If x^2 + x = 1
what is (x^5 + 8)/ x+1

Answer:

One number is -6 and the other number is 7.

Step-by-step explanation:

Let x be one of the numbers and y be the other number.

So 8x + 5y = -13.

Also, x + y = 1

These two equations are the algebraic version of the words in the problem.

We need to solve this system of equations. You may be studying solving systems of equations using substitution or elimination method or even matrices. I will show you here using elimination method, sometimes called addition or subtraction method.

We need to multiply x+y=1 by -5.

-5(x + y = 1)

-5x - 5y = -5

We can stack the two equation and add them together to eliminate one of the variables.

8x + 5y = -13

-5x - 5y = -5

___________ Add.

3x = -18

3x = -18 Now divide by 3.

x = -6

Put thus value back into one of the original equations.

x = -6

x + y = 1

Substitute.

-6 + y = 1

Add 6.

y = 7

When one number is -6 and the other number is 7, then both equations will be true.

=========================================================

Explanation:

Let's evaluate what i^97 would be

First let's list out a few powers of i. Recall that [tex]i = \sqrt{-1}[/tex]

[tex]i^0 = 1\\\\i^1 = i\\\\i^2 = (\sqrt{-1})^2 = -1\\\\i^3 = i*i^2 = i*(-1) = -i\\\\i^4 = i*i^3 = i*(-i) = -i^2 = -(-1) = 1\\\\[/tex]

In short,

[tex]i^0 = 1\\\\i^1 = i\\\\i^2 = -1\\\\i^3 = -i\\\\i^4 = 1\\\\[/tex]

The sequence is: 1, i, -1, -i, 1, ...

The process repeats once we get to the fourth item. In other words, the process repeats every 4 terms.

So to quickly compute i^97, we'll divide the exponent by 4 to look at the remainder.

97/4 = 24 remainder 1

The remainder 1 means i^97 = i^1 = i

If we got a remainder 2, then it would be equal to i^2

Remainder 3 means it's equal to i^3, and so on.

-------------------

Here's another way to see why i^97 = i

i^97 = i^(96+1)

i^97 = i^96*i^1

i^97 = i^(24*4)*i

i^97 = (i^4)^24*i

i^97 = 1^24*i

i^97 = 1*i

i^97 = i

This helps verify the previous section. Though I recommend using the remainder trick as it's faster.

----------------------

So because i^97 = i, this means:

i^97 - i = i - i = 0

This is why 0 is the final answer (choice B).

Because the squared equation can have negative roots.

If the equation you're given already includes the squared variable (and you don't multiply by the variable yourself), then you don't need to worry about the extraneous root. Both solutions will be correct because the variable was already squared.

You only need to worry about the extraneous root in the case of a quadratic equation if you made the equation quadratic by multiplying by a variable. Any time you square a negative number or a variable (which may be negative), you risk losing information by making it positive. That means that, if you square a variable (especially for variables on both sides of the equation, which can easily hide a negative) or a negative number, you should always do a quick plug-in and check.

Because the squared equation can have negative roots.

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The expression of the statement is 1.06x

Expressions are mathematical statements that are represented by variables, coefficients and operators

The statement is given as

The price of an item plus 6% sales tax

Let the price of the item be x

So, we have the sales tax amount to be

Sales tax amount = x * 6%

Evaluate the product

So, we have

Sales tax amount = 0.06x

So, the total amount is

Total = x + 0.06x

Evaluate the sum

So, we have

Total = 1.06x

Hence, the expression of the statement is 1.06x

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Applying the sine ratio, the length of CD is calculated as: 12.687 cm.

The sine ratio is stated as:

sin ∅ = opposite length / hypotenuse length of a right triangle.

Use the Pythagorean theorem to find BC:

BC = √(AC² - AB²)

AC = 12 cm

AB = 6 cm

Plug in the values

BC = √(12² - 6²)

BC = √(144 - 36)

BC = √108

Find the length of CD using the sine ratio:

∅ = 55

Opposite length = BC = √108

Hypotenuse length = CD

Substitute

sin 55 = √108/CD

(CD)(sin 55) = √108

CD = √108/sin 55

CD ≈ 12.687.

Therefore, applying the sine ratio, the length of CD is calculated as: 12.687 cm.

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Answer:

1. 9/10 x 3 = 93/10

2. 9/8

Espero que esto ayude a tener un buen día!

14. Constant of variation, k = 3/2

15. The graph does not represent a direct variation.

16. Constant of variation, k = 1/4

17. Constant of variation, k = 1

A direct variation is a proportional relationship where variable x varies directly with variable y. The equation of a direct variation is modelled by the equation below:

y = kx.

k is the constant of proportionality of the relationship between x and y. It is also referred as the unit rate. On a proportional or direct variation graph, it can be determined by using any point on the graph (x, y) to find k.

k = y/x.

All graphs that represent direct variations passes through the origin (0, 0). The coordinate of the constant of proportionality of a direct variation graph is (1, k), where the constant of variation = k, and x = 1.

14. The graph passes through the origin (0, 0), so it represents a direct variation.

Constant of variation, k = 3/2

15. The graph does not pass through the origin (0, 0), so it does  represent a direct variation.

16. The graph passes through the origin (0, 0), so it represents a direct variation.

Constant of variation, k = 1/4

17. The graph passes through the origin (0, 0), so it represents a direct variation.

Constant of variation, k = 1

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Step-by-step explanation:

=5(2,47y)+5(-2,03)

=12.35y-10,15

(−∞,2)

Im just writting this bc the app said the answer was to short :)

Answer:

30°, 45° and 105°

Step-by-step explanation:

2 + 3 + 7 = 12 parts

180/12 = 15 degrees each part

First angle (2 parts)

2(15) = 30°

Second angle (3 parts)

3(15) = 45°

Third angle (7 parts)

7(15) = 105°

Hope this helps

The solution (B) x=79.

Rewriting the equation to find the solution -

(x+2)³/₄=27

Raising both sides of the equation with exponent ⁴/₃

((x+2)³/₄)⁴/₃ = 27⁴/₃

Cancelling the exponents on Left Hand Side of the equation. Writing the value on Right Hand Side of the equation in exponent form

x + 2 =  (3³)⁴/₃

Cancelling 3 on Right Hand Side of the equation

x + 2 = 3⁴

Solving Right Hand Side of the equation

x + 2 = 81

Shifting 2 to Right Hand Side of the equation

x = 81 - 2

Performing subtraction on Right Hand Side of the equation

x = 79

Hence, the solution is (B) x=79.

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Answer:

Step-by-step explanation:

Given:-

–2g2h2

To solve the given expression, we'll substitute g with -5 and h with 2:-

[tex]\sf -2\left(-5\right)2\left(2\right)2[/tex]

Apply the following rule :- (a) = a

Now, we can follow the PEMDAS order of operations:-

Multiply:-

Multiply -2 * -5 = 10:-

Multiply 10 * 2 = 20:-

Multiply 20 * 2 = 40

and finally multiply 40 * 2 = 80!

Therefore, your answer is 80!

_____________________

Hope this helps!

Have a great day!

Answer:

80

Step-by-step explanation:

give hope brainliest

The graph for the function h(x) = x² + 2x is given by the graph -

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

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Answer: See attached.

Step-by-step explanation:

        This function will be a parabola (shaped like a "U")because it is a quadratic function. A quadratic function is in the form of y = ax² + bx + c. Our a value is 1, our b value  is 2, and we do not have a c value.

How would we graph this?

        Since a = 1, our quadratic function has a "slope" of 1. This means that we will count up one and right one, and up one and left one from the vertex and plot those points.

        Next, our b value is 2. This means we move the graph left 2 points from the parent function (y = x²).

        Lastly, we do not have a c value, so the graph is not transformed ("moved") up or down.

Substitute the √2 with a letter a to expand the expression. Multiply individual components of the first bracket with the second bracket. Apply the index power rule to simplify raised numbers.

(1-2√2)(1+2√2) = (1-2a)(1+2a)

1(1+2a)-2a(1+2a) = 1+2a-2a-2a2a = 1+2a-2a-4a^2

a = √2,

1+2√2 -2√2 -4(√2 )^2 = 1-4( 2^1/2x2)

1-4(2) = 1-8

= -7

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Step-by-step explanation:

when lines are parallel gradiant should be the same in both equations

or m in y=mx+c

A)

1. y=-3x-6

2. y=-3x+6

therefore A is parallell

B)

1. y=44x+7/2

2.y=2/3x-17

therefore not parallel

c)

1. y=8x/7-17/7

2. y=-23x/21+30/21

therefore not parallel

d)

1. y=-8x/7+6

y=-7x/8-12

therefore not parallel

might have missed something-am tired. let me know if you have an issue.

Answer:

C.

Step-by-step explanation:

Answer:

  1

-------

mn³

Step-by-step explanation:

              ¹/₂

( m²n⁻⁶ )

-----------

( m⁴p⁰ )

( mn⁻³ )

-----------

( m² )

m - m² = m⁻¹

   1

--------

 mn³

I hope this helps!

The equation of the straight line passing through the point (3, 3)

which is perpendicular to the line y=-1/2x-4 is y= 2x-3

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation for a straight line is y = mx + c. (1)

The line is parallel to the equation y=-1/2 x-4 ....(2),

meaning that the value of m in equation (1) is 2 y = 2x + c

The needed line has the equation y= 2x-3 since it goes through the point (3,3) where 3=2(3)+c provides c=-3.

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The the simplified form of the given expression 12.5 - 31/2 + 1 1/4 is -7/4.

Hence, option D) -7/4 is the correct answer.

Given the expression in the question;

12.5 - 31/2 + 1 1/4

First, convert the mixed fraction into an improper fraction.

1 1/4 = ( 1×4 + 1 )/4 = ( 4 + 1 )/4 = 5/4

Now, rewrite the expression as;

12.5 - 31/2 + 5/4

Find the common denominator

( 12.5/1 × 4/4 ) - ( 31/2 × 2/2 ) + ( 5/4 × 1/1 )

( 12.5/1 × 4/4 ) - ( 31/2 × 2/2 ) + ( 5/4 × 1/1 )

Perform the multiplication operation

50/4 - 62/4 + 5/4

Now, combine the numerators over the common denominator.

( 50 - 62 + 5 )/4

( -12 + 5 )/4

( -7 )/4

-7/4

The the simplified form of the given expression 12.5 - 31/2 + 1 1/4 is -7/4.

Hence, option D) -7/4 is the correct answer.

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For x = 80 and y = 130, l and m will be parallel to j and n respectively.

If two lines are parallel, then the sum of the interior angles is supplementary.

Thus, if m || n, then (x - 30) and (x + 50) will be supplementary

⇒ (x - 30) + (x + 50) = 180

x - 30 + x + 50 = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 80

Thus, if x = 80, then k will be parallel to l

Now, if m || n, then y and (x - 30) must be supplementary

⇒ (x - 30) + y = 180

x - 30 + y = 180

we found that x = 80

⇒ 80 - 30 + y = 180

50 + y = 180

y = 180 - 50

y = 130

Thus, if y = 130 then, k will be parallel to l.

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Problem 37

We subtract 1 from all three parts to isolate the variable x.

-5 < x+1 < 4

-5-1 < x+1-1 < 4-1

-6 < x < 3 is the final answer

========================================================

Problem 40

Let's isolate the 3x portion first. To do this, we add 1 to all three sides.

2 < 3x-1 ≤ 6

2+1 < 3x-1+1 ≤ 6+1

3 < 3x ≤ 7

Then we divide all parts by 3 to fully isolate x.

3/3 < 3x/3 ≤ 7/3

1 < x ≤ 7/3 is the final answer

When the value of the variable x is greater than or equal to -3, the result returned by the even function is 3.

x=-1x=−1x, equals, minus, 1, Then the correct option is C.

A true function f(x) is an even function if the yield value of the function f(-x) is the same as the value returned by the function f(x) for all values of x that fall within the domain of f.

It is recommended that the equation be saved in an even function:

f(-x) = f(x)

Therefore

f(x) = f(3) = 3

Let's assume that f(x) is a function that always returns even. Then there is also

f(-3) = f(3) = 3

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CQ

Select all input values for which f(x)=3f(x)=3f, left parenthesis, x, right parenthesis, equals, 3.

Choose all answers that apply:

(Choice A)

A

x=-5x=−5x, equals, minus, 5

(Choice B)

B

x=-3x=−3x, equals, minus, 3

(Choice C)

C

x=-1x=−1x, equals, minus, 1

(Choice D)

D

None of the above

Answer:

C.

D.

Step-by-step explanation:

For right triangle has a line of symmetry two sides of the triangle have the same length and two angles of the triangle have the same measure.

A triangle is a three-sided polygon that consists of three edges and three vertices.

A right angle triangle is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.

If a right triangle has a line of symmetry then two sides of triangle will have same length and two angles are equal.

For a triangle to have a line of symmetry, it must be an isosceles triangle, meaning two of it’s sides and two of it’s angles must be the same.

From there it follows that for a right triangle to have a line of symmetry it must be an isosceles right triangle, meaning it must either have two 90-degree angles, or two identical non-90-degree angles.

Hence for right triangle has a line of symmetry two sides of the triangle have the same length and two angles of the triangle have the same measure.

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Answer:

no solution or -3=4

Step-by-step explanation:

Answer:

gdjsgsghdbdgdjdnvshskdndhdhdhdbbdbdhdhdhd

Answer:

The width, x, is in the interval (0, 7), or 0 < x < 7.

Step-by-step explanation:

width = x

length = 7x + 7

area = x(7x + 7)

x(7x + 7) < 392

7x² + 7x - 392 < 0

x² + x - 56 < 0

(x - 7)(x + 8) < 0

We have two points of interest on the number line:

-8 and 7

That makes three intervals of interest:

(-∞, -8), (-8, 7), (7, ∞)

Now we test a number from each interval.

Try -10:

(x - 7)(x + 8) < 0

(-10 - 7)(-10 + 8) < 0

(-17)(-2) < 0

34 < 0 False

Interval (-∞, -8) does not work.

Try 0:

(x - 7)(x + 8) < 0

(0 - 7)(0 + 8) < 0

(-7)(8) < 0

-56 < 0 True

Interval (-8, 7) works.

Try 10:

(x - 7)(x + 8) < 0

(10 - 7)(10 + 8) < 0

(3)(18) < 0

54 < 0 False

Interval (7, ∞) does not work.

Since we are dealing with a rectangle, the length and width must be positive numbers.

The interval (-8, 7) works mathematically for the width, but it must be limited to positive numbers, so the width must be in the interval

(0, 7)

The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.

Types of triangles are isosceles, scalene and equilateral triangles. Two angles are said to be complementary if their sum is 90 degrees.

Two triangles are said to be congruent if all their corresponding sides and angles are congruent. This means that the triangles have equal angles and equal sides.

The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

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