v=u+ at
307 80 Marks
u=2
a=-7
Work out the value of v.
t = 0.5
Help

Answer:

(2x-3)(2x+1)

Step-by-step explanation:

4x^2 - 4x - 3

we need two numbers that give 12 when multiplied and 4 when subtracted

the numbers are 6 and 2 because 6*2=12 and 6-4=4.

4x^2 - (6-2)x -3

4x^2 -6x +2x -3

take common

2x(2x -3)+1(2x-3)

take (2x-3) as common

(2x-3)(2x*1 + 1*1)

(2x-3)(2x+1)

There are 720 permutations of {a, b, c, d, e, f, g} end with a. So the option 4 is correct.

If we choose components without repetition, P(7, 6) would imply that we are attempting to find a 7-permutation on the set {b, c, d, e, f, g}. This is not possible.

The same amount of these permutations finish in "a," "b," "c," and so forth.

The amount of permutations that finish in "a" is therefore just: 5040/7 = 720, the same as 6! = P (6,6)

P(7,6) is incorrect because it is asking for the number of 6-permutations on a set of 7 elements.

Since the last character must be a, there are only 6 elements that can be arranged in any order to form a permutation.

Therefore, the correct answer is P(6,6) = 6! = 720.

So the option 4 is correct.

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The equation of the line perpendicular to the green line, passing through the point (1, -4), is y = (-1/m)x + (-4 + 1/m) or y = (-1/m)x - (4 - 1/m) in slope-intercept form.

To find the equation of a line perpendicular to the given green line, we need to determine the slope of the green line first. However, since the equation of the green line is not provided, we cannot directly calculate its slope.

Nevertheless, we can still determine the equation of the perpendicular line using some general principles.

A line perpendicular to another line will have a slope that is the negative reciprocal of the slope of the original line. Let's assume the slope of the green line is m.

The negative reciprocal of m is -1/m. Therefore, the slope of the perpendicular line is -1/m.

Now, we can use the point-slope form of a line to find the equation of the perpendicular line. We have a point (1, -4) on the line, and the slope of the line is -1/m. Let's call the equation of the perpendicular line y = mx + b, where b is the y-intercept we need to determine.

Using the point-slope form, we can substitute the given point and slope:

-4 = (-1/m)(1) + b

Solving for b, we have:

b = -4 + 1/m

Therefore, the equation of the line perpendicular to the green line, passing through the point (1, -4), is y = (-1/m)x + (-4 + 1/m) or y = (-1/m)x - (4 - 1/m) in slope-intercept form.

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Answer:

-14°C

Step-by-step explanation:

The temperature at 12 noon = 10°C (given)

The temperature decreases by 2°C in 1 hour (given)

Thus, the temperature decreases by 1°C in 1/2 hour

Temperature 10°C above zero - Temperature 8°C below zero = 10 - (- 8) = 10 + 8 = 18°C

The temperature decreases by 18°C in 1/2 × 18 = 9 hours

Thus, from 10°C above zero to 8°C below zero it takes 9 hours

Total time = 12 noon + 9 hours

= 21 hours = 9 pm

Thus, at 9 pm temperature would be 8°C below zero.

(ii) The temperature at 12 noon = 10°C

The temperature decreases by 2°C every hour

The temperature decrease in 12 hours = - 2°C × 12 = - 24°C

At midnight, the temperature will be = 10°C + (-24°C) = -14 °C

Therefore, the temperature at mid night will be 14°C below 0.

The sequence is arithmetic. The common difference is 6. Answer: b

If a sequence is arithmetic, there exists a common difference d that is added to each term to get the next term. For instance, given the sequence 2, 5, 8, 11, 14, ...  to get each of the subsequent terms, we add 3. 2 + 3 = 5; 5 + 3 = 8, and so on.

The given sequence is 2,7,13,20, ...To determine whether it is an arithmetic sequence, we need to find the common difference d.

Subtract each subsequent term from its preceding term;7 - 2 = 513 - 7 = 620 - 13 = 7

Therefore, the common difference d is 6.

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\(-\cfrac{1}{2}x+\cfrac{1}{8}y=\cfrac{3}{4}\implies -\cfrac{x}{2}+\cfrac{y}{8}=\cfrac{3}{4}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8\left( -\cfrac{x}{2}+\cfrac{y}{8}\right)=8\left( \cfrac{3}{4} \right)} \\\\\\ -4x+y=6\implies y=4x+6\)

Check the picture below.

The measure of the angles e, d, a, and f will be 26°, 122°, 102°, and 58°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

By the supplementary property, the equation is given as,

f + 78° + 44° = 180°

f = 58°

By the complementary property, the equation is given as,

e + 64° = 90°

e = 26°

By the corresponding angles property, the equation is given as,

c = f

c = 58°

By the supplementary property, the equation is given as,

c + d = 180°

58° + d = 180°

d = 122°

By the corresponding angles property, the equation is given as,

b = 78°

By the supplementary property, the equation is given as,

a + b = 180°

a + 78° = 180°

a = 102°

The diagram is given below.

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Answer: 37

Step-by-step explanation:

: )

Answer:

37

Step-by-step explanation:

The value of SSE (sum squared error) is 40 in the given analysis of the variance problem if SST = 120 and SSR = 80. Option b is correct.

Here the words SSE means Sum Squared Error, SST means Sum of Squares Total and SSR means Sum of Square Regression.

In the SSE accuracy measure, errors are squared and then added. It is used when the data points are similar in magnitude.

The formula is SST = SSR + SSE ⇒ SSE = SST - SSR

The given values of the analysis of the variance problem are

SST = 120; SSR = 80

Then, the value of SSE = SST - SSR = 120 - 80 = 40

So, option b is correct.

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188.4 cm²  is the surface area of the cone .

What is known as a cone?

given   r = 4 cm

           l = 15 cm

the curved surface area = πrl

                                     = 3.14 * 4 * 15

                                      = 188.4 cm²

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Answer: 76 cm2

Step-by-step explanation:

I Did it trust

Answer:

x >-2

Step-by-step explanation:

3x-10<4(x-2)

3x - 10<4x-8

grouping liked terms

3x-4x<-8+10

-x<2

divide through by coefficient of x

x > -2

The angle 1 can be named as follows:

∠RST

∠TSR

∠S

There are various ways to name an angles. You can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.

Therefore, let's name the angle 1 indicated on the diagram as follows:

Hence, the different ways to name the angle 1 is as follows:

∠RST or ∠TSR

Or

∠S

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Step-by-step explanation:

In the picture.

The answer is X = 61°

Answer: -3/4

Step-by-step explanation: Lucky I just learned about this last week! Multiply 7 and -1 by -2 which makes the equation -14x + 2 = 14. Subtract 2 from both sides to make -16x = 12. Then divide each side by -16 and you get -3/4 = x.

Nice helping out!

Answer:

There are no solutions.

Step-by-step explanation:

Hello!

Isolate the absolute value equation first:

Now stop and think.

An absolute value equation always has a positive outcome, because you are finding the positive value of what's inside. The outcome here is negative, so there is no value of x that makes it so that the absolute value is negative.

So the solution is No Solutions.

The unlevered beta for Lincoln is closest to 0.95.

The unlevered beta represents the risk or sensitivity of a company's stock returns to market movements, assuming the company has no debt (or financial leverage). The beta value is typically provided by financial sources or can be calculated using regression analysis. Since no additional information is given about Lincoln or its industry, we cannot determine the exact unlevered beta. However, among the given answer options, 0.95 is the value that is closest to 1.0, which is often considered the average or baseline beta. A beta value greater than 1.0 indicates higher sensitivity to market movements, while a value less than 1.0 suggests lower sensitivity.

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The probability of winning at least once when playing the instant lottery twice is 0.19, or 19%.

To find the probability of winning at least once in the instant lottery when playing twice, we can use the complement rule.

The complement rule states that the probability of an event occurring (in this case, winning at least once) is equal to 1 minus the probability of the event not occurring (in this case, not winning both times).
Determine the probability of not winning in a single game, which is 1 - 0.1 = 0.9.
Calculate the probability of not winning both times, since outcomes are independent, by multiplying the probabilities of not winning each time: 0.9 * 0.9 = 0.81.
Finally, find the probability of winning at least once by subtracting the probability of not winning both times from 1: 1 - 0.81 = 0.19.

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Answer:

5.5 yd

Step-by-step explanation:

To find the side length of the cube, the volume is a clue. We know that all sides of a square are equal, and the volume of a cube is length×width×height. Since the length, width and height are all the same, we know it is V=x³. Since we know the volume, we can plug in and solve for x.

166=x³

In order to get x alone, we have to cube root both sides.

x≈5.5 yd

The Distance between the given parallel planes is 8.84.

According to the statement

we have given that the two parallel planes and we have to find the distance between them.

So, For this purpose, we know that the

First let us find a point on one plane. For this in plane 9z +3x - 3y = 2

assume x = 0 and y = 0 then and hence (0,0,2/9) on this plane.

Now we find the distance between point (0,0,2/9) and plane 6z -2y + 2x =0

So,

As distance from a point to plane is

\(D= \frac{|ax_1+by_1+cz_1+d|}{\sqrt{ (a^2+b^2+c^2)}}\)

And

now substitute the values in then

\(D= \frac{|2*0+ (-2)0+6*2/9+0|}{\sqrt{ 36 +4+4)}}\)

Then the value becomes

\(D= \frac{4/3}{\sqrt{ (44)}}\)

\(D= \frac{4\sqrt{44} }{3}\)

Then solve it

\(D= \frac{26.52}{3}\)

then

D = 8.84

So, The Distance between the given parallel planes is 8.84.

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Step-by-step explanation:

I always try to find the easiest way to solve this kind of questions.

The easiest percentage to calculate with is number 10.

first step , divide the whole amount of the money by ten.

as a result we get 40,000

second step, we were asked to calculate a20% so we will double the 10 percent

and the answer goes to 80,000.

Answer:

Step-by-step explanation: umm i think 6000000 i don't know it might be right because i guess you need to add

Answer:

complex

Step-by-step explanation:

Answer:

pretty sure it's compound

Step-by-step explanation:

Answer: 0.2

Step-by-step explanation:

Answer:

=> 6.5, 7.2 , 9.7

Step-by-step explanation:

By using Pythagorean theoram

H² = P² + B²

=> (9.7)² = (7.2)² + (6.5)²

=> 94.09 = 51.84 + 42.25

=> 94.09 = 94.09

A fraction is a way to describe a part of a whole.  The correct option is C.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

A proper fraction is a fraction whose numerator is smaller than the denominator. When a proper fraction is raised to a positive exponent greater than 1, then the product decreases but does not reach 0.

Hence, the correct option is C.

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Answer:

it's sideways please turn it so i can read it and help.

Step-by-step explanation:

Answer:

=408x3+1556x2−4008x+1564

Step-by-step explanation:\

(8x−4)(3x+17)(17x−23)