Find the measures of the angles formed by two intersecting lines if the
sum of the measures of three of the four angles is 270°

50 points! Please help quick!

find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex]  ; now find AD=AB-DB=21-15=6  .Then                AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]  

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in both right triangles

To find BD

BD² + CD² = BC²

BD² + 8² = 17²

BD² + 64 = 289 ( subtract 64 from both sides )

BD² = 225 ( take the square root of both sides )

BD = [tex]\sqrt{225}[/tex] = 15

Then

AD = AB - BD = 21 - 15 = 6

To find AC

AC² = AD² + CD²

AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )

AC = [tex]\sqrt{100}[/tex] = 10 → C

Answer:

28

Step-by-step explanation:

Answer:

(-5,31/2)

Step-by-step explanation:

open bracket

y=1/2x^2+5x+28

compare with y=ax2+bx+c

use formula (-b/2a,4ac-b2/4a)

Answer:

90

Step-by-step explanation:

From the given drawing, we have;

ΔRST is circumscribed about circle A

The center of the circle A = The point A

The line RT = A tangent to the circle A

The radius to the circle A = The line AP

According to circle theory, a line which is tangent to a circle is perpendicular to the radius of the circle drawn from the point of tangency

Where two lines are perpendicular to each other, then the angle formed between them = 90°

The angle formed between a tangent and the radius of the circle = m∠APT

Therefore;

m∠APT = 90°

Given:

The inequalities are:

[tex]y>\dfrac{2}{3}x+3[/tex]

[tex]y\leq -\dfrac{1}{3}x+2[/tex]

To find:

The graph for the given system of inequities.

Solution:

We have,

[tex]y>\dfrac{2}{3}x+3[/tex]

[tex]y\leq -\dfrac{1}{3}x+2[/tex]

The related equations are:

[tex]y=\dfrac{2}{3}x+3[/tex]

[tex]y=-\dfrac{1}{3}x+2[/tex]

Table of values

x                       [tex]y=\dfrac{2}{3}x+3[/tex]                        [tex]y=-\dfrac{1}{3}x+2[/tex]

0                             3                                           2

3                             5                                           1

Plot the points (0,3) and (3,5) and connect them by a straight line to get the boundary line [tex]y=\dfrac{2}{3}x+3[/tex].

Plot the points (0,2) and (3,1) and connect them by a straight line to get the boundary line [tex]y=-\dfrac{1}{3}x+2[/tex].

In [tex]y>\dfrac{2}{3}x+3[/tex], the sign of inequality is ">" it means the boundary line is a dashed line and shaded area lies above the boundary line.

[tex]y\leq -\dfrac{1}{3}x+2[/tex], the sign of inequality is "[tex]\leq [/tex]" it means the boundary line is a solid line and shaded area lies below the boundary line.

Therefore, the required graph is shown below.

Answer:

[tex]Sets = 27[/tex]

Step-by-step explanation:

Given

[tex]Coin = 1[/tex]

[tex]Toss = 5[/tex]

Required

Number of outcomes with at most 3 heads

First, we list out the sample space of a toss of coin 5 times

[tex](HHHHH)[/tex], [tex](HHHHT)[/tex], [tex](HHHTT)[/tex], [tex](HHTTT)[/tex], [tex](HTTTT)[/tex], [tex](TTTTT)[/tex], [tex](TTTTH)[/tex], [tex](TTTHH)[/tex], [tex](TTHHH)[/tex], [tex](THHHH)[/tex], [tex](HTHTH)[/tex], [tex](THTHT)[/tex], [tex](HHTHH)[/tex], [tex](TTHTT)[/tex], [tex](HTTHT)[/tex], [tex](THHTH)[/tex], [tex](THHHT)[/tex], [tex](HTTTH)[/tex], [tex](THHTT)[/tex], [tex](HTTHH)[/tex], [tex](HHTTH)[/tex], [tex](TTHHT)[/tex], [tex](TTHTH)[/tex], [tex](HHTHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](THTTH)[/tex], [tex](HTHHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](HHHTH)[/tex], [tex](TTTHT)[/tex]

Next, we list out all outcomes with at most 3 heads

, , [tex](HHHTT)[/tex], [tex](HHTTT)[/tex], [tex](HTTTT)[/tex], [tex](TTTTT)[/tex], [tex](TTTTH)[/tex], [tex](TTTHH)[/tex], [tex](TTHHH)[/tex], , [tex](HTHTH)[/tex], [tex](THTHT)[/tex], , [tex](TTHTT)[/tex], [tex](HTTHT)[/tex], [tex](THHTH)[/tex], [tex](THHHT)[/tex], [tex](HTTTH)[/tex], [tex](THHTT)[/tex], [tex](HTTHH)[/tex], [tex](HHTTH)[/tex], [tex](TTHHT)[/tex], [tex](TTHTH)[/tex], [tex](HHTHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](THTTH)[/tex], [tex](HTHHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](TTTHT)[/tex]

So, the number of set is:

[tex]Sets = 27[/tex]

Answer: 68

Step-by-step explanation: Complementary angles are angles that add up to 90. So, you need to do 90-22=68.

Answer:

Answer:

x=-3 and y=-2

Step-by-step explanation:

let the numbers be x and y

x+y=-5

x-y=-1

therefore x=-5-y

-5-y-y=-1

-2y=-1+5

-2y=4

y=-2

×=-5-(-2)

x=-5+2

x=-3

Answer: -2 and -3

Step-by-step explanation:

x + y = -5

x - y = -1 -> x = y - 1

(y - 1) + y = -5

y - 1 + y = -5

2y = 1 - 5

2y = -4

y = -2

x = y - 1 = -2 - 1 = -3

Answer:

A.

Step-by-step explanation:

4y = 12x + 16

3x = y - 4

=>

y = 3x + 4

using that in the first equation

4(3x+4) = 12x + 16

12x + 16 = 12x + 16

=> both lines/equations are identical, so they have infinitely many solutions.

Answer:

1/3 fraction of whole paint is used by mark

Step-by-step explanation:

Mark used  1/2 out of 3/2 cans.

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{2} = \frac{1}{2}*\frac{2}{3}=\frac{1}{3}[/tex]

The sum of the 15th square number and the 5th cube number is 350.

The 15th square number will be:

15² = 15 × 15

= 225

The 5th cube number will be:

5³ = 5 × 5 × 5

= 125

The sum of the numbers will be:

225 + 125

= 350

Therefore, we get that, the sum of the 15th square number and the 5th cube number is 350.

Learn more about sum here:

https://brainly.com/question/17695139

#SPJ1

Step-by-step explanation:

hope it helps

Answer: (a) P = 6W + 2

(b) L = 2W + 1

(c) Width = 13cm

Length = 27cm

Step-by-step explanation:

The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:

L = (2 × W) + 1

(b) L = 2W + 1

Therefore, P = 2(L + W)

P = 2( 2W + 1) + 2W

P = 4W + 2 + 2W

(a) P = 6W + 2

Since perimeter is given as 80cm. Therefore,

P = 6W + 2

6W + 2 = 80

6W = 80 - 2

6W = 78

W = 78/6

W = 13

Width is 13cm

Length = 2W + 1

Length = 2(13) + 1

Length = 27cm

The width of the rectangle is 13cm and the length is 27cm.

A rectangle is a quadrilateral. Opposite sides are equal. The four angles in a rectangle is equal to 90 degrees.

The formula for determining the perimeter of a rectangle = 2x (length + width)

P = 2(L + W)

80 = 2(1 + 2w + w)

80 = 2(1 + 3w)

40 = 1 + 3w

40 - 1 = 3w

39 = 3w

w = 13cm

Length = 1 + 2(13) = 27cm

To learn more about rectangles, please check: https://brainly.com/question/16595449

Answer:

I don't know I don't know about question

Answer:

because internal staggal angles are equal

Step-by-step explanation:

The first reason is wrong.

Angle EGH and DEG are internal staggal angles:

the two angles are on both sides of the cut line EG, and the two angles are between the two divided lines.

{the definition of internal staggal angle}

Answer:

20 Lines

Step-by-step explanation:

According to the Question,

Now,  the total pairs of points which can be formed is 9

And, the line passing through 2 such points 9c2 = 9! / (2! x 7!) = 9x4 ⇒ 36

Here, We have overcounted all of the lines which pass through three points.

And, each line that passes through three points will have been counted 3c2 = 3! / 2! ⇒ 3 times

Now, the sides of the square consist of 3 points. We have counted each side thrice, so 4*2 are repeated.

Answer:

(-7, -3)

Step-by-step explanation:

So the formula is (x, y) --> (-y, x) for a 90 degrees counterclockwise rotation.

To apply this formula to (-3,7), first identify which is the x-coordinate and which is the y-coordinate.

x-coordinate is -3 & y-coordinate is 7

Then you literally just substitute it into the formula like so:

(-y, x) -->(-(7), (-3)) --> (-7, -3)

Try to put parantheses around the coordinate when substituting to prevent confusion & incorrect negative signs.

Hope it helps and good luck (●'◡'●)

Answer:

(-7,-3)

Step-by-step explanation:

You could read (x,y)->(-y,x) as if I have the point (x,y), the image point is (opposite of y,x).

So shorthand the rule is just saying

(x,y)->(opposite of y, x)

(-3,7)->(-7,-3)

A few more examples:

(5,7)->(-7,5)

(-5,7)->(-7,-5)

(-5,-7)->(7-,5)

(5,-7)->(7,5)

This whole explanation comes down to reading-u as opposite of u.

Opposite just means to change the sign.

Another way to read -u is -1×u.

Example:

Q: evaluate -u if u=8

A: -8

Why? -u means -1×u or opposite or u. Take your pick in reading it. It's the same meaning just different ways of reading. -1×8=-8 or the opposite or 8 is -8.

Example:

Q: evaluate -u if u=-8

A: 8

Why? -u means -1×u or opposite or u. Take your pick in reading it. It's the same meaning just different ways of reading. -1×-8=8 or the opposite or -8 is 8.

Answer:

no solutions

Step-by-step explanation:

Hi there!

We're given this system of equations:

x+y=3

4y=-4x-4

and we need to solve it (find the point where the lines intersect, as these are linear equations)

let's solve this system by substitution, where we will set one variable equal to an expression containing the other variable, substitute that expression to solve for the variable the expression contains, and then use the value of the solved variable to find the value of the first variable

we'll use the second equation (4y=-4x-4), as there is already only one variable on one side of the equation. Every number is multiplied by 4, so we'll divide both sides by 4

y=-x-1

now we have y set as an expression containing x

substitute -x-1 as y in x+y=3 to solve for x

x+-x-1=3

combine like terms

-1=3

This statement is untrue, meaning that the lines x+y=3 and 4y=-4x-4 won't intersect.

Therefore the answer is no solutions

Hope this helps! :)

The graph below shows the two equations graphed; they are parallel, which means they will never intersect. If they don't intersect, there's no common solution

Answer:

2 sheep

Step-by-step explanation:

If you have 36 sheep  and you sell:

first day    1/2 of them  you sold               18

second day  1/3  them you sold                12

On thhe third day  1/9  them you sold       4

Therefore you sold 18 + 12  + 4  = 34

And you still have  2 sheep

Answer:

well your answer should be "F"

Step-by-step explanation:

we have

Y<-2x+10  -----> inequality A

The solution of the inequality A is the shaded area below the dashed line

Y = -2x+10

The y-intercept of the dashed line is (0,10)

The x-intercept of the dashed line is (5,0)

Y<1/2x-2 ----> inequality B  

The solution of the inequality B is the shaded area below the dashed line

Y= 1/2x-2

The y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (4,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution

therefore

The solution are the points

E, F and G

i hope this helps

Answer:

option d is correct answer

Given:

The limit problem is:

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

To find:

The value of the given limit problem.

Solution:

We have,

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

It can be written as:

[tex]=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{5x\times 2}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{10x}[/tex]

Applying limit, we get

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}[/tex]

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}[/tex]

Therefore, the value of given limit problem is [tex]-\dfrac{1}{50}[/tex].

Answer:

x = 24

Step-by-step explanation:

mathematically, in a cyclic quadrilateral, two opposite angles are supplementary

what this mean is that they add up to be 180

From what we have in the question, the two angles are supplementary and that means they add up to equal 180 degrees

thus, we have it that;

(4x + 9) + (3x + 3) = 180

4x + 3x + 9 + 3 = 180

7x + 12 = 180

7x = 180-12

7x = 168

x = 168/7

x = 24

Answer:

49

Step-by-step explanation:

The probability of choosing a red marble is equal to the number of red marbles over the number of total marbles there are.

Therefore, let the number of red marbles be [tex]x[/tex].

We have the following equation:

[tex]\frac{x}{84}=\frac{7}{12}[/tex]

Cross-multiplying, we get:

[tex]12x=7\cdot 84,\\x=\frac{84\cdot 7}{12},\\x=\boxed{49}[/tex]

Therefore, there are 49 red marbles in the bag.

Answer:

Step-by-step explanation:

H