Two adjacent angles of a paralle
logram are congruent. What is the measure of
each?

​

We are given:

aᵇ = bᵃ

b = 2a

Finding (a+b):

Finding a:

replacing b by 2a in the first equation, we get:

(a²)ᵃ = (2a)ᵃ

(a²)ᵃ = 2ᵃ * aᵃ

a²ᵃ / aᵃ = 2ᵃ                  [dividing both sides by aᵃ]

aᵃ = 2ᵃ                          [because xᵃ / xᵇ = xᵃ⁻ᵇ]

a = 2                             [raising both sides to 1/a]

Finding b:

We are given that b = 2a

now that we know what a equals, we will plug that value here

b = 2(2)

b = 4

Finding a+b:

We found that a = 2, b = 4

a + b = 2 + 4 = 6

Answer:

{2,6,14}

Step-by-step explanation:

The range are the f(x) values

the domain are the x values

So we have it that;

f(-1) = 4(-1) + 6 = 2

f(0) = 4(0) + 6 = 6

f(2) = 4(2) + 6 = 14

so we have the range as;

{2,6,14}

Answer:

c = 1/4

-1-1 = -2

-3-5 = -8  

Step-by-step explanation:

Answer:

it cost 80 dollars

Step-by-step explanation:

cost per bag for X brand =25 $

cost per bag for y brand = 20$

minimize Z=(25X +20 y)

further formulate the problem

the given constraints are

2x + y equal 12

2x + 9y equal 36

2x + 3y equal 24

well on the graph given plot of the constraints

the corner points are

(0;0)

(6;0)

(0;4)

(9;2.5)

minimum z occurs at (0:4)

value of Z(minimum cost)=80$

Answer:

(3,-5)

Step-by-step explanation:

The line y=-x is a positively sloped line that when reflected across changes all signs to their opposite counterpart. Positivee to negative, negative to positive.

We know that the initial temperature is -3 then it rises to 8 and drops by 6 degrees then you just need to subtract six from 8                                                         [tex]\displaystyle\ 8-6=2^\circ \\\\Answer: the\ secondary\ temperature \ will \ be equal \ to \ 2^\circ[/tex]

Step-by-step explanation:

— If the arc AB has length 3.2 cm, calculate (a) the length of the radius, (b) ... the length of the radius, (b) the length of the arc BC. r 0.8 rad С o r A .

Step-by-step explanation:

-5x+5y=15(multiply by 2)

3×-2y=-8(multiply by 5)

-10×+10y=30

15×-10y=-40

5x=-10

x=-2

Here,

-5x+5y=15.......(I)

and

3x-2y=8.....(II)

Now,

adding 3 in eqn (II)

so, 6x-5y=8

Now,

combining eqn (I) &(II)

-5x+5y=15

+6x-5y=8

[both 5y is cancelled ]

or, x=7

Now,

in eqn(i)

-5x+5y=15

or, -5*7+5y=15

or, -35+5y=15

or, -35-15=-5y

or, -50=-5y

or, -50/-5=y

[minus is cancelled ]

Therefore, y=10 and x=7

Answer:

2 and 3.

Step-by-step explanation:

2. and 3.

the total number of paintings depend upon the number of weeks that have passed as she adds 3 paintings every week to her collection.

1. can't be an option as output values depend upon the input values and hence not independent

4. can't be an option because each week that passes she adds 3 more paintings and since one input has 3 outputs, its not a function.

5. the number of weeks is the input value and number of paintings is the output value as you can later SEE how many paintings she has, not how many weeks it took her.

Answer:

(B, C, D)

Step-by-step explanation:

This scenario can be represented using this equation:

y = 3x + 7

y = total paintings after # of weeks (dependent variable)

x = # of weeks (independent variable)

3 = 3 paintings per week

7 = initial number of paintings

Let's evaluate each answer choice:

"The independent variable is represented by the ouput values"

No, this is wrong. The indepedent variable is the input values.

"The dependent variable is the total number of paintings"

This is correct. The total # of paintings is the output value, or the dependent variable.

"The total number of paintings depends on the number of weeks that have passed"

This is correct. The total # of paintings is the output value, or the dependent variable, because it depends on the # of weeks that pass by.

"This scenario is a function because for each week that passes, there will be exactly one total number of paintings"

This is correct. There is only one possible output for each input.

"The number of weeks is the output value"

No, this is wrong. The total # of paintings is the output value, not the # of weeks.

Hope it helps (●'◡'●)

Answer:

x = 14

Step-by-step explanation:

45 = 3(x + 1)

Distribute the 3

3(x) = 3x

3(1) = 3

We now have 45 = 3x + 3

Subtract 3 from both sides

45 - 3 = 42

3 - 3 cancels out

We now have 42 = 3x

Divide both sides by 3

42/3 = 14

3x / 3 = x

We're left with x = 14

Answer:

x = 14

Step-by-step explanation:

45 = 3(x + 1)

Distribute

45 = 3x + 3

-3           -3

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

42 = 3x

----    ----

3       3

14   =  x

Answer:

She has 9 choices for each different cheese.

For each of these cheeses there are 9 different wines,

So 9 * 9 = 81 and there are

81 possible different choices

Answer:

The experimental factor is the drug to alleviate inflammation paste form

Step-by-step explanation:

An experimental factor is an independent variable that is being controlled by the experimenter which are the input values which the experimenter sets specifically

In the given experiment, two teams, Team A and Team B are administered different treatments (inputs)

Team A is administered the paste form of the drug being experimented

Team B is administered a similar paste with no active ingredient

Therefore, the experimental factor is the drug being administered in paste form

Answer:

Step-by-step explanation:

by considering  2 + 3 = 95

3² = 9

2 + 3 = 5      

by considering  4 + 5 = 259

5² = 25

4 + 5 = 9  

by considering  6 + 7 = 4913

7² = 49

6 + 7 = 13  

by considering  8 + 9 = ????

9² = 81

8 + 9 = 17  

∴ 8 + 9 = 8117

B)  p and the q are switched

C) Neither p or q is negated

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

Explanation:

The original conditional "if P, then Q" has P and Q swap places to form the converse. So the converse would be "if Q, then P". We don't negate P, and we don't negate Q either.

Here is the full list

Side notes:

Answer:

0.4

Step-by-step explanation:

consider this like some lines overlapping each other.

one line (A) is 0.5 long, the other (B) 0.4 long.

together they are 0.8 long.

that means that they overlap at a length of 0.1 (they share a segment 0.1 long).

of the combined line of 0.8 that has 0.1 of a joined segment, the complimentary part of B is therefore 0.4 (0.8 minus the original length of B).

³√5 / ⁴√5 = ¹²√5 = 5^1/12

5^1/12

Answer:

the answer is  5/|1 5

Step-by-step explanation:

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3.

Answer:

-3,4 are the TWO integers whos product is -12 and whose sum is 1.

Step-by-step explanation:

-3×4=12

-3+4=1

Answer:

24.5 inches need to be cut

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Let m represent Mark's age and j represent Jeffrey's age.

Mark is five years older than Jeffrey. Hence:

[tex]m=j+5[/tex]

The sum of Mark's age and triple Jeffrey's age is 73. In other words:

[tex]m+3j=73[/tex]

We can substitute:

[tex](j+5)+3j=73[/tex]

Therefore, our answer is C.

Answer:

[tex]Bike = 7[/tex]

[tex]Car = 8[/tex]

[tex]Walk = 9[/tex]

[tex]Bus = 12[/tex]

Step-by-step explanation:

Given

[tex]Bus = 120^o[/tex]

[tex]Walk = 90^o[/tex]

[tex]Car = 80^o[/tex]

[tex]n = 36[/tex] --- pupils

Required

Determine the number of students in each category

This is calculated by dividing the measure of each category by 360; then multiply the result by the number of pupils:

So, we have:

[tex]Bus = \frac{120}{360} * 36 = \frac{1}{3} * 36 = 12[/tex]

[tex]Walk = \frac{90}{360} * 36= \frac{1}{4} * 36 = 9[/tex]

[tex]Car = \frac{80}{360} * 36 = \frac{80}{10} = 8[/tex]

To calculate the number of students that travel by bike, we have:

[tex]Car + Bike + Walk + Bus= n[/tex]

Substitute values

[tex]8 + Bike + 9+ 12= 36[/tex]

Collect like terms

[tex]Bike = 36 - 8 - 9 - 12[/tex]

[tex]Bike = 7[/tex]

Answer:

Look at picture

Step-by-step explanation:

Answer:

wht yr u in tis is too hard yk

Step-by-step explanation:

[tex] \sf Q) \: 19^{2} + 21^{2} = {?}[/tex]

[tex] \sf \to 19^{2} + 21^{2} [/tex]

[tex] \sf \to 361 + 441[/tex]

[tex] \sf \to 802[/tex] is the solution.

Answer:

m = -1

y intercept = -6

Step-by-step explanation:

The given equation of the line is ,

[tex]\implies y = -x -6[/tex]

We know that the Standard equation of Slope Intercept Form of the line is,

[tex]\implies y = mx + c[/tex]

Where ,

On comparing to the Standard form of the line we get ,

[tex]\implies Slope = -1 [/tex]

[tex]\implies y - intercept= -6 [/tex]

Slope: -1

Hope it helps.

Do comment if you have any query.

Answer:

x=14

y=24

Step-by-step explanation:

4y+42=8y-54

4y-8y=54-42

-4y/4=96/-4

y=24

solving for x

5x-28=7x-56

5x-7x=-56+28

-2x/-2=-28/-2

x=14