x = ?
f(x) = 3x - 7
f(x) = -1

y=-1x+4

---

hope it helps

sorry I had no idea how to explain

The given expression can be simplified using trigonometric identities. By using the identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b), we get:

cos(pi/4-x) = cos(pi/4)cos(x) + sin(pi/4)sin(x)

Substituting the given values of cos(x) and sin(x), we get:

cos(pi/4-x) = (1/sqrt(2))(-1/2) + (1/sqrt(2))(sqrt(3)/2)

Simplifying this expression, we get:

cos(pi/4-x) = -sqrt(2)/4 + sqrt(6)/4

The given expression involves the cosine of the difference between two angles. By using the identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b), we can simplify the expression in terms of the cosine and sine of the individual angles. We are given the value of cos(x) and we can use the identity sin^2(x) + cos^2(x) = 1 to find the value of sin(x). Once we have the values of sin(x) and cos(x), we can substitute them in the above identity to get the simplified expression.

In this particular problem, we are given the value of cos(x) and the fact that x is in the second quadrant, which implies that sin(x) is positive. Using these values, we can simplify the expression to get the final answer. It is important to note that the answer is requested in exact form as a fraction, and not as a decimal approximation.

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Answer:

Option (3)

Step-by-step explanation:

Coordinates of the centroid of a triangle with given vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by,

X-coordinates = \(\frac{x_1+x_2+x_3}{3}\)

Y-coordinates = \(\frac{y_1+y_2+y_3}{3}\)

For the given triangle FGH,

Coordinates of the vertices are,

F(-3, 1), G(2, 6) and H(4, 1)

X-coordinate of the centroid = \(\frac{-3+2+4}{3}\) = 1

Y-coordinate of the centroid = \(\frac{1+6+1}{3}\) = \(\frac{8}{3}\)

Therefore, coordinates of the centroid will be (1, \(\frac{8}{3}\) )

Option (3) will be the answer.

Answer: i think -22/3 and 6/17

Step-by-step explanation:

The statement is false because the element 2 does not meet the criteria of being an integer greater than 13.

To determine if {2} is an element of the set of integers greater than 13, we need to analyze the statement.

The set of integers greater than 13 can be represented as {x | x ∈ ℤ, x > 13}. This set contains all integers that are greater than 13.

Now, let's check if the element 2 is in this set. Since 2 is not greater than 13, it does not satisfy the condition x > 13. Therefore, {2} is not an element of the set of integers greater than 13.

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The meridians of longitude identify the degrees east and west of the Prime Meridian. These lines are scientifically based because they are determined by the Earth's rotation and provide a consistent and accurate system for navigation, mapping, and timekeeping.

1. The meridians of longitude are imaginary lines that run vertically from the North Pole to the South Pole on the Earth's surface.
2. The Prime Meridian, located at 0 degrees longitude, serves as the starting point for measuring degrees east and west.
3. The degrees of longitude are divided into 360 equal parts, with each degree representing one hour of the Earth's rotation.
4. The meridians of longitude allow us to determine specific locations on the Earth's surface and measure the angular distance from the Prime Meridian.
5. The scientific basis of meridians of longitude enables global coordination and facilitates activities such as international travel, communication, and scientific research.

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Answer:  -21

Step-by-step explanation:

11-32

The break-even quantity is 3 units. The profit for producing 470 units is $5624. 13 units must be produced for a profit of $120.here both cost and revenue are in dollars.

(a) To find the break-even quantity, we set the cost function C(x) equal to the revenue function R(x) and solve for x:

\(11x + 36 = 23x\)

\(36 = 12x\)

\(x = 3\)

Therefore, the break-even quantity is 3 units.

(b) The profit for producing 470 units can be calculated by subtracting the cost from the revenue:

\(Profit = Revenue - Cost\)

\(Profit = R(470) - C(470)\)

\(Profit = 23(470) - (11(470) + 36)\)

\(Profit = 10810 - 5186\)

\(Profit = $5624\)

The profit for producing 470 units is $5624.

(c) To find the number of units that must be produced for a profit of $120, we set the profit equation equal to $120 and solve for x:

\(Profit = Revenue - Cost\)

\($120 = R(x) - C(x)\)

\($120 = 23x - (11x + 36)\)

\($120 = 12x - 36\)

\(12x = 156\)

\(x = 13\)

Therefore, 13 units must be produced for a profit of $120.

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Answer:

1.5/12 is width of cell

Step-by-step explanation:

1. 2/3= 8/12

2. 8/12 times 1.5/12= 1/12

1/8 mm is the width of the cell.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, The length of a cell is 2/3 mm. If the area of the cell is 1/12 mm,

from the general formula of area :

Area = length * width

In our case

1/12 = 2/3 *width

multiply both sides by 3/2

width = 1/12 *3/2

Thus,

Width of cell = 1/8

therefore, the width of the cell is 1/8 mm.

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Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

Answer:

41 people

Step-by-step explanation:

If there are 68 people wearing swimsuits and 39 people are wearing sunglasses: 80 - 39 = 41. 41 people are wearing swimsuits but not sunglasses. This is only true aslong as everyone had to be wearing atleast a pair of sunglasses or a swimsuit.

Answer:

The y-intercept represents the number of mammals when they were originally counted.

The line y = 0 is an asymptote of the graph.

The y-intercept is 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

Step-by-step explanation:

Took the test

Answer:

The y-intercept represents the number of mammals when they were originally counted.

The line y = 0 is an asymptote of the graph.

The y-intercept is 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

Consider the ellipsoid given by the equation 3x^2+3y^2+z^2=75−5z^2.

The given equation can be rewritten in terms of the canonical form of an ellipsoid which is, x^2/a^2+y^2/b^2+z^2/c^2=1 where a, b, c are the lengths of the semi-axes of the ellipsoid. Therefore, the equation of the given ellipsoid becomes as follows:

x^2/5^2+y^2/5^2+z^2/√15^2=1

Let us differentiate the given equation with respect to x, y, and z.

∂z/∂x=−3x^2/2z.

Similarly, ∂z/∂y=−3y^2/2z.

Let us find z for the given point, x=−2,y=3, and z=−1 by substituting in the given equation. 3(−2)³(3)³+3(−1)³=75−5(−1)²81+3=75−5(9)54=75−45=30

∴z=−√10

Therefore, the slope of the tangent to the given ellipsoid at (-2, 3, -1) is as follows. dy/dx=−∂z/∂x/∂z/∂y=−3x^2/2z/−3y^2/2z=−y^2/x^2=−3^2/(-2)^2=9/4

Since the point (-2, 3, -1) lies on the tangent plane, its equation is as follows. 9x/4−3y+z+11=0

We have been given an ellipsoid and we need to find the symmetric equation of its normal line at (-2, 3, -1).We can find the normal vector at the given point as follows.

grad(x^2/5^2+y^2/5^2+z^2/√15^2)=⟨2x/25,2y/25,2z/√15^2⟩=⟨2x/25,2y/25,2√10/75⟩

By substituting x=−2,y=3,z=−√10 in the above equation, we get the normal vector at the given point as follows. ⟨−8/25,6/25,2√10/75⟩

Let P(x, y, z) be the general point on the line passing through (-2, 3, -1) in the direction of the normal vector ⟨−8/25,6/25,2√10/75⟩.

Therefore, the symmetric equation of the normal line is as follows. x−(−2)/−8/25=y−3/6/25=z−(−1)/2√10/75=8x+6y−5z−1=0

The slope of the tangent to the given ellipsoid at (-2, 3, -1) is 9/4.The equation of the tangent plane at the point (-2, 3, -1) to the given ellipsoid is 9x/4−3y+z+11=0.The symmetric equation of the normal line at the point (-2, 3, -1) to the given ellipsoid is 8x+6y−5z−1=0.

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Based on the number of minutes it takes each machine to make yoyos, the number of hours it would take for both machines to make 20 yoyos is 1 ¹/₁₀ hours.

Machine A makes a yoyo every five minutes while Machine B makes a yoyo every 10 minutes. In ten minutes therefore, the number of yoyos made by both machines is:
= (10 minutes / 5) + 1

= 2 + 1

= 3 yoyos

The number of minutes it would take to make 20 yoyos is:

= (20 / 3) x 10 minutes

= 66 minutes

In hours this is:

= 66 / 60 minutes per hour

= 1 ¹/₁₀ hours

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Answer:

Step-by-step explanation:

+18-9+5-3 = 11

It's on the eleventh floor and must go down 11 floors to return to the ground floor.

The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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Answer:

k = 42

Step-by-step explanation:

This is a complementary angle, meaning that the angles formed equal 90 degrees. We know it is complementary because the angle is shown was a tiny square, a sign that it is 90 degrees. Thus, the two angles (k+1) and 47 added together must equal 90. So, we can write an equation:

(k+1) + 47 = 90

k + 1 = 43

k = 42.

Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

Answer:

\(15,000\:\mathrm{mm^3}\)

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by \(V=s^2\cdot h\), where \(s\) is the base length and \(h\) is the height. Substituting given values, we have: \(V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}\)

The volume of a trapezoidal prism is given by \(V=\frac{b_1+b_2}{2}\cdot l\cdot h\), where \(b_1\) and \(b_2\) are bases of the trapezoid, \(l\) is the length of the height of the trapezoid and \(h\) is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases (\(\frac{b_1+b_2}{2}\)) multiplied by the trapezoid's height (\(l\)).

Substituting given values, we get:

\(V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}\)

Therefore, the total volume of the composite figure is \(5,880+9,120=\boxed{15,000\:\mathrm{mm^3}}\) (ah, perfect)

Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

\(V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark\)

Answer:

B number is right.

8 + (15 – 4) x 4 – 10 ÷ 5

8+11×4--10÷5

8+11×4-2

8+44-2

52-2

50

Answer:

yes get those raisins taylor

Step-by-step explanation:

woo! go taylor

By using the fact that the two triangles are equivalent, we will find that the value of n must be 18.4

Here we can see that the horizontal line divides the triangle in such a way that the left and right sides are divided in two halfs. (we can see this because both parts have the same symbol on them)

Also both of these triangles are equivalent, so:

if x is the measure of each part in the right side we can write the equivalent relation

11.3/x = (n + 4.2)/(2x)

Now wen solve this for n:

(11.3/x)*2x = (n + 4.2)

22.6 = n + 4.2

22.6 - 4.2 = n

18.4 = n

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Answer:

D. Cone

Step-by-step explanation:

i am sorry if incorrect

The percentage of expenditure which goes towards salaries is 78%

Company's expenditure:

Salaries: R105 000 000

Equipment: R10 000 000

Marketing: R2 000 000

Other: R8 000 000

Total expenditure= R105 000 000 + R10 000 000 + R2 000 000 + R8 000 000

= R135,000,000

percentage of the expenditure is salary= R105 000 000 / R135,000,000 × 100

= 0.78

= 78%

Therefore, 78% of the company's expenditure goes towards salary.

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The probability of A1 occurring given B1 is approximately 0.375, rounded to three decimal places.

To find the probability of P(A1|B1), we can use Bayes' theorem:

P(A1|B1) = (P(B1|A1) * P(A1)) / P(B1)

Given that A1 and A2 are complements, P(A2) can be calculated as 1 - P(A1), which means P(A2) = 0.7.

We are given P(B1|A1) = 0.6 and P(B1|A2) = 0.5.

Now, to calculate P(B1), we can use the law of total probability:

P(B1) = P(B1|A1) * P(A1) + P(B1|A2) * P(A2)

Substituting the given values, we get:

P(B1) = (0.6 * 0.3) + (0.5 * 0.7)

= 0.18 + 0.35

= 0.53

Finally, we can calculate P(A1|B1) using Bayes' theorem:

P(A1|B1) = (P(B1|A1) * P(A1)) / P(B1)

= (0.6 * 0.3) / 0.53

≈ 0.375

Therefore, the probability of A1 occurring given B1 is approximately 0.375, rounded to three decimal places.

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