1. In the figure below, a line intersects two parallel lines. Fill in the missing about how you might solve for the measurement help ASAP

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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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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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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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:

b

Step-by-step explanation:

make sure the y axis doesnt repeat

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

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

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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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

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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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]

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:

This system of equations can be solved using substitution or elimination methods.

Using substitution, we can solve for one of the variables in one of the equations and substitute that expression into the other equation.

Solving for x in the second equation:

x + 3y = 1

x = 1 - 3y

Substituting this expression for x into the first equation:

-4(1 - 3y) - 15y = -10

Expanding and solving for y:

-4 + 12y - 15y = -10

12y - 4 = -10

12y = -6

y = -1/2

Now that we know y = -1/2, we can substitute this value back into the expression for x:

x = 1 - 3(-1/2) = 1 + 3/2 = 7/2

So the solution to the system of equations is (7/2, -1/2).

Checking the solution in both equations:

-4(7/2) - 15(-1/2) = -4(7/2) + 15/

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 balance in the account after 16 years, given interest rate and the compounding period, is $ 10, 421. 83.

To find the balance after 16 years, the formula to be used is the compound interest formula which is:

= Amount invested x ( 1 + rate ) ^ number of periods

Rate :

= 6 % / 12 months per year

= 0. 5 %

The number of periods :

= 16 years x 12 months a year

= 192 periods

The value would be :

= 4, 000 x ( 1 + 0. 5% ) ¹⁹²

= $ 10, 421. 83

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The next number in this sequence is 63, which is the result of multiplying the previous number (39) by 2 and then adding 6.

The measure of other sides of a triangle are 15.11 units and 10.76 units.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

In the given triangle, ∠B=45°, ∠C=52° and AB=12 units.

By using angle sum property of a triangle,

∠A+∠B+∠C=180°

∠A+45°+52°=180°

∠A+97°=180°

∠A=83°

Now, by using sine rule, we get

sin83°/a=sin45°/b=sin52°/12

0.9925/a=0.7071/b=0.788/12

0.9925/a=0.788/12 and 0.7071/b=0.788/12

0.788a=11.91 and 0.788b=8.4852

a=11.91/0.788 and b=8.4852/0.788

a=15.11 units and b=10.76 units

Therefore, the measure of other sides of a triangle are 15.11 units and 10.76 units.

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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

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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Answer: x=35

Step-by-step explanation:

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

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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The value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.

We carry out specific operations in mathematics, such as addition, subtraction, multiplication, etc. Generally speaking, these operators accept two or more operands and output a result dependent on the operation carried out. Similar to this, in set theory, several operations are typically done on two or more sets to obtain a new set of elements depending on the operation. The number of elements supplied by the operation and processing the result of a collective set is represented by the union and overlap of sets. All of the components are taken into account in the outcome when there is a union, but only the ones that are shared when there is an intersection.

The union of the two sets depict all the terms present in both the sets.

Thus, the value of (A ∪ B) is:

(A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18}

The intersection of the sets depict all the common terms present in the two sets thus the value of (A ∩ B) is:

(A ∩ B) = {7}

Hence, the value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.

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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 base-nine system of 76 base 10 is 84

We will divide 76 by 9 and write down the remainder

9 | 76 R

9 | 8 | 4

9 |8 | 8

The remainder is then written from the bottom value giving us 84

Consequently, base 10 numbers can be converted to base 9 by dividing by 9 and writing the remainder in the reverse order of bottom to top.

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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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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

Answer:

              The area of the quadrilateral is C: 12 square feet.

Step-by-step explanation:

               In the photo, the quadrilateral is divided into two triangles, both having a base length of 4 feet and a height of 3 feet. Therefore, we can find the area of the entire quadrilateral by adding the areas of the two triangles together. Since the triangles have a base length of 4 feet and a height of 3 feet, their individual areas will be [tex]4*3*\frac{1}{2} =12*\frac{1}{2} = 6[/tex] square feet. As there are two triangles, we need to multiply the area of one triangle by 2 to get the total area of the quadrilateral, which would be [tex]6 * 2=12[/tex] square feet. Hence, we can conclude that the correct answer will be C.

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Answer:

22/22X22-22+22= 22÷5 =4.5

33/33X33-33+33=33÷5=6.6

The units of water the friends used in one month is 820 units.

The total units of water used as read by the meter = 789 units + 820 units

= 1609 units

Therefore, the friends used a total of 820 units of water.

Complete question:

A water meter shows how many units of water Riya and her friends use.

Riya reads the meter when they move in. It shows 789 units.

She reads the meter again after one month. It reads 820 units.

How many units of water did the friends use in one month?

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