Answer:
-3/22
Step-by-step explanation:
Hope this helps!
Answer: [tex]-\frac{3}{22}[/tex]
Step-by-step explanation:
To find the product, multiply the two fractions:
[tex]-\frac{2}{11} *\frac{3}{4} =-\frac{2*3}{11*4} =-\frac{6}{44} =-\frac{3}{22}[/tex]
What are all the real and complex solutions of x3 + 2x2 + 36x = –72? Round to the nearest tenth if necessary.
The roots of the equation x³ + 2x² + 36x + 72 = 0 are ( -2 , -6i , +6i )
What is Factorizing?
Brackets should be expanded in the following ways:
For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket
For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.
Given data ,
Let the equation be x³ + 2x² + 36x = -72
Adding 72 on both sides , we get
x³ + 2x² + 36x + 72 = 0
Now , on simplifying we get
Take the common factor x² in first two terms and 36 in last two terms
So ,
x² ( x + 2 ) + 36 ( x + 2 ) = 0
Now , taking ( x + 2 ) as common factor , we get
( x² + 36 ) ( x + 2 ) = 0
So , for the equation to be 0 , either ( x + 2 ) = 0 or ( x² + 36 ) =0
And , we can find the solutions to the equation as
x + 2 = 0
Subtracting 2 on both sides , we get
x = -2
So , one solution is -2
Now ,
( x² + 36 ) =0
Subtracting 36 on both sides , we get
x² = -36
x = √ ( -36 )
x = ± 6i
So , we got two more solutions as -6i and +6i
Hence , the roots of the equation are -2 , -6i and +6i
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3|x+3|−12=0
Step 3 of 4: Using the two equations found in Step 2, enter the solution set using set notation.
The solution set is X ∈{1, -7}
The set of values that satisfy a given set of equations or inequalities is known as a solution set. For example, the solution set for a set of polynomials over a ring is the subset on which the polynomials all vanish (evaluate to 0).
Given that 3(x+3) – 12 = 0
We have to find the solution set
3(x+3) – 12 = 0
3(x+3) = 12
X+3 = ±4
X + 3 = 4 or x + 3 = -4
X = 1 or x = -7
X ∈{1, -7}
Therefore the solution set is X ∈{1, -7}
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Workers in an office of 90 staff were asked their favourite type of take-away.
The results are summarised in the table.
Take-away Frequency Angle
Pizza 6 a
Curry 8 b
Fish & chips 21 c
Kebab 5 d
Other 50 e
What fraction of a person is one degree?
Give your answer in its simplest form.
The fraction of person that represents a degree is 1/4
What is Π chart ?A Π chart is a type of representation used in showing data representing the parts sometimes in degrees.
Π charts are made in circle and use the features of circle
Considering the problem at hand, the total number of workers in the office is 90
The total angle of a circle is 360
if 90 person is equivalent to 360 then one person would be
1 person = 360 / 90
1 person = 4 degrees
therefore 1 degree will be 1/4 person
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Determine whether (-9,-5) is a solution of 9x + 4y = 10.
...
Answer:
It is not a solution
Step-by-step explanation:
put in (-9,-5) in for x and y
9(-9)+4(-5)=10
-81-20=10
-101=10
This is false so (-9,-5) is not a solution to the equation 9x+4y=10
Find the inverse of the function.
y = x² + 4x + 4
I pretty much understand the concept on how to do this. Somebody on here already asked this exact question and got responded with a step by step answer, but I need someone to go more in depth. The part that confuses me most is the x² + 4x, how exactly do I write that out? The person who answered the other guy's question solved it by saying, "y = x² + 4x + 4 ⇒⇒⇒ factor the quadratic equation
y = (x+2)(x+2)". Where in the world did the (x+2)(x+2) come from?.. The video I'm learning from did not do that once whilst solving these problems. I really hope someone can help.
Inverse of the function is -2+x
What do you mean by inverse function?
A function that returns the initial value for which a function has produced an output is known as an inverse function. If f(x) is a function that produces the value y, then [tex]f^{-1}(y)[/tex] the inverse function of y, will provide the value x.
The function's inverse, represented by , [tex]f^{-1}[/tex] returns the original value that was used to create the output (x).
Given function is y = x² + 4x + 4
To find the inverse function, we need to express x as a function of y:
Substitue y=x
⇒ x = [tex]y^{2}+4y+4[/tex]
Substract x from the above equation we get,
[tex]y^{2}+4y+4[/tex] - x = 0
Solve the above equation using quadratic formula we get,
y = [tex]\frac{-4+\sqrt{16-4(4-x)} }{2}[/tex] [tex]=\frac{-4+\sqrt{16-16+4x} }{2}[/tex] = [tex]\frac{-4+2x}{2}=-2+x[/tex]
Similarly, y = -2-x
Therefore, [tex]f^{-1}=[/tex] -2+x , -2-x
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simplify - (y+2) +2y
Answer:
y-2
Step-by-step explanation:
How do you graph it?
Your round trip drive to work is 4 3/10 miles. How many miles do you drive to and from work in 3 days?
Answer:
Below
Step-by-step explanation:
4 3/10 * 3 = 43/10 * 3 = 129 / 10 = 12 9/10 miles
Out of 5,000 students 1,000 preferred diet drinks over sugared sodas. What percent preferred non diet drinks?
what is the value of tan 30?
The value of tan 30° after using trigonometric ratio is [tex]\frac{1}{\sqrt{3} }[/tex] .
What is trigonometric ratio?
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.
Here the given
=> tan30°
Now ,Tan 30 degrees in radians is written as
=>tan (30° × π/180°)
=> [tex]\frac{1}{\sqrt{3} }[/tex]
Therefore the value of tan30° is [tex]\frac{1}{\sqrt{3} }[/tex] .
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In 1965, the population of a certain town was 2010. In 1995, the population was 3620. If the population during this time period grew according to an exponential model, what will the population be in 2050?
According to the growth function, the population be in 2050 will be 10,635
Growth function:
The growth function refers the pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Given,
In 1965, the population of a certain town was 2010. In 1995, the population was 3620.
Here we need to find the population in 2050.
While we looking into the given problem, let us consider,
P refers the final population
A refers the the starting population, and
x refers the time passed
Now, we need to determine the value of the growth factor n and it can be calculated using the information for the years 1965 and 2010.
Here we know that, in 1965, the population of a certain town was 2010. In 1995, the population was 3620.
And the value of x is 30
So, it can be written as,
=> 3620 = 2010eⁿˣ³⁰
=> 3620/2010 = e³⁰ⁿ
=> 362/201 = e³⁰ⁿ
Here by applying ln to both sides of the equation:
⇒ln(362/201) = ln(e³⁰ⁿ)
By, using the laws of logarithms:
=> 30n = ln(362) - ln(201)
=> n = [ln(362) - ln(201)] / 30
=> n = 0.0196
Here we have to use this information to determine P in 2050.
Here the value of A will still be 2010, but x will be 85 years.
Here we have to apply these values then we get,
=> P = 2010e⁰°⁰¹⁹⁶ˣ⁸⁵
=> P = 2010e¹°⁶⁶⁶
=> P = 2010 x 5.2909
=> P = 10635
Therefore, there are 10635 in 2050.
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Calculate the standard score (z-score) of the given sample mean. Round your answer to two decimal places.
μ = 35 and o = 9; n = 60; x = 32
The standard score (z-score) of the given sample is -20.
Given,
[tex]u[/tex] = 35
[tex]o[/tex] = 9
n = 60
x = 32
To calculate standard score (z-score) use formula,
[tex]z=\frac{x-u}{\frac{o}{n} }\\\\z=\frac{32-35}{\frac{9}{60} }\\\\z=\frac{-3}{0.15}\\ \\z=-20[/tex]
Thus, the standard score(z-score) of given sample mean is -20.
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Eve is going to buy 30 pens from either shop A or shop B.
Shop A: pack of 10 pens for £2
Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.
What is the difference in cost for all 30 pens between the two shops?
PLSS HELPPPP
The difference in the cost of all 30 pens between two shops is,
£1.05
Given, Eve is going to buy 30 pens from either shop A or shop B.
Shop A: pack of 10 pens for £2
Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.
So, the cost of 30 pens from the shop A is,
as, a pack of 10 pens is of £2
1 pen = 2/10
30 pens = £6
Now, the cost of 30 pens from the shop B is,
as, a pack of 5 for £1.10
1 pen = 1.10/5 = £0.22
also buy 1 and get 1 at half price.
So, 2 pens = 0.22 + 0.11 = £0.33
Therefore, 30 pens = £4.95
So, the cost of 30 pens from shop A is £6 and from shop B is £4.95.
Hence, the difference in the cost of all 30 pens between two shops is,
£1.05
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Find
(Round your answer to the nearest hundredth)
The value of the unknown angle x would be 43 degrees.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We have been given a right-angle triangle with a perpendicular side of 6 units and a hypotenuse of 10 units.
The unknown angle is x which needs to find.
Therefore, applying trigonometry;
Sin x = perpendicular/hypotenuse
Sin x = 6/10
Sin x = 3/5
Sin x = 0.6
x = Sin inverse (0.6)
x = 43 degrees.
Hence, the value of the unknown angle x would be 43 degrees.
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1) 3x(x-3)+x(x-1)=50
2) 4x^2-10x=50
3) 2x^2-5x-25=0
How do you get from steps 1 to 2 to 3?
Step-by-step explanation:
okok
3x(x-3)+x(x-1)=50multiply inside the brackets then3x^2-9x+x^2-x=50then arrange then according to power and add or subtract 4x^2-10x=50 here is your step 2take 2 common form LHS as2(2x^2-5x)=50then you will get your step 3 as2x^2-5x=25.....25 comes from 50/2 and 2 is from LHSpaula is transferring photo files to an external hard drive to free up storage on her phone. The size of the files on her external hard drive in megabytes is give F , where F=38+6t and t is the time in seconds since the transfer began. how many megabytes of files are transferred to her hard drive every second
Every second, 44 megabytes of files will be transferred to her hard drive.
The size of the files on her external hard drive in megabytes is given F, where F = 38 + 6t and t is the time in seconds since the transfer began.
The function is below
F = 38 + 6t ....(i)
To determine the number of megabytes of files transferred to her hard drive every second
Substitute the value of t = 1 in the equation (i), and solve for F
F = 38 + 6(1)
F = 38 + 6
F = 44
So the number of megabytes of files = 44
Therefore, every second, 44 megabytes of files will be transferred to her hard drive.
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Make the subject of
x − 5 = t
A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 per day to rent the same car.
using a graphing calculator, find the number of days fpr which the costs are the same. round your answer the the nearest whole day
A. 9
B.3
C. 5
D. 8
Answer: The answer to this question would be: 5 days
In this question, there are two kinds of rent pricing and you are asked to find the number of days when both of them will charge the same price.
From the description, you can get an equation of each price which would look like this(x=number of day rent):
cost1= 110 + 46x
cost2= 70 + 54x
Then, the days when the price same would be:
cost1 = cost2
110 + 46x= 70+54x
110-70= 54x - 46x
40= 8x
x=5
Step-by-step explanation:
12²+6² ÷2 =
please help me
Answer:
162
Step-by-step explanation:
12²+6² ÷ 2
= 144 + 36 ÷ 2
= 144 + 18
= 162
A quadratic function
y
=
f
(
x
)
y=f(x) is plotted on a graph and the vertex of the resulting parabola is
(
−
5
,
6
)
(−5,6). What is the vertex of the function defined as
g
(
x
)
=
f
(
x
−
2
)
g(x)=f(x−2)?
Step-by-step explanation:
g(x) = the original function at x-2.
just means it is the same function as the original function, just moved 2 units to the right.
just think about it :
e.g.
g(3) is the same as the originated function at x=1.
g(4) is the same as the original function at x=2.
...
so, everything that happened for the original function at x, happens now for g at x+2.
therefore, again, things move 2 units to the right (positive x direction) .
that means the vertex "moves" from
(-5, 6) to (-3, 6)
the vertex of g(x) = (-3, 6)
NO LINKS!! Please help me with this problem. Find all points on the x-axis that are a distance 5 from P(-8,4)
Answer:
[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
The points that are a distance of 5 units from P(-8, 4) will be all the points on the circumference of a circle with center (-8, 4) and radius 5.
Substitute the center and radius into the formula to create an equation of the circle:
[tex]\implies (x+8)^2+(y-4)^2=25[/tex]
The y-value of any point on the x-axis is zero.
Therefore, to find the points on the x-axis that are 5 units from point P, substitute y = 0 into the equation of the circle and solve for x:
[tex]\implies (x+8)^2+(0-4)^2=25[/tex]
[tex]\implies (x+8)^2+(-4)^2=25[/tex]
[tex]\implies (x+8)^2+16=25[/tex]
[tex]\implies (x+8)^2+16-16=25-16[/tex]
[tex]\implies (x+8)^2=9[/tex]
[tex]\implies \sqrt{(x+8)^2}=\sqrt{9}[/tex]
[tex]\implies x+8=\pm3[/tex]
[tex]\implies x+8-8=\pm3-8[/tex]
[tex]\implies x=-8\pm3[/tex]
[tex]\implies x=-11, x=-5[/tex]
Therefore:
[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]
[tex]\sqrt{x}^4-6x^2+9[/tex]
explain how the value of a digit changes if the digit moves one place to the right or left.
When talking about a number line, the farther right the digit moves, the large the number. The farther left it goes, the smaller the number.
For example, 81 would be to the right of 80. And 79 would be on the left. The larger the negative number, the smaller it is. So -70 is smaller than -20.
I hope this helps!
If sin(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following. Use fractions and radicals only, no decimals. You do not need to rationalize the denominator.
sin(x/2) =
cos(x/2)=
Tan(x/2)=
please help
The value of sin(x/2)= √(1-√11/6)/2
The value of cos(x/2)=√(1+√11/6)/2
The value of tan(x/2) = 5/6/(√(1+√11/6)
What trigonometry of half angles?In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45 and so on. If θ is an angle, then the half angle is represented by θ/2.
In trigonometry, sin( x/2)= √(1-cosx)/2
cos( x/2)= √(1+cosx)/2
tan( x/2)=sinx/1+cosx
if sin (x) = 5/6
this means that 5 is the opposite and 6 is the hypotenuse, then the adjascent is
a= √(6^2-5^2)
a= √36-25
a= √11
therefore if cos x= √11/6
sin(x/2)= √(1-√11/6)/2
cos(x/2)= √(1+√11/6)/2
tan(x/2)=5/6/(√(1+√11/6)
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Brainliest if correct
Answer:
AAS
Step-by-step explanation:
let us say that angleDAB is 60 then angleADB is 30
due to the presence of line DB we can also say that angleDCB is 60 and angle CBD is 30
The graph below represents the paths of a squirrel traveling up and down a tree over time. The position of the squirrel can be calculated using the function p(t)=at^2+bt+c. What is the value of a? What is the value of b? What is the value of c?
The values of the variables a, b and c are; a = 5/19, b = -160/19, c = 960/19
How to interpret Quadratic graphs?
We are given the quadratic function formula as;
p(t) = at² + bt + c
Thus, the equation is now;
p(t) = at² + bt + 0
p(t) = at² + bt
From the graph, we see that when x = 8, y = 0. Thus;
p(8) = a(8²) + 8b + c = 0
64a + 8b + c = 0 ------(1)
From the graph, we know that the axis of symmetry is;
x = -b/2a
Thus;
16 = -b/2a
b = -32a -----(2)
From the graph, we see that when x = 5, y = 15. Thus;
p(8) = a(5²) + 5b + c = 0
25a + 5b + c = 15 ------(3)
Put -32a for b in eq 1 and 3 to get;
64a + 8(-32a) + c = 0
-192a + c = 0 ------(4)
25a + 5(-32a) + c = 15
-135a + c = 15 ------(5)
Subtract eq 4 from eq 5 to get;
192a - 135a = 15
57a = 15
a = 15/57
a = 5/19
Thus;
b = -32(5/19) = -160/19
-135(5/19) + c = 15
15 + (675/19) = c
c = 960/19
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Please help with this equation question?
Choose the pair of numbers that is not a solution to the given equation. . (1, 2) (0, ) (4, 3)
The pairs of numbers given, (1, 2) is not a solution.
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:
y= 2x+1 /3
Now, First value of x = 0
y= 2(0)+1 /3
y= 1/3
i.e., (0, 1/3)
and, Second value of x = 1
y= 2(1)+1 /3
y= 5/3
i.e., (1, 5/3)
and, Third value of x = 4
y= 2(4)+1 /3
y= 9/3
y=3
i.e., (4, 3)
Hence, from the pairs of numbers given, (1, 2) is not a solution.
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Simplify x^2-4/x^2+2
Answer:x^4+6
Step-by-step explanation:
you must combined both x squared to get x^4 and then add the opposite of -4 Which is +4 and what you do to one side you must do to the other therefore you add the 2 to it as well. in conclusion you get x^4+6. hope this helps:)
I need help fast please!
The time it takes to cover the distance between two cities by car varies inversely with the speed of the car.
The trip takes 7 hours for a car moving at 36 mph.
What is the speed of a car that makes the trip in 9 hours?
Answer:
28 mph
Step-by-step explanation:
Given that a car moving 36 mph takes 7 hours for a trip, you want to know the speed if the trip takes 9 hours.
Time and SpeedThe speed and time vary inversely for the same distance. If the time goes up by a factor of 9/7, the speed will go down by the inverse factor: 7/9.
7/9 × 36 mph = 28 mph
The speed of the car is 28 mph for the 9-hour trip.
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