Write an exponential function f so that the slope of a line from the point (0, f(0)) to the point (2, f(2)) is equal to 12.

The value of c is -12

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given: f(x) = x² +3x – 10 and  f(x - 2) = x²+ bx + c

f(x - 2)= (x-2)²+3x-6-10

           =  x² -4x+4+3x-16

           =x²-x-12

Thus comparing it to the given equation we get c=-12

Hence, the value of c is -12

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Company A charges $5.00 and 6 cents much more for x miles than Company B. The solution is obtained using arithmetic operations.

There are four basic operations which are listed as follows: Addition(‘+’): This operation deals with finding the sum. Subtraction(‘-’): This operation deals with finding the difference.   Multiplication(‘×’): This operation deals with finding the product. Division(‘÷’): This operation deals with finding the quotient.

In order to find how much more does company A charge than company B, we need to subtract the charges of company B from that of Company A.

So, on subtracting we get,

$55.50 and 15 cents - $50.50 and 9 cents = $5.00 and 6 cents per mile.

For x miles, we multiply $5.00 and 6 cents by x miles.

Also, we could convert dollars to cents by multiplying it by 100.

as $1 =100 cents.

5565 - 5059 cents = 506 cents.

For x miles, 506x cents.

Hence, Company A charges $5.00 and 6 cents much more for x miles than Company B.

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An equation for the cost of the cheaper brand is y = 60x + 1,800.

An equation for the cost of the more expensive brand is y = 50x + 2,600.

The cost of running the cheaper unit for 36 months is $3,960.

The number of months for which the cost of both brands would be equal is 8 months.

In order to write an equation that model this situation, we would assign variables to the time and cost respectively, and then translate the word problem into algebraic equation as follows:

Since a brand cost $1800 to buy with a monthly operation fee of $60, an equation for the cost of this cheaper brand is given by:

y = 60x + 1,800.

When x = 36 months, the cost of running the cheaper unit is given by:

y = 60(36) + 1,800.

y = $3,960.

For the more expensive brand, we have:

y = 50x + 2,600.

Next, we would determine the number of months for which the cost of both brands would be equal;

50x + 2,600 = 60x + 1,800

60x - 50x = 2,600 - 1,800

10x = 800

x = 800/10

x = 8 months.

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Complete Question:

Suppose your family is going to buy a new air conditioning unit. One brand costs $1800 to buy and $60 a month to operate. A more expensive brand cost $2600 to buy but only $50 a month to operate. Let “x” represent time in months.

a. write an equation for the cost of the cheaper brand

b. Write an equation for the cost of the more expensive brand.

c. What is the cost of running the cheaper unit for 36 months?

d. For how many months will the cost of both brands be equal?

Answer: $698.75

Step-by-step explanation: 7.5% of 650 is $48.75. 650 plus 48.75 = 698.75

Equation 4x222-12x+9=5 has a solution of x=  -√4-3.  It is said to be linear when an equation has the form y=mx+b .

In algebra, a linear equation is one with the form y=mx+b. B is the slope, and m is the y-intercept. Because y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables." Bivariate linear equations are those with two variables. There are various examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the formula y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

4x²2²-12x+9=5

8x2 - 12x +4 = 0

8x2 - 6x - 6x +4 = 0

2x(4x - 3) - 2(3x +2) = 0

Equation 4x222-12x+9=5 has a solution of x=  -√4-3 . It is said to be linear when an equation has the form y=mx+b .

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The required two-column proof that the triangles are congruent is explained below.

A triangle is a three sided plane shape whose the sum of internal angles is 180^o. Thus two or more triangles are said to be congruent when their corresponding sides and measure of internal angles are equal.

When two triangles are congruent, it can be proven in all respect that they are thus equal (considering their corresponding length of sides and measure of internal angles).

The two-column proof required in the question is given below:

       STATEMENT                                     JUSTIFICATION

1. <WXZ ≅ <YXZ                               Property of an angle bisector.

2. <XZW  ≅ <XZY                             Definition of a perpendicular bisector.

3. WX ≅ YX                                       Congruent sides of a triangle.

4. WZ ≅ YZ                                        Definition of a midpoint.

Therefore,

ΔWXZ ≅  ΔYXZ                                  Angle-Angle-Side theorem

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The constant of proportionality is 12. The equation to represent the relationship is :  b = 12p.

Constant proportional:

A constant of proportionality is a constant value for the ratio of two proportional quantities. If the ratio or product is constant, the two variables are proportional. The value of the constant of proportionality depends on the type of relationship between the two given quantities (positive versus inverse variation).

According to the question:

From the above mentioned , the individual ratio of number of birdhouse (b) cans of paints is:

Now,

For 1st  pair,

   b/ p = 3/ 1/4

⇒ b / p = 3 ×4 /1

⇒ b/ p = 12

Again,

For 2nd pair,

   b /p = 9/0.75

⇒ b /p = 12

For 3rd pair,

 b /p = 18/3/2

⇒ b /p = 18× 2/3

⇒ b/ p = 12

Finally,

For 4th Pair =

⇒ b/ p = 20/2.5

⇒ b/ p = 12

As all the ratios are equivalent, the relationship between number of birdhouse (b) and cans of paints (p) is proportional. The constant of proportionality is 12. The equation to represent the relationship is :  

                                            b = 12p.

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The formula for the area of the triangle with based and height is bh/2, where b is base and h is height of triangle.

The base of the triangle is the line in the triangle parallel to x-axis. The height of the triangle is its altitude and vertical line parallel to y-axis. Do remember that base and altitude or height of triangle are always perpendicular to each other.

Let us take an example to find the area. Assume the height to be 5 cm and base to be 4 cm. Keep the values in formula -

Area = 1/2 × 5 × 4

Area = 5 × 2

Area = 10 cm²

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Answer:

2

Step-by-step explanation:

By using the given formula and solving we get, the original value of the vase is 5000 pounds.

A percentage is a way to express a number as a fraction of 100. It is often denoted by the symbol "%". For example, 25% means 25/100 or 0.25. Percentages are often used to express rates of change or proportions.

A rate is a ratio that compares two quantities of different units, such as distance and time, or weight and volume. It is often represented as a fraction or a decimal and can be converted to a percentage by multiplying by 100.

The given formula tells us how the value of the vase changes over time, with the value increasing by a factor of 1.28 (28% increase) every year.

To find the original value of the vase, we need to know the value of the vase when n = 0.

Substituting n = 0 into the formula, we get:

value in pounds = 5000*1.28^0

When n = 0, 1.28^0 = 1, so the original value of the vase is:

value in pounds = 5000*1 = 5000 pounds

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The quadratic pattern with value of p and q has been proved.

A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Latin word for square, is where the word "quadratic" originates.

Here,

Given : 1st difference

p−4;

11−p;

q−11;

22−q;

2nd difference−2p+15;

q+p−22;

33−2q−2p+15=1−2p=−14p

=733−2q

=1q+p−22

=1−2q=−32or/of

q+7−22=1

q=16

Therefore , the solution of the given problem of quadratic comes out to be q =16

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Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a representation of a collection of integers.

A straight line of numbers is shown visually as a number line.

This line is used to compare integers that are spaced equally apart on an infinite line that extends horizontally on both sides.

The collection of integers can be shown on a number line much like other sets of numbers..

Hence, Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.

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It would take Sarah 136.36 minutes to walk 7.5 miles around spring lake park.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
Sarah walks laps around spring lake park. she can walk 4 laps in 108 minutes.

1 lap = 1.5 miles
4 lap = 6 miles

walking rate = 6 / 108 = 0.056 miles per minute

Now,
time = distance/walking rate
time = 7.5/0.056 = 136.36 minutes

Thus, It would take Sarah 136.36 minutes to walk 7.5 miles around spring lake park.

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Hana can put 4 fruits in each bowl. We can solve the given problem by finding the highest common factor using prime factorization.

The Highest Common Factor (HCF) of two numbers is the largest possible number that divides both numbers equally.

There are various methods for calculating the highest common factor between two numbers. The prime factorization method can be used to quickly determine the HCF of two or more numbers.

Examine the many attributes and components of HCF to learn more about it. Find the solutions to questions like what is the highest common factor for a collection of integers, how to quickly calculate the highest common factor, how to compute HCF using the prime factorization, and more to learn more fascinating details about them.

We found that the Highest common factor is 4

then 8 melons can be placed in 2 bowl having 4 melons in each bowl

12 pears can be placed in 3 bowls having 4 pears in each bowl

and lastly, 24 apples can be placed in 6 bowls having 4 apples in each bowl.

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Answer:

277.777778 Or about 277 meals

Step-by-step explanation:

We can find this out by converting 50 kg into grams. There are 1000 grams in a kg. So to convert 50 kg into grams we have to multiply by 1000. 50 x 1000 = 50000 g. 50000g / 180 g = 277.777778 or about 277.

The length of the straw placed inside the rectangular box is [tex]\sqrt{73}[/tex] inches.

A quadrilateral with parallel sides equal to one another and four equivalent vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel. The area of a rectangle is given as the product of the length and breadth of the rectangle.

The given parameters are:

The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

[tex]s=\sqrt{l^{2}+w^{2}+h^{2} }\\[/tex]

The equation becomes:

[tex]s=\sqrt{6^{2}+6^{2}+1^{2} }\\[/tex]

Evaluate the exponents:

[tex]s=\sqrt{73}[/tex] inches

=> s≈8.544 inches

Hence, the length of the straw is 8.544 inches.

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Therefore ,as a result, the  solution of the given problem of equation is  left side of the line's run is taken into consideration because the slope is positive.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A scientific statement that verifies the equality of two formalisms is known as an equation in algebra. For instance, the pieces ptdc + 6 and 12 are separated by an equal sign in the solution obd + 6 = 12. The relationship between the two variable on either flank of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 4x – 4 = 0.

Here,

provided: y + 1= (x-4)

The slope in this case turns out to be =>

=>y = x -5

We obtain m = 1 and an intercept of c = -5 when comparing with the equation y= mx + c.

As a result, the left side of the line's run is taken into consideration because the slope is positive.

We can swap the point for plot the graph by bringing the piece down by -5.

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A triangle's median is a straight path that joins a vertices to the midpoint of the following sectors across from it.

A triangle is a three-sided polygon that consists of three vertices, three sides, and three angles. Three types of triangles—scalene, isosceles, and equilateral—can be distinguished based on the length of their sides.

It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the size of its angles. A triangle's internal angles add up to 180 degrees. Two more terms—altitude and triangle median—are introduced to you in this essay.

A triangle's median is a straight path that joins a vertices to the midpoint of the following sectors across from it.

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Therefore , the solution of the given problem of graphs comes out to be we can simply deduce that the graph will initially start out declining, then quickly increase.

Graphs are used by mathematicians to rationally represent or chart facts or values. Typically, a graph tip will show a connection amongst two or more objects. A graph is a type of non-linear data structure that is made up of nodes, and vertices, and edges. affix the nodes, also referred as as vertices. This graph includes elements E=3,2,14,5 , having (2.5) and vertex V=1, 2, 3, 5. (3.5). (4.5). graphs of exponential growth in the form of statistics charting (bar charts, charts, line charts, etc.). the form of a triangle-shaped logarithmic graph

Here,

If she is first driving toward the gas station, then the graph will be declining.

She fills up her tank at the gas station, which causes the graph to move upward.

After that, the graph will start to decline as she approaches the market.

From the information,

we can simply deduce that the graph will initially start out declining, then quickly increase, and finally have a continuous reduction until we achieve our target.

Therefore , the solution of the given problem of graph comes out to be we can simply deduce that the graph will initially start out declining, then quickly increase.

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The x and y-intercepts of the given equation of line 8x - 5y = -11 are (-11/8,0) and (0,11/5) respectively.

Given the equation of line in the question;

8x - 5y = -11

To find the x-intercept, substitute in 0 for y  and solve for x.

8x - 5y = -11

8x - 5(0) = -11

8x - 0 = -11

8x = -11

x = -11/8

Hence, the x-intercept is (-11/8,0)

To find the y-intercept, substitute in 0 for x  and solve for y.

8(0) - 5y = -11

0 - 5y = -11

-5y = -11

y = -11 / -5

y = 11/5

Hence, the y-intercept is (0,11/5).

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By solving an exponential equation, we can see that the investment will be doubled after 10.6 years.

The investment can be modeled by the exponential equation:

P(x) = A*(1 + 6.75%/100%)^x

Where A is the initial value of the investment (the amount invested).

We can simplify this to get:

P(x) = A*(1 + 0.0675)^x

The investment will be doubled when:

2*A = A*(1 + 0.0675)^x

We want to solve this for x.

2 = (1 + 0.0675)^x

2 = (1.0675)^x

If we apply the natural logarithm in both sides:

ln(2) = ln((1.0675)^x)

ln(2) = x*ln(1.0675)

ln(2)/ln(1.0675) = x

10.6 = x

The investment will be doubled after 10.6 years.

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Answer:

Angle EFP = 115

Step-by-step explanation:

3x + 2.5 = 4x - 35

2.5 = x - 35

x = 37.5

3(37.5) + 2.5

= 112.5 + 2.5

= 115

The solutions to the system of equations in this problem is given as follows:

(0,1) and (0.25, 0).

The graph is given by the image presented at the end of the answer.

The equations that compose the system in this problem are given as follows:

We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.

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WY intersects UV at Y and hence the value of UV is 8.

They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

Given that WY intersects UV at Y.

Hence, the value of UY = YV.

Substitute the value of UY and YV as follows:

UY = YV

3x- 6 = x + 2

3x - x = 2 + 6

2x = 8

x= 2

Now, the value of UV = UY + YV

Substitute the values:

UV = UY + YV

UV = 3x - 6 + x + 2

UV = 4x - 4

Substitute the value of x as follows:

UV = (4)(2) - 4

UV =8 -4

UV = 4

Hence, the value of UV is 8.

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Answer:

1/2 x b x h

Step-by-step explanation:

b = length of the base of the triangle.

h = height of the triangle.

Therefore, the area of the triangle = 1/2 x b x h

Answer

slope: 1/5

x-intercept= 35

Step-by-step explanation:

0=1/5(X)-7

7=1/5x

7/1/5= 35
so

x-intercept is: (35,0)

The left side of the first equation is 2(3b+6) and the left side of the second equation is -2(6c-3). Both sides of the equations are products of a constant and a variable or a sum/difference of variables.

Answer:

2(3b+6) =78 : b=11

-2(6c-3) = -72 : c=6.5

Step-by-step explanation:

They are correct

The metal bar would displace 0.018 liters of water.

Volume is the measure of the amount of space occupied by an object or substance. It is often represented by the symbol 'V' and is typically measured in units such as liters (L), cubic meters (m^3), or gallons (gal). In three-dimensional space, the volume of an object is calculated by multiplying its length, width, and height (or depth). In two-dimensional space, the area of an object can be calculated by multiplying its length and width.

The volume of the metal bar is 3 cm x 3 cm x 2 cm = 18 [tex]cm^3[/tex]. The density of water is 1 g/[tex]cm^3[/tex]. To find the volume of water displaced, we need to convert the volume of the bar from cubic centimeters to liters.

1L = 1000[tex]cm^3[/tex]

So the volume of water displaced would be 18 [tex]cm^3[/tex] / 1000 = 0.018 L.

In summary, the metal bar would displace 0.018 liters of water.

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Answer:

Factored completely is: 3x^2 (x+3)(x-2)

according to your question - probs (x-2), no other choice

Step-by-step explanation:

have fun friend & have a good day friend :)