10 points!!!!!!!!!!!!!!!!!!!!!

Answer:

[tex]\textsf{a)} \quad v=12t^2-6t-18[/tex]

[tex]\textsf{b)} \quad a=24t-6[/tex]

c)   1.5 s

d)  -19.25 m

e)   24.5 m

Step-by-step explanation:

Displacement

[tex]x=4t^3-3t^2-18t+1[/tex]

(where t ≥ 0 and x is in meters)

To find the equation for velocity, differentiate the equation for displacement:

[tex]\implies v=\dfrac{\text{d}x}{\text{d}t}=12t^2-6t-18[/tex]

(where t ≥ 0 and v is in meters per second)

To find the equation for acceleration, differentiate the equation for velocity:

[tex]\implies a=\dfrac{\text{d}v}{\text{d}t}=24t-6[/tex]

(where t ≥ 0 and a is in meters per second squared)

The particle comes to rest when its velocity is zero:

[tex]\begin{aligned}v & = 0\\\implies 12t^2-6t-18 & = 0\\6(2t^2-t-3) & = 0\\2t^2-t-3 & = 0\\2t^2-3t+2t-3 & = 0\\t(2t-3)+1(2t-3) & = 0\\(t+1)(2t-3) & = 0\\\implies t & =-1, \dfrac{3}{2}\end{aligned}[/tex]

As t ≥ 0, the particle comes to rest at 1.5 s.

Substitute the found value of t from part (c) into the equation for displacement to find where the particle comes to rest:

[tex]\implies 4(1.5)^3-3(1.5)^2-18(1.5)+1=-19.25\: \sf m[/tex]

We have determined that the particle is at rest at 1.5 s.

Therefore, to find how far the particle traveled in the first 2 seconds, we need to divide the journey into two parts: before and after it was at rest.  

The first leg of the journey is the first 1.5 s and the second leg of the journey is the next 0.5 s.

At the beginning of the journey, t = 0 s.

[tex]\textsf{when }t=0: \quad x=4(0)^3-3(0)^2-18(0)+1=1[/tex]

Therefore, when t = 0, x = 1

When t = 1.5 s, x = -19.25 m (from part (d)).

⇒ Total distance traveled in first 1.5 s = 1 + 19.25 = 20.25 m

When t = 2, x = -15 m.

Therefore, the particle has traveled 19.25 - 15 = 4.25 m in the last 0.5 s of its journey.

Total distance traveled:

1 + 19.25 + 4.25 = 24.5 m

Refer to the attached diagram

When the particle is at rest, it changes direction.  If we model its journey using the x-axis, for the first leg of its journey (0 - 1.5 s) it travels in the negative direction (to the left). At 1.5 s it stops, then changes direction and travels in the positive direction (to the right), arriving at -15 at 2 seconds.

Answer:

Step-by-step explanation:

We know a total of 6000 is being turned into 510, in two accounts which equal to 15%, to find how much is in each account we can create the following equation:

[tex]5x+10x=510[/tex]

Solve for x

[tex]15x=510\\x=34[/tex]

Now multiply x by the corresponding percentages to find how much was invested into each percentage.

[tex]34*5=170[/tex]

[tex]34*10=340[/tex]

Therefore we now know that 170 dollars was invested into the 5% division, and 340 dollars was invested into the 10% division.

We can of course check our answer by adding 170+340 which equals our original investment of 510.

$1800 is invested at 5% and the remainder, $4200, is invested at 10%.

percentage, a relative value indicating hundredth parts of any quantity.

Let us consider the amount invested at 5% x.

The amount invested at 10% is then the remainder, which is:

$6000 - x

Now we can set up an equation for the total interest earned:

0.05x + 0.10($6000 - x) = $510

Simplifying and solving for x:

0.05x + $600 - 0.10x = $510

-0.05x + $600 = $510

-0.05x = -$90

Divide both sides by 0.05

x = $1800

Hence, $1800 is invested at 5% and the remainder, $4200, is invested at 10%.

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Option A is correct. The type of construction that we have here is the bisection of the <D.

The bisection of angle can be defined to be the construction of a ray that would help to divide a particular angle into two equal halves.

In this diagram we can see that the angle here is at D. Hence the construction is aimed at dividing this particular angle into 2. Therefore the answer to the question is The bisection of ∠D.

The bisector does the job of creating an equal measure. The given bisector is known to have the midpoint of the segment. It cuts through this angle and creates two different angles that are of the same size.

If we draw the line in that shape, we will be having the division of that angle. From the explanation here, we can see the answer is the first option

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When to use the law of cosine is explained below.

Using the labelled triangle, we have: sin D/d = sin E/e = sin F/f.

Using the sine law, the measure of angle M is: 74.9°.

The cosine law is given as, c = a² + b² - 2ab(cos C). It is used to solve a triangle with missing angle or side.

When we are given two sides and an angle between the two sides, and we need to find the third side.

When we are given the all three sides of a triangle and we need to find the angles of the triangle.

Using the labelled triangle DEF in the diagram below, the law of sines is:

sin D/d = sin E/e = sin F/f.

m∠N = 56°

n = 8.5 cm

m = 9.9 cm

Plug in the values into sin N/n = sin M/m:

sin 56/8.5 = sin M/9.9

sin M = (sin 56 × 9.9)/8.5

sin M = 0.9656

M = sin^(-1)(0.9656)

M = 74.9°

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For the given diagram, it has been proved that angle A is congruent to angle B.

Given Information:

Angle A and Angle B are such that,

Ray AC ║ Ray BE

Ray AD ║ Ray BF

Proof:

Since a straight line is the shortest line connecting two points in a plane,

Extend ray AD and ray BE, such that both intersect at point G.

Now, since, angle A and angle 1 both make corresponding angles,

∠A = ∠1 .......... (1)

Ray ADG is parallel to the ray BF.

Thus, again, angle B and angle 1 make corresponding angles,

∠B = ∠1 ............ (2)

From (1) and (2), as per transitive relationship of angles,

∠A ≅ ∠B

Hence proved.

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James is (B) 20 meters far from the finish line 9 seconds after the race has started.

To find the distance:

Therefore, James is (B) 20 meters far from the finish line 9 seconds after the race has started.

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The complete question is given below:

James covers a distance of 8 meters in the first second of a 100-meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started?

a. 11

b. 20

c. 28

d. 80

Answer:

4 degrees ( to nearest degree).

Step-by-step explanation:

The trig ratio you want is the tangent.

tan x = 10,000 / 160,000    where x is the angle of depression.

tan x = 0.0625

x = 3.576 degrees.

The null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.

Given that the significance level is 0.10.

We are required to form the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% the significance level.

Hypothesis is a statement which is tested for its validity. Null hypothesis is the statement which is accepted or not by z test,t test,f test ,chi-square test or any other test.

We have to take opposite of the statement to form a null hypothesis. Since we have to check whether the proportion of people who owns cats is larger than 60% of the significance level, we have to assume that it is smaller than 60% of the significance level.

60% of the significance level=0.60*0.10=0.06.

Null hypothesis is [tex]H_{0}[/tex]:μ<0.06

Hence the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.

Question is incomplete.The question should include the following:

Find the null hypothesis for the testing.

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Answer:

assuming it's a perfect world and that the fish lives in a 1 cubic meter fish tank 1*1.4422 will increase the volume my a factor of 3

a) The equation represents an ellipse.

b) The equation represents a circle.

c) The equation represents a parabola.

In this problem we have general equations of the form A · x² + B · y² + C · x + D · y + E = 0, which have to be modified into standard form to infer its graphical form. This procedure can be done by algebra properties:

16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0

[(4 · x)² + 2 · 12 · (4 · x)] + [(2 · y)² - 2 · 2 · (2 · y)] = - 84

[(4 · x)² + 2 · 12 · (4 · x) + 144] + [(2 · y)² - 2 · 2 · (2 · y) + 4] = 64

(4 · x + 12)² + (2 · y + 2)² = 64

4² · (x + 3)² + 2² · (y + 2)² = 64

(x + 3)² / 4 + (y + 2)² / 16 = 1 : Ellipse

x² + y² + 8 · x - 6 · y - 15 = 0

(x² + 8 · x) + (y² - 6 · y) = 15

(x² + 2 · 4 · x + 16) + (y² - 2 · 3 · y + 9) = 40

(x + 4)² + (y - 3)² = 40 : Circle

x² + 6 · x + 4 · y + 5 = 0

x² + 6 · x + 5 = - 4 · y

y = - (1 / 4) · x² - (3 / 2) · x - (5 / 4) : Parabola

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Step-by-step explanation:

clearly divergent.

the elements of the series are getting bigger and bigger intercepted by some constant "1" (but they don't help here - after every intercepting "1" are 2 numbers that are larger by 1 than the 2 numbers before the intercepting "1", and that continues into infinity, so, the numbers will go to infinity, and that shows that the series is divergent).

Answer:

Nope.  It would take 32 and 4/13 minutes, which is longer than 30 min.

Step-by-step explanation:

The distance is 35 miles and the speed 65 miles/hour

Dividie the distance by the speed to obtian the time required,

(35 miles)/(65 miles/hour) = 0.538 hours

No, 35 miles at the speed limit of 65 mph would require 0.538 hours, 0.038 hours more than 1/2 hour.  2 and 4/13 minutes more than 30 minutes.

Answer:

The painter was more productive in week a.

Step-by-step explanation:

Find the unit rate.  How many houses could be painted in 1 day?

6/2 means that she could paint 3 houses per day

5/4 means that she could paint 1.25 houses per day.

The painter was more productive in the last week.

In this problem, we need to find in which week did the painter paint the most.

To find the solution to this problem, first, we need to divide 6 by 2 (last week)

which equals 3.

Next, divide 5 by 4 (this week)

which equals 1.25

Now, compare the two quotients and identify the larger number (3 and 1.25).

Basically, we can see that the number 3 is larger.

This means that the painter could paint 3 houses per day in the last week, and 1.25 houses per day in this week.

Therefore, we can say that the painter was more productive in the last week.

I hope this helps :)

Justine only goes when her friend goes [Conditional probability].

Mom going to PROM and Justine going to PROM are separate events. [Independent events].

Mom can't go until she finishes the housework is dependent on events

independent events. [Dependent events]

The probability exists in the analysis of the possibilities of happening of a result, which exists acquired by the ratio between favorable cases and possible cases.

Conditional probability directs to the possibility that some outcome happens given that another possibility contains also occurred.

Justine only goes when her friend goes [Conditional probability]

Independent events exist as those possibilities whose occurrence exists not dependent on any other event.

Mom going to PROM and Justine going to PROM are separate events. [Independent events]

Dependent events exist that depend upon what occurred before.

Mom can't go until she finishes the housework is dependent on events

independent events. [Dependent events]

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Answer: x = 2

Step-by-Step Solution:

Given:

OH = WO = LW

OH = 2x + 1

WO = 3x - 1

LW = 5

To Find:

The value of 'x'

Solution:

We know, OH = WO = LW

So, equate any two of the values given :-

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

Hence, x = 2.

The area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex]

Given that the grid has squares with side lengths of 1.5 cm.

We are required to find the area of the composite figure.

The area of the composite figure is approximate to the area of the rectangle plus the are of the semicircle at the top of the rectngle plus the semicircle at the right side of the rectangle.

Finding the area of the rectangle.

A=(3*1.5)(4*1.5)=27 [tex]cm^{2}[/tex]

Finding the area of the semicircle at the top of the rectangle.

A=1/2 π[tex](2*1.5)^{2}[/tex]=4.5 π [tex]cm^{2}[/tex]

Finding the area of the semicircle at the right of the rectangle.

A=1/2 π[tex](1.5*1.5)^{2}[/tex]

=2.53π [tex]cm^{2}[/tex]

Total area =27+4.5π+2.53π

=27+7.03π

Use π=3.14

=27+7.03*3.14

=49.1 [tex]cm^{2}[/tex]

Hence the area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex].

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Answer:

180.

Step-by-step explanation:

100 contains 2  zero digits.

101 - 109 have 9 numbers,  110 to 200 have 11 numbers

so for 101 to 200 its 20 numbers

Its also 20 for 201 to 300  and for all sets of 100 up to 900.

- that is 7 * 20 = 140 numbers

Finally from 901 to 999 we have 18.

Total = 20 + 140 + 18

= 2 + 20 + 140 + 18

= 180.

The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given the expression:

[tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }\\ \\Simplifying:\\\\=\frac{\sqrt[4]{3x^2}}{2y}[/tex]

The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]

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Answer:

The answer is D

Step-by-step explanation:

The half-life of the substance is 1.94 years.

The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a [tex](1-r)^{x}[/tex] is the general form.

Here

a = the initial amount of substance

1-r is the decay rate

x = time span

The correct form of the equation is given as:

[tex]a=a_{0}[/tex]×[tex](0.7)^{t}[/tex]

where t is an exponent of 0.7 since this is an exponential decay of 1st order reaction

Now to solve for the half life, this is the time t in which the amount left is half of the original amount, therefore that is when:

a = 0.5 a0

Substituting this into the equation:

0.5 [tex]a_{0}=a_{0}[/tex]×[tex](0.7)^{t}[/tex]

0.5 = [tex](0.7)^{t}[/tex]

Taking the log of both sides:

t log 0.7 = log 0.5

t = log 0.5 / log 0.7

t = 1.94 years

The half life of the substance is 1.94 years.

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Answer:

-2/3

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

As we can see in the figure, lines m and n are parallel to each other. so we can apply Angle pair properties ~

So,

[tex]\qquad \sf  \dashrightarrow \: \angle1 \cong \angle2[/tex]

[ they form corresponding angle pair ]

and it's given that :

[tex]\qquad \sf  \dashrightarrow \: \angle2 \cong\angle 3[/tex]

therefore, by using above information. we can conclude that :

[tex]\qquad \sf  \dashrightarrow \: \angle1 \cong \angle3[/tex]

Answer:

3

Step-by-step explanation:

-2 * 3= -6

-1 * 3= -3

0 *3= 0

1 *3 = 3

2* 3 = 6

3 * 3 =9

Answer:

? = 3

Step-by-step explanation:

To find the value of ?, substitute one of the ordered pairs from the table [except (0, 0)] into the given formula and solve for ?.

Given formula:

[tex]\sf y=\boxed{?} \:x[/tex]

Substitute x = 1 and y = 3 into the formula:

[tex]\sf 3=\boxed{?} \:1[/tex]

To isolate ? divide both sides by 1:

[tex]\implies \sf \dfrac{3}{1}=\dfrac{\boxed{?} \:1}{1}[/tex]

[tex]\implies \sf 3=\boxed{?}[/tex]

Therefore, ? = 3:

[tex]\implies \sf y=3x[/tex]

Check by inputting another value of x from the table into the found formula and comparing the calculated y-value:

[tex]\sf x=-2 \implies y=3(-2)=-6 \quad \boxed{\sf correct}[/tex]

[tex]\sf x=3 \implies y=3(3)=9 \quad \boxed{\sf correct}[/tex]

Based on the graph of the budget function with the x-intercept and the y-intercept, the two ordered pairs that would fall on this line are (2, 0) (0, 5).

The x-intercept is the point on the graph where the budget function would cross the x-intercept.

At this point, the value of y would be 0 because the x-axis intersects the y-axis at y = 0.

An x-intercept of 2 would therefore have the point, (2,0).

The y-intercept would be the point where the y axis is crossed. At this point, x will be zero because the y-axis intercepts the x-axis at the value, x = 0.

A y-intercept of 5 would therefore yield a point of (0, 5).

In conclusion, option A is correct.

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Solving a system of equations we can see that:

Let's define:

When the airplane travels against the wind, the total speed is:

(A - W)

In this way, we know that the airplane travels 1350 miles in 5 hours, then:

(A - W) = 1350mi/5h

When the airplane travels with the wind, it takes 3.75 hours to travel the same distance, then:

(A + W) = 1350mi/3.75h

We have now a system of equations:

(A - W) = 1350mi/5h

(A + W) = 1350mi/3.75h

If we isolate A on the first equation, we get:

A = 270mi/h + W

Replacing that in the other equation we get:

270mi/h + W + W = 360 mi/h

Solving for W we get:

2*W = 360mi/h - 270mi/h = 90mi/h

W = 90mi/h = 45mi/h

And the airplane rate is:

A =  270mi/h + W = 270mi/h + 45mi/h = 315 mi/h

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Domain and Range of f(x) is given by:

Domain: {x | all real numbers} ;

Range: {y | y > 0}

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. A function's range is its potential output, whereas its domain is the set of all possible input data.

The function can be written as :

[tex]f(x)=\sqrt[\frac{2}{3} ]{108^{2x} } \\f(x)=108^{\frac{3}{2}^{2x} }[/tex]

Now that x is an exponent, all real values are possible for it. Therefore, all real numbers make up its domain for f(x). But value of f(x) cannot be less than 1 because for x = 0 the value of f(x) is 1 and also for any values of x, the value of f(x) can never be less than 1

So, Range of f(x) is all real numbers greater than 0

Hence, Domain and Range of f(x) is given by:

Domain: {x | all real numbers} ;

Range: {y | y > 0}

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Answer:

a^2+b^2=c^2

Step-by-step explanation:

leg1=a

leg2=b

hypotenuse=c

a^2+b^2=c^2

Answer:

u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

Step-by-step explanation:      

7. ∠I and ∠M are corresponding angles.

8. ∠J and ∠P are alternate exterior angles.

9. ∠K and ∠M are alternate interior angles.

10. ∠L and ∠M are consecutive interior angles..

11. ∠I and ∠O are alternate exterior angles.

12. 7. ∠K and ∠O are corresponding angles.

Angles that are formed outside the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate exterior angles.

Angles that are formed inside of the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate interior angles.

Angles that are formed inside of the parallel lines that are intersected by a transversal and lie on the same side of the the transversal are consecutive interior angles.

Angles that are formed in relative corner position on each of the parallel lines that are intersected by a transversal and lie along the transversal in the same side are called corresponding angles.

Thus, from the image given, we have the following special angles:

7. ∠I and ∠M are corresponding angles.

8. ∠J and ∠P are alternate exterior angles.

9. ∠K and ∠M are alternate interior angles.

10. ∠L and ∠M are consecutive interior angles..

11. ∠I and ∠O are alternate exterior angles.

12. 7. ∠K and ∠O are corresponding angles.

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The explicit form of the arithmetic function as described is; f(p) = 2(p-1) + 12. and the seventh term is; 24.

Since it follows from the task content, that the first term is 12 and the common difference is 2.

It therefore follows from convention that the explicit function is; f(p) = 2(p-1) + 12 and by substituting n= 7 into, the equation, we have; f(7) = 24.

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When graphing, the intersections of the graphs represent the solutions of the system.

When graphing a system of equations, you just need to graph both equations in the same coordinate axis.

The solutions of the system are all the points where the graphs of the two equations intersect.

This means that if there is only one intersection, there is one solution.

But we can have more than one intersection, like in the case where at least one of the equations is a polynomial of degree 2 or more.

And there is also the case that the graphs never intersect, like in parallel lines, in these cases we have no solutions.

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