36. Given that y varies directly with x,
what is the equation of direct variation
if y is 3 when x is 7?

Answer:47 is a prime and 81 is a composite

Step-by-step explanation:47={1,47}

81={1,3,9,18,27,81}

1. The number 47 is prime. The only factors are 1 and itself. We can check by dividing 47 over the list of primes smaller than 47. To be more efficient, we can stop once we reach sqrt(47) = 6.85. So we only need to check the primes {2, 3, 5} to show they are not factors of 47 to show that 47 is prime.

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

2. The number 81 is composite. It is not prime because it has factors other than 1 and itself.

There are 5 factors and they are

1, 3, 9, 27, 81

Note how each factor listed is a power of 3 (1 = 3^0, 3 = 3^1, 9 = 3^2, 27 = 3^3, 81 = 3^4)

The prime factorization of 81 is

81 = 3*3*3*3 = 3^4

Answer:

bbbbklhlhjljkhk

Step-by-step explanation:qwertyuiosdfghnjm,

xcvbnm,.sdfghuijk;m./

Answer:

[tex]\Large \boxed{tens}[/tex]

Step-by-step explanation:

We want to find out what 8 is in the number 1,082.

Let’s see the value of each number.

The 1 in 1,082 is in the one thousand place.

The 0 in 1,082 is in the hundreds place.

The 8 in 1,082 is in the tens place.

The 2 in 1,082 is in the ones place

We wanted to find what the value of 8 is, if you look above.. it says ‘The 8 in 1,082 is in the tens place’

Therefore the value of 8 is in the tens place.

If you have any questions, be free to ask!

Answer:

3

Step-by-step explanation:

As it's a parallelogram the cross splits each diagonal exactly in half, so each half is the same:

-9-6x = x-30

7x=21

x=3

Answer:

(1) B

(2) D

Step-by-step explanation:

(1)

Let the quadratic function be:

[tex]y = ax^{2} + bx + c[/tex]

For the point, (0,-1),

[tex]y = ax^{2} + bx + c[/tex]

[tex]-1=(a\times0)+(b\times0}+c\\-1=c\\c=-1[/tex]

Then the equation is:

[tex]y = ax^{2} + bx -1[/tex]

For the point (-1, -8) ,

[tex]y = ax^{2} + bx -1[/tex]

[tex]-8=(a\times (-1)^{2})+(b\times -1)-1\\-8=a-b-1\\a-b=-7...(i)[/tex]

For the point (1, 2) ,

[tex]y = ax^{2} + bx -1[/tex]

[tex]2=(a\times (1)^{2})+(b\times 1)-1\\2=a+b-1\\a+b=3...(ii)[/tex]

Add the two equations and solve for a as follows:

[tex]a-b=-7\\a+b=3\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a = -4\\a = -2[/tex]

Substitute a = -2 in (i) and solve for b as follows:

[tex]a-b=-7\\-2-b=-7\\b=5[/tex]

Thus, the quadratic function is:

[tex]f(x)=-2x^{2}+5x-1[/tex]

The correct option is (b).

(2)

The ordered pairs are:

(5, 7), (7, 11), (9, 14), (11, 18)

Represent them in an XY table as follows:

X : 5 | 7 | 9 | 11

Y : 7 | 11 | 14 | 18

Compute the difference between the Y values as follows:

Diff = 11 - 7 = 4

Diff = 14 - 11 = 3

Diff = 18 - 14 = 4

Now compute the difference between the Diff values:

d = 3 - 4 = -1

d = 4 - 3 = 1

Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.

The correct option is D.

Answer:

128

Step-by-step explanation:

20% of 64

= 0.2 × 64 = 12.8

10% = 12.8 , then

100% = 12.8 × 10 = 128

Answer:

The number is 128

Step-by-step explanation:

Let the number be represented by X

Therefore

20/100*64=10/100*X

---10X=1280

Now dividing both sides of the equation by 10 it will be

=10X/10=1280/10 which is

---X=128

Therefore the number is 128

1. -11     2.-3

Make sure to simplify the equation..

example: 3(2x - 7) = 6x - 21

because 3 x 2 = 6 and 3 x 7 = 21

Answer:

see explanation

Step-by-step explanation:

4a + 8               4

2a² + 8a            2a

12a² - 8a           4a

4 - 6a                2

Match each expression with its greatest common factor as follows;

4a + 8               4

2a² + 8a            2a

12a² - 8a           4a

4 - 6a                2

The largest number that is found in the common factors is called the greatest common factor.

The given expression are;

4a + 8              

2a² + 8a            

12a² - 8a      

4 - 6a              

The greatest common factor of the expression are as follows;

4a + 8  = 4(a+2) = common factor = 4    

2a² + 8a = 2a(a+4a) = common factor = 2a

12a² - 8a = 4a(3a-2) = common factor = 4a

4 - 6a = 2(2-3a) = common factor = 2

Learn more about the greatest common factor here;

https://brainly.com/question/15333869

#SPJ2

Answer:

[tex]\large \boxed{1296}[/tex]

Step-by-step explanation:

6 raised to 4 indicates that the base 6 has an exponent or power of 4.

[tex]6^4[/tex]

6 is multiplied by itself 4 times.

[tex]6 \times 6 \times 6 \times 6[/tex]

[tex]=1296[/tex]

Answer:

The number of minutes Nikki needs to listen to the radio to hear 20 commercials is 63.275 minutes

Step-by-step explanation:

The given dependent and independent variables are;

The number of minutes spent by Nikki listening = x

The number of commercials aired = y

The relationship between the independent variable, x ans the dependent variable, y, was given by the Nikki's graphing tool line of best fit as follows;

y = 0.338·x - 1.387

Therefore, the number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y is given as follows;

20 = 0.338·x - 1.387

20 + 1.387 = 0.338·x

0.338·x  =20 + 1.387 = 21.387

x =  21.387/0.338 = 63.275 minutes

The number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y = 63.275 minutes.

Answer:

C. 63 minutes

Step-by-step explanation:

Answer:

Reserve rate = 3%

Step-by-step explanation:

Reserve Ratio = Reserve Maintained with Central Bank / Deposit Liabilities × 100

Reserve maintained = $6,000

Deposit liabilities = $200,000

Reserve Rate = Reserve Maintained with Central Bank / Deposit Liabilities × 1000

=$6,000 / $200,000 × 100

=0.03 × 100

r=0.03 × 100

=3%

Therefore,

Reserve Rate =3%

Answer:

60

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer: True

Step-by-step explanation:

The number is going down in a way that cannot be written as a straight line so it is a nonlinear.

Answer:

1)

=6-15+7

=6-22

=-16 answer

2)

=7×40/5

=Then,7×8

=56 answer

Answer:

Points Q, J and M are not collinear

Step-by-step explanation:

Three points cannot be collinear if they are not coplanar (on the same plane), and M is on a different plane than Q. J is located on both planes.

Answer:

$49.50

Step-by-step explanation:

First, let's find how much total interest was made

For every year, 2.5% interest was made

Since we're finding the total for 4 years

It will be 4 x 2.5 = 10% total interest

Now let's find 10% of 45

45 x .1 = 4.5

This means we made $4.5 in those 4 years

Now we just add it to our starting amount

45 + 4.5 = 49.5

Answer:

If the concavity of f changes at a point (c,f(c)), then f′ is changing from increasing to decreasing (or, decreasing to increasing) at x=c. That means that the sign of f″ is changing from positive to negative (or, negative to positive) at x=c. This leads to the following theorem

Step-by-step explanation:

The previous section showed how the first derivative of a function,  f′ , can relay important information about  f . We now apply the same technique to  f′  itself, and learn what this tells us about  f . The key to studying  f′  is to consider its derivative, namely  f′′ , which is the second derivative of  f . When  f′′>0 ,  f′  is increasing. When  f′′<0 ,  f′  is decreasing.  f′  has relative maxima and minima where  f′′=0  or is undefined. This section explores how knowing information about  f′′

Let  f  be differentiable on an interval  I . The graph of  f  is concave up on  I  if  f′  is increasing. The graph of  f  is concave down on  I  if  f′  is decreasing. If  f′  is constant then the graph of  f  is said to have no concavity.

Note: We often state that " f  is concave up" instead of "the graph of  f  is concave up" for simplicity.

The graph of a function  f  is concave up when  f′  is increasing. That means as one looks at a concave up graph from left to right, the slopes of the tangent lines will be increasing. Consider Figure  3.4.1 , where a concave up graph is shown along with some tangent lines. Notice how the tangent line on the left is steep, downward, corresponding to a small value of  f′ . On the right, the tangent line is steep, upward, corresponding to a large value of  f′ .

Answer:

A. Regular pyramid

Step-by-step explanation:

If it has a vertex over the centre of the base, it has to be a pyramid.

Also, since the base is a regular polygon, the solid is a regular pyramid.

Answer:

The correct answer is

Step-by-step explanation:

Regular pyramid: A regular pyramid has a regular polygon base and a vertex over the center of the base.

Hope this helps....

Have a nice day!!!!

Answer:

47

Step-by-step explanation:

Using the follwing property

[tex]x^{2} -y^2=(x+y)(x-y)[/tex]

in which x=24 and y=23

so

[tex]24^2-23^2=(24-23)(24+23)\\=1(47)\\=47[/tex]

Answer:

47

Step-by-step explanation:

Lets say 24 is x and 23 is y.

the equation would be x^2 - y^2

this is = to (x-y)(x+y)

substitute the numbers in

(24-23)(24+23)

which simplifies to

(1)(47)

which equals 47

Answer:

the Mode Is 3

Step-by-step explanation:

You Have To Put the numbers from ascending order to descending order..The Numbers that appears the most is the mode

Answer:

9:45 A.M.

Step-by-step explanation:

First, add the time that took him to hike:

6:30 + 2 hours and 15 minutes = 8:45 A.M.

Next, add the 1 hour that he played volleyball for:

8:45 + 1 hour = 9:45 A.M.

So, he finished playing volleyball at 9:45 A.M.

Answer:

9:45 am

Step-by-step explanation:

He went at 6:30 am to a hike.

It took him 2 hours 15 minutes

=> 6 : 30

+  2    15

=> 8 : 45

He came back from the Hike at 8:45 am

He played volleyball for 1 hour.

=> 8 : 45

+  1

=> 9 : 45

He finished playing volleyball at 9:45 am

Answer:

The original number could be 85.

Step-by-step explanation:

Let the 2 digits be x and y.

Let the number be xy then, assuming that x is the larger digit:

x - y = 3.

x = y + 3

Also

10y + x + 10x + y = 143

Substituting for x:

10y + y + 3 + 10(y + 3) + y = 143

22y + 33 = 143

22y = 110

y = 5.

So x = y + 3 = 8.

Answer:

➥ 10(x + 3) + x + 10x + x + 3 = 143

➥ 10x + 30 + 12x + 3 = 143

➥ 22x + 33 = 143

➥ 22x = 143 - 33

➥ 22x = 110

➥ x = 110/22

➥ x = 5

The unit digit number = x = 5

The tens digit number = x + 3 = 5 + 3 = 8

The original number = 10(x + 3) + x

The original number = 10(5 + 3) + 5

The original number = 50 + 30 + 5

The original number = 85

Hence,the original number is 85.

Answer:

0.8 -4*0.8-7=0.8*2x-1

0.8-3.2-7=1.6x-1

0.8-10.2+1=1.6x

1.8-10.2=x1.6

-8.4=x 1.6

x= -8.4 / 1.6

x= - 5.25

Answer:

7.20 dollars

Step-by-step explanation:

1 1/4 can be expressed as 5/4 ((1*4+1) /4)

If price of 5/4 pound of turkey = $9

Price of 1 pound of turkey = $9 / (5/4)

( Same way you'd divide the price of 2 pounds by 2 to get the price of 1 pound)

$9 / (5/4) = $7.2

Answer:

y = (-3/4)x + 2

Step-by-step explanation:

Find the slope of this line.  Note how the first x-coordinate (-8) becomes 4, a jump of 12, and how the first y-coordinate (8) becomes -1, a decrease of 9.  Then the slope is

m = (change in y) / (change in x) = -9/12 = m = -3/4

Find the y-intercept from this data using the slope-intercept form:

y = mx + b becomes  8 = (-3/4)(-8) + b when x = -8, y = 8 and m = -3/4.

Solving this equation for b, we get:

                                     8 = 6 + b, so that b must be 2.

The desired equation is y = (-3/4)x + 2.

Answer:

Step-by-step explanation:

You gave very clear instructions on how to draw this graph, so that's what I did. What you need to remember in particular with limits is that you do not care in the least what happens AT the x value of 2, only what happens as it is being approached. Because we are asked the limit as x is approaching from the left and the right, this is a one-sided limit question. In order for the limit to exist as x approaches 2 (NOT from the left or the right), the limit would have to agree from the left and the right, and this one doesn't. Having said that there is "a horizontal line crossing the y-axis at 5 that ends at the open point (2, 5)..." is a limit approaching x from the left. Therefore,

[tex]\lim_{x \to 2^-} f(x)=5[/tex]

Having also said there is "...another horizontal line starting at the open point (2, -3) and continues to the right..." is a limit approaching x from the right. Therefore,

[tex]\lim_{x \to 2^+} f(x)= -3[/tex]

The closed point at (2, 1) is where x IS, and remember that we don't care about what happens AT x. So disregard this point in limits.

Answer:D

Step-by-step explanatiation:25th Percentile: 11

50th Percentile: 16

75th Percentile: 22

Interquartile Range: 11

Answer:

civil engineering..

hope it helps u

Step-by-step explanation:

There are answers to this problem based on how we interpret this question.

If the question is x^2 + x =2

=> x = 1

Since, 1^2 + 1 = 2.

Another way to interpret this question is 2x+ x = 2

=> 3x = 2

=> x= 2/3

The answer differs based on how we interpret this question.

Hope this helps you.

Answer:

-2

Step-by-step explanation:

The EASIEST way to do this is using the laws of the sum and products of roots.

When you multiply two roots together, you simply get c/a

So, let's start:

x^2 + x = 2

subtract the 2 to get a quadratic equation equal to 0

x^2 + x -2 =0

Now,

a=1

b=1

c=-2

plug b and a into c/a

-(2/1)= -(2)   =   -2

The answer is -2.

It's NOT 1. the answer would be 1 IF it was adding the roots.

Answer:

A'(-9, -3)

Step-by-step explanation:

The coordinates of A are (-3, -1).

The dilation factor is 3.

Multiply the coordinates of A by 3.

A'(-9, -3)

Answer:

Coordinates of A´ are (-3,-1), it is dilated by the factor of 3, The New coordinates will be:-

[tex](-3\times 3)=-9[/tex]

[tex](-1\times3)=-3[/tex]

[tex]A'(-9,-3)[/tex]

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