Solve the equation 12 + 2x = 16

Answer: (x,y)=(-2/3,15)

Negative 2 over three

Answer:

For addition and subtraction, use the standard + and - symbols respectively. For multiplication, use the * symbol. A * symbol is not necessary when multiplying a number by a variable. For instance: 2 * x can also be entered as 2x. Similarly, 2 * (x + 5) can also be entered as 2(x + 5); 2x * (5) can be entered as 2x(5). The * is also optional when multiplying with parentheses, example: (x + 1)(x - 1).

Step-by-step explanation:

Its right?

Answer:

cancel out as much of the equation as possible by doing inverse operations so add the 7 to both sides

x2 + 2x = 7

Divide by 2

x2 = 3.5

divide by 2 again

x = 1.75

now change x with 1.75 to check

1.75 x 2 = 3.5

3.5 + 3.5 - 7 = 0 so 1.75 is correct

Hope this helps

Step-by-step explanation:

Answer:

Initial value is 100

Step-by-step explanation:

A) rate of change would be dividing the number of songs wanted (100) by the number of weeks downloading (5)

100/5 = 20

 since the total quantity wanted is becoming less every week the rate of change would be negative so it becomes -20

Initial value is 100, which is the total number of songs they want

Answer:

Part A: 

initial value = 100 (total amount of songs to download)

rate of change = -20 songs/week (100-80 and so on)

Part B: 

y = -20x + 100

Answer:

D

Step-by-step explanation:

3x-4y=6

-4y=-3x+6

y=(3/4)x-(3/2)

positive slope with y-intercept at -3/2 corresponds to D

Graph includes the points (0,-3/2) and (2,0). Therefore, option D is the correct answer.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

The given linear equation is 3x-4y=6

Graph the line using the slope and y-intercept, or two points.

Slope: 3/4

y-intercept:

(0,-3/2)

Plot the points (0,-3/2) and (2,0)

Therefore, option D is the correct answer.

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Answer:

1/15

Step-by-step explanation:

Jesse drives to work. The distance Jesse’s car travels (d) on a number of gallons of gas (g) is given by the equation d = 15g. The constant of proportionality in terms of distance traveled per gallon of gas is 1/15.

the equation is...

d=15g

Now lets solve for 1 gallon of gas

d=15g

d=15(1)

d=15

This means that for every 1 gallon of gas, 15 (insert missing unit of distance here) can be driven.

15/1=15

1/15

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Answer:

D

Step-by-step explanation:

last one.

if a vertical line cuts the curve at more than one points ,then it is not a function.

Answer:

I agree that it is D

Step-by-step explanation:

Answer:

Correct option: 2 -> sqrt(37)

Step-by-step explanation:

To solve this problem, we just need to use the law of cosines. This law is used to find the third side of a triangle, when we have the two other sides and the angle between them.

The equation of the law of cosines is:

c^2 = a^2 + b^2 - 2 * a * b * cos(C)

So, we have that:

c^2 = 7^2 + 3^2 - 2 * 7 * 3 * (1/2)

c^2 = 49 + 9 - 21

c^2 = 37

c = sqrt(37)

Correct option: 2

Answer:

Step-by-step explanation:

definitely A

Answer:

Option 1) is correct

Step-by-step explanation:

Given: The graph shows the distance in miles, m, hiked from a camp in h hours.

To find: hourly interval that had the greatest rate of change

Solution:

Rate of change between two points refers to the vertical change divided by the horizontal change.

For hour 0 to hour 1:

rate of change = [tex]\frac{2-0}{1-0}=2[/tex]

For hour 2 to hour 3:

rate of change = [tex]\frac{4.5-3.5}{3-2}=1[/tex]

For hour 1 to hour 2:

rate of change = [tex]\frac{3.5-2}{2-1}=1.5[/tex]

For hour 3 to hour 4:

rate of change = [tex]\frac{5-4.5}{4-3}=0.5[/tex]

So, rate of change is greatest in interval: hour 0 to hour 1

The greatest rate of change between the interval 0 to 1 hour.

Given that,

The graph below shows the distance in miles, m, hiked from a camp in h hours.

We have to determine,

Which hourly interval had the greatest rate of change?

According to the question,

The greatest rate of change between the interval is determined by the rate of change between two points refers to the vertical change divided by the horizontal change.

1. The rate of change between 0 to 1 hours is,

[tex]\rm Rate \ of \ change = \dfrac{2-0}{1-0}\\\\ Rate \ of \ change= \dfrac{2}{1}\\\\ Rate \ of \ change= 2[/tex]

The rate of change between 0 to 1 hour is 2.

2. The rate of change between 2 to 3 hours is,

[tex]\rm Rate \ of \ change = \dfrac{4.5-3.5}{3-2}\\\\ Rate \ of \ change= \dfrac{1}{1}\\\\ Rate \ of \ change= 1[/tex]

The rate of change between 2 to 3 hours is 1.

3. The rate of change between 1 to 2 hours is,

[tex]\rm Rate \ of \ change = \dfrac{3.5-2}{2-1}\\\\ Rate \ of \ change= \dfrac{1.5}{1}\\\\ Rate \ of \ change= 1.5[/tex]

The rate of change between 1 to 2 hours is 1.5.

4. The rate of change between 3 to 4 hours is,

[tex]\rm Rate \ of \ change = \dfrac{5-4.5}{4-3}\\\\ Rate \ of \ change= \dfrac{0.5}{1}\\\\ Rate \ of \ change= 0.5[/tex]

The rate of change between 2 to 3 hours is 1.

Hence, The required greatest rate of change between the interval 0 to 1 hour.

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Answer:

B

Step-by-step explanation:

A is false. 0 + 1 - 2 = -1, not 0.

B is true.

(-2)-(-2) +0

= -2 + 2 + 0

= 0

C is false, since B is true.

Equation B 0=(-2)-(-2) +0 is true, which is simplified by subtraction.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

For equation A:

0 = 0+1-2

We can simplify the right-hand side of the equation by combining like terms:

0 = -1

This is not true, so we might be tempted to say that equation A is false.

For equation B:

0 = (-2)-(-2) + 0

We can simplify the right-hand side of the equation by performing the subtraction:

0 = 0 + 0 + 0

This simplifies to:

0 = 0

This equation is true.

Therefore, equation B is true.

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Answer:

6

Step-by-step explanation:

We can make:

A 3 sided shape and a 13 sided shape (3 + 13 = 16)

A 4 sided shape and a 12 sided shape (4 + 12 = 16)

A 5 sided shape and an 11 sided shape

A 6 sided shape and a 10 sided shape

A 7 sided shape and a 9 sided shape

2 8 sided shapes

Therefore the answer is 6.

Answer:

All of the angles are 60°, because 180÷3 is 60. so the measure of angle b plus the measure of angle a and angle c is equal to 180°. The measure of angle a + 120° is 180

Answer:

See below

Step-by-step explanation:

a and 120 form a straight line so they add to 180

a + 120 = 180

Subtract 120 from each side

a = 180-120

a = 60

The sum of the angles of a triangle add to 180

b+ a + 60 =180

b + 60 + 60 = 180

b+120 = 180

Subtract 120 from each side

b = 180-120

b = 60

Answer:

D

Step-by-step explanation:

This net when folded, will become a triangular prism, which is only represented by option D.

Answer:

Step-by-step explanation:

solve for v:  simplifying both sides of the equation, then the variable.

Exact Form:

v= 1/3

Decimal Form:

v=0.3

Answer:

x = - 5, x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given

(2x - 1)(x + 5) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

Answer:

x = - 5, x = 1/2

Step-by-step explanation:

(2x - 1)(x + 5) = 0

x + 5 = 0 so x = - 5

2x - 1 = 0 so 2x = 1 so x = 1/2

Answer:

Step-by-step explanation:

the answer is 15!

The square root of the number -√75 will be -3√5.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The square root of the number will be calculated as below:-

-√75 = - √( 3 x 3 x 5 )

        = -3√5

Therefore, the square root of the number -√75 will be -3√5.

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Answer:

-8y^7 - 5y^6 + 9y^5 + 3y^4 - 4y^3

Step-by-step explanation:

Please be sure to use " ^ " to indicate exponentiation.  Then,

your 9y5−4y3−8y7−5y6+3y4 becomes 9y^5 - 4y^3 - 8y^7 - 5y^6 + 3y^4.

We must now write that in descending order by powers of y:

-8y^7 - 5y^6 + 9y^5 + 3y^4 - 4y^3

Answer:

the answer is A

Step-by-step explanation:

Answer:

There are 616 total students

Step-by-step explanation:

boys : girls: total

5           3      5+3 = 8

There are 385 boys

385/5 = 77

Multiply each term by 77

boys : girls: total

5*77  3*77   8*77

385    539    616

There are 616 total students

Answer:

616 total students

Step-by-step explanation:

5 : 3

385 : x

5 x 77 : 3 x 77

385 : 231

385 + 231 = 616

Answer:

Step-by-step explanation:

1). Segment AB = [tex]\overline{AB}[/tex] (Option D)

   Segments are represented by an over-line/bar on the segment.

2). Length of segment AB = AB (Option B)

3). MN = 7 (Option C)

   Since the measure of segments MN and KL are equal from the figure attached.

4). [tex]\overline{KL}[/tex] is congruent to [tex]\overline{MN}[/tex]

   Given in the figure attached.

Answer:

1) Segment AB =d

2) Length of segment AB = b

3)MN=c

4) [tex]\widehat{KL}[/tex] is congruent to = a

Step-by-step explanation:

We are supposed to match the items

Options:

a.[tex]\widehat{MN}[/tex]

b. AB

C. 7

d. [tex]\widehat{AB}[/tex]

1) Segment AB

So, D option denotes the segment

So, 1) Segment AB =  [tex]\widehat{AB}[/tex]

2) Length of segment AB = Option b

So, Length of segment AB =AB

4) [tex]\widehat{KL}[/tex] is congruent to

So, referring the given figure we can say

[tex]\widehat{KL}[/tex] is congruent to [tex]\widehat{MN}[/tex]

So, [tex]\widehat{KL}[/tex] is congruent to option a

3)MN

Since [tex]\widehat{KL}[/tex] is congruent to [tex]\widehat{MN}[/tex](by 4)

So, KL = MN = 7

So, MN = 7

So, MN = option c

Hence

1) Segment AB =d

2) Length of segment AB = b

3)MN=c

4) [tex]\widehat{KL}[/tex] is congruent to = a

Answer:

the answer is20 inches

Step-by-step explanation:

a square has 4 sides so you divide the total of 80 by 4.

80÷4=20

The lines in the picture parallel because they are equal width apart , option (D) is correct.

Two straight lines in a plane such that even on getting extend till infinity they do not intersect each other and always at same distance from each other .

In the given picture the red line and black lines appears to have same distance between them .They are parallel not only because they are coplanar as coplanar lines can intersect each other.

Two lines travelling to infinity need not to be parallel always as they can intersect at some point and still travel to infinity.

If two lines of same size are there still they can have different perpendicular distance between them at diff points, they can be slightly tilted towards each other . Therefore they need not be parallel when they are of same size. And given lines are infinite therefore we cannot say that they are of same size also.

If two lines are equal width apart and never meet then it means the distance between them is always same therefore they are parallel,

Therefore, the lines in the  picture are parallel because they are equal width apart option (d) is correct.

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Answer:

Radius, r = 3.8 inch

Step-by-step explanation:

A roll of gift-wrapping paper can cover 232.2 sq. in. Jimmy wants to wrap a soccer ball that he is giving as a gift.

We need to find the maximum radius of the ball that Jimmy can wrap. The volume of a spherical shaped object is given by :

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

r = radius of the ball

[tex]r=(\dfrac{3V}{4\pi})^{1/3}\\\\r=(\dfrac{3\times 232.2}{4\times 3.14})^{1/3}\\\\r=3.8\ \text{inch}[/tex]

So, the maximum radius of the ball that Jimmy can wrap is 3.8 inches. Hence, this is the required solution.

The maximum radius of the ball that Jimmy can wrap is 3.8 inches.

The maximum radius of the ball is calculated from volume of a sphere.

V = ⁴/₃πr³

where;

232.2 = ⁴/₃πr³

3(232.2) = 4πr³

696.6 = 4πr³

r³ = 696.6/4π

r³ = 55.433

r = (55.433)^¹/₃

r = 3.8 in

Thus, the maximum radius of the ball that Jimmy can wrap is 3.8 inches.

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Step-by-step explanation:

Explanation:

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle. The intercepted arc might be thought of as the part of the circle which is "inside" the inscribed angle. (See the pink part of the circle in the picture above.)

A central angle is any angle whose vertex is located at the center of a circle. A central angle necessarily passes through two points on the circle, which in turn divide the circle into two arcs: a major arc and a minor arc. The minor arc is the smaller of the two arcs, while the major arc is the bigger. We define the arc angle to be the measure of the central angle which intercepts it.

The Inscribed Angle Conjecture I gives the relationship between the measures of an inscribed angle and the intercepted arc angle. It says that the measure of the intercepted arc is twice that of the inscribed angle.

The precise statements of the conjectures are given below. Each conjecture has a linked Sketch Pad demonstration to illustrate its truth (proof by Geometer's Sketch Pad!). The linked activities sheet also include directions for further "hands on" investigations involving these conjectures, as well as geometric problems which utilize their results.

The precise statement of the conjectures:

Conjecture (Inscribed Angles Conjecture I ): In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc..



Corollary (Inscribed Angles Conjecture II ): In a circle, two inscribed angles with the same intercepted arc are congruent.



Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.

Corollary (Inscribed Angles Conjecture III ): Any angle inscribed in a semi-circle is a right angle.



Proof: The intercepted arc for an angle inscribed in a semi-circle is 180 degrees. Therefore the measure of the angle must be half of 180, or 90 degrees. In other words, the angle is a right angle.

Answer:

x=10.93 or 10.9

Step-by-step explanation:

To find x we use sin

sin(40) = 0.6427876097  then * 17

= 10.9273

= 11

We can check and plug in answer as inverse to find other side

11/sin (40degree) x (90 degree) = 17.11

If we plug in the original 10.9273 we actually find 17

So we should show the correct amount 10.9273 and if rounding try 10.93

10.93/sin (40 degree) x sin (90 degree) = 17.00

Answer:

Total Students = 3a - 2b

Step-by-step explanation:

Given

Students in drama club = a

There are twice as many students in cooking club as in drama club;

So, Students in cooking club = 2a

Members of both clubs = b

Required

Expression for total students in cooking or drama club but not both;

To do this, number of students in individual clubs need to be calculated;

Let Students in drama club only  be represented by D and Students in cooking club only be represented by C

So,

D = Students in drama club - Members of both clubs

D = a - b

Similarly,

C = Students in cooking club - Members of both clubs

C = 2a - b

So, total students in cooking or drama club but not both D + C

Total students = a - b + 2a - b

Collect like terms

Total Students = a + 2a - b - b

Total Students = 3a - 2b

Answer:

C. 1/4 and q=4.

Step-by-step explanation:

I just got it correct on my test.

p=1/4 and q=4 which is correct option(c)

Slope of line is defined as the angle of line.

Let us get the equation of the two graphs

General equation form is;

y = mx + b

m is slope and b is the y-intercept

For the first one;

y intercept is -3

So the equation is;

y = mx -3

The x-intercept is 3/4

the value of y at the x-intercept is 0

0 = 3/4m -3

3/4m =3

m = 4

so, 4 × p

4p

q added to y-intercept;

q -3

Let us get the equation of the second plot

y-intercept is 1

Equation is;

y = mx +1

We can get slope using x-intercept

x-intercept is -1

0 = -1m +1

m = 1

So;

4p = 1

p = 1/4

For the value of q;

q -3 = 1

q = 1+3 = 4

Hence, p=1/4 and q=4

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Answer: -1.6 is not a possible r-value.

Step-by-step explanation:

R-values range from -1 to +1. Out of all these numbers, -1.6 does not belong. Hence, -1.6 is not a r-value.