What is the perimeter of a rectangle with a 7-inch width and a 16-inch length?

Answer:

20 inches squared

This is because the area of a triangle is height times base divided by 2.

So it is 10*4/2, so the answer is 20 inches squared.

The area of the right angle triangle is 20 square inches.

The area of a right angle triangle is given by the formula,

Area = 1/2 * base * height .

where the base and height are the legs of the given triangle.

It is given that the legs of a right triangle measure 10 inches and 4 inches.

Thus we have the base of the triangle as 4 inches and height of the triangle as 10 inches.

  Area = 1/2 * 4 * 10 square inches .

∴ Area =  20 square inches.

Therefore, the area of the right angle triangle is 20 square inches.

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Answer:

$57.75

Step-by-step explanation:

If 11 books cost $42.35,

11b=42.35

b=42.35/11

b=3.85

15 books will cost 15b.

15b

= 15*3.85

= 57.75.

15 Books will cost $57.75.

Answer:

57.75

Step-by-step explanation:

First I found the unit rate by dividing 42.35 by 11, which is 3.85.

second i multiplied the unit rate by 15 and got 57.75

Answer:

A. 36

Step-by-step explanation:

65+79=144

180-144=36

Answer: A

Step-by-step explanation:

Answer:

Angle measurements of 35°, 35°, and 110°

Angle measurements of 40°, 60°, and 80°

Step-by-step explanation:

If you specify only the three angles, you can have an infinite number of similar triangles of different sizes.

A is wrong. There can be only one triangle in which all three side lengths are specified.

C is wrong. The angles do not add up to 180°.

The descriptions which can describe more than one triangle is:

a)

Side lengths 6 ft, 8 ft and 10 ft.

First we check whether it form a triangle or not:

6+8=14>10

8+10=18>6

and

6+10=16>8

Yes, these side lengths form a triangle.

With the help of this only one unique triangle is possible.

b)

angle measurements of 35°,35° and 110°

First we check the sum of the angles:

35°+35°+110°=180°

Hence, more than one triangle is possible.

c)

angle measurements of 30°,40° and 50°

First we check the sum of these angles:

30°+40°+50°=120°≠180°

Hence, these angles measure do not form a triangle.

d)

angle measurements of 40°,60° and 80°

First we check the sum of these angles:

40°+60°+80°=180°.

Hence, more than one triangle is possible.

e)

side length of 4 cm, 6 cm and 9 cm.

First we check whether it form a triangle or not:

4+6=10>9

6+9=15>4

and

4+9=13>6

Hence, a unique triangle will be formed.

Answer:

So length is 7 in while width is 1 in.

Step-by-step explanation:

We are given W is 6 inches less than L which mean as an equation we have W=L-6.

We are given the area of this rectangle, LW=7.

So we have the system:

W=L-6

LW=7.

Replace the second W with what the first W equals:

LW=7

L(L-6)=7

Distribute:

[tex]L^2-6L=7[/tex]

Subtract 7 on both sides:

[tex]L^2-6L-7=0[/tex]

We are luck since the coefficient of L^2 is 1.  This means all we have to do is find two numbers that multiply to be -7 add at the same time add up to -6.

Those numbers are -7 and 1 since (-7)(1)=-7 and (-7)+(1)=-6.

So the factored form of our equation is:

(L-7)(L+1)=0

This gives us two equations to solve:

L-7=0  or L+1=0

L=7     or L=-1

L=-1 doesn't make sense for a length so L=7.

L=7 means the length is 7 inches.

If W=L-6 and L=7, then W=7-6=1.

The width is 1 inch since W=1.

So length is 7 in while width is 1 in.

Answer:I think it is 5000x32

Step-by-step explanation:

10,000 divided by 2 is 5,000

64 divided by 2 is 32

5,000 can’t go down into 100 the same amount of times for 32 to get to 8

The simplified form of 10,000 x 64 are,

⇒ 100x⁸

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

To find simplified form of √10,000x⁶⁴

Since, We can simplify as;

⇒ √10,000x⁶⁴

⇒ √(100)² (x⁸)²

⇒ 100x⁸

Thus, The simplified form of 10,000 x 64 are,

⇒ 100x⁸

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6x + 2 + 40 = 90

Let x = the unknown

6x + 42 = 90

6x = 90 - 42

6x = 48

x = 48/6

x = 8

Answer:

x=8

Step-by-step explanation:

We know that 40 + (6x+2)  +90 = 180   since the three angles form a straight line

40 + (6x+2)  +90 = 180

Combine like terms

132 + 6x = 180

Subtract 132 from each side

132-132 +6x= 180-132

6x = 48

Divide each side by 6

6x/6 = 48/6

x = 8

Answer:

x = 50

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 2 given angles in the lower triangle and subtract from 180 to find the third angle

third angle = 180° - (65 + 65)° = 180° - 130° = 50°

x = third angle = 50 ( vertical angles )

A triangle has to have three angles and they have to add up to 180 degrees so,

65+65=130

180-130=50

X=50 degrees because it is equal to the third angle.

Answer:

120 degrees

Step-by-step explanation:

You can just eyeball that it is greater than 90 degreees so it must be 120 degrees.

Answer:

Question 6: 6.8

Question 7: 8295

Step-by-step explanation:

Question 6:

Let's say that each hamburger costs x amount of dollars, and each soda costs y amount of dollars. For the first statement, we purchase 7 hamburgers (so 7 times x) and 3 sodas (3 times y) to add up to 27.95. As an equation, this means that 7x+3y=27.95. Similarly, for the second statement, 5x+4y=23.40.

Putting these two side by side, we get:

7x+3y=27.95

5x+4y=23.40

Using Gauss-Jordan elimination, we can multiply the first equation by -4/3 and then add that to the second equation, resulting in

[tex]-13x/3 = 27.95*(-4/3)+23.40\\[/tex]

Simplifying, we get

[tex]-13x = 27.95*(-4)+23.4*3\\\\-13x = -41.6\\\\x=3.2[/tex]

Question 7:

Take the number of students as x and the number of teachers as y. There are 35 times as many students as there are teachers, so 35y=x. We know that the students and teachers added up equal 8544-12=8532 (as 12 seats are empty in the auditorium that can seat 8544, 8532 must be occupied), so x+y= 8532. Since 35y=x, 35y+y+8532, 36y=8532, and y= 237. Since the number of students is equal to x, and x=35y, 35*y=35*237=8295 students.

Answer:

60

Step-by-step explanation:

We are given the triangles are congruent, that means the angles are the same measurement

<A = <X

<B = <Y

<C = <Z

We know A = 50  so X = 50

We know <Y = 70 so < B = 70

The three angles of a triangle add to 180

<A + <B + <C = 180

Substituting into the equation

50 + 70 + <C = 180

Combining like terms

120 + <C =180

Subtracting 120 from each side

120-120 +<C =180-120

<C = 60

Answer:

∠C = 60°

Step-by-step explanation:

Corresponding angles are congruent, thus

∠B = ∠Y = 70°

The sum of the 3 angles in ΔABC = 180°

∠C = 180° - (70 + 50)° = 180° - 120° = 60°

Answer:

The domain would be 0 to 4 seconds

Step-by-step explanation:

According to the given conditions a ball was lying on the ground but when it was hit by Vanessa it was in the air for 4 seconds. We have to find the domain.

We know that the domain is the input values. According to the given statement it would start at time 0 and end when it hit the ground at 4 seconds.

Therefore the domain would be 0 to 4 seconds.

[0,4] ....

a system of linear equations with infinite solutions, is simply one that has the same equation twice, but but but, one of the equations is in disguise.

so, say we can just  hmmm multiply the coefficient of the "x" variable, which is the slope, by something that gives us 1, recall same/same = 1, hmmm say let's multiply it by hmmmm 7/7.

[tex]\bf y=\cfrac{2}{3}x-5\implies \stackrel{\textit{multiplying the slope by }\frac{7}{7}}{\cfrac{2}{3}\cdot \cfrac{7}{7}\implies \cfrac{14}{21}}\implies \stackrel{\textit{so we get this equation}}{y=\cfrac{14}{21}x-5}[/tex]

now, let's notice that 14/21 simplifies to 2/3, so is really the same slope and the same y-intercept.

so if we use those two equations in a system of equations and graph them, what happens is, the first one will graph a line, the second one will graph another line BUT right on top of the first one drawn, so the two lines will just be pancaked on top of each other, making every point in each line, "a solution", since they're meeting at every point, and since lines go to infinite, "infinitely many solutions".

Answer:

Sample Response/Explanation: To have an infinite number of solutions, the equations must graph the same line. That means the equations must be equivalent. To form an equivalent equation, use the properties of equality to rewrite the given equation in a different form. Add, subtract, multiply, or divide both sides of the equation by the same amount.

Step-by-step explanation:

Answer:

a) maximum height is 156.25 ft

b) 6 seconds

Step-by-step explanation:

a) The maximum height can be found by finding the y-coordinate of the vertex. The vertex is the highest point in a parabola opened downward.

I start with by finding the t-coordinate of the vertex.

The t-coordinate of the vertex is [tex]\frac{-b}{2a}[/tex] where the expression [tex]-16t^2+92t+24[/tex] will need to be compared to [tex]at^2+bt+c[/tex].

We see that [tex]a=-16,b=92,c=24[/tex].

So the t-coordinate of the vertex is [tex]\frac{-b}{2a}=\frac{-92}{2(-16)}=\frac{-92}{-32}=\frac{23}{8}[/tex].

We can find the h, the height, that corresponds to this t by using the equation [tex]h=-16t^2+92t+24[/tex] where [tex]t=\frac{23}{8}[/tex].

So inserting 23/8 for [tex]t[/tex].

[tex]-16(23/8)^2+92(23/8)+24[/tex]

Plugging into calculator gives you 625/4.

So the maximum height is 625/4 or 156.25.

b) Let's find how long it takes the ball to hit the ground. If the ball is on the ground, then the distance between the ball and the ground is 0.  So we are looking to solve h(t)=0 for t.

So this is equation we are solving for t:

[tex]-16t^2+92t+24=0[/tex]

These numbers are big but since all the terms have a common factor we can make them slightly smaller.

That is, we are going to divide both sides by -4 and see

[tex]4t^2-23t-6=0[/tex]

It looks like it could be possible to factor.

a=4

b=-23

c=-6

We need to find two numbers that multiply to be ac and add up to be b.

a*c=4(-6)=-24

b=-23

So -24=-24*1 and -23=-24+1.

We are going to replace -23t with -24t+1t giving up something that should be factorable by grouping.

[tex]4t^2-23t-6=0[/tex]

[tex]4t^2-24t+1t-6=0[/tex]

Group the first 2 together and group the last two together:

[tex](4t^2-24t)+(1t-6)=0[/tex]

Factor what you can from each pair:

[tex]4t(t-6)+1(t-6)=0[/tex]

Now each term has a common factor of (t-6) so factor that out giving you:

[tex](t-6)(4t+1)=0[/tex]

Set both factors equal to 0 giving you

t-6=0              or               4t+1=0

  t=6               or               4t  =-1

  t=6               or                 t=-1/4

So it hit the ground in 6 seconds.

Final answer:

The maximum height of the ball is calculated to be at 2.875 seconds, and by inserting this time back into the height function, we get the max height. To determine when the ball hits the ground, we solve the quadratic function for when h(t) equals zero, finding that it occurs at approximately 5.4 seconds post launch.

Explanation:

To calculate the maximum height of the ball, we need to find the vertex of the quadratic function, which gives us the time when the maximum height is reached. The function is in the form h(t) = -16t^2 + 92t + 24. The time at which the maximum height occurs can be found using the formula -b/(2a), where a and b are coefficients from the quadratic function. Here, a = -16 and b = 92, so the time is t = -92/(2*(-16)) = 92/32 = 2.875 seconds. Inserting this back into the height function gives us the maximum height:

h(2.875) = -16(2.875)^2 + 92(2.875) + 24

Now, to find when the ball hits the ground, we need to find the positive root of the height function where h(t) = 0. The quadratic formula h(t) = -16t^2 + 92t + 24 is used to find the time values when the ball is at the ground level. Solving this equation, we get two possible times, and we're interested in the positive one since time cannot be negative.

Thus, we get that the ball reaches the ground at approximately 5.4 seconds.

Answer:

The range is all real numbers.

The domain is all reals numbers that are greater than -4.

Step-by-step explanation:

[tex]y=\log_3(x+4)[/tex] only exists when [tex]x+4[/tex] is positive.

You can take the log of a negative or 0 number.

So [tex]x+4>0[/tex] implies [tex]x>-4[/tex].  (I just subtract 4 on both sides.)

So the domain is x>-4. You should see this also when you graph the curve that the curve only exist to the right of -4.

Now the range.  The range is where the curve exist for the y-values.

The equivalent exponent form of [tex]y=\log_3(x+4)[/tex] is [tex]3^{y}=x+4[/tex]

We can solve this for x be subtract 4 on both sides:

[tex]x=3^y-4[/tex]

Now here y can be anything; there are no restrictions on the exponent.

Also if you look at the graph of [tex]y=\log_3(x+4)[/tex] you should see every y getting hit by the curve (look down to up; use the y-axis as a guide).

Let's think about the inverse I found above a little more (I'm going to swap x and y).

[tex]y=3^x-4[/tex].

If we look at the domain and range of this we can just swap it to get the domain and range of [tex]y=\log_3(x+4)[/tex].

[tex]y=3^x-4[/tex] is an exponential function of 3^x that has been moved down 4 units.

The range since it has been moved down 4 units is [tex](-4,\infty)[/tex].

The domain of an exponential function is all real numbers.  There are no restrictions on what you can plug in for x.

So swapping these to find the domain and range of [tex]y=\log_3(x+4)[/tex]:

Domain:  [tex](-4,\infty)[/tex]

Range : [tex](-\infty,\infty)[/tex]

Answer: For Edg is x> -4

And for the second on it is all real numbers

Answer:

2.5(x + 2y - 1).

Step-by-step explanation:

2.5x + ( 5y) -2.5

2.5x + 5y - 2.5  (we can just remove the parentheses without changing the value of the expression)

Each coefficient is divisible by 2.5 so by the distributive law:

2.5x + 5y - 2.5

= 2.5(x + 2y - 1).

By factorization of 2.5x + ( 5y) -2.5, the result is as follows-

2.5(x + 2y -1) is the expression equivalent to 2.5x + ( 5y) -2.5

What is factorization?

At first it is important to know about algebraic expression.

Algebraic expression consists of numbers and variables connected with addition, subtraction, multiplication and division.

Factorization is the process of breaking down of an algebraic expression into a product of algebraic expressions of smaller degree. Each smaller degree algebraic expressions are called factors.

Here,

2.5x + 5y - 2.5

2.5(x + 2y -1)

An expression that is equivalent to 2.5x + ( 5y) -2.5 is

2.5(x + 2y -1)

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Answer:

2

Step-by-step explanation:

because 2*2*2*2is equal to 16

The real fourth roots of 16 are: 2 and -2.

The detailed answer explains how to find the real fourth roots of 16 step by step, providing a clear solution.

The question: Find all real fourth roots of 16.

Step-by-step explanation:

Hi! It will be a pleasure to help you finding the solution to this problem, so let's solve each part:

[tex]\boxed{A. \ 1.50h+4}[/tex]

From the problem, we know the following data of the problem:

Our goal is to find the the expression for the total cost for parking at the beach for h hours. So:

Step 1: Since we have a fixed price, this value will appear in our expression:

[tex]4[/tex]

Step 2: Since Laval paid $1.50 for each hour, this can be represented as the following expression:

[tex]1.50h[/tex]

Finally, we can write total cost (C) as the sum of these two expressions:

[tex]C=1.50h+4[/tex]

Finally, our correct option is A:

[tex]\boxed{1.50h+4}[/tex]

5 hours

Here we have to find how many hours Laval spent at the beach knowing that he paid a total amount of $11.50. From the previous part, we know that our expression is:

[tex]C=1.50h+4 \\ \\ For \ C=11.50 \\ \\ 11.50=1.50h+4 \\ \\ Subtracting \ 4 \ from \ both \ sides: \\ \\ 11.50-4=1.50h+4-4 \\ \\ 7.5=1.50h \\ \\ Dividing \ both \ sides \ by \ 1.50 \\ \\ h=\frac{7.5}{1.50}=5[/tex]

Finally, he spent 5 hours at the beach

Answer:

Part A)

1) The graph in the attached figure N 1

2) The coordinate rule is (x,y) -----> (x,y+10)

3) The translation of the function up 10 units means that the initial deposit is $60 instead of $50

Part B)

1) The graph in the attached figure N2

2) The coordinate rule is (x,y) -----> (x-10,y)

3) The translation of the function right 10 units means that the initial deposit is equal to $10

Part C)

1) In each translation, the slope is the same (m=5) are parallel lines

2) The vertical translation would be up 40 units

Step-by-step explanation:

we have

[tex]f(x)=5x+50[/tex]

where

f(x) --> represents Jeremy's account balance

x ---> the time in years

Part A)

The translation of the function is up 10 units.

The rule of the translation is equal to

(x,y) -----> (x,y+10)

so

The new function will be

[tex]f(x)=5x+50+10[/tex]

[tex]f(x)=5x+60[/tex]

The graph in the attached figure N 1

The translation of the function up 10 units means that the initial deposit is $60 instead of $50

Part B)

The translation of the function is right 10 units.

The rule of the translation is equal to

(x,y) -----> (x-10,y)

so

we have

[tex]f(x)=5x+60[/tex] ----> function Part A

The new function will be

[tex]f(x)=5(x-10)+60[/tex]

[tex]f(x)=5x+10[/tex]

The graph in the attached figure N 2

The translation of the function right 10 units means that the initial deposit is equal to $10

Part C)

1. Look at the translations, what characteristic of the graph stayed the same in each translation?

In each translation, the slope is the same

The slope m is equal to m=5  

Are parallel lines

2. Look at the original graph and the graph of the translation right 10 units. What vertical translation of the graph in Part B would put the graph back to its original position?

we have

[tex]f(x)=5x+10[/tex]

The vertical translation would be up 40 units

The rule of the translation is equal to

(x,y) -----> (x,y+40)

so

The new function will be

[tex]f(x)=5x+10+40[/tex]

[tex]f(x)=5x+50[/tex]

The translation of the original linear function, f(x) = 5·x + 50, gives the

following values;

Part A:

Part B:

Part C:

The function for the amount of money in the account is; f(x) = 5·x + 50

Part A

1. The graph of the translation of the above function up 10 units gives

the function;

f(x) + 10 = 5·x + 50 + 10 = 5·x + 60

f(x) + 10 = 5·x + 60

Please find attached the graph of the function translated up 10 units created with MS Excel

2. The coordinate rule for a translation up 10 units is; [tex]\underline{(x, \ y + 10)}[/tex]

3. The meaning of the translation up 10 units means that amount in the

account at a point in time is increased by $10

Part B;

1. The function, f(x) = 5·x + 50, translated 10 units to the right gives;

f(x + 10) = 5·(x + 10) + 50 = 5·x + 100

Please find attached the graph of the function translated right 10 units created with MS Excel

2. The coordinate rule is (x, y) [tex]\underrightarrow{T_{(10, \ 0)}}[/tex] [tex]\underline{(x + 10, \ y)}[/tex]

3. A translation of the function to the right, means that the point in time at

which the graph starts, the account balance is $100, such that Jeremy

the time the interest is applied is 10 years longer, than the original time

added to the number of years in the given function, f(x) = 5·x + 50

Part C

1. The characteristic of the graph that stays the same is the slope

2. The vertical translation in the graph of the translation right 10 units

compared to the original graph is 50 units.

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Answer:

C. 16

Step-by-step explanation:

The distance between two points on the number line is the absolute value of the difference of their coordinates.

If the coordinates of two points on the number line are a and b, then the distance between the two points is

d = |a - b|

The coordinates here are -9 and 7.

distance = |-9 - 7| = |-16| = 16

Answer:

so b=-9 while c=12.

Step-by-step explanation:

If you have x-intercepts 1 and -4, then that means f(1)=0 and f(-4)=0.

You are given [tex]f(x)=-3x^2+bx+c[/tex]

So you have the system of equations to solve:

[tex]f(1)=-3(1)^2+b(1)+c=0[/tex]

[tex]f(-4)=-3(-4)^2+b(-4)+c=0[/tex]

Evaluating the exponents:

[tex]-3(1)+b+c=0[/tex]

[tex]-3(16)-4b+c=0[/tex]

Doing a little bit of multiplying:

[tex]-3+b+c=0[/tex]

[tex]-48-4b+c=0[/tex]

Let's add 3 on both sides of equation 1 and 48 on both sides of equation 2:

[tex]b+c=3[/tex]

[tex]-4b+c=48[/tex]

Subtracting the equations will eliminate c.

Let's do that:

[tex]5b+0c=-45[/tex]

[tex]5b=-45[/tex]

Divide both sides by 5:

[tex]b=\frac{-45}{5}[/tex]

Simplify:

[tex]b=-9[/tex]

If b=-9 and b+c=3 then -9+c=3 implies c=9+3=12.

so b=-9 while c=12.

To find b and c for the parabola y=-3x^2+bx+c with x-intercepts 1 and -4, we express the equation in its factored form, then expand it. From the expansion, we see that b=-9 and c=-12.

To find the values of b and c in the equation y = -3x^2+bx+c, where the x-intercepts are given as 1 and -4, we use the following steps:

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Answer:

1.19x=12

Step-by-step explanation:

The 12 represents his budget and 1.19 is the cost of each song, x is the amount of songs.

Answer: [tex]1.19x=12[/tex]

Step-by-step explanation:

Given : Doug can download new songs for $1.19 each.

Let the number of songs downloaded be x .

Then the total cost of x songs will be :-

[tex]1.19x[/tex]

To find the number of songs he can download for $12.00 , we need to put [tex]1.19x[/tex] equals to 12.

We get, the equation to show how many songs he can download for $12.00 will be

[tex]1.19x=12[/tex]

Answer:

A

Step-by-step explanation:

we have g(x) = 5x+3  

we know that 5x=f(x)

so g(x)=f(x)+3  

thus g(x) is obtained by adding 3 units to f(x)  

that's means the graph of g is obtained by translating the parent function f by 3 units up

Answer:

Step-by-step explanation:

There are two functions f(x) = 5x and g(x) = 5x + 3

This parent function f(x) has been translated to form a new function g(x) = 5x + 3

These linear functions can be represented by two lines y = 5x and y' = 5x' + 3

So when we shift line y = 5x by 3 units up on the y-axis then a new graph of

y = 5x + 3 will be formed.

Therefore, Option A is the answer.

To simplify the expression sin² X - sinX - 2 / sinX - 2, we need to factor the numerator and denominator separately and then cancel out the common factor of sin(X) - 2. The equivalent expression is sin(X) + 1.

To simplify the given expression, we can factor the numerator and denominator separately and then cancel out common terms. The numerator can be factored as (sin(X) - 2) (sin(X) + 1), and the denominator can be factored as (sin(X) - 2). By cancelling out the common factor of (sin(X) - 2), we are left with (sin(X) + 1) as the equivalent expression.

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Answer:

y =  -2x^2 -4x +1

Step-by-step explanation:

y-3 = -2 (x+1)^2

Foil (x+1)^2

(x+1)(x+1) = x^2 +x+x+1 = x^2 +2x+1

Substitute this back in

y-3 = -2(x^2 +2x+1)

Distribute

y-3 = -2x^2 -4x -2

Add 3 to each side

y-3+3 = -2x^2 -4x -2+3

y =  -2x^2 -4x +1

Answer:

b. [tex]\frac{1}{y^3}[/tex]

Step-by-step explanation:

Here we are given  [tex]y^{-3}[/tex] and are asked to simplify it. We are going to apply the law of exponents which says that

[tex]a^{-n}=\frac{1}{a^n}[/tex]

Hence applying this rule in our problem we get, where a=y and n=3

[tex]y^{-3}=\frac{1}{y^3}[/tex]

Hence our C) Option is correct

Answer:

I think 12.

Step-by-step explanation:

Answer:

27 ham sandwiches

Step-by-step explanation:

Let

x ----> the number of turkey sandwiches

y ----> the number of ham sandwiches

we know that

x=y -----> equation A

y=3(x-18) -----> equation B

substitute equation A in equation B

x=3(x-18)

x=3x-54

3x-x=54

2x=54

x=27 turkey sandwiches (initial)

therefore

The number of ham sandwiches is equal to

y=27 ham sandwiches

Note The options of this problem are incorrect, the number of sandwiches of ham must be greater than 18

Answer:

The ordered pair (3,1/2) is not a common point, the statement is false

The solution is the point (0.667, 6.333) (common point)

Step-by-step explanation:

we have

[tex]y=2x+5[/tex] -----> equation A

[tex]y=\frac{1}{2}x+6[/tex] ----> equation B

we know that

If a ordered pair is a common point between the two lines,

then

the ordered pair must satisfy both equations

step 1

Verify if the ordered pair (3,1/2) satisfy equation A

substitute the value of x and the value of y in the equation A and then compare the results

For x=3, y=1/2

[tex]\frac{1}{2}=2(3)+5[/tex]

[tex]\frac{1}{2}=11[/tex] ----> is not true

The ordered pair don't satisfy the equation A

therefore

The ordered pair is not a common points both lines

The statement is false

step 2

Find the common point between the two lines

[tex]y=2x+5[/tex] -----> equation A

[tex]y=\frac{1}{2}x+6[/tex] ----> equation B

Solve the system of equations by graphing

The intersection point both graphs is the solution of the system (common point)

using a graphing tool

The solution is the point (0.667, 6.333) (common point)

see the attached figure