To convert 7 m/m to yards per hour around the nearest 10th

What is a 15 of the sequence -7, 2, 11, ...? A. 128 B. 110 C. 136 D. 119

gregori [183]

Answer:

D. 119

Step-by-step explanation:

To find the common difference, we take the second term and subtract the first term

2-(-7) = 9

We check by taking the third term and subtracting the second

11-2 = 9

The common difference is 9

The formula for an arithmetic sequence is

an = a1 +d(n-1)

where a1 is the first term, d is the common difference and n is the number of the term in the sequence

a1=-7, d=9 and we are looking for the 15th term so n=15

a15 = -7 +9(15-1)

a15 = -7+9(14)

=-7 +126

= 119

3 0

4 years ago

Describe at least two similarities between constructing a perpendicular line through a point on a line and constructing a perpen

Sophie [7]

Two similarities between constructing a perpendicular line through a point on a line and constructing a perpendicular through a point off a line are;

1. Arcs are drawn to cross the given line twice on either side relative to the point

2. The perpendicular line is drawn using a straight edge by connecting the small arcs formed using the arcs from step 1, to the point on the line or off the line

Description:

1. One of the first steps is to place the compass on the point and from

point, draw arcs to intersect or cross the given line at two points.

2. The compass is placed at each of the intersection point in step 1 and

(opened a little wider when constructing from a point on the line) arcs are

drawn on one (the other side of the point off the line) side of the line with

the same opening (radius) of the compass to intersect each other.

3. From the point of intersection of the arcs in step 2, a line is drawn with a

straight edge passing through the given point.

Learn more about perpendicular lines here:

brainly.com/question/11505244

8 0

2 years ago

Need help ASAP! Anyone know?

VARVARA [1.3K]

Answer: x= 29°

Step-by-step explanation: Add angles D and C. Subtract from 180.

58/2 = 29

6 0

3 years ago

Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat

tensa zangetsu [6.8K]

Answer:

The volume of the largest rectangular box (V) = 81/4

Step-by-step explanation:

Step 1:-

Given volume of the largest rectangular box in the first octant

V = l b h

let (x ,y, z) be the one vertex in the given plane

V = f(x, y, z) = x y z

given plane. Ф (x, y, z) = x + 9y + 4z = 27 ........(1)

Step( ii):

By using Lagrange multipliers

Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0

Form Lagrange function F(x, y, z) = f(x, y, z) + λ Ф (x, y, z) where λ is called the Lagrange multipliers

F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)

Obtain the equations are δ F / δ x = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ y z + λ ( 1) = 0

⇒ y z = - λ ......(a)

Obtain the equations are δ F / δ y = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ x z + λ ( 9) = 0

⇒ $\frac{xz}{9}$ = - λ .......(b)

Obtain the equations are δ F / δ z = 0

δ f / δ x +λ δ Ф / δ z =0

x y + λ ( 4) = 0

⇒ $\frac{xy}{4}$ = - λ .......(c)

Step (iii):-

Equating (a) and (b) equations

we get $y z = \frac{xz}{9}$

cancel 'z' value we get x = 9y .......(d)

Equating (b) and (c) equations

we get $\frac{xy}{4} = \frac{xz}{9}$

cancel 'x' value on both sides , we get

4z =9y ......(e)

substitute (d) (e) values in equation (1) we get

x + 9y + 4z -27 = 0

9y + 9y + 9y -27 =0

27y -27 =0

y = 1

substitute y =1 in x = 9y

x = 9

substitute y =1 in 4z =9y

z = 9 /4

therefore the dimensions are x =9 , y=1 and z = 9 /4

Conclusion:-

The largest volume of the rectangular box V = x y z

substitute x =9 , y=1 and z = 9 /4

V = 9(1)(9/4) =81/4

The largest volume of the rectangular box (V) = 81/4

Verification :-

Given plane x + 9y + 4z = 27

substitute x =9 , y=1 and z = 9 /4

9 + 9 + 4(9/4) = 27

27 =27

so satisfied equation

3 0

3 years ago

Solve the inequality -7x + 12 = 75

yulyashka [42]

Answer:

-9

Step-by-step explanation:

-7x+12=75

-12 -12

-7x= 63

divide by -7 on both sides

x = -9

7 0

3 years ago