Answers
The values of x that make the equation true are approximately 5.7 and -0.7 .
The given equation is :
[tex]\frac{x+1}{x} = \frac{2}{x-4}[/tex]
Using cross multiplication this can be written as:
or, ( x + 1 ) ( x - 4 ) = 2 x
or, x² + x - 4x - 4 = 2x
Putting all the like terms together.
or, x² + x - 4x -2x - 4 = 0
or, x² - 5x - 4 = 0
Now we will use the quadratic formula to find the values of x :
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]
or, [tex]{\displaystyle x={\frac {5\pm {\sqrt {(-5)^{2}-4(1)(-4)}}}{2(1)}}\ \ }[/tex]
or, [tex]x = \frac{5+\sqrt{41}}{2} , \frac{5-\sqrt{41}}{2}[/tex]
or, x ≈ 5.7 , -0.7
The roots or zeros of the expression, which are also on the left side of the equation, are used to indicate the values of x that satisfy the equation.
There can only be two possible solutions to a quadratic problem. One argues that if there is only one remedy, there are many different causes of the problem. There are only four possibilities: one real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if each of the coefficients has a real value.
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Related Questions
which expression is equivalent to (2x3 +3x+7) / (x2 + x +10)
Answers
The simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.
Let us solve the given algebraic expression by the long division method:
We are given the expression:
(2x^3 + 3x + 7) / (x^2 + x + 10)
We need to perform the division of the given algebraic expression:
x^2 + x + 10 ) 2x^3 + 3x + 7 ( 2x - 2
2x^3 + 2x^2 + 20x
- - -
-2x^2 - 17x + 7
-2x^2 - 2x - 20
+ + +
-15x + 27
So,
quotient = 2x - 2
remainder = -15x + 27
Thus, the simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.
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Samantha invested $1000 in an account that pays 5% interest
compounded annually. Assuming no deposits or withdrawals are
made, find how much money Samantha would have in the account 18
years after her initial investment. Round to the nearest tenth (if
necessary).
Answers
The amount of money Samantha would have in the account 18 years after her initial investment is $2406.61
The principal amount = $1000
The interest rate = 5%
Time period = 18 years
The interest is compounded annually
The compound interest
A = [tex]P(1+\frac{r}{n})^{nt}[/tex]
Where A is the final amount
P is the principal amount
r is the interest rate
t is the time period
n is the number of times the interest applied
A = [tex]1000(1+0.05)^{18}[/tex]
A = 1000 × 2.40661
Multiply the terms
A = $2406.61
Hence, the amount of money Samantha would have in the account 18 years after her initial investment is $2406.61
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Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. How many liters of each does he need to make the needed 30 liters
of 60% acid solution?
Gabe needs ___ of the 40% solution.
Answers
He needs 10 litres of solution of 40% and 20 litres of 70% solution to make 30 litres of 60% acid solution.
According to the question,
We have the following information:
Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution.
Now, let's take x litres of 40% solution and y litres of 70% solution.
So, we have the following expressions:
x+y = 30
x = 30-y ....(1)
40x/100 + 70y/100 = 30*60/100
Dividing 100 on the numerator by 100 on denominator:
40x+70y = 1800
Dividing both sides by 10:
4x+7y = 180
Putting the value of x from equation 1:
4(30-y)+7y = 180
120-4y+7y = 180
120+3y = 180
Subtracting 120 from both the sides:
3y = 180-120
3y = 60
y = 60/3
y = 20
Now, putting this value of y in equation 1:
x = 30-y
x = 30-20
x = 10
Hence, he needs 10 litres of 40% solution and 20 litres of 70% solution to make 30 litres of 60% acid solution.
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In 1994, the moose population in a park was
measured to be 3280. By 1997, the
population was measured again to be 4120.
If the population continues to change
linearly:
Find a formula for the moose population, P,
in terms of t, the years since 1990.
P(t)
=
What does your model predict the moose
population to be in 2006?
Answers
To answer this question we will use The Linear Programming concept
The formula for the moose population is
The moose population in 2006 would be
We use the year 1990 as the base year for creating the equation of the moose population. We could assume that:
The moose population of the year: P(x)
The moose population in year 1990: a
The year difference to 1990: x
The linear change of the moose population: b
Hence, we could make some assumption about the relationship between each elements mentioned above, where the moose population of the year would be depends on the linear change of the population added into the original moose population in year 1990. We could write this relationship into the equation (i):
P(x) = a + bx ... (i)
Using data provided from the question, we could make some other equations and find the value of b:
P(x) = a + bx
P(4) = a + 4b = 3280 ---> year 1994 ... (ii)
P(7) = a + 7b = 4120 ---> year 1997 ... (iii)
We could do some eliminations between equations (ii) and (iii)
3280 = a + 4b
4120 = a + 7b -
840 = 3b
b = 280 ... (iv)
After finding the value of b, we could subtitute its value into equation (ii) to find the value of a:
3280 = a + 4b
3280 = a + 4(280)
3280 = a + 1120
a = 2160 ... (v)
After finding the value of a and b, we could rewrite the equation (i) by inserting the and b values.
P(x) = a + bx
P(x) = 2160 + 280x ... (vi)
Next, we will predict the moose population to be in 2006.
First, we should determine the value of x, the difference between the year 2006 to the base year 1990.
x = 2006 - 1990
x = 16 ... (vii)
We would subtitute the equation (vii) into equation (vi) to predict the moose population to be in 2006:
P(16) = 2160 + 280(16)
P(16) = 6640...(viii)
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What is the sum
5/7 + 1/2 + 3/4
Answers
Answer: The sum is 55/28.
Alternate Answer: 1 27/28
Step-by-step explanation:
In this equation, the common denominator between the three fractions would be twenty eight.
5/7 converts to 20/28
1/2 converts to 14/28
3/4 converts to 21/28
After adding all the new fractions together, you get 55/28.
Which graph represents the given equation? A. A parabola declines through (negative 1, 4), (negative 1, 3), (0, 2) and (1 point 5, negative 4 point 5) and rises through (2, negative 4), (3, 0) and (4, 6) on the x y coordinate plane. B. A parabola declines through (negative 4, 5), (negative 3 point 5, 2), (negative 3, 0) and (negative 1 point 5, negative 4 point 5) and rises through (0, negative 2), (1, 3) and (1, 4) on the x y coordinate plane. C. A parabola declines through (negative 2 point 3, 5), (negative 2, 2) and (negative 0 point 5, negative 3 point 1) and rises through (0, negative 2), (1, 4) and (1, 5) on the x y coordinate plane. D. A parabola declines through (negative 1, 5), (negative 0 point 5, 2), (0, negative 2) and (0 point 5, negative 3 point 1) and increases through (2, 2), (2 point 5, 5) on the x y coordinate plane.
Answers
The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.
How to obtain the graph of a quadratic function?To obtain the graph of a quadratic function, these three features have to be obtained from the function's definition:
The x-intercepts, which are the roots of the function.The y-intercept, which is the value of y when the function crosses the y-axis.The vertex, which is the turning point of the function.The function for this problem is defined as follows:
y = 1.5x² + 4x - 2.
Hence the numeric values of the coefficients are listed as follows:
a = 1.5, b = 4, c = -2.
Inserting these coefficients into a calculator, the x-intercepts of the function are given as follows:
x = -3.09 -> hence the function passes through point (-3.09, 0).x = 0.43 -> hence the function passes through point (0.43, 0).The y-intercept of the function is given by coefficient c = -2, hence the function also passes through point (0, -2).
The x-coordinate of the vertex is given as follows:
x = -b/2a = -4/3 = -1.33.
Hence the y-coordinate of the vertex is of:
y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.
Missing InformationThe problem asks for the graph of the following function:
y = 1.5x² + 4x - 2.
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A baker makes 164 cupcakes. To complete an order, he needs 36 more cupcakes. He packs the cupcakes in boxes t
each hold 9 cupcakes. How many boxes will the baker need to pack the whole order?
A) 14 boxes
B) 15 boxes
22 boxes
23 boxes
Answers
Explanation:
164 cupcakes plus another 36 is 200
200 divided by 9 is 22
Write a quadratic equation that goes through
the points (1,-3), (2,-5), and (-1,-11).
Answers
Answer:
1-3+2-5+-1-11
Step-by-step explanation:
I hope this helps :’)
if x- 37 equals to 93 find x
Answers
Answer:
x = 130
Step-by-step explanation:
x - 37 = 93 ( add 37 to both sides )
x = 130
Answer:
x=130
Step-by-step explanation:
x-37=93
x=93+37
x=130
x-37=93
-37-93= x (- / - =+ )
130=x
So, your answer is 130
One batch of pink paint uses 2 cups of red paint and 7 cups of white paint. Mai made a large
Amount of pink paint using 14 cups of red paint.
1. How many batches of pink paint did she make?
2. How many cups of white paint did she use?
Answers
Answer:
Mai made 7 batches of pink paint.
Mai used 49 cups of white paint.
Step-by-step explanation:
Part 1. Every 2 cups of red paint are 1 batch of pink paint. This means to find the number of batches of pink paint Mai made, we need to divide 14/2. 14/2 = 7. This means she made 7 batches of pink paint.
Part 2. For every 2 cups of red paint, there are 7 cups of white paint.
For every 1 cup of red paint, there are 3.5 cups of white paint.
This means that we need to multiply 14 x 3.5.
14 x 3.5 = 49.
This means she used 49 cups of white paint.
A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If .x machines are made, then the unit cost is given by the function C (x)=0.5x²-320x+68,684. What is the minimum unit cost?
Do not round your answer.
Answers
According to the concept of quadratic equation, the minimum cost for the x ray machine is $17, 484
Quadratic equation:
Basically, the polynomial equation with highest degree of two is called a quadratic equation.
The general equation is given by ax² + bx + c = 0, where a ≠ 0.
Given,
A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of machines made. If .x machines are made, then the unit cost is given by the function C (x)=0.5x²-320x+68,684.
Here we need to find the minimum unit cost.
Here we know that the standard form of a quadratic is given by:
=> ax² + bx + c
From this function, we have to calculate the value of x as,
=> x = -b/ 2a
While we compare the standard form with the given function,
=> C (x)=0.5x²-320x+68,684.
Then we get the value of
=> a = 0.5
=> b = -320
=> c = 68,684
So, the value of x is calculated as,
=> x = -(-320) / 2(0.5)
=> x = 320 / 1
=> x = 1
Now, we have to plug this value into original function would give us the minimum (unit cost):
=> C(320) = 0.5(320)²- 320 (320) + 68,684.
=> C(320) = 0.5(102400) - 102400 + 68, 684
=> C(320) = 51200 - 102400 + 68684
=> C(320) = 17, 484
Therefore, the minimum unit cost is $17, 484
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what is the derivative of tan(cos(t)) with respect to t at t=pi/2
Answers
The derivative of tan(cos(t) with respect to t at t= (π/2) is 1.
What is differentiation?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is tan(cos(t)). The derivation will be done as below,
[tex]\dfrac{d}{dx}tan(cos(t))=sec^2(cos(t)\dfrac{d}{dx}(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(t)sec^2(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(\dfrac{\pi}{2} )sec^2(cos\dfrac{\pi}{2})\\\\\dfrac{d}{dx}tan(cos(t))=sec^2(0)\\\dfrac{d}{dx}tan(cos(t))=1[/tex]
Therefore, the derivative of tan(cos(t) with respect to t at t= (π/2) is 1.
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A regular polygon has 20 sides. If one of its angles measures (5h − 12)°, what is the value of h?
Answers
The value of h in the given polygon is 34.8°
What is a regular polygon?A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides or edges of a polygon are made of straight line segments connected end to end to form a closed shape. The point where two line segments meet is called vertex or corners, and subsequently, an angle is formed. If a polygon contains congruent sides, then that is called a regular polygon.
The sum of the interior angles of a regular polygon = (n - 2) x 180
where n = number of sides of the polygon
here n = 20
Sum of the interior angle = (20 - 2) x 180
Sum of the interior angle = 3240°
which also means that 20(5h - 12) = 3240
100h -240 = 3240
100h = 3240+240
100h = 3480
h = 3480/100
h = 34.8°
In conclusion, the value of h = 34.8°
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Write the polynomial in standard form, name it using the degree and number of terms, identify the constant and the leading coefficient:(3x-8)^2(2x+5)
Answers
Answer:
It is a binomial, so it is (ax+b)^2. In this case, a=3, b=-8, and there are 2 terms. The constant is 64 and the leading coefficient is 9.
What's 237 to the square root?
Answers
Answer:
heyyy
Step-by-step explanation:
I need to know how to do these problems!
Answers
The height of the triangle pictured in the question is 2 units.
According to the question,
We have the following information:
Area of triangle = 8
Base of triangle = 8
We know that the following formula is used to find the area of triangle:
Area of triangle = 1/2*base*height
Area of triangle = 1/2*8*height
8 = 4*height
Dividing by 4 on both the sides:
Height = 8/4
Height of the triangle = 2 units
(Note that every physical quantity has some units of measurements. For example, the unit of measurement of area is square units.)
Hence, the height of the triangle pictured in the question is 2 units.
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Simplify -1 2/3 minus 9 2/5
Answers
Answer:
one ninths
Step-by-step explanation:
1/3-2/9 - fraction calculator. The result is 1/9 ≅ 0.1111111 = one ninth.
What equation that line passes through the point P(1/3,4) and has no slope.
Answers
The equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.
According to the question,
We have the following information:
Point through which line is passing = (1/3,4)
Slope of the line = 0
We know that the following formula is used to find the equation of the line passing through a point:
y-y' = m(x-x')
We have x' = 1/3 and y' = 4.
y-4 = 0(x-1/3)
y-4 = 0
Adding 4 on both sides of the equation:
y = 4
Hence, the equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.
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Increase 52 by 14% pl
Answers
Answer: 59.28
Step-by-step explanation:
your welcome :)
59.28
Travis had a box of 68 french fries. He gave 13 french fries to each of f friends. Which expression shows how many french fries he had left after giving some to his friends? A. 68 - f × 13 B. (68 + f) × 13 C. 68 + f × 13 D. (68 - f) × 13
Answers
The expression shows how many french fries he had left after giving some to his friends is 68 - 13 × f, so option A is correct.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
The total no of french fries = 68,
The no of friends = f,
The no of french fries given to each friend = 13
The equation according to the question is given as,
The french fries left = The total no of french fries - The no of french fries given to each friend × The no of friends
Substitute the values,
The french fries left = 68 - 13 × f
Therefore, the expression shows how many french fries he had left after giving some to his friends is 68 - 13 × f.
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5 customers entered a store over the course of 3 minutes. At what rate were the customers entering the store in customers per minute?
Answers
Answer: Par affluence
Step-by-step explanation: Car chaque 3 min le nombre de client augmentera
the question in the picture please help
Answers
The measures, using the binomial distribution, are given as follows:
a) Probability that exactly six arrive within two days: 0.735 = 73.5%.
b) Probability that exactly five arrive within two days: 0.232 = 23.2%.
c) Mean: 5.7 letters.
d) Variance: 0.285 letters².
e) Standard deviation: 0.534 letters.
What is the binomial distribution formula?The mass function, formula for the probability of x successes, is defined as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the mass function are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.Hence, in the context of this problem, the values of these parameters are given as follows:
n = 6, p = 0.95.
The probability that all six arrive within two days is of:
P(X = 6) = 0.95^6 = 0.735 = 73.5%.
The probability that five arrive within two days is:
P(X = 5) = 6 x 0.95^5 x 0.05 = 0.232 = 23.2%.
The statistical measures are calculated as follows:
Mean: E(X) = np = 6 x 0.95 = 5.7 letters.Variance: V(X) = np(1 - p) = 6 x 0.95 x 0.05 = 0.285 letters².Standard deviation: S(X) = sqrt(V(X)) = sqrt(0.285) = 0.534 letters.More can be learned about the binomial distribution at https://brainly.com/question/24756209
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Factor -4 out of -8+20 expression
Answers
Answer: -3
Step-by-step explanation:
Yearly budget 1200 you spend 350 what percentage is spent
Answers
Answer:
29.16% is spent
you have to divide 350 by 1200 then multiply by 100 then the answer will come
what is logarithm 4096^x=8
Answers
Answer:
Step-by-step explanation:
(4096)ˣ = 8
log ₂ (4096)ˣ = log ₂ 8
x·log ₂ (4096) = log ₂ 8
x = log ₂ 8 / log ₂ (4096)
x = log ₂ 2³ / log ₂ 2¹²
x = 3 / 12
x = 1 / 4
-4 represents the sand that lies under 4 feet of water. 4
represents a branch 4 feet above the water.
What does zero represent in this situation?
A. The distance between the sand and the branch
B. The distance to the branch
C. The surface of the water
D. The
distance
to the sand
176795
720-2
569095
$196
Answers
in this situation Zero represents, The surface of the water
-4 represents the sand that lies under 4 feet of water.
4 represents a branch 4 feet above the water.
Upon analysis, it can be said that as we move downwards, the value increases in negative sign
As we move upwards, the value increases in positive sign
The surface of water becomes the origin, as it is zero.
Therefore, , in this situation Zero represents, The surface of the water
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K
Question 1, 6.8.1
Part 1 of 5
The size P of a certain insect population at time t (in days). obeys the function P(t) = 300e0.05t
(a) Determine the number of insects at t=0 days.
(b) What is the growth rate of the insect population?
(c) What is the population after 10 days?
(d) When will the insect population reach 420?
(e) When will the insect population double?
(a) What is the number of insects at t=0 days?
0 insects
HW Score: 0%, 0 of 4 points
O Points: 0 of 1
**
Answers
a) At t = 0days : 300insects
b) The growth rate is 5.12% each day.
c) Population after 10days: P(10) =494.61
d) The population to reach 420 is equals roughly 70.129 hours
e) The insect population double in t=6.020 days , which is 144.48 hours.
What is Population?
Any whole group that shares at least one trait is referred to be a population. People do not make up all populations. Populations can include, but are not limited to, individuals, animals, organizations, structures, buildings, cars, farms, objects, or occasions.
Given: t in days, P(t)=300e(0.05t).
(a) The total number of insects at time t=0 days is equal to
P(0)=300(1)
P(0) =300.
(b) The growth rate is calculated as the percentage increase over time, which is equal to-
P(t+1)/P(t)=300e(0.05(t+1))/300e(0.05t)
P(t+1)/P(t) =e^(0.05(1))
P(t+1)/P(t) =1.0512
Therefore, the growth rate is 5.12% each day.
(c) Population after 10 days.
P(10)=300e^(0.05*10)
P(10) =300(1.6487)
P(10) =494.61
(d) When P(t)=420, the population will reach 420,
or 300e0.05t=420,
take log
0.05t=log(1.4), or
t = 2.922 days,
for the population to reach 420.
equals roughly 70.129 hours
(e) When P(t)=2*300=600 the population will double.
300e^(0.05t)=600
=> e^(0.05t)=600/300=2
Take log
(log 0.05t=log(2)),
t=6.020 days , which is 144.48 hours.
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Marc deposits $1000 into a savings account. The account pays 4% simple Interest on an annual basis. Is he does not add or withdraw money from the account, how much interest will he earn after 9 montgs?
A. $10
B.$20
C$30
D.$40
Answers
Answer:
C
Step-by-step explanation:
1000*0.04 = 40
(9/12) * 40 = 30
Determine whether the following probability is empirical or classical.
Virginia want to know how likely it is for her to win a backgammon game if she only needs to roll a double six to win.
A. Empirical
B. Classical
Answers
In this backgammon game, the probability used is Classical one.
Probability:
Probability refer the possible way of happening the particular event.
Given,
Virginia want to know how likely it is for her to win a backgammon game if she only needs to roll a double six to win.
Here we need to identify whether the given probability is empirical or classical.
In order to find the type of probability, first we have to know the definition of each of them.
So, classical probability means the the statistical concept that measures the likelihood (probability) of something happening where as the empirical probability means the probability that is based on historical data.
Therefore, based on the definition, the given situation is purely based on the classical probability.
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The price of a new computer is $1,393 at your local store. This is 20% less than what it costs at the brownstone mall. How much should it cost at the brownstone mall? Round to the nearest dollar.
Answers
Why?
First we have to find what 20% of 1,393 is.
20% = 0.20
0.20 x 1,393 = 278.6
Then we have to find what that takes away from the overall total.
1,393 - 278.6 = 1,114.4
And then since we are rounding up to the nearest dollar we can just ignore the .4