x2 =144 if and only if x =12 or x = -12

The number of positive integers n, that satisfy 3^n+81 the square of an integer is infinite.

Based on the information given, let 3n + 82 = p².

Therefore, 3n = p² - 81

= (p - 9)(p + 9)

Let p = 3q.

3n = (3q - 9)(3q + 9(

= 9(q - 3)(q + 4)

n = 3(q - 3)(q + 3)

n > 0 ; q >= 4 for n = 4, 5, 6....

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The function is written in vertex form the equation for is  mathematically given as

f(x) = 3(x – 4)2 – 38

This is further explained below.

Generally, To convert the expression "f(x) = 3x2 – 24x + 10," which is in quadratic form, into vertex form, which will look like this "y = a(x-h)2 + k," you will need to apply the technique of completing the square. This will allow you to convert the expression. In the beginning, we shall separate the x2 and x terms.

y = 3(x² - 8x) + 10

We start with a negative eight, divide that number by two to obtain a negative four, and then we square that number, which gets us sixteen. We combine these so that it forms a perfect square, and then we remove 16 so that it is not altered in any way. We will get:

y = 3(x² - 8x + 16 - 16) + 10

y = 3((x - 4)² ) - 48 + 10

y = 3(x - 4)² - 38

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Answer: option D

Step-by-step explanation:

Step-by-step explanation:

Let the cost of one tacos = t

Let the cost of one burritos = b

So, we have this system

                    t + b = 60      (eq-1)

2.50t + 4.00b = 175.50        (eq-2)

We take equation-1,

We can write,

              t + b = 60

              t= 60-b            (eq-3)

Substitute equation-3 into equation-2,

We can write,

          2.50t + 4.00b = 175.50

          2.50(60-b) + 4.00b = 175.50

 Multiply the values,

         2.5(60)-2.5b+4b = 175.5

         150-2.5b+4b = 175.50

Subtract the values,

           1.5b = 175.5-150

            1.5b = 25.5

             b = 25.5/1.5

Divide the values,

             b = 17

Replace the value 'b' in equation-3,

We can write,

              t= 60-b

              t= 60-17

              t=43

Therefore,

     Mariana sell 43 tacos yesterday.

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Answer:

Step-by-step explanation:

Solve for X:

Solve for 19:

It is recommended that the expressions

d = 400 - 256 and

d = 256 - 400 be considered when attempting to determine how much farther Adam can see to the horizon.

Since, the eye-level height of Pam is 256 feet above sea level, whereas the eye-level height of Adam is 400 feet above sea level.

Therefore, the formula that indicates how much farther Adam can see to the horizon should be taken to be

d = 400 - 256 and

d = 256 - 400.

This expression may be found by subtracting 400 from 256.

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CQ

Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level. What expression shows how much farther Adam can see to the horizon? In simplest terms, Adam can see a√b feet farther than Pam.

Answer:

A= 2 B= 6

Step-by-step explanation:

the dude above me is wrong

Answer: 2.12

Step-by-step explanation:

it's in the hundredths place

2       .   1           2

ones    tenths  hundredths

Answer:

List A: 2√2, 3√2, 4√2, …

List B: 2π, 3π, 4π, …

List C: 2log35, 3log35, 4log35, …

Step-by-step explanation:

In the last half hour 4  miles did Jesse ride his bike.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

Jesse rode his bike for 2 hours at a constant rate.

First 1.5 hours, he rode 12 miles.

According to given question we have

1.5 hours=12 miles

1 hours=12/1.5

0.5 hours=12*0.5/1.5

0.5 hours=4  miles

Therefore, in the last half hour 4  miles did Jesse ride his bike.

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The correct statements for this problem are given as follows:

20. Plane N contains line l.

21. Point P lies in line l.

22. PQ lies on plane N.

23. Line l and line m are coplanar.

24. Line l passes through P and Q.

25. Line m and line l intersect at P.

26. Points P and Q are colinear.

From the graph, we have these following items:

For item 20, we have that:

Line l is on plane N, hence:

Plane N contains line l.

For item 21, we have that point P is on both lines, m and l, hence:

Point P lies in line l.

For item 22, we have that points P and Q are on the plane N, hence:

PQ lies on plane N.

For item 23, we have that the lines are on the same plane, hence:

Line l and line m are coplanar.

For item 24, we have that points P and Q are both on line l, hence:

Line l passes through P and Q.

From it, we can also solve item 26, as follows:

Points P and Q are colinear.

And for item 25, the two lines intersect at point P, hence:

Line m and line l intersect at P.

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Answer:

Step-by-step explanation:

17

12

-----

do 7 x 2

14

then carry the 1

2x1 is 2 plus the 1 from before. it becomes 3

then do 1 x 7 then 1 x 1 but with an extra zero

so it becomes

17

12

---------

34

170

---------

then add it all together

34+170=204

Answer: 17*12=204

Step-by-step explanation:  because of G O O G L E

Answer:

Theorems are stated below

x = 6

Step-by-step explanation:

The following theorems can prove that 2 lines are parallel

Two lines are parallel if they’re cut by a transversal such that

The two angles shown are corresponding angles. They are corresponding because each is in the same position left side) in its group of four angles.

Corresponding angles are equal

Therefore,15x + 9 = 21x - 27

Subtract 9 from both sides:
15x = 21x - 27 - 9

15x = 21x  - 36

Subtract 21x from both sides

15x - 21x = - 36

-6x =  36

Divide by -6 both sides

-6x/-6 =  36/-6

x = 6

The two angles are
15x + 9 = 15(6) + 9 = 90 + 9 = 99°

and

21x - 27 = 21(6) - 27 = 126 - 27 =99°

And indeed they are equal

Answer:

1/16

Step-by-step explanation:

32= 2^5

Thus:

(2^5) ^-4/5

= (2)^ - 4

= (16) ^ - 1

= 1/16

Answer:

-8

Step-by-step explanation:

x - 16 = 3x

Solve for x

-2x = 16

x = -8

Answer:

3 / 20

Step-by-step explanation:

Take only after the decimal point part for calculation.

.15

Then, divide that value by 1.

.15

1

Multiply both numerator and denominator by 100 (because there are 2 digits after the decimal point so that is 102 = 100).

.15 × 100

1 × 100

=

15

100

;

To simplify

15

100

its lowest terms, find GCD (Greatest Common Divisor) for 15 & 100, which is 5. Here's How to Find GCD of 15 and 100?

15/5

100/5

After simplify or reduce the fraction.

3

20

Answer:

6 I belive it should land on 6

Answer:3 and 5/7

Step-by-step explanation:

The probability that the lot of the bulbs will fail inspection of the quality control inspector is 0.9856

Given data

p = 20%

sample drawn = 19 bulbs

20% of the bulbs in the lot are defective

n = 19

p = 20% = 0.20

if 20% of the bulbs are defective to find the non defective bulbs we solve as follows

q = 1 - p

= 1 - 0.20

= 0.80

Using binomial theorem,

[tex]P ( X = x) = (^n C _{x} ) * p x * (1 - p)n - x[/tex]

[tex]= 1 - P ( x < 1 )[/tex]

[tex]= 1 - P ( X = 0)[/tex]

[tex]= 1 - ( ^{19} C _{0} ) * 0.20^0 * (0.80)^{19}[/tex]

[tex]= 1 - 1 * 1 * 0.01441[/tex]

[tex]= 1 - 0.01441[/tex]

= 0.98559

= 0.9856 (to four decimal place)

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The value of a in Quadratic function ax^2 + bx + c is 1.

In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.

the polynomial function f(x)=Ax^2+Bx+C, where A 0 and A, B, and C R. A quadratic function is a second-degree polynomial function in which all the coefficients of the terms with a degree less than 2 are zeros.

Roots of the given equation are 4 and 7.

then the quadratic function whose roots are 4 and 7 is

x^2  - (4+11)x + (4*7)

x^2-11x+28

on comparing this to the Quadratic function ax^2+bx+c

the value of a is 1.

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Answer:

bjuk

Step-by-step explanation:

ftftrtt987652123456789

If f(x) = x² ₋ 4x ₋ 6 then we get the following answers for f(0),f(3) and f(-2) respectively. And the expression f(1/2) = f(7/2) and f(2₋h) = f(2₊h) is therefore proved.

f(0) = -6

f(3) = -9

f(-2) = 6

Given the function is f(x) = x² ₋ 4x ₋ 6

we need to find for f(0):

f(0) = 0² ₋ 4(0) ₋ 6

f(0) = ₋6

f(3) = 3² ₋ 4(3) ₋ 6

f(3) = 9 ₋ 12 ₋ 6

f(3) = ₋9

f(₋2) = (₋2)² ₋ 4(₋2) ₋ 6

f(₋2) = 4 ₊ 8 ₋ 6

f(₋2) = 6

we need to prove f(1/2)f(7/2)

now, f(1/2) = (1/2)² ₋ 4(1/2) ₋ 6

f(1/2) = 1/4 ₋ 2 ₋ 6

f(1/2) = 1 ₋ 8 ₋ 24 / 4

f(1/2) = ₋31/4

f(7/2) = (7/2)² ₋ 4(7/2) ₋ 6

f(7/2) = 49/4 ₋ 14 ₋ 6

f(7/2) = 49 ₋ 56 ₋ 24 / 4

f(7/2) = ₋31/4

therefore, f(1/2) = f(7/2)

f(2₋h) = (2₋h)² ₋ 4(2₋h) ₋ 6

f(2₋h) = (4 ₊ h² ₋ 4h) ₋ 8 ₊ 4h ₋ 6

f(2₋h) = h² ₊ 4 ₋ 4h ₋ 8 ₊ 4h ₋ 6

f(2₋h) = h² ₋ 10

f(2₊h) = (2₊h)² ₋ 4(2₊h) ₋ 6

f(2₊h) = 4 ₊ h² ₊ 4h ₋ 8 ₋ 4h ₋ 6

f(2₊h) = h² ₋ 10

therefore, f(2₋h) = f(2₊h)

Hence proved.

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The partial products of 3706 × 4 is ( 3000 × 4 ) + ( 706 × 4 ).

Calculating the product of two or more numbers is the procedure known as multiplication in mathematics. When two integers are multiplied together in mathematics, the result is a product or an expression that describes the factors to be multiplied.

The decimal numeral system is widely used to express both integer and non-integer numbers. The way of representing numbers in the decimal system is known as decimal notation.

The given product is 3706 × 4 and can be written as:-

3706 × 4 = [ 3000 + 706 ] × 4

3706 × 4 = ( 3000 × 4 ) + ( 706 × 4 )

Therefore, the partial products of the given expression is ( 3000 x 4 ) + ( 706 x 4 ).

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Answer: 5358

Step-by-step explanation:

282

x 18

----------

2538

+282

-----------

5358

Simple interest , 4368 is  the amount of money Marty would have at the end of the second year.

What does the term "simple interest" mean?

P = $4000 R = 4% T = 1

then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]

                = [tex]\frac{4000 * 4 * 1}{100}[/tex]  = 160

So, the total amount is ( 4000 + 160) = 4160

Second year

P = 4160 , R = 5%  T = 1

then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]

                      =  [tex]\frac{4160 * 5 * 1}{100}[/tex]  = 208

So, the total amount is ( 4160 + 208 ) =   4368

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Answer:

g(x) = - x² - 4

Step-by-step explanation:

g(x) is a reflection in the x- axis of f(x) followed by a vertical translation of 4 units down.

f(x) = x² , then

g(x) = - x² ( reflection in the x- axis )

g(x) = - x² - 4 ( a translation of 4 units down )

vertex of A = (x1,y1) =(2,4)

vertex of B = (x2,y2)= (12,2)

vertex of c = (x3,y3) = (8,6)

Midpoint :

The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

x= x1+x2/2

y=y1+y2/2

Now ,

D(7,3) is the midpoint of AB.

D (x',y') = (7,3)

vertex of A = (x1,y1)

vertex of B = (x2,y2)

x' = x1+x2/2

7 = x1+x2/2

14 = x1+x2 ...1

y' = y1+y2/2

3= y1+y2/2

6= y1+y2 .....2

E (x'',y'') = (10,4)

vertex of c = (x3,y3)

vertex of B = (x2,y2)

x''= x3+x2/2

y''=y3+y2/2

20= x3+x2 ....3

8 =y3+y2.......4

F (x''',y''') = (5,5)

vertex of c = (x3,y3)

vertex of A = (x1,y1)

10= x1 +x3 ...5

10 =y1+y3 .....6

For 1 & 3 & 5

14 = x1+x2 ...1

20= x3+x2 ....3

10= x1 +x3 ...5

Add all  1 & 3 & 5

44 = 2(x1+x2+x3)

22 = (x1+x2+x3) .....7

For 1 & 7

x3 = 8

For 3 & 7

x1 = 2

For 5&7

x2 = 12

For 2 , 4 & 6

6= y1+y2 .....2

8 =y3+y2.......4

10 =y1+y3 .....6

Add all  2 & 4 & 6

24 = 2 (y1+y2+y3)

For 2 & 8

y3 = 6

For 4 & 8

y1 = 4

For 6 & 8

y2 = 2

vertex of A = (x1,y1) =(2,4)

vertex of B = (x2,y2)= (12,2)

vertex of c = (x3,y3) = (8,6)

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Answer: He could put 8 blocks in 8 stacks

Step-by-step explanation:

Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find out how many blocks Ken could put in each stack, we need to divide the total number of blocks by the number of stacks.

So we have:

Number of blocks = 64

Number of stacks = x

To find out how many blocks can be put in each stack, we can set up the following equation:

64 / x = y

where y is the number of blocks in each stack.

Solving for y, we get:

y = 64 / x

So if Ken wants to put all 64 blocks into the same number of stacks, he can put:

64 blocks in 1 stack

32 blocks in 2 stacks

16 blocks in 4 stacks

8 blocks in 8 stacks

4 blocks in 16 stacks

2 blocks in 32 stacks

1 block in 64 stacks

Therefore,

Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.

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In linear equation, 2x - 5 is an expression for John's test grade.

What is linear equation in one variable?

Let Ariana's test grade = x

twice Ariana's test grade =  2x

then, John's test grade  = 2x - 5

an expression for John's test grade = 2x - 5

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