determine measure of the third angle

The unknown angles when line BD bisect the angle ABC is as follows:\

An angle bisector divides and angle into 2 equal angles.

Therefore, line BD bisect angle ABC.

Hence,

let's find m∠ABD

if m∠ABD = 6x + 4

m∠DBC =  8x - 4

Therefore,

m∠ABD  = m∠DBC

6x + 4 = 8x - 4

6x - 8x = -4 - 4

-2x = -8

x = -8 / -2

x = 4

Therefore,

m∠ABD = 6x + 4 = 6(4) + 4  = 24 + 4 = 28°

let's find m∠ABC

If m∠ABD = 5y - 3

m∠DBC = 3y + 15

Hence,

m∠ABD = m∠DBC

5y - 3 = 3y + 15

5y - 3y = 15 + 3

2y = 18

y = 18 / 2

y = 9

Therefore,

m∠ABC = m∠ABD +  m∠DBC

m∠ABC = 5(9) - 3 + 3(9) + 15

m∠ABC = 45 - 3 + 27 + 15

m∠ABC = 84°

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Answer:

8

Step-by-step explanation

we must find the total of the students to do that we look at when she grouped them in 7, 4 are left out so we multiple 4 miltiplied by 7 and we get 28, there are 4 left out so we add them. now we have a total of 32 students. 32 divided by 4 is 8

Answer:

Terms: 17xy, 4, 3x

Coefficients: 17, 3

Variables: x, y

Constants 4, 3

∣∣−175∣∣=175 Write an absolute value equation that has -17 and 5

Answer:

Step-by-step explanation:

I think you meant

-0.4 - x = -6(x - 3.1) + 6x

-0.4 - x = -6x + 6x + 18.6

-0.4 - x = 18.6

       -x = 18.6 + 0.4

       -x/-1 = 19/-1

           x = -19

check

-0.4 - (-19) = -6(-19 - 3.1) + 6(-19)

           18.6 = -6(-22.1) + (-114)

           18.6 = 132.6 - 114

           18.6 = 18.6

There are 20 markers with no tops and 46 markers with tops in the box.

So, there are 66 markers in the box.

Markers with tops:

Therefore, there are 20 markers with no tops and 46 markers with tops in the box.

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The correct question is given below;
There are 66 markers in the box. 20 markersdon't have tops. How many more markers have tops?

1.) 0.66666666666

2.) 3

3.) 5.2

4.) 0.875

5.) 11.875

6.) 1.10526315789

7.) 0.92

8.) 1.4

9.) 1.27272727273

10.) 12.44

11.) 11.36

Here ya go!

Answer:

1600

Step-by-step explanation:

1600

Answer:

1600

Step-by-step explanation:

Answer: x^29

Step-by-step explanation:

x^11 * x^18=

x^(11+18)=x^29

Answer:

= x²⁹

Step-by-step explanation:

x¹¹ · x¹⁸

= x¹¹ ⁺ ¹⁸

= x²⁹

Answer:

15

Step-by-step explanation:

9 seeds in 3 packets is a 3:1 ratio which means that there are 3 seeds per packet. With 5 packets you simply multiply 5 by 3

Answer:

b=100 c=80

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

The solution of the given system of equations is (4,0)

We can use 3 methods to solve a system of equations:

- graphical method

- elimination method

- substitution method.

The given system of equation is:

-2x + 8y = -8  ....... (1)

5x - 8y = 20  ........(2)

Notice that in the both equations the coefficients of y are -8 and 8, hence if we add those coefficients, they will be cancelled out.

Therefore, we will choose elimination method.

Add equation (1) and equation (2)

-2x + 8y = -8

5x - 8y = 20   +

3x        = 12

 x        = 12/3 = 4

Substitute x = 4 into equation (1):

-2x + 8y = -8

-2.(4) + 8y = -8

-8 + 8y = -8

Add 8 to both sides:

-8 + 8y +8 = -8 + 8

8y = 0

y = 0

Thus, the solution is (4,0)

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The total weight of the two animals is 5.9×10⁴ lbs.

In order to solve the question easily, firstly lets write the weight of each animal in standard form.

Weight of first animal = 5.36×10⁴

Weight of first animal = 53,600

Weight of first animal = 6.2×10⁴

Weight of first animal = 62,000

Now, the total weight of animals will be calculated by summing the two values.

Total weight = 53,600 + 62,000

Performing addition of total weight of animals

Total weight = 1,15,600 lbs

Writing the total weight in scientific notation -

Total weight = 1.15×10⁵ lbs

On rounding off, we get -

Total weight = 1.2×10⁵ lbs

Hence, the total weight of the two animals is 1.2×10⁵ lbs.

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The given series is an arithmetic series. The sum of its first 8 terms is 156.

To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.

If it is an arithmetic series, then:

    a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric series, then:

    a(n) = a(n-1) . r

where d is the common ratio.

The given series is:

       2+7+12+ . . . .

and the number of terms is 8.

In the given series:

a(1) = 2

a(2) = 7

a(3) = 12

Notice that the difference is constant,

 d = a(3) - a(2) = a(2) - a(1)

    = 7 - 2 = 5

Sum formula for the first n term of an arithmetic series is:

S(n) = n/2 . [2a(1) + (n - 1) . d]

Substitute n = 8, a(1) = 2, and d = 5

S(8) = 8/2 ( 2.(2) + (8 -1) .5)

S(8) = 4. 39 = 156

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[tex] \bf \implies \frac{ - 1}{2} [/tex]

[tex] \bf \longrightarrow({ - 2}^{3})( {3}^{0})({4}^{ - 2} )[/tex]

[tex] \bf \longrightarrow( - 8)(1)( \frac{1}{16}) [/tex]

[tex] \bf \longrightarrow( - 8)( \frac{1}{16})[/tex]

[tex] \bf \longrightarrow \frac{ \cancel{- 8}}{ \cancel{16}} \frac{ \cancel{ - 4}}{ \cancel{8}} \frac{ \cancel{ - 2}}{ \cancel{4}} \frac{ - 1}{2} [/tex]

[tex] \bf \longrightarrow \frac{ - 1}{2} [/tex]

Answer: b = 11/3 (or) 3.67

Step-by-step explanation:

Five less than the product of 3 and a number 6 equals .

five less = - 5

product of 3 and a number =  (multiply) 3 x b

equals 6 = = 6

3b - 5 = 6

3b = 6 + 5

3b = 11

b = 11/3

b = 3.67 ( rounded )

The value of the expression 6 - 1/4 - 2(1/1) as a mixed number is 2( 3/4 ).

Fraction: A number that is stated as a quotient in mathematics, when the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. A suitable fraction has a numerator that is less than its denominator.

Consider the expression,

6 - 1/4 - 2(1/1)

Let x = 6 - 1/4 - 2(1/1)

First solving the mixed fraction,

x = 6 - 1/4 - 2(1/1)

x = 6 - 1/4 - ( (2 ×1 + 1) / 1 )

x = 6 - 1/4 - ( 2 +1 / 1)

x = 6 - 1/4 - 3

x = 3 - 1/4

x = ( 12 - 1)/4

x = 11/ 4

x = 2( 3 /4 )

The value of 6 - 1/4 - 2(1/1) as a mixed fraction is 2( 3/4 ).

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Answer:

c. y = -1/2x - 4

Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c (m is the slope and c the y- intercept )

y = 2x + 8 ← is in slope- intercept form

with slope m = 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (8, - 8 ) into the partial equation

- 8 = - 4 + c ⇒ c = - 8 + 4 = - 4

y = - [tex]\frac{1}{2}[/tex] x - 4 ← equation of perpendicular line

The elevation of -10 feet is farther from the surface level of the ocean than an elevation of -8 feet.

Here, we are given two elevation levels from the surface of the ocean.

One elevation is of -10 feet and another one is of -8 feet.

An elevation of -10 feet implies that the distance from the surface level is 10 feet.

On the other hand an elevation of of -8 feet implies that the distance from surface level is 8 feet.

Thus, by comparing the distances, we can see that elevation of -10 feet is farther from the surface level of the ocean than an elevation of -8 feet. To be more precise, it is 2(10-2) feet farther than an elevation of -8 feet.

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Answer:

show a picture

Step-by-step explanation:

Answer:

About 22 mangoes.

Step-by-step explanation:

If we need to find the number of mangoes in a bag, and we have the total mass of the bag, and the average mass of a mango...

Total mass / Average mass = Number of mangoes

56kg / 13/5 kg = n

We can divide the fraction by flipping it and multiplying...

[tex]\frac{56}{1} /\frac{13}{5} = \frac{56}{1} *\frac{5}{13} \\\\56*5 / 13 \\\\280 / 13 = 21.54[/tex]

Because there are probably only whole mangoes in the bag, 21.5 is rounded up to 22 mangoes.

If a precise answer is necessary than stick with 21.54

Answer:

-3x+y=14

Step-by-step explanation:

add the x and -4x which gives you -3x

add the -y and 2y which is y

then -14 and 28 add up to 14

The range of the function is represented by y ∈ [- 0.5, 3].

Functions are relations between an input set named domain and an output set named range such that each element of the domain is related only to one element of the range. Graphically speaking, the range of the function is represented by the vertical axis of the Cartesian plane.

The picture shows that the range of the function is between - 0.5 and 3. Then, the range of the function is represented by y ∈ [- 0.5, 3].

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The 10th term of an arithmetic sequence is found to be a₁₀ = 115.

In Arithmetic Progression, the difference between two mathematical orders is a constant quantity (AP). Arithmetic Sequence is another name for it.

We'd come across a few specific terms in AP that had been labeled as:

As shown below, the AP can also be viewed in analysed in terms of common differences.

Now, as per the given question;

Let the 9th term be 'a₉' = 132.

The 11th term be 'a₁₁' = 98.

The 10th term be 'a₁₀'.

The AP must have contain equal common difference. So,

d = a₁₀ - a₉

d = a₁₀ - 132

And, also

d = a₁₁ - a₁₀

d = 98 - a₁₀

Since, a₁₀ - a₉ = a₁₁ - a₁₀ for forming an AP.

Equate the common difference.

a₁₀ - 132 = 98 - a₁₀

Bring the variable part on single side.

2a₁₀ = 98 + 132

2a₁₀ = 230

a₁₀ = 115.

Therefore, the value of the 10 th term is estimated as a₁₀ = 115.

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