Answers
Answer:
x=-15/2 and x=1
x=6 and x=3/4
Step-by-step explanation:
You have the following equations:
[tex]\frac{4x-3}{x+2}=\frac{2x}{x+5}[/tex]
[tex]\frac{2}{x-2}+\frac{3}{x}-\frac{9}{x+3}[/tex]
To solve both equations you can first multiply by the m.c.m of the denominators, and then solve for x, just as follow:
first equation:
[tex][\frac{4x-3}{x+2}=\frac{2x}{x+5}](x+2)(x+5)\\\\(4x-3)(x+5)=2x(x+2)\\\\4x(x)+4x(5)-3(x)-3(5)=2x(x)+2x(2)\\\\4x^2+20x-3x-15=2x^2+4x\\\\4x^2-2x^2+20x-3x-4x-15=0\\\\2x^2+13x-15=0[/tex]
In this case you use the quadratic formula:
[tex]x_{1,2}=\frac{-13\pm \sqrt{(13)^2-4(2)(-15)}}{2(2)}\\\\x_{1,2}=\frac{-13 \pm 17}{4}\\\\x_1=-\frac{15}{2}\\\\x_2=1[/tex]
Then, for the first equation the solutions are x=-15/2 and x=1
second equation:
[tex][\frac{2}{x-2}+\frac{3}{x}=\frac{9}{x+3}]x(x-2)(x+3)\\\\2x(x+3)+3(x-2)(x+3)=9x(x-2)\\\\2x^2+6x+3(x^2+3x-2x-6)=9x^2-18x\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\2x^2+6x+3x^2+3x-18-9x^2+18x=0\\\\-4x^2+27x-18=0[/tex]
Again, you use the quadratic formula:
[tex]x_{1,2}=\frac{-27\pm \sqrt{(27)^2-4(-4)(-18)}}{2(-4)}\\\\x_{1,2}=\frac{-27\pm 21}{-8}\\\\x_1=6\\\\x_2=\frac{3}{4}[/tex]
Then, the solutions for the second equation are x=6 and x=3/4
Related Questions
The graph is a marginal cost curve that compares expenses for producing apple pies. According to the graph, the marginal cost begins to increase when the producer makes two pies. three pies. four pies. five pies.
Answers
The correct answer is C. Four pies
Explanation:
Marginal cost refers to an increase in the cost of production as additional units are made. In the case of apple pies, the graph shows the cost for one is $1.00. Moreover, this decreases when two or three pies are produced because the cost is between $0.60 and $0.30. However, if the producer makes four or more units, the cost increases. For example, at four units the cost per unit is $0.60, while at six units the cost is $1.50. Thus, the marginal cost begins to increase at four pies.
Answer: four pies
Step-by-step explanation:
The graph is a marginal cost curve that compares expenses therefore it would equal four pies because the marginal cost rises on the graph starting at 4.
(Please answer!) What is the quotient (3x^3+10x+4)÷(x+2)? Answer choices below:
Answers
Answer:
The answer is option 2.
HELP, please!! What is the area of a trapezoid ABC?
Answers
Answer:
26 feet squaredStep-by-step explanation:
Area of trapezoid:
[tex] \frac{1}{2} \times \: sum \: of \: parallel \: sides \: \times height[/tex]
plugging the values:
[tex] \frac{1}{2} \times (21 + 5) \times 2[/tex]
Calculate the sum
[tex] \frac{1}{2} \times 26 \times 2[/tex]
Reduce the numbers with G.C.F 2
[tex]13 \times 2[/tex]
Calculate the product
[tex]26[/tex] feet squared.
Hope this helps...
Best regards!
Which shapes can be made from a planar cross section of a triangular pyramid? More than one can be correct: trapezoid, pentagon, isosceles triangle, rectangle, hexagon, scalene triangle, square, decagon, or equilateral triangle
Answers
Answer:
Triangle in isosceles, scalene or equilateral forms and
quadrilateral in trapezoid, rectangle or square forms
Step-by-step explanation:
Refer to pictures attached
Shapes can be formed are:
Trapezoid,when perpendicular to base
Rectangle or square,when angle cross section to base
Isosceles triangle,when base is isosceles triangle and parallel cross section to base,
or angle cross section
Scalene triangle,when base is scalene triangle and parallel cross section to base,
or angle cross section
Equilateral triangle,when base is equilateral triangle and parallel cross section to base,
or angle cross section
A line contains the points (3,1) and (−6,4). A line contains the points (3,1) and (−6,4). What is the equation for this line in slop-intercept form? What is the equation for this line in slop-intercept form?
Answers
Answer:
y = -1/3 x + 2Step-by-step explanation:
The equation of a line in slope-intercept form is expressed as y = mx+c
m is the slope of the line
c is the intercept
m = Δy/Δx = y₂-y₁/x₂-x₁
Given the points on a line to be (3,1) and (−6,4);
x₁ = 3, y₁ = 1, x₂ = -6 and y₂ = 4
m = 4-1/-6-3
m = 3/-9
m = -1/3
To get the intercept c, we will substitute any of the points given and the value of the slope into the equation y = mx+c. Using the point (3, 1) and m = -1/3
1 = -1/3(3)+c
1 = -1+c
c = 1+1
c =2
Substituting m = -1/3 and c = 2 into the sllpe intercept form of the equation will give;
y = -1/3 x + 2
Hence the equation for the line in slope-intercept form is y = -1/3 x + 2
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x + 7? A. It is the graph of y = x translated 7 units up. B. It is the graph of y = x where the slope is increased by 7. C. It is the graph of y = x translated 7 units to the right. D. It is the graph of y = x translated 7 units down.
Answers
The plus 7 at the end will shift the graph 7 units up. Replace y with f(x).
Then we have g(x) = f(x) + 7. Adding 7 to y = f(x) will increase the y value by 7.
The statement correctly describes the graph of y = x + 7 as choice A.
The graph is moved 7 units up
We have given that,
The graph of y = x.
What is the transformation of the graph?Each statement describes a transformation of the graph of y = x.
The plus 7 at the end will shift the graph 7 units up.
Replace y with f(x).
Then we have g(x) = f(x) + 7.
Adding 7 to y = f(x) will increase the y value by 7.
To learn more about the graph visit:
https://brainly.com/question/4025726
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Find the slope of the line that contains the following points. A(5, 6), B(10, 8) 5/2 2/5 14/15
Answers
Hey there! :)
Answer:
Slope = 2/5.
Step-by-step explanation:
Use the slope formula to solve for the slope of the line:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates of each point into the equation:
[tex]m = \frac{8 - 6}{10 - 5}[/tex]
Simplify:
m = 2/5. This is the slope of the line.
Please help me with this question.
Answers
Answer:
75% (I think)
Step-by-step explanation:
1/4 of babies have no hair
2/4 of babies have little hair
1/4 of babies have a lot of hair
Two pizzas with 8 inch and 16 inch diameters are each cut into 6 equal pieces. How does the area of each piece of the smaller pizza compare to the area of each piece of the larger pizza?
Answers
Answer:
Step-by-step explanation:
The easiest way to think about increasing area is by taking a square, if you double the dimensions, let's say they were 1 by 1 and then was made into a 2x2 square, you can fit four of the original cube (1x1) into the 2x2. So when the dimensions are doubled the area is quadrupled.
Even easier shortcut:
Take the cube idea, when the dimensions are messed with for anything, (works for volume too) always think of the smaller piece as 1x1 or 1x1x1. Then if the dimensions are double make it 2x2 or 2x2x2. If the dimensions are tripled then do 3x3 or 3x3x3, etc... 1x1=1x1x1, they are both equal to 1. So think of that as the numerator. the 2x2 in this case is equal to 4 so the smaller piece is 1/4 of the bigger one. Shown with volume if you double the dimensions of a cube that was 1x1x1 into 2x2x2. 1x1x1 still equals 1 so that's still the numerator and 2x2x2 is equal to 8 so the 1x1x1 cube is 1/8 of the 2x2x2, in other words you can fit eight 1x1x1 cubes into the 2x2x2 cube.
Hope this helps with area and volume.
Please answer this in two minutes
Answers
Answer:
k = 4Step-by-step explanation:
It is half of equilateral triangle where 2√3 is its hight so:
[tex]2\sqrt3=\frac{k\sqrt3}2\\\\4\sqrt3=k\sqrt3\\\\k=4[/tex]
Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2ab-6a+5b+___ Please include an explanation too!
Answers
Answer:
[tex]2ab - 6a + 5b - 15[/tex]
Step-by-step explanation:
Given
[tex]2ab - 6a + 5b + \_[/tex]
Required
Fill in the gap to produce the product of linear expressions
[tex]2ab - 6a + 5b + \_[/tex]
Split to 2
[tex](2ab - 6a) + (5b + \_)[/tex]
Factorize the first bracket
[tex]2a(b - 3) + (5b + \_)[/tex]
Represent the _ with X
[tex]2a(b - 3) + (5b + X)[/tex]
Factorize the second bracket
[tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]
To result in a linear expression, then the following condition must be satisfied;
[tex]b - 3 = b + \frac{X}{5}[/tex]
Subtract b from both sides
[tex]b - b- 3 = b - b+ \frac{X}{5}[/tex]
[tex]- 3 = \frac{X}{5}[/tex]
Multiply both sides by 5
[tex]- 3 * 5 = \frac{X}{5} * 5[/tex]
[tex]X = -15[/tex]
Substitute -15 for X in [tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]
[tex]2a(b - 3) + 5(b + \frac{-15}{5})[/tex]
[tex]2a(b - 3) + 5(b - \frac{15}{5})[/tex]
[tex]2a(b - 3) + 5(b - 3)[/tex]
[tex](2a + 5)(b - 3)[/tex]
The two linear expressions are [tex](2a+ 5)[/tex] and [tex](b - 3)[/tex]
Their product will result in [tex]2ab - 6a + 5b - 15[/tex]
Hence, the constant is -15
Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
Answers
Answer:
A. [tex] \frac{7x^2}{6x - 10} [/tex]
Step-by-step Explanation:
To get the quotient, which is the result of
What we get by dividing the above, we would turn the divisor upside down, while the division sign would change to multiplication. This rule applied is known as "multiplying by the reciprocal".
[tex] \frac{7x^2}{2x + 6} [/tex] ÷ [tex] \frac{3x - 5}{x + 3} [/tex]
[tex] \frac{7x^2}{2x + 6} * \frac{x + 3}{3x - 5} [/tex] => multiplying by the reciprocal.
[tex] \frac{7x^2}{2(x + 3)} * \frac{x + 3}{3x - 5} [/tex]
[tex] \frac{7x^2}{2} * \frac{1}{3x - 5} [/tex] => (x + 3) cancels (x + 3)
[tex] \frac{7x^2(1)}{2(3x - 5)} [/tex]
[tex] \frac{7x^2}{6x - 10} [/tex]
Quotient = [tex] \frac{7x^2}{6x - 10} [/tex]
Answer: A
Step-by-step explanation:
Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and leading coefficient. If the function is not a polynomial, state why. f(x)=x^4(2-x^3)+1
Answers
Answer:
The correct option is
This is a polynomial function of degree 7 with a leading coefficient of -1
Step-by-step explanation:
Functions that consist of a variable such as x raised to positive integer powers which are equal to or larger than zero added together to make the function are known as polynomial functions
Therefore, the function in the question which is f(X) = x⁴ × (2 - x³) + 1
Which can be expanded as follows
f(x) = 2·x⁴ - x⁷ + 1, which is the same as given as follow equation;
f(x) = -x⁷ + 2·x⁴ + 1
Which is polynomial function with a leading coefficient of -1 as it consists of only whole number positive powers of x including the powers of x 4 and 7
Therefore, the correct option is that f(x) is a polynomial function of degree 7 with a leading coefficient of -1.
I need help!!! Please Help!!
Answers
Answer:
Step-by-step explanation:
If you aren't supposed to do this on your calculator, then you'd have to figure out a way to get the bases of 10 to have the same power somehow in order to use the properties of exponents. This is the problem (you multiply the 2 dimensions together to find area, remember):
[tex](5.5*10^5)(4.2*10^4)[/tex]You cannot simply add the exponents on the 10's and say your power is 9...cuz it's not. It needs to be rewritten so that there is a power of 4 on the 10 in the parenthesis on the left. Do that this way:
[tex](5.5*10^4*10^1)(4.2*10^4)[/tex] Now you've got a common power of 4 between the 2 sets of parenthesis. 10 to the first is the same as 10, so multiplying that into the 5.5 gives us
[tex](55*10^4)(4.2*10^4)[/tex]
55 * 4.2 is 231 and 10 to the 4th times 10 to the 4th is 10 to the 8th.
[tex]231*10^8[/tex] But that's not in correct scientific notation. If we move the decimal to places to the left, we have to add 2 to the exponent of 8, giving us, finally,
[tex]2.31*10^{10}m^2[/tex]
Next use the hint to convert that to kilometers:
[tex]2.31*10^{10}m^2*\frac{1km^2}{1*10^6m^2}[/tex]
Dividing like bases means we subtract the lower exponent from the upper. 10 - 6 = 4, so the equivalent number of km squared is
2.31 × 10⁴ km²
Kilometers are comparable to miles, which is how we measure large things, like pieces of land. So it would be better to measure the forest in kilometers squared instead of meters squared.
Which of the following is the product of the rational expressions shown
below?
Answers
Answer:
The answer is b
Step-by-step explanation:
since 2*9=18 and (x)(2x+3)=2x^2+3x
Answer: B
Step-by-step explanation:
5x+8=3x-6 plz help me asap
Answers
Answer:
x = -7
Step-by-step explanation:
5x+8=3x-6
Subtract 3x from each side
5x-3x+8=3x-3x-6
2x+8 = -6
Subtract 8 from each side
2x+8-8 = -6-8
2x = -14
Divide by 2
2x/2 = -14/2
x = -7
Answer: x= -7
Step-by-step explanation:
[tex]5x+8=3x-6[/tex]
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
[tex]5x+8-8=3x-6-8[/tex]
[tex]5x=3x-14[/tex]
[tex]\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}[/tex]
[tex]5x-3x=3x-14-3x[/tex]
[tex]2x=-14[/tex]
[tex]\mathrm{Divide\:2\:\:on\:\:both\:sides\:}[/tex]
[tex]-14/2=-7[/tex]
[tex]x=-7[/tex]
Which of the points listed is the same distance from the y-axis as the point (−4, 7.5)?
Answers
Answer:
(-4, y) and (4, y), where y is any real number.
Step-by-step explanation:
The point (-4; 7.5) is 4 units from the y axis.
All points that lie on the line x = -4 and the line x = 4 have the same distance from the y-axis of 4 units.
If f(x)=5x/3+5, which of the following is the inverse of f(x)
Answers
Answer:
B
Step-by-step explanation:
to find the inverse of a function, repalace f(x) with x, and replace x with y, proceed to solve for y and the answer you get is B
Answer:
B
Step-by-step explanation:
f(x)=5x/3+5
y=5x/3+5
x=5y/3+5
now solve for y
3x=5y+15
5y=3x-15
y=3x/5-3 or 3(x-5)/5
Find the area of the shape shown below. I NEED HELP NOWWWWWW
Answers
Answer:
12.5 units[tex] {}^{2} [/tex]Step-by-step explanation:
Given figure : Trapezoid
Base sides,
a = 2.5
b = 7.5
Height ( h ) = 2.5
Now, finding the area:
[tex] \frac{1}{2} (a + b) \times h[/tex]
Plug the values
[tex] = \frac{1}{2 } \times (2.5 + 7.5) \times 2.5[/tex]
Calculate the sum
[tex] = \frac{1}{2} \times 10 \times 2.5[/tex]
Reduce the numbers with G.C.F 2
[tex] = 5 \times 2.5[/tex]
Calculate the product
[tex]12.5 \: \: {units}^{2} [/tex]
Hope this helps...
Best regards!
Use zero property to solve the equation.
F(x)=3x(x+7)-2(x+7)
Answers
Answer:
x = -7 or x = 2/3
Step-by-step explanation:
I'm assuming you meant solve for x when f(x) = 0.
f(x) = 3x(x + 7) - 2(x + 7)
0 = (x + 7)(3x - 2) -- Both terms have a common factor of (x + 7) so we can group them
x + 7 = 0 or 3x - 2 = 0 -- Use ZPP
x = -7 or x = 2/3 -- Solve
Molly was curious if quadrilateral A, B, C, D and E, F, G, H were congruent, so she tried to map one figure onto the other using transformations.
Answers
Answer: Choice C. No error. Molly is correct
Note how BC is 4 units high while FG is 5 units high. We don't have a match. So there is no way the figures are the same regardless of rigid transformations.
Answer:
Its c
Step-by-step explanation:
I got it right on khan academy
Reorder the following equations in ascending order of steepness: y= 15x + 5 y= 0.15x - 1 y=x y= x + 100
Answers
Answer:
y= 0.15x - 1, y = x, y = x + 100, y = 15x + 5.
Step-by-step explanation:
When the slope of a line is less than 1 (if the slope is a decimal), the slope will not be steep. But when the slope is more than 1, the slope will be steeper than the average.
According to that rule, the steepest will be y = 15x + 5.
The next steepest equations will be y = x and y = x + 100 (they are both at the same degree of steepness; the intercept does not impact the steepness of the line).
The least steepest will bey = 0.15x - 1.
So, the order, from least steep to most steep, will be y= 0.15x - 1, y = x, y = x + 100, y = 15x + 5.
Hope this helps!
Louis traveled 2,795 on an airplane from
Los Angeles to New York City. Then he
switched planes and traveled 3,460
miles to London. After that, he switched
planes again and traveled 889 miles from
London to Rome. How many miles did he
fly in all?
Answers
Louis traveled 7,144 miles
If you know the value of sin(30°), which of the following can you calculate directly through using the half angle formula?
cos(30°)
sin(45°)
sin(15°)
sin(60°)
Answers
Answer:
cos(30)
Step-by-step explanation:
Answer:
sin(15)
Step-by-step explanation:
By moving point G, how many triangles is it possible to draw, keeping the measure of just one angle constant (in this case, m∠FDE)? In how many instances are all three angle measures of ∆DEF equal to those of the original triangle, ∆ABC?
Answers
Step-by-step explanation:
Keeping, one angle FDE, many triangles are possible since length of no segment is fixed and only one angle is fixed.
At many instances, triangle ABC and DEF have same angle measurements. Referring to the image attached here.
As point G moved on the ray EF, many triangles with same angle measurements as of ABC can be formed.
Answer:
Since no segment length is fixed and only one angle is fixed, multiple triangles are possible while maintaining one angle FDE. Triangles ABC and DEF frequently have the same measured angles. referring to the picture that is attached. Numerous triangles with the same angle measurements as ABC can be constructed when point G moves along ray EF.
Step-by-step explanation:
ASAPPPPPP!! PLEASE help me!!!!!!!!!!
Answers
The volume of a sphere is calculated using the formula 4pi r^3/3=32pi/3. Solve for r and get r=2. Then plug into the formula for finding the area of a circle A=r^2pi so you get 4pi.
calcula la diagonal de un cuadrado cuyo lado tiene cada una de las siguientes medidas en centímetros. a.4 b.7 c.13
Answers
Answer:
[tex]4\sqrt{2}\\\\7\sqrt{2} \\\\13\sqrt{2}[/tex]
Step-by-step explanation:
Well the diagonal using pythagora's theorem:
[tex]x\sqrt{2}[/tex] where x is the lenght is the side of the square
so when x=4
[tex]4\sqrt{2}[/tex]
when x=7
[tex]7\sqrt{2\\}[/tex]
when x=13
[tex]13\sqrt{2}[/tex]
The length of diagonal is for (a=4) is [tex]4\sqrt{2}[/tex], for(a=7) is [tex]7\sqrt{2}[/tex] and for (a=13) is[tex]13\sqrt{2}[/tex].
Given side of squares.
We have to calculate the length of diagonal.
We know that in square shape,
length of diagonal [tex]=\sqrt{2} a[/tex], here a is the side of square.
So when square has a side of 4 then its diagonal becomes [tex]4\sqrt{2}[/tex].
when square has a side of 7 then its diagonal becomes [tex]7\sqrt{2}[/tex].
when square has a side of 13 then its diagonal becomes [tex]13\sqrt{2}[/tex].
Hence the length of diagonal is for (a=4) is [tex]4\sqrt{2}[/tex], for(a=7) is [tex]7\sqrt{2}[/tex] and for (a=13) is[tex]13\sqrt{2}[/tex].
For more details on length of diagonal of square follow the link:
https://brainly.com/question/16716787
A cylindrical container has a radius of 0.3 meter and a height of 0.75 meter. The container is filled with kerosene. The density of kerosene is 815 kg/m³. What is the mass of the kerosene in the container? Enter your answer in the box. Use 3.14 for π. Round your final answer to the nearest whole number.
Answers
Answer:
172.83 kg
Step-by-step explanation:
A cylindrical container has a radius (r) of 0.3 meter and a height (h) of 0.75 meter and density of 815 kg/m³.
The density of a substance is the mass per unit volume, it is the ratio of the mass of a substance to the volume occupied. The density is given by the formula:
Density = Mass / volume
The volume of a cylinder is given as:
V = πr²h
V = π × (0.3)² × 0.75 = 0.212 m³
Density = Mass/ volume
Mass = Density × Volume
Mass = 815 kg/m³ × 0.212 m³
Mass = 172.83 kg
Answer:
The answer is 173
Step-by-step explanation:
The other guy's answer was correct, but he forgot to round up to the nearest whole number so just in case you didn't notice the question saying that!
Which describes how to graph g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function?
Answers
Answer:
[tex]f(x) =\sqrt[3]{x}[/tex]
Step-by-step explanation:
Hello!
Considering the parent function, as the most simple function that preserves the definition. Let's take the function given:
[tex]g(x) = \sqrt[3]{x-5}+7[/tex]
To have the the parent function, we must find the parent one, let's call it by f(x).
[tex]f(x) =\sqrt[3]{x}[/tex]
This function satisfies the Domain of the given one, because the Domain is still [tex](-\infty, \infty)[/tex] and the range as well.
Check below a graphical approach of those. The upper one is g(x) and the lower f(x), its parent one.
Answer:
5 units to the right and 7 units up (B on edge)
Step-by-step explanation:
Please helpppp!!!
Solve: x^2 - 4x-5=0
Answers
Answer:
[tex]x=-1,5[/tex]
Step-by-step explanation:
[tex]x^2-4x-5=0[/tex]
In order to solve this quadratic, we have many methods. We can factor, complete the square, or use the quadratic formula. I'm going to factor since it's the easiest method.
To factor, find two numbers that when multiplied equal a(c) and when added equal b.
a=1, b=-4, and c=-5.
So we want two numbers that when multiplied equals 1(-5)=-5 and when added equals -4.
-5 and 1 are the possible numbers. Therefore:
[tex]x^2-4x-5=0\\x^2+x-5x-5=0\\x(x+1)-5(x+1)=0\\(x-5)(x+1)=0\\x=5, -1[/tex]