given that the line a is parallel to line b and that line c is parallel to line d, if m∠13 = (12x-22)° and m∠14 = (9x-29)°, find m∠2

Answer:

Step-by-step explanation:

[tex]\large \boldsymbol{ \boxed{\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b} }} \\\\\\ \sqrt{25x+75} +3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9x-18} \\\\ \sqrt{25} \cdot \sqrt{x+3}+3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9}\cdot \sqrt{x-2} \\\\5\sqrt{x+3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \ \ =2 +4\sqrt{x-3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \\\\(5\sqrt{x+3})^2 =(2+4\sqrt{x-3} )^2 \\\\ \ \ \ let \ \ t=x+3 \ \ ; \ \ \ t-6=x-3 \\\\ \big(5\sqrt{t} \ \big)^2=(2+\sqrt{t-6} )^2 \\\\[/tex]                                 [tex]\large \boldsymbol{} 25t=4+16\sqrt{t-6} +16(t-6) \\\\(9t+92)^2=(16\sqrt{t-6} )^2 \\\\81t^2+1656t+8464=256(t-6)\\\\81t^2+1400t+10000=0 \\\\ D=1400^2-324000=-128000=> \\\\D<0 \ \ no \ \ solutions[/tex]

Answer:

30

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

The equation modelling the statement is

[tex]\frac{x}{3}[/tex] - 1 = 2 ( [tex]\frac{x}{4}[/tex] - 3 ) ← distribute parenthesis by 2

[tex]\frac{x}{3}[/tex] - 1 = [tex]\frac{x}{2}[/tex] - 6 ( multiply through by 6 to clear the fractions )

2x - 6 = 3x - 36 ( subtract 2x from both sides )

- 6 = x - 36 ( add 36 to both sides )

30 = x

Complete question is;

In the triangles attached , DF is congruent to MN,DG is congruent to MP, angle D is congruent to angle P. Can you prove that triangle DFG is congruent to MNP.

Answer:

Proved below

Step-by-step explanation:

From the attached triangles, we can see that;

∠D corresponds to ∠M

∠F corresponds to ∠N

∠G corresponds to ∠P

But we are told that ∠D is congruent to ∠P. Thus, since we have 2 other congruent sides in the triangles, we can conclude that Side-Angle-Side Postulate (SAS) congruency theorem that triangle DFG is congruent to MNP.

Answer: Choice D

b greater-than 3 and StartFraction 2 over 15 EndFraction

In other words,

b > 3 & 2/15

or

[tex]b > 3\frac{2}{15}\\\\[/tex]

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

Explanation:

Let's convert the mixed number 2 & 3/5 into an improper fraction.

We'll use the rule

a & b/c = (a*c + b)/c

In this case, a = 2, b = 3, c = 5

So,

a & b/c = (a*c + b)/c

2 & 3/5 = (2*5 + 3)/5

2 & 3/5 = (10 + 3)/5

2 & 3/5 = 13/5

The inequality [tex]2 \frac{3}{5} < b - \frac{8}{15}\\\\[/tex] is the same as [tex]\frac{13}{5} < b - \frac{8}{15}\\\\[/tex]

---------------------

Let's multiply both sides by 15 to clear out the fractions

[tex]\frac{13}{5} < b - \frac{8}{15}\\\\15*\frac{13}{5} < 15*\left(b - \frac{8}{15}\right)\\\\39 < 15b-8\\\\[/tex]

---------------------

Now isolate the variable b

[tex]39 < 15b-8\\\\15b-8 > 39\\\\15b > 39+8\\\\15b > 47\\\\b > \frac{47}{15}\\\\b > \frac{45+2}{15}\\\\b > \frac{45}{15}+\frac{2}{15}\\\\b > 3+\frac{2}{15}\\\\b > 3\frac{2}{15}\\\\[/tex]

Side note: Another way to go from 47/15 to 3 & 2/15 is to notice how

47/15 = 3 remainder 2

The 3 is the whole part while 2 helps form the fractional part. The denominator stays at 15 the whole time.

Answer:

A. B. D.

Step-by-step explanation:

There are 6 possible values to roll. Since 3 values are even and 3 values are odd, the game should be 0.

Answer:

A, B, D

Step-by-step explanation:

EDG 2021

Brainliest?

Answer:

(8,11)

Step-by-step explanation:

1st line

y = x+ 3

We need to find the equation of the other line

We have two points (3, 1) and (4, 3)

Slope

m = (y2-y1)/(x2-x1)

   = ( 3-1)/(4-3)

   = 2/1 = 2

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y =2x+b

Using the point (4,3)

3 = 2(4)+b

3 = 8+b

3-8=b

-5 =b

y = 2x-5

We have 2 lines

y =x+3 and y = 2x-5

Setting them equal to each other

x+3 = 2x-5

Subtract x from each side

x+3-x = 2x-5-x

3 = x-5

Add 5 to each side

3+5 =x-5+5

8=x

Now we can find y

y =x+3

y = 8+3

y=11

Answer:

c (8,11)

Step-by-step explanation:

Answer:

không

Step-by-step explanation:

Answer:

I have no idea you can use the app paper.

Step-by-step explanation:

Hope it helps.

Answer:

85 i guess

Step-by-step explanation:

The mean of the distribution is 70 and the standard deviation of the distribution is 4.

The shaded area in the distribution below represents approximately 95% of the data. This means that the shaded area is equal to 1.96 standard deviations from the mean.

The 68-95-99.7 rule states that 95% of the data in a normal distribution falls within 2 standard deviations of the mean. So, the shaded area in the distribution below represents the area between 1.96 standard deviations below the mean and 1.96 standard deviations above the mean.

The mean of the distribution is the center of the shaded area. The standard deviation of the distribution is the distance from the mean to the edge of the shaded area.

In this case, the mean of the distribution is approximately 70. The standard deviation of the distribution is approximately 4.

Here is a step-by-step explanation of how to find the mean and the standard deviation:

Identify the shaded area in the distribution.

Remember that the shaded area represents 95% of the data.

Use the 68-95-99.7 rule to determine that the shaded area is between 1.96 standard deviations below the mean and 1.96 standard deviations above the mean.

Find the mean by averaging the two points on the distribution that are 1.96 standard deviations from the mean.

Find the standard deviation by subtracting the mean from one of the points on the distribution that is 1.96 standard deviations from the mean.

Therefore, the mean of the distribution is approximately 70 and the standard deviation of the distribution is approximately 4.

To learn more about standard deviation here:

https://brainly.com/question/13498201

#SPJ2

Answer:

y = 4x - 8

Step-by-step explanation:

y = 4x + b

4 = 4(3) + b

4 = 12 + b

-8 = b

Answer: 3f

Step-by-step explanation:

Answer:

CIRCUMFERENCE OF CIRCLE IS 2πr.

=2*3.14*6mi=results be the Answar

Answer:

[tex]log16x = \frac{1}{4} \\ x = \frac{ {10}^{ \frac{1}{4} } }{16} \\ x = 0.111[/tex]

Answer: [tex]100.544\ in.^3[/tex]

Step-by-step explanation:

Given

Diameter of the cone [tex]d=8\ in.[/tex]

Height of the cone [tex]h=6\ in.[/tex]

Volume of the Cone is given by

[tex]\Rightarrow V=\dfrac{1}{12}\pi d^2h[/tex]

[tex]\Rightarrow V=\dfrac{1}{12}\times \pi\times 8^2\times 6\\\\\Rightarrow V=16\pi \\\Rightarrow V=100.544\ in.^3[/tex]

The volume of the cone is [tex]100.544\ in.^3[/tex]

Answer:

60

Step-by-step explanation:

Since the angles are shown equal in the diagram, ABD=DBC=60

Answer:

lower limit = 5

upper limit = 10

class mark = lower limit + upper limit ÷ 2 = 7.5

class size = upper limit - lower limit

= 10-5 = 5

Step-by-step explanation:

I hope this help you have an great day and safe health

Answer:

4.5

Step-by-step explanation:

let,

k×9²=300

k = 300/81

or, k = 100/27

as two triangles are similar,

if smaller triangle's corresponding side is x (let), then,

kx²=75

100x²/27=75

x²=75×27/100

x=√81/4

x=9/2

x=4.5

Answer:

circumference = 25.12 yards

area = 50.24 yards squared or yd^2

Step-by-step explanation:

circumference = pi * d

3.14 * 8 =

25.12

area = pi* r^2

r = 1/2 of d = 4

area = pi * 16

3.14 * 16 =

50.24

Answer:

Area: 50.24yds^2            Circumference: 25.12yds

Step-by-step explanation:

Area: The formula for area of a circle is a = πr^2.

The radius (r) of the circle is 4yds because it is half the length of the diameter. The equation would like like this:

A = (3.14)(4)^2

A = (3.14)(16)

A = 50.24yds

Circumference: The formula for circumference is 2πr. We already know all of the variables so we can plug them in.

C = 2(3.14)(4)

C = 25.12yds

Hope this helps

Answer:

45

Step-by-step explanation:

Answer:

answer 1

Step-by-step explanation:

x^2+4x+7

=(x^2+4X+4)+3

=(x+2)^2+3

Answer:

7x^2 +7x

------------------

x^2 -9

Step-by-step explanation:

7x          (x+1)

------- * ----------

(x+3)    (x-3)

Multiply

7x^2 +7x

------------------

x^2 +3x-3x-9

7x^2 +7x

------------------

x^2 -9

Answer:

7x^2 +7x   /   x^2 -9

Step-by-step explanation:

Answer:

The last option

Step-by-step explanation:

In order for the graph to be a function it has to pass the vertical line test. If you draw a vertical line through the graph and it only intersects at one point then it is a function.

Answer:

it should be 2 as your answer

Answer:

A is the answer I pretty sure

Answer:

i think the answer is 502 m2

Answer:

The boat is going 21 MPH

Step-by-step explanation:

If the boat is going 84 miles in 4 hours, and you want to find the unit rate, divide 84 by 4.

84/4 = 21

Hope this helps!

9514 1404 393

Answer:

Step-by-step explanation:

The side ratios in a 30°-60°-90° triangle are 1 : √3 : 2. Since the hypotenuse of this triangle is 8 feet, the multiplier of these ratio values is (8 ft)/2 = 4 ft.

The triangle sides are ...

  4 ft : 4√3 ft : 8 ft

The ladder reaches 4√3 ≈ 6.9 ft up the wall. Its base is 4 ft from the building.

Step-by-step explanation:

C1:

The pattern for this: you add 1/2 every time.

C2:

3, 3 1/2, 4, 4 1/2

C3:

5 1/2

C4:

The 14th

C5:

10

D1:

You add twice as more than you did before, starting at 3.

D2:

48, 96, 192, 384

D3:

192

D4:

The 9th

D5:

384

Hope this all helps.

Answer:

C)

1) As the sequence progresses, each term in the sequence increases by 1/2.    2) 3 ; 3 1/2 ; 4 ; 4 1/2

3) The 10th term in the sequence is 5 1/2.

4) 7 1/2 is the 14th term in the sequence.

5) The 17th term is 9.

D)

1) As the sequence progresses, each term multiplies by 2.

2) 48 ; 98 ; 192 ; 384

3) The 7th term in the sequence is 192.

4) 768 is the 9th term in the sequence.

5) The 8th term in the sequence is 384.

Step-by-step explanation:

FOR C : 1 + 1/2 = 1 1/2, 1 1/2 + 1/2 = 2, 2 + 1/2 = 2 1/2, and so on. This pattern tells me the rule of the sequence. Continue this sequence to answer 1, 2, 3, 4, and 5.

FOR D: 3 x 2 = 6, 6 x 2 = 12, 12 x 2 = 24, and so on.  This pattern tells me the rule of the sequence. Continue this sequence to answer 1, 2, 3, 4, and 5.

Answer:

C. {x | x < [tex]\frac{10}{7}[/tex]}

Step-by-step explanation:

x must be less than 10/7

I hope this helps!

Answer:

158cm

Step-by-step explanation:

Martine had the height of 50cm when born.

Every year she grows at an average rate of 6cm

So the the first 18 years will be 6cm × 18 = 108cm

She will be 108cm + 50cm = 158cm tall by the time she turns 18 years

50cm + (6 × 18)cm

50cm + (6 × 18)cm50cm + 108cm

50cm + (6 × 18)cm50cm + 108cm158cm

Answer:

The stream's speed is 2 km/hr. We don't need to know the distance.

Step-by-step explanation:

Let the stream's speed = x

rate * time = d

The distance is the same going upstream as it is coming back down stream.

d_upstream = d_downsteam

(8 + stream)*3 = (8 - stream)*5

(8 + x)*3 = (8 - x)*5                    Remove the brackets

24 + 3x = 40 - 5x                      Subtract 24 from both sides.

3x = 40 - 24 - 5x

3x = 16 - 5x                               Add 5x to both sides

3x + 5x = 16

8x = 16                                      Divide by 8

x = 16/8

x = 2