(x + 1/x)² = x ² + 2 + 1/x ² = 10 + 2 = 12
==> x + 1/x = ±√12
MATHEMATICS
SECTION A (VERY SHORT ANSWERS)
1. Which of the following is irrational?
a V25
V12
b. Vs
c.
V3
2. V768 in its simplest form is:
dve
16
a.
16 V3
b. 64 V3 c.4 V3
d. 8 V3
3. The simplest rationalisation factor of 27 is:
a. b. 73
c. 27
d. 3
4. If x=2 and y = 3, then the value of xy + yt is:
a. 15
b. 17
c. 19
d. 21
a
2
5. The value of [ 8-43 + 22/12 is:
b. 2 ch d. 4
6. If p(x) = x2 – 3x + 2, then what is the value of p(0) + p(2).
7. Find the value of k, if (2x - 1) is a factor of the polynomial 6x2 + kx - 2.
8. Expand (x - y)
9. If x11 + 101 is divided by (x + 1), then what remainder do we get?
10. Find the value of x2 + 3, if(x - 5) = 13
SECTION B (SHORT ANSWERS
11. Express 0.123 in the form where p and q are integers and qf0
9
√7-√6
12. Rationalise the denominator of
√ + √6
13. Find the value of x if
&2x
14. If x2 + = 7 then find x3 +
15. If x + y + z = 10 and x2 + y2 + z = 40 find xy + y2 + zx and x3 + y + z3 - 3xyz
16. Factorize 8x3 - (2x - y)3
81
16
how many are 6 raised to 3 ???
Answer:
216
Step-by-step explanation:
When you say "6 raised to 3", it means you multiply 6, 3 times. Meaning:
6✖️6✖️6=216
Hope this helped!
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On a unit circle, the terminal point of 0 is (square root of 2/2, square root of 2/2) what is 0?
Answer:
Step-by-step explanation:
0 should never be used as a substitute for θ!
(√2/2, √2/2) = (cos(45°), sin(45°))
The value of θ if 0°< 0<360° on a unit circle where the terminal point of 0 is (√2/2, √2/2), is 45°.
What is a terminal point?The terminal point of a circle is defined as the measure of the angle in degrees or radians over the circle, at the endpoint on the coordinate plane.
On a unit circle, the terminal point of θ is,
(√2/2, √2/2) = (cos(45°), sin(45°))
The value of theta at the terminal point (square root of 2/2, square root of 2/2) is 45 degrees.
Thus, the value of θ if 0°< 0<360° on a unit circle where the terminal point of 0 is (square root of 2/2, square root of 2/2) is 45°.
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type in symbols to make 3,7,12,2 equal 45
Answer:
The answer is (3×7) + (12×2) .
[tex](3 \times 7) + (12 \times 2)[/tex]
[tex] = 21 + 24[/tex]
[tex] = 45[/tex]
Select the correct answer.
Brett is planning to build two new acrylic fish tanks. He wants the rectangular prism-shaped fish tanks to have the same width and
volume.
• For one of the fish tanks, he plans to make the height of the fish tank 2 cm less than twice the width and the length 4 times the
width.
• For the other fish tank, he plans to make the length 1 cm less than twice the width and the height 6 times the width.
If y represents the volume of the fish tanks, and x is the width of the fish tanks, which system of equations could represent this
situation?
Answer:8-8 and 12 and 6
Step-by-step explanation:
The system of equations based on the given information is represented by y = 8x³ - 8x² , y = 12x³ - 6x² .
Let's set up the equations based on the information:
x be the width of the fish tanks (in cm),
y be the volume of the fish tanks (in cubic cm).
For the first fish tank:
Height = 2x - 2 (2 cm less than twice the width)
Length = 4x (4 times the width)
Volume (V) of a rectangular prism = Length × Width × Height
V = (4x) × x × (2x - 2)
V = 4x² × (2x - 2)
V = 8x³ - 8x² (equation 1)
For the second fish tank:
Length = 2x - 1 (1 cm less than twice the width)
Height = 6x (6 times the width)
Volume (V) of the rectangular prism = Length × Width × Height
V = (2x - 1) × x × (6x)
V = (2x² - x) × 6x
V = 12x³ - 6x² (equation 2)
So, the system of equations representing the situation is:
V = 8x³ - 8x²
V = 12x³ - 6x²
Therefore, the correct answer is a system of equations are
y = 8x³ - 8x²
y = 12x³ - 6x²
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40) what is the area of a rectangular porch measuring 8 ft x 12/f
45) Create a stem and leaf plot to represent this set of data.
30, 62, 32, 63, 43, 77, 48, 78, 49, 82, 51, 84, 60,
please make sure to answer both questions
What is the tangent ratio of KJL? (Question and answers provided in picture.)
Answer:
Option (1)
Step-by-step explanation:
The given triangle JKL is an equilateral triangle.
Therefore, all three sides of this triangle will be equal in measure.
Side JK = JL = KL = 48 units
Perpendicular LM drawn to the base JK bisects the base in two equal parts JM and MK.
By applying tangent rule in ΔJML,
tan(∠KJL) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{\text{LM}}{\text{JM}}[/tex]
= [tex]\frac{\text{LM}}{24}[/tex]
Since, Sin(K) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° = [tex]\frac{\text{LM}}{48}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{LM}}{48}[/tex]
LM = 24√3
Now, tan(∠KJL) = [tex]\frac{\text{LM}}{24}[/tex]
= [tex]\frac{24\sqrt{3} }{24}[/tex]
Therefore, Option (1) will be the answer.
How many solutions does the system have?
Answer:
B. no solutionsStep-by-step explanation:
Left sides of both equations are the same sum (8x+2y), so the right sides also has to be the same. They are not so there is no solutions.
{If they are the same then system has infinitely many solutions.}
Write an equation in slope-intercept form of the line that passes through (-1, 4) and (0,2).
y =
Answer:
y =( -1/2 )x + 2
Step-by-step explanation:
first step is to determine the slope of the line ( which is the rise over the run) or symbolically slope is defined as m= ∆x / ∆y, so plugging those values we get...
m= ∆x / ∆y = (-1 - 0) / (4 - 2) = -1 / 2
so next is to find the zero( y-intercept) of the function by ....
y = mx + b
y = ( -1/2)x + b (since m is equal to -1/2)
2 = ( -1/2)0 + b
2= b
1. Three products from renewable resources are
Answer:
biomass energy (such as ethanol), hydropower, geothermal power, wind energy, and solar energy.
Algebra 1 need help ASAP
Answer:
It's A
Step-by-step explanation:
The money earned is 160 in 7 hours
The money earned is 100 in 3 hours
The slope = change in money / change in time
The slope = (160 - 100 ) / (7 - 3) = 60/4 = 15 dollars / hour
The slope means that for every hour he earns 15 dollars.
Given that v = u + 10t, find y when
u= 6 and t = 9.
Answer:
hey here is the answer
Step-by-step explanation:
Subject of the formula:
It is a variable which is expressed in terms of other variables involved in the formula.
Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.
For example:
In the formula v = u + at, v is the subject.
To find v in the example, we substitute the values u, a and t in the R.H.S. of the equation.
Changing the subject of the formula:
To change the subject of a formula, begin with the variable to become the new subject, and apply inverse operation as for solving equations in the opposite order to the order conventions.
1. To make ‘u’ the subject of the formula in v = u + at,
[subtract at from both sides]
v - at = u
or, u = v - at
2. To make ‘t’ the subject of the formula, v = u + at,
[subtract u from both sides]
v - u = at
or, (v - u )/a = t
or, t = (v - u)/a
Change the Subject of a Formula
The value of the equation is v = 96 when u = 6 and t = 9
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
v = u + 10t be equation (1)
when u = 6 and t = 9
Substitute the value of u and t in the equation , we get
v = 6 + 10 ( 9 )
On simplifying the equation , we get
v = 6 + 90
v = 96
Therefore , the value of v is 96
Hence , the equation is v = 96
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Suppose you are facing west. First you turn 180 degrees to the left. Then turn 45 degrees to the right. Then turn 90 degrees to the left. Then swap left with right. Then turn 180 degrees to the right. What direction are you facing now, if we are marking the directions with letters (North - N, South - S, East - E, West - W).
Answer:
we would be facing the North West
Please help its due in 30 minutes will mark braniliest
Answer:
Point A, B, and C are collinear points.
Step-by-step explanation:
When points lie on one line, meaning all of the points are on the same line --> this is known as collinear points.
udin memiliki 3 ember berisi ikan hias setiap ember berisi 320 ekor berapa banyak ikan hias udin semuanya
Answer:
960
Step-by-step explanation:
3 * 320 = 960
Udin memiliki, secara total, 960 ikan hias
(Udin has, in total, 960 ornamental fish)
Choose the inequality that represents the following graph.
Answer:
It is c
Step-by-step explanation:
because five is bigger than zero
Answer:
[tex]\sf x > 0[/tex]Step-by-step explanation:
The arrow points to all values greater than 0. And the point at 0 is not filled in. So, the inequality represents everything strictly greater than 0.
[tex]\bf x > 0[/tex]
___________________
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Have a great day!
It takes 250 \text{ g}250 g250, start text, space, g, end text of pasta and 240 \text{ ml}240 ml 240, start text, space, m, l, end text of sauce to make one batch of spaghetti, and it takes 600 \text{ g}600 g600, start text, space, g, end text of pasta and 700 \text{ ml}700 ml 700, start text, space, m, l, end text of sauce to make one batch of lasagna.
Answer:
250S + 600L > 4000
240S + 700L > 5000
Step-by-step explanation:
It takes 250 g of pasta and 240 ml of sauce to make one batch of spaghetti, and it takes 600g of pasta and 700ml of sauce to make one batch of lasagna.
Friedrich is a chef who wants to make spaghetti and lasagna using more than 4000 g of pasta and more than 5000 ml of sauce.
Let S denote the number of batches of spaghetti he makes and L the number of batches of lasagna he makes.
Write an inequality that represents the condition based on the number of grams of pasta.
Write an inequality that represents the condition based on the number of milliliters of sauce.
Scenario 1: Pasta
The chef wants to make spaghetti and lasagna using more than 4000 g of pasta.
S =the number of batches of spaghetti he makes
L =the number of batches of lasagna he makes.
We have, inequality based on the number of grams of pasta
250S + 600L > 4000
Scenario 2: Sauce
chef wants to make spaghetti and lasagna using more than 5000 ml of sauce.
S= the number of batches of spaghetti he makes
L= the number of batches of lasagna he makes.
We have, inequality based on the number of milliliters of sauce
240S + 700L > 5000
The two inequalities are:
250S + 600L > 4000
240S + 700L > 5000
If n equals 5 and b equals 4 what is n + b * 5
Answer:
25Step-by-step explanation:
Given,
n = 5
and, b = 4
Equation:
n + b × 5
= 5 + 4 × 5
= 5 + 20
= 25 (Ans)
help help help help help
reduce to lowest term. 2x^2- 18/x^2+4x-21
Answer:
[tex]\frac{2(x+3)}{x+7}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2x^2-18}{x^2+4x-21}[/tex] ← factorise numerator and denominator
2x² - 18 ( factor out 2 from each term )
= 2(x² - 9) ← difference of 2 squares
= 2(x - 3)(x + 3)
and
x² + 4x - 21 = (x + 7)(x - 3) , then
= [tex]\frac{2(x-3)(x+3)}{(x+7)(x-3)}[/tex] ← cancel common factor (x - 3) on numerator/ denominator
= [tex]\frac{2(x+3)}{x+7}[/tex]
What do you notice about the absolute value of the
difference between the two numbers of -5 and -1
Simplify 3 x times the fraction 1 over x to the power of negative 4 times x to the power of negative 3.
Answer:
3x^2
Step-by-step explanation:
Given:
(3x) * {(1/x)^-4 }* (x^-3)
=(3x) * {1 ÷ (1/x)^4} * {1/x^3}
=(3x) * {1(x/1)^4} * (1/x^3)
=(3x) * (x^4) * (1/x^3)
=(3x) (x^4) (1) / x^3
Multiply the denominators
=3x^5 / x^3
Can also be written as
=3*x*x*x*x*x / x*x*x
Divide the x
= 3*x*x / 1
=3x^2
What is the argument of -1 + √3 i?
30°
60°
120°
150°
Answer:30
Step-by-step explanation:
Pens cost 15 pence each. Rulers cost 20 pence each. Write down an expression for the cost of x pens and x rulers.
Answer:
C = 35x pence
Step-by-step explanation:
1 pen costs 15 , thus x will cost 15x
1 ruler costs 20, thus x will cost 20x
Total cost (C) will then be
C = 15x + 20x = 35x pence
The total cost of pens and rulers, C = 35x pence
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Cost 1 pens is 15.
Then, cost for x pen is 15x
Cost of 1 ruler is 20
Then, cost of x ruler is 20x
So, the total cost is
= 15x + 20x
= 35x
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2. Solve Equation Below Please Help!!
Answer:
n = 19
Step-by-step explanation:
get the -37 to the other side and solve it
Answer:
3rd answer
Step-by-step explanation:
-37+n=56
n=56+37
n=93
please help me
Expand ( p + 6 )( p - 3 )
Answer:
(p^2) + 3p - 18
Step-by-step explanation:
Have a nice day!
Answer:
2p+3
Step-by-step explanation:
(p+6)(p-3)
you have to open the brackets i.e
p+p+6-3
add p+p and you get 2p then you subtract positive 6 from 3 and you get 3
so your answer will be 2p+3
Help please!!! thx...
[tex]\\ \sf\longmapsto cos\theta=\dfrac{3}{\sqrt{13}}[/tex]
We know
[tex]\boxed{\sf sin^2\theta=1-cos^2\theta}[/tex]
[tex]\\ \sf\longmapsto \sin( \theta) = \sqrt{1 - { \cos}^{2} \theta } \\ \\ \sf\longmapsto \sqrt{1 - {( \frac{3}{ \sqrt{13} }) }^{2} } \\ \\ \sf\longmapsto \sqrt{1- \frac{ {3}^{2} }{ {( \sqrt{13)} }^{2} } } \\ \\ \sf\longmapsto \sqrt{1 - \frac{9}{13} } \\ \\ \sf\longmapsto \sqrt{\frac{13 - 9}{13} } \\ \\ \sf\longmapsto \sqrt{ \frac{4}{13} } \\ \\ \sf\longmapsto \frac{2}{ \sqrt{13} } [/tex]
Jasmine is having friends over to watch a football game. She has 2 1/2 hours until her guests arrive. She spends 2/5 of that time cleaning and the rest of the time preparing snacks. How much time does Jasmine spend preparing snacks?
Answer:
1 Hour and 30 Minutes
OR
1 1/2 Hours
Step-by-step explanation:
Convert 2 1/2 hours to minutes.
That is 150
Multiply 2/5 with 150.
Subtract that from 150.
It gives 120 minutes.
Convert that back to Hours.
You get 1 Hour and 30 Minutes or 1 1/2 Hours.
A fraction is a way to describe a part of a whole. The time that is spent by Jasmine to prepare for snacks is 2.1 hours or 2 1/10 hours.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
What is a Mixed Fraction?A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,
2 1/2
= (2×2 + 1)/2
= 5/2
= 2.5
Given that Jasmine has 2 1/2 hours until her guests arrive. She spends 2/5 of that time cleaning and the rest of the time preparing snacks. Therefore, the time spent on preparing snacks is,
Time spent on preparing for snacks = 2 1/2 - 2/5
= 5/2 - 2/5
= 2.5 - 0.4
= 2.1 hours
= 2 1/10
Hence, the time that is spent by Jasmine to prepare for snacks is 2.1 hours or 2 1/10 hours.
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Quiana took out a loan to pay for a new car. Initially she owned the lender $15,234.68. She has repaid $247.43 of the loan each month for the past 5 months. What is the net changed to the loan from Quiana's perspective over the past 5 months?
Answer:
[tex]Net\ Change = \$13997.53[/tex]
Step-by-step explanation:
Given
[tex]Debt = \$15,234.68[/tex]
[tex]Monthly\ Payment= \$247.43[/tex]
[tex]Duration = 5\ months[/tex]
Required
Determine the net change
First, we need to determine the total repaid amount;
[tex]Amount = Monthly\ Payment * Duration[/tex]
Substitute values for Monthly Payment and Duration
[tex]Amount = \$247.43 * 5[/tex]
[tex]Amount = \$1237.15[/tex]
The net change is the difference between the loan amount and the repaid amount
[tex]Net\ Change = Loan\ Amount - Repaid\ Amount[/tex]
[tex]Net\ Change = \$15,234.68 - \$1237.15[/tex]
[tex]Net\ Change = \$13997.53[/tex]
Hence, the net change over the period of 5 months is $13997.53
Answer: Quiana's initial loan amount is -15, 234.68. This is the total amount of money she must pay back to the lender.
Work out the mean for the data set below: 3, 5, 4, 3, 5, 6 Give your answer as a fraction. answer
Answer:
4 1/3
Step-by-step explanation:
3 + 5 + 4 + 3 + 5 + 6 = 26
26/6 = 4 2/6 (4 1/3)
Answer:
13/3
Step-by-step explanation:
To find the mean, add up all the numbers and divide by the number of terms
( 3+5+4+3+5+6) /6
26/6
Divide top and bottom by 2 to simplify the fraction
13/3