A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form.

Answer:

A

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is actually easier to ignore the left side for now, and work with the right side. The secant function can be represented in terms of cosine by putting a one over cosine. This relation below should be known:

\(sec(x)=\frac{1}{cos(x)}\)

So, if we replace the secants on the right with the above relation, you can make the right side in terms completely of cosine.

\(\frac{1-cos(x)}{1+cos(x)} =\frac{\frac{1}{cos(x)}-1 }{\frac{1}{cos(x)} +1}\)

I hope that's clear to see. Brainly equations are pretty small and blurry.

The next step is to get a common denominator for the right side. The term '1' is equivalent to cos(x)/cos(x). So we have the following:

\(\frac{1-cos(x)}{1+cos(x)} =\frac{\frac{1}{cos(x)}-\frac{cos(x)}{cos(x)} }{\frac{1}{cos(x)} +\frac{cos(x)}{cos(x)} }\)

Looks rather complex, but it simplifies everything by a lot. Combine it into one single fraction:

\(\frac{1-cos(x)}{1+cos(x)} =\frac{\frac{1-cos(x)}{cos(x)} }{\frac{1+cos(x)}{cos(x)} }\)

When you divide by a fraction, it is equivalent to multiplying by the reciprocal. This is an algebra 1 concept, so it should be familiar:

\(\frac{1-cos(x)}{1+cos(x)} =\frac{1-cos(x)}{cos(x)}*\frac{cos(x)}{1+cos(x)}\)

As you can see, the cos(x)'s will cancel, leaving:

\(\frac{1-cos(x)}{1+cos(x)} =\frac{1-cos(x)}{1+cos(x)}\)

QED

Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A.

Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A. This is due to the fact that for any symmetric matrix A, the image (column space) and kernel (null space) are orthogonal subspaces. Since v is in the image of A and w is in the kernel of A, their dot product must be zero, indicating orthogonality.

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here's the solution,

\( \boxed{\small{volume = area \: \: of \: base \: \: \times height}}\)

so,

=》

\(v = 25\pi \times 2\)

=》

\(v = 50\pi\)

if you solve for π then the value will be :

but in terms of π the value will be :

The volume of the cylinder is 157 unit³.

The amount of space occupied by a three-dimensional figure as measured in cubic units.

Given: B= 25π, h= 2 units

Base area= 25π

πr²=  25π

r²=25

r=±5 units

Now, Volume of cylinder= πr²h

                                         = 3.14* 5* 5* 2

                                         = 157 unit³

Hence, the volume of cylinder is  157 unit³.

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One car travel South at 64 mi/h and the other travels west at 48 mi/h. The distance between the cars increases with rate at 80 mi/h.

To find the rate of change, we need to find the derivative of the variables with respect to time.

Let:

p = distance between 2 cars

q = distance between car 1 and the start point

r = distance between car 2 and the start point

Using the Pythagorean Theorem:

p² = q² + r²

Take the derivative with respect to time:

2p dp/dt = 2q dq/dt + 2r dr/dt

dq/dt = speed of car 1 = 64 mi/h

dr/dt = speed of car 2 = 48 mi/h

The distance of car 1 and car 2 from the start point after 4 hours:

q = 64 x 4 = 256 miles

r = 48 x 4 = 192 miles

Using the Pythagorean theorem:

p² =256² + 192²

p = 320 miles

Hence,

2p dp/dt = 2q dq/dt + 2r dr/dt

p dp/dt = q dq/dt + r dr/dt

320  x dp/dt = 256 x 64 + 192  x 48

dp/dt = 80

Hence, the distance between the cars increases with rate at 80 mi/h

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The amount Anthony spent on each egg if he spent a total of $23.60 is $3.93 per egg.

Cost of each egg = Total cost of eggs ÷ Number of ostrich eggs

= $23.60 ÷ 6

= 3.933333333333333

Approximately,

Cost of each egg = $3.93

Therefore, the amount Anthony spent on each egg if he spent a total of $23.60 is $3.93 per egg

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Answer:

1. Altitude

2. Median

3. Angle bisector

4. Perpendicular bisector

Answer:

Hiii

Step-by-step explanation:

Hello to you too random person!

The exact values of all angles in the interval [0, 360°) that satisfy the given equations are:

data = 45°, 135°, 315°.

To solve the given trigonometric equations, we will consider each equation separately.

tan²(data) - 1 = 0:

First, let's rewrite tan²(data) as (sin(data)/cos(data))²:

(sin(data)/cos(data))² - 1 = 0

Now, we can factor the equation:

(sin²(data) - cos²(data)) / cos²(data) = 0

Using the Pythagorean identity sin²(data) + cos²(data) = 1, we can substitute sin²(data) with 1 - cos²(data):

((1 - cos²(data)) - cos²(data)) / cos²(data) = 0

Simplifying further:

1 - 2cos²(data) = 0

Rearranging the equation:

2cos²(data) - 1 = 0

Now, we solve for cos(data):

cos²(data) = 1/2

cos(data) = ± √(1/2)

cos(data) = ± 1/√2

cos(data) = ± 1/√2 * √2/√2

cos(data) = ± √2/2

From the unit circle, we know that cos(data) = √2/2 corresponds to angles 45° and 315° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 315°.

cos(data)sin(data) = 1:

Since cos(data) ≠ 0 (otherwise the equation wouldn't hold), we can divide both sides by cos(data):

sin(data) = 1/cos(data)

sin(data) = 1/√2

From the unit circle, we know that sin(data) = 1/√2 corresponds to angles 45° and 135° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 135°.

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The solution provided below describes the importance of SSS, AAA, SAS, ASA.

What is Similarity of Triangles?

Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.

Solution:

Side-Side-Side (SSS) - If equivalent sides in two triangles have the same ratio, then their corresponding angles are equal, and the triangles are identical (SSS similarity criterion).

Angle-Angle-Angle (AAA) - If all the three angles of one triangle are equal to the three angles of the other triangle in two triangles, then the two triangles are comparable (AAA similarity criterion).

Side-Angle-Side (SAS) - If one angle of one triangle equals one angle of another triangle, and the sides containing these angles have the same ratio (proportional), the triangles are comparable (SAS similarity criterion).

Angle-Side-Angle (ASA) - By ASA rule, two triangles are said to be similar if any two angles and the side included between the angles of one triangle are proportional to the corresponding two angles and side included between the angles of the second triangle.

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According to the rate of change, it is found that the hourly rate of temperature change at the bottom of the mountain was of -2.5 ºC per hour.

The average rate of change of a function is given by the change in the output divided by the change in the input.

In this problem, it is stated that at the top of the mountain, the average rate of change is of -2.5 ºC per hour, and at the bottom of the mountain the rate is the same, hence the hourly rate of temperature change at the bottom of the mountain was of -2.5 ºC per hour.

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Answer: Since we don't have the actual table, we can't provide an exact answer. However, we can explain the general method for solving this type of problem.

Let's say that Julie rented three types of bicycles: type A, type B, and type C. Let's also say that she rented a certain number of each type, and received a certain amount of money from each type. We can set up the following equations based on this information:

Cost to rent type A bike = (Amount received for type A rentals) / (Number of type A bikes rented)

Cost to rent type B bike = (Amount received for type B rentals) / (Number of type B bikes rented)

Cost to rent type C bike = (Amount received for type C rentals) / (Number of type C bikes rented)

We can then solve for each cost by plugging in the given numbers from the table. For example, if the table shows that Julie rented 10 type A bikes and received $200 in rental fees, we would have:

Cost to rent type A bike = $200 / 10 = $20

We can do this for each type of bike to find the cost to rent each kind of bicycle.

It's worth noting that the actual equations may look slightly different depending on the specific information provided in the table. For example, if the table gives the total number of bikes rented and the total amount received, we would need to use slightly different equations to solve for the individual costs.

The constant of proportionality between y and x is the same as the ratio of any corresponding y and x values in the table. Therefore, we need to check each table to see if the ratio of any corresponding y and x values is equal to 8/5.

Table 1:

x y

1 2

2 4

3 6

4 8

Ratio of y to x:

When x=1, y=2, so y/x = 2/1 ≠ 8/5

When x=2, y=4, so y/x = 4/2 = 2/1 ≠ 8/5

When x=3, y=6, so y/x = 6/3 = 2/1 ≠ 8/5

When x=4, y=8, so y/x = 8/4 = 2/1 ≠ 8/5

Table 2:

x y

1 1.6

2 3.2

3 4.8

4 6.4

Ratio of y to x:

When x=1, y=1.6, so y/x = 1.6/1 = 1.6 ≠ 8/5

When x=2, y=3.2, so y/x = 3.2/2 = 1.6 ≠ 8/5

When x=3, y=4.8, so y/x = 4.8/3 = 1.6 ≠ 8/5

When x=4, y=6.4, so y/x = 6.4/4 = 1.6 ≠ 8/5

Table 3:

x y

5 8

10 16

15 24

20 32

Ratio of y to x:

When x=5, y=8, so y/x = 8/5 = 1.6 = 8/5

When x=10, y=16, so y/x = 16/10 = 1.6 = 8/5

When x=15, y=24, so y/x = 24/15 = 1.6 = 8/5

When x=20, y=32, so y/x = 32/20 = 1.6 = 8/5

Therefore, Table 3 has a constant of proportionality between y and x of 8/5.

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Answer:

4 km wide and 6 km long.

Step-by-step explanation:

Let the width be x, then the length is x+2 km.

Area = width * length

Substituting the given values:

24 = x(x + 2)

24 = x^2 + 2x

x^2 + 2x - 24 = 0

(x + 6)(x - 4) = 0

x = -6, 4

As x must be positive, then x = 4.

So, the dimensions are 4 and 4+2

= 4, 6,

Answer:

width = 3.46 km and length = 6.93 km

Step-by-step explanation:

let the width be : X km

then the length would be: 2X km

as area is length x width

therefore:

2X x X = 24

2X² = 24

X² = 24/2

X² = 12

X = \(\sqrt{12}\)

X=  3.46

the width would be 3.46 km while the length would be 2X = (93.46) = 6.93 km

1. m may be higher or lower than the population mean.
2. The value of m is not necessarily representative of the population mean.
3. The sampling distribution of m is not necessarily normal.
4. The mean, median, and mode of the sample may all be different.

Assuming that the population from which you select your sample is not normal, the following statements about m (the mean of the sample) are true:
1. m may be higher or lower than the population mean.
2. The value of m is not necessarily representative of the population mean.
3. The sampling distribution of m is not necessarily normal.
4. The mean, median, and mode of the sample may all be different.

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When a population is not normal, it means that the distribution of the data is not symmetric and has non-uniform spread.

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Answer:

Step-by-step explanation:

a)1) As denominators are same, keep the same denominator for the result also

Add the numerators and write the new numerator.

\(\frac{3y}{4}+\frac{5y}{4}=\frac{3y+5y}{4}=\frac{8y}{4}\) = 2y

20 Reduce to simplest form by dividing the numerator and denominator by GCF

The probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes is 2/1 or simply 1, which means it is certain that the cycle time exceeds 60 minutes if it exceeds 55 minutes.

Given that the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes, we know that the probability density function is:

f(x) = 1 / (70 - 50) = 1/20, for 50 <= x <= 70

To find the probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes, we need to use conditional probability:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

We can simplify this by noticing that if X is greater than 55, then it must be between 55 and 70, and therefore:

P(X > 55) = P(55 <= X <= 70) = (70 - 55) / (70 - 50) = 1/4

Similarly, we can rewrite the numerator as:

P(X > 60 and X > 55) = P(X > 60)

since if X is greater than 60, it is also greater than 55.

Now, to find P(X > 60), we integrate the density function from 60 to 70:

P(X > 60) = ∫60^70 (1/20) dx = (1/20) × (70 - 60) = 1/2

Putting it all together:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

= P(X > 60) / P(X > 55)

= (1/2) / (1/4)

= 2

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Rhombus RSTU is congruent to WXYZ, and are translational images of each other because all their sides and angles are equal

Some of the properties of a rhombus are;

If Rhombus RSTU is congruent to WXYZ, then they are both translation images of each other because all their sides and angles are equal.

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Answer:

The answer is A.

Step-by-step explanation:

Because it takes 5730 years for half of a sample of carbon-14 atoms to decay. It says that 50% of the carbon atoms have decayed so that means that 5730 years have elapsed for that fossil.

Hope this helps!

Step-by-step explanation:

I'm sorry, but the statement you provided is not correct. The transitive property of angle congruence actually states that if ∠QRS ≅ ∠PQR and ∠PQR ≅ ∠XYZ, then ∠QRS ≅ ∠XYZ. In other words, if two angles are congruent to a third angle, then they are congruent to each other.

So, in your statement, if ∠QRS ≅ ∠PQR and ∠PQR ≅ ∠XYZ, then you can conclude that ∠QRS ≅ ∠XYZ.

The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;

1. AB:BC = 5:3

2. AB:CD = 1:1

3. m∠A : m∠C= 1 : 4

4. m∠B:m∠C = 4:1

5. AD: Perimeter ABCD = 3:16

A ratio is a representation of the number of times one quantity is contained in another quantity.

The shape of the quadrilateral ABCD in the question = A parallelogram

Length of AB = 15

Length of BC = 9

Measure of angle m∠A = 36°

Therefore;

1. AB:BC = 15:9 = 5:3

2. AB ≅ CD (Opposite sides of a parallelogram are congruent)

AB = CD (Definition of congruency)

AB = 15, therefore, CD = 15 transitive property

AB:CD = 15:15 = 1:1

3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)

Therefore; m∠A = m∠C = 36°

∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)

Therefore; ∠A + ∠D = 180°

36° + ∠D = 180°

∠D = 180° - 36° = 144°

∠D = 144°

m∠A : m∠C = 36°:144° =1:4

m∠A : m∠C = 1:4

4. ∠B = ∠D = 144° (properties of a parallelogram)

m∠B : m∠C = 144° : 36° = 4:1

5. AD ≅ BC (opposite sides of a parallelogram)

AD = BC = 9 (definition of congruency)

The perimeter of the parallelogram ABCD = AB + BC + CD + DA

Therefore;

Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48

AD:Perimeter of the ABCD  = 9 : 48  = 3 : 16

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Answer:

6,162.50 JA

Step-by-step explanation:

Is this true?

72.50x80= 6,162.50 JA

The objects are chosen depending on shape, pattern and texture.  The chosen objects are arranged such a way that they also have aesthetic appeal and harmonic configuration.

When choosing items for your still life composition, think about whether their shape, texture, or pattern is more significant.

After selecting your items, the next step is to arrange them in an aesthetically acceptable and harmonic configuration.

Take your time positioning them and move around your composition to try other angles. A changed viewpoint frequently causes a significant compositional shift.

Try to arrange the objects so that some of them overlap to make it apparent which is in front of which.

Create links that guide the viewer's attention around the composition.

As you rearrange the items, seek for the pleasant arrangement.

Delete some items and add others.

Once you've found one that suits you, move around and try a few more.

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We have eliminated the parameter t and obtained the equation of a circle centered at the origin with radius 1.

(a) To eliminate the parameter in the parametric equations x = cos(t) and y = sin(t), we can use the trigonometric identity that states sin²(t) + cos²(t) = 1.

We have:

x = cos(t)

y = sin(t)

Substituting these into the identity, we get:

sin²(t) + cos²(t) = 1

Simplifying, we have:

y² + x² = 1

(b) To find parametric equations for the rectangular equation u = e, we can let t = ln(u). Taking the natural logarithm of both sides of the equation, we get t = ln(u).

Thus, the parametric equations are:

x = cos(ln(u))

y = sin(ln(u))

By substituting t = ln(u), we have eliminated the parameter u and expressed the rectangular equation in terms of t.

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Answer: -22.5 degrees

Step-by-step explanation:

Answer:

r1/r2 = 2ω2/ω1

Step-by-step explanation:

The velocity of each pulley is expressed as v = ωr where;

v is the linear velocity of the pulley

ω is the angular velocity of the pulley

r is the radius of the pulley.

For the two pulleys, the velocity I'd both pulleys are the same.

v1 = v2

v1 is the linear velocity of first pulley

v2 is the linear velocity of the second pulley.

v1 = ω1r1

v2 = 2ω2(r2)

r1 and r2 is the radius of pulley 1 and pulley 2 respectively.

Since v1 = v2

ω1r1 = 2ω2(r2)

Divide both sides by r2

ω1r1/r2 = 2ω2(r2)/r2

ω1r1/r2 = 2ω2

Divide both sides by ω1

ω1r1/r2/ω1= 2ω2/ω1

r1/r2 = 2ω2/ω1

Answer:

20

Step-by-step explanation:

just add the 13 to A and B

Answer:

I believe it would be \(a_{n} = -4 *(-2)^{n-1}; -64\)   aka the second option.

Step-by-step explanation:

In this example we have \(a_{1} = -4, r =2, n=5\\\)

to find \(a_{5}\) we use formula \(a_{n}=a_{1} * r^{n-1}\)

. After substituting these values to above formula, we obtain:

\(a_{n}=a_{1} * r^{n-1}\\a_{5} = -4* (-2)^{5-1}\\ a_{5} =-4 * 16\\a_{5} =-64\)

hope this was helpful :)

Answer:

let the number of children and adult be 7x and 4x

as per question

7x=63

x=63/7=9

no. of adult= 4x= 4*9=36

Step-by-step explanation: