Triangle ABC is similar to triangle DEF What are the lengths of sides DF and EF ?

Answer:

[tex]\mathrm{A.\:}x+2y=a[/tex]

Step-by-step explanation:

In standard form [tex]ax+by=c[/tex], any point the line passes through will make the inequality true. We can simply use any point given to find the equation of the line:

We can write the following system of equations from two points from the table:

[tex]\begin{cases}d\cdot3a+e\cdot(-a)=f\cdot a\\d\cdot5a+e\cdot(-2a)=f\cdot a\end{cases}[/tex]

Solving, we get:

For [tex]a \notin 0[/tex],

[tex]d=1,\\e=2,\\f=1[/tex]

Therefore, our equation is:

[tex]dx+ey=fa,\\1x+2y=1a,\\\fbox{$x+2y=a$}[/tex].

Step 1: Find the sum of the interior angles

Use this formula: 180 x (n - 2)

n is the number of sides of the polygon

Work:

180 x (4 - 2)

180 x 2

360

Step 2: Find the angle right above the 94 degree angle

The entire angle (a circle) is equal to 360 degrees. To find the part we're looking for (inside of the polygon), we need to subtract the angle we already know from 360.

Work:

360 - 94

266

Step 3: Set up an equation to find the missing angle p

We now know every angle except p! And we know the sum of the interior angles. Knowing this information makes it really easy to set up an equation.

360 = 12 + 75 + 266 + p

360 = 353 + p

p = 7 degrees

Does this answer make sense?

Yes! Although the drawing may not be to scale, it is very possible that angle p could be 7 degrees because of how 12 degrees looks on this graph.

Hope this helps!! :)

Answer:

Step-by-step explanation:

Median: First write in ascending order. If number of data's is odd, median is the middle data.

If number of data's is even, then median = average of n/2th and (n+2)/2th term.

1) 1 , 3 , 5 , 5 , 6

Median = 5

2) 3,4,10,2,1

Ascending order: 1,2,3,4,10

Median = 3

3) 4, 5,7,11

Median = (5+7)/2 = 12/2 = 6

4) 1,1,2,6

Median = (1+2)/2 = 3/2 = 1.5

5) 2,2,3,3,,5,7

Median = 3+3/2 = 6/2 = 3

6)1,2,4,6,7,7

Median = (4+6)/2 = 10/2 = 5

7) 2,2,3,6,7,8

Median = (3+6)/2 = 9/2 = 4.5

8)1,2,3,14,17,18

Median = (3+14)/2 = 17/2 = 8.5

Mean= Sum of all the items÷ number of items

1)Mean = (1+2+3+2)÷4 = 8÷2 = 4

2)Mean=(4+3+2+4+2)÷5 = 15÷5 = 3

3)Mean = (5+4+6+1)÷4 = 16÷4 = 4

4)Mean = (2+5+1+4+7+5)÷6 = 24÷6 = 4

5)Mean =(10+11+9+12+8)÷5=50÷5 = 10

6)Mean = (1 + 2 + (-2)+1+(-2) )÷5 = -2÷5 = -0.4

7)Mean = (4+(-2)+3+(-3)+3)÷5 = 5÷5 = 1

8)Mean = (4+5.5+3+5.5)÷4=18÷4 = 4.5

Answer:

Median

1) 5

2) 3

3) 5+7=12/2=6

4)1+2=3/2=1.5

5)3+3=6/2=3

6) 4+6=10/2=5

7) 3+7=10/2=5

8)14+3=17/2=8.5

Mean

1) 2

2) 3

3)4

4)4

5) 10

6) 0

7) 1

8) 4.5

Step-by-step explanation:

Median is the middle number, make sure the list of in order from smallest to highest.

2) 1, 2, 3, 4, 10

if you have two numbers in the middle add them together then divide by 2

4) 1, 1, 2,6

5)2, 2, 3, 3, 5, 7

6) 1, 2, 4, 6, 7, 7

7)2, 2, 3, 7, 6,8

8)1, 2, 3, 14, 17, 18

Mean is when you add all the numbers together and divide by how many there are.

1) 1+3+2+2=8/4=2

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

Explanation:

The combination of angle x and the 93 degree angle forms x+93. This obtuse angle is congruent to 130 because these two angles are alternate interior angles and because line L is parallel to line M.

So,

x+93 = 130

x+93-93 = 130-93 .... subtracting 93 from both sides

x = 37

Answer:

[tex]k>-3[/tex]

Step-by-step explanation:

We have the equation:

[tex]-3x^2-6x+k=0[/tex]

Where a = -3, b = -6, and c = k.

And we want to determine values of k such that the equation will have real, unequal roots.

In order for a quadratic equation to have real, unequal roots, the discriminant must be a real number greater than 0. Therefore:

[tex]b^2-4ac>0[/tex]

Substitute:

[tex](-6)^2-4(-3)(k)>0[/tex]

Simplify:

[tex]36+12k>0[/tex]

Solve for k:

[tex]12k > -36[/tex]

[tex]k>-3[/tex]

So, for all k greater than -3, our quadratic equation will have two real, unequal roots.

Notes:

If k is equal to -3, then we have two equal roots.

And if k is less than -3, then we have two complex roots.

Answer:

[tex]\mathrm{Domain\:of\:}\:\frac{x-1}{x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-3\quad \mathrm{or}\quad \:x>-3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\cup \left(-3,\:\infty \:\right)\end{bmatrix}[/tex]

Therefore, the 4th option i.e. (−∞, −3) (−3, ∞) is the correct answer.

Step-by-step explanation:

Given the expression

[tex]f\left(x\right)=\frac{x-1}{x+3}[/tex]

We know that the domain is the set of all the input or argument values for which is the function is real and defined.

From the given expression, we need to make sure the denominator of a rational function can be anything but 0, because 0 would make the function undefined.

Thus, we need to find undefined points such as:

x+3 = 0

x = -3

Therefore, the function domain must be:

x < -3 or x > -3

In other words,

[tex]\mathrm{Domain\:of\:}\:\frac{x-1}{x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-3\quad \mathrm{or}\quad \:x>-3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\cup \left(-3,\:\infty \:\right)\end{bmatrix}[/tex]

Therefore, the 4th option i.e. (−∞, −3) (−3, ∞) is the correct answer.

Answer:

(1, 2/3) (-1, -1) are the points. use the slope formula to find the slope y2-y1/x2-x1

(-1 - 2/3) / (-1 -1) (answer both sides of the division side)

-5/3 / -2  (divide)

slope = 5/6  (the slope)

plug in values you know into point-slope form (y -y1) = m(x-x1)

y - (-1) = 5/6 (x - (-1) (i chose the easier point to plug in. two neg. make a pos. )

y +1 = 5/6 (x +1)  (use the distributive property)

y +1 = 5/6x+5/6  (subtract 1 from both sides)

y = 5/6x - 1/6  or B (this is the equation)

Step-by-step explanation:

I hope this helped :))

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete. However, a possible question is "calculate the depth of the lake after certain number of hours (say 2 hours)"

Given

[tex]Rate = \frac{1}{4}ft/hr[/tex]

[tex]Depth = 279ft[/tex]

First, we calculate the depth receded.

If the rate is 1/4ft per hour

Then

The Depth receded in 2 hours is:

[tex]Receded = \frac{1}{4} * 2[/tex]

[tex]Receded = \frac{2}{4}[/tex]

[tex]Receded = 0.5ft[/tex]

The new depth is then calculated as:

[tex]New\ Depth = 279ft - 0.5ft[/tex]

[tex]New\ Depth = 278.5ft[/tex]

Answer:

Step-by-step explanation:

Given: i. AB||DE

          ii. AC≅DC

Prove: ΔABC≅ΔDEC

From the two triangles, it can be observed that;

m<BAC≅m<EDC (alternate angles)

m<ABC≅m<DEC (alternate angles)

m<BCA≅m<ECD (vertically opposite angles)

m<BAC + m<ABC + m<BCA = m<EDC + m<DEC + m<ECD = [tex]180^{o}[/tex] (sum of angles in a triangle)

Since the three angles of the triangles are congruent respectively, then;

ΔABC≅ΔDEC (AAA congruence property)

Answer:

x equals 3 so multiply 3x3 and it will give you 9 and add that to 6 and you get 15. x equals 3 for the one that equals 5.

Answer:

3x + 16 = 15

3x = 15-16

3x = -1

x = -1/3

Answer:

Step-by-step explanation:

3/5(-60)(-2/3)=24

choice C

[tex]\huge\sf{Answer :- }[/tex]

Exterior angle of the polygon = ( 360/ n )°

where,

➙ ( 360/ 20 )°

➥ 18°

Answer:

answer of this qn will 360÷20= 18degree

Answer:

£4410

Step-by-step explanation:

Step one:

given data

Principal P= £4000

Rate= 5%= 0.05

time t= 2 years

Final amount A= ??

Required

The final amount

Step two:

The expression for the final amount of compound interest is

[tex]A= P(1+r)^t\\\\A=4000(1+0.05)^2\\\\A=4000(1.05)^2\\\\A=4000*1.1025[/tex]

A=£4410

Answer:

240

Step-by-step explanation:

-8(10×-3)

(10×3)=30

30×-8=240

Answer:

0+2+-4=-2

Step-by-step explanation:

Answer:

Someone help me with this question

Step-by-step explanation:

Answer:

The correct answer is,

Answer:

The value of x = 65.4°

Step-by-step explanation:

Given

hypotenuse = 12

To determine

The value of ∠x = ?

Using the trigonometric ratio

cos x = adjacent / hypotenuse

here:

substituting adjacent = 5, hypotenuse = 12 in the formula

cos x = adjacent / hypotenuse

cos x = 5 / 12

x = arccos (5/12)

x = 65.4°

Therefore, the value of x = 65.4°

Answer:

The answer is 65.3 to the nearest tenth

Step-by-step explanation:

You'll use the Pythagoras theorem to find the unknown side first

then you'll use the sin rule to solve for x

Answer:

y = 2x - 3.5

Step-by-step explanation:

2x² + 2y = 4x + 2x² - 7

2y = 4x + 2x² - 7 - 2x²

2y = 4x - 7

y = (4x - 7) / 2

y = 2x - 3.5

2x² + 2y = 4x + 2x² - 7

4x + 2y = 4x + 2x² - 7

4x + 2y = 4x + 4x - 7

4x+2y=8x-7

2y = 4x - 7

Answer:

3. Adjacent and Supplementry

Answer:

36:18= 16:9

2 eggs for every guest

Answer:

(2,4)

Step-by-step explanation:

the solution to a system of equations is where two lines intersect.

Answer: the last one

Step-by-step explanation:

um so the set begins with 40 and ends with 100 (look at that on the number line)

and so the median is essentially that middle line in the box, which is around 80

i assume yk how to calculate medians so I calculated the median of the first and the last answer

the first one was like 70, and the last one was like 78.9 which is close enough to 80

so i think its the last one

Answer:

It is answer number four.

Step-by-step explanation:

40 and 100 represent the outliers so both numbers must be included.

80 must also be included as it is the mean or average test grade.

Answer:

76

Step-by-step explanation:

To find the area you multiply both sides, the opposite of multiplication is division. Take 6992 and divide it by 92 to get the missing side of 76.

Answer:

321%

Step-by-step explanation:

hope I helped Kkkkkkkk

Answer:

65 %

Step-by-step explanation:

13/20 = 65/100

Answer:

65%

Step-by-step explanation:

20/100 =1/5

5*13=65

Answer:

Tomas has a 15% commission :)

Step-by-step explanation: Because 15% equals 15%