Locate the zero of the quadratic function

The answer calculates the original square footage of Eamon's home based on the $35 fee per square foot paid for adding 380 square feet past 25% of the original square footage. The original square footage of Eamon's home is 1,520 square feet.

Let's assume that the original square footage of Eamon's home was "x". According to the problem, he had to pay a fee of $35 for every square foot he added past 25% of the original square footage.

Therefore, the square footage he added to his home past 25% of the original square footage was:

380 - 0.25x

And the fee he paid was $2,800. So we can write an equation:

35(380 - 0.25x) = 2,800

Simplifying the equation, we get:

13,300 - 8.75x = 0

Solving for x, we get:

x = 1,520 square feet

Therefore, the original square footage of Eamon's home was 1,520 square feet.

Learn more about algebra here: brainly.com/question/24875240

#SPJ1

Step-by-step explanation:

Semir = n

Sarah = 2n - 5

Sarah's expression =. 2n-5

Sarah's equation = 18(2n-5)

Semir's equation = 18(2n-5) = 450

n = 15

Sarah walked 2(15) - 5 which is 25 miles.

SungSo:

18x + 72 = 450

x = 21

As per the travelling distance, if they meet in hours, then the rate of each cyclist is r₂ miles per hour.

Let's assume that the two towns are A and B, and the distance between them is d miles. Let the first cyclist start from town A and travel towards town B, and the second cyclist start from town B and travel towards town A. Let's also assume that the first cyclist travels at a rate of r₁ miles per hour, and the second cyclist travels at a rate of r₂ miles per hour.

Now, let's consider the time it takes for the two cyclists to meet. Since they are traveling towards each other, their combined speed is (r₁ + r₂) miles per hour. We can use the formula:

distance = speed × time

to find the time it takes for them to meet. Let t be the time taken for them to meet, then we can write:

d = (r₁ + r₂) × t

where d is the distance between the two towns.

Now, we need to solve for r₁ and r₂. We can use the fact that the two cyclists meet in hours to write:

t = d / (r₁ + r₂)

Substituting this expression for t in the equation we got earlier, we get:

d = (r₁ + r₂) × (d / (r₁ + r₂))

Simplifying this equation, we get:

r₁ + r₂ = d / t

Substituting the value of t, we get:

r₁ + r₂ = d / (d / (r₁ + r₂))

r₁ + r₂ = (r₁ + r₂)

This equation tells us that the sum of the rates of the two cyclists is equal to the distance between the two towns divided by the time it takes for them to meet.

We can now use algebra to solve for r₁ and r₂. Let's assume that r₁ is the faster cyclist, then we have:

r₁ = (d / t) - r₂

Substituting the value of t, we get:

r₁ = (d / (d / (r₁ + r₂))) - r₂

Simplifying this equation, we get:

r₁ = (r₁ + r₂) - r₂

r₁ = r₁

This equation tells us that the rate of the faster cyclist is equal to itself, which is obvious.

Now, we can find the rate of the slower cyclist by using the fact that:

r₂ = (d / t) - r₁

Substituting the value of t, we get:

r₂ = (d / (d / (r₁ + r₂))) - r₁

Simplifying this equation, we get:

r₂ = (r₁ + r₂) - r₁

r₂ = r₂

This equation tells us that the rate of the slower cyclist is also equal to itself, which is obvious.

Therefore, we can conclude that the rate of the faster cyclist is r₁ miles per hour, and the rate of the slower cyclist is r₂ miles per hour, where:

r₁ = (d / t) - r₂

r₂ = (d / t) - r₁

To know more about distance here

https://brainly.com/question/4199102

#SPJ4

To solve this problem, we need to first convert 5 minutes and 15 seconds to a decimal form of minutes.

5 minutes is equal to 5.0 minutes, and 15 seconds is equal to 15/60 = 0.25 minutes. Therefore, the total time in minutes is:

5.0 + 0.25 = 5.25 minutes

Next, we can multiply the number of copies made per minute by the total time in minutes to find the total number of copies made:

36 copies/minute x 5.25 minutes = 189 copies

Therefore, the copy machine makes 189 copies in 5 minutes and 15 seconds.

Scary drew a rectangle with a perimeter of 20 inches and its dimensions are 6 by 4 and the square is a 5 in × 5 in square.

We know that a square has 4 identical sides.

The square's perimeter is equivalent to the product of its four sides. The square's side length continues to be the same as the circumference measurement unit.

Perimeter = Side + Side + Side + Side = 4 Side

Perimeter = 4 × side of the square

If ‘a’ is the length of side of square, then perimeter is:

Perimeter = 4a unit

therefore,

20 = 4 × side length

side length = 20/4 = 5 in

it is a 5 in × 5 in square.

We know that a rectangle has 2 pairs of sides that are equally long inside their pair.

The entire distance that the rectangle's outer boundary covers is referred to as its perimeter. Its length is expressed in units. The perimeter calculation is provided by:

Perimeter, P = 2 (Length + Width)

and so, you have in this case a perimeter of

= 2 × 6 + 2 × 4

= 12 + 8

= 20 in

To learn more about perimeter, click here:

brainly.com/question/6465134

#SPJ4

Therefore, the area of the trapezoid is 60 cm².

A trapezoid is a four-sided polygon with two parallel sides (called bases) of different lengths, and two non-parallel sides (called legs). The legs of a trapezoid are usually not congruent and can be of different lengths. Trapezoids can have different shapes and sizes, but they always have at least one pair of parallel sides. The area of a trapezoid can be calculated using the formula:

[tex]Area = ((b_1 + b_2) * h) / 2,[/tex]

where b1 and b2 are the lengths of the parallel bases, h is the height or perpendicular distance between the two bases.

To calculate the area of a trapezoid, we use the formula:

[tex]Area = (b_1 + b_2) * h / 2[/tex]

where b1 and b2 are the lengths of the parallel sides of the trapezoid and h is the height (perpendicular distance) between the parallel sides.

In this case, we are not given which sides are the parallel sides and which one is the height, so we cannot directly apply the formula. However, we can make an educated guess based on the dimensions given.

Assuming that the two 8 cm sides are parallel, we can use the formula as follows:

[tex]Area = (b_1 + b_2) * h / 2[/tex]

[tex]Area = (8 cm + 16 cm) * 10 cm / 2[/tex]

[tex]Area = 120 cm^{2} / 2[/tex]

[tex]Area = 60 cm^{2}[/tex]

To know more about trapezoid, click here,

https://brainly.com/question/8643562

#SPJ1

a) No, there aren't shared rays.

b) Yes.

C) Vertical angles.

d) 2x = 50 + 8

e) x = 29.

Yes, clearly the two angles only share the common vertex which is B, all the rays startat that point, and in this case the rays for ABC are BA and BC.

Whie the rays for DBC are BD and BC.

So no, there aren't shared rays.

b) Yes, when the angles only share the vertex, these are called opposite or vertical angles, and it means that the two angles have the same measure.

c) As we said above, vertical angles.

d) The measures must be equal, then.

2x - 8 = 50

e) Solving that for x we will get:

2x = 50 + 8

2x = 58

x = 58/2 = 29

Learn more about vertical angles at

https://brainly.com/question/14362353

#SPJ1

The size of the bacterial population after 40 minutes.= 1572864000.

"A way to find a multiple unit value from a single unit value as well as the reverse."

In every case, we first count the unit or amount value before figuring out the more or less amount value.

This method is referred to as a unified procedure for this reason.

By dividing the set value by the quantity of sets, one can find numerous set values.

By dividing several set values by the total number of sets, one can determine a set value.

According to our question-

A = 1500(2)600/30

A = 1500(2)20

A = 1500(1048576)

A = 1572864000

Hence, The size of the bacterial population after 40 minutes.= 1572864000.

learn more about unitary method click here:

brainly.com/question/24587372

#SPJ1

The new variance is 0.41.

Given that the mean cost of a box of Cheerios oat crunch is $4.00 and the variance is 0.35.

The variance represents the average of the squared deviations from the mean, so we can write:

variance = (standard deviation)^2

The standard deviation is the square root of the variance, so we have:

standard deviation = sqrt(variance) = sqrt(0.35) = 0.59

Now, if the price of a box of Cheerios oat crunch increases by 25 cents, the new mean cost will be:

new mean = $4.00 + $0.25 = $4.25

To find the new variance, we need to calculate the new squared deviations from the mean and take their average. The squared deviation of each observation is given by:

(new cost - new mean)^2

We can simplify this expression by substituting the new mean and the original standard deviation:

(new cost - $4.25)^2 = (old cost - $4.00 + $0.25)^2 = (old cost - $4.00)^2 + 2($0.25)(old cost - $4.00) + $0.25^2

The first term on the right-hand side is the squared deviation of the original cost, the second term represents the change in the squared deviation due to the increase in price, and the third term is a constant that does not affect the variance.

To find the new variance, we need to take the average of these squared deviations. Since the original variance was 0.35, we have:

new variance = (1/n) * [sum of (new cost - new mean)^2]

where n is the number of observations (we assume it is large enough to use the normal distribution approximation). Using the expression above for the squared deviation, we can write:

new variance = (1/n) * [sum of (old cost - $4.00)^2 + 2($0.25)(old cost - $4.00) + $0.25^2]

We can simplify this expression by using the properties of summation:

new variance = (1/n) * [sum of (old cost - $4.00)^2] + (2/$n) * ($0.25) * [sum of (old cost - $4.00)] + ($0.25^2)

The first term is the original variance, the second term is zero (since the sum of deviations from the mean is always zero), and the third term is a constant that does not affect the variance. Therefore, the new variance is:

new variance = 0.35 + ($0.25)^2 = 0.41

Learn more about  statistical analysis:https://brainly.com/question/14724376

#SPJ11

We can conclude that the high school coach's claim is wrong, and the average pulse rate of students trying out for sports is not 62.4 bpm. The p-value is 0.014.

To compute the p-value, the following steps will be carried out in order;

State the null and alternative hypotheses and select a level of significance (α).

Then, apply the Z-test.

Statistical inference should be made.

The P-value should be calculated.

The findings must be interpreted.

This test is carried out to see whether the given data (sample) is enough to refute the null hypothesis that the mean population pulse rate is 62.4 bpm. ([tex]H_O[/tex]).

The alternate hypothesis ([tex]H_A[/tex]) is that the mean pulse rate is not equal to 62.4 bpm. ([tex]H_A[/tex]).

Hence; [tex]H_O[/tex]:

µ = 62.4 bpm [tex]H_A[/tex]: µ ≠ 62.4 bpm

We choose a level of significance of α= 0.05.

The significance level is usually referred to as alpha (α), which is a probability threshold that the sample data is used to assess.

When the null hypothesis is rejected, alpha (α) is the probability of making a Type I mistake.

When the null hypothesis is correct, it represents the probability of rejecting it.

We'll next use the Z-test in this scenario, which is the most common type of hypothesis test for population means when the population standard deviation (σ) is known.

The Z-test is performed using the following formula;

Z = (X - µ) / (σ / √n)

where; X = sample mean

µ = hypothesized population mean

σ = population standard deviationn = sample size

Substituting the values given;

Z = (65.0 - 62.4) / (10.3 / √32)Z = 2.17 (to 2 decimal places)

The p-value is calculated next;

P (Z > 2.17) = 0.014 (to 3 decimal places).

In conclusion, since the P-value is less than the significance level, we reject the null hypothesis.

For similar question on p-value

https://brainly.com/question/13786078

#SPJ11

Answer:5

Step-by-step explanation:

Answer:

B:25    

Plug it in to check                

The value of the expression when a = 5 and b = -3 is 35. We can calculate it in the following manner.

We can simplify the expression as follows:

2a² + b²+ 1 - a²

= a² + b² + 1

Substituting a = 5 and b = -3 into the expression, we get:

5² + (-3)² + 1

= 25 + 9 + 1

= 35

Therefore, the value of the expression when a = 5 and b = -3 is 35.

When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated. Formulas can be changed with values to assist us solve a variety of problems.

Learn more about simplify here brainly.com/question/29205070

#SPJ4

The function is f(x) = 15x + 25 and you would have 6 services if you were charged $25

We know that the hair salon charges a fixed rate of $25.00 for a haircut and then an additional $15 for any other services, therefore:

Let x = number of services, then we can obtain the function as:

f(x) = 15x + 25 (function)

when we further solve the function, we get the answer for how many services one would have if we were charged $25,

f(x) = 15x + 25

115 = 15x + 25

90 = 15x

6 = x

Now, we know that the function is f(x) = 15x + 25 and you would have 6 services if you were charged $25

To learn more about function, click here:

brainly.com/question/12431044

#SPJ4

If AD = 2x + 4 and CD = 4x - 4, and they share point D, then x must be equal to 4.

An equatiοn is a mathematical statement that indicates that twο expressiοns are equal.

Hοwever, we can use the fact that they share pοint D tο set them equal tο each οther and sοlve fοr x:

AD = CD

2x + 4 = 4x - 4

Collecting like terms:

2x - 4x = -4 - 4

-2x = -8

Dividing both sides by -2:

x = 4

Hence, if AD = 2x + 4 and CD = 4x - 4, and they share point D, then x must be equal to 4.

To learn more about equation, Visit

https://brainly.com/question/22688504

#SPJ1

Answer:

11.9m

Step-by-step explanation:

explanation in picture :)

please mark brainliest

Answer:

11.81 is the height

answer 48h. The maximum volume of a rectangular box without a lid can be found using the equation: V = l x w x h, where V is the volume, l is the length, w is the width, and h is the height.

To solve this problem, you need to first determine the length, width, and height of the box. Since you have 48 m2 of cardboard, you can rearrange the equation to solve for one of the variables.

48 m2 = l x w
w = 48/l

Once you have determined the width, you can then use the equation to solve for the length and the height.

V = l x 48/l x h
V = 48h

Therefore, the maximum volume of such a box is 48h, where h is the height of the box.

You can read more about volume at https://brainly.com/question/463363

#SPJ11

The optimal number of orange trees to plant per acre in order to produce the highest yield for the grower is 32.

Let x be the number of additional trees beyond 24 that are planted per acre. Therefore, the total number of orange trees planted per acre will be 24 + x.

The yield of oranges per tree decreases by 1 bushel for each additional tree planted, so the yield per tree can be expressed as:

40 - x

The total yield of oranges per acre can be calculated by multiplying the yield per tree by the total number of trees planted:

(40 - x)(24 + x)

To find the optimal number of trees to plant, we want to maximize this expression. We can do this by finding the maximum value of the quadratic expression (40 - x)(24 + x).

To do this, we can use the formula for the vertex of a quadratic function, which is:

x = -b / (2a)

where a and b are the coefficients of the quadratic expression in standard form (ax^2 + bx + c).

In this case, the quadratic expression is:

(40 - x)(24 + x) = -x^2 + 16x + 960

So, a = -1 and b = 16. Plugging these values into the formula for the vertex, we get:

x = -16 / (2(-1)) = 8

Therefore, the optimal number of additional trees to plant beyond the initial 24 trees is 8. The total number of trees to plant per acre is 24 + 8 = 32.

To check that this is indeed the optimal number, we can calculate the yield for adjacent values of x:

When x = 7: (40 - 7)(24 + 7) = 33 * 31 = 1023

When x = 8: (40 - 8)(24 + 8) = 32 * 32 = 1024

When x = 9: (40 - 9)(24 + 9) = 31 * 33 = 1023

Therefore, the optimal number of orange trees to plant per acre in order to produce the highest yield for the grower is 32.

Learn more about  optimization:https://brainly.com/question/28970005

#SPJ11

The area of the complex figure is 1863 m².

What is area?

Area is a measure of the size or extent of a two-dimensional surface or shape, such as a square, circle, or rectangle. It is the amount of space inside the boundaries of a shape, usually measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²).

The area of give figure :

= area of two rectangles + area of middle rectangle

we know that area of rectangle is length* breadth

so, area of give two rectangles = 2 × length × breadth

                                                  = 2 × 31 × 23

                                                   = 1426m²

similarly, area of the middle rectangle  = length × breadth

                                                                =  (69-23-23) × (31-12)

                                                                = 23 × 19

                                                                = 437 m²

∴ The area of give figure= 1426m²+437 m²

                                        = 1863 m²

To learn more about area visit the link:

https://brainly.com/question/2607596

#SPJ1

The probability of picking a red marble, then a green marble, and finally a blue marble is 0.091424%, or approximately 0.09%.

To find the probability of picking a blue marble, given that we have already picked a red and a green marble, we use the same method:

P(B|R and G) = P(R and G and B) / P(R and G)

where P(B|R and G) is the probability of picking a blue marble, given that a red marble and a green marble have been selected, and P(R and G and B) is the probability of picking a red marble, then a green marble, and finally a blue marble.

Using the given probabilities, we can plug in the values and simplify:

P(B|R and G) = (0.2 x 0.2857 x 0.228) / (0.2 x 0.2857) = 0.016

This means that if we have already picked a red marble, then a green marble, there is a 1.6% chance of picking a blue marble next.

Finally, to find the probability of picking a red marble, then a green marble, and finally a blue marble, we multiply the probabilities of each event together:

P(R and G and B) = P(R) x P(G|R) x P(B|R and G)

=> 0.2 x 0.2857 x 0.016 = 0.00091424 or 0.09%

To know more about probability here

https://brainly.com/question/11234923

#SPJ4

Therefore, the coordinates of the terminal points are: (0, 1),(-√2/2, -√2/2) ,(-1/2, -√3/2)

A coordinate is a set of numerical values that uniquely determines the position of a point in space. In two-dimensional space, a coordinate is typically represented by a pair of numbers (x, y), where x represents the horizontal distance from a reference point, and y represents the vertical distance from the same reference point. In three-dimensional space, a coordinate is represented by a triplet of numbers (x, y, z), where x, y, and z represent the horizontal, vertical, and depth distances from the reference point, respectively.

by the question.

Pi/2 is an angle in radians, and it corresponds to an angle of 90 degrees in degrees. The terminal point for this angle lies on the positive y-axis and has coordinates (0, 1).

315 degrees is an angle in degrees, and it corresponds to an angle of 7π/4 radians in radians. To find the terminal point for this angle, we can use the unit circle. Starting from the positive x-axis (the initial side), we rotate 315 degrees counterclockwise until we hit the terminal side. This corresponds to a rotation of 5π/4 radians. The terminal point lies in the third quadrant and has coordinates (-√2/2, -√2/2).

240 degrees is an angle in degrees, and it corresponds to an angle of 4π/3 radians in radians. To find the terminal point for this angle, we can again use the unit circle. Starting from the positive x-axis (the initial side), we rotate 240 degrees counterclockwise until we hit the terminal side. This corresponds to a rotation of 4π/3 radians. The terminal point lies in the third quadrant and has coordinates (-1/2, -√3/2).

To learn more about coordinate:

https://brainly.com/question/16634867

#SPJ1

Answer: $5.71

Step-by-step explanation:

Answer:

Step-by-step explanation:

12 quarters = $3

16 dimes = $1.60

17 nickels = $0.85

26 pennies = $0.26

Add everything up and you get $5.71

Answer:

2,007,000,000,000

Step-by-step explanation:

The numbers from left to right here are:

2 trillion

0 hundred billion

0 ten billion

7 billion

0 hundred million

0 ten million

0 million

0 hundredthousand

0 ten thousand

0 thousand

0 hundreds

0 tens

0 ones

If the width of the picture frame is greater than 35 inches, then the perimeter of the frame will be greater than 152 inches.

Let's first set up an equation for the perimeter of the picture frame. The perimeter is the sum of the lengths of all four sides, and we know that the length is 6 inches more than the width. Let's use x to represent the width:

Perimeter = 2(length + width)

Perimeter = 2(x + (x+6))

Perimeter = 4x + 12

Now, we want to find the values of x for which the perimeter is greater than 152 inches. We can set up an inequality:

4x + 12 > 152

Subtracting 12 from both sides:

4x > 140

Dividing both sides by 4:

x > 35

So the width must be greater than 35 inches in order for the perimeter to be greater than 152 inches.

Learn more about perimeter here:

https://brainly.com/question/30673291

#SPJ1

Answer:

the other line is over more the line that is on the left so its 6 units to the left

a. Discrete variable b. Continuous variable c. Continuous variable d. Discrete variable e. Continuous variable f. Continuous variable

In statistics, a variable is an attribute or characteristic that can be measured. They can be classified as either continuous or discrete. A continuous variable has values that can take any value within a given range while a discrete variable has values that can only be integers.

Classification of each variable:

a. The number of words spelled correctly by a student on a spelling test- Discrete variable

b. The amount of water flowing through the hoover dam in a day- Continuous variable

c. The length of time an employee is late for work- Continuous variable

d. The number of bacteria in a particular cubic centimeter of drinking water- Discrete variable

e. The amount of carbon monoxide produced per gallon of unleaded gas- Continuous variable

f. Your weight- Continuous variable

To know more about Discrete variable: https://brainly.com/question/18763328

#SPJ11

If the sequence is geometric, the common ratio 2:1.

In mathematics, an Sequence is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same item can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position.

The concept of series can be generalized as a family of indices, defined in terms of any set of indices.

According to the Question:

Given GP is 18,9,0,-9.

Common ratio =  second number/ first number

​                         =  18/9

                       ​ = 2

​So, the common ratio is  2:1

​

Learn more about Sequence:

https://brainly.com/question/30262438

#SPJ4

Answer:

121

Step-by-step explanation:

11x11=121

121+11=132

132-11=121