what is the slope and y intercept of the function k(x)=7/9x-2​

Answer:9

Step-by-step explanation: First you add the 3x to both sides(the -4x and the -3x) and then you get 15-1x=6. Next you subtract 15 from 15 and 6, so you get -1x=-9. So then you divide both sides by -1 (do -1x over -1 equals -9 over -1). Last you do the dividing and you get x=9.

Isolate the variable x by moving terms involving x to one side and constants to the other side. Simplify the equation step-by-step to find that x = 9.

To solve the equation 15 - 4x = 6 - 3x, we need to isolate the variable x. Follow these steps:

Therefore, the solution to the equation 15 - 4x = 6 - 3x is x = 9.

Answer:

Slope (m)

-0.2222

m = 2 / -9 = -0.222

Step-by-step explanation:

Answer: -3/7

Step-by-step explanation:

-3x + 5x +-3= 4x + 5x

7x=-3

x=-3/7

Answer:

5x + 3=4x

Step-by-step explanation:

Answer:

ΔB D E = ΔB F K, By rule A A S similarity

Step-by-step explanation:

a right angle is congruent to a right angle, so < B D E is congruent to

< B F K

< D B F is equal to < D B F

Side B D = B F is given

Thus, creating A A S similarity

Answer:

The percentage decrease in price of Air conditioner is 33.33%  

Step-by-step explanation:

Given as :

The initial price of air conditioner = Rs 27000

The reduce price of air conditioner = Rs 24000

Let the rate of percentage = x %

So,  % decrease = [tex]\frac{\textrm initial value - \textrm final value}{\textrm initial value}[/tex] × 100

Or,  % decrease = [tex]\frac{\textrm 27000 - \textrm 24000}{\textrm 27000}[/tex] × 100

Or , % decrease = [tex]\frac{3000}{27000}[/tex]  × 100

Or,  % decrease = [tex]\frac{100}{9}[/tex]

Or. % decrease = 33.33 %

Hence The percentage decrease in price of Air conditioner is 33.33%   Answer

Answer:

The second city is 54 miles behind the first city

Step-by-step explanation:

The first bus is assumed to go ahead of the second bus and is moving at 54 mph. The second bus is moving at a speed such as 54 mph is 60% (0.6) of its speed.  

The speed of the second bus is then 54/0.6 = 90 mph

When 1 and a half hour has passed, the first bus has moved a distance of

[tex]X_1=54\times 1.5[/tex] = 81 miles

The second bus (behind the first bus) has moved

[tex]X_2=90\times 1.5[/tex] = 135 miles

The problem states they both meet in that time, it can only be possible if the second bus departed a distance 135 - 81 = 54 miles behind the first city

So, the second city is 54 miles behind the first city

Answer:

4 5/12 or four and five twelfths or 4 and 5 over 12

Step-by-step explanation:

Answer:

-11/48

Step-by-step explanation:

11/16-11/12=132/192-176/192=-44/192

simplify

-11/48

PLEASE MARK BRAINLIEST!

Answer:

Your answer is

Step-by-step explanation:

11/16 = 33/48

11/12 = 44/48

33/48 - 44/48 = -11/48

Your answer is -11/48.

I hope this helps!

Answer:

Step V: Transitive property of Inequality

Step VI: Subtraction Property of Inequality

Step-by-step explanation:

In Step IV, the RHS of t=both the sides are equal.

So, they equated the LHS of both the sides.

This is the transitive property of equality which states that if a = b and c = b then a = c.

In this case, a = [tex]$ \angle {m_1} + \angle {m_2}  $[/tex]

b = 180⁰

c = [tex]$ \angle {m_2} + \angle {m_3} $[/tex]

Consequently, [tex]$ \angle {m_1} + \angle {m_2} = \angle {m_2} + \angle {m_3} $[/tex]

In step VI, [tex]$ \angle {m_2} $[/tex] is subtracted on both the sides. So, this is called as Subtraction Property of Equality.

Answer:

Sara will have US$ 2,251.02 in the bank after 4 years for her trip to Italy.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Investment of Sara during her 1st year of college = US$ 2,000

Duration of the investment = 4 years

Annual interest rate = 3%

2. Let's find the future value of this investment after 4 years, using the following formula:

FV = PV * (1 + r) ⁿ

PV = Investment of Sara during her 1st year of college = US$ 2,000

number of periods (n) = 4

rate (r) = 3% = 0.03

Replacing with the real values, we have:

FV = 2,000 * (1 + 0.03) ⁴

FV = 2,000 * (1.03) ⁴

FV = 2,000 * 1.12550881

FV = 2,251.02

Sara will have US$ 2,251.02 in the bank after 4 years for her trip to Italy.

Answer:

2240

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

When we differentiate the function, we get -32x + 32, which is the velocity function of the original.

When we differentiate again, we get -32, which is derived from the initial -16. This -32 represents the acceleration, because it is the 2nd derivative.

Hence, the answer is D, acceleration due to gravity.

Hey there! :)

Equation 1) -2x + y = 14

Equation 2) 4x - 6y = 4

Add 2x to both sides of equation 1 so that we can get the value of y.

y = 2x + 14

Now, plug the value of y into our second equation.

4x - 6(2x + 14) = 4

Simplify.

4x - 12x - 84 = 4

Add 84 to both sides.

4x - 12x = 4 + 84

Simplify.

-8x = 88

Divide both sides by -8.

x = -11

Now, plug our value of x into our first equation in order to find y.

-2x + y = 14

-2(-11) + y = 14

22 + y = 14

y = -8

Therefore, the systems of equation variables are : (-11, -8)

~Hope this helped! :)

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For solving such questions we need to know the linear inequations .

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Liner inequations can be solved with many methods . But here as mentioned we have to solve with substitution method .

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Substitution method is the method of finding the value of one variable from equation 1 and then substituting the value in the equation 2 .

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-2x + y = 14 --- ( i )

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4x - 6y = 4

2 ( 2x - 3y ) = 4

2x - 3y = 4 / 2

2x - 3y = 2 --- ( ii )

As given , -2x + y = 14

➠ y = 14 + 2x

Now, we will substitute the value of y in eq ( ii )

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➠ 2x - 3y = 2

➠ 2x - 3 ( 14 + 2x ) = 2

➠ 2x - 42 - 6x = 2

➠ 2x - 6x = 2 + 42

➠ -4x = 44

➠ x = 44 / - 4

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➠ x = -11

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[tex]\sf{\underline{\boxed{\huge{\blue{\mathbb{x = - 11 }}}}}}[/tex]

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➠ -2x + y = 14

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➠ - 2 × - 11 + y = 14

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➠ 22 + y = 14

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➠ y = 14 - 22

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➠ y = - 8

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[tex]\sf{\underline{\boxed{\huge{\blue{\mathbb{y = -8}}}}}}[/tex]

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Answer: 30

Step-by-step explanation:

1:7

x:210

find x

210 is 30 times bigger than 7 so 30 is 30 times bigger than 1

30 is the answer

Answer:

30 blueberries

Step-by-step explanation:

divide the total by the 7, it's a lot simpler since it's a 1:7 but yeah so it's 30:210 blueberries to strawberries

The equation of the line that parallel to x = -3 and passes through the point (4, -7) is y = -3x + 5

Solution:

The two forms of writing a point and slope in equation are point slope form and standard form.

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. The standard form of a line is just another way of writing the equation of a line.

The given point is (4,-7) and the slope is -3.

The slopes of parallel lines are always equal.

To write in standard form we will first write it in point slope form and then rearrange it into a standard from.

The equation of line in point slope form is given as:

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

[tex]\begin{array}{l}{y-(-7)=-3(x-4)} \\\\ {y+7=-3(x-4)} \\\\ {y+7=-3 x+12}\end{array}[/tex]

y = -3x + 5

Now, let us convert this equation to standard form

3x + y = 5

Thus the equation of line in point slope and standard form is found out

Answer:

x=-1189/36, y=242/9. (-1189/36, 242/9).

Step-by-step explanation:

-8x-16y=-166

8x+7y=-76

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

-9y=-242

9y=242

y=242/9

8x+7(242/9)=-76

8x=-76-1694/9

8x=-2378/9

x=(-2378/9)/8

x=-1189/36

Answer: Line C

Step-by-step explanation: She added 12 to one side and subtracted 12 from another side when she should've added 12 to both sides.

The correct answer and work would be:

8x-3(2x+4)=10

8x-6x-12=10

2x-12=10

2x=22

x=11

Answer:

[tex]0.2[/tex] miles per minute represents the speed of the bird and 3 miles represents the original distance of the bird from its nest.

Step-by-step explanation:

As there is no graph mentioned here but the information are quite sufficient to answer the question.

We have points [tex](0,3), (5,4),(10,5)...[/tex]

From these points we can find the slope of the line .

From point slope formula [tex]y-y_1=m(x-x_1)[/tex]

And assigning [tex](x,y) (0,3)[/tex] and [tex](x_1,y_1) (5,4)[/tex]

[tex]m=\frac{y_1-y}{x_1-x} =\frac{4-3}{5-0} =\frac{1}{5}=0.2[/tex]

This slope is also the speed of the bird which is [tex]0.2\ miles\ per\ minute.[/tex]

As by plugging the values of any coordinate point we can confirm this.

Lets put [tex](10,5)[/tex], y-axis is the distance so in [tex]10[/tex] minutes the the distance covered by the bird must be equal to to y-axis value which is [tex]5[/tex] miles.

[tex]y=0.2(x),y=0.2(10)=5\ miles[/tex]

Now as in [tex]t=0[/tex] the bird has started from y-intercept value [tex]3[/tex] so we can say that,the original distance of the bird from its nest is [tex]3\ miles[/tex].

So the correct choices are:[tex]B[/tex] and [tex]D[/tex]

The birds speed is [tex]0.2\ miles[/tex] per minute and is [tex]3\ miles[/tex] away from its nest.

Answer:

(d).

Step-by-step explanation:

The y-intercept (0, 3) is initial value of graph ⇒ (d). 3 miles; it represents the original distance of the bird from its nest

Answer:

1,187 bu/hr

Step-by-step explanation:

4.8 mi/hr

240 inches

Efficiency: 85% (0.85)

120 bushels/acre

1 acre = 6 272 640

1 mile = 63 360 inches

4.8 miles = 304 128 inches

120/6 272 640 x 240 = 5/1089 (bushels/inch)

5/1089 x 304 128 x 85% = 1 186.9 = 1187 bu/hr

Wow, that's hard for me :) Hope it's helpful

Answer:

- 0.183

Step-by-step explanation:

Given that [tex]\sin \theta = \frac{1}{3}[/tex]

and [tex]\frac{\pi }{2} < \theta  < \pi[/tex]

We have to find the exact value of [tex]\sin (\theta + \frac{\pi }{6} )[/tex].

Now, [tex]\sin \theta = \frac{1}{3}[/tex]

⇒ [tex]\theta = \sin ^{-1} (\frac{1}{3} ) = 19.47[/tex]

Now, since  [tex]\frac{\pi }{2} < \theta  < \pi[/tex],

So, [tex]\theta  = 180 - 19.47 = 160.53[/tex]

{Since [tex]\sin \theta = \sin (180 - \theta)[/tex]

Now, [tex]\theta + \frac{\pi }{6} = 160.53 + 30 = 190.52[/tex]

Hence, [tex]\sin (\theta + \frac{\pi }{6} )[/tex].

= [tex]\sin 190.52[/tex]

= - 0.183 (Approximate) (Answer)

The equation 6(x + 2) = 5(x + 7) simplifies to x = 23, indicating it has one unique solution. Substituting back into the original equation verifies the solution.

To classify the equation 6(x + 2) = 5(x + 7) as having one solution, no solution, or infinitely many solutions, we first simplify the equation:

This provides us with one solution for the equation, which means the equation has a single unique solution. When we substitute x = 23 back into the original equation, we get an identity, confirming that our solution is correct.

Equations with a single solution, no solution, or an infinite number of solutions are encountered often in algebra. For example, 1+x+x² = 0 may have real or complex solutions and can demonstrate the principle that an nth degree polynomial has n solutions, which can include repeated or complex roots. The equation 205+111x +4x² - 31x³ - 10x4 +5x5=0 is a higher-degree polynomial that may require numerous iterations to find a solution, emphasizing the complexity of finding solutions for polynomial equations.

Answer:

1.40f .

Step-by-step explanation:

One answer could be:

In March  the house had f + 40% of f

= f + 0.40f

= 1.40f

Answer:

If the February snowfall is valued as fs, the snowfall in March with an additional 40% could be expressed as:

Step-by-step explanation:

In the exercise it is mentioned that the snowfall in March was 40% higher than in February, if you wanted to express it in a mathematical function it could be mentioned that:

What could be represented as:

When calculating we would obtain:

Answer:

The answer is: y = 1/2x + 2

Step-by-step explanation:

Given equation: y = 1/2x + 5

Given point: (-2, 1)

The slope of the given line is 1/2. Parallel lines have the same slope.

Use the point slope form and solve for y:

y - y1 = m(x - x1)

y - 1 = 1/2(x - (-2))

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

y - 1 = 1/2x + 1/2 * 2

y - 1 = 1/2x + 1

y = 1/2x + 2

Proof:

f(-2) = 1/2(-2) + 2

= -1 + 2

= 1, giving point (-2, 1)

Hope this helps!! Have an Awesome Day!! :-)

Answer:

[tex]y=-30x+0[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem the linear equation represent a proportional relationship, because pass through the origin (0,0).

Find the value of the constant of proportionality k

For x=1, y=-30

substitute

[tex]k=\frac{-30}{1}=-30[/tex]

so

the linear equation is

[tex]y=-30x[/tex]

therefore

[tex]y=-30x+0[/tex]

Answer:

[tex]a=15[/tex]

[tex]b=\frac{1}{3}[/tex]

Step-by-step explanation:

we have an exponential function of the form

[tex]y=a(b^x)[/tex]

where

a is the initial value or y-intercept

b is the base

Looking at the graph

we can see the ordered pairs (0,15) and (1,5)

(0,15) ---> y-intercept

so

The value of a is equal to

[tex]a=15[/tex]

substitute

[tex]y=15(b^x)[/tex]

with the point (1,5) find the value of b

For x=1, y=5

substitute in the exponential function

[tex]5=15(b^1)[/tex]

solve for b

[tex]5=15(b)[/tex]

[tex]b=\frac{1}{3}[/tex]

therefore

The exponential function is

[tex]y=15(\frac{1}{3}^x)[/tex]

The solution to the differential equation [tex]\( \frac{dy}{dx} = \sqrt{x + 16} \)[/tex]with the initial condition y(0) = 0 is [tex]\( y = \frac{2}{3}(x + 16)^{3/2} - \frac{128}{3} \)[/tex].

To solve the differential equation [tex]\( \frac{dy}{dx} = \sqrt{x + 16} \)[/tex] with the initial condition y(0) = 0, we'll integrate both sides with respect to x.

Given:

[tex]\[ \frac{dy}{dx} = \sqrt{x + 16} \][/tex]

Integrating both sides:

[tex]\[ \int \frac{dy}{dx} \, dx = \int \sqrt{x + 16} \, dx \]\[ \int dy = \int \sqrt{x + 16} \, dx \]\[ y = \frac{2}{3}(x + 16)^{3/2} + C \][/tex]

Now, we'll apply the initial condition y(0) = 0 to find the value of the constant C:

[tex]\[ 0 = \frac{2}{3}(0 + 16)^{3/2} + C \]\[ 0 = \frac{2}{3}(16)^{3/2} + C \]\[ 0 = \frac{2}{3}(64) + C \]\[ C = -\frac{128}{3} \][/tex]

So, the particular solution to the differential equation with the initial condition is:

[tex]\[ y = \frac{2}{3}(x + 16)^{3/2} - \frac{128}{3} \][/tex]

Final answer:

It will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.

Explanation:

To determine the number of weeks it will take for the stock's price to reach $20.00 per share, we need to find the number of weeks it will take for the price to decrease from $62.50 to $20.00. Since the price is declining at a rate of 5% per week, we can set up an equation:

$62.50 - ($62.50  imes 0.05  imes  ext{number of weeks}) = $20.00

Simplifying the equation, we have:

$62.50 - (0.05  imes 62.50  imes  ext{number of weeks}) = $20.00

$42.50 = (0.05  imes 62.50  imes  ext{number of weeks})

Dividing both sides by 0.05 and 62.50, we get:

ext{number of weeks} =  rac{42.50}{0.05  imes 62.50}

Calculating this, we find that it will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.

Answer:

First blank -- B

Second blank -- A

Third blank -- C

Step-by-step explanation:

To find characteristics of a quadratic equation from just looking at the graph is very simple. Here are few points which you can keep in mind which solving these type of questions.

[tex]D=b^{2} -4ac[/tex]

if D > 0 then two distinct real roots (graph cuts x-axis at two distinct points)

if D = 0 then two equal real roots (graph touches x-axis)

if D < 0 then two imaginary roots (graph doesn't touch x-axis)

For graph A : D < 0 (as it has imaginary roots)

For graph B : D = 0 (as it touches the x-axis)

For graph C : D > 0 (as [tex]D=b^{2}-4ac=4^{2}-4 \times 1 \times (-2)=16+8=24[/tex])

Answer:

Graph B has one real root.

Graph A has a negative discriminant.

Graph C has an equation with coefficients

Step-by-step explanation:

Answer:

f(x) = (x + 4)(x - 4)(x + 3)

The other zeros of the function are at 4 and -3.

Step-by-step explanation:

Given function is f(x) = x³ + 3x² - 16x - 48.

Now, given that - 4 is a zero of the given function.

So, the function has a factor equals to (x + 4).  

Now, f(x) = x³ + 3x² - 16x - 48

⇒ f(x) = x³ + 4x² - x² - 4x - 12x - 48

⇒ f(x) = x²(x + 4) - x(x + 4) - 12(x + 4)

⇒ f(x) = (x + 4)(x² - x - 12)

⇒ f(x) = (x + 4)(x - 4)(x + 3)

Therefore, the other zeros of the function are at 4 and -3. (Answer)

Answer:

f(x) = (x + 4)(x - 4)(x + 3)

Step-by-step explanation:

Answer:

w(-15-w)= 0

w= 0 or (-15-w) = 0

Now,

-15-w =0

w= -15

So,The solution of w(-15-w) = 0

w= 0, -15

Answer:

w=-15,0

Step-by-step explanation:

w(-15-w)=0

-15w-w^2=0

-(w^2+15w)=0

w(w+15)=0

w=-15,0