The standard form of a parabola is y=ax² +bx+c. Find the equation to the parabola that
passes through the points (0,4), (2,4) and (-2,8).

By using the equation we can conclude that it will take 7 hours before the two tanks have the same amount of water.

So, the equation that will help to find the answer:

So, now solve for x as follows:

Therefore, by using the equation we can conclude that it will take 7 hours before the two tanks have the same amount of water.

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The result of the factorization of   8y^3-6y is 2y(4y^2-3) .

Factorization  can be described as the mathematical term, that is been used in expressing a particular number  as well as mathematical object to be writing inform of a  product of several factors.

From the question we were given the expression 8y^3-6y  to be factorized,

Then, this can be done as  2y(4y^2-3)

Therefore, the factorization of the given expression is 2y(4y^2-3) .

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11 cars needed to take 53 girls to mach if each car can take only 5 girls .

Answer:

Step-by-step explanation:

53 : 5 = 10.6

53:5=10,6

5        

 3 (rest)      

 0      

 30      

 30      

   0      

10 cars carry 5 girls (10 x 5 = 50) and one car carries 3, so you need 11 cars

Answer:

y = 3x + 1

Step-by-step explanation:

(2, 7); 3x - y = 5

(x₁, y₁)

3x - y = 5

-3x           -3x

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

-y = -3x + 5

÷-1    ÷-1   ÷-1

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

y = 3x - 5

y - y₁ = m(x - x₁)

y - 7 = 3(x - 2)

y - 7 = 3x - 6

  +7          +7

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

y = 3x + 1

I hope this helps!

Answer: y=3x+1

Step-by-step explanation:

[tex]3x-y=5\\3x-y+y=5+y\\3x=5+y\\3x-5=y+5-5\\3x-5=y\\So, \ y=3x-5\\[/tex]

A line parallel to line y=3x-5 will look like this: y=3x+b

The line passes throught the point (2,7), hence:

[tex]7=3(2)+b\\7=6+b\\7-6=6+b-6\\1=b\\Thus,\ b=1\\y=3x+1[/tex]

With the help of the ratio method, we conclude that 72 grams of sugar should be added.

So, 'n=5' will be the number of rings.

Let 's' be silver. Then,

Now, use the ratio method as follows:

Therefore, with the help of the ratio method, we conclude that 72 grams of sugar should be added.

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The correct question is given below:
A jeweler has five rings, each weighing 18 grams, made of alloys of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 50%. How much silver should he add?

The given equation x² + 6x - 5 can be written in the form of (x + a)² + b as

 (x + 3)² - 14.

In math, we can state that the process of "completing the square" is taking a quadratic equation of the form ax² + bx + c = 0 and changing it to write it in the form a(x + p)² + q = 0. Find the roots of a quadratic equation often using this method.

Given quadratic equation is x² + 6x - 5.

To convert it in the form (x + a)² + b, where a and b are numbers.

x² + 6x - 5

x² + 2 × 3x + 3² - 3² - 5 (convert the equation into a perfect square)

(x + 3)² - 9 - 5

(x + 3)² - 14

Hence, the required equation is (x + 3)² - 14.

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The value of the given function [tex]log_6x+log_6(x-1)=1[/tex] is x = 3 or x =-2

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g. since 1000 = 10 × 10 × 10 = 10^3, the "logarithm base 10" of 1000 is 3, or [tex]log_1_01000=3[/tex].

We know that

Log (a) + log (b) = log (ab)

So, [tex]log_6x+log_6(x-1)=1[/tex]

[tex]log_6(x(x-1))=1\\log_6(x^2-x)=1\\x^2-x=6^1\\x^2-x-6=0\\[/tex]

(x-3)(x+2)=0

So, x = 3 or x = -2

Therefore the value of the given Logarithmic function is x = 3 or x = -2

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Consecutive integer is  5.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.

Given Data

the letter n represents a positive integer {1,2,3,4…}

Consecutive = x +1

Here.

x = 4

Consecutive integer = x + 1

Consecutive integer = 4 + 1

Consecutive integer =  5

Consecutive integer is  5.

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(a) -5

(b) [tex]a_n=-2(-5)^{n-1}[/tex]

(c) [tex]a_{11}=2(-5)^{11-1}=19531250[/tex]

Answer:

1/12

Step-by-step explanation:

yellow=1/4

red=5/12

green=1/3

1/4 x 1/3= 1/12

Name : Trinomial.

Degree : 4

EXPLANATION

Monomial : A polynomial with just one term.

Binomial : A polynomial with two terms.

Trinomial : A polynomial with three terms.

From the question given;

(12x⁴ + 3x - 1) comprises of 3 terms, hence it is a trinomial.

The degree of a polynomial is the highest exponent in a term of a polynomial.

Hence, the highest exponent in the given expression is 4, this implies that the polynomial is of degree 4.

ok so at first if u have fractions like the first follow my instruction:

1st: u have 2/3---1/2, u will multiply 3 by 1 and 2 by 2 so u will get 6 and 4

but remember that 2/3 and 1/2 u cris cross it the left one comes first like 6 then 4 so it could balance and do the rest of the fractions like that.

2nd: if u have decimal u will check the number after the decimal but if the are the same u will compare the numbers before the decimal.

I hope it's usefull

Answer:

The y-intercept is -6.

Step-by-step explanation:

The number after the variable in an equation that is in slope intercept form(y=mx+b) is the y-intercept.

Answer:

k=2

Step-by-step explanation:

[tex]-3k+4=-2-6k \\ \\ 3k+4=-2 \\ \\ 3k=6 \\ \\ k=2[/tex]

6 2/3 liters of water should be mixed with 10 juiced lemons to obtain the same result as Four liters of water are mixed with 6 juices lemons to make lemonade.

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel.

A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4).

By using unitary method, 4 liters was water has 6 lemons

1 lemon will have 4/6 liter of water.

So 10 lemon will have

(4/6)*10=40/6

=20/3

=6 2/3 liters

Mix 10 freshly squeezed lemons with 6 2/3 liters of water to make lemonade as needed to combine the juice of six lemons with four liters of water.

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Given,

1 inch = 2.5 feet

∴ Area of garden = ( 5 x 2.5)  x  ( 1.5 x 2.5)  feet

Since, 80% area will be used as path with  crashed rock,

therefore, 12.5 x (1.5 x 2.5)/ 100 x 100 x 10 feet

= 37.5 sq. feet

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Answer: a

Step-by-step explanation:

We know that [tex]a^2 +b^2 =c^2[/tex]. The left hand side is the same as the sum of the areas of the two green squares, and the right hand side is the same as the area of the one large green square.

The interval that describes where the graph of this function is negative is: C. 2 < x < ∞

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

Generally speaking, a function is typically used for mapping an input variable to an output variable. In Mathematics, the value of y on the y-axis of a graph must be less than 0 (x < 0) for the graph of any function to be negative.

By critically observing the graph of this function, we can logically deduce that at point x = 2 is where the value of y becomes less than 0 (x < 0) and continues to infinity. Therefore, the graph of this function is negative is at an interval of 2 < x < ∞.

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Answer:

The graphs are not shown, but I can tell you that x < 3.5

Step-by-step explanation:

[tex]4x + 2 < 2x + 9[/tex]

[tex]2x + 2 < 9[/tex]

[tex]2x < 7[/tex]

[tex]x < 3.5[/tex]

Answer:

C

Step-by-step explanation:

Since the line is dotted, we can guarantee that it is either >/< and not <=/>=.
Since the shaded part takes up the higher values of y, we can guarantee that it is > and not </<=/>=.

Therefore, the answer is C.

Answer:

the answer to the question is B thank me later

Step-by-step explanation:

The value of x based on the equation illustrated as 0.4 + (3x - 1) = 9 will be 3.2.

It should be noted that an equation is important in Mathematics to show the relationship between the expressions that are given. This will be illustrated as:

0.4 + (3x - 1) = 9

Collect the like terms

0.4 + 3x - 1 = 9

3x = 9 - 0.4 + 1

3x = 9.6

Divide through by 3

3x / 3 = 9.6 / 3

x = 3.2

Therefore, x is 3.2.

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Membership to a video game club is $50 a year and $3 per game rented. At the end of the year Harvey had spent $296. he played games had he rented 82 games.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.

A set of numbers and operations make up a mathematical expression. The components of a mathematical expression that performs an operation are:

Operands: Operands are the numerical values that are employed in an operation. Different words are given to the operands depending on the type of operation.

Operator: An operator is the symbol used to represent a mathematical operation.

Solving the above;

Membership costs him= $50

Per game rented= $3

Amount he spent = $296

Therefore, Number of games he rented=[tex]\frac{296-50}{3}[/tex]

                                                                 = 82

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The equation of the line that passes through the point (8, 5) and perpendicular to y = −12x +7 is y = (1/12)x + 13/3.

We know that,

The product of the slopes of two perpendicular lines is -1.

The slope intercept form of a line is given by :-

y = mx + c

Comparing it with y = -12x + 7

We get,

m = -12 (slope of the line)

c = 7 (y-intercept of the line)

Let the slope of the line perpendicular to the given line be n.

Hence, we can write,

(-12)*n = -1

n = 1/12

Also, the line passes through (8,5).

Hence, we can write,

5 = (1/12)(8) + c

5 = 2/3 + c

c = 5 - 2/3 = 13/3

Hence, the equation of the line is given by :-

y = (1/12)x + 13/3

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Answer: The answer is y=-7x. yeah

If Camila filled up a 4-gallon in just 1/6 of a  minute, then the rate of water flow through the hose is 24  gallons/minute

Camila filled up a 4-gallon bucket in just 1/6 of a minute

Here we have to use the unitary method to find the rate of water flow through the hose

The quantity of water filled in 1/6 of a minute= 4 gallon

The quantity water filled in one minutes = The quantity of water filled in 1/6 of a minute ÷ (1/6)

Substitute the values in the equation

= 4÷(1/6)

= 4×6

= 24

The rate of water flow through the hose = 24 gallons/ minute

Hence, if Camila filled up a 4-gallon in just 1/6 of a  minute, then the rate of water flow through the hose is 24  gallons/ minute

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Answer:

Step-by-step explanation:

57m