Problem List Previous Problem Next Problem = (1 point) An alternating current E(t)=120sin(12t) has been running through a simple circuit for a long time. The circuit has an inductance of L=0.31 henrys, a resistor of R=7ohms and a capacitor of capcitance C=0.029 farads. What is the amplitude of the current I?

The vertical displacement of the mule comes out to be the difference between the final and the initial position which is 1190 m.

The displacement refers to the distance between the final and the initial position of an object. It is the shortest distance between these points is the displacement of the object. It is a vector quantity.

Vector quantity refers to the measurement in which both magnitude and direction are considered.

Starting point = 1290 m

Final point = 2480 m

Displacement = 2480 - 1920

= 1190 m

1190 m is the vertical displacement of the mule when traveling from one post to another.

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The question is in Spanish and when translated to English, it is:

On a mule trip to Duarte Peak, the rider observes a post 1,290 m above sea level, after 5 hours of walking he pays attention to another post that indicates 2,480 m above sea level. What has been its displacement in the vertical direction?

Answer:

0.8660

Step-by-step explanation:

sin24=opposite ÷hypotenus

sin24=opposite ÷5

cross multiply

sin24x5=opposite

sin24=0.4067x5

opposite =0.8660

Answer:

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

Given:

(i) We know 60 out of 110 can speak both languages, so as 60 out of 85. The number 60 is counted twice if we add them together.

Find the number of those speak either language:

(ii) Find the number of thise who can talk neither of these languages:

The car model that is least likely to have a brake failure is model d, and the probability of brake failure for this model is 0.0029%.

The given table provides the probabilities of brake failure for different car models. We need to identify the car model that has the lowest probability of brake failure and the corresponding probability.

From the table, we can see that the probability of brake failure is the lowest for model d, which is 0.0029%. To find this, we simply need to compare the probabilities given in the table and identify the smallest one.

It's worth noting that the total probability of brake failure across all car models is 0.0048%, which means that the probability of brake failure for any individual car model is quite low.

To express this in a more tangible way, we could say that out of 1000 new cars of model d, we can expect only about 2 or 3 to have brake failure. The low probabilities of brake failure suggest that new cars in general are quite safe and reliable when it comes to braking performance.

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The surface area of the pyramid is 390.8 cm².

The surface area of the triangular pyramid is calculated as follows;

S.A = base area   +  ¹/₂ (perimeter + slant height)

The height of the pyramid is calculated by applying Pythagoras theorem;

h = √ (28²  -  14²)

h = 24.2 cm

Area of the base = ¹/₂ x 28 cm x 24.2 cm = 338.8 cm²

The surface area of the pyramid is calculated as follows;

S.A = 338.8 cm²  + ¹/₂ (76 cm + 28 cm)

S.A = 390.8 cm²

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Answer:

1,425

Step-by-step explanation:

I got this one correct

the measurement of the couch in the scale drawing would be 15 inches.

We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.

When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.

When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.

When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.

One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.

You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.

To determine the measurement of the couch in the scale drawing, we can use the scale factor provided:

1/4 inch = 2 feet

This means that every 1/4 inch in the drawing represents 2 feet in real life.

To find the measurement of the couch in the drawing, we need to convert its actual size to the corresponding size in the drawing using the scale factor.

First, we can convert the actual size of the couch to feet:

10 ft = 10 ft x 12 inches/ft = 120 inches

Next, we can use the scale factor to convert the actual size to the corresponding size in the drawing:

1/4 inch = 2 feet

1 inch = 8 feet (multiplying both sides by 4)

So, 120 inches in real life is equal to:

120 inches / 8 feet per inch = 15 inches in the drawing

Therefore, the measurement of the couch in the scale drawing would be 15 inches.

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Using given function 9(x) = ln(3x+11), gl (x) B) 3(-3x + 11)^-1.

We are given 9(x) = ln(3x+11) and we need to find gl(x).

First, we can use the chain rule to differentiate ln(3x+11):

d/dx [ln(3x+11)] = 1/(3x+11) * d/dx [3x+11] = 3/(3x+11)

Now, we can use the given equation 9(x) = ln(3x+11) to find d/dx [9(x)]:

d/dx [9(x)] = d/dx [ln(3x+11)] = 3/(3x+11)

Therefore, gl(x) = d/dx [9(x)] / 3(x) = 3/(3x+11) * 1/3 = (3(-3x+11))^-1.

Therefore, the correct answer is B) 3(-3x+11)^-1.

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The value of the variables are a = 1 and b = -1

Given that the equations are;

a - 3 = 2b

4a + 5b- 8 = 0

Using the substitution method, we have;

Make 'a' the subject of formula from equation (1)

a = 2b + 3

Now, substitute the value of the variable in the second equation

4(2b + 3) + 5b - 8 = 0

expand the bracket, we have;

8b + 12 + 5b - 8 = 0

collect the like terms, we get;

8b + 5b = 0 - 5

add or subtract the values

5b = -5

b = -1

Substitute the value of b as =-1

a = 2(-1) +3

expand the bracket

a = -2 + 3

a = 1

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Answer:

40.7, my answer needs to be 20+ characters sooo....

As per the growth function, the value of the quantity after 97 years would be $67,458.85.

In your problem, you have a quantity with an initial value of 8200 that grows continuously at a rate of 0.55% per decade. To find the value of the quantity after 97 years, we can use the following growth function:

A(t) = A₀[tex]e^{kt}[/tex]

In this formula, A(t) represents the value of the quantity after time t, A₀ represents the initial value of the quantity (in this case, 8200), e represents Euler's number (a mathematical constant equal to approximately 2.718), k represents the growth rate (in this case, 0.0055 per decade), and t represents the time elapsed (in this case, 97 years).

To solve for the value of the quantity after 97 years, we simply plug in the values we know and solve for A(t):

A(t) = 8200[tex]e^{(0.0055/10\times97)}[/tex]

= 8200[tex]e^{0.5285}[/tex]

≈ 67,458.85

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Emilia make an error in step 3 she didn't use an x and y from the same coordinate pair.

In step 1 : point 1 : (5, 2.15)  point 2 : (12, 3.06)

In step 2 : m = [tex]\frac{12-5}{3.06-2.15}[/tex]

m = 7/0.91

m = 7.69

In Step 3 : y = mx + b

m = slope

Point used by Emilia (2.15 , 5)

But the point should be used be Emilia is (5, 2.15)

2.15 = 5(7.69) + b

b = y intercept

b = -36.3

step 3 is wrong she didn't use right coordinates of x and y

In step 4 : y = mx +b

y = 7.69x -36.3

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The model approximates the volume, V, in liters, of air in the lungs during a five-second respiratory cycle using the equation V = -0.0374t + 3 + 0.1525t^2 + 0.1729t.

The given equation represents a mathematical model for estimating the volume of air in the lungs during a respiratory cycle. It is a quadratic equation with three terms: -0.0374t, 0.1525t^2, and 0.1729t.

The term -0.0374t represents the linear decrease in volume over time, indicating that the volume decreases by 0.0374 liters for every second of the respiratory cycle.

The term 0.1525t^2 represents the quadratic relationship between volume and time squared, indicating that the rate of change of volume with respect to time is influenced by the square of time.

The term 0.1729t represents the linear increase in volume over time, indicating that the volume increases by 0.1729 liters for every second of the respiratory cycle.

Overall, this model provides an approximation of the volume of air in the lungs during a five-second respiratory cycle, taking into account both linear and quadratic relationships with time.

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Where the above graph and conditions are given,  the value of k that satisfies g(x) = f(x+k) is k = -2.

We can determine the value of k by using the given relationship between g(x) and f(x+k).

If g(x) = f(x + k), then we can substitute the given values of x in g(x) to get:

g(-1) = f(-1 + k) --> 5 = f(-1 + k)

g(0) = f(0 + k) --> 4 = f(k)

g(1) = f(1 + k) --> 3 = f(1 + k)

g(2) = f(2 + k) --> 2 = f(2 + k)

g(3) = f(3 + k) --> 3 = f(3 + k)

We know that f(x) is a v-shaped graph with a vertex at (0,2) and points at (-1,3) and (1,3). Therefore, we can conclude that f(k) = 4, which means that k is the x-coordinate of the vertex of f(x) shifted to the left or right.

Since the vertex of f(x) is at (0,2), and the x-coordinate of the vertex of f(x+k) is at k, we have:

k = 0 --> vertex of f(x+k) is at (0,2)

k = -1 --> vertex of f(x+k) is at (-1,2)

k = 1 --> vertex of f(x+k) is at (1,2)

k = 2 --> vertex of f(x+k) is at (2,2)

Therefore, the value of k that satisfies g(x) = f(x+k) is k = -2.

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The distance the boat travels to get to the beach is approximately 5.0 miles.

To see why, we can draw a right triangle on the coordinate plane, with one leg along the x-axis (going 3.5 miles east) and the other leg along the y-axis (going 4 miles south). The hypotenuse of this triangle is the straight distance from the marina to the beach, which is the distance the boat travels.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

c^2 = a^2 + b^2

c^2 = (3.5)^2 + (4)^2

c^2 = 12.25 + 16

c^2 = 28.25

c ≈ 5.0

Therefore, the distance the boat travels to get to the beach is approximately 5.0 miles.

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Therefore, the polynomial p(x) that satisfies the given conditions is:

p(x) = ax^3 + bx^2 + cx + d
p(x) = x^3 - 2x^2 + 3x + 23

So, p(2) = 1(2)^3 - 2(2)^2 + 3(2) + 23 = 9.

To find a polynomial p(2) of degree three, we need four pieces of information. We can use the given values to set up a system of linear equations:

-7a + 2b - 4c + d = 3
-a - b + c - d = 3
7a + b + c + d = -9
8a + 4b + 2c + d = -33

We can solve this system using any method of linear algebra. One way is to use row reduction:

[ -7  2 -4  1 |  3 ]
[ -1 -1  1 -1 |  3 ]
[  7  1  1  1 | -9 ]
[  8  4  2  1 | -33 ]

R2 + R1 -> R1:
[ -8  1 -3  0 |  6 ]
[ -1 -1  1 -1 |  3 ]
[  7  1  1  1 | -9 ]
[  8  4  2  1 | -33 ]

R3 - 7R1 -> R1, R4 - 8R1 -> R1:
[ -8  1 -3  0 |  6 ]
[  0 -7  8 -1 | 51 ]
[  0 -4  4  1 |-51 ]
[  0  4 26  1 |-81 ]

R4 + R2 -> R2:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0 -4  4  1 |-51 ]
[  0  4 26  1 |-81 ]

R3 + (4/3)R2 -> R2:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0  0 50  4 |-11 ]
[  0  4 26  1 |-81 ]

R4 - (4/3)R2 -> R2, R3 - (5/6)R2 -> R2:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0  0  8  4 |-34 ]
[  0  0  8  1 |-103 ]

R4 - R3 -> R3:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0  0  8  4 |-34 ]
[  0  0  0 -3 |-69 ]

Now we can back-substitute to find the coefficients of the polynomial:

d = -69/(-3) = 23
c = (-34 - 4d)/8 = 3
b = (30 - 34c + 3d)/(-3) = -2
a = (6 + 3b - 3c + d)/(-8) = 1

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Vertices faces and edges are only a few of the many attributes of three-dimensional shapes. The 3D shapes' faces are their flat exteriors. An edge is the section of a line where two faces converge.

1) cube

A vertex is the intersection of three edges. A solid or three-dimensional form with six square faces is called a cube. These are the characteristics of the cube.

Every edge is equal.

8 vertex

6 faces  

12 edges

2) Cuboid

When the faces of a cuboid are rectangular, it is often referred to as a rectangular prism. The angles are all 90 degrees each. It has a cuboid.

8 vertex

6 faces

12 edges

3) Prism

A prism is a three-dimensional form with two equal ends, flat faces, and identical sides.l cross-section down the length of it. The prism is typically referred to as a triangular prism since its cross-section resembles a triangle. There is no bend to the prism. A prism has also

6 vertex

9 edges

2 triangles and 3 rectangles

5 faces.

4) Pyramid

A pyramid is a solid object with triangle exterior faces that converge at a single point at its summit. The base of the pyramid may be triangular, square, quadrilateral, or any other polygonal shape. The square pyramid, which has a square base and four triangular faces, is the type of pyramid that is most frequently employed. Take a look at a square pyramid.

5 vertices

5 faces

8 edges

5) Cylinder

The term "cylinder" refers to a three-dimensional geometrical shape.two circular bases joined by a curving surface make up this figure. In a cylinder,

no vertex

2 edges

2 circles on flat faces

one curving face

6) Cone

A cone is a three-dimensional thing or solid with a single vertex and a circular base. A geometric shape known as a cone has a smooth downward slope from its flat, circular base to its top point or apex. In a cone

one vertex

1 edge

1 circle with a flat face.

one curving face

7) Sphere

A sphere is a perfectly round, three-dimensional solid figure, and every point on its surface is equally spaced from the point, which is known as the center. The radius of the sphere is the predetermined distance from the sphere's center.

a sphere is

zero vertex

zero edges

one curving face

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Based on the trend line and slope, Tony's expected salary of $70,000 after 15 years of employment at Company Z is reasonable, as it falls within the range of salaries predicted by the line of best fit.

First, we need to find the equation of the trend line. To do this, we use the least squares regression method to find the line that best fits the data. Let x be the years of employment and y be the annual salary. We can calculate the slope and y-intercept of the trend line using the following formulas

slope = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)

y-intercept = (Σy - slopeΣx) / n

where n is the number of data points, Σ represents the sum of, and ( )² denotes squared.

We can use the given data to calculate the values needed for the formulas. Let's denote the years of employment as x and the annual salary as y.

x: 1 2 3 4 5 6

y: 45 50 55 60 65 70

n = 6

Σx = 1 + 2 + 3 + 4 + 5 + 6 = 21

Σy = 45 + 50 + 55 + 60 + 65 + 70 = 345

Σxy = (145) + (250) + (355) + (460) + (565) + (670) = 1305

Σ(x²) = 1² + 2² + 3² + 4² + 5² + 6² = 91

Now we can plug these values into the formulas to find the slope and y-intercept

slope = (61305 - 21345) / (691 - 21²) = 5

y-intercept = (345 - 521) / 6 = 20

We can write the equation of the trend line in the form y = mx + b, where m is the slope and b is the y-intercept

y = 5x + 20

Finally, we can use this equation to estimate Tony's salary after 15 years of employment

y = 5(15) + 20 = 95

Based on the trend line and slope, we would expect Tony's salary to be about $95,000 after 15 years of employment.

This is higher than his expected salary of $70,000, so it may not be a reasonable expectation. However, it's important to note that the trend line is just an approximation and there may be other factors that could affect Tony's salary.

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Based on the observed outcome, it is therefore very or highly unlikely that Romain's probability is equal to that of the other brothers, and thus  it is possible that Romain is cheating.

Beneath the assumption that each brother has an break even with chance of getting picked in each draw, the likelihood of Romain not getting picked indeed once out of 12 times is:

P(Romain not picked) = (2/3)¹²

                                  = 0.0077

This is one that is less than 1%, which suggests that the observed result is made up of a likelihood less than 1% beneath the given speculation. Therefore, we need to reject the hypothesis that each brother has an equal chance of getting picked in all of the draw.

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See text below

Alexandre has two brothers: Hugo and Romain. Every day Romain draws a name out of a hat to randomly select one of the three brothers to wash the dishes. Alexandre suspected that Romain is cheating, so he kept track of the draws, and found that out of 12 draws, Romain didn't get picked even once. 1 Let's test the hypothesis that each brother has an equal chance of of getting picked in each draw versus 3 the alternative that Romain's probability is lower. Assuming the hypothesis is correct, what is the probability of Romain not getting picked even once out of 12 times? Round your answer, if necessary, to the nearest tenth of a percent. Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we will reject the hypothesis. What should we conclude regarding the hypothesis? Choose 1 answer: We cannot reject the hypothesis. B We should reject the hypothesis.

Annette's average speed was 40 mph if Annette drives her car 115 miles and has an average of a certain speed.

What is Average speed ?

Average speed is the total distance traveled divided by the total time taken to travel that distance. It is a measure of the overall speed of an object or person over a certain period of time.

Let's call Annette's original average speed "x". We can use the formula:

distance = speed x time

to set up two equations based on the given information.

For the first part of the trip:

115 = x * t1 (where t1 is the time it took Annette to travel 115 miles at speed x)

For the second part of the trip:

138 = (x + 8) * t2 (where t2 is the time it would have taken Annette to travel 138 miles at a speed of x + 8)

Since Annette traveled the same amount of time for both parts of the trip, we can set t1 equal to t2:

t1 = t2

We can solve for t1 in the first equation:

t1 = 115 : x

And we can solve for t2 in the second equation:

t2 = 138 : (x + 8)

Since t1 = t2, we can set the two expressions for t equal to each other:

115 : x = 138 : (x + 8)

Now we can solve for x:

115(x + 8) = 138x

115x + 920 = 138x

920 = 23x

x = 40

Therefore, Annette's average speed was 40 mph.

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The definite integral

[tex]-e^(2z)/u + 16e^z/u - 64ln(u)/u + C[/tex]

To evaluate this definite integral, we need to find the antiderivative of the integrand and evaluate it at the limits of

integration.

Let's start by using u-substitution:

Let [tex]u = e^z+8z[/tex]

Then [tex]du/dz = e^z+8[/tex]

And [tex]dz = 1/e^z+8 du[/tex]

Substituting this into the integral, we get:

[tex]∫(e^z) + 8/ (e^z+8z)^2 dz[/tex]

= [tex]∫(1/u^2)(e^z+8)^2 du[/tex]

= [tex]∫(1/u^2)(e^(2z)+16e^z+64) du[/tex]

= [tex]-e^(2z)/u + 16e^z/u - 64ln(u)/u + C[/tex]

Now we need to evaluate this antiderivative at the limits of integration.

Let's assume the limits are a and b:

= [tex][-e^(2b)/(e^b+8b) + 16e^b/(e^b+8b) - 64ln(e^b+8b)/(e^b+8b)] - [-e^(2a)/(e^a+8a) + 16e^a/(e^a+8a) - 64ln(e^a+8a)/(e^a+8a)][/tex]

Simplifying this expression is not easy, but it can be done with some algebraic manipulation.

Therefore, The definite integral

[tex]-e^(2z)/u + 16e^z/u - 64ln(u)/u + C[/tex]

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The percentage of companies with revenue between 50 million and 90 million dollar is: 87.6%

The formula for the z-score in this type of distribution is:

z = (x' - μ)/σ

where:

x' is sample mean

μ is population mean

σ is standard deviation

We are given:

μ = 70 million dollars

σ = 13 million dollars

Thus:

When x' = 50 million dollars, we have:

z = (50 - 70)/13

z = -1.54

When x' = 90 million dollars, we have:

z = (90 - 70)/13

z = 1.54

Using probability between two z-scores calculator, we have:

z = 0.87644 = 87.6%

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Each serving of cider contains 0.08 tablespoons of cinnamon.

Eric uses 2 tablespoons of cinnamon for a batch of cider that makes 25 servings. To find out how much cinnamon is in each serving, we need to divide the total amount of cinnamon used by the number of servings.

tablespoons/tablespoons= tablespoons per serving

2 tablespoons / 25 tablespoons = 0.08 tablespoons per serving

Therefore, there is 0.08 tablespoons of cinnamon in each serving of cider.

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a.  The ratio of Es to Ns in percentage is 64%

b. Probability that it will take at least five patients to find one patient on whom the medicine would not be effective is impossible to estimate this probability from the table.

c. The probability that the medicine will be effective on exactly three out of four randomly selected patients is  12.9%

a. The total number of patients in the table is 50.

To calculate the ratio of Es to Ns in percentage, we count the number of Es and Ns and divide the number of Es by the number of Ns and Es combined, and then multiply by 100. Counting the table, we find that there are 32 Es and 18 Ns. So, the ratio of Es to Ns in percentage is:

32 / (32 + 18) * 100 = 64%

b. To estimate the probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we need to look at the runs of Ns in the table. We can see that there are no runs of five or more Ns, so it is impossible to estimate this probability from the table.

c. To estimate the probability that the medicine will be effective on exactly three out of four randomly selected patients, we need to count the number of ways we can choose three Es and one N, and divide by the total number of possible outcomes of selecting four patients from the table. The total number of possible outcomes is:

50 choose 4 = 50! / (4! * (50-4)!) = 230300

The number of ways we can choose three Es and one N is:

32 choose 3 * 18 choose 1 = (32! / (3! * (32-3)!)) * (18! / (1! * (18-1)!)) = 32 * 31 * 30 / (3 * 2) * 18 = 32 * 31 * 30 * 18 / 6 = 297120

So, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is:

297120 / 230300 ≈ 0.129 or about 12.9% (rounded to the nearest tenth of a percent).

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The height of the outside is given as 17.44 meters

The equation of hyperbola is :

[tex]y^2 - x^2 = 38[/tex]

=>[tex]y^2/38 - x^2/38 = 1[/tex]

(of the form [tex]y^2/a^2 - x^2/b^2 = 1[/tex] and transverse axis is y-axis.)

Here, [tex]a^2 = b^2 = 38[/tex]

[tex]c^2 = a^2 + b^2 = 38+38 = 76[/tex]

( a is the distance of vertices from the center and c is the distance of foci from the center.)

Distance between walls = 2 a = [tex]2*\sqrt(38) = 12.33[/tex] meters at the center

and = [tex]2c = 2*\sqrt(76) = 17.44[/tex] meters at the end when the line joining

end points of the wall on one side is through the foci point.

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Answer:

(1, 4)

Don't worry, I feel the same way sometimes, :)

Step-by-step explanation:

Substitute the bottom equation into the top.

If y=3x+1, than the first y will equal 3x+1.

3x+1 = x+3

Subtract 1 from 3

3x = x+2

Subtract x from 3x.

2x=2

Divide everything by 2.

x=1

Now substitute it in the equation.

1. y=1 + 3

y=4

2. y= 3(1) + 1

y=3+1

y=4

(1, 4)

The function for Drake's monthly phone bill, C(t), is C(t) = 35 + 0.05t, where t represents the number of texts sent.

Drake has two components to his monthly phone bill: the base cost of $35 and the additional cost for texts sent. The base cost is fixed, meaning it does not change, so we can represent it as a constant value in the function (35).

The cost per text is $0.05, which means it varies depending on the number of texts sent (t). To find the total cost (C(t)), we need to add the fixed cost ($35) and the variable cost ($0.05 times the number of texts). Therefore, the function representing Drake's monthly phone bill cost is C(t) = 35 + 0.05t.

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To ensure that Circles X are congruent to Circle A, you need to ensure that they have the same size and shape. In other words, the radii of Circle X should be equal to the radius of Circle A.

Here are the steps you can follow to draw congruent Circles X:

Use a compass to measure the radius of Circle A.

Without changing the radius setting on your compass, place the tip of the compass at the center of where you want to draw Circle X.

Draw Circle X using the compass, making sure that the radius is the same as the radius of Circle A.

Check that Circle X and Circle A have the same size and shape. You can do this by measuring their radii with a ruler or by comparing their circumference.

By following these steps, you can ensure that Circle X is congruent to Circle A.

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The length of side a is 50 if the angle ∠bac is 50° and the length of side b is 20 and side c is 35 using cosine law.

Length of side b = 20

Length of side c = 35

Angle ∠bac =  50°

To calculate the length of the side a, we need to use the cosine law. The formula is:

[tex]a^2 = b^2 + c^2 - 2bc cos(A)[/tex]

Substituting the given values in the formula, we get:

[tex]a^2 = 20^2 + 35^2 - 2(20)(35)cos(50°)[/tex]

[tex]a^{2}[/tex] = 400 + 1225 + (1400)*(0.642)

[tex]a^{2}[/tex] = 1625 + 898.8

a = [tex]\sqrt{2523.8}[/tex]

a = 50

Therefore we can conclude that the length of side a is 50 using cosine law.

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