Question 5 of 5
Compare 7/8 and 8/9 by converting each fraction to a decimal. Which is larger?

a. The rocket splashes down after 31.23 seconds.

b.  The rocket is 1374.7 meters above sea level.

NASA launches a rocket at t=0 seconds.

Its height, in meters above sea-level, as a function of time is given by

h(t)=-4.9t²+142t+346.

Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?

When splash down occurs, h(t) = 0, therefore

-4.9t²+142t+346 = 0

find t using the quadratic formula; a=4.9, b=142, c=346

t = -142 ± √(142)² - 4(-4.9)(346) / 2(-4.9)

t = -142 ± 164.15 / -9.8

t = -142+164.15/-9.8 , -142-164.15/-9.8

t = 22.15/-9.8 , -306.15/-9.8

t = -2.26 , 31.23

time cannot be negative so t = 31.23

The rocket splashes down after 35.8229 seconds.

The max occurs on the axis of symmetry, use x=-b/(2a) to find it

t = -142/2(-4.9)

t = 142/9.8

t = 14.48 sec

replace t with 17.2449 in the equation

h(t) = -4.9(14.48)² + 142(14.48) + 346

= 1374.7 m

The rocket peaks at 1374.7 meters above sea-level.

Hence we get the answers.

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Answer:-0.9.45

Step-by-step explanation:

-0945

Answer: -0.6i

Step-by-step explanation:

[tex]0.4i-i=\\\\i(0.4-1)=\\\\i(-0.6)=\\\\-0.6i[/tex]

For the given line, the graph is given below -

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

For the given line,

y = 1/4x + 2

the coordinates will be -

for x = 4, y = 3

(4,3)

for x = 8, y = 4

(8,4)

for x = 0, y = 2

(0,2)

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Answer:

C

Step-by-step explanation:

to determine which ordered pair is not a solution , substitute the coordinates of the point into the inequalities and check the validity. Note that both inequalities must be true for the point to be a solution.

A (- 3, 3 )

3  ≥ - 3 - 5

3 ≥ - 8  ← true

3(3) < - 6(- 3) + 3

9 < 18 + 3

9 < 21 ← true

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

B ( - 1, 2 )

2 ≥ - 1 - 5

2 ≥ - 6 ← true

3(2) < - 6(- 1) + 3

6 < 6 + 3

6 < 9 ← true

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

C (4, 5 )

5 ≥ 4 - 5

5 ≥ - 1 ← true

3(5) < - 6(4) + 3

15 < - 24 + 3

15 < - 21 ← false

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

D (- 6, 0 )

0 ≥ - 6 - 5

0 ≥ - 11 ← true

3(0) < - 6(- 6) + 3

0 < 36 + 3

0 < 39 ← true

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

Both inequalities are true in A, B , D

Both inequalities in C are not true so (4, 5 ) is not a solution to the system

The benzene has a volume value of 149.99 mL

From the question, the given parameters are

Density of benzene = 0.8787 g/mL

Mass of benzene = 131.8 g

The volume of the benzene is then calculated using

Density = Mass/Volume

Make Volume the subject of the formula

So, we have

Volume = Mass/Density

Substitute the known values in the above equation

So, we have the following equation

Volume = 131.8/0.8787

Evaluate the quotients in the equation

Volume = 149.99

Hence, the volume of the benzene is 149.99 mL

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Answer:

C

Step-by-step explanation:

One of the quick ways of getting the answer is to graph the  equation. I have done that for you at the bottom of this answer. However, I think you want the written solution.

Equation

y = x^2 + 8x - 6                        Put brackets around the first 2 terms

y = (x^2 + 8x) - 6                      Take 1/2 the second term and square

8/2 = 4;   4^2 = 16                    Put 16 after the second term

y = (x^2 + 8x + 16)   - 6             Subtract 16 and put it after the 6

y = (x^2 + 8x + 16) -6-16           Combine

y = (x^2 + 8x + 16) - 22

The first 3 terms make a perfect square (x^2 + 8x + 16) = (x + 4)^2

So the answer is between C and A

y = (x + 4)^2 - 22

Answer:

0.5 ⋅ 103

Step-by-step explanation:

Answer:

The vertical angles are

1 and 3

2 and 4

Answer:

Y=-3x+7

Step-by-step explanation:

it hit the y axis at 7

And it is going down by 3

Answer:

Step-by-step explanation:

step 1: multiply both sides by 9π to get V9πr³=2

step 2: divide both sides by V9π to get r³=2/(V9π)

step 3: take the cubed root of both sides to get r=∛[2/(V9π)]

Number 20 from the set S:{−18, 2, 15, 20} will make the inequality five sixth "m" minus four less than one third "m" plus 5 false.

As per the question statement, we are supposed to find  the  integer(s) from the set S:{−18, 2, 15, 20} will make the inequality five sixth "m" minus four less than one third "m" plus 5 false.

Let's write the given statement in numeric form first, we get

[tex]\frac{5m}{6} -4 < \frac{m}{3} +5[/tex]

Let's solve the inequality for "m"

We get 3m/6 <9

or 3m <54

or m < 18

Therefore all values of m < 18 will make the inequality true and m>18 will make the  inequality false.

The value of m > 18 in the above given set S:{−18, 2, 15, 20} is 20, hence number 20 from the set S:{−18, 2, 15, 20} will make the inequality five sixth "m" minus four less than one third "m" plus 5 false.

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Answer: its 20 or 15 i belieive its 20 tho

Step-by-step explanation:

The relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds) has been plotted in the graph shown below.

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

Next, we would determine the initial altitude as follows:

y = mx + c

0  = (0.1 × 35)  + c

0 = 3.5 + c

c  = -3.5

Substituting the given points into the formula, we have;

y  = 0.1x - 3.5

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Complete Question:

Elon sat on the dock with his fishing rod, when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.1 meters per second. When it reached the water's surface after 35 seconds, Elon found it was only an old shoe...

Graph the relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds).

An 8-inch violin string has a frequency of 640 cycles per second using the  inverse variation equation.

Given: A 16-inch violin string is known to vibrate at 320 cycles per second.

We know that,

Using the frequency equation where l for the length of the string and f for the frequency.

f = k/l

320  = k/16

k = 5120

So, the equation becomes f = k/l

For l = 8

f = 5120/8

f = 640

Therefore, the frequency of an 8-inch-long violin string is 640 cycles per second.

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A line that passes through point (3,-5) and is perpendicular to y = -x+5 has the equation y = x - 8.

A straight line has an equation of y=mx + c, where m is the gradient and c is the constant, also known as the y-intercept, at which the line crosses the y-axis.

In order to put the equation in y-intercept (y = mx + b) form and determine the equation of a graphed line, first determine the slope and y-intercept.

It is given that a line's equation passes through point (3,-5) and is perpendicular to y = -x+5.

Slope of given line = -1

Slope of line perpendicular to the given line = Negative of the reciprocal of the slope of a given line = 1

We have the slope and point (3,-5) of the required line. So, we can find the constant of this equation.

y = mx + c

-5 = 1(3) + c

c = -5 - 3

c = -8

Substituting c = -8 and m = 1 to get the equation of required line.

y = mx + c

y = x - 8

As a result, the equation of a line passing through point (3,-5) and perpendicular to y = -x+5 is y = x - 8.

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Step-by-step explanation:

the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

a slope = 0 means that the y coordinate change is always 0, so y does not change anywhere on the line.

that makes y a constant c, and x can be any value completely independent of y.

the line is the summary of all points that have c as their y coordinate.

so, the general equation for such a line is simply

y = c

what is c ?

as we have one point on the line, remember the statement above : the line is the summary of all points that have c as their y coordinate.

that means (3, -4) must have the same y coordinate.

so, c = -4.

the equation of the line is therefore

y = -4

Answer:

[tex]\sf Area = 10\dfrac{7}{8} \yd^2[/tex]

Step-by-step explanation:

     Area = length *breadth

Convert the mixed fraction to improper fraction.

[tex]\sf 1\dfrac{1}{2}=\dfrac{3}{2} \ yd[/tex]

[tex]\sf area = \dfrac{3}{2}*\dfrac{58}{8}\\\\[/tex]

      [tex]\sf = \dfrac{3*29}{8}\\\\=\dfrac{87}{8}\\\\= 10\dfrac{7}{8} \ yd^2[/tex]

The representation of the radical expression; the cube root of five to the seventh power as an expression with a rational exponent is; five to the seven thirds power.

It follows from the task content that the radical expression given; ³√5⁷ is to be expressed as a rational exponent expression.

Recall that the converse of the rational exponent law of indices is such that; ³√x = (x)^⅓.

Hence, it follows that the expression given;

³√5⁷ = (5⁷)^⅓.

Also, it follows from the power of power law of indices that the expression above can be written as;

5^(7/3).

Ultimately, the equivalent rational exponent expression is; five to the seven thirds power; 5^(7/3).

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Answer:

Step-by-step explanation:

it is D i took the test

Answer: for number 1  13,416

Step-by-step explanation: i think that is the correct answer i could be wrong

In order to find how many pounds are in each bag, we just need to divide the total amount of blueberries by the number of bags.

So we have:

So in each bag there are 1/16 pounds of blueberry.

a) 20% 60 of  is 12

b) 25% of 24 is 6

c) 4% of 600 is 24

Here the problem we are dealing with is related to percentage, which could be a division or a proportion in which the value of the entire is continuously 100. is represented by the symbol "%".

a) let us consider the missing number to be x

so, the problem will be 20% of  x= 12

=> 20/1000* x= 12

=>20x= 12*100

=> x= 12*100/20 = 60

b) let the percentage be x

so, the problem will be x% of 24 =6

=>x/100* 24= 6

=>24x=600

=>x=600/24 =25

c)  here, we are given  4% of 600=?

=4/100* 600

=24

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Answer:

$100.14

Step-by-step explanation:

convert to a number

The probability that a group of four siblings includes all XY is 1/16 (6.5%), while the probability all XX offspring is 1/16 (6.5%). It is a simple genetic probability calculation.

Genetic probabilities and chromosomes

Females inherit two chromosomes X, whereas males inherit one chromosome X and one chromosome Y.

The probabilities of inherent two chromosomes X (females) are 1/2 (50%), while the probabilities of inherent one chromosome X and one chromosome Y (males) are also 1/2.

In consequence, the probability that a group of four siblings includes all XY is 1/16 (because it is equal to 1/2 x 1/2 x 1/2 x 1/2 = 1/16), the same for the probability all XX offspring (1/16).

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After doing some mathematical operations, we conclude that extra large pizza is 4x times heavier than small size pizza.

So, times extra large pizza is heavy than small pizza:

Now, perform operations as follows:

Therefore, after doing some mathematical operations, we conclude that extra large pizza is 4x times heavier than small size pizza.

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The correct question is given below:

Use the Table that shows the weights of three sizes of pizza.

Extra Large Pizza - 6 1/2

Medium Pizza - 3 1/4

Small Pizza - 1 5/8

(A) How many times as heavy is the extra large pizza than the small pizza?

Flight will reach Auckland at 11:22 am with respect to Auckland time.

We have the following given information which states as follows

A flight to Sydney to Auckland takes 3 hours and 12 minutes.

∴ Total journey time = 3hr 12min.

Auckland times is 2 hours ahead of Sydney's time.

∴ Change in time will be 2hr

The flight departed Sydney at 10:10 am

∴ Flight will reach Auckland after the journey time

∴ Flight will reach Auckland after 3hr 12min

∴ Flight will reach Auckland at 01:22 pm

But Auckland times is 2 hours ahead of Sydney's time.

∴ Change in time will be 2hr

∴ Flight will reach Auckland 2hr less than the considered reach time with respect to Sydney.

∴ Flight will reach Auckland at 11:22 am.

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Answer:

-2/3

Step-by-step explanation:

y=mx+c

m is the gradient/slope

m= y2-y1 / x2-x1

you can label any point as your x1y1 and x2y2, you will still get the same answer

Answer:

Answer down below!

Step-by-step explanation:

Using your knowledge of parallel lines, you know that parallel lines are most often time never touching, but on the same plane. The top of R and the bottom line of Q are parallel because they don't intersect each other.

We also notice that the shapes are the same length, so we have this conclusion!

Q and R are identical because they share opposite, parallel lines.

ANSWER

B) y = 1/2x - 6

EXPLANATION

We have that the line passes through (6 -3) and has a slope of 1/2.

To find the point-slope form of the equation, we have to use the formula:

where m = slope = 1/2

(x1, y1) = (6, -3)

So, we have:

y - (-3) = 1/2 (x - 6)

y + 3 = 1/2 x - (1/2 * 6)

y + 3 = 1/2 x - 3

=> y = 1/2x - 3 - 3

y = 1/2x - 6

The answer is Option B