Solve each equation.
2⁵x⁺¹=32

Answer:

gdjsgsghdbdgdjdnvshskdndhdhdhdbbdbdhdhdhd

(−∞,2)

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

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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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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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

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

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).

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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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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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

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

The angles which form a linear pair are 40° and 140°.

Linear pair is defined as the pair of angles which add up to 180 degrees.

When two straight lines intersect with one another then 4 angles are formed. Any two adjacent angles thus formed are a linear pair.

Let us consider one angle be x . Now another angle is 3.5 times this angle.

Therefore measure of second angle = 3.5x

Now if these two angles are a linear pair then their sum will be equal to 180°.

Therefore we can form a linear equation in x and solve to get the values of the angles.

∴3.5x + x = 180°

or, 4.5x = 180°

or, x = 180 ÷ 4.5

or, x = 40°

Measure of the second angle = 3.5 × 40° = 140°

Hence the two angles which form a linear pair are  40° and 140° .

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Based on the fact that Sierra wants to purchase a M dozen muffins and B boxes of cinnamon, the inequality to show how many items Sierra can buy is 3.50M + 4.25B ≤ 25

The amount that Sierra can spend at most is $25 which means that the boxes of cinnamon buns and the muffins should not exceed this $25.

The cost of the muffins is $3.50 each so the representation is:

= 3.50M

The cost of the cinnamon buns is 4.25B which can be represented as:

= 4.25B

The inequality is therefore:

3.50M + 4.25B ≤ 25

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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

Answer:

C.

Step-by-step explanation:

Using factorization, the factors of 2 x²+x-28 are x = - 4 and x = 7/2

The factorization approach simplifies any algebraic or quadratic equation by using the fundamental factorization formula, which represents the equations as the product of factors rather than extending the brackets. Any equation may have an integer, a variable, or the algebraic expression itself as a component.

Given equation is -

2 x²+x-28

we will use the method of factorization.

⇒ 2x² + 8x -7x -28

⇒ 2x(x+4) - 7(x+4)

⇒ (x+4) (2x - 7)

⇒ x = -4 and x = 7/2

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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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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.

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!

Answer:

True I think yes goodluck

Answer:

option D for you I have brainly plus and that's the answer I got.

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.

Answer:

see below

Step-by-step explanation:

solve for y

y-4/x = a

Add 4x to each side

y-4/x+4/x = a+4x

y =  a+4x

If the equation is

(y-4)/x = a

Multiply each side by x

(y-4)/x *x = a*x

y-4 = ax

Add 4 to each side

y = ax+4

Answer:

y = a + 4/x

Step-by-step explanation:

-add 4/x to both sides: y - 4/x + 4/x = a + 4/x

- simplify: y = a + 4/x

The exponential function that has a y-intercept of (0, 3) and passes through the point (2, 48) is y = 3 · 1.386ˣ.

Herein we are asked to derive the exponential formula of the form y = a · bˣ that has a y-intercept of (0, 3) and passes through the point (2, 48). By using logarithm properties, the expression can be modify into this linear-like expression:

㏑ y = ㏑ a · bˣ

㏑ y = ㏑ a + x · ㏑ b

By substituting x and y, we find the following system of equations:

㏑ 3 = ㏑ a                              (1)

㏑ 48 = ㏑ a + 2 · ㏑ b           (2)

By (1):

a = 3

(1) in (2):

㏑ 48 = ㏑ 3 + 2 · ln b

㏑ b = (1 / 2) · ㏑ (48 / 3)

b ≈ 1.386

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The total number of 3/4 bags of pecans that Lisa can make will be B. 16.

From the information, Lisa gathered and shelled 12 lbs of pecans from her backyard and she is going to make 3/4 Ib bags of pecans for gifts.

Therefore, the total number of 3/4 bags of pecans that Lisa can make will be:

= 12 ÷ 3/4

= 12 × 4/3

= 16

She can make 16 bags.

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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 unit rate at which Darrell walks is 1.5 meters per second.

Unit rate is defined as per unit time. Unit rate can be anything from speed, acceleration or any other measurement.

The quantity that is achieved in a single unit of time is called the unit rate.

The unit rate is calculated by dividing the total amount by total time that is taken to complete the total amount.

Here Darrell walks 90 meters in 60 seconds.

The unit time to be considered here is 1 second.

so Darrell walks a certain amount of distance in 60 seconds.

Therefore the unit rate in which he walks = total distance covered ÷ total time taken

∴ unit rate = 90 ÷ 60 meters per second = 1.5 meters per second.

Disclaimer : The complete question is : In 60 seconds, Darrell walks 90 meters. Find the unit rate at which Darrell walks.

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