Oabc is a square o is 0,0 a is -2,2 b is 0,4 c is 2,2 A single transformation of oabc is such that A is mapped to c. C is mapped to a O and b are invariant points Describe fully transformation

A solution to an equation that appears in the process of solving other equations is known as a extraneous solution.

The value of x = 2 then L.H.S = R.H.S, this equation has no extraneous solutions.

A solution to an equation that appears in the process of solving other equations is known as a extraneous solution.

To determine if a solution exists extraneous, we simply plug the solution into the original equation.

If it makes a true statement, then it exists not an extraneous solution, but if it makes a false statement, then it is an extraneous solution

Let the equation be,

√5x - 3 = √2x+3

squaring on both sides of the equation, we get

⇒ 5x - 3 = 2x + 3

⇒ 5x - 2x = 3 + 3

simplifying the above equation, we get

⇒ 3x = 6

Divide both sides of the equation by 3,

⇒ x/3 = 6/3

⇒ x = 2

The value of x = 2.

Substituting x = 2 in L.H.S

[tex]$\sqrt{5x-3} =\sqrt{10-3} =\sqrt{7}[/tex]

Substituting x = 2 in R.H.S

[tex]$\sqrt{2x+3} =\sqrt{4+3} =\sqrt{7}[/tex]

Since, L.H.S = R.H.S, this equation has no extraneous solutions.

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The equation to represent the given situation is 1/2X-5=11-5/6 using X as the variable.

What is an equation and how it can be formed?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

When we are given a mathematical problem that is or may be described using algebraic expressions, we form and solve equations. The information from the situation and the algebraic expressions can be used to create an equation. The equation can then be solved to obtain the answer.

Given the situation: If 5 is lessened by 1/2 of a number the result is the same as subtracting 5/6 from 11.

To write an equation for the given situation.

Let the number be X.

If 5 is lessened by 1/2 of the number, we get the expression 1/2X-5

Subtracting 5/6 from 11 gives the expression 11-5/6

Now, it is given that both the situations are same so equating both the expressions we get,

1/2X-5=11-5/6

⇒1/2X-5=61/6

Hence, the equation to represent the situation is 1/2X-5=11-5/6.

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After solving the equation we have concluded that if f(x)=-3 x+7 and g(x)=-7 x+3 , then the value of f(-3)-g(3) is -8

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

f(x) = -3x + 7

f(-3) = -3(-3) + 7 = 9 + 7 = 16

g(x) = -7x + 3

g(-3) = -7(-3) + 3 = 21 + 3 = 24

f(-3) - g(-3) = 16 - 24 = -8

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Given that line AT bisects angle CAR, the measure of angle TAR is 35 degree.

Given the data in the question;

Since Line AT bisects ∠CAR

m∠CAR = 2 × m∠CAT

9x + 7 = 2( 5x )

We solve for x

9x + 7 = 10x

10x - 9x = 7

x = 7

We know that a bisector divides a line or angle into two equal halves.

Hence, m∠CAT = m∠TAR

m∠TAR = m∠CAT = 5x

m∠TAR = m∠CAT = 5(7)

m∠TAR = m∠CAT = 35°

Given that line AT bisects angle CAR, the measure of angle TAR is 35 degree.

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Answer:

Step-by-step explanation:

c

C)The price of a shirt is $7, and the price of a cap is $3.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

x+y=10

2x + 4y = 26

solving, we get,

x=7  &  y=3

Hence,  C)The price of a shirt is $7, and the price of a cap is $3.

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The probability of selecting that both chips are purple is 3/40

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

It is Given that A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.

The probability of selecting that both chips are purple

= 6/20 x 5/20

= 30/400

= 3/40

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Answer:

Step-by-step explanation:

x + 80° = 5x ( being corresponding angle )

80° = 5x - x

4x = 80°

x = 80° / 4

x = 20°

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The summation notation for the series 500+490+480+ . . . . . . . +20+10 is

[tex]25500-10\sum\limits^{50}_{n=1} {n}[/tex]

A summation notation is used to express a long summation into a single notation.

The given series is:

    500+490+480+ . . . . . . . +20+10

This is an arithmetic series with:

a(1) = 500, and

d = 490 - 500 = -10

The last term is a(n) = 10. Find n first by using the nth term formula of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

10 = 500 + (n-1) . (-10)

10 = 500 -10n + 10

10 n = 500

n = 50

Write the explicit formula for the nth term:

a(n) = a(1) + (n-1) . d

a(n) = 500 + (n-1) . (-10)

a(n) = 500 -10n + 10

a(n) = 510 - 10n

The series is the summation notation from n=1 to n = 50

[tex]=\sum\limits^{50}_{n=1} {a(n)}[/tex]

[tex]=\sum\limits^{50}_{n=1} {(510-10n)}[/tex]

[tex]=\sum\limits^{50}_{n=1} {510} -\sum\limits^{50}_{n=1} {10n}[/tex]

[tex]=510\times50-10\sum\limits^{50}_{n=1} {n}[/tex]

[tex]=25500-10\sum\limits^{50}_{n=1} {n}[/tex]

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Answer:

I think the answer is ∞ which is the third option, undefined.

Answer:

Step-by-step explanation:

Hello, I have a Wonderfull website that can help you with this question. (Mathgenius.com) it should pull it up. its all and every subject you can imagine.

Answer:

Chicago to Cleveland- 350 miles

Cleveland to Cincinnati-250 miles

Cincinnati to Chicago-300 miles

Type of triangle formed? - Scalene

Step-by-step explanation:

so I first give each of them a letter, so I chose a for Chicago to Cleveland, b for Cleveland to Cincinnati, and c for Cincinnati to Chicago. Then I write some equations.
a+b+c =900

b=c-50

a=50+c

i then plug the a and b equation into the first one to get

50+c+c-50+c=900

The fifties cancel out, so we are left with 3c =900 so c=300

From this we can figure out the rest by substituting in 300 for c in the an and b equations.
300-50=250

300+50=350

He get the approximately $67 as the amount of interest rate.

According to the statement

We have to find that the interest does Jerome earn in one year.

So, For this purpose, we know that the

A Interest is the amount paid by someone who borrows a certain amount of money.

From the given information:

Jerome deposits $3700, in a certificate of deposit that pays 1.8% interest, compounded annually. How much interest does Jerome earn in one year.

Then

The amount deposited = $3700

The interest pays by the bank = 1.8%

Amount he get by the interest rate = 1.8% of 3700

Amount he get by the interest rate = 1.8 / 100 * 3700

Amount he get by the interest rate = 0.018 * 3700

Amount he get by the interest rate = 66.6.

So, He get the approximately $67 as the amount of interest rate.

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Answer:

3.75 dollars for the boys and 7.5 for girls

Step-by-step explanation:

Boys get x amount.

Girls get 2x

6x+2x=8x

30/8=3.75

Each boy receive the amount of $3.75 and Each girl receive the amount of $7.5

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

Let consider that each boy gets $x

It is given that each of the girls receives twice as much each of the boys

So, each girl receive the amount of 2x

Since there are 3 girls .

So, Three girls received the amount = 3(2x)=6x

2 boys get amount of 2x

Therefore,

6x+2x=8x

30/8

=3.75

Hence Each boy receive the amount of $3.75 and Each girl receive the amount of $7.5

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By combining the like terms, the simplified form of the the expression 2a+3b+4a is 6a+3b

Given,

The algebraic expression = 2a+3b+4a

Rearrange the terms

2a+3b+4a=2a+4a+3b

Combine the like terms

2a+4a+3b=6a+3b

Hence, by combining the like terms, the simplified form of the the expression 2a+3b+4a is 6a+3b

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Answer:

Step-by-step explanation:

x=72+23

x=95

Answer: x = 95

Step-by-step explanation:

Add 23 to both sides to isolate x

x - 23 + 23 = 72 + 23

x = 95

The volume of a cone that has a radius of 1 cm and a height of 3.4 cm is 3.56 cm³.

Volume of a cone is the space occupied by it in a three - dimensional space.

Volume of a cone is calculated using the formula:

[tex]V = \frac{1}{3} \pi r^{2} h[/tex]

where r is the radius of the base of the cone

[tex]\pi[/tex] is a constant having value 3.14

h is the height of the cone. It is the perpendicular height from the base.

According to the given condition,

r = 1 cm and h = 3.4 cm

Substituting these values in the equation above,

[tex]V = \frac{1}{3} \pi (1^{2}) (3.4)[/tex]

∴ V = 3.56 cm³.

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The equation in slope-intercept form is y = - (7/5x - 7 ).

The equation of a line is found using the slope-intercept form of a straight line. We need to know the slope of the line and the intercept where the line crosses the y-axis in order to use the slope-intercept formula. Consider a straight line with y-intercept b and slope m. For a straight line with slope "m" and y-intercept "b," the slope intercept form equation is: y = mx + b.

Given the equation is -

-7 x-5 y=35

Divide the equation by 5

-7/5x - y = 7

Rearrange the equation -

y = - (7/5x - 7 ) which is the equation in slope-intercept form.

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Answer:

Step-by-step explanation:

M(6,3)

A(4,-2)⇒A(x1,y1) just incase you understand

B(x2,y2),Now I will use the midpoint formula

[tex]M(\frac{x1+x2}{2} ,\frac{y1+y2}{2} )\\=(\frac{4+x2}{2} ,\frac{-2+y2}{2} )\\=separate(x)\\\frac{4+x2}{2} =6\\4+x2=12\\x2=12-4\\x2=8\\\\\frac{-2+y2}{2} =3\\-2+y2=6\\y2=3+2\\y2=5[/tex]

B(8,5)

Answer:

s = 5

Step-by-step explanation:

V=s^3

125 = s^3

s = 125^(1/3) (cube root)

s = 5

Never mind got it wrong

The value of a in the expression is 15.

It should be noted that an expression shows that relationship that exists between variables.

In this case, we are given the expression that 1/3a = -5

To find the value of a will be:

a/3 = 5

Cross multiply

a = 3 × 5.

a = 15

Therefore, the value of a in the expression is 15.

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1/3a = -5. Find the value of a.

Answer:14

Step-by-step explanation:X+8=asher's age X=Asher's sisters age

x+x+8 =20
2x+8=20
2x+8-8=20-8
2x=12
2x/2=12/2
x=6
x+8=asher's age
6+8=14

The slope of the line of each pair of points 3/2 , - (1/2) and -(2/3) , 1/3 is zero

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x.

We also refer to this tan as the line's slope.

We know that slope, slope = m =  [tex]\frac{y_2 -y_1}{x_2 -x_1}[/tex]

For the pair of points 3/2 , - (1/2)

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

   = 0/(-4)

Hence the slope is zero for these points.

For the pair of points -(2/3) , 1/3

m = [tex]\frac{3-3}{1-(-2)}[/tex]

   = 0/3

Hence the slope is zero for these points.

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Based on the graph, the expected total value of the donations in October would be $460.

When donations were 5 in number, the expected value was £30.

When donations were 8, the expected value was £50.

When donations were 15, the expected value was £90.

The slope of the line is:

= (90 - 50) / (15 - 8)

= 5.71

The y-intercept as seen on the graph is 0.

The equation of the line is therefore:

y = 5.71x

The expected value of £80 in donations is therefore:

y = 5.71 x 80

= $460

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So 1st off you divide 25.2 by 36 since it miles is the x and the cost is y

the unit rate is 0.7 since i divided those 2 numbers

now i just have to do 0.7 times 47

The answer is $ 32.9

sorry if its wrong?

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Answer:

The last one is incorrect

Step-by-step explanation:

Answer:

x=100

Step-by-step explanation:

√x-6+2=6

√x -4 =6

√x =6+4

√x = 10

squere both sides of the equation

x =100

Answer:

A. Jake made a mistake in step 2

Step-by-step explanation:

If you subtract a number from one side, you should do the same for the other. In step 2 Jake subtracted 7 from one side but not from another.

According to the given data the value of the  triangle's angle is m ∠ A =30

A triangle's inner angles always add up to 180°, whereas its outside angles are equivalent to the sum of its two inside angles. equal toward the combination of the two nearest interior angles Another method for calculating a triangle's exterior angle is to subtract overall angle of something like the vertex of concern from 180°.

m ∠ R=41

m ∠S=109

find m∠ A

We know that the total of the triangle's angles must equal 180°.

So ,

(​substitute given values)

m ∠R+ m ∠S +m ∠A =180

(add)

41 + 109 + m ∠A =180

(subtract 150 from both side)

150+m∠A =180

m ∠ A =30

According to the given data the value of the  triangle's angle is m ∠ A =30

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Given statement 'The component form of a vector describes the vector in terms of change in x and change in y.' is True.

For a vector V whose initial point is (x1, y1) and the terminal point is (x2, y2), the component form of a vector V is given as:  < x₂ – x₁, y₂ – y₁ >

The coordinates of the component form of vector are nothing but the ordered pair that describes the changes in the x-values and y-values.

Consider a vector v whose initial point is (1, 3) and the terminal point is   (3, 6).

The component form of vector v is:

<3 - 1, 6 - 3>

= <2, 3>

Here, 2 is the change in the x-values from initial point to terminal point and 3 is the change in the y-values  from the initial point to the terminal point.

Therefore, given statement 'The component form of a vector describes the vector in terms of change in x and change in y.' is True.

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