the table shows the rate at which justin can make widgets. how many widgets can justin make in 36 minutes?

Answer:

22/22X22-22+22= 22÷5 =4.5

33/33X33-33+33=33÷5=6.6

The function for the given zeros is f(x)=2x³-8x²+8x-32.

The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.

Given that, n=3.

x=4 and x=2i

We then know that the third root must be x=-2i

Now, f(x)=a(x-4)(x-2i)(x+2i)

= a(x-4)(x²-(-2i)²)

= a(x-4)(x²-(-4))

= a(x-4)(x²+4)

= ax²(x-4)+4(x-4)

f(x)= a(x³-4x²+4x-16)

f(1)=a(1³-4×1²+4×1-16)

-30=a(1-4+4-16)

a=2

Now, f(x)=2(x³-4x²+4x-16)

f(x)=2x³-8x²+8x-32

Therefore, the function is f(x)=2x³-8x²+8x-32.

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Step-by-step explanation:

we all know that development is positive change in society and fidelity is a process of fertilization of human in society that explain us development and fertilization are the process of positive changes in our environment and province

Step-by-step explanation:

It's a long answer. You have to find the area of the large triangle, the small triangle than subtract the two

A = 1/2(b)(h)

For the big triangle

A = 1/2(16)(4) = 1/2(64) = 32

For the small triangle

A = 1/2(8)(2)

We use 8 and 2 because that's half of 16 and 4, since at the bottom it says A and B are midpoints

A = 1/2(8)(2) = 1/2(16) = 8

Now we subtract

32-8 = 24 units

Size of the house should be 2900 ft².

Correct option is B.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for the line that expresses price of house

y = 0.06x + 60.5

where y is the price in thousand dollars, x is area in square feet.

Price of the house = $235000

⇒ y = 235

Then,

235 = 0.06x + 60.5

0.06x = $235 - 60.5

0.06x = 174.5

x = 174.5/0.06

x = 2908.33 ≈ 2900

Hence, 2900 ft² should be the size of the house.

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The local maximum for the graph below is given at point b.

A function has a local maximum when it changes from increasing to decreasing.

For the graphed function, we have that the function is increasing until point b, and then it starts to decrease, hence the local maximum is given at point b.

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The equation is f(x) = -0.4x + 60. The solution has been obtained by using slope - intercept form.

What is slope-intercept form?

The graph of the equation y = mx + b is a line with a slope of m and a y-intercept of b. The form of the linear equation is called the slope-intercept form, and the values of m and b are real integers.

We are given that f(-10) = 64 and f(15) = 54.

So, we get the points as (-10 , 64) and (15 , 54)

Using the slope intercept form, we get

Slope(m) = (54 - 64)/(15 + 10)

Slope(m) = -0.4

We know that y = mx + b

For calculating b. we will put in the values

⇒64 = -0.4(-10) + b

⇒64 = 4 + b

⇒b = 60

From this we get the equation as

f(x) = -0.4x + 60

Hence, the equation is f(x) = -0.4x + 60.

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The length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.

What is length?

The length of something measured from end to end or along its longest side, or the length of a specific section of something.

Convert the width from inches to feet:

Since there are 12 inches in a foot, the width in feet is:

9 / 12 = 0.75 ft

Calculate the length needed:

We know that the area of the gasket material is 19 sq ft, and the width is 0.75 ft. Let L be the length needed in feet. Then we have:

Area = Width x Length

19 sq ft = 0.75 ft x L

Solving for L, we get:

L = 19 sq ft / 0.75 ft

L = 25.33 ft (rounded to two decimal places)

Therefore, the length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.

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Answer:

hi

Step-by-step explanation:

[tex]x {}^{3} - 27 = {x}^{3} - {3}^{3} \\ = (x - 3)( {x}^{2} + 3x + 9) \\ {x}^{3} + 27 = {x}^{3} + {3}^{3} \\ = (x + 3)( {x}^{2} - 3x + 9)[/tex]

Answer:

Common ratio, r = 3

Step-by-step explanation:

Common ratio is given by the ratio of one of the terms to the previous term and is a constant for the entire sequence

Here the first term is 17

Second term is 51

Second Term ÷  First Term
= 51 ÷ 17 =3

Third Term ÷ Second Term
= 153 ÷ 51 = 3

So common ratio is 3

In general, if aₙ is the nth term and aₙ₊₁ then the common ratio is given by:
aₙ₊₁ / aₙ

Answer:

360

Step-by-step explanation:

Every 1/2pi is 90 degrees.

Going down the list...

1/2pi is 90

pi is 180

3/2pi is 270

2pi is 360

The capacity of the trophy that us 30 cm high is 0.4286 liter

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

7 cm height cup holds 100 ml. Therefore:

7 cm = 100 ml

For a 30 cm height trophy:

30 cm = 30 cm * 100 ml per 7 cm = 428.57 ml

1000 ml = 1 l

428.57 ml = 428.57 ml * 1 liter per 1000 ml = 0.4286 liter

The capacity of the trophy is 0.4286 liter

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The area of the attached figure is 32 square mm

The similar question is added as an attachment

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

A square a triangle and a parallelogram

The shapes can be combined to

a triangle and a parallelogram

So, we have

Area = Sum of individual areas

Using the dimensions of the shapes as a guide, we have the following:

Area = 0.5 * 2 * 8 + 4 * 6

This gives

Area = 32

Hence, the area is 32 square mm

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Answer:
5.6%

Step-by-step explanation:

2/100 x 100 = 2
100-2 = 98 Boys on new Honor Roll
1/10 x 80 = 8
80-8 = 72 Girls on  new Honor roll
180 Original Roll
170 On new Roll
x/100 x 180 = 170
x/100 = 17/18
x = 1700/18
x = 94.4444444
Round 94.4
5.6 percent decrease.

The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

Domain: The domain of the function is the set of all real numbers greater than -8, since the argument of the logarithm, x + 8, must be positive.

Range: The range of the function is all real numbers.

Asymptotes: The function does not have any vertical asymptotes.

Transformation: The function is a reflection of the standard logarithmic function over the x-axis, with a vertical scaling factor of -2. This means that the function will start from the origin and increase without bound.

Behavior near x = -8: As x approaches -8 from the right, the value of the function approaches negative infinity. As x approaches -8 from the left, the value of the function approaches positive infinity.

The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.

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According to the information in the graph, the cheapest route to travel through all cities would be: Atlanta - Dallas - San Francisco - Los Angeles - New York - Detroit - Atlanta.

To calculate the cheapest option to travel to all cities, we must identify our starting point in the city of Atlanta and analyze which is the cheapest option to travel. In this case, it would be the Detroit or Dallas option (at this point we can choose either one).

Once we choose Dallas, we must apply a location strategy so that the next move leaves us in a suitable position to go to the cities of the east coast. Therefore, the best option would be San Francisco and then Los Angeles.

After this, the best (cheaper) option would be to take transportation to New York, Detroit, and finally to Atlanta. Finally, we must add the values of the displacements to know what the total value is:

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Answer:

C. 5x²-7x-8

Step-by-step explanation:

(-3x²-5x +1 ) + (8x²-2x-9)

Grouping like terms:
(- 3x² + 8x²)  + (- 5x - 2x) + (1 - 9)

=> (5x²) + (-7x) + (-8)

=> 5x² - 7x - 8

52s represents the cost for the snowboard times s days.

What is an expression ?

An expression consists of one or more numbers or variables along with one more operation.

Given :

expression : 52s + 10

Since it represents , total cost to rent a snow board for s days plus the fee for the helmet

Therefore , 52 is the cost of the snowboard rental per day.

s represents the day(s) that the equipment is rented out.

Hence , 52s represents the cost for the snowboard times s days.

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Given question is incomplete , the complete question is given below:

At the ski shack customers can rent skis snowboards boots and poles by the day. josh rents a snowboard and a helmet. The expression 52s + 10 represents the toatak cost to rent a snow board for s days plus the fee for the helmet what dose the term 52s represent​

To prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.

What is the SSS Similarity Theorem?

The SSS Similarity Theorem states that two triangles are similar if the ratio of all three pairs of corresponding sides of two triangles are equivalent.

Given ΔUVW and ΔXYZ, where:

UV corresponds with XY, thus UV/XY = 50/40 = 1.25

WU corresponds with ZX, thus WU/ZX = 40/32 = 1.25

WV corresponds with ZY, thus WV/ZY = 60/48 = 1.25

Since all the ratio of all three corresponding sides of both triangles are equivalent, therefore both triangles can be proven to be similar by the SSS Similarity Theorem.

Therefore, to prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.

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Answer: x=35

Step-by-step explanation:

Answer:

10 miles

Step-by-step explanation:

Let's call the number of miles driven in a day "x". The total cost for Triangle Truck Rental can be expressed as:

Cost (Triangle) = $35 + 0.5x

The total cost for Circle Rent-A-Truck can be expressed as:

Cost (Circle) = $55 + 0.3x

We want to find the value of x such that Cost (Triangle) = Cost (Circle). So we can set the two expressions equal to each other and solve for x:

$35 + 0.5x = $55 + 0.3x

0.2x = $20

x = 100 miles

So the man would need to drive 100 miles in one day for both companies to have the same total cost.

The counterexample of the given conditional statement is "14 is even number and is divisible by 7."

Counterexamples are used in math to contradict a statement. Counterexamples are used to prove the limitations of possible theorems.

The given statement is "If a number is divisible by seven, then it is odd."

Number, 14, 28, 42, 56 are even numbers and they are divisible by seven.

Therefore, the counterexample of the given conditional statement is "14 is even number and is divisible by 7."

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Answer: the answer is 28

Step-by-step explanation: 28 is divisible by 7 and it is a even number

Answer: the shadow will extend 43.75m

Step-by-step explanation:

Using a system of equations, the number of each type of coffee that Julia and her husband should buy is as follows:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations can also be described as simultaneous equations.

The cost per pound of City Roast Columbian coffee = $6.50

The cost per pound of French Roast Columbian coffee = $8.20

The total quantity of the blend = 34 pounds

The cost per pound of the blend = $6.90

The total cost of the 34 pounds = $234.60 ($6.90 x 34)

Let the number of pounds of City Roast coffee = x

Let the number of pounds of French Roast coffee = y

x + y = 34 ... Equation 1

6.5x + 8.2y = 234.6 ... Equation 2

Multiply Equation 1 by 6.5:

6.5x + 6.5y = 221 ... Equation 3

Subtraction Equation 3 from Equation 2:

6.5x + 8.2y = 234.6

-

6.5x + 6.5y = 221

1.7y = 13.6

y = 8

Substitute, y = 8 in Equation 1:

x + y = 34

x = 34 - 8

x = 26

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The summary of the given data is Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56  . So option C is correct.

The middle  number of data in a collection is known as the median. Three alternative metrics are employed in mathematics to determine the average value for a given group of integers. They are the median,  mode, and mean. The measures of central tendency are this trio of measurements.

Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)

Median = {(n+1)/2}th term (for odd)

Based on the given information,

we can see that the box plot shows the values of 44, 48, 50.5, 53, and 56.

These values represent the minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum, respectively.

Therefore, the five-number summary for this data is:

Min = 44,

Q1 = 48,

Median = 50.5,

Q3 = 53,

Max = 56

So the answer is: Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56

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The original price of the upright bike is $3,600.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency.

Original price of the upright bike = sales price / percent discount

= $720 / (20/100)

$720 / 0.2

= $3,600

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The number as decimal is 26583.0

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

Number = 26583

Also, we have the required value of 5 to be

Required = 100

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

The number 5 must have a value of 100 in the new number i.e. 500

So, we have

Number = 26583

Rewrite as

Number = 26500 + 83

This means that we add 5 at the end

So, we have

Number = 26583.0

Hence, the new number is  26583.0

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By making the discriminant equal to zero, we can see that the quadratic equation has one real solution only for z = 10.

For a general quadratic equation:

a*x^2 + b*x + c = 0

We define the discriminant as:

D = b^2 - 4ac

The quadratic equation will have only one real solution only if the discriminant is equal to zero.

Here the quadratic is:

(z - 5)*x^2 - z*x + 5 = 0

Then the discriminant is:

(-z)^2 - 4*5*(z - 5)

And that must be equal to zero, then we need to solve:

z^2 - 20*(z - 5) = 0

z^2 - 20z + 100 = 0

Using the quadratic formula we will get:

[tex]z = \frac{20 \pm \sqrt{(-20)^2 - 4*1*100} }{2} \\\\z = \frac{20 \pm 0}{2} \\\\z = 10[/tex]

So the quadratic equation has one real solution only for z = 10.

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Answer:

Step-by-step explanation:

(a) (i) The mean of the original data set is denoted as μ and the constant value being added to each data point is denoted as c.

The formula for the new mean is simply μ + c, so the new mean is μ + 6 = 10 + 6 = 16.

(a) (ii) The standard deviation of the original data set is denoted as σ. Adding a constant value to each data point does not change the spread of the data set, so the new standard deviation is still σ = 3.

(b) (i) The mean of the original data set is denoted as μ and the constant value being multiplied to each data point is denoted as k.

The formula for the new mean is μ * k, so the new mean is μ * 6 = 10 * 6 = 60.

(b) (ii) The variance of the original data set is denoted as V. To find the new variance after multiplying each data point by k, we can use the formula: k^2 * V.

So, the new variance is 6^2 * V = 36 * V.

--------

Here is a definition of each variable:

μ: The mean of a set of data is the sum of all the values divided by the number of values. It represents the average value of the data set.

σ: The standard deviation of a set of data is a measure of the spread of the data set about the mean. It is the square root of the variance.

V: The variance of a set of data is the sum of the squares of the deviations of each value from the mean, divided by the number of values. It is a measure of the spread of the data set about the mean, but it is measured in squared units.

c: A constant value added to each data point.

k: A constant value multiplied to each data point.

Answer:

Step-by-step explanation:

-0.2x+3 / 2 = -0.6 =>

-0.2x = -(3/2) - 0.6 => (facotorize out -1)

x = ((3/2)-0.6)/0.2 =>

x = 4.5