the difference of two numbers is 24.if the smaller number is 38,find the greater one​

Answer:

common difference = 4

Step-by-step explanation:

common difference is the difference between the successive term and its preceding term.

let's take the successive term of -20 that is - 16

common difference (d) = successive term - preceeding term

= -16 -(-20)

= -16 + 20

= 4

if we take the successive term of -16 that is -12

we'll get the same common difference.

d = -12 -(-16)

d = -12 + 16

d = 4

this means that the common difference for an AP remains constant.

Answer: -3x+y=-4

Step-by-step explanation:

Standard form is Ax+By=C. In y=Mx+b form, it would be y=3x-4. To put it into standard form you subtract 3x from both sides. So then you have -3x+y=-4.

Answer:

[tex]{ \tt{ \tan(x) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan( \theta) = \frac{30}{16} }}[/tex]

Answer:

The speed is 20.8  m/s

Step-by-step explanation:

If a projectile ascends vertically, and after 3 seconds it reaches its maximum height, calculate the velocity that it carries to the middle of its downward trajectory

Let the maximum height is h and initial velocity is u.

From first equation of motion

v = u + at

0 = u - g x 3

u = 3 g.....(1)

Use third equation of motion

[tex]v^2 = u^2 - 2 gh \\\\0 = 9 g^2 - 2 gh \\\\h = 4.5 g[/tex]

Let the speed at half the height is v'.

[tex]v^2 = u^2 + 2 gh \\\\v'^2 = 0 + 2 g\times 2.25 g\\\\v'^2 = 4.5\times 9.8\times9.8\\\\v' = 20.8 m/s[/tex]

n(A∪B)=n(A)+n(B)−n(A∪B)=50+60−40=70

n(AΔB)=n(A∪B)−n(A∩B)

⇒70−40=30.

Answer:

Answer is derived according to the procedure of calculating LCM of any two numbers

Step-by-step explanation:

If you have any other questions

ask in comments

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

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

[tex]\\\\[/tex]

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

According to the question,

we have to find the LCM

Answer:

speed is 2t - 5

velocity is 2t - 5

a = 2 m/s²

Step-by-step explanation:

Given the position of a particle expressed as:

s(t) = t^2 - 5t + 1

speed v = ds/dt

ds/dt = 2t - 5

Hence the speed is 2t - 5

velocity can also  be expressed as the speed, hence, velocity is 2t - 5

Acceleration is the change in velocity with respect to time. Hence;

a = dv/dt

a = 2 m/s²

Answer:

X=20

a< = 125

Step-by-step explanation:

i think 51 is answer......

Answer:

Step-by-step explanation:

Answer:

⊥

Step-by-step explanation:

d and b meet at a 90 degree angle ( as shown by the box)

The lines are perpendicular (⊥)

Answer:

180m cubed

Step-by-step explanation:

Multiply the length, width, and height together: 6×6×5=180

Answer:

Formula of a rectangular prism:

L x W x H

Now we place in the numbers and solve:

5 x 6 x 6 = 180 m3

Answer:

70. 8x⁴

71. 3n - 10

72. a/5 + 12

Step-by-step explanation:

70. a number "x" raised to the fourth = x⁴

Product of 8 and x⁴ = 8 × x⁴

= 8x⁴

71. 3 times a number "n" = 3 × n = 3n

3n decreased by 10 = 3n - 10

72. Quotient of a number "a" and 5 = a/5

12 more than a/5 = a/5 + 12

Answer:

write your question properly

Step-by-step explanation:

Answer:

hope it helps you........

Answer:

x = 5

Step-by-step explanation:

1. Subtract 22 from both sides.

15x = 7x + 62 - 22

2. Simplify 7x + 62 - 22 to 7x + 40.

15x = 7x + 40

3. Subtract 7x from both sides.

15x - 7x = 40

4. Simplify 15x - 7x to 8x.

8x = 40

5. Divide both sides by 8.

x = [tex]\frac{40}{8}[/tex]

6. Simplify [tex]\frac{40}{8}[/tex] to 5.

x = 5

Answer:

20

Step-by-step explanation:

Multiply 4/7 with 35, this will get you 140/7, which simplifies to 20 employees

Answer:

hope this helps you

have a great day

Answer:

Step-by-step explanation:

it is a function because if you look on the x side 3 is repeating

Answer:

same y intercept

Step-by-step explanation:

The y intercept is when r = 0

Function 1

p = -3/2 r - 5

Let r = 0

p = 0-5

p = -5

Function 2

When r = 0  p = -5

They both equal -5, so they both have the same y intercept

Answer:

Option B

<F = 26°

<D = 64.01°

FD = 89

Answered by GAUTHMATH

For right triangle EFD,  m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89

The correct answer is an option (B)

It is the longest side of the right triangle.

For a right triangle,

[tex]a^{2}+ b^{2} = c^{2}[/tex], where c is hypotenuse and a, b area other two sides of the right triangle

For given example,

We have been given a right triangle EFD with hypotenuse FD.

Also, EF = 80, ED = 39

Using the Pythagoras theorem,

[tex]\Rightarrow FD^{2}= EF^{2} + ED^{2}\\\\ \Rightarrow FD^{2}= 80^{2} + 39^{2}\\\\ \Rightarrow FD^2 = 6400 + 1521\\\\ \Rightarrow FD^2 = 7921\\\\\Rightarrow FD = 89[/tex]

Consider, sin(F)

[tex]\Rightarrow sin(F)=\frac{ED}{FD} \\\\\Rightarrow sin(F)=\frac{39}{89}\\\\ \Rightarrow sin(F)=0.4382\\\\\Rightarrow \angle F=sin^{-1}(0.4382)\\\\\Rightarrow \angle F=25.98^{\circ}\\\\\Rightarrow \angle F\approx 26^{\circ}[/tex]

Now, consider sin(D)

[tex]\Rightarrow sin(D)=\frac{FE}{FD}\\\\ \Rightarrow sin(D)=\frac{80}{89}\\\\ \Rightarrow \angle D = sin^{-1}(0.8988)\\\\\Rightarrow \angle D = 64.009^{\circ}\\\\\Rightarrow \angle D \approx 64.01^{\circ}[/tex]

Therefore, for right triangle EFD,  m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89

The correct answer is an option (B)

Learn more about Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ2

We found that the height of the short wall "x" is 162.6 ft, the height of the tall wall "y" is 221.8 ft, and the distance between the canyon walls "z" is 162.6 ft.

To find the x, y, and z values we need to denote the right triangles from top to bottom as triangles 1, 2, and 3.

1. Finding the height of the short wall "x"

We can find the height of the short wall "x" (in triangle 3) with the following trigonometric function:

[tex] cos(\theta) = \frac{x}{H} [/tex]

Where:

H: is the hypotenuse = 230 ft

θ: is the angle between x and H.

Knowing that the sum of θ and the angle 45° must be equal to 90°, θ is:

[tex] \theta = 90 - 45 = 45 [/tex]

Hence, the height of the short wall "x" is:

[tex]x = cos(\theta)*H = 230cos(45) = 162.6 ft[/tex]                

2. Finding the height of the tall wall "y"  

The height of the tall wall "y" is given by the sum of the bases of the two first right triangles (the right triangles 1 and 2):

[tex] y = y_{1} + y_{2} [/tex]        

Where y₁ and y₂ can be calculated with the tangent and sine trigonometric functions.  

[tex]y_{1} = A*tan(20)[/tex]        

[tex] y_{2} = 230sin(45) [/tex]

Where A is the adjacent side to the angle 20°.

[tex] y = A*tan(20) + 230sin(45) [/tex]      

Since the right triangles 2 and 3 form a square, with all the sides equals to x, we have:        

[tex] A = z = y_{2} = x = 230cos(45) [/tex]        

We can use 230cos(45) or 230sin(45) to calculate y₂, so the height of the tall wall "y" is:      

[tex] y = y_{1} + y_{2} = A*tan(20) + 230cos(45) = 230cos(45)tan(20) + 230cos(45) = 221.8 ft [/tex]                        

3. Finding the distance between the canyon walls "z"

As we said above, the "z" value is the same as "x", then:

[tex]z = x = 230cos(45) = 162.6 ft[/tex]

Learn more about trigonometric functions here: https://brainly.com/question/14272510?referrer=searchResults

I hope it helps you!                                        

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

Explanation:

The table says that

That's 5+10+15 = 30 students out of 35 total.

The probability is therefore 30/35 = 0.8571 approximately which rounds to 0.86

There's roughly an 86% chance of picking someone who got an A, B or C.