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3 years ago

Question in pic. Plz open the pic for the question ..corect gets branliest

Mathematics

1 answer:

mel-nik [20]3 years ago

6 0

<h2><u>Answer with explanation</u>:</h2>

Given: In Δ ABC and ΔAEC,

AB=BC and AD=CD

i) In ΔADB and CBD, we have

AD = DC [given]

AB=BC [given]

DB= DB [given]

⇒ ΔADB ≅ΔCDB [By SSS congruence rule]

⇒ ∠ADB ≅∠CDB ...(i) [Corresponding parts of congruent triangles are congruent]

Since AC is a straight line,

∠ADB+∠CDB = 180° [Linear pair]

⇒∠ADB+∠ADB=180° [from (i)]

⇒2 ∠ADB=180°

⇒∠ADB=90° =∠CDB

Also ∠ADB+∠ADE=180° [Linear pair]

⇒∠ADE=180°-∠ADB = 180°-90°

⇒∠ADE=90°, i.e. ∠ADE is a right triangle.

Similarly, ∠CDB+∠CDE=180°

⇒∠CDE=90°

ii) Now, in ΔADE and CDE

AD= CD [given]

ED=ED [Common]

∠ADE= ∠CDE = 90°

⇒ΔADE ≅ CDE [By SAS congruence rule ]

⇒AE=EC [Corresponding parts of congruent triangles are congruent]

Hence proved.

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The second group of trainee astronauts are all sitting around the table, waiting to start their first day of training.

nexus9112 [7]

Answer:

Seat 1: Peter
Seat 2: Lia
Seat 3: Kenny
Seat 4: Jennie
Seat 5: Harvey
Seat 6: Joyce
Seat 7: Rick
Seat 8: Mark

Step-by-step explanation:

From Rule 6: Jennie is at Seat 4 and next to Harvey; and by rule 1 (Harvey has a higher seat number than Jennie)

Seat 4: Jennie
Seat 5: Harvey

From Rule 2: Peter is across from Harvey.

Since Seat 5 is across from Seat 1

Seat 1: Peter

From Rule 7: Peter is next to Lia.

Therefore, Lia can either be in Seat 2 or Seat 8, but by Rule 3 (Neither Joyce nor Lia is in seat 8), therefore, Lia is in Seat 2.

Seat 2: Lia

By Rule 5: Lia is next to Kenny, therefore:

Seat 3: Kenny

From Rule 4: Rick is across from Kenny, and Rick is also next to Joyce.

Seat 7 is across from Seat 3, therefore:

Seat 7: Rick

Since Rick is also next to Joyce (and by Rule 3, Joyce cannot be on Seat 8)

Seat 6: Joyce

Therefore, we have:

Seat 1: Peter

Seat 2: Lia

Seat 3: Kenny

Seat 4: Jennie

Seat 5: Harvey

Seat 6: Joyce

Seat 7: Rick

Since Mark has the remaining seat, Mark is on Seat 8.

4 0

3 years ago

A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the

d1i1m1o1n [39]

Answer:

The farmer should plant 14 additional trees, for maximum yield.

Step-by-step explanation:

Given

$Trees = 24$

$Yield = 104$

$x \to additional\ trees$

So, we have:

$Trees = 24 + x$

$Yield = 104 - 2x$

Required

The additional trees to be planted for maximum yield

The function is:

$f(x) = Trees * Yield$

$f(x) = (24 + x) * (104 - 2x)$

Open bracket

$f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x$

$f(x) = 2796 + 104x - 48x - 2x^2$

$f(x) = 2796 + 56x - 2x^2$

Rewrite as:

$f(x) = - 2x^2 + 56x + 2796$

Differentiate

$f'(x) = -4x + 56$

Equate $f'(x) = -4x + 56$ to 0 and solve for x to get the maximum of x

$-4x + 56 = 0$

$-4x =- 56$

Divide by -4

$x =14$

The farmer should plant 14 additional trees, for maximum yield.

5 0

3 years ago

What fraction is greater than 0.7 and less than 0.8

posledela

0.7=7/10
0.8=8/10
0.75=3/4 this is between 0.7 and 0.8

6 0

3 years ago

Help me please !!!!!!!!

murzikaleks [220]

Step-by-step explanation:

$\tan(45) = \frac{x}{13} \\ 1 = \frac{x}{13} \\ x = 13$

$\cos(45) = \frac{13}{y} \\ 2 \sqrt{2} = \frac{13}{y} \\ 2y \sqrt{2} = 13 \\ y = \frac{13}{2 \sqrt{2} }$

7 0

3 years ago

Lily has a bag of 140 marbles the bag has an equal number of green and blue marbles and an equal number of red and yellow marble

Allisa [31]

If there are equal amounts of blue and green marbles, then there are 56 of each; so 112 altogether. That leaves 28 red and yellow marbles; therefore 14 red marbles.

8 0

3 years ago