To solve the given operation firat we take LCM for both terms.
As denominator of first term is 3 and second term is [tex] 12x-8 [/tex]
Therefore, the Lcm is [tex]3(12x-8) [/tex]
Now solving and making same denominator for each term
[tex]\frac{7}{3} [/tex] [tex]\times [/tex] [tex] \frac{12x-8}{12x-8} [/tex]
On multiplying we get
[tex]\frac{7(12x-8)}{3(12x-8)} [/tex] [tex]=\frac{84x-56}{3(12x-8)} [/tex]
Now solving other term
[tex]\frac{8}{12x-8} [/tex] [tex]\times [/tex] [tex]\frac{3}{3} [/tex]
On multiplying we get
[tex]\frac{24}{3(12x-8)} [/tex]
Now solving the expression by putting the values
[tex]\frac{84x-56-24}{3(12x-8)} [/tex]
[tex]\frac{84x-80}{12(3x-2)} [/tex]
[tex]\frac{4(21x-20)}{12(3x-2)} [/tex]
On solving we get
[tex]\frac{21x-20}{3(3x-2)} [/tex]
There denominator of the expression is
[tex]9x-6 [/tex]
Hope this will help
Look at the box-and-whisker plot. What is the measure of the first quartile (Q1)?
A. 43.5
B. 47.5
C. 41.5
D. 50.0
The first quartile (Q1) in a box-and-whisker plot is the value at the left boundary of the box, which represents the median of the lower half of the dataset. According to the information provided, Q1 is 80, but none of the given answer options (A, B, C, D) match this value.
In the context of your question, which examines a box-and-whisker plot, the first quartile (Q1) corresponds to the value at the left boundary of the box. The first quartile represents the median of the lower half of the dataset, excluding the overall median. From the information provided, we can deduce that the first quartile (Q1) is 80, as represented by the left boundary of the box in a box plot provided elsewhere.
Therefore, the correct answer to your question would be the option that most closely matches the value of 80. However, since none of the options (A. 43.5, B. 47.5, C. 41.5, D. 50.0) match this value, there appears to be a discrepancy. It's possible that there is an error in the question options, or there might be a misinterpretation regarding the information provided. Make sure that you are referring to the correct box plot.
Please help! 15 Points! How do i do this? (View the picture down below)
Make 6 moves of [tex]\frac{2}{5}[/tex] to find the product.
Plot the product of the expression 6 ⋅ ( [tex]\frac{2}{5}[/tex] ) on the number line.
Ok, so what this question is really asking you is: [tex]2/5=0.4[/tex]
What is [tex]6*0.4[/tex] and that equals [tex]6*0.4=2.4[/tex]
Now because the the number is 2.4 plot that point
Rewrite using a single exponent. 7^4 - 7^4
A number added to its opposite is zero (0). No exponent is needed.
7^4 - 7^4 = 0
Is a 2x2 and 2x3 matrix multiplied undefined
Matrix multiplication is defined for M×K and K×N matrices to give an M×N result. Note that the middle two numbers (K) are the same.
Matrix multiplication of a 2×2 and 2×3 matrix will give a 2×3 matrix result. It is defined.
Make a frequency distribution and find the relative frequencies for the following number set. Round the relative frequency to the nearest tenth of a percent. Some of the answers will be used more than once and some may not be used. 10, 21, 21, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29 Number Frequency Relative Frequency 20 ______ ______% 21 ______ ______% 23______ ______% 24 ______ ______% 25 ______ ______% 26______ ______% 27 ______ ______% 28 ______ ______% 29 ______ ______%
Solution: We have to find the Frequency and Relative frequency of the given data:
Frequency is the number of times a number occurs.
Relative Frequency is the number of times a number occurs divided by the total number of items.
Therefore, the frequency and relative frequency are calculated as below:
Number Frequency Relative Frequency
20 1 [tex]\frac{1}{31} \times 100 =3.2\%[/tex]
21 4 [tex]\frac{4}{31} \times 100 =12.9\%[/tex]
22 2 [tex]\frac{2}{31} \times 100 =6.5\%[/tex]
23 4 [tex]\frac{4}{31} \times 100 =12.9\%[/tex]
24 3 [tex]\frac{3}{31} \times 100 =9.7\%[/tex]
25 2 [tex]\frac{2}{31} \times 100 =6.5\%[/tex]
26 3 [tex]\frac{3}{31} \times 100 =9.7\%[/tex]
27 5 [tex]\frac{5}{31} \times 100 =16.1\%[/tex]
28 3 [tex]\frac{3}{31} \times 100 =9.7\%[/tex]
29 4 [tex]\frac{4}{31} \times 100 =12.9\%[/tex]
Total 31
under the translation t(-7,3) the point (1,6) will become (-6,-3) true or false?
false
under the given translation
the point (1, 6 ) → (1 - 7, 6 + 3 ) → (- 6, 9 )
Is this correct? Please answer fast
if measure 1 = x+70 and measure 2 = 5x -54 what is measure 3.Write an equation and solve
What’s is the product of the two solutions of the quadratic equation ax^2+bx+c=0
The product of the two roots is c/a.
_____
Consider the equation
... a(x -p)(x -q) = 0
which has solutions x=p and x=q.
When multiplied out, it becomes ...
... a(x² -(p+q)x +pq) = ax² -a(p+q)x +apq = 0
When apq = c, the product pq is c/a.
Given: △KPS m∠P=105°, m∠S=30° PS=12 Find: PK.
Answer:
PK=8.49m
Explanation:
We have sine formula
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
By sine formula we have
[tex]\frac{PS}{sinK} =\frac{PK}{sinS} =\frac{KS}{sinP}[/tex]
We have PS = 12, ∠P=105° and ∠S=30°, so ∠K=180°-(105°+30°)=45°
Substituting
[tex]\frac{12}{sin45} =\frac{PK}{sin30} \\ \\ PK=8.49m[/tex]
The bird population on an island is declining at a rate of 2.2% per year. The population was 3500 in the year 2009.
Which answer is the best prediction of the population in the year 2014?
A 2730
B 3062
C 3132
D 3423
The population is multiplied by 100% -2.2% = 97.8% each year. After 5 years, the population will have been multiplied by this value 5 times, so will be ...
... 3500×0.978⁵ ≈ 3132
The appropriate choice is ...
... C. 3132
Point A is located at (4, 8) and point B is located at (14, 10) . What point partitions the directed line segment AB⎯⎯⎯⎯⎯ into a 1:3 ratio? (612, 812) (9, 9) (1112, 912) (6, 6)
The 1:3 ratio means that the distance from A to the point is 1/4 of the distance from A to B.
The difference of y-coordinates is 10-8 = 2. 1/4 of that is 2·1/4 = 1/2, so the point of interest will have y-coordinate 8 + 1/2 = 8 1/2. This apparently corresponds to the first selection:
... (6 1/2, 8 1/2)
The associative property changes the ____ of three addends or factors.
The associative property allows you to change the grouping of addends or factors without changing the value of the expression.
The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.
How can the Angle-Angle Similarity Postulate be used to prove the two triangles below are similar? Explain your answer using complete sentences, and provide evidence to support your claims
To use the AA postulate directly, you need to show that two corresponding angles are congruent. In order to show that here, you must calculate the value of one of the missing angle measures. Either of the missing angles can be found by invoking the fact that the sum of angles in a triangle is 180°.
After finding either missing angle, you can show that the measures of two angles in one triangle are identical to the measures of two angles in the other triangle, hence the triangles are similar by the AA postulate.
Answer:
I wrote the answer below :) hope it makes sense
Step-by-step explanation:
The Angle-Angle Similarity postulate can be used to prove that these two triangles are similar. To demonstrate I will use an example, and try to make sense to the reader. on triangle ABC, the 2 angles that are given to us are 32 degrees and 49 degrees. Since all triangles have an angle sum of 180 degrees, the missing degree would have to be 99 degrees. Same for the triangle A'B'C'. The 2 angles given are 99 degrees and 49 degrees, which means the missing angle has to be 32 degrees. Therefore, the triangles are similar.
I just took the test and this is correct.
Happy Holidays!
How is 2/3 related to 1/2
1/2 = 3/6
2/3 = 4/6
2/3 is greater than 1/2, so is to the right of 1/2 on the number line.
The difference is (4/6) -(3/6) = (4-3)/6 = 1/6.
2/3 is 4/3 times 1/2.
If f(x) = 4x + 1 and g(x) = x^2 - 5, find (f - g)(x)
Answer:
The Answer is B
Step-by-step explanation:
Subtract f-g
4x + 1 - x^2 - 5
Distribute the - sign
4x + 1 - x^2 + 5
Combine like terms
-x^2 + 4x + 1 + 5
-x^2 + 4x + 6
use the figure to find the measures of a and b thank you
Angles on the same side are the same, so angle 1 is 110°.
Angle 1 and 2 are supplementary, so they add up to 180. Since we know angle 1 is 110, angle 2 must be 70°
Jillian had
5
6
of a whole and took
3
6
away from it. How much does she have left?
2/6 is remaining from Jillian's whole.
[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Since the denominators of both fractions are common , that is 6
To subtract, subtract the numerators leaving the denominator
[tex]\frac{5}{6}[/tex] - [tex]\frac{3}{6}[/tex] = [tex]\frac{5-3}{6}[/tex] = [tex]\frac{2}{6}[/tex]
This fraction may be simplified by dividing the numerator/ denominator by 2
[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex] ← in simplest form
Find the area of the sector of a circle with diameter 34 feet and an angle of π/5 radians. (Round your answer to four decimal places.)
The area of the sector of a circle with diameter 34 feet and an angle of π/5 radians is approximately 9.0095 square feet.
Explanation:To find the area of the sector of a circle, we need to use the formula A = πr2θ/360, where A is the area, r is the radius, and θ is the angle in radians. The given diameter is 34 feet, so the radius is 17 feet. The angle is π/5 radians. Plugging these values into the formula, we get A = π(17)2(π/5)/360. Simplifying, we find A = 9.0095 square feet. Rounded to four decimal places, the area of the sector is 9.0095 square feet.
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To find the area of the sector of a circle, you use the formula A = 0.5 * r² * θ where r is the radius (half of the diameter) and θ is the angle in radians. After plugging in the provided values, you calculate the area to four decimal points.
Explanation:The subject is related to finding the area of the sector of a circle. The formula to calculate the area of the sector is A = 0.5 * r² * θ, where r is the radius and θ is the angle in radians. In the given problem, the diameter of the circle is given as 34 feet, so the radius will be 17 feet, and the angle is given as π/5 radians.
Step 1: First, note down the radius from the given diameter, which would be 17 feet, as radius = diameter/2.
Step 2: Plug the value of the radius and the angle into the formula for the area of a sector. The calculation will look like this: A = 0.5 * (17)² * (π/5).
Step 3: Calculate the area by multiplying the values. The final answer will be rounded to four decimal places.
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Lee converted 500 U.S. dollars to 625 Singapore dollars. If x represents U.S. dollars and s represents Singapore dollars, which of these equations represents the relationship between the two currencies?
Given
Lee converted 500 U.S. dollars to 625 Singapore dollars.
x represents U.S. dollars and s represents Singapore dollars.
Find out equations represents the relationship between the two currencies.
To proof
As given in the question
x represents U.S. dollars and s represents Singapore dollars.
converted 500 U.S. dollars to 625 Singapore dollars
500 x = 625 s
[tex]x = \frac{625}{500} s[/tex]
x = 1.25 s
This shows that the U.S dollars is equal to 1.25 times of singapore dollars.
Hence proved
PLEASEE HELPP!!!!
What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x4+5 ?
Enter your answer in the box.
y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{15}{2}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = 4x + 5 is in this form with slope m - 4
Given the slope of a line m, then the slope ([tex]m_{2}[/tex]) of a line perpendicular to it is
[tex]m_{2}[/tex] = - (1 / m ) = - [tex]\frac{1}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex] x + c is the partial equation of the perpendicular line
to find c, substitute ( 2, 7 ) into the partial equation
7 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = [tex]\frac{15}{2}[/tex]
y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{15}{2}[/tex] ← equation of perp. line
9 + 5 = x - 11
how to find the x number
9 + 5 = x - 11
combine like terms
14 = x - 11
add 11 to both sides
25 = x
or
x = 25
answer
x = 25
9+5=x-11
14=x-11
+11 +11
24=x
y=f(x)=-3x find f(x) when x is 3
f(3) = -9 for the function [tex]\( y = f(x) = -3x \) when \( x \) is 3.[/tex]
To find f(x) when ( x ) is 3 for the given function [tex]\( y = f(x) = -3x \),[/tex] you substitute 3 for ( x ) in the function: [tex]\[ f(3) = -3 \times 3 \][/tex]
Now, calculate the value: [tex]\[ f(3) = -9 \][/tex]
Therefore, when ( x ) is 3, f(x) is -9 for the function [tex]\( y = f(x) = -3x \).[/tex]
In more detail, this means that if you plug ( x = 3 ) into the function, it will result in ( y = -9 ). The function ( y = -3x ) represents a linear relationship where the coefficient of ( x ) is -3. This indicates that for each unit increase in ( x ), ( y ) decreases by 3 units. In the specific case of ( x = 3 ), substituting this value into the function gives [tex]\( y = -3 \times 3 = -9 \).[/tex]
This kind of analysis is fundamental in understanding the behavior of linear functions. It provides insight into how the function's output (y) changes in response to changes in the input ( x ). In this case, when ( x ) increases by 1, ( y ) decreases by 3, leading to the slope of -3 in the function ( y = -3x ).
Which lists the steps in the correct order to find the median of this data set?
24, 16, 23, 30, 18, 29
1. Put the numbers in order.
2. Cross off high/low pairs.
3. Add the leftover numbers.
4. Divide the sum by 2.
1. Put the numbers in order.
2. Cross of high/low pairs.
1. Cross off high/low pairs.
2. Add the leftover numbers.
3. Divide the sum by 2.
1. Cross of high/low pairs.
Answer:
1. Put the numbers in order.
2. Cross off high/low pairs.
3. Add the leftover numbers.
4. Divide the sum by 2.
Step-by-step explanation:
We know that the median represent the middle value in a data which gives the center of the measure.
Whenever we calculate the median of a data the first step we need to follow is to arrange the a data in either ascending or descending order.
After that choose that center-most data value (in odd number of data value) or calculate the mean of the center-most 2 numbers ( if even) which will be the median of the data.
Given data: 24, 16, 23, 30, 18, 29
Number of numbers = 6 (even)
1. Put the numbers in order.
16,18,23,24,29,30
2. Cross off high/low pairs., we left with the numbers :-
23,24
3. Add the leftover numbers.
23+24=47
4. Divide the sum by 2.
[tex]\dfrac{47}{2}=23.5[/tex]
Answer:
A.
Step-by-step explanation:
name a plane two different ways
A segment has endpoints (a,b) and (c,d). The segment is translated so that its image is 6 units up and 3 units left of the preimage. Are the two segments parallel, perpendicular, or neither? Also need a picture of the image and preimage, thanks!
Answer:
parallel
Step-by-step explanation:
Translation moves each point the same amount in the same direction. Essentially, the original segment becomes the side of a parallelogram, whose other side is the image, and whose ends are the vectors specifying the translation.
In the attachment, we have designated (a, b) as point A, and (c, d) as point B. We had to choose specific values for these in order to plot them, but the description of the effect of translation applies no matter what the point coordinates are chosen to be.
if 3x + 5y = 2 and 2x - 6y = 20 what is 5x - y
Hey!
We have:
... 3x + 5y = 2
... 2x - 6y = 20
In order to get 5x - y , we will need to add both the equations.
3x+5y=2
2x-6y=20
____________________________________________________
...5x - y = 22
Hence, the required answer is 22.
Hope it helps!
Linear equations in two variables are solved to obtain the values of variables. Thus, the value of the equation [tex]5x - y[/tex] is [tex]\bold{22}[/tex].
Given equations are mentioned below:
[tex]3x + 5y = 2\\2x - 6y = 20[/tex]
We need to determine the values of the expression [tex]5x - y[/tex].
For calculating the value of the above expression, first we need the value of the variables x and y.
How to calculate the values of the variables?The solution of linear equation in two variables can be calculated by different methods such as substitution, elimination and graphical methods.Here, in this question we used substitution method to calculate the desired value. Calculations:[tex]\begin {aligned}3x + 5y &= 2\\3x&=2-5y\\x&=\dfrac{2-5y}{3} \end{aligned}[/tex]
Now, substitute the value of the x in another expression and solve it further.
[tex]\begin{aligned}2 \times \dfrac{2-5y}{3} -6y&=20\\ \dfrac{4-10y}{3}-6y&=20\\4-10y-18y&=60\\28y&=-56\\y&=-2 \end{aligned}[/tex]
Now, calculate the value of x.
[tex]\begin{aligned}x&=\dfrac{2-5 \times -2}{3}\\&=\dfrac{12}{3}\\&=4 \end{aligned}[/tex]
Now, calculating the value of [tex]5x - y[/tex].
[tex]5\times4 - (-2)=22[/tex]
Hence, the value of the expression [tex]5x - y[/tex] is 22.
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What is the slope of your line perpendicular to y=5x-12
The slope of your line is the x-coefficient: 5.
The slope of a perpendicular line is the negative reciprocal of that: -1/5.
Use the three steps to solve the problem.
One number is 11 more than twice another number. If the sum of the numbers is twice their difference, find the numbers.
Let x be the bigger number and y be the smaller number.
One number is 11 more than twice another number. Thus,
x = 2y + 11
The sum of the numbers is twice their difference, thus,
x + y = 2(x-y), which simplifies to:
x + y = 2x - 2y
3y = x (Now plug this back to the first equation:
3y = 2y + 11, and solve:
y = 11
Plug in y = 11 to the first equation:
x = 2(11) + 11 = 22 + 11 = 33
Thus the numbers are: x = 33, y = 11.
Jordan and Sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up for the trip, and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla 3. only has enough materials to make 40 necklaces. (A) write two constraints to model the problem. Let x respresent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells. (B) can sharla afford the down payment with the money she earns selling her necklaces? Explain your answer Please HELP ASAPm
Amount needed for down payment = $650
Amount charged by Jordan for mowing 1 lawn = $25
Amount charged by Sharla for 1 necklace = $ 15
Let the number of lawns mowed by Jordan = x
Let the number of necklace made by Sharla = y
Part A:
[tex]25x+15y=650[/tex]
As it is given, Sharla can make 40 necklace so,
[tex]25x+15(40)=650[/tex]
Or it could be 25x=650 and 15y=650
Part B:
No, Sharla cannot afford the down payment because she makes $15 for every necklace and she only has 40 necklaces which is [tex]15*40=600[/tex]