WILL GIVE BRAINLIEST IF ANSWERED WELL!!!

Answer:

x = 1

Step-by-step explanation:

If you plug in 1 in both equations you will get 3 as your answer as it is the intersection of those two functions.

Answer:

9

Step-by-step explanation:

8x-13=5x+14

you subtract 5x from both sides and get

3x-13=14

then add 13 to both sides  and get

3x=27

then divide 3 from both sides

3/3=x

27/3=9

x=9

Answer:

x = 9

Step-by-step explanation:

8x - 13 = 5x + 14                                                                                                                                Subtract 5x from both sides of the equation                                                                    3x - 13 = 14                                                                                                                          Add 13 to both sides of the equation                                                                            3x = 27                                                                                                                                     Divide by 3 for both sides of hte eqation                                                                        x = 9

The value of dz/dt, using the chain rule, is (-3t^2 + 7t + 12)e^(3t). (The expression is obtained by substituting the given values and differentiating with respect to t using the chain rule.)

We are given:

z = (x + y)e^x

x = 3t

y = 4 - t^2

To find dz/dt, we need to differentiate z with respect to t using the chain rule. Let's substitute the given expressions into z:

z = ((3t) + (4 - t^2))e^(3t)

Now, we differentiate z with respect to t, applying the chain rule:

\(dz/dt = (d/dt)((3t + 4 - t^2)e^(3t))\)

\(= ((3 + (-2t))e^(3t)) + ((3t + 4 - t^2)(d/dt)(e^(3t)))\)

\(= (3 - 2t)e^(3t) + (3t + 4 - t^2)(3e^(3t))\)

\(= (3 - 2t)e^{(3t)} + 3(3t + 4 - t^2)e^{(3t)\)

\(= (3 - 2t + 9t + 12 - 3t^2)e^(3t)= (-3t^2 + 7t + 12)e^(3t)\)

Therefore, dz/dt is given by (-3t^2 + 7t + 12)e^(3t) based on the given values and applying the chain rule.

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The slope of the required line is -2 and the y-intercept of the required line is -10, giving the equation of the required line as \(y = -2x - 10.\)

Given the equation of the line: r - 2y = 5.Since the equation is not given in the form y = mx + b, we have to convert it to that form. Therefore, r - 2y = 5⇒ r = 2y + 5.Dividing both sides of the equation by 2, we get, y = (1/2)r - 5/2Comparing the given equation with y = mx + b, we get m = 1/2, b = -5/2.

Now, the given line is: y = (1/2)r - 5/2Since we need to find the equation of the line that is perpendicular to the given line, we need to find the slope of the line that is perpendicular to the given line. The slope of the given line is m = 1/2. The slope of the line that is perpendicular to this line is the negative reciprocal of 1/2.

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The values of the constants in the equation A = 6, B = -5, C = -3.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The variable in the equation 3 = –6n + 5 is n.

when written in the form An + B = C

Then 3 = –6n + 5

6n - 5  = -3

A = 6

B = -5

C = -3.

Hence, the values of the constants in the equation A = 6, B = -5, C = -3.

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A) The type of function that can be used to describe the value of the investment after a fixed number of years using option 1 and option 2 are respectively; Linear Function and Exponential function.

B) One function for each option to describe the value of the investment f(n), in dollars, after n years.;

Option 1; f(n) = n + 100

Option 2; f(n) = n + 100x

C) The amount from option 1 after 20 years would be 3000 and the amount from option 2 after 20 years would be 4900

A) For option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This reason is that, in option one, the amount increases by a fixed amount every year.

For option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. The reason is that, in option 2, the amount increase is higher than the previous year.

B) For option 1, the function is;

f(n) = n + 100

For option 2, the function is;

f(n) = n + 100x

C) After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference of 1900.

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Answer: Cube has more volume

Step-by-step explanation:

Volume of a cube = length³

= 8³ inch

= 512 inch³

Volume of cone = 1/3πr²h

= 1/3 × 3.14 × 4² × 8

= 133.97 inch³

Therefore, the cube has more volune

Answer:

37.24

Step-by-step explanation:

ok so there's a strategy I got taught ready?

100%- 96.

38%-x

~cross multiply~

100x= 3724

÷100      ÷100

________________

x=37.24

Hope this helps :D   p.s- i recommend using this strategy :D

Answer:

38.96

Step-by-step explanation:

Ok so its hard to explain but 38% u move the percent sign 2 times to the left and then u get 38. then u put 96 as the decimal there it is!

The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.

To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.

These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.

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The level of confidence used by the pollsters is 51%.

The level of confidence that the pollsters used can be calculated from the information given as follows:

Margin of error:2%

Sample size:4134 adults

Approval rating:54%

To get the level of confidence the pollsters used, you can utilize the formula:

Margin of error (ME) = z-score × Standard deviation (σ) ÷ √Sample size,

where z-score can be obtained from the z-table or calculator.

Since the formula above is for a two-tailed test, we need to divide the margin of error by 2 to obtain one tail margin of error (ME).

2% ÷ 2 = 0.01 (one-tail margin of error)

We want to find the z-score. So, we rearrange the formula above to give us:

Z-score = (Margin of error × √Sample size) ÷ Standard deviation

Z-score = (0.01 × √4134) ÷ 1.96 ≈ 0.03

Now we look up the z-table to find the level of confidence that corresponds to a z-score of 0.03, which is approximately 0.51 or 51%.

Therefore, the pollsters used a level of confidence of 51%.

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Assuming the amount of ingredients given are enough to make one batch, and the chef had enough celery and garlic.

We can see : For one batch to be made, 2 cups of onions and 3 cups of carrots are used.

-> 5 cups combined.

Since a total of 20 cups of the same ingredients were used, we can deduce the number of batches the chef made by dividing it by 5.

-> 20 : 5 = 4 (batches)

Answer:

0

Step-by-step explanation:

So we have the equation:

\(3(x+14)=42\)

Divide both sides by 3:

\(x+14=14\)

Subtract 14:

\(x=0\)

The value of x is 0

Answer: x=0

Step-by-step explanation:

Given

3(x+14)=42

Distributive property

3x+42=42

Subtract 42 from both sides

3x=0

Divide 3 on both sides

x=0

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

Given

3(x+14)=42

Divide 3 on both sides

x+14=14

Subtract 14 on both sides

x=0

Both ways are fine

Hope this helps!! :)

Answer:

6 + 3x

Step-by-step explanation:

3 * 2 and 3 *x

= 6 + 3x

you can not break that down any farther so it stays at "6 + 3x".

Hope this helps!

Answer:

3(2 + x) = 0

6 + 3x = 0

3x = -6

x = -6/3

x = -2

Hope this help. Do vote me for this. Thanks.

Exterior angle theorem and properties of the isosceles triangles are used

prove the specified relations.

Correct responses:

9. ΔPAT ~ ΔPTB by AA similarity postulate

15. \(\overleftrightarrow{HM}\)║\(\overleftrightarrow{JK}\) by basic proportionality theorem

9. A two column proof is presented as follows;

Statement \({}\)                                     Reasons

1. ∠PTA = ∠B \({}\)                           1.  Given

2. ∠PAT = ∠ATB + ∠B  \({}\)           2.  Exterior angle of a triangle theorem

3. ∠BTP = ∠ATB + ∠PTA \({}\)        3   Angle addition postulate

4. ∠BTP = ∠ATP + ∠B \({}\)             4.  Substitution property of equality

5. ∠PAT = ∠BTP \({}\)                      5.  Substitution property

6. ΔPAT ~ ΔPTB \({}\)                      6. AA similarity postulate

The Angle-Angle, AA, similarity postulate states that two triangles are similar if two angles in one triangle are each equal to two angles in the other triangle.

15. A two column proof is presented as follows;

Statement                        \({}\)                         Reasons

\(\displaystyle 1. \hspace{0.3 cm} \frac{GJ}{HK} = \frac{GK}{GM}\)                            \({}\)          1.  Given

2. ∠1 ≅ ∠G                          \({}\)                   2. Given

3. ΔKHG is an isosceles triangle\({}\)         3. Definition

4. HK = HG \({}\)                                            4. Legs of an isosceles triangle

\(\displaystyle 5. \hspace{0.3 cm} \frac{GJ}{HG} = \frac{GK}{GM}\)              \({}\)                         5. Substitution property

6. \(\overleftrightarrow {HM}\) ║ \(\overleftrightarrow{JK}\)                      \({}\)                    6. BPT, Basic Proportionality Theorem

Basic Proportionality Theorem, BPT, states that if a line parallel to one of the sides of a triangle, intersects the other two sides, then the line divides the other two sides in the same proportion.

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Answer: ..

Step-by-step explanation:

Wed: 0%

Thu: 30%

Fri: 50%

Sat: 80%

Sun: 100%

I got these answers by taking 100, and subtracting the rain percentage from it. For instance, if it was a 45% to rain, and a unknown amount for it to not rain, I would take 100 and subtract 45 from it, resulting in a 55% chance of it not raining.

The actual elevation of the Zambales Mountain Range relative to the ellipsoid is 1870m.

To calculate the actual elevation of the Zambales Mountain Range relative to the ellipsoid, we need to consider the given elevation referenced to the local geoid and the offset value between the geoid and the ellipsoid height.

The given elevation of the Zambales Mountain Range is 1790m, referenced to the local geoid.

The offset value between the geoid and the ellipsoid height is +80m. This means that the geoid height is 80m higher than the ellipsoid height.

To calculate the actual elevation of the mountain range relative to the ellipsoid, we add the elevation referenced to the geoid and the offset value: 1790m + 80m = 1870m.

Note: The offset value accounts for the difference between the geoid and the ellipsoid, ensuring that the elevation is calculated accurately with respect to the reference frame used for the given elevation.

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Positive 37,000 feet.

Step-by-step explanation:

In linear regression, the variance around the regression line represents the variability of the dependent variable (response variable) that is not explained by the regression model.

It measures the dispersion of the actual data points around the predicted values from the regression line.

The variance around the regression line can vary with different values of the predictor variable. This is because the relationship between the predictor variable and the response variable may not be constant across the entire range of the predictor variable. In other words, the spread or dispersion of the data points around the regression line may change as the predictor variable changes.

By examining the residuals (the differences between the observed values and the predicted values from the regression line) and calculating their variances, you can assess the variability of the data points around the regression line. This variability is an important aspect of understanding the goodness of fit of the regression model and the accuracy of the predictions.

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Let's assume the sum of the scores of the 28 students who took the test yesterday is 28 * 72 = 2016.

We know that the sum of the scores of all 30 students is (28 * 72) + x + y, where x and y are the scores of the two students who took the test this morning.

We also know that the mean of all 30 scores is 73. So we can write an equation:

[(28 * 72) + x + y]/30 = 73

Multiplying both sides by 30, we get:

2016 + x + y = 2190

So, x + y = 174.

We are given that the difference of the two scores is 22, so we can write another equation:

y - x = 22

Solving these two equations simultaneously, we get y = 98 and x = 76.

Therefore, the lower score from this morning is 76.

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Answer:

Points (0,0) and (1,-3) form a line that represents a proportional relationship.

Step-by-step explanation:

A proportional relationship is one in which the ratio of x and y is always the same.  (x/y) or (y/x) equals a constant, k.

Such a relationship will result in a straight line, if graphed.  In a linear equation such as y = 2x, it can be seen that the ratio of y/x will always be 2 (or (1/2) for x/y).

But the straight line must go through the origin (0,0).  If not, the relationship in no longer a constant, since the value of the y-intercept (b in y=mx+b) will cause deviations to a constant ratio of x and y.

See the attached graph.  All points are marked, and equations for the lines connecting them are also plotted.  Only the first set of points (0,0) and (1,-3) line on a straight line (Green line)with an intercept of (0,0),  The other lines either have an intercept (Purple and Yellow) or have no relationship (Red Line:  y is always equal to 2, regardless of the value of red)

The probability that the baseball player has exactly 3 hits in his next 7 at-bats can be calculated using the binomial probability formula.

To calculate the probability, we need to consider the player's batting average, which is the probability of getting a hit in a single at-bat. In this case, the batting average is 0.315, which means that the player has a 31.5% chance of getting a hit in each at-bat.

Since we want to find the probability of getting exactly 3 hits in 7 at-bats, we can use the binomial probability formula:

\(P(X = k) = C(n, k) * p^k * (1-p)^(^n^-^k^)\)

Where:

P(X = k) is the probability of getting exactly k hits,

C(n, k) is the combination formula for choosing k hits out of n at-bats,

p is the probability of getting a hit in a single at-bat,

and (1-p) is the probability of not getting a hit in a single at-bat.

Substituting the values into the formula, we have:

\(P(X = 3) = C(7, 3) * 0.315^3 * (1-0.315)^(^7^-^3^)\)

Calculating the values, we find the probability that the player has exactly 3 hits in his next 7 at-bats.

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The probability of drawing a red 7 and black face card is P ( A ) = 1/221

Given data ,

Let the probability of drawing a red 7 and black face card be P ( A )

Now , the compound probability is given by\

The number of red 7 cards = ( red of diamonds 7 + red of hearts 7 )

Probability of drawing a red 7 = 2/52

Now , the card is not replaced , so the total number of remaining cards = 51

And , number of black face cards = 6

Probability of drawing a black face card = 6/51

So , P ( A ) = 2/52 ( 6/51 )

P ( A ) = 12 / 2652

On simplifying , we get

P ( A ) = 1/221

Hence , the probability is P ( A ) = 1/221

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Answer:

The volume of the stacks is the total space occupied by the disks

Hope this helps!!!

Answer:

165°

..

..

..

..

..

..

.............

The first 3 non-zero terms only \(x^4 e^{-x/2} = x^4.\)

We can use the Maclaurin series for the trigonometric functions and exponential function to obtain the Maclaurin series for the given functions.

Here are the solutions:

\(f(x) = cos(7x^4)\)

The Maclaurin series for cosine is:

\(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Substituting 7x^4 for x, we get:

\(cos(7x^4) = 1 - (7x^4)^2/2! + (7x^4)^4/4! - (7x^4)^6/6! + .....\)

Simplifying, we get:

\(cos(7x^4) = 1 - 49x^8/2! + 2401x^16/4! - 117649x^24/6! + ...\)

The first three non-zero terms are:

\(cos(7x^4) ≈ 1 - 24.5x^8 + 168.1x^16 - 2042.5x^24 + ...\)

f(x) = sin(-πx)

The Maclaurin series for sine is:

\(sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...\)

Substituting -πx for x, we get:

\(sin(-\pi x) = -\pi x + (-\pi x)^3/3! - (-\pi x)^5/5! + (-\pi x)^7/7! -......\)

Simplifying, we get:

\(sin(-\pix) = -\pi x + \pi ^3 x^3/3! - \pi^5 x^5/5! + \pi^7 x^7/7! - ...\)

The first three non-zero terms are:

\(sin(-\pi x) \approx -\pi x + 5.17\pi ^3 x^3 - 10.8\pi ^5 x^5 + 14.7\pi ^7 x^7 - ...\)

\(f(x) = tan^-1(4x)\)

The Maclaurin series for the arctangent function is:

\(tan^-1(x) = x - x^3/3 + x^5/5 - x^7/7 + ...\)

Substituting 4x for x, we get:

\(tan^-1(4x) = 4x - (4x)^3/3 + (4x)^5/5 - (4x)^7/7 + .....\)

Simplifying, we get:

\(tan^-1(4x) = 4x - 64x^3/3 + 1024x^5/5 - 16384x^7/7 + ...\)

The first three non-zero terms are:

\(tan^-1(4x) \approx 4x - 21.33x^3 + 163.84x^5 - 1866.28x^7 + ...\)

\(f(x) = x^4 e^{-x/2}\)

The Maclaurin series for the exponential function is:

\(e^x = 1 + x + x^2/2! + x^3/3! + ...\)

Substituting -x/2 for x and multiplying by\(x^4\), we get:

\(x^4 e^{-x/2} = x^4 (1 - x/2 + x^2/2! - x^3/3! + ...)\)

Expanding the product, we get:

\(x^4 e^{-x/2} = x^4.\)

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Answer:

17.5

Step-by-step explanation:

let 'x' = each congruent side

let '2x - 7' = side of base

x + 2x - 7 = 63

3x = 70

x = 17.5

It gradually decreases as alcohol is metabolized. The function C(t)=0.135 t e^{-2.802 t}models the mean BAC measured in g/mL.

The maximum average BAC during 3 hours is 0.0001358 g/mL.

f(t) = α t e−βt --(1)

Let's rewrite this in a simple form:

f(t)= α eˡⁿ ᵗ e⁻βt = αe^(ln t −βt)

Since e^x is strictly increasing and it will be maximized exactly when its argument is maximized, so we can maximize instead:

g(t)=ln t −βt

differentiating with respect to t , and g'(t) = 0

g′(t)=1/t − β = 0

=> t =1/β

we have given a function

C(t)=0.135 t e⁻²·⁸⁰²ᵗ

if we compare it with (1) we get

β = 2.802, 0.135 = α

For it's maximized we need to check the second order condition, and that of g will differentiate again , g′′(t)= −1/t² < 0

We have to compute the derivative of C(t):

C′(t) = 0.135 t⋅(−2.802)e⁻²·⁸⁰²ᵗ + 1.35e⁻²·⁸⁰²ᵗ

For optimum at t₀ if C′(t₀)=0 and C′′(t₀)≠0. Here, we have

C′(t₀) = 0.135t₀⋅(−2.802)e⁻²·⁸⁰²ᵗ₀+ 0.135e⁻²·⁸⁰²ᵗ₀ =e⁻²·⁸⁰²ᵗ₀(−0.135* 2.802t₀+ 0.135)=0

It is clear that e⁻²·⁸⁰²ᵗ₀ not equal to zero for all t₀∈R, so that

=> −0.135* 2.802t₀+0.135=0

=> t₀ = 1/2.802 ≈0.36

let us consider t is in hours, so that it makes t₀ =0.36h≈21.41min. This is the only optimum and one should verify it is indeed a maximum, i.e. C′′(t₀)<0.

Now, easily compute the maximum average BAC, which is C(t₀)=C(0.36) = 0.135 (0.36)e⁻²·⁸⁰²⁽⁰·³⁶⁾

= 0.0486(0.3678) = 0.01787508

Hence, the maximum average BAC, is 0.017 g/dL.

Maximum average BAC during the first 3 hours,

t = 3 , C(t)=C(3) = 0.135 (3)e⁻²·⁸⁰²⁽³⁾ = 0.0001358 g/mL

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As per the law of sine, the value of ∠ABC is 13°

Law of sine:

In math, the law of sine refers the relationship between the sides and angles of non-right (oblique) triangles.

Given,

Triangle ABC is drawn with AB = 3.6 units. BC = 4.2 units, and BCA = 28°. Here we need to find the measure of ∠ABC.

According to the law of sine, the given measures of the given triangle  are written as,

=> sin 28°/4.2 = sin x°/3.6

Apply the value of sin 28° = 0.27, then we get,

=> 0.27/4.2 = sin x/3.6

=> 0.972/4.2 = sin x

=> sin x = 0.2314

=> x = sin⁻¹(0.2314)

=> x = 13°

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The absolute maximum and absolute minimum of the function f(x) = -6x³ + 9x² + 108x on the interval [-5, 5] are (3, 540) and (-2, -174), respectively.

First, we must differentiate the given function to find its critical points.

f(x) = -6x³ + 9x² + 108x

Now, let's take the derivative of this function:

f'(x) = -18x² + 18x + 108

To find the critical points, we need to solve for

f'(x) = 0

:0 = -18x² + 18x + 108

0 = -2x² + 2x + 12 (dividing by -9)

0 = x² - x - 6 (dividing by 2)

0 = (x - 3)(x + 2)

So, the critical points within the given interval are x = -2 or x = 3.

Now, we need to check the endpoints as well. i.e., when x = -5 and

x = 5f(-5) = -6(-5)³ + 9(-5)² + 108(-5)

= -1860f(5)

= -6(5)³ + 9(5)² + 108(5)

= 1740

Therefore, the absolute minimum value is at (-2, -174), and the maximum is at (3, 540). Therefore, the absolute maximum and absolute minimum of the function f(x) = -6x³ + 9x² + 108x on the interval [-5, 5] are (3, 540) and (-2, -174), respectively.

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