(a) find a combination of step functions that is equal to 4 when 2 ≤t ≤3 and equal to 0 otherwise. (b) write the following function in one line (i.e. without cases) using step functions: f(t)

Answer:

so basically Write a factor

Step-by-step explanation:

1 - write a factor and then multiply then divide that's all hopefully this is helpful:)

.

We have the inequality:

-4 < (3x - 2)/5 ≤ 6

We multiply all the sides by 5:

-4*5 < 5*(3x - 2)/5 ≤ 6*5

-20 < 3x - 2 ≤ 30

Now, we add 2 to all the sides of the inequality:

-20 + 2 < 3x - 2 + 2 ≤ 30 + 2

-18 < 3x ≤ 32

Finally, we divide by 3:

-18/3 < 3x/3 ≤ 32/3

-6 < x < 32/3

Now, using interval notation:

x = (-6, 32/3]

This means that x takes all the values greater than -6 and less or equal to 32/3. Graphically, this is:

The value of given code is 58 and the value of a=8, b=7, c=-3, d=6, e=1, f=2 for the given puzzles using the exponential identities applied to the puzzles. on substituting the given values to f(b+d)+a(e-c)= 2(7+6)+8(1-(-3))= 58.

The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 23. Keep in mind that a number raised to the power of one is itself.

If a>0 and b>0, the following applies to all real numbers x and y:

a^x.a^y = a^(x+y)

a^x/a^y = a^(x-y)

a^x.b^x=(ab)^x

(a/b)^x = a^x/b^x

a^0=1

a^-x= 1/ a^x

(x^a)^b= x^(ab)

For the puzzle 1,

we use the property a^x.a^y = a^x+y

x^4.x^a=x^12

4+a=12

a=8

For puzzle 2,

we use the property a^x/a^y = a^x-y

y^b/y^5=y^2

b-5=2

b=7

For puzzle 3,

we use the property a^-x= 1/ a^x

3^c=1/3^3

c=-3

For puzzle 4,

we use the property (x^a)^b= x^(ab)

(m^3)^2=m^d

d=3*2

d=6

For puzzle 5,

we use the property a^0=1

7^0=e

e=1

For puzzle 6,

we use the property a^x.a^y = a^(x+y)

4^-2.4^9.4^-5=4^f

f=-2+9-5

f=2

given code=f(b+d)+a(e-c)

=2(7+6)+8(1-(-3))

=2*13+8*4

=26+32

=58

Using the exponential identities applied to the puzzles, the value of the given code is 58 and the values of a=8, b=7, c=-3, d=6, e=1, f=2 for the given puzzles. when the given values are substituted into f(b+d)+a(e-c)= 2(7+6)+8(1-(-3))= 58.

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The number of golf ball after his friend gave him balls is y = 3b + b

He has 3 bags of golf balls with b balls in each bag.

His friend gave him 6 more balls.

Therefore, the number of balls jack has can be represented with the following equation.

b balls are in each of the 3 bags.

Therefore,

the number of balls in the whole bags = 3b

Hence, the number of balls after the friend gave him 6 more balls is as follows;

y = 3b + b

where

y = number of total  golf balls

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The evaluated functions are as follows:

The functions can be evaluated as follows:

Therefore,

f(x) = (1 / 4)⁻ˣ

For we to evaluate the function we have to substitute each value of x in the function.

Hence, let's evaluate the following:

we will replace x in the function by -2

f(-2) = (1 / 4)⁻⁽⁻²⁾

f(-2) = (1 / 4)²

f(-2) =  1 / 16

we will replace x in the function by 1

f(1) = (1 / 4)⁻¹

f(1) = 4

we will replace x in the function by 2.

f(2) = (1 / 4)⁻²

f(2) = 16

Therefore,

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As per the division operation, the hourly pay rate is $37.5

Division operation:

The division is a process of splitting a specific amount into equal parts.

Given,

You get paid $450 for 20 hours.

Here we need to calculate the hourly pay for us.

To find the hourly pay we have to perform the division operation.

The process of doing long division is,

Such that, we have to divide 450 by 12, then we get,

And the process of division is shown below.

So, the hourly pay for us is $37.5.

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Answer:252.5

Step-by-step explanation:

263-242=21

21/2=10.5

242+10.5=252.5

The halfway between 242 and 263 is 252.5

Answer:

1:25

Step-by-step explanation:

200/5000 (5kg = 5000g)

1/25

1:25

Answer:

X=6

Step-by-step explanation:

Simplify:

(2p^3x)^3 = 8p^54 into:

2p^3x = 2p^18

p^3x = p^18

3x = 18

x=6

The formula used for given problem is y = mx+ b.

Slope-intercept form: A line with m as the slope and m and c as the y-intercept makes up the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

This relationship is linear. Let y be the boiling point and let x be the altitude in feet.

We need the equation y = mx+ b for a linear one.

This is a linear relationship.  Let x = the altitude in feet and y be the boiling point

 For a linear equation, we want y = mx+ b

From the description m = -1.72/1000 and when x = 0, y = 212, so b = 212

  y = -1.72/1000 + 212

B)  When y = 190

    190 = -1.72/1000x + 212

    1.72x/1000 = 22

 x = 22000/1.72 ≈ 12791 feet

  When the boiling point is 190°​F, the elevation is about 12791 ft.

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Answer:

C

Step-by-step explanation:

the longest side in a right triangle is the hypotenuse.

using Pythagoras' identity in the right triangle

let the unknown side be x , then

x² + 9² = 15²

x² + 81 = 225 ( subtract 81 from both sides )

x² = 144 ( take square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12

Answer:

12 is the answer

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The exponent means to multiply x² by itself 3 times.

Answer:

They can invite at most 133 people

Step-by-step explanation:

132.97 rounded to the nearest "whole person" is 133

The quotient of the expression as given in the task content is; 27/40.

It follows from the task content that the quotient of the expression which is given in the task content is to be determined.

Since the given expression is; (3/8) ÷ (5/9).

Hence, it follows from division of fractions that the expression can be rewritten as;

(3/8) × (9/5)

= 27/40.

Ultimately, the quotient of the expression is; 27/40.

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The equation that represents the points scored by the Vols is  x-13=35

The solution of the equation is x = 48

Based on the information that is provided in the question, the points scored by Alabama is 13 less than the score of the Tennessee Volunteers. This means that the points of Tennessee Volunteers is 13 greater than that of Alabama.

Thus, in order to determine the points of Tennessee Volunteers, add the score of Alabama to 13. Addition is the process that is used to determine the sum of two or more numbers. The sign that represent addition is +.

Points scored by Tennessee Volunteers = points scored by Alabama + 13

x = 35 + 13

x = 48

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Solution:

Given:

g(-4) means the value of g(x) when x = -4

Substituting x = -4 into the function,

Also, showing the function on a graph using a graph plotter, the function is as plotted below;

The point when x = -4 corresponds to y = -4

Therefore,

We know that every equation expressed in terms of x can be graph in an x-y plane, in this case the equation is

if we want to move it up or down we add or substract the quantity of unities we are moving it. If we want to move it down two unities we substract 2 on the whole equation:

If we want to move it to the left or to the right we add or substract the quantity of unities we are moving it to the x term. If we add it means it is going to the left and if we substract it means it is going to the right. If we want to move it one unity to the right then we substract 1 from the x :

Then, the function:

is the result of moving

f(x) = x³

1 unit to the right and 2 units down

Answer:

y = -16 + 4x

-16 is the slope and the slope is also the y intercept, you can see on the graph how on the y axis the line crosses through -16 and 4 is the x intercept so that's how I know. I also used a graph calculator to check my answer.

Have a great night :)

Answer:

g× $12130.0012130.00.

Okay, here we have this:

Considering the provided points and information, we are going to calculate the requested slope, so we obtain the following:

m=(y2-y1)/(x2-x1)

m=(6-5)/(4-1)

m=1/3

Finally we obtain that the slope of the line is 1/3.

Answer:

y=14

Step-by-step explanation:

have a good day

The equation of the line that is parallel to the given line and passes through the point (–2, 2) is: B. y = 1/5(x) + 12/5

In order to determine the equation of this line, we would first of all calculate its slope. Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope\;,m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

By critically observing the graph of the line, we can logically deduce the following points:

Point (x, y) = (0, -3)

Point (x, y) = (-5, -4)

Substituting the given points into the formula, we have;

Slope = (-4 - (-3))/(-5 - 0)

Slope = (-4 + 3)/(-5)

Slope = -1/-5

Slope = 1/5

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m represents the slope.

Mathematically, the point-slope form of a line is given by this equation:

y - y₁ = m(x - x₁)

Where:

At point (-2, 2), we have:

y - 2 = 1/5(x - (-2))

y - 2 = 1/5(x + 2)

y - 2 = x/5 + 2/5

y = x/5 + 2/5 + 2

y = x/5 + 12/5

y = 1/5(x) + 12/5

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Complete Question:

What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?

y=1/5x+4

y=1/5x+12/5

y=-5x+4

y=-5x+12/5

Answer: B. y = 1/5x + 12/5

Step-by-step explanation: This is just a sum of what the person above me said.....and i can confirm this is the right answer bc i just did the quiz and scored 100% loll. Hope this helps! :D

Answer: n = 17

Step-by-step explanation:

2n + 3n -5 = 90

5n - 5 = 90

5n = 85

n = 17

Answer:

n = 19°

Step-by-step explanation:

The tiny square in the corner of the big angle shows that it is a right angle. Right angles have a measure of 90°. So the two angles labelled added together make a 90° angle.

2n + 3n - 5 = 90

Combine like terms.

5n - 5 = 90

Add 5.

5n = 95

Divide by 5.

n = 19

Answer is: 1

Explaination:

2 · 2 + 1/2 = 4 + 1/

2= 5/2

To find a new numerator:

a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2

= 4/2

b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5

c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs

Subtract: 5/2

- the result of step No. 4 = 5/2

- 3/2

= 5 - 3/2

= 2/2

= 2 · 1/2 · 1

= 1

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 2) = 2. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 2 = 4. In the following intermediate step, cancel by a common factor of 2 gives 1/1.

In other words - five halfs minus three halfs is one.

As per the properties of numbers, Step 1)  2 • 6 • 5 • 1 = (2 • 6) • (5 • 1) uses the option A. associative property of multiplication

Properties of numbers:

The properties of numbers are stated for real numbers.

The common properties are:

Commutative Property: a + b = b + a

Associative Property: a . (b . c) = (a . b) .(a . c)

Distributive Property: a × (b + c) = a × b + a × c

Identity property: a.1 = a

Given,

Here we have the following steps.

Step 1 2 • 6 • 5 • 1 = (2 • 6) • (5 • 1)

Step 2 = (6 • 2) • (1 • 5)

Step 3 = 12 • (1 • 5)

Step 4 = 12 • 5

In this one, we have to identify the property used in step 1.

While we looking into the step 1), we have identified that the product is the same regardless of the way in which the numbers are grouped.

Based on this concept, we have identified that the step is used the associative property of multiplication.

Therefore, step 1 is uses the concept associative property of multiplication.

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15 bags are expected for the journey for 9 people to fit backpacks in the trailer.

The fundamental principle of multiplication

To calculate the sum of two or more numbers, utilize the mathematical operation of multiplication. If an event can happen in m different ways and a second event can happen in n different ways after it, then the two events that happen in succession can happen in m n distinct ways.

Given that 5 backpacks can fit in the trailer for every 3 people.

Then 3 people = 5 backpacks

1 people = [tex]\frac{5}{3}[/tex] backpacks

therefore  If 9 people are going on the trip, then;

9 people = [tex]\frac{5}{3}*9[/tex] backpacks

= 5 x 3

= 15 backpacks

Hence, the trailer can fit 15 backpacks if 9 people go on the trip.

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The integer solutions in the inequality expression given as − 2 ≤ x < 3 are -2, -1, 0, 1 and 2

Inequalities are expressions that do not have equal value

As a general rule, inequalities are represented by the unequal symbols

The inequality expression is given as

− 2 ≤ x < 3

The above inequality implies that

The values in the range or domain are values greater than -2, but less than 3

This means that

-2 is inclusive of the range, while 3 is not inclusive of the range

Using the above as a guide, the values in the range are

-2, -1, 0, 1 and 2

Hence, the integer solutions are -2, -1, 0, 1 and 2

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Answer: 6.4

Step-by-step explanation: If rounding to one decimal place, your answer would be 6.4.

49.6 divided by 7.8 = 6.35897435...

Now, we see that after the 3 (The first decimal place) there is a five. Because we are rounding to the first decimal place the second decimal place will tell us to round up or down. In this case because it's a five, we would round up.

Answer:  -4.667/2.000 = -2.333

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :    y-(-7/3*x+5/2)=0

Simplify   [tex]\frac{5}{2}[/tex]

Equation at the end of step : y -  ((0 -  ([tex]\frac{7}{3}[/tex] • x)) +  [tex]\frac{5}{2}[/tex])  = 0

The left denominator is : 3  The right denominator is : 2

Least Common Multiple:      6

 y - [tex]\frac{(15-14x)}{6}[/tex]   = 0

y • 6 - [tex]\frac{(15-14x)}{6}[/tex] [tex]\frac{6y + 14x - 15}{6}[/tex]

[tex]\frac{ 6y + 14x - 15}{6}[/tex]

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 2.500 and for x=2.000, the value of y is -2.167. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.167 - 2.500 = -4.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -4.667/2.000 = -2.333

 x-intercept = 15/14 = 1.07143

 y-intercept = 15/6 = 5/2 = 2.50000