A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. which constraint could be part of the scenario? the pool is 1 meter deep. the pool is 2 meters deep. the toy falls at a rate of at least a negative one-half meter per second. the toy sinks at a rate of no more than a negative one-half meter per second.

Answer:

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Assuming the time changes at a constant rate, the equation for this is linear (so has the equation y=mx +c)

8am = -2

9am = -0.5

10am = 1.0

11am = 2.5

12pm = 4

m = change in each value or the slope , for this it is m=1.5

c = the y intercept, we find this by: when x=8 y must = 1.5 , which it isn't , y has to = -2 . So c = -3.5

The equation then is: y= 1.5*x - 3.5

The gradient/slope/m value is 1.5. The answer is 1.5

Part A: The amount of ice cream increases as the temperature increases. Part B: the slope is 2 and the y-intercept will be 5.

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

Part A: The relationship between the temperature of the city and the number of ice cream cones sold.

From the graph, the dots on the graph increase in the up-right direction.

Thus, The amount of ice cream increases as the temperature increases.

Part B: The line of best fit

First, if we draw a line through the points

we select any 2 points on the line:

( p,q) and (x,y) as (15, 35) and (0, 5).

The slope (m) is:

[tex]m = \dfrac{y-q}{x-p}[/tex]

[tex]m = \dfrac{5 - 35}{0-15}\\\\m = 2[/tex]

So, the line of best fit is:

y = mx + c

y = 2(x - 0) + 5

y = 2x + 5

The y-intercept will be when x = 0

y = 2x + 5

y = 0 + 5

y = 5

Thus, the slope is 2 and the y-intercept will be 5.

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Answer:

Is your teacher trying to confuse us or what?

Step-by-step explanation:

well 3/3 is full so it's just like 12/12, so 12 pieces of 1/12 piece are in 3/3

Answer:

See below ~

Step-by-step explanation:

Q1

⇒ S = {1, 2, 3, 4, 5, 6}

===========================================================

Q2

⇒ No. of possible outcomes = 6

===========================================================

Q3

(a)

⇒ P(6) = Number of 6's / Total numbers

⇒ P(6) = 1/6

(b)

⇒ P (negative) = No. of negative numbers / Total numbers

⇒ P (negative) = 0/6

⇒ P (negative) = 0

(c)

⇒ P (odd) = No. of odd numbers / Total numbers

⇒ P (odd) = 3/6

⇒ P (odd) = 1/2

Answer:

D

Step-by-step explanation:

can't really explain it just is the answer

hope this helps!

Answer:14.1%

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

it is easy first think but besides which school are you from

Answer:

Step-by-step explanation:

La cantidad numérica es donde escribes la cantidad del cheque con números/dígitos. Escribe los dólares en forma numérica y luego indica los centavos después del punto decimal. En el ejemplo a continuación, los dólares son ciento veinticinco (125) y los centavos son setenta y cinco (. 75).

Answer:.04/n

Step-by-step explanation:solidus represents division

The equation of the circle with the new point will be x² + ( y - 2 )² = 16.

The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the outer trace.

Given that:-

The equation of the circle will be formed as:-

We know that the general form of the circle is given as

( x - h )² + ( y - k )² = r²,

where ( h, k ) is the centre and r is the radius. When the circle is shifted 2 units up it means that now its centre will be ( 0, 2). So the equation will be:-

x² + ( y - 2 )² = 16

Therefore the equation of the circle with the new point will be x² + ( y - 2 )² = 16.

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Given that

[tex]\displaystyle \lim_{x\to0} f(x) = 4[/tex]

we can use the properties of limits to show

[tex]\displaystyle \lim_{x\to0} \frac14 f(x)^4 = \frac14 \lim_{x\to0} f(x)^4 = \frac14 \left(\lim_{x\to0} f(x)\right)^4 = \frac14 \times 4^4 = 4^3 = \boxed{64}[/tex]

Let's see

[tex]\\ \rm\Rrightarrow \lim_{x\to 0}\dfrac{1}{4}f(x)^4[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\lim_{x\to 0}f(x)^4[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\times 4^4[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{256}{4}[/tex]

[tex]\\ \rm\Rrightarrow 64[/tex]

Answer:

5/8

Step-by-step explanation:

The number of possible outcomes after flipping 3 coins is $2 \times 2 \times 2 = 8$. If the dime isn't heads, we need both the penny and nickel to be heads. If the dime is heads, the other two could be anything. So there are a total of $1+(2 \times 2)=5$ ways for us to get at least 6 cents. The answer is $\boxed{\dfrac58}.$

Answer:

find the measure of J

180-45=135

find the measure of K

360-135=225

The modal lengths of the ribbons are 60 cm and 110cm.

If the length 110 is removed, the new model length would be 60 cm.

Mode refers to a value that appears most frequently in a data set. Mode is a measure of central tendency. 110 and 60cm occur twice in the dataset. Thus, they are the mode lengths.

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Step-by-step explanation:

it is just a line covering all values smaller than -8 (that means left of -8).

so, it is a line starting at -8 and going all the way to the left (to the arrow on the left). and you make an empty (hollow) dot at -8, because the value -8 is not included (otherwise it would be p <= -8, and it would be a filled dot at -8).

From the steps shown in the table given, we can conclude that: D. in solving the equation, the subtraction property of equality was not applied.

If a + b = c, to apply the subtraction property of equality so that b is moved to the other side of the equation, we would have:

a + b - b = c - b

a = c - b

Thus, from the table given, the none of the steps showed that the subtraction property of equality was applied in solving the equation, so, the answer is: D.

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Answer:

42 miles

Step-by-step explanation:

If it's a constant 12 miles per hour then it would be

12 mph x 3 hours = 36

then you would add that with the 1/2 hour for

12 mph x 1/2 hours = 6

36 + 6 = 42 miles traveled

Answer:

A

Step-by-step explanation:y-5=6(x+1)

y-5=6x+6 Combine like terms so you add -5 to +6 which would be y=6x+11

Answer:

[tex]4(x-5)(3{x}^{2}+1)[/tex]

Step-by-step explanation:

1) Find the Greatest Common Factor (GCF).

1 - What is the largest number that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?

It is [tex]4.[/tex]

2 - What is the highest degree of [tex]x[/tex] that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?

It is 1, since [tex]x[/tex] is not in every term.

3 - Multiplying the results above,

The GCF is 4.

2)  Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

[tex]4(\frac{12{x}^{3}}{4}+\frac{-60{x}^{2}}{4}+\frac{4x}{4}-\frac{20}{4})[/tex]

3) Simplify each term in parentheses.

[tex]4(3{x}^{3}-15{x}^{2}+x-5)[/tex]

4) Factor out common terms in the first two terms, then in the last two terms.

[tex]4(3{x}^{2}(x-5)+(x-5))[/tex]

5)  Factor out the common term [tex]x-5[/tex].

[tex]4(x-5)(3{x}^{2}+1)[/tex]

The water consumption based on the information for three months will be 22267m³.

The total water consumption for the three months will be:

= 7219 + 7390 + 7658

= 22267m³

In conclusion, the information simply wants you to add the values of the water given.

Therefore, the water consumption based on the information for three months will be 22267m³.

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Answer: -329 sorry if i'm not right

The equations of the asymptotes of the given hyperbola are; y = ±(40/9)x

We are given;

Vertex at (0,−40)

Focus at (0, 41).

Thus, the equation of the asymptote of the given hyperbola is;

y = ±(40/(√41 - (-40))

y = ±(40/(√81)

y = ±40/9

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Answer:

See below

Step-by-step explanation:

If you just want the tip

[tex]0.20*161.86\approx\frac{1}{5}*160=32[/tex]

If you want the total bill

[tex]1.20*161.86\approx160+32=192[/tex]

The height of the prism is 5.67 units

How to determine height of the pyramid?

The given parameters are:

The volume of a right triangle pyramid is:

Volume = 0.5 * Height * Base dimensions

So, we have;

680 = 0.5 * Height * 15 * 16

Evaluate

Height = 5.67

Hence, the height of the prism is 5.67 units

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The area of polygons formulas to V=2.56m^2

We have to determine,

The volume of the pyramid.

The volume of a pyramid is found using the formula,

V = (1/3) Bh

where 'B' is the base area and 'h' is the height of the pyramid.

hight =2.4m

base=1.4+1.8

base=3.2m

V = (1/3) (3.2)(2.4)

V=2.56m^2

As we know the base of a pyramid is any polygon,

we can apply the area of polygons formulas to find 'B.

V=2.56m^2.

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Answer:

last option

Step-by-step explanation:

[tex]6x + 4y = 8 [/tex]

[tex]4y = 8 - 6x[/tex]

[tex]y = \frac{8 - 6x}{4} \\ [/tex]

[tex]y = \frac{8}{4} - \frac{6x}{4} \\ [/tex]

[tex]y = 2 - \frac{3x}{2} \\ [/tex]

[tex]y = - \frac{ 3x}{2} + 2 \\ [/tex]

y = -3/2x + 2

The equation of the exponential model is f(x) = 3 * 0.2^x

The table of data is given as:

x(-2,-1,0,1,2)

f(x)(71,13,3,0.6,0.1)

An exponential model is represented as:

f(x) = ab^x

When x= 0 and f(x) = 3;

We have:

ab^0 = 3

This gives

a = 3

When x= 1 and f(x) = 0.6

We have:

ab^1 = 0.6

This gives

ab = 0.6

Substitute 3 for a

3b = 0.6

Divide both sides by 3

b = 0.2

Substitute b = 0.2 and a =3 in f(x) = ab^x

f(x) = 3 * 0.2^x

Hence, the equation of the exponential model is f(x) = 3 * 0.2^x

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(2x−3)(x+3)

HAVE A NICE DAY!

Answer:

x=3/2 or x=-3

Step-by-step explanation:

first off equate the equation to zero

2x²+3x-9=0

then using factorisation method multiply 2 and -9 to get -18.

factors of -18 include +6 and -3

2x²+6x-3x-9=0

then factorise it

2x(x+3)-3(x+3)

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

2x=3 x+3=0

x=3/2 or -3

Answer:

7.5 m = 0.0075 km (Correct)

0.31 = 310 mm (Correct)

46 m = 4,600 cm (Correct)

457 mm =4.57 cm (Incorrect)

0.6 km = 6,000 m (Incorrect)

Step-by-step explanation:

Tell me if something is wrong.