Who wants to solve a question.

Answer:

x=2

Step-by-step explanation:

combine like terms to get 15x=30. divide by 15 on both sides to get x=2

Answer:

x=2

Step-by-step explanation:

1. Simplify the expression

4x+9x+2x=30

Simplify the arithmetic:

15x=30

2. Isolate the x

15x=30

Divide both sides by 15:

[tex]\frac{15x}{15}=\frac{30}{15}[/tex]

Simplify the fraction:

[tex]x=\frac{30}{15}[/tex]

Find the greatest common factor of the numerator and denominator:

[tex]x=\frac{2\cdot 15}{1\cdot 15}[/tex]

Factor out and cancel the greatest common factor:

[tex]x=2[/tex]

Why learn this

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

Terms and topics

The given sequence;–3.2, 4.8, –7.2, 10.8, is a geometric progression common ratio of -1.5.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

The given sequence ;

–3.2, 4.8, –7.2, 10.8, …

The common ratio

= -4.8/ 3.2

= - 1.5

The terms having a common ratio of -1.5 best describe the relationship between the successive terms in the sequence of the terms.

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jAlright, let's take this problem step-by-step:

What is the perimeter:

 ⇒ all the side-lengths added up

    ⇒ need to find side-length using distance formula

                [tex]Distance_._. Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                         - (x₁,y₁): first point

                         - (x₂,y₂): second point

Let's solve:

           ⇒ first point: (5,7)

           ⇒ second point: (3,3)

           [tex]Distance =\sqrt{(3-5)^2+(3-7)^2} =\sqrt{4+16} =\sqrt{20} =4.472[/tex]

          ⇒ first point: (5,7)

          ⇒ second point:(8,6)

           [tex]Distance=\sqrt{(8-5)^2+(6-7)^2} =\sqrt{9+1} =\sqrt{10}=3.162[/tex]

          ⇒ first point: (8,6)

          ⇒ second point: (3,3)

           [tex]Distance = \sqrt{(3-8)^2+(3-6)^2} =\sqrt{25+9} =\sqrt{34}=5.831[/tex]

Now let's solve for the perimeter:

  [tex]Perimeter = 4.472+ 3.126+ 5.831=13.429[/tex]

Answer: 13.43 (rounded to the nearest hundredth)

Hope that helps!

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perimeter of octagon

Now area

Area of square

Area of shaded region

Answer:

C.  647 square units

Step-by-step explanation:

To find the shaded area, subtract the area of the unshaded square from the area of the octagon.

Area of the octagon

[tex]\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \textsf{Area}=\sf \dfrac{8 \cdot 13 \cdot 15.69}{2}[/tex]

[tex]\implies \textsf{Area}=\sf \dfrac{1631.76}{2}[/tex]

[tex]\implies \textsf{Area}=\sf 815.88\:\:square \:units[/tex]

Area of the square

[tex]\implies \textsf{Area}=\sf 13^2=169 \:\:square \:units[/tex]

Area of the shaded region

= area of the octagon - area of the square

= 815.88 - 169

= 646.88

= 647 square units (nearest square unit)

Answer:

60

Step-by-step explanation:

2hrs = 120

120/30= 4

4×15=60

Answer:

60 pages :)

Step-by-step explanation:

First we turn the hours into minutes to make it easier :)

1 hr = 60 minutes

2 hrs = 120 minutes

Now that we have done that, we divide :)

120/30 =4

And now we multiply 1 more time :)

4 x 15 = 60

Have an amazing day!!

Please rate and mark brainliest!!

If the value of θ is 46.4°. Then the value of the cosine of θ will be 20/29.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The value of sine of θ is 21/29.

Then the value of θ will be

sin θ = 21/29

     θ = sin⁻¹(21 / 29)

     θ = 46.4°

Then the value of the cosine of θ will be

cos θ = cos 46.4°

cos θ = 20/29

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Answer:

x • (2xt + 7y)

Step-by-step explanation:

1. ((5xy-((x2)•t))+2xy)+(3x2•t)

2. Pull out like factors :

  2x2t + 7xy  =   x • (2xt + 7y)

Final result

x • (2xt + 7y)

Answer:

[tex]7xy + {x}^{2} t[/tex]

Step-by-step explanation:

[tex](5xy + 2xy) + ( - 2 {x}^{2} t + 3 {x}^{2}t) [/tex]

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 23 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 5x - x - 8 = 15 + 3x[/tex]

[tex]\qquad \tt \rightarrow \: 4x - 8 = 15 + 3x[/tex]

[tex]\qquad \tt \rightarrow \: 4x - 3x = 15 + 8[/tex]

[tex]\qquad \tt \rightarrow \: x = 23[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

x = 23

Explanation:

⇒ 5x - x - 8 = 15 + 3x

collect like terms

⇒ 5x - x - 3x = 15 + 8

add or subtract like terms

⇒ x = 23

Checking:

5(23) - 23 - 8 = 15 + 3(23)

115 - 23 - 8 = 15 + 69

84 = 84

The correct answer is option C which is x = y.

The angle formed by the line intersecting two parallel lines is called the alternate interior angle. This two angles are equal in magnitude.

In the given figure we can see that the angle x will be equal to the angle y because of the right opposite angles.

Since two parallel lines are cutting the upper part at x so the same lower part will be also x due to corresponding angles.

Now just right opposite to x there is an angle y so the angles x and y will be equal to each other.

Therefore the correct answer is option C which is x = y.

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Answer:

66m

Step-by-step explanation:

Answer:

66 m

Step-by-step explanation:

ok so if you think about it, when she runs diagonal she's creating a triangle where she is running along the hypotenuse. we can now use the Pythagorean Theorem a^2 + b^2 = c^2 to solve for the other side with two of them being known.

plug values in

100^2 + w^2 = 120^2

square known values

10,000 = w^2 = 14,400

subtract 10,000 from both sides

w^2 = 4400

take the square root

w = 66 (rounded to the nearest whole number)

The question is incomplete. Below you will find the missing content.

The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.

The correct option will be Option C: x=5t-3

y=4t-5

z=t

where t is the real number.

A matrix is in row echelon form when the first non-zero number from the left i.e. leading coefficient is always to right of the first non-zero number in the row above and rows consisting of all zeros are at bottom of the matrix.

The row echelon form of the matrix is given in the question.

from row-echelon form of the matrix, we can write the equation as,

x-5z=-3

y-4z=-5

Let's assume z=t, where t is the real number

now we can find x and y by putting z=t in the equation

x-5t=-3

⇒x=-3+5t

y-4t=-5

y=-5+4t

Now we get the solution of x,y,z in terms of t

x=5t-3

y=4t-5

z=t

where t is the real number.

So the correct option will be Option C: x=5t-3

y=4t-5

z=t

where t is the real number.

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Answer: -8

Step-by-step explanation:

Answer:

7(w+13)=35

7w + 91 =35

7w=35-91

7w= -56

7w/7 = -56/7

w=-8

Answer:

b(n) = -11 + (n-1)*8

Step-by-step explanation:

Let n be the sequence number, with n=1 the first number b(1) -11

The sequence changes by +8 each step.

b(1)   -11         + 8 =   -3

b(2)   -3          + 8 =    5

b(3)   5         + 8 =   13

b(4) 13

b(1) = -11

b(2) = -3.   or b(1) + 1*8

b(3) =  5,    or b(1) + 2*8

b(4) =  13,   or b(1) + 3*8

We note that each step adds a multiple of 8 to the initial value of -11.  This can be stated as (n-1)*8

The formula for this sequence would be b(n) = b(1) + (n-1)*8

b(n) = -11 + (n-1)*8

Check:  Does n=3 return the value of 5?

b(n) = -11 + (n-1)*8

b(3) = -11 + ((3)-1)*8

b(3) = -11 + (2)*8

b(3) = -11 + 16

b(3) = 5   YES

Any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In △ABD and △ACB,

∠A = ∠A (common)

∠ADB = ∠ABC (both are right angles)

Thus, △ABD ∼ △ACB (by AA similarity criterion)

Similarly, we can prove △BCD ∼ △ACB.

Thus △ABD ∼ △ACB,

Therefore, AD/AB = AB/AC.

We can say that AD × AC = AB².

Similarly, △BCD ∼ △ACB.

Therefore,

CD/BC = BC/AC.

We can also say that

CD × AC = BC².

Adding these 2 equations, we get

AB² + BC² = (AD × AC) + (CD × AC)

AB² + BC² =AC(AD +DC)

AB² + BC² = AC²

Hence proved

Thus, any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

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The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of Jake's tree is 17.325 trees.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

Given Josh is 31.2 meters away from the Red Pine tree. The angle of elevation from Josh to the top of the tree is 48º. Therefore, the height of the Josh tree will be,

Tan(48°) = Height of the tree/ Distance between Josh and tree

Height of the tree = Tan(48°) × 31.2 meter = 34.65 meters

Now, Jake's tree is half as tall as Josh's tree. Therefore, the height of Jake's tree is,

Height of Jake's tree = 34.65 meters = 17.325 meters

Hence, the height of Jake's tree is 17.325 trees.

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Answer:

25 < t < 350

Step-by-step explanation:

The mean lifetime of a bulb ranges from 25 to 350 hrs but the question is unclear.

Answer:

3.256*10³2

Step-by-step explanation:3.256 * 1000 = 3256 1000 =10³

the first definition of an element was made by

Answer:

parallel

a quadrilateral can be a parallelogram only and only if pair of opposite sides are equal and parallel.

Answer:

$17131.50

Step-by-step explanation:

23500 decrease 10% =

23500 × (1 - 10%) = 23500 × (1 - 0.1) = 21150

21150 decrease 10% =

21150 × (1 - 10%) = 21150 × (1 - 0.1) = 19035

19035 decrease 10% =

19035 × (1 - 10%) = 19035 × (1 - 0.1) = 17131.5

[tex]\textsf {Finding y :}[/tex]

[tex]\implies \mathsf {1^{2} + y^{2} = 3^{2}}[/tex]

[tex]\implies \mathsf {y^{2} = 8}[/tex]

[tex]\implies \mathsf {y = 2\sqrt{2}}[/tex]

[tex]\textsf {Finding z :}[/tex]

[tex]\implies \mathsf {(2\sqrt{2})^{2}+8^{2}=z^{2}}[/tex]

[tex]\implies \mathsf {z^{2} = 72}[/tex]

[tex]\implies \mathsf {z = 6\sqrt{2}}[/tex]

Answer:

z =8.49 or 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Do the Pythagorean theorem = [tex]a^{2} +b^{2} =c^{2}[/tex]

Length of hypotenuse = 8+1=9

length of one side = 3

so, a²+3²=9²

     a²+3²=9²

     a²=81-9

     a²=72

     a=√72=8.49 or 6[tex]\sqrt{2}[/tex]

At least 1 right angle = A, C and E

At least 2 sides of equal length = B and E

At least 1 pair of parallel sides= B and E

Parallel lines are those lines that are apart and they never meet till infinity.

Example of shapes that have sides with parallel line are the rectangle and parallelograms.

The shape B and E are rectangles and parallelograms respectively.

The shape that has angle 90° are right angle triangles and trapezium.

Therefore, the shapes that has right angles are A which is a trapezoid and E which is a rectangle.

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Answer:

B. -2

Step-by-step explanation:

-12x -2(x+9) = 5(x+4)

*ALWAYS REMEMBER YOUR BODMAS*

-12x -2x - 18 = 5x + 20

*group the like terms*

-14x - 5x = 20 + 18

-19x = 38

x = -2

The value of x that makes the equation true is: x = -2.

B. -2.

Here, we have to find the value of x that makes the equation true, we need to solve for x.

Let's solve the equation step by step:

-12x - 2(x + 9) = 5(x + 4)

Distribute the -2 and 5 on the right side of the equation:

-12x - 2x - 18 = 5x + 20

Combine like terms on both sides:

-14x - 18 = 5x + 20

Move the variable terms (5x) to one side of the equation and the constant terms to the other side.

Let's subtract 5x from both sides:

-14x - 5x - 18 = 5x - 5x + 20

-19x - 18 = 20

Move the constant term (-18) to the other side of the equation.

Let's add 18 to both sides:

-19x - 18 + 18 = 20 + 18

-19x = 38

Finally, divide both sides by -19 to isolate x:

x = 38 / -19

x = -2

So, the value of x that makes the equation true is: x = -2.

B. -2.

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Answer:

C

Step-by-step explanation:

7 × ln(x) = 2.4

ln(x) = 2.4/7 = 0.342857143...

x = e^0.342857143... = 1.408967466... ≈ 1.41

The sum of the interior angle is 1080 and each angle measure is 135 degrees.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have an octagon

In an octagon the number of sides = 8

The sum of the angles in the octagon is given by:

= (n - 2)×180

n = 8

= (8 - 2)180

= 6×180

The sum of the interior angle = 1080

Each angle = 1080/8 = 135 degree

Thus, the sum of the interior angle is 1080 and each angle measure is 135 degrees.

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