What is the solution of the inequality below for y ?

2x − 5y ≤ 15

Answer: [tex]2 sin(5 \theta) cos \theta[/tex]

Step-by-step explanation:

According to the trigonometric identities we have the following formula:

[tex]sin (x) + sin (y)=2 sin(\frac{x+y}{2}) cos(\frac{x-y}{2})[/tex]

Now, we have the following:

[tex]sin (6\theta)+ sin (4\theta)[/tex]

Where [tex]x=6\theta[/tex] and [tex]y=4\theta[/tex]

Hence:

[tex]sin (6\theta)+ sin (4\theta)=2 sin(\frac{6\theta+4\theta}{2}) cos(\frac{6\theta-4\theta}{2})[/tex]

[tex]sin (6\theta)+ sin (4\theta)=2 sin(\frac{10\theta}{2}) cos(\frac{2\theta}{2})[/tex]

Finally:

[tex]sin (6\theta)+ sin (4\theta)=2 sin(5\theta) cos(\theta)[/tex]

The inequality which represents the possible values for the number of cupcakes and donuts is : 4.50c + 1.75d = 450

Let :

Expressing the scenario as an inequality :

4.50c + 1.75d = 450

Therefore, the inequality which represents the possible values for the number of cupcakes and donuts is : 4.50c + 1.75d = 450

Answer:

The value of ∅ for the given trigonometrical equation is 60° .

Step-by-step explanation:

Given as :

The Trigonometrical equation

2 cos∅ + 2 = 3

Now, Solving this equation to get the value of ∅

∴ The equation can be written as

2 cos∅ = 3 - 2

or , 2 cos∅ = 1

or , cos∅ = [tex]\dfrac{1}{2}[/tex]

∴ ∅ = [tex]cos^{-1}(\frac{1}{2})[/tex]

I.e ∅ = 60°

So,The value of ∅ for the given trigonometrical equation = ∅ = 60°

Hence, The value of ∅ for the given trigonometrical equation is 60° . Answer

Answer:

164 minutes

Step-by-step explanation:

Assuming that Jerome's seed is maintained, we say that for every 1 mile, he takes 13 minutes and 40 seconds which is equivalent to[tex]13\frac {2}{3}[/tex] since 1 minute has 60 seconds hence [tex]\frac {40}{60}[/tex]=[tex]\frac {2}{3}[/tex]

Now if

1 mile = [tex]13\frac {2}{3}[/tex]

12 miles=??

We cross multiply hence 12\times[tex]13\frac {2}{3}=164[/tex]

Therefore, Jerome needs 164 minutes, equivalent to 2 hours 44 minutes

Answer:

[tex]768\ cm^{2}[/tex]

Step-by-step explanation:

Here is the correct question: The pyramid shown has a square base that is 24  centimeters on each side. The slant height is 16  centimeters. What is the lateral surface area?

Given: Side of sqaure base = 24 cm

           Slant height= 16 cm

Now, we have to compute to know lateral surface area of Pyramid with square base.

Formula, lateral surface area of pyramid= [tex]4(\frac{1}{2} \times b\times h)[/tex]

we know, side of sqaure base (b) is 24 cm and slant height (h) is 16 cm.

lateral surface area of pyramid= [tex]4\times (\frac{1}{2} \times 24\times 16)[/tex]

⇒lateral surface area of pyramid= [tex]4\times (192)[/tex]

Opening parenthesis.

∴lateral surface area of pyramid= [tex]768\ cm^{2}[/tex]

Answer:

1/256

Step-by-step explanation:

1/256

4^-4 as a fraction is 1/256. It cannot be further simplified because 1 and 256 have no common factors other than 1, making it the simplest form.

To express 4^-4 as a fraction and simplify it, we can apply the rule that states any non-zero number raised to a negative exponent is equivalent to 1 divided by that number raised to the positive exponent.

So, for 4^-4, we can write it as:

4^-4 = 1 / 4^4

Now, let's calculate 4^4:

4^4 = 4 * 4 * 4 * 4 = 256

So, we have:

4^-4 = 1 / 256

This is the fraction representation of 4^-4. To determine if it can be further simplified, we can check if the numerator and denominator have any common factors other than 1. In this case, 1 and 256 have no common factors other than 1.

Therefore, 1/256 is already in its simplest form. It represents the fraction equivalent of 4^-4, which is a small value. It means that 4 raised to the power of -4 is a very small positive number, specifically 1/256, indicating that the original number 4^-4 is less than 1 and quite close to zero in value.

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Answer: $9 per ticket

Step-by-step explanation: Unit price means the cost per unit. In this case, the cost per ticket.

Since we know that it costs $36 for 4 movie tickets, to find the cost for 1 movie ticket, we need to divide 4 into $36 or 4 into 36.

4 divides into 36 9 times. 9 x 4 is 36 and 36 - 36 is 0. So 4 divides into 36 9 times which means that each movie ticket costs $9.

So the unit price is $9 per ticket.

Answer:

D

Step-by-step explanation:

We need to find 2 roots of the quadratic function given and find the greater of the two roots.

We factorize the quadratic and find the two solutions first:

[tex]x^2-6x+5=0\\(x-5)(x-1)=0\\x=1,5[/tex]

So,

x = 1

and

x= 5

Out of the two, x = 5 is the greater root.

D is the correct answer.

To calculate the CPI for year 2 in a simple economy involving shirts and pants, we first find the total cost of the basket in both years considering the price increase. Then, using the formula for CPI, we find that the CPI for year 2 is 122.45, indicating an increase in the average price level compared to the base year.

To calculate the Consumer Price Index (CPI) for year 2 in a simple economy with only shirts and pants in the basket of goods, we first need to understand the concept of CPI. The CPI represents the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. Here, we're given that the price of each item increases by $1 in year 2, with the new prices being $21 for pants and $26 for shirts.

First, calculate the total cost of the basket in year 2:
Cost of 3 shirts in year 2 = 3 shirts * $26 per shirt = $78
Cost of 2 pairs of pants in year 2 = 2 pants * $21 per pants = $42
Total cost of the basket in year 2 = $78 + $42 = $120

To determine the CPI for year 2, we also need to know the base year's total cost, which isn't directly provided here.

However, assuming the base year (year 1) prices were $1 less for each item, the prices would have been $20 for shirts and $19 for pants.

Cost of the basket in year 1:

Cost of 3 shirts = 3 shirts * $20 per shirt = $60

Cost of 2 pairs of pants = 2 pants * $19 per pants = $38

Total cost of the basket in year 1 = $60 + $38 = $98

Finally, to calculate the CPI for year 2, we use the formula:

CPI for year 2 = (Total cost of the basket in year 2 / Total cost of the basket in year 1) * 100
= ($120 / $98) * 100 = 122.45

Therefore, the CPI for year 2 is 122.45, indicating prices have increased on average when comparing year 2 to the base year (year 1). This helps in understanding the inflation rate and cost of living increases for consumers.

The ounces of chocolate chips used by Mrs Jacob is 70 ounce

Solution:

Given that Jacob is making several batches of cookies and is using 84 total ounces of chips

Let "c" be the ounces of chocolate chips

Let "p" be the ounces of peanut butter chips

To find: ounces of chocolate chips used by Mrs Jacob

Given that There are 5 times as many ounces of chocolate chips as peanut butter chips

Thus we can frame a equation as:

ounces of chocolate chips = 5 x ounces of peanut butter chips

c = 5p -------- eqn 1

Jacob used 84 total ounces of chip. Therefore,

ounces of chocolate chips + ounces of peanut butter chips = 84

c + p = 84 ---- eqn 2

Substitute eqn 1 in eqn 2

5p + p = 84

6p = 84

Substitute p = 14 in eqn 1

c = 5(14) = 70

Thus the ounces of chocolate chips used by Mrs Jacob is 70 ounce

Answer:

96%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Percentage = (24/25) * 100 = 24* 4 = 96%

Answer:

D. A line can be contained in more than one plane .

Step-by-step explanation:

A. is wrong because a line can't be said as coplanar . We can draw infinite number of planes through a line .

B. is wrong because a line can be contained in infinite number of planes.

C. is wrong because a line can't be contained in a point as a line is a collection of points.

D. is the right answer as every line passes through infinite number of planes.

Final answer:

To find the amount of cloth left over, subtract the amount used from the total amount. Jaquan had 9.5 yards of cloth left over, which can be expressed as the fraction 19/50.

Explanation:

To find the amount of cloth left over, we need to subtract the amount used from the total amount. Jaquan bought 25 yards of cloth, used 4.9 yards for a decoration, and used 10.6 yards to make costumes. To find the amount left over, we subtract the sum of 4.9 yards and 10.6 yards from 25 yards: 25 - 4.9 - 10.6 = 9.5 yards.

The amount of cloth left over can be expressed as a fraction by dividing the amount left over by the total amount. So, 9.5 yards can be written as the fraction 9.5/25, which can be simplified by dividing both the numerator and denominator by 0.5 to get 19/50. Therefore, the amount of cloth left over is 19/50.

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Simplify 17q−q−8q−4  to  8q-48q−4.

8q - 4 = 20

8q = 20 + 4

8q = 24

q = 24/8

q = 3

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Answer:

B

Step-by-step explanation:

The 2 part of the ratio represents 39 instructors.

Dividing 39 by 2 gives the value of one part of the ratio, that is

39 ÷ 2 = 19.5 ← value of 1 part of the ratio, thus

number of employees = 12 × 19.5 = 234 → B

Answer:

-1

Step-by-step explanation:

A function assigns the values. The right-hand limit of this function at x=2 is -1.

A function assigns the value of each element of one set to the other specific element of another set.

The right-hand limit of the function when the value of x=2, can be found by substituting the value of x as 2 in the given function, therefore, the right-hand limit of this function at x=2 is,

g(x) = (x²-3)/(x-3)

g(2) = (4-3)/(2-3)

g(2) = -1

Hence, the right-hand limit of this function at x=2 is -1.

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The number that satisfies the condition that, when added to five and then doubled, is one less than the number itself is -11. We found this number by setting up an equation and solving for the variable.

Let's define x to be the number we're trying to find. According to the question, if the sum of this number and five is doubled, the result is one less than the number.

The equation based on the given information is 2(x + 5) = x - 1. To solve for x, let's distribute the 2 to both terms in the parentheses: 2x + 10 = x - 1.

Next, we need to get all the x terms on one side and the constant terms on the other side. We can do this by subtracting x from both sides, giving us: x + 10 = -1. Then, subtract 10 from both sides to isolate x: x = -11. So, the number we're looking for is -11.

If g(x)=15, x=...

g(x)=15

2x+9=15

x=3

answer: 3

Answer:

the answer is 3

Step-by-step explanation:

Answer:

The unit rate for her riding in miles per hour is given by 2 miles per hour.

Step-by-step explanation:

Amber rides m miles in h hours according to the equation m=2h .......... (1)

Putting h = 1 hour, we get m = 2 miles.

Therefore, Amber rides 2 miles height within a period of time 1 hour.

Therefore, the unit rate for her riding in miles per hour is given by 2 miles per hour. (Answer)

Again, differentiating equation (1) with respect to h we get,

[tex]\frac{dm}{dh} = 2[/tex] miles per hour.

So, here also we get the unit rate of her riding is 2 miles/hr.

Answer:

[tex] \: \: \: \: \: \: 15 - d = 6 \\ = > - d = 6 - 15 \\ = > - d = - 9 \\ = > d = 9[/tex]

Verification :

[tex] \: \: \: \: \: \: 15 - d = 6 \\ = > 15 - 9 = 6 \\ = > 6 = 6[/tex]

The equation of line in point slope form is y - 4 = 7x - 56

Solution:

Given that m = 7 and point is (8, 4)

We have to find the equation of line in point slope form

It emphasizes the slope of the line and a point on the line

The point slope form is given as:

[tex]y - y_1 = m(x - x_1)[/tex]

Where "m" is the slope of line

Substitute m = 7 and (x, y) = (8, 4) in above point slope form

[tex]y - 4 = 7(x - 8)[/tex]

[tex]y - 4 = 7x - 56[/tex]

Thus equation of line in point slope form is found

We can write the equation in standard form

The standard form of an equation is Ax + By = C. In this kind of equation, x and y are variables and A, B, and C are integers.

[tex]y - 4 = 7x - 56\\\\7x - y -52 = 0[/tex]

Step-by-step explanation:

Point B(2, 8) reflect to x-axis

It means the x value won't change, the only thing that will change is the y value.

According to it, we can know that B' is (2, -8)

(2, -8) → (-8, 2+4) = (-8, 6) = B''

Final answer:

To obtain the coordinates of B'' after a reflection across the x-axis and a translation of (x,y)
ightarrow(y,x+4), point B(2,8) becomes B'(2,-8) after reflection and then B''(-8, 6) after translation.

Explanation:

The student is asking about the results of performing a geometric transformation on a point in the coordinate plane. Specifically, point B(2,8) is first reflected across the x-axis, and then is translated according to the rule (x,y)
ightarrow(y,x+4). To find the coordinates of B'', we follow these steps:

Reflect B across the x-axis: The x-coordinate remains the same, but the y-coordinate changes sign, resulting in B'(2,-8).

Apply the translation rule: We then take the coordinates of B' and apply the rule. The x-value of B' becomes the y-value of B'' and the y-value of B', decreased by 4, becomes the new x-value. Therefore, B'' = (-8, 2+4) = (-8, 6).

The final coordinates of B'' after the reflection and translation are (-8,6).

Answer:

both are answered below

Step-by-step explanation:

[where x represents no. of carnations that he buys , y represents no. of roses that he buys ]

The true statements are:

A. Tree A's heights are less spread out than tree B's heights and

B. Tree A has lower average height than tree B

Explanation:

Standard deviation in this case represents the spreading out of heights of the trees, Since tree A has lesser standard deviation given equal to 5 , it is less spread out than B given equal to 12, hence option A. is true.

The average of a quantity is given by mean so, the average height can be compared by the given mean values of the trees. Since, A has lesser mean value (= 25) than B(=60), tree A is said to have lower average height than tree B hence option B. is true.

Answer:

A and B

Distance between two points is 7

Explanation:

This is a question based on reflection of point w.r.t line. During reflection we can see the mirror image with t-shirt print inverted.But the  distance from mirror remains same.

Assume a point (x,y), and it reflect in x-axis, then x-axis serves as the mirror, and the new point is (x,-y), because the distance from the mirror remains same. If the reflection of the point is (x,y) in y-axis, then y-axis serves as the mirror, and the new point is (-x,y). And if you reflect (x,y) in y=x line, then new point will be (y,x).

So considering the above question, if new point is (5, -3.5), then the original point must be (5, 3.5)

Distance between two points [tex]P(X_1, Y_1)[/tex] and [tex]Q(X_2, Y_2)[/tex]is given by:

d(P, Q) = [tex]\sqrt{ (X_2-X_1)^{2} + (Y_2-Y_1)^{2}}[/tex]

[tex]Y_2-Y_2 = (3.5) - (-3.5) = 3.5+3.5 = 7\\ \\X_2-X_1 = 5 - 5 = 0[/tex]

[tex]So \sqrt {(Y_2-Y_1)^{2} + (X_2-X_1)^{2}} = \sqrt { 7^{2} + 0^{2}} = \sqrt { 14+0} = \sqrt {14} = 7[/tex]

So distance = 7

Answer:

8/7

Step-by-step explanation:

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

m=(1-9)/(2-9)

m=-8/-7

m=8/7

Answer:

m= 8/7

Step-by-step explanation:

the formula to find slope is

m= y2-y1/x2-x1

Probability for male = 75/400 = 3/16

Probability for groups = 175/400 = 7/16

Probability for female = 150/400 = 3/8

There is a 3/8 probability of the song being sung by a female vocalist.

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The segment to draw is segment UT

Step-by-step explanation:

A line segment is a part of a line that is bounded by two two distinct  end points. In this case, segment UT is bounded by endpoints U and T. In the diagram, point R is not a segment but a point of intersection of segments BT and EU.

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Answer:

x = 26

Step-by-step explanation:

The parallel lines are Line l and Line m. The other line shown is the transversal.

When 2 parallel lines are cut by a trasversal it creates 4 euqual angles and another 4 equal angles of different measure.

The angle "5x + 7" is equal to the angle "8x - 71" since they are alternate exterior angles.

So, we can equate both expressions and use algebra to solve for "x". The process is shown below:

[tex]5x+7=8x-71\\8x-5x=71+7\\3x=78\\x=\frac{78}{3}\\x=26[/tex]

Hence,

the value of x is 26