does y=5/6x+2 and y=5/6x-2 have exactly one solution

Answer:

x = 8

Step-by-step explanation:

If NO is parallel to KJ then the sides LK and LJ are in proportion, that is

[tex]\frac{KN}{NL}[/tex] = [tex]\frac{JO}{OL}[/tex], substitute values

[tex]\frac{x+2}{x-3}[/tex] = [tex]\frac{x}{x-4}[/tex] (cross- multiply )

x(x - 3) = (x + 2)(x - 4) ← expand factors on both sides

x² - 3x = x² - 2x - 8 ( subtract x² - 2x from both sides )

- x = - 8 ( multiply both sides by - 1 )

x = 8

Answer:

8

Step-by-step explanation:

Answer:

the answer is a 18 because that would mean there are more red than any color in the bag

To make the probability of drawing a red marble 1/2 with the current bag of marbles, you would need to add 12 more red marbles.

To answer the question about how many additional red marbles must be added to the 18 marbles already in the bag so that the probability of randomly drawing a red marble is 1/2, we first need to understand how the probability of an event is calculated. Probability is calculated by dividing the number of ways an event can occur by the total number of outcomes. In this case, the event is drawing a red marble and the total number of outcomes is the total number of marbles in the bag.

Currently, there are 6 red marbles and 18 total marbles in the bag, so the probability of drawing a red marble is 6/18 = 1/3. We want this probability to increase to 1/2, so we need to add more red marbles. Let's represent the number of red marbles we need to add as x. To find x, we need to solve the following equation: (6 + x) / (18 + x) = 1/2.

Solving for x, we get x = 12. Therefore, you need to add 12 more red marbles to the bag to make the probability of drawing a red marble 1/2.

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Answer:

9

Step-by-step explanation:

1+8=9

Answer:

9

Step-by-step explanation:

1+8=9

Answer:

6

Step-by-step explanation:

5 times 4 is 20

20 divided by 10 is 2

2 plus 4 is 6

5 * 4 / 10 + 4

20 / 10 + 4

2 + 4

6

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Step-by-step explanation:

There are certain methods for solving a system of equations. Some of which are:

Substitution Method

Substitution method to solve a system of equations is suitable if a variable of a any equation seems isolated or could comfortably be isolated without any ration/fraction resulting.

For example, for the following system of equations

x - 2y = 11....[A]

x = 5 - y....[B]

substituting the value of x = 5 - y from equation [B] into equation [A], so that

(5 - y) - 2y = 11

5 - y - 2y = 11

3y = -6

y = -2

Elimination Method

Elimination method to solve a system of equations is suitable if both equation are in standard form, and just adding or subtracting the equations to determine an equation in one variable.

For example, for the following system of equations

2x + 7y = -5....[C]

5x - 7y = 12....[D]

Adding Equation [C] and Equation [D].

7x + 0 = 7

x = 1

Graphing Method

Sometimes graphing method may be used to solve the system of the equation and visualize the solution.

For example,

y = -2....[E]

y = 3x + 1....[F]

The solution for this system of equation is the point of intersection of both the lines, which is shown in attached figure. The point of intersection is (-1, -2).

Hence, the solution of this system of equations is (-1, -2), as shown in attached figure.

Keywords: system of equations, elimination method, substitution method, graphing method

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Answer:

Yes

Step-by-step explanation:

Answer:

yes it is

Step-by-step explanation:

3.456 could be written as a fraction, that means it is a rational number because rational number is any number that could be written as a fraction.

3.456=3456/1000

Answer:

2 packs

Step-by-step explanation:

Since there is 10 packs just divided it by how many notebooks were in the pack.

Answer:

Monthly sales = $15000

Step-by-step explanation:

Let x be the monthly sale.

Given:

The monthly salary of a show room attendant is the sum of a fixed  salary of $600 plus 8% of all monthly sales.

8% of monthly sale = [tex]\frac{8}{100}\times mothly\ sale[/tex]

8% of monthly sale = [tex]\frac{8}{100}\times x[/tex]

So, the monthly salary of attendant is.

[tex]Monthly\ salary = 600+8\ percent \ of\ monthly\ sales[/tex]

[tex]Monthly\ salary = 600+\frac{8}{100}\times x[/tex]

Monthly salary is given.

[tex]1800 = 600+\frac{8}{100}\times x[/tex]

[tex]1800 - 600 = \frac{8}{100}\times x[/tex]

[tex]1200 = \frac{8}{100}\times x[/tex]

[tex]x=\frac{1200\times 100}{8}[/tex]

[tex]x=\frac{120000}{8}[/tex]

[tex]x=15000[/tex]

Therefore, the monthly sale is $15000

Answer:

the tens place is going down one number each time

Step-by-step explanation:

To find the pattern of the data set we can subtract the 1st term to the 2nd term.

788 - 778 = 10

Now, multiply the 2nd term to the 3rd term to check.

778 - 768 = 10

Thus, the rule of the pattern is 10.

Best of Luck!

Answer:

  102 1/3

Step-by-step explanation:

To find the 6th term, add the common difference to the 5th term:

  103 + (-6 2/3) = 102 1/3

Answer:in Spanish: su calificación debe ser 60 para aprobar esta clase

Step-by-step explanation:

Answer:

That mean you must have 60 and above to pass and anything below that is failure

Step-by-step explanation:

Step-by-step explanation:

4. 4+11=15

to find the length of The first piece

4/15*75=20

to find the length of the second one

11/15*75=55

5. 4+1=5

to find the length of the first one

4/5*180=144

to find the length of the second one

1/5*180=36

7. 5+7+8=20

to find the length of the first one

5/20*40=10

to find the length of the second one

7/20*40=14

to find the length of the third one

8/20*40=16

4. The lengths of the two pieces are 20 inches and 55 inches.

5. The measures of the two angles are 144 degrees and 36 degrees.

6. The measures of the angles are 36 degrees, 60 degrees, and 84 degrees.

7. The lengths of the sides are 10 inches, 14 inches, and 16 inches.

4: A string that is 75 inches long will be cut into two pieces in the ratio of 4:11. Find the lengths of the two pieces of string.

The total length of the string is 75 inches.

The ratio given is 4:11.

First, find the total parts in the ratio by adding the two numbers: [tex]4 + 11 = 15[/tex].

Now, to find the length of each piece:

5: The ratio of two supplementary angles is 4:1. Find the measures of the two angles.

Supplementary angles add up to 180 degrees.

The given ratio is 4:1.

Find the total parts in the ratio: [tex]4 + 1 = 5[/tex].

Now, calculate the measures of the angles:

6: The ratio of the measures of the angles in a triangle is 3:5:7. Find the measure of each angle.

The sum of the angles in a triangle is 180 degrees.

The given ratio is 3:5:7.

Total parts in the ratio: [tex]3 + 5 + 7 = 15[/tex].

Now, calculate each angle's measure:

7: The ratio of the measure of the sides of a triangle is 5:7:8 and its perimeter is 40 inches. Find the measure of each side.

The perimeter of the triangle is 40 inches.

The given ratio is 5:7:8.

Total parts in the ratio: [tex]5 + 7 + 8 = 20[/tex].

Now, calculate the length of each side:

Answer:

there is not a triangle

Step-by-step explanation:

but if is has all 3 sides the same it is sss, if there is two sides and an angle in between them it is sas, and if there is a hypotenuse and then a leg then it is hl, or if it is none it is d

The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion. To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent. In the given options, B. SAS is the correct answer.

The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion.

To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent.

In the given options, B. SAS is the correct answer.

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Answer:

Median

Step-by-step explanation:

Median, in geometry, is a line segment that is drawn from the vertex or the corner of the shape that extends to the middle or the midpoint of the side opposite of that corner.

When you say opposite the corner, that means it is the one across it. Look at the attached picture for emphasis.

Answer:

the building is 90 feet tall

Step-by-step explanation:

each floor is 9 feet, there are 10 floors,

9 x 10 = 90 feet

Answer:

D

Step-by-step explanation:

Answer:

D. (sugar * frosting)/Flour

Step-by-step explanation:

Given that

The formula for sweetness of a cake is represented by S = sf/F

where the

sweetness of a cake is denoted with S

amount of sugar in a cake, with A

amount of frosting, with f

amount of flour with F.

To get the appropriate unit, all we need to do is to substitute the letter representation of each unit with the original word.

So,

S = sf/F becomes

S = (sugar * frosting)/Flour

We arrive at this by replacing s with sugar; f with frosting and F with Flour

Answer:

[tex]210[/tex] £

Step-by-step explanation:

Let amount that abby gets[tex]=x[/tex]

Given that [tex]\frac{Amount\ of\ abby}{Amount\ of\ Ben} =\frac{2}{7}[/tex]

[tex]Amount\ of\ ben=\frac{7}{2}\times Amount\ of\ abby\\ =\frac{7}{2}\ x[/tex]

Amount of chole + amount of Danesh [tex]=1.5\times[/tex]of abby

                                                                      [tex]=1.5 \ x[/tex]

[tex]x +\frac{7}{2} \ x + 1.5 \ x =360\\\\6x=360\\\\x=\frac{360}{6}\\\\x=60[/tex]

[tex]Amount\ of\ Ben =\frac{7}{2}\ x = \frac{7}{2} \times 60\\\\=7\times 30\\\\=210[/tex]

The amount got by Ben =  £210

£360 is shared between Abby, Ben, Chloe and Denesh.

The ratio of the amount Abby gets to the amount that Ben gets is 2:7.

Chloe and Denesh get 1.5 times the amount Abby gets.

We have to work out the amount of money that Ben gets.

Let the amount  Abby gets = x ...........(1)

According to the given situation

[tex]\rm \dfrac{Amount\; got\; by\; Abby }{Amount \; got \; by \; Ben }= \dfrac{2}{7}[/tex]

[tex]\rm Amount \; got \; by \; Ben = (7/2) x......(2)[/tex]

[tex]\rm Amouut\; goy \; by\; Chole + Amount\; got \; by \; Denesh = 1.5 x........(3)[/tex]

The total amount = £360

From equation (1) (2) and (3) we get

[tex]\rm x + (7/2)x + 1.5x = 360\\x(1+3.5 +1.5) = 360\\x (6) = 360 \\x = 360/6= 60[/tex]

The amount got by Abby = £60

So  the amount got by Ben = 3.5 (60)  =  £210

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Answer: 0.236 Liters.

Step-by-step explanation:

First you multiply 1.3 and 0.8 you get 1.064.

You subtract 1.3 and 1.064 and you get your answer 0.236 Liters.

Answer:

m∠C = 115°

Step-by-step explanation:

DE≈DF

ΔDEF is an isosceles triangle ∴ m∠DEF = m∠DFE = 1/2 (180-50) = 65

∴ m∠DFB = 180 -65 = 115

∵ DCBF is a parallelogram m∠DFB = m∠DCB = 115°

Answer:

I am not agree with him. Because -2 is the leading coefficient of this  polynomial.

Step-by-step explanation:

Pat multiplied the polynomials for a math assignment.

Then he found the product is [tex]-4x+8x^2-2x^3+5[/tex]

Now Pat wants to find the leading coefficient to this polynomial.

Pat's answer was -4.

But I am not agree with him.

Because for a given polynomial we can calculate the leading coefficient when comparing with degrees of the polynomial.

Leading coefficient means that the coefficient whose degree is the highest.

When compared with the given polynomial we have [tex]x^3[/tex] is the highest degree, so that -2 is the leading coefficient to this polynomial.

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

we know that

In a parallelogram opposite sides are parallel and congruent

In this problem

AB and CD are opposite sides

so

AB=CD

substitute the given values

[tex]6x-10=3x+5[/tex]

solve for x

[tex]6x-3x=10+5[/tex]

[tex]3x=15[/tex]

[tex]x=5[/tex]

Answer:

They have 18 vegetable plants.

Step-by-step explanation:

Given:

Emily's family loves to work together  in the garden.

They have a. preference for flowers as 80% of  their plants are flowers and the rest  are vegetables.

They have 90 plants  in the garden.

Now, to find the number of vegetable plants.

Total plants in the garden = 90.

80% of the plants are flowers.

So, number of plants which are flowers = 80% of 90.

[tex]=\frac{80}{100} \times 90[/tex]

[tex]=\frac{7200}{100}[/tex]

[tex]=72\ plants.[/tex]

The number of flower plants = 72.

Total plants = 90 (given)

So, to get the number of vegetable plants we subtract:

[tex]90-72=18\ plants.[/tex]

Thus, vegetable plants = 18.

Therefore, they have 18 vegetable plants.

Answer:

x=1, y=2. (1, 2).

Step-by-step explanation:

x-3y=-5

-3x+7y=11

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

x=3y+(-5)

x=3y-5

-3(3y-5)+7y=11

-9y+15+7y=11

-2y=11-15

-2y=-4

2y=4

y=4/2

y=2

x-3(2)=-5

x-6=-5

x=-5+6

x=1

Answer: fifty-two hundredths

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{5}{3}[/tex] x + 5 ← is in slope- intercept form

with slope m = - [tex]\frac{5}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular }[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{5}{3} }[/tex] = [tex]\frac{3}{5}[/tex]

Answer:

5/3

Step-by-step explanation:

Answer:

3x-2

Step-by-step explanation:

-2x-2+5x=-2x+5x-2=3x-2

Answer:

y=-70x+350

Step-by-step explanation:

Since x is the number of years since 1995, this means that at 1995, x=0. This also means that in 2000, x=5. The values of the stuffed animals were 350 in 1995 and 0 in 2000. The formula for slope is rise over run, so we can find the answer using this mathematical expression: y2-y1/x2-x1. Plugging in our values, we get 0-350/5-0 which simplifies into -350/5. This further simplifies into -70. Our slope is -70. The definition of y-intercept is the value of y when x=0. We know that x=0 at 1995 and the value for the stuffed animals was 350 at that time. This tells us that the y-intercept is 350. Slope-intercept form is y=mx+b, so plugging in our information, we get y=-70x+350.

The equation representing the data of Romi's stuffed animal inventory is y = -70x + 350

The given problem involves finding an equation in slope-intercept form to represent the data of Romi's stuffed animal inventory from 1995 to 2000. Let's first find the slope and y-intercept of the equation using the given data. We know that the inventory in 1995 was 350 and in 2000 was 0. We can use these two points to find the slope and y-intercept.

Slope (m) = (change in y)/(change in x) = (0 - 350)/(2000 - 1995) = -350/5 = -70

Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values

y = -70x + b

To find the value of b, we can substitute one of the given points into the equation. Let's use the point (0, 350).

350 = -70(0) + b

350 = b

Substituting the value of b back into the equation, we have the final equation:

y = -70x + 350

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Answer:

Around 39.2

Step-by-step explanation:

To do this question, you use the pythag theorem, a^2 + b^2 = c^2. You have the hypotenuse of the triangle, 40 feet in length, and you have a because it's 8 feet from the wall. You now have b^2 = 1600-64. b^2 = 1536. Take the square root, and you have the height of the latter on the wall is equal to 39.1918 or 39.2 rounded

Answer:

3 items are in B that are not in C

Step-by-step explanation:

a: only in a, not count those in b or c

b: only in b, not count those in a or c

c: only in c, not count those in a or b

A = a + b + c = 20

c = 7

a + b = 20 - 7 = 13

10 not in b, of course not in c ∴ a = 10

b = 13 -10 = 3