How do i solve this equation with steps

Answer:

13

Step-by-step explanation:

3(4)+1

12+1

13

Answer:

13

Step-by-step explanation:

Equation:

3n + 1

Let's substitute 4 into the equation as n.

3n + 1

3(4) + 1

Solve:

3(4) + 1

Multiply:

3(4) + 1

12 + 1

Add:

12 + 1

= 13

Therefore, the value of the expression is 13.

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Sathish will be going to pay a total of $64.8 for the gas.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

The First 150 and last 150 km will cover by Satish only

Since 6 liters covers 100 km

So,

Cost of 300 km (18 liters) ⇒ 18×1.2 = 21.6

Now,

The journey 2100 - 300 = 1800 km has been covered by all three

Split 1800/3 = 600 km of money Satish will pay

So,

Cost of 600km(36 liters) ⇒ 36 × 1.2 = 43.2

Total paid = 21.6 + 43.2 = 64.8.

Hence "Satis will be going to pay a total of $64.8 for the gas".

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Answer:

x° = 41.8°

Step-by-step explanation:

Use trigonometric functions to calculate angles from side lengths.

sOH - cAH - tOA.

Sine:  Opposite/Hypotenuse
Cosine:  Adjacent/Hypotenuse
Tangent:  Opposite/Adjacent

sin(x°) = 4/6

\(x=sin^-1(\frac{2}{3} )\)

x° = 41.8°

Answer:

4:5:1

Step-by-step explanation:

so first of all the ratio will be 140:70:35 but after we simplify it with 35 we'll get the final simplified ratio which is 4:5:1

The arc length of \(y=2x^{\frac32}\) over [0, 1] is given by the integral,

\(L=\displaystyle\int_0^1\sqrt{1+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx\)

Differentiate y with respect to x using the power rule:

\(\dfrac{\mathrm dy}{\mathrm dx}=\dfrac32\times2 x^{\frac32-1}=3x^{\frac12}\)

Then the integral becomes

\(L=\displaystyle\int_0^1\sqrt{1+\left(3x^{\frac12}\right)^2}\,\mathrm dx=\int_0^1\sqrt{1+9x}\,\mathrm dx\)

Substitute u = 1 + 9x and du = 9 dx :

\(L=\displaystyle\int_0^1\sqrt{1+9x}\,\mathrm dx=\frac19\int_1^{10}\sqrt u\,\mathrm du\)

\(L=\displaystyle\frac19\left(\frac23u^{\frac32}\right)\bigg|_1^{10}\)

\(L=\dfrac2{27}\left(10^{\frac32}-1^{\frac32}\right)\)

\(L=\boxed{\dfrac2{27}\left(10^{\frac32}-1\right)}\)

Answer:

850 ( 2 multiply by 15 divide by 100)

850 ( 2 multiply 0,15)

850 multiply 0,3

= R255, 00

The inverse of the given matrix would be C. C ⁻¹ [-4.5, -3.5]

[ - 4 , - 3 ]

The formula for finding the inverse of the matrix is;

= ( 1 / determinant ) x [ d , - b ]

[ - c , a ]

The inverse is therefore:

= 1 / 2 x [ 9 , 7 ]

=  [- 4. 5 , - 3 . 5 ]

= [ - 4 , - 3 ]

So, the inverse of the matrix C is:

[ - 4. 5 , -3. 5 ]

[ - 4 , - 3 ]

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The coordinates of the remaining vertices of the square ABCD with diagonal AC and given vertices A(1,3) and C(6,-2) are B(3, 0) and D(4, 1).

To find the coordinates of the remaining vertices of square ABCD with diagonal AC and given vertices A(1,3) and C(6,-2), we can follow these steps:

Find the midpoint of AC, which will be the center of the square. We can use the midpoint formula:

((1+6)/2, (3-2)/2) = (3.5, 0.5)

Find the direction of the sides of the square. Since the sides of a square are perpendicular to its diagonals, we can find the slope of the line AC and the negative reciprocal of that slope will give us the slope of the sides.

Slope of AC = (y2 - y1)/(x2 - x1) = (-2 - 3)/(6 - 1) = -1

Slope of sides = -1/(-1) = 1

Use the midpoint and slope to find the equations of the sides of the square. We know that the sides of the square pass through the midpoint of AC, so we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is the midpoint.

Side AB: y - 0.5 = 1(x - 3.5) => y = x - 3

Side BC: y - 0.5 = -1(x - 3.5) => y = -x + 4

Find the coordinates of the remaining vertices by finding the intersection points of the sides. We can solve the system of equations:

y = x - 3

y = -x + 4

to get the coordinates of the remaining vertices.

Solving for x, we get:

x - 3 = -x + 4 => 2x = 7 => x = 3.5

Substituting x into either equation to find y, we get:

y = x - 3 = 0.5

or

y = -x + 4 = 0.5

So the coordinates of the remaining vertices are:

B(3, 0) and D(4, 1)

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The figure will be a sphere with center T and radius 8 1/2 inches, that is, option D.

A circle is a closed curve constituting of the set of all points in a plane that are equidistant from a given point. This point is the center of the circle and the distance is the radius of the circle.

A circle is a 2-dimensional figure, and the two dimensional does not contain the set of all points in the 3-dimensional plane.

A sphere is a round geometrical object and is the set of all points that are equidistant from a given point, in the three-dimensional space.

Here, we are given that there is a point T and we need to describe the collection of all points in the same plane that are 8.5 inches from point T.

Going by the definitions given above, we can infer that it is a sphere with center T and radius 8.5 inches. If we take it to be a circle then it will not include the points in the 3D plane, hence, sphere.

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Your question was incomplete, check for the full content below-

Which describes the collection of all points in the same plane that are 8 1/2 inches from point T?

A.) Circle T with radius 8 1/2 inches

B.) circle T with diameter 8 1/2 inches

C.) circle T with radius 17 inches

D.) a sphere with center T and radius 8 1/2 inches

\(x7 - 2 \: or \: x \leqslant - 3\)

Answer:

Step-by-step explanation:

There are five dice, so whatever the first die rolls there is a 1/6 chance that the second die is the same number. If that occurs, there's a 1/6 chance that the third die is the same, ditto the fourth and the fifth. So probability of Yahztee in one roll is 1/6 x 1/6 x 1/6 x 1/6 = 1/1296.

Answer:

A 60% chance

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the equation for the nth term in the sequence, we need to determine the pattern or rule that generates the sequence.

From the given information, we can see that the sequence is not arithmetic because the differences between consecutive terms are not constant. Instead, the sequence appears to be quadratic because the second difference between consecutive terms is constant.

Using the given values of a₁, a₃, and a₅, we can find the first few differences:

a₃ - a₁ = 4 - (-6) = 10

a₅ - a₃ = 14 - 4 = 10

So, the first difference is 10, which indicates a linear term in the equation for an. We can now use the given value of a₁ and the first difference to find the constant term in the quadratic equation. Let d be the common difference, then we have:

a₂ = a₁ + d = -6 + 10 = 4

a₄ = a₃ + d = 4 + 10 = 14

a₆ = a₅ + d = 14 + 10 = 24 - 1

a₇ = a₆ + d = 24 - 1 + 10 = 33

Now, we can find the second difference between consecutive terms:

a₄ - 2a₃ + a₂ = 14 - 2(4) + (-6) = 0

a₆ - 2a₅ + a₄ = 19 - 2(14) + 4 = -5

a₇ - 2a₆ + a₅ = 33 - 2(19) + 14 = 9

Since the second difference is constant (-5), this confirms that the sequence has a quadratic term in its equation. Let's assume the equation for the nth term is:

an = an² + bn + c

Substituting the values we know, we get three equations:

a₁ = a₁² + b₁ + c --> -6 = c

a₃ = a₃² + b₃ + c --> 4 = 9a + b + c

a₅ = a₅² + b₅ + c --> 14 = 25a + 5b + c

Solving this system of equations, we get:

a = 1/2, b = 19/2, and c = -6

Therefore, the equation for the nth term in the sequence is:

an = (1/2)n² + (19/2)n - 6.

Answer:

144

Step-by-step explanation:

divide 50 by 3 and then multiply by 9

Answer:

1)-12/13

2)-1/3

3)0

4)-4/5

5)undefined

6)-4

7)5

8)3

9)4

10)-5/6

11)16

12)1/3

Answer: 1

Step-by-step explanation:

We can start by dividing both sides by 5. This gives us

\(6 + s = 7\)

Subtracting 6 from both sides gives us

\(s = 7-6=1\)

To check, we can put 1 back in the equation:

\(5(6+1) = 35\)

\(5(7) = 35\)

Since 5 * 7 is 35, 1 is the answer.

Answer:

= -42

Step-by-step explanation:

for -4,2 subsitute -42

sorry if im wrong:(

Answer:

170°

Step-by-step explanation:

180 - 10 = 170

5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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The coordinates of vertex D in the parallelogram are (-7, -10).

We have,

To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.

One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.

Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:

Find the vector representing one of the sides of the parallelogram.

We can use the vector AB.

Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)

= (6 - 8, -4 - 2)

= (-2, -6)

Add this vector to point C to find the coordinates of D.

Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)

= (-5 - 2, -4 - 6)

= (-7, -10)

Therefore,

The coordinates of vertex D are (-7, -10).

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Answer:

2.5 days

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work done per unit of time.

Given:

15 people working 5 hours per day can make 30 units of the product in 10 days.

From this information, we can calculate the work rate of these 15 people:

Work rate = Total units of the product / (Number of people × Number of hours × Number of days)

Work rate = 30 units / (15 people × 5 hours × 10 days)

Work rate = 0.04 units per person per hour

Now, we need to find how many days it will take for 10 people, working 10 hours per day, to make 10 units of the product.

Using the work rate formula:

Number of days = Total units of the product / (Number of people × Number of hours × Work rate)

Number of days = 10 units / (10 people × 10 hours × 0.04 units per person per hour)

Number of days = 2.5 days

Therefore, 10 people, working 10 hours per day, can make 10 units of the product in 2.5 days.

The correct answer is:

2.5 days

Answer:

The answer is 25

Step-by-step explanation:

Answer:

Ellipse

Step-by-step explanation:

From the given information:

Suppose the plane cuts the cone in such a manner that the plane is neither perpendicular nor parallel to the axis and also the angle of intersection is greater than the generator angle.

Then the conic section formed is an Ellipse.

The Conic Section that is formed from the intersection of the central axis at an angle between 40° and 90° will be An Ellipse.

Let us consider that the plane cuts the cone in such a manner that the plane is neither perpendicular nor parallel to the axis and also the angle of intersection is greater than the generator angle.

Thus, we can say that when the plane intersects the double-napped cone in such a manner that the angle between the vertex and the angle is greater than the vertex angle.

Then the resulting conic section formed is an Ellipse.

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Answer:

x = -3

y = -2

(-3, -2)

Step-by-step explanation:

x - 7y = 11

5x + 4y = -23

-----------------------

-5 (x - 7y = 11)

-5x + 35y = -55

--------------------------

-5x + 35y = -55

5x + 4y = -23

       39y = -78

     ÷39     ÷39

        y = -2

-----------------------------

x - 7y = 11

x -7(-2) = 11

x + 14 = 11

   -14    -14

x = -3

I hope this helps!

The steps to verify the identity cos(-Θ)/(1 + sin(-Θ)) = sec(Θ) + tan(Θ) are:

Start with the left-hand side of the identity: cos(-Θ)/(1 + sin(-Θ))

Use the fact that cos(-Θ) = cos(Θ) and sin(-Θ) = -sin(Θ) to rewrite the expression as: cos(Θ)/(1 - sin(Θ))

Multiply the numerator and denominator by (1 + sin(Θ)) to get: cos(Θ)(1 + sin(Θ))/((1 - sin²(Θ)))

Use the Pythagorean identity sin²(Θ) + cos²(Θ) = 1 to simplify the denominator to cos²(Θ): cos(Θ)(1 + sin(Θ))/(cos²(Θ))

Rewrite the expression using the definitions of secant and tangent: cos(Θ)/cos(Θ) + sin(Θ)/cos(Θ) = sec(Θ) + tan(Θ)

Simplify the expression to arrive at the right-hand side of the identity: sec(Θ) + tan(Θ)

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Image transcribed:

1. Put the steps in order to verify the identity.

cos(-Θ)/1 + sin(-Θ) = sec Θ + tan Θ

↑↓ (cos Θ/1 - sin Θ) (1+ sin Θ/1 + sin Θ)

↑↓ (cos Θ + sin Θ cos Θ) / (1-sin² Ө)

↑↓ cos Θ + sin Θ cos Θ)/ cos² Θ

↑↓ cos Θ/(1- sin Θ)

↑↓ 1/cos Θ + sin Θ/ cos Θ

↑↓ sec Θ +tan Θ

Answer:

1) x < 30

2) x > 20

3) x >= 250

4) x > 20

5-10) I cant see the numbers on the graph

Step-by-step explanation:

Answer:

For the graphs you have to basically make those words into a mathematical equation to make more sense like for the first problem in which..

x>30

remember, open circles mean that its it can't be greater for symbols like < and >

closed circles are for inequalities that are greater than or equal to or less than or equal to which are these symbols: ≤ and ≥

Answer:

Step-by-step explanation:

12q + 3r = 15

-12q - 12r = -132

-9r = -117

r = 13

12q + 3(13) = 15

12q + 39 = 15

12q = -24

q = -2

(-2, 13)

b is the answer

Answer:

(-2,13)

Step-by-step explanation:

i took the test and can confirm its 100% on edge