How many solutions does this system have? 12 x - 4 y = - 8. y = 3 x + 2.

Answer: 19 /4 or 4 3/4

Step-by-step explanation:

Turn 67/8 into a improper fraction, which is 55/8

Next, also convert 21/8 into an improper fraction, which is 17/8

Next, subtract 17/8 from 55/8 and you should get 38/8

Last, simplify 38/8 to do so divide 38/8 by 4/4 and you should get 19/4 and if you want it's optional to turn it into a mixed number.  

The estimate of the difference between the two fractions is: 4 3/4 = 4.75 ≈ 5.

To find the difference of two fractions means that subtract one from the other.

Thus:

Difference between 6 7/8 and 2 1/8 = 6 7/8 - 2 1/8

Change the mixed fraction to improper fractions

55/8 - 17/8

= (55 - 170/8

= 38/8 = 19/4

= 4 3/4 = 4.75 ≈ 5.

Therefore, the estimate of the difference between the two fractions is: 4 3/4 = 4.75 ≈ 5.

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Answer:

d) the height of red prism is three times the height of the blue prism.

Step-by-step explanation:

i) the volume of a rectangular prism is given by area of base [tex]\times[/tex] height.

ii) volume of the blue prism is = (base of blue prism) [tex]\times[/tex] (height of blue prism)

iii) volume of red prism is = (base of red prism) [tex]\times[/tex] ( height of the red prism)

               = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] ( base of blue prism) [tex]\height[/tex][tex]\times[/tex]  ( height of red prism)

iv) it is also given that

   volume of blue prism = volume of red prism

   ⇒    (base of blue prism) [tex]\times[/tex] (height of blue prism) = (base of red prism)[tex]\times[/tex] (height of red prism)

⇒(base of blue prism) [tex]\times[/tex] (height of blue prism) = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] ( base of blue prism)[tex]\times[/tex] (height of red prism)

⇒ (height of blue prism) = [tex]\frac{1}{3}[/tex] [tex]\times[/tex]  (height of red prism)

∴ height of red prism = 3 [tex]\times[/tex] height of blue prism

Therefore the correct option is

d) the height of red prism is three times the height of the blue prism.

Answer:

A

Step-by-step explanation:

The picture below illustrates a hyperbola.

The intersecting plane does not pass through the vertex of a right circular cone (the vertex of the cone is the point where two nappes meet).

As you can see from the diagram, the plane intersects both nappes of a right circular cone.

Hence, correct option is option A: The plane does not pass through the vertex and intersects both nappes of a right circular cone.

Answer:

Step-by-step explanation:

-3/4 = -0.75 (its terminating)

Answer:

Step-by-step explanation:

-3/4 = -0.75. It is terminating decimal

Answer:

2x⁴y²

Step-by-step explanation:

The question gives us the expression;

12x⁷y³ ÷ 6x³y

We are supposed to simplify the expression;

First we could divide the digits;

12 ÷ 6 = 2

Then we divide the like terms;

x⁷ ÷ x³

This means;

[tex]=\frac{x*x*x*x*x*x*x }{x*x*x}[/tex]

[tex]= x*x*x*x[/tex]

[tex]=x^4[/tex]

y³ ÷ y

That is;

[tex]=\frac{y*y*y}{y}[/tex]

[tex]=y*y[/tex]

[tex]=y^2[/tex]

Therefore, the simplified expression will be 2x⁴y²

Answer:

The values are [tex]x=\frac{7}{2}[/tex] and [tex]y=\frac{5}{2}[/tex]

The solution is ([tex]\frac{7}{2}[/tex],[tex]\frac{5}{2}[/tex])

Step-by-step explanation:

Given equations are [tex]5x=7y\hfill (1)[/tex] and

[tex]x+7y=21\hfill (2)[/tex]

To solve the given equations by elimination method:

Equation (1) can be written as  [tex]5x-7y=0\hfill (3)[/tex] and

Now multiply the equation (2) into 5 we get

[tex]5x+35y=105\hfill (4)[/tex]

Subtracting equations (3) and (4) we get

[tex]5x-7y=0[/tex]

[tex]5x+35y=105[/tex]

_________________

-42y=-105

[tex]y=\frac{105}{42}[/tex]

Therefore [tex]y=\frac{5}{2}[/tex]

Substitute  the value [tex]y=\frac{5}{2}[/tex] in equation (1) we get

[tex]5x=7\times \frac{5}{2}[/tex]

[tex]5x=\frac{35}{2}[/tex]

[tex]x=\frac{35}{2\times 5}[/tex]

[tex]x=\frac{7}{2}[/tex]

Therefore [tex]x=\frac{7}{2}[/tex] and [tex]y=\frac{5}{2}[/tex]

The solution is ([tex]\frac{7}{2}[/tex],[tex]\frac{5}{2}[/tex])

Answer:

[tex]v=\frac{0,25}{\pi } ft/min[/tex]

Step-by-step explanation:

There is a relation with the initial and final dimensions of the hopper according to the sand level when its high is 6 feet as follows:

[tex]\frac{h_{1} }{h_{2} }=\frac{r_{1} }{r_2}\\{r_2}=\frac{12ft*6ft}{18ft}\\ r_2=4ft[/tex]

Where the calculated [tex]r_{2}[/tex] is given with the 6 feet hgh.

Then we have the sand flow formula which is:

[tex]Q=A*v[/tex]

Where A represents the area of the transversal section and v  the velocity that we need to know, the area is:

[tex]A=\pi r^{2}\\ A=\pi *4^{2}\\ A=16\pi ft^{2}[/tex]

And finally the sand is dropping when the level is 6 feet high with the velocity (v) :

[tex]v=\frac{Q}{A} \\v=\frac{4}{16\pi }[/tex]

[tex]v=\frac{0.25}{\pi } ft/min[/tex]

The sand level in the hopper is dropping at a rate of approximately 0.08 feet per minute when the sand level is 6 feet high. This is calculated using related rates and the volume formula for a cone. The relationship between radius and height, derivative calculations, and the given sand emptying rate are essential for this solution.

To determine how fast the level of sand is dropping in the hopper, we need to use related rates. The volume V of the sand in the inverted cone is given by the formula:

V = (1/3)πr2h

In this case, the radius r and height h of the sand level are proportional because the shape is a cone. We can express the radius r in terms of the height h using similar triangles. Given the overall height is 18 feet and the radius is 12 feet, we have:

r = (12/18)h or r = (2/3)h

Substituting r into the volume formula:

V = (1/3)π[(2/3)h]2h = (4/27)πh3

We need the rate of change of the height (dh/dt) when h = 6 feet. Given dV/dt = -4 ft³/min (negative because the volume is decreasing), we use the chain rule for differentiation:

dV/dt = (dV/dh)(dh/dt)

First, find dV/dh:

dV/dh = d/dh [(4/27)πh3] = (4/27)π × 3h2 = (4/9)πh2

Using dV/dt = -4 ft³/min:

-4 = (4/9)π(h2)(dh/dt)

When h = 6 feet:

-4 = (4/9)π(62)(dh/dt)

-4 = (4/9)π(36)(dh/dt) = 16π(dh/dt)

Therefore:

dh/dt = -4/16π = -1/4π

dh/dt = -0.08 feet/min

So, the level of sand is dropping at a rate of approximately 0.08 feet per minute when the sand level is 6 feet high.

19 = 9x - 25 is the numerical expression for 19 is 25 less than the product of 9 and a number

Solution:

Given statement:

19 is 25 less than the product of 9 and a number

We have to write the numerical expression for given statement

Let the number be "x"

From given information,

19 is 25 less than the product of 9 and a number

"product" means multiplication

And "less than" means subtracted or reduced by

Therefore,

Product of 9 and a number is translated as [tex]9 \times x[/tex]

Therefore, given statement is written numerically as:

19 = 25 less than the product of 9 and a number

[tex]19 = (9 \times x) - 25[/tex]

[tex]19=9x-25[/tex]

Thus the expression is found

Answer:

x=0

y=-3

6x-5y=15

x=y+3

Replace x with y+3

6(y+3)-5y=15

Distribute

6y+18-5y=15

y= -3

x=0

The solution to the system of equations is x = 0 and y = -3.

To solve the system of equations:

1. 6x - 5y = 15

2. x = y + 3

We can substitute equation 2 into equation 1 to find the value of x, and then use that value to find the value of y.

Substituting equation 2 into equation 1:

[tex]\[6(y + 3) - 5y = 15\]\[6y + 18 - 5y = 15\]\[y + 18 = 15\]\[y = 15 - 18\]\[y = -3\]\\[/tex]

Now that we have found y, we can substitute this value back into equation 2 to find x:

[tex]\[x = (-3) + 3\]\[x = 0\][/tex]

So, the solution to the system of equations is x = 0 and y = -3.

Complete Question:

Solve the system of equations 6x-5y=15

x=y+3

x=

Y=

Answer: y= -3/4x + 1

Step-by-step explanation:

use the point to set up slope intercept to find you y-intercept (b)

(8,-5)

y=mx+b

-5=-3/4(8)+b

-5=-6+b

b=1

The equation of the line which passes through the point (8,-5) with a slope of -3/4, when written in slope-intercept form, is y = -3/4x + 1.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. You've been provided that the slope m of the line is -3/4 and it passes through the point (8,-5). You can substitute these values into the formula to find the y-intercept b.

Substituting the given values into the formula gives -5 = (-3/4)*8 + b, which simplifies to -5 = -6 + b. By adding 6 to both sides of the equation, you find that b = 1.

So the equation of the line in slope-intercept form is y = -3/4x + 1.

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Answer:

30 players.

Step-by-step explanation:

3 rows of 8 = 3 x 8 = 24. Plus an additional 6 players in the fourth row. 24 + 6 = 30.

The team photo consists of 30 players: 24 in the three full rows, each with 8 players, and 6 more players in the fourth row.

To find the total number of players in the team photo, you can simply add the number of players in each row together. In this case, there are three rows of 8 players each and a fourth row with 6 players.

First, calculate the total number of players in the three full rows, where each row has 8 players:

3 rows x 8 players/row = 24 players

Now, add the players from the fourth row:

24 players (from the full rows) + 6 players (from the fourth row) = 30 players

So, there are 30 players in the team photo.

In summary, the team photo includes 30 players, with 24 players in the three full rows of 8 each and an additional 6 players in the fourth row.

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Final answer:

To estimate the remaining advertisement budget, calculate the total possible maximum expense and subtract it from the initial budget, resulting in an approximate remaining amount of $14,300.

Explanation:

Mr. Kellen's starting budget for advertisements was $50,000. If I assume that each of the 7 advertisements costs about the maximum amount which is $5,100, the estimated total cost would be 7 times $5,100, which equals $35,700. So, a reasonable estimate of the amount of money remaining after paying for the advertisements is $50,000 - $35,700 = $14,300.

Answer: 0.47382

Step-by-step explanation:

The percent of 47.382 is dividing the figure by 100%

47.382/100= 0.47382

Answer: 0.53

Step-by-step explanation:

From variation ,

y ∞ x ------------------------------------------------1

y = kx , where k is called the constants of proportionality and must be calculated first before proceeding.

substitute for the values in equation 2 ,below

y   = kx -----------------------------------------------2

16 = k2.1

k   = 16/2.1

Now to find the value of x, make x the subject of the formula in equation 2

x  = y/k

   = 4/ 16/2.1

   = 4 ÷ 16/2.1

   = 4 x 2.1/16

   = 2.1/4

   = 0.525

 ≅ 0.53

Answer:

7/10

Step-by-step explanation:

4 1/2=9/2

3 4/5=19/5

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

9/2-19/5=45/10-38/10=7/10

Answer:

Θ = 45°

BA  = [tex]3\sqrt{2}[/tex] =  4.243

Step-by-step explanation:

i) the given triangle is a right angled isosceles triangle.

ii) the base and the height are both equal. height = base = 3 cm.

iii) from the rule of triangles the sum of all angles in a triangle is 180° and since the triangle is an right angled isosceles triangle one angle is 90° and the other two angles are equal.

 Therefore

Θ° + Θ° + 90° = 180°       ⇒   2Θ° = 180° - 90° = 90°    ∴ Θ = 45°

iv) the hypotenuse BA is given by the Pythagoras' theorem

∴ hypotenuse (BA) = [tex]\sqrt{base^{2} + height^{2} }[/tex] = [tex]\sqrt{BC^{2} + CA^{2} }[/tex]  = [tex]\sqrt{3^{2} + 3^{2} }[/tex] = [tex]3\sqrt{2}[/tex] = therefore BA  = [tex]3\sqrt{2}[/tex] =  4.243

To accurately determine the measure of angle Ø and the length of line BA, specific information or data related to the geometry or vectors involved is required. The measure of angle Ø may be calculated using geometrical principles or trigonometry, and the length of line BA could be determined by measuring or calculation if the context is known.

To find the measure of ∠Ø, you would typically need additional information such as the lengths of the sides of a triangle, the measures of other angles, or the coordinates of points if you are working with a graph. Similarly, to find the measure of line BA, information about the specific triangle, polygon, or coordinate grid where line BA exists is necessary. For example, using the Pythagorean theorem for a right-angled triangle or the distance formula for points on a coordinate grid.

If you are given the lengths of sides or the measures of angles, you can apply geometric principles or trigonometric ratios to calculate the desired measurements. Without the specific data or a provided figure, it's not possible to give an exact answer to these questions.

In the case of vector analysis, as mentioned in the reference provided, to measure line BA you would draw vectors on a graph and construct a parallelogram; the length of the diagonal could then be measured to find the result. For angles, you could use a protractor or apply trigonometric functions if you know the components of the vectors.

Answer:

The two numbers are 21 and 9.

Step-by-step explanation:

x+y=30

x-y=12

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

2x=42

x=42/2

x=21

21+y=30

y=30-21=9

Final answer:

The expression to determine how much more time Sacha spent on math than on science is y - x.

Explanation:

To determine how much more time Sacha spent on math than on science, we need to find the difference between the time spent on math and science. Let's say Sacha spent x amount of time on science and y amount of time on math. The expression that represents the difference between the time spent on math and science is y - x.

Therefore, the correct expression to determine how much more time Sacha spent on math than on science is y - x.

Answer:

Its C Hope dis helps!!!

Step-by-step explanation:

Without the actual data, we cannot definitively decide the correct exponential model for the population of the District of Columbia. The options provided all share the same initial quantity, with different growth factors. To pick one, we would need data on the annual population growth or decline.

The question is asking us to choose an exponential model of the form a ∙ bx that best represents the population of the District of Columbia for years after 2005. As we are not provided actual data on the population growth or decline, we can't definitively choose between the options. In this kind of model, a is the initial quantity (population in the year 2005), and b is the growth factor per the time period (in this case: annually). In all options provided we have the same initial quantity '550,521'. The difference is in the growth factors .993, .990, .992, and .991. Without the actual data, we cannot definitively pick one. However, if the population is declining each year, you'd expect the growth factor to be less than 1. In case if it's growing you'd expect it to be more than 1.

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Answer:

7)k=-7.02

8)n=-4

9)b=-14

10)-2=p

Answer:

y=16-3x/5

Step-by-step explanation:

I'm adding a pic of my solution. i hope you find it helpful.

The solution to the equation 3x + 5y = 16 for y is y = (16 - 3x) / 5. This is achieved by isolating y on one side of the equation.

To solve the equation 3x + 5y = 16 for y, you first need to isolate y on one side of the equation. This can be done in the following steps:

So, the solution for y in terms of x is y = (16 - 3x)/5.

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Answer:

A

Step-by-step explanation:

i used the process of elimination and got rid of answers that didnt make sense but based on the info given i could tell that x was 5 months because of where the point of 5 is on the graph

Answer:

It is D.

D. The average number of customers per night increased by 5 each month.

Step-by-step explanation:

The line is going up at  +5 for every month. This means 5 customers are being added every month

Answer:)

C. 50 feet^2

Step-by-step explanation:

Area of circle

A = Pi r^2 (radius is 7)

A= 153.86

Area of square

A = a^2

A= 10^2

A=100

From circle area substract square area

153.86 - 100 = 53.86

Answer:

The equation of the line is:  y = x + 4

Step-by-step explanation:

When we are given two points passing through a line, we can find the equation of the line by using two - point form.

Two - point form:    [tex]$ \frac{\textbf{y - y}_\textbf{1}}{\textbf{y}_{\textbf{2}} \textbf{-} \textbf{y}_{\textbf{1}}} = \frac{{\textbf{x - x}_\textbf{1}}}{\textbf{x}_{\textbf{2}} \textbf{-} \textbf{x}_{\textbf{1}} }$[/tex]

where [tex]$ (x_1, y_1) \hspace{3mm} \& \hspace{3mm} (x_2, y_2) $[/tex] are the points passing through the line.

Here, let us take two points (can be any two):

[tex]$(x _1, y_1) = (1, 5) $[/tex] and

[tex]$ (x_2, y_2) = (5, 9) $[/tex]

Therefore, we have:

[tex]$ \frac{y - 5}{9 - 5} = \frac{x - 1}{5 - 1} $[/tex]

[tex]$ \iff \frac{y - 5}{4} = \frac{x - 1}{4} $[/tex]

[tex]$ \iff y - 5 = x - 1 $[/tex]

[tex]$ \implies y = x - 1 + 5 $[/tex]

[tex]$ \implies y = \textbf{x + 4} $[/tex] which is the required answer.

Answer:

4 4/5 yards are left

Step-by-step explanation:

7 8/5-3 4/5

We know that 1/2 as a decimal is 0.5. Any decimal/fraction between 0.5 and 1 will be correct. For Example, 0.75 is greater than 0.5 but less then 1. 0.75 as a fraction is 3/4.

Best of Luck!

Answer:

Option A) Todd is older than 32

Step-by-step explanation:

we have

[tex]\frac{1}{2}x-6>10[/tex]

Solve for x

Adds 6 both sides

[tex]\frac{1}{2}x>10+6\\\\\frac{1}{2}x>16[/tex]

Multiply by 2 both sides

[tex]x>32[/tex]

so

Todd's age is greater than 32

therefore

Todd is older than 32

The complete function is: [tex]y = x+55[/tex]

Step-by-step explanation:

the given table represents a linear function

The linear function is represented by:

[tex]y = mx+b[/tex]

Here

m is the slope of function and b is the y-intercept

In this case, m will be calculated as:

[tex]m= \frac{Change\ in\ y}{Change\ in\ x}\\= \frac{61-60}{6-5}\\= 1[/tex]

Hence the slope is 1.

Putting in the equation

[tex]y = x+ b[/tex]

To find the value of b, we will put any pair of x and y in the equation

[tex]61 = 5 + b\\b = 60-5\\b = 55[/tex]

Hence,

The final equation for linear function is:

[tex]y = x + 55[/tex]

Keywords: Linear function, equation

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