Explain what x^(2/3) means using radicals and integer exponents.

Answer: Option C

[tex]x =8[/tex]

Step-by-step explanation:

To solve this problem use the properties of the logarithms.

We know that the inverse function of [tex]y = log_2 (x)[/tex] is [tex]y = 2 ^ x[/tex].

So when composing the function with its inverse function we have to:

[tex]2 ^ {log_2 (x)} = x[/tex].

Now apply this property on both sides of the equation

[tex]log_2(x) = 3\\\\2^{log_2(x)}=2^3\\\\x = 2^3\\\\x = 8[/tex]

the answer is the option C

Answer:

y = (-6/7)x + 11/7

Step-by-step explanation:

Going from  (-4, 5)  to  (3,-1), x increases by 7 and y decreases by 6.  Hence, the slope, m, of this line is m = rise / run = -6/7.

Making use of the slope-intercept form of the equation of a str. line, we have:

y = mx + b  →   5 = (-6/7)(-4) + b, or

                        5 = 24/7 + b.  Thus, b = 11/7, and

y = (-6/7)x + 11/7

The formula to find slope when you know two points is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =-1\\y_{1} =5\\x_{2} =3\\x_{1} =-4[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{-1 - 5}{3 - (-4)}[/tex]

[tex]\frac{-6}{7}[/tex]

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

x³ - 4x² - 16x + 24

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x(x² + 2x - 4) - 6(x² + 2x - 4) ← distribute both parenthesis

= x³ + 2x² - 4x - 6x² - 12x + 24 ← collect like terms

= x³ - 4x² - 16x + 24

A. x³ - 2x² - 16x + 24

To multiply 2 polynomials, apply the distributive property by using each term in 1 polynomial to multiply every in the other polynomial.

(x – 6)(x² + 2x – 4)

x(x² + 2x – 4) -6(x² + 2x – 4)

x³ + 2x² - 4x - 6x² - 12x + 24

Combine like terms

x³ - 2x² - 16x + 24

(x – 6)(x² + 2x – 4) equals: A. x³ - 2x² - 16x + 24

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The line of reflection between the two pentagons is the y-axis.

We can see this because all of the points in pentagon P'Q'R'S'T' have the same x-coordinate as their corresponding points in pentagon PQRST, but their y-coordinates are negated. For example, point P has coordinates (-4, 6), and its reflected image P' has coordinates (-4, -6).

The y-axis is the only line that passes through all of the midpoints of the segments connecting corresponding points in the two pentagons. Since reflection preserves distance, the line of reflection must be the perpendicular bisector of any segment connecting a point in one pentagon to its reflected image in the other pentagon.

Answer:

Equation: 7n = 8.61

Solution: n = $1.23

Step-by-step explanation:

7 binders = $8.61

1 binder = $n

The price of one binder is seven times the price of 7 binders.

7n = The price of 7 binders

The price of 7 binders is $8.61

7n = $8.61

Divide both sides of the equation by 7

n = $1.23

Answer: -2,4

Step-by-step explanation:

Center = (-2,4) are the coordinates of the center of the ellipse .

The major and minor axes' midpoints meet at the center of an ellipse. At their intersection, the axes are perpendicular. The foci are always on the major axis, and the constant sum of the distances between the foci is greater than the sum of the distances from the foci to any point on the ellipse.

The equation of an ellipse is [tex]\frac{\left(x - h\right)^{2}}{a^{2}} + \frac{\left(y - k\right)^{2}}{b^{2}} = 1[/tex]

where (h,k) is the center, b and a are the lengths of the semi-major and the semi-minor axes.

Our ellipse in this form is [tex]\frac{\left(x - \left(-2\right)\right)^{2}}{9} + \frac{\left(y - 4\right)^{2}}{36} = 1[/tex]

Thus, h = -2, k = 4

Center = (-2,4).

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Answer:

The maximum number of hours that can rent the canoe is 2 hours

Step-by-step explanation:

Let

h ----> the number of hours you can rent the canoe

we know that

The inequality that represent this situation is

[tex]14.5+6h\leq 32[/tex]

Solve for h

Subtract 14.5 both sides

[tex]6h\leq 32-14.5[/tex]

[tex]6h\leq 17.5[/tex]

Divide by 6 both sides

[tex]h\leq 17.5/6[/tex]

[tex]h\leq 2.9\ hours[/tex]

The maximum number of hours that can rent the canoe is 2 hours

The equation that represents the number of hours you can rent the canoe is h = ($32.50-$14.50)/$6.

The subject of this question is Mathematics and it appears suitable for a Middle School level. Given the scenario you presented, we will need to create a linear equation to determine the number of hours of canoe rental. In this case, the $14.50 is a fixed cost, like the $31.50 in one of your examples. Additionally, the $6 per hour to use the canoe is a variable cost. To create an equation that represents the amount of hours you can rent the canoe, we first deduct the fixed cost from your total budget. This gives you $32.50 - $14.50 = $18 left to work with. Each hour of canoe use costs $6, so we divide the remaining amount by 6 to find how many hours (h) you can rent the canoe. This gives us the equation, h = ($32.50-$14.50)/$6.

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Answer:

Since the money appreciates 4.2% each year, then:

2000=1600x(1.042)^n, where n is the number of years

Then:

1.25=1.042^n

ln 1.25=ln 1.042^n=n ln 1.042

n=5.424 years

Cate's $1600 stock investment, growing at 4.2% annually, will take approximately 5.21 years to reach a value of about $2000.

Given that Cate purchases $1600 worth of stock with an estimated increase in value by 4.2% each year, we are looking to find out after how many years the value will be about $2000. To determine this, we can use the formula for exponential growth, P = P_0 (1 + r)^t, where P is the future value, P_0 is the initial value, r is the rate of increase, and t is the time in years.

Cate's initial investment is $1600 (P_0), and we aim for a future value of $2000 (P). The annual growth rate r is 4.2%, or 0.042 when expressed as a decimal. Plugging these values into the formula and solving for t gives us:

So, it will take approximately 5.21 years for Cate's investment to reach a value of about $2000, assuming a steady 4.2% growth rate.

Answer:

A ray

Step-by-step explanation:

Answer:

ray

Step-by-step explanation:

Answer:

[tex]\cos (x-y)=\dfrac{1}{2}=0.5[/tex]

Step-by-step explanation:

Use formula:

[tex]\cos (x-y)=\cos x\cos y+\sin x\sin y[/tex]

Since

[tex]\sin x=-\dfrac{1}{2}[/tex]

and angle x is in the fourth quadrant, then cos x is greater than 0 and is equal to

[tex]\cos x=\sqrt{1-\sin ^2x}=\sqrt{1-\left(-\dfrac{1}{2}\right)^2}=\sqrt{1-\dfrac{1}{4}}=\sqrt{\dfrac{3}{4}}=\dfrac{\sqrt{3}}{2}[/tex]

Since

[tex]\cos y=\dfrac{\sqrt{3}}{2}[/tex]

and angle y is in the first quadrant, then sin y is greater than 0 and is equal to

[tex]\sin y=\sqrt{1-\cos ^2y}=\sqrt{1-\left(\dfrac{\sqrt{3}}{2}\right)^2}=\sqrt{1-\dfrac{3}{4}}=\sqrt{\dfrac{1}{4}}=\dfrac{1}{2}[/tex]

Hence,

[tex]\cos (x-y)=\cos x\cos y+\sin x\sin y=\dfrac{\sqrt{3}}{2}\cdot \dfrac{\sqrt{3}}{2}+\left(-\dfrac{1}{2}\right)\cdot \dfrac{1}{2}=\dfrac{3}{4}-\dfrac{1}{4}=\dfrac{1}{2}[/tex]

Answer:

A. 6x-150=2400

X=425

Step-by-step explanation:

Solve.

6x-150=2400

First, you add 150 from both sides of equation.

6x-150+150=2400+150

Then, simplify.

2400+150=2550

6x=2550

Divide by 6 from both sides of equation.

6x/6=2550/6x

Simplify to find the answer.

2550/6=425

X=425 is the correct answer.

A. 6x-150=2400 is the correct answer.

Answer:

6x – 150 = 2400

Step-by-step explanation:

Each plate of food was sold for $8, but cost the school $2 to prepare:

-2x + 8x = 6x

A school spent $150 on advertising for a breakfast fundraiser:

-150

After all expenses were paid, the school raised $2400 at the fundraiser:

6x – 150 = 2400

In case you want to solve it:

6x – 150 = 2400

+ 150 + 150

_________________

6x = 2550

___ _____

6 6

x = 425

So, four hundred twenty-five plates were sold.

I am joyous to assist you anytime.

Check the picture below.

Answer:

x = -4

Step-by-step explanation:

Distribute 2 inside the parentheses

[tex]2\times x = 2x\\ 2\times2=4\\ 2x+4 - 4[/tex]

Combine like terms

[tex]-4x + 2x = -2x + 4 = 12[/tex]

Subtract 4 from both sides

-2x = 8

x = -4

The solution of the linear equation 2(x + 2) – 4x = 12 will be negative 4.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given below.

2(x + 2) - 4x = 12

Solve for x in the equation 2(x + 2) - 4x = 12. Then we have

2(x + 2) - 4x = 12

2x + 4 - 4x = 12

-2x = 12 - 4

-2x = 8

x = -8/2

x = -4

The solution of the linear equation 2(x + 2) – 4x = 12 will be negative 4.

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Answer:

The equation 0 = ax2 + bx + c has no real roots or no solution.

Step-by-step explanation:

We are told that the graph of y = ax2 + bx + c is a parabola that opens up and has a vertex at (0, 5). Since the parabola opens up, the vertex (0, 5) will be the lowest point on the graph of the function. This implies that the parabola does not intersect the x-axis; the line y = 0. Therefore, the equation;

 0 = ax2 + bx + c will have no real roots or no solution. Find the attached.

Answer:

b d e f

Step-by-step explanation:

Answer:

Cats: 28; Dogs: 13

Step-by-step explanation:

54-26=28

48-35=13

54+48=102

102-61=41

28+13=41

Answer:

Step-by-step explanation:

To find each answer, we just have to complete the table.

We know that there are 54 cats in total, and 26 belong to 8th grade. So, 7th grade would be 54-26=28.

Also, we know that there are 48 dogs in total, if 35 belong to 8th grade, then 7th grade would be 48-35=13.

Therefore, 7th grade students have 28 cats, 13 dogs, and 41 pets in total. Therefore, the right choice is the second one.

The equation will be like this: y=ax+c. a is the slope and c is where the line crosses the (vertical) y axis - AKA the y-intercept.

As for the slope, it can be found like [(8-3)/(2-1)]. That gives 5. Another way to see it is to notice that between (1,3) and (2,8), the line moved up 5 points and went to the right only 1.

And for the y-intercept, make the equation y = 5x + c. Solve for c by filling x and y with information from any of the two points. Let's choose (1,3). Plugging in gives the equation 3=5(1)+c. C equals -2.

So, the final equation is:

y = 5x - 2

Answer:

y - 3 = 5(x - 1)

Step-by-step explanation:

Slope:  as we move from (1, 3) to (2, 8), x increases by 1 and y increases by 5.  Hence, the slope of this line is m = rise / run = 5/1, or just m = 5.

In point-slope form, the pertinent equation is

y - 3 = 5(x - 1)

Answer:

A) -sqrt(3)/3

Step-by-step explanation:

If you know your unit circle (attached), 11pi/6 has the value of (sqrt(3)/2,-1/2), where the coords are (cosine, sine).

Tangent is sine/cosine:

(-1/2)/(sqrt(3)/2)

We can convert this to multiplication by miltiplying the reciprocal of sqrt(3)/2:

(-1/2)*(2/sqrt(3))

Multiplied out to:

-2/(2sqrt(3))

We have to rationalize this by multiplying the numerator and denominator by sqrt(3):

-2(sqrt(3))/2sqrt(3)(sqrt(3)

two of the same square roots multiplied together equals the number without the sqrt:

-2(sqrt(3))/2*3

we can factor out 2 from the numerator and denominator:

-sqrt(3)/3

Therefore, the answer is A

Answer:

(-10, -8) and (-6, -4)

Step-by-step explanation:

we know that

The diagonals of a rhombus are perpendicular

If two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

step 1

Find the slope of the given diagonal

we have

(-11, -9) and (-5, -3)

m=(-3+9)/(-5+11)

m=-6/6=-1

Find the slope of the other diagonal

we have

m1=-1

Find m2

m1*m2=-1

(-1)*m2=-1

m2=1

step 2

Verify the slope of each of the endpoints of the other diagonal

The slope of the other diagonal must be equal to 1

so

case a) (-10, -4) and (-6, -8)

m=(-8+4)/(-6+10)

m=-4/4=-1

therefore

The points of case a) cannot be the end-points of the other diagonal

case b) (-8, -3) and (-5, -6)

m=(-6+3)/(-5+8)

m=-3/3=-1

therefore

The points of case b) cannot be the end-points of the other diagonal

case c) (-8, -4) and (-8, -8)

m=(-8+4)/(-8+8)

m=-4/0 -----> undefined

therefore

The points of case c) cannot be the end-points of the other diagonal

case d) (-10, -8) and (-6, -4)

m=(-4+8)/(-6+10)

m=4/4=1

therefore

The points of case d) can be the end-points of the other diagonal

Answer:

The answer is C) 57.46cm2

Step-by-step explanation:

To find the area of a trapezoid you add together the parallel lines and times the answer by the height. Then you divide it by 2.

Answer:

The answer is B, 160 cm2

Step-by-step explanation:

To find the area of a trapezoid we have to use the following equation:

A= 0.5*(b1*b2)*h

a= area

b1: base 1

b2: base 2

h: height

Then,

A= 0.5*(14cm+18cm)*10cm = 160 cm2.

Answer:

[tex]\frac{1}{a(a-4)}[/tex]

Step-by-step explanation:

Factor the denominator of the first fraction

a² - 16 ← is a difference of squares and factors as

a² - 16 = (a - 4)(a + 4), thus fraction becomes

[tex]\frac{a}{(a-4)(a+4)}[/tex] × [tex]\frac{a+4}{a^2}[/tex]

Cancel the factor (a + 4) on numerator/denominator and the a and a², leaving

[tex]\frac{1}{a(a-4)}[/tex]

Answer:

[tex]x=37.5[/tex]

Step-by-step explanation:

We need to find the solution to the following system of equations:

[tex]y = -\frac{4}{5} x[/tex] and [tex]y=-30[/tex]

By plugging the value of 'y' into the first equation we have that:

[tex]-30 = -\frac{4}{5} x[/tex] ⇒ [tex]30=\frac{4}{5} x[/tex]

Solving for 'x' we have:

[tex]x=37.5[/tex]

So, the solution to the system of equation is: (37.5, -30)

Answer:

[tex]x=\frac{5}{3}[/tex]

Step-by-step explanation:

Let do algebra and figure out the value of x:

[tex]\frac{4}{x-3}+5=2\\\frac{4}{x-3}=2-5\\\frac{4}{x-3}=-3\\4=-3(x-3)\\4=-3x+9\\3x=9-4\\3x=5\\x=\frac{5}{3}[/tex]

Note: assuming that the problem is [tex]\frac{4}{x-3}+5=2[/tex]

Answer:

The answer is 5/3

Step-by-step explanation:

Answer:

[tex]\boxed{A=6}\checkmark[/tex]

The answer should have positive sign.

Step-by-step explanation:

First you do is divide by -6 from both sides of an equation.

[tex]\frac{-6(2+a)}{-6}=\frac{-48}{-6}[/tex]

Then, simplify and solve the problem.

[tex]-48/-6=8[/tex]

[tex]2+a=8[/tex]

Next, you switch sides.

[tex]a+2=8[/tex]

You subtract by 2 from both sides of an equation./

[tex]a+2-2=8-2[/tex]

Finally, solve/simplify.

[tex]8-2=6[/tex]

A=6 is the correct answer.

Hope this helps you!

Have a nice day! :)

Answer:

They have the same slope but different y-intercepts, so they have no solution.

Step-by-step explanation:

As the slopes are the same (2) but the y-intercepts are different, it means that the straights are parallel. Parallel equations have no solution as the straights don't intercept each other.

Answer: They have the same slope but different y-intercepts, so they have no solution.

The given equations are [tex]y=2x+\frac{1}{4}[/tex] and [tex]y=2x-\frac{1}{4}[/tex].

We compare them with y = mx + b.

So the slope of both of them is m=2.

y-intercept for the first one is = b = 1/4

y-intercept for the second one is = b = -1/4

Hence, the lines are parallel and will never meet and will have no solution.

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Answer:

38

Step-by-step explanation:

Range is the largest number minus the smallest number

The largest number is 55 and the smallest number is 17

55-17 = 38

Answer:

[tex]70ft^2[/tex]

Step-by-step explanation:

Surface area is the sum of all sides of the area. Since it is a rectangular prism, each surface area will be multiplied by two to account for the opposite side (ex. top and bottom are the same area).

The front/back area is [tex]1*11[/tex] or 11. So the sum of the areas is 22.

The right/left area is [tex]2*1[/tex] or 2. So the sum of the areas is 4.

The top/bottom area is [tex]2*11[/tex] or 22. So the sum of the areas if 44.

We add these together to find the surface area.

[tex]22+4+44=70[/tex]

The surface area is [tex]70ft^2[/tex]

[tex]|\Omega|=6^4=1296\\|A|=1\cdot1\cdot5\cdot5\cdot\dfrac{4!}{2!2!}=25\cdot6=150\\\\P(A)=\dfrac{150}{1296}\approx11.6\%[/tex]

Answer: 243

Step-by-step explanation:

We have the expression

[tex]3(a + b + c)^2[/tex]

Note that the expression depends on 3 variables

a, b and c

in this case we want to evaluate the expression for

[tex]a = 2\\b = 3\\c = 4[/tex]

Then change the variable a by the number 2, the variable b by the number 3 and the variable c by the number 4

So we have

[tex]3(2 + 3 + 4)^2[/tex]

Now simplify the expression

[tex]3(9)^2[/tex]

[tex]3*81=243[/tex]

The answer is 243

ANSWER

[tex]243[/tex]

EXPLANATION

The given expression is

[tex]3 {(a + b + c)}^{2} [/tex]

We want to evaluate this expression for:

a = 2, b = 3, and c = 4.

We substitute the given values into the expression to get:

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

Let us perform the addition inside the parenthesis to get:

[tex]3(9)^{2} [/tex]

[tex]3(81) =24 3[/tex]

Therefore the given expression evaluates to:

[tex]243[/tex]

Answer:

First, we need to find the missing side which is BC ( using pythagorean theorem)

AB² + BC² = AC²

=> 16² + BC² = 20²

=> BC²          = 20² - 16² = 144

=> BC           = √144 = 12

Now apply the formulars:

Just to make things easier, let's point out exactly what will the hypotenuse, opposite side and adjacent side.

So in this case:

The hypotenuse will be AC

The opposite side (of angle A) is BC

The adjacent side (of angle A) is AB

Therefore:

sin A = opposite/hypotenuse = BC/AC = 12/20 = 3/5

cos A = adjacent/hypotenuse = AB/AC = 16/20 = 4/5

tan A = opposite/adjacent = BC/AB = 12/16 = 3/4