Lines, Angles, and Triangles please help solve

After solving the quadratic equation, the roots are (x - 2) and (x + 7).

To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.

The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.

As per the given equation in the question,

x² + 5x - 14 = 0

b² - 4ac

5² - 4(1)(-14)

25 + 56 = 81

Use the equation,

-b ± \(\sqrt{b^2-4ac}/2a\)

Substitute the values,

(-5 + 9)/2 = 2 and,

(-5 - 9)/2 = -7

Therefore, the root will be (x - 2) and (x + 7).

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Answer:

16

Step-by-step explanation:

Answer:

(-18±\(\sqrt{204}\))÷6

Step-by-step explanation:

Work Shown:

xy + 2x + 3x^2 = 4

d/dx[ xy + 2x + 3x^2 ] = d/dx[4]

d/dx[ xy ] + d/dx[ 2x ] + d/dx[ 3x^2 ] = d/dx[4]

y + xy' + 2 + 6x = 0

xy' = -6x-y-2

y' = (-6x-y-2)/x

y' = (-6x-y-2)/x

Complete the table representing a linear function with y = 10 and x = 9

The general form of a linear function is:

y = mx + c,

where m is the slope and c is the y-intercept

slope(m) = (y2-y1)/(x2-x1)

From the table:

point 1: x1 = 1, y1 = 0

point 2: x2 = 5, y2 = 40

slope(m) = (40-0)/(5-1) = 40/4 = 10

For the missing points:

x1 = 1, y1 = 0 and x2 = 2, y2 = y (unknown)

m = (y2-y1)/(x2-x1)

10 = (y-0)/(2-1)

10 = y/1

y = 10

x1 = 1, y1 = 0 and x2 =  x (unknown), y2 =90

m = (y2-y1)/(x2-x1)

10 = (90-0)/(x-0)

10 = 90/x

10x = 90

x = 90/10

x = 9

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Answer:

Inverse Property of Addition

Step-by-step explanation:

Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

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For the equation g(x) = 6 - 1, the graph of g(x) differs from the graph of f(x) by translating down 1 unit.

For the equation g(x) = 2 + 1, the graph of g(x) differs from the graph of f(x) by translating up 1 unit.

In the Desmos Graphing Calculator, when entering the equation f(x) = 6 and g(x) = 6-1, we can observe the difference between the graphs of f(x) and g(x).

The equation f(x) = 6 represents a horizontal line at y = 6. The graph of f(x) is a straight line parallel to the x-axis, passing through the y-coordinate 6.

On the other hand, the equation g(x) = 6 - 1 represents a line that is one unit below the line represented by f(x). The graph of g(x) is a parallel line to the graph of f(x), but shifted downward by one unit.

Therefore, the correct answer is:

The graph of g(x) differs from the graph of f(x) by translating down 1 unit.

Similarly, when entering the equation f(x) = 2 and g(x) = 2 + 1, we can observe the difference between the graphs of f(x) and g(x).

The equation f(x) = 2 represents a horizontal line at y = 2. The graph of f(x) is a straight line parallel to the x-axis, passing through the y-coordinate 2.

The equation g(x) = 2 + 1 represents a line that is one unit above the line represented by f(x). The graph of g(x) is a parallel line to the graph of f(x), but shifted upward by one unit.

Therefore, the correct answer is:

The graph of g(x) differs from the graph of f(x) by translating up 1 unit.

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Answer:

a) 1/8

b) 3/8

c) 0.125

d) 0.75

e) 25%

f) 100%

The method that determines the volume of the prism is simply multiply the area of the base by the height, and the result is 12.5 cm³. (option-a)

To determine the volume of the prism shown in the diagram, we need to multiply the area of the base by the height.

The base of the prism is a rectangle with dimensions 5 cm by 2 cm. Therefore, the area of the base is:

A = length x width = 5 cm x 2 cm = 10 cm²

The height of the prism is 2-¹ cm, which is equivalent to 5/4 cm.

Therefore, the volume of the prism is:

V = A x h = 10 cm² x 5/4 cm = 12.5 cm³

The expressions involving unit cubes and one-quarter cubes are not relevant to this problem and do not provide a method for finding the volume of the prism.

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The simplified form of the numerical expression (4√15) / √5 will be 4√3.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

The ratio is given below.

⇒ (4√15) / √5

Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To answer the problem properly and accurately, this rule must be followed.

⇒ (4√15) / √5

⇒ [4 × √(3 x 5)] / √5

⇒ (4 × √3 × √5) / √5

⇒ 4 × √3

⇒ 4√3

The simplified form of the numerical expression (4√15) / √5 will be 4√3.

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Answer:

3 feet

Step-by-step explanation:

A = l x w                    Formula

18.9 = 6.3 x w           Substitution

18.9/6.3 = w              Division

3 = w                         Solution

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Answer:  A  129

Step-by-step explanation:

Because the 2 chords are the same (lines in the circle), the 2 arcs are the same  create an equation that makes them equal

3x+24 = 4x -11             >bring x to one side by subtracting both sides by 3x

24 = x -11                     > add both sides by 11

35 = x

Now that we have solved for x you need to plug that back into the equation for BC

BC= 4x-11

BC = 4(35) - 11

BC =  140 - 11

BC = 129                   >A

Answer:

x at 1

Step-by-step explanation:

There is a corner at 1 making the function not differentiable

Answer: It is 20 m, multiply each number by 1.25

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 .

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Answer:

214 cubic feet (rounded to the nearest cubic foot)

Step-by-step explanation:

Step 1  Determine the volume of 1 box

Volume of a box or rectangular prism = dimensions multiplied by each other

Here, the given dimensions are 11 in by 8 in by 12 in

So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches

Step 2 Determine volume of all 350 boxes

Volume of 1 box = 1056

So volume of all 350 boxes = 1056 x 350 = 369600 cubic in

Step 3 Convert cubic in to cubic ft

To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)

369600 / 1728 = 214 cubic feet (to the nearest cubic foot)

214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in

The probability that a worker selected at random makes between $300 and $350 is 0.1359 Or 13.6%.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

Given, Weekly wages at a certain factory are normally distributed.

Mean(\(\overline{x}\)) = 400, S.D(\(\sigma\)) = 50.

Now, Since the wages are normally distributed we know,

\(z = \frac{x - \overline{x}}{\sigma}\).

Therefore,

z = (300 - 400)/50.

z = - 2.

And

z = (350 - 400)/2.

z = - 1.

Now, from the z-table,

P(z ≤ - 2) = 0.0228 and P(z ≤ - 1) = 0.1587.

Combining the two we have P( - 2 ≤ z ≤ - 1) =  0.1587 - 0.0228.

P( - 2 ≤ z ≤ - 1) = 0.1359.

As a result, the likelihood that a randomly chosen employee will earn between $300 and $350 is 0.1359, or 13.6%.

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Answer:

32

Step-by-step explanation:

Answer:

1) m=2/3

2) m=0

3)m = undefined

4 m=4

Answer:

The 95​% confidence interval for the mean birth weight of all ​non-premature babies is between 3350.4 grams and 3662.4 grams. This means that we are 95% sure that true mean birth weight of all non-premature babies is in this interval.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 41 - 1 = 40

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 40 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.0211

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 2.0211\frac{494.2}{\sqrt{41}} = 156\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 3506.4 - 156 = 3350.4 grams

The upper end of the interval is the sample mean added to M. So it is 3506.4 + 156 = 3662.4 grams

The 95​% confidence interval for the mean birth weight of all ​non-premature babies is between 3350.4 grams and 3662.4 grams. This means that we are 95% sure that true mean birth weight of all non-premature babies is in this interval.

Answer:

9.6 cm

Step-by-step explanation:

Since the shapes are similar, we can write a proportion. Let x be the length of MN.

9/12 = 7.2/x Write a proportion.

9x = 12(7.2) Use cross products.

9x = 86.4 Multiply.

x = 9.6 Divide both sides by 9.

Side MN is 9.6 cm.

Answer:

The answer is 47.5 and 72.5

Step-by-step explanation:

So,

Let the number be x and the other number be (x + 25).

Now,

x + (x + 25) = 120

x + x + 25 = 120

2x + 25 = 120

2x + 25 – 25 = 120 – 25

2x = 95

2x/2 = 95/2

x = 47.5

Thus, The number be x is equal to 47.5 and other which is more 25 than other number is (47.5 + 25) = 72.5

-TheUnknownScientist 72

Answer:

The numbers are 47.5 and 72.5

Step-by-step explanation:

Let "x" represent the larger number, then the smaller number would be equivalent to:

\(x-25\)

Larger Number + Smaller Number = 120

Therefore...

\(x+x-25=120\)

Combine like terms:

\(2x-25=120\)

Add 25 to both sides (note we are utilizing the Addition Property of Equality which essentially states that if you add a value to one side of the equation, you must add it to the other side as well):

\(2x=120+25\\2x=145\)

Divide both sides by 2 (note we are now utilizing the Division Property of Equality which essentially states that if you divide a value from one side of the equation, you must divide it from the other side as well; the same as the Addition Property of Equality, but with division instead):

\(x=\frac{145}{2}\\x=72.5\)

Therefore...

\(x-25=72.5-25=47.5\)

Answer:

false, no

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

The passenger train is traveling at 45 mph, and the freight train is traveling at 27 mph.

Step-by-step explanation:

Let's assume the speed of the passenger train is represented by x mph.

According to the given information, the freight train leaves the depot 2 hours before the passenger train. Therefore, when the passenger train starts, the freight train has already been traveling for 2 hours.

Let's represent the speed of the freight train as (x - 18) mph, which is 18 mph slower than the passenger train.

Now, we know that the passenger train overtakes the freight train in 3 hours. This means that the passenger train traveled for 3 hours, while the freight train traveled for 3 + 2 = 5 hours.

Since speed = distance/time, we can set up the following equation based on the distances covered by each train:

Distance covered by passenger train = Distance covered by freight train

Using the formula, distance = speed × time, we get:

x × 3 = (x - 18) × 5

Simplifying the equation:

3x = 5x - 90

90 = 5x - 3x

90 = 2x

Dividing both sides by 2:

45 = x

So, the speed of the passenger train is 45 mph.

The speed of the freight train is 45 - 18 = 27 mph.