6. Hayes's dad is paying for a $50 meal. He has a
coupon for 25% off for the meal. After the discount,
a 6% sales tax is applied. What does Hayes's dad pay
for the meal?

Answer:

Find all solutions for x by breaking the absolute value into the positive and negative components.

x = 3, -2

Deven bought the two plants one month ago. We can check that Plant A has a height of 10 cm and Plant B has a height of 11 cm after one month, so they have the same height again.

In this problem, we will use the unitary method to find out how many months ago Deven bought two plants that have the same height again. We will apply the concept of uniform growth rate and solve for the unknown variable using algebraic equations.

First, we need to set up equations for the height of each plant as a function of time. Plant A grows at a uniform rate of 10 cm per month, so its height after t months is given by:

Height of Plant A = 10t

On the other hand, Plant B has a variable growth rate, where it grows by n centimeters in the nth month after purchase. We can use the sum of an arithmetic series formula to find its height after t months:

Height of Plant B = (1 + 2 + 3 + ... + t) = 1/2 x t x (t+1) x n

Now, we need to find the time t when the heights of the two plants are equal. We can set up an equation and solve for t using the unitary method. Let's write:

Height of Plant A = Height of Plant B

10t = 1/2 x t x (t+1) x n

Dividing both sides by t, we get:

10 = 1/2 x (t+1) x n

Multiplying both sides by 2/n, we get:

20/n = t+1

Subtracting 1 from both sides, we get:

t = 20/n - 1

This is the formula we need to find out how many months ago Deven bought the two plants. We know that both plants had the same height when they were purchased, so we can set their initial height to zero. Therefore, we can use the formula for Plant A to find out how many months it took for it to reach the height of Plant B at its current growth rate:

10t = 1/2 x t x (t+1) x n

Simplifying, we get:

20 = t x (t+1) x n

Substituting t = 20/n - 1, we get:

20 = (20/n - 1) x (20/n) x n

Simplifying, we get:

20 = 20 - n

Therefore, n = 0, which is impossible since Plant B has been growing every month since it was purchased. This means that Deven made a mistake and the two plants cannot have the same height again. Alternatively, we can use the formula for Plant B to check if there is a solution:

10t = 1/2 * t * (t+1) * n

Substituting t = 20/n - 1, we get:

10(20/n - 1) = 1/2 x (20/n - 1) x (20/n) x n

Simplifying, we get:

200/n - 10 = 100/n - 10/n

Multiplying both sides by n, we get:

200 - 10n = 100 - 10

Solving for n, we get:

n = 10

Substituting n = 10, we get:

t = 20/n - 1 = 1

To know more about unitary method here.

https://brainly.com/question/28276953

#SPJ4

Find all possible values of x that make the equation true. There is an infinite number of solutions since x can take on any numerical value from 0 to 9.

To solve this equation, start by adding the two terms with the same variable. 2x + 2x = 4x. Next, add 5 and 3x to both sides of the equation. 4x + 5 + 3x = 4x + 5 + 3x. The equation is now 4x + 3x + 5 = 4x + 3x + 5. Simplify the equation by combining the two terms with the same variable. 7x + 5 = 7x + 5. The equation is now balanced and there are no terms with a variable. This means that there is an infinite number of solutions for x since any number from 0 to 9 can be used to make the equation true.

Learn more about number here

https://brainly.com/question/13583801

#SPJ1

The expression that is equivalent to cos3x/sinx cosx is B.

secxcos2x- cscxsin 2x.

How to solve cos3x/sinx cosx?Given an expression cos3x/sinx cosx.

The goal is to simplify it using trigonometric identities.

We know that the quotient identity of tan x is:

tan x = sin x / cos x

We can convert the above equation as:

cos x / sin x = 1 / tan x

Similarly, cot x = cos x / sin x

We can convert the above equation as:

sin x / cos x = 1 / cot x

Now, we can use the above equations to simplify the given equation.

Simplify cos3x/sinx cosx

We have:

cos3x/sinx cosx= cos2x * cosx / sinx cosx

= cos2x / sinx + cos2x / cosx

= cos2x/sinx + cos x

And, we know that

cos 2x =\(1 - 2sin^2x\)

= \(2cos^2x - 1\)

Substituting this value in the above equation, we get:

cos3x/sinx cosx = (\(2cos^2x - 1\)) / sinx + cos x

= secxcos2x- cscxsin 2x

Therefore, the expression that is equivalent to cos3x/sinx cosx is B.

secxcos2x- cscxsin 2x.

To know more about trigonometric visit:

https://brainly.com/question/29156330

#SPJ11

Answer:

-18/3

Step-by-step explanation:

Multiply the denominator and numerator by the same whole number.

Answer:

9

Step-by-step explanation:

Let first find the width of the subintervals

\( \frac{4 - 0}{4} = 1\)

We are using MRAM, so we will be using the midpoint interval height as the height.

So for the first rectangle

The midpoint of interval [0,1] is 0.5

The midpoint of the second interval [1,2]=1.5

The midpoint of the third interval [2,3]=2.5

The midpoint of the fourth interval [3,4]= 3.5

So let's set up an equation

Using Riemann sums, we are adding up rectangle areas so we will use the midpoint height (since we are using MRAM) and delta x(which is 1)

\(r = f(0.5)(1) + f(1.5)(1) + f(2.5)(1) + f(3.5)(1)\)

We will then get an area of

\(9\)

That is the approximate area.

The real area is 9.333333, so this is close somewhat.

The answer is 9

Answer:

12^(3/2)

Step-by-step explanation:

(2x6)^3/2

2x6=12

12^3/2= 41.5692193817

y=6x+6 is the equation of the tangent line to the curve at point (0,6)

In order to fing the equation of tangent of any graph we need 2 things.

i . A point on the graph at which tangent need to be drawn.

ii . Slope a line on that point.

solpe of line = \(y^'\)  =\(\frac{d(y)}{dx}\)

=> d(6\(e^xcosx\))/dx

in order to differentiate the above equation we have to use by parts

=> 6(\(e^xcox-e^xsinx\))

finding the slope at point(0,6)

\(y^'\) = 6*(1*1-1*0)

=>6

so slope is 6

now equation of line with slope 6 and point (0,6)

=> y-6 = 6(x-0)

=> y = 6x+6

To know more about tangent line click on below link:

brainly.com/question/23265136#

#SPJ4

Answer:

23 + 11 = 34

Bobby descended 34 meters

Answer:

23 is an integer

another 11 is an integer

23+11 = 34

total depth descended is 34.

The small jar is a better value, as the price per gram is lower than the large jar. It costs approximately 0.0037 GBP per gram compared to 0.0035 GBP per gram for the large jar.

To determine which jar is the best value, we need to calculate the unit price per gram of jam for each jar. For the large jar, the unit price is 0.35 pence per gram (154p/440g), while for the small jar, the unit price is 0.37 pence per gram (126p/340g). Thus, the large jar provides a better value for money in terms of the cost per gram of jam.

In conclusion, based on the unit price per gram of jam, the large jar is the better value option between the two sizes.

Learn more about value evaluation here: brainly.com/question/29181699

#SPJ4

Answer:

1

Step-by-step explanation:

because you can only cut it in a certain way that both pieces are the same measurements

Answer:

x=12

Step-by-step explanation:

4x+16=64

to isolate x, take 16 from both sides

4x+ 16(-16)=64-16

4x=48

divide 4 on each side

4x/4=x

48/4=12

x=12

The solution of the equation 4x+16= 64 is x = 12.

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

For this case, we've to solve for x, the equation \(4x + 16 = 64\)

Subtracting 16 from both the sides:

\(4x + 16 - 16 = 64 - 16\\4x + 0 = 48\\4x = 48\)

4x is actually 4 times x, and is written in short, where the multiplication sign is hidden. This is usually done when variables like x,y are there.

Dividing both the sides by 4, we can get x on one side, and rest of the constant values on the other side.

\(\dfrac{4x}{4} = \dfrac{48}{4}\\\\1 \times x = 12\\x = 12\)

(since 1 times any number is that number itself, and as x represents a number, so we got 1 times x =x).

Thus, the solution of the equation 4x+16= 64 is x = 12.

Learn more about solving equations here:

https://brainly.com/question/13072448

ANSWER

P(A and B) = 1/2

EXPLANATION

By the Bayes Theorem we have a relationship between the given probabilities:

In this problem P(B) = 4/7 and P(A|B) = 7/8:

The rate of decrease of volume of the sphere when its diameter is 6 cm is -96π cubic cm/min.

Given that the snowball is a sphere, we can use the formula for the volume of a sphere.

The formula for the volume of a sphere is

V = 4/3 πr³

We need to find out the rate of decrease of volume when the diameter is 6 cm.

To find the rate of decrease of volume, we need to differentiate the above formula. Differentiating the above formula w.r.t. time, we get

dV/dt = 4/3 π(3r²)(dr/dt)

Where r is the radius of the sphere and dr/dt is the rate of change of the radius.

Let d be the diameter of the sphere. Then we can write,r = d/2

Also, given that dr/dt = -2cm/min

Substituting the values in the equation for the rate of decrease of volume,

dV/dt = 4/3 π(3(d/2)²)(-2) = -8π/3 d²

As the diameter of the sphere is 6 cm, d = 6 cm.Substituting the value in the equation above, we get

dV/dt = -8π/3 (6)² = -96π cubic cm/min

for such more question on volume

https://brainly.com/question/463363

#SPJ11

Answer:

145 degrees

Step-by-step explanation:

The largest exterior angle would be the one with the smallest interior angle, which is 35 And exterior and interior angles is always 180.

180 - 35 = 145 degrees

I need the brainliest

Answer:

145 degrees

Step-by-step explanation:

I don't want the brainleist.

The Riemann Hypothesis is a conjecture in mathematics that states that all non-trivial zeros of the Riemann zeta function lie on a specific line in the complex plane, known as the critical line.

This critical line is defined as the set of complex numbers with a real part equal to 1/2. Additionally, the hypothesis suggests that the only other zeros of the zeta function are the negative even integers.

The Riemann zeta function is an important mathematical function that arises in number theory and has connections to prime numbers. The Riemann Hypothesis has been a central problem in mathematics for over a century, and its truth or falsehood has significant implications for the distribution of prime numbers.

Despite extensive efforts, the hypothesis remains unproven, and its proof or disproof continues to be an active area of research.

Learn more about Hypothesis here:

https://brainly.com/question/32562440

#SPJ4

Residual analysis is crucial before constructing a second-order regression model, as it allows us to identify any violations of the assumptions of least squares regression.

By conducting this analysis, we can ensure the validity and reliability of our model before proceeding with further model building. Residual analysis involves examining the residuals, which are the differences between the observed values and the predicted values from the regression model. By assessing the residuals, we can evaluate the assumptions underlying least squares regression, such as linearity, independence, and constant variance of errors.

Residual analysis helps us detect potential violations of these assumptions. For example, if the residuals exhibit a systematic pattern or curvature, it suggests that the relationship between the predictors and the response is nonlinear, indicating a need for a more complex model like a second-order polynomial. Additionally, if the residuals show heteroscedasticity (varying spread) or autocorrelation (dependence between residuals), the assumptions of constant variance and independence may be violated.

By conducting residual analysis before building the complete second-order model, we can identify these violations and take appropriate actions. This might involve transforming variables, adding interaction terms, or considering alternative modeling approaches. Residual analysis provides valuable insights into the data and guides the model-building process to ensure the resulting model is appropriate for the underlying relationships.

To learn more about residual click here:

brainly.com/question/31857773

#SPJ11

Answer:

208

Step-by-step explanation:

the formula is:

2*(width*lenght+height*lenght+height*width)

2*(6*8+4*8+4*6)

208

Answer:

\( \: \)

Step-by-step explanation:

In the given figure, it is given a net of cuboid where, the length is 8m, the breadth is 6m and the height is 4m and we have to find the surface area of the cuboid.

So, the formula for finding the surface area is ;

\(\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: Surface\: area_{(cuboid)}=2(lb + bh + lh )}}}}}} \: \: \bigstar \\ \\\)

Now, we'll substitute the values in the formula :

\(\\{ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(8.6 + 6.4 + 8.4 }}}}}}) \: \: \\ \\\)

\({ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(48 + 24 + 32 }}}}}}) \: \: \\ \\\)

\({ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(104 }}}}}}) \: \: \\ \\\)

\({ \longrightarrow \qquad{ { \pmb{ \frak{ { \: Surface\: area_{(cuboid)}=208 }}}}}}\: \: \\ \\\)

Therefore,

Answer:

y = -2/3x - 3

Step-by-step explanation:

y = mx + b

m = slope

(-3,-1) = (x,y)

Plus in the coordinates

-1 = -2/3(-3) + b

negative times negative = positive

-2/3 * -3 = 2

-1 = 2 +b

Use inverse operations

-2 --2

-3 = b

y = -2/3x - 3

Answer:

y = -2/3 x - 3

Step-by-step explanation:

since you have a point and a slope, you can use point - slope form

Answer:

A. T= S+I

B. T= 325m+ 3600

C. T= 11,400

Step-by-step explanation:

Answer:

Well give the other person brainiest because his or hers answer was a good a better answer than mines so give him brainiest  answer the question because i do not know this answer

Step-by-step explanation:

sorry for not answering.

The value of the given expression is found as: `1/tan0sec0 - 1/sin0cos0 + sec²0tan0 = sin0cos0` using the reciprocal identity.

a) We know that `1 - cos²0 = sin²0`.

Divide both sides by `cos²0` to get

`1/cos²0 - 1 = sin²0/cos²0`.

From the identity `sec²0 = 1/cos²0`, we get

`sec²0 - 1 = sin²0/cos²0`.

Now we can rewrite the given expression as `1/tan²0 = sec²0/csc²0 - 1`,

which simplifies to `(sec²0 - csc²0)/csc²0`.

Next, we use the Pythagorean identity `sec²0 = 1 + tan²0` and the reciprocal identity `csc0 = 1/sin0` to rewrite the expression as

`(1 + tan²0)/csc²0 - 1/csc²0`.

Combining the two terms over a common denominator, we get

`(1 + tan²0 - sin²0)/sin²0`.

Since `sin²0 + cos²0 = 1`, we have `sin²0 = 1 - cos²0`.

Substituting this into the expression gives `(1 + tan²0 - (1 - cos²0))/ (1 - cos²0)`, which simplifies to

`cos²0/(1 - cos²0)`.

We know that

`sec²0 - 1 = tan²0` so `sec²0 = tan²0 + 1`.

Substituting this into the expression gives

`(tan²0 + 1)/(1/sin²0) - 1/sin²0`,

which simplifies to `(tan²0 + 1 - 1)/sin²0`.

Finally, we get `tan²0/sin²0 = 1/tan²0`.

Therefore, `1/tan²0 = 1/tan²0`.

b) We know that

`1 + cos0 = sec0/cos0`

0

, so

`cos0 = (sec0 - 1)/sec0`.

Substituting this into the given expression gives

`(1/tan0)((sec0 - 1)/sec0)`, which simplifies to `(sec0 - 1)/(sec0tan0)`.

We also know that `tan0 = sin0/cos0`,

so

`sec0tan0 = sec0(sin0/cos0)

= (sin0/cos0)(1/cos0)

= sin0/cos²0`

.Substituting this into the expression gives

`(sec0 - 1)/(sin0/cos²0) = cos²0(sec0 - 1)/sin0`

.We know that

`1 + cot²0 = csc²0`, so `cot²0

= csc²0 - 1`.

Substituting this into the expression gives

`cos²0(sec0 - 1)/(1 + csc²0 - 1)`.

We know that

`csc0 = 1/sin0`,

so `csc²0 = 1/sin²0`

.Substituting this into the expression gives

`cos²0(sec0 - 1)/(1/sin²0)`,

which simplifies to `cos²0(sin²0)(sec0 - 1)`.

Since `1 - cos²0 = sin²0`, we have

`sec0 - 1 = tan²0/sec0`.

Substituting this into the expression gives

`cos²0(sin²0)(tan²0/sec0)`.

Using the Pythagorean identity `1 + tan²0 = sec²0`

and the reciprocal identity `cos0 = 1/sec0`, we can rewrite the expression as `cos0sin0`, which is equal to `sin0cos0`.

Know more about the reciprocal identity.

https://brainly.com/question/24156465

#SPJ11

Based on the test by result, Alex did better in the test by scoring 66.67%

Percentage scored by Alex = 40/60 × 100

= 0.66666666666666 × 100

= 66.6666666666666

= 66.67%

Therefore, Alex did better in the test

Learn more about percentage:

https://brainly.com/question/843074

#SPJ1

Let's solve for x by factoring this quadratic equation.

We first need to determine which two numbers multiply to -28 (c) but add to 3 (b).

The two numbers that multiply to -28 and add to 3 are 7 and -4.

Therefore, we can factor this equation like so:

Now, we can set this equation to 0 and solve for x.

If we look at each factor individually, we can determine the values of x:

Subtract 7 from both sides of the equation.

Now, let's look at the other factor:

Add 3 to both sides of the equation.

The solution of x^2 + 3x - 28 is x = -7, x = 4.

The value of α for which the system has a center as its critical point is α = -3.

The given system of equations is:

x₁' = αx₁ + 2x₂

x₂' = -3x₁ + 2x₂

To find the critical points, we set the derivatives equal to zero:

αx₁ + 2x₂ = 0

-3x₁ + 2x₂ = 0

From the first equation, we can solve for x1 in terms of x₂:

x₁ = (-2x₂) / α

Substituting this expression into the second equation:

-3((-2x₂) / α) + 2x₂ = 0

(6x₂ / α) + 2x₂ = 0

Multiplying through by α:

6x₂ + 2αx₂ = 0

Factoring out x₂:

6 + 2α) x₂ = 0

For x₂ to be nonzero, the term (6 + 2α) must be zero:

6 + 2α = 0

Solving for α:

2α = -6

α = -3

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ4

The value of the odds of pulling a red marble is equivalent to 1/9 from an urn filled with marbles of various colors.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

By definition, the theoretical probability is equal to the ratio of the favorable event to the total number of events.

Given that:

The probability of pulling a red marble at random is 1/10

Probability of not pulling red marble is = 1-(1/10)= 9/10

The odds of pulling red marble is (1/10)/(9/10)

The probability of odds of pulling red marble is 1/9.

To learn more about probability visit: https://brainly.com/question/14069444

#SPJ4

Answer:

$2.24 per Gallon

Step-by-step explanation:

36.96 divided by 16.5 is 2.24, then to check that multiple 2.24 by 16.5 and you get the total cost of 36.96. Hope this helps.

Step-by-step explanation:

Two angles are called supplementary when their measures add up to 180 degrees.

<ADB + <BDC = 180°

IT'S seen that BOTH ADB and BDC are 90 degrees

90+90= 180