157 * √24
a. rational
b. irrational

Answer:

What graph? add a photo?

Answer:

x = - 4 , x = - 2

Step-by-step explanation:

x² + 6x + 8 = 0

consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 6)

the factors are + 4 and + 2 , since

4 × 2 = 8 and 4 + 2 = 6 , then

(x + 4)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x + 2 = 0 ⇒ x = - 2

Answer:

2 solutions: ( -4,0 )

( -6,0 )

2 Non solution: ( 2,0 )

( 4,0 )

Answers:

Refer to the graph below

Two solution points are (-5,-4) and (-4,-3)

Non solution points are (0,3) and (1,4)

=========================================================

Explanation:

The boundary line for [tex]y \ge 3x+3[/tex] is [tex]y = 3x+3[/tex]

This linear equation has a y intercept of (0,3) and another point on the line is (1,6). Plot these two points and draw a straight line through them. This line is a solid boundary line because of the "or equal to" as part of the inequality sign. This means points on the boundary adjacent to the shaded region area part of the solution set.

Because of the "greater than" portion, we'll shade above the solid boundary line. This only works because y is isolated.

Keep in mind that we're also told that [tex]y < -2[/tex] which means we'll also shade the region below the boundary line [tex]y = -2[/tex]. This is a dashed line through -2 on the y axis. A dashed line does not include points on the boundary as part of the solution.

---------------

To summarize: We shade above y = 3x+3 (solid) but below y = -2 (dashed).

Refer to the diagram below to see what's going on.

The entire southwest region is shaded.

That blue shaded region represents all (x,y) points that make the system true.

For example, the point (-5,-4) is in the blue region.

Notice how plugging the coordinates into the first inequality gets us...

[tex]y \ge 3x+3\\\\-4 \ge 3(-5)+3\\\\-4 \ge -15+3\\\\-4 \ge -12\\\\[/tex]

which is a true statement. If you plugged y = -4 into [tex]y < -2[/tex], you would also get another true statement.

Both inequalities are true for (x,y) = (-5,-4) which confirms it to be a solution point.

You should also find that a point like (-4,-3) is another solution in the blue region following similar steps. There are infinitely many solution points to pick from. Feel free to choose others.

Non-solution points are such that they aren't in the shaded region. We could also pick points on the dashed boundary line as non-solutions.

Side note: you can pick points on the solid boundary as solution points, but those points must be adjacent to the shaded region. The point (0,3) is NOT a solution even though it's on the solid boundary line.

Answer:

2

I believe that the answer my friend

We happen to have

[tex]\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots[/tex]

which is to say, the base-8 representation of 1/7 is

[tex]\dfrac17 \equiv 0.111\ldots_8[/tex]

This follows from the well-known result on geometric series,

[tex]\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}[/tex]

if [tex]|r|<1[/tex]. With [tex]a=1[/tex] and [tex]r=\frac18[/tex], we have

[tex]\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots[/tex]

Uniformly multiplying each term on the right by an appropriate power of 2, we have

[tex]\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots[/tex]

Now observe that for [tex]n\ge4[/tex], each numerator on the right side side will contain a factor of 16 that can be eliminated.

[tex]\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}[/tex]

That is,

[tex]\dfrac{2^4}{16^4} = \dfrac1{16^3}[/tex]

[tex]\dfrac{2^5}{16^5} = \dfrac2{16^4}[/tex]

[tex]\dfrac{2^6}{16^6} = \dfrac4{16^5}[/tex]

etc. so that

[tex]\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots[/tex]

and thus the base-16 representation of 1/7 is

[tex]\dfrac17 \equiv 0.249249249\ldots_{16}[/tex]

and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.

The equation which best represents the scenario is, x²/2=271

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Perimeter is a length of the boundary surrounding the area

Area of rectangle=length x Breadth

Perimeter=2(length+breadth)

length=x

breadth=x/2

Area=271ft²

Area=length x breadth

So, using the given value we can write

271=x²/2

⇒x=√542

      =23.28ft

Therefore, the equation which best represents the scenario is, x²/2=271

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By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

In this question we have a rational function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:

[tex]x \to y[/tex]

[tex]f(x) \to x[/tex]

[tex]x = \frac{-2\cdot y + 2}{y+7}[/tex]

x · (y + 7) = - 2 · y + 2

x · y + 7 · x = - 2 · y + 2

2 · y + x · y = - 7 · x + 2

y · (2 + x) = - 7 · x + 2

[tex]g(x) = \frac{- 7\cdot x + 2}{x + 2}[/tex]

By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

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The value of the variable is 4√5. Then the correct option is C.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The similar triangles are shown in the diagram.

16 / x = x / 5

    x² = 16 × 5

      x = 4 √5

Then the value of the variable is 4√5.

Then the correct option is C.

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Damek can form 14 three-digit numbers from the given situation. Hence, only 14 possibilities.

There are five number cards on the table.

2- digit 1 card

1- digit 0 card

2- digit 2 card

There is a possibility of putting 1 or 2 in the hundredth place.

If 1 is put in the hundredth place then there are 3 possibilities for tenth place 1,0,2

If 1 is put there then there is a possibility of 2 numbers 0,2 in ones place

If 2 is put then there is a possibility of 3 numbers 0,1,2 in ones place

If 0 is put then there is a possibility of 2 numbers 1,2 in ones place.

So, there are 7=(2+3+2) possibilities that the hundredth place is filled by 1.

Similarly, there will be 7 possibilities that the hundredth place is filled by 2.

Hence, there are 14 possibilities as required by the problem.

So, the possibilities of 3-digit numbers are (given the number cannot start with 0) 14.

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Answer:

20 + 4y

Step-by-step explanation:

To have to fewest symbols possible, we must simplify the expression by multiplying 4 into the numbers within the parenthesis. Doing so we get:

[tex]4(5+y) = 4 * 5 + 4 * y = 20 + 4y[/tex]

Answer: 20+4y

Step-by-step explanation:

Hi, let me help you.

What we should do to simplify this expression is to "distribute" 4.

The parentheses around 5+y tell us to multiply 4 times both 5 and y. This is shown below.

[tex]\multimap\quad \tt 4\cdot5+4\cdot y[/tex]

[tex]\multimap\quad\tt 20+4y[/tex] is what we obtain upon multiplying

________________

Hope I helped. Best wishes.

Reach far. Aim high. Dream big.

____________________

Answer:

163.3

Step-by-step explanation:

3.14*r^2*h

h=13

4/2 = 2

r=2

2^2 = 4

3.14*4 = 12.56

12.56*13 = 163.28

Rounded = 163.3

I believe the answer is 163.3

Answer:

12 :D

Step-by-step explanation:

First we substitute all x's for -2 :)

f(-2)=−-2^3−3(-2)^2+8

Now we solve :)

f(-2)=−-2^3−3(-2)^2+8

f(-2)=− -8 −3(-2)^2 + 8

f(-2) = -8 - 3(-4) + 8

f(-2) = - 8 + 12 + 8

f(-2) = 4 + 8

f(-2) = 12 :)

f will equal 12 :)

Have an amazing day!!

Please rate and mark brainliest!!

The answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.

A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.

We have a rhombus shown in the picture.

The intersection point is P

From the definition of the rhombus: JK ≅ KM

According to the SAS congruency postulate, two triangles are congruent if a triangle has two sides and an included angle that are congruent to the two sides and an included angle of another triangle.

Thus, the answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.

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Answer:

56

Step-by-step explanation:

you first had to get the marked price so t you can get the profit.

just as illustrated in the picture above.

Answer:

1

Step-by-step explanation:

(2-0) / (6-4)

2/2

xxxxxxxx

Answer:

1

Step-by-step explanation:

Answer:

270 miles

Step-by-step explanation:

Since the unit rate is 30 miles per hour, the miles on 9 hours will be:

= 30 × 9

= 270 miles.

The correct answers are:

1. The equation |-x -4| = 8 will have two solutions. (True)

5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)

An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.

1. The equation |-x -4| = 8 will have two solutions. (True)

|-x - 4| = 8

-x -4 = ±8

-x -4 = 8 and -x -4 = -8

-x = 8 + 4 and -x = -8 + 4

-x = 12 and -x = -4

x = -12 and x = 4

Therefore, it has two solutions x ∈ {-12, 4}

2. The equation 3.4|0.5x - 42.1| = -20.6 will have one solution. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

3. The equation |1/2x - 3/4| = 0 will have no solutions. (False)

|(1/2)x - 3/4| = 0

(1/2)x - 3/4 = ±0

Since ±0 is the same

(1/2)x = 3/4

x = 2X3/4

x = 3/2

Therefore, it has one solution x = 3/2

4. The equation |2x – 10| = –20 will have two solutions. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)

|0.5x – 0.75| + 4.6 = 0.25

|0.5x – 0.75| = 0.25 - 4.6

|0.5x – 0.75| = -4.35

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

6. The equation |(1/8)x - 1| = 5 will have infinitely many solutions. (False)

|(1/8)x - 1| = 5

(1/8)x - 1 = ±5

(1/8)x - 1 = 5 and (1/8)x - 1 = -5

(1/8)x = 5 + 1 and (1/8)x = -5 + 1

(1/8)x = 6 and (1/8)x = -4

x = 6X8 and x = -4X8

x = 48 and x = -32

Thus, it has two solutions x ∈ {48, -32}

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Answer:

Step-by-step explanation:

Conditions

Let the girls = g

Let the boys = b

Equations

g + b = 1280

g = b + 70

Solution

Put the value for the girls (second equation) into the first equation.

b + 70 + b = 1280                           Subtract 70 from both sides

b + 70 - 70 + b = 1280 -70             Combine

2b = 1210                                        Divide both sides by 2

2b/2 = 1210/2  

b = 605                                          Substitute this value into the top equation

g + 605 = 1280                              Subtract 605 from both sides

g + 605 - 605 = 1280 - 605

g = 675

Answer

# boys = 605

# girls = 675

Answer:

It is both answers B and D

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The principal value of sin⁻¹(1) is 90°.

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

The principal value of sin⁻¹(1) is,

θ = Sin⁻¹(1)

θ = 90°

Hence, the principal value of sin⁻¹(1) is 90°.

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Answer:

g = 24 - 1/25m

Step-by-step explanation:

Since the Cadillac Escalade can travel 25 miles per gallon, each mile the Escalade travels is 1/25th of a gallon of gas.

This means that every mile the Escalade travels, 1/25th of a gallon is subtracted from the gas tank. Since the gas tank has a capacity of 24 gallons, the value of the gas tank is 24.

This leads us to the equation:

g = 24 - 1/25m

where g is the amount of gas left, and m is the number of miles driven.

Answer:

This is the answer to your question

Answer: tan^-1 (c/a)

Step-by-step explanation: An angle C ∈ ℝ such that angle C > 0 can be defined by the trigonometric ratio Arctangent (or rather tan^-1) where side "c" divided by side "a" ≠ 0.

By finding the probability, we can expect that 2 out of the 30 students will win the prize.

First, we should get the probability of winning this game.

Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.

Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:

p = 1/6

The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:

q = 1/5

The joint probability is then:

P = 2*(1/6)*(1/5) = 1/15.

Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.

Then the expected number of students that will win is equal to the probability times the total number of students:

(1/15)*30 = 2

So out of the 30 students, we can expect that 2 will win.

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Answer:

65 2 point questions, 5 4 point questions

Step-by-step explanation:

write a system of equations:

let x be the number of 2 point questions and y be the number of 4 point questions

2x + 4y = 150

x + y = 70 (since there are 70 total questions)

x + y = 70

subtract x from both sides

y = -x + 70

substitute y = -x + 70 into 2x + 4y = 150

2x + 4(-x + 70) = 150

2x - 4x + 280 = 150

-2x = -130

x = 65

substitute x = 65 into x + y = 70

65 + y = 70

subtract 65 from both sides

y = 5

Answer:

$960

Step-by-step explanation:

The discount is 20%, so we need to find 80% of the original price:

[tex].80 \times 1200 = 960[/tex]

Answer:

The equation of the blue graph is g(x)=(x-3)^{2} +1g(x)=(x−3)

2

+1 . Below is the explanation

Step-by-step explanation:

Given:

The graph of f(x)=x^{2}x

2

To find:

The equation of the transformed graph g(x).

The red graph f(x) is moved right 3 units and up 1 unit to get g(x).

When graph is moved right 3 units , 3 should be subtracted with x.

When graph is moved up 1 unit, 1 is added at the end.

So, our g(x)=(x-3)^{2} +1(x−3)

2

+1

The equation of the blue graph is g(x)=(x-3)^{2} +1g(x)=(x−3)

2

+1