Which point is a solution to the following graph:

The solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1

In this question, we have been given an equation.

2x / 3 - 1/2 = 2x + 5/6

We need to find the solution of given equation.

⇒ 2x / 3 - 1/2 = 2x + 5/6

⇒ (4x - 3)/6 = (12x + 5)/6

⇒ 4x - 3 = 12x + 5

⇒ 4x - 12x = 5 + 3

⇒ -8x = 8

⇒ x = -1

We need to check above solution.

so, substitute x = -1 in LHS of given equation.

LHS

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

= -2/3 - 1/2

= -(2/3 + 1/2)

= -[(4 + 3)/6]

= -7/6

Now, substitute x = -1 in RHS of given equation.

RHS

= 2(-1) + 5/6

= -2 + 5/6

= (-12 + 5)/6

= -7/6

For x = -1, LHS = RHS

Therefore, the solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1

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According to the question, to calculate the probability of the event which states that tossing a coin to get either head or tail

The total number of a coin is [tex]1[/tex]

And total number of possibilities are {H,T}

Therefore, the total number of favorable outcomes in which either head or tail can come: [tex]1[/tex]

As per question, the probability can be written as:

P(h or t) = P(h) + P(t)

            [tex]= \frac{1}{2} +\frac{1}{2} =1 = 100%[/tex]

Hence, the probability of getting either head or tail is [tex]1[/tex].

The given event is mutually exclusive because it has [tex]100[/tex] percent which is close to tenth of a percent. And these two events cannot happen at the same time also, so they are mutually exclusive.

What are mutually exclusive events?

Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.

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Answer:

y=-2x+6

Step-by-step explanation:

Please see attachment.

Hope this helps!

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Answer: 154º

Step-by-step explanation: vertically opposite angles => xº = 154º

Answer: 52

Step-by-step explanation: it might not be it. GOD BLESS.

Answer:

x = 2, x = -6

Step-by-step explanation:

Given quadratic function in vertex form:

[tex]f(x)=(x+2)^2-16[/tex]

The zeros of a function occur when f(x) = 0:

[tex]\implies (x + 2)^2 - 16 = 0[/tex]

Add 16 to both sides:

[tex]\implies (x + 2)^2 - 16+16 = 0+16[/tex]

[tex]\implies (x + 2)^2 =16[/tex]

Square root both sides:

[tex]\implies \sqrt{ (x + 2)^2} =\sqrt{16}[/tex]

[tex]\implies x+2= \pm 4[/tex]

Subtract 2 from both sides:

[tex]\implies x+2-2= -2 \pm 4[/tex]

[tex]\implies x= -2 \pm 4[/tex]

Therefore:

[tex]\implies x=-2+4=2[/tex]

[tex]\implies x=-2-4=-6[/tex]

The zeros of the given quadratic function are x = 2, x = -6.

Answer:

9/8 = 1  1/8

Step-by-step explanation:

The equation of the circle for a circular irrigation field with radius 12 and center at (7 , -10) is (x - 7)^2 + (y + 10)^2 = 144.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circular irrigation field, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (7 , -10)

r = 12

(x - 7)^2 + (y - -10)^2 = 12^2

(x - 7)^2 + (y + 10)^2 = 144

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The division will give a value of 0.15 × 10^10.

The information is to divide the quantity 1.365 times ten raised to the eighteenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.

This will be:

(1.365 × 10^18) / (9.1 × 10^8)

= 1.365/9.1 × 10^10

= 0.15 × 10^10

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Ben will receive £390

Alex and Ben share £520

They share this money in the ratio 1:3

The fraction of this amount that Ben will receive can be calculated as follows

1 + 3

= 4x

4x= 520

x= 520/4

x= 130

Ben Fraction= 130 × 3

= 390

Hence Ben's fraction of the money is £390

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Answer:

Let r be the number of rides and g be the number of games.

2.50g + 4.00r = 52.50

r = 2g

The equations are 2.5g +4r = 52.5 and g=2r.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Cost of game = $2.50

Cost of ride = $4

let g be the number of games

and, let r be the number of rides taken

total they played = $52.50

So, the equation can be

2.5g +4r = 52.5

and,  number of rides she went on is twice the number of games she played.

So, g = 2r

Hence, The equations are 2.5g +4r = 52.5 and g=2r.

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The probability for the arrow that land in the number 3 is 1/8.

Probability:

Basically, the word probability means the possibility of occurring the required event.

Given,

The spinner is divided into 8 equal sections.

Here we need to find if the arrow lands on a number, what is the probability that it will land on 3.

Let us consider that the spinner has 8 equal-sized sections numbered 1 to 8.

Since the sections have equal size, each section is equally probable.

The probability of falling on each section is therefore 1/8.

We know that, in the 8 sections,

There is only one 3 in this list.

So, the possibility of the event = 1

Hence, probability is

=> 1/8

Therefore, the probability for the arrow that land in the number 3 is 1/8.

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Answer:

Step-by-step explanation:

semplify

8/12 = 2/3

B)

1/3 + 1/3 = 2/3

Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. The given conclusion is deductive reasoning.

Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. Inductive thinking proceeds from the particular to the universal, whereas deductive reasoning proceeds from general premises to specific conclusions.

Given the statements,

From the given sentences, the first sentence is a general statement, the second statement is a specific statement. And, at the last, the third statement is a conclusion statement.

Hence, the given conclusion is deductive reasoning.

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Explanation:

Vertical angles are always congruent.

Set the two expressions equal to one another and solve for x.

6x - 6 = 3(x+6)

6x - 6 = 3x + 18

6x - 3x = 18 + 6

3x = 24

x = 24/3

x = 8

Then use this x value to find each angle

Both angles are 42 degrees each to confirm the answer.

Answer: science

Step-by-step explanation:

x=2

10-2(2x+1)=4(x-2)

10-4x-2=4x-8

10-2=8x-8

8=8x-8

16=8x

2=x

Answer:

X = 2

Step-by-step explanation:

[tex] \sf \: First, solve \: the \: brackets. [/tex]

[tex] \sf \: 10 - 2(2x + 1) = 4(x - 2) \\ \sf10 - 4x - 2 = 4x - 8 \: \: \: \: \: \: \: [/tex]

[tex] \sf \: Combine \: like \: terms .[/tex]

[tex] \sf8 - 4x = 4x - 8[/tex]

[tex] \sf \: Subtract \: 4x \: from \: both \: sides \: to \: remove \: 4x.[/tex]

[tex] \sf \: 8 - 4x - 4x = 4x - 8 - 4x \\ \sf8 - 8x = - 8[/tex]

[tex] \sf \: Subtract \: 8 \: from \: both \: sides \: to \: remove \: 8.[/tex]

[tex] \sf8 - 8 - 8x = - 8 - 8 \\ \sf - 8x = - 16[/tex]

[tex] \sf \: Divide \: both \: sides \: by \: -8.[/tex]

[tex] \sf \: x = 2[/tex]

The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints are A(2, 14) and C(0, 5).

Then the coordinates of the midpoint of a segment with the given endpoints will be

(x, y) = [(2 + 0) / 2, (14 + 5) / 2]

(x, y) = (2/2, 19/2)

(x, y) = (1, 9.5)

The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).

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Using the definition of slope, the points (3 , -5), (-3 , 3), and (0 , 2) are not collinear.

Three or more points are said to be collinear if they lie on a single straight line.

To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

m = (y2 - y1)/(x2 - x1)

Getting the slope of each pair of points:

(3 , -5) and (-3 , 3)

m = (y2 - y1)/(x2 - x1)

m = (3 - -5)/(-3 - 3)

m = 8/-6

m = -4/3

(-3 , 3) and (0 , 2)

m = (y2 - y1)/(x2 - x1)

m = (2 - 3)/(0 - -3)

m = -1/3

(3 , -5) and (0 , 2)

m = (y2 - y1)/(x2 - x1)

m = (2 - -5)/(0 - 3)

m = 7/-3

m = -7/3

Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is not equal with each other, then they are not collinear.

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Answer:

First option A

Step-by-step explanation:

Solved this by looking at the points of the graph from left to right. (-3,-2) is the first being the furthest left then so on.

Answer:

The last option:  x = 0

Step-by-step explanation:

The line of symmetry for a figure is a straight line that divides the figure into two congruent figures

The vertical line passing along the y axis is the line of symmetry and since it passes through all y values where x = 0, the equation is x = 0

The ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.

A three-dimensional object's total surface area exists the whole area of all of its external surfaces.

Let r be the radius of the circle and h be the height

To find volume of the hemispherical tank and its surface area.

Here,

TSA = Total Surface Area

CSA = Curved Surface Area

Volume of a hemisphere (V) = (2/3) πr³

TSA of the hemispherical tank(A) = CSA of the tank + CSA of the base.

TSA(A)  = 2πr² + πr² = 3πr²

The ratio of the volume of the hemispherical tank to its surface area is,

V/A = (2/3)πr³ / 3πr²

V/A = 2r/9

Therefore, the ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.

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Answer:

|2x + y - 3z|

Plug in the values

|-4 + 10 - 9|

= |-3|

= 3

Step-by-step explanation:

the answer is (3) because when all the letters are turned into numbers then solved it becomes [-4+10+(-9)] then you have to turn it into a positive because of the lines.

The next 2 terms if it is a geometric sequence is 360 and 480.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant. where r is the common ratio between successive terms.

Given:

The sequence in the form

[tex]f_{1} =120,[/tex]

[tex]f_{n} =f_{n-1}[/tex]         for n>2

According to given question we have

[tex]f_{1} =120,[/tex]

The formula would be:

[tex]f_{n} =f_{n-1}+f_{1}[/tex]         for n>2

[tex]f_{2} =f_{2-1}+f_{1} =f_{1}+f_{1} =240\\\\f_{3} =f_{3-1}+f_{1} =f_{2}+f_{1} =240+120=360\\\\f_{4} =f_{4-1}+f_{1} =f_{3}+f_{1} =360+120=480\\[/tex]

Therefore, the next 2 terms if it is a geometric sequence is 360 and 480.

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The restriction will be f-¹(x) range: y ≥ 0

Domain of a function:

The domain of a function refers to the set of all possible inputs for the function. For example, we get that the domain of f(x) = x² is all real numbers, and the domain of g (x) = 1 / x is all real numbers except for x = 0( as it will make the function indefinite.) Some special functions can also be defined whose domain are limited.

Range of a function:

The range of a function refers to the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.

So, the restriction will be f-¹(x) range: y ≥ 0 as x² will always be positive.

Therefore, the restriction will be f-¹(x) range: y ≥ 0.

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Tamika's number of visits required to earn a free movie ticket is 14 visits.

According to the question, the given data is;

Tamika has a points card for a movie theatre which are as follow;

Signup rewards = 20 points

Each visit reward = 10.5

Total points needed = 167

Let 'x' be the number of visits.

Total points earned for x number of visits: 10.5x.

Thus, the equation according to statement;

20 + (10.5 × x) = 167

10.5x = 167 - 20

10.5x = 147

x = 147/10.5

x = 14 visits.

Therefore, Tamika's number of visits required to earn a free movie ticket are 14 visits.

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Exercise 1

5 3/4 + (-1/4)

Multiply 5 and 4 to get 20.

20 + 3/4 - 1/4

Add 20 and 3 to get 23.

23/4 - 1/4

Since the fractions 23/4 and 1/4 have the same denominator, subtract their numerators to subtract them.

23 - 1/4

Subtract 1 from 23 to get 22.

22/4

Reduce the fraction 22/4 to its lowest expression by extracting and canceling 3.

11/4

Exercise 2

-2/3 + 1/6

Convert -2/3 and 1/6 to fractions with like denominators.

- 2×2/3 × 2 + 1/6

Simplify

-4/6 + 1/6

Since -4/6 and 1/6 have the same denominator, add their numerators to add them together.

-4 + 1/6

Add −4 and 1 to get −3.

-3/6

Reduce the fraction -3/6 to its lowest expression by extracting and canceling 3.

-1/2

Exercise 3

-8/5 + (-3/4)

Convert -8/5 and 3/4 to fractions with like denominators.

-32/20 - 15/20

Since -32/20 and 15/20 have the same denominator, subtract their numerators to subtract them.

-32 - 15/20

Subtract 15 from −32 to get −47.

-47/20

Answer:

x = 5

Step-by-step explanation:

[tex]12x = 70 - 2x[/tex]

[tex]14x = 70[/tex]

[tex]x = 5[/tex]

Answer:

Here :))

Step-by-step explanation: