need help with question 7. its due at 11:59 pm

Answer:

The measure of angle ∠ABD is 125°

Step-by-step explanation:

The given parameters are;

Triangle of ΔACD = Isosceles triangle

Triangle of ΔBCD = Isosceles triangle

m∠BAC = 33°

m∠BDC = 35°

Whereby ΔBCD and ΔACD have their vertex in the same direction, we can have;

[tex]\overline {AD}[/tex] ≅ [tex]\overline {AC}[/tex] Given sides legs of triangle ACD

[tex]\overline {BD}[/tex] ≅ [tex]\overline {BC}[/tex] Given sides legs of triangle BCD

[tex]\overline {BA}[/tex] ≅ [tex]\overline {BA}[/tex] Reflexive property

∴ ΔDAB ≅ ΔCAB  by SSS (Side-Side-Side) congruency rule

m∠BAC ≅ m∠BAD CPCTC (Congruent Parts of Congruent Triangles are Congruent)

∴ m∠BAC ≅ m∠BAD = 33° Definition of congruency

m∠BAC + m∠BAD = 33° + 33° = 66° = m∠DAC Angle addition postulate

m∠ADC = m∠ACD = (180 - m∠DAC)/2 = (180 - 66)/2 = 57° Base angles of an isosceles triangle

∴ m∠ADC = m∠ACD = 57°

m∠BDC = 35° = m∠BCD Base angles of isosceles triangle ΔBCD

m∠BCD + m∠DBC + m∠BCD = 180° Sum of the interior angles of a triangle theorem

m∠DBC = 180° - (m∠BCD +  m∠BCD) = 180° - (35° +  35°) = 110°

m∠DBC = 110°

∴ m∠ABD ≅ m∠ABC CPCTC

m∠ABD = m∠ABC Definition of congruency

m∠DBC + m∠ABD + m∠ABC = 360° Sum of angles at a point

m∠DBC + m∠ABD + m∠ABD = 360°

m∠DBC + 2 × m∠ABD = 360°

110° + 2 × m∠ABD = 360°

2 × m∠ABD = 360° - 110° = 250°

2 × m∠ABD = 250°

m∠ABD = 250°/2 = 125°

m∠ABD = 125°.

The measure of angle ABD is equal to [tex]125^\circ[/tex] and this can be determined by using the properties of the triangle.

Given :

Given that side [tex]\rm AD \cong AC[/tex].

Given that side [tex]\rm BD \cong BC[/tex].

[tex]\rm BA \cong BA[/tex] according to the reflexive property.

So, according to the above statements triangle DAB is congruent to triangle CAB by the SSS postulate.

Now according to CPCTC Angle BAD is congruent to angle BAC.

[tex]\rm \angle BAD + \angle BAC = 33 + 33 = 66^\circ[/tex]

[tex]\rm \angle DAC = 66^\circ[/tex]   (according to the angle addition postulate)

[tex]\rm \angle ADC = \angle ACD = \dfrac{180-\angle DAC }{2} = \dfrac{180-66}{2}=57^\circ[/tex]

[tex]\rm \angle BDC = \angle BCD = 35^\circ[/tex]

Now, according to the sum of the interior angle of the triangle theorem:

[tex]\rm \angle BCD+\angle DBC+\angle BDC = 180^\circ[/tex]

[tex]\rm \angle DBC = 180 - 35-35 = 110^\circ[/tex]

Therefore, the angle ABD and angle ABC are congruent according to the CPCTC.

Now, according to the definition of congruency angle ABD is equal to angle ABC.

Now, again according to the sum of angles at a point:

[tex]\rm \angle DBC + \angle ABD + \angle ABC = 360^\circ[/tex]

[tex]\rm \angle DBC + \angle ABD + \angle ABD = 360^\circ[/tex]

[tex]\rm \angle DBC + 2\times \angle ABD = 360^\circ[/tex]

[tex]\rm 110+2\times \angle ABD = 180^\circ[/tex]

[tex]\rm 2\times \angle ABD = 360-110[/tex]

[tex]\rm 2\times \angle ABD = 250^\circ[/tex]

[tex]\rm \angle ABD = 125^\circ[/tex]

For more information, refer to the link given below:

https://brainly.com/question/24580745

Answer:

x≥9

Step-by-step explanation:

x=people needed for the team

Answer:

X _>_9

Step-by-step explanation:

the domain is what x values the function takes on,

the range is what y values the function takes on

notice the open circle on (-8, -8) that means that it never actually touches (-8, -8)

however, there is a closed circle on (3, 4)

So, the domain is [tex](-8, 3][/tex]

and the range is [tex](-8, 4][/tex]

Answer:

D.

Step-by-step explanation:

The buoy sank a total of 11 2/3

Answer: 7 pies

Unit price: $3.50

Step-by-step explanation:

1. To find the unit price, you must divide the cost by the amount of pies

11 divided by 3 is 3.70

24.50 divided by 7 is 3.50

2. You now have the unit price. To find the better buy, you need to determine which price is lower.

3.50 < 3.70

3. The better buy is the 7 pies.

Answer:

100 dollairs

Step-by-step explanation:

do the math small brain

Answer: About  95% of her phone bills are between $36 and $60.

Step-by-step explanation:

If population is normally distributed , then by Empirical rule about 95% of the population lies within 2 standard deviations from mean.

Given: The amount of Jen's monthly phone bill is normally distributed with a mean of $48 and a standard deviation of $6.

Then, by Empirical rule

About 95% of her phone bills are between $(48 -2(6)) and $(48 +2(6))

i.e. About  95% of her phone bills are between $36 and $60.

Hence, About  95% of her phone bills are between $36 and $60.

Answer:

22

Step-by-step explanation:

42-9=33

33/1.50=22

Answer:

9807.

Step-by-step explanation:

First- you divide 9317 by 95 and you get 98.07 with a bunch of other numbers which you don´t include

Next - when you divide a number by another number and you get a decimal , move the decimal point all the way to the right counting the number of places you move the decimal too.

Last - put a decimal point in the quotient/answer space , exactly above the decimal point in the number under the division bar.

After you do all those steps, your last final answer that you will get is 9807.

Answer:

4 pounds of each item

Step-by-step explanation:

A supplier sells 2 1/4 pounds of mulch for every 1 1/3 pounds of gravel. The supplier sells 172 pounds of mulch and gravel combined. How many pounds of each item does the supplier sell? (Ratios and Rates)

Mulch = 2 1/4 pounds

= 9/4 Pounds

Gravel = 1 1/3 pounds

4/3 pounds

Total items sold = 172

Let x = pounds of each item the supplier sells

Mulch : gravel

9/4 : 4/3

Change into whole number by multiplying by 12

(9/4)12 : (4/3)12

= 108/4 : 48/3

= 27 : 16

Mulch : gravel = 27 : 16

27x + 16x = 172

43x = 172

Divide both sides by 43

x = 172 / 43

= 4

x = 4 pounds

Check

27x + 16x = 172

27(4) + 16(4) = 172

108 + 64 = 172

172 = 172

Therefore, the supplier sells 4 pounds of each item

Answer:

x = -3

Step-by-step explanation:

3 (2x +4) = -6

2x + 4 = -2

2x = -2 -4

2x = -6

x = -3

Answer:

25%

Step-by-step explanation:

y is 75% of what x was

Answer:

134

Step-by-step explanation:

Answer:

6(11+13)

Step-by-step explanation:I tryed it works thank you pls give me Brainliest <3 plsss

Answer:

-440

Step-by-step explanation:

hope this helps

have a good day

Answer:

-440

Step-by-step explanation:

Answer:

-3/4

Step-by-step explanation:

Answer: that is the simplest form.

Step-by-step explanation:

36 = 2*2*3*3

45 = 5*7

63 = 3*3*7

80 = 2*2*2*2*5

Then take each unique factor (2, 3, 5, and 7) and raise each the greatest power it has in any of the input numbers (2^4, 3^2, 5^1, 7^1) and multiply them, and that is your answer.

2*2*2*2*3*3*5*7 = 5040

Answer: supplementary angles

Step-by-step explanation: add them both you get 180

Answer: 16

Step-by-step explanation: If the ratio is 8 boys for every 7 girls and there are 14 girls, that means there are 2x the amount of girls in the ratio. 7 -> 14. This means that there are also 2x as many boys. 8 -> 16.

Answer:

3z-38

Step-by-step explanation:

Put an addition sign between the two equations and combine like terms. Write in order from highest degree to lowest (standard form). X's cancel out.

Answer:

Step-by-step explanation:

150 - total budget (150)

25 out of total budget (150 - 25)

solve 150 - 25 for (125)

125/10 = 12.5

the 150-25 is in parentheses so using PEMDAS, it will be completed first for an answer of (125). then 125 x .10 to divide.

the equation would be  -  (150-25).10  (OR)   (150-25)/10

(you can either choose to divide by a whole or multiply by a fraction.

Answer:

12 people

Step-by-step explanation:

25+10x=150

subtract 25 each side

10x=125

divide both sides by 10

x = 12.5

can't have half a body at a party.

hope this helps :)

Answer:

1 3 and 5

Step-by-step explanation:

Hope this helps

Answer:

1  3

Step-by-step explanation:

Answer:

(c)

Step-by-step explanation:

I completely guessed and got c first try

Answer:

37/6x=37

x=6

11/2x+2/3x=37

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

its 12. pick 12. hey its 12