Consider the following functions. f1(x) = x, f2(x) = x2, f3(x) = 2x − 4x2 g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for c1, c2, and c3 so that g(x) = 0 on the interval (−[infinity], [infinity]). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {c1, c2, c3} = $$ Correct: Your answer is correct. Determine whether f1, f2, f3 are linearly independent on the interval (−[infinity], [infinity]).

Correct answer: y = [tex]\frac{1}{3}[/tex]x + 2

To find out the slope, you would need to remember this slope formula: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. We can use the two points provided on the graph to figure out the slope. We can label (3, 3) as [tex]x_{1}[/tex] and [tex]y_{1}[/tex], and (0, 2) as [tex]x_{2}[/tex] and [tex]y_{2}[/tex]. Now we can plug these numbers into the slope formula to find out the slope:

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] → [tex]\frac{2-3}{0-3}[/tex] → [tex]\frac{-1}{-3}[/tex] → [tex]\frac{1}{3}[/tex]

To find out the y-intercept, just substitute (3, 3) into the slope-intercept formula ( y = mx + b ) with the slope that is substituted for 'm' that we already solved earlier.

y = mx + b

(3) = [tex]\frac{1}{3}[/tex](3) + b

3 = 1 + b

2 = b

You can also prove this true by looking at the graph provided. The line intersects at the y-axis at 2.

Now we know that m = [tex]\frac{1}{3}[/tex] and b = 2, we can substitute it into the slope-intercept formula. Thus, the answer is y = [tex]\frac{1}{3}[/tex]x + 2.

Hope this helps you! Let me know if you have any more questions related to this problem.

Answer: 0.42857142857

Step-by-step explanation:

Answer:

It would be 93 remainder 3/the second one.

Engineering has many applications in our country focused on the construction and development of new technological devices.

Engineering is a term that refers to the set of scientific principles necessary to design and build machines, structures, and others such as:

Engineering is characterized by:

According to the above, engineering has many applications in the country such as:

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Answer:

Base= 6

Height= 10

Step-by-step explanation:

Area of triangle= ½ ×base ×height

Let the base be 3x and the height be 5x.

Given that the area is 30,

½ ×base ×height= 30

½(3x)(5x)= 30

Multiply both sides by 2:

3x(5x)= 60

15x²= 60

x²= 60 ÷15

x²= 4

Square root both sides:

[tex]x = \sqrt{4} [/tex]

x= 2

(reject x= -2 since length has a positive value)

Length of base

= 3x

= 3(2)

= 6

Length of height

= 5x

= 5(2)

= 10

Answer:

9. 31/2 or 15.5( I think that's the answer)

10. B

Step-by-step explanation:

Hi this is the answer and explaination

I'm sorry if it's incorrect

hope's it's help

The circumcenter of a circle with a radius of 7 cm is, 44cm.

Circumference is the distance around the perimeter of a circular object. It is defined as the length of the circle that is found by multiplying the diameter of the circle by π (pi), which is approximately equal to 3.14.

The formula for the circumference of a circle is given by: C = 2πr,

Given that,

The radius of circle = 7 cm

Substituting the given value of radius as 7 and using pi = 3.14,

we get:

Circumference = 2 × 3.14 × 7

                         = 43.96

Rounding this to the nearest whole centimeter, we get:

Circumference ≈ 44

Therefore, the circumference of the circle with a radius of 7 centimeters is approximately 44 centimeters.

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Answer:

f×3-f×(-3)

3f+3f

solution:

6f

Step-by-step explanation:

hope it's can help

Answer:

Step-by-step explanation:

solution 1:

570 not man = 15% (cause 100% - 85%)

15% = 570

100% = w (for "whole package")

15w = 100 * 570

15w = 57000

w = 57000 / 15

w = 3800

solution 2:

15% = 570

85 = m (for "men)

15m = 570 * 85

15m = 48450

m = 48450 / 15

m = 3230

100% = 85% + 15%

100% = b (for "buch of people")

b = 3230 + 570

b = 3800

Answer:

(0,2) x (3,-2)

Step-by-step explanation:

Answer:

A and E

Step-by-step explanation:

The given problem shows a graph of a vertical line with an undefined slope, in which its equation is x = 3 (which matches Option A).

It is not considered a function because it has the same input for every given output.  This means that regardless of its y-coordinate, its corresponding x-coordinate will always be x = 3.  

The Vertical Line Test allows us to know whether or not a graph is actually a function. Remember that a function can only take on one output for each input. We cannot plug in a value and produce two output values.  Since the graph represents a vertical line, it automatically fails the vertical line test. Therefore, it is not a function.

Because it is not a function, Options B, C, and D are invalid answers.

Hence, the correct answers are Options A and E.

Answer:

232

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope intercept form is like so:

y = mx + b

mx is the slope

b is the y-intercept

Now in your equation:

y = 0.25x + 2

0.25x is the slope

2 is the y-intercept

Answer:

No pictures so can't help ya.

Answer:

800

Step-by-step explanation:

Hope this helps

Answer:

800, if it's higher than 50 you can round it to the next hundred

Composite number? I’m not sure if that’s what you’re working on but it’s a true statement.

Answer:

[tex] {x}^{2} - 4x + 9 = 0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-( - 4)\pm\sqrt{( - 4)^2-4(1)(9)}}{2(1)} \\x=\frac{ 4\pm\sqrt{ 16-36}}{2} \\ x=\frac{ 4\pm\sqrt{ - 20}}{2} \\ x=\frac{ 4\pm2i\sqrt{ 5}}{2} \\ x = 2\pm \: i\sqrt{ 5} \\ D = {b^2-4ac} \\D = { 16-36} \\ = - 20 < 0 \rightarrow \: x \in \: \mathbb{C} \: \\ x \: is \: complex [/tex]

Answer:

71/44

Step-by-step explanation:

Here the LCD is the product of the two denominators given:  11*8 = 88.

We rewrite 4/11 as 32/88 and 10/8 as 110/88.  Now the denominators are the same.

Combine  32/88 and 110/88.  We get the sum  142/88, which reduces to 71/44.

Answer:

-39/44.

Step-by-step explanation:

We need to find the lowest common multiple of 11 and 8.

This is 88.

Now to convert the 2 fractions to denominator 88 we multiply first by

8/8 and the second by 11/11:

4/11 - 10/8

= 32/88 - 110/88

= -78/88

= -39/44

Answer:

1.46%

Step-by-step explanation:

Pretend you have a number as a test dummy. We'll go with 100 for simplicity. A 14% increase to 100 would be 114. Then we can decrease 114 by 11%. We can find 11% of 114 with an equation like so: x/114 = 11/100. We can then cross multiply to get this" 100x = 1254, which can be simplified to x=12.54. Now, we can subtract 12.54 from 114, which will get us 101.46. Because percentage is based on 100, we can simply subtract 100 from 101.46, which gives us 1.46. So, the answer is 1.46%.

Hope this helps have a great day!!!!!

The number of student taking math is 37 while the number of students taking programming is 74

Universal set = 97

let

The number taking math = x

The number taking programming = 2x

The number of students that take exactly one subject = 53

The student taking neither of the subject = 15

The number of students taking only maths will be

The number of students taking only programming will be

let

n(m ∩ p) = y

Therefore,

x - y + 2x - y = 53

3x - 2y = 53

Also,

97 = x + 2x - y + 15

3x - y = 82

Therefore,

3x - 2y = 53

3x - y = 82

-y -(-2y) = 82 - 53

y = 29

3x - 29 = 82

3x = 82 + 29

3x = 111

x = 111/3

x = 37

Finally,

number of students taking maths = 37

number of student taking programming = 37×2 = 74

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Answer:

irrational numbers integers

Answer:

C. -4/3

Step-by-step explanation:

Parallel lines have the same gradient (steepness) and this means that they will never intersect.

Hope this helps!

The slope of the red line will be {m} = - 4/3.

The general equation of a straight line is -

y = mx + c

where -

{m} is the slope of the line.

{c} is the {y} - intercept.

Given is that the straight lines graphed below are parallel.

The slope of the red line could be calculated from the points through which the line passes. The points are : (- 3, 0) and (0, 4).

{m} = (- 4 - 0)/(0 + 3)

{m} = - 4/3

Since the lines are parallel, we can write the slope of the green line as same as that of the red line.

Therefore, the slope of the red line will be {m} = - 4/3.

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Answer:

hiik

Step-by-step explanation:

rvnlgsudffstdrestdftuisffjhigyhoffyxhcccdfidsudjifg

Answer:

Step-by-step explanation:

Pythagorean Theorem Formula: a² + b² = hypotenuse²

x² + 5² = 13²

x² + 25 = 169

x² + 25 - 25 = 169 - 25 (subtract 25 in both sides)

x² = 169 - 25

√x² = √144

x = 12

Answer:

r = -9

Step-by-step explanation:

the less the negative number is the more it is .

Answer:

3^18

Step-by-step explanation:

Hope it helps

Answer:

3^3

Step-by-step explanation: