Drag one number to each box (?) to make three true statements.
1
2
3
4
5
7
6
7
8
9

3/8 x ?/? > 1


3/8 x ?/? = 1


3/8 x ?/? < 1

Answer:

A = (1/2)(5.5)(8.5 + 12.5) = 57.75 m^2

Part A: The GCF of the expression 12x² + 18x - 12 is 6x.

Part B: The factored form of the expression 12x² + 18x - 12 is 6x(2x + 3) - 12x.

Part C: The result matches the original expression, which means our factoring is correct.

Part A: Finding the Greatest Common Factor (GCF)

To find the greatest common factor (GCF) of the given expression, we need to identify the largest term or number that can divide evenly into all the terms of the expression. In this case, we are dealing with three terms: 12x², 18x, and -12.

The coefficients of the three terms are 12, 18, and -12. The common factor of these coefficients is 6, as it can divide evenly into all of them.

The variable 'x' is present in both the first and second terms, and 'x' is also a common factor.

Combining the common factors of the coefficients and variables, we find that the GCF of the expression 12x² + 18x - 12 is 6x.

Part B: Factoring the Expression Completely

Now that we have determined the GCF of the expression, we can proceed to factor it completely.

We already found that the GCF is 6x. Factoring it out from each term, we get:

6x(2x + 3) - 6x(2)

We can simplify the expression further by multiplying the GCF with the remaining terms inside the parentheses:

6x(2x + 3) - 12x

Part C: Checking the Factoring

To check if our factoring is correct, we can multiply the factored expression back and see if it matches the original expression.

Multiplying the factored expression:

6x(2x + 3) - 12x

= 12x² + 18x - 12

The result matches the original expression, which means our factoring is correct.

To know more about expression here

https://brainly.com/question/14083225

#SPJ1

[tex]Given:\ x_{n+1}=\sqrt[3]{6x_{n}-1}\ ,\ x_{1}=4\\\\The\ iterative\ formula\ can\ be\ re-written\ as:\\x_{n}=\sqrt[3]{6x_{n-1}-1}\\\hrule\ \\x_2=\sqrt[3]{6x_{1}-1}\\x_2=\sqrt[3]{6(4)-1}\\x_2=\sqrt[3]{23}\approx 2.84\\\hrule\ \\x_3=\sqrt[3]{6x_{2}-1}}\\x_3=\sqrt[3]{17.04-1}\\x_3=\sqrt[3]{16.04}\approx 2.52\\\hrule\ \\x_4=\sqrt[3]{6x_{3}-1}}\\x_4=\sqrt[3]{15.12-1}\\x_4=\sqrt[3]{14.12}\approx 2.41[/tex]

The expressions 1 and 4 are having values less than 1.

Given are the expressions, we need to solve them,

1) -7 · 1/2 - 4

= -7/2-4

= -7-8 / 2

= -15/2

= -7.5 < 1

2) -7 · (1/2 - 4)

= -7 · -7/2

= 49/2

= 24.5 > 1

3) -7 · 1/2 · (- 4)

= -14/2 · (- 4)

= 56/2

= 28 > 1

4) -7 + 1/2 · (- 4)

= -7 -4/2

= -7 -2

= -9 < 1

5) -7 ÷ 1/2 · (- 4)

= -7 × 2 × -4

= -14 × -4

= 56 > 1

Hence, the expressions 1 and 4 are having values less than 1.

Learn more about expression click;

https://brainly.com/question/14083225

#SPJ1

Answer:

Step-by-step explanation:

To find the order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3, we need to calculate the average rate of change of each function over that interval and compare them.

For f(x), we have:

average rate of change = [f(3) - f(-1)] / (3 - (-1))

= [(3+3)^2 - 2 - ((-1)+3)^2 + 2] / 4

= 23

For g(x), we have:

average rate of change = [g(3) - g(-1)] / (3 - (-1))

= [0 - (-3/2)] / 4

= 3/8

For h(x), we have:

average rate of change = [h(3) - h(-1)] / (3 - (-1))

= [(62-14)/(3-(-1))]

= 12

Therefore, the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3 is:

g(x), f(x), h(x)

So the answer is option (b).

The standard form of the equation of a circle and the location of where Millie lives indicates;

12) The equation of the circle is; (x - 6)² + (y - 2)² = 25/π

13) Dave does not deliver to Millie

The equation for the area of a circle is A = π × Radius²

12) The length of a block = 250 inches

The distance of the post office = 6 blocks east and 2 blocks north

The area the postal carriers delivers mail = 25 square blocks

The coordinates of the location of the post office = (6, 2)

The radius of the circle ias therefore, r = √(25/π) ≈ 2.82

The equation of a circle is; (x - h)² + (y - k)² = r²

Where; (h, k) = (6, 2)

13) The coordinates of the location where Millie lives is (3, -3)

The distance of Millie's address 3 blocks south of the city hall, whereby the carrier Dave reaches about south 2.82 blocks, from 2 blocks north from the city hall, which is about 0.82 blocks south from the city hall.

Therefore, Dave's area does not extend to Millie's location and Dave does not deliver mail to Millie

Learn more on the equation of a circle here: https://brainly.com/question/30989368

#SPJ1

The sides of the triangle can be identified as follows:

6. The longest side is PR  7. The shortest side is QR

Based on the relationship between the sides of a triangle and its relative angle measures, we recall that the longest side will be opposite the largest angle measure and vice versa.

Therefore, we have the following:

m<Q = 83 degrees

m<P = 48 degrees

m<R = 180 - 83 - 48 = 49 degrees.

Angle Q is the largest angle, while angle P is the smallest.

Thus, we can conclude that:

6. The side that is the longest is PR

7. The side that is the shortest is QR

Learn more about the sides of triangles on:

https://brainly.com/question/30561079

#SPJ1

The probability that both M&Ms are green is 29% and the probability that John eats a red M&M then a green M&M is 25%

Here, we have

Red = 27

Green = 32

This means that

Total = 27 + 32

Total = 59

So, we have

P(Both green) = 32/59 x 31/58

Evaluate

P(Both green) = 29%

And, The probability of red M&M then a green M&M,

Here, we have

Red = 27

Green = 32

This means that;

Total = 27 + 32

Total = 59

So, we have

P(Red and green) = 27/59 x 32/58

Evaluate;

P(Red and green) = 25%

Read more about probability at

brainly.com/question/24756209

#SPJ1

The rectangular form of the complex number z = 3√2 cis (7π/4) is

z = -3 - 3i

We have,

To convert a complex number from polar form to rectangular form, we use the following formulas:

x = r cos(theta)

y = r sin(theta)

where r is the modulus of the complex number, and theta is its argument.

In this case, we have:

r = 3√2

theta = 7π/4

So:

x = 3√2 cos(7π/4) = 3√2 (-1/√2) = -3

y = 3√2 sin(7π/4) = 3√2 (-1/√2) = -3

Therefore,

The rectangular form of the complex number z = 3√2 cis (7π/4) is

z = -3 - 3i

Learn mroe about polar form here:

https://brainly.com/question/28976035

#SPJ1

The next step in the construction of a regular hexagon is A. Use a compass and straightedge to continue drawing an equilateral

A circle with the required radius must first be drawn in order to make a regular hexagon. Draw a second circle whose centre is one of the spots on the first circle using the same radius. These two circles' intersection points will form the vertices of an equilateral triangle. Three of these equilateral triangles, with their vertices on the circle, must be drawn inside a circle. At the circle's centre, these three triangles will have a common vertex.

Drawing three more equilateral triangles, each of which shares a side with one of the previously drawn triangles, is necessary to finish the building of a regular hexagon. Drawing equilateral triangles keeps on until there are six of them, each of which has a side in common with a preceding triangle.

Read more about hexagon on:

https://brainly.com/question/30384520

#SPJ1

Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

;>

The relationship between Dani's time and Candice's time, taking into account the fact that Dani took 5 minutes longer to run the course. it is Reasonable time to assume that the runners' rates were constant. Option C is the correct answer.

Let "t" be the time it took Candice to run the course.

Then, according to the problem statement, Dani took 5 minutes longer than Candice to run the course. Therefore, Dani's time is equal to Candice's time plus 5 minutes, which can be expressed as:

D = C + 5

where D is Dani's time and C is Candice's time.

This equation represents the relationship between Dani's time and Candice's time, taking into account the fact that Dani took 5 minutes longer to run the course. It can be used to solve problems related to the two runners' times, such as finding their individual times or comparing their rates. Option C is the correct answer.

It is important to note that this equation assumes that both runners ran the course at a constant rate. If the runners' rates varied throughout the course, then the equation would not accurately represent their times. However, for the purposes of this problem, it is reasonable to assume that the runners' rates were constant.

To know more about Reasonable time.

https://brainly.com/question/30204424

#SPJ11

The length of the enlarged photo should be approximately 8.57 inches.

The original photo and the enlarged photo are similar rectangles, we know that the ratio of their corresponding sides is the same.

Let's use "x" to represent the length of the enlarged photo.

We can set up a proportion to find the value of "x":

(original length) / (original width) = (enlarged length) / (enlarged width)

Substituting the given values, we get:

(5 inches) / (3.5 inches) = x / 6 inches

To solve for "x", we can cross-multiply and simplify:

5 inches × 6 inches = 3.5 inches × x

30 square inches = 3.5 inches × x

Dividing both sides by 3.5 inches:

x = 30 square inches / 3.5 inches

x = 8.57 inches (rounded to two decimal places)

For similar questions on length

https://brainly.com/question/28108430

#SPJ11

Answer:

5.25

Step-by-step explanation:

not much to show, go 3 topping across then up to see the price

Answer:

f : u = 12 : 9, so f : u : w = 12 : 9 : 5.

The Perimeter of the walkway is 18√5 ft.

Explanation:-

The perimeter of the rectangular walkway is the sum of the lengths of its four sides. If the width of the walkway is √5 ft and the length is 8√5 ft, then we can label the sides as follows:

Width = √5 ft

Length = 8√5 ft

Width = √5 ft

Length = 8√5 ft

The perimeter P is given by:

P = Width + Length + Width + Length

= 2(Width + Length)

= 2(√5 + 8√5)

= 2(9√5)

= 18√5 ft

Therefore, the perimeter of the walkway is 18√5 ft.

Read More About the Formula of Perimeter for different shape Object.

https://brainly.in/question/34547055

The slope of Line B would have to be -1/2.

Two lines are perpendicular to each other if the product of their slopes is -1. The slope of Line A is given as 2. Therefore, the slope of Line B would have to be the negative reciprocal of 2, which is -1/2. This ensures that the product of the slopes of Line A and Line B is -1, satisfying the condition for perpendicularity.

In general, if the slope of Line A is m, then the slope of a line perpendicular to Line A would be -1/m. This relationship holds because perpendicular lines form right angles, and the slopes of perpendicular lines are negative reciprocals of each other.

To learn more about perpendicular, here

https://brainly.com/question/12746252

#SPJ2

TU is parallel to MN.

Given that the slope of a line MN is -3, we need to find a line which is parallel to the MN.
So we know that the parallel lines are having equal slope so the line which is parallel to the MN it must have slope of -3.

Therefore,

Considering the line TU, find the slope = y₂-y₁ / x₂-x₁

= 10-1 / 5-8 = -9/3 = -3

Since, the slope of the line TU is -3 therefore we can say the lines TU and MN are parallel liens.

Hence TU is parallel to MN.

Learn more about slopes, click;

https://brainly.com/question/3605446

#SPJ1

The type of the conic basic x² - 4x + y² + 2y = 4 is a circle

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

x² - 4x + y² + 2y = 4

The above equation has the following features

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

A conic section that has the above features is a circle

This means that the type of the conic basic is a circle

Read more about conic section at

https://brainly.com/question/29192791

#SPJ1

Answer:

B. 40

Step-by-step explanation:

you would multiply 5 and 320 and then do the square root of the number

(c) 15i + 4b ≥ 100 inequality represents this scenario.

To represent the scenario described in the problem, we need to use an inequality that relates the amount of money Emily spends on ink and brushes to the total amount of money she has available. Let's call the amount of ink Emily buys "x" and the number of brushes "y". Then the total amount of money she spends is:

Total cost = 8x + 18y

We want to know when this total cost is less than or equal to $100, so we can write:

8x + 18y ≤ 100

This inequality means that the total cost of ink and brushes must be less than or equal to the amount of money Emily has available. Therefore, the answer is (c) 15i + 4b ≥ 100.

Correct Question :

Emily has $100 extra to spend on supplies for her T-shirt-making business. She wants to buy ink, i, which costs $8 a bottle, and ne brushes, b, which are $18 each. Which inequality below represents this scenario?

a) 4i+100 ≤ 15b

b) 15i + 4b ≤ 100

c) 15i + 4b ≥ 100

d) 4i + 15b ≤ 100

To learn more about inequality here:

https://brainly.com/question/30231190

#SPJ1

Answer:

P = (1/2)(6)(8)/(π(5^2))

= 12/(25π)

= .31 (about 31%)

Answer:Xmin:

-10

Xmax:

10

Ymin:

-10

Ymax:

10

Step-by-step explanation:

Let w be the weight on point s. Since the sum of the weights is 1, the weight on point t is 0.625, we can write:

w + 0.625 = 1

Subtracting 0.625 from both sides, we get:

w = 1 - 0.625 = 0.375

Therefore, the weight on point s is 0.375.

Answer: A

Step-by-step explanation:

Volume= LxWxH so we get 20x28x24 as given.

Volume= 13,440 which is the volume of the box given. ANd so if the box is 10,500cubic inches, we subtract to find the difference.

13,440-10,500= 2,940 Cubic Inches

Option A

Answer:

Part A:  13440 cubic inches.

Part B: A - 2940 cubic inches.

Step-by-step explanation:

The volume of the box = 24x20x28 = 13440 cubic inches.

The problem tells us that his gift is 10,500 cubic inches. So subtract that from the volume of the box.

13440-10500 = 2940 cubic inches. The answer is A.

Answer:

87

Step-by-step explanation:

I am not sure but try (143-104=39)39+21+27 you get 87

Answer:

Step-by-step explanation:

To compare the minimum y-values of the given functions, we need to find the minimum point of each function and compare their respective y-values.

For the function f(x) = 4 sin(2x-1) - 11, we know that the sine function oscillates between -1 and 1, and is multiplied by a factor of 4, which will change the amplitude of the function. We can find the minimum point of the function by setting its derivative equal to zero:

f'(x) = 8 cos(2x-1) = 0

cos(2x-1) = 0

2x-1 = (2n+1/2)π, where n is an integer

x = (2n+1/4)π + 1/2, where n is an integer

The minimum point will occur at x = (2n+1/4)π + 1/2, and the corresponding y-value can be found by substituting this value of x into the original function:

f(x) = 4 sin(2x-1) - 11

f((2n+1/4)π + 1/2) = 4 sin(2[(2n+1/4)π + 1/2]-1) - 11

f((2n+1/4)π + 1/2) = 4 sin(2nπ + π/2) - 11

f((2n+1/4)π + 1/2) = 4 (-1)^n - 11

We can see that the y-value of the minimum point alternates between -15 and -7 as n changes. Therefore, the smallest minimum y-value for the function f(x) is -15.

For the function h(x) = (x-2)² + 4, we know that it is a quadratic function with a minimum point at x=2. The y-value of the minimum point can be found by substituting x=2 into the function:

h(2) = (2-2)² + 4

h(2) = 4

Therefore, the smallest minimum y-value among the two given functions is 4, which is the minimum y-value of the function h(x) = (x-2)² + 4.

The equations of the three mediators of triangle ABC are:

x = 3 (the mediator of AB)

y = (-1/2)x + 5 (the mediator of AC)

y = (1/2)x + 2 (the mediator of BC)

The coordinates of A are (1,2) and the coordinates of B are (5,2), so the midpoint of AB is:

((1+5)/2, (2+2)/2) = (3,2)

The coordinates of A are (1,2) and the coordinates of C are (3,6), so the midpoint of AC is:

((1+3)/2, (2+6)/2) = (2,4)

The coordinates of B are (5,2) and the coordinates of C are (3,6), so the midpoint of BC is: ((5+3)/2, (2+6)/2) = (4,4)

The slope of BC is: (6-2)/(3-5) = -2

Leans more about equations on

https://brainly.com/question/1214333

#SPJ1