find the highest common factor of 36 and 48

Answer:

Answer:

Factors of 15: 1, 3, 5 and 15.

Factors of 17: 1 and 17.

Factors of 26: 1, 2, 13 and 26

Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.

Actually you can find all the answers in the Internet.

Answer:

Mixed number form 4 4/5 exact form 24/5

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

8/15

Answer:

2

Step-by-step explanation:

The average rate of change over [2, 8] is the change in the y-values over the change in the x-values.

[tex]\frac{f(8) - f(2)}{8 - 2}[/tex]

[tex]f(8) = 2(8) - 8 = 16 - 8 = 8[/tex]

[tex]f(2) = 2(2) - 8 = 4 - 8 = -4[/tex]

[tex]\frac{8 - (-4)}{8-2} = \frac{8 + 4}{8-2} = \frac{12}{6} = 2[/tex]

Answer:

Anything to a negative power is always the reciprocal. An example might be 2⁻² can be written as 1/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

45/11 miles per day or ~4.091 miles per day

Step-by-step explanation:

3 inches per second

24 hours in a day

60 minutes in 1 hour

60 seconds in 1 minute

Amount of inches per minute: 3 x 60 = 180 inches

Amount of inches per hour: 180 x 60 = 10,800 inches

Amount of inches per day 10,800 x 24 = 259,200 inches

To find the number of feet that 259,200 inches is, divide by 12.

259,200/12 = 21,600 feet per day

To find the number of miles that 21,600 feet is, divide by 5280.

21,600/5280 = 45/11 = 4.09090909091 = ~ 4.091

So, an ant could walk 45/11 miles per day or ~4.091 miles per day if it walked without taking a break.

Answer:

see explanation

Step-by-step explanation:

Since AL bisects ∠ KAT then ∠ 1 = ∠ 2

(30)

7x + 3 = 6x + 7 ( subtract 6x from both sides )

x + 3 = 7 ( subtract 3 from both sides )

x = 4

(32)

SAT is a straight line , then

∠ 1 + ∠ 2 + ∠ 3 = 180° , then

x + x + 4x = 180

6x = 180 ( divide both sides by 6 )

x = 30

(34)

Similar to (32)

x + 12 + x + 12 + 6x - 20 = 180 , that is

8x + 4 = 180 ( subtract 4 from both sides )

8x = 176 ( divide both sides by 8 )

x = 22

Answer:

30) x= 4

32) x=30

33) x=22

Step-by-step explanation:

All step by step explainations are in pic below

Answer:

[tex] {3}^{2} \times {3}^{ - 6} \\ = {3}^{2 + ( - 6)} \\ = {3}^{2 - 6} \\ = {3}^{ - 4} [/tex]

Answer:

3/2

Step-by-step explanation:

Csc(theta) = 1/Sin(theta)

So we have to find the side opposite theta.

a = 3*sqrt(5)

b = ?

c = 9

a^2 + b^2 = c^2

(3sqrt(5)) ^2 + b^2 = 9^2

9*5 + b^2 = 81

b^2 = 81 = 45

b^2 = 36

sqrt(b^2) = sqrt(36)

b = 6

Sin(theta) = 6/9

Csc(theta) = 1 / sin(theta) = 9/6

Csc(theta = 3/2

Problem 3

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

Explanation:

Use the pythagorean theorem to find the length of the missing side.

[tex]a^2 + b^2 = c^2\\\\a^2 + (3\sqrt{5})^2 = 9^2\\\\a^2+3^2*(\sqrt{5})^2 = 9^2\\\\a^2 + 9(5) = 81\\\\a^2 + 45 = 81\\\\a^2 = 81-45\\\\a^2 = 36\\\\a = \sqrt{36}\\\\a = 6\\\\[/tex]

This is the length of the missing vertical side. This side is opposite the angle theta.

[tex]\csc = \text{cosecant}\\\\\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{9}{6}\\\\\csc(\theta) = \frac{3*3}{3*2}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]

Alternatively, you can compute it like this

[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{6}{9}\\\\\sin(\theta) = \frac{2}{3}\\\\\csc(\theta) = \frac{1}{\sin(\theta)}\\\\\csc(\theta) = 1 \div \sin(\theta)\\\\\csc(\theta) = 1 \div \frac{2}{3}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]

Answer:

(6_4)(6+4)

6(6+4)-4(6+4)

36+24-24-16

36-16

Answer:

11. [tex]x^{5}[/tex]

12. 5*[tex]x^{2}[/tex]

13. x+21

14. 2x-8

Step-by-step explanation:

Answer:

180° Celsius is equal to approximately 356° Fahrenheit

Step-by-step explanation:

I hope this helps.

The value of 180 degree Celcius in Fahrenheit is 356.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Martha has a French cookie recipe that calls for baking the cookies for 14 to 18 minutes at 180∘C.

The temperature in Fahrenheit will be calculated as,

F = 1.8C + 32

F = ( 1.8 x 180 ) +32

F = 356

Therefore, the value of 180 degree Celcius in Fahrenheit is 356.

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Answer:

the answer is 2

Step-by-step explanation:

hope it helps

Answer:

2

Step-by-step explanation:

according to my calculator

Answer:

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

The line (y-1)=(2/3)(x+1) contains point (a,-3)

=> (-3-1) = (⅔)(a+1)

-4 = (⅔)(a+1(

(a+1)= -4 ÷ ⅔

a + 1 = -4 × 3/2

a+ 1 = -6

a = -6-1

a = -7

The value of 'a' will be;

⇒ a = - 7.

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The equation of line is,

⇒ (y - 1) = (2/3) (x + 1)

And, The point on the line = (a, - 3)

Now,

Since, The point on the line = (a, - 3)

Hence, It satisfy the equation of line.

Substitute x = a and y = - 3, we get;

⇒ (y - 1) = (2/3) (x + 1)

⇒ (- 3 - 1) = (2/3) (a + 1)

⇒ - 4 × 3 = 2a + 2

⇒ - 12 - 2 = 2a

⇒ 2a = - 14

⇒ a = - 7

Thus, The value of a = - 7

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Answer:

[-0.25 1.25]

[ ]

[-0.75 2.75]

If not satisfied than..

You can write it in other way as show in step by step

Step-by-step explanation:

Step 1:

First of all find the determinate.

Cross multiply the number 11 ✖ -1

= -11 ---eq1

And now cross multiply the number 3 ✖ - 5

= -15 ---eq2

Now we use eq 1 and 2

detA = (-11)-(-15)

Minus cancels minus

So it becomes

detA = -11 + 15

= 4

Step 2:

We find adjacent of the given.

[11 -5]

adjA= [ ]

[3 -1 ]

We change the places. The number 11 goes to in place of -1. -1 goes in place of 11.

And we change the signs of -5 and 3. -5 becomes 5 and 3 becomes -3.

We get

[-1 5]

adjA = [ ]

[-3 11]

Step 3:

Now we use the following formula

1

A^-1 = -------- adjA

detA

1 [-1 5]

A^-1 = ------- [ ]

4 [-3 11]

And now multiply

1

---- with each number of adjA.

4

And than subtract..

And you will get the inverse matrix

If the answer comes same than that's the answer for inverse matrix

Thank you.

Answer:

if we add 8 then the answer will be 30"

because

if 22is added 8 then it became 30

22+8= 30

simple

Answer:

area after 8 years is 2156km²

Step-by-step explanation:

Area of forest=4900 km²

decrease in area in 1 year=4900km² × 7%

decrease in area in 1 year= 343km²

decrease area in 8 years=343km² × 8

=2744km²

Remaining area= (4900-2744)km²

=2156km²

Note:If you have any question about it please ask.

Let the small , medium and large baskets be denoted by s,m & l

Formulating the equations

s+m+l= 80--------- equation1

$15.75s+ $25 m + $32.5l = $2086.25------equation2

2s=l---------equation 3

Using the technology  s=15, m=35 and l= 30

15+35+30= 80--------- equation1

$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2

2(15)=(30)---------equation 3

Yes because multiple variables can be easily calculated through matrices using technology

In Matrix form

[tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex] [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]     = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]

Let A= [tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex]

Z= [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]    

B = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]

Z= A⁻¹ B

A⁻¹= A mod/ det A

det A= -1

Using the technology  s=15, m=35 and l= 30

15 small baskets,

35 medium baskets

30 large baskets were sold.

Part C:

15+35+30= 80--------- equation1

$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2

236.25+ 875+ 975=$2086.25

$2086.25=$2086.25

2(15)=(30)---------equation 3

Answer 2:

Yes because multiple variables can be easily calculated using technology.

N.B There is a typing error in question its $2086.25 not 52086.25

Answer:

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Answer:

1) 43/40

2) 35/6

3) 43/40

4) -5/3

5) 1/6

Step-by-step explanation:

1)  -1 4/5 = -(1*5 +4)/ 5= -9/5

or          1= 5/5  so -1 4/5= -( 5/5+ 4/5)=-9/5

-2 7/8= -(2*8+7)/8=-23/8

=> -9/5 - ( -23/8)= -9/5 + 23/8 = (( -9*8)+(23*5))/40= (-72+ 115)/40

                                                                                =  43/40

2) 4 3/4= (4*4+3)/4= 19/4

-1 1/12= -(1*12+1)/12= -13/12

=> 19/4 - (-13/12)= 19/4 + 13/12 = ((19*3)+13)/12= (57+13)/12= 35/6

3) same like 1)

4) 3 1/3 = (3*3+1)/3= 10/3

=> 10/3 -5= (10- 3*5)/3= (10-15)/3= -5/3

5) -1/3 + 1/2= ((-1*2)+(1*3))/6 = (-2+3)/6= 1/6

Patterns are set of rules that guide the creation of a dataset. The observation from the first three designs are as follows:

The pattern

The first three design show that, as the design number increases (i.e. 1, 2, 3), the number of tiles used also increases (i.e. 7, 12, 19)

The expressions for the number of tiles

The design number and the number of tiles is represented as follows

[tex]1 \to 7[/tex]

[tex]2 \to 12[/tex]

[tex]3 \to 19[/tex]

From the designs, we observe that some tiles are at the middle, while other tiles are at the sides.

Design 1 has 1 tile at the center and 6 tiles at either sides.

So, we have:

[tex]1 \to 1 + 6[/tex]

[tex]2 \to 4 + 8[/tex]

[tex]3 \to 9 + 10[/tex]

Expand

[tex]1 \to 1^2 + 6 \to 1^2 + 2 \times 3 \to 1^2 + 2 \times (1 + 2)[/tex]

[tex]2 \to 2^2 + 8 \to 2^2 + 2 \times 4 \to 2^2 + 2 \times (2 + 2)[/tex]

[tex]3 \to 3^2 + 10 \to 3^2 + 2 \times 5 \to 3^2 + 2 \times (3 + 2)[/tex]

Notice the pattern,

The number of tiles in design n will be:

[tex]Tiles = n^2 + 2 \times (n + 2)[/tex]

Open bracket

[tex]Tiles = n^2 + 2n + 4[/tex]

Hence, the expressions for number of tiles in design n are:

[tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]

Technology to prove that both expressions are equivalent

To prove that [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] are equivalent using technology, the graphs of [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] can be plotted and then compared

The table and graph for the first 6 designs

The table entry for the first 6 designs is calculated as follows:

[tex]n = 1\ \ \ \ \ Tiles = 1^2 + 2 \times 1 + 4 = 7[/tex]        

[tex]n = 2\ \ \ \ \ Tiles = 2^2 + 2 \times 2 + 4 = 12[/tex]        

[tex]n = 3\ \ \ \ \ Tiles = 3^2 + 2 \times 3 + 4 = 19[/tex]        

[tex]n = 4\ \ \ \ \ Tiles = 4^2 + 2 \times 4 + 4 = 28[/tex]        

[tex]n = 5\ \ \ \ \ Tiles = 5^2 + 2 \times 5 + 4 = 39[/tex]        

[tex]n = 6\ \ \ \ \ Tiles = 6^2 + 2 \times 6 + 4 = 52[/tex]        

So, we have:

[tex]\begin{array}{cc}Design & {Tiles} & {1} & {7} & {2} & {12} & 3 & {19} & {4} & {28} & {5} & {39}& {6} & {52} \ \end{array}[/tex]

See attachment for the graph of the above table

All the points on the curve make sense in this scenario because all values are positive.

The pattern type

We have:

[tex]Tiles = n^2 + 2n + 4[/tex]

When an equation has a degree of 2, the equation is quadratic.

Hence, the pattern is quadratic.

The largest design that an empty sign of 10ft by 12ft can contain.

From the first three designs:

The number of tiles on a complete row and column are always the same.

Design 1 has 3 tiles in its complete row and column

Design 2 has 4 tiles in its complete row and column

Design 3 has 5 tiles in its complete row and column

The relationship between the design number (d) and the number of complete tiles (t) is:

[tex]d = t - 2[/tex]

For the 10ft by 12ft empty sign

[tex]t = 10[/tex] because [tex]10 < 12[/tex]

So, we have:

[tex]d = t - 2[/tex]

[tex]d = 10 - 2[/tex]

[tex]d = 8[/tex]

Hence, the largest design number is design 8

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Answer:

Option 1 is the correct equation.

Step-by-step explanation:

x = price of the student ticket.

One half price of x + $8 = adult ticket price ($15)

Answer:

The correct answer is A

Because taking the student ticket to be x

one half of x + 8 =15

Answer:

x > 2

Step-by-step explanation:

Distribute and cross-simplify 1/2 with parenthesis

4x + x + 2 > 12

Solve left side

5x + 2 > 12

Subtract 2 from both sides

5x > 10

Divide both sides by 5

x > 2

Answer:

92% of Income is  Rs 18400

Step-by-step explanation:

I = 18400/.92 = Rs 20000

Answer:

C. x^2 + 6x + 9

Step-by-step explanation:

(x+3)^2

using formula (a+b)^2= a^2 + 2ab + b^2,

(x)^2 + 2(x)(3) +(3)^2

=> x^2 + 6x + 9

Answer:

A

Step-by-step explanation:

(x)×2= 2x

(3)×2=6

x2 + 6....

Answer:

1st box is "a 90°clockwise rotation about the origin

2nd box is "a 180° rotation about the origin

3rd box is "a 90° counterclockwise rotation about the origin

3x = 18

Divide both sides by 3 and simplify

x=6

Answer:

Step-by-step explanation:

assuming  that you need to find the value of x

3x = 18

-divide both sides by 3

3x/3 = 18/3

-use the facts that 3/3 =1 and 18/3 = 3*6/3 = 6

x = 6