Find the equation perpendicular to y=-2x+10 through (10,7)

1. The solution to the quadratic equation, x² - 14x + 49 = 40, is x = 13.32 and x = 0.68

2. The solution to the quadratic equation, x² - x = 12, is x = -3 and x = 4

3. i. The factors of 2x² - 15x - 8 = 0 are (2x +1) and (x - 8)

ii. The x-intercepts of 2x² - 15x - 8 = 0 are x = -1/2 and x = 8

From the question, we are to solve the given quadratic equation by completing the square.

The given equation is

x² - 14x + 49 = 40

Solving the equation

x² - 14x + 49 = 40

x² - 14x = 40 - 49

x² - 14x = -9

Multiply the coefficient of x by 1/2 square and add to both sides

x² - 14x + (-7)² = -9 + (-7)²

(x - 7)² = -9 + 49

(x - 7)² = 40

x - 7 = ±√40

x = 7 ± √40

x = 7 ± 6.32

x = 7 + 6.32 OR 7 - 6.32

x = 13.32 OR 0.68

Solving x² - x = 12 by factoring

x² - x = 12

x² - x - 12 = 0

x² -4x + 3x - 12 = 0

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

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

x + 3 = 0 OR x - 4 = 0

x = -3 OR x = 4

Determining the factors of 2x² - 15x - 8 = 0

2x² - 15x - 8 = 0

2x² - 16x + x - 8 = 0

2x(x - 8) + 1(x - 8) = 0

(2x + 1)(x - 8) = 0

The factors are (2x +1) and (x - 8)

Determining the x-intercepts

(2x + 1)(x - 8) = 0

2x + 1 = 0 and x - 8 = 0

2x = -1 and x = 8

x = -1/2 and x = 8

Hence, the x-intercepts are -1/2 and 8

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The percentage of higher risk is unaffected by exposure as relative risk in unity.

In order to determine the strength of the relationship between exposures (treatments or risk factors) and outcomes, relative risk is employed in the statistical analysis of data from ecological, cohort, medical, and intervention studies. For instance, in a study looking at how the drug apixaban affected the occurrence of thromboembolism, 8.8% of patients receiving a placebo developed the condition, whereas only 1.7% of patients receiving the medication did. This means that the relative risk is.19 (1.7/8.8), meaning that patients receiving apixaban had 19% the disease risk of patients receiving a placebo. [4] In this instance, apixaban lowers the probability of disease, making it a protective rather than a risk factor.

Values of relative risk can be understood as long as the relationship between the exposure and the result is assumed to be causal.

RR = 1 denotes that the outcome is unaffected by exposure.

When the risk of the outcome is less than 1, this is referred to as a "protective factor."

RR > 1 indicates that the exposure, a "risk factor," has an effect on the outcome's risk.

Therefore, the percentage of higher risk is unaffected by exposure as relative risk in unity.

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Answer:

10/3 mile

Step-by-step explanation:

perimeter = 4 × side

perimeter = 4 × 5/6 mile

perimeter = 20/6 mile

perimeter = 10/3 mile

Answer:

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

One full circle is:

Three times the same distance:

Answer:

Distance travelled = 565.2 m

Step-by-step explanation:

Formula of circumference,

→ C = 2πr = π × d

The circumference of circle is,

→ π × d

→ (22/7) × 60

→ 1320/7

→ 188.4

Distance traveled after 3 rounds,

→ C × 3

→ 188.4 × 3

→ 565.2 m

Hence, Andi covered 565.2 m.

By using a Venn diagram, we can conclude that:

a. 10 businesses have a drive-up window and no outside seating

b. 4 Businesses have a drive-up window and outside seating, but no pay telephone

c. 20 businesses have no pay telephone

d. 9 businesses have only a drive-up window

e. 8 businesses have outside seating or a pay telephone

A Venn diagram is a diagram consisting of overlapping circles to illustrate the logical relationship between two or more sets of items.

In the question, there are 3 sets of criteria that describe the condition of the fast-food businesses in Valley Mills Drive: whether or not there is a drive-up window, outside seating, or a pay telephone.

Let d denotes the number of businesses that have the three criteria.

If a denotes the number of businesses that have drive-up window and outside seating only, then:

drive-up window and outside seating = a + d

                                                           12 = a + 4

                                                             a = 8

If b denotes the number of businesses that have outside seating and a pay telephone only, then:

outside seating and a pay telephone = b + d

                                                           6 = b + 4

                                                            b = 2

If c denotes the number of businesses that have drive-up window and a pay telephone only, then:

drive-up window and a pay telephone = c + d

                                                             5 = c + 4

                                                              c = 1

If x denotes the number of businesses that have drive-up window only, then:

have a drive-up window = a + c + d + x

                                    18 = 4 + 1 + 4 + x

                                    18 = 9 + x

                                      x = 9

If y denotes the number of businesses that have outside seating only, then:

have outside seating = a + b + d + y

                                17 = 4 + 2 + 4 + y

                                17 = 10 + y

                                  y = 7

If z denotes the number of businesses that have pay telephone only, then:

Have pay telephone = b + c + d + z

                               8 = 2 + 1 + 4 + z

                               8 = 7 + z

                                z = 1

Then we can draw a Venn diagram to illustrate those numbers to get a better illustration in answering the questions.

a. a drive-up window and no outside seating = c + x = 1 + 9 = 10

b. a drive-up window and outside seating, but no pay telephone = a = 4

c. no pay telephone = x + y + a = 9 + 7 + 4 = 20

d. only a drive-up window = x = 9

e. outside seating or a pay telephone = y + z = 7 + 1 = 8

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Answer:89

Step-by-step explanation:math

Answer:89

Step-by-step explanation:7p+5

This means 7 *p+5

Where we see the p we put in 12

We get 7*12+5=89

9x²-16x(3x+11)(7x-5)

9x²-48x²-176x(7x-5)

9x²-48x²-1232x²+880

-1271x²+880

Volume of solid generated by revolving the region bounded by the graph is 3817.53 unit

A volume is created while a plane figure rotating about an axis or around any straight line situated on the same plane.

We apply definite integration to calculate the required volume.

we are given the equation y = 5x² and y =0, x= 3

volume is calculated by using the formula, V = ∫π y² dx

                                                                      V = ∫₀³π (5x²) ² dx

On the y-axis x = 0 so upper limit x = 3 and lower limit x= 0

                                                          V= π × 25/5 [x⁵] ³₀

                                                        V = 15.71 [3⁵- 0]

  hence, the volume of solid = 3817.53 unit

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The answer of the given pattern is 38564.11

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

We are given the expression as

"-6000(1+1.1+1.1^2+...+1.1^7)"

Using the power series we get;

= -6000(1.1^8/0.1)

After the complete solution the answer is 38564.11

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Cindy was able to make $837 in commission thanks to her commission rate, which equates to $104.62 per hour.

Cindy is a travel agent. She receives a 9% commission based on the value of the trips she books. Today she spent eight hours arranging a $9,300 cruise for a newlywed couple

The commission that Cindy received can be determined by:

= Commission % x Price of booked trip

= 9% x 9,300

= $837

Consequently, the following is her hourly wage:

= Commission received / Hours worked

= 837 / 8

= $104.62

The bottom line is that  made $104.62 per hour plus $837 in commission.

Cindy was able to make $837 in commission thanks to her commission rate, which equates to $104.62 per hour.

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Answer: 20

Step-by-step explanation:

x = 2

6(2)+8 = 20

Answer: 20

Step-by-step explanation:

f(2)= 6(2)+8

=20

 plug in x with 2

The equation of line in slope in intercept form will be equal to y = 4x - 4.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the data provided in the question,

The formula for a line is y = mx + b, where m denotes the slope and b the y intercept.

So,

The equation can be written as,

y = 4x + b

As per the given point (2, 4),

4 = 4(2) + b

b = 4 - 8

b = -4

So, the final equation will be,

y = 4x - 4

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Answer:

7

Step-by-step explanation:

g(3)=4(3)-5

g(3)=12-5

g(3)=7

Answer:

g(3) = 7

Step-by-step explanation:

Given function:

[tex]g(x)=4x-5[/tex]

To find g(x3) substitute x = 3 into the function:

[tex]\begin{aligned}x=3 \implies g(3)&=4(3)-5\\&=12-5\\&=7\end{aligned}[/tex]

Therefore:

Answer:

slope = -3

Step-by-step explanation:

⭐ What is the equation of a line in slope intercept form?

The given line of best fit is written in slope-intercept form. All we have to do is identify which term is the slope.

[tex]y = -3x + 5[/tex]

-3 is the coefficient of x. Therefore, -3 is the slope.

Chorus over all view is about love, magic and war and following is the summary of his theme.

In the chorus, it is stated that "everything but death" has been vanquished by man, hinting at what Antigone will experience. Additionally, they sing of "unsavory ambition," or inordinate pride, which alludes to Creon's terrible fault, or hamartia.

The chorus in "Oedipus Rex" serves as the voice of the common people and offers perspective that the other characters in the play are unable to express. The chorus advances the plot by introducing new characters and providing answers to issues that arise.

The chorus declares that this play will not be about love, war, or valiant acts. Instead, it will detail the successes and failures of Dr. John Faustus, a German native of humble origins who attends the University of Wittenberg to study philosophy and divinity. He is so good at theology that he finally gets haughty, which is what brings him to ruin. In the end, Faustus decides to research necromancy, or magic.

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Answer:

The following equations are true when 3.27 is used:

÷ 1,000 = 0.0327

÷ 10 = 0.327

÷ 100 = 3.27

Note that the equations ÷ 102 and ÷ 1 are not true when 3.27 is used. The equation ÷ 102 is not true because 102 is not a multiple of 1,000, so dividing 3.27 by 102 will not result in a value that is close to 0. The equation ÷ 1 is not true because it is simply stating that 3.27 divided by 1 is equal to 3.27, which is true but not very interesting or useful.

The number of belts produced must be positive: X1, X2, X3 >= 0

The shadow price of a constraint can be understand as the change in the objective function value for a unit change in the right-hand side (RHS) value of the constraint, with all other variables held constant.

A constraint is a condition of an optimization problem that should be satisfied the condition.

Here we can formulate this problem as a linear programming model (LPM):

Consider X1 be the number of belt A produced per day

Let X2 be the number of belt B produced per day

Let X3 be the number of belt C produced per day

The objective function is to maximize the profit, that is;

3X1 + 5X2 + 4X3.

The constraints are as follows:

The time spent on machine M1 must be less than or equal to 8 hours per day then;

2X1 + 3X2 <= 8

The time spent on machine M2 must be less than or equal to 10 hours per day then;

3X1 + 2X2 + 5X3 <= 10

The time spent on machine M3 must be less than or equal to 15 hours per day then we have

2X1 + 2X2 + 4X3 <= 15

Thus number of belts produced must be positive:

X1, X2, X3 >= 0

To solve this LPM using the simplex algorithm, you can follow these steps:

w In standard form, the objective function is to minimize the cost, and all constraints are in the form of "less than or equal to" a certain value.

The pivot row is the row that corresponds to the smallest positive ratio between the right-hand side (RHS) value and the corresponding pivot column element the constraint 2X1 + 3X2 ≤ 8.

Now Interpret the shadow prices.

The shadow price of a constraint can be understand as the change in the objective function value for a unit change in the right-hand side (RHS) value of the constraint, with all other variables held constant.

It can help to understand the value of the constraints in the LPM and how they contribute to the optimal solution.

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Answer: A. x^3 +x^2-8x+4 B. 10

Step-by-step explanation: (f•g)(x) is the same as f(x) • g(x)

A. (x^2+3x-2) • (x-2) = (x^3+3x^2-2x) -(2x^2+6x-4) -> x^3 +x^2-8x+4

B. plug in -3 for x -> (-3)^3 + (-3)^2 -8(-3) + 4 -> 10

The store manager purchases 7 pens which can be determined by the concept of equations.

According to question store manager purchased a total of 15 pens and markers. So, let us assume the total number of pens =x and the total number of markers = y

The above statement gives us the equation as follows:

x + y=15

The statement each pen cost $3.50, and each marker cost $1.75 and the manager spent a total of $38.50 gives us the equation as follows:

3.50x +1.75 y=38.50

By solving both the equation on multiplying first eq by 3.50 gives

3.50x+3.50y=52.5

Subtracting the above two equations gives

1.75y=14

y=8

Putting value of y in first equation gives x=7

As we had assumed that the total number of pens = x

Hence, the total number of pens =7

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Answer:

Yes, it is proportional because it is a line that goes through (0, 0).

Step-by-step explanation:

Answer:

Yes, it is proportional because it is a line that goes through (0, 0).

Step-by-step explanation:

10.9 years long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.

Given that,

We have to find how long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.

We know that,

P = $1000

r = 6.35% = 0.635

n=12

A = $2000

A = P(1+r/n[tex])^{nt}[/tex]

2000 = 1000(1+0.635/12[tex])^{12t}[/tex]

2= (1+0.635/12[tex])^{12t}[/tex]

log2= log(1+0.635/12[tex])^{12t}[/tex]

log2= 12t×log(1+0.635/12)

t=log2/12×log(1+0.635/12)

t≈10.9 years.

Therefore, 10.9 years long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.

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Step-by-step explanation:

To find the number of years it will take for Enola's investment to triple in value, we can use the formula for simple interest:

I = P * r * t

where I is the total interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the number of years.

Since the investment will triple in value, the total interest earned will be equal to two times the initial investment, or 2 * $8,600.00 = $17,200.00. Substituting these values into the formula and solving for t, we get:

$17,200.00 = $8,600.00 * 5.1% * t

t = $17,200.00 / ($8,600.00 * 5.1%) = 3.28 years

Rounding this value to the nearest tenth of a year, we get t = 3.3 years. Therefore, it will take approximately 3.3 years for Enola's investment to triple in value.

no 48 es un numero irracional

Cualquier número real que no se puede escribir como el cociente de dos números enteros, p/q, donde p y q son ambos números enteros, se denomina número irracional. Por ejemplo, la raíz cuadrada de 2 no se puede expresar como un número entero o una fracción.

Explicación detallada:

48 se puede expresar como [tex]\frac{48}{1}[/tex] aquí se puede ver que la forma p/q está presente. Entonces es un número racional.

no 48 es un numero irracional.

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48 is not an irrational number

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is called an irrational number. For example, the square root of 2 cannot be expressed as a whole number or a fraction.

48 can be expressed as  [tex]\frac{48}{1}[/tex] here you can see that the p/q form is present. So it is a rational number.

48 is not an irrational number.

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Answer:

Anna needs 801 boxes.

Step-by-step explanation:

You need to know how many groups of 9 are in 7209.

Use division to find this answer.

7209 ÷ 9 = 801

Anna needs 801 boxes.

Answer:

hey

Step-by-step explanation:

Answer:

Angle e = Angle a, as they are alternate angles.

Angle f = Angle c, as they are alternate angles.

Angles a, b, and c add up to 180°, as they are on a straight line.

Therefore, angles e, f and b also add up to 180°.

Answer:

282.6in^2

Step-by-step explanation:

Surface area of a cylinder = 2πrh+2πr^2

plugging in r=5 and h=4 gives

2π20+2π25

40π+50π = 90π

90*3.14=282.6in^2

The response will be -10 if the stated statement is accurate.

This same square root and cubed root are the two radicals we see most frequently. Since the square root is so often employed, it is customary to presume that any radical written without the need for an index is a square root. The figure above constitutes a radical taken as a whole.

An phrase that has a root, often a square or cube root, is referred to as a radical. A radical is made up of three main parts, namely: It expresses the degree of radicand multiplication. If the root symbol's numeric component is absent, it is assumed as 2 (square root). The symbol √ means “root of”.

= 6 - 4²

= 6 - 16

= - 10

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The correct questions are-

6 - 4²

Answer: 5

Step-by-step explanation:

x=7-2

x=5

Answer:

x=5

Step-by-step explanation:

5+2=7  or 7-2=5