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3 years ago

Please answer this now in two minutes

Mathematics

1 answer:

Firlakuza [10]3 years ago

7 0

Answer:

x = 6.6

Step-by-step explanation:

Data obtained from the question include the following:

Angle X = 15°

Angle Y° = 23°

Side y = 10

Side x =..?

The value of side x can be obtained by using the sine rule as shown below:

x/Sine X = y/Sine Y

x/Sine 15 = 10/Sine 23

Cross multiply

x × Sine 23 = 10 × Sine 15

Divide both side by Sine 23

x = (10 × Sine 15) / Sine 23

x = 6.6

Therefore, the value of x is 6.6.

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Landon finds that the school cafeteria has 8,000 milliliters of grape juice, 4.2 liters

KengaRu [80]

Answer:

1) Part A)

Liters Mililiters

1 1,000

5 5,000

8 8,000

14 14,000

2) Part B)

One way to convert 4.2 liters to milliliters is to  multiply  the number of liters by the number of milliliters in 1 liter. This means there are  4,200 milliliters in 4.2 liters. The cafeteria has the greatest amount of  orange juice, the second greatest amount of  grape  juice, and the least amount of  cranberry juice.

Explanation:

1) Data:

Grape juice: 8,000 mililiters

Cranberry juice: 4.2 liter

Orange juice: 12,000 mililiters

There are 1,000 mililiers in 1 liter

2) Part A:

Table:

The table is garbled. This is what the tables could look like:

Liters Mililiters

1 1,000

5 5,000

8 8,000

14 14,000

You can see that the table shows a direct relationship between the number of mililiters and the number of liters:

1,000/1 = 1,000
5,000/5 = 1,000
8,000/8 = 1,000

14,000/14 = 1,000

number of mililiters / liters = 1,000

3) Part B)

Fill in the blanks to explain how Landon can convert 4.2 liters of cranberry juice to mililiters so he can compare the amounts of the different juices:

i) One way to convert 4.2 liters to milliliters is to  multiply  the number of

liters by the number of milliliters in 1 liter.

As demonstrated above there is a direct relationship between the number of mililiters and the number on liters, then you must multiply the number of liters by the proportionality constant to find the number of mililiters.

ii) This means there are  4,200 milliliters in 4.2 liters.

That is the product 4.2 × 1,000 = 4,200.

iii) The cafeteria has the greatest amount of  orange juice, the second greatest amount of  grape  juice, and the least amount of  cranberry juice.

Rank the amounts:

12,000 > 8,000 > 4,200

↑ ↑ ↑

orange grape cranberry

8 0

3 years ago

Identify the functions that are continuous on the set of real numbers and arrange them in ascending order of their limits as x t

Studentka2010 [4]

Answer:

g(x)<j(x)<k(x)<f(x)<m(x)<h(x)

Step-by-step explanation:

1. $f(x)=\frac{x^2+x-20}{x^2+4}$

The denominator of f is defined for all real values of x

Therefore, the function is continuous on the set of real numbers

$\lim_{x\rightarrow 5}\frac{x^2+x-20}{x^2+4}=\frac{25+5-20}{25+4}=\frac{10}{29}=0.345$

3. $h(x)=\frac{3x-5}{x^2-5x+7}$

$x^2-5x+7=0$

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function h is defined for all real values.

$\lim_{x\rightarrow 5}\frac{3x-5}{x^2-5x+7}=\frac{15-5}{25-25+7}=\frac{10}{7}=1.43$

2. $g(x)=\frac{x-17}{x^2+75}$

The denominator of g is defined for all real values of x.

Therefore, the function g is continuous on the set of real numbers

$\lim_{x\rightarrow 5}\frac{x-17}{x^2+75}=\frac{5-17}{25+75}=\frac{-12}{100}=-0.12$

4. $i(x)=\frac{x^2-9}{x-9}$

x-9=0

x=9

The function i is not defined for x=9

Therefore, the function i is not continuous on the set of real numbers.

5. $j(x)=\frac{4x^2-7x-65}{x^2+10}$

The denominator of j is defined for all real values of x.

Therefore, the function j is continuous on the set of real numbers.

$\lim_{x\rightarrow 5}\frac{4x^2-7x-65}{x^2+10}=\frac{100-35-65}{25+10}=0$

6. $k(x)=\frac{x+1}{x^2+x+29}$

$x^2+x+29=0$

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function k is defined for all real values.

$\lim_{x\rightarrow 5}\frac{x+1}{x^2+x+29}=\frac{5+1}{25+5+29}=\frac{6}{59}=0.102$

7. $l(x)=\frac{5x-1}{x^2-9x+8}$

$x^2-9x+8=0$

$x^2-8x-x+8=0$

$x(x-8)-1(x-8)=0$

$(x-8)(x-1)=0$

$x=8,1$

The function is not defined for x=8 and x=1

Hence, function l is not defined for all real values.

8. $m(x)=\frac{x^2+5x-24}{x^2+11}$

The denominator of m is defined for all real values of x.

Therefore, the function m is continuous on the set of real numbers.

$\lim_{x\rightarrow 5}\frac{x^2+5x-24}{x^2+11}=\frac{25+25-24}{25+11}=\frac{26}{36}=\frac{13}{18}=0.722$

g(x)<j(x)<k(x)<f(x)<m(x)<h(x)

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3 years ago

One cube has a volume of 192 cm3, and another has a volume of 375 cm3. How much longer is the edge of the larger cube than that

vesna_86 [32]

Answer:

134

Step-by-step explanation:

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