Solve the system of equations by substitution - 5x+8y= -86
y=6x-43 ​

9514 1404 393

Answer:

  a) f(-2.5) = 62.6875; f(-1.5) = -13.0625; (-2.5, -1.5) contains a real root

  b) there are 1 each of positive and negative real roots; 2 complex roots

  c) -2 and 1/3 are the rational real roots

  d) x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}

Step-by-step explanation:

a) f(-2.5) = 62.6875; f(-1.5) = -13.0625. The function changes sign between -1.5 and -2.5, so there is a real root in that interval.

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b) The given coefficients have one sign change, so there is one positive real root. Changing the signs of odd-degree terms makes the signs + - + - -, so there are three sign changes. There are 1 or 3 negative real roots, and possibly 2 complex roots. The constant term is non-zero, so zero is not a root. Here's your table:

  positive real roots: 1

  negative real roots: 1 or 3

  complex roots: 2 or 0

  zero roots: none

The graph is attached. It shows 2 real roots, one positive and one negative, so there are 2 complex roots. (There are 4 roots in total, so if only 2 are real, the other 2 are complex.)

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c) Possible rational roots are of the form ...

  ±{1, 2}/{1, 3, 9}

Listed, they are ...

  ±{1/9, 2/9, 1/3, 2/3, 1, 2}

The actual real roots are -2 and 1/3.

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d) The graph shows the real roots to be -2 and 1/3. The original leading coefficient of 3 is the product of the leading coefficients of the factors. Writing the factor (x -1/3) as (3x -1) lets us reduce the leading coefficient of the quadratic term from 9 to 3. The result of dividing factors (x+2) and (3x-1) from the original function is shown in the attachment. It is a parabola with vertex (-1/3, 2/3), so the factorization is ...

  f(x) = (x +2)(3x -1)(3(x +1/3)² +2/3)

The roots of the quadratic term are ...

  3(x +1/3)² = -2/3

  x +1/3 = ±√(-2/9)

  x = (-1 ±i√2)/3

So, the entire list of roots is ...

  x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}

_____

Additional comment

The roots of a quadratic are easily found by knowing its leading coefficient and its vertex. If factoring known real roots from a higher-degree polynomial results in a quadratic, then the remaining complex roots are easily found. A graphing calculator is a wonderful tool for this process.

Answer: Yes!

Step-by-step explanation:

Yes, graphite is composed of 100%carbon. With this, can we say that graphite is an element or compound of carbon? Compound is composed of two or more elements combined in a substance in definite proportions, in the form of molecules held together by chemical bonds.

Answer:

The constant proportionally of the graph is:

Step-by-step explanation:

We know that when 'y' varies directly with 'x', we get the equation

y ∝ x

y = kx

k = y/x

here 'k' is called the constant of proportionality.

From the graph, it is clear that:

at x = 0.5, the value of y = 4

so substituting x = 0.5 and y = 4 in the equation

k = y/x

k = 4/0.5

k = 8

at x = 1, the value of y = 8

so substituting x = 1 and y = 8 in the equation

k = y/x

k = 8/1

k = 8

Therefore, the constant proportionally of the graph is:

Answer:

[tex]42x^{2}[/tex]

Answer:

y = 15 m<a = 78 m<b = 68

Step-by-step explanation:

(5y+3) + (4y+8) --> 9y + 11

9y + 11 = 146

y = 15

plug in 15 into the equations for the angles and you get

m<a = 78

m<b = 68

Answer:

Use the BODMAS method and at the end work the fraction left by adding it to 15

My answer was 15.274

Answer:

8

Step-by-step explanation:

so my school uses the method called kcf (keep change flip)

keep the 4

change the division sign to a multiplication sign

flip 1/2 to 2/1

4x2=8

Answer:

8 i first said two but used a caculater and found out it was 8

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Let's solve your equation step-by-step.

−6+7x=50

Step 1: Simplify both sides of the equation.

7x−6=50

Step 2: Add 6 to both sides.

7x−6+6=50+6

7x=56

Step 3: Divide both sides by 7.

7x/7 = 56/7

x=8

have a wonderful day

Answer:

Step-by-step explanation:

Left figure:

area of rectangle = 4×6 = 24 cm²

area of triangle = ½×(base of triangle)×(height of triangle) = ½×6×4  = 12 cm²

area of shape = 24+12 = 36 cm²

Right figure:

area of rectangle = 6×8 = 48 m²

area of triangle = ½×(base of triangle)×(height of triangle) = ½×8×(8-6) = 8 m²

area of shape = 48+8 = 56 m²

9514 1404 393

Answer:

  84 = j × 7

Step-by-step explanation:

A product results from multiplying two numbers. Here, the two numbers are said to be "Julie's score" and 7. "Julie's score" is represented by j, so the product is ...

  j × 7

Then the translation can be ...

  84 is the product of j and 7

  84 = j × 7

__

In algebra, we can indicate a product without the multiplication symbol, simply by writing the factors next to each other. Generally, we write the numeric factor first:

  84 = 7j . . . . another way to write the answer

Note that this latter method does not seem to appear in the forms available for your answer box.

Answer:

The correct answer will be $725

Answer:I believe it is $725

Step-by-step explanation: 12.50(1+0.16)

= 14.5 then 14.5 times 50 = 725

Hello! :)

[tex]\large\boxed{A = 32.5cm^{2}}[/tex]

We can use the following area to solve for the area of the trapezoid pictured:

[tex]A = \frac{1}{2}(b_{1} + b_{2})h[/tex]

Where:

h = height

b1 = bottom base

b2 = top base

Plug in the given values:

[tex]A = \frac{1}{2}(9 + 4)(5)[/tex]

Simplify:

[tex]A = \frac{1}{2}(65)\\\\A = 32.5 cm^{2}[/tex]

Answer:  10

Step-by-step explanation:  

(5 x 18) / 9 = 90/9 = 10

Answer:

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

The option B i.e.(1,6), (2,7),(4,9), (0,5) represents the function.

Step-by-step explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

Checking option A:

(2, 4), (0, 2), (2, -4), (5,3)

Here, the input x = 2 is repeated twice.

Thus, option A does not represent the function as the input x = 2 is duplicated and we can not have duplicated inputs as there should be only 1 output for each input.

Checking option B:

(1,6), (2,7),(4,9), (0,5)

It is clear that no input value is repeated. In other words, each input or x-value of the X set has a unique y-value or output of the Y set.

Thus, the option B represents the function.

Checking option C:

(0, 2), (2, 3), (0, -2), (4,1)

Here, the input x = 0 is repeated twice.

Thus, option C does not represent the function as the input x = 0 is duplicated and we can not have duplicated inputs as there should be only 1 output for each input.

Checking option D:

(1, 2), (1, -2), (3, 2), (3, 4)

Here, the input x = 1 is repeated twice, and also x = 3 is repeated twice,

Thus, option D does not represent the function as we can not have duplicated inputs as there should be only 1 output for each input.

Conclusion:

The option B i.e.(1,6), (2,7),(4,9), (0,5) represents the function.

Add the two houses together:

135000 + 160000 = 295,000

Multiply the total by the percentage:

295,000 x 0.06 = $17,700

He earned $17,700

Answer:

-4

Step-by-step explanation:

3x-2(6-x)=7x+2(5+x)-6

First, distribute.

3x+ −12+ 2x = 7x + 10 + 2x −6

Combine like terms on each side.

5x − 12= 9x + 4

To solve for x, pick a side to solve. I will solve the right x.

5x - 12 = 9x + 4

-5x         -5x

-12 = 4x + 4

Subtract 4 to isolate the variable.

-16 = 4x

Divide 4.

-4 = x

The triangles are classified below.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

An equilateral triangle is a triangle where all three sides are equal.

The right triangle is a triangle where one angle is 90 degrees.

An isosceles triangle is a triangle where two sides are equal.

An obtuse triangle is a triangle where the angle is greater than 90 degrees

An acute triangle is a triangle where the angles are less than 90 degrees.

A scalene triangle is a triangle where all three sides are different.

Now,

Side 5 cm, 5 cm, 5 cm, and 5 cm is an equilateral triangles.

Since all the sides are the same.

Sides of 3 cm, 5 cm, and 5 cm is an isosceles triangle.

Since the two sides are the same.

Sides of 3 cm, 5 cm, and 7 cm is a scalene triangle.

Since all three sides are different.

Angles of 40°, 50°, and 90° is a right triangle.

Angles of 40°, 60°, and 80° is an acute triangle.

Angles of 40°, 40°, and 100° is an abtuse triangle.

Thus,

The triangles are classified above.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ5

Answer:

Check question number 9 in that file you may be able to understand the problem

Step-by-step explanation:

Answer:

keith buy 11 pencils at the cost of 165 paise

Step-by-step explanation:

6 pencils cost = 90 paise

so 1 pencil cost = 15 paise

Answer:

36%= 9/25 in fraction form (:

Answer:

36/100 sorry if wrong

Step-by-step explanation:

Answer:

5m^2

Step-by-step explanation:

Given data

Length of board= 2.50m

Width of board= 2m

The cover need should have the same area as the board

Area= Length*Width

Area= 2.5*2

Area=5m^2

Hence the area of the cover is 5m^2

Answer:

19

Step-by-step explanation:

Answer:

19

Step by step explanation:

Answer:

discrete, the class boundaries are;

16 - 25

26 - 35

36 - 45

46 - 55

56 - 65

66 = 75

continuous, the class boundaries are;

16 to less than 26

26 to less than 36

36 to less than 46

46 to less than 56

56 to less than 66

66 to less than 76

Step-by-step explanation:

Given that;

Range of the dataset = maximum value - minimum value = 74 - 16 = 58

total number of data set n = 50

Rule : [tex]2^{k}[/tex] ≥ n

substitute value of n

[tex]2^{k}[/tex] ≥ 50

k × log(2) = log( 50 )

k × 0.3010 = 1.69897

k = 1.69897 / 0.3010

k = 5.64

Hence, we have a total of 6 number of classes needed to be constructed.

so,

class width = 74 - 16 / 6 = 58 / 6 = 9.67

If the Data is discrete, the class boundaries are;

16 - 25

26 - 35

36 - 45

46 - 55

56 - 65

66 = 75

If the Data is continuous, the class boundaries are;

16 to less than 26

26 to less than 36

36 to less than 46

46 to less than 56

56 to less than 66

66 to less than 76

Answer:

C.

Step-by-step explanation:

There's no problem for now but it still needs to be monitored in case something might happen.

Answer: C. g^(-1) (x)= 1/(x+ 2)

Step-by-step explanation:

y=1/x-2

x=1/y-2

1/y-2=x

1/y=x+2

1=(x+2)y

1=xy+2y

xy+2y=1

(x+2)y=1

y=1/(x+2)

answer: g^(-1) (x)= 1/(x+ 2)

-39/100 is the answer according to me ..

Plz mark me as brainliest if u found it helpful