Can someone help me out?

What set of reflections would carry rectangle ABCD onto itself?

Dvinal [7]

Answer:

y=x, x-axis, y=x, y-axis

Explanation:

Reflecting the figure across three axes just moves it from one quadrant to another. It does not map the figure to itself.

Reflecting across the line y=x moves it from quadrant II to IV or vice-versa. If it is in quadrant I or III, it stays there. So the sequence of reflections x-axis (moves from I to IV), y=x (moves from IV to II), x-axis (moves from II to III), y=x (stays in III) will not map the figure to itself.

However, the last selection will map the figure to itself. The initial (and final) figure location, and the intermediate reflections are shown in the attached. The figure starts and ends as blue, is reflected across y=x to green, across x-axis to orange, across y=x to red, and finally across y-axis to blue again.

7 0

3 years ago

After running a regression, you plotted the residual against the predicted value. You observed that the residuals seem to increa

DENIUS [597]

Answer:

A. the error term has a constant variance

Step-by-step explanation:

Firstly, note that it is observed the residuals increase as the predicted value increases. Now the natural logarithm transformation will change will change a skewed variable into a normal distributed value, which leads to a linear regression between the both variables, since they (the independent and dependent variables) are normal. A key assumption of linear regression is Homoscedasticity, therefore the error term obtains the same finite variance.

So as soon as the transformation is applied, the error term will therefore have a constant variance.

4 0

3 years ago

11/6358 long agurithum

miss Akunina [59]

Answer:

Least common multiple:

lcm (578; 11) = 6,358 = 2 × 11 × 172;

Numbers have no common prime factors: 6,358 = 578 × 11.

Step-by-step explanation:

Approach 1. Integer numbers prime factorization:

578 = 2 × 172;

11 is a prime number, it cannot be broken down to other prime factors;

Multiply all the prime factors, by the largest exponents.

Least common multiple:

lcm (578; 11) = 2 × 11 × 172;

lcm (578; 11) = 2 × 11 × 172 = 6,358

Numbers have no common prime factors: 6,358 = 578 × 11.

Integer numbers prime factorization

Approach 2. Euclid's algorithm:

Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

Step 1. Divide the larger number by the smaller one:

578 ÷ 11 = 52 + 6; Step 2. Divide the smaller number by the above operation's remainder:

11 ÷ 6 = 1 + 5; Step 3. Divide the remainder from the step 1 by the remainder from the step 2:

6 ÷ 5 = 1 + 1; Step 4. Divide the remainder from the step 2 by the remainder from the step 3:

5 ÷ 1 = 5 + 0; At this step, the remainder is zero, so we stop:

1 is the number we were looking for, the last remainder that is not zero.

This is the greatest common factor (divisor).

Least common multiple, formula:

lcm (a; b) = (a × b) / gcf, hcf, gcd (a; b);

lcm (578; 11) =

(578 × 11) / gcf, hcf, gcd (578; 11) =

6,358 / 1 =

6,358;

lcm (578; 11) = 6,358 = 2 × 11 × 172;

8 0

2 years ago

A perfectly straight 24 ft tall tree grows on the edge of the bank of a 45 foot wide river. A bird sitting at the top of the tre

True [87]

Answer:

Distance covered by the bird before meeting the water is: 51.264 ft

Step-by-step explanation:

Notice that if the bird catches the fish in 2 seconds, then the fish was able to dive down a total of 6 feet before being caught:

$distance=Vel\,* time=3\,\frac{ft}{s} *\,2\,\,s=6 \,\,ft$

So the bird needs to fly in the direction of the hypotenuse of a right angle triangle (see attached image) that has one leg of length (24 ft + 6 ft) = 30 ft, and another one 22.5 ft (half the width of the river.

Such hypotenuse is (using Pythagoras theorem):

$hyp =\sqrt{(60\,ft)^2+(22.5\.ft)^2} =\sqrt{4106.25} \,ft=64.08\,ft$

Now, in order to find the distance D the bird covers from the top of the tree to the water (marked in red in our image), we use similar triangles. The bigger triangle is that of legs 60 ft and 22.5 ft and hypotenuse 64.08 ft.

The smallest triangle we use in the proportion is the one shaded yellow in the image, which has one leg equal to 24 ft, and unknown hypotenuse:

So we make the proportion between known legs, and hypotenuses:

$\frac{24\,ft}{30\,ft} =\frac{D}{64.08\,ft} \\D=\frac{64.08\,ft\,*\,24\,ft}{30\,ft} \\D=51.264\,ft$

7 0

3 years ago

What is an equation of the line that is perpendicular to y=−4/5x+3 and passes through the point (4, 12) ?

PilotLPTM [1.2K]

The slope of the given line is -4/5. The line perpendicular to that line will have a slope that is the opposite reciprocal. In other words, the perpendicular slope will be 5/4. If it passes through (4, 12), we have an x and a y value to use in y=mx+b. y is 12, x is 4, and we have a slope of 5/4. Filling in accordingly: $12= \frac{5}{4}(4)+b$ and 12 = 5 + b. So b = 7. Rewriting with our new slope and b value, $y= \frac{5}{4}x+7$ . And there you go!

3 0

3 years ago