Given f(x) = 4x − 8 and g(x) = −3x + 1, what is (f − g)(x)?

The corresponding sides and angles of both the triangles [pre-image and the image] are congruent

Hence,The corresponding sides and angles of both the triangles [pre-image and the image] are congruent

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Answer:

y = -2x + 1

Step-by-step explanation:

y = mx + b  you must find the m (slope) and the b (y intercept) to write the equation for the graph.

The slope is negative.  If you start on the very left side of the graph and follow it, you will see that it goes in a down hill direction.  That means that the slope is negative.  If I start on the very left and the line goes up from there, the slope is positive.  If the line is a straight horizontal line, then the slope is zero, it does not go up or down.

The slope is -2.  Select one of the dots and travel to the next dot, but you can only move horizonaly and vertically.  You cannot move diagonally.  You will notice that the two closes dots are two units up (or down) and only 1 unit left (or right) depending on which dot you start at.  Since you move 2 units up and 1 unit left that is a slope of 2.  2/1 = 2.

The b (y-intercept) is just where you see the line cross the y axis.  It crosses it at 1.

Answer:

  y = -2x + 1

Step-by-step explanation:

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

Pick any two points on the line.

(-1,3) & (2,-3).

Find the Slope.

     [tex]\sf \boxed{Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                 [tex]\sf = \dfrac{-3-3}{2-[-1]}\\\\=\dfrac{-6}{2+1}\\\\=\dfrac{-6}{3}\\\\=-2[/tex]

m = -2.

Equation of the line:

     y = -2x + b

Substitute any one point in the above equation and find the y-intercept. (-1,3)

     3 = -2*(-1) + b

     3 = 2 + b

3 - 2  = b

      b = 1

Equation of the line:

        y = -2x + 1

The probability that the number is a multiple of four is 0.25.

we know that if a number is multiple of four then its last 2 digits must be divisible by four.( i.e. ten's and one's places)

We are given only four numbers 1,2,3,4 , which can't be repeated.

So here , in this case , such numbers with last two digits divisible by four are 12,24 and 32 only

Having last two digits ‘12’ ;

the first two digits can be formed using 3 and 4 only . This can be done in (2!) = 2 ways.

Similar case will be happening with 24 and 32 as well.

So the total ways of getting a multiple of four will be = 2 + 2 + 2

                                                                                        = 6 ways

Now total numbers that can be made from given four digits = [tex]P_{4} ^{4}[/tex]

                                                                                                  = 24

So the probability of getting a multiple of four is = 6/ 24

                                                                                 = 0.25

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Answer:

y = [tex]\sqrt{(k-a)}[/tex]

Step-by-step explanation:

k= y^2 + a

k-a= y^2

y^2 = k-a

y = (k-a)^(1/2)

y = [tex]\sqrt{(k-a)}[/tex]

Answer:

[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]

Step-by-step explanation:

To make y-term as the subject of formula means to solve for y-term. First, subtract both sides by a-term, this’ll at least isolate y².

[tex]\displaystyle{k-a=y^2+a-a}\\\\\displaystyle{k-a=y^2}[/tex]

Everything that you do or add to one of both sides, that side will also be done too. (e.g Suppose we have x + 1 = y. If we add 2 to left then 2 should also be added to right too so we’ll have x + 1 + 2 = y + 2)

Then square root both sides to get rid of the exponents of y-term:

[tex]\displaystyle{\sqrt{k-a}=\sqrt{y^2}}[/tex]

If we substitute y = any numbers, we’ll always get positive result. Therefore, this means that y-term can be any positive or negative values. Hence, write plus-minus to the left side then evaluate the square root of y² to y:

[tex]\displaystyle{\pm \sqrt{k-a}=y}[/tex]

Therefore, the new equation written in term of y is:

[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]

The value of x is 18 which is option B.

Given:

Two pyramids are similar.

if two figures are similar then the ratio of their sides are equal.

So, 24/8 =  x/6

24*6 = 8*x

144 = 8x

divide by 8 on both sides

8x/8 = 144/8

x = 144/8

x = 18.

Therefore the value of x is 18 which is option B.

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Answer:

[tex] - 3 \leqslant w < 1[/tex]

Step-by-step explanation:

as shown in picture attached

The equations using any method for the given situation illustrated that:

Equation for Jordan: 225 + 45w

Equation for RayAnn: 150 + 60w

Let the number of weeks be represented by w.

Jordan saved $225 and continues to save $45 each week. The equation for this will be:

= 225 + (45 × w)

= 225 + 45w

RayAnn saved $150 and continues to save $60 each week. The equation will be:

= 150 + (60 × w)

= 150 + 60w

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The solution is Pack #1

The pack which offers Toby the best deal is Pack #1

What is an Equation?

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.

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 data ,

Let the price per card of each pack be = A

Now , the equation is

a)

Pack #1

The number of cards = 12 cards

The cost per pack = $ 29

The equation is

So , the cost of 1 card = cost per pack / number of cards

                                    = $ 2.416

Therefore , the cost of one card in pack 1 is $ 2.416

b)

Pack #2

The number of cards = 24 cards

The cost per pack = $ 89

The equation is

So , the cost of 1 card = cost per pack / number of cards

                                    = $ 3.708

Therefore , the cost of one card in pack 2 is $ 3.708

c)

Pack #3

The number of cards = 24 cards

The cost per pack = $ 213

The equation is

So , the cost of 1 card = cost per pack / number of cards

                                    = $ 8.875

Therefore , the cost of one card in pack 3 is $ 8.875

And ,

cost of one card in pack 3 is $ 8.875 > cost of one card in pack 2 is $ 3.708 > cost of one card in pack 1 is $ 2.416

Therefore , the cost of one card in pack 1 is $ 2.416 and this is the best deal

Hence , The pack which offers Toby the best deal is Pack #1

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Answer: -893

Step-by-step explanation: -900 -(+16) = 884 +(-8) = -893

Answer:

-892

-900+16-2^3=-900+16-8=-900+8=-892

Answer: always, always

Step-by-step explanation:

Every circle is similar to every other circle.

Answer:

k = - 6 , c = 8

Step-by-step explanation:

f(x) = x² + kx + c

given f(2) = 0 , substitute (2, 0 ) into f(x)

0 = 2² + 2k + c

0 = 4 + 2k + c ( subtract 4 from both sides )

- 4 = 2k + c → (1)

given f(- 3) = 35 , substitute (- 3, 35 ) into f(x)

35 = (- 3)² - 3k + c

35 = 9 - 3k + c ( subtract 9 from both sides )

26 = - 3k + c → (2)

subtract (2) from (1) term by term to eliminate c

- 4 - 26 = 2k - (- 3k) + (c - c)

- 30 = 2k + 3k

- 30 = 5k ( divide both sides by 5 )

- 6 = k

substitute k = - 6 into (1) and solve for c

- 4 = 2(- 6) + c

- 4 = - 12 + c ( add 12 to both sides )

8 = c

then

k = - 6 and c = 8

The required number is 94.

Let the digit on unit's place be 'x'

Digit on ten's place be 'y'

Therefore,

Original number = 10y + x

Given, the sum of the digits = 11

=> x + y = 11 →(I)

When the digits are reversed, new number = 10x + y

Therefore,

(10y + x) - (10x + y) = 63

10y + x - 10x - y = 63

9y - 9x = 63

=> y - x = 7 →(II)

Adding (I) and (II) we get

2y = 18

y = 9

Substituting the value of y in (I) we get

x + 9 = 11

x = 2

Therefore,

Original number = 10y + x = 10(9) + 4 = 94

The required number is 94.

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Answer:

x=3 y=4

Step-by-step explanation:

-4x= -6y+12      -1

8x-4y = 8         -2

-4x+6y=12        -1

8x-4y = 8         -2

multiply first equation by 2:

2(-4x+6y=12)

= -8x+12y=24

add with 2nd equation;

-8x+12y=24

       +

8x-4y=8

-8x+8x=0

+12-4y=8y

24+8=32

0+8y=32

y=32/8

y=4

input y into any equation to get x:

-4x= -6(4)+12

-4x = -24+12

-4x= -12

-x= -12/4

x=3

The solutions to the given equation are -5/2 and  -3. These answer can get after using quadratic formula.

The quadratic formula is a formula that offers a quadratic equation's solution. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

In the literature, there are numerous ways to derive the quadratic formula. The common one uses the completing the square method in a straightforward manner.

The given equation is :

-11x = 2x² +15

Move terms to the left side

-11x -(2x^2 +15) =0

Rearrange terms

-2x^2 - 11x -15 = 0

Common factor

-(2x^2+ 11x +15) =0

Divide both sides by the same factor

2x^2 +11x +15 =0

Use the quadratic formula

x = -11 ± √11² - 4 * 2*15/2*2

x =-11±1/4

Solve

x = -5/2

x= -3

The value of x will be -5/2 or -3.

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The simple interest using I = prt if Oliver borrowed $1,500 to purchase a riding lawn mowerat the rate of f 12% for 6 monthsis

The concept that will be used is the concpt of simple interest and thei can be calculates using the simple interst formular which is

I = [(prt)/100]

where p = principal =  $1,500

     I = intereste rate

     t=time

Then this can be expressed as

I= (prt)/100

I =  ($1,500* 6/12 * 12 )/100

=  $90

In conclusion the simple interest is now  $90 which is the second option that is given.

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a) a/5 + 3 = 8

Step 1 : Minus both sides by 3

a/5 + 3 - 3 = 8 - 3 -> a/5 = 5

Step 2 : Multiply both sides by 5

a/5 x 5 = 5 x 5 -> a = 25.

b) (3b)/7 - 1 = 5

Step 1 : Add both sides by 1

(3b)/y - 1 +1 = 5 + 1 -> (3b)/7 = 6

Step 2 : Multiply both sides by 7

(3b)/7 x 7 = 6 x 7 -> 3b = 42

Step 3 : Divide both sides by 3

3b : 3 = 42 : 3 -> b = 14.

The sum of a number w is more than -12 becomes w > -12

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

We have been given that the sum of a number w is more than -12.

Now the sum of a number = w

It is more than -12 means the inequality form as;

w > -12

Therefore, the overall expression becomes w > -12

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By applying the lowest common multiple approach, Kyra may have acquired up to 12 rocks.

What does common factor mean?

A common factor is a whole number that is a factor of at least two other numbers. The highest common factor is the largest factor that will divide into two or more numbers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).

The least common multiple of 2, 3, and 4 can be used to determine how much rock Kyra has.

Several of:

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

3 = 3, 6, 9, 12, 15, 18, 21

4 = 4, 8, 12, 16, 20

The smallest number that 2, 3, and 4 have in common is 12. There are therefore 12 rock piles in Kyra's possession.

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The slope of the line is 1.11

Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line.

Given that, engineers measure angles in gradients, which are smaller than degrees,

Slope = (-200+100)/(-180+90) = -100/(-90) = 10/9 = 1.11

Hence, The slope of the line is 1.11

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Answer:

1.11

Step-by-step explanation:

it's correct.

The equation which represents a cubic polynomial function with zeroes 2, 3 and 5 is; f(x) = x³ - 10x² + 31x - 30.

It follows that if a polynomial function has zeroes, a, b and c; The factors of such polynomial function are; (x - a), (x - b) and (x - c).

Therefore, since the given polynomial function has zeroes, 2, 3 and 5, the polynomial function is;

f(x) = (x - 2) (x - 3) (x - 5)

Therefore, by simplification; we have;

f(x) = (x² - 5x + 6) (x - 5)

f(x) = x³ - 5x² + 6x - 5x² + 25x - 30.

f(x) = x³ - 10x² + 31x - 30.

Therefore, the required cubic polynomial function is; f(x) = x³ - 10x² + 31x - 30.

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The x-intercept of the given graph of the function is (10,0) while the y-intercept is (0,15).

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand the behavior of the graph.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

As per the given equation,

y = (-3/2)x + 15

At y-intercept,

x = 0 so, y = 0 + 15 = 15 thus, (0,15)

At x-intercept

y = 0

0 = (-3/2)x + 15

x = 10 thus, (10,0)

Hence "The x-intercept of the given graph of the function is (10,0) while the y-intercept is (0,15)".

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For the complete question and graph image attached below,

For the equation A=s² for s. Assume s > 0, then s = [tex]\sqrt{A}[/tex].

What are squares and square roots?

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value.

For the given equation, A = s², we have to find the value of s.

thus, taking the square root on both sides, we get

                                     s = [tex]\sqrt{A}[/tex].

Hence, the value of s = [tex]\sqrt{A}[/tex].

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There is a change of 1/2 for Adam to get strictly more heads than Ben.

The likelihood that Ben will get more heads than Adam is equal to the likelihood that Ben will get more tails than Adam. (by symmetry)

If Ben and Adam each have n+1 (101) coins, then Ben will receive more heads or even more tails than B, but never both.

Considering (1) and (2), we find that there is a 50% chance that Adam will get more heads than Ben.

Thus, there is a change of 1/2 for Adam to get strictly more heads than Ben.

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The number of books each boy had based on the 3:1 ratio of the books remaining is 34 books

A ratio is a quantitative expression of the relationship between two values that indicates the relative proportion of each amount.

The initial number of books Ben had = The initial number of books Charlie has

The number of books Ben gave away = 16 books

The number of books Charlie gave away = 28 books

The ratio of the number of books Ben and Charlie had left is 3:1

Let x represent the number of books each of them initially have. Representing the numbers as a ratio gives;

The number of books Ben had left = x - 16

The number of books Charlie had left = x - 28

[tex]\dfrac{x - 16}{(x - 16) + (x - 28)} = \dfrac{3}{3+1}[/tex]

Which gives; [tex]\dfrac{x - 16}{(2\cdot x - 44) } = \dfrac{3}{4}[/tex]

4 × (x - 16) = 3 × (2·x - 44)

6·x - 4·x = 3×44 - 4×16 = 68

2·x = 68

x = 68 ÷ 2 = 34

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Answer:

1.5

Step-by-step explanation:

3÷2=1.5

The solution of the quadratic equation will be;

⇒ x = - 1 ± √5 / 8

⇒ x = –1 Plus or minus Start Root Start Fraction 5 Over 8 End Fraction End Root.

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The quadratic equation is,

⇒ 8x² + 16x + 3 = 0

Now,

Solve the equation as;

⇒ 8x² + 16x + 3 = 0

⇒ 8x² + 16x = - 3

⇒ 8 (x² + 2x) = - 3

Now, Using completing the square as;

⇒ 8 (x² + 2x + 1) = - 3 + 8

⇒ 8 (x + 1)² = 5

⇒  (x + 1)² = 5 / 8

⇒ (x + 1) = ±√5 / 8

⇒ x = ±√5/8 - 1

⇒ x = - 1 ± √5/8

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The angle amount of m is 128⁰

Angle can also refer to the length of a rotation or an angle. The Greek word , which means "crooked, curled," and the English word "ankle," are related words. Both stem from the Proto-Indo-European root  which means "to bend" or "bow," in some way.

A plane angle, according to Euclid, is the inclination to each other of two intersecting lines in a plane that are not perpendicular to one another. Proclus asserts that an angle must be either a quality, a number, or a connection. Eudemus used the first idea, viewing an angle as a departure from a straight line; Carpus of Antioch used the second idea, viewing an angle as the distance or space between intersecting lines; and Euclid used the third idea. Vertical angles, opposing angles, or vertically opposite angles refer to a pair of angles that are directly across from one another and are created by two straight lines meeting to form a "X". Vert is the shorthand for them. opp.

The vertical angle theorem states that angles that are vertically opposing are equal. The assertion shown that since both of a pair of vertical angles are supplementary to both of the neighboring angles, the vertical angles are equal in measure, according to Eudemus of Rhodes' attribution of the proof to Thales of Miletus. When Thales visited Egypt, it is recorded in history[9] that he noticed the Egyptians measuring the vertical angles whenever two intersecting lines were drawn to ensure that they were equal. Thales came to the conclusion that one might establish

4x+6=7x-21

3x=27

x=9

x+x+42+42=360

2x+84=360

x=128⁰

Therefore, the angle amount of m is 128⁰

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The proportional relationship that gives the cost of x pounds of rice is given as follows:

y = 3x.

A proportional relationship is a special case of a linear function, with slope represented by k and intercept of 0, hence the output variable y is obtained with the multiplication of the input variable x and the slope k, as follows:

y = kx.

In this problem, the input and the output are given as follows:

You can buy 3 pounds of rice for 9 dollars use, hence the constant representing the cost per pound is given as follows:

k = 9/3 = 3.

Hence the equation is:

y = 3x.

This problem is incomplete but we suppose that it asks for a proportional relationship giving the cost of x pounds of rice.

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