The term to term rule of a sequence is "multiply by 3 and add 1". The third term is 13. Work out the first term of the sequence.

Answer:

the correct answer is b. Initially the car is 420 miles from its destination.

Step-by-step explanation:

Answer:

aₙ = 30 - 5n

Step-by-step explanation:

25,20,15,10, ...

We see from the given series that it is AP with:

Then formula is:

Answer:

(5, 2)

Step-by-step explanation:

(5, 6) go down 4 units means subtract 4 from the y

(5, 2)

The point to end up will be (5, 2).

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

In the first quadrant you start at (5, 6 ) and move 4 units down.

Now,

Since, In the first quadrant you start at 5, 6 and move 4 units down.

Hence, The end up point = (5, 6 - 4)

                                       = (5, 2)

Thus, The point to end up will be (5, 2).

Learn more about the coordinate visit:

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Answer:

4 1/3

Step-by-step explanation:

3 + 5 + 4 + 3 + 5 + 6 = 26

26/6 = 4 2/6 (4 1/3)

Answer:

13/3

Step-by-step explanation:

To find the mean, add up all the numbers and divide by the number of terms

( 3+5+4+3+5+6) /6

26/6

Divide top and bottom by 2 to simplify the fraction

13/3

Answer:

Weight of wastage=179.775kg

weight of rice cultivated= 585.225 kg

percentage of rice cultivated=76.5%

Step-by-step explanation:

Area of land=100 square meters

Cultivated rice=765kg

Wastage=23.5%

1) Weight of the wastage=23.5% of 765kg

=23.5/100 × 765

=17977.5 / 100

=179.775 kg

2) Weight and percentage of rice cultivated.

weight of rice cultivated = 765 kg - 179. 775 kg

= 585.225 kg

percentage of rice cultivated = 100 - 23.5

= 76.5%

3) if area is increased 40 times in size

New area=1000 square meters × 40

=40,000 square meters

Cultivated rice= 765kg × 40

=30,600 kg

Cultivated rice excluding wastage=585.225 kg × 40

=23,409 kg

Answer:

Step-by-step explanation:

Time spent in studies = [tex]1 \frac{3}{4} [/tex]

Time spent in playing cricket = [tex]2 \frac{1}{2} [/tex]

Now, let's find the hours that he spent at all:

[tex] \mathsf {1 \frac{3}{4} + 2 \frac{1}{2} }[/tex]

Convert mixed fraction into improper fraction

[tex] \mathsf{ = \frac{7}{4} + \frac{5}{2} }[/tex]

Take the LCM

[tex] \mathsf{ = \frac{7 + 5 \times 2}{4} }[/tex]

Multiply the numbers

[tex] \mathsf{ = \frac{7 + 10}{4} }[/tex]

Add the numbers

[tex] \mathsf{ = \frac{17}{4} }[/tex]

Convert the improper fraction into mixed fraction

[tex] \mathsf{ = 4 \frac{1}{4} }[/tex] hours

Hope I helped!

Best regards!

Answer:

360,000

Step-by-step explanation:

When you square something you multiply it by itself. With that in mind, 600 square or 600^2 would be 600x600 which equals 360,000. Please mark as brainliest.

Answer:

3.03 • 10⁻³ is scientific notation

0.00303 is decimal form

Answer:

The x coordinate of P is [tex]\frac{4}{3}[/tex].

Step-by-step explanation:

Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:

[tex]\frac{dy}{dt} = 2\cdot x \cdot \frac{dx}{dt} -2\cdot \frac{dx}{dt}[/tex]

According to the statement of the problem, these variables are known:

[tex]\frac{dx}{dt} = 6[/tex] and [tex]\frac{dy}{dt} = 4[/tex]

Hence, the x coordinate of P is found by direct substitution:

[tex]4 = 2\cdot x \cdot (6)-2\cdot (6)[/tex]

[tex]4 = 12\cdot x -12[/tex]

[tex]x = \frac{4}{3}[/tex]

The x coordinate of P is [tex]\frac{4}{3}[/tex].

Answer:

x = 21.25 , y = 5

Step-by-step explanation:

In a parallelogram

Consecutive angles are supplementary

Opposite angles are congruent, thus

125 + 4x - 30 = 180

4x + 95 = 180 ( subtract 95 from both sides )

4x = 85 ( divide both sides by 4 )

x = 21.25

8y² = 125 ( divide both sides by 5 )

y² = 25 ( take the square root of both sides )

y = [tex]\sqrt{25}[/tex] = 5

Answer:

169.74

Step-by-step explanation:

this problem is like a triangle, the sun, mars, and earth are the three points, so you just use a^2 + b^2 =  c^2 so basically

93^2 + 142^2 = c^2

8649 + 20164 = 28813

28813 square root = 169.74

Answer:

  2 × (14 – 9) – (17 – 14) = 7

Step-by-step explanation:

Evaluate the choices to see which is true.

(2 x 14) – 9 – (17 – 14) = 7   ⇒  28 -9 -3 ≠ 7

2 x (14 – 9) + (– 17 – 14) = 7   ⇒  2(5) +(-31) ≠ 7

(2 x 14) – (9 – 17) – 14 = 7   ⇒   28 -(-8) -14 ≠ 7

2 x (14 – 9) – (17 – 14) = 7   ⇒   2(5)- 3 = 7 . . . . true

Answer:

ray df or ray fd because both of these letters are consecutive in both of the angles.  

Step-by-step explanation:

Answer:

Answer is Ray FD

Step-by-step explanation:

Given the following angles, what ray is the common side of ∠CFD and ∠DFE?

A. Ray FC

B. Ray FE

C. Ray FD

Answer:

Step-by-step explanation:

Given the expression [tex]sin^{-1} 1/2[/tex], the following steps must be taken to evaluate the expression.

[tex]Let\ y = sin^{-1}1/2[/tex]

[tex]y = sin^{-1} 0.5[/tex]

From the calculator, the value of y wil give;

[tex]y = 30\\\\y = 30.00 (to\ the \ nearest \ hundredth)[/tex]

Hence [tex]sin^{-1} 0.5 = 30.00[/tex].

Answer:

Step-by-step explanation:

The answer is 0.52

Hope that helped

Answer:

Step-by-step explanation:

Multiplying y by a value greater than 1 results in a vertical stretch. When the sign of it is negative there is a reflection over the x-axis. The appropriate choice is shown below.

__

The second attachment shows how the graph is flipped and stretched.

Answer:

2 hrs, 24 min

Step-by-step explanation:

Sally:  in one hour, she can paint 1/4 of the room.

Joe: in one our, he can paint 1/6 of the room

Hour one: 1/4+1/6=3/12+2/12=5/12

1÷5/12=1*12/5=12/5

12/5= 2 & 2/5 hours, or 2.4 hours, or 2 hrs 24 minutes

Answer: 2.4 hours

Step-by-step explanation:

1/4 1/6

LCM

3/12+2/12=5/12 repricical 12/5 =2.4

Answer:

Step-by-step explanation:

In order to find the amount Adel paid we use ratio and proportion

3kg of rump steak = £ 42

Therefore

4kg of rump steak = [tex] \frac{4 \times 42}{3} [/tex]

We have the final answer as

Hope this helps you

Answer:

£56

Step-by-step explanation:

since 3kg costs £42

1kg will be £42/3 which will be equal to £14

4kg will cost £14×4 which will be £56

Answer:

A.

Step-by-step explanation:

from what the question states im assuming it was 3 times 5 less than a number is no more than 272.

if we look at a it fits it perfectly.

3 times 5 less than a number is no more than 272 =

   3(x-5) = 272.

Hope it helps <3

Answer:

y<−13

y−9>4+2y

Simplify both sides of the inequality

y−9>2y+4

Subtract 2y from both sides

y−9−2y>2y+4−2y

−y−9>4

Add 9 to both sides.

−y−9+9>4+9

−y>13

The divide both sides by -1

Answer:

[tex]\boxed{y < -13}[/tex]

Step-by-step explanation:

Hey there!

To solve for y we‘ll combine like terms and use the communicative property.

y - 9 > 4 + 2y

+9 to both sides

y > 13 + 2y

-2y to both sides

-y > 13

Divide -1 by both sides

y < -13

Hope this helps :)

Answer:

-8.05

Step-by-step explanation:

In order to solve for C you first have to subtract 17.6 from both sides.

2c=(6/4)-17.6

6/4 is 1.5

1.5-17.6=-16.1

2c=-16.1

c=-8.05

Answer:

1.5

Step-by-step explanation:

2c+17.6=6/4

2c+176/10=6/4

2c+88/5=6/4

2c=6/4-88/5

2c=30-352/20

2c=-322/20

2c=-161/10

c=-8.05

Proof:

2c+17.6=6/4

2(-8.05)+17.6=6/4

-16.1+17.6=6/4

1.5=1.5

Hope this helps ;) ❤❤❤

1) 9.8 cm

3) 194.68 kilo litters

Step By Step Explanation

Sister these questions are related to volume of cylinder.

You need to use this formula πr²h [ Where r is radius and h is height or depth]

_______________________________________

3)

Given:

Diameter = 4m

Therefore radius = 2m

Depth is 31/2 m

To Find:

How many kilo litters will it hold ?

Actually It's asking about Volume.

Solution:

You know, volume = πr²h

[tex] = \pi {(2 \: m)}^{2} \times ( \dfrac{31}{2})m[/tex]

[tex] = 3.14 \times 4 \: {m}^{2} \times \dfrac{31}{2} m[/tex]

[tex] = \: 62 \times 3.14 \times {m}^{3} \sf [\because \: {m}^{3} = kilolitters][/tex]

[tex] = \sf 194.68 \: \: kilolitters[/tex]

_______________________________________

1)

Given:

Diameter = 14 cm

[tex] \sf \therefore \: radius \: = 7 \: cm[/tex]

height = 20 cm

Diameter of other cylinder = 20 cm

[tex] \sf \therefore \: radius = 10 \: cm[/tex]

To Find:

Deep of water in other cylinder

Consider the depth of water be x

Solution:

Volume of water will remain constant in both

So,

[tex]V_1 = V_2[/tex]

[tex] \sf \: \pi {(r_1)}^{2} h_1 = \pi {( r_2 )}^{2} h_2[/tex]

[Eliminating π from both sides]

[tex] {(7)}^{2} \times 20= {(10)}^{2}x[/tex]

[tex]49 \times 20 = 100x [/tex]

[tex]x = \dfrac{49 \times 2}{10} [/tex]

[tex]x = \dfrac{98}{10} \implies \: 9.8[/tex]

Therefore the required value of x is 9.8 cm .

Answer:

101

Step-by-step explanation:

Given the following :

Number of soldiers = 10201

They are queued such that the number of queues = number of soldiers in each queue

Let number of queues = q

Therefore, if number of queues equals number of soldiers per Q,

Then ;

q × q = 10201

q^2 = 10201

Take the square root of both sides

q = √10201

q = 101

Number of soldiers per queues = 101

Answer:

Step-by-step explanation:

The equation that Dimitri and Jillian were trying to solve is expressed as

(x+1)(x+3) = 12. They are both solving this equation to get the value of x.

Based on the their suggestion, Jillian strategy would have been the best and the only one that will work for us in solving the equation but he didn't take cognizance of 12 when using the formula in his second step hence None of them are correct. The following steps should have been taken;

Step 1: Multiply out the expression (x+1)(x+3)

= (x+1)(x+3)

= x(x)+ 3x+x+1(3)

= x² + 3x + x + 3

= x² + 4x + 3

He got x² + 4x + 3 on expansion

Step 2: He should have rewrote the equation as shown;

x² + 4x + 3 = 12

x² + 4x + 3 -12 = 0

x² + 4x -9 = 0

Step 3: He used the quadratic formula to factorize the expression x² + 4x + 3 where a = 1, b = 4 anad c = -9

x = (-b±√b²-4ac)/2a

x = (-4±√(4)²-4(1)(-9))/2(1)

x = -4±√16+36/2

x = (-4±2√13)/2

x = (-4+2√13)/2 or  (-4-2√13)/2

x = -2+√13 or -2-√13

Hence Neither of them is correct. Jillian is almost correct but he should have equated the equation to zero by taking 12 into consideration before factorizing.

Answer:

Hey there!

12^2+5^2=c^2

144+25=c^2

c=13

Let me know if this helps :)

Answer:

[tex]\Large \boxed{\mathrm{D) \ 13}}[/tex]

Step-by-step explanation:

[tex]\sf We \ can \ apply \ Pythagorean \ theorem.[/tex]

[tex]c=\sqrt{a^2 +b^2 }[/tex]

[tex]\sf Plug \ in \ the \ values.[/tex]

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

[tex]\sf Evaluate.[/tex]

[tex]c=\sqrt{25+144}[/tex]

[tex]c=\sqrt{169}[/tex]

[tex]c=13[/tex]

Answer:

Step-by-step explanation:

y = r x

r is the constant of proportionality

To find r pick any values of x and y provided and substitute it into the above formula and solve for r.

That's

using

x = 2

y = 22

We have

22 = 2r

Divide both sides by 2

Therefore the constant of proportionality is 11

Hope this helps you

Answer:

base and altitude both are 6 cmand 6cm

Answer:

t = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Since the points are collinear they lie on the same line.

Thus the slopes between any of the 3 points are equal.

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 8, 5) and (x₂, y₂ ) = (2, - 1)

m = [tex]\frac{-1-5}{2+8}[/tex] = [tex]\frac{-6}{10}[/tex] = - [tex]\frac{3}{5}[/tex]

Repeat using

(x₁, y₁ ) = (- 8, 5 ) and (x₂, y₂ ) = (0, t) and equate to previous m

m = [tex]\frac{t-5}{0+8}[/tex] = [tex]\frac{t-5}{8}[/tex] = - [tex]\frac{3}{5}[/tex] ( cross- multiply )

5(t - 5) = - 24 , that is

5t - 25 = - 24 ( add 25 to both sides )

5t = 1 ( divide both sides by 5 )

t = [tex]\frac{1}{5}[/tex]