Q). The sum of four consecutive natural numbers is 166. What are the numbers? ​

The motion of the rock thrown from the cliff which goes downwards due to

the gravitational force, is a free fall motion.

Reasons:

The given function that represents the height of the of the rock in feet x seconds after being thrown is; f(x) = 16·x² + 4·x + 125

At the initial height before being thrown from the cliff, we have;

The time, x = 0

The initial height is therefore;

The initial height f(0) = 16 × (0)² + 4 × (0) + 125 = 125

125 represents A. The initial height of the rock

Learn more about motion under gravity here:

https://brainly.com/question/7596138

Answer:

Somewhat illegible but looks like the equation should be:

S = u t + 1/2 a t^2

100 = 20 + 1/2 * a * 4    where t = 2

a* 4 = 160

a = 40

Answer:

1/4

Step-by-step explanation:

Divide both the numerator and denominator by the GCD 9 ÷ 9

36 ÷ 9

Reduced fraction: 1/4 Therefore, 9/36 simplified to lowest terms is 1/4.

Answer:

2640mm

Step-by-step explanation:

I'm assuming you need the area of the rectangle which the circles don't take up.

First, to find the area of the whole rectangle:

length x width

to find length:

the length is 1 circle, therefore it is the diameter of the circle, which is 32 x 2 = 64mm

to find width:

the width is 3 circles, which is the radius 6 times, so 32 x 6 = 192mm

So, area of rectangle = 64 x 192 = 12288mm

Now to find the area the circles take up:

area of 1 circle =

[tex]\pi \times {r}^{2} [/tex]

=

[tex]\pi \times {32}^{2} [/tex]

=

[tex]1024\pi[/tex]

As we have 3 circles, we multiply this by 3:

[tex]1024\pi \times 3 = 3072\pi[/tex]

Finally we subtract the area of the three circles from the area of the rectangle:

[tex]12288mm - 3072\pi = 2637[/tex]

As we need to round it to 3 significant figures, the answer is 2640mm

Answer:

Inequality: 30 - 3d ≤ 20

Rate of decrease from Monday to Thursday: greater than or equal to 10/3 degrees Celsius per day

Step-by-step explanation:

Translate theconditions into mathematical terms:

HIgh temperature on Monday = T₀ = 30°C.

The temperature decrease at a constant rate in the next 3 days. Call d such rate, so T₃ = T₀ - 3d = 30 - 3d

That the pool is open when the high temperature is higher than 20°C means that, if the pool is closed, then the temperature is less than or equal to (≤) 20°C:

30 - 3d ≤ 20

And that is the requested inequality.

From that, you can solve for the rate of temperature decrease, d:

Add 3d to both sides: 30 ≤ 20 + 3d

Subtract 20 from both sides: 10 ≤ 3d

Divide both sides by 3: 10/3 ≤ d

Apply symmetry property: d ≥ 10/3

Hence, the rate of temperature decrease is greater than or equal to 10/3 degrees Celsius per day, from Monday to Thursday.

Answer:

30 - 3d ≤ 20

d≥10/3

Step-by-step explanation:

Answer:

50

110

90

=250

Step-by-step explanation: 90+50+110

I HOPE THIS HELPS

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

Work Shown:

(2 cm)/(7 m) = (7.5 cm)/(x meters)

2/7 = 7.5/x

2x = 7*7.5

2x = 52.5

x = 52.5/2

x = 26.25

7.5 cm on paper corresponds to 26.25 meters in real life.

side note: 26.25 meters = 86.122 feet approximately

Answer:

y=mx+b

Step-by-step explanation:

The slope-intercepts formula, the y = y coordinate, m = slope, x = x coordinate, b = y intercept

Answer:

92 1/12      

Step by step explanation:                                

The discriminant is greater than 0, so there are two real roots and it can be determined by using nature of roots.

Given that,

Equation; [tex]\rm 3x^2 - 8x + 5 = 5x^2[/tex]

We have to determine,

Which statement about the following equation is true?

According to the question,

To determine the true statement about the equation following all the steps given below.

Equation; [tex]\rm 3x^2-8x+5=5x^2[/tex]

Simplify the equation for the roots of the equation,

[tex]\rm 3x^2-8x+5=5x^2\\\\\rm5x^2- 3x^2+8x-5=0\\\\ 2x^2+8x-5=0\\\\ 2x^2+8x-5=0\\\\2x^2+8x=5\\\\2x(x+4)=5\\\\Then, \ 2x = 5, \ \ x = \dfrac{5}{2} \\\\And\ \ x+4=5, \ \ x=5-4, \ \ x=1[/tex]

The equation has two real roots and x is 1 and 5/2.

Hence, The discriminant is greater than 0, so there are two real roots.

For more details about Discriminate refer to the link given below.

https://brainly.com/question/10706429

Answer:

 -78

Step-by-step explanation:

Simplify -6 1/2 to -13/2

Then multiply by 12

-13/2 x 12/1= -156/2

Simplify -156/2 to -78

Hopes This Helps :)

Answer:

B

Step-by-step explanation:

So a reflection over the x is a change in the y value.

Only point (2,0) is on the x-axis, so it will not move.

Since 3 is greater than -3, hence (-1, 3) lie in the solution set. Option C is correct

In order to determine the points that lie in the solution set of the inequality y > 3x +10, we will substitute the x-coordinate and see if y is greater than the result.

For the coordinate point (1, 10)

y > 3(1) +10

y > 13

Since 10 is not greater than 13, hence (1,10) does not lie in the solution set.

For the coordinate point (4, 20)

y > 3(4) +10

y > 22

Since 20 is not greater than 22, hence (4,20) does not lie in the solution set.

For the coordinate point (-1, 3)

y > 3(-1) +10

y > -7

Since 3 is greater than -3, hence (-1, 3) lie in the solution set.

Learn  more on inequality here: brainly.com/question/24372553

Answer:

there is no way to solve for y, but if your solving for x then x=4/5 and in decimal form it is x=0.8    hope that helps

Step-by-step explanation:

Answer:

it means you replace y with 18 so

33(18)

so 33*18=594

Hope This Helps!!!

Answer:

594

Step-by-step explanation:

33y

33(18)

33 x 18 = 594

General method:

Given numbers are 1.3 bar and 1.4 bar

Two rational numbers between them

= 1.3222... and 1.43333...

Mean Method:

Let X = 1.333... → → →eqn(i)

since the periodicity is 1 then multiply eqn(i) with 10

⇛10×X = 1.333...×10

⇛10X = 13.333... → → →eqn(ii)

Subtract eqn(ii)-eqn(i)

10X = 13.333...

X = 1.333...

(-)

____________

9X = 12.000...

____________

⇛9X = 12

⇛X = 12/9

⇛X = 4/3

and

Let X = 1.444... → → →eqn(i)

since the periodicity is 1 then multiply eqn(i) with 10

⇛10×X = 1.444...×10

⇛10X = 14.444...→ → →eqn(ii)

Subtract eqn(ii)-eqn(i)

10X = 14.444...

X = 1.444...

(-)

____________

9X = 13.000...

____________

⇛9X = 13

⇛X = 13/9

Now we have 12/9 and 13/9

The rational number between them by mean method (a+b)/2

⇛{(12/9)+(13/9)}/2

⇛(25/9)/2

⇛25/18

and Second rational number

⇛{(12/9)+(25/18)}/2

⇛{(24+25)/18}/2

⇛(49/18)/2

⇛49/36

Answer: The two rational numbers between them are 25/18 and 49/36.

also read similar questions: INSERT TWO RATIONAL NUMBERS BETWEEN 2 AND 3. How to find them?

https://brainly.com/question/85169?referrer

Answer:

I don't think I can remember every skill I was taught through the years but in Kindergarten we used Number Sense so we could understand the meaning of more and less also there's estimation and  PEMDAS. I've also learned how to round up so that the solution is at least around those numbers if the skill is to be applied.

hope that helps

Step-by-step explanation:

Answer:

1.50 + 40= $41.50

Step-by-step explanation:

if Greg only had $1.50 and then he got an additional $40, he now has $41.50.

Answer:

I don't know

Step-by-step explanation:

Because I don't have a protractor and a scaled representation of the image you sent.

Answer:

D.) AFD and EFD

Step-by-step explanation:

supplementary angles equal 180° and this is the only set that produces 180 when added together. the supplementary angle is basically the whole straight line

Hey there!

7/6

= 7 ÷ 6

= 1.166667

Therefore, your answer is: 1.166667 which is approximately 1.67 or 1.7

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

gradient = 2

Step-by-step explanation:

Calculate the gradient (slope) m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (6, 10) ← 2 points on the line

m = [tex]\frac{10-0}{6-1}[/tex] = [tex]\frac{10}{5}[/tex] = 2

Answer:

0.1 i think

Step-by-step explanation:

each line is 0. *number* until u reach 1 then it goes to 1.*number*

Answer:

0.1

Step-by-step explanation:

[tex]\huge \bf༆ Answer ༄[/tex]

Let's solve for x ~

Hence, value of x is -3

[tex]\text{Given that,}\\\\y = -\dfrac 4{15} x + 24\\\\\text{When x = 120,}\\\\y = -\dfrac 4{15} (120) + 24\\\\\implies y = - \dfrac{480}{15} +24\\\\\implies y=-32+24 \\\\\implies y = -8[/tex]

Answer:

32x + 37

Step-by-step explanation:

f(g(x)) = 8(4x+5) - 3

= 32x + 40 - 3

= 32x + 37

Answer:

the answer is b. sss is not possible

Answer:

2. "a number is greater than 17.2"

Step-by-step explanation:

m > 17.2 can be read by saying "the number m is greater than the number 17.2" which also can be read as 2. "a number is greater than 17.2"

Answer:

24 !!

Step-by-step explanation:

Simple, x got doubled, and since y varies directly as x, 12 doubled = 24. I hope this helps!!!