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Answer:

It will take the boulder approximately 4.28 seconds to hit the road

Step-by-step explanation:

The given height of the cliff from which the boulder falls, h = 90 feet

The equation that can be used to find the time it takes the boulder to fall is h = u·t + (1/2)·g·t²

Where;

h = The height of the cliff = 90 ft.

u = The initial velocity of the boulder = 0 m/s (The boulder is assumed to be at rest when it falls)

g - The acceleration due to gravity ≈ 9.81 m/s²

t = How long it will take for the boulder to hit the road below

Plugging in the values gives;

90 = 0 × t + (1/2)×9.81×t² = 4.905·t²

∴ t = √(90/4.905) ≈ 4.28

The time it takes the boulder to hit the road, t ≈ 4.28 seconds.

Answer:

Step-by-step explanation:

Five rational number from 68 to 72

69, 70 , 71, 71.1 , 71.2

Answer:

B) 5 units

Step-by-step explanation:

The distance between these points (0, 2) and (5, 2) will be 5 units. Then the correct option is B.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

The two pints are given below.

(0, 2) and (5, 2)

Then the distance between these points (0, 2) and (5, 2) will be given as,

D² = (5 - 0)² + (2 - 2)²

D² = 5²

D = 5 units

The distance between these points (0, 2) and (5, 2) will be 5 units. Then the correct option is B.

Learn more about the distance between two points here:

https://brainly.com/question/18296211

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Answer:

(5/1)(4-0)-(-5)(-4-3)

Step-by-step explanation:

You could also get an undefined number by putting any number divided by 0.

Answer:

Area=12.56

Circumference= 12.56

Step-by-step explanation:

Area formula is [tex]\pi r^{2}[/tex]

Circumference is [tex]2\pi r[/tex]

Answer:

radius=diameter/2

=4/2=2

circumference of a circle= 2πr

=2*3.14*2

=12.56ft

area of a circle=πr2

=3.14*2*2

=12.56ft

Answer:

-6 and -1

Step-by-step explanation:

The excluded values are the values of x that satisfy [tex]2x^{2} + 14x + 12 = 0[/tex]

Let us solve the equation [tex]2x^{2} + 14x + 12 = 0[/tex]

It's a quadratic equation

Thus, let us calculate the discriminant Δ

Δ [tex]= 14^{2} - 4 .2.12 = 100[/tex]

the discriminant is greater than 0, so the equation has two solutions

[tex]x = \frac{-14 - 10}{4} = \frac{-24}{4} = -6[/tex]  or  [tex]x = \frac{-14+10}{4} = \frac{-4}{4} = -1[/tex]

the excluded values are -6 and -1

Answer:

440cm³

Step-by-step explanation:

Area of trapezium base=

[tex] \frac{1}{2} \times (a + b) \times h[/tex]

[tex] \frac{1}{2} \times (8 + 14) \times 4[/tex]

[tex] \frac{1}{2} \times 22 \times 4 \\ = \frac{88}{2} \\ = 44 {cm}^{3} [/tex]

Volume=Area or trapezium x Height between trapezium ends

[tex] = 44 \times 10 \\ = 440 {cm}^{3} [/tex]

Answer:

2(x+3)

Hope u get it correct!!!

Step-by-step explanation:

Answer:

3966

Step-by-step explanation:

Use order of operations to solve this problem:

In your case, there are no parentheses or exponents, so we can skip right the the multiply and divide step. The first multiplication is 98*63=6174. The next step is to do 32*69=2208. Then you minus 6174-2208=3966.

Hope this helps!

Answer:No

Step-by-step explanation: It is on 3x-3

The point (15, 29) does not satisfy the line y = 2x - 3, and the point (15, 29) is not lying on the line.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

We have a line:

y = 2x - 3

If the point (15, 29) is on the lie then it must satisfy the line.

Therefore putting this point in the equation of the line.

Put x = 15, and y = 29, we get:

29 = 2×15 - 3

     = 30 - 3

29 ≠ 27

29 cannot be equal to 27 it means the point (15, 29) does not satisfy the line and the point is not lying on the line.

Thus, the point (15, 29) does not satisfy the line y = 2x - 3, and the point (15, 29) is not lying on the line.

Learn more about the linear equation here:

brainly.com/question/11897796

The answer would be $53

Answer:

The equation is unsolvable when the 'a' variable is in it, so if we take it out, then all of them would make the equation open up.

Sorry for not giving a definite answer, but that is what I got.

Hope that this helps!

Answer:

20 students

Step-by-step explanation:

Given that

There are 200 students surveyed

And, the percentage of each games is as follows;

For tennis it is 10%

For basketball it is 30%

For football it is 35%

for baseball it is 25%

We need to find the number of students choose tennis

So, it should be

= 10% of 200

= 20 students

Answer:

B or C

Step-by-step explanation:

if its refering to the answer of 11 × X then the answer is C, but if its not the answer might be B.

Answer:

Number of additional inches= x

Number of additional topping= y

Total cost= 8+1.5(x)+0.75(y)

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hope it helps...

have a great day!!

Answer:

Area =  1053.59²

Step-by-step explanation:

Area = Area of cylinder + Area of rectangular prism

Area of cylinder = 2 π r h + 2 π r²             [ r = 4, h = 8]

                        = 2 π r ( h + r)

                        = 2 π x 4 ( 8 + 4)

                        = 301.59 ft²

Area of rectangular prism = 2 ( 12 x 8 + 8 x 14 + 14 x 12)  = 752 ft²

Area = 301. 59 + 752 = 1053.59²

Answer:

1376

Step-by-step explanation:

Step 1   14 × 8 × 12 = 1344

Step 2   28 × 4 = 32

Final Step  1344 + 32 = 1376

Step-by-step explanation:

the answer is in the above image

Answer:

$13.4

Step-by-step explanation:

Given that :

Tip percentage = 20%

Amount of bill = $67.13

Rounding the bill Amount to then nearest dollar :

$67.13 = $67

Tip amount = 20% of $67

Tip amount = 0.2 * $67

Tip amount = $13.4

Answer:

m = -4

Step-by-step explanation:

The given y= -4x + 5 exactly matches the format of the slope-intercept equation   y = mx + b.

Thus, the gradient (slope) of the given line is -4.

Answer: 500 cables

Step-by-step explanation:

The population refers to the individuals or the items which are of interest fltonthe researcher during an experiment.

Since the computer department received 10 boxes containing 50 cables each, then the population will be gotten as:

= 10 × 50

= 500 cables

Answer:

yeah me too

Step-by-step explanation:

Answer:

(b) is true

Step-by-step explanation:

Given

Molly

[tex]a = 500[/tex] --- starting balance

[tex]m = 10[/tex] --- monthly rate

Her brother

[tex]a = 100[/tex] ---- starting balance

[tex]r = 10\%[/tex] --- annual rate

Required

Determine which option is true

First, we calculate her brother's function.

The function is an exponential function calculated as:

[tex]y = ab^x[/tex]

Where [tex]b = 1 + r[/tex]

So, we have:

[tex]y = ab^x[/tex]

[tex]y = 100 *(1 + 10\%) ^x[/tex]

[tex]y = 100 *(1 + 0.10) ^x[/tex]

[tex]y = 100 *(1.10) ^x[/tex]

Hence:

[tex]g(x) = 100 *(1.10) ^x[/tex]

Next, we calculate Molly's function (a linear function)

The monthly function is:

[tex]y = mx + a[/tex]

So, we have:

[tex]y = 10x + 500[/tex]

Annually, the function will be:

[tex]y = 10x*12 + 500[/tex]

[tex]y = 120x + 500[/tex]

So, we have:

[tex]f(x) = 120x + 500[/tex]

At this point, we have:

[tex]f(x) = 120x + 500[/tex] ---- Molly

[tex]g(x) = 100 *(1.10) ^x[/tex] ---- Her brother

Next, we test each option

(a): Molly's account will have a faster rate of change over [32,40]

We calculated Molly's function to be:

[tex]y = 120x + 500[/tex]

The slope of a linear function with the form: [tex]y = mx + b[/tex] is m

By comparison:

[tex]m = 120[/tex]

Since Molly's account is a linear function, the rate of change over any interval will always be the same; i.e.

[tex]m = 120[/tex]

For his brother:

Rate of change is calculated using:

[tex]m = \frac{g(b) - g(a)}{b - a}[/tex]

[tex]m = \frac{g(40) - g(32)}{40 - 32}[/tex]

[tex]m = \frac{g(40) - g(32)}{8}[/tex]

Calculate g(40) and g(32)

[tex]g(x) = 100 *(1.10) ^x[/tex]

[tex]g(40) = 100 * 1.10^{40} =4526[/tex]

[tex]g(32) = 100 * 1.10^{32} = 2111[/tex]

So, we have:

[tex]m = \frac{4526 - 2111}{8}[/tex]

[tex]m = \frac{2415}{8}[/tex]

[tex]m = 302[/tex]

By comparison: [tex]302 > 120[/tex]

Hence, her brother's account has a faster rate over [32,40]

(a) is false

(b): Molly's account will have a slower rate of change over [24,30]

[tex]m = 120[/tex] --- Molly's rate of change

For his brother:

[tex]m = \frac{g(b) - g(a)}{b - a}[/tex]

[tex]m = \frac{g(30) - g(24)}{30 - 24}[/tex]

[tex]m = \frac{g(30) - g(24)}{6}[/tex]

Calculate g(30) and g(24)

[tex]g(x) = 100 *(1.10) ^x[/tex]

[tex]g(40) = 100 * 1.10^{30} =1745[/tex]

[tex]g(32) = 100 * 1.10^{24} = 985[/tex]

So, we have:

[tex]m = \frac{g(30) - g(24)}{6}[/tex]

[tex]m = \frac{1745 - 985}{6}[/tex]

[tex]m = \frac{760}{6}[/tex]

[tex]m = 127[/tex]

By comparison: [tex]127 > 120[/tex]

Hence, Molly's account has a slower rate over [24,30]

(b) is false

(c): Molly's account will have a slower rate of change over [0,4]

[tex]m = 120[/tex] --- Molly's rate of change

For his brother:

[tex]m = \frac{g(b) - g(a)}{b - a}[/tex]

[tex]m = \frac{g(4) - g(0)}{4 - 0}[/tex]

[tex]m = \frac{g(4) - g(0)}{4}[/tex]

Calculate g(4) and g(0)

[tex]g(x) = 100 *(1.10) ^x[/tex]

[tex]g(4) = 100 * 1.10^4 =146[/tex]

[tex]g(0) = 100 * 1.10^{0} = 100[/tex]

So, we have:

[tex]m = \frac{g(4) - g(0)}{4}[/tex]

[tex]m = \frac{146 - 100}{4}[/tex]

[tex]m = \frac{46}{4}[/tex]

[tex]m = 11.5[/tex]

By comparison: [tex]120>11.5[/tex]

Hence, Molly's account has a faster rate over [0,4]

(c) is false

Answer:

Length = 6.5 meters

Width = 4.5 meters

Step-by-step explanation:

Given,

Perimeter of a rectangle is twice the sum of it's length and width.

Length is 2 meters more than twice its width, let the length be x meters so the width becomes (x-2) meters

perimeter of the rectangle,

2{x+(x-2)} meters which is 22 meters (given)

so,

2{x+(x-2)}=22

or, 2(x+x-2)=22

or, 2(2x-2)=22

or, 2x-2=11

or, 2x=13

or, x=6.5

so the length is 6.5 meters and the width is 6.5-2 = 4.5 meters.

Answered by GAUTHMATH

Answer:

The largest number of mini cakes Nicole can make with the butter she has is 9.

Step-by-step explanation:

Given that Nicole has 2/3 of the butter needed to make a cake, and the same amount of butter is needed to make 1 cake as it does to make 14 mini cakes, to determine what is the largest number of mini cakes Nicole can make with the butter she has, the following calculation must be performed:

2/3 = 0.666

1 = 14

0.666 = X

0.666 x 14/1 = X

9.333 = X

Therefore, the largest number of mini cakes Nicole can make with the butter she has is 9.

Answer/Step-by-step explanation:

Recall: SOH CAH TOA

✔️Find <A:

Reference angle (θ) = A

Opposite side = 14 cm

Hypotenuse = 20 cm

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin A = 14/20

A = [tex] sin^{-1}(\frac{14}{20}) [/tex]

m<A = 44° (nearest whole number)

✔️Find <C:

Reference angle (θ) = C

Adjacent side = 14 cm

Hypotenuse = 20 cm

Apply CAH:

Cos θ = Adj/Hyp

Substitute

Cos C = 14/20

C = [tex] cos^{-1}(\frac{14}{20}) [/tex]

m<C = 46° (nearest whole number)

✔️Find AB:

Reference angle (θ) = C = 46°

Opposite side = AB

Hypotenuse = 20 cm

Apply SOH:

Sin θ = Opp/Hyp

Sin 46° = AB/20

20*Sin 46° = AB

AB = 14.4 cm (one decimal place)

Answer:

It is A

Step-by-step explanation:

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