which graph correctly represents 3x+y > 7

By the application of algebraic procedures and logarithm properties, the roots of the logarithmic equation [tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex] are x = 2 and x = -1.

In this question we need to solve a logarithmic equation by means of algebraic procedures and logarithm properties:

[tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex]

[tex]\log \sqrt{x\cdot (x-1)} = 1[/tex]

[tex]\log \sqrt{x^{2}-x} = 1[/tex]

[tex]\frac{1}{2}\cdot \log (x^{2}-x) = 1[/tex]

[tex]\log (x^{2}-x) = 2[/tex]

[tex]x^{2}-x = 2[/tex]

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

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

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

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

[tex]x^{2} - 2 = x[/tex]

[tex]x^{2}-x-2 = 0[/tex]

[tex](x-2)\cdot (x + 1) = 0[/tex]

[tex]x = 2 \,\lor \,x= -1[/tex]

By the application of algebraic procedures and logarithm properties, the roots of the logarithmic equation [tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex] are x = 2 and x = -1.

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The value of y is 2.33924.

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

Given:

(1/8)²-3y = [tex]2^{y}[/tex]-2

1/64 - 3y =  [tex]2^{y}[/tex]-2

1/64+ 2 =  [tex]2^{y}[/tex]+3y

129/2 =  [tex]2^{y}[/tex]+3y

Taking log on both side

log 129 - log 2 = y log 2 + 3 log y

2.11 - 0.301 = 0.301 y + 3 log y

1.809 = 0.301 y + 3 log y

1.809/3= 0.1 y + log y

0.603 = 0.1 y + log y

y = [tex]10^{\frac{603-100y}{1000}}[/tex]

y= 2.33924

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Answer:

y=0.5(x−1)

Step-by-step explanation:

Explanation: To find the inverse of a function, you have to substitute y for x in the equation and simplify to get a normal equation again. In this case, f(x) is y.

y=2x+1

x=2y+1

2y+1=x

2y=x−1

y=0.5(x−1)

Answer

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

Step-by-step explanation:

To find the inverse of a function  [tex]f(x)=2x+1[/tex] , we substitute x and y for each other and then solve for y to get a new function.

We rewrite the original function as:

[tex]x=2y+1[/tex]

And then we solve for y:

[tex]x-1=2y[/tex]

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

This is our answer.

Answer:

720 Course Schedules

Step-by-step explanation:

When you choose the first course, there are 6 to choose from. When you scoose the second, there are only 5. This keeps going until the 6th course where there is only 1 choice.

You multiply these choices together. You should get 6×5×4×3×2×1

6×5=30

30×4=120

120×3=360

360×2=720

720×1=720

You then end up with 720 course schedules.

Answer:

14.285714285714 %

Step-by-step explanation:

suppose the weekly payment is of x dollars

Then

Previous payment : $(x/40) per hour

New payment : $(x/35) per hour

Then

The percentage increase in the hourly rate of pay is :

[tex]=\frac{\frac{x}{35} -\frac{x}{40} }{\frac{x}{40} } \times100[/tex]

[tex]=\frac{\frac{5x}{1400} }{\frac{x}{40} } \times100[/tex]

[tex]=\frac{5x}{1400} \times \frac{40}{x} \times100[/tex]

[tex]=\frac{200}{1400} \times100[/tex]

[tex]=\frac{1}{7} \times100[/tex]

[tex]=14.285714285714[/tex]

The highest rate on increasing is of 12x -6y = -24; Option B is the correct answer.

The options are given in the image attached with the answer

A function is a law that relates a dependent variable and an independent variable.

It is asked among the options given , which is increasing at the highest rate.

To increase at a rate , the value of the slope , m should be > 0

For the Option 1

for a straight line function , the slope is given by

m = ( y₂ -y₁)/(x₂-x₁)

m = ( -3 -3)/(2- (-1)) = -6 /3 = -2

Therefore the function is decreasing

For Option 2

12x - 6y = -24

-6y = -12x -24

y = 2x +4

m = 2 (increasing)

For option 3

m = (-4 + 5)/(2-1) = 1

For Option 4

(8,0) (0,-4)

m = (-4 -0) /(0-8) = 4/8 = 1/2

The highest rate on increasing is of 12x -6y = -24

Therefore Option B is the correct answer.

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Answer:

The correct answer is A

Step-by-step explanation:

2 is exactly 7 units away from -5.

Answer:

Step-by-step explanation:

Gradient is the slope, the rise over run, change in y over change in x.

For line A

6/3=2

Gradient=2

For Line B

5/5 =1

Gradient =1

Answer:

•The coordinates of line A (0,1) and (1,3)

gradient formula : y2-y1/x2-x1

gradient :

3-1/1-0=2

Actually you can take any other coordinates for reference!

example :

the other coordinates of line A (0,1) and (2,5)

=5-1/2-0

=2 (same)

•The coordinates of line B (3,2) and (4,1)

Gradient : =1-2/4-3

=-1

or

the coordinat B =(7,-2) and (-2,7)

=7-(-2)/-2-7

=9/-9

=-1

Note:The line to the right has a positive gradient, and the line to the left has a negative gradient

Step-by-step explanation:

[tex] = {5}^{ \frac{3}{2} } [/tex]

[tex] = \sqrt[2]{ {5}^{3} } [/tex]

[tex] = \sqrt{ {5}^{3} } [/tex]

Answer:

3.31 x 10^4

Step-by-step explanation:

3.111 x 10^4 is 31110

2 x 10^3 is 2000

31110 + 2000 = 33100 or 3.31 x 10^4

Answer:

b) 3.31 × 10⁴

Explanation:

[tex]\sf \rightarrow \left(3.11\cdot 10^4\right)+ \left(2\cdot 10^3\right)[/tex]

remove parenthesis

[tex]\rightarrow \sf 3.11\cdot \:10^4+2\cdot \:10^3[/tex]

simplify

[tex]\rightarrow \sf 31100+2000[/tex]

add the numbers

[tex]\sf \rightarrow 33100[/tex]

convert to scientific form

[tex]\sf \rightarrow 3.31 \ x \ 10^4[/tex]

The forward differences for this data is 1, 1, 1, 1, 1, 1 (since 10 - 9 = 1, 11 - 10 = 1, etc). Since we only need one iteration of differences, a linear polynomial will fit the data exactly.

Answer:

C

Step-by-step explanation:

2 equal angles are said to be congruent

Answer:

2(4ax+2bx+2a+5b)

Step-by-step explanation:

Answer:

y = -x +1

Step-by-step explanation:

p1 (-3,4)

p2 ( 3, -2)

line equation y = mx + b

The slope m equals

[tex] \frac{y2 - 21}{x2 - x1} [/tex]

[tex] \frac{ - 2 - 4}{3 - - 3} = \frac{ - 6}{6} = - 1[/tex]

y = - x + b

from any point

-2 = -3 + b

b = 1

line equation = y = -x +1

The result of the expression in exponential form is 9^-4

Given the expression below

[tex]9^2 \times 9^{-6}[/tex]

According the product law, since the base are equal, we will add the exponent to have:

[tex]9^2 \times 9^{-6}=9^{-6+2}\\9^2 \times 9^{-6} = 9^{-4}[/tex]

Hence the result of the expression in exponential form is 9^-4

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The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the meal cost, hence:

Total cost = x + 0.2x + 0.0725x

15 = 1.2725x

x = 11.79

The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.

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The correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.

The given inequality is -3(2x-5)<5(2-x).

Inequality is a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

At first simplify each side

LHS of inequality -3(2x - 5) = -3(2x) + -3(-5) [∵(-)(-) = (+)]

⇒ -3(2x - 5) = - 6x + 15

Now, RHS of the inequality 5(2 - x) = 5(2) + 5(-x) [∵(+)(-) = (-)]

⇒ 5(2 - x) = 10 - 5x

Now, - 6x + 15 < 10 - 5x

Subtract 15 from both sides

That is, - 6x < -5 - 5x

Add 5x to both sides

That is, - x < - 5

Remember the coefficient of x is negative, and then when you divide both sides by it you must reverse the sign of inequality.

Now, the coefficient of x is -1

So, divide both sides by -1

Then, x > 5.

Hence, the correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.

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Answer:

See below

Step-by-step explanation:

To construct a circle, one must know the center point of the circle, and the circle's radius.
The circle that circumscribes a triangle (called a circumcircle), has a circumcenter (center point) that is the point of concurrency (a point where more than two lines intersect at the same point) of all three perpendicular bisectors (perpendicular lines that happen to cut a given line segment exactly in half) of the sides of the triangle.

Construct the circle with a center at the circumcenter, and a radius out to any one of the vertices of the triangle.  The circumcenter is equidistant from all three vertices, so the circle draw will contain all three vertices.

To construct perpendicular a bisector, recall that a perpendicular bisector is a line containing all points that are equidistant the end points of a line segment (each point on the line is the same distance from both segment endpoints simultaneously).

So, if we can find two points that are the equidistant from the two segment endpoints, we'll have two points on the line, and to draw any line, one only needs two distinct points, and the straightedge.

Finding a point that is equidistant from two given points

Set the compass to any radius that is larger than half the distance between the two endpoints.  If uncertain of a "good" choice, one can simply choose the length of the line segment itself as a radius.

Setting the center of the compass circle on one endpoint, draw an arc such that the arc will pass through the perpendicular line we're trying to construct twice.  If uncertain, draw the entire circle.  Keeping the radius saved.

With the same radius, setting the center of the compass circle to the second endpoint, draw and arc such that the arc intersects the first circle two times.  If it doesn't intersect two times, the radius chosen at the beginning was too small.  Start the entire process over with a larger radius.

These two points of intersection are equidistant from the two endpoints of the line segment, and thus, they are on the perpendicular bisector of the line segment.

Using those two points, and a straightedge, draw the line containing those two points, and extend it generously in both directions.

Steps 1-5 in pink; steps 6-10 in green; steps 11-15 in blue (see diagram):

Note:  Since all three perpendicular bisectors intersect at the same point, it is only necessary to find two of three, not all three.  So, one could skip constructing one of those three perpendicular bisectors (either steps 1-5, 6-10, or 11-15), and still be able to construct the circumcircle correctly.

Hello! I hope you are having a nice day. My name is Galaxy and I will be helping you with this problem. We can solve this problem in 2 steps, respectively Theory and Solving.

I'll go ahead and start with the Theory.

Before we attempt to solve the problem mathematically, we must first figure out how we're going to solve this problem.  

We know that we have a line and a point, we can start by graphing the equation and point that we've received.

Now that we have our points plotted and our equations graphed, we can start to see that something odd is happening, the given point is on the line itself.

We can check this by inputting the points into our equation:

[tex](-4)+2(-3)=-10?\\(-4)+(-6)=-10?\\-10=-10[/tex]

This proves that our point is on the line that we were given.

According to the basic rules of Euclidean Geometry, we know that parallel lines can never intersect each other and due to this there cannot be any solution to this problem.

Any other line using this point would intersect the given line, and due to this, this problem has no real solutions.

* The only line that can use these points and graph is the line provided, and that cannot work due to the lines intersecting at an infinite number of points.

Cheers,
Galaxy.

Answer:

[tex]\fbox {r = 34}[/tex]

Step-by-step explanation:

Finding IQ and RJ by tangent rule :

⇒ IQ = QK = 10

⇒ KR = RJ = 8

Finding PJ :

⇒ PJ = 32 - 8

⇒ PJ = 24

∴ But PJ = PI (by tangent rule)

⇒ PI = 24

Finding r :

⇒ PI + IQ

⇒ 24 + 10

⇒ r = 34

Answer:

m=120

k=60

Step-by-step explanation:

a trapezoid has 360 degrees. subtract 120 degrees to get 240 degrees. we know that m=2k. 240=2k+2k which is 4k. 240 is 4k. k=60. m=2k, so mulitply 60 by 2 to get m=120

Answer:

300-6x

Step-by-step explanation:

Trust me

value of a = 3

value of b = 2

a + b = 3 + 2 = 5 .

Answer:

[tex]\pi \times radius \times hieght[/tex]

Answer:

(5,-5)

x=5

y=-5

Step-by-step explanation:

How to solve using elimination method.

First, add the two equations.

   2x - 3y = 25

+  5x + 3y = 10

7x=35

The y values got eliminated.

Next, divide 7 from both sides.

7x/7=35/7

x=5

Next, plug-in x=5 into one of the equations.

2(5) - 3y = 25

10-3y=25

Subtract 10 from both sides.

-3y=15

Divide -3 from both sides.

y=-5

Remember a positive divided by a negative is a negative.

Hope this helps!

If not, I am sorry.

Answer:

[tex]\fbox {False}[/tex]

Step-by-step explanation:

To convert a degree measure to radian measure, multiply with π/180.

⇒ 180 × π/180

⇒ π radians

false is the answers

please mark me as brainlest

Answer:

[tex]x=-18, y=-44[/tex]

Step-by-step explanation:

[tex]y=3x+10\\y=2x-8\\\\3x+10=y\\2x-8=y\\3x-y=-10\\2x-y=8\\\\-2(3x-y=-10)\\3(2x-y=8)\\\\-6x+2y=20\\6x-3y=24\\-y=44\\y=-44\\-44=3x+10\\-54=3x\\x=\frac{-54}{3} \\x=-18\\\\x=-18, y=-44\\[/tex]

CHECK

[tex]-44=3(-18)+10\\-44=-54+10\\-44=-44\\\\-44=2(-18)-8\\-44=-36-8\\-44=-44[/tex]

The linear relation of the height as a function of the number of weeks is:

y = 0.5*x

A general linear relation is written as:

y = a*x + b

Where a is the slope.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, we have the points of the form (week, height).

(4, 2)

(6, 3)

(8, 4)

If we use any two of these we can get the slope, so using the first two:

a = (3 - 2)(6 - 4) = 1/2 = 0.5

y = 0.5*x + b

To get the value of b, we can use the first point, it says that when x = 4, we have y = 2, then:

2 = 0.5*4 + b

2 = 2 + b

0 = b

Then the linear relation of the height as a function of the number of weeks is:

y = 0.5*x

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Answer:

it's helps with learning the difference of thr compound