at a basketball game, a vender sold a combined total of 166 sodas and hot dogs. The number of hot dogs sold was 54 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold. ​

[tex]\sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex]      or     [tex]\sf \dfrac{54a-52}{24}[/tex]

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[tex]\sf \rightarrow 7\left(\dfrac{5}{14}a-\dfrac{5}{21}\right)-\dfrac{1}{12}\left(3a+6\right)[/tex]

use distributive method

[tex]\sf \rightarrow \dfrac{5a}{2}-\dfrac{5}{3}-\dfrac{a}{4}-\dfrac{1}{2}[/tex]

group terms

[tex]\rightarrow \sf \rigtharrow \dfrac{5a}{2}-\dfrac{a}{4}-\dfrac{5}{3}-\dfrac{1}{2}[/tex]

make the denominators same

[tex]\rightarrow \sf \rigtharrow \dfrac{2(5a)}{4}-\dfrac{a}{4}-\dfrac{2(5)}{6}-\dfrac{3(1)}{6}[/tex]

simplify

[tex]\rightarrow \sf \rigtharrow \dfrac{10a-a}{4}-\dfrac{10+3}{6}[/tex]

answer in separate constants

[tex]\rightarrow \sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex]

make the denominators same

[tex]\rightarrow \sf \dfrac{6(9a)}{24}-\dfrac{4(13)}{24}[/tex]

simplify

[tex]\rightarrow \sf \dfrac{54a}{24}-\dfrac{52}{24}[/tex]

join both fractions

[tex]\rightarrow \sf \dfrac{54a-52}{24}[/tex]

Answer:

 [tex]\boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]

Step-by-step explanation:

[tex]7(\dfrac{5a}{14} - \dfrac{5}{21} ) - \dfrac{(3a + 6)}{12}[/tex]

Step-1: Simplify the distributive property

⇒ [tex]\dfrac{35a}{14} - \dfrac{35}{21} - \dfrac{(3a + 6)}{12}[/tex]

Step-2: Make common denominators

⇒ [tex]\dfrac{35a \times 3}{14 \times 3} - \dfrac{35 \times 2}{21 \times 2} - \dfrac{7 \times (3a + 6)}{12 \times 7}[/tex]

⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{7 \times (3a + 6)}{84}[/tex]

Step-3: Simplify the distributive property

⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a + 42}{84}[/tex]

Step-4: Rewrite (21a + 42)/84 in a different way

⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a}{84} + \dfrac{42}{84}[/tex]

Step-5: Add/Subtract if necessary

⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}}[/tex]

Step-6: Simplify the fractions

⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}} = {\dfrac{9a}{4} - \dfrac{49}{42}} = \boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]

Answer: Roses 2.70 Lillies 2.45 Carnations 1.60

Step-by-step explanation:

I dont know if its wrong its mostly correct but hope it helps

Answer: 13°

Explanation: x = tan^-1 ( 9/40) ≈ 13°

Answer:

5.907

Step-by-step explanation:

I believe if you multiply 3 times 1.79 you get 5.37 then if you multiply 0.3 times 1.79 you get 0.537. If you combine the 2 you get 5.907. I think this is correct not sure though D:

Answer:

238

Step-by-step explanation:

You have to find the area for each box and then you add all of them together

Answer:

238 mm²

Surface area of rectangular prsim = 2(lw + lh + wh)

Here,

length = 11 mm

width = 4 mm

height = 5 mm

area:

Two solids with the same surface and different volumes are a cube of side length of 1 unit, and a sphere of radius of 0.69 units.

First, let's define a cube of a side length of 1 unit. The surface of this cube is equal to 6 times the area of one of the faces, or:

S  = 6*(1 unit square) = 6 units square.

And the volume is equal to the side length cubed, so we have:

V = (1 unit)^3 = 1 unit cubed.

Now, let's find a sphere with the same surface than our cube. For a sphere of radius R, the surface is:

S = 4*3.14*R^2

Then we must have:

4*3.14*R^2 = 6 units square

R = √(6/(4*3.14)) units = 0.69 units.

And the volume of this sphere is:

V = (4/3)*3.14*R^3 = (4/3)*3.14*(0.69 units)^3 = 1.38 cubic units.

So the sphere has the same surface and more volume.

If you want to learn more about solids, you can read:

https://brainly.com/question/10171109

Step-by-step explanation:

2mm : 16m

so to get 1mm you need to divide 16 by 2

16/2 is 8 therefore

1mm : 8m

1 millimeter represents 8 meters in real life

hope that helps :)

The small does 2 1/2 for 1/4 of the large. Multiply by 4 to get a full rotation of the large one:

2 1/2 x 4 = 10

answer: D. 10

Answer:

y= -12/x + 3

Step-by-step explanation:

Here's my answer

Answer:

the common factors for both are 1,2,3,6

The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.

For the graph, the domain lie across the x-axis. The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

Note that point where the circles are shaded shows a closed interval

Learn more on domain and range here: https://brainly.com/question/1942755

Answer:

Missing Angle = 26⁰ ( corresponding angles )

Answer:

I believe it is Dissolve.

Answer:

its A becauss i tryed b and th en i tried A so its a

Answer:

see below

Step-by-step explanation:

10^33/2

Rewriting the numerator as 10 * 10 ^ 32

10 * 10 ^32

--------------------

2

10/2 = 5

5 * 10 ^32

Therefore

10^33/2=5*10^32

Answer: False

Step-by-step explanation:

68%

Key Takeaways. The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

Answer:

12.12

Step-by-step explanation:

7^2+x^2=14^2, as by the Pythagorean theorem.

49+x^2=196,

x^2=147,

square root of 147;

it's close to 144,

thus, 12.12

Answer:

If the broker Josef employed to purchase these stocks and bonds charges a commission of $72 for each ten shares of stock bought or sold and a commission of 4% of the market value of each bond bought or sold, then the bonds have a yield 1.35 percentage points higher than that of the stocks.

Step-by-step explanation:

Answer:

yes you are correct :)))

Answer:

5/32 square miles or 0.15625 square miles

Step-by-step explanation:

1/4 miles × 5/8 miles

=5/32 square miles or 0.15625 square miles

Answer:

its yes

Step-by-step explanation:

because it's x 2  I hope this helps      

Answer:

112m

Step-by-step explanation:

A = lw

A = 10(26)

A = 260

1380 - 260 = 1120

1120 = 10(w)

1120 / 10 = 112

Answer:

[tex](2x - 5)^2[/tex]

Step-by-step explanation:

[tex]y = 4x^2 -20x + 25\\\rightarrow (2x - 5)(2x - 5)\\\rightarrow (2x - 5)^2\\\\\text{checking...}\\(2x - 5)^2 = (2x - 5)(2x - 5) = 4x^2 - 10x - 10x + 25 = 4x^2 - 20x + 25[/tex]

The operation between a rational and a irrational number that results in a rational number is a multiplication, hence the expression ab could represent a rational number.

If a number can be represented by a fraction, it is rational, otherwise, it is irrational.

The addition/subtraction of a rational and an irrational numbers is irrational, while the multiplication is rational, hence the expression ab could represent a rational number.

More can be learned about rational numbers at https://brainly.com/question/10814303

Answer:

which one's anwer you want

2. length= 65 ft width=24 m area=135 in2

Answer:

104

Step-by-step explanation:

1st term + or - common difference (term -1)

common difference is +6

2 + 6 (18-1)

2 + 6 (17)

2 + 102

104

Answer:

33

Step-by-step explanation:

For 4 triangles area 4*(1/2)*4*3=24

base square area 3*3=9

all together 24+9= 33  

Answer:

•WHAT IS PERIMETER?

>> PERIMETER MEANS THE SUM OF ALL SIDES OF FIGURE

NOW,LET'S SEE YOUR GIVEN QUESTION.

THE FIGURES 2 SIDES DATA IS GIVEN

•6CM

•5.5CM

THEREFORE : 6 + 5.5

: 11.5 CM

THE PERIMETER OF FIGURE IS 11.5 CM