Write the ratio as a fraction in simplest form.

51:9

Given:

The expression is

[tex]13\sqrt {22b}-10\sqrt{22b}, b>0[/tex]

To find:

The equivalent expression.

Solution:

We have,

[tex]13\sqrt {22b}-10\sqrt{22b}[/tex]

Taking out common factors.

[tex]=(13-10)\sqrt {22b}[/tex]

[tex]=(3)\sqrt {22b}[/tex]

[tex]=3\sqrt {22b}[/tex]

The expression [tex]3\sqrt {22b}[/tex] is equivalent to the given expression.

Therefore, the correct option is D.

Answer:

I would need to know the number of radios she made each day.

Step-by-step explanation:

lets say she assembled 2 radios a day, which means we would do 0.54 x 2 (that would be 1.08) and then times it by 6 ***not incuding sunday***

you would get $6.48

then for sunday we would do 0.62 x 2 (that would be 1.24) .

now we add 6.48 and 1.24 to get $7.72 a week.

Answer:s=10.50 and p=27

Step-by-step explanation:

Answer:

Step-by-step explanation:

The key to answering this is to know that the only time you'll change the direction of the sign is when you multiply or divide by a negative number.

-46 - 8x > 22

-8x > 22 + 46

-8x > 68

x < 68/-8        (we divided by -8 so the inequality changed direction)

x < -17/2

Step-by-step explanation:

-46 - 8x > 22: Original problem

-46 - 8x + 46 > 22 + 46: Bringing all the constants to one side of the inequality

-8x > 68: Simplification

x < 68/-8 : You have to flip the inequality symbol because you are dividing by                                

                  a negative number..

x< -8.5 : The answer!!!!!

Checking your answer....

-46 - 8x > 22 : Original problem

-46 - 8(-8.5) > 22 : Substitution

-46 + 68 > 22 : Simplification

22 > 22 : Answer check successful!!!

(22 is not greater than 22 but we know that the answer cannot be -8.5 because the inequality states that x is less -8.5. This process was only for the purpose of checking not for the purpose of proving)

Hope this helps!!!!

Answer:

44°

Step-by-step explanation:

8x-4 = 6x+8

8x - 6x = 8 + 4

2x = 12

x = 12/2

x = 6

then:

8*6 - 4 = 48 - 4 = 44°

The measure of angle 1:

44°

Step-by-step explanation:

subtract b to get P-b=2a. divide each side by 2 to get (P-b)/2=a

Answer:

Step-by-step explanation:

[tex]2a +3(a +7)-(3a +3)\\\\Expand\: 3(a +7) :\\3a+21\\\\=2a+3a+21-\left(3a+3\right)\\\\-(3a+3)=-3a-3\\\\=2a+3a+21-3a-3\\\\Simplify\\\\=2a+18[/tex]

Answer: 6.68km/litre

Step-by-step explanation:

Distance(d) = 187km ( to 3 significant figures)

Petrol(p) = 28litres ( to 2 significant figures)

A number, x, rounded to 1 significant figure is 200

Write down the error interval for x

Calculating the lower and upper bound for both 'd' and 'p'

Upper bound 'd' = 187.5km

Lower bound 'd' = 186.5km

Upper bound 'p' = 28.5km

Lower bound 'p' = 27.5km

Therefore,

Petrol consumption (C) = d/p

Upper C = 187.5 / 28.5 = 6.57894

Lower C = 186.5 / 27.5 = 6.781818

Accuracy answer for C = (6.57894 + 6.781818) / 2 = 6.680379

= 6.68km/ litre ( to 3 significant figures)

To achieve a reasonable level of accuracy, the upper and lower bounds of P and D was used to calculate C, which was then averaged.

Using 3 significant figures ensure that we capture the C better, instead of early rounding.

Answer:

12.90%

Step-by-step explanation:

Given ;

Original price = 171.50

Sale price = 149.37

To find the % markdown :

Markdown = Purchase price - sale price

171.50 - 149.37 = 22.13

(Markdown / purchase price) * 100%

(22.13 / 171.50) * 100%

0.1290379 * 100%

= 12.90%

Answer:

yes True

Step-by-step explanation:

thank you so much

Answer:

9 sleeves for 22.99

Step-by-step explanation

The first pack has a unit rate of $11.49/ 4 balls

=$2.8725

The second pack has a unit rate of $16.79/6balls

=$2.798 per ball

the third pack has a unit rate of $22.99/9balls

=2.554

So, I would definitely go for the third pack since it has the least cost.

Answer= s > 10/2

s > -10/-2

s > 10/2

Answer:

5

Step-by-step explanation:

Step-by-step explanation:

sogzglzotsoypysotaota9t8ts

It would be 120 ye  f  = 8  E = 3 1/2  

Answer:

the answer is b

Step-by-step explanation:

12:

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Given that,

Initial cost of a t-shirt = $30

Final cost of a t-shirt = $37.50

We need to find percent of change. The percentage change in any value is given by :

[tex]\%=\dfrac{\text{final value-initial value}}{\text{initial value}}\times 100\\\\=\dfrac{37.5-30}{30}\times 100\\\\=25\%[/tex]

Hence, the percentage error is 25%.

Answer:

look in explanation

Step-by-step explanation:

1) bisector means cutting an angle in half. the small lines between segment SM and MT mean they are congruent. this means MW is a bisector. Since both halves of ST are congruent, we know SM = 19. 19+19=38

2) same logic here, M bisects ST. set both halves of ST equal to each other and solve.

3x-6=x+8

2x+14

x=7

plug back in to find MT (7)+8=15. MT=SM so double 15 to get ST. ST=30

3) the bisector will be exactly halfway between the points.

4) find difference between x and y values, and divide by 2

2-2=0 0/2=0 x moves 0

13-1=12 12/2=6 y moves 6

so add 0 and 6 to 2,1 to get (2,7)

5) same process

6--6=12 12/2=6

6-0=6 6/2=3

add 6 and 3 to -6,0 to get (0,3)

6) find the change in x and y between the coordinate sets. (x: 1- -1=2) (y: 2-4=-2) take the opposite of those values and add them to M

(x:1-2=-1) (y:2+2=4)

(-1, 4) are the other coordinates for C

7) take the same steps

(x:3-1=2) (y:7-1=6)

use -2 and -6

(x:3-2=1) (y:7-6=1)

(1,1) are other coordinates for C

8) use distance formula

sqrt (x1-x2)^2 + (y1-y2)^2

sqrt(1--1)^2 +(2-4)^2

sqrt (2)^2 +(-2)^2

sqrt 4+4

sqrt 8

9) same process

sqrt (-1-3)^2+(-5--8)^2

sqrt (-4)^2 +(3)^2

sqrt 16+9

sqrt 25

5

Answer:

Step-by-step explanation:

The quotient of

Answer:

The equation is;

C = kg

c is the cost in $

k is the proportionality constant $/can

g is the number of cans

cost of 5 cans of coffee is $46.25

Step-by-step explanation:

From the question, 2 cans of ground coffee costs $18.50

Let c be the cost and g be the number of ground coffee

18.50 = k * 2

where k is the constant of proportionality;

k = 18.5/2

k = 9.25

So, the cost of 5 coffee cans will be;

c = 9.25 * 5 = $46.25

Answer:

x=5

Step-by-step explanation:

Angles in a triangle adds up to 180 degrees

so 105 + (6x+20) + (7x-10) = 180

simplify

115+13x=180

subtract 115 to each side

13x=65

divide by 13

x=5

check work

105 + (6(5) + 20) + (7(5) -10)

105 + (30 +20) +(35 - 10)

105 + 50 + 25 = 180

1. 1\10

2. 1/4

3.16

Step-by-step explanation:

your welcome

Answer:

13.33 pink roses

Step-by-step explanation:

We are told the floral arrangements are proportional , hence:

6 white roses = 8 pink roses

10 white roses = x

Cross Multiply

6 white roses × x = 10 white rose × 8 pink roses

x = 10 white roses × 8 pink roses/6 white roses

x = 13.333333333 pink roses

x ≈ 13.33 pink roses

Answer:

I believe it is $21.24 im sure

Answer: 2100 square feet

Step-by-step explanation: 60 x 35=2100

Answer:

2100 ft squared!

Step-by-step explanation:

The formula to find the area of a rectangle is L * W = A

Where A is the total area, and L and W are the dimensions.

Since we know what the dimensions of the rectangles are, we can replace L and W to find out the area. This will look like this: 60 * 35 = A

Now we just have to multiply 60 and 35 to find A. This will simplify to 2100, which means the total are of the rectangle, or in this case, the soccer field, is 2100 ft squared!

Answer:

The measure confirming that PQRS would be 25

Step-by-step explanation:

It's easier if you draw it down.

1. We need to make this shape a parallelogram and the way we will do that is by making angle Q and angle S the same, because in parallelograms those opposite angles are required to be the same.  

                             \

                        155 \

P \ -------------------------\ Q

    \                         25 \

      \                               \     so that's your shape  

   S   \______________\ R

2.We were given that the exterior angle of Q measures 155, and since exterior and interior angles combined make 180, then we can assume that the interior angle of Q is 25.

3. As mentioned before, in a parallelogram, opposite angles are the same and  therefore PSR (which is just asking for the middle letter, S) is equal to 25 because Q is also 25.  

Answer:

mark of the fifth exam = 60

Step-by-step explanation:

Mean = sum of all marks / number of exam

Mean = 70

Number of exam = 5

Let x =

Mean = sum of all marks / number of exam

70 = (65 + 80 + 76 + 69 + x) / 5

Cross product

70 × 5 = (290 + x)

350 = 290 + x

350 - 290 = x

x = 60

mark of the fifth exam = 60

Answer: i think its c

Step-by-step explanation:

Answer:

5 for the green box and 9 for the purple one

Step-by-step explanation:

Answer:

(2,1)

Step-by-step explanation:

2x - 2y = 2

5x + 2y = 12

2x + 5x = 7x

-2y + 2y = 0

2 + 12 = 14

7x = 14

7x/7 = 14/7

x = 2

2x - 2y = 2

2(2) - 2y = 2

4 - 2y = 2

-2y = 2 - 4

-2y = -2

-2y/-2 = -2/-2

y = 1

Answer:

(4, 22)

Step-by-step explanation:

y = 5x + 2

y  = 3x + 10

Since both equations are equal to y, we can have both equations equal to each other).

5x + 2 = 3x + 10

5x + 2 - 3x - 2 = 3x + 10 - 3x - 2

5x - 3x = 10 - 2

2x = 8

2x/2 = 8/2

x = 4

(Substitute the x value to any equation to solve for y).

y = 5x + 2

y = 5(4) + 2

y = 20 + 2

y = 22

So, the answer is (4, 22).

Hope this helped! <3

it is -23 I think

Step-by-step explanation:

(-5)+(-18)=-23