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Can a triangle be formed with side lengths 5, 6, 12? Explain.

No, because 5 + 6 < 12
Yes, because 5 + 6 > 12
No, because 12 − 6 < 6
Yes, because 12 − 6 < 5

For the function f(x) = 7/8x² - 14, the x-intercepts are x = -4 and x = 4.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the x-intercepts of the function f(x), we need to solve the equation f(x) = 0.

f(x) = 7/8x² - 14

Substitute f(x) with 0 -

0 = 7/8x² - 14

Add 14 to both sides -

7/8x² = 14

Multiply both sides by 8/7 -

x² = 16

Take the square root of both sides -

x = ±4

Therefore, the x-intercepts of the function f(x) are x = -4 and x = 4.

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Answer:

10

Step-by-step explanation:

5x+37=87

5x=87-37

5x=50

X=50÷5

X=10

Answer:

Step-by-step explanation:

The equivalent value of {x} is equivalent to 2.046.

The cosine function (or cos function) in a triangle is the ratio of the adjacent side to that of the hypotenuse.

Given is the expression as -

cos(47) = x/3

We have the expression as -

cos(47) = x/3

{x} = 3 cos(47)

{x} = 3 x 0.682

{x} = 2.046

Therefore, the equivalent value of {x} is equivalent to 2.046.

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The polynomial in this problem is factored as follows:

x² - 12x + 27 = (x + 9)(x + 3).

The polynomial for this problem is defined as follows:

x² - 12x + 27.

The format to factor the polynomial is given as follows:

x^2+(a+b)x+ab=(x+a)(x+b)

Which means that:

The two numbers that satisfy this are:

-9 and -3.

As a product of it's linear factors, the polynomial is factored as follows:

(x + 9)(x + 3).

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Answer:

\(\huge\boxed{\overrightarrow{u}-\overrightarrow{v}=\left<-10;\ -3\right>}\)

Step-by-step explanation:

\(\overrightarrow{u}=\left<-8;\ 4\right>;\ \overrightarrow{v}=\left<2;\ 7\right>\\\\\overrightarrow{u}-\overrightarrow{v}=\left<-8;\ 4\right>-\left<2;\ 7\right>=\left<-8-2;\ 4-7\right>=\left<-10;\ -3\right>\)

Answer:

Step-by-step explanation:

-u-v = 6,-11

u-v = -10,-3

v-u = 10,3

The missing variables on item 2 are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 60º, we have that:

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

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Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

Answer:

A

Step-by-step explanation:

Only one that make sense

Answer:

115-2*180

= 245

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

there are 2 triangles so the angles in all add up to 360. (108*2) then you subtract all the known angles.

Answer:

10

Step-by-step explanation:

Answer:

first step is to minus 28.7 - 6.7=22 (I did the minus because I want to get the remaining length of the rope )

step 2 : is to divide 22 by 2 (because the question said they should divide it into two pieces )

then the answer you get from the division of 22/2 which is 11 that would be the final answer

meaning each tire swing is 11m

Answer:

Step-by-step explanation:

so we know that there are 193 students going on this field trip and then it said that their are 5 buses each bus has 18 seats two students can sit in each seat so we muliply 18 by 2 which is and get 36, 36 can go on each bus multiply that by 5 and get 180 180 can go and there will be 13 not going

Given that a randomly selected applicant has more than 10 years of experience, the likelihood that they have a graduate degree is roughly 0.4016.

To find the probability that a randomly chosen applicant has a graduate degree given that they have over 10 years of experience, we need to use conditional probability. We can use the formula:

P(grad degree | over 10 years of experience) = P(grad degree and over 10 years of experience) / P(over 10 years of experience)

From the given information, we know that:

P(grad degree and over 10 years of experience) = 51 (number of applicants with over 10 years of experience and a graduate degree)

P(over 10 years of experience) = 127 (number of applicants with over 10 years of experience)

So, plugging in these values:

P(grad degree | over 10 years of experience) = 51 / 127

Using a calculator, we get:

P(grad degree | over 10 years of experience) ≈ 0.4016

Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they have over 10 years of experience, is approximately 0.4016.

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Answer:

B

Step-by-step explanation:

\(m = \frac{0 - ( - 2)}{ - 2 - 0} = - 1\)

use the point (-5,3)

y-3=-(x-(-5)) = y-3= -(x+5)

Answer: B. y - 3 = -(x + 5)

Step-by-step explanation:

Find two easy points on the graph to calculate the slope:

The slope is calculated using \(\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\), so substitute in the values:

\((x_{1}, y_{1}) = (-2, 0)\\(x_{2}, y_{2}) = (0, -2)\\ \frac{y_{2}-y_{1} }{x_{2}-x_{1}} =\frac{(-2)-0}{0-(-2)} =\frac{-2}{0+2} =\frac{-2}{2} =-1\)

The y-intercept is where it intersects the y-axis. It's -2.

Therefore, if you put it together, the function would be y = -x - 2                    

Solve each answer choices and find the one that matches the function:

B.\(y-3=-(x+5)\\y-3=-x-5\\y=-x-5+3\\y=-x-2\)

This table shows the frequency of each number obtained after throwing the die 35 times

To prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.

Numbers: 1, 2, 3, 4, 5, 6

Frequency: 5, 14, 6, 4, 5, 1

Based on the given numbers, the frequency table would look like this:

Number   | Frequency

1                      5

2                     14

3                      6

4                      4

5                      5

6                       1

This table shows the frequency of each number obtained after throwing the die 35 times.

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Answer:

0.0392 = 3.92% probability that the test result is positive.

Step-by-step explanation:

Probability of a positive test:

95% of 1%(person has the disease)

100 - 97 = 3% of 100 - 1 = 99%(person does not have the disease).

What is the probability that the test result is positive?

\(p = 0.95*0.01 + 0.03*0.99 = 0.0392\)

0.0392 = 3.92% probability that the test result is positive.

Answer:

Step-by-step explanation

Okay so lets solve step by step/

15% can be written as a  fraction: 15/100

The of in the equation means multiplying.

15/100= 3/20

3/20*9= 270/20

27/2 is answer

According to the information, we can infer that the correct expression is (10 * 7) + (2 * 7) (option D).

To find the correct expression we must look at the graph and interpret the information it has. In this case, some tiles are white and others are gray, so they would represent different elements. In this case, the white area is 10 * 7 tiles, so this would be the first part of the expression.

On the other hand, the second part of the expression would be 7 * 2, which represents the length, length and width of the gray area. According to the above, the correct expression would be (10 * 7) + (2 * 7), the first part in parentheses represents the white area and the second part in parentheses represents the gray area.

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Work Shown:

450 calories = 20 ounces

450/20 calories = 20/20 ounces ..... divide both sides by 20

22.5 calories = 1 ounce

This smoothie has 22.5 calories per ounce.

y= 1/5 x6^2 + 6/5 x + 11/10

The coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the Coordinates of Luke's house on the coordinate grid.

The grid representing Kyle's house. However, based on the given information, we can determine the coordinates of Kyle's house relative to Luke's house.

If Luke's house is located at the point (x, y), then Kyle's house is located 4 units to the left of Luke's house, which means the x-coordinate of Kyle's house is (x - 4). Similarly, Kyle's house is located 2 units up from Luke's house, which means the y-coordinate of Kyle's house is (y + 2).

Therefore, the coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the coordinates of Luke's house on the coordinate grid.

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The graph of the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

Is in the image at the end.

Here we have the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

To graph this, we just need to graph both of the linear equations, and we need to shade the region below the first line (the one with positive slope) and the region above the second line, the one with negative slope.

Then the graph of the system of inequalities is the graph you can see in the image at the end of the answer.

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Answer:

x = 7 - 3y

Step-by-step explanation:

6y + 2x = 14 (divide all by two)

3y + x = 7 (move 3y to the right to isolate x)

x = 7 - 3y

Answer:

7-3y=x

Step-by-step explanation:

6y+2x=14

2x=14-6y >>> isolate x variable

x=7-3y >>> simplify because everything is divisible by 2

We can see in the graph that f(x) and g(x) are parallel lines. This means that to transform f(x) into g(x), we can shift it horizontally or vertically.

Part A: Applying a vertical or horizontal shift to f(x) will result in g(x).

For part B, we need to find the transformations.

We can take two points of each function:

f(x): (0, -10) and (5, 0)

g(x): (0, 6) and (-3, 0)

Then, if we apply vertical shift in (0, -10), we should get the point (0, 6). Then, we can solve:

If we apply a horizontal shift, the point (5, 0) should transform into (-3, 0). Then:

Part B:

Horizontal shift: k = -8

Vertical shift: k = 16

For part C we need to write an equation for each transformation.

Given a function h(x), a vertical shift of k units is written:

And a horizontal shift of k units:

Vertical shift: This transformation adds 16 units in the y-coordinate.

Horizontal shift: This transformation subtracts 8 from the x-coordinate:

Answer:

(d) -12

Step-by-step explanation:

3a = _____

a = -4

3(-4) = ___

3(-4) = -12

The answer is (d) -12