What is the image point of (1,4)(1,4) after a translation left 5 units and down 5 units?

Answer: (1, 34) and (2, 17)

Step-by-step explanation:

Step 1: Divide 34 by the smallest prime factor.

34/2 = 17

Step 2: Since 17 itself is a prime number, therefore, it is divisible by 17 only.

17/17 = 1

Step 3: Now further division is not possible. Thus, we will consider 2 and 7 as the prime factors of 34.

The quadrilateral with vertices (2 , 5), (4 , 8), (7 , 6), and (5 , 3) is a rectangle.

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)

In a rectangle, each pair of adjacent side/line is perpendicular with each other, thus, the slope is negative reciprocal of one another. Also, opposite sides are parallel, thus their slopes are equal.

let A = (2 , 5)

B = (4 , 8)

C = (7 , 6)

D = (5 , 3)

(8 - 5)/(4 - 2) = (3 - 6)/(5 - 7)

3/2 = -3/-2

3/2 = 3/2

(6 - 8)/(7 - 4) = (3 - 5)/(5 - 2)

-2/3 = -2/3

(8 - 5)/(4 - 2) = (6 - 8)/(7 - 4)

3/2 = -2/3

(6 - 8)/(7 - 4) = (3 - 6)/(5 - 7)

-2/3 = 3/2

(3 - 6)/(5 - 7) = (3 - 5)/(5 - 2)

3/2 = -2/3

(3 - 5)/(5 - 2) = (8 - 5)/(4 - 2)

-2/3 = 3/2

Using the slope of the line connecting the vertices, we have proved that the quadrilateral with vertices (2 , 5), (4 , 8), (7 , 6), and (5 , 3) is a rectangle.

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The word “quantity” indicate to use a variable

The phrase is given as:

quantity

In an algebraic expression, phrases are used to indicate variables

So, anywhere the word is used, it implies that we make use of a variable

Take for instance:

A quantity is more than 2 means x > 2

Hence, the word “quantity” indicate to use a variable

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Answer: x=

7.5

Step-by-step explanation:

Answer:7.5

Step-by-step explanation:

move all unknowns to one side by either adding or subtracting from both sides

so, subtract 4x from both sides and you get 2x-10=5

now mode -10 to the other side by adding 10 to both sides. you get 2x=15

divide both sides by 2 to get x by itself

you get x=7.5

The amount that Jared needs before taxes for his new computer is $606.19

What does before-tax price mean?

The before-tax price means the amount that Nick needs to acquire the laptop before considering the sales  tax of 7.25%, but after having factored in the layway fee of 1.2%

before-tax price=cost of computer*(1+layway fee %)

cost of computer=$599

layway fee=1.20%

before-tax price=$599*(1+1.2%)

before-tax price=$ 606.19

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The point-slope form be y - 7= 0.4(x - 6) then 0.4x - y = -4.6 be the standard form.

Given:

(x1, y1) = (6, 7)

The value of m = 2/5

The point-slope form is given by, y - y1 = m(x - x1)

substitute the values in the above equation, we get

y - 7 = 2/5(x - 6)

simplifying the equation,

y - 7 = 0.4(x - 6)

Therefore, the point-slope form is y - 7= 0.4(x - 6)

Standard form is Ax + By = C

Since, slope-intercept form is y = 0.4x + 4.6

⇒ 0.4x - y = -4.6

Therefore, 0.4x - y = -4.6 is the standard form.

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The required solution for the given arithmetic problems are,
A) 2/5
B) 72 / 125
C) 6, 3/4, 12/5, and 3/10
D) 4, 1/6 and 6

A) 12/25 times 15/18.
Division of two fractions performed as multiplication of numerator of one fraction with a denominator of another function over a denominator of one function with a numerator of another function.
= 12 / 25  * 15 / 18 = 2 / 5

Similarly

b) 12/25 divided by 15/18.
= [12 / 25 ] / 15 / 18
= 12 / 25 * 18 / 15
= 72 / 125

C) 6 and 3/4 times 1 and 2/5
 6 * 1 = 6
3 / 4 * 1 = 3/4
6 * 2/5 = 12/5
3/4 * 2/5 = 3 / 10

D) 4 and 1/6 divided by 1 and 2/3.
= 4 / 1 = 4
= 1/6  / 1 = 1/6
= 4 / 2/3 = 6
= 1/6 / 2/3 = 1/4

Thus, the required solution for the given arithmetic problems is mentioned above.

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The smallest domain element of the relation is 2

The domain of the function is the set of input values of the graph

The relation is given as

R = {(2, 3), (3, 3), (4, 4), (5, 7), (7, 9), (12, 11), (14, 13)}.

Remove the y values to determine the domain

So, we have

Rx = {2, 3, 4, 5, 7, 12, 14}

The smallest element in the above list is 2

So, we have

Smallest Rx = 2

Hence, the smallest domain element of the relation is 2

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Answer:

true

Step-by-step explanation:

Explicit formulas for arithmetic sequences are derived from terms in arithmetic sequences. It helps to find each term in arithmetic progression easily. The arithmetic progression is a1, a2, a3, ..., an. where the first term is denoted as 'a', we have a = a1, and the tolerance is denoted as 'd'. The tolerance formula is d = a2 - a1 = a3 - a2 = an - an - 1. The nth term of the arithmetic progression represents the explicit formula for the arithmetic progression.

Explicit formula: an= a + (n − 1) d

Explicit formula: Sn = n/2 [2a+(n-1) d]

Where,

nth term in the arithmetic sequence

a = first term in the arithmetic sequence

d = difference (each term and its term difference) previous term, i.e., d = an-an-1

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An equation in slope intercept form the line which goes through the points (0,3) and (4,-5) is;

⇒ 2x + y = 3

Here,

The line passes through the points (0,3) and (4,-5).

We have to find an equation in slope intercept form the line which goes through the points (0,3) and (4,-5).

What is Equation of line?

The equation of line passes through the point (a, b) with slope m is;

y - b = m (x - a)

Now,

The line passes through the points (0,3) and (4,-5).

Hence, The slope is given as;

[tex]m = \frac{y_{2}-y_{1} }{x_{2}- x_{1} } = \frac{-5-3}{4-0} = -2[/tex]

Therefore, the equation of line is;

y - y₁ = m (x - x₁)

y - 3 = -2 (x - 0)

y - 3 = -2x

2x + y = 3

Hence, An equation in slope intercept form the line which goes through the points (0,3) and (4,-5) is;

⇒ 2x + y = 3

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Answer:

Hope this helps :)

24.263 = 24.3

341.276 = 341.28

299.61 = 300

4,123.499 = 4,123

5.246 = 5.25

Step-by-step explanation:

When rounding first look at the number next to the place that is told to rounded to (for example, they tell you to round to nearest tenth, then look at the place value next to it). If that number is 1, 2, 3, or 4 then round down, and if that number is 5, 6, 7, 8, or 9 then round up.

The equation of the line 2x - y = 9 expressed in slope-intercept form is y = 2x - 9 with a slope equal to 2.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the equation of the line 2x - y = 9, which is in standard form, transform it into slope-intercept form by isolating the variable y in one side.

2x - y = 9

y = 2x - 9

Hence, the equation of the line in slope-intercept form is y = 2x - 9 where the slope is equal to m = 2.

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Answer:

Mean:  76

Median:  69

Mode:  63

Range: 46

Standard deviation: 15.5

Step-by-step explanation:

Given:

If each value in the data set is increased by a constant k, the mean, median, and mode will be increased by k.  

The range and standard deviation will remain unchanged.

Therefore, if each value in the data set is increased by 14:

Step-by-step explanation:

12 degres below 0 is -12°C ..so the temperature rose from -12°C to 24°C

The difference now from Morning to afternoon is

=24°C-(-12°C)

=24°C+12°C

=36°C

Finding the equation of the parabola, it is found that the height of the diving board is of 24 feet.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

From the maximum height, it is found that the vertex is at (1,25), hence:

h = 1, k = 25.

Hence:

y = a(x - 1)² + 25.

You hit the water 6 feet from the diving board, hence y(6) = 0, meaning that we use it to find a as follows:

0 = a(6 - 1)² + 25

25a = -25.

a = -1.

Hence:

y = -(x - 1)² + 25.

The height of the diving board is y(0), hence:

y = -(0 - 1)² + 25 = -1 + 25 = 24 feet.

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By substitution, the solution of the system of equations,  x + 6y = 2 and 5x + 4y = 36, is (8 , -1).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + 6y = 2     (equation 1)

5x + 4y = 36     (equation 2)

Using the first equation, find the value of one variable, lets say x, in terms of the other.

x + 6y = 2     (equation 1)

x = 2 - 6y

Substitute the value of x to the second equation.

5x + 4y = 36     (equation 2)

5(2 - 6y) + 4y = 36

10 - 30y + 4y = 36

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

10 - 30y + 4y = 36

-30y + 4y = 36 - 10

-26y = 26

y = -1

Substitute the value of y in the equation of x.

x = 2 - 6y

x = 2 - 6(-1)

x = 2 + 6

x = 8

Hence, the solution of the given system of equations is (8 , -1).

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Answer:

A

Step-by-step explanation:

x² - 14x

using the method of completing the square

add ( half the coefficient of the x- term )² to x² - 14x

x² +2(- 7)x + (- 7)²

= x² - 14x + 49

= (x - 7)² ← perfect square

The missing terms are 1.4, 0.8, 0.2

The series is ,

2, __, __, __, -0.4,...

To find the missing terms of the arithmetic sequence , we need to find the the common difference (d).

So formula to find the value of d

[tex]t_{n}[/tex] = a+ (n-1)d

Where [tex]t_{n}[/tex]= nth term of the series

           a = first value of the sequence

           n = number of terms

Here

          [tex]t_{5}[/tex]= -0.4

          a = 2

          n = 5

-0.4= 2 + 4d

d = -0.6

Now we will add -0.6 from the first number of the series, so we get

[tex]t_{2}[/tex] = 2+(-0.6)

   =2-0.6

   = 1.4

[tex]t_{3}[/tex] = 1.4 - 0.6

   = 0.8

[tex]t_{4}[/tex] = 0.8 - 0.6

    0.2

Therefore the Missing terms of the series = 1.4, 0.8, 0.2

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the order of titles according to the correct description boxes is  (0, 4.9), (-3,10), (-9, -3) and then (4.9, 10) respectively.

We first look at the graph, and then, we analyze it, completing the tiles.

From the graph, the function is increasing in two intervals (-10,-9) and (4.9,10). The function is increasing over two interval, (-10, -9) and (4.9,10) , so the corresponding tile is (4.9, 10) for increasing in two intervals.

Between -9 and 4.9 the function is decreasing, so the corresponding tile is (0, 4.9).

An interval where the function is above the x-axis, so between -9 and -3, and then above 10, so the corresponding tile is (-9,-3) for interval over which the difference is positive.

Interval over which the difference is negative is when an interval where the function is below the x-axis, so before -10, and then between -3 and 10. Thus the corresponding tile is (-3,10).

Therefore, we can conclude the following relations

interval in which difference of the number of sales is decreasing→ (0, 4.9)

interval over which difference of the number of sales is negative→ (-3,10)

interval over which difference of the number of sales is positive→  (-9, -3)

interval in which difference of the number of sales is increasing→ (4.9, 10)

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The sum of the given finite series is -5050

The summation notation is used to expressed a long summation into a single formula.

Expand the sum of the given finite series:

[tex]\sum\limits^{100}_{n=0} {(-1)n} =0-1-2-3-...-100[/tex]

The right side is an arithmetic series. We can ignore the 0 in the first term, so the arithmetic series is:

-1 -2 - 3 -4 - ... - 100

We get:

a(1) = -1

d = -2 - (-1) = -1

a(n) = -100

n = 100

Substitute these parameters into the sum formula:

S(n) = n/2 [a(1) + a(2)]

S(100) = 100/2  [-1 + (-100)]

S(100) = 50 . (-101) = -5050

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Answer:

[tex]x = 1 + \frac23c[/tex]

Step-by-step explanation:

Hello!

Solve for x by isolating the variable.

The solution for x is [tex]x = 1 + \frac23c[/tex].

Using the converse of same-side interior angle theorem, the complete proof that shows why lines l and m are parallel is explained below.

According to the converse of same-side interior angle theorem, if two same-side interior angles that are formed on two lines that are intersected by a transversal are supplementary, then the two lines are parallel to each other.

To prove that lines l and m are parallel to each other, the following proof with statements and reasons that justify each are given below:

Statement                                                 Reasons                                        

1. <2 and <5 are supplementary             1. Given

2. <3 ≅ <2                                                 2. Vertical angles theorem

3. <3 and <5 are supplementary            3. Transitive property

4. l║m                                                        4. converse of same-side interior        

                                                                     angle theorem

Thus, using the converse of same-side interior angle theorem, the complete proof that shows why lines l and m are parallel is given above.

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The simplification of difference of the given two rational expressions [tex]\frac{x}{x^{2} -4}+\frac{1}{x+2}[/tex] is equal to 2(x-1)/ (x-2)(x+2).Restriction on the variables is given by x≠ -2,  x≠ 2.

As given in the question,

Given expression is [tex]\frac{x}{x^{2} -4}+\frac{1}{x+2}[/tex]

Simplify the given two rational expressions by factorizing them,

[tex]\frac{x}{x^{2} -4}+\frac{1}{x+2}\\\\= \frac{x}{(x-2)(x+2)}+\frac{1}{x+2}\\\\= \frac{x+x-2}{(x-2)(x+2)}\\\\= \frac{2x-2}{(x-2)(x+2)}\\\\= \frac{2(x-1)}{(x-2)(x+2)}[/tex]

Restriction on the variables is given by  x≠ -2,  x≠2.

Therefore, the  simplification of difference of the given two rational expressions [tex]\frac{x}{x^{2} -4}+\frac{1}{x+2}[/tex] is equal to 2(x-1)/ (x-2)(x+2). Restriction on the variables is given by x≠ -2,  x≠ 2.

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For the given inequality 6 x+9<7 x, x is greater than 9

Inequality is the relation between two expressions linked by the arithmetic expression other than equal sign. Such as less than (<), greater than (>), less than equal to (<=) and greater than equal to (>=).

Let's solve the inequality

6 x+9<7 x

Separate the variables and constants by moving them on the same side. Such as

9<7x-6x

9<x

We want to keep the variable on the left side. Then, just interchange the positions.

x>9

Therefore, it is clear that x is greater than 9.

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The given expression:

(3/8)*( 1 + √49)^2 - (4 - 1)^3

Can be simplified to -3.

So we have the equality:

(3/8)*( 1 + √49)^2 - (4 - 1)^3 = -3

Which means that the first option is the correct one.

Here we have the expression:

(3/8)*( 1 + √49)^2 - (4 - 1)^3

(I think is something like that)

And we want to simplify it, so first let's simplify the things inside the two parentheses.

The first one is:

1 + √49

We know that 7*7 = 49, then the square root of 49 is 7.

1 + √49 = 1 + 7 = 8

The other one is:

4 - 1 = 3

Replacing that in the expression we get:

(3/8)*( 1 + √49)^2 - (4 - 1)^3 = (3/8)*(8)^2 - (3)^3

Now we can solve the exponents:

8^2 = 8*8 = 64

3^3 = 3*3*3 = 27

Replacing that we get:

(3/8)*64 - 27 = 3*8 - 27 = 24 - 27 = -3

We conclude that the given expression:

(3/8)*( 1 + √49)^2 - (4 - 1)^3

Can be simplified to -3.

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Answer: take a picture of it please

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

To answer the problem:

PK * PN = PL^2

Let PN = x

8x = 10^2

8x = 100

x = 100/8

x = 12.5

KN = PN - PK

12.5 - 8 = 4.5 would be the length of segment KN.

Step-by-step explanation:

when x increases by 1. y decreases by 7.

e.g. from (-4, 7) to (-3, 0).

the slope is therefore -7/1 = -7.

the slope is always the factor of x in the equation.

y = -7x + b

b is the y-intercept (the y value when x = 0).

let's use e.g. (-3, 0) to get b :

0 = -7×-3 + b = 21 + b

b = - 21

so, the full equation is

y = -7x - 21