What is the equation of the line that passes through the point (-4, 2) and has a
slope of -5/4

Equation/Question:

-6x-(-8)=2

Answer/Way I did it:

1. Remove parentheses.

-6x+8=2

2. Subtract 8 from both sides.

-6x=2-8

3. Simplify  2-8 to  -6.

-6x=-6

4. Divide both sides by -6.

x=1

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

Checking:

Equation/Question:

−6x−(−8)=2

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

1. Let x=1.

−6×1+8=2

2. Simplify  -6×1  to  −6.

-6+8=2

3. Simplify  -6+8 to  2.

2=2

Done by NeighborhoodDealer

Answer:

x(7y)x(7y)

Step-by-step explanation:

The given expression: 7(xy)7(xy)

i.e. a product of 7 and xy.

The operation used here: Multiplication.

Commutative property of multiplication :-

a\times b=b\times aa×b=b×a for any numbers a and b.

Associative property of multiplication :-

a\times(b\times c)=(a\times b\times c)a×(b×c)=(a×b×c) for any numbers a , band c.

Now, 7(xy)=(7x)y7(xy)=(7x)y [Associative property of multiplication]

=(x7)y=(x7)y [Commutative property of multiplication]

=x(7y)=x(7y) [Associative property of multiplication]

Answer: 56

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

You can use a calculator to figure this out!

The answer is 21. Hope this Helps!

Answer:

Segment Addition Postulate.

Step-by-step explanation:

The segment addition postulate justifies the statement:

\(AQ+QB=AB\)

To help this make sense, you are namely adding segments on a line in order to achieve a complete line segment.

Hi!

These can be set up as systems of equations.

Let b = the number of birds, and let d = the number of dogs.

b + d = 21

2b + 4d = 76 (this is because birds have 2 legs and dogs have 4 legs.)

You can solve this using either elimination or substitution.

Consider marking brainliest.

The cost for two stations that are 10 miles apart will be $8.21.

What is cost?

Cost denotes the amount of money that a company spends on the creation or production of goods or services. It does not include the markup for profit. From a seller's point of view, cost is the amount of money that is spent to produce a good or product.

Given equation is;

y = 0.354x+4.669

Where x represents the number of miles traveled.

For measuring the cost for two stations that are 10 miles apart;

x=10

Putting in given equation

y=0.354(10)+4.669

y=3.54+4.669

y=8.209

Rounding off to nearest hundredth;

y=$8.21

The cost for two stations that are 10 miles apart will be $8.21

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Answer:

60

Step-by-step explanation:

\(a+b+c=180\\\frac{b+c}{2}=a \rightarrow b+c=2a\\\\a+2a=180\\3a=180\\a=60\)

Therefore, the value of a is 60 degrees

The physical diameter of the sun will be 1309000km and the percentage of difference between the diameters will be 5.8%.

From the information, the sun has an angular diameter of about 0.5° and an average distance from the Earth of about 150 million km. The angular diameter in radians will be:

= 0.5π / 180

= 0.008727 radians

Distance from the sun = 150 × 10^6

The physical diameter of the sun will be:

= 150 × 10^6 × 0.008727

= 1309000km

The difference between the diameters will be:

= 1390000 - 1309000

= 8.1 × 10^4.

The percentage of difference will be:

= (8.1 * 10^4) / 1390000 × 100

= 5.8%

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Apply right triangle proportions:

20 (16) = x (x)

320 = x^2

√320 = x

x = 8√5

Answer:

M(-6,-7), N(-2,-1), P(0,6)

Rotation Formula 180 degrees: (x,y) -> (-x,-y)

Rotation Formula  90 degrees clockwise: (x,y) -> (y,-x)

M) (-7.6) -> (7,-6) -> (-6,-7)

N) (-1,2) -> (1,-2) -> (-2,-1)

P) (-6,0) -> (6,0) -> (0,6)

Answer:

96

Step-by-step explanation:

to be honest i just looked it up on google

Step-by-step explanation:

one foot cost 3 so a fourth of one foot is one fourth of three which is .75 and .75 x 3 is 2.25

Answer:

Option B. 4

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 60 °

Opposite (Fe) = 4√3

Adjacent (DE) = x

The value of x can be obtained by using the Tan ratio as illustrated below:

Tan θ = Opposite / Adjacent

Tan 60 = 4√3 / x

√3 = 4√3 / x

Cross multiply

√3 × x = 4√3

Divide both side by √3

x = 4√3 /√3

x = 4

Thus, the length of DE is 4

Answer:

Dylan is 10 years old, and Genesis is 11.

Step-by-step explanation:

If Genesis and Dylan's age are consecutive integers, and Genesis is older, we can represent their ages as:

Dylan's age: x

Genesis' age: x+1

This would mean Genesis is a year older than Dylan.

The product of their ages is 110.

We can write an equation:

x×(x+1)=110

x²+x=110 (Distribute x)

x²+x-110=0 (Move 110 to the other side)

You can solve this by the quadratic equation, by factoring or by completing the square

I'll solve it by the quadratic equation:

We must first find the coefficients a, b and c, and then plug it into the formula.

\(x = \frac{ - 1 + - \sqrt{ {1}^{2} - 4 \times 1 \times - 110} }{2 \times 1} \\ x = \frac{ - 1 + - \sqrt{1 + 440} }{2} \\ x = \frac{ - 1 + - 21}{2} \)

Since we have a ± symbol, we get 2 real solutions, x1 and x2.

x=-1±21/2

x1=-1+21/2

x1=20/2

x1=10

x2=-1-21/2

x2=-22/2

x2=-11

Since their age can't be negative, x2 can't be a solution, so Dylan's age must be 10, and Genesis' age must be 11.

Hope this helps, and let me know if you need help with another method to solve this problem!

90 dL times L/dL equals 9 L

To understand why 90 dL times L/dL equals 90L, it's important to understand the units involved and how they cancel out.

First, dL stands for deciliter, which is a unit of volume equal to one-tenth of a liter.

L, on the other hand, stands for liter, which is a unit of volume equal to 1000 milliliters or one cubic decimeter.

So, 90 dL represents a volume of 90 deciliters, while L/dL represents a ratio of liters to deciliters.

Specifically, L/dL means "liters per deciliter," which is a way of expressing a conversion factor between liters and deciliters.

Multiplying 90 dL by L/dL involves multiplying 90 dL by the conversion factor of L/dL, which is 1 liter per 10 deciliters. The deciliter units cancel out, leaving only the liter units.

Therefore, we can rewrite the calculation as follows:

90 dL x (1 L/10 dL) = (90/10) L = 9 L

So, the result is 9 L, which is equivalent to 90 dL times L/dL.

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Answer: continental drift

Step-by-step explanation: as far as I'm aware, they developed the theory of plate tectonics by the continental drift theory and that the world looks like a puzzle, I may be wrong but this is all I know

The unknown angle in the cyclic quadrilateral is as follows:

m∠CML = 109 degrees

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's find m∠CML as follows:

Using the arc angle and opposite angle of a quadrilateral theorem,

6x + 25 = 1 / 2 (7x + 14 + 106)

6x + 25 = 1 / 2(7x + 120)

6x + 25 = 7 / 2 x + 60

6x - 7 / 2 x  = 60 - 25

6x - 3.5x = 35

2.5x = 35

divide both sides by 2.5

x = 35 / 2.5

x = 14

Therefore,

m∠CML = 6x + 25 = 6(14) + 25 = 84 + 25 = 109 degrees

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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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(a) The critical points of the given system of equations are (0,0), (2,2), and (-2,-2).

(b) Near the critical point (0,0), the linear system is: \(\frac{dx}{dt} = 2y, \frac{dy}{dt} = -2x\). Near the critical point (2,2), the linear system is: \(\frac{dx}{dt} = -2y, \frac{dy}{dt} = 2x\) Near the critical point (-2,-2), the linear system is: \(\frac{dx}{dt} = 2y, \frac{dy}{dt} = -2x\)

(c) The eigenvalues of the linear system near (0,0) are: ±2i. The eigenvalues of the linear system near (2,2) are: ±2i. The eigenvalues of the linear system near (-2,-2) are: ±2i. These eigenvalues indicate that the nonlinear system is stable near each of the critical points.

(d) The phase portrait of the nonlinear system will be a series of circles centered at each of the critical points and will show that the system is stable near each of the critical points.

A critical point of a system of equations is a point at which the derivative of the system is equal to zero.

To find the critical points of the given system, we can set the derivative of each equation equal to zero and solve for x and y. For the first equation, this gives us:

\(\frac{dx}{dt}\) = (2 + x)(y - x) = 0

If we set the derivative equal to zero, then either (2 + x) = 0 or (y - x) = 0. If (2 + x) = 0, then x = -2. If (y - x) = 0, then y = x.

For the second equation, setting the derivative equal to zero gives us:

dy/dt = (4 - x)(y + x) = 0

If we set the derivative equal to zero, then either (4 - x) = 0 or (y + x) = 0. If (4 - x) = 0, then x = 4. If (y + x) = 0, then y = -x.

Therefore, the critical points of the given system are (-2,0), (4,0), and (0,0).

Next, we can find the corresponding linear system near each critical point by finding the Jacobian matrix of the given system at each critical point. The Jacobian matrix is a matrix of the partial derivatives of the system with respect to x and y.

At the critical point (-2,0), the Jacobian matrix is:

[(2 + x)(y - x) (2 + x)(y - x)]

[(4 - x)(y + x) (4 - x)(y + x)]

Evaluating this matrix at the point (-2,0) gives us:

[(-2)(0 - (-2)) (-2)(0 - (-2))]

[(-2)(0 + (-2)) (-2)(0 + (-2))]

= [4 4]

[-4 -4]

At the critical point (4,0), the Jacobian matrix is:

[(2 + x)(y - x) (2 + x)(y - x)]

[(4 - x)(y + x) (4 - x)(y + x)]

Evaluating this matrix at the point (4,0) gives us:

[(4)(0 - 4) (4)(0 - 4)]

[(4 - 4)(0 + 4) (4 - 4)(0 + 4)]

= [-8 -8]

[0 0]

At the critical point (0,0), the Jacobian matrix is:

[(2 + x)(y - x) (2 + x)(y - x)]

[(4 - x)(y + x) (4 - x)(y + x)]

Evaluating this matrix at the point (0,0) gives us:

[(2)(0 - 0) (2)(0 - 0)]

[(4 - 0)(0 + 0) (4 - 0)(0 + 0)]

= [0 0]

[0 0]

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Answer:

-5x=-10

Step-by-step explanation:

Adding both equations will result in this

Answer:

18

Step-by-step explanation:

Answer:

1. m is the correct one

2. h is the correct one

The question that can be represented by the equation: ?× 1 5\8 = 1\3 is a. What fraction of the trip has Andre completed?.

It was stated that  from home to a festival that is 1 5\8 kilometers away, and later after some moments we were told that He takes a quick rest after walking 1\3 kilometers.

Then if we were to know the fraction of the trip has Andre completed, then the calculation will be ?× 1 5\8 = 1\3 which makes the option A that was chosen to be correct.

Therefore, option A  is correct.

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CHECK THE MISSING OPTIONS;

a. What fraction of the trip has Andre completed?

b. How many more kilometer does he have to walk to get to the festival?

c. What fraction of the trio is left.

d. How many kilometers is it from home to the festival and back home?

The firm's federal income tax is $57,168.

To calculate the firm's federal income tax, we need to determine its taxable income first. Taxable income is calculated by subtracting deductions from the firm's total income.

In this case, the firm's total income consists of income from operations, interest income, and dividend income.

Total income:

Income from operations = $231,000

Interest income = $23,100

Dividend income = $29,700

Total income = $231,000 + $23,100 + $29,700 = $283,800

Next, we deduct expenses from the total income. In this case, the only relevant expense is the interest paid to bondholders:

Total expenses = Interest paid to bondholders = $11,000

Taxable income = Total income - Total expenses = $283,800 - $11,000 = $272,800

Now, we can calculate the federal income tax by applying the federal tax rate of 21% to the taxable income:

Federal income tax = Taxable income * Federal tax rate

Federal income tax = $272,800 * 0.21 = $57,168

Therefore, the firm's federal income tax is $57,168.

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Answer:

Step-by-step explanation:

Given

Number of servings:

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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Answer:

32 mph

Step-by-step explanation:

We want to find the patrolman's rate in miles per hour during the shift. Since we want to find miles per hour, we must divide the miles he drove by the number of hours.

rate = miles / hours

He drove 272 miles.

rate = 272 miles / hours

He drove for 8 hours and 30 minutes. There are 60 minutes in 1 hour. One half of 60 is 30. Therefore, we can also say he drove eight and a half, or 8.5 hours.

rate= 272 miles / 8.5 hours

rate = 32 miles / hour

rate= 32 mph

His average rate during the shift was 32 miles per hour.

Answer:

32 mph

Step-by-step explanation:

To answer this, find the average rate of change

 272 mi

------------- = 32 mph

 8.5 hr