[tex]\frac{-5}{8} * \frac{2}{3}[/tex]
Multiply the top with the top and the bottom with the bottom:
[tex]\frac{(-5)*2}{8*3}[/tex]
[tex]\frac{-10}{24}[/tex]
Then you can simplify:
[tex]\frac{-5}{12}[/tex]
Hope this helped!
Answer:
-5/12
Step-by-step explanation:
Multiply the top of both fractions and the bottom of both fractions, -5*2=-10,8*3=24
so -10/24 can be simplified to -5/12
(3Q) Find the amplitude and period of f(t)= -tan.0t
Answer:
It has no amplitud and the period is 5pi/2
Step-by-step explanation:
Given a function of the following type:
f(t) = AtanB(t + C)
The function has no amplitud, given that it doesn't have maximum or minimum value. And the period is given by: pi/B
In this case, we have f(t)= -tan0.4t. Then:
B = 0.4
⇒ Period = pi/0.4 = 5pi/2
Therefore, the answer is: It has no amplitud and the period is 5pi/2
Describe the vertical asymptotes and holes for the graph of y=x-6/x^2+5x+6
Answer:
For the equation
[tex]y=\frac{x-6}{x^2+5x+6}[/tex]
There are vertical asymptotes at x=-2 and x=-3
There are no holes
Step-by-step explanation:
The equation for this graph can be factored in its denominator to get
[tex]y=\frac{x-6}{(x+2)(x+3)}[/tex]
This means that there are VA's at x=-3 and x=-2
(There are no holes as there is not a factor that cancels out.)
A function assigns the values. The asymptotes and the holes for the graph lie at x=-2 and x=-3.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The vertical asymptotes and the holes for the graph can be found by factorizing the denominator of the given function. Therefore, the factorisation of the denominator is,
x² + 5x + 6 =0
x² + 2x + 3x +6 =0
x(x+2)+3(x+2)=0
(x+2)(x+3)=0
x = -2, -3
Hence, the asymptotes and the holes for the graph lie at x=-2 and x=-3.
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What is the simplified form of 2 over x squared minus x minus 1 over x ? (2/x^2-x) - (1/x)
answers:
x-1/x(x+1)
1-x/x(x+1)
3-x/x(x-1)
x+2/x(x-1)
Answer:
3-x/x(x-1)
Step-by-step explanation:
Given
2/(x^2-x)- 1/x
To simplify, we can take x as common from the denominator of first term
= 2/(x(x-1))- 1/x
Taking LCM of denominators and then using the rules of addition and subtraction of numerators using denominator’s LCM
= (2(1)-(x-1))/(x(x-1))
Solving the brackets
=(2-x+1)/(x(x-1))
= (-x+3)/(x(x-1))
The term can also be written as:
= (3-x)/(x(x-1))
(3-x)/(x(x-1)) is the correct answer ..
To simplify the expression 2/x^2 - x - 1/x, we need to find a common denominator for the two fractions in the expression, which is x(x+1). The simplified form is (x + 2)/(x(x+1)).
Explanation:To simplify the expression 2/x^2 - x - 1/x, we need to find a common denominator for the two fractions in the expression. The common denominator is x(x+1). Multiplying the numerator and denominator of the first fraction by x+1 and the numerator and denominator of the second fraction by x, we get:
(2(x+1))/(x(x+1)) - (1*x)/x(x+1) (2x + 2 - x)/(x(x+1)) (x + 2)/(x(x+1))
So, the simplified form of 2/x^2 - x - 1/x is (x + 2)/(x(x+1)).
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Solve x in the diagram below.
X=(3x+10)
The solution to the equation X=(3x+10) is -5, which was found by isolating x on one side of the equation.
Explanation:To solve the equation X = 3x + 10 for x, you begin by isolating the variable. First, subtract 3x from both sides, yielding -2x = 10. To find the value of x, divide both sides by -2. This results in x = -5. So, the solution for x in the given equation X = 3x + 10 is x = -5. This process involves balancing both sides of the equation to isolate the variable, and by subtracting 3x and then dividing by -2, we find that x equals -5, making it a clear and concise solution to the equation.
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What is the standard form of this complex number (1+2i)/(1+I)
Answer: 3/2 + i/2
Step-by-step explanation: Simplify and write eht enaswer in standard form, a + bi.
Hope this helps! :) ~Zane
What is the results when 4x^3+11x^3-9x^2-8x+30 is divided by x+3
Answer:
4x^3 -x^2 -6x +10
Step-by-step explanation:
You can perform the division of (4x^4 +11x^3 -9x^2 -8x +30)/(x +3) by polynomial long division or by synthetic division. The latter is shown below.
The result of the division is ...
4x^3 -x^2 -6x +10
PLEASE HELP!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
B is the only graph that starts at both intervals of 2, which would be 2, and -2
Please don't delete my question! Here they are:
1. (fraction) 7/9 divided by 5/6 (fraction)
2. Write the answer is simplest form: (fraction) 1 3/8 + 4 1/2 (fraction)
3. 13 is what percent of 16?
PLEASE HELP
Answer:
1. 14/15
2. 5 7/8
3. 81.25%
Step-by-step explanation:
1. (fraction) 7/9 divided by 5/6 (fraction)
7/9 ÷ 5/6 =
= 7/9 * 6/5
= (7 * 6)/(9 * 5)
= 42/45
= 14/15
2.
1 3/8 + 4 1/2 =
= 1 + 3/8 + 4 + 1/2
= 1 + 4 + 3/8 + 4/8
= 5 + 7/8
= 5 7/8
3.
percent = part divide by whole times 100
13/16 * 100 =
= 81.25%
Answer/Step-by-step explanation:
1. 14/15
7/9 divided by 5/6
7/9 X 6/5: multiply by the reciprocal
7/3 X 2/5: reduce the numbers
7/3 X 2/5=14/15
2. 1 3/8 + 4 1/2
1+4: add all whole numbers first
3/8 +1/2 : then add the fractions
5 7/8: is your final answer in its simplest form
3. Convert fraction 13 / 16 to a Answer: 81.25%
How do you solve #5? Show your work...
Answer: 162
Step-by-step explanation:
3(2+4(5+2^3)]
3(2+4(5+8)
3(2+(4)(13))
3(2+52)
(3)(54)
=162
A gym membership at Gym A costs $12 every month plus a one-time membership fee of $36, and a gym membership at Gym B costs $20 every month plus a one-time $20 membership fee. After about how many months will the gym memberships cost the same amount?
After 2 months, the gym memberships at Gym A and Gym B will cost the same amount, based on the membership cost equations of each gym.
Explanation:We need to determine after how many months the total costs of gym memberships at Gym A and Gym B will be the same. The cost of a gym membership at Gym A is described by the equation C = 12m + 36, where C represents the total cost and m represents the number of months. For Gym B, the cost is given by the equation C = 20m + 20.
To find the number of months where the costs are equal, we set the two equations equal to each other:
12m + 36 = 20m + 20
Subtracting 12m from both sides gives us:
36 = 8m + 20
Subtracting 20 from both sides gives us:
16 = 8m
Dividing both sides by 8 gives us:
m = 2
Therefore, after 2 months, the total costs for gym memberships at both Gym A and Gym B will be the same.
Given f(x)=4x^2-9 and g(x)=2x+3 find each value
Given f(x)=4x^2-9 and g(x)=2x+3 find each value
FIND EACH VALUE
1. (f+g)(x)
2. (f-g)(x)
3. (fg)(x)
4. f(g(3))
5. g(f(3))
Given,
f(x)=4x^2-9
g(x)=2x+3
1.
(f+g)(x)=f(x) + g(x)
=4x^2-9+2x+3
=4x^2+2x-6
2.
(f-g)(x)=f(x)-g(x)
4x^2-9-2x-3
=4x^2-2x-12
when x=3, then,
f(3)=4×(3)^2-9=27
g(3)=2×3+3=9
5.
f(g(3))=f(9)=4×(9)^2-9
=312
5.
g(f(3))=g(27)=2×27+3=57
Answer:
listen to romap they are correct
Step-by-step explanation:
In the inequality, y > -5x + 1 What is the slope? ___________ What is the y-intercept? _____________ Is it a dashed or solid line? ______________ Do you shade above or below? _____________ Graph the inequality. Make sure to include the shading to indicate the solutions to the inequality.
Answer:
See below
Step-by-step explanation:
The given inequality is
[tex]y\:>\:-5x+1[/tex]
The corresponding linear equation is y=-5x+1.
This line is of the form y=mx+b
The slope of this line is m=-5 and b=1 is the y-intercept.
Since the inequality sign is '>' the boundary line is a dashed line.
We test the origin to see if the inequality will be satisfied.
[tex]0\:>\:-5(0)+1[/tex]
[tex]0\:>\:1[/tex]
This statement is false so we shade above the dashed line.
The graph of the inequality is shown in the attachment.
What is the explicit formula for this geometric sequence
Answer:
a(n) = a(1)*(1/4)^(n - 1)
Step-by-step explanation:
The first four terms of this sequence are 64, 16, 4, 1.
Let the common ratio be r. Then 64r = 16, and r = 1/4.
The first term is 64.
The general term is then
a(n) = a(1)*(1/4)^(n - 1)
What is the system of equations?
y=-5x+3
y=1
A. (0.4, 1)
B. (0.8, 1)
C. (1, 0.4)
D. (1, 0.8)
ANSWER
A. (0.4, 1)
EXPLANATION
The given system of equations is:
y=-5x+3
y=1
We equate the two equations to obtain;
[tex] - 5x + 3 = 1[/tex]
Group the similar terms to obtain;
[tex] - 5x = 1 - 3[/tex]
[tex] - 5x = - 2[/tex]
We divide both sides by -5 to get,
[tex]x = \frac{ - 2}{ - 5} [/tex]
[tex]x = \frac{ 2}{ 5} [/tex]
[tex]x = 0.4[/tex]
Therefore the solution is (0.4,1)
Answer:
[tex]\large\boxed{A.\ (0.4,\ 1)}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=-5x+3\\y=1\end{array}\right\\\\\text{Put the value of y from the second equation to the first equation:}\\\\1=-5x+3\qquad\text{subtract 3 from both sides}\\\\-2=-5x\qquad\text{divide both sides by (-5)}\\\\\dfrac{-2}{-5}=x\to \boxed{x=0.4}[/tex]
Please Help Soon!! I'm in a rush!!!
To best estimate the quotient in scientific notation, what number should replace m?
m=9-5 so answer is m=4
Answer:
[tex]m=4[/tex]
Step-by-step explanation:
We have been given an equation. We are asked to find the value of m for our given equation.
[tex]\frac{6.22\times 10^9}{1.79\times 10^5}=3\times 10^m[/tex]
Let us solve left side of our given equation using exponent property for quotient [tex]\frac{a^b}{a^c}=a^{b-c}[/tex].
[tex]\frac{6.22\times 10^9}{1.79\times 10^5}=\frac{6.22}{1.79}\times 10^{9-5}[/tex]
[tex]\frac{6.22\times 10^9}{1.79\times 10^5}=3.18\times 10^{4}[/tex]
Therefore, the value of m would be 4 for our given equation.
identify the correct trigonometry formula do you use to solve for the given angle
The correct trigonometry formula [tex]tan^{-1}[/tex] (71°) . Therefore , [tex]tan^{-1}[/tex](71°) is correct .
The correct trigonometry formula to use to solve for the given angle is the tangent formula.
This is because you are given the side opposite to the angle (48) and the side adjacent to the angle (34), and you need to solve for the angle itself (71°).
The tangent formula is:
tan(angle) = opposite / adjacent
In this case, you would have:
[tex]tan^-1[/tex] = 48 / 34
[tex]tan^-1[/tex] = 0. 708333 degree
[tex]tan^-1[/tex] = 0.71 degree
[tex]tan^-1[/tex] (0.71)
= 35.3112 degree.
Therefore, the correct answer is tan(71°).
Ann took a taxi home from the airport. The taxi fare was
$
2
.
1
0
$2.10dollar sign, 2, point, 10 per mile, and she gave the driver a tip of
$
5
$5dollar sign, 5. Ann paid a total of
$
4
9
.
1
0
$49.10dollar sign, 49, point, 10.
Write an equation to determine the distance in miles
(
x
)
(x)left parenthesis, x, right parenthesis between the airport and Ann's home.
Find the distance between the airport and Ann's home.
miles
Answer:
20.9, rounded answer: 21 miles
Step-by-step explanation:
x= distance between the airport and Ann's home.
since Ann is paying $2.10 per mile let 2.10 be the coefficient
our equation:
5 is our constant since that's how much Ann trips the driver
since the total is equal to 49.10, that's what our equation will be equal to
2.10x+5=49.10
sub "5"
2.10x+5-5=49.10-5
2.10x=44
divide both sides by "2.10"
2.10/2.10x=44/2.10
x=20.9
we can round 20.9 to 21
I don’t know what the answer is I wish I could help
An animal shelter spends $3.50 per day to care for each bird and $4.00 per day to care for each cat. Makayla noticed that the shelter spent $161.50 caring for birds and cats on Wednesday. Makayla found a record showing that there were a total of 43 birds and cats on Wednesday. How many birds were at the shelter on Wednesday?
By setting up and solving a system of equations based on the total costs and number of animals, it is determined that there were 21 birds at the shelter on Wednesday.
To solve how many birds were at the shelter on Wednesday, we can set up a system of equations based on the costs and the total number of animals. Let the number of birds be b and the number of cats be c.
The total cost for birds and cats is $161.50, and there are 43 birds and cats together. This gives us two equations:
$3.50b + $4.00c = $161.50
b + c = 43
We can solve this system of equations by first expressing c in terms of b from the second equation:
c = 43 - b
Now we can substitute c into the first equation:
$3.50b + $4.00(43 - b) = $161.50
After simplifying:
$3.50b + $172.00 - $4.00b = $161.50
Combining like terms:
-$0.50b = -$10.50
Dividing by -0.50:
b = 21
So, there were 21 birds at the shelter on Wednesday.
Input in standard form the equation of the given line.
The line through (0, -3) and (3, 0)
Answer:
x-y-3=0
Step-by-step explanation:
The slope of the line that passes through the points (0,-3) and (3,0) is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\ \\=\dfrac{0-(-3)}{3-0}\\ \\=\dfrac{3}{3}\\ \\=1[/tex]
The equation of the line is
[tex]y=m(x-x_1)+y_1\\ \\y=1\cdot (x-0)+(-3)\\ \\y=x-3\\ \\x-y-3=0[/tex]
What is the value, after 7 years, of a 2014 Ford Mustang that originally cost $25,000.00 if the depreciate at a rate of 8% per year? Round your answer to the nearest dollar.
Answer:
$14,236
Step-by-step explanation:
25000 x 0.92 = 23000 = 1 Year
23000 x 0.92 = 21600 = 2 Years
19872
18282.24
16819.66
15474.09
14236 = 7 Years
The answer would be 14000
what is 75% of 180?
Hello There!
75% of 180 is 135.
Converting Percent To Decimal.
p = 75%/100 = 0.75
Y = 0.75 * 180
Y = 135
Make a proportion ([tex]\frac{part}{whole}[/tex])...
The whole is 180 but we need to find the part which would be x
75 % is also a part of 100% (the whole)
The proportion would look like this...
[tex]\frac{x}{180} =\frac{75}{100}[/tex]
Now cross multiply to solve for x. The work for this is below.
100x = 13500
To isolate x divide 100 to both sides
100x/100 = 13500/100
x = 135
So...
135 is 75% of 180
Hope this helped!
student tickets for the football game cost $12 each and adult ticket cost $20 $1,720 was collected for the 100 tickets sold at the last game which system of equations can be used to solve for the numbers of each kind of ticket sold
Answer:
B) x+y=120; 12x+20y=1720
Step-by-step explanation:
If variables are defined as ...
x = number of student tickets sold
y = number of adult tickets sold
then the problem statement can be modeled by ...
x + y = 120 . . . . . . the total number of tickets sold is 120
12x + 20y = 1720 . . . . . the total collected from ticket sales was $1720
___
Total revenue is the sum of the revenues from sales of each ticket type. The revenue from a given ticket type is the product of that ticket price and the number sold.
The top of a ladder rests at a height of 15 feet against the side of a house. If the base of the ladder is 6 feet from the house, what is the length of the ladder? Round to the nearest foot.
Answer:
The length of the ladder is [tex]16\ ft[/tex]
Step-by-step explanation:
Let
L ----> the length of the ladder
we know that
Applying the Pythagoras theorem
[tex]L^{2}=15^{2} +6^{2}[/tex]
[tex]L^{2}=261[/tex]
[tex]L=\sqrt{261}\ ft[/tex]
[tex]L=16\ ft[/tex]
Answer:
Answer:
The length of the ladder is
Step-by-step explanation:
Let
L ----> the length of the ladder
we know that
Applying the Pythagoras theorem
Step-by-step explanation:
PLEASE HELP 14 POINTS
Answer:
A equals 254.46
C equals 56.54
Step-by-step explanation:
Area
pie (3.14) times the radius (9) times ^2 is equal to
254.46
Circumference
(2) times pi (3.14) times radius of (9) to get
56.54
Area of a circle formula = [tex]\pi[/tex]r² where r means radius and [tex]\pi[/tex] means 3.14
3.14(9)^2 = 254.34 = area
Circumference formula: 2[tex]\pi[/tex]r
2(3.14)(9) = 56.52 = circumference
The triangles are similar. What is the value of x? 48,52,20 / 12,x,5
Answer:
The value is 13
Step-by-step explanation:
You can notice that 48/12 is 4 and 20/5 is 4. Therefore, divide 52 by 4
The value of x is 13.
Similar triangle :Two triangles are said to be similar when corresponding angles of both triangles are congruent and ratio of corresponding sides are in equal proportion.
Given that, sides of one triangle are 48, 52, and 20.
Sides of other triangle are, 12, x and 5
Since, corresponding sides are in the proportion.
[tex]\frac{48}{12}=\frac{20}{5}=\frac{52}{x} \\\\x=\frac{52}{4}=13[/tex]
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Which is the logarithmic form of 4^5 = 1024
Answer:
[tex]Log_41024=5[/tex]
Step-by-step explanation:
The change of form formula (exponential to logarithm) is:
[tex]a^x=b\\Log_ab=x[/tex]
Looking at the problem given, we can simply write the logarithmic form as:
[tex]4^5=1024\\Log_41024=5[/tex]
This is the answer.
Please help will give brainliest
Answer:
19°
Step-by-step explanation:
In triangle ABC, ∠A=120°, a=8, b=3.
Use the sin rule:
[tex]\dfrac{a}{\sin \angle A}=\dfrac{b}{\sin \angle B}\\ \\\dfrac{8}{\sin 120^{\circ}}=\dfrac{3}{\sin \angle B}\\ \\8\sin \angle B=3\sin 120^{\circ}\\ \\8\sin \angle B=3\cdot \dfrac{\sqrt{3}}{2}\\ \\\sin \angle B=\dfrac{3\sqrt{3}}{16}\approx 0.3248\\ \\\angle B\approx 18.95^{\circ}\approx 19^{\circ}[/tex]
What is the product of (4x)(-3x^8)(-7x^3)
(4x)(-3x^8)(-7x^3)
4 (-3)(-7) = 84
x(-x^8)(-x^3) = x^(1 + 8 + 3) = x^12
Answer: 84x^12
Answer:
C
Step-by-step explanation:
A survey was conducted among 100 students of age groups 7−12 years and 13−18 years to find their favorite book genre. The students had to select any one genre out of detective, adventure, and biography. Out of the 50 students in the age group 7−12 years who participated in the survey, 23 liked adventure or biography. The total number of students of both age groups who liked detective books was 28.
Using a two-way table, compute the total number of students in the age group 13−18 years who liked adventure or biography.
23
27
49
51
The correct answer is C. 49.
Remember that there are 100 students divided into 7-12 and 13-18 age group. So there should be 50 for each. The table should go like this:
7-12 age group
23 adventure or biography
27 - detective
so you just have to subtract 50 from 23, which makes it 27. The remaining belongs to the 13-18 age group.
13-18 age group
1 - detective
49 - adventure or biography.
Answer:
49
Step-by-step explanation:
Total number of students =100
Out of the 50 students in the age group 7−12 years who participated in the survey, 23 liked adventure or biography.
So, 50-23 = 27 Out of the 50 students in the age group 7−12 years who participated in the survey liked detective
Now we are given that The total number of students of both age groups who liked detective books was 28.
No. of students of age group 13-17 who like detective books = Students of both age group like detective - No.of students of 7−12 years who liked detective = 28-27 =1
So ,The total number of students of both age groups who liked adventure or biography was 100-28 = 72
Since the age group 7−12 years who participated in the survey, 23 liked adventure or biography.
So, the age group 13-17 years who participated in the survey liked adventure or biography = 72-23=49
Age group Adventure or Biography Detective Total
7-12 23 27 50
13-18 49 1 50
Total 72 28 100
So, Option C is true.
The total number of students in the age group 13−18 years who liked adventure or biography. is 49
For v=-3i-7j, find the unit vector in the same direction of v, and write your answer as a linear combination of the standard unit vectors I and j.
Answer:
[tex]-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}[/tex]
Step-by-step explanation:
The given vector is:
v = -3i-7j
The unit vector is found by dividing the vector by its magnitude
[tex]Unit\ vector\ of\ v=\frac{v}{||v||}[/tex]
We have to find the magnitude first
So,
[tex]||v||=\sqrt{(-3)^{2} +(-7)^{2}}\\ =\sqrt{9+49}\\ =\sqrt{58}[/tex]
The unit vector is:
[tex]\frac{-3i-7j}{\sqrt{58} } \\=>-\frac{3i}{\sqrt{58}}-\frac{7j}{\sqrt{58}}\\=>(-\frac{3i}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}}) -(\frac{7j}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}})\\=>-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}[/tex]
Therefor the last option is the correct answer ..
The unit vector in the same direction as v = -3i-7j is found by calculating the magnitude of v and then dividing v by its magnitude. The result is (-3/sqrt(58))i + (-7/sqrt(58))j.
Explanation:Finding the Unit VectorTo find the unit vector in the same direction as v = -3i-7j, we first need to calculate the magnitude (length) of v. The magnitude of a vector can be calculated using the Pythagorean theorem as applied to vector components, so for our vector v, the magnitude |v| would be sqrt((-3)^2 + (-7)^2) = sqrt(9 + 49) = sqrt(58).
Next, we find the unit vector by dividing the vector by its magnitude. This gives us: (-3/sqrt(58))i + (-7/sqrt(58))j.
Therefore, the unit vector in the same direction as v is (-3/sqrt(58))i + (-7/sqrt(58))j.
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