Rebecca can swim 90 meters in 2 minutes. If you graph this with minutes on the x-axis and meters on the y-axis, what will be the slope of the line?


May I please have some help with this problem?

Answer:

Yes, because there are two pairs of congruent corresponding angles

Step-by-step explanation:

Two triangles are similar if they have the same angles. For triangle UVT on the left, we know that the sum of angles in a triangle is 180 degrees. There is one missing angle there, so the sum of angles is

80 + 55 + missing angle = 180

subtract 80+55 = 135 from both sides

45 = missing angle

Therefore, the angles in UVT are 45, 55, and 80

Similar, for XWY,

missing angle + 45 + 55 = 180

subtract 45 + 55= 100 from both sides

missing angle = 80

The angles for XWY are 45, 55, and 80. The angles are the same for both triangles, and there are three pairs of congruent corresponding angles (45, 55, and 80). Therefore, the triangles are similar

QUESTION:- SOLVE EQUATION BY FACTORISATION

EQUATION:-

[tex] {x}^{2} + x - 72 = 0[/tex]

ANSWER:-

[tex] {x}^{2} + x - 72 = 0\\{x}^{2} + 9x - 8x - 72 = 0 \\ x(x + 9) - 8(x +9) = 0 \\ (x - 8)(x + 9) = 0 \\ [/tex]

NOW FOR VALUE OF X ->

[tex]x - 8 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 9 = 0\\ x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 9[/tex]

Given:

The given expression is:

[tex]6x^2y-3xy-24xy^2+12y^2[/tex]

To find:

Part A: The expression by factoring out the greatest common factor.

Part B: Factor the entire expression completely.

Solution:

Part A:

We have,

[tex]6x^2y-3xy-24xy^2+12y^2[/tex]

Taking out the highest common factor 3y, we get

[tex]=3y(2x^2-x-8xy+4y)[/tex]

Therefore, the required expression is [tex]3y(2x^2-x-8xy+4y)[/tex].

Part B:

From part A, we have,

[tex]3y(2x^2-x-8xy+4y)[/tex]

By grouping method, we get

[tex]=3y(x(2x-1)-4y(2x-1))[/tex]

[tex]=3y(x-4y)(2x-1)[/tex]

Therefore, the required factored form of the given expression is [tex]3y(x-4y)(2x-1)[/tex].

The answer would be D.

Answer: D

Step-by-step explanation:

Pretend that C is 12, pi is 3, and d is 4. 4=3/12, 4=3*12, 4=12-3, or 4=12/3? The only one that works is that last one, so the and is D: d=C/pi

Step-by-step explanation:

9514 1404 393

Answer:

  24

Step-by-step explanation:

The front face is an 8-sided star, so has 8 edges. We presume the back face is the same, so it also has 8 edges. Each of the front vertices is connected by an edge to each of the corresponding back vertices, so there are 8 more edges connecting front and back.

The total number of edges is 8 + 8 + 8 = 24.

We have to figure out what the product of DA is,

[tex]\begin{bmatrix}-1&2&3\\8&-4&0\\6&7&1\\ \end{bmatrix}\begin{bmatrix}1\\3\\5\\ \end{bmatrix}=\begin{bmatrix}a\\b\\c\\ \end{bmatrix}[/tex]

We know that,

[tex]\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix}=\begin{bmatrix}ax+by+cz\\dx+ey+fz\\gx+hy+iz\\\end{bmatrix}[/tex]

So,

[tex]a=-1\cdot1+2\cdot3+3\cdot5=-1+6+15=20[/tex]

[tex]b=8\cdot1+(-4)\cdot3+0\cdot5=8-12=-4[/tex]

[tex]c=6\cdot1+7\cdot3+1\cdot5=6+21+5=32[/tex]

So the solution is,

[tex]a,b,c=\boxed{20,-4,32}[/tex]

Hope this helps :)

Answer:

8.4

Step-by-step explanation:

jjdijendjndoendidnie

Answer:

(2,0)

Step-by-step explanation:

the x intercept is when 'y' is equal to 0 :

0 = 3x - 6

6 = 3x

x = 2

Answer:

(2,0)

Step-by-step explanation:

y = 3x-6

The x intercept is found by setting y = 0 and solving for x

0 = 3x-6

Add 6 to each side

6 = 3x-6+6

6 =3x

Divide each side by 3

6/3 = 3x/3

2 =x

The x intercept is

(2,0)

9514 1404 393

Answer:

  x = √2

Step-by-step explanation:

A graph indicates the only solution is near x=√2.

__

Square both sides, separate the radical and do it again.

  [tex]\displaystyle(2-x)\sqrt{\frac{x+2}{x-1}}=\sqrt{x}+\sqrt{3x-4}\qquad\text{given}\\\\(2-x)^2\cdot\frac{x+2}{x-1}=x+(3x-4)+2\sqrt{x(3x-4)}\qquad\text{square}\\\\\frac{(2-x)^2(x+2)}{x-1}-4x+4=2\sqrt{x(3x-4)}\qquad\text{isolate radical}\\\\\left(\frac{(2-x)^2(x+2)-4(x-1)^2}{x-1}\right)^2=x(3x-4)\qquad\text{square}\\\\(x^3-6x^2+4x+4)^2=4(x-1)^2(3x^2-4x)\qquad\text{multiply by $(x-1)^2$}[/tex]

Now, we can put this polynomial equation into standard form and factor it.

  [tex]x^6 -12x^5+32x^4-76x^2+48x+16=0\\\\(x-2)^2(x^2-2)(x^2-8x-2)=0\qquad\text{factor it}\\\\x\in \{2,\pm\sqrt{2},4\pm3\sqrt{2}\}[/tex]

The original equation requires that we restrict the domain of possible solutions. In order for the radicals to be non-negative, we must have x ≥ 4/3. In order for the left side of the equation to be non-negative, we must have x ≤ 2. So, the only potential solutions will be in the interval [4/3, 2].

The only values in the above list that match this requirement are {√2, 2}. We know that the right side of the equation cannot be zero, so the value x=2 is also an extraneous solution.

The only solution is x = √2.

_____

Additional comment

For solving higher-degree polynomials, I like to use a graphing calculator to help me find the roots. The second attachment shows the roots of the 6th-degree polynomial. They can help us factor the equation. (There are also various machine solvers available that will show factors and roots.)

Answer:

0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 102, standard deviation of 12:

This means that [tex]\mu = 102, \sigma = 12[/tex]

Sample of 63:

This means that [tex]n = 63, s = \frac{12}{\sqrt{63}}[/tex]

What is the probability that the mean of the sample would differ from the population mean by greater than 3.4 watts?

Below 102 - 3.4 = 98.6 or above 102 + 3.4 = 105.4. Since the normal distribution is symmetric, these probabilities are equal, and thus, we find one of them and multiply by two.

Probability the mean is below 98.6.

p-value of Z when X = 98.6. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{98.6 - 102}{\frac{12}{\sqrt{63}}}[/tex]

[tex]Z = -2.25[/tex]

[tex]Z = -2.25[/tex] has a p-value of 0.0122.

2*0.0122 = 0.0244

0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.

Answer: Choice A) M = 0.25n + 100

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

Explanation:

For now, I'll treat n as x, and M as y.

In other words,

Let's select two points from this graph. I'll pick (200,150) and (400,200)

The slope of the line through those points is

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

m = (200-150)/(400-200)

m = 50/200

m = 0.25

Now we'll use the point (x,y) = (200,150) along with that slope value to find the y intercept b

y = mx+b

150 = 0.25*200+b

150 = 50+b

150-50 = b

100 = b

b = 100

You could also use (x,y) = (400,200) and you should get the same b value.

In fact, any other point from this graph works as well.

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

Since m = 0.25 and b = 100, we go from y = mx+b to y = 0.25x+100

This then translates over to M = 0.25n + 100 which is choice A

To help verify this, let's say we plugged in n = 100

M = 0.25*n + 100

M = 0.25*100 + 100

M = 25 + 100

M = 125

Which is confirmed by what the graph shows. I'll let you check the other points as well.

Answer:

hope u will understand...if u like this answer plz mark as brainlist

Answer:

[tex]\displaystyle p(x) + q(x) = \frac{2x}{(x+1)(x-1)}[/tex]

The result is indeed another rational expression.

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle p(x) = \frac{1}{x+1}\text{ and } q(x) = \frac{1}{x-1}[/tex]

And we want to perform the operation:

[tex]\displaystyle p(x) + q(x)[/tex]

And show that the result is another rational expression.

Add:

[tex]\displaystyle = \frac{1}{x+1} + \frac{1}{x-1}[/tex]

To combine the fractions, we will need a common denominator. So, we can multiply the first fraction by (x - 1) and the second by (x + 1):

[tex]\displaystyle = \frac{1}{x+1}\left(\frac{x-1}{x-1}\right) + \frac{1}{x-1}\left(\frac{x+1}{x+1}\right)[/tex]

Simplify:

[tex]=\displaystyle \frac{x-1}{(x+1)(x-1)} + \frac{x+1}{(x+1)(x-1)}[/tex]

Add:

[tex]\displaystyle = \frac{(x-1)+(x+1)}{(x+1)(x-1)}[/tex]

Simplify. Hence:

[tex]\displaystyle p(x) + q(x) = \frac{2x}{(x+1)(x-1)}[/tex]

The result is indeed another rational expression.

Answer:

(6,-6)

Step-by-step explanation:

First let's identify the current coordinates of D

It appears that D is located at (2 , -2)

Now let's find the coordinate of D if it were dilated by a scale factor of 3.

To find the coordinates of a point after a dilation you simply multiply the x and y values of the pre image coordinates by the scale factor

In this case the scale factor is 3 and the coordinates are (2,-2)

That being said let's apply the dilation rule

Current coordinates: (2,-2)

Scale factor:3

Multiply x and y values by scale factor

(2 * 3 , -2 * 3) --------> (6 , -6)

The coordinates of D' would be (6,-6)

Answer:

16 is answer

Step-by-step explanation:

3(2)^2+4(1)^2= 3(4)+4(1)=12+4=16

Let's use Gaussian elimination. Consider the augmented matrix,

[tex]\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right][/tex]

• Add row 1 to row 2, and add -1 (row 1) to row 3:

[tex]\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right][/tex]

• Add -2 (row 2) to row 3:

[tex]\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right][/tex]

• Add -2 (row 3) to row 2:

[tex]\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right][/tex]

• Add row 2 and row 3 to row 1:

[tex]\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right][/tex]

So the inverse is

[tex]\begin{bmatrix}1&-1&-1\\-1&2&3\\1&1&4\end{bmatrix}^{-1} = \boxed{\begin{bmatrix}5&3&-1\\7&5&-2\\-3&-2&1\end{bmatrix}}[/tex]

Answer:

The answer is C

Step-by-step explanation:

PLATO

Answer:

The guy above me is correct

Step-by-step explanation:

2022

Answer:

number of seeds planted per square foot

Step-by-step explanation:

response is the yield explained by how many seeds are planted

Answer:

the answer is 56 cubic units

Answer:

Step-by-step explanation:

one angle is 50

Answer:

The figure is not symmetrical

Answered by GAUTHMATH

9514 1404 393

Answer:

  smaller : larger = 3 : 4

Step-by-step explanation:

The scale factor is the ratio of corresponding dimensions. If we use the width dimensions, we have ...

  smaller/larger = 9/12 = 3/4

The scale factor is 3/4.

Answer:

where is your diagram?

Step-by-step explanation:

Answer:

-2 <× <35

i hop i helped you sold the question

Answer:

the answer is C

Step-by-step explanation:

Answer:

The answer is in the picture below

Step-by-step explanation:

Sorry just realised the answers were different ;-;

Answer:

The arm spans for Class A are roughly symmetric, while those for Class B are skewed left.

Step-by-step explanation:

Answer:

It's too short. Write at least 20 characters to explain it well.

Answer:

C. 4x^2 + 9x + 12

Step-by-step explanation:

4x^2 + 9x + 12 is a polynomial.

Answer:

the answer is c

Step-by-step explanation: