The height of a projectile that is thrown upward from ground level with an initial velocity of 98 meters per second can be modeled by the equation h = −4.9t2 + 98t, where h is the height in meters and t is the elapsed time in seconds. Find the time it takes for the projectile to hit the ground

Answer: [tex]f^{-1}(x)=\frac{x-1}{2}[/tex]

Step-by-step explanation:

To find the inverse of a function start by replacing f(x) with x and replace the original x with y.

[tex]f(x)=2x+1\\x=2y+1[/tex]

Now solve for y

[tex]x=2y+1\\x-1=2y+1-1\\x-1=2y\\\frac{x-1}{2} =\frac{2y}{2}\\\frac{x-1}{2} =y[/tex]

Finally, replace y with the inverse of f(x), [tex]f^{-1}(x)[/tex]

Let's first look only at the numerator: 5x^2 - 5

Consider this question: What do both terms have in common?

The answer is 5, both terms contain a 5, so we can factor it out.

5(x^2 - 1)

Now let's look at the denominator, considering the same question: 3x^2 + 3x

This time, both terms contain a 3 and an x.

3x(x^2 + 1)

Now we are here: [ 5(x^2 - 1) ] / [ 3x(x + 1) ]

In the numerator, the binomial factors out into (x + 1)(x - 1). There is also an (x + 1) in the denominator, so those to binomials cancel out. That leaves us with the following expression:

5(x - 1) / 3x

Correct Answer: C

Hope this helps!

Answer:

i got 8.5

Step-by-step explanation

i have a triangle area calculator lol..

The length of the base of the triangle is B = 8.5 inches

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the area of the triangle be A = 25.5 inches²

Let the height of the triangle be H = 6 inches

Let the base of the triangle be B

Now , area of the triangle = ( 1/2 ) x Length x Base

On simplifying , we get

25.5 = ( 1/2 ) x ( 6 ) x ( B )

On simplifying , we get

3B = 25.5

Divide by 3 on both sides , we get

B = 8.5 inches

Hence , the base of triangle is B = 8.5 inches

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Answer:

last statement is correct.

Answer:

D is correct

Step-by-step explanation:

Brainliest would be appreciated

Answer:

B.

Step-by-step explanation[tex]\sqrt[3]{216} =6[/tex]

The area is 4(x+3). If we multiply the 4 out we have 4x + 12 as the area using the distributive property.

Expression: 4x+12

The original dimensions are x+3 and 4. If they are doubled, we have new dimensions 2x+6 and 8. The area is then 8(2x+6) = 16x + 48.

Area: 16x+48

Explanation: The ratio of the area of the original rectangle to the area of the larger rectangle is and will always be (4x+12)/(16x+48) = 1/4. Therefore, the ratio will be the same for any positive value of x.

The location of the light bulb is (15, 0). Check the reason for the answer been (15, 0) below.

This is also known as  paraboloid or paraboloidal reflector. It is a kind of  dish or a mirror that is said to have a reflective surface which is often used to take in or project any kind of energy e.g., light, sound, etc.

For the above question, the formula is:

y² = 2px

The focus is (p/2, 0)

x- 10 = u

y2 = 20u

So, the focus for U  =  ( [tex]\frac{20}{4}[/tex]; 0)

The focus for x =  ( [tex]\frac{20}{4}[/tex]; 10, 0)

= 5 , 10, 0

= (15, 0)

Therefore, the answer is (15, 0)

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Duck Feet. Duck feet are visually obvious adaptations. All duck species have webbed feet that help them swim. These feet extend laterally when a duck pushes back with its legs and provide maximum surface area for increased efficiency in movement.

hope it helps...!!!

Answer:

☑ 3 is a constant.

☑ 5 is a coefficient

Step-by-step explanation:

It is a sum of two terms.

It a product of different terms

5 and 4 are coefficients.

Answer:

[tex] \: [/tex]

Step-by-step explanation:

[tex] \: [/tex]

To find the radius of the circle we must know this formula first :

[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: 2 \pi r \: =Circumference_{(circle)}}}}}}} \: \: \bigstar \\ \\[/tex]

Now substituting the values in the formula :

[tex]\\{ \longrightarrow \qquad{ {{ \tt{ \: 2 \times 3.14 \times r \: =34.48}}}}} \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ \tt{ 6.28 \times r \: =34.48}}}}} \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ \tt{ r \: = \frac{34.48}{6.28} }}}}} \\ \\ [/tex]

[tex]{ \longrightarrow \qquad{ \pmb {{ \frak{ r \: = 5.490 }}}}} \\ \\ [/tex]

Therefore,

Step-by-step explanation:

Well there is no direct formula for calculating the orthocentre

well the process of finding the orthocentre is to find the altitudes of all the sides and then find their intersection points

Here in this question

The given triangle represents a right angled triangle with right angled at L(-3,2)

We know that the ortho centre in a right angled triangle is the right angled vertex

-----------------------------------------------------------------------

Hence the required orthocentre is (-3,2) and it is on the Triangle

-----------------------------------------------------------------------

Answer:

5) 162

6) 61.6

Step-by-step explanation:

Area of triangle = [tex]\frac{1}{2} b*h[/tex]

Area of rectangle = w * l

5)

Left triangle Area  = [tex]\frac{1}{2} 4*3[/tex]

= 2*3

=6

Right triangle Area = [tex]\frac{1}{2} 7*8[/tex]

=[tex]\frac{56}{2}[/tex]

=28

Rectangle Area = 16*8 = 128

Total Area = 128+28+6 = 162

6)

12-10 = 2

base of each traingle is 2/2 = 1

Left triangle = right triangle =  [tex]\frac{1}{2} 5.6*1[/tex] = 2.8

Rectangle = 10*5.6 = 56

Total = 2.8+2.8+56 = 61.6

Mean is the ratio of the sum of data to the ample size. The remaining four cards that could be on the card are 8, 8, 16 and 22

Mean is the ratio of the sum of data to the ample size. Median is the middle number after rearrangement while the mode is the most occurring number.

Given the sequence of numbers in order of size as 5, _, _, _, _ 24

Since 2 number falls in the middle and the median is 14, hence:

x +y/2 = 14

Since 8 is the mode, we can assume x = 8 in order to determine "y" as shown

8+y/2 = 14
8+y = 28
y = 16

The sequence of numbers will become 5, 8, 8, 16, _ 24 (8 was repeated twice being the mode)

The last unknown number can then be any value between 16 and 24. Using 22 as the last unknown value, the remaining four cards that could be on the card are 8, 8, 16 and 22

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Answer:

sa: 34cm2

Step-by-step explanation:

2x5 = 10

2x1 = 2

5x1 = 5

(10 + 2 + 5)2 = 20 + 4 + 10 = 34

Answer:

(3, 0) and (-14, 0)

Step-by-step explanation:

Answer:

the first option, acute

Step-by-step explanation:

a straight line is equal to 180

34+64=96

180-96=84

84 degrees so its an acute angle

Answer:

47/10

Step-by-step explanation:

[tex]4\frac{7}{10} =\frac{(4)(10)+7}{10} =\frac{47}{10}[/tex]

Hope this helps

Answer:

47/10

Step-by-step explanation:

Hello!

To convert a mixed number to an improper fraction, we:

Let's simplify:

Another way to represent this:

Your answer is 47/10

Answer:

A) 5 inches of snow.

B) The fourth quarter of the box plot.

C) The first quarter of the box plot.

Step-by-step explanation:

A) 5 inches because that's where the farthest line to the left reaches.

B) The info is most concentrated in the fourth quarter of the box plot.

C) The info is least concentrated in the first quarter of the box plot.

Assume we're measuring something using numerical quantities. We put a dot above that figure in the number line for each frequency of that object we observe.

As a result, the number of total dots in the dot plot corresponds to the entire number of measurements of the values of whatever we performed.

Martina created this box plot to represent the number of inches of snow that fell during the winter in several different cities.

A) Because the longest line to the left reaches that point, the measurement is 5 inches.

B) The fourth quadrant of the box plot contains the greatest information.

C) The initial quadrant of the box plot contains the least amount of information.

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Answer:

I think yes is the correct answer

Step-by-step explanation:

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE let

Answer:

Yes

Step-by-step explanation:

Because they are different

Answer:

3?

Actually I dont understand

The number of different assignments that are possible for this case when the teacher wants to assign 4 of the 15 practice problems is 1,365 ways.

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex]  ways.

For this case, the teacher have to choose 4 problems out of 15 practice problems so that assignments are different.

An assignment would be different than other if the 4 questions in one assigment are not exactly same in the second assigment, and their order won't matter (assumingly).(no counter statement is given in the question's statement) against this assumption).

Those 15 problems are assumingly distinguishable (here we used general logic that each problem would be somewhat different if not fully, and thus, no two problems being indistinguishable).

Then, we can use the combinations to find the number of ways any 4 problems out of 15 practice problems available can be chosen, as shown below:

[tex]^{15}C_4= \dfrac{15!}{4! \times (15-4)!}\\\\\\^{15}C_4=\dfrac{15!}{4! \times 11!} = \dfrac{15 \times 14 \times 13 \times 12 \times 11 \times \cdots \times 2 \times 1}{(4 \times 3 \times 2 \times 1) \times ( 11 \times \cdots \times 2 \times 1)}\\\\\\^{15}C_4=\dfrac{15 \times 14 \times 13 \times 12 }{4 \times 3 \times 2 \times 1} = 1365[/tex]

Thus, the number of different assignments that are possible for this case when the teacher wants to assign 4 of the 15 practice problems is 1,365 ways.

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a. how much will you pay

b. A square meter costs P 145.75

c. multiplication

d. 146.75 × 102.3 (not sure)

e. P 15,017.25

Answer:

y=rx x-3

Step-by-step explanation:

answer is 3

Alice picked 25 apples from the garden and she wants to share the apples with her 6 friends. She wants to determine how many apples each friend would get.

Division is a mathematical operation taht entails grouping a number into equal parts using another number. The sign used to denote division is ÷.

Based on the sign in the question, you are to divide 25 by 6. In order to do this, group 25 into 6 groups. The result is 4 remainder 1.

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Answer:

24.8 ft (1 dp)

Step-by-step explanation:

Arc length of semicircle = [tex]\pi r[/tex]  (where r is the radius)

Given:

⇒ Arc length = 2 × 3.14 = 6.28 ft

Use Pythagoras' Theorem [tex]a^2+b^2=c^2[/tex] to find the hypotenuse of the right triangle with legs 2 ft and 4 ft:

[tex]\implies 2^2+4^2=c^2[/tex]

[tex]\implies c^2=20[/tex]

[tex]\implies c=\sqrt{20}=2\sqrt{5}\:\sf ft[/tex]

Therefore:

perimeter = 6 + 6.28 + 6 + 2 + 2√5

                = 24.75213596...

                = 24.8 ft (1 dp)

Perimeter of semicircle

#Rectangle

For triangle

Use Pythagorean theorem

Total Perimeter

Answer:

y = -x+10

Step-by-step explanation:

We have a point at ( 2,8) and a point at ( 4,6)

We can find the slope using

m = ( y2-y1)/(x2-x1)

   = ( 6-8)/ ( 4-2)

   = -2/2

  = -1

The slope is -1

We can see that it intercepts the y axis at 10 ( x=0 point)

Using the slope intercept form  y = mx+b  where m is the slope and b is the y intercept

y = -x+10

Answer:

the area is 6cm2

Step-by-step explanation:

1/2 bh

1/2 4 x 3

1/2 12

6

Answer:

4000 mL

Step-by-step explanation:

there are 1000 millilitres in 1 liter

in 4 liters there would be 1000 * 4 = 4000 millilitres

Answer:

4,000 ml

Step-by-step explanation:

hope this helps  *_*  :)