please help 15 points

What is the closed linear form for this sequence given a1 = 27 and an + 1 = an - 2?
A) an = 14 - n
B) an = 30 + 2n
C) an = 27 + 4n
D) an = 29 - 2n

ANSWER

[tex]34 {units}^{2} [/tex]

EXPLANATION

The width of the rectangle is |AB|

A(-1,4) and B(3,3)

We use the distance formula,

[tex]d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]

This implies that,.

[tex]d = \sqrt{ {(3- - 1)}^{2} + {(3 - 4)}^{2} } [/tex]

[tex]d = \sqrt{ {(4)}^{2} + {( - 1)}^{2} } [/tex]

[tex]d = \sqrt{ 16+ 1 } [/tex]

[tex]d = \sqrt{17} [/tex]

The length is BC

C(1,-5) and B(3,3)

[tex]d = \sqrt{ {(3- 1)}^{2} + {(3 - - 5)}^{2} } [/tex]

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

[tex]d = \sqrt{4 + 64 } [/tex]

[tex]d = \sqrt{68} [/tex]

[tex]d = 2 \sqrt{17} [/tex]

The area is

[tex] = l \times w[/tex]

[tex] = 2 \sqrt{17} \times \sqrt{17} [/tex]

[tex]2 \times 17 = 34 {units}^{2} [/tex]

Answer:

[tex]f(x)=\frac{1}{4}x-4[/tex]

Step-by-step explanation:

To find the equation of a linear function , we pick two points from the graph

LEts pick two points (0,-4) and (4,-3)

Equation of linear function is [tex]f(x)=mx+b[/tex]

where m is the slope and b is the y intercept

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

(0,-4) is (x1,y1) and (4,-3) is (x2,y2)

[tex]slope m= \frac{y_2-y_1}{x_2-x_1}=\frac{-3+4}{4-0} =\frac{1}{4}[/tex]

y intercept is the point where the graph crosses y axis

y intercept [tex]b=-4[/tex]

Linear function becomes

[tex]f(x)=\frac{1}{4}x-4[/tex]

Answer:

a)26,31,36

Step-by-step explanation:

add by 5

26, 31, 36  next three terms in the sequence.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Given

a = 6

d = 11-6 = 5

aₙ = a + (n-1)d

n = 5, 6, 7

a₅ = 6 + (5-1)5

a₅ = 6 +20 = 26

a₆ = 6 + (6-1)5

a₆ = 6 +25 = 31

a₇ = 6 + (7-1)5

a₇ = 6 +30 = 36

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Answer:

12xy^2z^2

Step-by-step explanation:

The GCG or greatest common factor is the greatest value of number or expression which will divide into both expressions. Here 24 and 36 are both divisible by 12. Both also have the variables xy^2z^2. This means the GCG is 12xy^2z^2.

Answer:

f(x) reflect over the x-axis, vertically stretch by a factor 3, and

shift down 1 unit ⇒ 2nd answer

Step-by-step explanation:

* To solve this problem you must to know some fact about

  transformation

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

- A vertical stretching is the stretching of the graph away from

 the x-axis

• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically

 stretched by multiplying each of its y-coordinates by k.

- A vertical compression is the squeezing of the graph toward

 the x-axis.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed

 by multiplying each of its y-coordinates by k.

• if k should be negative, the vertical stretch or compress is

 followed by a reflection across the x-axis.  

* Now lets solve the problem

- From the graph

∵ The line passes through the points (0 , -1) and (-1 , 2)

∴ The slope of the line = (2 - -1)/(-1 - 0) = 3/-1 = -3

∵ The graph intersect the y-axis at point (0 , -1)

∵ The equation of any line ⇒ y = mx + c , where m is the slope

   of the line and c is the y-intercept

∵ m = -3 and y-intercept = -1

∴ y = -3x - 1 ⇒ g(x) = -3x - 1

∵ f(x) = x

* From all the transformation above

# -3x means the graph reflected over the x-axis, vertically stretch

  by a factor 3

# -1 means shift down 1 unit

# g(x) = -3f(x) - 1

∴ f(x) reflect over the x-axis, vertically stretch by a factor 3, and

  shift down 1 unit

* The second answer

B. 15m, 20m, 25m

use pythagorean theorem

a²+b²=c²

225+400=625

the square root of 625 is 25

Answer:

FIGURE IT OUT THIS IS SUPER BASIC YOU REALLY NEED TO DO THIS BY YOURSELF

Step-by-step explanation:

girl slope intercept form is just when you isolate y and whatever you do to one side you do to the other you just minus the extra term which isn't y and then you divide whatever is multiplied to y on each term and it's that easy

Answer:

2. y = -8x + 9

3. y = -1/6x - 1/3

4. y = -4/3x + 3

Step-by-step explanation:

the goal for 2, 3, and 4 is to get them into y = mx + b form. to do this, we need to isolate y on one side of the equation

2. 8x + y = 9 < subtract both sides by 8x

y = -8x + 9

3. x + 6y = -2 < subtract x from both sides

6y = -x - 2 < divide both sides by 6 to get y alone

6y/6 = y

-x - 2 / 6 = -1/6 - 1/3

y = -1/6x - 1/3

4. 4x + 3y = 9 < subtract 4x from both sides

3y = -4x + 9 < divide both sides by 3 to get y isolated

3y/3 = y

-4x + 9/3 = -4/3x + 3

y = -4/3x + 3

Answer: Option B

No solutions

Step-by-step explanation:

We have the following system of equations

[tex]2x - y = -6[/tex]    (1)

[tex]-4x + 2y = -9[/tex]   (2)

To solve the system using the substitution method, solve the first equation for the variable y

[tex]y=2x+6[/tex]

Now substitute the value of y in the second equation

[tex]-4x + 2(2x +6) = -9[/tex]

[tex]-4x + 4x +12=-9[/tex]

[tex]12=-9[/tex]

2 is not equal to -9, the system is inconsistent. The system has no solution

Answer:

No solution

Step-by-step explanation:

Given equations are 2x-y=-6 and -4x+2y=-9.

Now we need to solve that system of equation using substitution method.

solve 2x-y=-6 for y

2x-y=-6

-y=-6-2x

y=6+2x

Plug this value of y into other equation -4x+2y=-9

-4x+2(6+2x)=-9

-4x+12+4x=-9

12=-9

Which is a false equation.

Hence there is no solution to the given system.

Answer:

27.6

Step-by-step explanation:

https://brainly.com/question/12181840

credit to Calculista

Answer:

a=63.75

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer: a = -250

Step-by-step explanation:

1. Solve the left side: 0.5a + 0.5a = a

2. Subtract 0.9a to the other side which gives: a - 0.9a = -25

3. Solve the left side again: 0.1a = -25

4. Divide 0.1a to the right side to isolate a: a = -25/0.1

5. Now divide -25 / 0.1 to get a = -250

Answer:

Step-by-step explanation:

(f•g)(x) = f(g(x)) = f(1/x) = 1/x +7

You need to multiply the amount she makes per hour by the number of hours (t) she works.

The equation would be y = 16.8t

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

5d^2+4d-3-(2d^2-3d+4)

We need to find the correct difference.

Collect the like terms together.

5d^2+4d-3-(2d^2-3d+4)\\\\=5d^2+4d-3-2d^2+3d-4\\\\=5d^2-2d^2+4d+3d-3-4\\\\=3d^2+7d-7

Hence, First option is correct

Answer:

1st one :)

Step-by-step explanation:

Answer:

4 packages of fruits, 5 packages of chocolate

Step-by-step explanation:

We need to find the lowest common multiple of 12 and 15.

12 is ( 2 * 2 * 3) and 15 is (5 * 3).

The lowest common multiple would be three.

Then we can multiply 12 by 5 and 15 by 2 * 2.

The are both equal to 60.

Then we divide:

60 / 15 = 4, which is the amount of packages for the fruits

60/ 12 = 5, the packages of chocolates.

IF THIS WAS NOT THE ANSWER YOU WERE LOOKING FOR, PLEASE COMMENT.

To find the smallest number of packages needed to have the same amount of both fruit and chocolate pastries, calculate the LCM of 15 and 12, which is 60. Thus, one needs 4 fruit pastry packages and 5 chocolate pastry packages.

The student's question relates to finding the least common multiple (LCM) of two numbers, in this case, the number of pastries in each package. Mrs. Patterson's bakery sells fruit pastries in packages of 15, and chocolate pastries come in packages of 12. To find how many of each type of package one needs to buy to get the same number of both types of pastries, we need to calculate the LCM of 15 and 12.

The LCM of 15 and 12 is 60. This means the smallest number of fruit pastry packages (of 15) needed is 60 / 15, which equals 4. Similarly, the smallest number of chocolate pastry packages (of 12) needed is 60 / 12, which equals 5. Therefore, the person would need to buy 4 fruit pastry packages and 5 chocolate pastry packages to have an equal number of pastries.

well I know for a fact that the equation for a parabola is

[tex]ax^{2} + bx + c[/tex]

so obviously it is an equation for an ellipse, sadly I am not exactly sure whether the answer is b or c.(I'm leaning towards b)

hopefully I helped out by eliminating 2 options.

Brainliest people comment what the answer is!!!!

Have a great day

Answer:

Option d)

[tex]3x^2+y^2+6x-6y+3=0[/tex]

Step-by-step explanation:

we are given with the equation

[tex]3x^2+y^2=9[/tex]

Dividing both sides by 9 and simplifying we get

[tex]\frac{x^2}{3}+\frac{y^2}{9}=1[/tex]

[tex]\frac{x^2}{(\sqrt{3})^{2}}+\frac{y^2}{3^{2}}=1[/tex]

Which represents an ellipse. Hence we have an ellipse in our problem. And also  it is obvious that any translation or rotation of this ellipse will again result into en ellipse.

If we see the first two options , they are the equations of the parabolas hence they can not be answer to the problem.

Let us see the third equation.

It is

[tex]3x^2+y^2+3x-3y+3=0[/tex]

Let us transform this equation in perfect square form.

[tex]3x^2+3x+y^2-3y+3=0[/tex]

[tex]3(x^2+x)+y^2-3y+\frac{9}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x^2+x+\frac{1}{4}-\frac{1}{4})+y^2-3y+\frac{9}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x^2+x+\frac{1}{4})-3\times\frac{1}{4}+y^2-3y+\frac{9}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x+\frac{1}{2})^{2}+(y+\frac{3}{2})^{2}-3\times\frac{1}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x+\frac{1}{2})^{2}+(y+\frac{3}{2})^{2}=0[/tex]

Which represents the equation of an circle , Although Circle also comes in the category of an ellipse but it clearly not the same as we have in the problem in which the minor and major axis are different.

Hence this is also not our answer. So we have a clue that as the first three options are not correct , the right answer must be the forth one. Let us confirm it by converting it into a perfect square.

The equation given is

[tex]3x^2+y^2+6x-6y+3=0[/tex]

[tex]3x^2+6x+y^2-6y+3=0[/tex]

[tex]3(x^2+2x)+y^2-6y+9-9+3=0[/tex]

[tex]3(x^2+x+1-1)+y^2-6y+9-9+3=0[/tex]

[tex]3(x^2+x+1)-3+y^2-6y+9-9+3=0[/tex]

[tex]3(x+1)^{2}+(y-3)^{2}-3-9+3=0[/tex]

[tex]3(x+1)^{2}+(y-3)^{2}-9=0[/tex]

[tex]3(x+1)^{2}+(y-3)^{2}=9[/tex]

Which certainly represents an ellipse. hence this is our correct answer.

Answer:

- 2 and 10 with the difference with each other is 8 and the sum is twelve

Step-by-step explanation:

PLLZZZ MARK AS BRAINLIEST PLZZZZZ

Answer:

74

Step-by-step explanation:

52+22 = 74 this is the expression

Answer:

w = 21.4 ft

Step-by-step explanation:

Area of Trapezoid = Area = (a+b)/2 * h

Where a and b are the bases of trapezoid, and h is the height.

In the figure we are given:

a= 32.3 ft

b=w=?

h= 22.9 ft

Area = 614.865 ft²

Putting values in formula

Area = (a+b)/2 * h

614.865 = (32.3 + w) / 2 * 22.9

1229.73 = 32.3 + w * 22.9

1229.73 / 22.9 = 32.3 +w

53.7 -32.3 = w

=> w = 21.4 ft

The answer is negative 96

The answer to 8(-12) is - 96

Answer:

[tex](x+3)^2 + (y-4)^2 = 1[/tex]

Step-by-step explanation:

Equation of a circle can be found by

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]

Given center 3,-4 i.e

a= 3 and b=-4

and radius r = 1

Putting the values of a,b and r in the equation we get:

[tex](x-(-3))^2 + (y-4)^2 =(1)^2\\(x+3)^2 + (y-4)^2 = 1[/tex]

Answer:

[tex] {3}^{7} \times \frac{1}{ {3}^{4} } [/tex]

Answer:

a(n) = 12 * (13)^(n-1)

Step-by-step explanation:

First step is to determine what's the scale/multiplication factor between each term:

156 / 12 = 13

2028 / 156 = 13

So, since we got 13 between 1st, 2nd and 3rd term, we can be confident it's the right multiplication factor.

an would be the first term (12) multiplied by a factor of 13. So,

[tex]an = 12 * (13)^{n-1}[/tex]

If we try for n > 1, we have

a(2) = 12 * (13)^(2-1) = 12 * 13 = 156

a(3) = 12 * (13)^(3-1) = 12 * 13² = 12 * 169 = 2028

It matches!

Answer:

61.2

Step-by-step explanation:

The product of 918.642 and 1/10 is 91.8642.

Dividing this by 1.5 yields 61.2, which has been rounded off from 61.2428.

this is the answer to question one

3:1:2 = 90:30:60

and the answer to the second one

Answer: The answer to the cube one is 13 times 13 which gives u 169 and one of those is red so the ratio is 1 red cube to 168 black cubes or 1:168

Answer:

1/3

Step-by-step explanation:

There are 2 u's in August and there are 6 total letters if you divide 2/6. you get 1/3

The probability of selecting a 'u' is 1/3.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

The letters in the word August are placed into a bag.

There are two 'u' in the word August.

And the total letters are 6.

So, the probability of selecting one u,

= 2 / 6

= 1 / 3

Therefore, 1/3 is the probability.

To learn more about the probability;

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Answer:

Final answer is  [tex]a_0=-9[/tex]

Step-by-step explanation:

Given equation is [tex]5-a_0=14[/tex]

Now we need to solve the given equation [tex]5-a_0=14[/tex] for the unknownd variable  [tex]a_0[/tex] .

We can do that by isolating [tex]a_0[/tex]

To isolate [tex]a_0[/tex], let's subtract 5 from both sides

[tex]5-a_0-5=14-5[/tex]

[tex]-a_0=9[/tex]

multiply both sides by -1

[tex]-a_0(-1)=9(-1)[/tex]

[tex]a_0=-9[/tex]

Hence final answer is  [tex]a_0=-9[/tex]

ANSWER: 60 female lions

In the ratio there are 21 male lions and 20 female lions, in total 41 lions. Create a proportion relating the total number of lions in the ratio (41) and in the problem (123), and the number of female lions in the ratio (20) and in the problem (unknown).

20/41 = x/123

Cross multiply and solve

20(123)=41x

2460=41x

60=x

Answer:

X=20. Our x coordinate is 20.

Step-by-step explanation:

Based from the given slope of 1/2 and a y-intercept of -6, our equation of a line is y=x/2 -6. To remove the fraction we can multiply the equation by 2 to get 2y=x-12. Using this substitute the value of y coordinate 4.

2(4)= x-12

8+12 =x

X=20.

Answer:

20

Step-by-step explanation:

since the line has a slope of 1/2, the x coefficient of the line is 1/2. Since the y intercept is -6, we have the equation of the line

x/2 - 6 = y

Since in this case y = 4, we have

x/2 - 6 = 4

x/2      = 10

x          = 20

So the x coordinate is 20 when the y coordinate is 4.

Hope it helps and if it does, please mark me brainliest...

Answer:

B. 1

Step-by-step explanation:

Your answer for A is correct.

The time it take for the sub to hit the water will be the time between when the submarine started to get lowered and when its distance from the water was zero.

The sub started to get lowered at x = 0.

Now we need to solve for the smallest positive zero of the function.

This function factors to (x - 1)(x - 7)

From this we can tell that the submarine is a water level for time x = 1 and x = 7.

The smallest of these is 1, so that is when the submarine first hit the water and 7 is when it came back out.

The sub started getting lowered at x = 0 and hit the water at x = 1 and because x is in seconds, it took 1 second for the sub to hit the water.