Using the Addition Method, solve for x in the following system of linear equations.

2y + x = 4

y - 3x = 2


a.) x = 1

b.) x = 2

c.) x = 8

d.) x = 0

Answer:

a) -0.5 = -1/2

b) -2/1/4 = -2/4

c) -5/6/7 = -5/42

d) 7.2 = 72/10

Step-by-step explanation:

Answer:

7 maybe? (I'm assuming any two neighboring digits is greater than or equal to 8)

Step-by-step explanation:

Ok so it's important to establish which combinations of numbers have a difference of 8+. The most obvious one is (0, 8), and (1, 9), but there's also (0, 9). In my explanation I'll express a three digit number as: [tex]100a+10b+c[/tex] where a, b, and c will form the three digit number. It's important to understand that: [tex]a\ne0[/tex], because if it was 0, then it would be a two digit number, because there would be no hundreds place. So let's start with the (0, 8) combination. a=8 and b=0, and c can have 2 different values. So we get the two numbers: [tex]809, 808[/tex]. Now let's using the (1, 9) which can be rearranged where (a=1, b=9) OR (a=9, b=1) since this combination doesn't have a 0 as one of the values. So let's start with a=1, b=9, this leaves 2 values for c. This gives you the numbers: [tex]190, 191[/tex]. Now let's use the a=9, b=1 combination. This only leaves 1 values for c since 8-1 = 7, meaning c can only equal 9. This gives you the following number: [tex]919[/tex]. Now for the last combination: (0, 9). In this combination a has to be 9, and b has to be 0. This gives you 2 values for c. This gives you the following two numbers: [tex]909, 908[/tex]. Combining all these numbers we get the following numbers: [tex]909, 908, 919, 809, 808, 190, 191[/tex]

Answer:

The product is the difference of squares is [tex]$$(9c-2d)(9c+2d)=81{{c}^2}-4{{d}^2}$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(9 c-2 d)(9 c+2 d)=(9 c)^{2}-(2 d)^{2} \\&(9 c-2 d)(9 c+2 d)=81 c^{2}-4 d^{2}\end{aligned}$$[/tex]

Answer:

126 sq. meters

Step-by-step explanation:

A = lw

= 9(14)

= 126 sq. meter

Answer:

51 units²

Step-by-step explanation:

First, split the polygon into two pieces so that the left side is a triangle, and the right side is a rectangle.

Then, find the area of the rectangle. Count how many units the width and the height is. The height is 7 units, and the width is 6 units. Multiply the two measurements to get the area of the rectangle.

7×6=42.

The area of the rectangle is 42.

Now, find the area of the triangle. Count how many units the width and the height is. The height is 6, the width is 3. Use the area of a triangle formula. The formula is:

1/2×b×h

1/2×3×6=3×3=9

The area of the triangle is 9.

Add the areas together to find the area of the total polygon.

42+9=51.

The area of the polygon is 51 units².

Hope this helps!

If not, I am sorry.

Answer:

C = 100 degrees

B = 70 degrees

Step-by-step explanation:

OPPOSITE ANGLES OF A CYCLIC QUADRILATERAL ARE SUPPLEMENTARY, WHENEVER YOU ADD THEM THEY SHOULD GIVE YOU 180 DEGREES.

SOLUTION

A + C = 180

80 + C = 180

C = 100

D + B = 180

110 + B = 180

B = 70

The result of the decrease of the number 14.4 by 0.2 of it is of 14.2.

The equivalent operation is the subtraction of a by b.

In this problem, we want to decrease the number 14.4 by 0.2 of it, hence the operation is:

14.4 - 0.2 = 14.2.

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Answer:

6

Step-by-step explanation:

To answer this simply subtract 7 from 13 to find the answer.

13-7=6

Hope this helps!

If not, I am sorry.

Answer: 6

Step-by-step explanation: i just did the work

The area of the triangle with sides of 51cm, 37cm, and 30cm, is calculated to be 496.37cm².

The area of a triangle can be computed by the formula √{s(s - a)(s - b)(s - c)}, where a, b, and c, are the three sides of the triangle, and s is the semi-perimeter of the triangle, that is, s = (a + b + c)/2.

In the question, we are asked to find the area of the triangle, whose sides are 51cm, 37cm, and 30cm.

Thus, we take a = 51cm, b = 37cm, and c = 30cm.

The perimeter of the triangle = a + b + c = 51cm + 37cm + 30cm = 118cm.

Hence, the semi-perimeter of the triangle, s = (a + b + c)/2 = 118cm/2 = 59cm.

Hence, using the formula for the area of the triangle:

√{s(s - a)(s - b)(s - c)}

= √{59(59 - 51)(59 - 37)(59 - 30)} cm²

= √{59 * 8 * 18 * 29} cm²

= √246384 cm²

= 496.37 cm².

Thus, the area of the triangle with sides of 51cm, 37cm, and 30cm, is calculated to be 496.37cm².

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The absolute value equation with the wanted solutions is:

|x| - 1/2 = 0

Here we want to find an absolute value equation such that the solutions are:

x = -1/2 and x = 1/2.

Remember that the absolute value equation always changes the sign, such that the outcome is positive.

This means that:

|1/2| = 1/2

|-1/2| = 1/2

Then a trivial equation with these two solutions is:

|x| - 1/2 = 0

Where the two solutions are x = 1/2 and x = -1/2.

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The area, in square centimeters, of the shaded quarter of the circle is π cm² OR 3.14 cm²

From the question, we are to determine the area of the shaded quarter of the circle

The shaded quarter of the circle is a sector.

The area of a circle is given by the formula,

[tex]A = \frac{\theta}{360^\circ}\times \pi r^{2}[/tex]

Where A is the area

θ is the angle subtended

and r is the radius

First, we will calculate the radius of the circle

The radius of the circle equals the length of a side of the square.

From the given information,

Area of the square = 4 cm²

∴ s² = 4 cm²

s =√4 cm²

s = 2 cm

∴ A side of the square is 2 cm in length

Thus,

r = 2 cm

and

θ = 90°

Then,

[tex]A = \frac{90^\circ}{360^\circ}\times \pi \times 2^{2}[/tex]

[tex]A = \frac{1}{4}\times \pi \times4[/tex]

[tex]A = \pi \ cm^{2}[/tex] OR 3.14 cm²

Hence, the area, in square centimeters, of the shaded quarter of the circle is π cm² OR 3.14 cm²

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Answer:

Step-by-step explanation:

Things we already know:

Angle B = 56 degrees

Angle C = 90 degrees

Side CB = 7 units

We need to find angle A and sides AC and AB.

We know that every triangle has its angles equal to 180 degrees

angle A + B + C = 180 degrees

angle A + 56 + 90 = 180 degrees

angle A + 146 = 180 degrees

subtract 146 from both sides.

angle A = 34 degrees

Now we know angle A.

To find side AC, we can use the tangent of theta.

The hyp (hypothenuse) = AB

The adjacent side = CB

And the opposite side = AC

The tangent of theta is the opposite side divided by the adjacent side.

[tex]tan(56) = \frac{AC}{7}[/tex]

Now we just need to solve for AC.

multiply 7 on both sides, to cancel it out on the right side.

7tan(56) = AC

10.3 = AC

Now we know the side AC.

AC = 10.3 units

To find the hypothenuse, we can use the sine, cosine, or the Pythagorean theorem.

I will choose the Pythagorean theorem, though.

[tex]7^{2} +10.3^{2} =AB[/tex]^2

49 +106.09 = AB^2

AB = 155.09 units^2

AB = 12.4 units

And now we know everything about this triangle.

A = 34 degrees

C = 90 degrees

B = 56 degrees

AC = 10.3 units

CB = 7 units

AB = 12.4 units

Hope I Helped!

Answer:

-11x^8 + 3

Step-by-step explanation:

-8x^8 + (-3x^8 + 3)

-8x^8 - 3x^8 + 3

-11x^8 + 3

His average speed for the entire trip is 46.6 mph

We have,

30 miles at 40 mph

time taken at this speed = 30/40 = 3/4 hours

..

75 miles at 50mph

time taken = 75/50 = 3/2 hours

Total time taken = 3/4 +3/2 hours=3+6 /4

=9/4 hours

Total distance traveled = 30+75 = 105 miles

Average speed = 105/ 9/4

=105*4/9

46.6 mph is the average speed.

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The value of x is 8√3

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

In triangle having angle 60.

sin 60 = P/ 8√2

√3/2= P/8√2

2P=8√2* √3

P= 4√6

Now again

sin 45= 4√6/x

1/√2 = 4√6/x

x= 4√6*√2

x= 8√3

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Answer:

n=45

Step-by-step explanation:

[tex]n=\dfrac{54.100}{120} \\\\n=45[/tex]

Equation of a line is given by y - y1 = m(x - x1); where m is the slope.

y - 4 = 2/5 (x - (-2))

y - 4 = 2/5 (x + 2)

Hope this helps! :)

Answer:

Step-by-step explanation:

y = 2/5x + p

We now that passes through (–2, 4)

 2/5 × (-2) + p = 4

⇔ -4/5 + p = 4

⇔ p = 4 + 4/5

⇔ p = 20/5 + 4/5

⇔ p = 24/5

⇒ y = 2/5x + 24/5

Answer:

slope = m = 7/5

y-intercept = b = -3

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

y = 7/5 x - 3

slope = m = 7/5

y-intercept = b = -3

Answer:

Step-by-step explanation:

If a line's equation has the form y=mx+b, then finding the slope can be done within 2 seconds.

∴ m is the Slope,

and the slope is always multiplied by the x co-ordinate.

b is the y-intercept,

and it's added to the product of the slope and the x co-ordinate.

Both the slope and the y-intercept can be any real number.

∵, slope = [tex]\boxed{\rm{Slope=7/5}}[/tex]

∵, y-intercept = [tex]\boxed{\rm{Y-intercept=-3}}[/tex]

done !!

[tex]\orange\hspace{300pt}\above2[/tex]

Answer:

y = 2x + 8

Step-by-step explanation:

  Parallel lines have same slope.

 y = 2x - 4

Slope = 2

Point (-2 ,4)

Equation of line in point-slope form:

         y - y₁ = m(x - x₁)

        y - 4  = 2(x - [-2] )

       y - 4   = 2(x + 2)

       y -4   = 2x + 4

             y = 2x + 4 + 4

        [tex]\sf \boxed{y = 2x + 8}[/tex]

Step-by-step explanation:

First, we need to find that top angle, which we'll call angle x. We can say 26 is the hypotenuse, and 12 is the adjacent, so we know that:

[tex] \cos(x) = \frac{12}{26} [/tex]

Let's solve this, to find X:

[tex]x = { \cos }^{ - 1}( \frac{12}{26} )[/tex]

Now that we know what X is, we can use trig to find the missing side, which we'll call y. 48 is the adjacent, and y is the hypotenuse, therefore:

[tex] \cos(x) = \frac{48}{y} [/tex]

To find y, let's rearrange:

[tex]y = \frac{48}{ \cos(x) } [/tex]

And now let's figure out calculate the value of y (I'm leaving the value of X as just X for the equations, but you will need it to calculate first):

[tex]y = 0.767833242[/tex]

540 students gained admission

The given parameters are:

Students = 1200

Proportion that gain admission. p = 9/20

The number of student that gain admission is calculated as:

Admission = p * Students

So, we have:

Admission= 9/20 * 1200

Evaluate

Admission= 540

Hence, 540 students gained admission

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The probability of a success and a failure is as follows,

P(success) = one - fourth

P(failure) = three - fourth

Definition of Probability

The area of mathematics that deals with numerical representations of the likelihood that an event will occur or that a statement is true is known as Probability. An event's probability is a number between 0 and 1, where, 0  generally denotes the event's impossibility and 1 denotes certainty of that event.

Calculating the Probability

The formula for finding the probability of an event to occur is given by,

P = (favorable outcomes)÷(total number of outcomes)

Now, it is given that each multiple choice question consists of 4 choices.

And, out of these four choices, only one answer is true.

Then, if Laila guesses the answer, the probability of choosing the right answer is given by,

P(success) =1/4

Thus, the probability of choosing the wrong answer will be,

p(failure) = 1 - P(success)

⇒ P(failure) = 1 - (1/4)

⇒ P(failure) = 3/4

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Answer:

The product is the difference of squares is [tex]$$\left(xy-9\right)\left(xy+9\right)={{x}^2}{{y}^2}-81$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(x y-9)(x y+9)=(x y)^{2}-(9)^{2} \\&(x y-9)(x y+9)=x^{2} y^{2}-81\end{aligned}$$[/tex]

Answer:

the answer is A

Step-by-step explanation:

put it in the calculator

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

When you have a negative exponent like [tex](\frac{a}{b})^{-x}[/tex] you simply take the reciprocal and then the denominator takes the exponent. So it becomes [tex]\frac{b}{a^{x}}[/tex].

So now you simply plug -2 as x. This gives you [tex]2(4)^{-2}[/tex]. and 4 is essentially [tex]\frac{4}{1}[/tex]. So it becomes [tex]\frac{1}{4^2}[/tex] which is [tex]\frac{1}{16}[/tex]. So multiplying it by 2 you get [tex]\frac{2}{16}[/tex]. Which can be written as [tex]\frac{2}{8 * 2}[/tex] so the 2's cancel out and the fraction becomes [tex]\frac{1}{8}[/tex]

Displacement at t = 0 :

Displacement at t = 1 :

Displacement between t = 0 and t = 1 :

∴ The displacement between t = 0 and t = 1 is -4√2 meters.

Answer:

[tex]-4\sqrt{2} m[/tex]

Step-by-step explanation:

Similar question to the previous one you asked, and I swear I will not make the same mistake again :)

First we will find the displacement at t = 0 and t = 1 to find both displacements.

t = 0,

[tex]x(0)=4cos(\pi (0)+\frac{\pi }{4} )=4cos(\frac{\pi }{4} )\\=4(\frac{\sqrt{2} }{2} )\\=2\sqrt{2} m[/tex]

t = 1,

[tex]x(1)=4cos(\pi (1)+\frac{\pi }{4} )=4cos(\pi +\frac{\pi }{4} )\\=4(-\frac{1}{\sqrt{2} } )\\=-\frac{4}{\sqrt{2} }[/tex]

Total Displacement = Final Position - Initial Position

= x(1) - x(0)

= [tex]-\frac{4}{\sqrt{2} } -2\sqrt{2} \\=-4\sqrt{2} m[/tex]

|AC|^2 = |AB|^2 + |BC|^2  is indeed the Pythagorean theorem which implies that adding the hypotenuse square as well as the two sides of a right triangle equals the hypotenuse square.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).

Calculating value by using the Pythagorean theorem:

The smallest side of the triangle in this instance contains 2 dots, which equals.

The triangle's bigger side has 3 dots.

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Answer:

15; -580; 936

Step-by-step explanation:

1. 10a-15=10*3-15=15

2. -5b^3+7b+10=-5*5^3+7*5+10=-580

3. 6abc+4a^2=6*3*5*10+4*3^2=936

Answer:

well.. 1/1/1 would be 1.

8 x 3 = 24

24x 1 = 24

sooo the answer would be 24...

Step-by-step explanation:

The product of the given expression 8 × 1/1/1 x 3 would be equal to 24.

When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction.

A proper fraction is also called fraction which is less than 1.

And an improper fraction is ≥ 1

A mixed fraction contains a sum of whole number and a proper fraction.

We know that 1/1/1 would be 1.

So,

8 x 3 = 24

24x 1 = 24

Thus, the answer would be 24.

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