positive,negative,zero and undefined slope

Answer:b

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

The first quadrant is the top-right one

If a point is in the first quadrant, the x- and y-values of the point are both positive

Let's go through the one by one.

A) Translating the quadrilateral right 4 units will make the new S to be \((-3+4, -7)=(1, -7)\), which is not in the first quadrant.

B) Reflection the quadrilateral across \(x=4\) will not change the y-value of any points. So, the new S will stay below the x-axis, and thus will never be in the first quadrant, because it will always have a negative y-value.

C) This one is tricky. We can prove(the proof is just taking cases of which quadrant) that if a point is in the second or fourth quadrant, it's reflection across the line \(y=-x\) will always be in the same quadrant it started in(i.e. reflect a point in the second quadrant, you get a point in the second quadrant). We know that P is in the second quadrant, so the new P will also be in the second quadrant. Therefore, the new quadrilateral will not be entirely in the first quadrant.

D) We intuitively(and can prove) that because R is right underneath Q, the new R will be directly to the left of Q, with the same distance as Q to original R. So, the new R will be \((-10, 12)\) using above method. This point is not in the first quadrant.

E) We know intuitively(and can prove) that a reflection across the line \(x=3\) will make the entire quadrilateral in the first and fourth quadrant. However, When we translate up, the new S, the lowest point on the quadrilateral, will be above the x-axis, making all the points in the first quadrant! Therefore, E works.

F) When we reflect across the x-axis, any points in the second quadrant go to the third quadrant. So, the new P will be in the third quadrant. However, when we translate up 13 units, the new P will go to the second quadrant. It will never cross the y-axis, and will always have a negative x-coordinate. Therefore, P will not be in the first quadrant.

Summing up the cases that work, we get that \(\boxed{E}\) is the only answer.

The transformations of quadrilateral PQRS which would result in the image of the quadrilateral being located only in the first quadrant of the coordinate plane is:

This refers to the axis of a two dimensional Cartesian system which is one side out of four quarters of a circle or given shape.

From the given image, we can see that the first quadrant is at the top.

With this, we can see that the transformation which would make the quadrilateral PQRS to be in the first quadrant is a reflection across x=3, then a translation up 8 units.

This is because when we translate up, then we can see that the x-y values of the point are positive and which would make the translation up 8 points.

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Abbey's acceleration is 0 m/s². Acceleration is the rate of change of velocity with respect to time.

If Abbey is running down the field at a constant speed of 10 m/s, then her velocity is not changing. Therefore, her acceleration is 0 m/s².

Mathematically, we can represent acceleration using the equation:

a = (v₂ - v₁) / t

Where,

a = acceleration

v₁ = initial velocity

v₂ = final velocity

t = time

In Abbey's case, her initial velocity (v₁) and final velocity (v₂) are the same, since she has a constant speed. Therefore,

v₂ - v₁ = 10 m/s - 10 m/s = 0 m/s

And since there is no change in velocity, her acceleration is 0 m/s².

So, Abbey's acceleration is 0 m/s².

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Answer:

3\(\sqrt{13}\)

Step-by-step explanation:

Calculate the distance using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (- 9, 8) and (x₂, y₂ ) = (- 3, - 1)

d = \(\sqrt{(-3-(-9))^2+(-1-8)^2}\)

  = \(\sqrt{(-3+9)^2+(-9)^2}\)

  = \(\sqrt{6^2+81}\)

   = \(\sqrt{36+81}\)

   = \(\sqrt{117}\)

   = \(\sqrt{9(13)}\)

   = \(\sqrt{9}\) × \(\sqrt{13}\)

   = 3\(\sqrt{13}\)

Answer: I think it's B. (7b - 4)²

Step-by-step explanation:

Answer: O B. (7b-4)²

Here is how it's done:

49b2−56b+16

=(7b−4)(7b−4) or (7b-4)²

Answer:

11

Step-by-step explanation:

I’m pretty sure. Just add it

Answer:

11

Step-by-step explanation:

Absolute value only applies to negative numbers. It will make negative numbers positive. As you can see in the problem, they are asking for the absolute value of positive numbers, so you can ignore the absolute value signs and add normally.

Hope it helps! Comment if you have any questions!

Answer: 24

Step-by-step explanation:

6 sides on the dice. 4 sections on the spinner.

6 times 4 = 24

24 possible outcomes.

Answer: y = -1.5x - 3

Step-by-step explanation:

We'll assume this is a straight line, with the form y=mx+b. m is the slope (the rate that y changes with a change in x) and b is the y-intercept (the value of y when x=0).

Once we can determine both m and b, we'll have an equation that answers this question. First, m.

m, the slope, is known as the Rise/Run. We can use the two given points to calculate this value. Take the two points, (-4,3) and (2,-6), and calculate the change in x (the Run), by subtrating the initial point (I'll choose (-4,3)) from the final point ((2,-6)). For x that is: 2-(-4) = 6. For y: -6-3 = -9. When x moved +6 units, y went down by 9, or -9. The slope is the Rise (-9) over the Run (6), or (-9/6). The slope of this line is - 1.5.

We now have y = -1.5x + b. To find b, use wither of the two points. I'll use (2,-6) because I like even numbers, but fell free to use the other. Both will give the same answer for b. [Try it].

Using (2,-6), we get:

y = -1.5x + b

-6 = -1.5*(2) + b

-6 = -3 + b

b = -3

The equation is y = -1.5x - 3

=====

For fun, try the other point, (-4,3) to find the value of b:

y = -1.5x + b

3 = -1.5*(-4) + b

3 = 6 + b

b = -3 The Same!

The Wilcoxon signed-rank test is employed to see if there is a substantial difference between two related samples. Here the new cognitive therapy group and placebo group are related samples as they both belong to the same sample of cognitive therapy's study. The Wilcoxon signed-rank test is performed on the rank-based data as the data is not normally distributed. Following is the calculation for Wilcoxon’s signed rank test:The null hypothesis for the Wilcoxon signed-rank test is that there is no difference between the new cognitive therapy and placebo treatments. While the alternative hypothesis is that there is a difference between the two treatments.

The Wilcoxon signed-rank test is performed as follows:
Rank all the data, with the lowest value being ranked 1 and the highest value being ranked 12.
Calculate the difference between the new cognitive therapy and placebo group scores.
Take the absolute values of the differences.
Rank the differences in ascending order and ignore the signs.
Calculate the sum of the ranks of the new cognitive therapy group.
Calculate the test statistic T.
For this dataset, the calculations of the Wilcoxon signed-rank test are as follows:
Data Ranked (New therapy) Difference Absolute Difference Ranked Differences + Rank Therapy Differences - Rank Placebo 5 1 4 3 4 4 6 2 4 4 2 2 4 4 8 7 1 1 1 12 10 2 2 3 5 1 6 13 12 1 8 7 7 4 4 1 5 5 5 1 14 13 1 2 1 15 7 8 7 7 5 9 10 3 5 8 56 12 44 12 12 11 7 Total 49
Calculating T:

\($$T =\) \(\frac{Total\ of\ positive\ ranks - \frac{n(n+1)}{4}}{\sqrt{\frac{n(n+1)(2n+1)}{24}}}$$\)

Here, n is the number of pairs, which is 12.
T = 3.52
Using the Wilcoxon signed-rank test table, the critical value at the 0.05 level for n = 12 is 18.
Since T (3.52) is less than the critical value (18), the null hypothesis cannot be rejected.
There is no evidence to suggest that there is a difference between the new cognitive therapy and placebo treatments.

The equation of the line containing the points (4, 6) and (8, 4) in slope-intercept form is y = (-1/2)x + 8.

To find the equation of a line containing the points (4, 6) and (8, 4) in slope-intercept form, we need to determine the slope (m) and the y-intercept (b) of the line.

The formula to calculate the slope (m) is given by:

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

Using the coordinates (4, 6) and (8, 4), we have:

m = (4 - 6) / (8 - 4)

m = -2 / 4

m = -1/2

Now that we have the slope, we can choose either of the given points and substitute its coordinates (x, y) into the slope-intercept form equation (y = mx + b) to find the y-intercept (b). Let's use the point (4, 6):

6 = (-1/2)(4) + b

6 = -2 + b

b = 8

Therefore, the slope (m) is -1/2 and the y-intercept (b) is 8. Plugging these values into the slope-intercept form equation, we get:

y = (-1/2)x + 8

Hence, the equation of the line containing the points (4, 6) and (8, 4) in slope-intercept form is y = (-1/2)x + 8.

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Answer:

8

Step-by-step explanation:

41-4t

Hope this helps ^^

Answer:

Fraction Equivalent Fractions

4/5 8/10 12/15

1/6 2/12 3/18

5/6 10/12 15/18

1/7 2/14 3/21

Step-by-step explanation:

We say that 1/2 is equivalent to 2/4. Fractions are determined to be equivalent by multiplying the numerator and denominator of one fraction by the same number. This number should be such that the numerators will be equal after the multiplication.

Step-by-step explanation:

The expression 1/4 - 2/3 - (1/2 + 5/6) is equivalent to -7/4.

Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.

The given expression is,

1/4 - 2/3 - (1/2 + 5/6)

To solve the expression, first simplify bracket term,

1/4 - 2/3 - (8/6)

(3 - 8)/12 - 8/6

-5/12 - 8/6

-21/12

-7/4

The simplified form of the expression 1/4 - 2/3 - (1/2 + 5/6) is -7/4.

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Answer:

1: 2cm

2: 5cm

Step-by-step explanation:

Answer:

First one is 2, second is 5

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

The figure shown is a trapezoid

Area of a trapezoid = 1/2(bottom base length + top base length) × height

Bottom base length = 7 units

Top base length = 1 unit

Height = 4 units

So area = 1/2 ( 7 + 1 ) × 4

==> add 7 and 1

Area = 1/2 (8) × 4

==> multiply 1/2 and 8

Area = 4 × 4

==> multiply 4 and 4

Area = 16

Answer:

I'm not 100% sure but I think if you graph them all

where they intersect is the solution

Answer:

The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

Step-by-step explanation:

The breadth and length is 64m and 74m

breadth=x

length=x+10

perimeter for 3 rounds=3y

3y*50=13800

y(perimeter)=276

2(l+b)=286

2(x+10+x)=276

2(2x+10)=276

4x+20=276

4x=276-20

x=256/4

x=64

breadth=64m

length=74m

The complete question is,

rectangular land is 10m longer than its breadth cost of fencing around it is 3 rounds at rs 50 per meter is rs 13800. find length and breadth

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The breadth and length of the land is 64m and 74m.

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The first five terms of the sequence defined by the recurrence relation are 1, 2, 27, 146, and 603, and a closed formula for a subscript n is a subscript n = \(2^n - 3(1^n) + 5^n\).

(a) To find the first five terms, we can use the recurrence relation and the given initial terms:

a_0 = 1

a_1 = 2

a_n = 3a_{n-1} - a_{n-2} + 10a_{n-3}

a_2 = 3a_1 - a_0 + 10a_{-1} = 3(2) - 1 + 10(0) = 5

a_3 = 3a_2 - a_1 + 10a_0 = 3(5) - 2 + 10(1) = 23

a_4 = 3a_3 - a_2 + 10a_1 = 3(23) - 5 + 10(2) = 80

a_5 = 3a_4 - a_3 + 10a_2 = 3(80) - 23 + 10(5) = 259

Therefore, the first five terms of the sequence are: 1, 2, 5, 23, 80.

(b) To solve the recurrence relation, we first find the roots of the characteristic equation:

\(r^3 = 3r^2 - r + 10\)

(r-2)(r-1)(r-5) = 0

So the roots are r=2, r=1, and r=5.

a_n = \(c_1(2^n) + c_2(1^n) + c_3(5^n)\)

To find the values of the constants c_1, c_2, and c_3,

a_0 = 1 = c_1 + c_2 + c_3

a_1 = 2 = 2c_1 + c_2 + 5c_3

c_1 = 1

c_2 = -3

c_3 = 1

Therefore, the closed formula for a_n is a_n = \(2^n - 3(1^n) + 5^n\)

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Consider the recurrence relation a subscript n space equals space 3 a subscript n space minus space 1 end subscript space plus space 10 a subscript n space minus space 2 end subscript with first two terms a subscript 0 = 1 and a subscript 1 = 2.

(a) Write out the first 5 terms of the sequence defined by this recurrence relation.

(b) Solve the recurrence relation. That is, find a closed formula for an.

Step-by-step explanation:

very difficult............

Answer:

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The solution of the expression -3(3x+1) - (2+x) =0 is,

x = -1/2  or -0.5

The given mathematical expression is ,

-3(3x+1) - (2+x) =0

To solve it,

Expand the expression

⇒ -9x - 3 - 2 - x = 0

We can write it as,

⇒ -10x - 5 = 0

Add 5 both sides,

⇒ -10x - 5 + 5 = 5

⇒            -10x  = 5

Divide both sides by -10 we get

⇒                x  = -5/10

⇒                x  = -1/2

Hence,

The required value of x = -1/2.

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Answer:

4. But if u meant like rounding it would be 123.5

Step-by-step explanation:

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

Not accurate

Step-by-step explanation:

3+9+9=21

Answer:

purple graph is for x+y>3

black graph is for x+y<-4

Step-by-step explanation:

I recommend u use desmos. it'll really help

hope u have a nice day :)

9514 1404 393

Answer:

  Compounded continuously, $5,02

Step-by-step explanation:

Compounded quarterly, the amount in the account will be ...

  A = 6500(1 +.0325/4)^(4·5) ≈ 7641.89

Compounded continuously, the amount in the account will be ...

  A = 6500e^(.0325·5) = 7646.91

So, the account compounding continuously has the higher yield, by the amount of ...

  $7646.91 -7641.89 = $5.02

Answer:

x=138

Step-by-step explanation:

68+70+a=180

138+a=180

a=42

180-42=x

x=138