determine the values of the missing entries. reduce all fractions to the lowest terms
9x-6y= 18

Answer and Explanation:

The problem provides the following information:

Hypotenuse

=

h

y

p

=

5129

ft

Vertical drop

=

o

p

p

=

1275

ft

To find the angle of depression, the best trigonometric ratio to use is the sine ratio. After equating it with the ratio of the opposite side over the hypotenuse, get the inverse of the sine ratio as shown:

sin

θ

=

o

p

p

h

y

p

θ

=

sin

−

1

(

o

p

p

h

y

p

)

θ

=

sin

−

1

(

1275

ft

5129

ft

)

θ

=

sin

−

1

(

0.2485864691

)

θ

=

14.3938824691

≈

14.4

∘

The angle of depression is

14.4

The answer to this question is:

The actual distance between the two towns = 130 km

Given that according to  the map scale,

Distance between two towns = 2.6cm

Given that the scale of map =

                                           1cm = 50km

So, we are asked to find the actual distance between them.

For finding the distance between two towns, we have to multiply the distance from the map by the scale of the map.

Distance between two towns * scale of the map

= 2.6 * 50 km

= 130 km

Therefore, actual distance between the two towns = 130 km

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The coefficient matrix for the given system of equations is as follows:

[tex]\left[\begin{array}{ccc}2&-6&-1\\-10&9&5\\3&0&5\end{array}\right][/tex]

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The augmented matrix of a system is composed as follows:

In standard notation, this system is given as follows:

Hence the augmented matrix is given by:

[tex]\left[\begin{array}{ccc}2&-6&-1\\-10&9&5\\3&0&5\end{array}\right][/tex]

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We get the values of RS and RT as 6 and 17 respectively after solving the equations.

We are given the equations:

RS = 2x - 8

ST = 11

RT = x + 10

Now, we know that:

RS + ST = RT.

Substituting the values, we get that:

2 x - 8 + 11 = x + 10

2 x + 3 = x + 10

2 x - x = 10 - 3

x = 7

Now substituting it to find RS and RT:

RS = 2 x - 8

RS = 2 ( 7 ) - 8

RS = 14 - 8

RS = 6

RT = x + 10

RT = 7 + 10

RT = 17

Therefore, we get the values of RS and RT as 6 and 17 respectively after solving the equations.

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Answer:

Step-by-step explanation:

2(2x-5)=3x+x-2x

4x-10=3x+x-2x

4x-10=2x

4x-10+10=2x+10

4x=2x+10

2x=10

2/2

10/2=5

x=5

The solution to the equation 2(2x-5) = 3x + x - 2x is x = 5

Given data:

To solve the equation 2(2x - 5) = 3x + x - 2x, we will simplify and solve for x.

Step 1: Distribute the 2 to the terms inside the parentheses:

4x - 10 = 3x + x - 2x

Step 2: Combine like terms on both sides of the equation:

4x - 10 = 2x

Step 3: Subtract 2x from both sides to isolate the variable x:

4x - 2x - 10 = 0

Simplifying:

2x - 10 = 0

Step 4: Add 10 to both sides to eliminate the -10 term on the left side:

2x - 10 + 10 = 0 + 10

Simplifying:

2x = 10

Step 5: Divide both sides by 2 to solve for x:

(2x)/2 = 10/2

Simplifying:

x = 5

Hence, the solution is x = 5.

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Answer: 300mL + 500mL = 800 mL

2000 mL - 800 mL = 1200mL

The patient can have 1200 milliliters of liquid for the rest of the day.

It means there's a 90 percent chance that 8:00 AM train from Princeton to New York will arrive on time, and 10 percent chance it’s 8:00 AM train from Princeton to New York will not arrive on time.

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood of a particular event happening.

It means there's a 90 percent chance that 8:00 AM train from Princeton to New York will arrive on time, and 10 percent chance it’s 8:00 AM train from Princeton to New York will not arrive on time.

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Answer:

10

Step-by-step explanation:

Use the distance formula to determine the distance between two points.
√[(x₂ - x₁)² + (y₂ - y₁)²]

Answer:

the answer is A

that is 828263

Answer:

7√2

7√2 is irrational since √2 is irrational

Step-by-step explanation:

3√2 + 2√8 = 3√2 + 2 × 2√2 = 3√2 + 4√2 = 7√2

7√2 is irrational since √2 is irrational

The width and length of the rectangle given its area is 8.5 meters and 28 meters respectively.

Area of a rectangle = Length × width

238 = (4w - 6) × w

238 = 4w² - 6w

4w² - 6w - 238 = 0

a = 4

b = -6

c = -238

w = -b ± √b² - 4ac / 2a

= -(-6) ± √(-6)² - 4(4)(-238) / 2(4)

= 6 ± √36 - (-3808) / 8

= 6 ± √36 + 3808 / 8

= 6 ± √3844 / 8

= 6 ± 62 / 8

= 68/8 or -56/8

w = 8.5 or -7

So,

w = 8.5 meters

Recall,

Length of the rectangle = (4w - 6) meters

= 4(8.5) - 6

= 34 - 6

= 28 meters

Therefore, the width and length of the rectangle given its area is 8.5 meters and 28 meters respectively.

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The largest interval in which the function is continuous is given by:

(-∞, -3).

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

A function is also not continuous for the values of x which are outside the domain of the function, hence a fraction is not continuous at the zeroes of the denominator.

In this problem, the zeroes of the denominator of the function are:

x = -3, x = 4.

Hence the continuity intervals are:

The largest one is the first, as |-3| < |4|, meaning that it is a larger distance from infinity.

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The complete table of values is

x     |   f(x)

-1.4  |  -13.92

-0.7 |  -7.48

0    |  -3

0.7 |   -0.48

1.4 |  0.08

The function is given as:

f(x) = -2x^2 +5x - 3

Next, we calculate the values of the functions at the given x values

So, we have:

f(-1.4) = -2(-1.4)^2 + 5(-1.4) - 3 = -13.92

f(-0.7) = -2(-0.7)^2 + 5(-0.7) - 3 = -7.48

f(0) = -2(0)^2 + 5(0) - 3 = -3

f(0.7) = -2(0.7)^2 + 5(0.7) - 3 = -0.48

f(1.4) = -2(1.4)^2 + 5(1.4) - 3 = 0.08

Hence, the complete table of values is

x     |   f(x)

-1.4  |  -13.92

-0.7 |  -7.48

0    |  -3

0.7 |   -0.48

1.4 |  0.08

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Answer: 291 with a remainder of 375

Step-by-step explanation: What you need to do first is multiply the senior tickets by 37 which is 370. Now subtract 4,740 by 370 which equals 4370. Then divide 4370 by 15. 4370 divided by 15 equals 291. Multiply 291 by 15 (just to find the remainder) which equals 4,365. 4,740 subtracted by 4,365 equals 375. So the answer is 375

The given functions can be solved using composition functions.

Function composition is a mathematical procedure where two functions, f and g, are taken and a function, h = g f, is produced such that h(x) = g(f(x)). The function g is applied in this operation on the outcome of applying the function f to x.

function (x)-2x+5.

(a) f(3) = 2(3) + 5

= 11

(b) f'(x)

y = 2x + 5

y - 5 = 2x

x = y - 5 / 2

f'(x) = x - 5 / 2

g is the function g(x)-²-25.

(c)  g(x)-²-25

g(-3) = (-3)² - 25

g(-3) = -16

(d) g(f(x)) = g(2x + 5)² - 25

= 4x² + 25 + 20x - 25

⇒ 4x² + 20x

r'(x) = 2x + 5

(ii) g(x) - 0

⇒ g(x)

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The fraction of the bag that are red and yellow are  [tex]\frac{17}{30}[/tex].

To calculate the total fraction of red and yellow candies in the bag of skittles we add the two fractions together.

To add the two fractions together but first rewrite the fractions with a common denominator;

[tex]\frac{4}{15} =\frac{8}{30}[/tex]

[tex]\frac{3}{10} =\frac{9}{30}[/tex]

[tex]\therefore\frac{8}{30} +\frac{9}{30} \\\\=\frac{17}{30}[/tex]

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Answer:

8u + 7z + 15

Step-by-step explanation:

Let's solve the problem,

→ 3z + 6 + 4z + 9 + 8u

→ 8u + (3z + 4z) + (6 + 9)

→ 8u + 7z + 15

Thus, solution is 8u + 7z + 15.

Answer:

8u±7z±15

Step-by-step explanation:

3z±6±4z±9±8u

8u±3z±4z±9±6

8u±7z±15

Hope its helpful for you

The average number of viewers over the two weeks will be 3.85 × 10⁴.

It should be noted that based on the information, the TV show had 3.6 x 10⁴ viewers in the first week and 4.1 x 10⁴ viewers in the second week.

Therefore, the average number of viewers over the two weeks will be:

= [(3.6 × 10⁴) + (4.1 × 10⁴)] / 2

= 3.85 × 10⁴

Therefore, the average number of viewers over the two weeks will be 3.85 × 10⁴.

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The values of all the required angles are; m∠5 = 42°; m∠8 = 138°; m∠10 = 138° and m∠11 = 42°

Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines.

Now, we are given that; m∠1 = 42°

By corresponding angles, we can say that;

m∠1 = m∠5

Thus; m∠5 = 42°

Now, we know that sum of angles on a straight line is equal to 180° i.e. they are supplementary angles.

Now, from the diagram, we can see that m∠5 and m∠8 are supplementary angles and as such;

m∠5 + m∠8 = 180°

42 + m∠8 = 180

m∠8 = 180° - 42°

m∠8 = 138°

Now, m∠9 is a corresponding angle to both m∠1 and m∠5. Thus, we can say that; m∠9 = 42°. However, m∠9 is supplementary to m∠10. Thus;

m∠10 = 180 - 42

m∠10 = 138°

Lastly, m∠10 and m∠11 are supplementary angles and as such;

m∠10 + m∠11 = 180°

138 + m∠11 = 180

m∠11 = 180° - 38°

m∠11 = 42°

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Answer:

230lb

Step-by-step explanation:

The Boy weighs 90 lb on earth and 34.5 on the Moon.

90/34.5= 2.608695652

The boys weight on earth divided by his weight on the moon is equal to the difference in weight

So for a 600 lb guy

600/2.608695652 = 230

The guys Earth weight divided by the difference in weight is equal to his moon weight.

Answer:

the answer is to the question is 691648

Answer:

I think to solve for X you have to place like terms on the other side like:

x4 = 4

x=4 - 4 (4 becomes negative)

x=0

The hole having the diameters likely between 4.048 and 4.0553 is 17.

Maximum value of diameter = 4.05 + 0.0028 = 4.0528

Minimum value of diameter = 4.05 - 0.0028 = 4.0472

So, the diameters of the holes are in AP with common difference

= (2 × 0.0028) / 20 = 0.00028

So, the AP is:

4.0472, 4.04748, 4.04776, 4.04804, …, 0.0.0528

So, the first 3 terms are not included between 4.048 and 4.0553

Hence, the answer is 20 - 3 = 17

Therefore, the hole having the diameters likely between 4.048 and 4.0553 is 17.

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The differentiation of the given function is expressed as; 2x - √3(y) = 0

We want to differentiate the function;

x² - √3(xy) + 2y² = 12

To differentiate this means to express as;

x²(dy/dx)  - √3(xy)(dy/dx) + 2y²(dy/dx) = 12(dy/dx)

This gives us;

2x - √3(y) + 0 = 0

2x - √3(y) = 0

Thus, the differentiation of the given function is expressed as;

2x - √3(y) = 0

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Answer:

y = 0, one solution

Step-by-step explanation:

15y + 14 = 14 y + 14

-14y          -14y

y + 14 = 14

-14        -14

y = 0

so one solution

Answer:1. X=9

              2. x

=

Step-by-step explanation:

Answer:

USE air math

Step-by-step explanation:

hope that helps

Answer:

your answer is 7/2