What is the solution to the equation 1/2x + 3 = 2/3x + 1

A. obtuse. The angle R is obtuse.

An obtuse angle is an angle greater than 90° and less than 180°. So, in the image attached we can see that the angle R is greater than 90° and less than 180°.

Answer:

The translation is 2 units at left and 7 units up

Step-by-step explanation:

we have that

The rule of the translation is

(x, y) → (x – 2, y + 7)

That means----> The translation is 2 units at left and 7 units up

Answer:

2 units at left and 7 units up

Step-by-step explanation:

If the rule as a mapping for the translation of a rectangle is (x, y) → (x – 2, y + 7), 2 units at left and 7 units up describes this translation.

Answer:

P(4, - 1 )

Step-by-step explanation:

The ratio 1 : 1 represents the midpoint of segment AB

Using the midpoint formula

[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

with (x₁, y₁ ) = (13, 1) and (x₂, y₂ ) = (- 5, - 3), so

P = [0.5(13 - 5), 0.5(1 - 3) ] = [0.5(8), 0.5(- 2) ] = (4, - 1 )

the midpoint P has the coordinates (4, −1).

To find the coordinates of point P that partitions segment AB in a 1:1 ratio, also known as the midpoint, we use the midpoint formula. Given the coordinates A(13,1) and B(−5,−3), the midpoint formula is ((x1 + x2)/2, (y1 + y2)/2).

Applying the values from A and B:

Therefore, the midpoint P has the coordinates (4, −1).

Answer:

The third table is an arithmetic sequence . Its difference is -1.4.

Step-by-step explanation:

In an arithmetic sequence the difference between one term and the next is a constant

8.7 - 1.4 = 7.3

7.3 - 1.4 = 5.9

5.9 - 1.4 = 4.5

4.5 - 1.4 = 3.1

Answer:3rd table

Step-by-step explanation:

Answer:

Angle D is 70, I believe

Angle D would be supplementary to A

Answer:

(-2,-7)

Step-by-step explanation:

Answer:

x= -2

Step-by-step explanation:

-b/2a = x

-(12)/2(2) = x

-12/6 = x

-2 = x

[tex]\bf V=(x)(4x+3)(4x)\implies \cfrac{V}{4x}=(x)(4x+3)[/tex]

Answer:

[tex]V=(x)(4x+3)(4x)=16x^2+12x[/tex]                        

Step-by-step explanation:

Given : Expression [tex]V = (x)(4x+3)(4x)[/tex]

To find : Suppose you multiplied the cereal box dimensions in a different order ?

Solution :

The given expression is the product of three numbers,

[tex]V = (x)(4x+3)(4x)[/tex]

First we multiply first two terms,

[tex](x)(4x+3)=4x^2+3x[/tex]

Substitute back,

[tex]V = (4x^2+3x)(4x)[/tex]

Then multiply the left terms,

[tex]V =16x^2+12x[/tex]

Therefore, [tex]V=(x)(4x+3)(4x)=16x^2+12x[/tex]

Answer:

its the second choice 2 + n< 14

Answer:

B.

Step-by-step explanation:

P(something not happening)+P(something happening)=1 or 100%.

So if we have

P(something not happening)+40%=100%

Then the P(something not happening)=60% since 60%+40%=100%.

Yes I was using the event="something not happening" as the complement of something happening.

In fancy notation, some people might write:

[tex]P(A)+P(A')=1[/tex]

or

[tex]P(A)+P(A^c)=1[/tex]

Answer:

First exercise: [tex]x=7[/tex]

Second exercise: [tex]x=2[/tex]

Step-by-step explanation:

According to the Intersecting Secants Theorem the products of the segments of two secants that intersect each other outside a circle, are equal.

Knowing this, in order to solve the first exercise and the second exercise, we can write  the following expressions and solve for "x":

For the first exercise, we get:

[tex](5)(5+x)=6(6+4)\\\\25+5x=60\\\\5x=60-25\\\\x=\frac{35}{5}\\\\x=7[/tex]

For the second exercise, we get:

[tex](4)(4+x)=3(3+5)\\\\16+4x=24\\\\4x=24-16\\\\x=\frac{8}{4}\\\\x=2[/tex]

Answer:

False; this is the law of syllogism.

Step-by-step explanation:

Law of Detachment is:

1) p->q

2) p

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

Conclusion: q

Law of syllogism is:

1) p->q

2) q->r

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

Conclusion: p->r

Answer:

A. S

Step-by-step explanation:

The edge of the circle would be M and there is a line to the center showing the radius. The second letter shows the center.

point S is the centre of the given circle.

You need to know some details about a circle, such as its equation or certain locations on the circle, in order to locate its center.

Drawing the perpendicular bisectors of each chord will allow you to determine the circle's center if you are aware of the location where two perpendicular chords connect. The center of the circle is where the perpendicular bisectors intersect.

Therefore, based on the given figure, the centre is the point S.

Learn more on centre of a circle here: https://brainly.com/question/29458405

#SPJ2

Answer:

b. winter wear, appropriate for around 20-45°F c.

Step-by-step explanation:

Answer:

b. winter wear, appropriate for around 20-45°F

Step-by-step explanation:

When it is 6:00 hours in Honolulu, it is 15:00 hours in London, this means that there are 15 - 6 = 9 hours of difference.

Paul got into London at 12:00 p.m, that is, at 12 - 9 = 3:00 p.m. Friday Honolulu time. Paul’s flight left Honolulu at 2:00 p.m. Thursday, so he spent 25 hours flighting.

When the flight started, the temperature in London was 30 °C, after 25 hours the temperature dropped 25 °C, so it was 30 - 25 = 5 °C.

To convert from °C to °F, we use the following formula:

(x °C × 9/5) + 32 = y °F

Replacing with x = 5

(5 °C × 9/5) + 32 = 41 °F

Answer:

The function that shows total sales, including the first hour is

[tex]S(x)=15(x-1)+120[/tex]  or [tex]S(x)=15x+105[/tex]  

Step-by-step explanation:

Let

s(x) -----> function that represent the sales after the first hour

S(x) ----> function that represent the total sales (including the first hour)

x -----> the  number of hours

we know that

The linear equation that represent the total sales is equal to

[tex]S(x)=s(x)+120[/tex] -----> equation A

we have

[tex]s(x)=15(x-1)[/tex] -----> equation B

substitute equation B in equation A

[tex]S(x)=15(x-1)+120[/tex]

[tex]S(x)=15x-15+120[/tex]

[tex]S(x)=15x+105[/tex]  

Therefore

The function that shows total sales, including the first hour is

[tex]S(x)=15(x-1)+120[/tex]  or [tex]S(x)=15x+105[/tex]  

Answer:

the order is

2,4,1,3

(the 1st answer is the 2nd option)

Answer:

1. (a² - b)/(a³b²)= 1/ab² - 1/a²b

2. (b - a)/a³b³ = 1/a³b² - 1/a²b³

3. (2 - ab²)/(a²b³) = 2/a²b³ - 1/ab

4. (2 - a)/a³b³ = 2/a³b³ - 1/a²b³

Step-by-step explanation:

To do this we'll break down fraction to least term through division.

The solution is as follows

1. (a² - b)/(a³b²)

Splitting the fraction;

a²/a³b² - b/a³b²

= 1/ab² - 1/a²b

2. (b - a)/a³b³

Splitting the fraction.

b/a³b³ - a/a³b³

1/a³b² - 1/a²b³

3. (2 - ab²)/(a²b³)

Splitting the fraction.

2/a²b³ - ab²/a²b³

2/a²b³ - 1/ab

4. (2 - a)/a³b³

Splitting the fraction

2/a³b³ - a/a³b³

2/a³b³ - 1/a²b³

The equation of the line is y = 0.6*x - 1, the graph is in the image at the end.

How to find the linear equation?

A linear equation in the slope-intercept form can be written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the points (−5,−4) and (5,2), so the slope is:

a = (2 + 4)/(5 + 5) = 6/10 = 0.6

y = 0.6*x + b

And it passes through (5, 2), then:

2 = 0.6*5 + b

2 - 0.6*5 = b

-1 = b

The equation is:

y = 0.6*x - 1

The graph is in the image below.

Answer:

y+4=-2(x-4)

Simplified- y=-2x+4

Step-by-step explanation:

y+4= -2(x-4)

y+4= -2x+8

-4. -4

y=-2x+4

Answer:

[tex]\large\boxed{\bigg(4\times10^8\bigg)^2=1.6\times10^{17}}[/tex]

Step-by-step explanation:

[tex]\text{The sicientific notation:}\ a\times10^k,\ \text{where}\ 1\leq a<10\ \text{and}\ k\in\mathbb{Z}.\\\\\bigg(4\times10^8\bigg)^2\qquad\text{use}\ (ab)^n=a^nb^n\\\\=4^2\times\left(10^8\right)^2\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=16\times10^{16}\ -\ \text{this is not a scientific notation yet}\ a=16>10\\\\=1.6\times10\times10^{16}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=1.6\times10^{17}[/tex]

Answer:

1.6 x 1017

Step-by-step explanation:

Answer:

y-1=0

Step-by-step explanation:

I'm going to write into y=mx+b form first.

m is the slope and b is the y-intercept.

First step is to find the slope.

To find the slope given two points you can use m=(y2-y1)/(x2-x1).

Instead, I like to line up the points and subtract vertically.  Then put 2nd difference on top of 1st difference.

Let's do that:

 (-2,1)

- (2,1)

--------

 -4, 0

The slope is 0/-4=0.  That means the line is horizontal and is of the form y=a number.

If you look at the points, you see the y-coordinate doesn't change.  The y-coordinate is always 1.  So the equation for the line is y=1.

If we subtract 1 on both sides we get y-1=0.

So general form is Ax+By+C=0 which is why I decide to move the one on the other side of the equation.  

If I had noticed earlier that the y-coordinates were the same I would have stopped and say y=whatever y-coordinate I seen. However, I really didn't take notice of that until after I found the slope.

E is exponents, D is division, A is addition

Answer:

E- exponent D- division A- addition

Step-by-step explanation:

PEMDAS is an acronym which means

P- parenthesis

E- exponents

M- multiplication

D- division

A- addition

S- subtraction

used for two or more operation in a single expression, the order of letters in the PEMDAS tells us what to calculate first, second, third and so on, until the calculation is complete.

Answer:

3 and 9

if f(x)=x^2+13 and g(x)=12x-14

Step-by-step explanation:

So when we are looking for the intersection of two functions, we are trying to figure out when they are the same.  When you think same, you should think equal (=).

So we want to find when f(x)=g(x) for x.

f(x)=g(x)

[tex]x^2+13=12x-14[/tex]

Let's get everything to one side.

Subtracting 12x and adding 14 to both sides.

[tex]x^2+13+14-12x=0[/tex]

I'm going to reorder the left hand side and also simplify the 13+14 part:

[tex]x^2-12x+27=0[/tex]

Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.

Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.

So the factored form of our equation is

[tex](x-3)(x-9)=0[/tex]

Since the product is 0, then at least one of the factors must be 0.

So we want to solve both x-3=0 and x-9=0.

x-3=0 can be solved by adding 3 on both sides. This gives us x=3.

x-9=9 can be solved by adding 9 on both sides. This gives us x=9.

The intersection of f and g happens at x=3 or x=9.

Answer:

x = 9 and x = 3

Step-by-step explanation:

Given

f(x) = x² + 13 and g(x) = 12x - 14

To find the points of intersection equate the 2 functions, that is

f(x) = g(x)

x² + 13 = 12x - 14 ← subtract 12x - 14 from both sides

x² - 12x + 27 = 0 ← in standard form

Consider the factors of the constant term ( + 27) which sum to give the coefficient of the x- term ( - 12)

The factors are - 3 and - 9, since

- 3 × - 9 = + 27 and - 3 - 9 = - 12, hence

(x - 3)(x - 9) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 9 = 0 ⇒ x = 9

The functions intersect at x = 3 and x = 9

Answer:

-2 + i

Step-by-step explanation:

The midpoint is the average:

[ (-7 + 4i) + (3 − 2i) ] / 2

Combine like terms:

(-4 + 2i) / 2

Divide:

-2 + i

The graph of y=(x-1)^2-3 can be transformed to the graph of y=1/2(x+4)^2 by stretching it vertically and shifting it horizontally to the left.

The graph of y=(x-1)^2-3 transformed to produce the graph of y=1/2(x+4)^2 can be done by manipulating the equation and observing its effect on the graph.

Step 1: Identify the transformation of the parent function y=x^2

Step 2: The transformation y=1/2(x+4)^2 indicates a vertical stretch by a scale factor of 1/2 and a horizontal shift to the left by 4 units.

Therefore, the graph of y=(x-1)^2-3 is transformed to the graph of y=1/2(x+4)^2 by stretching it vertically and shifting it horizontally to the left.

A: The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.

B: The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.

C: The graph is translated left 5 units, compressed horizontally by a factor of One-half, and translated down 3 units.

D: The graph is stretched horizontally by a factor of One-half, translated left 5 units, and translated down 3 units.

Answer:

The graph is stretched horizontally by a factor of 1/2, translated left 5 units and up 3 units.

Step-by-step explanation:

I put both equations into a graphing calculator and compared them. Five units left and 3 up agree with answers A and B. The second equation showed a wider parabolic than the first one, which agrees only with answer C. Therefore, it is my opinion that neither answer is correct. I chose D, but since this is a unit test I can't go in and see if I was correct or not.

Answer:

The line containing the midpoints of two sides of a triangle is parallel to the third side ⇒ proved down

Step-by-step explanation:

* Lets revise the rules of the midpoint and the slope to prove the

  problem

- The slope of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- The mid-point of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

* Lets solve the problem

- PQR is a triangle of vertices P (0 , 0) , Q (2a , 0) , R (2b , 2c)

- Lets find the mid-poits of PQ called A

∵ Point P is (x1 , y1) and point Q is (x2 , y2)

∴ x1 = 0 , x2 = 2a and y1 = 0 , y2 = 0

∵ A is the mid-point of PQ

∴ [tex]A=(\frac{0+2a}{2},\frac{0+0}{2})=(\frac{2a}{2},\frac{0}{2})=(a,0)[/tex]

- Lets find the mid-poits of PR which called B

∵ Point P is (x1 , y1) and point R is (x2 , y2)

∴ x1 = 0 , x2 = 2b and y1 = 0 , y2 = 2c

∵ B is the mid-point of PR

∴ [tex]B=(\frac{0+2b}{2},\frac{0+2c}{2})=(\frac{2b}{2},\frac{2c}{2})=(b,c)[/tex]

- The parallel line have equal slopes, so lets find the slopes of AB and

  QR to prove that they have same slopes then they are parallel

# Slope of AB

∵ Point A is (x1 , y1) and point B is (x2 , y2)

∵ Point A = (a , 0) and point B = (b , c)

∴ x1 = a , x2 = b and y1 = 0 and y2 = c

∴ The slope of AB is [tex]m=\frac{c-0}{b-a}=\frac{c}{b-a}[/tex]

# Slope of QR

∵ Point Q is (x1 , y1) and point R is (x2 , y2)

∵ Point Q = (2a , 0) and point R = (2b , 2c)

∴ x1 = 2a , x2 = 2b and y1 = 0 and y2 = 2c

∴ The slope of AB is [tex]m=\frac{2c-0}{2b-2a}=\frac{2c}{2(b-c)}=\frac{c}{b-a}[/tex]

∵ The slopes of AB and QR are equal

∴ AB // QR

∵ AB is the line containing the midpoints of PQ and PR of Δ PQR

∵ QR is the third side of the triangle

∴ The line containing the midpoints of two sides of a triangle is parallel

  to the third side

Answer:

b,c

Step-by-step explanation:

That guy above took so long

Answer:

90

Step-by-step explanation:

90-20%=72

72-20-52

plus everything else doesnt match up and with taxes involved so the oroginal price was 90

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

Te formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

We have two points: (2, -3) and (4, 2). Substitute:

[tex]m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}[/tex]

[tex]y-(-3)=\dfrac{5}{2}(x-2)\\\\y+3=\dfrac{5}{2}(x-2)[/tex]

Convert it to the standard form [tex]Ax+By=C[/tex]:

[tex]y+3=\dfrac{5}{2}(x-2)[/tex]           multiply both sides by 2

[tex]2y+6=5(x+2)[/tex]        use the coordinates of the point

[tex]2y+6=5x+10[/tex]          subtract 6 from both sides

[tex]2y=5x+4[/tex]              subtract 5x from both sides

[tex]-5x+2y=4[/tex]        change the signs

[tex]5x-2y=-4[/tex]

Answer:

x=1

Step-by-step explanation:

1/2x-3/4=3/8-5/8

Combine like terms on the right hand side

1/2x-3/4=-2/8

Simplify the fraction

1/2x-3/4=-1/4

Add 3/4 to each side

1/2x-3/4+3/4 = -1/4+3/4

1/2x = 2/4

Multiply each side by 2

1/2x *2 = 2/4*2

x = 4/4

x=1

Answer:

the answer its 1

Step-by-step explanation:

Answer:

$1050

Step-by-step explanation:

To solve, multiply your two expenses against your $6000 and find the difference.

The man spends 1/5 of his salary on children's education.

To find how much he spends on his children's education in dollars, multiply 1/5 against $6000.

[tex]\frac{1}{5} *6000\\1200[/tex]

The man spends $1200 on children's education.

The man spends 5/8 of his salary on his aged mother and unemployed sister.

Repeat the same process as the first step, this time multiplying 5/8 against $6000.

[tex]\frac{5}{8} *6000\\3750[/tex]

The man spends $3750 on his aged mother and unemployed sister.

Add these two expenses together.

[tex]1200+3750\\4950[/tex]

The man has combined expenses of $4950.

To find how much money he has left, subtract his expenses from his $6000 income.

[tex]6000-4950\\1050[/tex]

The man has $1050 remaining.

Answer:

5 hours

Step-by-step explanation:

The total amount of the repair is $265 and includes parts and an hourly rate. We are told the parts are $90. Subtract the price of the parts, $90, from the total of $265.

$265 - $90 = $175

The $175 is only due to the hourly rate.

Now we divide the total due to the hours by the hourly rate to find the number of hours.

175/35 = 5

Answer: 5 hours