Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given.
a = 6; d = -3
an = ?; 214 = ?
O A. an = 9-3n; 14 = - 15
O B. a, = 9+ 3n; 214 = -33
O c. a, = 6 - 3n; 214 = - 33
OD. an = 9 - 3n; 214 4 = -33

Answer:

104,758

Step-by-step explanation:

Answer:

$52

Step-by-step explanation:

Given data

Beth can buy T-shirts in packs of 5 for $5.55

Cost per shirt

=5.55/5

=$1.11

To buy 40 shirt

=1.11*40

=$44.4

In packs of 2 for $4.82

cost per shirt

=4.82/2

=$2.41

To buy 40 shirt

=2.41*40

=$96.4

Hence the best buy in packs of 5 for $5.55

and the cost per shirt is $1.11

He will save

=96.4-44.4

=$52

Answer:

dα/dt  =  - 0,25  rad/sec

Step-by-step explanation:

The vertical wall, the ground from the vertical wall up to the ladder, and the ladder shape a right triangle. angle α  will be the angle between the ladder and the ground, then:

cos α  = distance between the wall and the down end of the ladder (x)  /  length of the ladder

cos α   =  x/ L

- sin α * dα/dt   =  dx/dt * L /L²

- sin α * dα/dt   =  dx/dt /L

When   the down end of the ladder is 8 ft apart from the wall

cos  α   =  8 / 10   =  0,8  then    cos² α  +  sin²α  = 1

sin² α  =  1 - cos²α        sin²α =  1 - (0.8)²    sin²α  = 0.36

sin α  = 0.6

dα/dt  =  ?

dx/ dt  =  3/2

L  = 10 ft

x  =  8 ft

By substitution

- 0.6*dα / dt   = (3/2) / 10

dα/dt  =  -  1.5 / 6

dα/dt  =  - 0,25  rad/sec

(-) means the angle is decreasing

Step-by-step explanation:

hope this helped you :)) !!

Answer:

Option one (x-2)(x-3)

Step-by-step explanation:

We have x²-5x+6 =0

X²-3x-2x+6=0

X(x-3)-2(x-3)=0

(x-2)(x-3)=0

Answer:

25.7 in

Step-by-step explanation:

perimeter = 1/2(2)πr + 10 = 15.7 + 10 = 25.7 in

Answer:

5.600

Step-by-step explanation:

Answer:

Solution given:

x+x+10°+40°+2x+10=360[complete turn]

4x+60°=360

4x=360-60

x=300/4=75

now

2x+10=2×75+10=160° is your answer

Answer:

one square, four triangles

Step-by-step explanation:

It's a pyramid, so there's only 1 base.

A square has 4 faces, so to build up the pyramid from its base, we need 4 triangles to stick with the square base and to form a sharp vertex.

Answer: The width is 10.2 inches, the perimeter is 71.4, the area is 260.1.

Step-by-step explanation: So first i divided 25.5/5 which equals 5.1. The ratio is 2:5 so I know that i have to multiply 5.1x2 which is 10.2, thats how you get the width. The perimeter I just did 25.5+25.5+10.2+10.2 =71.4. For the area I just multiplied 25.5x10.2=260.1.

The width of the rectangle is 10.2 inches.

The perimeter of the recatngle is 71.4 inches.

The area of the rectangle is 260.1 square inches.

The perimeter of rectangle is given by;

[tex]\rm Perimeter \ of \ rectangle=2 (Length + width)[/tex]

The sides of a rectangle are in the ratio 2:5.

If the longer side of the rectangle is 25.5.

The shortest side of the rectangle is;

[tex]=\dfrac{25.5}{5}\\\\=5.1 \rm \ inches[/tex]

The width of the rectangle is;

[tex]\rm Width=2\times 5.1\\\\Width =10.2[/tex]

The width of the rectangle is 10.2 inches.

The perimeter of the recatngle is;

[tex]\rm Perimeter \ of \ rectangle=2 (Length + width)\\\\\rm Perimeter \ of \ rectangle=2 (25.5+10.2)\\\\\rm Perimeter \ of \ rectangle=2 \times 35.7\\\\\rm Perimeter \ of \ rectangle=71.4 \ inches[/tex]

The perimeter of the recatngle is 71.4 inches.

The area of the rectangle is;

[tex]\rm Area=length \times width\\\\Area=25.5\times 10.2\\\\Area=260.1 \ square \ inches[/tex]

The area of the rectangle is 260.1 square inches.

Learn more about rectangle here;

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The value of the expression is 86.

To evaluate the given expression, we need to simply put the given value of x in the mentioned expression. Subsequently, further operations will be performed based on the sequence in order of operators.

Value = 150 - (2 + x)³

Keep the value of x in the mentioned expression

Value = 150 - (2 + 2)³

Performing addition inside the bracket to find the value

Value = 150 - 4³

Taking cube on Right Hand Side of the equation

Value = 150 - 64

Performing subtraction to find the value of equation

Value = 86

Hence, the evaluation will give the result 86.

Learn more about evaluation of expression -

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Answer:

10

Step-by-step explanation:

Rolling a single six-sided die, you would get two 1/6th of the time because there is one two out of the six sides.

So 60 rolls would be 60*(1/6)=60/6=10

Answer:

x = 13

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = x^2

25+144 = x^2

169 = x^2

Taking the square root of each side

sqrt(169) = sqrt(x^2)

13 =x

Answer:

13

Step-by-step explanation:

[tex] \sqrt{5^{2} + 12^{2}} = \sqrt{169} \\ \\ \sqrt{169} = 13[/tex]

a²+b²=c²

Answer:

12.8 square meters

Step-by-step explanation:

244.48/19.1=12.8

Answer: Hm 1 second

Step-by-step explanation: 1 sec

Answer:

hope it helps.

Answer:

21.1cm

Step-by-step explanation:

Hello :)

The volume of a sphere can be found by this equation:

[tex]V=\frac{4}{3} \pi r^3[/tex] where V stands for volume and r stands for the radius in the sphere.

Since the volume is actually given to us and we need to find the radius, we can substitute in the numbers we know, and isolate the variable we are trying to find so we can get a concise answer.

[tex]V=\frac{4}{3} \pi r^3[/tex]

[tex]32398=\frac{4}{3} \pi r^3[/tex]

Now, let's isolate the r variable by dividing 4/3 and pi to the other side.

[tex]\frac{32398}{\frac{4}{3}\pi } =r^3[/tex]

We can get rid of the exponent by square rooting by 3.

[tex]\sqrt[3]{\frac{32398}{\frac{4}{3}\pi}} =r[/tex]

If we plug this into the calculator, the r=21.1

Which means the radius of the sphere is 21.1 cm.

Answer:

21.1 CM

[tex] \: \: \: \: \: \: \: [/tex]

Answer:

2.8 miles

Step-by-step explanation:

From the attached sketch of the solution diagram, let x = distance of plane from runway :

The sketch gives a right angled triangle ; hence, we can apply trigonometry :

To obtain x :

Sin θ = opposite / hypotenus

Sin 5 = 1266 / x

0.0871557 * x = 1266

x = 1266 / 0.0871557

x = 14525.720 feets

Converting feets to mile :

1 mile = 5280 feets

14525.720 feets = 14525.720 / 5280

2.751 miles

To the nearest tenth of a mile ; 2.8 miles

Answer:

18 centimeters.

Step-by-step explanation:

Since you already know the length (height) divide 20 by 5 = 4.

This gives you the width (4), add up all the sides ( 4 + 4 + 5 + 5).

The sum comes out to be 18.

Answer:

23x+1........ .... .........

Answer:

6x-48=4x-10

2x=38

x=19

Answer:

Step-by-step explanation:

90 + 34 = (l)

(l) = 124

Answer:

25%

Step-by-step explanation:

25% us the answer. First: work out the difference (decrease) between the two numbers you are comparing.

Decrease = Original Number - New Number

Then: divide the decrease by the original number and multiply the answer by 100.

Let's split this up into two shapes: a half-circle and a triangle.

First, we'll find the area of the half-circle. The formula for the area of a circle is: A = 3.14 * r^2. Therefore, the area of a half circle will be: A = 1/2 * 3.14 * r^2. Using our new formula, let's plug in what we know and solve.

A = 1/2 * 3.14 * 8^2

A = 1/2 * 3.14 * 64

A = 3.14 * 32

A = 100.48 m^2

Next, let's find the area of the triangle. The formula for the area of a triangle is: A = 1/2 * base * height. Using our formula, let's plug in what we know and solve.

A = 1/2 * 12 * 8

A = 6 * 8

A = 48 m^2

Finally, we need to add the area of the half-circle and the area of the triangle to find the area of the shape.

100.48 + 48

148.48 m^2

Hope this helps!! :)

Step-by-step explanation:

area of the triangle

[tex] \frac{1}{2} (12)(8) \\ \frac{1}{2} (96) \\ 48[/tex]

area of the half circle

[tex] \frac{1}{2} \pi {(8)}^{2} \\ \frac{1}{2} (3.14)(64) \\ \frac{1}{2} 200.96 \\ 100.48[/tex]

area of entire shape

[tex]48 + 100.48 \\ 148.48 {m}^{2} [/tex]

Answer:

h

Step-by-step explanation:

multiplication and inference

Answer:  (x, y) = (-26, 10)

This means x = -26 and y = 10 pair up together

===============================================================

How to get that answer:

Add the equations straight down. Think of having 3 separate columns for the three different like terms.

After all that, we're left with the simpler equation 3y = 30. That solves to y = 10 after dividing both sides by 3.

Plug this back into any equation involving x and y. Solve for x

3x+9y = 12

3x+9(10) = 12

3x+90 = 12

3x = 12-90

3x = -78

x = -78/3

x = -26

We have found that x = -26 and y = 10 pair up together to form the solution.

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

Checking the answer:

Plug (x,y) = (-26, 10) into the first equation

3x+9y = 12

3(-26)+9(10) = 12

-78+90 = 12

12 = 12

We get a true equation since the same thing is on both sides.

Repeat the same idea for the second equation

-3x-6y = 18

-3(-26) - 6(10) = 18

78 - 60 = 18

18 = 18

The second equation is true as well.

Both equations are true, so the solution (x, y) = (-26, 10) is confirmed.

Answer:

-26, 10

Step-by-step explanation:

See the steps below:)