Given the following piecewise defined functions, evaluate each of the problems below.
h(x) ={7, when x<0
{x+1, when 0 ≤x ≤4
{√x-1, when x>4
1.h(0)
2.h(10)
3.h(-3)
4.h(3)

Answers

Answer 1

The values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4

How to evaluate each of the function values from the piecewise function?

The piecewise function is given as:

h(x) = {7, when x<0

         {x+1, when 0 ≤x ≤4

          {√x-1, when x>4

Next, we solve the function values

1. Function h(0)

This means that x = 0

To do this, we make use of h(x) = x + 1 because x= 0 is in its domain

So, we have

h(0) = 0 + 1

h(0) = 1

2. Function h(10)

This means that x = 10

To do this, we make use of h(x) = √x - 1 because x= 10 is in its domain

So, we have

h(10) = √10 - 1

h(10) = √9

h(10) = 3

3. Function h(-3)

This means that x = -3

To do this, we make use of h(x) = 7 because x= -3 is in its domain

So, we have

h(-3) = 7

4. Function h(3)

This means that x = 3

To do this, we make use of h(x) = x + 1 because x= 3 is in its domain

So, we have

h(3) = 3 + 1

h(3) = 4

Hence, the values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4

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Related Questions

is james scored a 40 on a test with a mean of 38 and the standard deviation was for whataburger z-score be

Answers

The value of z-score for James is 0.2

Step-by-step explanation:

From the formula of z-score we know that

z-score = individual score - mean / standard deviation

Given

James score = 40

Mean = 38

Standard deviation = 10 (missing in question)

To find

z-score =?

Let's put the values in the formula

z-score = 40-38/ 10

z-score = 0.2

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Subtract (5.3 x 108) − (8.2 x 106).

2.9 x 102
5.218 x 102
2.9 x 108
5.218 x 108

Answers

Answer: 5.218*10^8 ==> Option 4

Step-by-step explanation:

(5.3 x 10^8) − (8.2 x 10^6)=

(5.3*10^2 x 10^6) − (8.2 x 10^6)=

(5.3*100*10^6)-(8.2*10^6)=

(530*10^6)-(8.2*10^6)=

(530-8.2)*10^6=

(530.0-8.2)*10^6=

521.8*10^6=5.218*10^8 ==> Option 4

How many boxes of cereal can you buy with $42 if one box costs $5.25? As Equation Review

Answers

You can buy 8 boxes of cereal

Answer:

8

Step-by-step explanation:

$ 42 / 5.25 $ / box = x  = 8 boxes

The list of ingredients for chocolate
brownies given at right will make 16
brownies.
Use the list to decide how much of
each ingredient is needed to make 6
brownies.
2
3
5 ounces unsweetened chocolate
1/2 cups sugar
cup butter
2 teaspoons vanilla
2 eggs
1 cup flour
www
cup(s) of butter is needed.
(Simplify your answer. Type an integer, simplified fraction, or mixed number.)
ounce(s) of chocolate are needed
(Simplify your answer. Type an integer, simplified fraction, or mixed number.)

Answers

The following ingredients are needed to make 6 brownies:

Cups of butter needed  is 1/4 cups

Ounces of chocolate needed is 1 7/8

Cups of sugar needed is 9/16

Ounces of vanilla needed is 3/4

How much ingredients are needed?

Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero. An example of an integer is -1.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below

A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator.

Cups of butter needed = (2/3 x 6) / 16

4 / 16 = 1/4 cups

Ounces of chocolate needed = (5 x 6) / 16

= 30 / 16 = 1 14/16 = 1 7/8

Cups of sugar needed = ( 1 1/2 x 6) / 16

(3/2 x 6) / 16 = 9/16

Ounces of vanilla needed = ( 2 x 6) / 16

= 12 / 16 = 3/4

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Calculate the electric potential energy in a capacitor that stores 1.0 x 10^-10 C
of charge at 100.0 V. Use PE = 1/2QAV.
OA. 1.0 x 10-8 J
OB. 1.0 x 102 J
O C. 5.0 × 10¹ J
OD. 5.0 × 10-9 J

Answers

The electric potential energy is 5.0 × 10^(-9) J

How to calculate the electric potential energy?

The formula to calculate the electric potential energy in a capacitor is;

E = 1/2 * C * V²

Where;

E = electric potential energy

C = capacitance = charge

V = voltage applied

We are given;

Voltage applied; V = 100 V

Capacitance (Charge) = 1 × 10⁻¹⁰ C

Plugging in the relevant values gives

E = 1/2  * 1 × 10⁻¹⁰ *  100

E = 1/2 * 1 × 10⁻⁸

E = 0.5  × 0⁻⁸ volts

E = 5.0 × 10^(-9) J

Thus, we conclude that the electric potential energy is 5.0 × 10^(-9) J

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Tallie wants to buy a new iPhone. The iPhone costs
$850. She has saved $325 to put down as an initial
payment and will pay another $75 each month until
the phone is paid off. How many months will it take
for Tallie to pay for her new iPhone?

Answers

Answer:

7 months to pay it off.

Step-by-step explanation:

see attached for details.

a) 3² x 3* = 37
Find the value of x.
b) 78 + 7 = 76
Find the value of y.
c) (q¹)² = q¹²
12
Find the value of z.
Marks

Answers

 z =  3  or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]   is the value of z in linear equation.

What in mathematics is a linear equation?

There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.

a ) Simplify using exponent rule with same base  = a[tex]a^{n} . a^{m} = a^{n + m}[/tex]

Based on the given conditions, corresponding exponents are equal                                                                              = [tex]3^{2 + x} = 3^{7}[/tex]

Rearrange unknown terms to the left side of the equation                                                                           = 2 + x = 7

 Calculate the sum or difference                                                                               x = 5

b) Calculate the power 5764801 + [tex]7^{y}[/tex] = 117649

Rearrange unknown terms to the left side of the equation

         7^{y} = 117649 - 5764801

The equation is not defined.

c)  the equations  z =  3  or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]

   answer    z =  3  or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]

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Please help due tonight.

Answers

Answer:  Choice C

This is the result of subtracting 3x from both sides. The inequality sign does not flip. It only flips if we multiply or divide both sides by a negative number.

Mrs. Figueroa made a spaghetti dinner for the cheerleaders after practice. She purchased four and three fourths pounds of beef for $3.99 per pound. How much money did she spend on the beef for the spaghetti?

$7.25
$8.87
$9.98
$18.95

Answers

Answer is $18.95 for beef

Step by step

4 3/4 pounds x $3.99 per pound

Change your fraction into a decimal and multiply

4.75 x 3.99 = 18.95

Or

4 3/4 x 3.99

Change to improper fraction

19/4 x 3.99

Multiply across

75.81/4

Divide = $18.95

Problem solved!!



Answer:

$18.95

Step-by-step explanation:

for #13-14 determine if the lines are parallel, perpendicular or neither 10x +5y=-5 and y=-2x+6

Answers

Answer:

48

because. Of the time

Solve the inequality 34q−23q<512q−112 and write the solution in interval notation.

Answers

Answer:   [tex]q=\frac{112}{501}[/tex]

Step-by-step explanation:

1) Add similar elements: 11q < 512q - 112

2) Subtract 512q from both sides: 11q - 512q < 512q - 112 - 512q

3) Simplify: -501q < -112

4) Multiply both sides by -1 to reverse the inequality: (-501q)(-1) > (-112)(-1)

5) Simplify: 501q > 112

6) Divide both sides by 501: [tex]\frac{501q}{501} > \frac{112}{501}[/tex]

7) Simplify: [tex]q=\frac{112}{501}[/tex]

the limit of​ f(x) as xa describes what happens to​ f(x) when x is​ near, but not equal​ to, the value a.

Answers

If x is near but not equal​ to, the value an is that f(a) then the function will not continue.

What is the limit?

Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.

In another word, limit is a mathematical concept in which we find out the value of any function at a point by its adjacent very close point.

If a function f(x) is defined near to x = a but not a then there will be no continuity of that function at that point.

To exist a limit at x = a

LHL = RHL

But for continuity

LHL = RHL = f(a)

Hence "If x is near but not equal​ to, the value an is that f(a) then the function will not continue".

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of the 35 flavors of ice cream at an ice cream parlor, 25 flavors contain some sort of nuts, 12 are fat-free, and 8 both fat-free and contain nuts. how many of the flavors at the ice cream parlor neither are fat-free nor contain nuts?

Answers

The number of ice creams according to the probability,  Neither contain nuts nor are fat free is 6.

According to the statement

We have to find that the ice creams that neither are fat-free nor contain nuts.

So, For this purpose, we know that the

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.

From the given information:

There are 35 flavors of ice cream at an ice cream parlor, 25 flavors contained ice creams.

Contain nuts = 25

Are fat free = 12

Are both = 8

Then

Contain nuts or are fat free = 25+12-8 = 29

Total = 35

Neither contain nuts nor are fat free = 35-29 = 6.

So, The number of ice creams according to the probability,  Neither contain nuts nor are fat free is 6.

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Help with all answers

Answers

The value of m∠1 is 158° as the two line x and y are parallel.

Two lines are said to be parallel if they do not meet at any point and the perpendicular distance between them is always the same.

A straight line intersecting both the parallel lines is called a transversal.The alternate interior or exterior angles formed are always equal.The corresponding angles are equal.The co-interior angles are supplementary.

In the given figure it is given that x║y and m∠2 = 22°.

Now let us use the above principles to solve the value of the other angles.

m∠2+m∠1 = 180°(linear pair)

or, m∠1= 180°-22°

or, m∠1=158°

m∠2+m∠3 = 180°(co-interior angles are supplementary)

or,m∠3=158°

m∠2=m∠4(Corresponding angles are equal)

or, m∠4=22°

m∠2=m∠5 (vertically opposite angles are equal)

or, m∠5=22°

m∠6=m∠1 (vertically opposite angles are equal)

or, m∠6=158°

m∠2=m∠7(alternate angles are equal)

or, m∠7=22°

m∠3=m∠8 (vertically opposite angles are equal)

or, m∠8=158°

Hence all the above angles are calculated using the properties of parallel lines.

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If the length of a certain rectangle is increased by 1, then the area of the rectangle is increased by 12. If instead, the width is increased by 2, then the area of the rectangle is increased by 42. What is the area of the original rectangle?

Answers

Answer:   Let the length and breadth of a rectangle are x and y units , its area is x.y units^2

Step-by-step explanation: sorry no explanation


Given: B is midpoint if AC
C is the midpoint if BD
Prove: AB is congruent to CD

Answers

Answer:

See proof below

Step-by-step explanation:

If B is the midpoint of AC, then AB = BC

If C is the midpoint of BD then BC = CD

Using the transitive property of equality, if a = b and  b = c  then a =c

We apply this to the above line segments and get

If AB = BC and BC = CD then AB=CD
For two line segments to be congruent they must have the same length

So AB is congruent to CD

a market woman bought n eggs at the rate of 12 eggs at €60. 8 of the eggs were broken so she sold the remaining at the rate of 4 eggs at €24 and made a profit of €12. how many eggs did she buy.​

Answers

Answer:26 eggs

Step-by-step explanation: yes

The market woman bought 60 eggs.

The market woman bought n eggs at the rate of 12 eggs for €60.

So, the cost price of each egg is given by:

Cost price per egg = €60 / 12 = €5

The total cost of n eggs is the cost price per egg multiplied by the number of eggs (n):

Total cost = €5 * n = 5n

After buying n eggs, 8 of them were broken.

So, the market woman had (n - 8) eggs left to sell.

She sold the remaining eggs at the rate of 4 eggs for €24.

The selling price of each egg is given by:

Selling price per egg = €24 / 4 = €6

The total selling price of the remaining (n - 8) eggs is the selling price per egg multiplied by the number of remaining eggs (n - 8):

Total selling price = €6 * (n - 8) = 6n - 48

The profit is the difference between the total selling price and the total cost:

Profit = Total selling price - Total cost

Since the problem states that the market woman made a profit of €12, we can set up the equation:

6n - 48 - 5n = 12

Solve for n.

Combine like terms:

n - 48 = 12

Add 48 to both sides:

n = 60

So, the market woman bought 60 eggs.

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7. Vernon filled his gas tank with 16 gallons of
gas. The table shows the linear relationship
between the amount of gas remaining in his
tank and the miles driven. What is the rate of
change of gallons of gas per mile driven?
Miles Driven
Gas (gal)
0,16
84,12
105,11
336,0

* coordinates is a chart x representing miles driven y representing gas(gal)

Answers

Vernon put 16 liters of gas in his tank. 21 miles per gallons of gas are consumed each mile that is driven.

Given that,

Vernon put 16 liters of gas in his tank.

The table depicts the linear relationship between the mileage driven and the amount of gas in his tank.

We have to find how many gallons of gas are consumed each mile that is driven.

From the table we can say

The total Distance is 336

The total gallons of gas is 16

Rate= Total distance/Total gallons

Rate=336/16

Rate=21 miles per gallons

Therefore, 21 miles per gallons of gas are consumed each mile that is driven.

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Given f(x) = 2(3 - x) - 2x, what is the value of f(x) = -10? ​

Answers

Substitute the value of x for -10 so
2(3- - 10) - 2 (-10)
2*(26) - 20
52 -20= 32
So f(-10)= 32

The value of x for f(x) = 2 (3-x) -2x at f(x) = -10 is 4.

To find the value of f(x) when f(x) equals -10, we substitute -10 into the equation and solve for x.

Given:

f(x) = 2(3 - x) - 2x, we have:

-10 = 2(3 - x) - 2x

Let's simplify the equation step by step:

-10 = 6 - 2x - 2x

-10 = 6 - 4x

-10 - 6 = -4x

-16 = -4x

To solve for x, divide both sides by -4:

x = (-16) / (-4)

x = 4

Therefore, when f(x) = -10, the value of x is 4.

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Which of the following is equivalent to (7y + 5x) + 8x?

35xy + 8y
7y + 13x
8x(7y + 5x)
7y + 40x

Answers

Answer:

7y + 13x

Step-by-step explanation:

Let's simplify step-by-step.

7y+5x+8x

Combine Like Terms:

=7y+5x+8x

=(5x+8x)+(7y)

=13x+7y

The expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x which is correct answer would be option (B).

What is algebra?

Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.

What is the algebraic expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.

⇒ (7y + 5x) + 8x

Open parenthesis and combine like terms to get the solution,

⇒ 7y + 5x + 8x

⇒ (5x + 8x) + (7y)

⇒ 13x + 7y or

⇒ 7y + 13x

Therefore, the expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x.

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a gas station sells regular gas for $2.10 per gallon and premium gas for $2.90 a gallon. at the end of a business day 280 gallons of gas had been sold, and receipts totaled $652. how many gallons of each type of gas had been sold?

Answers

200 gallons of regular gas and 80 gallons of premium gas were sold.

Let the amount of regular gas sold be x gallons. So, the amount of premium gas sold will be (280 - x).

Now, forming the equation using the given information, to find the amount of each type of gallon.

Equation -

2.10x + 2.90(280 - x) = 652

Performing multiplication with values inside bracket in Left Hand Side

2.10x + 812 - 2.90x = 652

Rewriting the equation -

812 - 652 = 2.90x - 2.10x

Performing subtraction

160  = 0.8x

Rewriting the equation according to x

x = 160÷0.8

Performing division to find the value of x

x = 200

So, 200 gallons of regular gas was sold.

Amount of premium gas sold = 280 - 200

Performing subtraction

Amount of premium gas sold = 80 gallons

Hence, 200 gallons of regular gas and 80 gallons of premium gas was sold.

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√21 √9/√63 indadicate opretion and simplifying

Answers

Sorry in my keyboard there is no symbol for squareroot

Amys weight this year is 50 pounds lessthan twice her weight from last year. if she weighs 120 pounds this year, what equation can be used to find her weight from last year?

Answers

Answer:

190

Step-by-step explanation:

(120*2) - 10 = 190

hope this helped !!

finding the rise and the run on the graph

Answers

Answer:

rise = 4, run = 5. The slope would be 4/5

Step-by-step explanation:

You go up by four then right by 5

At Cheng's Bike Rentals, it costs $46 to rent a bike for 9 hours. How many hours of bike use does a customer get per dollar? Answer each part. If necessary, round your answers to the nearest hundredth.

Answers

Answer:

0.20 hours

Step-by-step explanation:

Bike rental is $46 for 9 hours.

We want to find hours per dollar, so divide time by cost:

9 hours / 46 dollars = 0.19565217... hours/dollar

Rounded to nearest hundredth:

0.20 hours

What is the measure of x?

Answers

You subtract 135 from 180 to get the angle of the arc. Once u have the arc you divide by two to get the angle u need (angle B) which 22.5

what are corresponding angles

Answers

Corresponding Angles are any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.
the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

What is the slope of the line that passes through the points (10, 8) and (7, 14)?
Write your answer in simplest form.

Answers

Answer:

-0.2667

Step-by-step explanation:

m =y2 - y1

x2 - x1

=14 - (10)

-7 - (8)

=14 - 10

-7 - 8

=4

-15

researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. the researchers attend political debates and record how frequently each candidate displays positive facial expressions. which research method are the researchers using? a. random sample b. case study c. naturalistic observation d. survey

Answers

researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. c. naturalistic observation

What is naturalistic observation?

A study technique called naturalistic observation includes watching participants in their natural settings. Many psychologists and other social scientists employ this strategy. It is an approach to qualitative research that emphasizes gathering, analyzing, and describing non-numerical data.

When performing lab research would be impractical, expensive, or would adversely influence the subject's behavior, it may be helpful. Naturalistic observation is to capture behavior as it happens in its natural environment without intervention or efforts to change any of the factors. In a lab context, people frequently act differently than they would in the wild. Sometimes, researchers wish to watch their subject's behavior "in the wild".

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Use the distributive property to solve the equation. 5x/2-x=x/6-8/3.

Answers

Answer:

Step-by-step explanation:

i know

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