PLEASE HELP
If a = 1, find the values of b, c, and d that make the given expression equivalent to the expression below.
Answers
Once you have simplified the expression, you get
[tex] \dfrac{-x-9}{2x-4} [/tex].
But, the problem stipulates that a must equal 1. We can equivalently factor out the negative sign and put it on the denominator with no change to write
[tex] \dfrac{x+9}{-(2x-4)} = \dfrac{x+9}{-2x+4}[/tex].
So, seeing where each coefficient corresponds between the two expressions, you get a = 1, b = 9, c = –2, and d = 4.
Equivalent expressions are expressions with the same value.
The values of the variables are:
[tex]\mathbf{a = 1}[/tex] [tex]\mathbf{b = 9}[/tex] [tex]\mathbf{c = -2}[/tex] [tex]\mathbf{d = 4}[/tex]
The expression is given as:
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49}}[/tex]
Expand
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x^2 + 9x - 7x - 21}{-2x^2 +4x -6x + 12} \cdot \frac{2x^2 + 14x + 9x + 63}{6x^2 + 21x - 14x - 49 } }[/tex]
Factorize
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x(x + 3) - 7(x + 3)}{-2x(x -2) -6(x - 2)} \cdot \frac{2x(x + 7) + 9(x + 7)}{3x(2x + 7) - 7(2x - 7) } }[/tex]
Factor out the terms
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(3x - 7) (x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{(3x - 7) (2x - 7) } }[/tex]
Cancel out 3x - 7
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]
Factor out -2
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{-2(x +3)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]
Cancel out x + 3
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{1}{-2(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) }}[/tex]
Rewrite as:
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x + 9)(x + 7)}{ -2(x - 2)(2x - 7) } }[/tex]
Expand
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{2x^2 + 25x + 63}{ -4x^2 + 22x - 28}}[/tex]
Factorize again
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x+ 7)(x + 9)}{(2x + 7)(-2x + 4)}}[/tex]
Cancel out common factors
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{x + 9}{-2x + 4}}[/tex]
From the question, we have:
[tex]\mathbf{\frac{ax + b}{cx + d}}[/tex]
So, we have:
[tex]\mathbf{\frac{ax + b}{cx + d} = \frac{x + 9}{-2x + 4}}[/tex]
By comparison, we have:
[tex]\mathbf{a = 1}[/tex]
[tex]\mathbf{b = 9}[/tex]
[tex]\mathbf{c = -2}[/tex]
[tex]\mathbf{d = 4}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/24242989
Related Questions
In calculating the present value of $1,000 to be received 5 years from today, the discount factor has been calculated to be .7008. what is the apparent interest rate?
Answers
from the present value table, the percentage corresponding to discount factor of 0.7008 in 5 years is 7%
therefore using the formula:
FV=PV(1+r/100)^n
where:
FV=$1000
PV=?
r=7%
hence:
1000=PV(1+7/100)^5
PV=1000/(1+7/100)^5
PV=712.986
A solid is composed of squares and equilateral triangles. Its net is shown below:
The area of each triangle is 1.5 square units. The surface area of the triangular prism is _____ square units. (Input whole number only.)
Answers
2*2=4
4*3= 12
There are 2 triangles so
2*2=4
4/2=2
2*2=4
4+12= 16
Answer:
So I am going one is kind of the same but it says six units and then it says the area of each triangle is 16 square units and I was trying to follow the step-by-step explanation from somebody else and I got 52 but I don’t know if I did that right
Step-by-step explanation:
How can Brady use fraction strips to show that 3 4 and 7 8 are NOT equivalent?
Answers
Next Brady needs seven strips that each represent one eighth (1/8). He needs to line them up end to end. The new long strip he has created represents 7/8.
If the two long strips he created were equal then 3/4 would equal 7/8 but as they are not equal this is not the case. Since the strip for 7/8 is longer, the fraction 7/8 is greater than 3/4.
To demonstrate that 3/4 and 7/8 are not equivalent, Brady can use fraction strips to visually compare the colored portions of the strips, which will clearly show that 7/8 is greater than 3/4 as it has more colored sections.
Explanation:To show that 3/4 and 7/8 are not equivalent using fraction strips, Brady can follow these steps:
Take one strip and divide it into four equal parts to represent the fraction 3/4. Color three of these parts.Take another strip, divide it into eight equal parts to represent the fraction 7/8, and color seven of these parts.Compare the two colored strips side by side.Brady will observe that the strip representing 7/8 has more colored sections than the strip representing 3/4, even though the strips are the same length. This visual comparison confirms that 3/4 is less than 7/8, thus they are not equivalent fractions. The fraction 7/8 is only one-eighth away from being a whole, whereas 3/4 is one-fourth away.
help me please asap ill mark brainliest nd plz be correct
Answers
7 = 2x-11
18 = 2x
x = 18/2 = 9
AI = 3(9) +7 = 27 +7 = 34
5x - 11 = 3x + 7
2x = 18
x = 9
so
AI= 3(9) + 7 = 27 + 7 = 34 = BI = CI
answer
34
WILL MARK AS BRAINLIEST!!
What is the value of x?
Need help fast!
Answers
.. x = 3*8 in = 24 in
Why is it most logical to let x represent Dianna’s current age?
Answers
in 3 years, she's going to be " x + 3 " years old.
33 years ago, she was " x - 33 " old.
how much is 4 times that anyway? well 4(x-33), that's 4 times as 33 years ago her age.
now, we know in 3 years, x+3, she'll be "4 times as old as she was 33 years ago", 4(x-33), therefore, those amounts are equal then,
[tex]\bf \stackrel{\textit{3 years from now}}{x+3}~~=~~\stackrel{\textit{4 times as old as she was 33 years ago}}{4(x-33)} \\\\\\ x+3=4x-132\implies 135=3x\implies \cfrac{135}{3}=x\implies 45=x[/tex]
why is it most logical to use "x" for her age today?
well, because 3 years from now is just x + 3
and
33 years ago is x - 33, 4 times that is 4( x - 33 ).
works very well as a point of reference.
Diannas current age is what your being asked to find
Diannas age is the unknown in the problem
The given relatioships can be written in terms of diannas current age
Solve the system shown.
Answers
x+12y=68 (i)
x=8y-12 (ii)
2. Let's substitute the equation (ii) into the equation (i):
x+12y=68
(8y-12)+12y=68
3. Then, you have:
8y-12+12y=68
4. When you clear "y", you have:
20y-12=68
20y=68+12
20y=80
y=80/20
y=4
5. You already have the value of "y". Now, you must substitute this value into the equation (ii):
x=8y-12
x=8(4)-12
x=32-12
x=20
6. Therefore, the result is:
x=20
y=4
Do 1.5 cm, 3 cm, 1.5 cm make a triangle and what kind
Answers
The lengths 1.5 cm, 3 cm, and 1.5 cm cannot form a triangle because the sum of the lengths of the two shorter sides is equal to the length of the longest side, which does not satisfy the Triangle Inequality Theorem.
The question asks if lengths 1.5 cm, 3 cm, and 1.5 cm can form a triangle, and if so, what kind of triangle it would be. To determine whether these lengths can form a triangle, we use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For these lengths:
1.5 cm + 1.5 cm = 3 cm1.5 cm + 3 cm > 1.5 cm1.5 cm + 3 cm > 1.5 cmWe see that when we add the lengths of the two shorter sides (1.5 cm + 1.5 cm), it equals the length of the longest side (3 cm). According to the Triangle Inequality Theorem, the lengths do not meet the condition for forming a triangle because the sum must be greater than, not equal to, the length of the third side. Therefore, these lengths cannot form a triangle.
Anybody have a correct answer?
Answers
The formula for the Lateral Area of Square-based Pyramid
L.A = [tex] \frac{1}{2} [/tex] (Perimeter of the base) x Apothem
Given:
Apothem = 10 in
Side length = 5 in
Perimeter of Square = 4 x side = 4 x 5 = 20 in
L.A = [tex] \frac{1}{2} [/tex] (20)(10)
= [tex] \frac{1}{2} [/tex] (200)
= 100 in²
Answer:
100
Step-by-step explanation:
What is 5/15 written as a decimal???
What is 4/15 written as a decimal???
What is 3/15 written as a decimal???
Answers
There are a couple ways we can use to convert a fraction to a decimal, but let's stick with the easiest one.
To convert a fraction to a decimal, simply divide the numerator (top part of the fraction) by the denominator (bottom part).
The first fraction is 5/15. Its numerator is 5, and its denominator is 15. Divide the top by the bottom.
5 ÷ 15 = 0.3333333333
Because this decimal keeps repeating, it is called a "repeating fraction."
We don't want to write all those 3's over and over again, so to indicate that it is a repeating decimal, simply put a bar above the 3.
Convert the other two fractions using the same method:
4 ÷ 15 = 0.266666667
Remember to put a bar above the repeating number.
3 ÷ 15 = 0.2
Since this decimal does not repeat, it is called a "terminating decimal". You do not have to put a bar above the 2.
Don't forget this method!
Need quick help please?! Using the Angle Bisector Theorem solve for x.
Show all work.
Answers
15/3 = (4x+1)/5
5 = (4x+1)/5
4x+1 = 25
4x = 24
x = 6
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
We have been given a triangle and we are asked to solve for x using angle bisector theorem.
Angle bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side of triangle into segments that are proportional to the other two sides.
Using angle bisector theorem we can set an equation as:
[tex]\frac{4x+1}{5}=\frac{15}{3}[/tex]
Let us solve for x by multiplying both sides of our equation by 5.
[tex]\frac{4x+1}{5}*5=\frac{15}{3}*5[/tex]
[tex]4x+1=5*5[/tex]
[tex]4x+1=25[/tex]
Let us subtract 1 form both sides of our equation.
[tex]4x+1-1=25-1[/tex]
[tex]4x=24[/tex]
Upon dividing both sides of our equation by 4 we will get,
[tex]\frac{4x}{4}=\frac{24}{4}[/tex]
[tex]x=6[/tex]
Therefore, the value of x is 6 units.
solve for x in the equation x^2+10x+12=36
Answers
x^2 +10x + 12 = 36
x^2 + 10x + 12 - 36 = 0
x^2 +12x - 2x - 24 = 0
x(x + 12) - 2(x +12) = 0
(x + 12) x (x - 2) = 0
x + 12 = 0
x - 2 = 0
x = -12
x = 2
your answer for the first x is x = -12, and your answer for the second x will be
x = 2
let me know if you have any further questions
:)
Answer: The required value of x is 2 or -12.
Step-by-step explanation: We are given to solve for x in the following equation :
[tex]x^2+10x+12=36~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be solving the given equation by the method of factorization.
From equation (i), we have
[tex]x^2+10x+12=36\\\\\Rightarrow x^2+10x+12-36=0\\\\\Rightarrow x^2+10x-24=0\\\\\Rightarrow x^2+12x-2x-24=0\\\\\Rightarrow x(x+12)-2(x+12)=0\\\\\Rightarrow (x-2)(x+12)=0\\\\\Rightarrow x-2=0,~~~~~~x+12=0\\\\\Rightarrow x=2,~-12.[/tex]
Thus, the required value of x is 2 or -12.
I WILL GIVE BRAINLIEST, PLS HELP-A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
Enter your answer in the box.
ft²
Answers
which numerical expression would provide the solutions to the equation 7x^2 + 4x - 8 = 14
Answers
7x^2 + 4x - 8 = 14-----------------> 7x²+4x-22=0
Step 1
Solving a second degree equation
x1=[-b+√(b²-4ac)]/2a
x2=[-b-√(b²-4ac)]/2a
a=7
b=4
c=-22
then
x1=[-4+√(4²-4*7*(-22))]/(2*7)-----------> [-4+√(632)]/(14)
x1=-(-4+25.14)/14=1.51
x2=[-4-√(4²-4*7*(-22))]/(2*7)-----------> [-4-√(632)]/(14)
x2=-(-4-25.14)/14=-2.08
the solutions of the system is
x1=1.51
x2=-2.08
to check the result
using a graph tool
see the attached figure
the answer is
the numerical expressions is
x1=[-b+√(b²-4ac)]/2a
x2=[-b-√(b²-4ac)]/2a
The quadratic equation 7x^2 + 4x - 8 = 14 does not have any real solutions.
Explanation:The given equation is a quadratic equation of the form at² + bt + c = 0, where a = 7, b = 4, and c = -22. To find the solutions, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values, we get:
x = (-4 ± √(4² - 4(7)(-22))) / (2(7))
Simplifying further, we get:
x = (-4 ± √(16 - 616)) / 14
x = (-4 ± √(-600)) / 14
The expression inside the square root is negative, which means there are no real solutions to the equation.
Help please !!!!!!!!!!!!!!!!!???!?
Answers
---------------------------------------------
The idea is to go through each answer choice and see if that value is in the range. To do so, draw a horizontal line from that value at the y axis and see if it crosses the graph.
So for example, for choice A, we draw a horizontal line through -2 on the y axis. You'll see that the horizontal line crosses the green part of the piecewise function graph. So y = -2 is in the range. Similar situations will happen for B and C as well.
The only time that this doesn't happen is when y = 5. Draw a horizontal line through 5 on the y axis. This horizontal line is too high to cross through any part of the piecewise function. So y = 5 is not in the range.
Which is why the answer is choice D
Which concept can be used to prove that the diagonals of a parallelogram bisect each other?
a)congruent triangles
b)similar triangles
c)congruent rectangles
d)similar rectangles
Answer: Jiren is too strong. (congruent triangles)
Answers
Hope I helped you :D
Answer:
Option: A is correct (congruent triangles)
Step-by-step explanation:
To prove that he diagonals of a parallelogram bisect each other we have to go through the following steps:
Angle DBA is congruent to angle BDC. Angle CMD is congruent to angle AMB. Triangle CMD is congruent to triangle AMB. Segment AM is congruent to segment MC. M is the midpoint of segment AC. Segment BD bisects segment AC. Segment BM is congruent to segment MD. M is the midpoint of segment BD. Segment AC bisects segment BD.Hence we have to use the concept of congruent triangles in order to prove that the diagonals of a parallelogram bisect each other.
Hence, option A is correct
Cody graphed a quadratic equations, y = -(x+3)^2 + 1. What were cody's mistakes?
Answers
The vertex of cody's graph was ploted in x = 3, where it should be x = -3
This changes the position of the parabola
Answer:
the answer is d
Step-by-step explanation:
The vertex and the axis of symmetry are graphed incorrectly.
The digits 8,7,6,5,4,3,2,1 are written in a pattern over and over again. what will be the 5479th digit
Answers
The 5479th digit is 2.
What is Division?One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation can be used to quickly and easily fix such issues. In this case, we must divide 30 by 5.
given:
8 digits written in that same order ( 8,7,6,5,4,3,2,1 ) over and over again
So, we have to find 5479th digit
= 5479/8
= 684 7/8
Now, The 684 quotient tells us how many complete times the sequence goes through the cycle of 8,7,6,5,4,3,2,1, and the 7 remainder tells us which member of the cycle is the 5479 digit.
Since the 7th member of the cycle is 2.
Hence, the 5479th digit is 2.
Learn more about division here:
https://brainly.com/question/21416852
#SPJ2
Please HELP NEEDED ASAP APPRECIATED !! Brainlestwill be given
Answers
sqrt(x) = x^(1/2) so
(x^(1/2) )^5 = x^(5/2)
The answer closest to the bottom of the page <<<<===== answer.
In a homicide case 33 different witnesses picked the same man from a line up. the line up contained 5 men. if the identifications were made by random guesses, find the probability that all 33 witnesses would pick the same person. round to seven decimal places.
Answers
we know that
the probability
that a witness picks a particular person by chance-----> P=1/5
the probability
that all 7 witnesses would pick the same person-----> P=1/5^7=0.0000128
the answer is the option B 0.0000128
There are a variety of problems in which the number of witnesses change, for example
....find the probability that all 9 witnesses would pick the same person
in this case, the probability would be-------> P=1/5^9=0.000000512
Final answer:
The probability that Nancy is a robber given Bob's identification is around 33.2%, considering Bob's accuracy and the base rate of robbers in the population.
Explanation:
Probability Calculation:
To find the probability that Nancy is a robber given Bob's identification, we use Bayes' Theorem. Given that Bob is 99% accurate in identifying suspects, the calculation reveals that the probability that Nancy is a robber is around 33.2%.
Base Rate Fallacy: It is crucial to consider the base rate of robbers in the population to avoid common statistical errors in interpreting the probability of an event.
Brainliest!
World’s Busiest Airports
Airport
Total Passengers (millions)
Atlanta, Hatfield
80.2
Chicago, O’Hare
72.1
Los Angeles
68.5
Dallas/Ft Worth
60.7
London, Heathrow
64.6
Find the mean number of passengers in the world’s five busiest airports.
a.
69.22 million
c.
80.2 million
b.
346.1 million
d.
60.7 million
Answers
Hope this helps <3
In the diagram, AB = 12, DX = 2.5, and BX = 5. Find CD. Show all work.
Answers
See attached image.
For this case what you should see is that you have two similar triangles.
We then have the following relationship:
((AB) / (BX)) = ((CD) / (DX))
We cleared CD:
CD = ((AB) / (BX)) * (DX)
Substituting the values:
CD = ((12) / (5)) * (2.5)
CD = 6
Answer:
CD = 6
helpppppppppppppppppppppppppppppppp
Answers
By us looking at this expression, [tex](fg)(5)[/tex], this would be clear to show us that (fg) would be multiplied by 5. So, in your options, this would be something that we would want to find, a multiplication expression.
Your correct answer to this question would be A.) Let's look! So, the first part of the option A.) is [tex]f(5)[/tex] and from this, it would auto matically be multiplied. Now it would also be the same as the other part of the expression, which so sum it all up, this would be the best answer that would be equivalent to the expression above.
Your correct answer would be . . . . .
[tex]\boxed{\boxed{f(5)*g(5)}}[/tex]
Hope this helps you greatly!
one face of a cube an area of 49 square centimeters. what is the volume of the cube
Answers
Force exerted by the ball on the kickers foot.
Answers
F = (42*0.65)/(0.018) = 1516.7 N
To the correct number of sig figs it is 1500 N
Find a second-degree polynomial p such that p(1) = 5, p'(1) = 7, and p''(1) = 10.
Answers
p'(x) = 2ax +b
p''(x) = 2a
You require
.. 2a = 10
.. 2a +b = 7
.. a + b + c = 5
Thus a=5, b=-3, c=3, and
.. p(x) = 5x^2 -3x +3
The given conditions suggest a second-degree polynomial of form p(x) = ax^2 + bx + c. By solving the given conditions a = 5, b = -3, and c = 3, yielding the polynomial p(x) = 5x^2 - 3x + 3.
Explanation:The question is asking for a second-degree polynomial, which can generally be written in the form p(x) = ax^2 + bx + c. Given that p(1) = 5, that means a + b + c = 5. The derivative of p(x), p'(x) = 2ax + b, and p'(1) = 7, so 2a + b = 7. The second derivative, p''(x) = 2a, and p''(1) = 10, so 2a = 10 or a = 5. We can substitute a = 5 into the first two equations to find the values of b and c. So, b = -3 and c = 3. Therefore, the original function is p(x) = 5x^2 - 3x + 3.
Learn more about Second-degree polynomial here:https://brainly.com/question/31062879
Quadrilateral ABCD is inscribed in this circle. what is the measure of angle C?
Answers
angle c = 180 - 2x - 38
angle c = 142 - 2x
Answers...........................?
Answers
Your calculator can help with this if you don't happen to know already that 1/5 of 5/4 = 1/4.
A Hummingbird moves its wings at a rate of 5520 wingsbeats a minute. Write this rate in wingbeats per second?
Answers
The required rate of wingbeats per second is 92.
A Hummingbird moves its wings at a rate of 5520 wingsbeats a minute. Write this rate in wingbeats per second?
Rate of change is defined as the change in value with rest to the time is called rate of change.
given rate = 5520 wingsbeats a minute.
now to convert it in seconds divide it by 60
= 5520/60
= 92 wingsbeats a second
Thus, The required rate wingbeats per second is 92.
Learn more about rate of change here: https://brainly.com/question/13103052
#SPJ2
What is the area of the polygon
Answers
Formula:
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 22 x 9
Area of triangle = 99 square units