PLZ HELP PLZ
I WOULD APPRECIATE IT PLZ
19 and 20

PLZ HELP PLZI WOULD APPRECIATE IT PLZ19 And 20

Answers

Answer 1

let given points be

(x1,y1)=(-3,-3)

and(x2,y2)=(3,1)

equation of given line ,

(y-y1)= ((y2-y1)/(x2-x1))×(x-x1)

therefore, 2x-3y+3=0.........(i)

comparing (i ) with ax+by+c=0 we get

a=2

b= -3

c=3

then the line parallel to (i) is

ax+by+k=0 where k = -bc

that is, 2x-3y+9=0 is the required equation

Answer 2

Answer:

19. y = 2/3x - 10/3

20. y = -3/2x - 4

Step-by-step explanation:

First off, we need to find the equation of the line shown. There are two coordinates given. The slope of the line is (1 - -3) / (3 - -3) = 4 / 6 = 2/3. The line obviously intersects the y-axis at -1, so the equation of the line is y = 2/3x - 1.

19. If a line were to be parallel to the given line, the line would have to have a slope of 2/3. So, we have y = 2/3x + b.

To solve for b, all you need to do is substitute the coordinates given, (2, -2), and solve.

-2 = (2/3) * 2 + b

b + 4/3 = -2

b = -6/3 - 4/3

b = -10/3.

So, the equation of the line is y = 2/3x - 10/3.

20. If a line were to be perpendicular to the given line, the line would have a slope that is the negative reciprocal of the given line's slope. The slope would be -3/2. So, we have y = -3/2x + b.

To solve for b, once again, put in the given coordinates, (-4, 2), and solve.

2 = (-3/2) * (-4) + b

b + 6 = 2

b = -4

So, the equation of the line is y = -3/2x - 4.

Hope this helps!


Related Questions

Complete the solution of the equation. Find th
value of y when x equals -4.
- 8x + y = 37
Enter the correct answer.​

Answers

Answer:

64

Step-by-step explanation:

The perimeter of a triangle is 7 a − 11 b . If two of its sides are 2 a + b and a − 9 b , what is the third side?

Answers

Answer:

To find the missing side we need to calculate the sum of the two given sides and then subtract that from the perimeter.

7a - 11b - (2a + b + a - 9b)

= 7a - 11b - (3a - 8b)

= 7a - 3a - 11b + 8b

= 4a - 3b

Use the graph to complete the statement. O is the origin. Ry−axis ο Ry=x: (2,3) A. (-2, -3) B. (3, -2) C. (2, -3) D. (-3, 2)

Answers

Answer:

D

Step-by-step explanation:

Given

[tex]R_{y-axis}[/tex] ○ [tex]R_{y=x}[/tex] : (2, 3 )

Then the order of reflections is from right to left, that is

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(2, 3 ) → (3, 2 )

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , thus

(3, 2 ) → (- 3, 2 ) → D

a bonus of 4200 is shared by 10 people who works for a company.40% of the bonus is shared equally between 3 managers the rest of the bonus is shared equally between 7 sales people.Peter, one of the sales people says," if the bonus is shared equally between 10 people i will get 25% more money. Janet a manager, says," no you wont get that much extra. show that Janet is correct by working out how much peter thinks he would get and how much he would actually get.

Answers

Step-by-step explanation:

if each the bonus is shared equally each will get 420

if 40% is shared by managers each manager will get 560

if 7 sales persons share 60% each will get 360

therefore Peter salesperson will get 360

but he thinks he will get 336 because if 420 is 125% that is including his extra 25% then hundred percent of the 420 is 336 which is not what he will get there for Janet is correct

Use the Quadratic Formula to solve y=3x2+9x-13

Answers

The answer is y= 3x^2+9x-13

Hope it help u

Can someone help me out with these math questions?
You can pick one to answer or chose to answer both!
I’d appreciate the help thank you!

Answers

For both questions I used F.O.I.L. to expand from factored form. Hope this helps!
Answer: 1. -12x^2 + 48x - 48
2. -20x + 50

Explanation:
1.
-3(2x-4)^2
= -3(4x^2 - 2(2)(4) + 16)
= -3(4x^2 -16 + 16)
= -12x^2 + 48x - 48

2.
(2x-5)^2 - (2x-5)(2x+5)
= 4x^2 - 2(2)(5)x + 25 - (4x^2 - 25)
= 4x^2 - 20x + 25 - 4x^2 + 25
= -20x + 50

Determine the intercepts of the line.

Answers

Y int.: (0,-1.2)
X int.: (-0.7,0)

A square with side length c has an area of 81 square centimeters. The following equation shows the area of the square. c^2 = 81. What is the side length of the square in centimeters?

Answers

Answer:

9 cm

Step-by-step explanation:

c^2=81

Take the square root of both sides.

The square root of c^2 is c.

The square root of 81 is 9.

c=9

Answer:

C = 9 centimeters

Step-by-step explanation:

First, look at the area of a square, which formula is c^2 or in standard format - s^2. Thus, we can say, c^2 = 81. Then, we can simplify, and put c = √81. Since 81 is a perfect square, 9 *  9 = 81. Thus the answer is 9 centimeters.

Solve using derivatives.
I have no clue where to start on this I really need help please.
Please show steps and diagram.

Answers

Answer:

Below in bold.

Step-by-step explanation:

The surface area of the box

= x^2 + 4hx  where x = a side of the square base and h is the height.

So x^2 + 4hx = 8

The volume of the box

V = x^2h

From the first equation we solve for h

4hx = 8 - x^2

h = (8 - x^2) / 4x

Now we substitute for h in the formula for the volume:

V = x^2 * (8 - x^2) / 4x

V =  8x^2 - x^4 / 4x

V =  2x - 0.25x^3

Finding the derivative:

V' = 2 - 0.75x^2 =  0  for max/mimn values

x^2 = 2/ 0.75 = 2.667

x = 1.633.

So the  length and width of the base is 1.633 m and the height

= ( 8 - 2.667) / (4*1.633)

= 0.816 m

The maximum volume =  0.816 *  2.667 =  2.177 m^2.

The answers are correct to the nearest thousandth.

Susie needs to melt some chocolate to use in a recipe she found in a cookbook. The cookbook calls for melting the chocolate at a low temperature of 30 degree celsuis . What temperature in degrees Fahrenheit will she need to set her stove to melt the chocolate? Round your answer to the nearest whole degree. The solution is

Answers

Answer:

The temperature needed to melt the chocolate = 86  degree Fahrenheit.

Step-by-step explanation:

The given temperature = 30 degrees Celsius.

Now we have to calculate the temperature in Fahrenheit. So just covert the given degree Celsius into Fahrenheit. Therefore multiply the 30 with 9/5 and add the 32 so the remaining answer is the temperature in the Fahrenheit. Below is the calculation to convert the degree Celsius into Fahrenheit.

Temperature = 30 × 9/5 + 32 = 86 Fahrenheit.

Seven lamps labeled A through G are arranged in a row. Each lamp has its own switch. Now lamps A, C, E, and G are on and other lamps are off. Ben starts to flip each switch from A to G the following way: if the lamp is on, he turns it off; if the lamp is off, he turns it on. He repeats the pattern until he flips the switches 2011 times. Which lamps are on finally? dont bully me im in 5th grade also this is due in 4 days

Answers

Answer:

O=on

X=off

OXXOXOX  after 2011 flips.

Step-by-step explanation:

There are many ways to get the answer.

A. Actually flip them 2011 times.

One way is to put 7 cards on the table, and name them A to G, with A,E,C,G facing up, and the other facing down.

Now flip the cards in order A to G 2011 times and find the answer.  

Since you have four days to find the answer, you only have to flip about 500 times a day.

B. Simplify procedure A above.

Do the same as above, actually flip the cards, but only 14 times.

You will find that the cards are restored to the original position after 14 flips.  

If we divide 2011 by 14, we get a quotient of 143 with a remainder of 9.

We know we don't have to make 143 sets of 14 flips.  We only need to make 9!

Then again, we know that after 7 flips, the lights will be all opposite.

If O=on, and X=off then the situations are

OXOXOXO  initial

XOXOXOX  after 7 flips

OXXOXOX  after 9 flips, which is also after 2011 flips, and that is the final answer.

Find the least common multiple of x2 + 4x + 3 and x2 + 7x + 12.

Answers

Answer:

( x+1) (x+3) (x+4)

Graphically represent the increase in emission of greenhouse gasses in India over a period of 5 years.

Answers

Answer:

Check it below

Step-by-step explanation:

According to GHG platform India, in the period between [2011-2015] there was a growth of emissions in tons of Carbon Dioxide. As it follows below.

The Energy sector is the segment that contributes the most with this, followed by the Agricultural and the Industries and the Waste.

Find the percentage change: The price was $60. Now it is $40.

Answers

Answer:

33.33%

Step-by-step explanation:

The percentage was a decrease.

Let the percent be x.

60 × (1 - x%) = 40

60 × (1 - x/100) = 40

1 - x/100 = 40/60

-x/100 = 40/60 - 1

-x/100 = -1/3

x/100 = 1/3

x = 1/3 × 100

x = 33.33333

Solve this equation with a variable term on both sides. 5.1y = –0.3y – 21.6 What is the solution? y =

Answers

Answer:

y = -4

Step-by-step explanation:

5.1y = –0.3y – 21.6

5.1y + 0.3y = -21.6

5.4y = -21.6

y = -4

Answer:

y=  -4

Step-by-step explanation:

Solve this equation with a variable term on both sides.

5.1y = –0.3y – 21.6

What is the solution?

y =  -4

HELP PLZ Javier and his study group designed a word problem, equation, table, and graph that were all supposed to represent the same information, as shown below. Word Problem A movie theater charges $8.00 for each ticket. What is the total cost, y, for x tickets? Equation y = 8x Graph Movie Theater Costs A graph with number of tickets sold on the x-axis and total cost on the y-axis. A line goes through points (8, 1), (16, 2). Table A 2-column table with 4 rows. Column 1 is labeled x with entries 5, 8, 12, 13. Column 2 is labeled y with entries 40, 64, 96, 104. Which piece of information does not represent the same information as the other three parts? word problem equation graph table

Answers

Answer:

Graph

Step-by-step explanation:

The graph swapped the y and x axis values.

Answer:

Graph

Step-by-step explanation:

PLEASE HELP ! ! ! pleaseeeee ! ! ! ! ! :C

Answers

Answer:

5/2

Step-by-step explanation:

When you multiply exponents, you add the powers, and when you subtract exponents, you subtract the powers.

Step 1: Move negative exponents

[tex]\frac{2^25^6}{2^35^35^2}[/tex]

Step 2: Combine exponents

[tex]\frac{2^25^6}{2^35^5}[/tex]

Step 3: Remove like terms

[tex]\frac{5^1}{2^1}[/tex]

Step 4: Exponent

5/2

which best describes how the graph of g(x) = radical 25/9x
relates to the graph of the parent function, f(x)= radical x?

Answers

Answer:

Step-by-step explanation:

g(x) = radical 25/9x would be clearer if written as g(x) = radical (25/9)x.  Note that radical (25/9) = (5/3).

The graph of g(x) = radical (25/9)x would have the same shape as that of g(x) = radical x EXCEPT that it would be stretched vertically by a factor of (5/3).

Answer: g(x) = radical 25/9x would be clearer if written as g(x) = radical (25/9)x. Note that radical (25/9) = (5/3).

The graph of g(x) = radical (25/9)x would have the same shape as that of g(x) = radical x EXCEPT that it would be stretched vertically by a factor of (5/3).

Step-by-step explanation:

PLEASE HELP ME I DO NOT HAVE TIME AND NEED TO PASS

Answers

Answer:

X=8.8 and Y=1

Step-by-step explanation:

additional expenses made after purchasing an article added to its actual cost are called————

Answers

Answer:

by definition : Additional expenses made after buying an article are included in the cost price and are known as overhead expenses.

Step-by-step explanation:

What is the solution set of {xlx<-3}{xlx>5)?
all real numbers
all numbers except -3 and 5
the empty set
the numbers between -3 and 5

Answers

Answer: C. Empty set

Explanation:

The first set {x | x < -3} means we're talking about numbers smaller than -3. This includes -4, -5, -6, etc

The second set {x | x > 5} means we're talking about numbers larger than 5. So things like 6,7,8,...

Combining both at the same time, we want to find a number that is both smaller than -3 and larger than 5. This is impossible as no such number exists. You can pick one or the other, but not both.

There are no solutions. Since there are no solutions, the solution set is the empty set.

Three numbers are in ration 3: 4: 8. The sum of the two larger numbers exceeds twice the smallest by 48. Find the numbers.

Answers

Answer:

24, 32, 64

Step-by-step explanation:

12x=6x+48

-6x  -6x

6x=48

x=8

8(3)=24

8(4)=32

8(8)=64

Answer:

24, 32, 64

Step-by-step explanation:

1st=3x

2nd=4x

3rd=8x

2(3x)+48=4x+8x

6x+48=12x

48=6x

x=8

SO:

1st =24

2nd= 32

3rd= 64

ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.

Answers

Answer:

[tex]t = 2.86 \: s[/tex]

The ball remains in the air for 2.86 seconds.

Step-by-step explanation:

A baseball is hit into the air, and its height above the ground is described by the function

[tex]H(t) = -16t^2 + 45t + 2[/tex]

Where H(t) represents the height of the ball t seconds after it is hit.

The ball remains in the air before it hits the ground.

When the ball hits the ground,

[tex]H(t) = 0[/tex]

So,

[tex]0 = -16t^2 + 45t + 2[/tex]

The equation may be solved using the quadratic formula.

[tex]$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

Where

[tex]a = -16 \\\\b = 45 \\\\c = 2 \\\\[/tex]

So,

[tex]t=\frac{-(45)\pm\sqrt{(45)^2-4(-16)(2)}}{2(-16)} \\\\t=\frac{-45\pm\sqrt{(2025 - (-128)}}{-32} \\\\t=\frac{-45\pm\sqrt{(2153}}{-32} \\\\t=\frac{-45\pm 46.4004}{-32} \\\\t=\frac{-45 + 46.4004}{-32} \: and \: t=\frac{-45 - 46.4004}{-32}\\\\t= -0.04 \: and \: t = 2.86 \\\\[/tex]

Since the time cannot be negative, discard the negative value and accept the positive value

[tex]t = 2.86 \: s[/tex]

Therefore, the ball remains in the air for 2.86 seconds.

What is the quotient of 8 1/4×3/4

Answers

Answer:

6 3/16

Step-by-step explanation:

8.25x.75=6.1875, or 6 & 3/16

Answer:

[tex]6\frac{3}{16}[/tex]

Step-by-step explanation:

[tex]8 \frac{1}{4} * \frac{3}{4} \\\\\frac{33}{4} * \frac{3}{4} = \frac{99}{16} \\\\\frac{99}{16} = 6\frac{3}{16}[/tex]

Hope this helps! :)

- Clout Answers

Brainliest is greatly appreciated :)

What is the quotient? StartFraction a minus 3 Over 7 EndFraction divided by StartFraction 3 minus a Over 21 EndFraction StartFraction negative (a minus 3) squared Over 147 EndFraction StartFraction (a minus 3) squared Over 147 EndFraction 3 –3

Answers

Answer:

Correct answer is

[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]

Step-by-step explanation:

Let us rephrase the given statement mathematically.

We are given the fractions as:

[tex]\dfrac{a-3}{7}[/tex]

to be divided by:

[tex]\dfrac{3-a}{21}[/tex]

To find:

[tex]\dfrac{a-3}{7}\div\dfrac{3-a}{21}[/tex]

Now, let us have a look at the division rule in fractions:

[tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex]

is equivalent to

[tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]

In other words, we say that the second fraction [tex]\frac{c}{d}[/tex] is changed to [tex]\frac{d}{c}[/tex] and [tex]\div[/tex] is changed to [tex]\times.[/tex]

Now solving the given fraction by applying above rules:

[tex]\dfrac{a-3}{3}\div\dfrac{3-a}{21}[/tex]

[tex]\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{3-a}\\\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{-(a-3)}\\\Rightarrow \dfrac{1}{1}\times \dfrac{3}{-1}\\\Rightarrow -3[/tex]

So, correct answer is:

[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]

Answer:

d on edg

Step-by-step explanation:

taking test rn

in a box of chocolates, 1/5 of the chocolates contains nuts. the rest do not.
write down the ratio of the number of chocolates that contains nuts to the number of chocolates that do not contain nuts .
give you answer in the form 1: n

Answers

Answer:

the ratio would be 1:4

Step-by-step explanation:

ratio of those who has nuts:

1/5

ratio of those who dont:

1-1/5=4/5

one against another:

1/5 : 4/5 = 1:4 = with : without

Expand the following:
a) x(x + 2)
b) x(2x - 5)
c) 2x(3x + 4)
d) 6x(x - 2)

Answers

Answer:

[tex]a. \: {x}^{2} + 2[/tex]

[tex]b. \: 2 {x}^{2} - 5x[/tex] [tex]c. \: 6 {x}^{2} + 8x[/tex] [tex]d. \: 6 {x}^{2} - 12x[/tex]

solution,

[tex]a. \: x(x + 2) \\ \: \: = x \times x + 2 \times x \\ \: \: = {x}^{2} + 2x[/tex]

[tex]b . \: x(2x - 5) \\ \: = x \times 2x - x \times 5 \\ \: \: = 2 {x}^{2} - 5x[/tex]

[tex]c. \: 2x(3x + 4) \\ \: = 2x \times 3x + 2x \times 4 \\ \: \: = 6 {x}^{2} + 8x[/tex]

[tex]d. \: 6x(x - 2) \\ \: \: = 6x \times x - 6x \times 2 \\ \: \: = 6 {x}^{2} - 12x[/tex]

Hope this helps...

Good luck on your assignment..

Evaluate: [tex]3-2^2+4*3+5[/tex]

Answers

Answer:

16

Step-by-step explanation:

Apply PEMDAS:

Solve the exponent, multiply from left to right, and then subtract and add from left to right.

[tex]3-2^2+4*3+5\\\\3-4+4*3+5\\\\3-4+12+5\\\\-1+12+5\\\\11+5\\\\\boxed{16}[/tex]

Answer: 16

Step-by-step explanation:

The important thing to remember here is the Order of Operations

The Order of Operations states that first solve Parentheses, then Exponents, then Multiplication and Division, then Addition and Subtraction.

There are no parentheses.

Exponents: 3 - 4+4*3+5

Multiplication and Division: 3 - 4 + 12 + 5

Addition and Subtraction:

-1+12+5

11+5

16

Hope it helps <3

The question is in the picture attached

Answers

Answer:

≈ 10.7 ft

Step-by-step explanation:

We have 2 secants to a circle from an external point.

The product of the measure of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.

let the internal part of the right secant be x , then

6(6 + x) = 4(4 + 12) = 4 × 16 = 64 ( divide both sides by 6 )

6 + x ≈ 10.7 ( subtract 6 from both sides )

x ≈ 4.7

length of pass = 6 + 4.7 = 10.7

A right triangle has a side of length 1 fourth and a hypotenuse of length 1 third. What is the length of the other side?

Answers

Answer:

The other side = [tex]\frac{1}{12}[/tex] units

Step-by-step explanation:

A right triangle has a side of length [tex]\frac{1}{4}[/tex] units and;

the hypotenuse is [tex]\frac{1}{3}[/tex]

According to Pythagorean theorem,

a² + b² = c² , where a and b are the two legs of a triangle and c is the hypotenuse.

Lets say a² = [tex](\frac{1}{4}) ^2[/tex]   and  c² = ([tex](\frac{1}{3} )^2[/tex]

b² = c² - a²

b² = [tex]\frac{1}{9}[/tex] - [tex]\frac{1}{16}[/tex] = [tex]\frac{1}{144}[/tex]

So b = [tex]\sqrt{1/144}[/tex] = [tex]\frac{1}{12}[/tex] units.

So the other side = [tex]\frac{1}{12}[/tex] units.

Other Questions
Around the world, people tend to prefer: baby boys. baby boys, except in the U.S. where girls are preferred. baby girls, except in the U.S. where boys are preferred. baby girls. Matt invested $1500 into a stock of his choice. After two years, he had received$400 in dividends. He sold the stock and received a total of $1600. What is Matt'srate of return on investment? Refer to the following partial ANOVA results from Excel (some information is missing). Source of Variation SS df MS F Between groups 210.2778 Within groups 1483 74.15 Total 2113.833 The number of treatment groups is:_______. a- 4 b- 3 c- 2 d- 1 Need help with this activity ?Save for LaterFinish: SuIComplete the following conversation between two friends about a new student. Use the correct form of saber or conocer, according to the context.1) MARA: (1)t al estudiante nuevo? (2) sabes (t) cmo se llama?CARMEN: (YO) (3)que su apodo (nickname) es Beto.MARA: (4)si Beto habla espaol?CARMEN: Si, (5)que habla espaol.MARA: 2(6)dnde vive?CARMEN: Yo no (7) sdnde vive, pero mi hermano (8)que Beto vive cerca de launiversidadMARA: (9)t a Maribel, la hermana de Beto?CARMEN: No, yo no (10)a Maribel.MARA: Vamos a conocerlos!CARMEN: Vamos!Finish: Submit for Grading Determine the radius of an Al atom (in pm) if the density of aluminum is 2.71 g/cm3 . Aluminum crystallizes in a face centered cubic structure with an edge leng crossword, help me please The breaking down and changing of rocks at or near Earth's surface is called _____. What are some similarities and differences between group 1, 0 and 7 elements on the periodic table? A cell has a defect in its receptor for growth factors, preventing growth factors from attaching to and signalling the cell. Based on this, which prediction below is most likely?A. The cell will remain dormant in GO phase.B. The cell will grow uncontrollably and continue to divide as long as it has food.C. The cell will replicate its DNA but be unable to begin mitosis.D. The cell will begin DNA replication but will be unable to complete S phase. Please help me with this. Attention all smart people!!! Read this excerpt from The Tell-Tale Heart by Edgar Allan Poe. Then fill in the blanks in the paragraph that follows.TRUE! nervous very, very dreadfully nervous I had been and am; but why will you say that I am mad? The disease had sharpened my senses not destroyed not dulled them. Above all was the sense of hearing acute. I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad? Hearken! and observe how healthily how calmly I can tell you the whole story.It is impossible to say how first the idea entered my brain; but once conceived, it haunted me day and night. Object there was none. Passion there was none. I loved the old man. He had never wronged me. He had never given me insult. For his gold I had no desire. I think it was his eye! yes, it was this! He had the eye of a vulture a pale blue eye, with a film over it. Whenever it fell upon me, my blood ran cold; and so by degrees very gradually I made up my mind to take the life of the old man, and thus rid myself of the eye forever.In these opening lines, the reader is presented with a narrator who wants to kill "the old man" because of his eye. The author uses the lines to present a conflict. Based on this excerpt, this stage of the plot is most likely to occur in . Calculate the percent ionization of nitrous acid in a solution that is 0.249 M in nitrous acid. The acid dissociation constant of nitrous acid is Help please ASAP :) please give answers to both questions If (ax+b)(bx+a)=26x^2+ Box(x) +26, where a, b, and Box are distinct integers, what is the minimum possible value of Box, the coefficient of x?Question in latex: If $(ax+b)(bx+a)=26x^2+\Box\cdot x+26$, where $a$, $b$, and $\Box$ are distinct integers, what is the minimum possible value of $\Box$, the coefficient of $x$? A Chinese supporter of the Boxer Rebellion would most likely agree withwhich statement? Find the total surface area of this triangular prism... Helppp!!!! please!!! A firm sells peanuts in a perfectly competitive market. Upon increasing production output from 60 packages to 75 packages, the total revenue increased from $300to $375. What was the marginal revenue of this increase in production HELPPP DO NOT LOOK IT UP PLS In the 1790s, despite a lack of specific constitutional authority to do so, Congress chartered a national bank, arguing that the institution was necessary to regulate the value of currency, a power that the Constitution did grant to Congress. The chartering of a national bank was therefore an example of