use r =27 & x =3

[tex]-\frac{r}{9}+ 5x[/tex]

Answer:

so both tables are proportional

1. in the green table

y divided by x =

1/5 for each row

2. in the blue table

y divided by x =

2/5 for each row

Step-by-step explanation:

/ means divided by

divide y by x

for both tables

in each table

if y divided by x

show the same number

for every row

then its proportional

1. in the green table

y divided by x =

1/5 for each row

2. in the blue table

y divided by x =

2/5 for each row

so both tables are proportional

Solution given:

it is a right angled isosceles triangle

so

perpendicular [p]=base[b]=5

hypotenuse [h]=x

we have

by using Pythagoras law

p²+b²=h²

5²+5²=h²

50=h²

h=[tex]\sqrt{50}[/tex]

x=[tex]\bold{5\sqrt{2}}[/tex]

Answer:

A = 127.48 rounded

Step-by-step explanation:

Area of a circle:  

A = [tex]\pi r^{2}[/tex]

A = [tex]\pi[/tex][tex](6.37)^{2}[/tex]

A = 127.48 rounded

Answer:

It's 127.47

First we take the radius and square it

6.37^2

then we multiply it by pi

40.5769 x π = 127.47

Answer:

9 < x

6 - f

t × 6

1/2n

Step-by-step explanation:

Given expressions:

9 less than x

Less than (<)

9 less than x = 9 < x

6 minus f

Minus (-)

= 6 - f

t multiplied by 6

Multiplication (×)

= t × 6

one half of a number n

One half = 1/2

one half of a number n

= 1/2 × n

= 1/2n

= n/2

The closer to 1 the r value the closer the dots make a straighter line.

A positive value the distance move up to the right, a negative value the dots move down to the right.

A = r = -0.33

B = r = -0.75

C = r = 0.72

D = r = 0.89

Answer:

d

Step-by-step explanation:

Answer:

yes , k = 9

Step-by-step explanation:

The equation of a proportional relationship is

y = kx ← k is the constant of proportion

To find k divide both sides by x

[tex]\frac{y}{x}[/tex] = k

Check each ordered pair in the table

k = [tex]\frac{18}{2}[/tex] = 9

k = [tex]\frac{45}{5}[/tex] = 9

k = [tex]\frac{63}{7}[/tex] = 9

Thus the relationship is proportional with k = 9

Answer:

[tex]q < 33[/tex]

Step-by-step explanation:

[tex]q < 11 \times 3[/tex]

[tex]q < 33[/tex]

Answer:

33

Step-by-step explanation:

q/3<11

q=11×3

q=33

:. The answer is 33.

Answer:

-49

Step-by-step explanation:

-3^2=-9

(2-6)*10=-40

(-9) + (-40) = -49

Answer:

1134

Step-by-step explanation:

We have 3 digits:

a, b, c

a 3 digit number can be written as:

a*100 + b*10 + c*1

Such that these numbers can be:

{1, 2, 3, 4, 5, 6, 7, 8, 9}

Let's assume that:

a < b < c

Then the 3 smaller numbers are:

a*100 + b*10 + c

a*100 + c*10 + b

b*100 + a*10 + c

The 3 larger numbers are:

b*100 + c*10 + a

c*100 + a*10 + b

c*100 + b*10 + a

We know that the sum of the 3 smaller numbers is equal to 540, then:

(a*100 + b*10 + c) + (a*100 + c*10 + b) + (b*100 + a*10 + c) = 540

Let's simplify this:

(a + a + b)*100 + (b + c + a)*10 + (c + b + c) = 540

(2a + b)*100 + (b + c + a)*10 + (2c + b) = 540

The sum of the 3 larger numbers is equal to X, we want to find the value of X:

(b*100 + c*10 + a) + (c*100 + a*10 + b) + (c*100 + b*10 + a) = X

Now let's simplify the left side:

(b + c + c)*100 + (c + a + b)*10 + (a + b + a)*1 = X

(b + 2*c)*100 + (c + a + b)*10 + (2a + b) = X

Then we have two equations:

(2a + b)*100 + (b + c + a)*10 + (2c + b) = 540

(b + 2*c)*100 + (c + a + b)*10 + (2a + b) = X

Notice that the terms are inverted.

By looking at the first equation, we can see that:

(2c + b) = 10    (because the units digit of 540 is 0)

Then, we can see that:

(b + c + a + 1 ) = 14   (the one comes from the previous 10)

finally:

(2a + b + 1) = 5   (the one comes from the previous 14)

Then we can rewrite:

(2*c + b) = 10

(b + c + a) = 14 -1  = 13

(2a + b) = 5 - 1 = 4

Now we can replace these 3 in the equation:

(b + 2*c)*100 + (c + a + b)*10 + (2a + b) = X

(10)*100 + (13)*10 + 4 = X

1000 + 130 + 4 = X

1134 = X

The sum of the 3 largest numbers is 1134.

Answer:

1/9

You are being asked to "complete the square"

you need to find a value to make the quadratic a "perfect square:

the focus is -2/3 you need to "add" one half of -2/3 squared to the

equation (1/2 * -2/3)^2 .... (-2/6)^2 .... 4/36 .... 1/9

Step-by-step explanation:

Answer two 20p coins make 40p

Step-by-step explanation:

Answer:

20 number of 20p makes £4.

Step-by-step explanation:

Let the number of 20p be x

Therefore,

                [tex]x \times 0.20 = 4\\\\x = \frac{4}{0.20} = \frac{4 \times 100}{ 20} = 4 \times 5 = 20[/tex]

Answer:

$7.58/lb

Step-by-step explanation:

raw roast: $5.99 per lb

deli roast: $2.99 for 100g

We know the price per lb of the raw roast.

Let's find the price per lb of the deli roast.

1 lb = 454 grams

454 grams / 100 grams = 4.54

1 lb is 4.54 times 100 g

If we multiply the price of 100g of deli roast by 4.54, we get teh price per lb.

$2.99/lb * 4.54 = $13.57/lb

raw roast: $5.99/lb

deli roast: $13.57/lb

difference in price of 1 lb: $13.57 - $5.99 = $7.58

Answer: $7.58/lb

Answer:

.01669 $/g or $7.57 $/lb

Step-by-step explanation:

$2.99/100g = .0299 $/g

1 lb = 453.59237 g.

$5.99/453.59237 g= .0132$/g

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]0 \to[/tex] Correct

[tex]1 \to[/tex] Defective

Required

The probability that the next is defective

The question is incomplete because the list of bottles that came out is not given.

However, the formula to use is:

[tex]Pr = Num ber\ o f\ d e f e c t i v e \div T o t a l\ b o t t l e s[/tex]

Take for instance, the following outcomes:

[tex]0\ 1\ 0\ 0\ 0\ 1\ 0\ 0\ 1\ 1\ 0\ 0\ 0\ 1[/tex]

We have:

[tex]Total = 14[/tex]

[tex]D e f e ctive = 9[/tex] --- i.e. the number of 0's

So, the probability is:

[tex]Pr = 9 \div 14[/tex]

[tex]Pr = 0.643[/tex]

Answer:

1/20

Step-by-step explanation:

000000000000100000

It is asking the probability of a defective bottle

there is one defective bottle out of 20

Answer:

64

Step-by-step explanation:

2x2x2x2x2x2 = 64

Answer:

8 Times, Mark would expect to roll a one 'Eight times'

Answer:

b + 24

Step-by-step explanation:

b and 24 would be b + 24

............................

...............................................................................................................................................................................................................................................................................................................

Answer:

Option C.

Step-by-step explanation:

For a given set of N elements:

{x₁, x₂, ..., xₙ}

The mean is given by:

[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]

And the variance is given by:

[tex]v = \frac{(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_n - M)^2}{N}[/tex]

Then for our set:

{70, 80 ,75, 75, 80}

We have 5 elements, then N = 5

The first thing we need to find is the mean.

[tex]M = \frac{70 + 80 + 75 + 75 + 80}{5} = 76[/tex]

Then the variance will be:

[tex]v = \frac{(70 - 76)^2 + (80 - 76)^2 + (75 - 76)^2 + (75 - 76)^2 + (80 - 76)^2}{5} = 14[/tex]

The correct option is C, 14.

We have that

x - 3y = 12 and -x + y = 4

We add the 2 equations together

x - 3y + (-x + y) = 16

-> -2y = 16

-> y = -8 (1)

We plug y = -8 into -x + y =4

-> -x - 8 = 4

-> -x = 12

-> x = - 12 (2)

From (1) and (2) we could conclude that the answer is B

Answer:

Step-by-step explanation:

x - y = 30

Substitute 15 for y.

x - (15) = 30

Add 15 to both sides.

x = 45

Answer:

[tex]{ \tt{h(t) = - 10t + 6}} \\ - 44 = - 10t + 6 \\ - 10t = - 50 \\ t = 5[/tex]

Answer:

h(5)

Step-by-step explanation:

Equate - 10t + 6 and - 44 and solve for t

- 10t + 6 = - 44 ( subtract 6 from both sides )

- 10t = - 50 ( divide both sides by - 10 )

t = 5 , that is

h(5) = - 44

Answer:

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

Step-by-step explanation:

We want to solve the equation:

[tex]\displaystyle \sqrt{x^2-4x+8}+x=2-x[/tex]

We can isolate the square root. Subtract x from both sides:

[tex]\sqrt{x^2-4x+8}=2-2x[/tex]

And square both sides:

[tex](\sqrt{x^2-4x+8})^2=(2-2x)^2[/tex]

Expand:

[tex]x^2-4x+8=4-8x+4x^2[/tex]

Isolate the equation:

[tex]3x^2-4x-4=0[/tex]

Factor:

[tex]\displaystyle (3x+2)(x-2)=0[/tex]

Zero Product Property:

[tex]3x+2=0\text{ or } x-2=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle x=-\frac{2}{3}\text{ or } x=2[/tex]

Now, we need to check for extraneous solutions. To do so, we can substitute each value back into the original equation and check whether or not the resulting statement is true.

Testing x = -2/3:

[tex]\displaystyle \begin{aligned} \sqrt{\left(-\frac{2}{3}\right)^2-4\left(-\frac{2}{3}\right)+8}+\left(-\frac{2}{3}\right)&\stackrel{?}{=}2-\left(-\frac{2}{3}\right)\\ \\ \sqrt{\frac{4}{9}+\frac{8}{3}+8}-\frac{2}{3}&\stackrel{?}{=}2+\frac{2}{3} \\ \\ \sqrt{\frac{100}{9}}-\frac{2}{3}& \stackrel{?}{=} \frac{8}{3}\\ \\ \frac{10}{3}-\frac{2}{3} =\frac{8}{3}& \stackrel{\checkmark}{=}\frac{8}{3}\end{aligned}[/tex]

Since the resulting statement is true, x = -2/3 is indeed a solution.

Testing x = 2:

[tex]\displaystyle \begin{aligned}\sqrt{(2)^2-4(2)+8}+(2) &\stackrel{?}{=}2-(2) \\ \\ \sqrt{4-8+8}+2&\stackrel{?}{=}0 \\ \\ \sqrt{4}+2&\stackrel{?}{=}0 \\ \\ 2+2=4&\neq 0\end{aligned}[/tex]

Since the resulting statement is not true, x = 2 is not a solution.

Therefore, our only solution to the equation is x = -2/3.  

Step-by-step explanation:

Hey there!

Given;

[tex] \sqrt{ {x}^{2} - 4x + 8} + x = 2 - x[/tex]

Take "X" in right side.

[tex] \sqrt{ {x - 4 + 8}^{2} } = 2 - 2x[/tex]

Squaring on both sides;

[tex] {( \sqrt{ {x}^{2} - 4x + 8 } )}^{2} = {(2 - 2x)}^{2} [/tex]

Simplify;

[tex] {x}^{2} - 4x + 8 = {(2)}^{2} - 2.2.2x + {(2x)}^{2} [/tex]

[tex] {x }^{2} - 4x + 8 = 4 - 8x + 4 {x}^{2} [/tex]

[tex]3 {x}^{2} - 4x - 4 = 0[/tex]

[tex]3 {x}^{2} - (6 - 2)x - 4 = 0[/tex]

[tex] 3 {x}^{2} - 6x + 2x - 4 = 0[/tex]

[tex]3x(x - 2) + 2(x - 2) = 0[/tex]

[tex](3x + 2)(x - 2) = 0[/tex]

Either;

3x+2 = 0

x= -2/3

Or;

x-2 = 0

x= 2

Check:

Keeping X= -2/3,

√(x²-4x+8 ) +X = 2-x

√{(-2/3)²-4*-2/3+8}+(-2/3) = 2+2/3

8/3 = 8/3 (True)

Now; Keeping X= 2

√{(2)²-4*2+8}+2 = 2-2

8 ≠0 (False)

Therefore, the value of X is -2/3.

Hope it helps!

Answer:

$1.70

Step-by-step explanation:

To figure out how much each apple costs, divide $1.50 by the quantity of apples (6). The answer to that is $0.25, so multiply it by the two apples to get $0.50.

For the oranges, divide $3 by 5. The answer for that is $0.60. Multiply that by the two oranges to get $1.20.

Then, add $0.50 to $1.20 to get a total of $1.70

Answer:

$1.70

Step-by-step explanation:

We know that you can buy 6 apples for $1.50 and 5 oranges for $3.00. So let's look at the cost for one individual apple first.

To find the amount/apple we can divide $1.50 by 6. Here's another way to look at it:

Assume A is cost per apple.

6A = $1.50

6A/6 = $1.50/6

A = $0.25

Now to find the amount for 2 apples, you want to multiply the amount it costs for one apple by 2, because you are multiplying the quantity by 2 as well.

A= $0.25

A *2 = $0.25 * 2

2A = $0.50

So for two apples, it is 50 cents.

We can use a similar process for oranges but with a different price and quantity.

Assume R is cost per orange.

5R = $3.00

5R/5 = $3.00/5

R = $0.60

To find the amount for two oranges we multiply the cost by two.

R = $0.60

R*2 = $0.60*2

2R = $1.20

Finally, we want the total amount for apples AND oranges so we find the sum.

$0.50 + $1.20 = $1.70

Answer:19 You can use addition 12+7=19 19-7=12

Answer:

y= x + 3

Step-by-step explanation:

we know that

The linear equation in slope-intercept form is equal to

y= mx + b

where

m is the slope

b is the y-intercept

step 1:

Find the slope

Take two points from the graph

see the attached figure

about (37,40) and (47,50)

The formula to calculate the slope between two points is equal to: y2-y1

                                                                                                               x2-x1              

substitute

M= 50-40/47-37

10/10 = 1

step 2:

Find the y-intercept

we have: m=1

point (37,40)

substitute in the linear equation: 40= (1) (37) + b

solve for b: 3

therefore

The linear equation is: y = x + 3

Answer:

The answer is 90cm

Step-by-step explanation:

Hello,

Lateral area = (3+3+3+3)*6=4*3*612*6=72 (cm²)

Bases area= 2*3²=18 (cm²)

Total area= 72+18=90 (cm²)