Solve for x:

[tex] \frak{2 ( 3x + 1 ) + 3 ( 5x + 2 ) = x - 1}[/tex]
[tex] \\ \\ \\ [/tex]
Thank uh -,-​

Answer:

1 positive solution (and 1 negative)

the greatest solution is about 2.87

Step-by-step explanation:

so, it is

x² + 2x + 7 = 21

x² + 2x - 14 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 2

c = -14

x = (-2 ± sqrt(2² - 4×1×-14))/(2×1) =

= (-2 ± sqrt(4 + 56))/2 = (-2 ± sqrt(60))/2 =

= (-2 ± sqrt(4×15))/2 = (-2 ± 2×sqrt(15))/2 =

= -1 ± sqrt(15)

x1 = -1 + sqrt(15) = 2.872983346... ≈ 2.87

x2 = -1 - sqrt(15) = -4.872983346...

Answer:

The volume of this rectangular prism is 112mm.

Step-by-step explanation:

[tex]volume \: = \: length \times width \times height \\ v = 6.4mm \times 2.5mm \times 7mm \\ v = 112mm[/tex]

Answer:

265

Step-by-step explanation:

You subtract 275 minus 10

$247.5 was the original amount on the credit card

Lets simplify the problem,

Total amount after late fee = $275

Late fee deduction = 10%

Original amount = 275 - 10% of 275

= 275 - 27.5

= $247.5

So $247.5 was the original amount on the credit card before the late fee.

Percentage:

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

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Answer:

Step-by-step explanation:

380 rows in total

bcs

use sense

The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2

An equation is an expression that shows the relationship between two or more number and variables.

[tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18} \\\\=\frac{(x +3)(x +4)}{x-3} .\frac{(x-3)(x-3)}{2(x+3)(x-3)} =\frac{x+4}{2}[/tex]

The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What are we solving for?}[/tex]

[tex]\mathsf{56 = w(w + 10) }[/tex]

[tex]\huge\textbf{How are we going to solve for the}\\\\\huge\textbf{equation?}[/tex]

[tex]\mathsf{56 = w(w + 10)}[/tex]

[tex]\mathsf{w(w + 10) = 56}[/tex]

[tex]\mathsf{w(w) + w(10) = 56}[/tex]

[tex]\mathsf{w(w) + 10(w) = 56}[/tex]

[tex]\mathsf{w^2 + 10w = 56}[/tex]

[tex]\huge\textbf{Subtract \boxed{\bf 56} to both sides:}[/tex]

[tex]\mathsf{w^2 + 10w - 56 = 56 - 56}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{w^2 + 10w - 56 = 0}[/tex]

[tex]\huge\textbf{Factor the left side of the equation:}[/tex]

[tex]\mathsf{(w - 4)(w + 14) = 0}[/tex]

[tex]\mathsf{(w - 4)\times(w + 14) = 0}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{w - 4 = 0\ or\ w + 14 = 0}[/tex]

[tex]\mathsf{w = 4\ or \ w = -14}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\mathsf w = 4\ or \ \mathsf w = -14}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The sum of two terms are:

The sum of two numbers is one that tells you to find the sum of two or more numbers, and as such, you have to add the numbers altogether.

t₅, ₃ =  5 + 3

= 8

t₁₁, ₂ = 11 + 2

= 13

t₁₅,₁₃ =  15 + 13

= 28.

Hence the correct sum of two terms are:

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The number of apples in the basket are; 24 apples

Let there be X number of apples and Y number of oranges.

Thus by the given ratio we can say that;

x/y = 3/8   -----(1)

(x — 1)/y = 1/3

3x — 3 = y   ----(2)

Substitute 3x - 3 for y in eq 1 to get;

x/(3x - 3) = 3/8

8x = 9x - 9

9x - 8x = 9

x = 9

Thus;

y = 3(9) - 3

y = 24 apples

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Answer:

y = 3x + 5

Step-by-step explanation:

x = number of years

• bush grows 3cm per year

• the initial height is 5cm

3cm per year times x number of years: y = 3x

Add the initial height of 5cm: y = 3x + 5

The probability of randomly getting a red or green counter is:

P = 39%/100% = 0.39

We know that 40% of the counters are red or white. Then 60% of the counters are blue or green.

Now we know that the ratio of red to white is 3:5

Then the percentage of red counters is:

(3/8)*40% = 15%

And the ratio of blue to green is 3:2

Then the percentage of red counters is:

(2/5)*60% = 24%

Then the percentage of counters that are either red or green is:

15% + 24% = 39%

Then the probability of randomly getting a red or green counter is:

P = 39%/100% = 0.39

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a) ∠PQR=65° (alternate interior angles theorem)

∠PRQ = 60° (linear pair)

x = 55° (angles in a triangle add to 180°)

b) ∠APQ and ∠PQR are congruent alternate interior angles.

The equivalent equation is (4x² + 9)(4x² - 9) and the zero's are x =± 3 / 2 and x = ± 3 / 2i

The equivalent equation can be found by factoring. Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.

Therefore,

f(x) = 16x⁴ - 81 = 0

Hence,

9 × 9 = 81

4x² × 4x² = 16x⁴

Therefore,

16x⁴ - 81  = (4x² + 9)(4x² - 9)

Hence,

The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).

The zero's of the function are as follows:

4x²  = 9

x² = 9 / 4

x =± 3 / 2

4x² = -9

x² = - 9 / 4

x =√-9 / 2

x = ± 3 / 2i

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That year FTE was 26.

According to statement

Labor hours worked that year = 55,267

Total number of hours paid that year = 59,995

The total number of hours during the year

8 hours × 5 days × 52 weeks = 2080 hours

Now we find the FTE per year

So, FTE/YEAR = Labour works on that year / total number of hours in year

Substitute the values in it then

FTE/YEAR = 55267/2080

FTE/YEAR = 26

So, That year FTE was 26.

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Answer:

I have wrote just answer.

The percentage of dogs who didn't try to bite the groomer is; 65%.

If follows from the task content that the number of dogs is 300 of which, 0.35 faction of the whole tried to bite the groomer.

Hence, the faction that did not try to bite the groomer is; 0.65 which corresponds to 65% when expressed as a percentage.

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Answer:

Addition form: x = 75 + √3 (675 − P) / 3

or

Subtract form: x = 75 − √3 (675 − P) / 3

Answer:

x = 20

Step-by-step explanation:

x°

2x°

(x + 10)°

little box on the bottom left means this is a right angle which is 90°

add up all the angles and make it equal to 90°

( x° + 2x° + (x + 10)° ) = 90°

4x + 10 = 90

4x = 80

x = 20

Since we can see the "square" at the bottom left corner of the angle, the square indicates that the angle is a right angle (which measures 90°).

We can also see three smaller angles forming the right angle. Therefore, the sum of the measure of the smaller angles = 90°.

According to the diagram, the measures of the smaller angles are x°, 2x°, and (x + 10)° respectively. Then we get the following equation:

[tex]\implies x + 2x + (x + 10) = 90\°[/tex]

Here, we had the equation: [tex]\underline{x + 2x + (x + 10) = 90\°}[/tex]

[tex]\implies x + 2x + x + 10 = 90\°[/tex]              [tex]\text{(Ope} \text{ning the parentheses)}[/tex]

[tex]\implies 4x + 10 = 90\°[/tex]                             [tex]\text{(Combining like terms)}[/tex]

[tex]\implies 4x + 10 - 10 = 90 - 10[/tex]          [tex]\text{(Subtracting 10 on both sides)}[/tex]

[tex]\implies 4x = 80[/tex]                                    [tex]\text{(Simplifying both sides)}[/tex]

[tex]\implies \dfrac{4x}{4} = \dfrac{80}{4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Dividing 4 on both sides)}[/tex]                            

[tex]\implies \boxed{x = 20}[/tex]                                      [tex]\text{(Simplifying both sides)}[/tex]

Therefore, the value of x, in the diagram provided, is 20.

Ms. Drake will earn [tex]\$ 170[/tex] in this time from the investment of [tex]\$ 1000[/tex] at a simple interest with rate of interest [tex]8.5\%[/tex]

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Conversely, for compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

Formula for finding simple interest is [tex]\frac{principal \times rate \ of \ interest \times time}{100}[/tex]

Given principal of Ms. Drake is [tex]\$1000[/tex]

Rate of interest is [tex]8.5 \%[/tex]

Time is [tex]2[/tex] years.

Interest [tex]=\frac{1000 \times 8.5 \times 2}{100}[/tex]

            [tex]=\frac{17000}{100}\\=170[/tex]

Therefore, Ms. Drake will earn [tex]\$ 170[/tex] in this time.

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The probability of event X or Y is P = 0.7, or, in percentage form, the probability is 70%.

First, two events are mutually exclusive if these events can't happen at the same time.

This means that if happens X, with a 30% of probability, then Y can't happen.

If happens Y, with a 40% of probability, then X can't happen.

Then the probability of X or Y (the probability that one of these two events happens, not both) is just the addition of the two individual probabilities.

Then we have:

P(X or Y) = 0.3 + 0.4 = 0.7

Or, in percent form, we get:

P(X or Y) = 70%

The probability of event X or Y is just 70%.

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Hello,

an other method

Pythagorean theorem :

x² + x² = 6²

2x² = 36

x² = 36/2

x² = 18

x = √18 (and not -√18 because x ≥ 0)

x = √(9 × 2)

x = √(3² × 2)

x = 3√2

Answer A

Answer:

C.  (x,y) ⇒ (x + 8, y − 3)

Step-by-step explanation:

See attached image.

The cost spent on fill the box with sand is 405$.

According to the statement

we have given a square sandbox with length 9 ft and depth of 1 ft.

and the rupees of sand per cubic ft is $5

then

Now, we have to find the volume of sandbox with the given length and depth.

So, for this purpose we use Volume formula

V = (a)^3

V = 9*9*1

V = 81 cubic feet

And the cost of sand per cubic feet is $5.

then

The cost of sand for 81 cubic per feet is calculate by multiplication formula then

Total cost of sand = 81*5

Total cost of sand = 405$

So, The cost spent on fill the box with sand is 405$.

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Answer:

4

Step-by-step explanation:

[tex] {3}^{2} + {x}^{2} = {5}^{2} \\ \\ 9 + {x}^{2} = 25 \\ \\ {x}^{2} = 16 \\ \\ x = 4[/tex]

The probability you will roll a sum of 9 is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability you will roll a sum of 9 = total times a sum of 9 is derived / total sample spaces

The probability you will roll a sum of 9 = 4/36 = 1/9

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By applying trigonometric identities, the value of tan(x) = 14, gives;

[tex]sin(2 \cdot x) = \frac{28}{197} [/tex]

[tex]cos(2 \cdot x) = -\frac{195}{197} [/tex]

[tex]tan(2 \cdot x) = -\frac{28}{195} [/tex]

Given;

tan(x) = 14

sin(x) is negative

By definition, we have;

[tex]sin(2 \cdot x) = \mathbf{\frac{2 \cdot \: tan(x)}{1 + {tan(x)}^{2} }} [/tex]

Which gives;

[tex]sin(2 \cdot x) = \frac{2 \times 14}{1 + {14}^{2} } = \frac{28}{197} [/tex]

Similarly, we have;

[tex]cos(2 \cdot x) = \mathbf{\frac{1- tan(x)^2}{1 + {tan(x)}^{2} }} [/tex]

Which gives;

[tex]cos(2 \cdot x) = \frac{1- 14^2}{1 + {14}^{2} } = -\frac{195}{197} [/tex]

[tex]tan(2 \cdot x) = \mathbf{\frac{sin(2 \cdot x) }{cos(2 \cdot x) } } [/tex]

Which gives;

[tex]tan(2 \cdot x) = \frac{ \frac{28}{197}}{-\frac{195}{197} } = -\frac{28}{195} [/tex]

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Generally speaking, Harriot's notation was clearer than Viète's, which made it simple for him to connect Viète's identities.

Harriot made significant contributions to the theory of equations and developed a more straightforward notation for algebra.

The employment of special notation is algebra's most evident characteristic. Variables are the symbols that are used to represent numbers.

A symbolic system known as notation is used to represent mathematical concepts and objects.

The primary components of notation are letters, symbols, figures, and signs. Notation can be made using symbols, characters, numbers, or a combination of these, such as the factorial symbol.

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Answer:

605

Step-by-step explanation:

We are starting at 110 and not zero, so I need to find have the distance between 110 and 110 and add that to 110.

110 + 1/2(1100 - 110)  Subtract what is in the parentheses

110 + 1/2(990) Find 1/2 of 990

110 + 495

604

Answer:

A

Step-by-step explanation: