Complete both transformations below.
Then enter the final coordinates of the figure.
(1,-3)
A
C (2,-5)
B
(5,-1)
A" ([?], [])
B" ([ ], [])
C" ([],[])
1) Reflect across y - axis
2) <4.5>

The given sequence is

1, 1/2, 1/4, 1/8......

we can see that the ratio of the consecutive terms is the same. We have

1/2/1 = (1/4)/(1/2) = (1/8)/(1/4) = 1/2

This means that it is a geometric sequence

To find the amount of the substance left after 21 half lifes, we would find the 21st term of the sequence. The formula for finding the nth term of a geometric sequence is

an = a1r^(n - 1)

a1 = 1

n = 21

r = 0.5

Thus,

a21 = 1 * 0.5^(21 - 1) = 0.5^20

a21 = 0.00000095367

a21 = 1/1048576

The answer makes sense in the problem context because it follows the common ratio that was established at the begining.

The slope of the line that passes through (2, 2) and (10, 6) is; 1/2.

The slope of parallel lines is the same. Slopes of perpendicular lines are negative reciprocals of each other. The slope of a line or straight object is the ratio of how much amount of rising occurs in correspondence to the increment in the run.

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

We have been given that the line that passes through (2, 2) and (10, 6).

Let ( p,q) and (x,y) are (2, 2) and (10, 6) respectively.

Slope = [tex]m = \dfrac{y-q}{x-p}[/tex]

m = (2-6)/(2-10)

m = 4/8

m = 1/2

Then the slope is 1/2.

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Before we can proceed in graphing the complex number, let's get the sum of the two given complex numbers first.

When adding complex numbers, simply combine similar terms like real-to-real and complex-to-complex only.

So, we have:

Hence, the sum of the two complex numbers is 1 - 4i.

When plotting a complex number in the plane, the real number acts as the x-coordinate and the complex number acts as the y-coordinate.

Hence, the x-coordinate is 1 while the y-coordinate is -4.

Here's the graph of the sum.

Answer:

5

Explanation:

Given the below function;

To find u when c = 1, all we have to do is substitute the value of c into the above equation and solve for u;

Answer:

f(n) = 8000(1.67)ⁿ⁻¹

Explanation:

The equation for exponential growth has the following form:

Where a is the initial amount, r is the growth rate and x is the variable.

In this case, we know the amount after the first year and the growth rate and the variable is the number of years. So, replacing a by 8,000 and r by 0.67 and x by (n-1) because we will not include the 1st year, we get:

Therefore, the explicit equation for f(n) is:

1) If the function g(x) =-2x² +3 is translated vertically upward then we need to add 7 units, to that.

2) So the function h(x) is going to

h(x) = g(x) +7

h(x) = -2x² +3 +7

h(x) =-2x² +10

We're given:

One of the forms of a quadratic equation is vertex form:

[tex]y=a(x-h)^2+k[/tex]

Plug in the vertex:

[tex]y=a(x-h)^2+k\\y=a(x+5)^2-5[/tex]

Plug in the given point and solve for a:

[tex]3=a(-7+5)^2-5\\3=a(-2)^2-53=4a-5\\8=4a\\a=2[/tex]

Plug 2 into the equation as a:

[tex]y=2(x+5)^2-5[/tex]

[tex]y=2(x+5)^2-5[/tex]

Step-by-step explanation:

Hello ,nice too meet you✨

Spanish club has 48 tickets which must be sold to reach the fund-raising goal as profit of $600.

What is profit?

In mathematics, the term profit can be explained as the amount which is on the standard cost price. For the profit, the amount of the commodity can be designed by the shopkeeper which is bigger amount as per the cost price.

According to the question, the total profit from the Spanish club fundraiser varies directly with the number of dinner tickets sold.

If the sale of 14 tickets results in a profit of : $175.

Therefore, Profit in 1 ticket = 175/14 = 12.5 dollars

Let us assume 'x' tickets are sold in order to reach the fund-raising goal of $600.

x = (14/175)(600) = 48

x = 48 tickets

Hence, 48 tickets must be sold to reach the fund-raising goal as profit of $600.

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In triangle XYZ, measure as shown below

Step 1: Using Cosine rule

Hence the value of x = 33.004

ok

To solve this problem, I'll use trigonometric functions,

The trigonometric function that relates the opposite side and the hypotenuse is sine

Formula

sin 48 = Opposite side / hypotenuse

hypotenuse = 105 ft

opposite side = H

Substitution

sin 48 = H/105

Solve for H

H = 105*sin 48

Simplification

H = 105*0.743

Result

H = 78 ft

Answer:

At the same rate, she will travel 638 miles if she drives 11 hours.

Step-by-step explanation:

[tex]\frac{754 miles}{13 hours\\} = \frac{x}{11 hours}[/tex]

x=11*754/13

x=638

A V-shaped graph belongs to an absolute value function or a piecewise function, never to a linear function (these are graphed only with a single line).

This is really trivial question.

So the answer is really trivial, as you can see.

But let's explain it a little bit more.

The only functions that have V-shaped graphs are piecewise functions (formed of two linear equations) or absolute value equations, neither of these are exactly linear (but they are made of "linear like parts").

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For you to input the information in a Matix you only have to consider the coefficients corresponding to each variable in each equation, in this case the matrix is:

1 -1 4 : 4

6 -8 1 : -1

4 1 0 : 0

This is the matrix for the given equations

The dividend when the divisor is 8 and the quotient is 96 with a remainder of 3 is 771.

The dividend in mathematics is the value that is divided by another value to obtain the result. The dividend is the starting point for any division method. The dividend is one of four critical components of the division process. It is the whole that is to be divided into equal parts.

A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another integer to produce n. In this case, n is also said to be a multiple of m.

In this case, the dividend will be:

= (96 × 8) + 3

= 768 + 3

= 771

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The coordinates of the vertices of the original shape are given to be:

The transformed shape coordinates are given to be:

On observation, the shapes show a dilation and a shift in position.

The image has a scale factor of 1/2, meaning it is reduced by 1/2. Therefore, the original coordinates will be reduced to give:

The translation of the initial image can be gotten by subtracting the corresponding coordinates:

All the differences are the same. This means that the image moves to the right by 4 units and down by 1 unit.

The dilation rule with a scale factor of k is given to be:

The translation rule for a units to the right and b units down is given to be:

Combining both rules, we have:

Given:

Therefore, the transformation is given to be:

Answer:

d

Step-by-step explanation:

The number of years must be non-negative.

This eliminates all of the options except for d.

Solving for x, the value of x is 37/53

An expression that has been created utilizing integer variables, constants, and algebraic operations is known as an algebraic expression. As an illustration, the algebraic expression 3x2 2xy + c

Given,

51x + 2x = 37

To resolve the x equation

51x + 2x = 37

Including the xs

53x = 37

53 divided between the two sides

53x/53 = 37/53

x = 37/53

As a result, by solving for x in the subsequent steps, we obtain:

x = 37/53

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Question: What is the number of terms in this expression? m/5 + 4.6

Answer:

Two terms

Explanation:

Addition and subtraction separate terms but division and multiplication do not, so they are two terms in the below expression;

The terms are m/5 and 4.6

Step 1

The original blueprint of the family has a scale of 2inches=5feet

The family wants to use a new blueprint that shows the length of the living room to be 15 inches.

Step 2

The width of the living room is

Hence, the length of the living room is

So the new scale is;

The width of the new print is;

Hence the scale of the new print is; 5inches = 8feet

Width of new blue print=9.375inches

Answer:

Slope:

7/3

y-intercept:

(0, −3)

Step-by-step explanation:

For this question, we can see our function has two variables ("x" and "y"). So all we h=need to do is to substitute the different values of "x" to get the corresponding values of "y". So, let's calculate as follows:

Once we got all y-values we can finish our table as follows:

And that is our final answer.

The linear equations are x  +  y  =  10 and (11.90)x  +  (13.10)y  =  (12.86)(10) and the value of x and y are 2 and 8 respectively.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A coffee distributor needs to mix a(n) Queen City coffee blend that normally sells for $11.90 per pound.

Let x and y be the quantity of Queen City coffee (lbs) and the quantity of Arabian Mocha coffee (lbs)

From the data given;

The equations can be framed:

x  +  y  =  10

(11.90)x  +  (13.10)y  =  (12.86)(10)

After solving the substitution method:

x = 2

y = 8

Thus, the linear equations are x  +  y  =  10 and (11.90)x  +  (13.10)y  =  (12.86)(10) and the value of x and y are 2 and 8 respectively.

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A direct proportional relation can always be express as an equation of the form:

where k is the constant of proportionality. (This means that y has to be the result of multiplying a number by x)

Now, let's see at the option we have.

a)

Solving the equation for y we have:

Since we can write the equation in the form as a direct proportional relationship we conclude that option a shows a directly proportional relationship and that the constant is -1.

b)

For this case we have the equation:

From it we already can see that this means that x is directly proportional to y and that the constatn of porportionality is 0.125.

Now if we want we can solve the equation for y, then we have:

this equation shows that y is directly proportional to x and that the constant of proportionality is 8.

Notice that the the constant of proportionality changes if we write the relation as x directly proportional to y or if we write it as y directly proportional to x. Either way the relation express the same and it is directly proportional.

c) and d)

For this equations that we have a division in which one of the variables is the divisor (or the denominator); this means that the equation show a relation between x and y but their are not directly proportional. In fact this means that the equations show an inversely proportional relations.

The equation of tangent is y = -2x + 20. The slope of the tangent line is negative 2. And coordinate of point A is (10, 0). And the length of AB is 22.36 units.

The equation of the circle with center at origin and radius r is given as,

x² + y² = r²

The slope of the tangent line to the circle at points (8, 4) is given as,

2x + 2y (dy/dx) = 0

dy / dx = - 8 / 4

m = - 2

Then the equation of the line is given as,

y = -2x + c

The equation is passing through (8, 4), then we have

4 = -2(8) + c

c = 4 + 16

c = 20

The equation is y = -2x + 20. Then the x-intercept is given as,

y = 0

-2x + 20 = 0

2x = 20

x = 10

Then the length of the line is given as,

AB² = (10 - 0)² + (0 - 20)²

AB² = 100 + 400

AB = √(500)

AB = 22.36 units

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Given:

The graph of modulus function is given.

The modulus function is defined as,

For the given graph,

Hello! First, let's write the equation:

Answer:

a. x ≥ 6

Explanation:

If a number is at least 6, then, the number is greater than or equal to 6.

Since the symbol ≥ means greater than or equal, the correct answer is:

a. x ≥ 6

Let:

The slope is given by: