puzzle one find the values of the unknown variables a b c d e and f substitude the values of the unknown numbers​

The value of the expression when z = 10 is 1000

The given parameters are

z = 10

z^3 - 3(z-10)

Substitute z = 10 in z^3 - 3(z-10)

So, we have

10^3 - 3(10-10)

Evaluate the expression

10^3 - 3(10-10) = 1000

hence, the value of the expression when z = 10 is 1000

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The lines are neither, nor perpendicular

The equations of the lines are given as

5x + 2y = 14

y = -5x + 9

Make  y the subject in both equations

So, we have

y = -2.5x + 7

y = -5x + 9

The slopes of the above equations are

m1 = -2.5

m2 = -5

The above slopes are neither equal not opposite reciprocals

Hence, the lines are neither, nor perpendicular

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Answer: [tex]\frac{1}{\sqrt{2}}[/tex]

Step By Step Explanation:

[tex]=\frac{2\sqrt{2}}{2\cdot \:2}[/tex]

[tex]=\frac{\sqrt{2}}{2}[/tex]

[tex]=\frac{\sqrt{2}}{\sqrt{2}\sqrt{2}}[/tex]

[tex]=\frac{1}{\sqrt{2}}[/tex]

Answer: n=18

Step-by-step explanation:

f(n) = -3(n - 1); -51

-51=-3(n - 1)

-51/(-3)=-3(n - 1)/(-3)

n-1=17

n+1-1=17+1

n=17+1

n=18

The number of each type of vehicle sold are :

SUVs : 300

Passenger cars : 270

Number of SUVs were sold more than passenger cars = 30

Total number of cars sold = 540

Let the number of Passenger car sold = x

Then, The number of SUVs sold = x + 30

So, Total number of cars sold = Number of Passenger car sold + Number of SUVs sold

     540 = x + (x + 30)

2x + 30 = 540

       2x = 540

         x = 540/2

         x = 270

We got, the number of Passenger car sold (x) = 270

The number of SUV's sold = x + 30

The number of SUV's sold = 270 + 30 = 300

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Answer:

36.5 is median Temperature for girls

Step-by-step explanation:

Let's first calculate the median Temperature for boys to show you how it is done;

Below are the Temperature, they are not in ascending order

37.0,36.1,37.1,37.3,36.3,36.4,36.7,36.7,36.7,35.8

Now let's arrange them in ascending order

35.8, 36.1, 36.3, 36.4, (36.7, 36.7, )36.7, 37.0, 37.1, 37.3

In the middle are 36.7 and 36.7 as seen in the bracket

to find median = 36.7+36.7/2

➟ 73.4/2

➟ 36.7

∴36.7 is median Temperature for boys

Now that I've shown you example with boys temperature let's go find the actual temperature which is girls

Below are temperature for girls

34.7,35.8,35.9,36.2,36.4,36.6,36.6,36.8,36.8,36.9

Let's arrange them in ascending order

34.7, 35.8, 35.9, 36.2,( 36.4, 36.6, )36.6, 36.8, 36.8, 36.9

In the middle are 36.4 and 36.6 as seen in the bracket

to find median = 36.4+36.6/2

➟ 73/2

➟ 36.5

∴36.5 is median Temperature for girls

The single power that is equivalent (4³)² to is 4^6.

This is a term in mathematics to refer to the exponents. The given expression is four to the power of three all to the power of two. Exponents helps to represent equations and makes it easier to remember  and handle.

Given data

(4³)²

This could be solved using the laws of indices

(4³)² =  4³ * 4²

4³ * 4² = 4³ *² = 4^6

Hence we can say that the single power that is equivalent (4³)² to is 4^6.

base = 4

power = 6

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The length of the interval AB is 7.21 units.

Given,

From the graph we can have the triangle ABC.

Length of side AC = 6 - 2 = 4 units

Length of side BC = 7 - 1 = 6 units

We have to find the length of AB.

By using Pythagorean theorem we can determine the length of AB.

Hypotenuse² = Altitude² + Base²

AB² = AC² + BC²

AB² = 4² + 6²

AB² = 16 + 36

AB² = 52

AB = [tex]\sqrt{52}[/tex] = 7.21

That is, the length of the interval AB is 7.21 units.

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The inequality stated may be expressed as 2m - 5/4 ≤ 7/8.

There are four sorts of inequality.

A < B means that A is less than B.

A > B means a is greater than B.

A ≥ B, a is bigger than or equal b.

A ≤ B, a is less than or equal.

In light of the posed query

The maximum difference between two numbers, m and 5/4, is equivalent to an inequality of the form 2m - 5/4 < 7/8.

The difference between two numbers, "m," and 5/4 is 2m - 5/4, which can only represent "less than" or "equal to."

∴ The formula for the given statement is 2m - 5/4 < 7/8.

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The total cost of wallpaper is $4 per square foot as calculated from the surface area of the rectangular prism.

The total surface area is the total area of all the surfaces of an object. The surface area is calculated by the area of the surface in the form of the 2 dimensional representation.

Here the box is in the form of an rectangular prism , which means that the box is in the form of a cuboid.

From the figure we can see that the dimensions of the box are :

length = 6 feet

width = 5 feet

height = 3 feet

We know that the total surface area of a rectangular prism is given by:

2×(length × width + width  ×height + height × length)

or, 2 × (6×5 + 5×3 + 3×6)

or, 126 ft²

Now the total cost for wallpaper is $504 .

Now to calculate the cost per square feet we will divide the total money by the total surface area.

∴Cost of the wallpaper per square foot=$(504÷ 126) per ft² = $4 per ft²

Hence the cost of the wallpaper is $ 4 per ft² .

Disclaimer: The figure of the prism is attached below.

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To get a perfect square, the smallest number to be multiplied by 6300 is 7.

Multiplication is the process of calculating the result when a number is taken times. Each of the numbers is referred to as a factor of the product, which is the outcome of a multiplication.

Consider the number 6300 which can also be written as:

6300 = 2 × 2 × 3 × 3 × 5 × 5 × 7

Now, 2, 3, and 5 are in pairs. Only 7 is not in pair.

Now, we will multiply 6300 by 7.

Then,

6300 × 7 = 44100

Therefore, the number 44100 is the number that makes the perfect square.

Let's say x² = 44100,

Taking square root on each side of the equation:

x² = 44100

√x² = √44100

x = √[ 21 × 21 × 10 × 10 ]

x = 210

Therefore the smallest number by which 6300 is multiplied to get a perfect square is 7.

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The 2,722 to the nearest thousand is 3000.

In the given statement is :

What is 2,722 rounded to the nearest thousand

Number is => 2722

Hence, the 2,722 to the nearest thousand is 3000.

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There will be roughly 12,000 bacteria after 12 hours.

So, there are 5300 bacteria  and it gets doubles in 10 hours:

Then,

Therefore, there will be roughly 12,000 bacteria after 12 hours.

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Answer: y=6x−8

Step-by-step explanation:

From the given stem-and-leaf plot, we have that:

a) The maximum number of cups of coffee sold on a single day is of 78.

b) In 5 days, less than 60 cups were sold.

c) The average sales is of 65 cups of coffee a day.

The questions are missing, and they are given by the image at the end of the answer.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

Considering the key in this problem, the measures(number of cups of coffee sold each day) are given as follows:

50, 52, 58, 59, 60, 63, 63, 65, 69, 69, 72, 75, 77, 78.

Hence:

a) The maximum number of cups of coffee sold on a single day is of 78.

b) In 5 days, less than 60 cups were sold.

The average of a data-set is given by the sum of all observations in the data-set divided by the number of observations, hence:

M = (50 + 52 + 58 + 59 + 60 + 63 + 63 + 65 + 69 + 69 + 72 + 75 + 77 + 78)/14 = 65.

The average sales is of 65 cups of coffee a day.

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Answer:

-23

Step-by-step explanation:

Just add left to right

Answer:

8

Step-by-step explanation:

[tex]g(x)=3^2+2x-4=5+2x \\ \\ g(1.5)=5+2(1.5)=8[/tex]

Answer:

It means that the -4 is one of the solutions for this polynomial. In other words, -4 is a point in the x axis of the graph where the function touches said axis.

The value of the polynomial at P(-4) will be 0.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given that the polynomial function is P(x) = x³ + 11x² + 34x + 24. The value of the function at P(-4) will be calculated as:-

P(x) = x³ + 11x² + 34x + 24

P(-4) = (-4)³ + 11(-4)² + 34(-4) + 24

P(-4) = -64 + 176 - 136 + 24

P(-4) = 200 - 200

P(-4) = 0

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Answer: 2,730

Step-by-step explanation:

Explained in mental math proccess:

In 455, the one value will be multiplied by 6. 5x6= 30.

In 455, the tens value will be multiplied by 6. 50x6= 300.

In 455, the hundreds value will be multipled by 6. 400x6= 2,400.

Find the sums of all products multiplied by 6. 30+300+2,400= 2,730.

455x6= 2,700

Answer:

$396.84

Step-by-step explanation:

To solve for this question, we can use the formula:

Cost of Paint per Gallon × Amount of Paint needed in Gallons

Cost = $29.95 per gallon x 13.25 gallon

= $396.84 (Rounded off to 2 decimal places)

Answer:

$396.84

Step-by-step explanation:

We can set up this equation

29.95*13.25

Multiply

396.8375

Round

$396.84

Answer:

Exact Form: 43/8

Decimal Form: 5.375

Rounding to the Nearest whole number: 5

Answer:

D) b/7 + 18 =16

Step-by-step explanation:

Let's solve your equation step-by-step.

b/7+18=16

Step 1: Simplify both sides of the equation.

1/7b+18=16

Step 2: Subtract 18 from both sides.

1/7b+18−18=16−18

1/7b=−2

Step 3: Multiply both sides by 7.

7*(1/7b)=(7)*(−2)

b=−14

The equation: 1/2 + 1/6 = 2/3

Is true.

Here we have the equation:

1/2 + 1/6 = 2/3

First, we need to find a common denominator for the two fractions, if we multiply and divide the first one by 3 we get:

(3/3)*(1/2) = 3/6

Replacing that in the equation:

3/6 + 1/6 = 2/3

4/6 = 2/3

Now we can simplify the fraction in the left by dividing both numerator and denominator by 2:

4/6 = 2/3

2/3 = 2/3

Thus, the equation is true.

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So the x of the vertex is -b/2a which is -6/-2 which is 3. -2*9+6*3+12 is 18+18+12 so the vertex is (3, 48). The vertical intercept is 12.

The required intersection would be at the point (55, 460) in the given graph which shows a round of golf is 55 and a total cost is $460.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

We have been given that the graph represents the following situation.

Golfers must first pay a $75 membership fee and an additional $7 for each round of golf in order to play at Gulf Shores Range.

Golfers at the Royal Estates Country Club pay $5 for each game of golf, but membership costs $185.

Since the x-axis represents a round of golf and the y-axis represents a total cost.

According to the graph,

Here is a round of golf = 55 and a total cost = $460

So the intersection represents this situation at the point (55, 460).

Therefore, the required intersection would be at the point (55, 460) in the given graph.

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