11. A number plus four equals nine.


Please I need help with my math homework

The equations of the functions from the zeros are f(x) = 4x² + 5x - 6 and f(x) = 3x² - 15

Function (a)

Given that

(3/4,0) and (-2,0).

Since the two points have the same y-coordinate of 0, the quadratic function is of the form

f(x) = (x - p)(x - q), where p and q are the x-coordinates of the two points.

Plugging in the given values, we get

f(x) = (x - 3/4)(x + 2)

So, we have

f(x) = 4x² + 5x - 6

Function (b)

Here we have

(-√5, 0), (√5, 0) and (-3, 12)

This function can be represented as

f(x) = a(x - p)(x - q)

So, we have

f(x) = a(x - √5)(x + √5)

Expand

f(x) = a(x² - 5)

Using the last point, we have

a((-3)² - 5) = 12

4a = 12

a = 3

So, we have

f(x) = 3(x² - 5)

Expand

f(x) = 3x² - 15

Hence, the function is f(x) = 3x² - 15

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Answer:

127°

Step-by-step explanation:

I added a photo of my solution

Answer:

--------------------------------

The formed quadrilateral has two right angles, because of tangent segments.

One angle is marked as 53°, and the missing angle is x.

We know the sum of interior angles of a quadrilateral is 360°.

Find the missing angle:

The equation [tex]f(x) = -x^2 + 5x + 14[/tex] models the flight path of a quaffle thrown into the air during a game of quidditch.

The equation [tex]f(x) = -x^2 + 5x + 14[/tex] can be used to model the height of the quaffle, where x represents the time in seconds after the quaffle is thrown.

To find the maximum height of the quaffle, we need to find the vertex of the parabola described by the equation. The following formula can be used to determine the vertex's x-coordinate:

x = -b / 2a

where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c[/tex]. In this case, a = -1, b = 5, and c = 14, so we have:

x = -5 / 2(-1) = 5/2

The y-coordinate of the vertex can be found by plugging this value of x into the equation:

[tex]f(5/2) = -(5/2)^2 + 5(5/2) + 14 = 23.5[/tex]

Therefore, the maximum height of the quaffle is 23.5 feet, and it occurs 2.5 seconds after the quaffle is thrown.

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Answer:

Step-by-step explanation the answer will be 20 each

:

The formula for the Pythagorean theorem in 3 dimensions is [tex]d^2 = a^2 + b^2 + c^2.[/tex]

What is Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be extended to 3 dimensions using the same principle.

In the case of a cube with base a, width b, and height c, we can imagine a right triangle that is formed by one of the diagonals of the cube and one of the faces. Let d be the length of this diagonal.

By the Pythagorean theorem in 3 dimensions, we have:

[tex]d^2 = a^2 + b^2 + c^2[/tex]

To see why this is the case, imagine that we have a right triangle in three dimensions, with sides of length a, b, and c.

The hypotenuse of this triangle is the diagonal of a rectangular box with sides of length a, b, and c. By the Pythagorean theorem, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the other two sides, which gives us the formula above.

Therefore, the formula for the Pythagorean theorem in 3 dimensions is [tex]d^2 = a^2 + b^2 + c^2.[/tex]

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Answer:

ii. is the answer

hope this helped

The correct statements are:

The median is six and one-fourth.

The mode cannot be determined from the given information.

The range is five and three-fourths.

The median measures the central tendency in a dataset, which is the middle value when the data is arranged in order from lowest to highest (or highest to lowest). If the dataset has an odd number of values, the median is the middle value. If there is an even number of values in the dataset, the median is the average of the two middle values.

The median is six and fourth: This statement is true based on the given information that there are 11 marks on the line plot above 6 and fourth, and 11 marks below.

The mode is seven and two-fourths: This statement is false based on the given information. The mode is the value that appears most frequently in the dataset, and there are no values that appear more than once in the given data.

The range is five and three-fourths: This statement is true based on the given information. The range is the difference between the highest and lowest values in the dataset, which in this case is 5 and three-fourths (8 minus 2 and one-fourth).

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The cost of each lily is $3.50, and the cost of each rose is $2.25.

Let's use the variables L and R to represent the cost of each lily and each rose, respectively.

From the problem, we can write a system of two equations based on the information about the two arrangements:

5L + R = 19.75 (equation 1)

6L + 3R = 27.75 (equation 2)

To solve for L and R, we can use elimination. First, we can multiply equation 1 by 3:

15L + 3R = 59.25 (equation 3)

Then, we can subtract equation 2 from equation 3:

9L = 31.5

Solving for L, we get:

L = 3.50

Now we can substitute this value back into either equation 1 or equation 2 to solve for R. Let's use equation 1:

5L + R = 19.75

5(3.50) + R = 19.75

17.50 + R = 19.75

R = 2.25

Therefore, the cost of each lily is $3.50, and the cost of each rose is $2.25.

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Natalie saved amount $23 by using the coupon.

The discount rate is the interest rate used to determine the present value of future cash flows in a discounted cash flow (DCF) analysis. This helps determine if the future cash flows from a project or investment will be worth more than the capital outlay needed to fund the project or investment in the present.

The data is available from the question is:

The discount through coupon is d = 50%.

The original price of camera is c = $46.00

The discount on the amount is:

[tex]d = (\frac{50}{100}) 46[/tex]

d = 23

Thus, the amount saved is $23.

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The standard deviation for the given Poisson distribution is 0.8.

A Poisson distribution is used to model the number of events occurring in a fixed time interval when the events occur independently and at a constant rate. The mean and variance of a Poisson distribution are equal, and both are given by λ, the rate parameter.

Here, the given information is that the company receives an average of 0.64 purchase orders per minute. Therefore, λ = 0.64.

The formula for the variance of a Poisson distribution is σ² = λ, where σ is the standard deviation. Thus, substituting λ = 0.64 in this formula, we get σ² = 0.64. Taking the square root of both sides, we get σ = √0.64 = 0.8.

Therefore, the correct answer is 0.8.

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Answer:

70

Step-by-step explanation:

If y=30 when x=6, 5x=y (because they are in direct proportion).

So, when x=14 replace x.

5*14=y

y=70

you can prove this because 70/14=30/6=5

so, the proportions are equal

Thus, the most he could weigh that is the upper bound of the given condition is 84kg.

What about weigh?

The word "weigh" is not frequently used by itself in arithmetic. The notion of weight or mass, for example, can be used when measuring or comparing quantities. While mass is a measurement of the quantity of matter inside an object, weight is a measure of the gravitational force acting on it. Weight can be viewed as the force a standard gravitational field applies to an object in the setting of measurement. Weight or mass may be denoted in mathematical equations by variables such as "w" or "m," and the units used to measure them may change based on the situation.

Define upper bound:

In mathematics, an upper bound is a number that is greater than or equal to all the elements in a given set. More formally, let S be a set of real numbers. A number u is an upper bound for S if and only if for all x in S, we have x ≤ u.

For example, consider the set S = {2, 4, 6, 8}. The number 10 is an upper bound for S because 2 ≤ 10, 4 ≤ 10, 6 ≤ 10, and 8 ≤ 10. However, the number 7 is not an upper bound for S because 8 > 7.

Note that an upper bound need not be an element of the set S itself. For instance, the set of all negative real numbers does not have any upper bound among the negative real numbers, but 0 is an upper bound for this set.

It's worth noting that an upper bound may or may not be a member of the set S. If an upper bound is a member of S, then it is called a "maximum" or "greatest" element of S. However, if an upper bound is not a member of S, then S has no maximum element.

According to the given information:

Brain weigh himself at 84kg to the nearest kg as (given) , because uses the method of round off.

Thus, the range of weigh:

⇒ 83.5 ≤ Weigh ≤ 84.4.

Thus, the most he could weigh is 84.4kg.

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The cost of 8 family passes to the amusement park is $432 when a family pass to the amusement park costs $54.

To find the cost of 8 family passes to the amusement park, we can use the Distributive Property of multiplication over addition. The Distributive Property states that a(b + c) = ab + ac, where a, b, and c are numbers. In this case, we can use the Distributive Property to write:

8 x $54 = (5 x $54) + (3 x $54)

We can see that we have broken 8 down into two smaller numbers that we can multiply by $54 individually, and then add together. The first term, 5 x $54, represents the cost of 5 family passes, while the second term, 3 x $54, represents the cost of 3 family passes. Adding these two values together, we get:

(5 x $54) + (3 x $54) = $270 + $162 = $432

Therefore, the cost of 8 family passes to the amusement park is $432.

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This proportion represents the estimated probability that Chad will get a hit on more than 2 of every 10 pitches he receives.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To simulate the probability that Chad will get a hit on more than 2 of every 10 pitches he receives using random digits, follow these steps:

1. Divide the pitches into groups of 10. For each group of 10 pitches, record the number of hits that Chad gets.

2. Generate a random digit between 0 and 9 for each pitch in the group. If the digit is 0, 1, 2, or 3, consider it a hit. If the digit is 4, 5, 6, 7, 8, or 9, consider it a miss. Repeat this process for each group of 10 pitches.

3. Count the number of groups of 10 pitches in which Chad gets more than 2 hits.

4. Repeat steps 2 and 3 a large number of times (for example, 1000 times) to get an estimate of the probability that Chad will get a hit on more than 2 of every 10 pitches he receives.

5. Calculate the proportion of times in which Chad gets more than 2 hits in a group of 10 pitches.

Therefore, this proportion represents the estimated probability that Chad will get a hit on more than 2 of every 10 pitches he receives.

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Answer:

28

Step-by-step explanation:

Average of first 6 scores is 12, so the total of those 6 scores is 6 × 12 = 72.

Average of next 12 scores is 36, so the total of those 12 scores is 12 × 36 = 432.

Total of all 18 scores is 72 + 432 = 504.

Overall average is 504 ÷ 18 = 28.

The answer of the given question based on the finding the similarity statement by relating the three triangle is the three triangles appear to be similar by the Angle-Angle (AA) similarity theorem.

The Angle-Angle (AA) similarity theorem is  statement used in geometry to determine whether two triangles are similar. It states that if two angles of one triangle are congruent to two angles of another triangle, then  two triangles are similar.

More specifically, this theorem states that if two pairs of corresponding angles in two triangles are congruent, then triangles are similar. In other words measure of one angle in one triangle is equal to corresponding angle in other triangle, and measure of another angle in first triangle is equal to corresponding angle in other triangle.

Based on the given diagram, the three triangles appear to be similar by the Angle-Angle (AA) similarity theorem.

In the diagram, we can see that all three triangles have two pairs of congruent angles, which are labeled as angle A and angle B. Therefore, we can conclude that the three triangles are similar by AA similarity.

We can write this similarity statement as: Triangle ABC ~ Triangle DEF, Triangle ABC ~ Triangle GHI, and Triangle DEF ~ Triangle GHI.

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5000 parts must be tooled by the machine to ensure 4500 are acceptable as One tenth of the parts tooled by a machine are rejects.

One-eighth of the parts tooled by a machine are rejected.

Now, let's take the number of parts made by the machine to be x.

Now, the number of acceptable parts will be:

Total number of parts - number of rejected parts

x - (x/10)

(10x-x)/10

9x/10

Now, we have the number of acceptable parts as 4500.

So, we have:

9x/10 = 4500

9x = 4500*10

x = (4500*10)/9

x = 5000

Hence, the total number of parts tooled by the machine is 5000 in which 4500 are acceptable one.

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The experimental probability is the same as the expected probability for the blue marble, since the experimental probability of pulling a blue marble is 0.1 and the expected probability is also 0.1.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a mathematical concept that quantifies the chance of an event happening, ranging from 0 (impossible) to 1 (certain). Probability is commonly expressed as a fraction or a decimal between 0 and 1, or as a percentage between 0% and 100%

To determine the expected probability of pulling a certain color from the bag, we need to calculate the ratio of the number of marbles of that color to the total number of marbles in the bag.

Expected probability of pulling a red marble = 12/40 = 0.3

Expected probability of pulling a blue marble = 4/40 = 0.1

Expected probability of pulling a yellow marble = 8/40 = 0.2

Expected probability of pulling a green marble = 16/40 = 0.4

To calculate the experimental probability, we need to divide the frequency of each color by the total number of pulls, which is the sum of all the frequencies:

Experimental probability of pulling a red marble = 40/100 = 0.4

Experimental probability of pulling a blue marble = 10/100 = 0.1

Experimental probability of pulling a yellow marble = 20/100 = 0.2

Experimental probability of pulling a green marble = 30/100 = 0.3

So, the experimental probability is the same as the expected probability for the blue marble, since the experimental probability of pulling a blue marble is 0.1 and the expected probability is also 0.1. For all other colors, the experimental probability is different from the expected probability.

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the amount of soil needed is 27 cubic feet.

Answer:

Step-by-step explanation:

Rate of commission = commission / total sales

Rate of commission = $1,393.74 / $15,486

Rate of commission = 0.0898 or 8.98%

Diego's rate of commission is 8.98%.

As a result, the following regression model best fits the data: y ≈ 3.38x + 9.37 rounded to the closest hundredths.

The link between a dependent variable and one or more independent variables can be modeled statistically using linear regression. The dependent variable can be treated as a linear function of the independent factors since this sort of regression analysis presupposes a linear relationship between the variables. Finding the line of best fit that minimizes the gap between the observed data points and the anticipated values of the dependent variable is the objective of linear regression. The equation y = mx + b, in which y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept, is represented by the line of best fit, which is a straight line.

given

Using a graphing calculator, we may display the data points and identify the line of best fit in order to determine the regression model that best matches the data.

We obtain the following scatter plot by entering the data into a graphing calculator:

We can observe from the scatter plot that the data seems to have an approximately linear trend. We may utilize the calculator's linear regression tool to determine the line of best fit.

We obtain the following equation by applying a linear regression on the data:

y = 3.38x + 9.37

The regression equation is as follows, rounded to the closest hundredths:

y ≈ 3.38x + 9.37

As a result, the following regression model best fits the data: y ≈ 3.38x + 9.37 rounded to the closest hundredths.

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The complete question is:-  Use a graphing calculator to graph the data and to find a regression model that best fits the data. Round values to the nearest hundredths.

Answer:

No

Step-by-step explanation:

A prime number cannot be divided exactly by any number other than itself and 1.

For example, 17 is a prime number, since it can only be exactly divided by 17 and 1.

85 is NOT a prime number, since it CAN be divided by 5.

A particular type of cell doubles in number every hour.Write an exponential function that can be used to findthe number of cells present, y, at the end of x hours ifthere are initially 4 of these cells?The exponential function that can be used to find the number of cells present, y, at the end of x hours, given that there are initially 4 cells is: y = 4 * 2^x This is because the number of cells doubles every hour, so if there are 4 cells to start with, after one hour there will be 8 cells (doubling the initial number), after two hours there will be 16 cells (doubling the number after one hour), and so on. The exponent in the function represents the number of hours elapsed, and the base of the exponent is 2, representing the doubling of cells every hour.

The equation of parabola for the given equation through which it satisfied the relation is     [tex]( \frac{1}{30} )x^2 + (\frac{1}{30} )x - 1[/tex].

What about parabola?

A parabola is a U-shaped curve that is formed by the graph of a quadratic function of the form y = [tex]ax^2 + bx + c[/tex]. The parabola is symmetric around its axis of symmetry, which is a vertical line passing through the vertex of the parabola. The vertex is the point where the parabola changes direction, either from increasing to decreasing or from decreasing to increasing. The direction of the opening of the parabola (upward or downward) is determined by the sign of the coefficient a in the quadratic equation. Parabolas are used in various fields, such as physics, engineering, and mathematics, to model various real-life phenomena.

Define equation:

An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). It represents a mathematical relationship between two or more variables or constants, and is used to solve problems and make predictions.

In mathematics, equations can take various forms, including linear equations, quadratic equations, trigonometric equations, differential equations, and more. Depending on the type of equation, the variables may represent real or complex numbers, vectors, matrices, functions, or other mathematical objects.

According to the given information:

As, we know about the condition of the parabola,

Hence:

[tex]y = Ax^2 + Bx + C y-intercept: x=0 and y = -1\\\\ C = -1 y = Ax^2 + Bx - 1 (5,0) \\ \\0 = 25A + 5B - 1 (-6,0) \\\\ 0 = 36A - 6B - 1 1 \\\\ = 25A + 5B1 = 36A - 6B \\ \\ 0 = -11A - 11B 11B = -11A B = -A kX^2 - kx - 1 , k=A=-b (5,0)\\\\25k + 5k - 1 = 030k = 1k = 1/30 \\\\(-6,0)36k - 6k - 1 = 0\\\\30k = 1k=30 (\frac{1}{30} )x^2 + (\frac{1}{30} )x - 1 ,[/tex]

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Answer:

it's above

Step-by-step explanation:

yeah

The distance the visitor should run to minimize the time it takes to reach the rock formation is 3/4 miles.

A unitary method is a mathematical technique used to solve problems involving proportional relationships between different quantities.

Let's use the unitary method to find the time it takes to complete the journey.

Time taken to run = Distance / Rate = x / 4

Time taken to swim = Distance / Rate = (3 - x) / 3

Total time taken = Time taken to run + Time taken to swim

= x / 4 + (3 - x) / 3

To minimize the total time taken, we need to find the value of x that minimizes the above expression. Let's differentiate it with respect to x and equate it to zero.

d/dx (x/4 + (3-x)/3) = 1/4 - 1/3 = -1/12

-1/12 = 0 (at minimum)

Solving for x, we get:

x = 3/4

The visitor should run westward along the shoreline until reaching the point 3/4 miles away from the tent, and then swim the remaining 2 1/4 miles to reach the rock formation.

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The measure of angle T in the given quadrilateral is 92.5 degrees.

A quadrilateral is said to be inscribed in a circle if all four of its vertices are located on the circumference of the circle. In other terms, the quadrilateral is "enclosed" by the circle. The opposing angles of a quadrilateral are supplementary (add up to 180 degrees) and the product of the measurements of the two diagonals equals the sum of the products of the measures of the pairs of opposite sides when a quadrilateral is inscribed in a circle, both of which are important features. Inscribed quadrilateral geometry difficulties can be resolved by using these characteristics.

The sum of the angles in a quadrilateral is 360 degrees.

angle R + angle S + angle T + angle U = 360 degrees

79 degrees + 96 degrees + x + angle U = 360 degrees

Angle T and angle U are opposite angles in quadrilateral RSTU, therefore congruent.

175 degrees + 2x = 360 degrees

2x = 185 degrees

x = 92.5 degrees

Hence, the measure of angle T is 92.5 degrees.

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it takes Jason 6 seconds to hit the water after he jumps off the cliff. To determine when Jason hits the water, we need to find the value of t when h(t) = 0.

This is because the height of Jason is measured in feet and when he hits the water, he will be at a height of zero.

So we can set h(t) equal to zero and solve for t:

[tex]-16t^2 + 16t + 480 = 0[/tex]

Dividing both sides by -16, we get:

[tex]t^2 - t - 30 = 0[/tex]

Now we can use the quadratic formula to solve for t:

t = [-(-1) ± √[tex]((-1)^2[/tex] - 4(1)(-30))] / (2(1))

t = [1 ± √(121)] / 2

t = [1 ± 11] / 2

We get two possible solutions: t = 6 or t = -5. However, since time cannot be negative in this scenario, we can disregard t = -5 and conclude that Jason hits the water after 6 seconds.

Therefore, it takes Jason 6 seconds to hit the water after he jumps off the cliff.

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