All computers are on sale for 10% off the original price.If x is the original price of the computer,then the function that represents the price after only a 10% discount is
P(x)=x - 0.1x
P(x)=0.9x
The function that gives the price,C,if only a $150 coupon is used is: C(x)=x-150

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]

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 value of y for x = 8 is 60  .

Step-by-step explanation:

Given expression as :

For x = 2  , y = 15

Let the equation be written with constant k'

So, y = k x

Or, k = [tex]\dfrac{y}{x}[/tex]

∴   k =  [tex]\dfrac{15}{2}[/tex]

Now, again

For x = 8

equation can be written as

   y = k x

Or,  y =  [tex]\dfrac{15}{2}[/tex] × 8

Or,  y = [tex]\frac{15\times 8}{2}[/tex]

∴    y = 15 × 4

I.e  y = 60

Hence The value of y for x = 8 is 60  . Answer

Answer:

In descending order the function are represented as [tex]D>F>A>B>E>C[/tex]

Step-by-step explanation:

Whether it is increasing or is the larger or smaller number it all depends on its slope.

Equation of line [tex]y=m(x)+c[/tex],and [tex]m[/tex] is the slope.

So we will work with the slopes of each equations and arrange them in descending order.[Greater to larger number sequence]

Slopes are [tex]\frac{4}{3}, \frac{5}{4}, \frac{-2}{1},\frac{7}{4}, \frac{6}{5}, \frac{8}{5}[/tex]

We will equate the denominator by taking LCD of it then multiply numerator and denominator with a fix number which can bring all the denominator same.

LCD of the denominator [tex](1,3,4,5)=60[/tex]

Example:

[tex]\frac{4}{3}=\frac{4\times 20}{3\times 20}= \frac{80}{60}[/tex]

Similarly we will equate all the fractions.

So the slope are [tex]\frac{80}{60}, \frac{75}{60}, \frac{-120}{60},\frac{105}{60}, \frac{72}{60}, \frac{96}{60}[/tex]

In descending order the numbers are:

[tex]\frac{105}{60},\frac{96}{60}, \frac{80}{60}, \frac{75}{60},\frac{72}{60},\frac{-120}{60}[/tex]

According to the option the right choice are as follows:

[tex]D>F>A>B>E>C[/tex]

To find increasing functions, examine the slope of each equation, which must be positive for the function to be increasing. Functions A, B, D, E, and F are increasing, with D having the largest unit rate. C is a decreasing function and is not classified with the others.

To determine which functions are increasing, we look at the coefficient of x in each equation since that represents the slope of the line. For a function to be increasing, its slope (unit rate) must be positive. Comparing the slopes will help us classify each function as having a larger unit rate or a smaller unit rate than the function represented in the graph. Without the specific function from the graph for comparison, we'll just compare the given functions to each other.

Based on the slopes, D has the largest unit rate, followed by F, A, B, and E, in that order. Function C is not increasing and thus not part of this classification.

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: -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:

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: 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

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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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:

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:

4/3t

Step-by-step explanation:

1/2t.........90m

x t.............4h->240m

x=(240m*1/2t)/90m

x=120/90

x=4/3t

The construction crew can clear 8/3 tons of dirt in 4 hours.

To find out how much dirt the construction crew can clear in 4 hours, we need to first determine their rate of clearing dirt. The question states that they can clear 1/2 ton of dirt in 90 minutes. To calculate their rate, we divide the amount of dirt cleared (1/2 ton) by the time taken (90 minutes):

Rate = 1/2 ton / 90 minutes

Simplify the rate:

Rate = 1/2 × 2/90 ton/minute = 1/180 ton/minute

Now, to find how much dirt they can clear in 4 hours, we multiply their rate by the number of minutes in 4 hours:

Dirt cleared = Rate × Time

Dirt cleared = 1/180 ton/mintue × 4 hours × 60 minutes/hour

Simplify the units:

Dirt cleared = 1/180 × 4 × 60 ton

Calculate the result:

Dirt cleared = 8/3 ton

Therefore, the construction crew can clear 8/3 tons of dirt in 4 hours.

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Answer:

y = 2x

Step-by-step explanation:

Note the relationship between x and y, that is

x = - 42 → y = - 84 ← that is y = 2x

x = - 14 → y = - 28 ← that is y = 2x

x = 14 → y = 28 ← that is y = 2x

x = 42 → y = 84 ← that is y = 2x

Thus the linear equation is y = 2x

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the table we have the points (14, 28) and (42, 84).

Substitute:

[tex]m=\dfrac{84-28}{42-14}=\dfrac{56}{28}=2[/tex]

Put the val;ue of a slope and the coordinates of the point (14, 28) to the equation of a line:

[tex]28=2(14)+b[/tex]

[tex]28=28+b[/tex]    subtract 28 from both sides

[tex]28-28=28-28+b\\\\0=b\to b=0[/tex]

Finally we have:

[tex]y=2x+0=2x[/tex]

Answer:

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

Step-by-step explanation:

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:

[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:

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:

-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:

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:

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!! :-)

D. Reflexive Property of SSS

Answer:

D

3. Reflexive Property of (Congruence) ≅

4. SSS (Side to Side to Side Congruence rule)

Step-by-step explanation:

3. Any geometric figure compared to itself is congruent to itself so this is why:

[tex]\overline{AC}\cong \overline{CA}\\\angle B\cong \angle B\\(...)[/tex]

4. Since we have a parallelogram, therefore we can say:

[tex]\overline{BC}\cong \overline{DA}\\\\\overline{BA}\cong \overline{DC}\\\\\overline{CA}\cong \overline{AC}\\[/tex]

Both triangles ABC and CDA satisfy the side to side to side congruence, since their 3 sides are congruent.

So, It's D.

P.S.

Notice that the angle measure information is not included in the data above that's why we cannot say it is SAS congruence.

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]

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:

1.40f .

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:

During January it decreased by $3,530.

Step-by-step explanation:

Given data:

Value of stocks in January 1st = $8,474

Value of stocks on March 1st = $3,323

Decrease value during February = $1,621

To find the decrease value during January.

Solution:

Let the decrease value in dollars during January be = [tex]x[/tex]

So, value of stocks in dollars on 1st February will be = [tex]8474-x[/tex]

So, value of stocks in dollars on 1st March will be = [tex]8474-x-1621[/tex]

So, we have

[tex]8474-x-1621=3323[/tex]

[tex]6853-x=3323[/tex]

Subtracting both sides by 6853.

[tex]6853-x-6853=3323-6853[/tex]

[tex]-x=-3530[/tex]

Multiplying both sides by -1.

∴ [tex]x=3530[/tex]

Thus, during January it decreased by $3,530.

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.

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:

They could make 14 full stacks

Step-by-step explanation:

All you need to is divided the 269 by the 18 cartons and it will equal 14.944444444

so that means only 14 full stacks and you can't round because that would not make sense

Answer:

Slope (m)

-0.2222

m = 2 / -9 = -0.222

Step-by-step explanation: