To ensure that the mass of an average grain of rock salt stays the same, what should you multiply the first factor 1.2 by so that 10 negative 2 becomes 10 negative 4

Answer:

67 ≤ x ≤ 73

Step-by-step explanation:

The absolute value of a real number x is the non negative value of x. Therefore the absolute value of x (|x|) = x for x ≥ 0 and -x for x < 0.

An expression |x - a| = b signifies that x - a = b or -(x - a) = b

Given that |x − 70| ≤ 3, hence:

|x − 70| ≤ 3

x - 70 ≤ 3 or -(x - 70) ≤ 3

x ≤ 3 + 70 or x - 70 ≥ -3

x ≤ 73 or x ≥ -3 + 70

x ≤ 73 or x ≥ 67

67 ≤ x ≤ 73

Hence the solution of |x − 70| ≤ 3 is 67 ≤ x ≤ 73

Answer:

273 tiles

Step-by-step explanation:

Given

Square tile

[tex]Side=\frac{1}{2} ft[/tex]

Bathroom floor

[tex]Length = 10\frac{1}{2}ft[/tex]

[tex]Width = 6\frac{1}{2}ft[/tex]

Required

Determine the number of tiles to cover the floor

First, we calculate the area of the floor:

[tex]A_{floor} = Length * Width[/tex]

[tex]A_{floor} = 10\frac{1}{2} * 6\frac{1}{2}[/tex]

Convert to decimals

[tex]A_{floor} = 10.5 * 6.5[/tex]

[tex]A_{floor} = 68.25ft^2[/tex]

Next, we calculate the area of the square tile:

[tex]A_{tile} = Side * Side[/tex]

[tex]A_{tile} = \frac{1}{2} * \frac{1}{2}[/tex]

Convert to decimal

[tex]A_{tile} = 0.5 * 0.5[/tex]

[tex]A_{tile} = 0.25ft^2[/tex]

The number of tiles is then calculated as:

[tex]Tiles = \frac{A_{floor}}{A_{tile}}[/tex]

[tex]Tiles = \frac{68.25ft^2}{0.25ft^2}[/tex]

[tex]Tiles = \frac{68.25}{0.25}[/tex]

[tex]Tiles = 273[/tex]

Answer:

-6g + 7h

Step-by-step explanation:

Answer:

D. x[tex]\geq[/tex]26

Step-by-step explanation:

Its x >_ 26

______________

Answer:

1) 4x² + 3x

Step-by-step explanation:

Add/Combine like terms:

2x² - 6x² = -4x²

6x - (+3x) = 3x

5 - (+5) = 0

Simplify: -4x² + 3x

Answer:

5/6

Step-by-step explanation:

Answer:

1 1/2 - 2/3 = 5/6

Step-by-step explanation:

I hope i helped ^^

Answer:

a) 12cm

b) 360cm²

c) 2160cm cubed

Step-by-step explanation:

a)

you would use Pythagoras theorem  for A

so half of 18 is 9

15² - 9² = 144

the square root of 144 is 12

the height is 12cm

b)

18 x 20 = 360cm²

c)

csa x L

csa = b x h divide by 2

18 x 12 = 216cm²/2 = 108cm²

108xm² x 20cm = 2160cm cubed

Answer: (1,-3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function:

a) Maximum height is the vertex. The ball reaches the maximum after:

b) Time the ball was in the air:

Solving we get approximately t = 13 seconds

c) Maximum height is at vertex, we found t above:

Answer:

The mercury will not freeze because the freezer is warmer than the freezing point of mercury.

Step-by-step explanation:

A "freezing point" is a point that allows a liquid to solidify. This is lower than the melting point (of course). However, specific liquids freeze at varying freezing points.

For example, the freezing point of water is 0°C while the freezing point of Mercury is -39°C. This means that water will only freeze once it reaches a temperature of 0°C or lower than this. Same goes for Mercury–it needs to reach the temperature of -39°C or lower in order to freeze.

Answer: Decisions and Determinations -If a Medicare appeal request does not result in a dismissal, adjudication of ... dismissal by providing an explanation for the late filing to the MAC within 6 months of the dismissal of the.

Step-by-step explanation:g brain

Answer:

∠2

Step-by-step explanation:

∠2 + ∠3 = 90°

complimentary angles add up to 90°

Answer:

257cm

Step-by-step explanation:

Can I get brainliest pls

Answer:

159

Step-by-step explanation:

35x-1 =-35 plus 34x20

Answer:

Gwen has already burned 100 calories when Tristan and Keith started, and he continues to burn 10 calories per minute.The equation for Gwen is

y = 100 + 10x

Question 2)`Tristan is burning 125 calories every 10 minutes. His burning calories rate is 12.5 calories per minute. The equation for Tristan is

y = 12.5x

Question 3)Keith is burning 300 calories in 30 minutes. His rate per minute is 10 calories per minute. The equation for Keith isy = 10x

Step-by-step explanation:

Answer:

5.60 ganeyryjfj3ym5uhwrbeyny3nte y

Answer:

50

Step-by-step explanation:

first of all thimk about how many 12s there is in 60 (which is 1hr=60)  and thats 5, so multiply 5 by 10 because in each 12 mins its 10 km which gives you 50 as the answer

Answer:

2

Step-by-step explanation:

The slope of the line with equation y=2x+3 is 2 . So, any line parallel to y=2x+3 has the same slope 2 .

Hello!

Parallel lines have the same slope. So if one line has a slope of 2, the line parallel to it has a slope of 2 as well.

Therefore, the slope is 2. Hope it helps.

If you have any questions, feel free to ask.

~A forlorn teen

[tex]MagicalNature[/tex]

Answer:

WHAT?!

Step-by-step explanation:

Answer:

[tex]P(x)=-5x^3-40x^2-45x+90[/tex]

Step-by-step explanation:

Equation of a Polynomial

Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:

[tex]P(x)=a(x-x1)(x-x2)(x-x3)[/tex]

Where a is the leading coefficient.

We know the three roots of the polynomial -6, -3, and 1, thus:

[tex]P(x)=a(x+6)(x+3)(x-1)[/tex]

Since the y-intercept of the polynomial is y=90 when x=0:

90=a(0+6)(0+3)(0-1)

90=a(6)(3)(-1)=-18a

Thus

a = 90/(-18) = -5

The polynomial is:

[tex]P(x)=-5(x+6)(x+3)(x-1)[/tex]

We must write it in standard form, so we have to multiply all of the factors as follows:

[tex]P(x)=-5(x^2+6x+3x+18)(x-1)[/tex]

[tex]P(x)=-5(x^2+9x+18)(x-1)[/tex]

[tex]P(x)=-5(x^3-x^2+9x^2-9x+18x-18)[/tex]

[tex]P(x)=-5(x^3+8x^2+9x-18)[/tex]

[tex]\boxed{P(x)=-5x^3-40x^2-45x+90}[/tex]

Answer:

D

Step-by-step explanation: edge 2021

Answer:

x= 4.5

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer: y=4/3x-8

Step-by-step explanation:

Answer:

The rate of change of Function A is less than the rate of change of function B.

Other than that, everything else you put is correct.

Step-by-step explanation:

None.

Answer:

Option A, B and D are correct options.

Step-by-step explanation:

First we will find rate of change of function A and function B

Rate of Change of Function A

The formula used to calculate rate of change is: [tex]Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}[/tex]

We have x_1=1, y_1=5, x_2=2, y_2=7

Putting values in formula and finding rate of change

[tex]Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:Change=\frac{7-5}{2-1}\\Rate\:of\:Change=\frac{2}{1}\\Rate\:of\:Change=2[/tex]

So, Rate of change of Function A = 2

Now, finding y-intercept.

y-intercept is found by putting x =0

Looking at the function, we can write the equation: y=2x+3

Now, put x =0

y=2(0)+3

y=3

So, when x =0, y=3

So, y-intercept is 3 for function A.

Rate of Change of Function A

The formula used to calculate rate of change is: [tex]Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}[/tex]

We have x_1=1, y_1=1, x_2=2, y_2=4

Putting values in formula and finding rate of change

[tex]Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:Change=\frac{4-1}{2-1}\\Rate\:of\:Change=\frac{3}{1}\\Rate\:of\:Change=3[/tex]

So, Rate of change of Function B = 3

Now, finding y-intercept.

y-intercept is found by putting x =0

Looking at the graph, when x=0, y is -2

So, y-intercept is -2 for function B.

We get following answers:

Rate of change of Function A = 2

Rate of change of Function B = 3

y-intercept is 3 for function A.

y-intercept is -2 for function B.

So, The correct options are:

The rate of change of function A and B are positive

The rate of change of function A is less than the rate of change of function B. (Because 2 is less than 3)

The y-intercept of function A is positive, while y-intercept of function B is negative.

So, Option A, B and D are correct options.

Hey there!

We simply have to do 182/2.8, and you will get the area (65m^2).

We know that the formula for area is length x width, and the formula for volume is length x width x height. In the volume formula, we can see it can also be area x height to get volume. So, we know that area x height = volume, right? And in this equation, we are given volume and height. If          V = ha, with V = volume; h = height; a = area, we can divide "h" on both sides, and we get V/h = a, or volume divided by height is area. To solve for the above equation, we can plug the numbers in the formula: 182/2.8 = a, or 65 = a.

Hope this helps! Have an amazing day, and remember, you've got this!

Answer:

See the proof below

Step-by-step explanation:

Given the following coordinates

P(2, −1)

Midpoint of PQ M(3, 0)

We can get the coordinate point Q using the midpoint formula;

M(X,Y) = (x1+x2/2, y1+y2/2)

X = x1+x2/2

3 = 2+x2/2

6 = 2+x2

x2 = 6-2

x2 = 4

Y = y1+y2/2

0 = -1+y2/2

0 = -1 + y2

y2 = 0+1

y2 = 1

Hence the coordinate of Q is (4, 1)

Next is to get the coordinate of R

Given the midpoint of QR to be N(5, 3)

(5,3) = (4+x2/2, 1+y2/2)

5 = 4+x2/2

10 = 4+x2

x2 = 10-4

x2 = 6

1+y2/2 = 3

1+y2 = 6

y2 = 6-1

y2 = 5

Hence the coordinate of R is (6,5)

Given the coordinates M(3, 0) and N(5, 3)

Slope is expressed as:

m = y2-y1/x2-x1

m = 3-0/5-3

m = 3/2

Slope of MN = 3/2

Get the slope of PR

Given the coordinates P(2, −1) and R (6,5)

Slope of PR = 5-(-1)/6-2

Slope of PR = 5+1/4

Slope of PR = 6/4 = 3/2

Since the slope of MN is equal to that of PR, hence MN is parallel to PR i.e MN || PR

To show that MN = 1/2PR, we will have to take the distance between M and N and also P and R first as shown:

For MN with coordinates  M(3, 0) and N(5, 3)

MN = √(x2-x1)²+(y2-y1)²

MN = √(5-3)²+(3-0)²

MN = √2²+3²

MN = √13

Get the length of PR where P(2, −1) and R (6,5)

PR = √(6-2)²+(5+1)²

PR = √4²+6²

PR = √16+36

PR = √52

PR = √4*13

PR = √4*√13

PR = 2√13

Since MN = √13

PR = 2MN

Divide both sides by 2

PR/2 = 2MN/2

PR/2 = MN

Hence MN = 1/2 PR (Proved!)

Answer:

48%

Step-by-step explanation:

(24/50)2

= 48/100

= 48%