Solve the inequality4x + 13 ≥ 27

It will take 80 gallons of water to fill the fish tank.

The amount of space occupied by a three-dimensional object or region of space.

Given that, Anna is going to clean the fish tank, which measures 48 inches long by 11 inches wide by 35 inches high

The fish tank is cuboidal,

Volume of cuboid = length*width*height

Therefore, volume of fish tank = 48*11*35 = 18,480 in³

1 gallon = 231 in³

So, 18,480  in³ = 18,480/231 gallons = 80 gallons

Hence, Volume of tank = 80 gallons

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The area of triangle using vertices is D)  A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

What is area of triangle using vertices ?

 The length of a triangle's three sides must first be determined if the triangle's vertices are known. The distance formula can be used to determine the length. when the vertices in the coordinate plane are known, the process to determine the triangle's area. Consider the triangle PQR, whose coordinates P, Q, and R are [tex](x_1,y_1)(x_2,y_2)[/tex], and [tex](x_3,y_3)[/tex] respectively.

If the triangle's area is zero and its vertices are P[tex](x_1,y_1)[/tex] Q[tex](x_2,y_2)[/tex], and R[tex](x_3,y_3)[/tex] then (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]] = 0 and its points are collinear.

Here the given vertices are, [tex](x_1,y_1),(x_1,y_2)[/tex] and [tex](x_3,y_3)[/tex] then the area of triangle is ,

=> A =  (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]

=> A =  (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_1(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]

=> A = (1/2)[ [tex]x_1y_2-x_1y_3+x_1y_3-x_1y_1+x_3y_1-x_3y_2[/tex]]

=> A = (1/2) [[tex]x_1y_2-x_1y_1+x_3y_1-x_3y_2[/tex]]

=> A = (1/2) [[tex]x_1(y_2-y_1)-x_3(y_2-y_1)[/tex]]

=> A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

Hence the correct option is D)  A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

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Answer:

[tex]d=7[/tex]

[tex]a_9=59[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]3[/tex] and the second term is [tex]10[/tex], then each successive term in the sequence is [tex]7[/tex] more than the previous term. The common difference is [tex]7[/tex] ( [tex]d=7[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=7n-4[/tex]

Therefore, the ninth term in the sequence is:

[tex]a_9=7(9)-4[/tex]

[tex]a_9=63-4[/tex]

[tex]a_9=59[/tex]

Answer:

  (e)  b h a k

Step-by-step explanation:

You want the order of operations involved in the transformation ...

  g(x) = a(bx -h) +k

The Order of Operations tells you that multiplication takes precedence over addition, and expressions inside parentheses are evaluated first.

We note there is an expression in parentheses here: (bx -h). In that expression is a multiplication operation (bx) and an addition operation (_-h).

The multiplication is done first, so evaluating this expression in parentheses, we ...

Once the parenthetical expression is evaluated, we proceed to the main event. Again, multiplication and addition are required. That means the next two steps are ...

In summary, the operations we perform during evaluation of the transformation successively apply the parameters ...

  b h a k

The correct statement:  

1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10

incorrect statement:  2/5 equal to 1/3

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

a) 4/12

Writing into Simplest form

4/12 = 1/3

b) 4/6

Writing into Simplest form

4/6 = 2/3

c) 2/5 cannot be simplified to 1/5

d) 5/10

Writing into Simplest form

5/10= 1/2

Hence, The correct statement:  1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10 and incorrect statement:  2/5 equal to 1/3.

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Answer:

68°

Step-by-step explanation:

The angles are equal to each other.  Set them equal and solve for x

5x + 18 = 8x - 12  Subtract 5x from both sides of the equation

18 = 3x - 12  Add 12 to both sides of the equation

30 = 3x  Divide both sides by 3

10 = x

Now that you have found x plug is back into  5x + 18

5(10) + 18

50 + 18 = 68

Answer:

∠ FLJ = 68°

Step-by-step explanation:

∠ EKG and ∠ FLJ are alternate exterior angles and are congruent , then

8x - 12 = 5x + 18 ( subtract 5x from both sides )

3x - 12 = 18 ( add 12 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

Then

∠ FLJ = 5x + 18 = 5(10) + 18 = 50 + 18 = 68°

The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and  2c(c - 3)/[(c - 3)(5c - 9)(c - 8)].

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given expression,

8/(5c² - 6c - 27) , 2c/(5c² - 31c - 72)

Now, take the first denominator,

5c² - 6c - 27 = 5c² - 15c + 9c - 27

⇒ 5c(c - 3) - 9(c - 3)

⇒ (c - 3)(5c - 9)

Take the second denominator

5c² - 31c - 72 = 5c² - 40c + 9c - 72

⇒ 5c(c - 8) + 9(c - 8)

⇒ (c - 8)(5c + 9)

Therefore, the expression converts as,

8/[(c - 3)(5c - 9)] , 2c/[(c - 8)(5c + 9)]

8/[(c - 3)(5c - 9)] = 8(c - 8)/[(c - 3)(5c - 9)(c - 8)]

2c/[(c - 8)(5c + 9)] = 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]

The denomiantor of both expression are same.

Hence "The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and  2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]".

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The structured question below,

The statement that correctly describes the graph of the relationship is (d) A line that goes through (0, 0) and (4.3, 17.2).​

The table of values is given as

x 4.3 9.2 3.4

y 17.2 36.8 13.6

The table shows a proportional relationship

This means that the line of the graph must pass through the origin i.e. (0, 0)

From the table of values, we have the following point

(4.3, 17.2)

This means that the line of the graph goes through (0, 0) and (4.3, 17.2).​

Hence, the true statement is (d)

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Answer:

No, it is not proportional because 9.2 over 18.4 does not equal 17.6 over 52.8.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is 4

Answer:

40%

Step-by-step explanation:

The given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given that the graph of the function has increased and decreasing orders on the coordinate plane.

The interval in which the given graph of the function is increasing is,

(-∞,-6)

(-4,-1)

(3,6)

(8,∞)

Therefore, the given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

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Answer:

the answer to 2dp is 2536.02

Answer: C.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

[tex]16x {}^{3} + 1[/tex]

Step-by-step explanation:

We need to differentiate the following function,

[tex]\longrightarrow f(x) = 4x^4 + x [/tex]

Let ,

[tex]\longrightarrow y = f(x) [/tex]

So that ,

[tex]\longrightarrow y = 4x^4+x [/tex]

Differentiating both sides wrt x ,

[tex]\longrightarrow \dfrac{dy}{dx}= \dfrac{d(4x^4+x)}{dx}\\[/tex]

[tex]\longrightarrow\dfrac{dy}{dx}= \dfrac{d(4x^4)}{dx}+\dfrac{dx}{dx}\\ [/tex]

[tex]\longrightarrow \dfrac{dy}{dx} = 4(4)x^{4-1} + 1 \\ [/tex]

[tex]\longrightarrow \underline{\underline{ \dfrac{dy}{dx}= 16x^3 +1}}[/tex]

Answer:

5 pounds

Step-by-step explanation:

1 kg = 2.205 lbs.

2.25×2.205

⇒4.96125

Answer:

Step-by-step explanation:

The measure of h from the triangle is h = 55

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

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

And , the measure of ∠ABC = 40°

Now , Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

So , the measure of ∠ACB = ∠BAC = y° = 70°

And , 2h + y° = 180° ( angles on a straight line )

On simplifying , we get

2h + 70° = 180°

Subtracting 70 on both sides , we get

2h = 110

Divide by 2 on both sides , we get

h = 55

Hence , the measure of h = 55

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The complete question is attached below :

(2h)

40°

(2h)

What is the value of h of the triangle?

O h=20

O h=35

O h=55

O h=70

If FG = 10x − 10, GH = x + 4, and FH = 16, FG is 10

information given in the question include

FG = 10x − 10

GH = x + 4

FH = 16

The problem is solved using substitution. this involves replacement of a variable with another that are same.

An instance of this a line FH having points FG and GH

FH contains FG and GH, hence adding both FG and GH gives FH

FH = FG + GH

plugging in the values

16 = 10x - 10 + x + 4

collecting like terms

16 = 11x - 6

16 + 6 = 11x

22 = 11x

rearranging the equation

11x = 22

x = 2

FG = 10x − 10

substituting the value of x

FG = 10 * 2 − 10

FG = 20 - 10

FG = 10

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The expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

So, the expression is:

Now, use Pascal's Triangle to expand as follows:

Therefore, the expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

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The interest she is pay total is $2340.822 when Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.

Given that,

For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.

We have to find will she pay interest at all.

We know that,

i=p×r×t

Here,

i is interest.

p is principal amount.

r is rate of interest

t is time.

So, p is $6380

r is 12.23%

t is 3 years

So,

i= 6380×0.1223×3

i= $2340.822

Therefore, the interest she is pay total is $2340.822 when Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.

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The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

The location of a circle in the Cartesian plane is represented by a circle equation. We can write the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.

The standard equation of a circle with center at

(a, b) and radius is r.

So, the standard equation circle is

(x -a)² + (y- b)² = r²

Given:

As, we know the standard form for equation of a circle is

(x-a)² + (y-b)² = b =r²

where (a, b) is the center of the circle and r is the radius of the circle.

We have

diameter = 12 units

radius = 12/2 = 6 units

So, the center will be at (0, 3)

Thus, the equation of circle

(x-0)² + (y-3)² = 6²

x²+ (y-3)² = 36

Hence, the Equation of Circle is x²+ (y-3)² = 36.

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Answer: $8.55

because 6.65 divided by 7 is 0.95 and 0.95 multiplied by 9 is 8.55

so the answer is $8.55

The difference of a linear, quadratic reation.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation.

Trigonometric ratios describe these operations. The ide and trigonometric functions In the previous chapters, we discovered that the polynomial equation is the equation that results from equating a polynomial function to zero. A linear equation results from equating a function to zero if it is a linear polynomial. We get a quadratic equation if the function is a quadratic polynomial.

When we graph a linear equation, we get a straight line, however with a quadratic equation, we get a parabola.

Unlike the slope of a linear polynomial, the slope of a quadratic polynomial is constant.

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A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

It would take 8 months of membership for the total money paid of $321.91.

An equation is an expression that shows the relationship between two or more numbers and variables. A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

Let x be the number of months subscribed. Hence,

For Fitness :

Total payment = 33.99 x + 49.99

if you paid a total of $321.91 then the number of months subscribed will be;

321.91  = 33.99 x + 49.99

33.99 x = 321.91  - 49.99

33.99 x = 271.92

x = 271.92/33.99

x = 8

It would take 8 months of membership for the total money paid of $321.91.

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The quotient estimated value of 394.6/9 is 43.84

A quotient is the number which is generated when we perform division operations on two numbers. Basically, it is the result of the division method. There are four main terminologies used in the arithmetic division such as divisor, dividend, quotient and remainder. For example, 15/3= 5 .The number that is being divided ( 15) is called the dividend, and the number that it is being divided by (3) is called the divisor. The result of the division(5) is the quotient.

Therefore the quotient of 394.6/9= 43.84

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The solutions to the inequality whose graph is as represented in the attached image are;

It follows from the task content that the graphical solutions for the inequality are represented on the graph and the points which are solutions for the inequality are to be identified.

Therefore, the points which are solutions for the inequality are points which are located in the shaded region of the graph.

Hence, such points include;

The answer choices B, D and F represents points on the border line of the inequality graph and since the line is broken, they are not solutions to the inequality.

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