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3 years ago

Write the equation of the line that passes through (2, 4) and has a slope of –1 in point-slope form.

1 answer:

3 0

Y - y1 = m(x - x1).....this is point slope form
slope(m) = -1
(2,4)...x1 = 2 and y1 = 4
now we sub
y - 4 = -1(x - 2) <===

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Bridget, June and Colin share £88 in a ratio 3:3:2. How much money does each person get?

astra-53 [7]

Answer

33,33 and 22

Step-by-step explanation:

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2 years ago

an athlete completes a race in 55.72 seconds how many times greater is the digit in the tens place than the digit in the ones pl

Inessa05 [86]

7 is 5 greater than the 2

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3 years ago

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Vaughn is laying sod in his backyard. A diagram of his backyard is bel ow

Orlov [11]

Answer: $A=944\ ft^2$

Step-by-step explanation:

You need to use the following formula that is used to find the area of a trapezoid:

$A=(\frac{M+m}{2})h$

Where "M"and "m" are the bases of the trapezoid and "h" is the height of the trapezoid.

Based on the information given in the exercise, you can identify that:

$M=c=36\ ft\\\\m=a=23\ ft\\\\h=b=32\ ft$

Knowing these values, you can substitute them into the formula:

$A=(\frac{36\ ft+23\ ft}{2})(32\ ft)$

Finally, you must evaluate in order to find its area. This is:

$A=(\frac{59\ ft}{2})(32\ ft)\\\\A=\frac{1888\ ft^2}{2}\\\\A=944\ ft^2$

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2 years ago

Prove that H c G is a normal subgroup if and only if every left coset is a right coset, i.e., aH = Ha for all a e G

Kaylis [27]

$\Rightarrow$

Suppose first that $H\subset G$ is a normal subgroup. Then by definition we must have for all $a\in H$ , $xax^{-1} \in H$ for every $x\in G$ . Let $a\in G$ and choose $(ab)\in aH$ ( $b\in H$ ). By hypothesis we have $aba^{-1} =abbb^{-1}a^{-1}=(ab)b(ab)^{-1} \in H$ , i.e. $aba^{-1}=c$ for some $c\in H$ , thus $ab=ca \in Ha$ . So we have $aH\subset Ha$ . You can prove $Ha\subset aH$ in the same way.

$\Leftarrow$

Suppose $aH=Ha$ for all $a\in G$ . Let $h\in H$ , we have to prove $aha^{-1} \in H$ for every $a\in G$ . So, let $a\in G$ . We have that $ha^{-1} =a^{-1}h'$ for some $h'\in H$ (by the hypothesis). hence we have $aha^{-1}=h' \in H$ . Because $a$ was chosen arbitrarily we have the desired .

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2 years ago

John made a small rectangular table for his workroom. If the sides of the table are 32 inches and 26 inches, what should the tab

matrenka [14]

Answer:

The table should measure diagonally about 41.23 inches.

Step-by-step explanation:

To find the diagonal of a rectangle we use the formula :

$a^{2}$ + $b^{2}$ = $c^{2}$

A and B both represent the side lengths of the rectangle, while C is the diagonal part. Knowing this formula, let's plug in the values for A and B and see what happens.

$32^{2}$ + $26^{2}$ = $c^{2}$

1024 + 676 = $c^{2}$

1700 = $c^{2}$

The square root of 1700 is (rounded to the hundreth's place) = 41.23

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2 years ago