Using the quadratic equation to solve 3x 2 + 11x - 4 = 0, the value of b 2 - 4ac is.

The solution of the graph to the inequality Ix+3122 x = -11 or x = 5

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

We are given that;

Inequality= Ix+3122

Now,

First, rewrite it as |x+3|/22 ≤ 4/11

Then, find the equation of the boundary line by replacing ≤ with =: |x+3|/22 = 4/11

This means x+3 = ±(4/11)*22

So x = -3 ± 8

x = -11 or x = 5

Therefore, by inequalities the answer will be x = -11 or x = 5

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Both expressions result in the same answer of 15 when evaluated.

An expression is a combination of numbers, variables, and operators that represents a mathematical computation or relationship. Expressions can be as simple as a single number or variable, or as complex as a combination of several numbers, variables, and operators.

Part A:

To subtract 13 from the product of 4 and 7, we can write the expression as:

4 x 7 - 13

Part B:

5 x (4 x 7 - 13) can be simplified using the order of operations (PEMDAS) as follows:

First, we perform the operation inside the parentheses:

4 x 7 - 13 = 28 - 13 = 15

Then, we multiply 5 by the result of the operation inside the parentheses:

5 x 15 = 75

Therefore, the expression 5 x (4 x 7 - 13) simplifies to 75.

Now let's compare this with the expression we wrote in Part A:

4 x 7 - 13 = 15

As we can see, the expression in Part A is equivalent to the simplified expression in Part B.

Therefore, both expressions result in the same answer of 15 when evaluated.

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The distance from first base to third base (Hypotenuse) in a baseball diamond is approximately 127.3 feet.

A baseball diamond is a square with 90 feet (27.4 meters) on each side, with the corners connected by two diagonal lines. The bases are located at each corner of the square, and the pitching rubber is located in the center of the diamond, 60 feet 6 inches (18.4 meters) away from home plate. The distance from home plate to first base and from home plate to third base is 90 feet (27.4 meters),

The distance from first base to third base in a baseball diamond is the diagonal of the square, which can be found using the Pythagorean theorem.

The length of one side of the square (the distance from home plate to first base or third base) is 90 feet.

Using the Pythagorean theorem:

c² = a² + b²

where c is the length of the diagonal (the distance from first base to third base), and a and b are the lengths of the sides of the square.

Plugging in the values we know:

c² = 90² + 90²

c²  = 8,100 + 8,100

c²  = 16,200

Taking the square root of both sides:

c = √(16,200)

c = 127.28 feet

c [tex]\approx[/tex] 127.3 feet when rounded to one decimal place.

Therefore, the distance from first base to third base in a baseball diamond is approximately 127.3 feet.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

A baseball diamond is a square which is 90 feet on the side. What is the distance from the first base to the third base?

Answer: 16.3 cm

Step-by-step explanation:

2.5 meters = 98.4252 inches.

(Round to 98.4)

98.4 - 11.5 = 86.9

(keep subtracting till you can't subtract 11.5 anymore w/o getting a negative number)

6.4 in = 16.3 cm (multiply the length value by 2.54)

16.3 cm left over.

Answer:

[tex]120 cm long each[/tex]

Answer:

Step-by-step explanation:

To find the surface area of the solid given the net, we need to identify all of the faces and add up their areas. Looking at the net, we can see that the solid consists of a rectangular prism and two triangular prisms attached to its sides.

To find the area of the rectangular prism, we need to multiply the length, width, and height. From the net, we can see that the length is 12 units, the width is 5 units, and the height is 8 units. So, the area of the rectangular prism is:

Area = length * width * height

Area = 12 units * 5 units * 8 units

Area = 480 units²

To find the area of the triangular prisms, we need to multiply the base, height, and half the width. From the net, we can see that the base of each triangular prism is 12 units and the height is 8 units. To find the width, we can use the Pythagorean theorem:

width² = height² + base²/4

width² = 8² + 12²/4

width² = 64 + 36

width² = 100

width = 10 units

So, the area of each triangular prism is:

Area = 1/2 * base * height * width

Area = 1/2 * 12 units * 8 units * 10 units

Area = 480 units²

Now, we can add up the areas of all three faces to find the total surface area:

Surface area = area of rectangular prism + area of two triangular prisms

Surface area = 480 units² + 480 units² + 480 units²

Surface area = 1440 units²

Therefore, the surface area of the solid given the net is 1440 units². None of the answer choices match exactly, but the closest one is A. 1292 units².

Answer:

669.75

Step-by-step explanation:

14.10 x 40 hours = 564 plus

21.15 x 5 hours =105.75

add 564 + 105.15= 669.75

Total wage of joe for 45 hours is $669.75 .

Given,

Rate of work for 40 hours = $14.10

So,

Let us calculate the wage for first 40 hours.

14.10 x 40 hours = 564 plus

Now wage for the next 5 hours,

21.15 x 5 hours =105.75

Total wage of joe will b ethe total wage of 45 hours .

Thus,

$564 + $105.15 = $669.75

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Answer:

Step-by-step explanation:

To find the slope of the line represented by the table of values, we need to use the formula:

slope = (change in y) / (change in x)

We can choose any two points from the table to calculate the slope. Let's choose the first and last points: (-7, 9) and (8, -15).

change in y = (-15) - 9 = -24

change in x = 8 - (-7) = 15

slope = (change in y) / (change in x) = -24/15 = -8/5

Therefore, the slope of the line represented by the table of values is -8/5.

Answer:

We know that the wire was cut into 24 equal pieces and the length of each piece is 70 cm.

So, the total length of the wire = 24 x 70 cm = 1680 cm

We also know that 100 cm = 1 meter. Therefore,

1680 cm = 16.8 meters

Hence, the length of the wire is 16.8 meters.

We can write the equation for the area of rectangle as -

Area = 6x².

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is a segmented rectangle as shown in the question.

Assume that the side of each cube inside the rectangle is {x} units.

We can write the area of the rectangle as -

Area = 6 × Cube Area

Area = 6x²

Therefore, we can write the equation for the area of rectangle as -

Area = 6x².

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Answer:

Step-by-step explanation:

To calculate the future value of the investment, we can use the formula:

FV = P * (1 + r/n)^(n*t)

where:

P = the principal amount ($1300 in this case)

r = the annual interest rate expressed as a decimal (8% = 0.08)

n = the number of times the interest is compounded per year (12 for monthly compounding)

t = the number of years of the investment (10 years in this case)

Plugging in the values, we get:

FV = $1300 * (1 + 0.08/12)^(12*10)

FV = $1300 * (1.00666667)^(120)

FV = $1300 * 1.115969

FV = $1,464.75

Therefore, the future value of the investment after 10 years at an APR of 8% compounded monthly would be $1,464.75.

To find the cycle decomposition of (1,2,4)(5,4,1)(2,8) ∈ S8, we can start by applying the permutation to each element in [8] until we end up back where we started.

Starting with 1, we have:

(1,2,4)(5,4,1)(2,8)(1) = (5,2,8)

So 1 goes to 5, which goes to 2, which goes to 8, which goes back to 1. We have found a cycle (1 5 2 8).

Next, we can try 3:

(1,2,4)(5,4,1)(2,8)(3) = (3)

So 3 stays where it is, which means it forms a cycle by itself: (3).

Moving on to 6:

(1,2,4)(5,4,1)(2,8)(6) = (6)

So 6 also forms a cycle by itself: (6).

Next, we can try 7:

(1,2,4)(5,4,1)(2,8)(7) = (7)

So 7 also forms a cycle by itself: (7).

Finally, we try 8:

(1,2,4)(5,4,1)(2,8)(8) = (4,1,5,2)

So 8 goes to 4, which goes to 1, which goes to 5, which goes to 2, which goes back to 8. We have found another cycle: (2 4 1 5).

Putting it all together, we have the cycle decomposition:

(1 5 2 8)(3)(4 1 5 2)

To determine the order of this permutation, we need to find the least common multiple of the lengths of its cycles. The lengths are 4, 1, and 4, so the LCM is 4. Therefore, the order of (1,2,4)(5,4,1)(2,8) ∈ S8 is 4.

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As a result, $300's worth of labor would cost $1,600 overall because there are $1,000 in total fixed costs and $2.00 in variable unit costs.

A variable in mathematics is a symbol or letter that designates a quantity that is subject to variation or value shift. Variables are a basic idea in algebra and other branches of mathematics, and they are used to model real-world situations in mathematical expressions and equations. Variables are frequently used in algebra to represent unknowable values that we are trying to discover, such as an equation's roots or a line's slope. They can also be used to symbolize values that change with time, space, or temperature, among other variables.

given

We must apply the following formula to determine the overall expense for 300 labor hours:

Total price = Fixed price Plus (Variable unit cost x Number of units)

In this case, the variable unit cost is $2 and the set cost is $1,000. We must convert labor hours to units in order to determine the total amount of units. According to the assumption that one unit of work costs one hour, 300 units would be needed.

There are 300 pieces total.

When we enter these numbers into the algorithm, we obtain:

Overall cost: $1,000 plus ($2 multiplied by 300)

Final price equals $1,000 plus $600.00.

Cost in total is $1,600.00.

As a result, $300's worth of labor would cost $1,600 overall because there are $1,000 in total fixed costs and $2.00 in variable unit costs.

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The complete question is :- If the total fixed cost is equal to $1,000.00 and the variable unit cost is $2.00, what will be the total cost for 300 labor hours?

Any point that is 1/4 units away from the origin represents the 25% mark.

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers

Given is a point on the number line that best represents the 25% mark.

The number line is not given, so we will discuss the method to find the 25% mark on the number line. For a point on the number line, its distance from the origin should be (25/100 = 1/4 units) away from the origin. Any point that is 1/4 units away from the origin represents the 25% mark.

Therefore, any point that is 1/4 units away from the origin represents the 25% mark.

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The 98% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is given as follows:

(1160.9, 1339.7).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 7 - 1 = 6 df, is t = 3.1427.

The parameters are given as follows:

[tex]\overline{x} = 1250.3, s = 75.3, n = 7[/tex]

Hence the lower bound of the interval is of:

1250.3 - 3.1427 x 75.3/sqrt(7) = 1160.9.

The upper bound of the interval is of:

1250.3 + 3.1427 x 75.3/sqrt(7) = 1339.7.

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Answer:

  y = 1 +cos(3/2(x+π/3))

Step-by-step explanation:

You want the equation of a cosine graph.

The usual transformations applied to a parent function are ...

The difference between the maximum and minimum of a cosine function is (1) -(-1) = 2. We observe that same difference on this graph, so there is no vertical scaling.

The maximum of a cosine function is found at (0, 1). On this graph, the nearest maximum is at (-π/3, 2). Subtracting the usual location gives the values of the horizontal and vertical translation:

  (h, k) = (-π/3, 2) - (0, 1) = (-π/3, 1)

The period (from one peak to the next) of the graph is π -(-π/3) = 4π/3. The usual period of the cosine function is 2π, so this graph has been "expanded" by the factor (4π/3)/(2π) = 2/3.

Putting these transformations into the equation for the cosine function, we get ...

  y = cos((x -(-π/3))/(2/3)) +1

  y = 1 +cos(3/2(x +π/3)) . . . . equation of the graph

You can eliminate the inner parentheses by writing this in the equivalent form ...

  y = 1 +cos(3/2x + π/2)

The required reflected equations are g(x) = -x² + 4 and h(x) = x² - 4.

Graph reflections entail projecting a graph over a particular line. Functions with reflecting graphs are those whose graphs mirror one another. The following guidelines can be used to plot reflecting functions over the x and y axes: The graph of f(x) mirrored over the x-axis is represented by -f(x).

The graph of f(x) = x² - 4 is a parabola that opens upwards and has a vertex at (0, -4).

To reflect the graph across the x-axis, we need to negate the y-coordinate of each point on the graph.

This is equivalent to multiplying f(x) by -1. Therefore, the equation for the reflected graph across the x-axis is

g(x) = -f(x) = -(x² - 4) = -x² + 4

To reflect the graph across the y-axis, we need to negate the x-coordinate of each point on the graph.

This is equivalent to replacing x with -x in the equation for f(x). Therefore, the equation for the reflected graph across the y-axis is

h(x) = f(-x) = (-x)² - 4 = x² - 4

Thus, required reflected equations are g(x) = -x² + 4 and h(x) = x² - 4.

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Answer:

is 3mil

300000000000000000000000000

Step-by-step explanation:

because i said so

Answer:

the answwer is is 679 and second answer is 189

Volume of the capsule = 770.73 mm³

Volume of the cylinder = 502.65 mm³

A three-dimensional solid shape's volume is described as the space it occupies. It is challenging to visualize in any shape, yet it may be contrasted with others.  

Any two-dimensional shape's area is determined by dividing the object into equal square units. The volume of solid shapes will also be divided into equal cubical units when calculated.

Given in the question,

Length of the side of the capsule, l = 10mm

Radius of the capsule, r = 4mm

Volume of the capsule, V = π r² ((4/3) r + l)

Putting the value of π, r and l, we get:

⇒ V = 3.1415 × 4² (4 × 4/3 + 10)

⇒ V = (3.1415 × 16 × 46)/3

⇒ V = 770.73 mm³

Now in case of the cylinder,

Volume of the cylinder, V = π a² l

⇒ V = 3.14 × 4² ×10

⇒ V = 502.65 mm³

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Answer:

28ft

Step-by-step explanation:

7+7+7+7=28

there are 4 equal sides to a square, to find perimeter you add up the length of each side, which in this case is 28

Answer:

x = 25°

y = 65°

Step-by-step explanation:

One angle is marked with the small square showing it is a right angle. Two pieces are x and 65°. These will add together to make 90°.

Use this idea to write an equation:

x + 65° = 90°

subtract 65 from both sides.

x = 90 - 65

x = 25°

x + y also add up to 90°.

x + y = 90°

25° + y = 90

subtract 25°

y = 65°

The length of the line segment MN is given as follows:

5.83 units.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The endpoints of the line segment MN is given are given as follows:

M(5,6) and N(2,1).

Hence the length of the segment is given by the distance of these two points:

L = sqrt((5-2)² + (6-1)²)

L = sqrt(34)

L = 5.83 units.

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Answer: 272ft^2

Step-by-step explanation:

Area of the Rectangle:
20*12=240ft^2
Area of the Triangle:
20-12=8ft which is the length of the missing leg of the triangle
8*8/2=64/2=32ft^2
Area of the Whole:
240+32=272ft^2

Answer:

  272 ft²

Step-by-step explanation:

You want the area of a figure composed of a rectangle and a triangle.

The dashed line in the diagram helps you see that the shape is that of a triangle combined with a rectangle. The base length of the triangle is shown as 8 ft, but the height is not shown. It needs to be computed.

The rectangle is 12 ft from its bottom to the dashed line, so the triangle height is ...

  20 ft - 12 ft = 8 ft . . . . . . . height of triangle

The area of a triangle is given by the formula ...

  A = 1/2bh . . . . . base b, height h

The area of this triangle is ...

  A = 1/2(8 ft)(8 ft) = 32 ft²

The formula for the area of a rectangle is ...

  A = LW

For this rectangle, the area is ...

  A = (20 ft)(12 ft) = 240 ft²

The area of the figure is the sum of the areas of its parts.

  garden area = (32 ft²) +(240 ft²)

  garden area = 272 ft²

The function y = 3x + 5 can be written as:

x = (y - 5) / 3

To find the inverse function, we need to solve for y:

y = 3x + 5

Interchange x and y:

x = 3y + 5

Solve for y:

3y = x - 5

y = (x - 5) / 3

Therefore, the inverse function of y = 3x + 5 is:

y = (x - 5) / 3

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The equation for the surface area of the rectangular prism is given as follows:

S = 2(hw + lw + lh).

In which:

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

Hence for this problem you must identify the three dimensions from the image, then replace in the formula and calculate the surface area.

The problem is incomplete, hence the general procedure to obtain the surface area of the prism is presented.

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The area of a rectangle is given by the formula A = lw, where l is the length of the rectangle and w is the width of the rectangle.

Width is defined as the measurement of something from side to side, or the measurement of the size of a two-dimensional object. It is usually the shortest measurement of a rectangular object, and is usually used in conjunction with length to measure the size of an object. The measurement of width is usually taken from the widest part of the object or surface.

Since the area of the rectangle is given to be 42 square centimeters, we can set up the equation 42 = lw.
The equation P = 2l + condenser tubes, wherein l is the rectangle's length and w is its width, yields the radius of a rectangle.
Since the perimeter of the rectangle is given to be 26 centimeters, we can set up the equation 26 = 2l + 2w.
Solving these two equations simultaneously, we find that the length of the rectangle is 10 centimeters and the width of the rectangle is 4 centimeters.
The image below shows the rectangle with the given dimensions and the point on the grid that represents one vertex of the rectangle.

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Answer:

1/4 and 1/4

Step-by-step explanation:

Slope F(0) to f(4): 1/4

Slope f(4) to f(8): 1/4

Answer:

the product of (3 + 2i)(5 – 2i) is 19 + 4i.

Step-by-step explanation:

To multiply the complex numbers (3 + 2i)(5 – 2i), we can use the FOIL method:

(3 + 2i)(5 – 2i)

= 3(5) + 3(-2i) + 2i(5) + 2i(-2i) [multiply First terms, Outer terms, Inner terms, and Last terms]

= 15 - 6i + 10i - 4(i²) [simplify i² to -1]

= 15 + 4 + 4i [combine like terms]

= 19 + 4i

Therefore, the product of (3 + 2i)(5 – 2i) is 19 + 4i.

Answer:

-4i^2+4i+15

Step-by-step explanation:

steps colored in picture

Answer:

Step-by-step explanation:

You want the number of text messages sent by each of Yolanda, Ryan, and Henry if they sent a total of 127, and Ryan sent 7 more than Yolanda, while Henry sent 4 times as many as Yolanda.

The relationships expressed in the problem statement can be written as equations:

Using the last two equations to substitute into the first, we have ...

  y +(y +7) +(4y) = 127

  6y = 120 . . . . . . . . . . . . subtract 7

  y = 20 . . . . . . . . . . . divide by 6

  r = 20 +7 = 27

  h = 4·20 = 80

Yolanda sent 20 text messages, Ryan sent 27, and Henry sent 80.