Express the following linear equations in the form ax + by + c = 0 and indicate the values of a , b , c in each case :

i ) -2x + 3y = 6
ii) 2x = -5y​

The the 21st, 26th, 65th, and 75th percentiles are 19.45, 21.7, 27.85, and 29.50.

Here, n=8

P21=(21(n+1)100)th value of the observation

=(21⋅9/100)th value of the observation

=1st observation +0.89[2nd-1st]

=15+0.89[20-15

= 19.45

P26 = (26(n+1)100)th value of the observation

=(26⋅9/100)th value of the observation

=2nd observation +0.34[3rd-2nd]

=20+0.34[25-20]

=20+0.34(5)

= 21.7

P65= (65(n+1)100)th value of the observation

=(65⋅9/100)th value of the observation

=5th observation +0.85[6th-5th]

=27+0.85[28-27

= 27.85

P75 = (75(n+1)100)th value of the observation

=(75⋅9/100)th value of the observation

6th observation +0.75[7th-6th]

=28+0.75[30-28]

= 28 + 1.50

= 29.50

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Answer:

1/256

Step-by-step explanation:

4^-4 is the same thing as 1/4*1/4*1/4*1/4 which is 1/256

Answer:

1/256

Step-by-step explanation:

4⁻⁴ = 1/(4⁴) = 1/256

Answer:

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Step-by-step explanation:

Your question has already been answered.

Here is the link to the answer:

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Hope this helps!

If not, I am sorry.

The equation that represents the volume of the storage container(rectangular prism) in terms of its width is 12w + 6w²

volume of a rectangular prism = lwh

where

Therefore,

h = 6 ft

l = 2 + w

Hence,

volume of the rectangular prism = (2 + w) × w × 6

volume of the rectangular prism = (2w + w²)6

volume of the rectangular prism = 12w + 6w²

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Answer: 2/13

Step-by-step explanation:

To solve this word problem expression, we can first convert the mixed number to an improper fraction so it's easier to work with.

1 1/3 = 4/3

Adding 4/3 to 0.4, we get 5.2/3.

4/15 divided by 5.2/3 is 4/26, or 2/13

For the given geometric sequence, we have:

[tex]a_1 = 9\\\\a_n = (-1/3)*a_{n-1}[/tex]

So the correct option is B.

Here we have the geometric sequence:

[tex]a_n = 9*(-\frac{1}{3} )^{(n - 1)}[/tex]

To get the initial value of the geometric sequence, we just need to replace n by 1, so we get:

[tex]a_1 = 9*(-\frac{1}{3} )*(1 - 1) = 9[/tex]

Now, notice that the common ratio is (-1/3), this means that each term of the sequence is (-1/3) times the previous term.

[tex]a_n = (-1/3)*a_{n-1}[/tex]

Then the correct option is B.

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Answer:

OB

Step-by-step explanation:

no clear explanation for this answer. a picture to demonstrate how i archived it will be shared

The scale factor from triangle ABC to DEF would be,

⇒ 1 / 3

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Two triangle ABC and DEF is shown in figure.

Hence, We can formulate;

The scale factor from triangle ABC to DEF would be,

⇒ AC / DF

⇒ 3 / 9

⇒ 1 / 3

Thus, The scale factor from triangle ABC to DEF would be,

⇒ 1 / 3

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The parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units

This is a way of changing the position of an object on an xy-plane.

Given the parent function expressed as  y = (x – 5)^2 + 7

From the resulting image after translation, we can see that the parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units

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The t-test is a type of inference statistic used to determine if there is a significant difference between the means of two groups that may be related to a particular characteristic. The t-test is one of many tests used to test statistical hypotheses.

Inference statistics have two main purposes. Estimates for population groups (for example, the average SAT score for all 11th graders in the United States). Hypothesis testing to draw inferences about the population

One-way ANOVA is a common method for comparing three or more group means. The usual goal is to determine if the mean (or median) of at least one group is different from the other. Subsequent multiple comparison tests are often used to determine where differences occur.

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The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x

An equation is an expression that shows the relationship between two or more variables and numbers.

The products of the two polynomials (x² + x – 2) and (4x² – 8x) is:

= 4x⁴ - 8x³ + 4x³ - 8x² - 8x² + 16x

= 4x⁴ - 4x³ - 16x² + 16x

The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x

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Answer:

x<3

Step-by-step explanation:

3x - 4 < 17 - 4x

So, the -4 shall cross to the other side and replace the -4x which will now take the place of where the -4 used to be and the signs of both digits will change to a positive (+)

Remember the inequality sign (<) shall not change

so now the equation shall appear like this;

3x + 4x < 17 + 4

add both sides and it will appear like this;

7x < 21

simplify both sides by 7 and you'll get

x < 3

Answer:

4 legs from the bed and 4 from the chair im guessing since not all have 4

Hope This Help

Answer:

4 legs from the bed and 4 from the chair

Step-by-step explanation:

im a math wizard fr

A function assigns the values. The cost of advertising for 10 minutes will be equal to £100.

A function assigns the value of each element of one set to the other specific element of another set.

Let the number of minutes of advertising be represented by x, and the cost of advertising be represented by y.

Given the function through which the cost of advertising can be determined. Therefore, the cost of advertising for the 10 min program will be when the value of x is 10. Therefore, the cost of advertising for 10 mins will be £100.

Hence, the cost of advertising for 10 minutes will be equal to £100.

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The equation with infinitely many solutions is:

9x + 80 - 1x = 8*(x + 10)

An equation has infinitely many solutions when the dependence on x vanishes.

If you look at the third equation, we get:

9x + 80 - 1x = 8*(x + 10)

If we simplify the left side and expand the right side, we get:

8x + 80 = 8x + 80

So we have the exact same thing in both sides, this means that the equation is true for any value of x, so the equation has infinite solutions.

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The width is 1 meter.

Given,

Jarom is working for a landscaping company and is responsible for building the stone border around a rectangular pond.The pond measures 6 meters by 15 meters. The manager told Jarom that the budget only allowed enough stone for 46 square meters

Let the border be width  = x

then the area of the border will be

2(6x) + 2(15x) +4x2 = 46

= 12x +30x+ 4x2 = 46

= 4x2 + 42x - 46 = 0

=> x =( -42 +- √42² +4*4*46)/8

x =1 , x = -11.5

since the width is 1 meter.

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Answer: D

Step-by-step explanation:

See attached image.

Answer:

Axis of symmetry: x = 2

Vertex: (2,4)

Step-by-step explanation:

Answer:

B E F

Step-by-step explanation:

as the graphic shows, f(x) = 0 means that the y value is 0. and that means these are the points, where the curve intersects the x-axis.

they are already marked in the graphic :

for x = -1, 2, 4

The inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6

The function is given as:

f(x) = 6x + 4

Rewrite as:

y = 6x + 4

Swap x and y

x = 6y + 4

Subtract 4 from both sides

6y = x - 4

Divide through by 6

y = (x - 4)/6

Rewrite as:

f^-1(x) = (x - 4)/6

Hence, the inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6

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Hello!

Let's subtract!

⇒ 6x² - 2x + 6 - (6x² - 7x - 2)

⇒ 6x² - 2x + 6 - 6x² + 7x + 2

⇒ 5x + 8

∴ The difference will be equal to 5x + 8.

Answer:

Your answer is 5x+8

Step-by-step explanation:

= 6x^2-2x+6 - (6x^2-7x-2)

= 6x^2-2x+6 - 6x^2+7x+2

= 6x^2- 6x^2-2x+7x+6+2

=5x+8

Hope its helpful!

Answer:

4th option

Step-by-step explanation:

L = larger softball and S = smaller softball ,then

L + S = 80 → (1) ← equation based on number of softballs ordered

2.75L + 3.25S = 245 → (2) ← equation based on cost

subtract S from both sides in (1)

L = 80 - S → (3)

substitute L = 80 - S into (2)

2.75(80 - S) + 3.25S = 245 ← distribute parenthesis and simplify left side

220 - 2.75S + 3.25S = 245

220 + 0.5S = 245 ( subtract 220 from both sides )

0.5S = 25 ( divide both sides by 0.5 )

S = 50

substitute S = 50 into (3)

L = 80 - 50 = 30

50 small softballs and 30 large softballs were ordered

Answer:

the 4th answer option

Step-by-step explanation:

L, S are the number of balls of that size.

so, L + S = 80. as we order a total of 80 balls.

then each large ball costs $2.75. and each small ball costs $3.25.

so, the total price is

2.75L + 3.25S = 245

as we order balls in total for $245.

so, this set of 2 equations with 2 variables allows us to find the solution.

one defines the total number of balls, and one defines the total amount of money spent by using the individual prices for each type of ball.

the advantage of variables is that we can define the rising and dependencies before we have to calculate any of them specifically.

and once we have all of them defined, then we can start solving the numbers.

To solve the expression, the steps are add 19 and multiply by 5

Given the equation;

-3 = -19 + d/5

First,

Collect like terms

-3+ 19 = d/5

Add the values on the left side

We have

16 = d/5

Cross multiply

16 × 5 = d

We then have

d = 80

Thus, to solve the expression, the steps are add 19 and multiply by 5

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Using supplementary angles, it is found that the measure of angle x is of 65º.

Angles are called supplementary if the sum of their measures is of 180º.

In this problem, angles x, 25, and 90º are supplementary, hence:

x + 25 + 90 = 180

x = 180 - (25 + 90)

x = 65º.

The measure of angle x is of 65º.

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Answer:

○ The distance between a and b on the number line is 0.47 units.

Explanation:

The first statement is not true because the distance between a and b on the number line is not 0.47.

Distance between a and b = 5.25 - (-5.72)

                                             = 10.97

• The second statement is true because the sum of a and b is negative:

Sum = a + b

        = -5.72 + 5.25

        = -0.47

• The third statement is true because the quotient of a and -b is:

a ÷ -b

⇒ -5.72 ÷ -5.25

⇒ 1

And the quotient of -a and b is:

-a ÷ b

⇒ -(-5.72) ÷ 5.25

⇒ 1

This shows that the quotients are the same.

• The fourth statement is true because the product of a and -b:

a × -b

⇒ -5.72 × -(5.25)

⇒ 30.03 ,

is positive.

Explanation:

For choice A, order matters. This is because of the positions of first place and second place are different from one another. Since order matters, we have a permutation for choice A and can rule it out.

Choices C and D are ruled out for the same reason.

Choice B is a combination. It doesn't matter what the order of the CDs are. All that matters is the group overall rather than the individual CDs.

9) The x-intercepts are when y=0. From the factored form, we know the x-intercepts are (-1,0) and (3,0).

10) The y-intercept is when x=0. From the standard form, we know the y-intercept is (0, -3).

If the Height of Eiffel Tower in Paris is 1063 feet tall and we took an elevator 3/4 up the tower then we would be 797.25 feet from the ground.

Given The height of the Eiffel Tower is 1063 feet tall. We have taken an elevator that is 3/4 up the tower.

Height is the measurement of someone  from head to foot or from base to top. It is the distance upward.

Height of The Eiffel tower is 1063 feet.

We have taken 3/4 up the elevator.

Then the height from ground to us can be calculated by multiplying 1063 by 3/4 which will be as under:

=1063*3/4

=729.25 feet

Hence if the height of the Eiffel Tower is 1063 feet then we would be 729.25 up from the ground if we have taken elevator 3/4 up the tower.

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