please help me solve this problem one problem for 15 points

X =12

Step-by-step explanation:

Supplementary Angels means the angles are added up to 180 degrees.

So , <1 + <2 = 180

Given that,

<1 = 2x +6

Now lets find the size of <2.

We know that,

Angles in a Straight line is also added up to 180 degrees.

So,

<2+ < 3 = 180

Let's Solve.

[tex] < 2 + < 3 = 180 \\ < 2 +( 3x - 6) = 180 \\ < 2 = 180 - (3x - 6) \\ < 2 = 180 - 3x + 6 \\ < 2 = 186 - 3x[/tex]

Now we know the size of <2

lets find out the value of x

[tex] < 1 + < 2 = 180 \\ 2x + 6 + 186 - 3x = 180 \\ 186 + 6 - 180 = 3x - 2x \\ 12 = x[/tex]

Let's check whether the answer is correct.

We know that <1 =<3 (Alternative Angles)

[tex] < 1 = < 3 \\ 2x + 6 = 3x - 6 \\ 2 \times 12 + 6 = 3 \times 12 - 6 \\ 24 + 6 = 36 - 6 \\ 30 = 30[/tex]

Have a nice day

Answer:

y = 1/2x - 3

Step-by-step explanation:

The line intercepts with the y-axis at -3 and its pattern is going right two and up one.

Answer:is that 3i or what?

-

Step-by-step explanation

Answer:

It's answer is d) 9

.........

Answer:

8640

Step-by-step explanation:

According to question,

P= 6000

T=3 year 8 months = 11/3 years

R= 12% per annum

Simple interest is given by :

[tex]SI=\frac{PRT}{100} \\SI=\frac{6000*12}{100} *\frac{11}{3} \\SI=24*11\\SI=2640 Rs[/tex]

Now,

Amount = P+SI

Amount=6000+2640

Amount=8640 Rs

8640 Rs amount which will clear her debt

Answer:

x=-3×-5×-7

-3×-5=15

15×-7=-105

=-105

Answer:

% increase = 100 x [(new price) - (original price)] / (original price)] = 100 (9.67 - 9.56) / 9.56

% increase ≅ 1.2% (to the nearest tenth)

Answer:

[tex]{ \tt{ = 2 \frac{1}{2} }} \\ \\ = \frac{5}{2} \\ \\ { \tt{ = 2.5}}[/tex]

Answer:

Step-by-step explanation:

When you ask "which of the following"

you must include the choices

Answer:

0.5x = 25.5

Step-by-step explanation:

Peter was thinking of a number x, then he halves it's

Answer:  Choice C) integers from 1 to 10 inclusive

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

Explanation:

The "U" means "set union". We form a larger set that contains any number that's in set A, set B, or both.

So,

A U B = {stuff from set A,  stuff from set B}

A U B = {1,3,5,7,9,       2,4,6,8,10}

A U B = {1,2,3,4,5,6,7,8,9,10}

A U B = set of integers from 1 and 10 inclusive

That makes choice C the final answer.

Choice B is very close to it, but that verbally describes the set {2,3,4,5,6,7,8,9} which leaves out 1 and 10. The "inclusive" makes sure to involve the endpoints 1 and 10, as well as everything in between.

Answer:

[tex]x=54^{o}[/tex]

Step-by-step explanation:

Angles of straight line: 126 and x = 180

[tex]x+126=180[/tex]

[tex]x=180-126[/tex]

[tex]x=54^{o}[/tex]

{CHECK: [tex]54+126=180[/tex]}

hope this helps.....

Step-by-step explanation:

[tex] \frac{ \frac{4x}{5 + x} }{ \frac{6x}{x + 2} } [/tex]

[tex] \ \frac{2(x + 2)}{3(5 + x)} [/tex]

[tex] \frac{2x + 4}{3x + 15} [/tex]

Answer:

2x+4 over 3x+15

Step-by-step explanation:

First divide 4x over 5+x by 6x over x+2 when multiplying 4x over 5+x by the reciprocal of 6x over x+2

Step 2: cancel out 2x in both numerator and denominator

Last step:use distributive property to multiply 2 by x+2 and 3 by x+5

Answer:

(2,0)

x-value: [1+3]/2 = 4/2 = 2

y-value: [2+-2]/2 = 0/2 = 0

Step-by-step explanation:

Given:

Total bill = $67.65

Mr. Scott paid with four $20 bills.

To find:

The amount of change he have received.

Solution:

It is given that, Mr. Scott paid with four $20 bills. So, the total amount paid by him is:

[tex]\$20\times 4=\$80[/tex]

Total bill = $67.65

Now,

Amount of change = Total amount paid - Total bill

                               = $80 - $67.65

                               = $12.35

Therefore, he should have received $12.35.

Answer:

3.3 m

Step-by-step explanation:

the height = 2/3 × 5 = 10/3 = 3.3 m

Please delete my answer. I made a mistake

Answer:

-9/ 11 ____-5/11 _____ - 2/11

Step-by-step explanation:

-2/11, -5/11, -9/11

All the numbers are negative ; the fraction which is largest is 9/11 ; then 5 /11 ; then 2 /11 ; however, since they are negative, they largest fraction becomes the least value.

Numbers on a number line are arranged from least to highest. Hence the numbers will be arranged in a number line as follows :

-9/ 11 ____-5/11 _____ - 2/11

Answer:

it is x

Step-by-step explanation:

The volume of a shape is the amount of space in it.

The graph that satisfies the above condition is the (b) graph X:

The volume of a rectangular-shaped swimming pool is

[tex]\mathbf{V=l \times w \times h}[/tex]

Where:

[tex]\mathbf{l,w,h \ge 0}[/tex] ---all the dimensions are greater than 0

[tex]\mathbf{l,w,h \ge 0}[/tex] means that:

From the given graphs, the graph that satisfies the above condition is the graph X:

This is so because it crosses the x-axis three times, and it does not pass through the origin

Read more about volumes at:

https://brainly.com/question/13338592

Given:

The expressions are [tex](x+1),\ (x-1)[/tex] and [tex](x^2-1)[/tex].

To find:

The least common multiple of given expressions.

Solution:

The expressions are [tex](x+1),\ (x-1)[/tex] and [tex](x^2-1)[/tex]. The factor forms of these expressions are:

[tex](x+1)=1\times (x+1)[/tex]

[tex](x-1)=1\times (x-1)[/tex]

[tex](x^2-1)=(x-1)(x+1)[/tex]                 [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

The least common multiple is the product of all distinct factors with its highest degree. So,

[tex]L.C.M.=1\times (x+1)\times (x-1)[/tex]

[tex]L.C.M.=(x+1)(x-1)[/tex]

[tex]L.C.M.=x^2-1^2[/tex]                [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]L.C.M.=x^2-1[/tex]

Therefore, the least common multiple of given expressions is [tex]x^2-1[/tex].

Answer:

smaller piece is 65cm

larger piece is 115cm

Step-by-step explanation:

let 's' = smaller piece

let '180-s' = larger piece

3(180-s) = 85 + 4s

540 - 3s = 85 + 4s

540 = 85 + 7s

455 = 7s

s = 455/7 which is 65cm

larger piece = 180-65 or 115cm

The sum of two numbers and their difference is 30.

Answer:

Below.

Step-by-step explanation:

The first term (where k = 1)

= 3(2)^1-1

= 3*1

= 3,

The last term ( k = 10)

= 3(2)^(10-1)

= 3(2)^9

= 3* 512

= 1536.

Answer:

3

1536

A

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

Triagle GIA and Triangle GNT are congruent.

Answer:

(2x - y )2 - (y + 2)2 = 4 (x - y - 1)

Step-by-step explanation:

[tex](2x -y) 2 - ( y + 2 ) 2 = (4x -2y) -(2y + 4) \\\\[/tex]

                             [tex]= 4x - 2y -2y - 4\\\\=4x - 4y - 4\\\\=4(x-y-1)[/tex]

Answer:

Yes they are congruent and it is explained below

Step-by-step explanation:

There are 5 postulates when testing for congruency and they are;

SSS, SAS, ASA, AAS and HL.

S represents side

A represents angle

H represents hypotenuse

L represents leg

Now, in this our question, we can see that the 3 angles and the three sides of both triangles are equal to each other.

Thus, we can make use of SSS postulate whereby we say the 3 sides of the first triangle are equal to the 3 sides of the second triangle.

Thus, they are congruent.

Answer:

B) 5

Step-by-step explanation:

The given parameters are;

The number of shots at the basket = 5 shots

The number of ways to make exactly 4 shots is given by combination as follows;

The number of ways to shoot exactly 4 shots = ₅C₄ = 5!/(4!×(5 - 4)!) = 5

The number of ways to shoot exactly 4 shots = 5 ways

Step-by-step explanation:

a. increased b. discreased c. increased d. decreased

p+q = 12

Squaring both the sides

(p+q)^2 = 12^2

p2 + q2 + 2pq = 144

p2 + q2 + 2x 22 = 144

p2 + q2 = 144 - 44

p2 + q2 = 100

Answer:

q2=

Step-by-step explanation:

The formula for p^2+q^2p

2

+q

2

is

p^2+q^2 = (p+q)^2 -2pqp

2

+q

2

=(p+q)

2

−2pq

Answer:

25/30 and 12/30

Step-by-step explanation:

6 and 5 have a least common multiple of 30

6*5 = 30

5/6 * 5/5 = 25/30

2/5 *6/6 = 12/30

Answer:

10/12       4/10

Step-by-step explanation:

Answer:

? = 24/23 or 1 1/23

Step-by-step explanation:

In order to do this you have to:

1) Isolate the variable

            -  you do this by dividing each side by factors that don't contain the variable

            - you divide because it is the opposite of multiplication

Hope this helps!

Option c is correct formula