What is the y-intercept

Using the values given in the table to evaluate each expression, the value of each expression is (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.

To evaluate the expressions, we need to use the values given in the table for f(x) and g(x). The composition of functions (f∘g)(x) means that we plug the value of g(x) into the function f(x).

a. (f∘g)(1) = f(g(1)) = f(0) = 5

b. (f∘g)(2) = f(g(2)) = f(-3) = 8

c. (g∘f)(2) = g(f(2)) = g(3) = -7

d. (g∘f)(3) = g(f(3)) = g(2) = -3

e. (g∘g)(1) = g(g(1)) = g(0) = 1

f. (f∘f)(3) = f(f(3)) = f(2) = 3

Therefore, the answers are (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.

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The vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c

The space curve given is r(t) = sin t i + e^t j + ln(t+1) k. To find the tangent vector of the curve at a given point, we need to take the derivative of the curve with respect to t. The derivative of the curve is r'(t) = cos t i + e^t j + (1/(t+1)) k.

At the point (0, 1, 0), t = 0. So, the tangent vector at this point is r'(0) = cos 0 i + e^0 j + (1/(0+1)) k = <1, 1, 1>.

Now, we need to find which of the given vectors is perpendicular to the tangent vector. Two vectors are perpendicular if their dot product is equal to 0. So, we need to find the dot product of the tangent vector with each of the given vectors and see which one is equal to 0.

a. <1, 1, 1> • <0, 1, 0> = 0 + 1 + 0 = 1 (not perpendicular)
b. <1, 1, 1> • <-1, 0, -1> = -1 + 0 - 1 = -2 (not perpendicular)
c. <1, 1, 1> • <1, 0, -1> = 1 + 0 - 1 = 0 (perpendicular)
d. <1, 1, 1> • <1, -1, 1> = 1 - 1 + 1 = 1 (not perpendicular)
e. <1, 1, 1> • <1, 0, 1> = 1 + 0 + 1 = 2 (not perpendicular)

Therefore, the vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c.

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Answer:

To find the percentage of the money collected from entry fees over the 3 days that was collected on Day 2, we need to first find the total amount collected for all three days.

Total amount collected = $750 + $400 + $300 = $1450

Then, we need to find what fraction of the total was collected on Day 2:

Amount collected on Day 2 = $400

Fraction of total collected on Day 2 = $400 / $1450

Finally, we convert the fraction to a percentage:

Fraction of total collected on Day 2 = $400 / $1450 = 0.2759

Percentage of total collected on Day 2 = 0.2759 x 100% = 27.59%

Therefore, approximately 27.59% of the money collected from entry fees over the 3 days was collected on Day 2.

The solution for u-(3)/(4)=5(1)/(3) u is 2(5)/(12).

The additive property of equality states that if the same amount is added to both sides of an equation, the equation remains true. In this case, we can use the additive property of equality to solve for u by isolating the variable on one side of the equation.

Step 1: Add (3)/(4) to both sides of the equation to cancel out the subtraction on the left side of the equation.
u-(3)/(4)+(3)/(4)=5(1)/(3)+(3)/(4)

Step 2: Simplify the left side of the equation.
u=5(1)/(3)+(3)/(4)

Step 3: Find a common denominator for the fractions on the right side of the equation and combine them.
u=20(1)/(12)+(9)/(12)

Step 4: Simplify the right side of the equation.
u=29/(12)

Step 5: Convert the improper fraction to a mixed number.
u=2(5)/(12)

Therefore, the solution for u is 2(5)/(12).

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Yes, a probability of 4/5 indicates that an event is likely to happen.

Probability refers to the measure of the likelihood of an event occurring, typically expressed as a number between 0 and 1. It is used to quantify uncertainty and is widely used in various fields such as mathematics, statistics, economics, science, and engineering.

Yes, a probability of 4/5 indicates that an event is likely to happen. It means that out of 5 possible outcomes, 4 outcomes are favorable to the event. In other words, there is an 80% chance that the event will occur.

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A store scanner has a red laser wavelength of 650 nm. While a green laser pointer has a wavelength of 502 μm. The ratio of green to red wavelengths is 0.77.

To find this ratio, we need to divide the wavelength of the green laser by the wavelength of the red laser:

502 μm / 650 nm = 0.77

Note that we need to convert the units of the green laser wavelength from micrometers (μm) to nanometers (nm) in order to divide it by the red laser wavelength, which is already in nanometers. To do this, we multiply the green laser wavelength by 1000:

502 μm * 1000 = 502000 nm

So the ratio of green to red wavelengths is 502000 nm / 650 nm = 0.77.

This ratio indicates that the green laser has a shorter wavelength than the red laser. Generally, shorter wavelengths correspond to higher energy and higher frequency light. In the case of lasers, this means that the green laser is capable of producing a more intense and focused beam of light than the red laser.

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The statements that are true about the function when graphed on a coordinate plane include the following:

C. The relative minimum of the function is (3, 0)

E. When t > 3, the function is increasing.

In order to determine the minimum and maximum of this function, we would have to determine the critical points where the derivative of the function is equal to zero or undefined, and then evaluate the function at these critical points and at the endpoints of the interval.

By taking the first derivative of the given function and factorizing, we have:

f(t) = t³ - 6t² + 9t

f'(t) = 3t² - 12t + 9  

3t² - 12t + 9 = 0

t² - 4t + 3 = 0

(t - 3)(t - 1) = 0

t = 3 and t = 1

Therefore, the critical points of the function are at t = 1 and t = 3.

By taking the second derivative of the given function and factorizing, we have:

f''(t) = 6t - 12

At point t = 1, we have:

f''(1) = 6(1) - 12 = -6 (it is less than zero).

Therefore, f(t) has a local maximum at t = 1.

At point t = 3, we have:

f''(3) = 18 - 12 = 6 (it is greater than zero).

Therefore, the function f(t) has a local minimum at t = 3.

At t = 4, f''(4) = 24 - 12 = 12

At t = 5, f''(5) = 30 - 12 = 18

In conclusion, the relative minimum of the function is (3, 0) and when t > 3, the function would increase.

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Answer: 50%

Step-by-step explanation: There are 5 out of 10 employees at the water slide. 10 in this situation is going to be 100%

since there is only 5 out of 10 employees that are temporary

it would be 50%

Answer: 50%

Step-by-step explanation:

we can use the fact that anything multiplied by 1 results in the same value to simplify the expression:

   (3x + 2)(x - 5) / (3x + 4)(x - 5)  =  (3x + 2)/(3x + 4)

To obtain an equivalent expression for (3x+2)/(x-5) with a denominator of (3x+4)(x-5), we can use the distributive property to expand the numerator and denominator:

   (3x + 2) / (x - 5)  =  (3x + 2)(x - 5) / (3x + 4)(x - 5)

From here, we can use the fact that anything multiplied by 1 results in the same value to simplify the expression:

   (3x + 2)(x - 5) / (3x + 4)(x - 5)  =  (3x + 2)/(3x + 4)

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Answer: It will take the rope 5 seconds to reach the ground if it continues travelling at a speed of 10 m/s

Step-by-step explanation:If the rope is going 10 m/s down a 50 m cliff,

50/10=5 It will take it 5 seconds becuase it is going at a speed of 10 meters a second

Looking at the table, we can see that the addends follow a pattern where each subsequent pair of addends adds up to 1/5. Specifically, the missing addend is 2/5 - 3/10, which equals 1/10. The missing sums are 1/2 and 4/10.

The addends in the table are as follows:

1/10 + 1/5 = 3/10, 1/5 + 1/5 = 2/5

3/10 + 1/5 = 1/2

We can observe that the first two pairs of addends add up to 1/5 less than the subsequent sums. This pattern indicates that the missing addend must be

1/5 - 1/10 = 1/10

which would make the third pair of addends add up to

1/2 - 1/10 = 4/10

Therefore, the missing sums are 1/2 and 4/10, respectively. This pattern can be helpful in solving similar problems where pairs of addends add up to a specific sum or difference.

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John must score 286 on his 8th game to achieve an average score of 215.

What is an Average?

Average, also known as the mean, is a mathematical concept that represents the central value of a set of numbers. It is found by dividing the sum of the numbers by the total count of the numbers.

To find out what John must score on his 8th game to achieve an average score of 215, we need to use the formula for calculating the average or mean:

Average = (Sum of Scores) / (Number of Scores)

We can use this formula to solve for the unknown score:

215 = (159 + 182 + 225 + 240 + 198 + 200 + 230 + x) / 8

Multiplying both sides by 8, we get:

1720 = 159 + 182 + 225 + 240 + 198 + 200 + 230 + x

Simplifying, we get:

1720 = 1434 + x

Subtracting 1434 from both sides, we get:

x = 286

Therefore, John must score 286 on his 8th game to achieve an average score of 215.

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Angle, when two straight lines or rays intersect at a single endpoint,  then an angle is created.

The exterior angle of a triangle equals the sum of opposite interior angles. The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.

∠XYZ  = ∠YWX + ∠WXY

10x - 5   = 3x + 17 + 3x + 2

10x - 5 = 6x + 19

10x - 6x  = 24

4x  = 24

x = 6

∠WXY =  3x + 2

= 3*6 + 2

= 20°

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Answer:

x=8.3 recurring

Step-by-step explanation:

1÷0.12=8.3 recurring

x=8.3 recurring

or as a fraction 8 1/3

Answer:

5,184 from my knowledge

Answer:

(x + 4)2 = -26 x = -4 ± √26

Step-by-step explanation: x2 + 8x + 30 = 0

x2 + 8x = -30

x2 + 8x + (8/2)2 = -30 + (8/2)2

(x + 4)2 = -22

x + 4 = ±√22

x = -4 ± √22

math sucks lol

Therefore, the total tax owed by a Single filer with a taxable income of equation $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.

When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.

Assuming that the taxable income of $57,000 is for the tax year 2021 and the person is filing as Single, we can use the following marginal tax rates to compute the tax owed:

Tax Rate Taxable Income Range

10% $0 - $9,950

12% $9,951 - $40,525

22% $40,526 - $86,375

24% $86,376 - $164,925

32% $164,926 - $209,425

35% $209,426 - $523,600

37% $523,601 or more

To compute the tax owed, we need to apply each tax rate to the corresponding portion of the taxable income and add up the results. Here's how we can do that:

The first $9,950 of taxable income is taxed at 10%, so the tax on this portion is $9950 x 0.1 = $995.

The next $30,575 ($40,525 - $9,950) of taxable income is taxed at 12%, so the tax on this portion is $30,575 x 0.12 = $3,669.

The remaining $17,475 ($57,000 - $40,525) of taxable income is taxed at 22%, so the tax on this portion is $17,475 x 0.22 = $3,844.50.

Therefore, the total tax owed by a Single filer with a taxable income of $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.

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Answer:

$9.84

Step-by-step explanation:

At the rates given and the quantities purchased,

Maya will pay
Green Beans:   3 lbs x $1.19/lb = $3.57

Zucchini:  2 lbs x $0.99/lb = $1.98

Lettuce: 1 pound x $1.29/lb = $1.29

Sweet Corn: 6 ears x $0.50 per ear = $3.00

Total paid
= $3.57 + $1.98 + $1.29 + $3.00

= $9.84

We have to, A is linearly dependent for all values of c, the set of all vectors of the form (2a + b + c, 2a + 2b, 0) and the only value of c for which (4, 1, 3) is in Span(A) is c = 1.

a) A is linearly dependent for all values of c because there are more vectors than there are dimensions in the vector space. This means that one of the vectors can be expressed as a linear combination of the other vectors. Specifically, the vector (0, 0, c) can be expressed as a linear combination of the other vectors: (0, 0, c) = c*(2, 2, 0) + 0*(1, 2, c) + 0*(1, 0, 0).

b) For c = 0, the set of vectors A becomes {(2, 2, 0),(1, 2, 0),(0, 0, 0),(1, 0, 0)}. The span of this set of vectors is the set of all linear combinations of these vectors. Since the third vector is the zero vector, it does not contribute to the span. The span of the remaining vectors is the set of all linear combinations of the form a*(2, 2, 0) + b*(1, 2, 0) + c*(1, 0, 0). This is the set of all vectors of the form (2a + b + c, 2a + 2b, 0), which is a plane in R3 that contains the origin and is parallel to the xy-plane.

c) To find all values of c for which (4, 1, 3) is in Span(A), we need to find all values of c for which there exist scalars a, b, and d such that (4, 1, 3) = a*(2, 2, 0) + b*(1, 2, c) + d*(1, 0, 0). This gives us the following system of equations:2a + b + d = 42a + 2b = 1bc = 3We can solve this system of equations to find the values of a, b, and c. From the first equation, we can express d in terms of a and b: d = 4 - 2a - b. Substituting this into the second equation gives us 2a + 2b = 1 - 4 + 2a + b, which simplifies to b = 3. Substituting this value of b back into the third equation gives us 3c = 3, which gives us c = 1. Therefore, the only value of c for which (4, 1, 3) is in Span(A) is c = 1.

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The factored form is 2y(x - y) - 11x.

Factored form of a polynomial is when the polynomial is written as a product of its factors. Each factor is either a polynomial or a number. Factored form is useful for identifying the zeros of a polynomial and for solving polynomial equations.

To simplify the given expression, we need to combine like terms and factor if possible.

First, let's combine the like terms:

x^2 + 3xy - 4y^2 - 6x + 3y - x^2 - xy + 2y^2 - 5x - 3y

= 2xy - 2y^2 - 11x

Next, let's see if we can factor the expression:

2xy - 2y^2 - 11x

= 2y(x - y) - 11x

Since we cannot factor any further, the simplified expression in factored form is:

2y(x - y) - 11x

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The numbers in the cards are:

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

Cards = 45, 45 and 46

Next, we have

Multiples of 2, 3 and 4

Using the above as a guide, we have the following:

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The result of the formula "20 - 4.65" is 15.35, which corresponds to the amount of change the customer gets.

Expressions are separated by mathematical sign i.e positive or negative.

The expression "20 - 4.65" represents the amount of change a customer would receive after ordering from the menu board.

The first part of the expression, "20", represents the amount of money the customer paid for their order. This is the total cost of the items they purchased from the menu board.

The second part of the expression, "4.65", represents the amount of money that the customer spent on their order. This is the subtotal of the items they purchased before tax and any other fees that may be added to the bill.

To calculate the change the customer receives, you subtract the amount the customer spent from the amount they paid. So in this case, the expression "20 - 4.65" gives us the answer of 15.35, which represents the amount of change the customer receives.

As for what the customer ordered, we cannot know for sure based on this expression alone. It's possible that the customer ordered a single item that cost exactly $4.65, or they may have ordered multiple items that added up to that subtotal. Without more information about the menu board and the prices of the items, it's impossible to determine exactly what the customer ordered.

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The height of the building is approximately 27.62 feet. Rounded to the nearest hundredth, the answer is 27.62 feet.

In arithmetic, we use angles and distance to determine an object's height. The distance between the items is measured horizontally, and the height of an object is determined by the angle of the top of the object with respect to the horizontal.

Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It is used to determine the distance between any two objects, including heavenly bodies or other objects, as well as the height of towers, buildings, mountains, etc. Astronauts, surveyors, architects, and navigators are the main users.

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Given that the polynomial has a zero at 5 with multiplicity 2, its complete factorization is (x - 5)²(z + 9)(z - 2).

To factor the given polynomial z⁴ - 3z³ - 63z² + 355z - 450, given that it has a zero at 5 with multiplicity 2, we can use the fact that (z - 5)² is a factor of the polynomial. We can then use synthetic division to find the other factors.

First, we divide the polynomial by (z - 5) using synthetic division:
5   |   1  -3  -63  355  -450
    |       5    10  -265  450
        1   2  -53    90       0

The result of the division is z³ + 2z² - 53z + 90 . Divide it by (z - 5) again since the multiplicity is 2.
5   |   1   2  -53    90
    |       5    35   -90

        1   7   -18      0

The result of the second division is z² + 7z - 18. This polynomial can still be factorized as (z + 9)(z - 2).

So, the final answer is:

z⁴ - 3z³ - 63z² + 355z - 450 = (x - 5)²(z + 9)(z - 2).

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let's recall that a year has 12 months, thus 15 months is really 15/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$9800\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{15}{12}\dotfill &\frac{5}{4} \end{cases} \\\\\\ I = (9800)(0.05)(\frac{5}{4}) \implies I = 612.5[/tex]

Answer:

24

Step-by-step explanation:

The sum of the three angles in a triangle is always 180 degrees.

Let x be the measure of the third angle.

Then we have:

102 + 54 + x = 180

Simplifying the left side:

156 + x = 180

Subtracting 156 from both sides:

x = 180 - 156

x = 24

Therefore, the measure of the third angle is 24 degrees.

The value of x from the similar triangles is x = 4

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔQRS

Let the second triangle be ΔLMN

Now , the measure of ∠QRS = measure of ∠NLM

And , the triangles are similar

Now , the corresponding sides of similar triangles are in the same ratio

On simplifying , we get

LM / RQ = LN / QS

( 2x + 4 ) / 8 = 9 / 6

Multiply by 8 on both sides , we get

2x + 4 = ( 3/2 ) 8

2x + 4 = 12

Subtracting 4 on both sides , we get

2x = 8

Divide by 2 on both sides , we get

x = 4

Therefore , the value of x is 4

Hence , the similar triangles are solved

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Answer: See attached.

Step-by-step explanation:

    Since the first equation uses a ≤ symbol, we know we will use a solid line. This is because it is less than and equal to. Then, we will graph it as a regular slope-intercept line.

    This line has a slope of 5 and a y-intercept of -2. This means we will start at (0, -2) and move five units up for every unit right, or five units down for every unit left.

    For the next equation, it uses a > symbol so we will use a dashed line. This is because it is not equal to, only greater than. Same as the previous. We will graph it as a slope-intercept line, but using a dashed line instead of a solid line.

    This line has a slope of -2 and a y-intercept of positive 5. This means we will start at (0, 5) and move two units down for every unit right, or two units up for every unit left.

Answer: $15

Step-by-step explanation:

Remember percent makes the decimal move two places

The cost of Frank's shirt is 12 + 12(0.25)

12 + 3 = $15

Hope this helps!

In the word problem, the time (in seconds) the ball was in the air is D)0.50 seconds.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here expression which describes height is,

h(t)= [tex]-18t^2+3t+2[/tex]

Now h(t)=0 then,

=> [tex]-18t^2+3t+2=0[/tex]

=> [tex]18t^2-3t-2=0[/tex]

=> [tex]18t^2-3t=2[/tex]

=> 3t(6t-1)=2

=> 3t=2 , 6t-1=2

=> t=2/3 , 6t=3

=> t=2/3 , t=1/2

=> t= 0.5 seconds.

Hence  the time (in seconds) the ball was in the air is D)0.50 seconds.

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