PLEASE HELP


Bob drives on an interstate highway in Pennsylvania at a constant rate for three hours. A graph of the distance he travels based on the time he drives is shown below.


A car driving at the speed limit on this highway is represented by

Does Bob drive within the speed limit? Explain

Answer:

Parallel: y= -(7x/3)-20

Perpendicular: y= 3x/7 - 24/7

Step-by-step explanation:

Slope of parallel line: -7/3

So the equation is y=-7x/3+a

Solve for A:

−6=(−7/3)⋅(−6)+a

So A is -20 and the equation is y=-7x/3=20

Slope of perpendicular line: 7/3

So the equation is y=3x/7 + a

Solve for A:

-6=(3/7)*(-6)+a

Therefore, a= -24/7

So the equation is y= 3x/7 - 24/7

Answer:

Equation of the parallel line: [tex]y = -\frac{7}{3}x - 20[/tex]

Equation of the perpendicular line: [tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

Step-by-step explanation:

To find the equation of a parallel line, we already know that the slope is the same as the original line, so let's find the equation of our original line. We are given:

-7x - 3y = 5

So, we will add 7x to both sides to leave y on a side by itself:

-3y = 7x + 5 (This is the slope-intercept form which is what we will be using)

Then, divide by -3 to isolate y, giving us:

[tex]y= -\frac{7}{3} x - \frac{5}{3}[/tex]

Since it is a parallel line, our slope is the same, giving us:

[tex]y = -\frac{7}{3}x + b[/tex]

Now, the slope of a line is [tex]\frac{rise}{run}[/tex]. Rise is the gain in y, and run is the gain in x. So, since we want to find the y-intercept, we need x to be 0, so let's say for every 3 we gain on the x-axis, we lose 7 on the y-axis (because we need one of the two values to have a negative so that our overall fraction is negative). Now, since we have the point (-6, -6) We need to gain 6 on the x-axis. Meaning, we need to use our slope twice. This means that we will need to also multiply our -7 by 2. So we have:

(-6 + 6, -6 - 14)

Giving us:

(0, -20)

Which is our y-intercept. So our equation for the parallel line is:

[tex]y = -\frac{7}{3}x - 20[/tex]

Now, for the perpendicular line, we need to get the negative reciprocal of the slope of our original line. Our original line's slope was [tex]-\frac{7}{3}[/tex]. So, the negative reciprocal of that is [tex]\frac{3}{7}[/tex]. So, our equation is:

[tex]y = \frac{3}{7}x + b[/tex]

Now, we will find the y-intercept. Since we need to gain 6 on the x-axis, but we have a normal gain of 7, we will need to multiply both our run and rise (3 and 7 respectively) by [tex]\frac{6}{7}[/tex]. Giving us that our x coordinate is:

[tex](-6 + 7 * \frac{6}{7} , -6 + 3 * \frac{6}{7} )[/tex]

Simplifying gives us:

[tex](-6 + 6 , -6 + \frac{18}{7} )[/tex]

Adding the x coordinates gives us:

[tex](0, -6 + \frac{18}{7})[/tex]

Now, to make this simple, we will put -6 over 7. To achieve this, we will need to multiply -6 by 7, giving us -42. So, we have:

[tex](0, -\frac{42}{7} + \frac{18}{7})[/tex]

42 - 18 = 24. So, we get:

[tex](0, -\frac{24}{7})[/tex]

So, the slope of the perpendicular line is:

[tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

So, these are the two equations of the parallel and perpendicular lines respectively:

Parallel: [tex]y = -\frac{7}{3}x - 20[/tex]

Perpendicular: [tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

Hope this helped!

A triangle with the lengths of the sides 6cm , 8cm , and 10cm is a right angled triangle using Pythagoras theorem.

As given in the question,

In the given triangle,

lengths of the sides of the triangle is given by :

6cm , 8cm , and 10cm

In the given measurement longest side is 10cm.

Using Pythagoras theorem :

( Hypotenuse ) ² = (Base)² + ( Altitude)²

Here

( 6 )² + ( 8 )²

= 36 + 64

= 100

= 10²

It satisfy the condition of Pythagoras theorem.

It is a right angled triangle with hypotenuse = 6cm.

Therefore, the given lengths of the sides of the triangle represents it is a right angled triangle.

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The solution for "m" for the equation is 8.3.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given expression

5m + 2 - 3.9m = 2.1(m — 3)

5m + 2 -3.9m = 2.1m - 3(2.1)

1.1m + 2 = 2.1m - 6.3

compare variables on one side and constant other,

2  + 6.3 = 2.1m - 1.1m

8.3 = m

Hence the value of m is 8.3.

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If to the nearest whole number, then 2. If to the nearest tenth, then 1.5.

0.579 + .94 is 1.519.

When rounding to the nearest whole number, if the first number after the decimal point is 5 or higher, round up. If 4 or lower, then round down.

It must be less effective than 100%. Any time you switch from one source of energy to another, especially if there is effort involved, there is a cost.

An enzyme is a protein that must retain its three-dimensional structure in order for it to function as a "lock and key." A little alteration to the enzyme structure might render it inoperative.

Denaturation of proteins is common. The protein's structure can change as a result of environmental factors including pH and temperature. An increase in temperature should hasten the process, but an excessive increase might harm the enzyme. Therefore, the situation in which there is no change to the enzyme structure would be the "ideal" one.

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Note : The complete question could be as bellow,

A second set of measurements were taken, and the efficiency was found to be greater than 100%. What reasons most likely explain why the second set had a different efficiency? Select all that apply:

Used the reciprocal of the efficiency formula

Raised the resistance force in a shorter amount of time

Used the incorrect conversion factor from pounds to Newtons for force Incorrect values for the resistance distance

Inaccurate readings from force sensor for effort force

Increase efficiency from reduced friction

The US GDP (Gross Domestic Product) for 2014 was reported to be the nearest hundredth is 17. 56 trillion dollars. The current US population is about 320 million people to the nearest hundredth.

The gross domestic product (GDP) is a commonly used indicator of the value added produced by the production of goods and services in a country over a certain time period (GDP). As a result, it also takes into account the money made from that manufacturing or the sum of money spent on finished goods and services (fewer imports). Although the gross domestic product (GDP) is the most important indicator for gauging economic activity, other metrics may be better suitable for gauging people's material well-being.

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The inequality that models the situation is:

x + 2y ≥ 12

We know that a Mecnahinc named Zeke plans to work a maximum of 12 hours (12 hours is an allowed value) tomorrow.

And we know that he works doing tune-ups and oil changes.

Let's define the variables:

We know that It takes 1 hour to perform a tune-up and 2 hours to perform an oil change.

Then the total number of hours worked by Zeke is given by the expression:

x*1 + y*2

And that must be equal to or smaller than 12, so we will get the inequality:

x + 2y ≥ 12

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His pay to play this game per draw is $0.1413

0.015 of an event is a measurement of how likely an event can occur as an outcome of a random experiment.

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.

Given;

Money mark recieves for diamond=$0.45

Money mark recieves for queen=$0.60

Money mark recieves for queen of diamonds=$0.80

Now,

Probability of getting a diamond = 13/52

Price of one heart =$0.45

Pay for one heart = 13/52×0.45=$0.1125

Probability of getting a queen =4/52

Price of one queen =$0.60

Pay for one queen =4/52×$0.60=$0.0115

Probability of getting a queen of diamonds =1/52

Price of one queen =$0.80

Pay for one queen =1/52×$0.80=$0.015

Total pay for one draw= $0.1125+$0.0115+$0.0173=$0.015

=0.1413

Therefore, the pay per draw by probability will be $0.1413

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No , half and halve represents different forms which is given by :

Half represent the noun form , adjective form or the adverb form where as halve represents the verb form.

Difference between half and halve is as follow :

Therefore, half and halve are not same they represents different forms which is given by : half is the noun form , adjective form or the adverb form where as halve represents the verb form.

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Devon's expression had the greatest value which is 20.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a mathematical value or relationship. Expressions can be simple or complex, and they can take on many different forms depending on the context.

They are also used to represent real-world problems, and also used to evaluate mathematical expressions to get numerical results.

Step-by-step explanation:

Let's use t=1 to compare all the expressions:

1. -5(12t+9)

if t = 1, -5(12+9) = -5(21) = negative number

2. 2(-6t-8)

if t = 1, 2(-6-8) = 2(-14) = negative number

3. -6(-2t+18)

if t = 1, -6(-2+18) = -6(16) = negative number

4. (-4(-3t-2)

if t = 1, -4(-3-2) = -4(-5) = 20 positive number

Therefore, Devon's expression had the greatest value which is 20.

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Therefore ,as a result, 42/5 is the value of the first term in the equation for the arithmetic mean.

The arithmetic average or means of the group is calculated as the sum of each value in a list divided by the total number of things in that list. The progression in mathematics is the same as this. The average of the integers 5, 7, and 9 is 4, as shown by the equation 5 + 7 + 9 being equal to 21, and 21 divided by 3 (there are actually three numbers) being equal to 7.

Here,

Given :

5 a + 10 d = 70 in the first five terms (1)

The first ten terms add up to 10 a + 45 d = 210. (2)

This means that in order to solve the system for a, multiply equation (1) by 2, then subtract it from equation (2):

=> 10a - 10a + 45d - 20d = 210-140

=> 25d = 70

=> d = 70/25

=> d = 14/5

A value then becomes:

5a + 10*14/5 = 70;

5a = 70-140/5;

5a = 350-140/5;

a = 42/5.

42/5 is the response.

As a result, 42/5 is the value of the first term in the equation for the arithmetic mean.

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Answer:

the answer is 45 cm^2

how many questions are left lol

Using proportions, it is found that Product A sold 345600 units.

In this problem, we have that Product B sold 70% less, that is, 30% of Product C, which sold 39,000 units, hence:

B = 0.3 x 33000 = 9900.

Product A sold 3.5 times more than Product B. So, the number of units sold by Product A is given by:

A = 3.5 x 9900 = 346500.

Therefore, Product A sold 345600 units.

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On solving the provided question, we can say that by linear equation we have 2.5x * cereals = y

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.

2.5 cups of this particular cereal,

the following linear equation, you could calculate how many calories and grams of fiber you were eating.

let x = cereals we eat y = calories

so, equation - 2.5x * cereals = y

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If Annual Salary: $24,872; personal exemptions: $1,500.  the income tax withheld per pay is: $29.57 per pay period.

Total taxable income = $24,872 - $1,500

Total taxable income = $23,372

The first $10,000 is taxed at a rate of 2.75%.  The tax owed on the first $10,000 is:

$10,000 * 0.0275

= $275.

The remaining $13,372 ($23,372 - $10,000) is taxed at a rate of 3.25%, so the tax owed on this amount is:

$13,372 * 0.0325

= $434.57

The total tax owed is:

$275 + $434.57

= $709.57

Since the person is paid semimonthly, we divide the annual tax owed by 24 to find the tax withheld per pay period:

$709.57 / 24

= $29.57 per pay period

Therefore the income tax withheld per pay is: $29.57 per pay period.

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Given

let the value of geometric mean be a and b

a=12

b=7

we know that,

Geometic mean(G.M)=√ab

=√12×7

=√84

=9.16

the geometric mean of 12 and 7 is 9.16

A visual representation of data where numbers on the left side of a chart show one part of each value and numbers on the right side of the chart show the other is called a bar chart. A bar chart is a chart that uses rectangular bars to represent different values or categories. Each bar has a length that represents a value or a category. The left side of the chart is called the y-axis, or the vertical axis, and the right side of the chart is called the x-axis, or the horizontal axis. The x-axis typically shows the categories, and the y-axis shows the values of those categories. The height of each bar represents the value of the data point, with the height on the y-axis and the categories on the x-axis. This type of graph is useful for comparing the relative sizes of different groups or categories, as well as spotting trends and patterns.

Answer:

i think 48.00

Step-by-step explanation:

10% of 50 is 5 while 6% of 50 is 3 so 50-5+3 is 48

Answer:

153.958 [tex]cm^{2}[/tex]

Step-by-step explanation:

a = [tex]\pi r^{2}[/tex]

a = 3.142([tex]7^{2}[/tex])     The radius is half of the diameter 14/2 = 7

a = 3.142(49)

a = 153.958

Answer:

degree is 7

leading coefficient:-20

Step-by-step explanation:

degree is the highest exponent

leading coefficient is the coefficent with the highest degree

hope this helps :)

The longest portion is 18 inches longer than the shortest portion.

What is algebraic equation ?

An algebraic equation is a mathematical statement that shows that two expressions are equal. It typically consists of a combination of numbers, variables and mathematical operations such as addition, subtraction, multiplication, and division.

We know that the ratio of the portions is 1:2:4, so we can use this ratio to find the length of each portion by dividing 42 inches by the sum of the ratio, 1+2+4 = 7.

So each portion is 42 inches / 7 = 6 inches.

The longest portion is 4 times the length of the shortest portion, which is 6 inches. So the longest portion is 4 * 6 inches = 24 inches.

24 - 6 = 18 inches ,

Therefore, the longest portion is 18 inches longer than the shortest portion.

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Answer: x<4

Step-by-step explanation:

19>15+x

4>x

x<4 is the answer

Answer:

Since 15+x is less than 19. 15+x cannot equal to or greater than 19. If x is greater or equal to 4, the answer will be equal to or greater than 19 which is not true for the equation shown above.

So x is less than 4.

Giselle worked 12 hours as a carpenter

She also worked 18 hours as a blacksmith

Giselle worked as both a carpenter and a blacksmith

She earned $20 per hour working as a carpenter

She also earned $25 per hour working as a blacksmith

She worked for 30 hours to earn $690

Let x represent the number of hours that she worked as a carpenter

Let y represent the number of hours that she worked as a blacksmith

x + y= 30........equation1

20x + 25y= 690......equation 2

From equation 1

x + y= 30

x= 30-y

Substitute 30-y for x in equation 2

20(30-y) + 25y= 690

600-20y+25y= 690

collect the like terms

600+5y=690

5y= 690-600

5y= 90

y= 90/5

y= 18

Substitute 18 for y in equation 1

x+y= 30

x+18= 30

x= 30-18

x= 12

Hence Giselle worked 12 hours as a carpenter and 18 hours as a blacksmith

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Answer:

50276 rounded to the nearest hundred is 50300.

Rounding to the nearest hundred means finding the number that is closest to the original number, but ends in two zeroes. In this case 50300 is the nearest number ending in two zeroes to 50276.

Answer:50300

Step-by-step explanation:

In 50276, the number 2 is in the hundreds place. If the number in the tens place if equal or bigger to 0 round up to get 50300.

For the given scenario appropriate answer is A: 1, 7, 34, 7, 1, which is the best indicator that the variable is modeled with a normal approximation

A normal distribution is the sampling distribution of averages or proportions from a large number of independent trials that approximately follows the normal curve. The expectation of a sample proportion or average is the corresponding population value.

The normal approximation is used to approximate probabilities because it is often easier to use the area under the normal curve compared to the sum of many discrete values.

"

Complete question:

Clara recorded 50 numerical observations on a certain variable and then calculated the mean x¯ and the standard deviation s for the observations. To help decide whether a normal model is appropriate, she created the following chart. The figure presents a number line. The number line has four tick marks labeled from left to right as x bar minus 2 s, x bar minus s, x bar plus s, and x bar plus 2 s. The 4 tick marks create 5 intervals on the number line. From left to right the intervals are labeled a, b, c, d, and e. The intervals at the ends of the number line, a and e, appear to be the same length, the intervals labeled b and d appear to be the same length and the interval in the middle, labeled c, appears to be twice the length of interval b. In Clara’s chart, the letters a,b,c,d,and e represent the number of observations falling in each interval. Which of the following list of counts for a,b,c,d,and e, respectively, is the best indicator that the variable can be modeled with a normal approximation?

A 1, 7, 34, 7, 1

B 1, 10, 28, 10, 1

C 2, 8, 30, 8, 2

D 2, 4, 38, 4, 2

E 5, 5, 30, 5, 5

"

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Answer:

[tex]-\frac{1}{64}[/tex]

Step-by-step explanation:

We have:

[tex][( \frac{1}{15} - \frac{2}{5}) * (-\frac{3}{4})^{3}] / (-9)[/tex]

Now, we will multiply the second fraction in the first parentheses by [tex]\frac{3}{3}[/tex] so we can subtract it from the [tex]\frac{1}{15}[/tex]. Then, we will multiply all of the [tex]\frac{3}{4}[/tex]'s. This gives us:

[tex][( \frac{1}{15} - \frac{2}{5} * \frac{3}{3} ) * (-\frac{3}{4} * -\frac{3}{4} * -\frac{3}{4})] / (-9)[/tex]

Which simplifies to:

[tex][( \frac{1}{15} - \frac{6}{15} ) * (-\frac{27}{64})] / (-9)[/tex]

Simplifying:

[tex][(-\frac{5}{15} ) * (-\frac{27}{64})] / (-9)[/tex]

Multiplying in our brackets gives us:

[tex]\frac{9}{64} / (-9)[/tex]

Now, using the rule of KCF (Keep, Change, Flip), we will keep our first fraction, change our division sign to a multiplication sign, and make the last number its reciprocal. This gives us:

[tex]\frac{9}{64} * -\frac{1}{9} = -\frac{1}{64}[/tex]

So, the equation simplified is [tex]-\frac{1}{64}[/tex].

Hope this helped!

The required time for Cormac to catch Leif is, 2.85 minute

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

Given that,

Cormac runs at a speed = 105 m/minute

Leif runs at a speed = 65 m/minute

Leif is 100 m away from the Cormac,

So, total distance covered by Leif =  100 + Distance covered After Cormac started

Distance covered After Cormac started = 65t

Distance covered by Cormac =  100t

To catch Leif,

100t = 65t + 100

35t  =  100

   t  = 2.85 minute

Hence, the required time is 2.85 minute

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The width of the bookcase is 6 feet and height is 4 feet if the carpenter expects to use 28 feet of lumber to make it.

Let w = the width and h = the height of the bookcase. The width of the lumber you are using is not given.

Also, Let the height is x.

and, the width is 3x -14.

Since, we stated that this equals 28 feet and also that w = 3h - 14, we can insert this into the equation and use it to solve for h:

Now,

The total amount of lumber used to make the bookcase is:

L = 4w + 2h             -------------------------- (1)

Now Putting Width and height in the Equation (1):

⇒ 28 = 4(3h - 14) + 2h

⇒ 28 = 12h - 56 + 2h

⇒ 28 = 14h - 56

⇒ 84 = 14h

⇒ h = 84/14

      = 6 feet

Putting the value of height, h= 6 feet in

w = 3x -14

⇒ w = 3(6) - 14 = 4.

Therefore,

The width is 4 feet and the height is 6 feet.

Complete Question:

A bookcase is to have 4 shelves including the top as pictured below.

The width is to be 14 feet less than 3 times the height. Find the width and the height if the carpenter expects to use 28 feet of lumber to make it.

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