Find the first term and the common difference of the arithmetic sequence whose 6th term is 30 and 12th term
is 54.

Answer:

2.25

Step-by-step explanation:

The lower number will always be on the right side unless its negative numbers , So the lower number is 2.25 , Why it isn't 1.26 is because its much far from 2.26 and so cannot be counted . Thanks

Step-by-step explanation:

-3x - 3 <= 6

-3x <= 9

x >= -3

your answer options are not clear to me.

so, please pick the one corresponding to all x >= -3.

for any value of x greater or equal to -3 that inequality is true.

The solution of inequality is,

⇒ x ≥ - 3

We have to given that,

An inequality to solve,

⇒ - 3x - 3 ≤ 6

Now, We can simplify the inequality as,

⇒ - 3x - 3 ≤ 6

Add 3 both side,

⇒ - 3x ≤ 6 + 3

⇒ - 3x ≤ 9

Divide by 3;

⇒ - x ≤ 9/3

⇒ - x ≤ 3

⇒ x ≥ - 3

Therefore, The solution of inequality is,

⇒ x ≥ - 3

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Answer:

[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{x^{5}y}[/tex]

Required

The equivalent expression

We have:

[tex]\sqrt[3]{x^{5}y}[/tex]

Rewrite as an exponent

[tex]\sqrt[3]{x^{5}y} = (x^{5}y)^\frac{1}{3}[/tex]

Open bracket

[tex]\sqrt[3]{x^{5}y} = x^{5*\frac{1}{3}}y^\frac{1}{3}[/tex]

[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]

Answer:

The answer is 2.)

Step-by-step explanation:

Given initial velocity=135 ft/s

& cliff=76 foot

Given quadratic equation

⇒                      (let h=0 it is given)

⇒  

⇒  

⇒    t=8.96≈9 s (the other root is negative)

Hence, rocket will take 9 s to hit the ground after launched.

Answer:  Choice D

0 = 16t^2 + 135t + 76;  9 s

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

Explanation:

The equation we start with is

[tex]h = -16t^2 + vt + c\\\\[/tex]

where v is the starting or initial velocity, and c is the starting height.

We're told that v = 135 and c = 76

We let h = 0 to indicate when the object hits the ground, aka the height is 0 ft.

That means the equation updates to [tex]0 = -16t^2 + 135t + 76\\\\[/tex]

Based on that alone, the answer is between A or D

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

We'll use the quadratic formula to solve for t

We have

So,

[tex]t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\t = \frac{-135 \pm \sqrt{135^2 - 4(-16)(76)}}{2(-16)}\\\\t = \frac{-135 \pm \sqrt{23,089}}{-32}\\\\t \approx \frac{-135 \pm 151.9506}{-32}\\\\t \approx \frac{-135 + 151.9506}{-32} \ \text{ or } \ t \approx \frac{-135 - 151.9506}{-32}\\\\t \approx \frac{16.9506}{-32} \ \text{ or } \ t \approx \frac{-286.9506}{-32}\\\\t \approx -0.52971 \ \text{ or } \ t \approx 8.96721\\\\[/tex]

We ignore the negative t value because a negative time duration makes no sense.

The only practical solution here is roughly 8.96721 which rounds to 9.0 or simply 9 when we round to the nearest tenth (one decimal place).

In short, the object will hit the ground at the 9 second mark roughly. Or put another way: the object is in the air for about 9 seconds.

From this, we can see that the final answer is choice D.

Keep in mind that we aren't accounting for any wind resistance. Considering this variable greatly complicates the problem and requires much higher level mathematics. So we just assume that there is no wind at this moment.

Answer:

15.5

Step-by-step explanation:

Yes

Answer:

Side = 2 * height / sqr root 3

Side = 2 * 6 * sqr root 3 / sqr root 3

Side = 12

Step-by-step explanation:

Answer:

Required probability:

Required probability:

At least 2 students pass:

Number of x's:

Answer:

80 miles

Step-by-step explanation:

Please find attached the graph used in answering this question

On the graph, the distance travelled is on the vertical axis while the gallons consumed in on the horizontal axis

from the graph, the following can be deduced :

0 gallons is consumed when the car travels 0 mile

1 gallon is consumed when the car travels 30 miles

2 gallons is consumed when the car travels 60 miles

total mile travelled when the gallons consumed is : 2 2/3 x 30

8/3 x 30 = 80 miles

Answer: ∠A = 20°; ∠B = 59°; ∠C = 101°

Step-by-step explanation:

According to the problem:

All interior angles within a triangle adds up to 180°:

∠A + ∠B + ∠C = 180°

[tex]A+(4A-21)+(5A+1)=180\\\\A+4A+5A-21+1=180\\\\10A=180+21-1\\\\10A=200\\\\A=20\°[/tex]

Substitute in the value of ∠A into the other equations:

∠B = 4 · ∠A - 21° = 4(20°) - 21° = 80° - 21° = 59°

∠C = 5 · ∠A + 1° = 5(20°) + 1° = 100° + 1° = 101°

Answer:

plant B

Consistent means better so plant be had more better yields

Answer:

x>_-1

10x + 3 - 5x_< 14x + 12

-9_<9x

Answer:

Step-by-step explanation:

10x +3-5x < (nhỏ hơn hoặc bằng) 14x=12

10-14x-5x< bằng 12 -3

-9x< bằng 9

x > bằng -1

Answer:

Step-by-step explanation:

The inscribed angles are made up of the remote interior angles of this hexagon, of which each of them measures 120 degrees. That means that if this is measure of the inscribed angle, the arc this angle intercepts is twice the degree measure of the inscribed angle. The arcs then will all measure 240 degrees.

Answer:

Student has made an error

Step-by-step explanation:

If two figures are said to be congruent, this implies that area of both is same and both as exactly same or copy or each other.

But from the graph, it can be stated that height of figure JKLM is 4 units whereas that of other is 6 unit.

Hence explained !

Diameter = radius x 2

So, the radius is half of the denominator.

10 / 2 = 5

A = pi x r^2

A = pi x 5^2

A =  3 x 25

A = 75 ft^2

Hope this helps!

Answer:

Approximately 9.2

Step-by-step explanation:

For right triangle, if you know 2 sides, you can find the third using pythagorean theorem, a^2 + b^2 = c^2. 'a' and 'b' are the lengths of the legs, while 'c' is the hypotenuse. You can plug in what you know into this formula:

9^2 + 2^2 = c^2

81+4 = c^2

c = √85, or approximately 9.2

Answer:

see below

Step-by-step explanation:

take f(x)=5x-6, which is y=5x-6

switch the y for x and x for y and you get

x=5y-6

then add 6 on both sides and you get

x+6=5y

now divide both sides by 5 and you get

y=(x+6)/5

which is the inverse of the original function

Answer:

Solution given:

f(x)=5x-6

let f(x)=y

we get

y=5x-6

Interchanging role of x and y

x=5y-6

x+6=5y

y=[tex]\bold{\frac{x+6}{5}}[/tex]

so

f-¹=[tex]\bold{\frac{x+6}{5}}[/tex]

shown

This is a polynomial in [tex]2^x[/tex] that can be factorized:

[tex]2^{2x}-5\cdot2^x+4 = 0[/tex]

[tex]\left(2^x\right)^2-5\cdot2^x+4=0[/tex]

[tex]\left(2^x-4\right)\left(2^x-1\right)=0[/tex]

[tex]2^x-4=0\text{ or }2^x-1=0[/tex]

[tex]2^x=4\text{ or }2^x=1[/tex]

Since 4 = 2² and 1 = 2⁰, you get the two solutions x = 2 and x = 0.

Answer:

X>3

Step-by-step explanation:

-2.5x +5 < -2.5

-2.5x < -2.5-5

-2.5x< -7.5

X> -7.5/-2.5

X>3

Answer:

[see below]

Step-by-step explanation:

Point slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

(x1, y1) - a point

m - slope

We are given the point of (2, -7), and the slope of -5.

[tex]y-y_1=m(x-x_1)\rightarrow y-(-7)=-5(x-2)\rightarrow\boxed{y+7=-5(x-2)}[/tex]

Hope this helps.

Answer:

-4,0

0,1

8,3

======

x: -4, 0, 8

f(x) = 1/4(x) + 1

Plug in x values into f(x)...

f(-4) = 0

f(0) = 1

f(8) = 3

The required value of x is 36

Step-by-step explanation :

Let the required number be x.

Three fourth of number = (3/4)x

One third of number = (1/3) x

According to the question ;

3x/4 = x/3 + 15

→ 3x/4-x/3 = 15

→ 9x - 4x / 12 = 15

→ 5x = 15 x 12

⇒ x = 180 / 5

⇒ x = 36

Step-by-step explanation:

= 3+3x-1+3x^4 , g(x) = -x^3+x^2-x+2-x^4. tính f(x)+g(x) và f(x) -g(x)

By analyzing the graph we conclude that the value that is an input is x = 4.

For the inputs, we need to look at the horizontal axis. In the graph we can see a closed dot at x > 0 (we can't see the exact value).

This means that the minimum of the domain is positive.

From that, we conclude that the only correct option, that we can be sure that belongs to the domain (set of the inputs), is x = 4, the third option.

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Answer:

Option C,

y² = 18x, since the graph opens right

Answered by GAUTHMATH

Answer:

C.

Step-by-step explanation:

212/4 = 53, so 53/1, or 53 miles are driven every hour.

Answer:

[tex]\angle CFD =105^o[/tex]

Step-by-step explanation:

Given

[tex]\angle D FE = \angle DE F = 75^o[/tex]

See attachment

Required

Determine the measure of [tex]\angle CFD[/tex]

[tex]\angle CFD[/tex] and [tex]\angle DFE[/tex] are on a straight line.

So:

[tex]\angle CFD + \angle DFE = 180^o[/tex] --- angle on a straight line

Substitute known values

[tex]\angle CFD + 75^o = 180^o[/tex]

Collect like terms

[tex]\angle CFD =- 75^o + 180^o[/tex]

[tex]\angle CFD =105^o[/tex]

Answer:

65%

Step-by-step explanation:

120 * x = 78

78/120 = x

.65 = x

Answer:

35%

Step-by-step explanation:

First, set up the equation.

Then solve.

78-120 is -42.

Divide by 120. -0.35.

Multiply by 100. -35.

The negative sign means that it is decreasing, so you can take it away.

I hope this helps!

Area of the triangle = 1/2 x base x height

Area of triangle = 1/2 x 6 x 8.3 = 24.9 square feet.

Area of rectangle = length x width

Area of rectangle = 33.2 x 12 = 398.4 square feet.

To find the number of triangles that can fit in the rectangle divide the area of the rectangle by the area of the triangle:

398.4 / 24.9 = 16

Answer: 16 triangles

Answer:

F.  m/10.

Step-by-step explanation:

10 miles = 1 inch

1 mile = 1/10 of an inch so

m miles = m/10 inches.