Which graph is defined by the function given below?
y = (x-3)(x-3)

The value of a in terms of b is given as [tex]a = 8b^3[/tex]

Given the equation solved by Leo expressed as [tex]b=\frac{1}{2}\sqrt[3]{a-1}[/tex]

We are to solve the equation for the variable "a"

Given;

[tex]b=\frac{1}{2}\sqrt[3]{a-1}[/tex]

Cross multiply

[tex]2b=\sqrt[3]{a-1}[/tex]

Cube both sides of the equation:

[tex](2b)^3=(\sqrt[3]{a-1})^3 \\8b^3=a-1[/tex]

Add 1 to both sides of the equation:

[tex]8b^3+1=a-1+1\\8b^3=a\\Swap\\a=8b^3[/tex]

Hence the value of a in terms of b is given as [tex]a = 8b^3[/tex]

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Answer:

That is an improper fraction

Step-by-step explanation:

When the numerator (the top) is greater than the denominator (The bottom) then the fraction is improper

Hope this helps!

Answer:

Improper fraction

Step-by-step explanation:

Answer:

Step-by-step explanation:

When James is twice as old as John, the difference in their ages will be John's age: 10. That is 5 years from now, so John's age now is 10 -5 = 5.

John is 5 years old.

__

3 years ago, John was 2 and James was 12. Their total age at that time was 14.

Answer:

Step-by-step explanation:

x + 4y = 8

-x           -x

4y = -x + 8

divide by 4

y= -1/4x + 2

then graph

The equation that matches the given points is g(x) = -1.4x + 7.6

The standard form of a linear  equation is expressed as [tex]g(x)=mx + b[/tex]

Using the coordinate points (3, 3.4), (4,2)

[tex]m=\frac{2-3.4}{4-3}\\m=\frac{-1.4}{1}\\m=-1.4[/tex]

Substitute m = -1.4 and the coordinate (4, 2) into the formula:

[tex]2=4(-1.4)+b\\2=-5.6+b\\b=2+5.6\\b=7.6[/tex]

Get the required equation:

[tex]g(x)=mx+b\\g(x)=-1.4x+7.6[/tex]

Hence the equation that matches the given points is g(x) = -1.4x + 7.6

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[tex]\huge\boxed{Good\:evening!:)}[/tex]

2(2c+12)=68

4c+24=68

4c=68-24

4c=44

Divide both sides by 4:

c=11

[tex]\huge\boxed{Hence,\:the\:answer\:is\:11.:)}[/tex]

[tex]\huge\underline{Hope\:it\:helps!}[/tex]

[tex]\huge\sf{Good\:luck.}[/tex]

[tex]\boxed{DreamyTeenager\:here\:to\:help}[/tex]

Answer:

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

The total weight W of such a plane is equal to

W = w + gf

where

w = weight of plane without fuel

g = number of gallons of fuel

f = weight of 1 gallon of fuel.

When carrying g = 10 gallons, the total weight is W = 1955, so

1955 = w + 10f

When carrying g = 42 gallons, the weight is W = 2131, so

2131 = w + 42f

We want to find W when g = 52, and to do this we first need to find the weight of the plane w and the weight of 1 gallon of fuel f.

Solve the system of equations,

w + 10f = 1955

w + 42f = 2131

We can combine the equations like so to eliminate w and solve for f :

(w + 42f) - (w + 10f) = 2131 - 1955

32f = 176

f = 11/2 = 5.5

Then solving for w, we get

w + 10 (5.5) = 1955

w + 55 = 1955

w = 1900

So, when the plane carries g = 52 gallons of fuel, the total weight is

W = 1900 + 52 (5.5) = 2186

Answer:

4:11:7

Step-by-step explanation:

Find the GCF, or greatest common factor of the 3 numbers. In this case it is 12. To simplify, divide each number by 12

Answer:

4:11:7

Step-by-step explanation:

please mark me as brainlest

Answer: The element described is aluminum.

Answer:

The answer is 15

Step-by-step explanation:

15*3=45-5=40

The rational zero test is also known as the rational root test, and it is used to determine the potential root of a function.

(a) 1/2 is not a possible zero of the function

The function is given as:

[tex]f(x) =x^3 - 5x + \frac 25[/tex]

For a function,

[tex]f(x) = px^n +......q[/tex]

The list of possible roots is:

[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]

Multiply both sides of [tex]f(x) =x^3 - 5x + \frac 25[/tex] by 5

[tex]5f(x) = 5x^3 - 25x + 2[/tex]

So, we have:

[tex]p= 5[/tex]

[tex]q = 2[/tex]

The factors are:

[tex]p =\pm 1, \pm 5[/tex]

[tex]q =\pm 1, \pm 2[/tex]

So, the possible roots are:

[tex]Roots = \pm\frac{1,2}{1,5}[/tex]

Split

[tex]Roots = \pm1, \pm \frac 15, \pm 2, \pm \frac 25}[/tex]

Hence, 1/2 is not a possible zero of the function

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Answer:

rectangle

Step-by-step explanation:

Answer:

Rectangle

Step-by-step explanation:

FG's slope is the opposite reciprocal of GD's, so they are perpendicular. The same with the other sides.

The opposite sides have the same length.

Answer:

272×620=168,640

Step-by-step explanation:

If koala airlines carries 272 in average then the answer is 168,640

Answer:

number of adult shirts sold (a) = 20

number of youth shirts sold (b) = 10

Step-by-step explanation:

a = number of adult shirts sold

y = number of youth shirts sold

30 = a + y

$324.50 = 11.50a + 9.45y

This is the resulting system of equations from the given information in the problem.

Solve for y in the first equation and then substitute the equation for y into the second equation :

a+y=30 --> y=30-a

324.50 = 11.50a + 9.45(30-a)

Solve for a.

324.50 = 11.50a + 283.5 - 9.45a

41 = 2.05a

a = 20

Now that we have solved for a, we can back substitute into our equation for y and solve.

y=30-(20)

y = 10

CHECK:

(20)+(10) = 30 True

(11.50)(20) + (9.45)(10) = 324.5  True

The solution is Option C.

The height of the wall to the top of the ladder is 15 feet

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Let the height of the wall be represented as h = AB

Now , Larry liens a 16 foot ladder against a wall

So , the hypotenuse of the triangle AC = 16 feet

And , the base is 5 feet away from the wall

So , the base of the triangle BC = 5 feet

The height of the wall h is given by the Pythagoras theorem ,

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

AC² = AB² + BC²

16² = AB² + 5²

On simplifying the equation , we get

Subtracting 5² on both sides of the equation , we get

AB² = 16² - 5²

AB² = 256 - 25

AB² = 231

Taking square root on both sides of the equation , we get

AB = 15.19

AB ≈ 15 feet

Therefore , the value of h is 15 feet

Hence , the height of the wall is 15 feet

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#SPJ2

Lin should aim the ball at 7.8 feet away from point  B

From the question (see attachment), we have the following equivalent ratios:

[tex]AB : BE = DC :CE[/tex]

This is so because triangles ABE and DCE are similar triangles.

Such that:

[tex]BE + CE = 20[/tex]

[tex]AB = 16[/tex]

[tex]DC = 16 + 9 = 25[/tex]

So, we have:

[tex]AB : BE = DC :CE[/tex]

[tex]16 : BE = 25: CE[/tex]

Make CE the subject in [tex]BE + CE = 20[/tex]

[tex]CE=20 - BE[/tex]

Substitute 20 - BE for CE in [tex]16 : BE = 25: CE[/tex]

[tex]16 : BE = 25: 20 - BE[/tex]

Express as ratio

[tex]\frac{16 }{ BE} = \frac{25}{ 20 - BE}[/tex]

Cross multiply

[tex]16(20 - BE) = 25BE[/tex]

Open bracket

[tex]320 - 16BE = 25BE[/tex]

Collect like terms

[tex]25BE + 16BE = 320[/tex]

[tex]41BE = 320[/tex]

Divide both sides by 41

[tex]BE = 7.8[/tex]

Hence, she should aim at 7.8 feet away from point  B

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Answer:You want to make a bank shot. Sketch the path of the cue ball so it will bounce off of the bottom side and knock the yellow stripe 9 ball into the top middle pocket.

Step-by-step explanation:

Answer: 8 or -6

Step-by-step explanation:

x^2 - 2x = 48

x^2 - 2x - 48 = 0

(x-8)(x+6) = 0

x = 8 or -6

Answer:

34-13.95 = 20.05

Step-by-step explanation:

Answer:

20.05

Step-by-step explanation:

34 - 13.95 = 20.05

Answer: 38 miles per gallon ; 342 miles.

Step-by-step explanation:

The miles/gallon that he got on the trip will be:

= 228/6

= 38 miles per gallon.

When he used 9 gallons of gas, the distance travelled will be:

= 38 × 9

= 342 miles

Answer:

Question :

Jamar drove 228 miles and used 6 gallons of gas.

Solution :

a) How many miles/gallon did he get on the trip?

[tex]{\implies{\sf{\dfrac{228}{6}}}}[/tex]

[tex]{\implies{\sf{ \cancel{\dfrac{228}{6}}}}}[/tex]

[tex]{\implies{\sf{\underline{\underline{\red{36 \: miles/gallon}}}}}}[/tex]

Hence, he get 38 miles/gallon for his trip.

[tex]\rule{200}2[/tex]

b) On another trip, he used 9 gallons of gas. How far did he travel?

[tex]{\implies{\sf{38 \times 9}}}[/tex]

[tex]{\implies{\sf{\underline{\underline{\red{342 \: miles}}}}}}[/tex]

Hence, he traveled 342 miles by using o gallon og gas.

[tex]\underline{\rule{220pt}{3pt}}[/tex]

Answer:

Answer in the image

Step-by-step explanation:

By the binomial theorem,

[tex]\displaystyle \left(x^2-\frac1x\right)^6 = \sum_{k=0}^6 \binom 6k (x^2)^{6-k} \left(-\frac1x\right)^k = \sum_{k=0}^6 \binom 6k (-1)^k x^{12-3k}[/tex]

I assume you meant to say "independent", not "indecent", meaning we're looking for the constant term in the expansion. This happens for k such that

12 - 3k = 0   ===>   3k = 12   ===>   k = 4

which corresponds to the constant coefficient

[tex]\dbinom 64 (-1)^4 = \dfrac{6!}{4!(6-4)!} = \boxed{15}[/tex]

Answer:

AB = 21

Step-by-step explanation:

Tales' theorem

[tex]\frac{12}{14} =\frac{18}{AB}[/tex]

[tex]AB=\frac{(14)(18)}{12}[/tex]

[tex]AB=21[/tex]

Hope this helps

(i)Given that:

AE || BD

AB = ? [Let AB be x]

BC = 3

ED = 12

DC = 4

We know that

By Basic Proportionality Theorem,

AB/BC = ED/DC

On substituting these values in the above formula

⇛ AB / 3 = 12 / 4

On applying cross multiplication then

⇛ x(4) = (12)3

⇛ 4x = 36

Shift the number 4 from LHS to RHS.

⇛ x = 36÷4

⇛ x = 36/4

Therefore, AB = 9

Answer: The value of AB for the given problem is 9.

Similarly,

(ii) Given that:

EB || DC

AE = 14

ED = 12

AB = ? [Let AB be X]

BC = 18

We know that

By Basic Proportionality Theorem,

AE / ED = AB / BC

On substituting these values in the above formula

⇛ 14 / 12 = x / 18

On applying cross multiplication then

⇛ 14(18) = (12)x

⇛ 252 = 12x

Shift the number 252 from LHS to RHS.

⇛ X = 256÷12

⇛ X = 21

Therefore, AB = 21

Answer: The value of AB for the given problem is 21

Additional comment:

Basic Proportionality Theorem

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F, G, and H all lie on the same line. If FG/GH = 1, then FG = GH, which is to say the distance between F and G is equal to the distance between G and H. This means either F and H are the same point, or G is the midpoint of F and H.

They're not the same point, because the x-coordinate of H is 7 times that of F. So G must be halfway between F and H.

Then the x-coordinate of G is

(a + 7a)/2 = 8a/2 = 4a

Answer:

−5<n≤2 I think, I don't really understand the question either I'm sorry!!!!

Answer:

Both plans would cost $100 if 6 gigabytes of data are used.

Explanation:

From the question, the system of equation are correctly represented by using small letter c to represent the total cost in dollars for both equations as already assumed in the question as follows:

c = 52 + 8d ........................... (1)

c = 82 + 3d ........................... (2)

Since c is common to both, equations (1) and (2) can therefore be equated and d solved for as follows:

52 + 8d = 82 + 3d

8d - 3d = 82 - 52

5d = 30

d = 30 / 5

d = 6

Substituting d = 6 into equation (1), we have:

c = 52 + (8 * 6)

c = 52 + 48

c = 100

Since d = 6 and c = 100, it therefore implies that both plans would cost $100 if 6 gigabytes of data are used.

Answer:

y = 2x + 9.

Step-by-step explanation:

Using the point-slope form:

y - y1 = m(x - x1)   where m = the slope and (x1, y1) is a point on the line.

So here we have:

y - 1 = 2(x - (-4))

y - 1 = 2(x + 4)

y - 1 = 2x + 8

y = 2x + 9.

Answer:

First one

Step-by-step explanation:

For every 1 in x the y goes up by 3