Determine if (4,1) is a solution for the system of equations. Explain answer

y = -x + 5
y = 2x - 7

The graph of the function and its inverse is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) = 3 + 2ln(x)

Express as an equation

So, we have

y = 3 + 2ln(x)

Swap x and  y in the above equation

x = 3 + 2ln(y)

Next, we have

2ln(y) = x - 3

Divide by 2

ln(y) = (x - 3)/2

Take the exponent of both sides

[tex]y = e^{\frac{x - 3}{2}}[/tex]

Next, we plot the graphs

The graph of the functions is added as an attachment

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Answer:

the radius of the cylinder is approximately 2.26 feet.

Step-by-step explanation:

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * radius^2 * height

Given that the volume is 400 feet, the height is 25 feet, and using π ≈ 3.14, we can rearrange the formula to solve for the radius:

400 = 3.14 * radius^2 * 25

Divide both sides of the equation by (3.14 * 25):

400 / (3.14 * 25) = radius^2

Simplifying:

400 / 78.5 ≈ radius^2

5.09 ≈ radius^2

To find the radius, we take the square root of both sides:

√5.09 ≈ √(radius^2)

2.26 ≈ radius

Rounding to the nearest hundredth, the radius of the cylinder is approximately 2.26 feet.

Answer:

Step-by-step explanation:

Volume Formula for a cylinder is  V=πr²h

Substitute the following:    400 = 3.14(r²)(25)

r=[tex]\sqrt{\frac{V}{\pi h} }[/tex]

r=[tex]\sqrt{\frac{400}{\pi 25} }[/tex]

r≈2.25676ft

Answer:

180 meters

Step-by-step explanation:

To find the perimeter of the actual swimming pool, you need to first find the length and width of the actual swimming pool by multiplying the length and width of the pictured swimming pool by the scale factor of 1200 cm.

Now that we know that the perimeter of the actual pool is 18000 centimeters, we need to convert that to meters! Keep in mind that:

Now we can divide 18000 by 100:

18000 cm ÷ 100 = 180 m

Therefore, the perimeter of the actual swimming pool is 180 m.

The values in the expression is as follows:

a = 2

b = 0

c = -1

The expression can be solve using the exponential law. Therefore,

g = 2³ × 3 × 7²

h = 2 × 3 × 7³

Therefore, let's solve the following:

g/h = 2ᵃ × 3ᵇ × 7ⁿ

Therefore,

g = 2³ × 3 × 7² = 2 × 2 × 2 × 3 × 7 × 7

h = 2 × 3 × 7 × 7 × 7

Hence,

g / h =  2 × 2 × 2 × 3 × 7 × 7 / 2 × 3 × 7 × 7 × 7

Hence,

g / h = 2 × 2 / 7

g . h = 2² × 3° × 7⁻¹

Hence,

a = 2

b = 0

c = -1

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The measure of the indicated arc angle is 134 degrees.

The angle subtended by the arc at the centre of the circle is the angle of the arc.

Therefore, the central angle of an arc is the angle at the centre of the circle between the two radii subtended by the arc.

Hence, the central angle is also known as the arc's angular distance.

Therefore, the measure of an arc is the measure of its central angle.

Hence, the measure of the indicated arc is 134 degrees.

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The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.

The integral of f(x) = ex - e with respect to x can be computed as follows:

∫[0, 2] (ex - e) dx

Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:

∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx

Integrating each term separately:

= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2

= (e2 - e0) - (e0 - e0)

= e2 - 1

The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

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Answer:

  B.  linear

Step-by-step explanation:

You want to know the type of function represented by the table of values ...

When the differences in x-values are 1 (or some other constant), the differences in y-values will tell you the kind of function you have.

Here, the "first differences" are ...

They are constant with a value of 4.

The fact that first differences are constant means the function is a first-degree (linear) function.

The table represents a linear function.

__

Additional comment

The function is y = 4x. That is, y is proportional to x with a constant of proportionality of 4.

The level at which differences are constant is the degree of the polynomial function. The differences of first differences are called "second differences," and so on. A cubic function will have third differences constant.

If differences are not constant, but have a constant ratio, the function is exponential.

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Answer:

Step-by-step explanation:

I cannot see the graphs.

The limit of the trigonometric expression is equal to 0.

In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:

[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]

Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:

[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]

Third, use known limits to determine the result:

0

The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.

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The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.

To complete the given number sequence, let's analyze the pattern and identify the missing terms.

Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:

The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.

Using this pattern, we can determine the missing terms as follows:

To obtain the third term, we add 2 to the second term:

7 + 2 = 9

To find the fifth term, we add 3 to the fourth term:

16 + 3 = 19

To determine the seventh term, we add 4 to the sixth term:

__ + 4 = 23

Therefore, the missing terms in the sequence are 9, 19, and 23.

By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.

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The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;

1. ΔAJK ~ ΔSWY according to the SAS similarity postulate

2. ΔLMN ~ ΔLPQ according to the AA similarity postulate

3. ΔPQN ~ ΔLMN

LM = 12, QP = 8

4. ΔLMK~ΔLNJ

NL = 21, ML = 14

Similar triangles are triangles that have the same shape but may have different sizes.

1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;

24/16 = 3/2

18/12 = 3/2

The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.

2. The ratio of the corresponding sides in each of the triangles are;

MN/LN = 8/10 = 4/5

PQ/LQ = 12/(10 + 5) = 12/15 = 4/5

The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule

3. The alternate interior angles theorem indicates;

Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;

ΔPQN ~ ΔLMN by the AA similarity postulate

LM/QP = (x + 3)/(x - 1) = 18/12

12·x + 36 = 18·x - 18

18·x - 12·x = 36 + 18 = 54

6·x = 54

x = 54/6 = 9

LM = 9 + 3 = 12

QP = x - 1

QP = 9 - 1 = 8

4. The similar triangles are; ΔLMK and ΔLNJ

ΔLMK ~ ΔLNJ by AA similarity postulate

ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)

ML/NL = LK/LJ = (24 - 8)/24

(24 - 8)/24 = (6·x + 2)/((7·x + 7)

16/24 = (6·x + 2)/(7·x + 7)

16 × (7·x + 7) = 24 × (6·x + 2)

112·x + 112 = 144·x + 48

144·x - 112·x = 32·x = 112 - 48 = 64

x = 64/32 = 2

ML = 6 × 2 + 2 = 14

NL = 7 × 2 + 7 = 21

MN = 2 + 5 = 7

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Answer:

BC = 24 units

Step-by-step explanation:

This is an isosceles triangle which always has:

In this triangle, the legs CA and BA are congruent so CA = BA and the angles C and B are congruent to each other so angle C = angle B.

Thus, we can find x by setting CA and BA equal to each other:

(3x - 15 = x + 33) + 15

(3x = x + 48) - x

(2x = 48) / x

x = 24

Thus, x = 24

Since the length of BC is x and x = 24, BC is 24 units long.

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

Step-by-step explanation:

a) To solve the equation tan θ = 1/√3, we can find the angle whose tangent is 1/√3 by taking the inverse tangent (arctan) of 1/√3.

θ = arctan(1/√3)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies tan θ = 1/√3 is approximately 30.0°.

b) To solve the equation 2cos θ = √3, we can isolate the cosine term by dividing both sides of the equation by 2.

cos θ = √3 / 2

Now, we can find the angle whose cosine is √3/2 by taking the inverse cosine (arccos) of √3/2.

θ = arccos(√3/2)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies 2cos θ = √3 is approximately 30.0°.

Step-by-step explanation:

Common difference , d, is  9

Sn = n/2 ( a1 + a33)                a33 = a1 + 32d = 2 + 32(9) = 290

S33 = 33/2 ( 2+290) = 4818

The measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.

The measure of the numbered angles is calculated by applying the following formula as follows;

Rhombus has equal sides and equal angles.

angle 2 = angle 57⁰ (alternate angles are equal)

angle 1 = 90⁰ (diagonals of rhombus intersects each other at 90⁰)

angle 3 = angle 4 (base angles of Isosceles triangle )

angle 3 = angle 4 = ¹/₂ x 90⁰

angle 3 = angle 4 = 45⁰

Thus, the measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.

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Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.

We need to follow these steps:

Calculate the discount on the Silverado:

Discount = 33% of $57,999

Discount = 0.33 * $57,999

Discount = $19,079.67

Subtract the discount from the original price of the Silverado:

Price after discount = $57,999 - $19,079.67

Price after discount = $38,919.33

Subtract Brianna's down payment from the price after discount:

Amount owed = Price after discount - Down payment

Amount owed = $38,919.33 - $15,670

Amount owed = $23,249.33

So, Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.

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Answer:

When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).

So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.

Answer:

A = [tex]\frac{4}{3}[/tex] π

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{120}{360}[/tex] ( r is the radius of the circle )

here r = FG = 2 with central angle = 120° , then

A = π × 2² × [tex]\frac{1}{3}[/tex]

  = [tex]\frac{4}{3}[/tex] π

Answer:

Let's denote the height of the triangle as "h" inches.

According to the given information, the base of the triangle is 3 inches more than two times the height. Therefore, the base can be expressed as (2h + 3) inches.

The formula to calculate the area of a triangle is:

Area = (1/2) * base * height

Substituting the given values, we have:

7 = (1/2) * (2h + 3) * h

To simplify the equation, let's remove the fraction by multiplying both sides by 2:

14 = (2h + 3) * h

Expanding the right side of the equation:

14 = 2h^2 + 3h

Rearranging the equation to bring all terms to one side:

2h^2 + 3h - 14 = 0

Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:

h = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the values are:

a = 2

b = 3

c = -14

Substituting these values into the quadratic formula:

h = (-3 ± √(3^2 - 4 * 2 * -14)) / (2 * 2)

Simplifying:

h = (-3 ± √(9 + 112)) / 4

h = (-3 ± √121) / 4

Taking the square root:

h = (-3 ± 11) / 4

This gives us two possible solutions for the height: h = 2 or h = -14/4 = -3.5.

Since a negative height doesn't make sense in this context, we discard the negative solution.

Therefore, the height of the triangle is h = 2 inches.

To find the base, we substitute this value back into the expression for the base:

base = 2h + 3

base = 2(2) + 3

base = 4 + 3

base = 7 inches

Hence, the base of the triangle is 7 inches and the height is 2 inches.

Step-by-step explanation:

-The answer for the height is 5.5 units.

-The base of the triangle is aproximately 2.5454 units.

To answer this problem, you have to set an equation with the information you're given. If you do it correctly, it should look like this:

7=1/2(3+2h)

-Now, you have to solve for h:

7=1.5+h

7-1.5=h

5.5=h

-Now that you have the height, you plug it in into the triangle area formula to solve for the base:

7=1/2(b)5.5

7=2.75b

7/2.75=b

b≈2.5454

-To make sure that the corresponding values for the base and height are correct, we plug the values in and this time we are going to solve for a(AREA):

A(triangle)=1/2(2.5454)(5.5)

A=1/2(13.9997)

A=6.99985 square units

-We round the result to the nearest whole number and we get our 7, which is the given value they gave us.

Answer:

52% used.

Step-by-step explanation:

13/25=52/100=52%

Answer:

In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg. So AC = 80√3.

In a 45°-45°-90° triangle, both legs are congruent. So BC = 80.

AB = AC - BC = (80√3 - 80) meters

= 80(√3 - 1) meters

= about 58.56 meters

The distance between points A and B is approximately 138.6 meters.

To find the distance between points A and B, we can use the concept of trigonometry and the given information.

Let's denote the distance between points A and B as x.

From point A, the angle of elevation to the top of the cliff at point D is 30°. This means that in the right triangle formed by points A, D, and the top of the cliff, the opposite side is the height of the cliff (80.0 m) and the adjacent side is x. We can use the tangent function to calculate the length of the adjacent side:

tan(30°) = opposite/adjacent

tan(30°) = 80.0/x

Simplifying the equation, we have:

x = 80.0 / tan(30°)

Using a calculator, we can find the value of tan(30°) ≈ 0.5774.

Substituting the value, we get:

x = 80.0 / 0.5774

Calculating the value, we find:

x ≈ 138.6 meters

In light of this, the separation between positions A and B is roughly 138.6 metres.

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The cafeteria can conclude that a majority of the senior high school students like the newly served snack.

To determine if more than 50% of the students like the newly served snack, we need to analyze the responses of the 60 randomly selected students.

Analyzing the responses:

Out of the 60 students surveyed, we have:

- Number of students who responded with "1" (liking the snack): 32 students.

- Number of students who responded with "0" (not liking the snack): 28 students.

To determine the percentage of students who liked the snack, we divide the number of students who liked it by the total number of students surveyed and multiply by 100: (32/60) * 100 = 53.33%.

Since the percentage of students who liked the newly served snack is 53.33%, which is greater than 50%, we can conclude that more than 50% of the students like the snack based on the given survey results.

Therefore, the cafeteria can conclude that a majority of the senior high school students like the newly served snack.

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Answer:

It's 7.81

Step-by-step explanation:

Answer:

KL = 6

Step-by-step explanation:

We see that the length of IL includes IJ, JK, and Kl and is 26.

Since IL = 26 and IJ + JK + KL = IL, we can subtract the sum of the lengths of IJ and Jk from IL to find KL:

IL = IJ + JK + KL

26  = 9 + 11 + KL

26 = 20 + KL

6 = KL

Thus, the length of KL is 6.

We can confirm this fact by plugging in 6 for KL and checking that we get 26 on both sides of the equation when simplifying:

IL = IJ + JK + KL

26 = 9 + 11 + 6

26 = 20 + 6

26 = 26

Thus, our answer is correct.

Answer:

f(x)=5/(x-6)

Step-by-step explanation:

f(x)=(5x-5)/(x^2-7x+6)

f(x)=[5(x-1)]/[(x-1)(x-6)]

f(x)=5/(x-6)

Answer:

x=50

Step-by-step explanation:

Make this equal to 180.

x+3x-35+x-35 = 180

5x = 180 + 70

5x=250

x=50