Which of the following statements are true?


The prime factorization of 21 is 3 x 7.
The LCM of 14 and 21 is 42.
The prime factorization of 14 is 2 x 7.
14 is a composite number.
21 is a prime number.
The GCF of 14 and 21 is 14.

The value of side z will be equal to 99.32 cm.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.

Given that:-

In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°

So by applying the formula given below:-

z²   =   x²  +  y²  -  2xyCos(142)

z²   =   79²  +   27²   -  2 ( 79 x 27  x  Cos142  )

z    =    99.32  cm

Hence the value of side z will be equal to 99.32 cm.

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The number if 18-year old 12-year old students that took part in the survey is 320.

Looking at the survey chart one can see that the total number of 18year old that partook of the survey are:

30 + 20 + 60 + 70 + 40 + 60 + 40

= 340

From the diagram , 18 year old = 60

                                 12 year old = 40

The differences will be:

= 60 - 40

= 20

Therefore, The number if 18-year old 12-year old students that took part in the survey is 320 and  the number of more 18-year old students than 12-year old students that spent between  25 and  35 mins on social media is 20.

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Answer:

O (5,-3.5)

Step-by-step explanation:

Answer:

4 kg

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Add to find total mass:

2.5 + 3.5 + 3.5 + 5 + 5.5 = 20

Since there is a total of 5 bags and want to evenly distribute divided by 5,

20 / 5 = 4

Answer:

40.6°

Step-by-step explanation:

formula of area of triangle

1) √[(s)(s-a)(s-b)(s-c)] , s= (a+b+c)/2

2) 1/2ab sin c

calculate the area first

s= (9.6+6.3+8.1)/2

=12

area= √[(12)(12-9.6)(12-6.3)(12-8.1)]

= √640.224

= 25.3026

1/2(9.6)(8.1) sin c = 25.3026

sin c = 25.3026(2)/(9.6*8.1)

sin c = 0.6508

c = sin-¹ 0.6508

c = 40.6 (nearest tenth)

Answer:

$766.48

Step-by-step explanation:

area = length × width

area = 11 m × 8 m = 88 m²

cost = 88 m² × $8.71/m²

cost = $766.48

Based on the AFN equation, the AFN for the coming year will be -$16000.

Last year's sales =$200,000

Sales growth rate = g = 40%

Forecasted sales = S0 × (1 + ) = 280,000

∆S = change in sales = S1 − S0 = $80,000

Last year's total assets = A*0 = A*0 since full capacity $135,000

Forecasted total assets = A*1 = A*0 × (1 + g) = $189,000

Last year's accounts payable = $50,000

Last year's accruals= $20,000

L*0 = payables + accruals = $70,000

Profit margin = M = 20.0%

Target payout ratio = 25.0%

Retention ratio = (1 − Payout) = 75.0%

AFN = (A*0/S0)ΔS – (L*0/S0)ΔS – Margin × S1 × (1 − Payout)

AFN = $54,000 – $28,000 – $42,000

= -$16,000

The complete question goes thus:

Chua Chang & Wu Inc. is planning its operations for next year, and the CEO wants you to forecast the firm's additional funds needed (AFN). Data for use in your forecast are shown below.

Last year's sales = $200,000

Sales growth rate = 40%

Last year's accounts payable = $50,000

Last year's notes payable = $15,000

Last year's accruals = $20,000

Based on the AFN equation, what is the AFN for the coming year?

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Answer:

3±√2/3 = x

Step-by-step explanation:

As you already have the vertex, the equation for this is y = a(x – h)^2 + k,

so by plugging all this in using the vertex coordinates, you get y = 3(x - 3)^2-2, so, if you divide everything by three you get 2/3 = (x - 3)^2

This means that the two x-intercepts are:

The speed of landing is 15.69 ft/sec.

"Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.    

The three basic derivatives (D) are: (1) for algebraic functions, D(xn) = nxn − 1, in which n is any real number; (2) for trigonometric functions, D(sin x) = cos x and D(cos x) = −sin x; and (3) for exponential functions, D(ex) = ex."

Let the length of the rope = r

Height of the balloon = h

we are given dr/dt = 15ft/sec

at any time t we know:

[tex]r = 125 + 15*t[/tex]

By the Pythagoras theorem we know:

[tex]h^2 + 125^2 = r^2[/tex]

We have to find dh/dt at time t = 20 sec

[tex]d/dh(h^2 + 125^2) = d/dt(r^2)[/tex]

By chain rule:

[tex]d/dh(h^2 + 125^2)*dh/dt\\ = d/dr(r^2)*dr/dt\\2h*dh/dt = 2r* dr/dt\\h*dh/dt = r*dr/dt\\dh/dt = (r/h)*dr/dt[/tex]

[tex]= [(125 + 15*20)/(425^2 - 125^2)^1/2]*15[/tex]--------------------- at time t = 2

=15.69 ft/sec

Hence dh/dt = 15.69 ft/sec

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Let's consider the relationship between the circumference and the radius:

 ⇒ first, consider the equation for finding the circumference

      [tex]Circumference = 2\pi *radius[/tex]

Let's consider the known information

Let's plug the known information to find the radius:

  [tex]Circumference = 2\pi *radius\\36\pi =2\pi *radius\\radius = 18[/tex]

Thus the radius is 18 cm

Answer: 18 cm

Hope that helps!

Answer:

see below    

Step-by-step explanation:

Just graph           y = 4/5 x

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . .

We are asked to solve the equation [tex]\mathrm{-6z+2+3=15}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Notice that we can add 2+3 right off the bat:

[tex]\star~\mathrm{-6z+5=15}[/tex]

Subtract 5 from both sides of the equal sign:

[tex]\star~\mathrm{-6z=10}[/tex]

Divide both sides by -6:

[tex]\star~\mathrm{z=\cfrac{10}{-6}}[/tex]

Simplify!

[tex]\star~\mathrm{z=-\cfrac{5}{3}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Step-by-step explanation:

remember what a rational number is ?

any number that can be expressed by a/b, with a and b being integer numbers, and b different to 0.

so,

-7 = -7/1 rational

sqrt(10) irrational, because there is no rational number that multiplied by itself is 10.

sqrt(16) = sqrt(4×4) = 4 = 4/1 rational

52% = 52/100 rational

1.235 = 1235/1000 rational

Answer:

  d.  $1,740

Step-by-step explanation:

The annual after-tax salary is found by subtracting the tax from the salary. The tax is found by multiplying the tax rate by the salary. The monthly after-tax income is 1/12 of the annual after-tax income.

__

  annual tax = 0.28 × $29,000 = $8,120

  annual take-home pay = $29,000 -8,120 = $20,880

  monthly take-home pay = annual pay / months per year

  = $20,880 / 12 = $1,740 . . . . net monthly income

_____

Additional comment

The net pay will be (1 - 0.28) = 0.72 times the nominal salary. The monthly pay will be 1/12 of the annual pay. These combined factors give a monthly net pay of (0.72)(1/12) = 0.06 times the annual pay.

  0.06 × $29000 = 6×$290 = $1740

Answer: 433.5 square miles or 433 1/2 square miles

Step-by-step explanation

[tex]SA = 6x^{2}[/tex]

[tex]SA = 6 *(8.5)^{2} \\\\SA = 6*72.25\\\\SA = 433.5[/tex]

The measure of the central angle is 2.15 radians if the radius of the circle is 7 in.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

The radius of the circle = 7 in

Arc length = 15 in

We know,

s = rθ

s is the arc length, θ is the central angle, and r is the radius of the circle.

15 = 7θ

θ = 15/7

θ = 2.142 radians ≈ 2.15

Thus, the measure of the central angle is 2.15 radians if the radius of the circle is 7 in.

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Answer:

incomplete question

Step-by-step explanation:

in order to calculate for the surface area of a rectangular box we would need 3 measurements:
length
width
height

you only provided 2

Answer: AAS

Step-by-step explanation:

We know that [tex]\angle TSN \cong \angle HSU[/tex] because they are vertical angles, meaning the triangles are congruent by AAS.

Answer:

A. median

Step-by-step explanation:

the median is the middle of the shape :)

Answer:

THE ANSWER IS A

Step-by-step explanation:

CORRECT IF I WRONG

Answer:

if ur in college then how do u not know this

Step-by-step explanation:

use ur brain

Answer:

25°

Step-by-step explanation:

hope it helps you solve the question

274

hope that helps

:D

btw i used long division

In the given question, we have to perform this experiment and test if the inequality is true or not.

Adding the same value to both sides of the inequality will not change the inequality sign

data;

In the first case, we would do follow the process

[tex]6 * 7 * 4 < 7 * 7 * 6\\168 < 294[/tex]

In the second case;

[tex]11 > - 2\\\\5 + 11 > -2 + 5\\3 + 16 > 3 + 3\\4+ 19 > 6 + 4\\23 > 10[/tex]

In all the scenarios, the operations did not affect the inequality sign because we are doing it equally to all side and at the end of the day nullifies each other.

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Answer:

761.25 m³

Step-by-step explanation:

l = 15 , w = 14.5 , h = 3.5

Volume of a rectangular prism is given by the formula :

V = lwh

V = 15 × 14.5 × 3.5

V = 761.25

Units will be m³

I am attaching an image for visual understanding

Hope this helped and brainliest please.

Answer:

35/14 as a decimal = 2.5 · 35/14 in decimal form = 2.5 · Thirty-five fourteenths as a decimal = 2.5 · 35 over 14 as a decimal = 2.5

9880 different possibilities are there in Sally's new combination option second 9880 is correct.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Total unique numbers consists in a Sally locker = 3

From the digits 0 to 39

Total numbers = 40

Apply combination formula:

= C(40, 3)

= 40!/(3!37!)

= 9880

Thus, 9880 different possibilities are there in Sally's new combination option second 9880 is correct.

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