Which absolute value function defines this graph?

Answer:

ab+bc+ac = 7+21 + 28 =56

so the answer is 56

Observe that

[tex]a^2 + b^2 + ab = 7 \iff a^2 + b^2 - 2\cos(120^\circ) = \left(\sqrt 7\right)^2[/tex]

[tex]b^2 + c^2 + bc = 21 \iff b^2 + c^2 - 2\cos(120^\circ) = \left(\sqrt{21}\right)^2[/tex]

[tex]a^2 + c^2 + ac = 28 \iff a^2 + c^2 - 2\cos(120^\circ) = \left(\sqrt{28}\right)^2[/tex]

Drawing a comparison to the law of cosines, we see the first equation defines a triangle with sides [tex]a[/tex], [tex]b[/tex], and [tex]\sqrt 7[/tex]; the second equation defines one with sides [tex]b[/tex], [tex]c[/tex], and [tex]\sqrt{21}[/tex]; and the third equation defines another one with sides [tex]a[/tex], [tex]c[/tex], and [tex]\sqrt{28}[/tex]. We can then join these triangles at a point D to form a new triangle ABC with sides [tex]\sqrt7,\sqrt{21},\sqrt{28}[/tex]. (See attached sketch)

Now, the area of ABC is the sum of the areas of ABD, BCD, and ACD. The area of any of these triangles is equal to half the area of a parallelogram spanned by the sides involving the vertex D. The area of a parallelogram with adjacent sides [tex]x[/tex] and [tex]y[/tex] and with angle [tex]\theta[/tex] between them is [tex]ab\sin(\theta)[/tex].

For example, triangle ABD has area

[tex]\mathrm{area}_{\Delta ABD} = \dfrac12 \times ab \sin(120^\circ)[/tex]

Then the total area of triangle ABC is

[tex]\mathrm{area}_{\Delta ABC} = \dfrac12 \sin(120^\circ) (ab + ac + bc)[/tex]

We use Heron's formula to find the area of ABC. If [tex]s[/tex] is its semiperimeter, i.e.

[tex]s = \dfrac{\sqrt7 +\sqrt{21} + \sqrt{28}}2[/tex]

then, with a lot of algebraic simplification,

[tex]\mathrm{area}_{\Delta ABC} = \sqrt{s (s-\sqrt7) (s - \sqrt{21}) (s - \sqrt{28})} = \dfrac{7\sqrt3}2[/tex]

Finally, we find

[tex]\dfrac{7\sqrt3}2 = \dfrac12 \sin(120^\circ) (ab + ac + bc) \implies ab + ac + bc = \dfrac{\frac{7\sqrt3}2}{\frac12\times\frac{\sqrt3}2} = \boxed{14}[/tex]

[tex]\left(\frac{-2+13}{2}, \frac{5-7}{2} \right)=\boxed{\left(5.5, -1)}[/tex]

Using a system of equations, it is found that the number of golfers in the cafeteria is of 5.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

The number of baseball players is one less than twice the number of golfers, hence:

x = 2y - 1.

Since x = 9:

9 = 2y - 1

2y = 10

y = 5.

There are 5 golfers in the cafeteria.

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Using the binomial distribution, it is found that the probabilities are given as follows:

a) 0.2036 = 20.36%.

b) 0.0011 = 0.11%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

p = 0.95, n = 5.

Item a:

The probability is P(X = 4), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{5,4}.(0.95)^{4}.(0.05)^{1} = 0.2036[/tex]

Item b:

The probability is P(X < 3), hence:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.95)^{0}.(0.05)^{5} \approx 0[/tex]

[tex]P(X = 1) = C_{5,1}.(0.95)^{1}.(0.05)^{4} \approx 0[/tex]

[tex]P(X = 2) = C_{5,2}.(0.95)^{2}.(0.05)^{3} = 0.0011[/tex]

Then:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0.0011 = 0.0011.

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Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a<  b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

We are given

-5 < 4x+3 ≤ 8

⇒ (add -3 to all sides to get ) -5+(-3) < 4x+3+(-3) ≤8+(-3)

⇒-8 < 4x ≤ 5

⇒[tex]\frac{-8}{4} < x \leq \frac{5}{4}[/tex]

⇒-2<x<5/4

Hence, the solution is -2<x<5/4.

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Answer:

No.

Step-by-step explanation:

This problem in scientific notation would be 9.3 * 10^10.

Step-by-step explanation:

T = 55 + 6w

after 8 week $103

Answer:

.7692307692 or 10/26

Step-by-step explanation:

You solve this problem by finding the total number of sports playing students and dividing it by the total, in this case 26. Since we know there are 5 students that play both sports, you subtract that 5 from the total number of basketball plyers and baseball players, so 16-5=11 and 9-5=4, then add those together, so 11+4=15. From there you add back in the students that play both which is 5, so 15+5=20. 20/26 is your answer.

Answer:

y = 2/3x + 4/3

Step-by-step explanation:

Voy a suponer que necesitas resolver para y.

2x + 3y = 4

3y = -2x + 4

y = -2/3x + 4/3

Answer:

Look below!

Step-by-step explanation:

From the picture, the answer is A.

From the points, calculate the slope using y2-y1/x2-x1

you will find that the slope is -1

parallel lines have the same slope

so y = -x+1 is the correct answer

now,

parallel lines never intersect

therefore, they have no solution.

                                          17/52

Step-by-step explanation: There are 13 clubs in a deck of fifty-two cards and there are four jacks in a fifty-two deck.  So adding that up it's 17 out of 52 = 17/52.   And you can not reduce it.

Answer:

10π cm

Step-by-step explanation:

c = 2πr

c = (2*5) * π

c = 10π

Answer:

[tex]648[/tex]([tex]x^{3} + 3x^{2} - 4x + 2[/tex])

Step-by-step explanation:

When factoring an expression like this, you need to divide all of the parts by a common number or variable. In this case, the only thing all of these numbers share is that they are divisible by 648. So, you would divide each number by 648 to simplify it, getting 1, 3, 4, and 2. Put these numbers in front of their respective variables, and put 648 outside of the parentheses to get the final answer.

Answer:

(3x – 6)4

Step-by-step explanation:

Answer:

93 boxes

Step-by-step explanation:

sixth row has 23 boxes

fifth row has 20 boxes

fourth row has 17 boxes

third row has 14 boxes

second row has 11 boxes

first row has 8 boxes

the total is thus 23+20+17+14+11+8=93

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: log_{6}(25) - log_{6}(5) [/tex]

[tex]\qquad \tt \rightarrow \: log_{6}(5) {}^{2} - log_{6}(5) [/tex]

[ property : x² = 2 log x ]

[tex]\qquad \tt \rightarrow \: 2 \: log_{6}(5) {}^{} - log_{6}(5) [/tex]

[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

it it a parallelogram

Step-by-step explanation:

it has 2 sets of 2 parallel lines

With the information given, we can not prove this quadrilateral is a parallelogram. Explanation is given.

A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

In order to prove, quadrilateral is a parallelogram:

We can prove either one of these following method;

1. Establish the congruence of the two pairs of opposing sides.

2. Show that the two opposing side pairs are parallel.

3. Show that one pair of opposed sides is parallel and congruent.

Here, we have AB = CD

And we have line AD and BC.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

AD and BC are at equal distance.

That means, AD II BC.

And to solve further, we do not have any statements.

Therefore, with given information, we can not prove this quadrilateral is a parallelogram.

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The value of x is 38 degree.

A triangle is a polygon with three sides , three angles and three sides .

The sum of all angles in a triangle is equal to 180 degree

The angles of the triangle given are

83 degree and 59  degree and x degree

83 + 59 + x = 180

x = 38 degree

Therefore the value of x is 38 degree.

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Answer:

625

Step-by-step explanation:

here we are in an inverse proportion situation :

As the number of days increases

when the number of students decreases and vice versa.

__________________

Say n is the original number of students.

___________________________________________

After 15 days, the rest of food is enough for n students for 45 days,

or enough for n+500 students for 25 days.

Then

45n = 25×(n + 500)

Then

45n = 25n + 25×500

Then

45n - 25n = 25×500

Then

20n = 12500

Then

n = 12500÷20

  = 625

and thus , there were 625 students in the hostel.

Answer:

11 boys walk to school each day

Step-by-step explanation:

*The following will be assumed: the only genders of students in the class are male or female; the only options for getting to school are walking or not walking

If there are 32 students in the class total, and there are 15 boys,

32 - 15 = 17

there are 17 girls.

If 8 of these girls do not walk to school,

17 - 8 = 9

9 girls walk to school

So, if 20 total students walk to school, and 9 of those are girls

20 - 9 = 11

11 boys walk to school each day.

Answer:

11

Step-by-step explanation:

The equation in the vertex form of g(x) is:

[tex]g(x) = (x + 1)^2 - 38[/tex]

We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).

So first, let's rewrite f(x) to its vertex form:

[tex]f(x) = x^2 - 4x - 32[/tex]

The vertex is at:

[tex]x = -(-4)/2*1 = 2[/tex]

The y-value of the vertex is:

[tex]f(2) = 2^2 - 4*2 - 32 = -36[/tex]

Then the vertex form of f(x) is:

[tex]f(x) = (x - 2)^2 - 36[/tex]

If we move this vertex 2 units below, and 3 units to the left, then we have:

[tex]g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38[/tex]

That is the equation for g(x) in vertex form.

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Answer:

C. 3x - 9

Step-by-step explanation:

3x – y = 9 ___(1)

8x – 4y = 0 ___(2)

From (1) eq.

3x – y = 9

– y = 9 – 3x

y = - (-3x + 9)

y = 3x – 9

Hence, 3x - 9 should be substituted in the second equation to get the required answer.

Answer:

c

Step-by-step explanation:

solve for y in the first equation

y = 3x - 9

when you substitute, you will get a value of 9 for x and 18 for y

#1

Find slope

y=-3x+5 is the equation as there is no other having slope -3

#2

slope

y=x-4 as no other have slope m

#3

y intercept is -1

y=2x-1 is the equation as it has y intercept -1

#4

y intercept is -4

(9x³+5)/(2x - 3)

split up (9x³+5)

9x³/2x-3 + 5/2x-3

attached solution.

Answer:

$165554

Step-by-step explanation: I  use the Law of Cosines to find one of the angles of the triangle.  Then use the formula for the area of the triangle: A = (1/2)absinC.

C= 92.856 degree

Area = (1/2)(112)(148)sin(92.856°) = 8277.7 ft^2

To find the price just need to take 8277.7 time 20 = 165554

So the answer is $165554

Answer:

a

Step-by-step explanation:

substitute x = 10 into f(x) , that is

f(10) = 2(10) + 3 = 20 + 3 = 23

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[tex]\large \bold {ANSWER}[/tex]

[tex]\large \bold {SOLUTION}[/tex]

Given the first-degree function:

[tex]\Large\begin{array}{c}\rm f(x)=2x+3\end{array}[/tex]

We were asked to determine the value of f(10), so, to find its value, just replace the 10 where there is x in the function, see:

[tex]\begin{gathered}\Large\begin{array}{c}\rm f(x)=2x+3\\\\ \rm f(10)=2\cdot 10+3\end{array}\end{gathered}[/tex]

You see, we put that dot there, which indicates multiplication, because when a number is next to a letter it indicates that it is multiplying, thus:

[tex]\begin{gathered}\Large\begin{array}{c}\rm f(10)=2\cdot 10+3\\\\ \rm f(10)=20+3\\\\ \red{\boxed{\rm f(10)=23}}\checkmark\end{array}\end{gathered}[/tex]

Hence, the value of f(10) in this function is equal to 23.

Answer:

I solved 26 problems correctly.