solve the system of equations 2y - 3x = -27 5y + 3x = 6 PLEASE EXPLAIN STEPS!
(photo included)

Answer:

2

Step-by-step explanation:

[tex]5x^2 +3x +2 = 0\\\\\text{Apply the quadratic formula,}~ x=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\\text{In this case,}~a= 5, ~ b = 3~ \text{and}~ c = 2\\\\ \\x=\dfrac{-3\pm \sqrt{3^2 -4\cdot 5 \cdot 2}}{2\cdot 5}\\\\~~~=\dfrac{-3 \pm \sqrt{9-40}}{10}\\\\~~~=\dfrac{-3 \pm \sqrt{-31}}{10}\\\\~~~=\dfrac{-3 \pm i\sqrt{31}}{10}\\\\\text{So, there are 2 solutions,}~ x=\dfrac{-3 + i\sqrt{31}}{10}~ \text{and} ~x=\dfrac{-3 -i\sqrt{31}}{10}[/tex]

Another  way to find the number of solutions is by looking at the highest exponent(Degree), which indicates the number of solutions.  

[tex]\\ \rm\rightarrowtail 5x^2+3x+2=0[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm \sqrt{9-40}}{10}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{-31}}{10}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{31}i}{10}[/tex]

Answer:

The answer is 34

Step-by-step explanation:

Now,

Common Difference (d)

d = a₂ – a₁ = 304 – 310 = -6

d = a₃ – a₂ = 298 – 304 = -6

Here, common difference is same everywhere

So,

aₙ = a + (n – 1) × d

a₄₇ = 310 + (47 – 1) × (-6)

a₄₇ = 310 + 46 × (-6)

a₄₇ = 310 – 276

a₄₇ = 34

Thus, The 47th term of this sequence is 34.

Answer:

-1/4

Step-by-step explanation:

14x - 2x + 3 = 0
12x + 3 = 0
12x = -3
12x/12 = -3/12
x = -1/4

Answer:

64 ounces

Step-by-step explanation:

Since 1 lb = 16 oz, just do 4 × 16 = 64

If puppy weighs 4 pounds then the weigh in ounces is 64 ounces.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

There are 16 ounces in a pound.

1 pound= 16 ounces.

Given that puppy weighs 4 pounds.

We have to find the wight in ounces.

To convert pounds to ounces, we need to multiply the weight in pounds by 16.

The puppy weighs 4 pounds x 16 ounces/pound

= 64 ounces

Hence, if puppy weighs 4 pounds then the weigh in ounces is 64 ounces.

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The probability is 0.1429.

The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:

5/7(4/6)(3/5)(2/4) = 120/840 = 0.1429.

The probability that everyone in the group is a girl is 2/7.

Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.

Total number of students in a class = 7

Number of boys students = 2

Number of girls students = 5

The probability that everyone in the group is a girl is;

[tex]\rm Probability =\dfrac{Total \ number \ of \ girls}{Total \ number \ of \ boys}\\\\Probability=\dfrac{2}{7}[/tex]

Hence, the probability that everyone in the group is a girl is 2/7.

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The thermometer is a device that is used to measure the temperature gradient. Anders needs to set the boiling point of water at 100° C.

The thermometer is a device that is used to measure the temperature gradient or the temperature of a body/object.

The boiling point of water is 100°C, therefore, Anders needs to set the boiling point of water at 100° C.

Thus, Anders needs to set the boiling point of water at 100° C.

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teddy bears = 80

hope it helps..!!!

Answer:

y= 2x-5

Step-by-step explanation:

The slope formula is m=(y2-y1)/(x2-x1)

-3-1 / 1-3 = -4/-2= 2=m

The Y interception- y=mx+b using coordinates (3,1)

1=2(3)+b

1=6+b (subtracting 6 on both sides to isolate b)

-5=b

plug it in

y=2x-5

let's keep in mind that Profit = Revenue - Costs.

so each guitar costs originally "d" dollars online.

you buy the kits at half price, 50% of the original price, well, the original price is "d", half "d" is just 0.5d, and there's a shipping charge of $4.50.  So the Cost to get one kit alone for you is 0.5d + 4.50.

After some work, you resell the kits online for 1.5d + 4.5, so since that's the selling price that is your Revenue for one kit.

[tex]\stackrel{\textit{\Large Profit}}{\stackrel{Revenue}{(1.5d~~ + ~~4.50)}~~ - ~~\stackrel{Costs}{(0.5d~~ + ~~4.50)}}\implies 1.5d+4.5-0.5d-4.5 \\\\\\ 1.5d-0.5d+4.5-4.5\implies 1d\implies d[/tex]

Answer:

According to the graph:

H^2 + 10^2 = 21^2

Solve as:

H = 18.19 feet

So the height is 18.19 feet

Answer:

-90 degrees counter clock wise

Step-by-step explanation:

it goes the opposite of a clock so it would be called -90 degrees counter clockwise, you could also say 270 degrees clockwise if the other isnt an option.

Answer:

Step-by-step explanation:

1.cos

2.sin

3.cos

4.tan

5.sin

6.tan

Step-by-step explanation:

remember the basic trigonometry setup ?

the norm circle (radius = 1) with a horizontal and a vertical line through the center of the circle.

and then there is an angle at the center indicated by the horizontal line and an inclined (by that angle) radius line connecting the center and the circle arc.

this inclined radius line is then the baseline (Hypotenuse) of a right-angled triangle, and the legs of that triangle are sine and cosine of the angle at the center (sine is the vertical leg, cosine is the vertical leg).

in essence (at least it works for me), when given such right-angled triangle problems, I always try to rotate and/or flip this triangle until it looks like the described situation above.

the only other thing to remember is that for triangles inside circles with a different radius than 1, everything is multiplied by the actual radius (it really happens also for the norm circle, but multiplying by 1 does not really change anything, right ?).

so, now for the given problems :

1)

x is the radius of the circle.

we can make 68° the defining angle of that trigonometric situation. so, the top right vertex would be the center of the circle with radius x.

then

30 = cos(68)×x

x = 30/cos(68)

= 80.08401488...

2)

60 is the radius of the circle.

x is the defining angle.

then

15 = sin(x)×60

sin(x) = 15/60 = 1/4

x = 14.47751219...°

3)

x is the radius of the circle.

22° is the defining angle.

then

14 = cos(22)×x

x = 14/cos(22)

= 15.0994864...

4)

the unnamed side is the radius of the circle. let's call it "s".

54° is the defining angle.

then

47 = cos(54)×s

x = sin(54)×s

x/47 = sin(54)×s / (cos(54)×s) = sin(54)/cos(54) = tan(54)

x = 47×tan(54) or 47×sin(54)/cos(54)

= 64.68995026...

5)

14 is the radius of the circle.

41° is the defining angle.

then

x = sin(41)×14

= 9.184826406...

6)

the unnamed side is the radius of the circle. let's call it "s".

x is the defining angle.

then

57 = cos(x)×s

9 = sin(x)×s

9/57 = sin(x)×s / (cos(x)×s) = sin(x)/cos(x) = tan(x)

x = 8.972626615...°

Answer:

1. Degree= 6, trinomial

2. degree= 4, binomial

Step-by-step explanation:

1. The largest exponent is 6 making it the degree and there are three terms because (m^5n^2), (mn^2), (n^6).

2. Since (9a^2bc^2) has the more than 1 exponent, you add them and the  degree is 4. There are two terms because (2a^3b), (9a^2bc^2).

Answer:

[tex] = 2 \times 4 = 8 \\ = 5 \times 5 = 25 \ \\ \frac{1}{2} \times 5 \times 3 = 7.5 \\ 7.5 + 8 + 2.5 = 18[/tex]

Answer:

no they dont form a Pythagorean triple

Step-by-step explanation:

a2 + b2 = c2

Answer:

12

Step-by-step explanation:

it would be 12 if it is unknown so 12 because y and x are used for unknown numbers.

i hope i got it right just tell me if this is wrong, please

The expression for the smaller number is q = x - 4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the greater number be p = x

Let the smaller number be q

If the greater number is x, then the other number must be 4 less than x.

We can express this algebraically as:

On simplifying the equation , we get

q = x - 4

Hence , the other number is x - 4.

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Answer:

right angled triangle

Step-by-step explanation:

the only triangle that this formula can be used to find a side is the right angled triangle

Answer:

is it 7?

Step-by-step explanation:

if he rode for 8 seconds and it says she rode for 2 seconds FEWER are you not subtracting from 8 to get 7?

no. the word technology spans every invention ever created. we don't.

Answer:

Yes, We as a society rely too much on technology because it is the new thing that everyone wants or needs. Technology can buy your groceries and food with a single click.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

480

Step-by-step explanation:

[tex]80*6[/tex] = 480

Answer:

She will travel 480 miles in 6 hours

Step-by-step explanation:

All you need to do is Multiply 80 by 6 to get an answer of 480.

Hope that helps!

After converting yards to miles:

2640 yards =  1.5 miles

Given,

2640 yards= ________ miles

Now,

To convert to yard to miles the conversion factor is 0.000568182.

So,

1 yard ⇒ 0.000568182 miles

Multiply 2640 on both sides,

2640 yards ⇒ 1.5 miles.

Therefore 2640 yards is equivalent to 1.5 miles.

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Answer:

ok so lets make this into a algrebra equation

22.2(mil)=0.34x

divide by 0.34

65294117.6471=x

x=65294118

Hope This Helps!!!

Answer: x=12, (MR)=55

Step-by-step explanation:

The statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity

If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.

For the considered case, the function is:

[tex]f(x) = \dfrac{2x}{1-x^2}[/tex]

The missing options are:

So we need to find the limit of the function as x approaches infinity.

[tex]lim_{x\rightarrow \infty}f(x) = lim_{x\rightarrow \infty}\dfrac{2x}{1-x^2} = lim_{x\rightarrow \infty}\dfrac{2x/x^2}{1/x^2 - 1} = lim_{x\rightarrow \infty}\dfrac{2/x}{1/x^2 - 1}\\\\lim_{x\rightarrow \infty}f(x) = \dfrac{lim_{x\rightarrow \infty}(2/x^2)}{lim_{x\rightarrow \infty}(1/x^2 - 1)} = \dfrac{0}{0-1} = \dfrac{0}{-1} = 0[/tex]

Since the value of the function approaches 0 as x approaches infinity, so as its graph will do.

Thus, the statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity

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Answer:

43 ffhfhfhfhfhfhchchchchchc

Answer:

It will take 225 days for Evie's chicken to lay 45 eggs

Step-by-step explanation:

Volume of right prism is 1800 in³, So option 'B' is the correct answer to the following question.

What information do we have?

Height of the prism is labeled = 15 in.

Base of the prism is a triangle with the base = 30 in

Height labeled = 8 in

Volume of right prism = Area of base triangle × Height

Volume of right prism = (1/2)(b)(h) × Height

Volume of right prism = (1/2)(30)(8) × 15

Volume of right prism = (30)(4) × 15

Volume of right prism = 120 × 15

Volume of right prism = 1800 in³

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Answer:

The answer is B. 1800 [tex]in^{3}[/tex]

Step-by-step explanation:

I took the test

Answer:

20 2/5 cm

Step-by-step explanation:

4 ( 5 1/10)

4 × 51/10

2×51/5

0.4x51

=20 2/5

Answer:

1. -3          2. y=-1

Step-by-step explanation: