Show graphically that the system of linear equations 5x – y = 14 ; x – 2y =1 has a unique solution. Write the coordinates where line x – 2y =1 intersects the X-axis. Write the solution.
Answers
The graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)
The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)
How to Determine the Solution to the System of Equations?Given the linear equations:
5x – y = 14 ---> equation 1
x – 2y = 1 ---> equation 2
Rewrite both equations in slope-intercept form as y = mx + b, where b represents the y-intercept of the line and m represents the slope.
5x - y = 14
-y = -5x + 14
y = 5x - 14 (slope is 5 and y-intercept is -14)
x - 2y = 1
-2y = -x + 1
y = 1/2x - 1/2 (slope is 1/2, and the y-intercept is -1/2).
Therefore, the graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)
The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)
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Related Questions
The letters a and b represent nonzero constants. Solve ax+b=41 for x .
Answers
The given equation is solved to x as x=(41-b)/a.
The given equation is ax+b=41.
We need to solve the given equation for x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, the equation ax+b=41 can be solved as follows:
Keep the variable x on the left-hand side of the equation and bring a to the right-hand side of the equation.
That is, x=(41-b)/a (when you bring a variable from LHS to RHS or vice versa the mathematical operations become inverse that is multiplication changes to division)
Therefore, the given equation is solved to x as x=(41-b)/a.
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9y=99
Ingrese su respuesta...
Answers
The value of y for which the left hand side of the equation is equal to Right hand side is 11.
What is a solution of a linear equation?Solution of a linear equation is the value of the variable for which the left hand side and right hand side of the equation are equal.
Given is the following equation -
9y = 99
In order to solve the equation. we have to find the value of y for which 9y is equal to 99. Now -
9y = 99
Divide both sides by 9 -
9y/9 = 99/9
y = 11
Therefore, the value of y for which the left hand side of the equation is equal to Right hand side is 11.
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[The given question is written in Spanish. The following is the statement converted onto English as
9y=99 Enter your answer.}
when addition or subtraction is performed, answers are rounded to the least significant decimal place
Answers
For addition and subtraction problems, the answer should be rounded to the least significant decimal places as the measurement with the least number of decimal places
The rightmost digit of a decimal number is the least significant digit or least significant figure. Another way to look at the least significant figure is to consider it to be the rightmost digit when the number is written in scientific notation. Least significant figures are still significant.
Count the number of significant figures in the decimal portion only of each number in the problem. Add or subtract in the normal fashion. Final answer may have no more significant figures to the right of the decimal than the least number of significant figures in any number in the problem.
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Solve the inequality and express your answer in interval notation.
x^2-12x+5<0
Answers
Answer:
you solve the main number and you can plus the 1+1 the answer is 2 2=2 the main berb on this answer is no
Step-by-step explanation:
jalok
Answer:
The answer is A.
Step-by-step explanation:
What is the inequality shown
Answers
Answer:
-4 [tex]\leq[/tex] x [tex]\leq[/tex] 3
Step-by-step explanation:
The filled in dots mean that those numbers are included
1. As c decreases, does the value of x increase, decrease, or stay the same for each equation? Assume c is positive.
Equation | Value of x
x + c = 0 |
—————-|——————
-CX=-C |
—————-|——————
X/C=1 |
Answers
The complete statements are:
As c increases in x + c = 0, the value of x decreasesAs c increases in -xc = -c, the value of x stay the sameAs c increases in x/c = 1, the value of x increasesHow to determine the complete statements?
To do this, we evaluate each equation
So, we have
Equation 1
x + c = 0
Make x the subject
x = -c
The above implies that x and c are additive inverses
Hence, as c increases, the value of x decreases
Equation 2
-xc = -c
Divide both sides by -c
So, we have
x = 1
The above implies that c does not have any effect on the value of a
Hence, as c increases, the value of x stay the same
Equation 3
x/c = 1
Make x the subject
x = c
The above implies that x and c have the same value
Hence, as c increases, the value of x increases
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(ross p1.15) consider a group of 20 people. if everyone shakes hands with everyone else, how many handshakes take place?
Answers
190 handshakes take place.
What is Combinations?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. The sequence in which the chosen components are chosen is crucial in permutations, too. For instance, the arrangements ab and ba are distinct in permutations but equivalent in combinations (regarded as one arrangement).
Combinatorics is the study of combinations, although mathematics and finance are two other fields that employ combinations.
EXPLNATION : For a handshake you need two people. Therefore, select two from twenty, that is, 20C2 ways. It is 20*19/2 = 190.
In general, if there are ’n’ number of people there can be nC2 handshakes.
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Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Mariam's account has gone into overdraft. Her balance is $-20.21. To get back to a positive balance, she plans to deposit money at a steady rate of $20.79 per week. How much will be in her account after 4 weeks?
Answers
Using a linear function, it is found that $62.95 will be in her account after 4 weeks.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The initial balance is the intercept.The weekly deposit is the slope.Hence, her balance after x weeks is given by the following function:
B(x) = -20.21 + 20.79x.
Her balance after 4 weeks is given by:
B(4) = -20.21 + 20.79(4) = $62.95.
Hence $62.95 will be in her account after 4 weeks.
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Which expressions are equivalent to 4m-2+(-8m)4m−2+(−8m)4, m, minus, 2, plus, left parenthesis, minus, 8, m, right parenthesis ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-2(4m+1) +4m−2(4m+1)+4mminus, 2, left parenthesis, 4, m, plus, 1, right parenthesis, plus, 4, m
(Choice B)
B
2(2m-1)-8m2(2m−1)−8m2, left parenthesis, 2, m, minus, 1, right parenthesis, minus, 8, m
(Choice C)
C
None of the above
Answers
Answer:
Ohayooooooooooooooooooooo
A&B
Me podrian ayudar con estos dos problemas? porfavor es urgente:(
Answers
leonard can wash 6 cars in 4.5 hours. assuming that he always washes cars at this same rate, answer the following. how many cars can he wash in 9 hours?
how long will it take him to wash one car?
how many cars can he wash in one hour
Answers
He wash 12 cars in 9 hours.
And, He take 45 minutes to wash a car.
And, He wash one and one third part of cars in one hour.
Given that;
Leonard can wash 6 cars in 4.5 hours.
He always washes cars at this same rate.
We have to find number of wash cars in 9 hour and time to wash one car and number of wash cars in one hour.
What is relation between hour and minutes?
The relation between hour and minutes is ;
1 hour = 60 minutes.
Now, we have;
Leonard can wash 6 cars in 4.5 hours.
Time for wash 6 cars = 4.5 hour
So, Time for wash 1 car = 4.5 ÷ 6 = 0.75 hour
Since, 1 hour = 60 minutes
Hence, Time for wash 1 car = 0.75 x 60 = 45 minutes
And, In time 4.5 hour, number of wash cars = 6
So, In 1 hour, number of wash cars = 6/4.5 = 1 1/3
Hence, Number of wash cars in one hour is one and one third part of car.
In 9 hour, number of wash cars = (6/4.5) * 9 = 12
Hence, Number of wash cars in 9 hours is 12.
So, He wash 12 cars in 9 hours.
And, He take 45 minutes to wash a car.
And, He wash one and one third part of cars in one hour.
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2. Which of the following expressions simplifies to -15a + 30?
a. -3(-5a + 10)
b. 5(-3d-6)
c. -15(a + 2)
d. 6(-2.5a + 5)
Answers
Answer:
D
Step-by-step explanation:
D, because 6* -2.5a = -15a and 6*5= 30 so it equals -15a+30.
these are the means and standard deviations for samples of building heights in two different cities. city a city b mean: 120 ft mean: 240 ft standard deviation: 20 ft standard deviation: 12 ftselect the two true statements.
Answers
The average building height and the standard deviation for two separate cities' samples are shown. The true statements are:
City A’s heights are more spread out than city B’s heights.
City A has a lower average height than city B.
What is average?In daily life, an average is a number chosen to represent a group of numbers; it is often the sum of the numbers divided by the total number of numbers in the group (the arithmetic mean). The average of the integers 2, 3, 4, 7, and 9, for instance, is 5, which equals 25. An average could alternatively be another statistic like the median or mode, depending on the situation. The median is sometimes used in place of the mean since the mean would be unnaturally high if it included the personal incomes of a few billionaires. The median is the amount below which 50% of personal incomes fall and above which 50% of personal incomes rise.
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unit 2 sample work due aug 29 3 of 103 of 10 items question order the integers from least to greatest: -9, 5, 2, -8, 0, 10, -12 0, 2, 5, -8, -9, 10, -12 0, 2, 5, -8, -9, 10, -12 -12, -9, -8, 0, 2, 5, 10 -12, -9, -8, 0, 2, 5, 10 -9, -8, 0, 2, 5, 10, -12 -9, -8, 0, 2, 5, 10, -12 -8, -9, -12, 0, 2, 5, 10
Answers
The integers from least to greatest is -12<-9<-8<0<2<5<10.
The given set of numbers are -9, 5, 2, -8, 0, 10, -12.
We need to order the integers from least to greatest.
What is ascending order of integers?Ascending order refers to the arrangement of numbers or other items in increasing order from smallest to largest. Numbers that we see on a number line from left to right are examples of ascending order. We usually represent it by putting commas between numbers or by using the 'less-than symbol (<)' between numbers.
With negative numbers, the highest number with the negative sign has the least value.
So, -12<-9<-8<0<2<5<10.
Therefore, the integers from least to greatest is -12<-9<-8<0<2<5<10.
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with a random sample, each individual has the same chance of being selected. with a simple random sample, all samples of the same size have the same chance of being selected.
Answers
A subset of a statistical population called a simple random sample is one in which each member has an equal chance of being chosen.
What is Probability sampling?
A probability Slice is a process of opting for a sample from a population when the selection is grounded on the randomization principle, frequently known as chance or arbitrary selection. In general, a probability slice is more delicate, time-consuming, and precious than a non-probability slice.A random/ arbitrary sample is similar to a straightforward arbitrary sample. The distinction between the two is that any object in the population has an equal probability of being named with a simple arbitrary slice. Every item doesn't inescapably have an equal chance of being chosen in an arbitrary slice.
A random/ arbitrary sample is one that was named at arbitrary. It should really be labeled as a sample that was chosen at arbitrary. In order to help bias and other negative goods, arbitrary samples are employed. In fact, it's not as easy as it seems to opt for a arbitrary sample that involves further than simply opting for 100 people from a population of 1000. Make sure your arbitrary sample is actually random/ arbitrary before using it.
The liability of a straightforward random/ arbitrary slice, a subset of a statistical population called a simple random/ arbitrary sample is one in which each member has an equal chance of being chosen. A straightforward arbitrary sample is intended to offer an objective definition of a group.
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The rectangle below has an area of x^2+8x+15x
2
+8x+15x, squared, plus, 8, x, plus, 15 square meters and a width of x+3x+3x, plus, 3 meters.
What expression represents the length of the rectangle?
A rectangle with a width of x plus three and an unknown length. The area of the rectangle is x squared plus eight x plus fifteen.
Answers
The length of the given rectangle is x + 5 meters.
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.Given:
Area of rectangle = x² + 8x + 15 sq.metersWidth = x + 3 metersTo find: Length of the rectangle
Finding:
Let 'a' be the length of the rectangle.
We know that area of a rectangle = length * width
On substituting the given values in the above formula, we get:
=> x² + 8x + 15 = a (x + 3)
=> a = [tex]\frac{x^2+8x + 15}{x+3}[/tex]
=> a = [tex]\frac{(x+5)(x+3)}{x+3}[/tex]
=> a = x + 5
Hence, The length of the given rectangle is x + 5 meters.
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Simplify. (7^{6})^{2}(7
6
)
2
Answers
The result of the exponent given is 7^12
Solving exponentsIn order for us to solve the exponential expression given, we will use the law of exponent below;
(a^m)^n = a^mn (multiply the powers)
Given the expression
[tex](7^{6})^{2}[/tex]
Multiply the exponents to have;
7^6(2)
7^12
Hence the result of the exponent given is 7^12
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Anna does sit-ups to get ready for her first triathlon. When she starts, she does a sit-up every 222 seconds. But, as she gets tired, each sit-up takes longer and longer to do.
Answers
Answer:
No, the number of sit-ups Anna does, are not proportional to the time she spends doing them.
Step-by-step explanation:
When Anna starts, she does a sit-up every 22 seconds.
Gwen davis is a middle school math teacher. she starts today's lesson by introducing the topic of percent increase and percent decrease and reviewing decimals and percents. then, she develops student understanding by explaining and modeling the process of solving percent increase and percent decrease problems. based on the strategy gwen has chosen, what should her next step be
Answers
Grew Davis next step would be to give homework for the students and conduct a test in the next week .
Gwen Davis is a middle school math teacher.
she starts today's lesson by introducing the topic of percent increase and percent decrease and reviewing decimals and percent
How do I calculate a percentage decrease?
Percentage decrease formula can be obtained by simply dividing the decreased value by the original value and multiplying that with 100. Here, Decreased Value = Original Value – New Value.
How do you calculate a 20% increase?
Multiply the original value by 0.2 to find the amount of a 20 percent markup, or multiply it by 1.2 to the original value
Hence , Grew Davis next step would be to give homework for the students and conduct a test in the next week .
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Factor completely.
100-9x²
someone help please
Answers
Answer:
[tex](10+3x)(10-3x)[/tex]
Step-by-step explanation:
[tex]100-9x^2\\\sqrt{100} =10\\\sqrt{9} =3\\3*-3=-9\\\sqrt{x^2} = x \\(10-3x)(10+3x)[/tex]
________________________________________________________
Considering both terms are perfect squares, factor using the difference of squares formula:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
In this situation, a = 10 and b = 3x. With this, now plug in your data into the formula.
(10 + 3x) (10 - 3x)
_________________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Estimate the average rate of change over the interval [-1, 0]. Show your work below or on the graph.
Answers
ax + bx = c please help I’m so confused
Answers
Answer:
[tex]x = \frac{c}{a + b} a = - b[/tex]
Solve 0. 504 ÷ 8.
answer choices:
−7. 496
0. 063
0. 630
4. 32
Answers
Answer:
0.063
Step-by-step explanation:
0.504 divided by 8 is 0.063
Hope It Helps
Sorry If I'm Wrong
Answer: The answer is 0.630
Step-by-step explanation: The picture proves my answer :D
PLS HELP!!!
Fine the measure of the angle indicated in bold. Then find the measure of the other indicated angle.
Answers
The answer for the following questions are:
x= 3x= 10x= 43 = x3 = xx= 8x= 8x=9x=5 x=6What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint.
11. 5+35x + 24x - 2 = 180 (linear pair)
59x = 177
x= 3
12. 15 + 10x = -5 + 12x (corresponding angle)
20 = 2x
x= 10
13. 13x -4 + 8 +9x =180 (linear pair)
22x +4 = 180
22x = 176
x= 4
14. 24x + 3 = 25x (alternate interior angle)
3 = x
15. 32x + 4 = 1 + 33x ( corresponding angle)
3 = x
16. 13x+ 11 = 15x - 5 (alternate interior angle)
-2x = -16
x= 8
17. 15x + 8x -4 = 180 (linear pair)
23x = 184
x=8
18. 9x +16 = 11x -2 ( Vertically opposite angle)
-2x = -18
x=9
19. 5+ 17x = 19x -5 (alternate interior angle)
2x = 10
x=5
20. 8x - 3 + 23x -3 =180 ( Linear pair)
31x = 186
x=6
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Which relation is a function of x?
O {(1, 2), (7, 6), (3, 2), (1, 0), (5, 6)}
y
2
-6
X
0
0
0
0
9
-7
Ox=3y²-7
X=
-5-4-3-2
5
4
3
2
-2
2 3 4 5 x
Answers
Answer:
x=3y2-7
x=3×1-7
x=3-7
x=-4
Jane ordered a few moving boxes from a local store as she is relocating to Atlanta.
She returned 28 damaged boxes. She allotted the remaining boxes equally for
each of the four rooms from which her belongings had to be packed. If 5 boxes
were used for each
room, how many boxes did she receive from the store
initially?
Answers
48 boxes did she receive from the store initially in probability.
How does probability explain work?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.Basic probability is governed by three primary rules: the addition rule, the multiplication rule, and the complement rule.Since there is a 50% chance that the outcome will be heads, we can anticipate 50 heads. But when we actually test it, we may get 48 heads, 55 heads, or anything else at all, though it will typically be a figure close to 50.Based on the given conditions formulate = 28 + 5 * 4
Calculate the product or quotient = 28 + 20
calculate the sum or difference = 48
get the result = 48
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Select the correct answer from the drop-down menu.
Right triangle MNR is represented with the right angle at vertex M. Angle R measures 34 degrees and angle N measures 56 degrees. Point Q lies on segment RN and point P lies on segment MP. Segments MQ and PQ are drawn. Angle MQP measures 56 degrees.
In the figure, sin ∠MQP =
. Plato
Answers
The required measure of the sine of angle ∠ MQP for Right triangle MNR is evaluated as 0.83.
As given in the question, the Right triangle MNR is represented with the right angle at vertex M. Angle R measures 34 degrees, and angle N measures 56 degrees.
We have to determine sin ∠MQP.
The angle can be defined as the one line inclined over another line.
Here,
For right-angle triangle MNR,
To calculate the sin of the angle in the right angle triangle we need hypotenuse and perpendicular.
But in the question value of angle ∠MQP is given, So directly,
sin 56 = 0.83.
Thus, the required value of the sine of angle ∠MQP is 0.83.
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Answer:
hlpp
Step-by-step explanation:
Emma is planning how much she needs to make next week. She can only work 25 hours, and she needs to make a total of $620. What is the dollar value of sales Emma will need to make?
Answers
Answer:
The corrects answer is: Emma will need to make sales totaling $800 next week to meet her goal.
Step-by-step explanation:
The approximate mean age is _____ years.
(Round to one decimal place as needed.)
Age
0-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Frequency
23
22
24
15
31
48
34
18
4
Answers
In the figure, the radius of the large circle is three times the radius of the small circle. About what percent of the large circle is covered by the small circle?
I NEED THIS NOW PLEEEEEASE!!
Answers
The percent of the large circle is covered by the small circle will be 33.3%.
How to calculate the percentage?It should be noted that the radius of the small circle will be r.
The radius of the big circle will be 3r.
Therefore, the percent of the large circle is covered by the small circle will be:
= r / 3r × 100
= 1/3 × 100
= 33.3%
The percent of the large circle is covered by the small circle will be 33.3%.
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