The finances of a group of pet owners were analyzed to determine how much they were spending on their pets each year. Would (3,7.2) be a viable solution for the function

Answer:

The direction cosines are:

\(\frac{5}{\sqrt{42} }\), \(\frac{1}{\sqrt{42} }\)  and  \(\frac{4}{\sqrt{42} }\)  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

Step-by-step explanation:

For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.

If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.

Where;

cos α = \(\frac{a . i}{|a| . |i|}\)               ---------------------(i)

cos β = \(\frac{a.j}{|a||j|}\)               ---------------------(ii)

cos γ = \(\frac{a.k}{|a|.|k|}\)             ----------------------(iii)

And from these we can get the direction angles as follows;

α =  cos⁻¹ ( \(\frac{a . i}{|a| . |i|}\) )

β = cos⁻¹ ( \(\frac{a.j}{|a||j|}\) )

γ = cos⁻¹ ( \(\frac{a.k}{|a|.|k|}\) )

Now to the question:

Let the given vector be

a = 5i + j + 4k

a . i =  (5i + j + 4k) . (i)

a . i = 5         [a.i is just the x component of the vector]

a . j = 1            [the y component of the vector]

a . k = 4          [the z component of the vector]

Also

|a|. |i| = |a|. |j| = |a|. |k| = |a|           [since |i| = |j| = |k| = 1]

|a| = \(\sqrt{5^2 + 1^2 + 4^2}\)

|a| = \(\sqrt{25 + 1 + 16}\)

|a| = \(\sqrt{42}\)

Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e

cos α = \(\frac{5}{\sqrt{42} }\)

cos β =  \(\frac{1}{\sqrt{42} }\)              

cos γ =  \(\frac{4}{\sqrt{42} }\)

From the value, now find the direction angles as follows;

α =  cos⁻¹ ( \(\frac{a . i}{|a| . |i|}\) )

α =  cos⁻¹ ( \(\frac{5}{\sqrt{42} }\) )

α =  cos⁻¹ (\(\frac{5}{6.481}\) )

α =  cos⁻¹ (0.7715)

α = 39.51

α = 40°

β = cos⁻¹ ( \(\frac{a.j}{|a||j|}\) )

β = cos⁻¹ ( \(\frac{1}{\sqrt{42} }\) )

β = cos⁻¹ ( \(\frac{1}{6.481 }\) )

β = cos⁻¹ ( 0.1543 )

β = 81.12

β = 81°

γ = cos⁻¹ ( \(\frac{a.k}{|a|.|k|}\) )

γ = cos⁻¹ (\(\frac{4}{\sqrt{42} }\))

γ = cos⁻¹ (\(\frac{4}{6.481}\))

γ = cos⁻¹ (0.6172)

γ = 51.89

γ = 52°

Conclusion:

The direction cosines are:

\(\frac{5}{\sqrt{42} }\), \(\frac{1}{\sqrt{42} }\)  and  \(\frac{4}{\sqrt{42} }\)  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

The equation of a line that has a slope of 3 and passes through (8, 9) will be y = 3x - 15.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is 2. Then the equation is written as,

y = 3x + c

The equation is passing through (8, 9). Then the value of c will be

9 = 3(8) + c

9 = 24 + c

c = - 15

Then the equation will be given as,

y = 3x - 15

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The normal fraction given which is 123/8 can be written as the mixed number 15 3/8.

To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. The whole number part of the result will become the whole number part of the mixed number, and the remainder will become the numerator of the fraction part.

In this case, we have 123/8. To divide 123 by 8, we can use long division method.

So, the whole number part is 15, and the remainder is 3. Therefore, we can write:

123/8 = 15 3/8

This means that 123/8 is equal to 15 and 3/8. The whole number part, 15, represents the number of whole units that can be formed using 8 parts each. The fraction part, 3/8, represents the remaining amount that cannot form a whole unit of 8 parts.

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Answer:

reflection of the axis y=4

Step-by-step explanation:

becuase it is reflected on itself

Answer:

Reflect Triangle A by the line y = 4

Step-by-step explanation:

The answer is reflect Triangle A by y = 4 because the two triangles are symmetric.

Answer:

Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:

m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)

m∠4 = m∠2 (since angles 2 and 4 are vertical angles)

Substituting m∠4 = m∠2 into the first equation, we get:

m∠2 + m∠3 = 180

Now we can solve for m∠2 and m∠3:

m∠3 = 43 (given)

m∠2 = 180 - m∠3 = 180 - 43 = 137

Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:

m∠1 = 180 - m∠2 = 180 - 137 = 43

Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.

Answer:

5/6 quarts of water

Step-by-step explanation:

2/3 same as 4/6. 4/6 + 1/6 = 5/6

Answer:

Y=30

X=40

Step-by-step explanation:

for Y is because 46-16=30

for X is because 180÷3=60

80+60=140

180-140=40

Answer:

David share is 36 sweets

Step-by-step explanation:

let Lucy share be x

let David share be y

Lucy has 27 more

x=y+27

total sweet is x+y

y+27 +y= 2y+27

total ratio = 4+7=11

David share=

\(y = \frac{4}{11} \times (2y + 27)\)

\(11y = 4(2y + 27)\)

\(11y = 8y + 108\)

\(11 y- 8y = 108\)

\(3y = 108\)

y=108/3= 36

Answer:

Step-by-step explanation:

Distance from point N to M can be calculated using the Pythagoras theorem. According to Pythagoras theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Here, side LN is the hypotenuse, and NM and ML are the other two sides. Therefore, LM can be calculated using the Pythagorean theorem as follows:

NM² + ML² = LN²

7.5² + 8.3² = LM²

56.25 + 69.29 = LM²

125.54 = LM²

LM = √125.54

LM ≈ 11.2

Therefore, the distance from point N to M is equal to the length of the side LM which is approximately 11.2. Hence, the correct option is not available in the given alternatives.

Answer:

B. (-4, -8) Is the answer to the problem

Step-by-step explanation:

Otherways to say:

1. The second option

2. B

3. II

4. (-4, -8)

Edge Format:

(-8, -4)

(-4, -8)

(-4, 4)

(4, -4)

That way, there is no reason not to give brainliest or bellow 5 stars.

The solution to the system of the equations is (-4, -8).

"It is a finite set of equations for which we find the common solution."

"It is statement which consists of equal symbol between two algebraic expressions."

For given example,

we have the first equation,

\(y =\frac{1}{2}x-6\)

and the second equation x = -4

Substitute x = -4 in the first equation,

⇒ y = (1/2)×(-4) - 6

⇒ y = -2 - 6

⇒ y = -8

Therefore, the solution to the system of the equations is (-4, -8).

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Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) \(\times\) 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

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Answer:

The question is not complete

Answer:

The constant of proportionality is 0.3

Step-by-step explanation:

» The graph shows a direct proportiinality.

\({ \rm{y \: \alpha \: x}}\)

» Therefore, input the constant;

\({ \rm{y = kx}}\)

» When x is 5, y is 1.5:

\({ \tt{1.5 = (k \times 5)}} \\ { \rm{k = 0.3}}\)

Answer:

0.3

Step-by-step explanation:

On a graph, proportional relationships are straight lines that extend through the origin.  

Slope of a graph = constant of proportionality of the equation

Let (5, 1.5) = \((x_1,y_1)\)

Let (20, 6) = \((x_2,y_2)\)

Formula of a slope: \(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(\implies m=\dfrac{6-1.5}{20-5}=0.3\)

So as the slope = 0.3, the constant of proportionality = 0.3

Answer:

79591

Step-by-step explanation:

Answer:

79591

Step-by-step explanation:

Estimate would be 79600

Recall that for |x| < 1, we have

\(\displaystyle \frac1{1-x} = \sum_{n=0}^\infty x^n\)

Differentiating both sides gives

\(\displaystyle \frac1{(1-x)^2} = \sum_{n=0}^\infty nx^{n-1} = \sum_{n=0}^\infty (n+1)x^n\)

and multiplying both sides by 8 gives the series for f(x) :

\(f(x)=\displaystyle \frac8{(1-x)^2} = \boxed{8\sum_{n=0}^\infty (n+1)x^n}\)

and this converges over the same interval, |x| < 1, so that the radius of convergence is 1.

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The inequalities which satisfy the number line shown is x>2 and x>=2.

We are given that;

The number line showing inequality

Now,

x>2 satisfies the equation by the given number line

x>=2 satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

Therefore, by the number line the answer will be x>2 and x>=2 .

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Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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Answer: The answer is:  "False" ;  

                since the expression IS, in fact, "factorable."

__________________________________________

Step-by-step explanation:

__________________________________________

x² + (-7) + 12 =

x² - 7 + 12 ;  

What factors of "12" (that is: "+12") ;

add up to "-7" ?      -4, -3 ;   -4 * -3 = +12 ;

                                              -4 + (-3) = -4 - 3 = -7 ;

__________________________________________

So, we can factor the expression:  (x - 4) (x -3) ;  

__________________________________________

The answer is: "False" ; since the expression IS, in fact, "factorable."

__________________________________________

Answer: 16 pounds of grain.

Step-by-step explanation: 36 divided by 9 is 4, which means we have to multiply bin C by how much bin J was multiplied by, which is 4, so 4x4 is 16.

(let me know if you would like me to explain more on this)

Answer:

33.6 degrees F

Step-by-step explanation:

8000/1000 = 8

8(1.9) = 15.2 degree drop

48.8 - 15.2 = 33.6 degrees F

Answer:

The value of b equals to

\( \frac{5}{72} \)

Step-by-step explanation:

steps given below

given expression

\(b + \frac{3}{8} = \frac{4}{9} \\ \)

subtract

\( \frac{3}{8} \)

from both sides

\(b + \frac{3}{8} - \frac{3}{8} = \frac{4}{9} - \frac{3}{8} \\ b = \frac{4}{9} - \frac{3}{8} \)

To, continue find the L.C.M of 9 and 8 thus, it's 72

So, plug 72 and solve the expression as follows

\(let \: \frac{a}{c} - \frac{b}{c} = \frac{a - b}{c} \\ b = \frac{32 - 27}{72} = \frac{5}{72} \)

Hope it helps!

Answer: 15

Step-by-step explanation:

To solve this problem, we first need to translate the given information into a system of equations. Let's call the first number x and the second number y. Since the sum of the two numbers is 22, we know that x + y = 22.

The second statement says that three times one number increased by five is the same as twice the other number decreased by four. We can translate this into an equation by substituting x and y for the two numbers and using the given information:

3x + 5 = 2y - 4

Now that we have a system of equations, we can solve for x and y. First, we'll solve for x by adding four to both sides of the second equation:

3x + 9 = 2y

Then, we can divide both sides by three to get the value of $x$:

x = {2y - 9} / {3}

Next, we can substitute this expression for x into the first equation to solve for y:

y + {2y - 9} / {3} = 22

We can simplify this equation by multiplying both sides by three:

3y + 2y - 9 = 66

Combining like terms on the left side, we get:

5y - 9 = 66

Then, we can add nine to both sides to solve for y:

5y = 75

Finally, we can divide both sides by five to find the value of y:

y = 15

Now that we know the value of $y$, we can substitute it back into the expression for $x$ to find the value of $x$:

x = \frac{2 \cdot 15 - 9}{3} = \frac{27}{3} = 9

Since we want the larger of the two numbers, the answer is 15

Answer:

Use graph paper to create a scatter plot. Draw the x- and y- axes, ensure they intersect and label the origin. Ensure that the x- and y- axes also have correct titles. Next, plot each data point within the graph. Any trends between the plotted data sets should now be evident.

The fish tank requires 7900 square cm of glass.

First, choose three fish for our tank. Let's choose a neon tetra, a guppy, and a corydoras catfish.

According to the guideline given, each fish requires 4,000 cubic centimeters of water for every inch of a fish's length. Determine the total length of the three fish to calculate the required water volume.

Assuming the neon tetra is 1 inch long, the guppy is 2 inches long, and the corydoras catfish is 3 inches long, the total length of the fish is 1+2+3=6 inches.

To accommodate these three fish, we need 6 inches x 4,000 cubic centimeters of water per inch = 24,000 cubic centimeters of water.

To design the fish tank. Make it a rectangular prism shape with the dimensions of 50 cm x 30 cm x 40 cm (length x width x height).

To calculate the amount of glass necessary to build the tank, to find the surface area of the glass required. There are five sides to the tank (four sides and the base), find the area of each and add them up.

The front and back sides each have an area of 50 cm x 40 cm = 2000 square cm.

The two side walls each have an area of 30 cm x 40 cm = 1200 square cm.

The base has an area of 50 cm x 30 cm = 1500 square cm.

So, the total surface area of glass required is:

2(2000 square cm) + 2(1200 square cm) + 1500 square cm = 7900 square cm.

Therefore, 7900 square cm of glass is needed to build our fish tank.

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Answer:

6n+30

Step-by-step explanation:

Step 1:

Multiply 6 and n

Step 2:

Multiply 6 and 5

Step 3:

Put together!

have a great day and thx for your inquiry :)

Answer:

the answer is A

Step-by-step explanation:

distributive property states

a(b+c)=ab+ac

therefore

6(n+5)=6n+30

Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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Answer:

24

Step-by-step explanation: