The expressions (x-5)/(x+3) and 4/(x-3) can be rewritten with a common denominator of (x+3)(x-3) to become ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).
Explanation:The expressions stated are: (x-5)/(x+3) and 4/(x-3). In order to rewrite these expressions with a common denominator, you need to multiply the denominators together to create a common denominator. Therefore, the common denominator would be (x+3)(x-3).
Next, each expression must be rewritten so that they have this common denominator. For the first expression, we multiply the numerator and denominator by (x-3) so we get: ((x-5)(x-3))/((x+3)(x-3)).
For the second expression, we multiply the numerator and denominator by (x+3) so we get: 4(x+3)/((x+3)(x-3)). So, the expressions rewritten with a common denominator are ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).
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To find a common denominator for the given expressions, multiply the denominators together. The expressions, rewritten with the common denominator, are [tex](x-3)*(x-5)/(x+3)(x-3)[/tex] and [tex]4*(x+3)/(x+3)(x-3).[/tex]
Explanation:The goal here is to find a common denominator for the expressions x-5/x+3 and 4/x-3. A common denominator can be found by multiplying the denominators of both expressions together. So for these expressions, the common denominator would be [tex](x+3)*(x-3).[/tex]
Then you multiply the top and bottom of each fraction by the missing factor from the other denominator. The expressions rewritten with a common denominator would then be:
For the first expression, multiply (x-5) by (x-3), which gives (x-3)*(x-5).For the second expression, multiply 4 by (x+3), which gives 4*(x+3).So the expressions with a common denominator are: [tex](x-3)*(x-5)/(x+3)*(x-3)[/tex]and [tex]4*(x+3)/(x+3)*(x-3).[/tex]
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Please explain your answer
Answer: Blueberry = $6, Pumpkin = $17
Step-by-step explanation:
Let B represent blueberry pie and P represent pumpkin pie.
Kim: 12B + 8P = 208
- Krystal: 10B + 8P = 196
2B = 12
B = 6
Input B = 6 into either of the equations to solve for P
10B + 8P = 196
10(6) + 8P = 196
60 + 8P = 196
8P = 136
P = 17
what is the answer for this math problem
7/8 is tricky to do on a computer, but I will say that it is 87.5 percent or 0.875.
Do you know how to do normal long division? This is like that. Just after the decimal point, drop a 0 down.
I hope this helps!
Answer:
7/8 = .875 7/8=87.5%
Step-by-step explanation:
Divide 1/4(.25) by 2 and you get 1/8(.125)
Multiply .125 by 7 which gives you .875.
For the percent just multiply .875 by 100
Hope this helps.
Express 45 = x as a logarithmic equation.
Answer:
[tex]5 = log_{4}x[/tex]
Step-by-step explanation:
You know that [tex]45=4^{5}[/tex]
Then: [tex]4^{5}=x[/tex]
Taking log with base 4 in both sides, we have:
[tex]log_{4} 4^{5}=log_{4}x[/tex]
Applying the logarithmic rules, we have:
[tex]log_{4}4^{5}=log_{4}x[/tex] → [tex]5log_{4}4=log_{4}x[/tex]
→ [tex]5 = log_{4}x[/tex]
In conclusion, 45 = x expressed as a logarithmic equation equals: [tex]5 = log_{4}x[/tex]
Answer:
[tex]4^5=x[/tex] as a logarithmic equation [tex]\log_4 (x)=5[/tex]
Step-by-step explanation:
Given : Expression [tex]4^5=x[/tex]
To find : Express the expression as a logarithmic equation?
Solution :
Expression [tex]4^5=x[/tex]
Taking log with base 4 both side,
[tex]\log_4(4^5)=\log_4 (x)[/tex]
Using logarithmic property, [tex]\log_a a^b=b[/tex]
[tex]5=\log_4 (x)[/tex]
Therefore, [tex]4^5=x[/tex] as a logarithmic equation [tex]\log_4 (x)=5[/tex]
What is the area of the kite? Height of 6ft base of 14ft. 21 square feet 40 square feet 42 square feet 84 square feet
Answer:area is 84
Step-by-step explanation:
6*14
Answer:
its c 42 square feet
Step-by-step explanation:
-2x + 3 < 5
solve and show steps please
Answer:
x < -1
Step-by-step explanation:
5 - 3 = 2
-2x < 2
x < -1
Answer:
Answer is x > -1
Step-by-step explanation:
Because -2x + 3 < 5
-3 -3 minus 3 on both sides
Then: -2x < 5
-2 -2 divide negative 2 on both sides
And get x > -1, Because if you divide by negative numbers the sign always flips.
Sorry i had to reedit it's -1 because you divide my bad.
Hope my answer has helped you and if not i'm sorry.
What is the solution to the inequality? 17 < 9 + x
Answer:
x > 8
Step-by-step explanation:
Given
17 < 9 + x ( subtract 9 from both sides )
8 < x , hence
x > 8
Which is a factor of x2 + 5x – 24?
O
(x-6)
(x + 6)
(X-8)
(X + 8)
Answer:
the answer would be d
Step-by-step explanation:
Find the indicated side of the triangle.
Please Help!!!
Answer:
Step-by-step explanation:
So you can use the special formula for 30-60-90 triangle or you can use the whole Soh Cah Toa thing.
I honestly prefer trig. so a is the opposite side of the 30 deg and 12 is the hyp. This should scream sine to you since sine goes with opposite/hypotenuse.
sin(30 deg)=a/12
Multiply both sides by 12
giving a=12 sin(30)
Type into calculator unless you know your unit circle well.
a=6
Answer:
a = 6
Step-by-step explanation:
Since the triangle is right use the sine ratio to find a
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{12}[/tex]
Multiply both sides by 12
12 × sin30° = a, hence
a = 6
Find the standard deviation of 21, 31, 26, 24, 28, 26
Given the dataset
[tex]x = \{21,\ 31,\ 26,\ 24,\ 28,\ 26\}[/tex]
We start by computing the average:
[tex]\overline{x} = \dfrac{21+31+26+24+28+26}{6}=\dfrac{156}{6}=26[/tex]
We compute the difference bewteen each element and the average:
[tex]x-\overline{x} = \{-6,\ 5,\ 0,\ -2,\ 2,\ 0\}[/tex]
We square those differences:
[tex](x-\overline{x})^2 = \{36,\ 25,\ 0,\ 4,\ 4,\ 0\}[/tex]
And take the average of those squared differences: we sum them
[tex]\displaystyle \sum_{i=1}^n (x-\overline{x})^2=36+25+4+4+0+0=69[/tex]
And we divide by the number of elements:
[tex]\displaystyle \sigma^2=\dfrac{\sum_{i=1}^n (x-\overline{x})^2}{n} = \dfrac{69}{6} = 11.5[/tex]
Finally, we take the square root of this quantity and we have the standard deviation:
[tex]\displaystyle\sigma = \sqrt{\dfrac{\sum_{i=1}^n (x-\overline{x})^2}{n}} = \sqrt{11.5}\approx 3.39[/tex]
To find the standard deviation of the set 21, 31, 26, 24, 28, 26, first calculate the mean, then the squared deviations from the mean, followed by the variance, and finally take the square root of the variance. The standard deviation is approximately 2.52.
The question asks how to find the standard deviation of the numbers 21, 31, 26, 24, 28, 26. To calculate the standard deviation, follow these steps:
Find the mean (average) of the data set. Subtract the mean from each number to get the deviations from the mean, then square each result. Find the average of these squared deviations, which is the variance. Take the square root of the variance to get the standard deviation.
Let's calculate it together:
Mean = (21 + 31 + 26 + 24 + 28 + 26) / 6 = 26 Squared deviations: (5^2) + (5^2) + (0^2) + (2^2) + (2^2) + (0^2) = 38 Variance = 38 / 6 = 6.33 (rounded to two decimal places) Standard Deviation = √6.33 = 2.52 (rounded to two decimal places)
Therefore, the standard deviation of the data set is approximately 2.52.
Which of the following is the general term for the sequence a, -a, a, -a, . . . ?
Answer:
a(-1)^(n-1).
Step-by-step explanation:
This is a Geometric Sequence with common ratio r = -1.
The general term is a(-1)^(n-1).
The general term for the sequence a, -a, a, -a, ... is given by the mathematical formula (-1)^(n+1) * a, where n is the term's position in the sequence, starting at n=1 for the first term.
Explanation:The general term for the sequence a, -a, a, -a, ... can be described using a formula that alternates between a and -a as the sequence progresses. This pattern is a common example of a simple mathematical sequence where the terms alternate in sign.
To express this sequence as a general term, we can use the concept of the n-th term in a sequence. If we let n represent the position of the term in the sequence (starting with n=1 for the first term), we could describe the n-th term using the formula (-1)^(n+1) * a. This formula takes advantage of the fact that raising -1 to an even power results in 1, and raising it to an odd power results in -1, thus alternating the sign of a as n increases.
For example, if n=1, the formula gives (-1)^(1+1) * a = 1 * a = a. If n=2, the formula gives (-1)^(2+1) * a = -1 * a = -a, and so on.
On Thursday the high temperature was 0 °C. If it was three degrees colder on Friday, what was the temperature?
Answer:
-3 degrees C
Step-by-step explanation:
We need to subtract 3 degrees from Thursdays temperature
0 - 3
-3 degrees C
Find a1, for the given geometric series. Round to the nearest hundredth if necessary. Sn= 44,240, r= 3.8, n= 9
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=9\\ r=3.8\\ \stackrel{S_n}{S_9}=44240 \end{cases}[/tex]
[tex]\bf 44240=a_1\left( \cfrac{1-3.8^9}{1-3.8} \right)\implies 44240\approx a_1\left( \cfrac{-165215.101}{-2.8} \right) \\\\\\ 44240\approx a_1(59005.393)\implies \cfrac{44240}{59005.393}\approx a_1\implies \stackrel{\textit{rounded up}}{0.75=a_1}[/tex]
When all the terms of a geometric sequence are added, then that expression is called geometric series. The first term of the given geometric series is 0.75.
What is a geometric series?When all the terms of a geometric sequence are added, then that expression is called geometric series.
What is the sum of terms of a geometric sequence?Let's suppose its initial term is, the multiplication factor is r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
Given the sum of the geometric series is 44,240, while the number of terms is 9. Also, the common ratio of the series is 3.8. Thus, we can write,
Sₙ = a(rⁿ-1)/(r-1)
44240 = a(3.8⁹ - 1)/(3.8 - 1)
44240 = a 59005.3933
a = 0.75
Hence, the first term of the given geometric series is 0.75.
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Please look at attachment. Has all info needed. Need help
Step-by-step explanation:
When the object hits the ground, h = 0.
0 = -21.962x + 114.655
x = 5.2
From the table, the object landed at x = 4.6 seconds. So the line of best fit predicts a time 0.6 seconds greater than actual.
The original height is when x = 0.
h = -21.962(0) + 114.655
h = 114.7
So the line of best fit predicts the object was dropped from a height of 114.7 meters. This is higher than the actual 100 meters.
At x = 3.5:
h = -21.962(3.5) + 114.655
h = 37.8
So the line of best fit estimates the object reached a height of 37.8 meters after 3.5 seconds.
We know that at x = 0, h = 114.7. This is more than 4 meters from the actual initial height of 100 m.
Therefore, the answer must be A.
Answer:
A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
Step-by-step explanation:
what is the area of the polygon given below?
Answer:
C 340 square units
Step-by-step explanation:
Divide it into smallest pieces.
I see two rectangles that I'm going to do.
The long rectangle reading the paper from bottom to top is a 4 by (4+11+4) rectangle.
The wide rectangle reading the paper from left to right is a 24 by 11 rectangle.
We need to find the area of both of these rectangles and then just add them together to get the total area.
So first rectangle has area 4(19)=76 and the second rectangle has area 264. The sum of these two numbers are 340 square units.
Hello There!
The answer would be 340 square units
First, let's find the area of our small rectangle located to the left. The formula for a rectangle is width*height so we would multiply19 because we know that on our right rectangle the height is 11 and we would add 4 to that and add another 4 to that to get our length of our rectangle on the left.
Next, we multiply 24 by 11 because we are using our same formula for the rectangle on the right and once we multiply, we get a product of 264.
Finally, we add 264 and our area of the rectangle on the right together and get a sum of 340 square units.
Have A Great Day!
Durind the summer, Ms. Stevenson likes to swim. Her goal next summer is to swim1,456 laps. If she swims 28 laps a day, how many days will it take Ms. Stevenson to reach her goal?
Answer:
52
Step-by-step explanation:
1456/ 28 = 52 days
Answer:
52 days
Step-by-step explanation:
If she swims 28 laps a day, it will take her 52 days to reach her goal.
1,456/28 = 52
Nick borrowed $1250, to be repaid after 5 years at annual simple interest rate of 7.25%. how much interest will be due after 5 years? how much will nick have to repay.
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1250\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ t=years\dotfill &5 \end{cases} \\\\\\ I=(1250)(0.0725)(5)\implies 453.125 \\\\\\ \stackrel{\textit{he'll have to repay}}{1250+453.125}\implies 1703.125[/tex]
Please help me now please
Answer:
The model represents the expression:
A. 7/8 ÷ 1/8
Step-by-step explanation:
In the question, the number line model represents 7/8 divided into 7 equal units. Each arrow represents a unit and there are a total of seven arrows.
The size of each unit is 1/8 as shown.
Showing that 1/8 divides 7/8 into 7 divisions:
7/8 ÷ 1/8
= 7/8 x 8/1
= 7/1 x 8/8
= 7 x 1
= 7
Hence, the number line represents seven divisions given by 7/8 ÷ 1/8.
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to
$(6)-1
276)+1
(6)
2(6) + 1
36-1
26+1
(6)-1
(6)+1
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to (r/s)(6) is: A. [tex]\frac{3(6) - 1}{2(6)+1}[/tex]
In Mathematics, an algebraic expression is a type of mathematical equation which is typically used for showing the relationship existing between two (2) or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.
Based on the information provided, the quotient of the two expressions can be computed as follows;
[tex]\frac{r(x)}{s(x)} =\frac{3x - 1}{2x+1} \\\\[/tex]
When the value of x is 6, the output value of the expression
[tex]\frac{r}{s}(6) =\frac{3(6) - 1}{2(6)+1}[/tex]
Complete Question;
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to (r/s)(6)?
Solve system of equations 2x + 2y + 5z = 7 6x + 8y + 5z = 9 2x + 3y + 5z = 6
Answer:
the values of x, y and z are x= 2, y =-1 and z=1
Step-by-step explanation:
We need to solve the following system of equations.
We will use elimination method to solve these equations and find the values of x, y and z.
2x + 2y + 5z = 7 eq(1)
6x + 8y + 5z = 9 eq(2)
2x + 3y + 5z = 6 eq(3)
Subtracting eq(1) and eq(3)
2x + 2y + 5z = 7
2x + 3y + 5z = 6
- - - -
_____________
0 -y + 0 = 1
-y = 1
=> y = -1
Subtracting eq(2) and eq(3)
6x + 8y + 5z = 9
2x + 3y + 5z = 6
- - - -
______________
4x + 5y +0z = 3
4x + 5y = 3 eq(4)
Putting value of y = -1 in equation 4
4x + 5y = 3
4x + 5(-1) = 3
4x -5 = 3
4x = 3+5
4x = 8
x= 8/4
x = 2
Putting value of x=2 and y=-1 in eq(1)
2x + 2y + 5z = 7
2(2) + 2(-1) + 5z = 7
4 -2 + 5z = 7
2 + 5z = 7
5z = 7 -2
5z = 5
z = 5/5
z = 1
So, the values of x, y and z are x= 2, y =-1 and z=1
Michael and Tom are brothers. Their combined age is 20, and Tom is 4 years older than Michael. What are Michael and Tom’s ages?
Answer:
Micheal is 8, and Tom is 12 years old.
Step-by-step explanation:
To solve this, we can set each of their ages as a variable. Let's say Michael's age is x.
We know Tom is 4 years older than Michael, so Tom's age is x+4.
We also know that their combined age is 20, so if we add both of their ages, we should get 20.
Solving;
[tex]x + (x+4) = 20\\2x+4 = 20\\2x=16\\x=8.[/tex]
So Michael's age is 8, and Tom is 12.
Answer:
Tom is 12 and Michael is 8
Step-by-step explanation:
The diagram shows a sector of a circle with radius 15 cm.
Calculate the perimeter of this sector.
Answer:
≈ 36.81 cm ( to 2 dec. places )
Step-by-step explanation:
The perimeter (P) of the sector is calculated as
P = circumference of circle × fraction of circle + radii
= 2π × 15 × [tex]\frac{26}{360}[/tex] + 30
= 30π × [tex]\frac{26}{360}[/tex] + 30
= [tex]\frac{26\pi }{12}[/tex] + 30 ≈ 36.81 cm
Answer:
36.81 cm to the nearest hundredth (or 30 + 13 π / 6).
Step-by-step explanation:
The perimeter of the circle of which this sector is a part = 2 π 15
= 30 π cms
So the length of the curved part of the sector = 26 * 30 π / 360
= 2.167π
The perimeter = 2(15) + 2.167 π
= 36.81 cm.
determine the slope of each pair with fractions
Answer:
Step-by-step explanation:
The slope here is -3.
This answer is found by using the formula I clipped below.
Hope that Helps!
Y=2x
x+y=9
Solve using substitution
Answer:
x = 3; y = 6
Step-by-step explanation:
x + 2x = 9
3x = 9
x = 3
The graphs of f(x) =2/3x and g(x) =2/3x-2 are shown below.
Y1=2/3x , Y2=2/3x-2
those are the graph of the functions
Julian spent $15.00 to purchase some notebooks that cost $3.50 each and some pens that cost $4.50 each. Assuming he bought at least one notebook, what is the greatest number of pens Julian could have purchased?
Answer:
If Julian bought 1 notebook, he would only have enough money for 2 pens
Step-by-step explanation:
Pen = $4.50
Notebook = $3.50
2 pens = $9.
9 + 3.50 = 12.50.
15 - 12.50 = 2.50.
$2.50 is not enough money for another notebook or pen.
Answer:
2 notebooks.
Step-by-step explanation:
To evaluate this you just have to create an equation to solve this problem, it says that Julian has $15 in total, and he has to buy at least one notebook, so you´d have to withdraw the money of a notebook from the total, and the pens cost 4.50 each, we will be expressing the number of pens by "X" and the number of notebooks by "y" so your equation would be like this:
[tex]4.5x+3.5y=15[/tex]
The number of notebooks is one, so you can put it into the equation:
[tex]4.5x+3.5y=15[/tex]
[tex]4.5x+3.5(1)=15[/tex]
Now you clear "x"
[tex]4.5x=15-3.5[/tex]
[tex]4.5x=11.5[/tex]
[tex]x=\frac{11.5}{4.5}[/tex]
[tex]x=2.55[/tex]
Since he can not buy .55 of a pen, he will only be able to buy 2 pens.
simplify
(18-9.(-4/3)+10×2)
Answer:
what is the period after the 9?
Answer:
50
Step-by-step explanation:
Evaluate the products before addition
18 - (9 × - [tex]\frac{4}{3}[/tex] ) + (10 × 2)
= 18 - (- 12) + 20
= 18 + 12 + 20
= 50
what values complete this function
Answer:
f(x) = - (x - 3) (x + 4)
Step-by-step explanation:
* Lets explain the graph
- The graph is a parabola, which is the graph of the quadratic function
- The general form of the quadratic function is f(x) = ax² + bx + c
- a is the coefficient of x², if a > 0 the parabola is oped upward, if a < 0
the parabola is opened down ward
- c is the y-intercept of the parabola means the curve intersect the
y-axis at point (0 , c)
- The roots (zeroes) of the quadratic function are the x-intercept of the
parabola means values of x when f(x) = 0
* Now lets solve the problem
- The parabola is downward
∴ The coefficient of x² is negative
- The y-intercept is 12
∴ c = 12
- The x-intercepts are 3 , -4
∴ The zeroes of the function are 3 , -4
∴ x = 3 ⇒ subtract 3 from both sides
∴ x - 3 = 0
∴ x = -4 ⇒ add 4 for both sides
∴ x + 4 = 0
- The factors of f(x) are (x - 3) and (x + 4)
∴ f(x) = -(x - 3)(x + 4)
- Lets find the general form of the function to be sure from the answer
- Multiply the two brackets
∵ f(x) = - [(x)(x) + (x)(4) + (-3)(x) + (-3)(4)] = - [x² + 4x + -3x + -12]
∴ f(x) = - [x² + x - 12] ⇒ multiply the bract by the (-)
∴ f(x) = -x² - x + 12
- Lets check the value of the y-intercept
∵ a = -1 , c = 12
∴ The coefficient of x² is -ve ⇒ the parabola is downward
∴ The y-intercept is 12
∴ f(x) = - (x - 3) (x + 4) is the answer
Can someone please help me out with this question?
Answer:
[tex]\frac{300}{t}[/tex] chairs at each table
Step-by-step explanation:
Total number of chairs : 300
Total number of tables : t
If we divide 300 chairs equally among t tables, then each table must have 300 chairs ÷ t tables = [tex]\frac{300}{t}[/tex] chairs at each table.
About 60% of the normal human
being's body weight is composed of
water. How much of a 125 pound
person is water weight?
F 72 pounds H 76 pounds
G 75 pounds I 80 pounds
The water weight of a 125lb person is 75lbs.
What is the solution to the system of equations below? y = 3/4 x - 12 and y = 4x - 31
(–4, –15)
(–4, –12)
(4, –9)
(4, –47)
Answer:
(4,-47) is the solution
Step-by-step explanation:
4 is x
-47 is y
Just substitute these numbers into the equations and your solution must equal y which is - 47. This solution did equal -47 so its the one
Answer:
X= -4 Y= -15
Step-by-step explanation:
Got Correct On Mypath.