Complete the explicit formula for the sequence.

42, 47, 52, 57, 62, ...

Answer:

Length=8 Width=5

Step-by-step explanation:

Set this up as a system of equations with l standing for length and w standing for width.

w+3=l

l×w=40

Substitute rhe first equation into the 2nd one.

w(w+3)=40 --------> w^2+3w=40

Move all the terms to the left side

w^2+3w-40=0

Factor

(w+8) (w-5)

Set both factors equal to 0.

w+8=0 -----> w=-8

w-5=0 ------> w=5

Since distance cannot be negative we can eliminate -8. So w=5

Plug it back into any one of the equations and solve for l.

5+3=l -----> 8=l

So the answer is the length is 8 and the width is 5.

The dimensions of the rectangle are:

Length = 8 meters.

width = 5meters.

We are given that the length of a rectangle is 3 meters longer than its width and the area of a rectangle is 40 square meters.

We need to find the length and width of the rectangle.

A rectangle is a closed 2-dimensional shape that has two dimensions, the length, and the width. Length is the longer side and width is the shorter side of the rectangle.

The area of a rectangle is given by :

A = Length x Width.

Let the area, length, and width of the rectangle be A, L, and W.

The length of a rectangle is 3 meters longer than its width.

We can write it as,

L = 3 + W

The area of a rectangle is 40 square meters.

We can write it as,

A = 40 square meters

We can write it as,

L x W = 40

Substituting  L = 3 + W.

(3 + W) W = 40

[tex]3W + W^2 = 40\\W^2 + 3W = 40 \\W^2 + 3W - 40 = 0[/tex]

This is a quadratic equation and we will apply middle-term factorization.

[tex]W^2 + 3W - 40=0\\W^2 + (8-5)W - 40=0\\W^2 + 8W - 5W - 40=0\\W(W + 8) - 5 ( W + 8)=0\\(W+8)(W - 5)=0\\W+8 = 0~~and~~W-5=0\\W = -8~~and~~W=5[/tex]

The distance can not be negative so W = -8 is eliminated.

We have, W = 5

Substituting W = 5 in L = 3 + W.

We get,

L = 3 + 5 = 8

L = 8.

The dimensions of the given rectangle are:

Length = L = 8 meters.

Width = W = 5 meters.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ2

Answer:

30

Step-by-step explanation:

Answer: 91

Step-by-step explanation:

Angle between the two vectors u and v is option (a) 0 degree

Vector, in mathematics, a quantity that has both magnitude and direction

Given,

u=(-2,3)

v=(-6,9)

Angle between the two vectors θ =[tex]cos^{-1} \frac{u.v}{|u| |v|}[/tex]

[tex]u.v=(-2)(-6)+(3)(9)\\u.v=12+27\\u.v=39[/tex]

[tex]|u|=\sqrt{-2^{2}+3^{2} } \\|u|=\sqrt{13}[/tex]

[tex]|v|=\sqrt{-6^{2}+9^{2} } \\|v|=\sqrt{117}[/tex]

Angle between two vectors θ =[tex]cos^{-1} \frac{u.v}{|u| |v|}[/tex]

θ=[tex]cos^{-1} \frac{39}{\sqrt{13}.\sqrt{117} } \\cos^{-1}\frac{39}{39}\\ cos^{-1}1=0[/tex]

Hence, the angle between the vectors u and v is 0 degree

Learn more about vector here

https://brainly.com/question/13322477

#SPJ2

Answer:

38

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

1-4 round down 5-10 round up

Answer: Here we answer "What is the square root of 674 (√674) in simplest radical form?"

The square root of 674 in its simplest form means to get the number 674 inside the radical √ as low as possible.

The square root of 674 is already in the simplest radical form. Therefore, the answer is:

√674

hope this helps.. Stay safe and have a great day/night!!! :D

The square root of 674 is expressed as √674 in the radical form.

A square root of a number is a value that, when multiplied by itself, gives the number.

Given that, what is the square root of 674 in the simplest radical form,

The square root of 674 is expressed as √674 in the radical form,

The square root of 674 rounded up to 7 decimal places is 25.9615100. It is the positive solution of the equation x² = 674.

Hence, the square root of 674 is expressed as √674 in the radical form.

Learn more about square root, click;

https://brainly.com/question/29286039

#SPJ5

Answer:

the answer is  [tex]x=10,\:y=-1[/tex]

Step-by-step explanation:

Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.

hope this helps :)

*see attachment for diagram

Answer:

✔️m<BAC = 72°

✔️m<BCD = 108°

Step-by-step explanation:

Given:

m<ABC = (4x - 16)°

m<ACB = (5x + 7)°

Find the numerical value of m<ABC, m<ACB, m<BAC, and m<BCD.

First we need to determine the value of x.

The ∆ given is an isosceles triangle with two equal sides, therefore, the angles opposite the two equal sides would also be equal.

Therefore:

(4x - 16)° + 2(5x + 7)° = 180° (sum of ∆)

Solve for x

4x - 16 + 10x + 14 = 180

Add like terms

14x - 2 = 180

Add 2 to both sides

14x = 182

Divide both sides by 14

x = 13

Find the measure of each angle by plugging in the value of x where necessary:

✔️m<ABC = (4x - 16)° = 4(13) - 16

m<ABC = 36°

✔️m<ACB = (5x + 7)° = 5(13) + 7

m<ACB = 72°

✔️m<BAC = m<ACB (both are base angles of the isosceles ∆, so they are equal)

Therefore,

m<BAC = 72°

✔️m<BCD = m<ABC + m<ACB (exterior angle theorem of a triangle)

m<BCD = 36 + 72 (Substitution)

m<BCD = 108°

Therefore, the angle measures that are correct are:

✔️m<BAC = 72°

✔️m<BCD = 108°

Answer:

x = 20

Step-by-step explanation:

If A || B, then ∠2 should equal to ∠3 (Alternate angles).

3x - 10 = x + 30

Isolate like terms.

3x - x = 30 + 10

Evaluate like terms.

2x = 40

Find x.

x = 40 ÷ 2

x = 20

Answer:

x = 20.

Angles 2 and 3 are measured as 50 degrees.

Step-by-step explanation:

Angles 2 and 3 are congruent, meaning that they are equal.

Set the two equations equal to each other and solve for x.

3x-10=x+30 (subtract x from the left side and add 10 to the right. This gets the x's and the plain numbers on the same side of the equation)

2x=40 (Divide by 2)

x = 20

Check your work by plugging in 20 for x in each expression. If the two expressions are equal when you do so, then you know you've worked out the problem correctly.

Angle 2:

3(20)-10

60 - 10 = 50

Angle 3:

20 + 30 = 50

Both expressions equal 50 when plugging in 20 for x, so this is the correct answer.

The value of x from the quadratic equation is x = { 2 , -12 }

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 10x = 24   be equation (1)

Adding 5² on both sides of the equation , we get

x² + 10x + 25 = 24 + 25

( x + 5 )² = 49

Taking square roots on both sides , we get

x + 5 = ±7

Subtracting 5 on both sides , we get

x = 2

And , x = -12

Hence , the quadratic equation is solved and value of x is x = -12 or x = 2

To learn more about quadratic equations click :

https://brainly.com/question/25652857

#SPJ7

Answer:QR = 54

Step-by-step explanation:

(B) [tex]\frac{78-87}{8-2}[/tex]

Therefore, (B) [tex]\frac{78-87}{8-2}[/tex] can be simplified to find the slope of the trend line in the scatter plot.

Know more about the slope of the trend line here:

https://brainly.com/question/3688621

#SPJ2

Answer:

dude i can't even see that sorry

Step-by-step explanation:

I like your cut G

Answer:

Step-by-step explanation:

Step one:

given

monthly allowance= $21

from January to June= 6 months

total savings = 21*6= $126

cost of gift = $110

Step two:

Ian will have enough money to buy the gift

since he saved $126 which is greater than the cost of the gift of $110

he would have a balance of $16

Answer:

-9

Step-by-step explanation:

Slope = (y2 - y1)/(x2 - x1)

 (r - 11)/(4 - (-1)) = (r - 11)/5

So, (r - 11)/5 = -4

r - 11 = -20

r = -9

I dont know wht

way you are doing this but hope it helps

Answer: A: no, because each vertex is not multiplied by the same scale factor.

Step-by-step explanation: got it right on Edge 2020!

Answer:

0.00039

Step-by-step explanation:

Answer:

N=CD C=2-3 sentance

Step-by-step explanation:

Answer:

The rate of change is 0 because 0/1=0.

Step-by-step explanation:

hope this helps

Answer:

x>1

Step-by-step explanation:

Answer:

-2, 0, 2, 4, 6  these are the answers for the boxes and they are in order. solution x<1

Step-by-step explanation:

if you look at the box you will see that it says x and 2x at the bottom. The x at the top is the same as the one at the bottom. So they want you to multiply the number in the row of x by the number below x I hope this helps

Answer: I don't know if you wanted it to be solved or re-written but the answer is x=4/3 and re-written is 3x=4

Answer: C

Step-by-step explanation:

proportional relationship will have an equation that goes through the origin (0,0)  

The equation for C will not go through the origin because it has a y-intercept of -1  and the line will be going through (0,-1) instead of (0,0).

All the other equations will be going through the origin because they have no y intercepts.

Answer: The number is 974

Step-by-step explanation:

First, any 3 digit number can be written as:

N = a*100 + b*10 + c

Where a, b, and c are single-digit numbers.

a is the hundreds digit

b is the tens digit

c is the unit digit

We can write the clues as:

#1: a + b + c = 20

#2: b = a - 2

#3: c = a + b - 12

Then we have a system of equations:

a + b + c = 20

b = a - 2

c = a + b - 12

To solve this, we need to isolate one of the variables in one equation and then replace this in the other equations, we can see that b is already isolated in the second equation, then we can replace that in the first and third equations:

a + (a - 2) + c = 20

c = a + (a - 2) - 12

Now we can see that c is isolated in the second equation, then we can replace that in the first one to get:

a + (a - 2) + (a + (a - 2) - 12) = 20

Now we can solve this for a:

a + a - 2 + a + a -2 - 12 = 20

4*a - 16 = 20

4*a = 20 + 16

4*a = 36

a = 36/4 = 9

With this, we can find the values of b and c.

b = a - 2 = 9 - 2 = 7

c = a + b - 12 = 9 + 7 - 12 = 4

Then the 3-digit number is:

N = a*100 + b*10 + c = 9*100 + 7*10 + 4 = 974

N = 974

Answer: The shirt's price after reduction = $ 84.15

Step-by-step explanation:

Given: Price of shirt= $ 85

Marked up percent = 10%

Reduced percent = 10%

Price after mark up = (Price of shirt) + 10% of (Price of shirt)

= $ (85+10% x 85)

= $ (85+(0.1) x (85))

= $ (85+8.5)

= $ 93.5

Price after 10% reduction = (Price after mark up)- 10% of (Price after mark up)

= $ (93.5-0.1 x 93.5)

= $ (93.5-9.35)

= $ 84.15

Hence, the shirt's price after reduction = $ 84.15

Answer:

It is D.

Step-by-step explanation:

Answer:

x = -1/2

Step-by-step explanation:

First, subtract 2 from both sides to get 7/x alone. Then muliply both sides by x to get rid of 7/x's denominator. Divide both sides by -14 to get rid of x's coefficient and to get x alone. You will then get -1/2 as your answer.

2 + 7/x = -12

-2             -2

7/x = -14

*x       *x

7 = -14x

÷-14    ÷-14

- 1/2 =x

x = -1/2

Answer:

149866

Step-by-step explanation:

Hope this helps.

Answer:

149866.

This is because the '.3' part means that you do not have to round the '6' up.

Answer:  can't be done

Step-by-step explanation:

Answer:

The principal, real, root of:

27−−√3

=3

All roots:

3

−1.5+2.59807621i

−1.5−2.59807621i

27 is a perfect cube

Answer:

26.6

Step-by-step explanation:

(12*5)-(8.35*4)

60-33.4

26.6