The recursive formula for an arithmetic sequence is:
a1 = -10
an = an-1+3
What is the 3rd term in the sequence?
A. -16
B. -30
C. -7
D. -4

Answer: x = 7

Step-by-step explanation:

First, we will plug 4 in for y. Then, to solve we will isolate the variable "x" in the equation.

  Given:

8x – 2y = 48

  Plug in the y value of 4:

8x – 2(4) = 48

  Multiply -2 times 4:

8x – 8 = 48

  Add 8 to both sides of the equation:

8x = 56

  Divide both sides of the equation by 8:

x = 7

Answer:

x=7

Step-by-step explanation:

8x – 2y = 48

Let y=4

8x -2(4) = 48

8x - 8 = 48

Add 8 to each side

8x-8+8= 48+8

8x = 56

Divide by 8

8x/8 = 56/8

x = 7

Answer:

If two things have the same shape and size then they are congruent to one another. If they are only the same shape but not size, then they are similar.

If two things have the same shape and size then they are congruent to one another.

If they are only the same shape but not size, then they are similar.

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The explicit formula for the sequence is 3n -10

An arithmetic sequence is a series of terms which have  common difference between its consecutive numbers.

The sequence given is

−7, −4, −1, 2, 5, …

The common difference between each term is d =3

-4-(-7) = 3

-1-(-4) =3

The nth term for a sequence is given by

[tex]\rm T_n = a +(n-1)d[/tex]

Here a is the first term = -7

n is the no. of terms  = n

d is the common difference = 3

Therefore the equation will be

[tex]\rm T _n = -7 + (n-1) * 3[/tex]

[tex]\rm T _n[/tex] = -7 +3n -3

[tex]\rm T _n[/tex] = 3n -10

Therefore the explicit formula for the sequence is 3n -10 .

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From the given diagram <msr is a right angle (equal to 90 degrees) and <mrh is acute since it is less than 90degrees.

The given diagram is a rhombus that has the following properties

From the figure shown, we can see that;

<msr is a right angle (equal to 90 degrees)

<mrh is acute since it is less than 90degrees.

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Answer:

A (it must be acute)

Step-by-step explanation:

The point (0, 0) is a solution to which of these inequalities are satisfied. so option B. y-7<2x-6is the only correct answer.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

The point (0, 0) is a solution to which of these inequalities are satisfied.

A. y+7<2x - 6

      7 < -6

So, it is incorrect.

B. y-7<2x-6

      -7 < -6

So, it is correct.

C. y-6<2x-7

         -6 < -7

So, it is incorrect.

D. y+7<2x+6

7 < 6

So, it is incorrect.

Hence, option B is the only correct answer.

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Answer: The Actual area of the dining room is 252 square feet.

Explanation:

How to Find the Actual Area Using Scale?

Given that the area of the house on a blueprint = is 7 square inches.

The scale of the blueprint = is 1 inch: 6 feet.

Therefore, we would have the following proportion:

The area on the blueprint/actual area = square of the scale

7/actual area = 1²/6²

7/actual area = 1/36

Actual area = (7)(36)

Actual area = 252 square feet.

Mrs. Phillips needs to buy 8 packs of floor boards

In contrast to a square, a rectangle is a planar figure having four equal neighboring sides, four straight sides, and four right angles. An enclosed 2-D form called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposing sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.

As per the figure attached Mrs. Phillips floor plan can divided into two rectangles

The area of rectangle is as follow:

Area = length(l) x Width(w)

Area of part 1 will be:

A = 6 x 2 = 12 m²

Area of part 2 will be :

a = 3 x 2 = 6 m²

Total area of floor = A + a

Total area of floor = 12 + 6

Total area of floor = 18 m²

Given one pack of floor boards will cover 2.5 m².

So total pack of floor block needed will be as follow:

Total pack of floor block = Total area of floor/Area covered by one pack of floor boards

Total pack of floor block = 18/2.5

Total pack of floor block = 7.2 packs ≈ 8 packs

Hence Mrs. Phillips needs to buy 8 packs of floor boards

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The maximum number of visits you can make with each membership is 104.

Gym membership refers to the cost to register, attend, and use a gym as a member for an agreed period.

Some gym memberships require one-time payments made monthly or annually.

Assume that the annual gym fee is $200 for Saturdays and Sundays only.

Thus, in this scenario, the maximum number of visits you can make with each membership is 104.

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9x + 3 = 30
9x = 27
x = 3

Then 3x + 1 = 3 * 3 + 1 = 10

[tex]9x + 3 = 30 \\ \\ 9x = 30 - 3 \\ \\ 9x = 27 \\ \\ x = \frac{27}{9} \\ \\ x = 3.[/tex]

putting x = 3 in 3x + 1

[tex]3x + 1 \\ \\ 3 \times 3 + 1 \\ \\ 9 + 1 \\ \\ 10.[/tex]

The value of 3x + 1 is 10.

The equation of the function is f(x) = x(x + 2)(x -1)(x -3)

From the graph, we have the following highlight:

The above means that:

f(x) approaches positive infinity irrespective of the x value

Hence, the end behavior of the function is:

[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]

Since, the function opens upward.

Then the sign of the leading coefficient is positive

This is the point, where the graph crosses the x-axis.

From the graph, we have the zeros to be:

x = -2, x = 0, x = 1 and x = 3

Since the graph crosses the x-axis at this point, then the multiplicity of the zeros is 1

In (c), we have:

x = -2, x = 0, x = 1 and x = 3

Rewrite as:

x + 2= 0, x = 0, x - 1 = 0 and x - 3 = 0

Multiply these values

f(x) = x(x + 2)(x -1)(x -3)

Hence, the equation of the function is f(x) = x(x + 2)(x -1)(x -3)

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Answer:

yeheheehejehejejejjejjejejejejje

Answer:

[tex]m \times H=\left[\begin{array}{c c c}\boxed{-9} & \boxed{36} & \boxed{-\dfrac{9}{2}}\end{array}\right][/tex]

Step-by-step explanation:

Calculate the value of m

Given:

[tex]3\left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]=\dfrac{2}{3}m \times \left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right][/tex]

Therefore:

[tex]\implies 3=\dfrac{2}{3}m[/tex]

[tex]\implies m=3 \times \dfrac{3}{2}[/tex]

[tex]\implies m=\dfrac{9}{2}[/tex]

Calculate the value of H

Given:

[tex]\left(H+ \left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]\right)+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]=\left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]+\left(\left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]\right)[/tex]

Therefore:

[tex]\implies H= \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]

Calculating m × H

[tex]\implies m \times H=\dfrac{9}{2} \times \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]

[tex]\implies m \times H=\left[\begin{array}{c c c}\dfrac{9}{2}(-2) & \dfrac{9}{2}(8) & \dfrac{9}{2}(-1)\end{array}\right][/tex]

[tex]\implies m \times H=\left[\begin{array}{c c c}-9 & 36 & -\dfrac{9}{2}\end{array}\right][/tex]

The equation represents the amount of juice that remains, y, after x students are served is y = negative one-half x + 32; option C

y = 32 - 1/2x

This can also be written as;

y = -1/2x + 32

Therefore, the correct answer is option C; y = -1/2x + 32

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Answer:

y = [tex]\frac{1}{5}[/tex] x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{5}[/tex] x + 4 ← is in slope- intercept form

with slope m = [tex]\frac{1}{5}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{1}{5}[/tex] x + c ← is the partial equation

to find c substitute (5, - 4 ) into the partial equation

- 4 = 1 + c ⇒ c = - 4 - 1 = - 5

y = [tex]\frac{1}{5}[/tex] x - 5 ← equation of parallel line

Answer:

x = 3/2 ± [tex]\sqrt{5}[/tex] /2

Step-by-step explanation:

4x²-12x+9 = 5

Rearrange:

4x²-12x+4 = 0

Solve using the quadratic equation:

x = 3/2 ± [tex]\sqrt{5}[/tex] /2  

The probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The question is incomplete.

The complete question is:

Insurance company executives surveyed 200 young adults about their first motor vehicle. The results of the survey are given in the following two-way table(please refer to the attached picture)

A survey participant is randomly selected. Let F be the event that the participant’s first motor vehicle had four cylinders and let C be the event that the participant’s first motor vehicle was a car. What is the value of P(F or C)?

We have to find the value of P(F or C):

[tex]\rm P( F \ or \ C) = \dfrac{118+6+18+16+2}{118+6+18+16+12+20+2+6+2}[/tex]

[tex]\rm P( F \ or \ C) = \dfrac{160}{200}[/tex]

P(F or C) = 0.80

Thus, the probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.

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A number written in scientific notation has a Negative Exponent that indicates the digits used in the number and is always written with 1 digit to the left of the decimal place.

The coefficient is always a number larger than or equal to one and less than ten in scientific notation. There is an integer exponent. When using scientific notation to write integers bigger than ten

As a result, when a number is smaller than 1, it will have a negative exponent in scientific notation.

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Answer: In the first week, Micah bought 11 gallons of gas,

and in the second week, he bought 8 gallons of gas

Step-by-step explanation:

In the first week, Micah bought x gallons of fuel at $2.39/gallon

In the second week, he bought (x - 3) gallons at $2.49/gallon

Formulating an equation and solving for x gallons of fuel:

x × 2.39 + (x - 3) × 2.49 = 46.21

2.39x + x × 2.49 − 3 × 2.49 = 46.21

2.39x + 2.49x − 7.47 = 46.21

4.88x − 7.47 = 46.21

4.88x = 53.68

[tex]\frac{4.88x}{4.88} = \frac{53.68}{4.88}[/tex]

x = 11

Therefore,

In the first week, Micah bought 11 gallons of gas

In the second week, he bought (11 - 3) = 8 gallons of gas

The e vertex of the decagon will be in the top position after rotating it counterclockwise by 3 times the smallest angle of rotation.

Which vertex will be in the top position of the regular decagon?

A regular decagon has 10 sides of equal lengths with points labeled 'a' through 'j' clockwise. It is given that the point a is the top-left point. Hence, the the vertex which is in the the top position currently is 'b'.

Now, the smallest angle of rotation will be the angle between the two sides of the decagon.

In the first rotation by the smallest angle in counterclockwise direction, point 'c' will come to the top position. In the second rotation by the smallest angle in counterclockwise direction,  point 'd' point will become the top most vertex. Finally, after the third similar rotation, 'e' vertex will be in the top position of the decagon. (Refer the attached diagram)

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It looks like you're saying

[tex]f(x) = ax^2 + bx + c[/tex]

and you're asked to find [tex]a,b,c[/tex] given [tex]f(0)=-4[/tex], [tex]f(1)=-1[/tex], and [tex]f(-1)=-5[/tex].

Evaluate [tex]f[/tex] at the three given points:

[tex]x=0 \implies f(0) = \boxed{c = -4}[/tex]

[tex]x=1 \implies f(1) = -1 = a + b + c \implies a+b = 3[/tex]

[tex]x=-1 \implies f(-1) = -5 = a - b + c \implies a - b = -1[/tex]

[tex](a+b) + (a-b) = 3 + (-1) \implies 2a = 2 \implies \boxed{a=2}[/tex]

[tex]a-b = -1 \implies \boxed{b=3}[/tex]

and the mapping is [tex]f(x) = 2x^2 + 3x - 4[/tex].

Answer: The perimeter of this triangle is 13.47.

Step-by-step explanation:

First you should choose your first two points on the triangle that are on the same line. In this case I'll start with C = (3,3) and B = (8,6)[tex]d = \sqrt{(3 - 8)^2 + (3-6)^2}[/tex]

*Note: Keep X and Y consistent in the distance equation.

The distance for CB = 5.831

After finding this distance continue onto a new set of points to find a new length of the triangle, my second set of points will be A = (5,7) and B = (8,6) to find the length of AB.

[tex]d = \sqrt{(5 - 8)^2 + (7-6)^2}[/tex]

The distance for AB = 3.162

Now you're going to need to use your final to points, in this case for me A and C, and find the length of your final segment. So, I'll use point A = (5,7) and point C = (3,3).

[tex]d = \sqrt{(5 - 3)^2 + (7-3)^2}[/tex]

The distance for AC =4.472

Then find the perimeter by adding up the three side lengths.

AB + CB + AC = P

[tex]5.831 +3.162+4.472=13.465[/tex]

Finally, round 13.465 to the nearest hundredth, 13.47.

*Note: Make sure not to round your answer until the end of the problem to avoid less accurate or even wrong answers.

Answer: A,B,C

Step-by-step explanation: A,B,C is the answer

Answer:

Length = 30

Width = 17

Step-by-step explanation:

Let L = length of rectangle and W = Width

The first sentence gives the equation

W = L/2 + 2 ==>

2W = L +4 ==>

L = 2W - 4 ....  (1)

The perimeter of the rectangle is 2(L+W) = 2L +2W

Second sentence gives us the equation

4L = 2L + 2W + 26 ===>
2L = 2W + 26 ......   (2)

(2) - (1) ==> L = 30   (2W cancels out)

From (1), W = 30/2 + 2 = 15 + 2 = 17

Check:
Using these values and substituting in equation 2 gives us
2 * 30 = 2* 17 + 26
60 = 34 + 26
which matches

Answer:

no

Step-by-step explanation:

if I use any numbers too  .the numbers can not be constant numbers so this equation is not a direct variation

7 - 5 = 2

6- 4 = 2                                                        

not contstant

Answer:

4020 grams

Step-by-step explanation:

4kg=4000g

2 dag= 20g

Total: 4000g + 20g = 4020g

Answer:

4020 grams

Step-by-step explanation:

1 kg = 1000 g
1 dag = 10 g
4 x1000= 4000
2 x 10 = 20
4000 + 20

Answer:

  (4, -2)  (see attached)

Step-by-step explanation:

Vector addition on a graph is accomplished by placing the tail of one vector on the nose of the one it is being added to. The negative of a vector is in the direction opposite to the original.

__

The components of the vectors are ...

  u  = (1, -2)

  v = (-6, -6)

Then the components of the vector sum are ...

  2u -1/3v = 2(1, -2) -1/3(-6, -6) = (2 +6/3, -4 +6/3)

  2u -1/3v = (4, -2)

The sum is shown graphically in the attachment. Vector u is added to itself by putting a copy at the end of the original. Then the nose of the second vector is at 2u.

One-third of vector v is subtracted by adding a vector to 2u that is 1/3 the length of v, and in the opposite direction. The nose of this added vector is the resultant: 2u-1/3v.

The resultant is in red in the attachment.

The answer is (4, -2) hope this helps!

The real number of the given expression is a=-2.

Given that the expression is [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex]

Real numbers is known as the union of both rational and irrational numbers. Real numbers can be both positive or negative and are denoted by the symbol “R”.

To compute the value of a.

In the given expression multiply both sides with (a³+7) as

[tex]\frac{(a^3+7)}{a^3+7}-7=\frac{-a^3(a^3+7)}{a^3+7}[/tex]

Simplify the expression as,

1-7(a³+7)=-a³

Expand out terms of the left hand side

1-7a³-49=-a³

-7a³-48=-a³

Taking out minus common from both sides and cancel them

-(7a³+48)=-(a³)

7a³+48=a³

Add -a³-48 on both sides

7a³+48-a³-48=a³-a³-48

6a³=-48

Divide both sides with 6

(6÷6)a³=(-48÷6)

a³=-8

write -8 in the expansion form which is (-2)×(-2)×(-2)=-8

a³=(-2)³

From above it says that

a=-2

Hence, real number that satisfy [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex] is a=-2.

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