Write down an algebraic rule to show the relationship between the number of lines
(L)and pattern number (n).​

Step-by-step explanation:

height= 4b

length = 2 + b

volume = 60in³

or, l ×b × h = 60in³

or, (2+b) × b × 4b = 60in³

or, 4b²(2+b) = 60in³

or, 8b² + 4b³ = 60

or, 2b² + b³ = 15

or, b³ + 2b² -15= 0

b= 1.95

l= 2+1.95=3.95

h= 4×1.95 = 7.8

Answer:

a) red

b) red

c) the blue one is y=1/2x+1

Step-by-step explanation:

Answer:

[tex]\frac{(\sin 18^\circ)}{75} = \frac{(\sin 35^\circ)}{x}[/tex]

Step-by-step explanation:

Incomplete question:

[tex]\angle CBD = 53^\circ[/tex]

[tex]\angle CAB = 35^\circ[/tex]

[tex]AB = 75[/tex]

See attachment for complete question

Required

Determine the equation to find x

First, is to complete the angles of the triangle (ABC and ACB)

[tex]\angle ABC + \angle CBD = 180[/tex] --- angle on a straight line

[tex]\angle ABC + 53= 180[/tex]

Collect like terms

[tex]\angle ABC =- 53+ 180[/tex]

[tex]\angle ABC =127^\circ[/tex]

[tex]\angle ABC + \angle ACB + \angle CAB = 180[/tex] --- angles in a triangle

[tex]\angle ACB + 127 + 35 = 180[/tex]

Collect like terms

[tex]\angle ACB =- 127 - 35 + 180[/tex]

[tex]\angle ACB =18[/tex]

Apply sine rule

[tex]\frac{\sin A}{a} = \frac{\sin B}{b}[/tex]

In this case:

[tex]\frac{\sin ACB}{AB} = \frac{\sin CAB}{x}[/tex]

This gives:

[tex]\frac{(\sin 18^\circ)}{75} = \frac{(\sin 35^\circ)}{x}[/tex]

Step-by-step explanation:

sin18

∘

)

=

x

(sin35

∘

)

Step-by-step explanation:

Incomplete question:

\angle CBD = 53^\circ∠CBD=53

∘

\angle CAB = 35^\circ∠CAB=35

∘

AB = 75AB=75

See attachment for complete question

Required

Determine the equation to find x

First, is to complete the angles of the triangle (ABC and ACB)

\angle ABC + \angle CBD = 180∠ABC+∠CBD=180 --- angle on a straight line

\angle ABC + 53= 180∠ABC+53=180

Collect like terms

\angle ABC =- 53+ 180∠ABC=−53+180

\angle ABC =127^\circ∠ABC=127

∘

\angle ABC + \angle ACB + \angle CAB = 180∠ABC+∠ACB+∠CAB=180 --- angles in a triangle

\angle ACB + 127 + 35 = 180∠ACB+127+35=180

Collect like terms

\angle ACB =- 127 - 35 + 180∠ACB=−127−35+180

\angle ACB =18∠ACB=18

Apply sine rule

\frac{\sin A}{a} = \frac{\sin B}{b}

a

sinA

=

b

sinB

In this case:

\frac{\sin ACB}{AB} = \frac{\sin CAB}{x}

AB

sinACB

=

x

sinCAB

This gives:

\frac{(\sin 18^\circ)}{75} = \frac{(\sin 35^\circ)}{x}

75

(sin18

∘

)

=

x

(sin35

∘

)

Step-by-step explanation:

#44 y = 180-122 = 58

x = (180-58)/2 = 61

Answer:

B keeping his debt above 30% of his credit card limit.

Step-by-step explanation:

1. Formula for simple interest,

[tex]a = p(1 + rt)[/tex]

where

a = Final amount

p = Principal amount

r = annual interest rate

t = time in years

given p = 1250

r = 4.25/100 (r is a raw number, not percentage, so we need to divide 100 here to get the raw number)

t=4

Substitute values into formula to get a.

[tex]a = 1250(1 + (\frac{4.25}{100})(4)) \\ = 1250(1 + 0.17) \\ = 1250(1.17) \\ = 1462.50dollars[/tex]

Let's use the simple interest to calculate Henry's final amount first.

p = 5000

r = 4.2/100

t = 4

[tex]a = 5000(1 + ( \frac{4.2}{100} )(4)) \\ = 5000(1 + 0.168) \\ = 5000(1 .168) \\ = 5840 \: dollars[/tex]

To calculate the interest paid, just use the final amount minus the principal amount

[tex]a - p = 5840 - 5000 \\ = 840dollars[/tex]

Now we will do the exact same method for Ingrid.

p = 5,000

r = 3.9/100

t = 6

[tex]a = 5000(1 + ( \frac{3.9}{100} )(6)) \\ = 5000(1 + 0.234) \\ = 5000(1.234) \\ = 6170 \: dollars[/tex]

[tex]a - p = 6170 - 5000 \\ = 1170dollars[/tex]

Difference in interest between 2 of them =

Interest of Ingrid Loan - Interest of Henry Loan

= 1170 - 840

= $330

Answer:

Suppose we have a system of two linear equations, this can be written as:

y = a*x + b

y = c*x + d

Now, we have 3 possible cases here.

The solutions of the system are the points where the graphs of the linear equations do intersect.

Then, if for example, we have two parallel lines (two parallel lines never intersect) we have no solutions.

And we know that two lines are parallel if they have the same slope and different y-intercept.

Then the system:

y = a*x + b

y = a*x + c

has no solutions.

If we have both equal lines, then the lines intersect in infinitely many points, meaning that we have infinite solutions, then the system:

y = a*x + b

y = a*x +b

has infinite solutions.

And if the lines intersect only one time we have one solution, and this happens when the slopes are different, so the system:

y = a*x + b

y = c*x + d

has only one solution.

Now, if we have more equations:

y = a*x + b

y = c*x + d

y = k*x + n

We have more equations than variables, then this system only has one solution of the 3 lines intersect at the same point, which is really rare.

One case where we have a solution here is if the 3 equations have the same y-intercept:

y = a*x + b

y = c*x + b

y = d*x + b

where the solution is the point (0, b)

Of course, there are other possible solutions, but these are not as formulaic as this ones.

Answer:

The value of a₂₇ is 788

Step-by-step explanation:

a₁₉ = 548

a₃₃ = 968

Now,

a₁₉ = 548 can be written as

a + 18d = 548 ...(1) and

a₃₃ = 968 can be written as

a + 32d = 968 ...(2)

Now, from equation (2) we get,

a + 32d = 968

a + 18d + 14d = 968

548 + 14d = 968 (.°. a + 18d = 548)

14d = 968 - 548

14d = 420

d = 420 ÷ 14

d = 30

Now, for the value of a put the value of d = 30 in equation (1)

a + 18d = 548

a + 18(30) = 548

a + 540 = 548

a = 548 - 540

a = 8

Now, For a₂₇

a₂₇ = a + 26d

a₂₇ = 8 + 26(30)

a₂₇ = 8 + 780

a₂₇ = 788

Thus, The value of a₂₇ is 788

-TheUnknownScientist

Answer: radius is is 12.

Step-by-step explanation:

Explanation: A circle with equation of the form x2+y2=r2 will have radius r=√144=12 .

Sorry, I'm not sure on the bottom part

We know,

The general equation for circle is –

[tex] { \boxed{\bf{\rm \red {(x \: - \: a)² \: + \: (y \: - \: b)² \: = \: r²}}}} [/tex]

[tex] \bf (a, \: b) \: = \: center \: coordinates [/tex]

[tex] \bf r \: = \: radius [/tex]

[tex] \bf a \: = \: 0 \: , \: b \: = \: 0 \: , \: r \: = \sqrt{144} \: = \: 12 [/tex]

[tex] \bf Center \: coordinates \: = \: (0, \: 0) [/tex] [Answer]

[tex] \bf Radius \: = \: 12 [/tex] [Answer]

__________________________________________________

NOTE – Refer the above attachment.

__________________________________________________

Answer:

Two packs of buns and three hotdog packages

Step-by-step explanation:

Answer:

[tex]y\leq 4[/tex]

Step-by-step explanation:

The range is about the y values, and by looking at this parabola we can see that the maximum value is a 4. So the range would be the maximum and below (where the parabola extends to). So the values in the range would be equal to 4 and less than since the parabola is negative.

Hope this helps :)

Answer:

pretty sure that's C

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

600 ft

Step-by-step explanation:

Mark as brainilest

And I'm only 80% sure that is the correct

Step-by-step explanation:

[tex]y = -\frac{2}{3}x + 4[/tex]

[tex]y = \frac{1}{3}x - 2[/tex]

Since both equations are set equal to [tex]y[/tex], we can take the right-hand side of each equation and set them equal to each other to solve for [tex]x[/tex]:

[tex]-\frac{2}{3}x + 4 = \frac{1}{3}x - 2[/tex]

[tex]-\frac{2}{3}x - \frac{1}{3}x = -2 - 4[/tex]

[tex]-x = -6[/tex]

[tex]x = 6[/tex]

Now we can plug this value into either equation to solve for [tex]y[/tex]:

[tex]y = \frac{1}{3}x - 2[/tex]

[tex]y = \frac{1}{3}(6) - 2[/tex]

[tex]y = 2 - 2[/tex]

[tex]y = 0[/tex]

So the solution to the system of equations is [tex](6, 0)[/tex]

Answer:

printf(“%d”, i++);

Step-by-step explanation:

Answer:

count += 1

OR

count = count + 1

Step-by-step explanation:

count = 0

numbers = int(input("Enter a number: "))

while number > 0:

    number = number // 10

    count +=1

print("Total number of digits", count)

Answer:

18.18%

Step-by-step explanation:

66 - 54 = $12

% change - 12/66 * 100

simplify - 12/66 --> 2/11

2/11 * 100

200/11

18.18%

Answer: 4

Step-by-step explanation:

u+3=7

u=7-3

u=4

Answer:

c

Step-by-step explanation:

edg 21 ^u^

Answer:

The person above me is correct. :D

Step-by-step explanation:

Answer:

1. BC=25

2. DC=30

Step-by-step explanation:

In a parallelogram, pairs of opposite sides are always equal. The side opposite of AD is BC, so if AD=25, BC=25. Likewise, if side AB=30, side DC=30. Of course, this is assuming the shape is a parallelogram. If it is not, there is no way of determining the side lengths.

lmk if im wrong, hope this helps :)

Answer:C

Step-by-step explanation:332 square in

Answer:

The answer is C, 332 in.2.

Step-by-step explanation:

Just did the unit test on edge. Hope this was able to help, have a good day <3 :)

Answer:

hyperbola

Step-by-step explanation:

Sana makatulong

Answer:

Answer:

1 A 2 A 3 an 4 A 5 Their 6 a, Their 7 they'er 8 there

Step-by-step explanation:

Answer:

a) b ≈ 100

b) m ≈ 30

Step-by-step explanation:

Answer:

14.4 in

Step-by-step explanation:

25 in is the longer leg so you have to do [tex]\frac{25}{\sqrt3}[/tex]

Answer:

14.4 on edge 2021

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

so multiplies see och the rest of the world and the second half and the other hand if you have a good and the second one is the only way only a and the other is the first time I saw one he and only best o

Answer:

33b-8 is the perimeter

Step-by-step explanation:

Triangle is an Isosceles triangle so two side is equal

2(12b - 8) + 9b + 8

Distribute

24b - 16 + 9b + 8

Combine like terms

33b -8

Answer:

To transform the given expression to the sum of cubes, calculate first the cube root of the terms. The cube root of the first term, 64x^6 is 4x^2 and that of the second term, 27 is 3.

Thus, the answer to this is (4x^2)^3 + 3^3