Question 1
Match the equation with its graph. Identify the slope and the y-intercept.

y=2x+1

The width of the pool is approximately 4.01 feet.

Mrs. Sanford plans to build a rectangular pool in her backyard, which will hold 9,000 gallons of water. The pool's height is 15 feet and its length is 20 feet. To determine the width of the pool, we need to first convert gallons to cubic feet, as 1 gallon equals approximately 0.1337 cubic feet.

So, 9,000 gallons * 0.1337 = 1,203.3 cubic feet of water. Now, we know that the volume of a rectangular pool is calculated using the formula V = LWH (Volume = Length * Width * Height). We have the volume (1,203.3 cubic feet), the height (15 feet), and the length (20 feet), so we can solve for the width (W):

1,203.3 = 20 * 15 * W
1,203.3 = 300 * W
W = 1,203.3 / 300
W ≈ 4.01 feet

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Answer:

7 4/10

Step-by-step explanation:

Answer:

7 4/10

72/5

7 2/5 is the answer

\(\huge\tt\pink{Answer}\)

A≈852.83cm²

Radius

7cm

Height

31cm

60 degrees is the measure of arc BC from the figure

The given diagram is a circle with several arc angles

arcAWB = 120 degrees

The line AC is a diameter

Since the sum of angles on a straight line is 180 degrees, hence:

arc AWB + arcBC = 180

arcBC = 180 - arc ZWX

arcBC = 180 - 120

arcBC = 60 degrees

Hence the measure of the arc BC from the diagram is 60 degrees

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Answer:

4000 + 400x = 3750 + 450x

Step-by-step explanation:

The number of cars where the offer would be equal is 5 cars.

4000 + 400x = 3750 + 450x  Subtract 400x from both sides of the equation

4000 = 3750 + 50x  Subtract 3750 from both sides of the equation

250 = 50x  Divide both sides by 50

5 = x

If you sell less than 5 cars a month, take job A.  If you sell more than 5 cars a month, take job B.

Answer:

300 mins

Step-by-step explanation:

1 hours = 60 mins

5 hours = 5×60=300 mins

Answer:

300

Step-by-step explanation:

5 * 60 (minutes in an hour) = 300

The fraction of the cake that was ron's pieces is 1/5.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Since Mrs Jones gave 1/5 of a cake to her neighbour, the remaining fraction will be:

= 1 - 1/5

= 4/5

The fraction of the cake that was ron's pieces will be:

= 2/(1+3+4) × 4/5

= 2/8 × 4/5

= 8/40

= 1/5

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Answer:

706.86

Step-by-step explanation:

have a good day! :D

It is shown that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |1/f(x) - 1/f(y)| < ε/(2kM) for all x, y in a. This proves that 1/f is uniformly continuous on a.

What is uniformly continuous?

Uniform continuity is a property of a function in which for any given value ε > 0, there exists a corresponding value δ > 0 such that for all pairs of points in the function's domain whose distance is less than δ, the difference in the function's values at those points is less than ε. In other words, a function is uniformly continuous if its rate of change does not vary significantly over its entire domain, and small changes in its input result in correspondingly small changes in its output.

To show that 1/f is uniformly continuous on a, we need to prove that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |1/f(x) - 1/f(y)| < ε for all x, y in a.

Given that f is uniformly continuous on a, we know that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |f(x) - f(y)| < ε/k for all x, y in a.

We also know that |f(x)| > k for all x in a.

Using these facts, we can begin by manipulating the expression |1/f(x) - 1/f(y)|:

|1/f(x) - 1/f(y)| = |(f(y) - f(x))/(f(x)f(y))|

Since |f(y) - f(x)| < ε/k, we can substitute this into the above expression:

|1/f(x) - 1/f(y)| < |(ε/k)/(f(x)f(y))|

Now, we need to find a way to relate f(x)f(y) to |x - y|.

Since f is uniformly continuous, we know that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |f(x) - f(y)| < ε/k for all x, y in a.

This implies that |f(x)f(y)| < k(f(x) + f(y)) < 2kM, where M is the supremum of |f(x)| over a.

Thus, we have:

|1/f(x) - 1/f(y)| < ε/(2kM)

Therefore, we have shown that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |1/f(x) - 1/f(y)| < ε/(2kM) for all x, y in a. This proves that 1/f is uniformly continuous on a.

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Step-by-step explanation:

1.2

area of triangle = ½ × base × height

so,

height = 5cm

base = 4cm

now,

→ 1/2 × 4 × 5

→ 2 × 5 = 10 cm²

therefore, area of the ∆AED is 10cm².

1.3

area of rectangle = l × b

length = 8cm

breadth/width = 5cm

now,

area of BCDE

→ 8 × 5 = 40 cm²

now,

area of,

→ ABCD = BCDE - ∆AED

→ ABCD = 40 - 10 = 30

therefore, required area of ABCD is 30cm².

hope this answer helps you dear...take care and may u have a great day ahead!

Answer:

gg

Step-by-step explanation:

ggxgg=gggg

Based on the provided voltage readings, the polarity of the single-phase transformer can be identified as follows: the dot notation represents the primary winding, while the numerical labels indicate the corresponding terminals.

The primary and secondary windings are denoted by L1 and L2, respectively. The polarities can be determined by observing the voltage readings across various terminal combinations.

To identify the polarity of a single-phase transformer, you can analyze the voltage readings obtained from different terminal connections. In this case, let's consider the given readings.

When measuring the voltage between L1 and L2, we obtain a reading of 121 volts. This indicates the voltage across the primary and secondary windings in the same direction, suggesting a non-reversed polarity.

Next, measuring the voltage between terminals 1 and 4 while connecting terminals 2 and 3 results in a reading of 26.47 volts. This implies that terminals 1 and 4 have the same polarity, while terminals 2 and 3 have opposite polarities.

Similarly, when connecting terminals 2 and 4 and measuring the voltage between terminals 1 and 3, a reading of 7.32 volts is obtained. This indicates that terminals 1 and 3 have the same polarity, while terminals 2 and 4 have opposite polarities.

For the combination of terminals 6 and 7, a voltage reading of 25.78 volts is measured between terminals 5 and 8. This suggests that terminals 5 and 8 have the same polarity, while terminals 6 and 7 have opposite polarities.

Lastly, when connecting terminals 5 and 7 and measuring the voltage between terminals 6 and 8, a reading of 5.42 volts is obtained. This indicates that terminals 6 and 8 have the same polarity, while terminals 5 and 7 have opposite polarities.

By considering the polarity relationships observed in these readings, we can conclude that the primary and secondary windings of the single-phase transformer have the same polarity. The dot notation indicates the primary winding, and the numerical labels represent the terminals.

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Answer:

$77.18

Step-by-step explanation:

A = total amount

P = principal

I = interest

A = P(1 + r/n)^n·t

A = 70(1+.05)²

A = 70(1.05)²

A = 77.175

I = A - P

To reference cell C2 on the flooring prices worksheet, you would enter "Flooring Prices!C2" in the formula bar.

The term "Flooring Prices" refers to the name of the worksheet and the exclamation mark separates the worksheet name from the cell reference. By entering this formula, you can retrieve the value or formula in cell C2 on the Flooring Prices worksheet. This method is particularly useful when you need to refer to cells in other worksheets within the same workbook. By specifying the worksheet name, you can avoid confusion and ensure that the formula references the correct cell. It is important to note that if the worksheet name contains spaces, you need to enclose it in single quotation marks ('Flooring Prices') when entering the formula.

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Answer:

B

Step-by-step explanation:

AB=6 therefore Pto Q should be 6

6^2=36

8^2=64

add them together

=100

square root 100=10

divide by 2=5

Four pounds of jelly beans: $6.82

First, calculate the cost of 1 lb by dividing the price by the number of pounds:

6.82 / 4 = $1.705 per pound

Now, multiply by 2:

1.705 x 2 = $3.41

Answer:

i did too lol

Step-by-step explanation:

Answer:

Don't worry you might meet someone later in time

Step-by-step explanation:

A triangular prism is a type of geometric shape. It has a total of five faces, including two congruent triangles and three rectangular faces that connect them. To calculate the surface area of a triangular prism, we need to add up the area of each face.

Given that the dimensions of the triangle and rectangular face are given in the question, we can apply the appropriate formulas.Area of triangle = 1/2 × base × heightArea of rectangle = length × widthLet's start by calculating the area of the two triangles. Since the dimensions of the triangle are all equal (3 inches), we can assume that it's an equilateral triangle. So the height of the triangle will be sqrt(3) times the base (1.732 x 3). Therefore,Area of triangle = 1/2 × base × heightArea of triangle = 1/2 × 3 × 1.732 × 3Area of triangle = 7.794 sq inWe have two triangles, so the total area of the triangles will be 2 × 7.794 = 15.588 sq inNow let's calculate the area of the three rectangular faces.

We are given two dimensions for the rectangular faces (6 in and 7 in), so we can use the formula:Area of rectangle = length × widthFor the first rectangular face:Area of rectangle = length × widthArea of rectangle = 6 × 3Area of rectangle = 18 sq inFor the second rectangular face:Area of rectangle = length × widthArea of rectangle = 7 × 3Area of rectangle = 21 sq inFor the third rectangular face:Area of rectangle = length × widthArea of rectangle = 7 × 6Area of rectangle = 42 sq in.

The total surface area of the triangular prism will be the sum of the areas of the two triangles and the three rectangular faces:S.A = 15.588 + 18 + 21 + 42S.A = 96.588 sq inTherefore, the surface area of the triangular prism is 96.588 sq in.

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If we take a simple random sample of size n=500 from a population of size 5,000,000, the variability of our estimate will be  (c) about the same as the variability for a sample  size n=500 from a population of size 50,000,000.

The variability of an estimate primarily depends on the sample size (n) rather than the population size. Since both scenarios have a sample size of 500, the variability will be approximately the same.

The correct answer is (d) slightly greater than the variability for a sample size n = 500 from a population of size 50,000,000. This is because the larger the population size, the smaller the sampling variability. In other words, if we take a sample of the same size from a larger population, there will be more variability due to the increased number of potential outcomes. However, the difference in variability between a population size of 5,000,000 and 50,000,000 is not significant enough to make a substantial impact on the estimate.

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Answer:

Perpendicular

Step-by-step explanation:

In the first part, it is necessary to show that there exists a value x in the interval (0, π) for which f(x) = 0. This can be done by demonstrating that f(x) changes sign in the interval. The fixed-point method is then applied to find the root using three iterations and achieving four digits of accuracy. The specific formula for the fixed-point method is not provided, but it involves iteratively applying a function to an initial guess to approximate the root.

In the second part, the error bound is determined by comparing the actual root P with the approximation π/3. The error bound represents the maximum possible difference between the true root and the approximation. The calculation of the error bound involves evaluating the function f(x) and its derivative within a certain range.

In the third part, the number of iterations needed to achieve an approximation with an accuracy of 10^-5 is determined. This requires using the given information of two iterations and five digits to estimate the additional iterations needed to reach the desired accuracy level. The calculation typically involves measuring the convergence rate of the fixed-point iteration and using a convergence criterion to determine the number of iterations required.

Overall, the questions involve demonstrating the existence of a root, applying the fixed-point method, analyzing the error bound, and determining the number of iterations needed for a desired level of accuracy. The specific calculations and formulas are not provided, but these are the general steps involved in solving the problem.

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Answer:

Because the airline allows each suitcase to hold up to 50 pounds, and it doesn't force them to hold exactly 50 pounds

Answer:

Step-by-step explanation:

b/c she doesn't have to have exactly 50 pounds,  she can have any were from 0 to 50 pounds  in each suit case.   They are not going to charge her more, if she only brings 49 pounds :DDDD  It's the same charge up to and including 50 pounds.  If she brings 51 pounds then maybe she would get charged more :P    But not for 50 pounds or less .  :)  Make sense?

Answer:10

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

\(48° + x = 90(angle \: at \: a \: right \: angle)\)

\(therefore \: x = 90°- 48°\\ = 42°\)

Answer:

B = 42

Step-by-step explanation:

B + 48 = 90 ... because they are complement angles

B = 90 - 48

B = 42 ...... so the unknown angle is 42

Answer:

x               y

4              180

8              360

12             540

Step-by-step explanation:

hope this helpss

To simplify the given polynomial expression, we can start by combining like terms.

First, let's simplify the first part of the expression: (3x^2 - x - 7) - (5x^2 - 4x - 2).

Combining like terms, we have: (3x^2 - 5x^2) + (-x + 4x) + (-7 - 2).

This simplifies to: -2x^2 + 3x - 9.

Next, let's simplify the second part of the expression: (x + 3)(x + 2).

Using the distributive property, we expand this expression: x(x + 2) + 3(x + 2).

Multiplying, we get: x^2 + 2x + 3x + 6.

Combining like terms, this simplifies to: x^2 + 5x + 6.

Now, we can combine the simplified parts of the expression:

(-2x^2 + 3x - 9) + (x^2 + 5x + 6).

Combining like terms, we get: -x^2 + 8x - 3.

Therefore, the simplified polynomial expression is: -x^2 + 8x - 3.

The degree of the polynomial is determined by the highest power of x in the expression. In this case, the highest power is 2 (x^2), so the degree of the polynomial is 2.

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Answer:

b. trigonal pyramidal

The shape of the NH3 (Ammonia) molecule is described as Trigonal Pyramidal. It has a tetrahedral electron-pair geometry due to three bonding pairs and one lone pair. The presence of lone pair causes the bond angles to be slightly smaller than an ideal tetrahedron.

The shape of the NH3 (Ammonia) molecule is best described as Trigonal Pyramidal. This can be understood by examining the molecule's molecular and electron-pair geometry. In case of ammonia, the central nitrogen atom is bonded to three hydrogen atoms and it also has one lone pair of electrons. The electron pair geometry therefore is tetrahedral which are distributed in three bonding pairs and one lone pair.

However, the molecular structure, which is the shape that considers only the bonding pair of electrons, is derived from this and appears as a Trigonal Pyramidal structure. The bond angles in this structure are slightly smaller than the ideal 109.5° angle in a regular tetrahedron due to the presence of the lone pair. The lone pair occupies more space than the bonding pairs, causing slight deviation from the ideal angles.

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The solution to the system of equations is d = 100 and m = 1/4. Multiplying each term in the second equation by 2 helped us to eliminate the variable d and solve for m.

To solve the system of equations, we can use the elimination method, which involves adding or subtracting the two equations to eliminate one of the variables.

In this case, if we add the two equations as they are, we won't be able to eliminate one of the variables.

Multiply each term in the second equation by 2, we will get:

4d + 200m = 450

4d + 800m = 600

Now, we can subtract the first equation from the second equation to eliminate d:

(4d + 800m) - (4d + 200m) = 600 - 450

600m = 150

m = 1/4

Substituting this value of m back into either of the original equations, we can solve for d:

4d + 200(1/4) = 450

4d + 50 = 450

4d = 400

d = 100

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The volume of the parallelepiped is 299³ units.

So,

The volume of parallelopiped can be calculated using the steps below.

Now, the volume of parallelopiped is increasing:

\(v=\left|\begin{array}{lll}-5 & -5 & 1 \\-1 & 6 & 1 \\6 & 3 & 7\end{array}\right|\)

The matrix's determinant is:

⇒ -5(42 - 3) +5(-7 -6) +1(-3 - 36)

⇒ -5(39) +5(-13) +1(-39)

⇒ -195 -65 -39

⇒ |-299| = 299

Therefore, the volume of the parallelepiped is 299³ units.

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Answer:

they both must go through (0, 0) and both must be straight lines

Step-by-step explanation:

linear/proportional