what is the value of x? pls help!

Answer:

The answer to your question is tan²Ф

Step-by-step explanation:

Trigonometric identities are equalities that relate trigonometric functions  and are true for every value of it. There are many trigonometric functions and are useful in trigonometry.

The trigonometric identity that is the answer to this question is tan²Ф.

                    tan²Ф  + 1 = sec²

Option E) I and III only is the correct answer

Step-by-step explanation:

First of all we have to define the disjoint events and independent events

Disjoint events:

Two events are said to be mutually exclusive or disjoint if they cannot occur at the same time. There will be no common elements in their outcomes.

Independent Events:

Two events are said to be independent if the probability of occurrence of one event doesn't affect the probability of occurrence of other event.

Moreover,

The sum of probability of an events occurrence and its complement is 1.

So by looking at the definitions we can say that statement I and statement III are true

Hence,

Option E) I and III only is the correct answer

Keywords: Probability, events

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Answer:

14 free throw baskets , 25 two point baskets and 11 three point baskets

Step-by-step explanation:

Let n₁ represent the number of free-throw baskets, n₂ represent the number of two point baskets and n₃ represent the number of three point baskets.

Now, from the question, the number of two point baskets, n₂ is greater than the free throw baskets by 11. This is written as n₂ = n₁ + 11. Also, the number of three point baskets n₃ is three less than the number of free point baskets. This is written as n₃ = n₂ - 3. Since our total number of points equals 97, it follows that, sum of number of points multiplied by each point equals 97. So, ∑(number of points × each point) = 97. Thus,

n₁ + 2n₂ + 3n₃ = 97. Substituting n₂ and n₃ from above, we have n₁ +2(n₁ + 11) + 3(n₁ - 3) = 97.

Expanding the brackets, we have, n₁ + 2n₁ + 22 + 3n₁ - 9 = 97

collecting like terms, we have 6n₁ + 13 = 97

6n₁ = 97 - 13

6n₁ = 84

dividing through by n₁ we have, n₁ = 84/6 =14

so n₁ our free throw baskets equals 14. Substituting this into n₂ our number of two point baskets equals n₂ = n₁ + 11 = 14 + 11 = 25. Our number of three point baskets n₃ = n₁ - 3. So, n₃ = 14 -3=11

Final answer:

To find the combination of scores for Team A's 97 points, we define variables for each scoring method, set up equations based on the given relationships, and solve to find that Team A made 10 free throws, 21 two-point baskets, and 13 three-point baskets.

Explanation:

In a basketball game where Team A scored 97 points by a combination of two-point baskets, three-point baskets, and one-point free throws, we can define the following variables based on the information given: Let x represent the number of free throws, y the number of two-point baskets, and z the number of three-point baskets. From the statements, we know that y = x + 11 and x = z - 3. The total points can be represented by the equation: 1x + 2y + 3z = 97.

Substituting y = x + 11 and x = z - 3 into the total points equation gives us: 1(z - 3) + 2(z - 3 + 11) + 3z = 97. Simplifying this equation gives 6z + 17 = 97, leading to 6z = 80, and thus z = 13.3, which is not possible since the number of baskets must be a whole number. Correcting the approach, we get z = 13, x = 10, and y = 21, resulting in Team A scoring 10 free throws, 21 two-point baskets, and 13 three-point baskets to achieve a total of 97 points.

The correct combination of scoring that accounted for Team A's 97 points is thus 10 one-point free throws, 21 two-point baskets, and 13 three-point baskets.

Question 1:

For this case we must rewrite the following equation:

[tex]-3x + y = 5[/tex]

If we add 3x to both sides of the equation we have:

[tex]y = 5 + 3x[/tex]

Thus, we have that an equivalent expression is option C.

Answer:

Option C

[tex]y = 5 + 3x[/tex]

Question 2:

For this case we must solve the following equation:

[tex]-5x + 5 = -40[/tex]

Subtracting 5 from both sides of the equation we have:

[tex]-5x = -40-5\\-5x = -45[/tex]

Dividing between -5 on both sides of the equation we have:

[tex]x = \frac {-45} {- 5}\\x = 9[/tex]

Answer:

Option B

Answer:

a) nearest jump is JL = 1380 inches = 115ft

b) number of jumps in 1 mile N= 46 jumps

Step-by-step explanation:

Given that the jump length is proportional to the body length.

If 2 inch grasshopper can jump 40 inches.

JL = k(BL)

k = JL/BL

where JL = jump length = 40 inches

BL = Body length = 2 inches.

k = 40/2 = 20

The constant of proportionality is 20.

For the athlete :

BL = 5ft 9 inches = 5(12)+9 = 69 inches.

The jump length of the athlete is:

JL = k(BL) = 20(69)

JL = 1380 inches. = 115ft

The number of jumps in 1 mile is

1 mile = 63360 inches

N = 63360/1380

N = 45.9 = 46

N= 46

Therefore, 46 jumps would be needed.

Answer:

The correct option is D) -9/16

Therefore the final expression when X is equal to -1 and Y is equal to 4 is

[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]

Step-by-step explanation:

Given:

[tex]9x^{-5}y^{-2}[/tex]

Evaluate when x = -1 and y = 4

Solution:

When x = -1 and y = 4 we hane

[tex]9x^{-5}y^{-2}=9(-1)^{-5}(4)^{-2}[/tex]

Identity we have

[tex]x^{-a}=\dfrac{1}{x^{a}}[/tex]

As we know  minus sign multiplied by odd number of times the number is multiplied and the assign remain same that is minus. Therefore,

[tex](-1)^{5}=-1\times -1\times -1\times -1\times -1\\(-1)^{5}=-1[/tex]

Now using the above identity we get

[tex]9x^{-5}y^{-2}=\dfrac{9}{(-1)^{5}}\times \dfrac{1}{(4)^{2}}[/tex]

[tex]9x^{-5}y^{-2}=\dfrac{9}{-1}\times\dfrac{1}{16}[/tex]

[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]

Therefore the final expression when X is equal to -1 and Y is equal to 4 is

[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]

Final answer:

The dependent variable in the study of the effect of handedness on athletic ability, which is measured on a 12-point scale, is A. Discrete and quantitative since it cumulates as whole-number scores.

Explanation:

In the study of the effect of handedness on athletic ability, the dependent variable is athletic ability measured on a 12-point scale. The nature of this variable can be determined by considering how the data behaves. Since athletic ability is rated using a numerical score on a fixed scale, it is a quantitative type of data. Furthermore, because the scores are given as whole numbers on a scale (from 1 to 12), they are discrete values, which refer to data that result from counting.

Therefore, the dependent variable in this study is A. Discrete and quantitative. This conclusion is based on the information that the athletic ability is measured numerically and cannot take infinitely varying values but is rather confined to integer values on the scale.

Answer: the height of the ramp above the water at the highest point is 2.0832ft

Step-by-step explanation:

The ramp makes an angle of 10 degrees with water and forms a right angle triangle.

The height of the ramp above the water at the highest point represents the opposite side of the right angle triangle.

The length of the ramp represents the hypotenuse of the right angle triangle. Therefore, to determine the height of the ramp above the water at the highest point, h , we would apply the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 10 = h/12

h = 12Sin10 = 12 × 0.1736

h = 2.0832

The height of the ramp above the water at the highest point is approximately 4.87ft.

To find the height of the ramp above the water at the highest point, we can use trigonometry. The height of the ramp is represented by the opposite side of the angle, while the adjacent side is the length of the ramp. We can use the formula: Opposite = Adjacent * tan(Angle). Plugging in the values, we get: Opposite = 28ft * tan(10 degrees). Evaluating this expression on a calculator, we find that the height of the ramp above the water at the highest point is approximately 4.87ft.

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Answer:

9 months for 360 dollars

Step-by-step explanation:

360÷40=9

Answer:

Step-by-step explanation:

The co-ordinates of C is (W, -V).

The co-ordinate of C indicates that it is in the fourth quadrant.

A lies diagonally opposite to that of C, that is A is in the second quadrant.

Since, the rectangle is centered at the origin, the mod values of the points' co-ordinates will be same.

Hence, the co-ordinates of A will be (-W, V), as it is in the second quadrant.

Only the option D tells the same.

Answer:

D    

Step-by-step explanation:

Answer:

Step-by-step explanation:

F(x)=(5 t^2+t  )x to x+3

=5((x+3)^2-x^2)+(x+3-x)

=5(x^2+6x+9-x^2)+3

=5 (6x+9)+3

=30x+48

F'(x)=30

Answer:

  y = 4cos((π/5)x) +3

Step-by-step explanation:

The graph shows the peak of the function to be at x=0, so a cosine function is an appropriate choice for the model.

The value of A is half the difference between the minimum and maximum, so is ...

  A = (1/2)(7 -(-1)) = 4

The value of C is the average of the maximum and the minimum, so is ...

  C = (1/2)(7 +(-1)) = 3

The value of k must be chosen so that for one full period, kx is 2π. We note that one minimum is at -5, and the next is at +5, so the period of this waveform is (5 -(-5)) = 10. Then ...

  k·10 = 2π

  k = π/5 . . . . . divide by 10 and reduce the fraction

Now, we have all the parameters of our function:

  y = 4cos((π/5)x) +3

To find a function that matches a given graph, the amplitude, frequency, and phase shift must be determined. The amplitude is calculated by determining the maximum and minimum values of y, the frequency is found by comparing the distances in the cycles, and the phase shift is calculated by looking at the middle of the oscillation.

In order to find a function that matches the graph given, we need to determine certain aspects of the waveform such as the amplitude, frequency, and phase shift. This is done through carefully analysing the graph. In general, A resembles the amplitude or the 'height' of the wave. This can be determined by calculating half the distance between the maximum and minimum values of y. The coefficient k is linked to the frequency of the function, which can be figured out by the distance between alike points in the cycle (like peak to peak, or trough to trough). And finally, C corresponds to any vertical shift of the function which can be understood by checking the 'middle' of the oscillation. If the wave seems to be shifted to the right or left of the y-axis, then you would use a phase shift in the sine or cosine function. Remember, cosine and sine functions are similar in shape, but a cosine waveform begins at a peak, while a sine waveform begins at zero.

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Answer:

fyfyfiulhvt

Step-by-step explanation:

xerytuyuytref

Answer:

The answer to your question is the Square pizza is a better deal.

Step-by-step explanation:

Data

Square pizza

side = 45 cm

cost = 450

Circular pizza

diameter = 50 cm

cost = 480

Process

1.- To solve this problem calculate the area of both pizzas

Area square pizza = side x side

                               = 45 x 45

                               = 2025 cm ²

Area of circular pizza = π(50/2)²

                                    = 1962.5 cm²

2.- Compare the area of the pizza to its cost

Square pizza = 2025 / 450 = 4.5

Circular pizza = 1962.5 / 480 = 4.1

From this data we conclude that the square pizza is a better deal.

Answer:

Vector equation, ř = <1, 0, 5> + <1, 3, 1>t

The Parametric Equation is:

x = 1 + t

y = 3t

z = 5 + t

Step-by-step explanation:

<a, b, c> is a vector perpendicular to the plane ax + by + cz + d = 0.

By this, a vector perpendicular to the plane

x + 3y + z = 0

is

<1, 3, 1>

The Parametric Equation of a line through the point

[tex](x_0, y_0, z_0)[\tex]

and parallel to the vector <a, b, c> is given as

[tex]x = x_0 + at[\tex]

[tex]y = y_0 + bt[\tex]

[tex]z = z_0 + ct[\tex]

So, the Parametric Equation is

x = 1 + t

y = 3t

z = 5 + t

The vector form of the line is

ř = <1, 0, 5> + <1, 3, 1>t

Answer:

The answer to your question is below

Step-by-step explanation:

*A(x)=3x³ + 2x² - x           This polynomial is not divisible by (x - 1)

                                       Factor completely    3x(x + 1)(3x - 1)

*B(x)=5x³ - 4x² - x            This polynomial is divisible by (x - 1)

                                       factor completely   3x(x - 1)(5x + 1)

*C(x)=2x³ - 3x² + 2x - 1     This polynomial is divisible by (x - 1)

                                        Synthetic division      2   - 3  + 2  -1      1

                                                                                   2    -1    1                

                                                                            2    -1      1    0

*D(x)=x³ + 2x² + 3x + 2   This polynomial is not divisible by (x - 1)

                                        Synthetic division    1    2   3   2   1

                                                                                1    3   6                      

                                                                           1    3   6   8                  

Answer:

B(x) and C(x)

Step-by-step explanation:

B(x) and C(x)

Answer: Possible production sequences= 4,838,400

Step-by-step explanation: Total machine operation =13

Machines divided into 2 sets.

Set 1= 5 machines

Set 1=5!= 5×4×3×2×1=120 ways

Set 2= 13-5 =8 machines

Set 2= 8!=8×7×6×5×4×3×2×1=40,320 ways

Total number of ways to sort the two sets =120×40,320= 4,838,400

Answer:

[tex]E=5.76\times 10^{-8}N/C[/tex]

Step-by-step explanation:

We are given that

Charge of atomic nucleus,q=+40 e=[tex]40\times 1.6\times 10^{-19}C[/tex]

Because

1 e=[tex]1.6\times 10^{-19} C[/tex]

Charge of atomic nucleus=[tex]64\times 10^{-19}C[/tex]

Distance of charge form the center of nucleus=r=1 m

We have to find the magnitude of  electric field at distance r

[tex]E=\frac{Kq}{r^2}[/tex]

Where K=[tex]9\times 10^9Nm^2/C^2[/tex]

Using the formula

[tex]E=\frac{9\times 10^9\times 64\times 10^{-19}}{1}=576\times 10^{-10}N/C[/tex]

[tex]E=\frac{576}{100}\times 10^2\times 10^{-10}=5.76\times 10^{2-10}=5.76\times 10^{-8}N/C[/tex]

Using identity[tex]a^x\cdot a^y=a^{x+y}[/tex]

Hence, the magnitude of electric field=[tex]E=5.76\times 10^{-8}N/C[/tex]

Answer:

182 seconds

Step-by-step explanation:

Given:

Time taken for first lap is 50 seconds and each subsequent lap takes 20% longer than previous

Solution:

Time taken for first lap = 50 sec

For second lap

Each subsequent lap takes 20% longer than previous

Previous lap time = 50 sec

second lap = 50 + 20% of 50

second lap [tex]=50+(\frac{20}{100}\times 50)[/tex]

second lap [tex]= 50 + 10[/tex]

second lap [tex]= 60\ sec[/tex]

For third lap

Each subsequent lap takes 20% longer than previous

Previous lap time = 60 sec

Third lap = 60 + 20% of 60

[tex]Third\ lap = 60 + (\frac{20}{100}\times 60)[/tex]

[tex]Third\ lap = 60+2\times 6[/tex]

[tex]Third\ lap = 60+12[/tex]

[tex]Third\ lap = 72\ sec[/tex]

Time taken for 3 laps is equal to sum of all three laps time.

[tex]Tiem\ taken\ for\ 3\ lap = 50+60+72[/tex]

[tex]Tiem\ taken\ for\ 3\ lap = 182\ sec[/tex]

Therefore, it takes 182 seconds (3 min, 2 seconds) to run three laps

The number of units of tiles he will need is 18.96 units

Step-by-step explanation:

The parallelogram ABCD has a right triangle ABD with A as 90°

The length of segment AB is given as 3.16 units and that of the diagonal BD is 7.07 units.

Apply Pythagorean relationship to find length of segment AD=BC

The sum of squares of the sides equals the square of the hypotenuse.

a²+b²=c²

In this case, side a=3.16 units, b=AD and c=hypotenuse=7.07

Applying the formula;

a²+b²=c²

3.16²+b²=7.07²

9.99+b²=49.99

b²=49.99-9.99

b²=40

b=√40=6.3245 =6.32

AD=BC=6.32 units

Find the perimeter of the quadrilateral

=3.16+3.16+6.32+6.32=18.96 units

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Answer:

18.96 units

Step-by-step explanation:

I took the test.

Answer:  2685

==========================================

Explanation:

When we want to add up the first n terms of an arithmetic sequence, the formula to use is

S = (n/2)*( 2*a+d(n-1) )

where

S = sum of the first n terms

n = number of terms

a = first term

d = common difference

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

In this case,

S = unknown

n = 30

a = -12

d = 7

which means,

S = (n/2)*( 2*a + d*(n-1) )

S = (30/2)*( 2*(-12) + 7*(30-1) )

S = 15*(-24 + 7*29)

S = 15*(-24 + 203)

S = 15*(179)

S = 2685

This answer is confirmed using a spreadsheet. Basically I had the spreadsheet generate 30 terms based on a pattern I gave it of the first two terms. Then I used the "SUM" function to add up all 30 terms quickly getting 2685.

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

Side note:

Another formula we could use is

S = (n/2)*(a_1 + a_n)

where

a_1 = first term

a_n = nth term, when n = 30 this is the 30th term

The a_n part is equal to a_n = a_1 + d(n-1), and when you add this to the a_1 already in the S formula, that accounts for the 2*a_1 back in the first formula mentioned at the top of the page.

Answer:sum of the first 30 terms is 2685

Step-by-step explanation:

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

n = 30 terms

a = - 12

d = 7

Therefore, the sum of the first 30 terms, S30 would be

S30 = 30/2[2 × - 12 + (30 - 1)7]

S30 = 15[- 24 + 203)

S30 = 15 × 179 = 2685

Answer:

Step-by-step explanation:

When A and B are brought together then they repel i.e. A and B have same charge, either negative or positive

When B and C are brought together then they also repel. This implies that nature of charge on  B and C is same          

Answer: the total cups of flour that the three ladies used is 10 5/12 cups

Step-by-step explanation:

Gayle used 3 1/4 cups of flour.

Converting 3 1/4 cups of flour to improper fraction, it becomes 13/4 cups of flour.

Irma used 2 2/3 cups of flour. Converting 2 2/3 cups of flour to improper fraction, it becomes 8/3 cups of flour.

Wynell used 4 1/2 cups of flour. Converting 4 1/2 cups of flour to improper fraction, it becomes 9/2 cups of flour.

Therefore, the total number of cups of flour that Gayle, Wynell and Irma used would be

13/4 + 8/3 + 9/2 = (39 + 32 + 54)/12

= 125/12 = 10 5/12 cups of flour.

Answer:

The three ladies used  10 5/12 of flour total!

Step-by-step explanation:

Answer:

The correct option is c.)

Step-by-step explanation:

If someone says that an investment had a rate of return of 10% It matters if the person means a nominal rate of return or a real rate of return because real rates take inflation into account. Nominal rates are not adjusted for inflation. Nominal rates of return usually appear to be higher than the real rates of return.

Therefore the correct option is c.)

The solution set is [tex]x=-\frac{11}{2}[/tex]

Step-by-step explanation:

The given expression is [tex]3(x-2)=5(x+1)[/tex]

Multiplying the terms, we get,

[tex]3x-6=5x+5[/tex]

Subtracting 3x from both sides of the equation,

[tex]-6=2x+5[/tex]

Subtracting 5 from both sides of the equation,

[tex]-11=2x[/tex]

Dividing both sides by 2, we get,

[tex]-\frac{11}{2} =x[/tex]

Thus, the solution set is [tex]x=-\frac{11}{2}[/tex]

The graph the solution set [tex]x=-\frac{11}{2}[/tex] is to plot this value in the number line.

The graph for the solution set [tex]x=-\frac{11}{2}[/tex] is attached below:

The cost of one granola bar is $0.60 and cost of one apple is $0.35

Step-by-step explanation:

Let,

Cost of one granola bar = x

Cost of one apple = y

According to given statement;

4x+y=2.75     Eqn 1

2x+3y=2.25   Eqn 2

Multiplying Eqn 2 by 2

[tex]2(2x+3y=2.25)\\4x+6y=4.50\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 1 from Eqn 3

[tex](4x+6y)-(4x+y)=4.50-2.75\\4x+6y-4x-y=1.75\\5y=1.75[/tex]

Dividing both sides by 5

[tex]\frac{5y}{5}=\frac{1.75}{5}\\y=0.35[/tex]

Putting y=0.35 in Eqn 2

[tex]4x+0.35=2.75\\4x=2.75-0.35\\4x=2.40[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4}=\frac{2.4}{4}\\x=0.60[/tex]

The cost of one granola bar is $0.60 and cost of one apple is $0.35

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The cost of one granola bar is $0.60, and the cost of one apple is $0.35.

To solve the problem, we need to set up a system of linear equations based on the information given:

Georgia paid $2.75 for 4 granola bars and 1 apple.

Addison paid $2.25 for 2 granola bars and 3 apples.

Let G be the cost of one granola bar and A be the cost of one apple.
4G + A = 2.75
2G + 3A = 2.25

Multiply the first equation by 3
3(4G + A = 2.75)
=> 12G + 3A = 8.25
(12G + 3A) - (2G + 3A) = 8.25 - 2.25
10G = 6
G = 0.60
Substitute the value of G back into the first equation,
4(0.60) + A = 2.75
2.40 + A = 2.75
A = 0.35

Therefore, the cost of one granola bar is $0.60 and the cost of one apple is $0.35.

Answer:

110

Step-by-step explanation:

triangle = 180° total so

180- 82 = 98

98 ÷ 2 = 49

y = 49

4 sided shape = 360° total

35 + 35 + 49 + 49 + 82 = 250

360 (total) - 250 = 110

hope this helps

Mary's Plan A and Plan B workout sessions both last 0.75 hours, or 45 minutes each. This was determined by setting up a system of equations based on the number of clients and total hours trained on Wednesday and Thursday, and solving for the duration of each plan.

To determine how long each of Mary's workout plans lasts, we need to set up a system of equations based on the information given. Let Plan A be x hours per session, and Plan B be y hours per session.

On Wednesday, Mary had 7 clients who did Plan A and 9 clients who did Plan B for a total of 12 hours. Thus, we have the equation:
7x + 9y = 12.

On Thursday, there were 5 clients who did Plan A and 3 who did Plan B for a total of 6 hours, leading to the equation:
5x + 3y = 6.

We can now solve the system of equations. Multiplying the second equation by 3 gives us:

7x + 9y = 12

15x + 9y = 18

Subtracting the first equation from the second equation, we get:
8x = 6
x = 6÷8
x = 0.75 hours (or 45 minutes).

Now, using the value of x, we can solve for y in either equation. We'll use the first equation for simplicity:
7(0.75) + 9y = 12
5.25 + 9y = 12
9y = 12 - 5.25
9y = 6.75
y = 6.75/9
y = 0.75 hours (or 45 minutes).

Therefore, both Plan A and Plan B last 0.75 hours, or 45 minutes, per session.

Answer:

a is an element of A; a is a rational number

(a+1) is element of B

Step-by-step explanation:

(a+1) = sup(A), which are the elements of B.

(a+1) + 1 = sup(B)

Recall a+1 = sup(A),

Therefore,

sup(A )+ 1 = sup(B)

sup(B) = sup(A) + 1 ___proved

Sup(A) means supremum of set A. It means least element of another set (say set B), that is greater than every element in set A

Answer:

 B: Based on the data, this is an example of correlation.

Step-by-step explanation:

It's the correct answer because there somewhat related and as the ice cream trucks get more sales the weather gets warmer. They both have a positive increase.

Based on the data, this is an example of correlation and causation. Option A is correct

Correlation is defined as the two things depends on each other.

Here,

People would like to buy ice cream in warm weather this statement is correlation and causation is people would like to by ice cream cause the increase in temperature.  

Thus, Based on the data, this is an example of correlation and causation.

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