[tex]\bf \cfrac{x}{4x+x^2}\implies \cfrac{\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(4+x)}\implies \cfrac{1}{4+x}\qquad \{x|x\in \mathbb{R}, x\ne -4\}[/tex]
if you're wondering about the restriction of x ≠ -4, is due to that would make the fraction with a denominator of 0 and thus undefined.
To simplify the expression x/4x + x^2, we combine like terms and factor out a common factor.and This simplified expression cannot be reduced further.
Explanation:To simplify the expression x/4x + x^2, we need to combine like terms. First, let's simplify the fraction by finding a common denominator. The common denominator for 4x and x is 4x. Therefore, the fraction becomes x/(4x) + x^2. Next, let's combine the fractions by adding the numerators and keeping the same denominator. This gives us (x + 4x^2)/(4x). Finally, we factor out the common factor x from the numerator, resulting in x(1 + 4x)/(4x). This simplified expression cannot be reduced further.
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I Need Help!! What’s The Answer
Answer:
23°Step-by-step explanation:
Angles (2x + 14)° and (x + 7)° are complementary angles.
If two angles are complementary, then they add up to 90°.
Therefore we have the equation:
(2x + 14) + (x + 7) = 90 combine like terms
(2x + x) + (14 + 7) = 90
3x + 21 = 90 subtract 21 from both sides
3x = 69 divide both sides by 3
x = 23
Which graph represents the function p(x) = |x - 1l
Answer:
D) (the fourth one)
Step-by-step explanation:
The function will never go below 0 since the absolute of a negative number is a positive number, so C is out of the question.
The equation of an absolute function is f(x) = a|x-h|+k
h is the offset on the x axis, and the equation of this function is |x-(1)|, so that means the function is shifted one to the right, making it D.
Do you think that there is a rule you could use to predict the number of times your heart would beat in 15 seconds after you did 100 jumping jacks? Explain your answer.
Answer:
Yes
Step-by-step explanation:
The more you jump, the higher your blood flow becomes, since your heart needs to pump more blood to the working areas. This really doesn't belong in math though.
Answer: yes
Step-by-step explanation: but i am not that sure how i can explain it, here look at the guys answer above. Also thank the guy above, not me.
If you spent 24 weeks working on a project for your job and was rewarded with 3 days of vacation, write the ratio of time on vacation to time working as a fraction in lowest terms.
The ratio of time on vacation to time working as a fraction in lowest terms when working 24 weeks and rewarded with 3 days of vacation is 1/56.
If you spent 24 weeks working on a project for your job and were rewarded with 3 days of vacation, the ratio of time on vacation to time working as a fraction in lowest terms can be calculated as follows:
Convert weeks to days: 24 weeks x 7 days/week = 168 days workedCalculate the fraction: 3 days vacation / 168 days worked = 1/56Therefore, the ratio of time on vacation to time working as a fraction in lowest terms is 1/56.the burj khalifa a building in dubai united arab emirates is about 828 meters tall
Answer:
true
Step-by-step explanation:
Solve the system of equations.
2x+2y+3z=4
5x+3y+5z=5
3x+4y+6z=5
Answer:
B. [tex]x=3,\ y=20,\ z=-14[/tex]
Step-by-step explanation:
Consider the system of three equations:
[tex]\left\{\begin{array}{l}2x+2y+3z=4\\5x+3y+5z=5\\3x+4y+6z=5\end{array}\right.[/tex]
Multiply the first equation by 5, the second equation by 2 and subtract them:
[tex]\left\{\begin{array}{r}2x+2y+3z=4\\4y+5z=10\\3x+4y+6z=5\end{array}\right.[/tex]
Multiply the first equation by 3, the second equation by 2 and subtract them:
[tex]\left\{\begin{array}{r}2x+2y+3z=4\\4y+5z=10\\-2y-3z=2\end{array}\right.[/tex]
Multiply the third equation by 2 and add the second and the third equations:
[tex]\left\{\begin{array}{r}2x+2y+3z=4\\4y+5z=10\\-z=14\end{array}\right.[/tex]
Fro mthe third equation
[tex]z=-14[/tex]
Substitute it into the second equation:
[tex]4y+5\cdot (-14)=10\\ \\4y=10+70\\ \\ 4y=80\\ \\y=20[/tex]
Substitute y=20 and z=-14 into the first equation:
[tex]2x+2\cdot 20+3\cdot (-14)=4\\ \\2x+40-42=4\\ \\2x-2=4\\ \\2x=6\\ \\x=3[/tex]
The solution is
[tex]x=3,\ y=20,\ z=-14[/tex]
If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
Answer:
Their point of intersection will always be on the line y = x.
Step-by-step explanation:
We have a function f(x) and its inverse is the function f⁻¹(x).
The domain and range of a function replaces each other for the inverse of that function.
So if f(x) and f⁻¹(x) are inverse of each other
and f(a) = b
then a = f⁻¹(b)
Another example to make it clear is that
f(5) = 25
f⁻¹(25) = 5
The function and its inverse will intersect each other at the point where f(x) = f⁻¹(x) which is only possible when a = b.
Hence, a function and its inverse will always intersect at a point on the line x=y.
The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?
Answer:
53
Step-by-step explanation:
Let's make some equations.
The number is two-digit, so let's make it [tex]xy[/tex]
Also, the two digits add up to 8, so [tex]x+y=8[/tex]
Now the value of [tex]xy=10x+y[/tex]
and the value of [tex]yx=10y+x[/tex]
Since we know that when we reverse the digits the number is less than the resulting number by 18, we can formulate an equation.
[tex]10y+x=10x+y+18[/tex]
Solve this equation.
[tex]9y-9x=18[/tex]
[tex]9(y-x)=18[/tex]
[tex]y-x=2[/tex]
Now let's use the equation we made earlier.
Change [tex]x+y=8[/tex] into [tex]y=8-x[/tex]
Solve the system of equations.
[tex]y-x=2[/tex]
[tex]y=8-x[/tex]
[tex]8-x-x=2[/tex]
[tex]8-2x=2[/tex]
[tex]-2x=-6[/tex]
[tex]x=3[/tex]
[tex]y-3=2[/tex]
[tex]y=5[/tex]
So the original number is 53.
Answer:
C
Step-by-step explanation:
2 Points
What is the vertex of the graph of the function below?
y = x2 + 10x + 24
O A. (-4,-1)
O B. (-5, -1)
O C. (-5,0)
O D. (4,0)
SUBMIT
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10}x\stackrel{\stackrel{c}{\downarrow }}{+24} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{10}{2(1)}~~,~~24-\cfrac{10^2}{4(1)} \right)\implies (-5~,~24-25)\implies (-5~,~-1)[/tex]
The vertex of the quadratic function y = x² + 10x + 24 is located at point B. (-5, -1). This is found by using the formula -b/2a for the x-coordinate and substituting the x coordinate into the function for the y-coordinate.
Explanation:The vertex of a quadratic function (a function in the form of y=ax²+bx+c) is the point that represents the minimum or maximum of the function graph. In this case, we are looking to find the vertex of the function y = x² + 10x + 24. The formula to find the x-coordinate of the vertex of a quadratic function is -b/2a. In this function, a = 1 and b = 10, giving us -10/(2*1) = -5 for the x-coordinate of vertex. We then substitute -5 into the function for x to determine the y-coordinate, resulting in y = (-5)² + 10*-5 + 24 = -1. Therefore, the vertex of the function is (-5,-1). So, the correct choice is B. (-5, -1).
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Jonathan makes a weekly allowance of $25. He also makes $9.50 an hour at his job. Because of his age, he can work no more than 20 hours a week.
a) Write a function for the amount of money he makes each week based on the amount of hours, h, he works.
b) What is the domain of the function for this situation?
c) Sketch the graph of the function over the domain you chose.f
Final answer:
Jonathan's weekly income is determined by a linear function M(h) = 9.5h + 25, with the domain being 0 ≤ h ≤ 20 to reflect his work hour limitations. A sketch of this function would show a linear increase from an initial allowance of $25, rising by $9.50 for each hour worked up to 20 hours.
Explanation:
Jonathan makes a weekly allowance of $25 and earns $9.50 per hour at his job, with a maximum work limit of 20 hours per week.
a) Function for Jonathan's weekly earnings:
The function M(h) = 9.5h + 25 represents the amount of money Jonathan makes each week, where h is the number of hours he works.
b) Domain of the function:
The domain of this function, considering Jonathan's work hour limitation, is 0 ≤ h ≤ 20. This range is because Jonathan cannot work more than 20 hours a week due to his age restrictions.
c) Sketch of the graph:
The graph would start at the point (0, 25), which represents Jonathan's weekly allowance without any worked hours. Then, it would rise linearly at a slope of $9.50 for each additional hour worked, up to the point (20, 215), which represents the maximum amount Jonathan can earn by working 20 hours plus his weekly allowance. Note: The actual graph is not displayed here but can easily be sketched using the described points and slope.
what are the possible combinations that can be made
A net and the prism it will form when it is folded are shown below.
What is the surface area of the prism in square centimeters?
A)724 square centimeters
B)972 square centimeters
C)1,089 square centimeters
D)1,320 square centimeters
Answer:
Option A)724 square centimeters
Step-by-step explanation:
we know that
The surface of the prism is equal to the area of its six rectangular faces
The surface area is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the base
P is the perimeter of the base
H is the height of the prism
we have
[tex]L=12\ cm[/tex]
[tex]W=11\ cm[/tex]
[tex]H=10\ cm[/tex]
Find the area of the base B
[tex]B=LW[/tex]
[tex]B=(12)(11)=132\ cm^{2}[/tex]
Find the perimeter of the base P
[tex]P=2(L+W)[/tex]
[tex]P=2(12+11)=46\ cm[/tex]
Find the surface area SA
[tex]SA=2(132)+(46)(10)=724\ cm^{2}[/tex]
I know there is too many questions but please help me answer them I will give you 20 points thank you so much for all the people who is going to help me
Answer:
25%
1/3
100%
5/4
2.5
Step-by-step explanation:
Convert all the values into decimals and order them from least to greatest.
can someone please solve 2/8 = n/20
Answer:
[tex]n=5[/tex]
Step-by-step explanation:
We have the following expression [tex]\frac{2}{8} = \frac{n}{20}[/tex] and we must solve for variable n.
To solve the equation multiply by 20 on both sides of the equality and you will get the following
[tex]20*\frac{2}{8} = 20*\frac{n}{20}[/tex]
[tex]\frac{20*2}{8} = \frac{20n}{20}[/tex]
[tex]\frac{40}{8} = n[/tex]
[tex]n= \frac{40}{8}[/tex]
Finally we have that:
[tex]n=5[/tex]
Answer:
n=5
Step-by-step explanation:
2/8 = n/20
Using cross products
2 * 20 = 8*n
40 = 8n
Divide each side by 8
40/8 = 8n/8
5 =n
What is pie? What is the best type of pie? Why does the pie emoji look nothing like pie?
Answer:
Pie: Pie is a dessert that has pastry from top to bottom and has filling in the middle.
Best type of pie: In my opinion: Key Lime Pie
Pie Emoji: No clue, you'll have to email Apple or Samsung (or whatever your phone provider is) and ask them to update or change the emoji.
Step-by-step explanation:
These are very important questions
Factor the following polynomial completely.
x^4y+8x^3y-6x^2y^2-48xy^2
Answer:
xy(x+8)(x^2-6y)
Step-by-step explanation:
To long to explain, but you can just google it if you just need the answer
Answer:
xy(x^2 - 6y)(x + 8 ) .
Step-by-step explanation:
The Greatest Common Factor of this expression is:
xy so dividing by this:
= xy(x^3 + 8x^2 - 6xy - 48y).
Factoring the expression in the parentheses by grouping:
= xy [ x^2( x + 8) - 6y (x + 8)]
= xy(x^2 - 6y)(x + 8 ) (answer).
a scale drawing of a square has a side length of 2 cm. The drawing has a scale of 1cm : 8ft. Find the actual perimeter and area of the square
Answer: Area: 256 ft squared Perimeter: 64 feet
Step-by-step explanation: If the scale is 1 cm to 8 ft then if you multiply 1 cm by 2 you get 2 cm. Then you multiply 8 by 2 to get 16 feet. Once you get 16 feet, you can do 16 times 16 to find the area and 16 times 4 to find the perimeter.
could anyone solve how to get x? thank you^
Answer:
40 deg
Step-by-step explanation:
This is just m anglex=.5(58+22)=.5(80)=40
Answer:
x = 40
Step-by-step explanation:
When 2 chords intersect inside a circle then the measure of the angle formed is half the sum of the arcs intercepted by the angle and it's vertical angle, so
x = 0.5(58 + 22)° = 0.5 × 80° = 40°
1. What is the slope of the line?
2. What is the slope of the line?
Answer:
1/4
Step-by-step explanation:
Answer:
[tex]slope =\frac{1}{4}[/tex]
slope is undefined
Step-by-step explanation:
WE need to find the slope of two lines
to find out slope we use formula
[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]
To find slope we pick two points from the line
(-4,0) and (0,1) is (x1,y1) and (x2,y2)
[tex]slope =\frac{1-0}{0+4}=\frac{1}{4}[/tex]
[tex]slope =\frac{1}{4}[/tex]
To find slope we pick two points from the line
(1,0) and (1,1) is (x1,y1) and (x2,y2)
[tex]slope =\frac{1-0}{1-1}=\frac{1}{0}[/tex]
When denominator =0 then the slope is undefined
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. During one particular week, the two cars went a combined total of 1225 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
first car:
Second:
Answer:
First car: 35 gallons
Second car: 15 gallons
Step-by-step explanation:
Assuming [tex] x [/tex] to be the gas consumed by 1st car and [tex] 50 - x [/tex] to be the gas consumed by 2nd car.
We know that:
Distance traveled = fuel efficiency × gas consumed
[tex]20x+35(50-x)=1225[/tex]
[tex]20x+1750-35x=1225[/tex]
[tex]35x-20x=1750-1225[/tex]
[tex]15x=525[/tex]
[tex]x=35[/tex]
So [tex]50 - x = 50-35=15 [/tex]
Therefore, first car consumed 35 gallons while second car consumed 15 gallons.
Answer:
First car: 35 gallons
Second car: 15 gallons
Step-by-step explanation:
Set up a system of equations.Let be "x" the number of gallons consumed by the first car and "y" the number of gallons consumed by the second car.
Then:
[tex]\left \{ {{x+y=50} \atop {20x+35y=1,225}} \right.[/tex]
Applying the Elimination method, multiply the first equation by -20, then add both equations and solve for "y":
[tex]\left \{ {{-20x-20y=1,000} \atop {20x+35y=1,225}} \right. \\.......................\\15y=225\\y=15[/tex]
Substitute this value into the first equation and solve for "x":
[tex]x+15=50\\x=35[/tex]
How many solutions can be found for the equation 3x − 2 = 3x + 5?
a)zero
b)one
c)two
d)infinitely manyHow many solutions can be found for the equation 3x − 2 = 3x + 5?
Answer:
Zero
Step-by-step explanation:
there is no solution the sides are uneven. if you solve for it 3x and 3x cancels out each other leaving you with -2=5
Answer:
Zero
Step-by-step explanation:
Periodt
what is the slope of the line shown below (-3,1) (5,1)
Answer:
A. 1/4
Step-by-step explanation:
The line is upwards so slope will be positive. (either A or C will be the answer)
Now to solve for slope to find out
Two coordinate points on graph (-3,-1) ad (5,1)
Slope = (y2 - y1)/(x2 - x1)
Slope = (1 + 1)/(5 + 3) = 2/8 = 1/4
Answer:
[tex]A.\frac{1}{4}[/tex]
Step-by-step explanation:
Hello, I think I can help you with this
The slope is the inclination of the line with respect to the abscissa axis, if you know two points it can be calculated using
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\[/tex]
where
[tex]P1(x_{1},y_{1})\\P2(x_{2},y_{2})[/tex]
Step 1
put the values into the equation
Let
[tex]P1(-3,-1) \\P2(5,1)\\\\m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\m=\frac{1-(-1)}{5-(-3) } \\m=\frac{1+1}{5+3} \\m=\frac{2}{8} \\m=\frac{1}{4}[/tex]
Have a great day
This photo 2 of This question read it and find out what is The difference in feet between The Minimum and Maximum heights of a car on The ferris wheel
Answer:
From the looks of things, it seems to be 140 ft, the maximum height being 150 ft and the minimum height being 10 ft. Find the difference, and that should be your answer :)
Answer:C 140
Step-by-step explanation:
which statement is true
if a base of a parallelogram is 8 inches long and the altitude to the base is 10 inches what is the area of the parallelogram
Answer: [tex]80 in^2[/tex]
Step-by-step explanation:
The area of a parallelogram can be calculated with the following formula:
[tex]A=b*h[/tex]
Where "b" is the base and "h" is the height or altitude.
You know that the base of this parallelogram is 8 inches long and the altitude to the base is 10 inches, then:
[tex]b=8in\\h=10in[/tex]
You need to substutite these values into the formula.
Therefore, the area the parallelogram is:
[tex]A=(8in)(10in)\\\\A=80in^2[/tex]
If a circle has a radius of 13 and a sector defined by a 7.4 degree arc, what is
the area, in cms, of the sector? Round your answer to the nearest tenth.
Answer:
A = 10.9 cm^2
Step-by-step explanation:
If a circle has a radius of 13 and a sector defined by a 7.4 degree arc, the area, in cms, of the sector is 10.9 cm^2 or 10 cm^2 to the nearest tenth.
without actual calculation find (25)^3-(75)^3+(50)^3
Answer:
Simplified to -281250
Step-by-step explanation:
Which set of side lengths forms a right triangle 2,3,13 4,6,10 9,12,18 15,36,39
Answer:
15,36,39
Step-by-step explanation:
primitive pythag: 5, 12, 13 *3
Answer:
The Answer is D
Step-by-step explanation:
What is the slope of the line that passes through (-2, 5) and (3, 9)?
Answer: 4/5
Step-by-step explanation:
1. you need to know the formula which is m = y2-y1/x2-x1
2. you plug in the numbers which would be 9-5/3-(-2)
3. you get your answer as 4/5
4. the answer is 4/5
Answer:
○ b ⅘
Step-by-step explanation:
-y₁ + y₂\-x₁ + x₂ = m
[tex] \frac{4}{5} = \frac{ -5 + 9}{2 + 3}[/tex]
I am joyous to assist you anytime.
drag each tile to the table to multiply each row heading by each column heading
Answer:
drag each result in the corresponding box according to the results
Step-by-step explanation:
Hello
The product of two or more powers of equal base "a" is equal to the power of base "a" with exponent equal to the sum of the respective exponents.
[tex]a^{m}*a^{n} =a^{n+m}[/tex]
Step 1
[tex]d*2d^{2}\\[/tex]
[tex]d*2d^{2}=(2*1)d^{(2+1)}\\d*2d^{2}=2d^{3} \\[/tex]
Step 2
[tex]-9*2d^{2}\\[/tex]
[tex]-9*2d^{2}=(-9*2)d^{(2+0)}\\-9*2d^{2}=-18d^{2} \\[/tex]
Step 3
[tex]d*11d\\[/tex]
[tex]d*11d=(1*11)d^{(1+1)}\\11*d^{2}=11d^{2} \\[/tex]
Step 4
[tex]-9 * 11d\\[/tex]
[tex]-9 * 11d = (-9*11)d^{1+0}=-99 d[/tex]
Step 5
[tex]d*-4=-4d[/tex]
Step 6
[tex]-9*-4 = ( -*- ) (9*4)= 36[/tex]
Step 7
Now, drag each result in the corresponding box .
Have a great day
Answer:
Your welcome :)
Step-by-step explanation: