15. Kate plays a card game with two friends. She gives 5 cards to each player. Ten plus what number is equal to the total number of cards Kate gives out? Write an equation to show and solve the problem.​

Answer:

y=1/5x-31/5 (or y=0.2x-6.2 in decimals)

Step-by-step explanation:

x=5y-8     (original equation)

x+8=5y (Addition Property of Equality)

1/5x+8/5=y (Division Property of Equality, slope of original equation is 1/5)

y-y1=m(x-x1)    (point-slope formula)

y-(-5))=1/5(x-(6)) (plug in the slope that was found earlier and the point given in the question)

y+5=1/5(x-6)

y+5=1/5x-6/5   (Distributive Property of Multiplication)   Note:  5 = 25/5

y=1/5x-31/5 (Subtraction Property of Equality, and there's your answer)

y=0.2x-6.2 (This is the same answer, but written with decimals)

Step-by-step explanation:

you drew already the right things, you have everything.

so, what is the problem ?

the most common form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and solve for b.

so, for the 2 marked points you showed correctly the differences :

x changes by +8 (from -4 to 4).

y changes by -2 (from 3 to 1).

so the slope is -2/+8 = -1/4

the y-intercept we also see directly in the chart : +2.

Answer: The answer is the last option, Option D.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\impliedby y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{5}}x-8[/tex]

so we're really looking for the line of a slope of 3/5 and passing through (0,-3)

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{0}) \\\\\\ y+3=\cfrac{3}{5}x\implies y=\cfrac{3}{5}x-3[/tex]

The equation of a line in point slope form is expressed according to the formula;

y-y0 = m(x-x0)

Given the following parameters

m = -3

(x0, y0) = (-4, 1)

Substitute into the formula above will givee;

y - 1 = -4(x+4)

y -1 = -4x - 16

y = -4x - 15

Next is to plot the graph of the line y = -4x - 15 on the coordinate plane as shown:

Learn more graphs here: https://brainly.com/question/19011142

The best selection for the quadrilateral with the given vertices is: parallelogram.

Recall:

Parallel lines are lines do not intersect and they are equal distant apart.

The opposite side of a parallelogram are of equal length.

Thus, the points of the vertices of the quadrilateral has been graphed in the diagram shown below:

Point A (-2,0)

Point B (0,4)

Point C (6,4)

Point D (4,0)

Find the distance between each vertices using the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Distance between Point A (-2,0) and Point B (0,4):

[tex]AB = \sqrt{(0 -(-2))^2 + (4 - 0)^2} \\\\\mathbf{AB = \sqrt{20} }[/tex]

Distance between Point B (0,4) and Point C (6,4):

[tex]BC = \sqrt{(6 - 0)^2 + (4 - 4)^2} \\\\\mathbf{BC = 6 }[/tex]

Using the same distance formula, CD = √20 while AD = 6

This means that the opposite sides of the quadrilateral with the given vertices are equal in length. Parallelogram has two pairs of equal sides.

Therefore, the best selection for the quadrilateral with the given vertices is: parallelogram.

Learn more about Parallelogram on:

https://brainly.com/question/12167853

Step-by-step explanation:

formula y2-y1 / x2-x1

m = 5 / -10 = 1 / -2 = -0.5

Answer:

0

Step-by-step explanation:

Answer:

8 tablespoons1/2 cup4 ounces10 tablespoons plus 2 teaspoons2/3 cup5.2 ounces12 tablespoons3/4 cup6 ounces16 tablespoons1 cup8 ounces

Answer:

  13

Step-by-step explanation:

The average of any 5 consecutive numbers is the 3rd one (the middle one of the group). The third consecutive number starting from 11 is 13.

The average of {11, 12, 13, 14, 15} is 13.

Step-by-step explanation:

when the scale says 1:500000, then that means 1 unit in the map corresponds to 500000 units in reality.

and so, 3.2 cm on the map are

3.2 × 500000 cm in reality.

3.2 × 500000 = 1,600,000 cm = 16,000 m = 16 km

Answer:

x = 11/7

Step-by-step explanation:

[tex]7x+6-2x=12x-7+2\\\\5x+6=12x-5\\\\5x+6-5x=12x-5-5x\\\\6=7x-5\\\\6+5=7x-5+5\\\\11=7x\\\\\frac{11}{7}=\frac{7x}{7}\\\\\frac{11}{7}=x[/tex]

Answer:

The is answer is 19.1x8.6= 164.26

Step-by-step explanation:

Answer:

Finally, Juno and her satellite were able to return home to her family.

Step-by-step explanation:

Answer:

Finally, Juno and her satellite were able to return home to her family

Step-by-step explanation:

Answer:

.37 resolutions

Step-by-step explanation:

2×22/7×35

44.5×=220

0.37 revolutions

Problem 1

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

Explanation:

The first task is to determine the function for f(x). Because it's linear, it's in the form y = mx+b. Let's find the slope m.

Select any two columns to pick out (x,y) points from the f(x) function. I'll pick the first two columns to select the points (-6,15) and (-4,11). Apply the slope formula to these two points to get...

m = (y2-y1)/(x2-x1)

m = (11-15)/(-4-(-6))

m = (11-15)/(-4+6)

m = -4/2

m = -2

Then use this m value along with any of the points of the table to determine the y intercept b. I'll use the point (-6,15)

y = mx+b

b = y-mx

b = 15-(-2)*(-6)

b = 15-12

b = 3

The y = mx+b equation becomes y = -2x+3 and that leads directly to the function f(x) = -2x+3.

Repeat all of those steps but do so for g(x) this time. I'll skip those steps over but you should get the function g(x) = 5x-6.

The y intercepts of f(x) and g(x) found were 3 and -6 respectively. Subtract those values to find the y intercept of h(x) = (f-g)(x) = f(x)-g(x).

So we get 3-(-6) = 3+6 = 9 which leads to the location (0, 9).

=========================================================

Problem 2

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

Explanation:

Through trial and error, the factor by grouping method, or using your graphing calculator, factor the denominator to get

g(x) = x^3+2x^2-x-2 = (x+2)(x+1)(x-1)

The factors (x+2), (x+1) and (x-1) lead to the roots of x = -2, x = -1, and x = 1 in that order. Those three roots of g(x) will make g(x) = 0 and cause a division by zero error in the denominator. So we must kick out those three values from the domain. Every other real number is allowed in the domain. So that's how we get the notation for choice A. It starts off saying x is a real number. Then it goes onto say that -2, -1 and 1 aren't allowed.

So overall the domain is described as: "x can be almost any real number except x cannot be -2, cannot be -1, and it cannot be 1".

Side note: We don't involve the numerator function at all.

=========================================================

Problem 3

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

Explanation:

The height is x, which we can factor out like this

2x^3-5x^2-3x

2x^2*x - 5x*x - 3*x

x(2x^2-5x-3)

Effectively you would use the distribution rule in reverse.

Now let's factor the remaining expression in the parenthesis.

I'll use the factor by grouping method.

2x^2-5x-3

2x^2-6x+1x-3

(2x^2-6x) + (1x-3)

2x(x-3) + 1(x-3)

(2x+1)(x-3)

Therefore, the full factorization is

x(2x+1)(x-3)

which shows we have the dimensions of x, (2x+1) and (x-3). The order doesn't matter so we could easily have (2x+1) the length and (x-3) the width, or we could have it the other way around.

You can verify that (2x+1)(x-3) expands out to 2x^2-5x-3 using either the FOIL method or the box method.

the slope is -14/6 or the simplified version is -7/3

Answer:

The answer is A im new to this id.k if you need help with the image or not sorry if that dosent answer your question but the answer is A for that picture.

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

(4x-20+x-1)/8 = (3x-9+4x-16)/12

(5x-21)/8=(7x-25)/12

(5x-21)/8 x 12/1 = (5x-21)/2 x 3/1 = (15x -63)/2

15x - 63 = 14x - 50

x=13

Answer:

The answer is C

Step-by-step explanation:

(I'm not completely sure)

A Perform the indicated operations. Show your solution in the given space below.

Answer:

C Negative Association

Step-by-step explanation:

Youll notice how the overall "line" of the graph goes down, the dots on the graph proceeding into the negative

Answer:

hmm it's like ut I do know and my answer

Answer:

b(-1)= -6

b(0)= -4

b(4)=  4

Step-by-step explanation:

2(-1) - 4

-2-4=-6

2(0) - 4

0 - 4 = -4

2(4) - 4

8 - 4 = 4

Answer:

-6, -4, 4

Step-by-step explanation:

Answer:

the portion of the drama clubs budget needed for each type of expense

Step-by-step explanation:

the number of inches of snow received each year by a ski resort

- you should use line graph to see data changing in consistent time period

the portion of the drama clubs budget needed for each type of expense

- you can use box plot to see the box plot to show median and q1 q3 of the expenses.

the number of heads and tails that came up in 100 coin flips

- you should use pie chart to see the percentages in entire population  

the number of votes received by each of four candidates

- you should use bar graph to compare 4 comparable object.

The portion of the drama clubs budget needed for each type of expense

A data set is a set of information. A data set corresponds to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row represents a specific record of the data set in question.

a) The number of inches of snow received each year by a ski resort

you should use a line graph to see data changing in the consistent time period

b) The portion of the drama club budget needed for each type of expense

you can use the box plot to see the box plot to show the median and q1 q3 of the expenses.

c) The number of heads and tails that came up in 100 coin flips

you should use a pie chart to see the percentages in the entire population  

d) The number of votes received by each of the four candidates

you should use a bar graph to compare 4 comparable objects.

Therefore a portion of the drama club's budget is needed for each type of expense.

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Answer: That would be distributive

Step-by-step explanation: