Complete the following proof. Given: (BD) is the perpendicular bisector of (AC) Prove: ∢A≅∢C
Statement Reason
1. (BD) is the perpendicular bisector of (AC) 1. Given
2. Point B is the midpoint of (AC) 2. Definition of perpendicular bisector
3. 3. Definition of midpoint
4. ∢ABD and ∢CBD are right angles 4. Definition of perpendicular bisector
5. ∢ABD and ∢CBD are congruent 5. All right angles are congruent.
6. 6. Reflexive property of congruence
7. 7.
8. ∡A≅∡C 8.

Answer:

Let x and y be the numbers, with x the larger one.

x - y = 5

2y = x + 18

Then solve this system of equations:

x - y = 5

x - 2y = -18

Subtract bottom equation from top equation and get

y = 23

So x = y + 5 = 23 + 5 = 28

Answer:

There is no Question or no images...

Step-by-step explanation:

Answer:

$16.48

Step-by-step explanation:

Split this up into the four years.

For the first year, multiply 200 x .02 to get 4

Add 4 onto your total. ($204.00)

For the second year multiply 204 x .02 to get 4.08

Add 4.08 onto your total. ($208.08)

For the third year multiply 208.08 x .02 to get 4.1616 but round to 4.16

Add 4.16 onto your total ($212.24)

For the fourth year multiply 212.24 x .02 to get 4.2448 but round to 4.24

Add 4.24 onto your total (216.48)

Now subtract 200 from your total

216.48-200 = 16.48

She will be payed $16.48 in interest.

Answer:

x = 40°

y = 30°

Step-by-step explanation:

Given parallelogram ABCD :

∠A = ∠C

3x = 120

x = 120 ÷ 3

∠B + ∠C = 180°

2y + 120 = 180

2y = 180 - 120

2y = 60

y = 60 ÷ 2

Answer:

x = 40°

y = 30°

Step-by-step explanation:

Given the diagram of a parallelogram, where:

∠A = 3x°, ∠B = 2y°, and ∠C = 120°

The given problem also requires us to find the values of x and y.

In reference to the Parallelogram Opposite Angles Theorem, where it states that: if a quadrilateral is a parallelogram, then it will have congruent opposite angles.  In other words, ∠A ≅ ∠C , and ∠B ≅ ∠D.

Hence, we can establish the following equality statement to solve for the value of x:

m∠A = m∠C

3x° =  120°

Divide both sides by 3 to solve for x:

[tex]\displaystyle\mathsf{\frac{3x^{\circ}}{3}=\:\frac{120^{\circ}}{3}}[/tex]

x = 40°

Therefore, the value of x = 40°.

In order to solve for y, we must refer to the Parallelogram Consecutive Angles Theorem, where it states that if a quadrilateral is a parallelogram, then its consecutive angles are supplementary whose sum add up to 180°.

In the given diagram, ∠A and ∠D, ∠B and ∠C are consecutive angles.  

We can establish the following equation to solve for the value of y:

m∠B + m∠C = 180°

2y° + 120° = 180°

Subtract 120° from both sides:

2y° + 120° - 120° = 180° - 120°

2y° = 60°

Divide both sides by 2 to solve for y:

[tex]\displaystyle\mathsf{\frac{2y^{\circ}}{2}=\:\frac{60^{\circ}}{2}}[/tex]

y = 30°

Therefore, the value of y = 30°.

Answer:

Answer Below

Step-by-step explanation:

7: Not congruent; Only one angle and only side is shown for each triangle

8: ASA; Two angles shown with a side put in-between

9: SSS; Should be self-explanatory (only sides are shown)

10: ASA; Angles with side shoved between

11: Not Congruent; Triangles are separated and only one side are shown

12: Not Congruent; Angles said to be congruent are on different angles

Answer:35 m

Step-by-step explanation:

North: 5+6+4. East: 4+16. 15+20

Answer: $149.8

Step-by-step explanation:

Find the 1% of the 140 which is 1.4 because 140/100 = 1.4

Times by 7 to get 7%. 1.4 x 7 = 9.8

Add them together. 140+9.8 = 149.8

Answer:

B The values for y are square roots of negative numbers.

Answer:

b

Step-by-step explanation:

Answer:

0.43%

5.4

Step-by-step explanation:

To convert 0.0043 to a percentage, multiply the number 0.0043 by 100

0.43%

In decimal form, 540 percent equals

5.4

Answer:

Step-by-step explanation:

6x + 5 = 4x + 45

6x - 4x = 45 - 5

2x = 40

x = 20

6x + 5 = 6.20 + 5 = 125°

Answer:

for line b - the slope is 0, not undefined. an undefined slope is a vertical line.

for line d - the slope is -1/3. slope is written rise over run, so just count the units that it goes down and how many it goes right. it goes down 1 and right 3, so it is -1/3.

Answer:

D : 0

Step-by-step explanation:

f(0) = 0

Answer:

Max area = 100

10 10 sides

Step-by-step explanation:

here given perimeter for fencing is 40 feet

for it to have maximum area sides

sides length is perimeter / 4

so l = 40/4 = 10

so it is 10 × 10 square

Area = 100

This is the maximum area

Step-by-step explanation:

x = -2 and x = -5

x + 2 = 0 and x + 5 = 0

(x + 2)(x + 5) = 0

x² + 5x + 2x + 10 = 0

x² + 7x + 10 = 0

Option → B

Answer:

x=121

Step-by-step explanation:

Answer:

x = 121°

Step-by-step explanation:

180 - 115 = 65°

The angle beside 115° is 65°.

A full circle is 360° so

360 - 304 = 56°

Add the two angles

65 + 56 = 121°

Subtract it to 180° to find the other angle

180 - 121 = 59°

Now subtract again to 180° to find the angle in the other side

180 - 59 = 121°

Answer:

a number

Step-by-step explanation:

not a letter

Answer:

A rectangle doesn't have equal sides

Both sides are not equal

Answer:   1 is none 2=A   3=B   4=C

Step-by-step explanation:

see it in shapes

Answer:

1. none

2. a

3. b

4. c

Step-by-step explanation:

1: This represents the net of a triangular prism, for it has a square in the middle, two triangles, and two other squares/rectangles. However, there is no triangular prism among the three solids, so the answer for this is none.

2: This represents the net of a cone, for it has a circle as the base and a sector that gives the cone it's curved surface. There is one cone among the three solids, and the answer for this one is A.

3: This represents the net of a tetrahedron, for it consists of 4 equilateral triangles and having one of the triangles as its base. Therefore, the answer for this one is B.

4: This represents the net of a square pyramid, composed of a square as the base and 4 triangles surrounding it. There's one square pyramid among the answer choices, so the answer for #4 is C.

Answer:

160

Step-by-step explanation:

Answer:

a = b² + 3c

Step-by-step explanation:

The square of the number b is b² and 3 times c is 3c , then

a = b² + 3c

Answer:

8 2/3

Step-by-step explanation:

2 2/3×3 1/4

Change to improper fractions.

2 2/3=8/3

3 1/4=13/4

8/3x13/4=26/3

=8 2/3

Hope this helps :)

Step-by-step explanation:

smallest value 30° largest value 150°.

Answer:

30, 150

Step-by-step explanation:

sin θ = 1 / 2

sin 30 = 1 / 2

θ = 30

So,

the smallest value of θ is 30.

sin ( 180 - 30 ) = sin 150 = 1 / 2

So,

the larger value of θ = 150.

Answer:

8(3x + 1)

Step-by-step explanation:

8 and 24 are multiples of 8

(8/8) + (24x/8) = 1 + 3x

The equation with distributive property is 8(1 + 3x)

-Chetan K

Answer:

Step-by-step explanation:

[tex]\frac{6}{4.5}=\frac{4}{x}[/tex]

6x = 4 × 4.5

6x = 18

x = 3

Answer:

how am I supposed to graph?

Step-by-step explanation:

Answer:

Step-by-step explanation:

18.

LHS

[tex]\frac{cos^{2}a-sin^{2}b }{sin^{2}a.sin^{2}b}[/tex]

= [tex]\frac{cos^{2}a }{sin^{2}a.sin^{2}b} -\frac{sin^{2}b }{sin^{2}a.sin^{2}b}[/tex]

= [tex]\frac{cos^{2}a}{sin^{2}a}[/tex] × [tex]\frac{1}{sin^{2}b}[/tex] - [tex]\frac{sin^{2}b}{sin^{2}b}[/tex] × [tex]\frac{1}{sin^{2}a}[/tex]

= [tex]cot^{2}a[/tex] × [tex](1+cot^{2}b)[/tex] - 1 × [tex](1 + cot^{2}a)[/tex]

= [tex]cot^{2}a[/tex] + [tex]cot^{2}a.cot^{2}b[/tex] - 1 - [tex]cot^{2}a[/tex]

= [tex]cot^{2}a.cot^{2}b[/tex] - 1

Then you can conclude that LHS = RHS

19. It's weird. I tried a few ways like simplifying, dividing both numerator and denominator on LHS by tan or sin or cos but it didn't work out.

Answer:

1) 9/10 + 4/5 + 5/6 = 2 8/15

2) 14/15 + 2/9 + 1/5 = 1 16/45

==============================================

Solution:

[tex] \bold{1)} \: \tt \frac{9}{10} + \frac{4}{5} + \frac{5}{6} \\ \\⟹ \tt \frac{9}{10} + \frac{4}{5} \\ = \tt \frac{9 \times 1}{10 \times 1} + \frac{4 \times 2}{5 \times 2} = \frac{9 + 8}{10} = \frac{17}{10} \\ \\ ⟹\tt \frac{17}{10} + \frac{5}{6} \\ = \tt \frac{17 \times 3}{10 \times 3} + \frac{5 \times 5}{6 \times 5} = \frac{51 + 25}{30} = \frac{76}{30} \: or \: 2 \frac{16}{30} = 2 \frac{8}{15} \\ \\ \\ \\ \bold{2)} \tt \: \: \frac{14}{15} + \frac{2}{9} + \frac{1}{5} \\ \\⟹ \tt \frac{14 \times 3}{15 \times 3} + \frac{2 \times 5}{9 \times 5} = \frac{42 + 10}{45} = \frac{52}{45} \\ \\⟹ \tt \frac{52}{45} + \frac{1}{5} \\ = \frac{52 \times 1}{45 \times 1} + \frac{1 \times 9}{5 \times 9} = \frac{52 + 9}{45} = \frac{61}{45} = 1 \frac{16}{45} [/tex]