What is the equation of the line that passes through the points (-5,-3) and has a slope of -1?

Answer:

1,4

Step-by-step explanation:

Answer:

1:4

Step-by-step explanation:

uh if im not dumb i think its 1:4 because thats the x coordinate to the y coordinate

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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The expression for the identity is given as;

cos(∠ABC-60°) = 3/10 - 2/5√3

Option D

From the information given, we have that the expression is given as;

cos(∠ABC-60°)

This is simplified as;

cos (B - 60)

Now, let us expand the bracket, we get;

(1/2)cos(B) + (sqrt(3)/2)sin(B).

We have that the identities are expressed as;

cos B = 3/5

sin B = 4/5

Substitute the values, we get;

cos(∠ABC-60°) = 1/2 × 3/5 - √3/2 × 4/5

divide the values, we have;

cos(∠ABC-60°) = 3/10 - 2/5√3

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Answer:

Brand A: $0.05

Brand B: $0.07

Brand A is the better buy

Step-by-step explanation:

Brand A: 72x = 3.89

Brand B: 96x = 6.62

Brand A:

72x = 3.89

/72    /72

x = $0.05 (this one is the better buy)

Brand B:

96x = 6.62

/96     /96

x = $0.07

Hope this helps!

Answer:

1/625

Step-by-step explanation:

You can reduce it to:

5^-8/5^-4

which becomes

1/5^4

which is 1/625

The point estimate of the population mean is 21.

The point estimate of the population mean is the midpoint of the confidence interval.

To find the midpoint, add the lower and upper bounds of the interval and divide by 2. In this case, the lower bound is 17 and the upper bound is 25, so the point estimate of the population mean is (17 + 25) / 2 = 21.

On the other hand, the margin of error is a measure of the precision of the estimate. It is the amount by which the estimate could be off and still be considered accurate. The margin of error is typically expressed as a percentage of the point estimate. In this case, the margin of error would depend on the level of confidence you have in the estimate and the size of the sample you used to generate the interval. Without more information, it is not possible to determine the margin of error.

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Answer:

1

Step-by-step explanation:

a fourth is 1/4 meaning Fourth = 1/4

Th equation is \(3v=54\\\).

Given,

product of 3 and vidya's height is 54

v is represented as vidya's height.

Representation of equation is as follows:

The product of 3 and vidya's height can be written as \(3*v=3v\)

and their product is 54,

\(3v=54\).

Thus, the equation is \(3v=54\\\).

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Answer:

1

Step-by-step explanation:

(-2)^0 = a^0 = 1

Anything raised to the 0 power is 1

Answer:

115.24

Step-by-step explanation:

15.35*4.25=65.2375

65.2375+50=115.2375

115.2375≈ 115.24

Answer:

$84.95

Step-by-step explanation:

50+15.35=65.35

15.35+4.25=19.6

65.35+19.6=84.95

Answer:

x=20

Step-by-step explanation:

if the angles are the same the it would be solved like an equation.

equation: 120=5x+20

this would be solved by subtracting 20 from both sides to make the equation look like:

100=5x the divide 5 by both sides to get x=20

The probability of those that favors building the health center is 0.196

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.

In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the health center.

According to the scenario, 70% of the community favoured in building a health centre.

Hence , p=0.7.

In order to find the probability, binomial theorem will be used as follows :

= 0.196

Hence, The probability is 0.196

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

5+9+10+11+12+13=60 divided by 6 = 10

Mean = Sum of all observations/Number of observations

Mean = 12 + 13 + 9 + 5 + 11 + 10/6

=60/6

= 10

dont forget to like and mark me

Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

The most appropriate choice for equation of line in slope intercept form will be given by-

\(y = -\frac{1}{2}x - 4\)  is the required equation of line

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = \(tan\theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

The given equation of line is y = 2x-5

Slope of this line = 2

Slope of the line perpendicular to this line = \(-\frac{1}{2}\)

The line passes through (2 , -5)

Equation of the required line = \(y - (-5) = \frac{1}{2}(x - 2)\)

                                                    \(y +5=-\frac{1}{2}x+1\\y = -\frac{1}{2}x +1 -5\\y = -\frac{1}{2}x -4\)

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Gender is categorical nominal, end-of-the-year stock classification is categorical and ordinal, and distance is quantitative and ratio.

Quantitative variables are measured with numbers. Some examples include:

Weight measured in kilos

The distance measured in meters or kilometers

Time measured in seconds or hours

On the other hand, a categorical variable is defined by features, categories, or concepts rather than numbers. Here is an example:

Breeds of dogs: Poodles, Boston Terriers, German shepherds, etc.

Moreover, variables can be classified as:

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If Caleb's school is five blocks due north of his home,  the figure that is  closest to the straight-line distance from Caleb's s  is (D) 1,481 ft.

Distance can be defined as how far an object is from another object.

Using Pythagoreans theorem

Hypotenuse =√Perpendicular² + Base²

Where:

Perpendicular = 275 feet ×5 = 1375ft

Base = 275 feet × 2 = 550ft

Let plug in the formula

Hypotenuse =√ 1375 ft² + 550ft

Hypotenuse =√1,890,625 + 302,500

Hypotenuse =√2,193,128

Hypotenuse = 1,480.9ft

Hypotenuse = 1,481ft (Approximately)

Therefore the correct option is D.

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Answer:

(a) 27 degrees (nearest degree)

(b) 17.9 m  (to one decimal place)

Step-by-step explanation:

Wow, that's along ladder, perhaps for the firemen!

From diagram,

(a)

sin(x) = 9 / 20 = 0.45

x = arcsin(0.45) = 26.74 degrees

(b)

height of wall ladder reaches

h = 20*cos(x) = 20*cos(26.74) = 17.86 m

Answer:

Step-by-step explanation:

Answer:

(0, 2)

Step-by-step explanation:

The value of river garden's common stock is $24.79.

In order to determine the value of the common stock, the constant dividend model would be used.

According to this model, the value of a common stock is determined by its dividend, the growth rate and the required return.

Value of the stock = Dividend / (required return - growth rate)

The first step is to determine the dividend of the common stock.

Dividend = pay out ratio x expected earnings

Dividend = 0.45 x $3.25

Dividend = $1.46250

Value of the stock = $1.46250 / (0.124 - 0.065)

Value of the stock = $24.79

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Answer:

Step-by-step explanation:

Based on the coldest temperature in Buffalo and the difference in the temperature of Chicago, the equation that can be used to find the coldest temperature in Chicago is C. C - 12 = -39; -27°

When temperatures are warmer, it means that they are higher. This means that to find the coldest temperature in Chicago, you need to add 12°F to the temperature of Buffalo.

The formula would therefore be:

C = -39 + 12

Making the Buffalo temperature the subject gives;

C - 12 = -39

The coldest temperature in Chicago is:

= -39 + 12

= -27°F

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Answer: x = 12.124

y = 14

Step-by-step explanation:

In a 30, 60, 90 triangle, the side opposite the 30° angle is half the length of the hypotenuse. So y = 14.

7/sin(30) = 14

You can use the Pythagorean Theorem to calculate x.

14^2= 7^2 + x^2

196 - 49 = x^2

147 = x^2

sr/rt 147 = sq/rt x^2

12.124 = x

Or with trig

7/tan(30)= 12.124

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The probabilities are given as follows:

3. P(rides bus|owns a car) = 1/3.

4. P(red|organic) = 3/5.

The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For item 3, the outcomes are given as follows:

Hence the probability is:

P(rides bus|owns a car) = 8/24 = 1/3.

For item 4, the outcomes are given as follows:

The error was in identifying the total outcomes, and the probability is:

P(red|organic) = 18/30 = 3/5.

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Answer:

D, E

Step-by-step explanation:

In the table, r = 3p, and by converse, p = 1/3r. These options are D and E

Answer:

This is not college level stuff.

But the answer is D. r = 3p and E. p =r/3

Step-by-step explanation:

As you can see in the graph, all the r values are 3 times the p values, 9 = 3 x 3, 21 = 3 x 7, 24 = 3 x 8 and  so on. So, the equation is r = 3p. The same is also vice versa, r/3 = p.

Answer:

D

Step-by-step explanation: