These are the first four terms of a sequence, -2, 1, 8, 19. Write down the next term of this sequence.​

The equation of line having slope of 5/2 is given as 2y -5x = 8.

As, per the given question;

The slope of the line is given as; m = 5/2

The coordinates of the passing points (-2, -1).

Thus, (x₁, y₂) = (-2, -1).

The equation of the becomes.

(y - y₁) = m (x – x₁)

Put the values;

y - (-1) = (5/2)(x - (-2))

Simplifying

y + 1 = (5/2)(x + 2)

2y + 2 = 5x + 10

2y -5x = 8

The equation of line is calculated as 2y - 5x = 8.

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Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

[tex]5x + 3x = 8 +48[/tex]

  ⬇️

8x = 8 + 48

          ⬇️

  8x = 56

Divide both sides of the equation by the coefficient of the variable;

[tex]x = \frac{56}{8}[/tex]

Cross out common factors;

[tex]x=7[/tex]

If Lee is laying out a design for the tiles of a section of his bathroom floor and he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design then the number of white and black tiles Lee will use is equal to 4 and 24 respectively.

The number of white and black tiles Lee will use can be determined by using an algebraic expression.

As 1 white tile is used for every 6 black tiles, an algebraic expression can be represented as,

x + 6x = 28

By solving the value of x, the number of each type of tile that Lee will use can be calculated,

x + 6x = 28

7x = 28

x = 28 ÷ 7

x = 4

As there is one white tile for every six black tiles,

White tiles = 1(x) = 1(4) = 4

Black tiles = 6(x) = 6(4) = 24

Hence the number of white tiles Lee will use is equal to 4 and the number of black tiles Lee will use is equal to 24.

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A circle is a curve sketched out by a point moving in a plane. The diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that radius of the circle is x/8 units. Therefore, the diameter and the circumference of the circle can be written as,

Diameter of circle = 2 × (Radius of the circle)

                             = 2 × (x/8) units

                             = x/4 units

Circumference of circle = 2 × π × (Radius of the circle)

                                       = 2 × π × (x/8) units

                                       = (x/4)π units

Hence, the diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.

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Answer:

f(-4) = -7

g(-7) = 9

Step-by-step explanation:

f(x) = 2x + 1

f(-4) = 2(-4) + 1 = -8 + 1 = -7

g(x) = x^2 - 40

g(-7) = (-7)^2 - 40 = 49 - 40 = 9

Answer:

4°=1

g g g g g g g g g g

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x+5=6x-3​

subtract 6x

2x-6x+5=6x-6x-3

-4x+5=-3

subrtract-5

-4x+5-5= -3-5

-4x=-8

divide-4

-4x÷-4=-8÷-4

x=2

The sum of the given finite series is 75

The given series is:

[tex]\sum\limits^{10}_{n=5} {(20-n)}}[/tex]

To find the sum of this series,

Expand the summation notation by using the properties of sum operator:

Σ(a+b) = Σa + Σb

Hence,

[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]

If a is a constant, then Σa = k. a, where k is the number of terms = upper limit - lower limit + 1

Using this property:

[tex]\sum\limits^{10}_{n=5} {20} = (10 - 5+1)\times20=6\times20=120[/tex]

Expand

[tex]\sum\limits^{10}_{n=5} {n}=5+6+7+8+9+10=45[/tex]

Hence,

[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]

= 120 - 45 = 75

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Answer: The value of x is 20.

Algebraic function :

Given function is,  

We have to find the value of x when

The value of x is 20.

Step-by-step explanation: hope this helps

Answer:

c = (y+8)/d

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

the plane is 180 degrees

subtract 2x4

172

divide by 4

43

BOOM

Answer:

15y+14

Step-by-step explanation

Answer: 14 + 15y

Step-by-step explanation:

E = Eileen’s age = 3y

M = Mum’s age

Total Age = 14 + 3y + 4(3y)

                =  14 + 15y

Total age in 7 years time is their current ages plus 7 years for each (14 years)

Eileen is 3y, and her mum is 4 times that, which is 12y, meaning that their total ages are 3y + 12y, or, 15y.

Total age is then 15y + 14. Since we don’t know what y equals, we cannot add these two terms, and we can just leave them like that!

So, the answer is 14 + 15y.

We can say that if the measure of angle 1 = (7x-19), and the measure of angle 2 = (x+5), then the measure of angle 2 is 18°.

Define supplementary angle.

Supplementary angles are those two angles whose sum is always equal to 180 degrees.

Mathematically, a supplementary angle is calculated as follows:

Q + R = 180

Since the angles on this line segment are supplementary angles, we have:

Angle (1) + Angle (2) = 180° - Angle 3

Substituting the given values into the formula, we get;

7x - 19 + x + 5 = 180 - 90

8x - 14 = 90

8x = 90 + 14

8x = 104

x = 104/8

x = 13

Now, we can calculate the length of angle 2 by putting the 'x' value:

Angle 2 = x + 5

Angle 2 = 13 + 5

Angle 2 = 18°

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The conditional probability formula for P(B | A) has been derived from two dependent events P(A and B).

When the outcome from one event influences the outcome of the other, two events are referred to as dependent.

Derivation of conditional probability from two dependent events P(A and B) is-

The probability multiplication rule is used to derive the conditional probability formula, P(A and B) = P(A)×P(B|A).

This rule is also known as P(AB). The Union symbol (∪) represents "and," as in event A occurring and event B occurring.

Step 1: Write the multiplication rule down:

           P(A and B) = P(A)*P(B|A)

Step 2: P(A) divides both sides of the equation:

           P(A and B) / P(A) = P(A)*P(B|A) / / P(A)

Step 3: On the right side of the equation, cancel P(A):

           P(A and B) / P(A) = P(B|A)

Step 4: Rewrite the equation as follows:

           P(B|A) = P(A and B) / P(A)

Therefore, P(B | A) conditional probability formula is compiled from two dependent events P (A and B).

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the estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104,000 and Actual 1,305 × 81 = 105,706

The correct option is D.

In the given statement is:

Find 1, 305 x 81. Then estimate to check your answer.

The estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104000 and Actual 1,305 × 81 = 105706

How to estimate and then compute the product check that your answer is reasonable?

The product expression is given as

1,305 × 81

As an estimate, we have

1305 = 1300

81 = 80

So, we have:

1,305 × 81 ≈ 1300 * 80

Evaluate the product

1,305 × 81 ≈ 104000

For the actual product, we have

The estimate and the actual product both approximate to 100000

Hence, the estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104,000 and Actual 1,305 × 81 = 105,706

The correct option is D.

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The population of city 10 years ago before 30% decrease in population was 500,000

In the given statement is :

A city has a population of 350,000.The population has decreased by 30% in the past ten years.

The formula for calculating the percent change between two values over the time is given by:

[tex]p=\frac{A-B}{B}[/tex]×[tex]100[/tex]

where,

'p' represents the percent change

'A' represents the New value

'B' represents the Old value

Since, p is the percent (decreased) = -30

Substitute the given values and solve for B;

then;

[tex]-30=\frac{350,000-B}{B}[/tex] × 100

Divide both sides by 100 we get;

[tex]-0.3=[/tex] [tex]\frac{350,000-B}{B}[/tex]

By cross multiply we get;

-0.3B = 350,000 - B

Add both sides B, we get

-0.3B + B = 350,000

0.7B = 350,000

Divide both sides by 0.7 we get;

B = 500,000

Therefore, The population of city 10 years ago before 30% decrease in population was 500,000

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The first step in simplifying the expression 2(x+3)+5 = 2x+2(3)+5.

Given expression in 'x' is 2(x+3)+5.

In order to simplify this expression, we need to expand it by opening the parenthesis. That is, we need to distribute 2 over (x+3) first. For this we multiply 2 into (x+3) and then only we can add 5 to it.

So, 2(x+3) +5 = 2x + 2(3) +5

                     = 2x +6 +5

                     = 2x+11

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Answer:

5

Step-by-step explanation:

[tex]d=\frac{|-3(5)-4(5)+10|}{\sqrt{(-3)^2+(-4)^2}}=5[/tex]

The diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.

An average is a mean or the central value obtained by dividing the sum of all data values by the number of data values.

Diver            Crabs observed     Dives     Average Crab per dive

Scuba Sam              33                     11               3

Wet Suit Willy          81                     18              4.5

Deep Diving Dan  104                    26              4

Thus, the diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.

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The value of f(-3) is 15.

The given function is f(x) = -3x+6. Now, f(-3) = x = -3

Substituting and Evaluating the value of x in the equation f(x) = -3x+6, we get

f(-3) = -3(-3)+6f(−3)=−3(−3)+6

f(-3) = 9+6f(−3)=9+6

f(-3) = 15f(−3)=15

∴ The value of f(-3) for the function f(x) = -3x+6 is equal to 15.

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Answer: $39.62

Step-by-step explanation: To get the answer to the cost of Peter's three items, I took the prices of the three and added them together. This amount would be the amount he paid WITHOUT TAX.

Part a

[tex]\frac{\pi}{3} > \frac{\pi}{4} \implies f(\pi/3)=\sin(\pi/3)=\boxed{\frac{\sqrt{3}}{2}}[/tex]

Part b

[tex]\frac{\pi}{6} \leq \frac{\pi}{4} \implies f(\pi/6)=2+\cos(\pi/6)=\boxed{2+\frac{\sqrt{3}}{2}}[/tex]

Part c

[tex]\frac{\pi}{4} \leq \frac{\pi}{4} \implies f(\pi/4)=2+\cos(\pi/4)=\boxed{2+\frac{1}{\sqrt{2}}}[/tex]

Identify the property illustrated by the equation.5+(-5)=0  Additive Inverse

What is an additive Inverse ?

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For the given situation, we can clearly say that the change in one quantity will cause a change in the second quantity as well.

Correlation is a relationship between the values ​​of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.

Causality means that one event causes another. Causality can only be determined by well-designed experiments. In such experiments, similar groups receive different treatments, and the results of each group are examined.

From the above information, we concluded that a person's age and the number of cassette tapes he/she owns are correlated more he lives the more he buys the cassette tapes. So we can make relation from this,

Person's Age ∝ Number of Cassette

This clearly states that by increasing/changing one quantity we will increase/change the other quantity as well.

Similarly, now that they have a direct relation if we decrease the Age of the person, the number of Cassette's will also decrease. A positive correlation we can call it.

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Answer:

(0, - 9 )

Step-by-step explanation:

the y- intercept is where the line crosses the y- axis

the line crosses the y- axis at (0, - 9 ) and is the y- intercept

The resultant velocity is about 12.3 feet per second at a heading of 8.4°east of north, <1.8, 12.14>

In this question,

Amy is paddling her canoe across a lake at a speed of 10 feet per second headed due north.

The wind is blowing 40°C east of north with a velocity of 2.8 feet, per second.

We need to find Amy's resultant velocity.

We write the direction vector for Amy in component form.

Due north is equivalent to 90° from the horizontal.

x-component:

x = 10 cos(90°)

x = 0

And y-component:

y = 10 sin(90°)

y = 10

The component form for Amy’s vector is <0, 10>.

Now we write the direction vector for wind in component form.

40 east of north is equivalent to 50° from the horizontal.

x-component:

x = 2.8 cos(50°)

x = 1.8

And y-component:

y = 2.8 sin(50°)

y = 2.14

The component form for the wind’s vector is <1.8, 2.14>

Add the vectors for Amy and the wind.

<0, 10> + <1.8, 2.14> = <1.8, 12.14>

Now, we determine the vector's magnitude by using Pythagoras theorem.

Let v be the velocity of Amy.

Let θ be the angle made by Amy with the horizontal

⇒ tan(θ) = |y/x|

⇒ tan(θ) = |12.14 / 1.8|

⇒ θ = 81.6°

81.6° with the horizontal is equivalent to 8.4° east of north.

Therefore, the resultant velocity is about 12.3 feet per second at a heading of 8.4°east of north, <1.8, 12.14>

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Using Gaussian elimination, the solution to the given system of equations is given as follows:

x = 5, y = -11, z = 3.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the equations are given as follows:

(I suppose there was a typing mistake on the first equation, as Gaussian elimination can only be applied to solve linear systems).

For Gaussian elimination, the first step is building the matrix of the system, in which:

Hence, the matrix of the system is given as follows:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]

Then, we need to make the coefficient of x zero in the second and third rows, hence:

Then the matrix will be given by:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]

Now we need to make the coefficient of y on the third row zero, hence:

R3 -> 11R2 + 5R3.

Then:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]

From the third row, we have that:

40z = 120

z = 120/40

z = 3.

From the second row, we have that:

5y - 10z = -85

5y - 30 = -85

5y = -55

y = -11.

From the first row, we have that:

2x - y + 4z = 33

2x + 11 + 12 = 33

2x = 10

x = 5.

Hence the solution of the system is given by:

x = 5, y = -11, z = 3.

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Step-by-step explanation:

I'm not sure but this is the solution hehe