Peggy is thinking of a number such that when twice the number is added to three times one more than the number she gets the same result as when she multiplies four times one less than the number. What number is Peggy thinking of?

Answer:

Graph A

Step-by-step explanation:

As we know, in 3 minutes he washes 18 dishes. Without even doing any math, you can see that this is the only graph that represents that. The others show that he washes two dishes in 12 minutes, which doesn’t make sense.

Ned's rate of washing dishes is 6 dishes per minute. The graph representing the number of dishes Ned can wash in any number of minutes would be an upward sloping line originating from the origin. The slope of this line, or the rate of change, signifies Ned's dish-washing rate.

This is a typical problem in Mathematics subject related to speed or rate, specifically, it involves a rate of washing dishes. Ned can hand-wash 18 dishes in 3 minutes. Thus, Ned's rate of washing is 18 dishes per 3 minutes, or 6 dishes per minute.

The relationship between the dishes and the minutes is a direct proportional relationship since the amount of dishes Ned can hand-wash increases directly as the time increases.

To reflect this in a graph, we would have a straight, upward sloping line originating from the graph's origin (0,0). The slope of this line, or the rate of change, signifies the rate at which Ned can wash dishes.

Given that Ned can wash 6 dishes per minute, each point on the line should increase by 6 dishes for each increment of 1 minute on the time axis. Hence the correct graph would be a straight line with a slope of 6.

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Brian should purchase Choice C of fabric

Solution:

Given that Brian wants to purchase a piece of fabric  that is between 49 and 53 inches long

So piece of fabric should be between: 49 and 53 inches

Let us convert feet to inches

[tex]4\frac{3}{4} feet = \frac{4 \times 4 + 3}{4} = \frac{19}{4} feet[/tex]

Now convert to inches

We know that,

1 feet = 12 inches

[tex]\frac{19}{4} feet = \frac{19}{4} \times 12 = 57 inches[/tex]

But this choice is greater than given condition that piece of fabric should be between: 49 and 53 inches

So this is not correct

[tex]4\frac{1}{2} feet = \frac{2 \times 4 + 1}{2} = \frac{9}{2} feet[/tex]

Now convert to inches

[tex]\frac{9}{2} feet = \frac{9}{2} \times 12 inches = 54 inches[/tex]

But this choice is greater than given condition that piece of fabric should be between: 49 and 53 inches

So this is not correct

[tex]4\frac{1}{3} feet = \frac{3 \times 4 + 1}{3} = \frac{13}{3} feet[/tex]

Now convert to inches

[tex]\frac{13}{3} feet = \frac{13}{3} \times 12 inches = 52 inches[/tex]

So this 52 inches lies between 49 and 53 inches

So Brian should purchase Choice C of fabric

3 small boxes and 6 large boxes were sent to the retailer.

Step-by-step explanation:

Number of books held by small boxes = 30

Number of books held by large boxes = 40

Total books held by boxes = 330

Let,

x represent the number of small boxes

y represent the number of large boxes

According to given statement;

y = 2x     Eqn 1

30x+40y=330    Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]30x+40(2x)=330\\30x+80x=330\\110x=330[/tex]

Dividing both sides by 110

[tex]\frac{110x}{110}=\frac{330}{110}\\x=3[/tex]

Putting x=3 in Eqn 1

[tex]y=2(3)\\y=6[/tex]

3 small boxes and 6 large boxes were sent to the retailer.

Keywords: linear equation, substitution method

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Answer:

The possible values of v are 6 and -6

Step-by-step explanation:

The opposite operation of an absolute value is to add a ± to the other side, so when we solve for v we get

|v|=6

v=±6

Which is the same as

v=-6 and 6

Answer:

C

Step-by-step explanation:

|6| and |-6| have the same meaning. Both are equal to 6

The answer is C

Answer:

The last system is that one with exactly one solution:

–2x + 7y = –5  

2x + 7y = –9

Step-by-step explanation:

We can easily check the number of solutions that each system has in this problem, since the equations contain most of them combinations of terms in y and in x that can be easily cancelled out via simple term by term addition.

Going through them system by system, and adding term by term the equations which are in standard form we get:

(1) –5x – 10y = 24  

      5x + 10y = 16  

---------------------------

     0x  +  0y   = 40  which sates a mathematical absurd: "0 = 40", and therefore there are no x and y solution values that could verify such. This also means that the lines represented by the system do NOT intersect (they are parallel lines)

(2)  3x + 4y = –7  

   –3x – 4y = 7  

   --------------------

    0x   + 0y  = 0 which gives that zero equals zero, which any pair (x, y) belonging to any of the two equations can verify, so an infinite number of solutions (the lines in the system overlap)

(3) –12x + 8y = 16  

      12x – 8y = 16  

      -------------------

       0x  +  0y   = 32 which sates a mathematical absurd: "0 = 2", and therefore there are no x and y solution values that could verify such. This also means that the lines represented by the system do NOT intersect (they are parallel lines)

(4)  –2x + 7y = –5  

        2x + 7y = –9

      ---------------------

        0x + 14y = -14

This is the only system that shows solution. It allows us first to solve for "y" in the resultant equation: 14 y = -14 giving us the value y = -14/14 = -1

and then using it the unique value for x can be determined:

        2x + 7y = –9

        2x + 7 (-1) = -9

        2x -7 = -9

        2x = -9 + 7

        2x = -2

          x = -2/2 = -1

Therefore, the pair (-1, -1) is the unique solution to the system

Answer:

Step-by-step explanation:

Trust me guys. The guy above me has a full explanation, but if you are just looking for a simple answer, then I gotchu

Money earned after working for 15 hours and making 8 deliveries is $ 534

Solution:

Given that pizza delivery person earns 30 per hour plus 10.50 for each delivery made

The expression used to find the earnings for him is given as:

30h + 10.50d

Where "h" is the number of hours and "d" is the number of deliveries

We have to find the money earned by him after working for 15 hours and making 8 deliveries

Therefore we get, h = 15 and d = 8

Substitute h = 15 and d = 8 in given expression

Money earned = 30(15) + 10.50(8)

Money earned = 450 + 84 = 534

Thus money earned after working for 15 hours and making 8 deliveries is $ 534

Answer:

i think C

Step-by-step explanation:

Answer:

$150.

Step-by-step explanation:

$250 - 0.20 *250 = $200.

Final price = 200 - 0.25*200

= $150.

Answer:

The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour .

Step-by-step explanation:

Given as :

The speed = s = 2000 ft per min

Now, ∵ 5280 feet = 1 miles

so, 1 feet = [tex]\dfrac{1}{5280}[/tex] miles

∴ 2000 feet =  [tex]\dfrac{1}{5280}[/tex] × 2000 miles

i.e 2000 feet = 0.378 miles

Again

∵ 1 minute = [tex]\dfrac{1}{60}[/tex] hour

So, The speed in miles per hour

s = [tex]\dfrac{distance}{time}[/tex]

∴ s = [tex]\frac{0.378}{\frac{1}{60}}[/tex]

i.e s = 2.268 miles per hour

Hence, The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour . answer

To convert 2000 ft./min. to miles per hour, multiply by appropriate conversion factors, and round the result, yielding 22.7 miles per hour.

To convert 2000 ft./min. to miles per hour, follow these steps:

Convert feet to miles: 2000 ft/min x (1 mile/5280 ft) = 0.3788 miles/min

Convert minutes to hours: 0.3788 miles/min x 60 min/hr = 22.73 miles/hr

Rounded to the nearest tenth, 2000 ft/min is 22.7 miles per hour.

Answer:

x=-19/5

Step-by-step explanation:

-3x=2x+19

-3x-2x=19

-5x=19

x=19/-5

Answer:

get x to one side by subtracting 2x from 2x+19

new equation:

-3x-2x=19

-5x=19

divide both sides by -5

x=-19/5

or x=-3 4/5

Answer:

Step-by-step explanation:

4 cm to 25 miles = 20 cm to x miles

4 / 25 = 20 / x

cross multiply

4x = (25)(20)

4x = 500

x = 500/4

x = 125 miles <=====

Answer:

The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Scale on a map: 4 cm = 25 miles

2.  What is the actual distance in miles represented by a line that is 20 cm on map ?

For calculating the distance in miles represented, we will use the following equation:

Actual distance in miles represented = Miles in the scale/Centimeters in the scale * 20

Replacing with the real values:

Actual distance in miles represented = 25/4 * 20 = 25 * 5 = 125

The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.

Answer:

The point lie outside the circle

Step-by-step explanation:

step 1

Find the distance between the center of the circle and the given point

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

(0,0) and (-3,-7)

substitute the values

[tex]d=\sqrt{(-7-0)^{2}+(-3-0)^{2}}[/tex]

[tex]d=\sqrt{58}\ units[/tex]

step 2

Compare the distance with the radius

If d=r ----> the point lie on the circle

If d > r -----> the point lie outside the circle

If d < r -----> the point lie inside the circle

we have

[tex]d=\sqrt{58}\ units[/tex]

[tex]r=\sqrt{53}\ units[/tex]

so

[tex]\sqrt{58}\ units > \sqrt{53}\ units[/tex]

[tex]d > r[/tex]

therefore

The point lie outside the circle

Answer:

C outside the circle

Step-by-step explanation:

khan

Answer:

0.33...acre

Step-by-step explanation:

1/4=0.25

3/4=0.75

-------------

0.25/0.75=x/1

cross product

0.75*x=0.25*1

0.75x=0.25

x=0.25/0.75

x=0.3

Answer:

The thickness of 1 card  = 0.0025 inches

Step-by-step explanation:

Here, the total number of cards in the stack = 250 cards

The total height of the stack = 5/8 inch = 0.625 in.

[tex]\textrm{Thickness of one card} = \frac{\textrm{The total thickness of the stack}}{\textrm{The total cards in the stack}}[/tex]

[tex]\implies \textrm{Thickness of one card} =\frac{0.625}{250} = 0.0025[/tex]

Hence, the thickness of 1 card  = 0.0025 inches

Answer:  4y + x - 22 = 0

Step-by-step explanation:

Recall that  for two lines to be perpendicular m1m2 = -1 ie, the product of their gradients must = -1

from the equation given, y - 3 = 4(x + 2), we need to rearrange it in the form

y = mx  + c in order for us to ascertain the gradient.

y -3 = 4x + 8

y = 4x + 8 + 3

y = 4x + 11

Therefore, m1 = 4 while m2 = -1/4

The coordinate of the line = (-2, 6) . We now use this to find the value of c.

6 = -1/4 x -2 + c

6 = 1/2 + c

multiply by 2

12 = 1 + 2c

12 - 1 = 2c

11 = 2c

c = 11/2

now to find the equation of the second line

y = -x/4 + 11/2

now multiply through by 4

4y = -x + 22

4y + x - 22 = 0 is the required equation

Question:

Ten subtracted from the quotient of a number and 5 is 18. What is the number?

Answer:

140 is the number.

Step-by-step explanation:

Let consider the number as ‘X’

Quotient of a number and 5 can be written as

                         [tex]X \div 5[/tex]

Ten subtracted from the quotient of a number and 5 can be written as

                        [tex](X \div 5) - 10[/tex]

Ten subtracted from the quotient of a number and 5 is 18 can be written as

                        [tex](X \div 5) - 10 = 18[/tex]

By solving the above equation, find ‘X’

                        [tex](X \div 5) = 18 + 10[/tex]

                        [tex]\frac{X}{5} = 28[/tex]

                        [tex]X = 28 \times 5 = 140[/tex]

Answer:

well it would kinda depend on their age,and size,but the average height of an ADULT male is : 5.6 ft

ADULT female:5.2ft

(remember it would depend on their age,but some people might even have medical reasons to be shorter or taller than their original height too. At a age children don't HAVE to be that exact height,but atleast close enough to that height.)

(changes may occur depending on medical reasons,or age too!)

Answer:

365.35

Step-by-step explanation:

USE A CALCULATOR!!!!

Answer:

  [tex]32\text{ for }x=0.\overline{40}[/tex]

Step-by-step explanation:

It looks like you want the sum of digits of the product ...

  [tex]x = (0.\overline{6})(0.\overline{60})=\dfrac{2}{3}\cdot\dfrac{20}{33}=\dfrac{40}{99}=0.\overline{40}[/tex]

Since the decimal fraction starts off with 4 and has an even number of repeating digits, there will be 8 4's and 7 0's in the sum of the first 15 decimal digits:

  sum = 8×4 +7×0 = 32

The sum of the first 15 digits after the decimal point is 32.

Answer:

The answer is 123.

Step-by-step explanation:

Given that-

( [tex]x + \frac{1}{x}[/tex] ) = 3.....................(i)

To find -

( [tex]x^{5} + \frac{1 }{x^{5} }[/tex] ) = ?

Now squaring both sides of equation (i)-

( [tex]x^{2}  + \frac{1}{x^{2} } + 2[/tex] ) = 9

( [tex]x^{2} + \frac{1}{x^{2} }[/tex] ) = 7....................(ii)

On cubing equation (i) both sides-

( [tex]x^{3} + \frac{1}{x^{3} } + 3 ( x + \frac{1}{x} )[/tex] ) = 27

( [tex]x^{3} + \frac{1}{x^{3} } + 3 * 3[/tex] ) = 27

( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 27 - 9

( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 18.....................(iii)

Multiply equation (i)  and equation (ii)-

( [tex]x^{2} + \frac{1}{x^{2} }[/tex] )  ( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 7 × 18

( [tex]x^{5} + \frac{1}{x^{5} } )+ ( x + \frac{1}{x} )[/tex] = 126

( [tex]x^{5} + \frac{1}{x^{5} } ) = 126 - 3

( [tex]x^{5} + \frac{1}{x^{5} } ) = 123

Answer:

So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.

Step-by-step explanation:

We are given a function and we have to find the intervals in which the function has positive value.

y = [tex]x^{2} +12x+27[/tex]

y =(x + 3)(x + 9)

For the function to be positive , y ≥ 0

(x + 3)(x +  9) ≥ 0

Here there are two cases , either both should be positive or both should be negative.

If both are positive,

(x + 3)≥0 and (x + 9)≥0

So, x ≥ -3

If both are negative,

(x + 3)≤0 and (x + 9)≤0

So, x ≤ -9

So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.

The intervals on which the function y = x² + 12x + 27 is positive are

x > -3 and x > -9

For the function given to be positive, it has to be greater than zero.

Since the expression is greater then zero, hence;

x² + 12x + 27 > 0

Factorize the resulting expression

x² + 3x + 9x + 27 > 0

x(x+3) + 9(x+3) > 0

(x+3) (x+9) > 0

x+3 > 0 and x + 9 > 0

x > -3 and x > -9

Hence the intervals on which the function y = x² + 12x + 27 is positive are

x > -3 and x > -9

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Answer:

1.5a - 0.5

Step-by-step explanation:

Add like terms

4.4 - 2.9 = 1.5

7.3 - 6.8 = 0.5

Final answer:

To find the sum of the two expressions -2.9a+6.8 and 4.4a-7.3, you need to combine the like terms. Simply add or subtract the coefficients of like terms while keeping the variable the same, the sum of the two expressions -2.9a+6.8 and 4.4a-7.3 is (4.4a - 2.9a) + (6.8 + (-7.3)). .

Explanation:

To find the sum of the two expressions -2.9a+6.8 and 4.4a-7.3, you need to combine the like terms. Like terms are terms that have the same variable raised to the same power. In this case, -2.9a and 4.4a are like terms because they both have the variable 'a' raised to the first power. Similarly, 6.8 and -7.3 are also like terms because they don't have any variables. To combine like terms, simply add or subtract their coefficients while keeping the variable the same.

So, -2.9a + 4.4a can be combined as (4.4a - 2.9a) and 6.8 - 7.3 can be combined as (6.8 + (-7.3)).

Therefore, the sum of the two expressions -2.9a+6.8 and 4.4a-7.3 is (4.4a - 2.9a) + (6.8 + (-7.3)).

Answer:

y=3x+6

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-0=3(x-(-2))

y-0=3(x+2)

y=3x+6+0

y=3x+6

Answer:

The answer is B

Step-by-step explanation:

You just have to subtract the lowest temp by the highest temp

Answer:

?

Step-by-step explanation:

It could be

Answer:

Yes

Step-by-step explanation:

Yes because it is a one-to-one relation. Every x-value maps to a unique value of y.

Answer:

(i) 5

(ii) - 1

(iii) - 1

(iv) 0

(v) 1

(vi) 1

Step-by-step explanation:

See the graph attached to this question.

The blue graph shows y = f(x) and the red graph shows y = g(x).

(i) (f + g)(- 3) = f(-3) + g(-3) = 4 + 1 = 5

(ii) (g - f)(- 2) = g(- 2) - f(- 2) = 2 - 3 = - 1

(iii) (fg)(2) = f(2) × g(2) = (- 1) × (1) = - 1

(iv) [tex](\frac{g}{f})(3) = \frac{g(3)}{f(3)} = \frac{0}{- 3} = 0[/tex]

(v) (fog)(1) = f[g(1)] = f(1) = 1

(vi) (gog)(- 1) = g[g(-1)] = g(2) = 1  (Answer)

After using the graph with the values of f and g we find the values as follows:

(i) (f+g)(-3) = 5

(ii) (g-f)(-2) = -1

(iii) (fg) (2) = -1

(iv) (g/f) (3) = 0

(v) (f o g) (1) = 1

(vi) (g o g)(-1) = 1

i) ( f +g ) (-3)

= ( f (-3) + g(-3) )

Values we got from the graph are:

f(-3) = 4

g(-3) = 1

After substituting these values in the given equation we get

( f + g) (-3) = 5

ii) ( g - f ) (-2)

= ( g(-2) - f(-2) )

Values we got from the graph are:

g(-2) = 2

f(-2) = 3

After substituting these values in the given equation we get

( g - f ) (-2) = - 1

iii) ( fg) (2)

= ( f(2) g(2))

Values we got from the graph are:

f(2) = -1

g(2) = 1

After substituting these values in the given equation we get

( fg)(2) = -1

iv) (g/f) (3)

( g(3) / f(3) )

Values we got from the graph are:

g(3) = 0

f(3) = - 3

After substituting these values in the given equation we get

( g / f ) (3) = 0

v) ( f o g ) (1)

= ( f(1) o g(1) )

Values we got from the graph are:

g(1) = 1

f(1) = 1

After substituting these values in the given equation we get

( f o g ) (1) = 1

vi) ( g o g ) (-1)

= ( g(-1) o g(-1) )

Values we got from the graph are:

g(-1) = 2

g(2) = 1

After substituting these values in the given equation we get

( g o g ) (-1) = 1

Work is provided in the image attached.

Answer:

5 times

Step-by-step explanation:

$25 - $10 (fixed rate) = $15

$15 / $3 = 5 times.

Mia must watch her brother 5 times within the week to make the desired amount. Hope this helps :)

Answer:

A) 8, 15, 17.

Step-by-step explanation:

Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option  (the hypotenuse) that means that those numbers could be the sides of a right triangle.

The Pythagorean theorem states that: [tex]a^2+b^2=c^2[/tex]

Thus:

[tex]\sqrt{a^2+b^2}=c[/tex]

Option A:

[tex]\sqrt{8^2+15^2}=17[/tex] → 17 = 17 OK!

Option B:

[tex]\sqrt{6^2+8^2}  = 10[/tex] → 10 ≠ 12 NO

Option C:

[tex]\sqrt{9^2+11^2} = [tex]\sqrt{202}[/tex][/tex] → [tex]\sqrt{202}[/tex] ≠ 21 NO

Option D:

[tex]\sqrt{4^2+13^2} = \sqrt{185}[/tex] → [tex]\sqrt{185}[/tex] ≠ 16 NO

Answer:

100

Step-by-step explanation:

It will help in the future to memorize your time tables

10*10 is basically 10 plus 10, 10 times but in a easier form

10+10+10+10+10+10+10+10+10+10=100

10+10=20

20+10=30

30+10=40

40+10=50

50+10=60

60+10=70

70+10=80

80+10=90

90+10=100