Find the vertex and axis of symmetry

To change the base of an exponential function, we can use the formula:

log_b(a) = log_c(a) / log_c(b).

To change the base of an exponential function, you can use the property that logarithms with different bases are related by the following equation:

log_b(a) = log_e(a) / log_e(b)

Where log_b(a) is the logarithm of a to the base b and log_c(a) is the logarithm of a to the base e.

For example: To change log_3(7) to log_e(x)/log_e(y), we can use the property that logarithms with different bases are related by the following equation:

logb(a) = logc(a) / logc(b)

So log_3(7) = log_e(7) / log_e(3)

To find x and y we can use the logarithm properties and the definition of logarithm:

log_e(x) = log_e(7)

x = 7

log_e(y) = log_e(3)

y = 3

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Answer:

5

Step-by-step explanation:

You should do cross multiplication.

Multiply 3 by 10 and 6 by 'h'

So 3×10=6h

6h=30

h=30÷6=5

Marking of points A and B in 4 cm apart and shaded the region that is closer to B than to A and within 3 cm of B, in the coordinate plane.

The cartesian coordinate system includes a two dimensional plane known as the Cartesian Plane. Rene Descartes created the cartesian plane in the 17th century. The cartesian plane's ability to connect Euclidean geometry and algebra is its most significant characteristic.

Numerical coordinates can be used to describe any point on a cartesian plane. An ordered pair is used to express a point's coordinates on a cartesian plane. These points are also signed, and their distance from two perpendicular lines known as axes is fixed.

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Answer:

2+2%2%5+51%895%+8+81%9+61%+5%+8+%15+%

Answer:

(- 8, - 6 )

Step-by-step explanation:

y = 2x + 10 → (1)

y = x + 2 → (2)

substitute y = 2x + 10 into (2)

2x + 10 = x + 2 ( subtract x from both sides )

x + 10 = 2 ( subtract 10 from both sides )

x = - 8

substitute x = - 8 into either of the 2 equations and evaluate for y

substituting into (2)

y = - 8 + 2 = - 6

solution is (- 8, - 6 )

The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left

You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal.  The graph is a diagram that illustrates the statement.

The given inequality is 2(b + 2) > 24

Opening the brackets to get

2b+4≥24

2b≥24-4

This implies that 2b≥20

Making b the subject

b≥20/2

b≥10

Conclusively the graph is a number line with closed point at 10 with arrow pointing left

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An ordered pair is a refers to the of the x coordinate and the y coordinate of a point. They have two values which is written in a specific order and is quoted by parentheses.

It is used when we need to solve some problems and it also has utilization in the field of statistics.

Ordered pair are also used in coordinate geometry, they are used to portray geometric objects and figures in open space which helps to improve visual perception.

Ordered pairs are used to represent the center, vertices, and length of the sides of a square, circle, rectangle, or polygon with coordinates.

Example:  ( 2 , 4).

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Total number of prime numbers which are twin are infinite and its general form is given ( 6n - 1 , 6n + 1 ) apart from ( 3, 5 ) where 'n' represents the natural number.

As given in the question,

Prime numbers are those numbers which have only two factors one and the number itself.

Prime numbers which are twins are defined as when the difference between two prime number is equal to 2.

Example of twin prime numbers are as follow :

( 3, 5 ) , ( 5, 7 ) , ( 11 , 13 ) , ( 17 , 19 ) , ( 29 , 31 ), ( 41, 43 ) ,...........,(6n - 1 , 6n + 1 )

where 'n' represents the natural number.

5 is the only prime number which exist in two pairs of twin prime numbers.

Apart from ( 3,5 ) all the twin prime numbers divided by 12.

Therefore, there are infinite prime numbers which are representing as a twin prime numbers.

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the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5). We were then asked to find the number of years elapsed when the trees are at the same height.

In this problem, we were given two different trees, one that is 3 feet tall and growing at a rate of 1 foot per year, and another that is 5 feet tall and growing at a rate of 0.75 feet per year. The ordered pair (3,1) represents the 3-foot tall tree growing at a rate of 1 foot per year and the ordered pair (5,0.75) represents the 5-foot tall tree growing at a rate of 0.75 feet per year.

To find the number of years elapsed when the trees are at the same height, we need to solve the equation:

3 + 1t = 5 + 0.75t

t = (5 - 3)/(1 - 0.75) = 2/0.25 = 8

So the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5).

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To calculate how many flowers of each kind Marisol created, use the formulae x+y=96 and x+3y=192. Marisol used 48 tulips in total to produce Garden Delight bouquets on Monday and Tuesday.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Let x be Spring Mix bouquets and y be the Garden Delight bouquets.

x+y=96

x+3y=192

2y=96

y=48

x=48

The system of equations that you can use to find how many bouquets of each type Marisol made is x+y=96 and x+3y=192. The total number of tulips Marisol used to make Garden Delight bouquets on Monday and Tuesday is 48.

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Answer:

The result can be shown in multiple forms.

Point Form: ( 2, − 2 )

Equation Form: x = 2 , y = − 2

Step-by-step explanation:

1. Eliminate the equal sides of each equation and combine them.
2x − 6 = − 5x + 8

2. Solve 2x − 6 = −5x +8 for x.

x = 2

3. Evaluate y when x = 2.

y = − 2

The solution to the system is the complete set of ordered pairs that are valid solutions.

( 2, − 2 )

The result can be shown in multiple forms.

Point Form: ( 2, − 2 )

Equation Form: x = 2 , y = − 2

Answer:

x = 2

y = -2

Step-by-step explanation:

Substitute equation 1 into equation 2 then solve for x:

2x - 6 = -5x + 8

7x = 14

x = 14/7 = 2

Now substitute x=2 into either equation to solve for y:

y = 2(2) - 6 = -2

The expression that represents the cost (in dollars) of renting a paddleboard for h hours is r + xh

From the question, we have the following parameters that can be used in our computation:

Cost of rents:

Charging a rental fee plus an hourly rate.

Using the above as a guide, we have the following:

Initial rental fee = r

Hourly rate = x

The cost for h hours can then be represented as

C(h) = Initial rental fee + Hourly rate * Number of hours

Substitute the known values in the above equation, so, we have the following representation

C(h) = r + x * h

Evaluate

C(h) = r + xh

Hence, the expression is r + xh

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The slope of the line passing through the equation 4x - 3y = 12 is given by Slope m = -3/4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

4x - 3y = 12   be equation (1)

Now , on simplifying the equation , we get

Adding 3y on both sides of the equation , we get

3y + 12 = 4x

Subtracting 12 on both sides of the equation , we get

3y = 4x - 12

Divide by 3 on both sides of the equation , we get

y = ( 4/3 )x - 4

It is of the form y = mx + b where m is the slope and b is the y-intercept

So , slope m₁ = 4/3

Now , the line is perpendicular to the line y = ( 4/3 )x - 4

So , the product of their slopes is -1

And , m₁ x m₂ = -1

Substituting the values in the equation , we get

m₂ = ( 3/4 ) x -1

m₂ = -3/4

Hence , the slope of the line is -3/4

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The perimeter of a soccer field is 304 meters. The field is 96 meters long. So, its wide becomes: 56 m

The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it. The perimeter of the form is equal to the algebraic sum of each side's length. For the various geometric forms, there are formulae accessible. The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths.

Given that,

The perimeter of a soccer field is 304 m

length of the field is 96 m

wide = ?

As we know,

perimeter = 2 (length + width)

or, 304 = 2 (96 + width)

or, 304 = 192 + 2 width

or, width = 112 /2

or, width = 56 m

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The three different forms of slope formulas are m=(y-b)÷x, m=(y-y₁)÷(x-x₁), and m=(-A)÷B.

The slope gives the steepness of a straight line. The three different forms of the slope of a linear equation are slope-intercept form, point-slope form, and standard form.

From the equation of slope-intercept form y=mx+b, the slope is calculated using the formula, m=(y-b)÷x. Here, the slope is m and the y-intercept is b.

From the equation of the point-slope form (y-y₁)=m(x-x₁), the slope is calculated using the formula, m=(y-y₁)÷(x-x₁). Here, points on the line are x₁ and y₁.

From the equation of standard form Ax+By=C, the slope is m=(-A)÷B. Here, constants or integers are A, C, and B.

In general, the slope is calculated using the formula, m = (Δy)÷(Δx)= (y₂-y₁)÷(x₂-x₁). Here, in the line, the coordinate of the first point is (x₁, y₁), and the second point is (x₂, y₂).

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We know that the bank charges $2.25 per month plus $0.10 per bill paid using the service. Let x be the number of bills paid using the service.

The total cost of the service is:

Cost = 2.25 + 0.10x

We also know that the charges are always between $3.50 and $5.00. So we can write this as an inequality:

3.50 <= Cost <= 5.00

To find the number of bills, we can substitute the expression for cost into the inequality:

3.50 <= 2.25 + 0.10x <= 5.00

We can solve this inequality by isolating x on one side:

0.10x >= 1.25

x >= 12.5

So the number of bills paid using the service is greater than or equal to 12.5.

She could pay exactly 12 bills, 13 bills, 14 bills and so on.

The solution is x >= 12.5

Let's call the number of bills paid per month as "x"

We know that the total cost is:

$2.25 (fixed monthly fee) + $0.10x (cost per bill paid)

We also know that the total cost is between $3.50 and $5.00

Therefore, $3.50 <= $2.25 + $0.10x <= $5.00

To solve for x, we can first isolate x by subtracting $2.25 from both sides of the inequality:

$1.25 <= $0.10x <= $2.50

Now we can divide both sides of the inequality by $0.10 to get:

12.5 <= x <= 25

It means that the number of bills paid per month using the service is between 12 and 25 bills, Debbie can pay at least 12 bills and at most 25 bills.

The solution of equation: 2y + 8x = 2(y + 4)x.

For the stated equation:

= 2y + 8x

As. 2y and 8x both are divisible by 2 .

So, Taking two common from both.

= 2(y + 4x)

Thus, the solution of the equation becomes: 2(y + 4x).

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Answer:

9 units

Step-by-step explanation:

The y values are the same, this means that this is a horizontal line.  The distance from -5 to 9 is 14 units.

Answer:

14

Step-by-step explanation:

using the distance formula to determine the distance between the two points

Answer:

x = 5, -5, 3, -3

Step-by-step explanation:

First, substitute u = x^2 into the equation, and we have

u^2 - 34u + 225 = 0

u = x^2

Factor u^2 −34u +225 using the AC method, and we get

( u - 25) ( u - 9) = 0

We know If any individual factor on the left side of the equation is equal to

0, the entire expression will be equal to 0, so

u - 25 = 0

u - 9 = 0

Next, we set u - 25 equal to 0  and solve for u, and we get

u = 25

Then set u - 9 equal to 0 and solve for u, and we get

u = 9

The final solution is all the values that make (u−25)(u−9) = 0  true.

u =25,9

Substitute the real value of u=x^2 back into the solved equation.

x^2 = 25

(x^2)^1 = 9

x^2 = 25

x = 5, -5

Now we solve the second equation

(x^2)^1 = 9

x = 3, -3

So, the answers are: 5, -5, 3, -3

Answer:12/9

Step-by-step explanation:

subtract 9 from 21 and 21 will give you 12 silver coins which will be 12 silver coins to 9 gold coins

Answer:

0

Step-by-step explanation:

h(x) = 3 – 3/x

h(3) = 3 – 3/3

h(3) = 0/3

h(3) = 0

i hope this helped

A number line marked with zero, one twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, ten twelfths, eleven twelfths, and one. From the zero point to the three twelfths mark, a red line is painted.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.

Here,

Multiply one times three, and four by three.

It will equal to three out of twelve or 3/12.

=1/4

A number line marked with zero, one twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, ten twelfths, eleven twelfths, and one. From the zero point to the three twelfths mark, a red line is painted.

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The required reflection of the points N(-3, 1), G(0, 4), B(-1, 1) across the y-axis are N(3, 1),  G(0, 4), B(1, 1) .

Point (x, y) is reflected across the x-axis as (x, -y). The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse.

We have,

N(-3, 1), G(0, 4), B(-1, 1)

While, find reflected points we are considering y-axis as mirror,

Then,

Reflection of point N(-3, 1) across the y-axis

⇒ N(3, 1)

Reflection of point G(0, 4) across the y-axis

⇒ G(0, 4)

Reflection of point B(-1, 1) across the y-axis

⇒ B(1, 1)

Thus, required reflected points are  N(3, 1),  G(0, 4), B(1, 1) .

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AA: y=40x+2

BB: y=34x+3

When the length of one side and the angle of one corner of a right-angled triangle are provided as 16 and 69°, respectively, trigonometric ratios are used to compute the value of b as 35.38.

The values of all trigonometric functions depending on the side ratio of a right-angled triangle are known as trigonometric ratios. The ratios of a right-angled triangle's sides to any acute angle are the angle's trigonometric ratios.

given

one side = 16

angle = 69°

one angle = 90° as right angle triangle

another angle = 69°+ 90° + x = 180°

= 155° + x = 180°

x = 25°

a / sin69° = 16 / sin25°

a = 35. 38

When the length of one side and the angle of one corner of a right-angled triangle are provided as 16 and 69°, respectively, trigonometric ratios are used to compute the value of b as 35.38.

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Answer:

parallelogram

Answer: a₁ = 5, a₂ = 6, a₃ = 13 are the only ones I could figure out, I apologize.

Step-by-step explanation: I hope this helps a little!

It is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm because the sum of two sides are greater than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 25 and 5

25 + 5 > 24

30 > 24

Now we add 25 and 24

25 + 24 > 5

49 > 5

Now we add 5 and 24

5 + 24 > 25

29 > 25

It is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm because the sum of two sides are greater than third sides.

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B. MLYZ and C. LN = XZ are not true, since these letters do not correspond to any sides or angles in the given triangles.

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." Given the statement "ALMN = AXYZ," we can assume that triangle ALMN is congruent to triangle AXYZ.

With that in mind, the following congruences are true:

A. ZX=ZN (Corresponding parts of congruent triangles)

D. MN = YZ (Corresponding parts of congruent triangles)

E. ZY ZMo (not a valid statement)

F. ZZ = ZL (not a valid statement)

B. MLYZ and C. LN = XZ are not true, since these letters do not correspond to any sides or angles in the given triangles.

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