A parabola can be drawn given a focus of ((7,6) and a directrix of y=-8y=−8. What can be said about the parabola?

Number of integers 'p' for which there exist a triangle with the given side length 3p -1 , 3p , p² + 1 is equal to five that is 1, 2, 3, 4, 5.

Using triangular inequality of triangle :

sum of two sides > third side

a. 3p - 1 + p² + 1 > 3p

⇒p² > 0

True result.

b. 3p + p² + 1 > 3p - 1

⇒ p² > -2

True result.

c. 3p - 1 + 3p > p² + 1

⇒ p² -6p + 2 < 0

Roots are : p = [ -(-6) ± √(-6)² -4(1)(2) ] /2(1)

                     = ( 6 ± √28 ) 2

                     = 5.6 or 0.35

Integer value of p are in between 0.35 to 5.6 are :

1, 2, 3, 4, 5

Therefore, the integer value of 'p' for the given side length of the triangle is equal to five that is 1, 2, 3, 4, 5.

For how many positive integers 'p' does there exist a triangle with sides of length 3p-1 , 3p , and p² + 1 ?

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Answer:

23

Step-by-step explanation:

just divide 34.5 and 1.5 that gives you the ammount of days she worked on her project

Answer:

g(x) = 4x - (1/2)

Second choice

Step-by-step explanation:

Using points: (-2, -8.5) and (-1, -4.5)

            y2 - y1      -4.5 - (-8.5)      -4.5 + 8.5        4

slope = -----------  = ---------------  =  --------------- =   --- = 4

             x2 - x1         -1 - (-2)              -1 + 2            1

Answer:

the answer should be g(x) = 4x - (1/2)

Step-by-step explanation:

The greatest sum that Gregory can get is given as follows:

1173.

When two three digit numbers are added, the numbers in the equivalent positions are added with each other, that is, the third digit is added with the third digit, the second with the second and the third with the third.

Hence the greatest sum would be obtained as follows:

Hence the sum would be given as follows:

642 + 531 = 1173.

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The factorization of three polynomials (x2 - 8x + 15) = (ax + b)(cx + d) is (x-5) (x-3)

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

The general equation of a straight line is given by the expression y = mx + c, where m is the gradient and y = c is the point at which the line intersects the y-axis.

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The graph that shows the new position of the rectangle after a translation is; Option C

When it comes to transformation in mathematics, there are different types such as reflection, dilation, rotation, translation.

Now, we are dealing with translation which is defined as a transformation of a shape in a plane that preserves the length, which tells us that the object is transformed without getting its dimensions affected.

In this case, we see the rectangle in the graph and we can conclude that the translation of the rectangle shows the correct translation would be the second option because it shows that the length is preserved without getting its dimensions or shape altered.

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Answer:

Step-by-step explanation:

the answer is 18 I think?

Answer:

18

Step-by-step explanation:

6 (legs) x 3 (ants) = 18 legs

It can also be represented as 6+6+6 (18)

hope this helps :)

Therefore , the solution of the given problem of percentage comes out to be a value is 55.

In mathematics, a percentage is a number any figure that is stated as a proportion of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. The "%" symbol, however, is frequently used to denote it. The % amount has no dimensions and is flat. Because the numerator of percentages is 100, they are effectively fractions. To show that a number is a percentage, the percent sign (%) should be put in front of it. On a test, for instance, you would receive a 75% if you gave the answer 75 out of the total questions.

Here,

Given :

=> 20 /100 * a =11

=> a  = 11 *100 /20

=> a  = 1100 /20

=> a = 55

Thus , a is 55 .

Therefore , the solution of the given problem of percentage comes out to be a value is 55.

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The largest value of all four operations is 54

In order to determine the largest value of all the four operations, one needs to plug in the values into the different operations given and then generate their values. By so doing, the following deductions are made:

(f * g)(3) = 2 * (3^2) * (3 - 4 * (2 * 3)) = 54

(f - g)(4) = 2 * (4^2) - (4 - 4 * (2 * 4)) = 40

f(g(2)) = 2 * (2^2) = 8

(f + g)(1) = 2 * (1^2) + (1 - 4 * (2 * 1)) = -3

So, the largest value of all four operations is 54. Therefore, the correct answer is as given above

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The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.

The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.

A motor oil store has two tanks: one holds 12 gallons of oil, and the other holds 2 gallons of oil. In order to determine which tank will require to fill the bottles, the following computation must be done:

Quarts to gallons is 4 to 1.

1/4 x 60 = X

60/4 = X

15 = X

Since the motor oil vendor requires 15 gallons of oil, he must use both tanks but will still be short by 1 gallons

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The correct option regarding the relationship between the population of the village and time is given as follows:

A. The population is decreasing over time.

The variables of the scatter plot are given as follows:

From the points on the scatter plot, we have that when the value of t increases, the value of P decreases.

This means that the scatter plot shows a decreasing relationship, and thus the correct option is given by option A.

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The following number is rational by writing it as a ratio of two integers. 52.4726172617261... = 52497370/999900.

In mathematics, any number that can be written as p/q where q ≠0 is considered a rational number. Additionally, every fraction that has an integer denominator and numerator and a denominator that is not zero falls into the category of rational numbers. The outcome of dividing a rational number, or fraction, will be a decimal number, either a terminating decimal or a repeating decimal.

The following number is rational by writing it as a ratio of two integers. 52.4726172617261...

let 52.4726172617261...=x

100x=5247.26172617.....

100x=5247+0.2617+0.00002617+....

S0, 0.2617+0.00002617+... is a geometric series,

[tex]S=\frac{a}{(r-1)}\\\\a=0.2617,r=0.0001\\\\s=\frac{0.2617}{0.9999}\\\\S=\frac{2617}{9999}\\\\now,\\100x=5247+\frac{2617}{9999}\\100x=\frac{52,467,370}{9999}\\\\x=\frac{52467370}{999900}[/tex]

So, 52.472617...can be written by x.

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Answer: where is the expression

Step-by-step explanation:

Let x be the number of $1 bills and y be the number of $10 bills.

We know that:

x + y = 59 (the total number of bills)

x + 10y = 239 (the total monetary value of the bills)

We can use the first equation to solve for one of the variables in terms of the other. For example:

x = 59 - y

We can substitute this expression for x into the second equation:

(59 - y) + 10y = 239

59 + 9y = 239

9y = 180

y = 20 (the number of $10 bills)

We can use this value of y to find the number of $1 bills by substituting it back into the first equation:

x + y = 59

x + 20 = 59

x = 39 (the number of $1 bills)

Therefore, the motel clerk has 39 $1 bills and 20 $10 bills.

The answers to all the parts is mentioned above.

Given are the geometrical figures as shown.

{ 9 } -

We can write the proportional relationship {since both triangles are similar} as -

5/8 = x/10

{x} = 50/8

{x] = 6.25

{ 10 } -

We can write the proportional relationship {since both triangles are similar} as -

x/20 = 10/16

{x} = 200/16

{x} = 12.5

TY = 20 - 12.5

TY = 7.5

Therefore, the answers to all the parts is mentioned above.

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Answer:

The number is 7

Step-by-step explanation:

1. Create the equation needed to solve this

Lets think of a number as x. We have a number multiplied by 6 and have 4 added to it.

We get:

6x + 4

Now this sum is equal to the product of 2 and 23. We connect this to get

6x + 4 = 2(23)

We can simplify this to

6x + 4 = 46

2. Solve for x

6x + 4 = 46

Subtract 4 from both sides

6x = 42

Divide both sides by 6

x = 7

Therefore the number is 7

Answer:

Rolando pays $63 for 20 rides

Step-by-step explanation:

this was the question right???

The total cost that he paid for the parking for 5 days is $26.00.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

The graph above shows the cost of parking at the airport,

since the graph is a straight line so it is the condition for a linear equation,

from the graph, the y-axis shows the price in dollars and the x-axis shows the number of days,

line of the graph passes from coordinates (0, 6) and (6, 30)

equation of line is y = mx + c

where c is initial cost when x is 0, y is 6

c = 6

and m = (y₂- y₁)/(x₂ - x₁)

m = (30 - 6)/(6 - 0)

m = 4

equation of line is,

y = 4x + 6

cost for 5 days,

x = 5

y = 4(5) + 6

y = 26

cost is $26.00

Hence cost for 5 days is $26.00, option C is correct.

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The probability of randomly drawing seven vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles is low. One time throughout the simulation's 500 iterations, all seven tiles were vowels.

Part A: What is the probability of randomly drawing 7 vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles?

Part B: To imitate one repetition of the process, you would use a table of random digits or a calculator to randomly generate seven digits, each between 0 and 9. The variable you would measure is the number of vowels drawn.

Part C:

Random Digits: 4, 2, 5, 7, 8, 8, 4

Vowels: 2, 8, 8, 4

Part D: This result suggests that it is possible to randomly draw all vowels in one draw, although it is unlikely.

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Answer: As the loan is amortized, Boris will make a series of equal payments each month for the duration of the loan, with each payment comprising of both interest and principal. The amount of interest in each payment will decrease over time, while the amount of principal in each payment will increase.

To calculate the monthly payments, we can use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

Where:

M = monthly payment

P = the principal or the loan amount = 91500

i = interest rate as a decimal = 3.3%/12 = 0.00275

n = total number of payments = 40 years x 12 months/year = 480

By substituting the values in the formula:

M = 91500 [ 0.00275 (1 + 0.00275)^480 ] / [ (1 + 0.00275)^480 - 1]

M = $439.65

So the monthly payment that Boris will make is $439.65. This amount will stay the same throughout the loan term, but the proportion of interest to principal in each payment will change as the loan is amortized.

Step-by-step explanation:

Let where is an integer greater than 9. compute the number of values of for which the sum of the squares of the digits of is at most 25.

The question asks us to count the number of values of for which the sum of the squares of the digits of is at most 25. To solve this problem, we can use a loop to iterate through all possible values of starting from 9 and up. For each value of , we can then calculate the sum of the squares of the digits of by using modulo and division operations to extract each digit and square it. If the sum of the squares of the digits of is at most 25, we can add 1 to the count of values. After the loop completes, we will have the total number of values of for which the sum of the squares of the digits of is at most 25.

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The rate of change of the angle of elevation is approximately - 2.597 degrees per second (-0.045 radians per second). (Correct choice: C)

In this problem we find the case of a drone that travels horizontally, at constant height (h), in meters. The rate of change of the angle of elevation (θ'), in degrees per second, can be found from trigonometric functions and derivatives:

tan θ = y / x

Where:

By derivatives:

sec² θ · θ' = - y · x⁻² · x'

θ' = - (y · x⁻² · x') / sec² θ

Where x' is the speed of the drone, in meters per second.

If we know that y = 5 m, θ = π / 6 and x' = 5 m / s, then the rate of change of the angle of elevation is:

x = y / tan θ

x = (5 m) / tan (π / 6)

x ≈ 2.887 m

θ' = - [(5 m) · (2.887 m)⁻² · (5 m / s)] / sec² (π / 6)

θ' ≈ - 2.597 degrees per second (- 0.045 radians per second)

Note - Please notice that negative sign indicates that angle is decreasing.

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Two equations that have the same solution as the given equation are;

2.3. p - 10.1 = 6.49. p - 4

230.p - 1010 = 650.p - 400 - p

The correct options are B and C.

The given equation is; 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

Simplifying the above equation by collecting like terms gives;

2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4

2.3·p - 10.1 = 6.49·p - 4

Both sides of an equation will remain equal, when both sides are multiplied by the same amount.

Multiplying both sides of the original equation by 100 gives the same solution as follows;

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

a) The expected annual rainfall is 15 million tons.

b) The standard deviation is the square root is 15 million tons.

c) Pgamma(4, shape = 3, scale = 5)

d) Pgamma(5, shape = 3, scale = 5) - Pgamma(2, shape = 3, scale = 5)

a) The expected annual rainfall accumulated in this lake is given by the mean of the gamma distribution, which is alpha * gamma. In this case, the expected annual rainfall is 3 * 5 = 15 million tons.

b) The standard deviation of the annual amount of rainfall in this lake is given by the square root of the variance, which is the square root of alpha * gamma². In this case, the standard deviation is the square root of 3 * 5² = 15 million tons.

c) To find P(X < 4), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.

pgamma(4, shape = 3, scale = 5)

This will return the probability that X is less than 4, which is the cumulative probability.

d) To find P(2 < X < 5), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.

pgamma(5, shape = 3, scale = 5) - pgamma(2, shape = 3, scale = 5)

This will return the probability that X is between 2 and 5, which is the cumulative probability.

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Answer:

all

Step-by-step explanation:

all of them

Answer:

We multiply 3/4 with the reciprocal of 3/8 which is 8/3. This leaves us with 3/4x8/3 which equals 24/12. This can be simplified into 2.

The inequality equation for the given graph is option B: y ≤ 1/3x - 4.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The given inequality equations are -

y ≥ 1/3x - 4

y ≤ 1/3x - 4

y ≤ 1/3x + 4

y ≥ 1/3x + 4

In a graph of an inequality, the symbols (<,>) are represented using a dotted line and the symbols (≤,≥) are represented using a straight line.

Now, write the inequality in equation form -

y = 1/3x - 4

y = 1/3x + 4

Substituting the values of x and y with origin (0,0) -

0 = 1/3(0) - 4

0 = -4

0 = 1/3(0) + 4

0 = 4

Putting the inequality symbol back -

y ≥ -4

This statement is false as seen in the graph.

y ≤ -4

This statement is true as seen in the graph.

y ≤ 4

This statement is false as seen in the graph.

y ≥ 4

This statement is false as seen in the graph.

Therefore, the equation for the graph is y ≤ 1/3x - 4.

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