A number with the same value but written differently

Answer:

a. y(t) = - 1/2gt² + y₀ b. [tex]t = \frac{v_{0} +/- \sqrt{v_{0} ^{2} + 2 y_{0}g } }{g }[/tex]

Step-by-step explanation:

Let the quadratic function y(t) = v₀t - 1/2gt² + y₀ represent the quadratic function that models the height above the ground of the projectile.

a. Maximum Height

At maximum height, the velocity, v₀ = 0, so substituting v₀ = 0 into the equation, we have

y(t) = v₀t - 1/2gt² + y₀

y(t) = 0 × t - 1/2gt² + y₀

y(t) = 0 - 1/2gt² + y₀

y(t) = - 1/2gt² + y₀

b. Time when the projectile reaches the ground

The time when the projectile reaches the ground is gotten when y(t) = 0, So

y(t) = v₀t - 1/2gt² + y₀

0 = v₀t - 1/2gt² + y₀

re-arranging, we have

1/2gt² - v₀t - y₀ = 0

Using the quadratic formula,

[tex]t = \frac{-(-v_{0}) +/- \sqrt{(-v_{0}) ^{2} - 4 X (-y_{0}) X\frac{g}{2} } }{2 X \frac{g}{2} } \\= \frac{v_{0} +/- \sqrt{v_{0} ^{2} + 2 y_{0}g } }{g }[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \sqrt{61} \: \: units}}}}}[/tex]

Step-by-step explanation:

Let R ( -3 , 2 ) be ( x₁ , y₁ ) and D ( 3 , -3 ) be ( x₂ , y₂ )

Using distance formula

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

[tex] \dashrightarrow{ \sf{ \sqrt{ {(3 - ( -3)) }^{2} + {( - 3 - 2)}^{2} } }}[/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{ {(3 + 3)}^{2} + {( - 3 - 2)}^{2} } }}[/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{ {6}^{2} + {( - 5)}^{2} } }}[/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{ 36 + 25 } }}[/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{61} }}[/tex] units

Hope I helped!

Best regards! :D

Answer:

1

Step-by-step explanation:

2-6/6

You divide before subtraction

2-1

1

Answer: Around 28 planes take off every hour

Step-by-step explanation: 336 / 12 = 28

Answer:

30 planes per hour

Step-by-step explanation:

Divide the number of plane takeoffs by the number of hours.

Answer:

x  = 3[tex]\sqrt{2}[/tex]

step-by step:

x -√2=√8

x = [tex]\sqrt{12}[/tex]

x = [tex]\sqrt{6 * 2}[/tex]

x = [tex]\sqrt{2 * 2 * 3}[/tex]

x  = 3[tex]\sqrt{2}[/tex]

Answer:

x = 3 sqrt(2)

Step-by-step explanation:

x -√2=√8

Add sqrt(2) to each side

x - sqrt(2) + sqrt(2) = sqrt(8)+ sqrt(2)

x = sqrt(8)+ sqrt(2)

Rewriting sqrt(8)  as sqrt(4) sqrt(2) = 2 sqrt(2)

x = 2 sqrt(2)+ sqrt(2)

x = 3 sqrt(2)

Answer:

-13

Step-by-step explanation:

Answer:

-13 is your answer

when a negative and a positive are next to each other they equal and negative l. So your final equation would be -8-5

Answer:

52 raisins

Step-by-step explanation:

we have dimensions of the box

L = 5cm ; W = 2.5cm ; H = 2.5cm

V(raisin) = 0.6 cm³

V(box) = L×W×H

= 5cm×2.5cm×2.5cm

= 31.25 cm³

Vbox/Vraisin = 31.25cm³/0.6cm³ = 52.08(3) = 52 raisins

Answer:

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume is approximately 46.90 minutes

Step-by-step explanation:

The given parameters are;

The diameter of  the balloon  = 55 feet

The rate of increase of the radius of the balloon when inflated = 1.5 feet per minute

We have;

dr/dt = 1.5 feet per minute = 1.5 ft/min

V = 4/3·π·r³

The maximum volume of the balloon = 4/3 × 3.14 × 55³ = 696556.67 ft³

When the volume is two-thirds the maximum volume, we have;

2/3 × 696556.67 ft³ = 464371.11 ft³

The value of the radius, r₂ at that point is found as follows;

4/3·π·r₂³ = 464371.11 ft³

r₂³ = 464371.11 ft³ × 3/4 = 348278.33 ft³

348278.333333

r₂ = ∛(348278.33 ft³) ≈ 70.36 ft

The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)

The time for the radius to increase to the above length ≈ 70.369 ft/(1.5 ft/min) ≈ 46.90 minutes

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume ≈ 46.90 minutes.

Answer:

Composite

Step-by-step explanation:

It can be divided by numbers other than 1 and itself. It can be divided by 1, 3, and 9.

Answer:

9 is composite number because it has more than 2 factors.

it's factors are 1,3,9 ....

hope its helpful to u if yes then brainlist me and mark as brainlist

Answer:

x = 38° , y = 104°

Step-by-step explanation:

2x = 76°

(opposite angles are equal)

76 ÷ 2 = 38°

360 - (76×2) = 208

208 ÷ 2 = 104°

Dobereiner could find only three triads; . i.e total of 9 elements only. However the total number of elements were more than that of those encompassed in Dobereiner's Triad. Thus, Dobereiner's could not be classify most of the elements known at that time

Answer:

The answer was obtained by first taking the measurement for the temperature drop, the duration of the temperature drop, and the rate at which the temperature is dropping which are -28 F, 4 hours, and dropping at a steady rate.

The measured temperature drop of -28 F, is then divided by the duration of the drop which is 4 hours, to get the amount the temperature drop each our as -28F/4 = -7 F per hour

Step-by-step explanation:

The rate at which the local meteorologist claims that the temperature is going to drop = Steady rate

The duration over which the local meteorologist states that the temperature is going to drop = 4 hours

The amount by which the temperature is observed to drop = -28F

The rate at which the temperature is observed to drop = The same amount each hour

Therefore, the temperature drop per hour = -28F/4 = -7 F per hour

Answer:

1,3

2,4

5,5

Step-by-step explanation:

x,y

0,2

Answer:

(1,3),(2,4),(3,5)

Step-by-step explanation:

Remember that when plotting points, the x value comes first and then the y value.

Look at the graph, x value then y value, to find the point locations.

Cheers.

with this information provided all we have to do now is substitute

[tex]f(1):\\h=1 \\f(h) = 10h\\f(1) = 10*1 = 10[/tex]

so, first row:

[tex]f(h)=10 \\ h=1[/tex]

we repeat the same process with the rest of the values

[tex]f(4.5)\\h=4.5\\f(h)=10h\\f(4.5)=10*4.5 = 45[/tex]

second row:

[tex]f(h)=45\\h=4.5[/tex]

repeat that once more

[tex]f(10)\\h=10\\f(h)=10h\\f(10)=10*10= 100[/tex]

third and final row:

[tex]f(h)=100\\h=10[/tex]

and we're done, hope this helps. <3

Answer:

46.15%

Step-by-step explanation:

(6 ÷ 13) × 100 = 46.15384615

= 46.15%

Hello! :)

Answer:

[tex]\huge\boxed{NP = 7}[/tex]

Given:

MP = 24

MN = 17

Write an expression to represent NP:

MP = MN + NP

24 = 17 + NP

Isolate NP:

24 - 17 = NP

NP = 7.

Answer:

7cm is the correct answer

Step-by-step explanation:

Hope this is helpful for you

Answer:

C. $80

Step-by-step explanation:

To determine how much money will four people save altogether one way using the lower rate, you have to calculate the cost of buying four tickets with the regular airfare and the cost of buying four tickets with the special discount and then, find the difference:

Regular airfare=$125

125*4=$500

Airfare with discount=$105

$105*4=$420

$500-$420=$80

According to this, the answer is that four people will save $80 using the lower rate.

Answer:

−0.989010989010

Step-by-step explanation:

what is the 45th term of a sequence generated by the formula tn=(-1)^n * (2n/2n+1)?

When n= 45

tn=(-1)^n*(2n/2n+1)

tn = (-1)^45 * ( 2(45) / 2(45) + 1

= -1 * 90 / (90+1)

= -90 / 91

= −0.989010989010

The 45th term of the sequence generated by the formula tn=(-1)^n*(2n/2n+1) is −0.989010989010

Answer:

9, with a remainder of 1, OR 9.2

Step-by-step explanation:

The length of the other leg is 13.1

Given.

The length of the hypotenuse of a right triangle is 30 inches.

The length of one leg is 27 inches.

To the nearest tenth, we need to find the length of the other leg.

It states that in a right-angled triangle the square of the hypotenuse is equal to the square of the other two sides.

We have,

Length of the hypotenuse = 30 inches.

Length of One leg = 27 inches.

Let the length of the other leg be x.

Now,

Applying the Pythagorean theorem.

30² = 27² + x²

900 = 729 + x²

Subtracting 729 on both sides

900 - 729 = 729 + x² - 729

171 = x²

x² = 171

x = 13.07669

Rounding to the nearest tenth

We get,

x = 13.1

Thus the length of the other leg is 13.1

Learn more about the finding length of a side of a right-angled triangle here:

https://brainly.com/question/13515866

#SPJ2

Answer:

The product of the square root of a prime number and a nonzero rational number is a irrational number.

Step-by-step explanation:

Given that,

When is the product of the square root of a prime number and a nonzero rational number a irrational number.

We know that,

Prime number :

Prime number is that number whose has a two factor. first factor is one and second is themselves.

The square root of a prime number is irrational number.

Rational number :

Rational number is that number which is in fraction form.

For example : [tex]\dfrac{p}{q}[/tex]

Here, p and q are integers

We need to proof the product of  the square root of a prime number and a nonzero rational number is a rational number

Using given data

Suppose, the square root = √5

Rational number  = [tex]\dfrac{2}{3}[/tex]

We need to calculate the product of the square root of a prime number and a rational number

Using formula of product

[tex]R=P\timesQ[/tex]

Where, P = square root of a prime number

Q= rational number

Put the value into the formula

[tex]R=\sqrt{5}\times\dfrac{2}{3}[/tex]

[tex]R=\dfrac{2\sqrt{5}}{3}[/tex]

Hence, The product of the square root of a prime number and a nonzero rational number is a irrational number.

Answer:

Absolute value equation: |x - 13| = 5

Step-by-step explanation:

The midpoint between 8 and 18 is;

(8 + 18)/2 = 26/2 = 13

This means that the distance between 13 and either 8 or 18 will be 5.

Now, the absolute value equation will have to say that the distance between x and 13 is 5.

Thus, plugging those numbers into the pattern of |x - m| = b. Where m is the midpoint and b is the distance from midpoint to either values of x.

This gives us the absolute value equation: |x - 13| = 5

Answer:

c.) x = -3

Step-by-step explanation:

Solve for x:

-10 x = 2 (9 - 2 x)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

-10 x = 18 - 4 x

Hint: | Move terms with x to the left hand side.

Add 4 x to both sides:

4 x - 10 x = (4 x - 4 x) + 18

Hint: | Look for the difference of two identical terms.

4 x - 4 x = 0:

4 x - 10 x = 18

Hint: | Combine like terms in 4 x - 10 x.

4 x - 10 x = -6 x:

-6 x = 18

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -6 x = 18 by -6:

(-6 x)/(-6) = 18/(-6)

Hint: | Any nonzero number divided by itself is one.

(-6)/(-6) = 1:

x = 18/(-6)

Hint: | Reduce 18/(-6) to lowest terms. Start by finding the GCD of 18 and -6.

The gcd of 18 and -6 is 6, so 18/(-6) = (6×3)/(6 (-1)) = 6/6×3/(-1) = 3/(-1):

x = 3/(-1)

Hint: | Simplify the sign of 3/(-1).

Multiply numerator and denominator of 3/(-1) by -1:

Answer: x = -3

Answer:

C

Step-by-step explanation:

40+20=60

A.10(4+2) = 60

B.5(8+4) = 60

C.4(10+16) = 104

D.2(20+10) = 60

Answer:C

Step-by-step explanation:

First we find out what 40+20 is which is 60

So now we go through each choice to see if any doesn’t equal 60

A.10(4+2)

10*6=60

B.5(8+4)

5*12=60

C.4(10+16)

4*26=104

D.2(20+10)

2*30=60

As you can see C is 104 not 60 so c is the answer

Answer:

-6/2 is a product and it is 5/2 is the sum i think maybe reduced I am working on it too actually

Hey there! I'm happy to help!

To find the number halfway between two numbers, you simply add them and then divide by two.

1.4142133+1.41422=2.8284333

2.8284333/2=1.41421665

That is one number in between these two. Now, we can find the number in between the middle number and the second number. This is another number in between our two numbers.

(1.41421665+1.41422)/2=1.414218325

You could keep on doing this and find tons of numbers in between these two.

Therefore, two numbers between 1.4142133 and 1.41422 are 1.41421665 and 1.414218325.

Have a wonderful day! :D

Answer:

1.  y = (-5x/2) + -3

2. y = (3x/2) + 7

Step-by-step explanation:

For both these problems, we simply need to apply point-slope form.

1.  The point (0, -3) and the slope that is perpendicular to the line is the reciprocal of the coefficient, slope = -5/2.

From here, we simply apply the formula:

y - y0 = m ( x - x0)

y - -3 = -5/2 ( x - 0 )

y + 3 = -5/2 x

y = (-5x / 2) + -3

2.  The point (0, 7) and the slope that is parallel to the line must maintain the same slope.  First, we need to rewrite the equation into slope-intercept:

-3x + 2y = 10

2y = 3x + 10

y = 3x/2 + 5

Now we want to apply the point-slope form

y - y0 = m ( x - x0 )

y - 7 = (3/2) (x - 0)

y - 7 = 3x / 2

y = 3x/2 + 7

Cheers.

Answer:

12.8 is the square root i think like u could simplify the square toot of 165 since it isnt a whole number

Step-by-step explanation:

sorry if its wrong

Let the number of cards equal x.

Set up an equation for both companies, set equal to each other and solve for x.

0.10x + 12 = 0.12x + 10

Subtractb0.10x from both sides:

12 = 0.02x + 10

Subtract 10 from both sides:

2 = 0.02x

Divide both sides by 0.02:

X = 2/0.02

X = 100

100 cards would be the same price for both companies.