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Which of the following would best be solved using completing the square?

A) 2x^3 - 12x^2 + 5x - 30 = 0

B)5x^2 + 7x = 12

C) x^2 = 81

D) x^2 + 4x - 21 = 0

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Answer:

9.8 feet

Step-by-step explanation:

let area of triangular base be A square feet.

volume of prism = A x height(or length in this case)

498.33 = A x 9

A = 498.33 / 9 = 1/2 x 11.3 x base

...

thus, base = 9.8 feet

The solution to 4 superscript log subscript 4 baseline (x 8) baseline = 4 squared for the variable x is 8.

The exponent of the log rule says that the raising a logarithm with a number to its base is equal to the number.

For example, let k is the number and a is the base. Thus,

[tex]a^{\log a(k)}=k[/tex]

The logarithmic equation given in the problem is,

[tex]4^{\log_4(x+8)}=4^2[/tex]

Compare the equation with the expression of exponent of log rule, we get,

[tex]x+8=4^2\\x+8=16\\x=16-8\\x=8[/tex]

Thus, the solution to 4 superscript log subscript 4 baseline (x 8) baseline = 4 squared for the variable x is 8.

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Answer:

8

Step-by-step explanation:

Answer: 58/19 or 3¹/119

Step-by-step explanation: Area = 58

Length is 19 Width is Area/ Length

Answer:

There’s nothing really different between the UK and the US when it comes down to Tests and Schools. The UK have harder tests but a laughable school grading scale, while the US has slightly easier tests but a harsher grading scale.

Answer: It all depends on the category you are comparing the UK has grading Scales of 1-9 but in the US you have A,B,C,D,F which are is way harder to understand in my opinion.

The measurement is the closest to the length of endpoints of CD in units is 4.5 units. Option D is the correct option.

The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = \sqrt{(x-p)^2 + (y-q)^2}[/tex]

The coordinates of the endpoints of CD are C(2, 5) and D(4, 9). Put the values of coordinate point in the above formula as,

[tex]D = \sqrt{(4-2)^2 + (9-5)^2}\\D = \sqrt{2^2 + 4^2}\\D = \sqrt{4 + 16}\\D=4.47\\D\approx4.5\rm\; units[/tex]

Thus, the measurement is the closest to the length of endpoints of CD in units is 4.5 units. Option D is the correct option.

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Let's see

#a

Take 28

#2

Take 9,10

Answer:

Two-digit number greater than 25:   32

Rewrite 32 as the difference of 2 numbers: 40 - 8

Therefore, x = 40  and  y = 8

[tex]\begin{aligned}\implies (40-8)^2 & =40^2-2(40)(8)+8^2\\ & = (4 \cdot 10)^2-(80)(8)+64\\ & = 4^2 \cdot 10^2-640+64\\ & = 16 \cdot 100-640+64\\ & = 1600-640+64\\ & = 960+64\\ & = 1024\end{aligned}[/tex]

Let a = 10

Let b = 11

[tex]\begin{aligned}\implies 10^3+11^3 & =(10+11)(10^2-10 \cdot 11+11^2)\\& = 21(100-110+121)\\ & = 21(-10+121)\\ & = 21(111)\\& = 21 (100 + 10 + 1)\\ & = (21 \cdot 100)+(21 \cdot 10)+(21 \cdot 1)\\ & = 2100 +210+21\\ & = 2310 + 21\\ & = 2331\end{aligned}[/tex]

Answer:

9 weeks :)

Step-by-step explanation:

First we subtract :)

2145 - 952.50 = 1192.50

Now we divide :)

265/2 = 132.5

Now we divide 1 more time :)

1192.50/132.50 = 9

It will take 9 weeks :)

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Answer:

so whats the question now?

Step-by-step explanation:

Answer:

2 2/5 (For the word problem)

For the graph (In order)

4/5

1 1/4

12/30 (Or 2/5)

2 6/12 (or 2 1/2)

Step-by-step explanation:

1:

12 pounds make 5 pies, turn it into a fraction.

12/5

Now turn it into a mixed number. How many fives can go into 12?

Two fives equal ten, subtract it from twelve. Bring the amount of fives to the left.

2 2/5

2: Oh, that's really easy.

Four divided by five is 4/5

Five divided by four is 5/4 which as a mixed number is 1 1/4

3: 12 divided by thirty is 12/30, you can simplify it by dividing both sides of the denominator by three, then two. But if it's not required then just don't 12/30

4: 30 divided by 12 is 30/12, how many twelves can go into 30? Two.

30 - 24 = 6

2 6/12

Step-by-step explanation:

Answer:

105.53 m

Step-by-step explanation:

Distance covered until 60°

Distance covered until 30°

Distance in interval (d)

Answer:

The answer would be 48 cm^2

Step-by-step explanation:

You have to do 9x4 and then add 6x2 to that.
9x4 is 36 and 6x2 is 12.
36+12 is 48. Hope this helps! :)

Answer:

The answer would be 48 cm^2

Answer:

90/140.

Step-by-step explanation:

75 + 15 = 90. Then 90 + 50 is 140.

Answer:

5 miles: $10

8 miles: $16

20 miles: $40

Step-by-step explanation:

Since each mile costs $2 and that it asks you to figure out the price for 5 miles, 8 miles and 20 miles, you multiply 2 with the amount of miles travelled

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

12y-19= 6y+1

12y-6y = 1 +19

6y = 20

y = 20/6

y= 10/3 or 3.33..

Answer:

A gallon is a

greater

unit than a pint, so

we multiply

the number of gallons by 8

to find the number of pints. Therefore, 4 gallons is equal to 32

pint(s).

The value of 4 gallons will be equal to 32 pints.

Expressions can also include functions, trigonometric functions, logarithmic functions, and other mathematical operations. They are used to represent mathematical ideas and formulas and can be manipulated and simplified using algebraic techniques.

Expressions can be evaluated, meaning that they can be simplified to a single value. The value of an expression depends on the values of any variables or numbers within the expression.

We need to divide the number of gallons by 0.125 (since there are 8 pints in a gallon)

To find the number of pints. Therefore, 4 gallons is equal to,

32 pints.

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Answer:A, commutative

Step-by-step explanation: The commutative property of multiplication states that

the order in which we multiply numbers does not change the product.

Answer:

A. Commutative

Step-by-step explanation:

I believe it's a because you didn't use +/- so I assumed it was multiplication in which case, the commutative property of multiplication, which states that the order we multiply in does not affect the product.

Answer:

A = 5x³ + 17x² - 35x - 30

Step-by-step explanation:

the shaded area (A) is calculated as

A = outer area - inner area

   = (5x + 3)(x² + 4x - 10) - 3x(2x - 1) ← distribute parenthesis

   = 5x³ + 20x² - 50x + 3x² + 12x - 30 - (6x² - 3x)

  = 5x³ + 23x² - 38x - 30 - 6x² + 3x ← collect like terms

  = 5x³ + 17x² - 35x - 30

Answer:

5x^3+ 17x^2- 35x-30 Or x=-4.63 or 1.9

Step-by-step explanation:

Area of rectangle =L×B

for smaller rectangle :

after applying the formula, the equation becomes:

6x^2 - 3x

For bigger rectangle:

Applying the same formula, the equation becomes:

5x^3+ 23x^2- 38x- 30

Area of shaded region =

Area of bigger rectangle- Area of smaller rectangle

= 5x^3+17x^2 -35x-30

going further solving the above equation

Area of shaded region: -4.96 or 1.9

Answer:

1390 cm^3

Step-by-step explanation:

9 x 7 x 10 = 630 cm^3 for the rectang prism top

area * 10 for the bottom

8 x ( 12 + 7)/2   * 10 = 760 cm^3  for the trap base

total = 1390 cm^3

Answer:

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

Step-by-step explanation:

[tex]\textsf{General form of a quadratic function}:f(x)=ax^2+bx+c[/tex]

Equation 1

[tex]\begin{aligned}f(1) &=0\\ \implies a(1)^2+b(1)+c &=0\\ a+b+c &=0 \end{aligned}[/tex]

Equation 2

[tex]\begin{aligned}f(-1) &=-4\\ \implies a(-1)^2+b(-1)+c &=-4\\ a-b+c &=-4 \end{aligned}[/tex]

Equation 3

[tex]\begin{aligned}f(2) &=5\\ \implies a(2)^2+b(2)+c &=5\\ 4a+2b+c &=5 \end{aligned}[/tex]

Add Equation 1 and Equation 2:

[tex]\begin{array}{r l}a+b+c & =0 \\+\quad a-b+c & =-4 \\\cline{1-2} 2a+2c & =-4 \end{array}[/tex]

[tex]\implies a+c=-2[/tex]

Substitute [tex]a+c=-2[/tex] into Equation 1 and solve for b:

[tex]\begin{aligned}\implies a+b+c &=0\\ b-2 &=0\\ b &=2\end{aligned}[/tex]

Substitute [tex]a=-2-c[/tex]  and  [tex]b=2[/tex]  into Equation 3 and solve for c:

[tex]\begin{aligned} \implies 4a+2b+c&=5\\ 4(-2-c)+2(2)+c &=5\\-8-4c+4+c &=5\\ -3c &=9\\ c &=-3\end{aligned}[/tex]

Substitute found value of c into [tex]a=-2-c[/tex] and solve for a:

[tex]\implies a=-2-(-3)=1[/tex]

Therefore, a = 1, b = 2 and c = -3

Substitute the found values into the general form of a quadratic function to form the final equation:

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

Answer:

5006 is and 4896

Step-by-step explanation:

math is the best letsgoooo

that is the circumference of its circular base.

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=9\\ V=27\pi \end{cases}\implies 27\pi =\cfrac{\pi r^2 (9)}{3}\implies 27\pi =3\pi r^2 \\\\\\ \cfrac{27\pi }{3\pi }=r^2\implies 9=r^2\implies \sqrt{9}=r\implies \underline{3=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \qquad C=2\pi (\underline{3})\implies C=6\pi[/tex]

The circumference of the cone will be;

⇒ 6π

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The volume of a right cone = 27π units³

And, The height = 9 units

Now,

Since, We know that;

The volume of cone = πr²h / 3

⇒ 27π = π × r² × 9 / 3

⇒ 27 = r² × 3

⇒ r² = 27/3

⇒ r² = 9

⇒ r = 3

Since, The circumference of the cone = 2πr

                                                            = 2 × π × 3

                                                            = 6π

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[tex]2(x - 9) = 9 \div ( - \frac{1}{3} ) \\ [/tex]

[tex]2(x - 9) = 9 \times ( - 3)[/tex]

[tex]2(x - 9) = - 27[/tex]

[tex] \frac{2(x - 9)}{2} = \frac{ - 27}{2} \\ [/tex]

[tex]x - 9 = - 13.5[/tex]

[tex]x - 9 + 9 = - 13.5 + 9[/tex]

[tex]x = - 4.5[/tex]

Thus option B is the correct answer.

charlotte buys a rectangular rug with an area of 27/4 square meters.

The width of the rug is 3/2 meters. So the length of the rectangular rug is 9/2 meters.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

charlotte buys a rectangular rug with an area of 27/4 square meters.

The width of the rug is 3/2 meters.

Area of the rectangular rug = 27/4 square meters

Let us assume the length of the rug = x meters

Then,

Area of the rug =  length × Width

[tex]27/4 = (3/2) \times x\\\\x = (27/4) \times (2/3) \\x = 9/2[/tex]

So the length of the rectangular rug is 9/2 meters.

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