100 points please answer!!!!!!!!!
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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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Answer:

? = 4.492385

About 4.5 pounds

Step-by-step explanation:

m = money spent

80 - 44.6 = m

m = 35.4

m / 7.88 = ?

? = 35.4 / 7.88

? = 4.492385

About 4.5 pounds

Answer:

She bought 5 pounds of coffee

Step-by-step explanation:

If you subtract 80-40.60 you would get 39.4/39.40 and since each pound was 7.88 you divided 39.40 and 7.88 and you would get 5

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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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: The answer is y=-7x. yeah

Answer:

  Part A: no. The bikes/skateboards labels are reversed

  Part B: 8/25 = 0.32; Fraction of students with both bikes, skateboards

Step-by-step explanation:

Given a segmented bar chart, you want to know if it was drawn correctly, and you want to know the value and meaning of the greatest joint relative frequency.

You want to know if the given segmented bar chart is an appropriate representation of the data in the 2-way table.

The bar chart is created incorrectly.

There are at least a couple of problems with the chart.

The largest number in the table is 80. The fraction that is of the whole is ...

  80/(70+30+80+70)

  = 80/250 = 8/25 = 0.32

The greatest relative frequency is 0.32. It represents the fraction of students who have both bikes and skateboards.

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Tate and Nathan will leave $ 19.48 to the server to cover up the bill and the tip when they go out to dinner at Red Robin.

As given in the question,

Since Tate and Nathan both order burgers for $12.49 each,

Total amount payable is

$12.49 + $12.49= $24.98.

Now 18% tip is equal to

18% of $24.98

(18/100) × 24.98

= $4.4964

= $4.50 (rounded to nearest cent).

Total gross amount payable (including 18% tip) is

24.98 + 4.50 = $29.48.

Now subtracting the birthday coupon for $10.00 off,

the net amount payable in the bill is

29.48 - 10.00

= $ 19.48

= 19.48 cents

Therefore, after using the coupon, they will leave the server $19.48 to cover the bill and the tip.

The complete question is:

Tate and Nathan go out to dinner at Red Robin They both order burgers for $12.49 each. Tate has a birthday coupon for $10.00 off, but the boys want to leave an 18% tip before subtracting the cour

After using the coupon, how much money will they leave the server to cover the bill and the tip? Round to the nearest cent.

a. $14.49

b. $2768

c. $4.79

d.$19.48

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Answer:

1/12

Step-by-step explanation:

yellow=1/4

red=5/12

green=1/3

1/4 x 1/3= 1/12

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

thus ;

[tex]f( - 3) = 3 \times ({ - 3})^{2} - ( - 3) + 5[/tex]

[tex]f( - 3) = 3 \times 9 + 3 + 5[/tex]

[tex]f( - 3) = 27 + 8[/tex]

[tex]f( - 3) = 35[/tex]

_____________________________________________

[tex]f(4) = 3 \times ({4})^{2} - (4) + 5[/tex]

[tex]f(4) = 3 \times 16 - 4 + 5[/tex]

[tex]f(4) = 48 + 1[/tex]

[tex]f(4) = 49[/tex]

_____________________________________________

So :

[tex]2f( - 3) = 2 \times 35 = 70[/tex]

And ,

[tex] - f(4) = - 49[/tex]

so :

[tex]2f( - 3) - f(4) = [/tex]

[tex]70 - 49 = [/tex]

[tex]21[/tex]

(a) -5

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

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

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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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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The solution of the given system of equation is 136

Fractions are expressed as ratio of two integers. Given the expression below;

20/3.4 = 800/y

Cross multiply to have:

3.4. * 800 = 20 *y

3.4 * 800 =20y

2720 = 20y

Swap

20y = 2720

Divide both sides by 20

20y/20 = 2720/20

y = 136

Hence the solution to the given equation on cross multiplying is 136

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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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1. Noah reads 9 pages.

2. The price of one pizza is $9.

3. Lin shares her stickers is 9.

1.Given,

Elena read three times as many pages as Noah.

and, She read 27 pages.

Now, According to the question:

3x = 27

x = 27/3

x = 9

Hence, Noah reads 9 pages.

2. Given,

Diego paid $27 to have 3 pizzas delivered

and, $35 to have 4 pizzas delivered

In the question, In place of $ 35 should be $36

So, we take the $36

Now, Diego paid $27 to have 3 pizzas delivered

$36 to have 4 pizzas delivered

Let x be the price of 1 pizza

then, 4x = 36

x = 36/4

x = $9

Hence, The price of one pizza is $9.

3. Given,

Lin has 27 stickers.

and, She gives 3 stickers to each of her friends.

Now, 27 is divided by 3  = 9

Hence, Lin shares her stickers is 9.

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The angle AOB has a measure of 72 degrees

The formation of angles is as a result of the intersection of multiple lines intersect.

The given parameters are:

The above means that

AOB = BOC

So, we have

6x - 12 = 3x + 30

Evaluate the like terms

3x = 42

Divide by 3

x = 14

Substitute x = 14 in AOB= 6x -12°

So, we have

AOB= 6 x 14  -12°

Evaluate

AOB= 72°

Hence, the measure of the angle is 72 degrees

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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]

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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Answer:

Step-by-step explanation:

57m

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?

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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Answer:

the answer to the question is B thank me later

Step-by-step explanation:

On subtracting "3a – 7b + 12c" from "-5a – 21b + 3c" we get -

- 8a - 14b - 9c

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign −.

Given is to subtract "3a – 7b + 12c" from "-5a – 21b + 3c".

Assume that -

A = 3a – 7b + 12c

B = -5a – 21b + 3c

B - A = (-5a – 21b + 3c) - (3a – 7b + 12c)

B - A = -5a - 21b + 3c - 3a + 7b - 12c

B - A = -5a - 3a - 21b + 7b + 3c - 12c

B - A = - 8a - 14b - 9c

Therefore, on subtracting "3a – 7b + 12c" from "-5a – 21b + 3c" we get -

- 8a - 14b - 9c

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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.

Answer:

k=2

Step-by-step explanation:

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

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.