side a is 30.6 feet ⇒ to the nearest tenth
→ By using cross multiplication between the 2nd and the 3rd fractions
∴ b × sin 100.4 = 48.8 × sin 41.5
→ Divide both sides by sin 100.4
∴ b = 32.87596206
∴ The length of side b is 32.9 feet ⇒ to the nearest tenth
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
x = 6
Step-by-step explanation:
first find the angle
51 + 72 + x = 180
123 + x = 180
x = 180 - 123
x = 57
so the third angle is 57
now find the value of x in the given expression
8x + 9 = 57
8x = 57 - 9
8x = 48
x = 48/8
x = 6
now check whether the value of x is correct or not by evaluating the value of x in expression
8x + 9 = 57
8(6) + 9 = 57
48 + 9 = 57
57 = 57
so its true
Method 2
51 + 72 + (8x + 9) = 180
123 + 8x + 9 = 180
132 + 8x = 180
8x = 180-132
8x = 48
x = 48/8
x = 6
now again you can check by evaluating the value of x in the above expression
HEEEEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLPPPPPPPPPPPPPPPPPPPP
Luke loaned $3500 to his sister. His sister agreed to repay Luke in a year, with 2% simple interest on the $3500. What is the total amount that Luke’s sister will repay?
Answer:70
Step-by-step explanation:
Answer:
70
Step-by-step explanation:
Does anyone know ?!!!
Answer:
72 square units
Step-by-step explanation:
area of a paralellogram = bh
Base = 6
Height = 12
6 x 12 = 72 square units
Ra'Shaela is going to the store to buy candy. She has $3.45 in dimes and
quarters in her pocket. Write an equation to represent the number of dimes
and quarters that Ra'Shaela could have in her pockets
Write the given trinomial if possible as a square of a binomial or as an expression opposite to a square of a binomial: 15ab-9a^2-6 1/4b^2
Answer:
[tex] - \bigg(3a - \frac{5}{2} b) \bigg)^{2} [/tex]
Step-by-step explanation:
[tex]15ab-9a^2-6 \frac{1}{4} b^2 \\ \\ = 15ab-(3a)^2-\frac{6 \times 4 + 1}{4} b^2 \\ \\ = 15ab-(3a)^2-\frac{24+ 1}{4} b^2 \\ \\ = 15ab-(3a)^2-\frac{25}{4} b^2 \\ \\ = 15ab- (3a)^2- \bigg(\frac{5}{2} b \bigg)^2 \\ \\ = - \{ - 15ab + (3a)^2 + \bigg(\frac{5}{2} b \bigg)^2 \} \\ \\ = - \{ (3a)^2 + \bigg(\frac{5}{2} b \bigg)^2 - 15ab \} \\ \\ = - \bigg(3a - \frac{5}{2} b \bigg)^{2} [/tex]
A parking lot has seventy-six parking spaces numbered from 1 to 76. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 31?
The probability that the number on the parking space where Jillian parks is greater than or equal to 31 is 45/76 or 0.5921 .
Given, Jillian parks her car randomly in a parking slot of 76 spaces.
Total number of Parking spots : 76
Number of parking spots above number 31 : 76 - 31 = 45
Probability = Successful events/ Total events
Probability = 45/76
The probability that the number on the parking space where Jillian parks is greater than or equal to 31 is 45/76 .
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Avni designs a game in which a player either wins or loses 4 points during each turn. Which equation represents all numbers of points, p, a player may have after his or her first turn of the game? A. p = 4 B. p = –4 C. |p| = 4 D. |p| = –4
Answer:
C |p| = 4
Step-by-step explanation:
If a player wins 4points during each turn, then, the total points will be +4points
If the player looses 4points, total points lost will be -4points
The total number of point p the player can have will be represented as;
|p| = 4 (since is both positive and negative 4 )
Note that the nodulus of a variable will return both positive and negative value of that variable
in un rombo l'area e' di 234,95c2 , mentre l'altezza misura 12,7cm
Answer:
la diagonale più lunga dovrebbe essere 37cm.
Step-by-step explanation:
Se cerchi la diagonale più lunga la formula dovrebbe essere questa:
A=p*(q/2)
234,95 = 12,7*(x/2)
234,95/12,7 = x/2
18,5 = x/2
18,5*2 = x
37 = x
Order the following integers from least to greatest -25,-41,36,28,and16
Is ABC a right angle? Why or why not?
Answer:
3.Yes, because triangle ABC has a 90 degree angle.
4.No, because triangle XYZ doesn’t have a 90 degree angle.
Name how the triangles are congruent in this image
help plz idk okhehehehehe
An industrial factory makes / yards of chain every minute. The cost of each yard of chain is $2.00. What is the total cost for all chain produced in 10 minutes?
Answer:
Cost = $86.67
Step-by-step explanation:
Given
Yards = 4⅓ (missing part of the question)
Cost per yard = $2.00
Required
Determine cost of chains produced in 10 minutes
If 4⅓ yards is made in a minute, then
4⅓ * 10 yards are made in 10 minutes
Total = 4⅓ * 10
Total = 13/3 * 10
Total = 130/3 yards
Cost of a yard of chain is $2.00.
Cost of 130/3 yards would be:
Cost = $2.00 * 130/3
Cost = $260.00/3
Cost = $86.67 (approximated)
Hence, the required cost is approximately $86.67
Jeremiah uses
1/3
cups of veggies for every
1/5
cup of dip when making a snack mix. Enter the number of cups of veggies Jeremiah uses for 1 cup of dip.
1 and 2/3 cups of veggies
Arthur is playing a television game show. He starts with 0
points. Arthur answers questions with the following point
values: 30, -20, 10, -20, 60, -100
What is the point value of a question Arthur can answer so
that he has 0 points again
A. -60
B. -40
C. 40
D. 60
Answer: -40
Step-by-step explanation:
1. 30 -20 = 10
2. 10 + 10 = 20
3. 20 - 20 = 0
4. 0 + 60 = 60
5. 60 - 100 = -40
Sombody tell me what the y intercept is
Answer:
1
Step-by-step explanation:
The line is crossing over the y-axis on the 1.
Answer:
(0,1)
Step-by-step explanation:
The y-intercept is always the point where the line crosses the y-axis.
can somone help me pls ?
[tex]\huge\mathtt{Hello!}[/tex]
[tex](6x - 23) = (4x + 9)[/tex]
[tex]6x -4x = 9 + 23[/tex]
[tex]2x = 32[/tex]
[tex]x = 16[/tex]
It is because the sides are equal, so the angles opposite to them also are equal.
Have a nice day!
Evaluate the expression.
1.2 exponent 2
answer choices =
1.44
14.4
1.728
1.5
Answer:
1.44
Step-by-step explanation:
Answer:
the answer is 1.44
Step-by-step explanation:
Because the exponent of a number says how many times to use the number in a multiplication. In 1.2 exponent 2 the "2" says to use 1.2 twice in a multiplication, so 1.2'2 = 1.2 × 1.2 = 1.44 In words: 1.2'2 could be called "1.2 to the power 2" or "1.2 to the second power.
Your welcome
what is the 7th term of the geometric sequence below? 7,-14,28,-56
Answer:
The 7th term of given sequence is: 448
Step-by-step explanation:
Given sequence is:
7,-14,28,-56
Here
a1 = 7
a2 = -14
a3 = 28
First of all we have to find the common ratio. The common ration is the ratio between two consecutive terms of a geometric sequence and is same for all consecutive terms of a geometric sequence.
So,
[tex]r = \frac{a_2}{a_1} = \frac{-14}{7} = -2\\r = \frac{a_3}{a_2} = \frac{28}{-14} = -2\\[/tex]
The common ratio is -2.
The general formula for geometric sequence is given as:
[tex]a_n = a_1r^{(n-1)}[/tex]
Putting values
[tex]a_n = 7.(-2)^{n-1}[/tex]
For 7th term, putting n=7
[tex]a_7 = 7*(-2)^{7-1}\\= 7 * (-2)^6\\= 7 *64\\= 448[/tex]
Hence,
The 7th term of given sequence is: 448
Answer:
A
Step-by-step explanation:
The original price of a desk was $80. And its price was marked
down to $70 during the holiday. What was the percentage of
discount for the desk during the holiday?
Answer:
Required Answer:-Amount of discount =80-70=10$
percentage:-
[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac{10}{80}}\times 100 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {10}{4}}5 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {50}{4}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 12.5\% [/tex]
Answer: the answer is 12.5
Step-by-step explanation: