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4 years ago

Question 1

Mathematics

1 answer:

Ahat [919]4 years ago

5 0

Answer: x = 22

Explanation:

1) Corresponding sides and correspoding angles of congruent triangles are equal.

2) When you name two congruent triangles the order of the vertices signal which sides and angles are congruents.

That triangle ABC is congruent to triangle DEF means that these are the corresponding parts, which are congruent to each other:

∠A and ∠D are congruent
∠B and ∠ E are congruent
∠C and ∠F are congruent
Segment AB and segment DE are congruent
Segment BC and segment EF are congruent
Segment AC and segment DF are congruent

In the figures, it is given that the segment DF measures (1/2)x - 1 and the corresponding segment AC measures 10 units.

Hence, you set this equation: (1/2)x - 1 = 10

Solving for x:

(1/2)x = 10 + 1
(1/2)x = 11
x = 2(11)
x = 22 ← answer

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In trapezoid ABCD, AC is a diagonal and ∠ABC≅∠ACD. Find AC if the lengths of the bases BC and AD are 12m and 27m respectively.

xz_007 [3.2K]

Answer:

Length of diagonal is 18 m

Step-by-step explanation:

Given in trapezoid ABCD. AC is a diagonal and ∠ABC≅∠ACD. The lengths of the bases BC and AD are 12m and 27m. We have to find the length of AC.

Let the length of diagonal be x m

In ΔABC and ΔACD

∠ABC=∠ACD (∵Given)

∠ACB=∠CAD (∵Alternate angles)

By AA similarity theorem, ΔABC~ΔACD

∴ their corresponding sides are proportional

$\frac{x}{27}=\frac{12}{x}=\frac{AB}{CD}$

Comparing first two, we get

⇒ $\frac{x}{27}=\frac{12}{x}$

⇒ $x^2=27\times 12$

⇒ $x=\sqrt324=18$

hence, the length of diagonal is 18 m

4 0

3 years ago

A 30 ft building casts a shadow that is 75 ft. long. A nearby tree casts a shadow that is 35 ft. long. How tall is the tree?

Whitepunk [10]

Answer:

The tree is 14 ft. tall.

Step-by-step explanation:

Height of the building/ Height of the tree = Shadow of building/ Shadow of tree

30/x = 75/35 Cross multiply

75x = (30)(35)

75x = 1050

x = 1050/75

x = 14

5 0

3 years ago

Inequality Word Problems 100 POINTS!!!

Rina8888 [55]

Answer:

1. 4 nights

2. $154

Step-by-step explanation:

1. The airfare is a fixed cost, and the cost of staying at the hotel for n nights is 98 * n. So, we add this up: 478 + 93n. This cost can be no more than 850 because that's Jenna's budget limit. So, we have:

478 + 93n ≤ 850

Subtract 478 from both sides:

93n ≤ 372

Divide by 93:

n ≤ 4

The maximum number of nights is 4 nights.

2. Abigail currently has $45 and she needs m more dollars in order to achieve her goal of at least $199. Seeing "at least", we know that we need to use the ≥ sign:

45 + m ≥ 199

Subtract 45 from both sides:

m ≥ 154

Abigail still needs at least $154.

Hope this helps!

3 0

3 years ago

Read 2 more answers

Determine whether each table represents a linear quadratic or exponential function

Kryger [21]

Answer:

Table A: exponencial function

Table B: quadratic function

Table C: linear function

Step-by-step explanation:

Table A:

for x from 1 to 2, Y increased by 6

for x from 2 to 3, Y increased by 18

for x from 3 to 4, Y increased by 54

So we can see that the values of Y are being multiplied by 3 for each increment of x, so this table represents an exponencial function.

Table B:

for x from 1 to 2, Y increased by 6

for x from 2 to 3, Y increased by 10

for x from 3 to 4, Y increased by 14

The increment of Y is higher than a linear increment and smaller than an exponencial increment, so this is the quadratic function.

Table C:

for x from 3 to 6, Y increased by -2

for x from 6 to 9, Y increased by -2

for x from 9 to 12, Y increased by -2

The increment of Y is constant for the same increment of X, so this is a linear function.

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3 years ago

The point ( -3, 15 ) undergoes a translation of 9 units right and 10 units down. What are 5he coordinates of the new point.

Ipatiy [6.2K]

A point is set up like (x,y)

Since horizontal movement is movement in the x-axis, the x part of the point would change.

Since horizontal changes appear as the opposite inside the parentheses, 9 units right would be -9

-3-9= -12

A change up or down is a change in the y-axis. So, 10 units down would be 15-10=5

So, the new point is (-12,5)

8 0

4 years ago

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