for which values of (A) the system has at least one solution

For Which Values Of (A) The System Has At Least One Solution

Answers

Answer 1

Answer

The values of a that ensures that the system has at least one solution is

a > (21/127)

Explanation

We are told to find the values of a that ensures that the system has at least one solution. The system of equations include

3 (a - 5x) < 1 + x

2 - (x/2) > 3 + 5 (x - a)

To do this, we need to solve the expressions

3 (a - 5x) < 1 + x

3a - 15x < 1 + x

We can rewrite this as

1 + x > 3a - 15x

x + 15x > 3a - 1

16x > 3a - 1

Divide both sides 16

[tex]\begin{gathered} \frac{16x}{16}>\frac{3a-1}{16} \\ x>\frac{3a}{16}-\frac{1}{16} \end{gathered}[/tex]

We then solve the second one. But to do this, let's multiply through by 2

2 - (x/2) > 3 + 5 (x - a)

4 - x > 6 + 10 (x - a)

we can rewrite as

6 + 10 (x - a) < 4 - x

6 + 10x - 10a < 4 - x

10x + x < 10a - 6 + 4

11x < 10a - 2

Divide both sides by 11

[tex]\begin{gathered} \frac{11x}{11}<\frac{10a-2}{11} \\ x<\frac{10a}{11}-\frac{2}{11} \end{gathered}[/tex]

The two solutions are

x > (3a/16) - (1/16)

x < (10a/11) - (2/11)

To find a lasting solution, we need the inequality sign to be the same, so, we need to multiply through one of the equations by -1

x > (3a/16) - (1/16)

-x < (-3a/16) + (1/16)

So, the system of equations become

-x < (-3a/16) + (1/16)

x < (10a/11) - (2/11)

We can then add the two equations

-x + x < (-3a/16) + (1/16) + (10a/11) - (2/11)

0 < (-3a/16) + (10a/11) + (1/16) - (2/11)

0 < -0.1875a + 0.9091a + 0.0625 - 0.1818

0 < 0.7216a - 0.1193

Rewrite

0.7216a - 0.1193 > 0

0.7216a > 0.1193

Divide both sides by 0.7216

(0.7216a/0.7216) > (0.1193/0.7216)

a > 0.1653

a > (21/127)

Hope this Helps!!!


Related Questions

Inverse & Composition of Functions
1. Find the inverse of f(x) = x² + 2

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Answer: √x−2,−√x−2

Step-by-step explanation:

Find the 9th term of the geometric sequence 4, -16, 64, ...

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Answer:

4 to the 9th power :D

Step-by-step explanation:

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Carter has 60 balloons , of the balloons are black, and is of the balloons are white. The rest of theballoons are red. How many red balloons Carter has? Show your calculations in the space provided

Answers

we have 60 balloons

black balloons are =4/12*60

and that is =20 black balloons

red balloons= 3/12*60=5*3=15

the rest are white

white balloons= 60- 20 black-15 red=25 white balloons

Christine gets $71 for working the weekend. She buys $53 in clothes and then
makes another $45 babysitting. How much does she have now?

Answers

Answer:

63 i think!

Step-by-step explanation:

71-53 is 18. 18+45 is 63!

Im so so so sorry if im wrong, have a nice day friend!: )

It’s 71-53=18
18 +45=63 dollar left


A cylinder with a radius of 1 yd and a height of 2 yd

Answers

The volume is 6.28 yard

Navy paint is made by mixing 8 cups of blue paint with 2 cups of black paint. If he only has 1 cup of blue pain, how much black paint should he use?

Answers

For 1 cup of blue paint, 1/4 cups of black paint is needed

How to determine the amount of black paint?

The given parameters are

8 cups of blue paint needed for 2 cups of black paint

This means that

8 cups of blue paint needed = 2 cups of black paint

Divide both sides of the equation by 8

So, we have the following equation

8/8 cups of blue paint needed = 2/8 cups of black paint

Evaluate the quotient

So, we have the following equation

1 cup of blue paint needed = 1/4 cups of black paint

Hence, the amount of black paint is 1/4

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all the odd numbers from 51 to 5001 are written what is the total number of digits used

Answers

Answer:

9404 digits

Step-by-step explanation:

The numbers written:

51, 53, 55, 57, 59, . . . 97, 99 [5*5=25 numbers; 50 digits]

101, 103, 105, . . . 997, 999 [9*50=450 numbers; 1350 digits]

1001, 1003, 1005, . . . 4997, 4999, 5001 [40*50+1=2001 numbers; 8004 digits]

Total:

50 + 1350 + 8004 = 9404 digits

Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. Work out the probability that tina takes two blue counters in fraction.

Answers

Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. The probability that tina takes two blue counters in fraction is 15/72

What is the probability?

Given parameters:

Bag A= 5 red + 3 blue

Bag B = 4 red + 5 blue

Hence,

Total counters in bag A = 5 +3 = 8

Total counters in bag B = 4 + 5 = 9

Now let determine the probability that she takes two blue counters

Probability =  3 /8 × 5 /9

Probability = 15 / 72

Therefore 15 / 72 is the probability that two blue was taken.

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What is the completely simplified form of the expression 2(1 - 3x) - (5x + 1)?

A) -11x + 1
B) -8x + 1
C) -11x + 3
D) -8x + 3

Answers

Answer:

A

Step-by-step explanation:

2(1-3x)-(5x+1)

=2-6x-5x-1

=1-6x-5x

=1-11x/-11x+1

The amount of vinegar that melody used for a recipe can be written as a whole number which could be the amount of vinegar that Melody used?A. -3.75 tspB. 1.5 tspC. 2 1/3 tspD. 12/3

Answers

Given:

The amount of vinegar that melody used for a recipe can be written as a whole number.

So, we will check the options to find which one represents a whole number

The whole number does not contain numbers after the decimal point and also the denominator will be 1

So, the answer is option D) 12/3 = 4

Justin places a bet on the giants to win the superbowl. the odds are 2:3. a) Are the giants expected to win? why or why not?b) Find P(Giants win)=

Answers

To convert the odds to a probability, we can divide the odds by one plus the odds.

then, in this case we have the following:

[tex]\begin{gathered} \text{odds:} \\ 2\colon3=\frac{2}{3} \\ \Rightarrow1+\frac{2}{3}=\frac{5}{3} \end{gathered}[/tex]

then, we have that the probability is:

[tex]\frac{\frac{2}{3}}{\frac{5}{3}}=\frac{2\cdot3}{5\cdot3}=\frac{2}{5}[/tex]

thus, the probability that the Giants will win the superbowl is 2/5=0.4=40%

As we can see, we cannot expect for sure that the giants will win

Pls help me with this ill give brainlist

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What’s the question?

Find the value of x in the diagram. ΔPQR ~ ΔSTU

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X is 12.5 by using cross multiplication.

determine the domain of each function yx-3x=3y-1

Answers

Domain of the given function yx-3x=3y-1 is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3}.

What is a domain?

The dependent variable and the independent variable are the two types of variables used to define a function.

The domain of a function is a set of all possible values of x which is an independent variable. For example The domains of function f(x)=x² can be all real numbers.

Despite x=0, the domain of g(x)=1/x can contain any real number.

The input values to a function are referred to as domains, while the output values are referred to as the range. The data flow is as follows:

Domain → Function → Range

We are aware that the value of x is the function's domain. Therefore, the domain is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3} for the provided function.

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The proportion of a population with a characteristic of interest is p = 0.37. What is the standard deviation of the sampling distribution when the sample size is 1,600?

Answers

The standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 is equal to 0.0121.

What is a sample proportion?

A sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.

Mathematically, sample proportion can be calculated by using this formula:

[tex]\hat{p} = \frac{x}{n}[/tex]

Where:

x represent the number of individuals with a specified characteristic.n represent the total number of individuals in a sample.

In Mathematics, the standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 can be calculated by using this formula:

Standard deviation (SD) = √(p(1 - p)/n)

Substituting the given parameters into the formula, we have;

Standard deviation (SD) = √(0.37(1 - 0.37)/1,600)

Standard deviation (SD) = √(0.37(0.63)/1,600)

Standard deviation (SD) = √(0.2331)/1,600)

Standard deviation (SD) = √0.0001457

Standard deviation (SD) = 0.0121.

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If 3 dogs eat 4 pounds of food per day, how many dogs eat 15 pounds of food?

Answers

11 dogs will eat 15 pounds of food.

According to the question,

We have the following information:

3 dogs eat 4 pounds.

We have to find how many dogs will eat 15 pounds.

We have the following expression:

4 pounds = 3 dogs

We can treat dog as a non-living object or a product.

So, we can find the parts devoted to 1 pound:

1 pound = 3/4

Now, we have to find the same for 15 pounds:

15 pounds = (3/4)*15

15 pounds = 11.25

Now, note that the number of dogs can not be in points. So, we will round it off to form a whole number.

So, 15 pounds = 11 dogs

Hence, 15 pounds of food is enough for 11 dogs.

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following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed

Answers

Points which would fall on the line produced by the point-slope form equation y - 3=1/2(x - 7) when graphed are as follow:

c. (1,0)

d. (3, 1)

As given,

Equation of given line

y - 3=1/2(x - 7)

Points which would fall on the line produced by the point-slope form:

a.(0,1)

x=0

y-3=1/2(0-7)

⇒ y=-1/2

b.(1,-1)

x=1

y-3=1/2(1-7)

⇒y=0

c.(1,0)

x=1

y-3=1/2(1-7)

⇒y=0

Required point

d.(3,1)

x=3

y-3=1/2(3-7)

⇒y=1

Required point

Therefore, points which would fall on line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed are as follow:

c. (1,0)

d. (3, 1)

The complete question is :

Which of the following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed?

a. (0,1)      b. ( 1,-1)       c. (1,0)       d. (3,1)

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Plllsss help answer the question in the picture below!!!!!

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The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.

What is the difference between standard deviation and histogram?

It always displays the median and the middle 50% of the data. For data displayed in histograms, a similar spread measurement is helpful. The term for it is the standard deviation. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.

The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The sum of the bar heights is therefore one. Only discrete variables (right), where the histogram heights now total to unity, are suitable for relative frequency analysis.

A measurement of how far points deviate from the mean is the standard deviation. The first histogram includes fewer points that are close to the mean and more points that are distant from the mean (scores of 0, 1, 9, and 10). (scores of 4, 5 and 6). As a result, its standard deviation will be higher.

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2) A toy store is having a sale on puzzles. For each puzzle, Naomi buys she
gets 75% off of a second puzzle. The original price of each puzzle is
$16.50. Naomi bought 4 puzzles. How much did she spend?

Answers

Naomi bought 4 puzzles and she spend total $21.91

What is percentage?

The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.

Given that : A toy store is having a sale on puzzles. For each puzzle, Naomi buys she gets 75% off of a second puzzle. The original price of each puzzle is $16.50. Naomi bought 4 puzzles

Naomi first puzzle price is $16.50

she get 75% off on as second puzzle

=[tex]16.50(\frac{75}{100} )[/tex]

=12.375

=16.50 - 12.375

= 4.125

So , second puzzle price is 4.124

=[tex]4.125(\frac{75}{100} )[/tex]

=3.09

= 4.125 - 3.09

=1.03

So , third puzzle price is 1.03

=[tex]1.03(\frac{75}{100} )[/tex]

=0.7725

=0.2575

So ,fourth puzzle price is 16.50+4.124+1.03+ 0.2575

=21.91

Total naomi spend 0.2575

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find the ratio of the boxes and the circles there are 7 boxes and 10 circles

Answers

The ratio of boxes to the circles is 7: 10

two trains travel at a constant speed. Train a travels 1400 miles in 5 hours and train b travels 2100 miles in 7 hours. Which train travels faster?

Answers

Train b

Explanation: 1400 divided by 5 times by 7= 1960 miles

45.6 divided by 0.03

Answers

Answer:

1,520

Step-by-step explanation:

classify the system as "consistentdependent", "consistent independent", or "inconsistent". choose the best description of its solution. if the system hs exactly one solution give it solution.

Answers

The solution of a system is the point where the lines described by the equations of the system intersect, If a system has no solution, it is said to be inconsistent, In this case, both lines have the same slope (-3/2) which means that they are parallel each other, then they will never intersect, and the system has no solution and is inconsistent

State the zero(s) of the function.
f(x) = x³ - 2x² - x + 2
O a
O b
Ос
Od
1 and 2
-1, 1, and 2
-1, 0, and 1
-2, -1, and 1

Answers

Answer:

-1, 1, and 2

Step-by-step explanation:

[tex]x^3 - 2x^2 - x+2=0 \\ \\ x^2(x-2)-(x-2)=0 \\ \\ (x^2-1)(x-2)=0 \\ \\ (x-1)(x+1)(x-2)=0 \\ \\ x=-1, 1, 2[/tex]

URGENT!!!!!!!!!
Thank you to whoever solves it right!

Answers

Answer:

D

Step-by-step explanation:

The plane was at 24,000+ feet above the ground and then it ROSE (indicating an addition of feet to the original) 7,00+ feet.

Hope that helps

Can you please explain? I have the other options also.

Answers

Given

[tex]f(x)=\frac{1}{3}\lvert x+4\rvert-4[/tex]

The graph

Which number is equivalent to 3^(4)÷3^(2)

Answers

Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

This problem comes straight from a standardized test given in New York in 2014.

Find the volume of the cone, use 3 for π

Answers

Given:

Cone with diameter of 14 ft, and height of 4 ft.

First, determine the radius of the cone, by dividing the diameter by 2.

[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{14\text{ ft}}{2} \\ r=7\text{ ft} \end{gathered}[/tex]

Now that we have the radius, substitute π = 3, r = 7 ft, and h = 4 ft to the formula of the volume of the cone.

[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{(3)(7\text{ ft})^2(4\text{ ft})}{3} \\ V=\frac{3(49\text{ ft}^2)(4\text{ ft})}{3} \\ V=\frac{588\text{ ft}^3}{3} \\ V=196\text{ ft}^3 \\ \\ \text{Therefore, the volume of the cone is }196\text{ ft}^3. \end{gathered}[/tex]

13. The model represents an equation. 1 1 1 1 À AC X DOOD D0000 solue.) What value of x makes the equation true? 15.

Answers

Answer:

The equation is true when x = 2.25

Explanation:

On the left side of the equation, there are 3 triangles with value -x and 10 triangles with value 1. So, the expression for the left side of the equation is:

3*(-x) + 10*(1)

-3x + 10

For the right side, we have 5 triangles with value x and 8 triangles with value -1. So, the expression for the right side is:

5*x + 8*(-1)

5x - 8

Now, we can write the equation as:

-3x + 10 = 5x - 8

So, solving for x, we get:

-3x + 10 + 3x = 5x - 8 + 3x

10 = 8x - 8

10 + 8 = 8x - 8 + 8

18 = 8x

18/8 = x

2.25 = x

Therefore, the equation is true when x is equal to 2.25

Tickets of a program at college cost $4 for general admission or $3 with a student ID. If 181 people paid to see a performance and$616 was collected, how many of each type of ticket were sold?In a program at college tickets ?were sold for general admission and?tickets were sold with a student ID.

Answers

Tickets were sold for a program at a college .It cost $4 for general admission or $3 with a student ID.

Let

number of people that used student ID = x

number of people that used the general admission cost = y

[tex]x\text{ + y = 181}[/tex][tex]3x\text{ + 4y = 616}[/tex][tex]\begin{gathered} x+y\text{ = 181} \\ 3x+4y=616 \\ x=181-y \\ 3(181-y)+4y\text{ = 616} \\ 543-3y+4y=616 \\ y=616-543 \\ y=73 \\ x+73=181 \\ x=181-73 \\ x=108 \end{gathered}[/tex]

108 used the student ID ticket while 73 used the general admission ticket .

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