The number x = - 5/7 .
How do you frame an equation?The following steps are necessary to construct a linear equation in one variable from the provided word problem:
Step I: Read the problem attentively and make separate notes for the provided and necessary quantities.
Step II: Use 'x', 'y', 'z', etc. to represent the unknowable quantities.
Step III: Next, convert the issue into a mathematical formulation or statement.
Step IV : Utilizing the conditions provided in the problem, form a linear equation in one variable in
Step V: Verify the equation for the unknown quantity
Let the number be x
Thus according to the question :
( twice a number) × 6 = 11 (number) - 5/7
(2x)6 = 11 x - 5/7
12x = 11 x- 5/7
x= - 5/7
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Question 2 of 25The coach of a college basketball team categorizes the number of pointsscored by the team in each game, with the categories being 51 - 57, 58 - 64,65 - 71, and 72 or more. If the following data represent the numbers ofpoints scored in the last 10 games, how many games were in the 51 - 57category?51, 70, 63, 59, 56, 75, 60, 55, 67, 64O A1B. 2O c. 4O D. 3
In the table, we can see that the highest number corresponds to the cats who failed. Then, if a comparative bar chart represents the data, the bar representing the number of cats that failed will be the tallest.
AnswerA. Cats who failed
Ken exercise at a park first he run 3 miles in 30 minutes.Then he rests for 15 minutes.Then he runs 2 miles in 15 minutes.Finally he walks 1 mile in 15 minutes.Assume each running and walking segment was done at a constant rate.skecth a graph to represent ken's exercing at the park.the fisrt segment should begin at (0,0).
The horizontal axis represents the time in hours, and the vertical axis represents the number of miles ran.
So for the first part we have 3 miles in 30 minutes (0.5 hour), so we can draw a line from point (0, 0) to point (0.5, 3)
For the second part, he rests for 15 minutes (0.25 hour), so the y-value doesn't change, therefore we have a horizontal line from (0.5, 3) to (0.75, 3).
Then, we have 2 miles in 15 minutes, so we have a line from (0.75, 3) to (1, 5).
And finally, 1 mile in 15 minutes, so a line from (1, 5) to (1.25, 6).
Sketching the graph, we have:
Carrots costs $0.99 per pound. Broccoli costs $1.50 per pound. Jack buys 3.5 pounds of carrots and 1.25 pounds of broccoli. What is Jack’s total bill?
Answer: his total bill is 7.24
Step-by-step explanation:
You volunteer at a nursing home for 3 hours a day. You volunteered 6 hours last week and 12 hours this week. How many days did you volunteer?
The graph shows the linear parent function.Y5-55----Which statement best describes the function?
From the picture, we have the graph of the linear parent function f(x) = x.
We have the following statements as descriptions of the function:
A. The function is negative when x < 0.
From the graph, we see that the function takes negative values for x < 0. This statement is true.
B. The function is negative when x < 0 and also when x > 0.
The first part of this statement is true, but the second is not because that we see that the function takes positives values for x > 0. So this statement is false.
C. The function is never negative.
If we see the graph, the function is negative when x < 0. So this statement is false.
D. The function is negative when x > 0.
Again, seeing the graph we note that the function takes positive values for x > 0. So this statement is false.
So the only statement that it is true, is option A.
help help help help help help help
rectangle perimeter ; 36 unitswidth; xlength ; 4x - 2solve for x
Perimeter = 36 units
width = x
length = 4x - 2
Equation of perimeter = 2width + 2length
Substitution
36 = 2(x) + 2(4x - 2)
Expanding
36 = 2x + 8x - 4
36 = 10x - 4
36 + 4 = 10x
40 = 10x
x = 40/10
x = 4
2. Multiply the matrices.
Result of matrix multiplication [tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] = \left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right] [/tex].
What is a matrix?A matrix is a series of numbers forming a square or rectangle arranged in rows and columns enclosed in square brackets [ ] or regular brackets ( ).
Solution:
[tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] [/tex]
[tex] \left[ \begin{array}{cc} - 1 \times 2 + 2 \times 7 + 0 \times 1 & - 1 \times ( - 3) + 2 \times ( - 1) + 0 \times 2 \\3 \times 2 + ( - 2) \times 7 + 4 \times 1&3 \times ( - 3) + ( - 2) \times ( - 1) + 4 \times 2\\ - 5 \times 2 + ( - 1) \times 7 + 6 \times 1&( - 5) \times ( - 3) + ( - 1) \times ( - 1) + 6 \times 2 \end{array}\right ][/tex]
[tex]\left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right ][/tex]
Would you please check this answer for me? Use elimnation to solve the system of equations:2x+2y=162x+3y=14My answer: (10, - 2)
Equation
[tex]\begin{gathered} 2x+2y=16 \\ 2x+3y=14 \\ \end{gathered}[/tex]Let's multiply -1 by Eq 1
[tex]\begin{gathered} -2x-2y=-16 \\ 2x+3y=14 \\ 2x-2x+3y-2y=-16+14 \\ y=-2 \end{gathered}[/tex]Now for x
[tex]\begin{gathered} 2x+2y=16 \\ x=\frac{16-2y}{2} \\ x=\frac{16-2\cdot(-2)}{2} \\ x=\frac{16+4}{2} \\ x=\frac{20}{2} \\ x=10 \end{gathered}[/tex]The answer would be (10, -2)
Raffle tickets are being sold for a fundraiser. The function a(n) relates theamount of money raised to the number of tickets sold, n.It takes as input the number of tickets sold and returns as output the amountof money raisedan) = 4n - 20Which equation represents the inverse function n(a), which takes the moneyraised as input and returns the number of tickets sold as output?O A. n(e) -47,20O B. n(e) – +20OC. n() - 0-20OD. n(a) -3 -20
A
Since The equation is
[tex]a(n)\text{ = 4n-20}[/tex]To find its inverse we have to proceed to some steps
a= 4n-20
1) Swap a for n, in this case,
n=4a-20
2) Isolate n on the left side by subtracting 4a on both sides:
n -4a =4a-4a -20
n-4a=-20
3) Subtract n on both sides
a-a-4n =-20-a
-4n=-20 -a
4) Multiply it by -1
4n = 20 + a
5) Divide by 4, there you have it. The inverse function:
[tex]n(a)=\frac{20+a}{4}[/tex]To find its in
Determine whether the triangles are similar. If so, what are the similarity statement and the postulate or theorem used? (image attached)thank you ! :)
ANSWER
ΔOMN ~ ΔOJK; SAS
EXPLANATION
As we can observe in the diagram, the triangles share angle O and we have information about the sides forming that angle, so the postulate to use, in case they are similar, is SAS.
If two triangles are similar, then the ratio between corresponding sides is constant.
Let's assume that the similar triangles are triangle OMN and triangle OJK. Then, the previous statement is,
[tex]\frac{OM}{OJ}=\frac{MN}{JK}=\frac{ON}{OK}[/tex]Replace the side lengths for the first and last ratios - since we don't know the lengths of sides MN and JK,
[tex]\begin{gathered} \frac{30+10}{30}=\frac{3+1}{3} \\ \\ \frac{40}{30}=\frac{4}{3} \\ \\ \frac{4}{3}=\frac{4}{3} \end{gathered}[/tex]The ratio between corresponding sides is constant, 4/3. Hence, triangles OMN and OJK are similar, by SAS.
Suppose that the functions s and t are defined for all real numbers x as follows.
s(x)=x-3
t(x) = 3x+4
Write the expressions for (s•t) (x) and (s-t) (x) and evaluate (s+t) (-2).
7 is the value of function s and t .
What is function explain?
A relation between a set of inputs and a set of allowable outputs is called a function, and it has the property that every input is associated to exactly one output. When every element in set A has one end and only one image in set B, then the mapping from set A to set B is a function. Let A & B be any two non-empty sets.Four main categories can be used to classify the many sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.s(x)= x-3
t(x) = 3x+4
(s•t) = ( x -3 ) ( 3x + 4 )
= ( 3x² + 4x - 3x² - 12 )
= 4x - 12
(s-t) (x) = ( x-3 ) - ( 3x+4 )
= x-3 - 3x + 4
= -2x + 1
(s + t) (-2) = x-3 + 3x+4
= 4x + 1
(s + t) (-2) = 4 * - 2 + 1
= 8 - 1 = 7
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a bucket contains 15 blue pens 35 black pins and 40 Red Pins. You pick one pin at random find the theoretical probabilities below . Express your answer as a percent to the nearest whole number p(black)=???p(blue or black)=???
The number of blue pen is 15
The number of black pens is 35
The number of red pens is 40
The total number of pens in the bucket = Blue pens + black pens + red pens
The total number of pens = 15 + 35 + 40
= 90
Therefore, the total number of pens in the bucket = 90 pens
The probability that black pen is picked is
Probablity = possible outcomes/ total outcomes
P(black) = 35 / 90 x 100%
P(black) = 0.3888 x 100%
P(black) = 38.88%
P(black) = 39%
P(blue or black)
If its pick at random without replacement then
If the first pick is blue, then the total number of pen in the bucket remains 89
For the first pick will be 15/90
Since the remaining pens is 89, then the second pick is
35/89
Then we have
15/90 + 35/89
LCM is 8010
8010 x 15 / 90 + 35 x 8010 /89 / 8010
89 x 15 + 35 x 90 / 8010
P(blue / black) = 1335 + 3150 / 8010
P(blue or black) = 4485 / 8010
P(blue or black) = 0.559 x 100%
P(blue or black) = 55.9%
P(blue or black) = 56%
A 20-foot support post leans against a wall, making a 70° angle with the ground. To the nearest tenth of a foot, how far is the base of the post from the wall?
The following problem can be well explained by the diagram shown below:
Hence by the trigonometry of the figure use the trigonometric ratio of cos to get:
[tex]\begin{gathered} \cos 70=\frac{BC}{AC}=\frac{x}{20} \\ x=20\cos 70 \\ x=6.8404\approx6.8 \end{gathered}[/tex]Hence the support is 6.8 feet away from the wall.
Option A is correct.
I need help with my math
Callan hikes at the rate of 3 miles per hour, that means, the table of values of values would be completed as follows;
Hours, x Miles, y
1 3
3 9
5 15
The ordered pair above is derived by multiplying every hour by 3 to arrive at the number of miles.
The graph is now shown as;
7 is added to 11 divided by a number r write the algebraic expression
Answer: 7+(11/r)
Step-by-step explanation:
Given the replacement set: {−9, −10, −11, −12}.
Which value of x correctly solves this equation?
3.2x−5=−40.2
Enter your answer in the box.
Answer:
x = -11
Step-by-step explanation:
You want to know the value of x that correctly solves the equation 3.2x -5 = -40.2.
SolutionThis 2-step linear equation is solved in the usual way:
Step 1: isolate the variable term
3.2x -5 +5 = -40.2 +5 . . . . . . . . . add 5 to both sides
3.2x = -35.2 . . . . . . . . . . . . . simplify
Step 2: isolate the variable
3.2x/3.2 = -35.2/3.2 . . . . . . . . . . divide both sides by the coefficient of x
x = -11 . . . . . . . . . . . . . . . . . . simplify
Is -7. a rational number
A rational number can be represented by dividing two integers.
So, it can be represented as a ratio of 2 integers.
-7 = -7/1
-7 is a rational number
An aeroplane flies between two cities that are 8100 km apart.
The aeroplane takes 9 hours to complete the journey.
Calculate the average speed of the aeroplane, in km/h.
Answer:
7,290,000.answer
Step-by-step explanation:
1 km= 100000 m
1 hour = 60 minute
8100 km = 810000 m
9 hour=540 minute
60/540.00 cancel
6/54 will be than cut 6×9=54
SO,multiply 810000×9 = 7,290,000
Answer:
The answer is 7,290,00
Step-by-step explanation:
1 km= 100000 m
1 hour = 60 min
8100 km = 810000 m
9 hour=540 min
60/540.00 cancel
6/54 will be than cut 6×9=54
so ,multiply 810000×9 = 7,290,000
A car was valued at $41,000 in the year 1994. The value depreciated to $13,000 by the year 2004
Firstly, we have to write the general depreciation fomula as follows;
[tex]V(t)=I(1-r)^t[/tex]where V(t) represents the value of the commodity after a certain t years
I is the initial value of the item
r is the annual percentage change (rate of depreciation)
t is the number of years
a) Here, we want to calculate the annual rate of change
According to the data given in the question;
V(t) = $13,000
I = $41,000
r = ?
t = 2004-1994 = 10 years
Now, we proceed to substitute these values, to find the find of r as follows;
[tex]\begin{gathered} 13,000=41,000(1-r)^{10} \\ (1-r)^{10\text{ }}\text{ = }\frac{13,000}{41,000} \\ (1-r)^{10\text{ }}=\text{ }\frac{13}{41} \\ \\ (1-r)\text{ = }\sqrt[10]{\frac{13}{41}} \\ \\ 1-r\text{ = 0.8915} \\ r\text{ = 1-0.8915} \\ r\text{ = 0.1085} \end{gathered}[/tex]b) To write r in percentage form, we have to multiply the answer in 'a' above by 100
We have this as ;
[tex]0.1085\times100\text{ = 10.85 \%}[/tex]c) Here, we want to get the car value by year 2009
In that instance;
V(t) = ?
I = $41,000
r = 0.1085
t = 2009-1994 = 15
Substituting these values, we have;
[tex]\begin{gathered} V(15)=41,000(1-0.1085)^{15} \\ V(15)\text{ = \$7,321.56} \end{gathered}[/tex]To the nearest 50 dollars, this is $7,300
A local hamburger shop sold a combined total of 598 hamburgers and cheeseburgers on Wednesday. There were 52 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?
In the local hamburger shop the total number of hamburgers sold on Wednesday , based on the given data is :
325 hamburgers.
Explanation:A General Rule for Equation Solving
Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.here form a equation based on given data ;
let , Hamburgers be = x
let, Cheeseburgers be = y
here , No. of burgers (hamburgers and cheeseburgers )sold = 598
here,
x + y = 598 =>(1)
y = x - 52 => (2)
solving 2 equations ,
x + ( x - 52 ) = 598
x + x - 52 = 598
2x = 598 + 52
x = 650 /2
x = 325
on Wednesday 325 hamburgers were sold.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
(8x-18)°
40°
110°
The value of the variable x associated to the triangle is equal to 6.
What is the variable associated to internal angles of a triangle?
Triangles are figures with three sides and three internal angles. According to Euclidean geometry, the sum of the measures of the internal angles is equal to 180° and we must solve the following equation for x:
(8 · x - 18) + 40 + 110 = 180
(8 · x - 18) + 150 = 180
(8 · x - 18) = 30
8 · x = 48
x = 6
The triangle has internal angles of 30°, 40° and 110° and the value of variable x is 6.
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the average daily rainfall is typically 5/8 of an inch. Last year, the average daily rainfall
was only 3/8 of an inch. What percent of the typical average daily rainfall fell last year in Green Valley?
Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors. He has 16 cookies and 24 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates he can make to share?
The greatest number of plates he can make to share is 6.
What is the greatest number of plates he can make to share?From the information, Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors and he has 16 cookies and 24 brownies to share.
It should be noted that this illustrates that we have to find the highest common factor for 16 and 24.
This will be:
18 = 2, 3, 6, 9 and 18.
24 = 2, 3, 4, 6, 8, 12 and 24
The highest common factor is 6.
Therefore, the number will be 6 plates.
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Explain how travelling to a ski resort to go skiing could influence travel time
A ski trip requires a lot of planning.You must choose your travel dates, choose the ideal location, identify the best ski resorts for your family in the area, book lodging, purchase lift tickets, schedule lessons, consider your equipment and clothing needs, and possibly book flights or a rental car.
Describe the possible effects that traveling to a ski resort might have on travel time?
Beyond making reservations, there are more actions to be taken.Making decisions, locating the best offers, and making reservations take time.While some tasks should be completed in advance, others can wait till later.Before heading to the slopes, use this helpful planning timeline to help you save some green (and your sanity). Planning is more necessary when skiing with children as it differs from skiing alone.When there was an incredible snowstorm, I remember those last-minute college ski excursions that somehow came together, allowing me to jump in an SUV with someone else and crash on their lily pad with them and 10 to 20 other pals.I have happy recollections of those ski holidays when I was a younger frog. Perhaps I have forgotten the sleepless nights spent in the company of snorers and surviving on sugar and coffee, but those things were unavoidableBut now, on our mountainous excursions, Leap, my husband, who is learning to ski, and two tadpoles are also hopping along.The majority of our preferred ski resorts involve travel by plane, which is difficult to arrange at the last minute due to our tight schedules.In addition, it appears that my standards and working hours have changed, and now I no longer consider sleeping on a couch or the floor with complete strangers to be a vacation. As a result, I must think carefully and plan ahead for my ski trips in order to accommodate a family with a toddler, a tween, and adults.You should begin planning your ski vacation up to a year in advance.Choose the ski region or areas you want to go to.For instance, focus on a specific area; perhaps you want to look into the Denver region, Lake Tahoe, or Utah.Find the finest ski resort for your family by researching ski resorts in those areas.Check out mountain statistics and trail maps to determine if there are any runs that your family will enjoy.In comparison to other resorts, you might notice that one has more terrain for beginner to intermediate skiers. When there aren't any lift tickets or lessons available, it might be difficult to compare pricing during the off-season. To illustrate, imagine that you decide to go skiing in Colorado the next winter a year in advance.To help you plan and get an idea of costs so you can budget, look at the prices of different resorts in the area during peak and off-peak seasons on their websites more than a year in advance. You can also compare the costs of different resorts in the area at both peak and off-peak times.You may discover that Keystone and Breckenridge are more affordable while still providing excellent family-friendly amenities than places like Vail and Beaver Creek.To learn more about ski resort refer
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rewrite 13% into equivalent fraction
The number 13% as an equivalent fraction is 13/100
How to rewrite the percentage into equivalent fraction?From the question, the given parameter is
13%
This above number is a percentage or percentile
So, we have
Percentage = 13%
Next, we multiply the percentage by 1
So, we have
Percentage = 13% x 1
Express 1 as 100/100
So, we have
Percentage = 13% x 100/100
Evaluate the product of 13% and 100
So, we have
Percentage = 13/100
Rewrite as
Fraction = 13/100
The fraction cannot be further simplified
Hence, the equivalent fraction of 13% is 13/100
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Molly has 250 trading cards. She gives n trading cards to her friend Carol. Marcus has 430 trading cards. He gives away three times as many cards as Molly does. How many trading cards did Molly give away if Molly and Marcus have the same number of trading cards left?
Molly gave away 90 trading cards out of 250 trading cards to her friend Carol.
Initially molly had 250 cards.
She gave away n trading cards to her friend.
Now molly has (250 - n) trading cards.
Initially Marcus had 4430 trading cards.
The number of cards that Marcus gave away is is three times of molly.
Cards gave away by Marcus = 3n
Now, Marcus is left out with (430 - 3n) trading cards/
After giving away the cards,
Molly and Marcus had same number of trading cards.
So, we can write,
250-n = 430-3n
Now, we have a linear relation between the number of cards given away and the remaining cards,
Further solving,
2n = 180
n = 90.
So, Molly gave away 90 cards.
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find the perimeter of ABC with vertices A(-4,4), B(4,-1) and C(-4,-1)
Answer: A=-16 B=-5 C=-3
Step-by-step explanation:
Hi I have tried calling but I can’t do anything
For the given functions, we will find the first derivative of each function
Note:
a, and b are constants
y, f, and g are functions
2) y = (a+bf)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g*b\frac{df}{dx}-(a+bf)\frac{dg}{dx}}{g^2}[/tex]=============================================================
3) y = (x+f)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g(1+\frac{df}{dx})-(x+f)\frac{dg}{dx}}{g^2}[/tex]==========================================================
4) y = (x+f)³
We will use the exponent rule to find the derivative as follows:
[tex]y^{\prime}=3(x+f)^2(1+\frac{df}{dx})[/tex]===========================================================
5) y = ax² + bg² + f
so, y' will be as follows:
[tex]y^{\prime}=2ax+2bg\frac{dg}{dx}+\frac{df}{dx}[/tex]==========================================================
help l need help with this
Answer:
Step-by-step explanation:
Answer: Y = 3x + 3
Simply plug in points on graph calculator.
Answer:
Step-by-step explanation:
I think it might be y=3/1+6 ??? i might be wrong