MATHEMATICS MIDDLE SCHOOL

In Triangle DEF, if angle D is congruent to angle E, DE= x + 4, EF= 4x - 8, and DF= 7X - 35 find X and the measure of each side

Answers

Answer 1

Answer:

If angle D is congruent to angle E, then the triangle DFE is an isosceles triangle (look at the picture).

Therefore DF ≅ EF.

DE = x + 4, EF = 4x - 8, DF = 7x - 35

The equation:

7x - 35 = 4x - 8 add 35 to both sides

7x = 4x + 27 subtract 4x from both sides

3x = 27 divide both sides by 3

x = 9

DE = x + 4 → DE = 9 + 4 = 13

EF = 4x - 8 → EF = 4(9) - 8 = 36 - 8 = 28

DF = 7x - 35 → DF = 7(9) - 35 = 63 - 35 = 28

Answer:

x = 9, DE = 13, EF = 28, DF = 28.

Answer 2

Answer:

In Triangle DEF, if angle D is congruent to angle E, then this is an isosceles triangle, meaning DE = DF. By setting these values equal and solving the algebraic equation, we find x = 6.5. Therefore, the lengths of sides DE, DF, and EF are 10.5, 10.5, and 18 respectively.

In triangle DEF where angle D is congruent to angle E, it implies that triangle DEF is an isosceles triangle because two angles in the triangle are congruent. In an isosceles triangle, the two congruent sides are equal. Therefore, DE = DF.

The lengths of these sides are represented as 'x + 4' and '7x - 35' respectively. So we can set up the following equation:

x + 4 = 7x - 35

Solve this equation to find the value of x.

By subtracting 'x' on both sides and adding '35' on both sides, you get:

6x = 39

Dividing both sides by '6' to isolate 'x', we get:

x = 6.5

So, the lengths of the sides DE and DF are:

DE = x + 4 = 6.5 + 4 = 10.5

DF = 7x - 35 = 7 * 6.5 - 35 = 10.5

EF = 4x - 8 = 4 * 6.5 - 8 = 18

Therefore, the lengths of the sides DE, DF, and EF are 10.5, 10.5, and 18 respectively.

Learn more about Isosceles Triangle here:

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Using these coordinates, (3, 1/4) and (-2, -1) write an equation in Point-Slope, Slope-Intercept, and Standard Form.

Answers

Answer here $\text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 } = (-1 - (1)/(4))/(-2 - 3) = ( - (5)/(4))/(-5)= ( - (5)/(4)\cdot4)/(-5\cdot4) =(-5)/( -20) =\boxed{ \bf{ (1)/(4)}}$

The slope is 1/4.

The equation in point-slope form is:
y - (-1) = 1/4(x - (-2))
$\boxed{\bf{y + 1 = (1)/(4)(x+2)}}$

In slope-intercept form, it is:
y + 1 = 1/4(x+2)
$\boxed{\bf{y = (1)/(4)x - (1)/(2)}}$

In Standard form it is:
y = 1/4x - 1/2
1/2 = 1/4x - y
Multiply both sides by 4
2 = x - 4y
$\boxed{\bf{x-4y=2}}$

I hope that helps. :)

Heeeeeeeeeelp......

Answers

Answer:

x+7

Step-by-step explanation:

So it's been a while since I took Geometry, so I don't know what principle makes these angles equal to each other, but I know that they are in fact equal. So that means that 6x +3 = 45. Subtract 3 from each side gets you 42+6x, then divide each side by 6, which gets you your answer of x=7.

| 15. Aliyah runs approximately 5.4 miles per hour.She is training for a half-marathon and plans
to run 9 miles on Tuesday and 12 miles on
Thursday. How many minutes longer will her
run be on Thursday compared to Tuesday?

Answers

Answer: 33.33 minutes longer.

Step-by-step explanation :

We need to remember the following formula:

$t=(d)/(V)$

Where "t" is the time, "d" is the distance and "V" is the speed.

We know that she runs approximately 5.4 miles per hour, then:

$V=5.4\ (mi)/(h)$

Since she plans to run 9 miles on Tuesday, her run's time on Tuesday will be:

$t_1=(9\ mi)/(5.4\ (mi)/(h))\n\nt_1=(5)/(3)\ h$

Making the conversion from hours to minutes, we get:

$((5)/(3)\ h)((60\ min)/(1\ h))=100\ min$

Since she plans to run 12 miles on Thursday, her run's time on that day will be:

$t_2=(12\ mi)/(5.4\ (mi)/(h))\n\nt_2=(20)/(9)\ h$

Making the conversion from hours to minutes, we get:

$((20)/(9)\ h)((60\ min)/(1\ h))=133.33\ min$

Finally in order to find how many longer will her run be on Thursday compared to Tuesday, we need to make the following subtraction:

$t_2-t_1=133.33\ min-100\ min=33.33\ min$

Solve the missing measure of a square, when P=76in
Formula: P=4s

Answers

$P=4s\n P=72\ in\n 72=4s\n s=18\$

Answer: s = 19 (each side of the square is 19)

Step-by-step explanation:

p = 4s

plug in value for p

76 = 4s

divide by 4

19 = s

each side is 19

Vicki puts 10 books on a shelf. The 10 books take up 28 cm. What is the mean (average) thickness of her books? Can I have it worked out as well plz? I really need to understand it.

Answers

Average thickness of book = Total thickness/mo. of books
= 28 cm/ 10
= 2.8 cm
Thus, on average, each book has 2.8 cm thickness.

If the ten books are 28cm thick then the average thickness is 28 (the total thickness) divided by 10 (the number of books).

28cm divided by 10 is 2.8cm.

So the average thickness is 2.8cm!

Is 900 cm greater than 9,000 mm