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What is the equation of the following line? Be sure to scroll down first to see
all answer options.
10
-10
(0,0)
(10,-2)
10
Rest of the options are
D.y=- 1/5x
E. Y=5x
F.y=x

Answer: c

Step-by-step explanation:

Answer: The discount percentage is 23.4%

Step-by-step explanation:

The discount percentage can be calculated by taking the difference between the original price and the sale price, dividing that by the original price, and then multiplying by 100 to get a percentage.

From the curve in the graph the function values are

h(3) = 2

h(5) = 6

h(6) = 5

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line.

The quadratic equation represents a parabolic curve on a graph

Examining the graph the function values can be deduced noting that the values 3 5 6 and in h(3), h(5) and h(6) are points in the x axis or the domain

The function values are points on the y axis corresponding to tracing the x values to the curve

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Sum of the series will be (19/30)

Partial differentiation is the method of determining a function's partial derivative. By holding the other variable constant, one may use this method to get the partial derivative of a function with respect to one variable.

An equation having an unknown function of two or more variables and its partial derivatives with respect to these variables is known as a partial differential equation. A partial differential equation has the highest-order derivatives as its order. is a partial differential equation of order 2, as an illustration.

Ordinary differential equations, often known as ODEs, are equations for which only one variable's derivatives are considered. Consequently, there is just one independent variable. PDEs are equations that rely on the partial derivatives of a number of distinct variables.

Using partial fractions, we have

[tex]\frac{6}{(n+8)(n+10)}=\frac{A}{n+8}+\frac{B}{n+10}\\\\=\frac{A(n+10)+B(n+8)}{(n+8)(n+10)} \\\\ 6=A(n+8)+B(n+10)[/tex]

Put n=-8,

we have 6=0+2B=>B=3

Put n=-10,

we have 6=-2A =>A=-3

[tex]$$\begin{aligned}& \sum_{n=1}^{\infty} \frac{6}{(n+8)(n+10)}=\sum_{n=1}^{\infty}\left(\frac{3}{n+8}-\frac{3}{n+10}\right) \\& =3 \sum_{n=1}^{\infty} \frac{1}{n+8}-\frac{1}{n+10} \\& =3\left[\left(\frac{1}{9}-\frac{1}{11}\right)+\left(\frac{1}{10}-\frac{1}{12}\right)+\left(\frac{1}{11}-\frac{1}{13}\right)+\left(\frac{1}{12}-\frac{1}{14}\right)+\ldots\right] \\& =3\left[\frac{1}{9}+\frac{1}{10}\right]=\frac{19}{30}\end{aligned}$$[/tex]

other terms will be cancelled out

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The correct question should be:

Find the sum of the convergent series: [tex]$$\sum_{n=1}^{\infty} 6 /(n+8)(n+10)$$[/tex]

Answer: x = 15

Step-by-step explanation: Combine like terms

7 x plus 4 x plus x equals 180

12 x equals 180

2

Divide both sides by the same factor

12 x equals 180

the fraction with numerator 12 x and denominator 12 end fraction equals the fraction with numerator 180 and denominator 12 end fraction

3

Simplify

Solution

x equals 15

Answer: x3 +y3 20

Step-by-step explanation:

An inequality to determine at what times the car will be ahead of the truck is; 63x > 55x + 30

The graph of the inequality is attached and the solution is (3.75, 236.25).

We are told that;

x represent the number of hours that the car and truck travel

The truck is traveling at an average rate of 55 mph. Thus, the expression 55x represents the distance the truck travels in x hours.

The car is traveling at a rate of 63 mph. Thus, the expression 63x represents the distance the car travels in x hours.

In the beginning, the truck was 30 miles ahead of the car. So, we need to solve the inequality:

63x > 55x + 30

Use technology to graph y = 63x and y = 55x + 30 gives us;

The intersection point is (3.75, 236.25)

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The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

We should know that a circle is a set of points on a circle that are equal from a fixed point

The standard form for finding the equation of a circle is expressed as;

(x-a)² + (y-b)² = b=r²

where; (a, b) is the center of the circle

r is the radius of the circle

Given the following

Diameter = 12 units

radius = 12/2 = 6 units

If the center lies on the y-axis, the center will be at (0, 3)

Therefore, Substituting into the formula, we will have (x-0)² + (y-3)² = 6² which is equivalent to x²+ (y-3)² = 36

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The length of measurement would be in a scale drawing of 180 m is 24 cm.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, the scale is 2 cm = 15 m.

So, 1 m =2/15

A scale drawing of 180 m

Now, 180 m = 2/15 ×180

= 2×12

= 24 cm

Therefore, the length of measurement would be in a scale drawing of 180 m is 24 cm.

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Answer:

2 only

Step-by-step explanation:

Answer:2 and 4

Step-by-step explanation:

if you divide 164 by all the numbers you only get whole numbers when you divide it by 2 and 4  not 3 and 6

The limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined.

We can see that the denominator [tex]x^2[/tex][tex]y^2[/tex] goes to 0 as (x,y) approaches (0,0), and that can cause the function to go to infinity. However, the numerator (cos(xy) -1) does not have a specific value as (x,y) approaches (0,0) the cosine function oscillates between -1 and 1 as xy approaches zero, and therefore it does not approach a specific value.

The term (x,y) → (0,0) means that x and y are approaching 0 independently. There are different paths in which x and y can approach zero. Hence, by the squeeze theorem, we can see that if we approach (x,y) to (0,0) along the path y = mx, where m is a nonzero constant, the function goes to infinity, but if we approach (x,y) to (0,0) along the path x = 0 or y = 0, the function goes to -1.

Therefore, the limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined, as the function does not approach a specific value along all paths.

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Answer:

To find the value of the quantity after 46 years, we can use the formula for continuous compound interest:

A = P(1 + r)^t

Where:

A = final amount

P = initial amount (4400)

r = rate of growth (0.5%)

t = number of years (46)

We need to convert the percentage rate to decimal form, so we divide the rate by 100

0.5/100 = 0.005

Now we can substitute the values into the formula:

A = 4400(1 + 0.005)^46

A = 4400(1.005)^46

A = 4400 * 1.294624

A = 5685.89

Therefore, the value of the quantity after 46 years is 5685.89, to the nearest hundredth.

Step-by-step explanation:

Answer: a. To find the speed at which Zahara's dad drives, we need to divide the distance traveled by the time it took to travel that distance. The formula is: speed = distance/time.

So, speed = 159 miles / 3 hours = 53 miles per hour

b. Since Zahara's trip and Jorge's trip took the same amount of time, the only way that Jorge could have traveled a shorter distance than Zahara is if he drove slower. So, it can be inferred that Jorge drives slower than Zahara's dad.

Step-by-step explanation:

An object O is displayed in front of a plane mirror in the figure. The image of the object is visible from locations B and C.

An object's image is created by a plane mirror by reflecting light rays that originate from the object. The object and its image appear to be equally distant from the mirror because the image created by a plane mirror is imaginary, upright, and the same size as the object.

As light from the object enters the plane mirror, it reflects each beam in accordance with the Law of Reflection. At the intersection of the reflected beams' extensions, the image is visible.

Therefore, the location must be on the reflected ray's path for the image to be visible. Here, locations B and C are on the path of the reflected ray. So the image is visible in these locations. But not in locations A and D.

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On solving the provided question, exponents, resale value be $5339 after 4 years.

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) means 2 x 2 x 2 = 8.  and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.

y = cn^x

y is the new price, c is the starting price, n is the rate of increase (or decrease), and x is the number of years. I won't bore you with the various names this exponent use has in calculus and economics.

In our instance:

By calculating how much of the price will remain, we can determine n.

1.00 — 0.25 = 0.75

f(x) = (22500)(0.75)^x

f(5) = (22500)(0.75)^5

=5339.35

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Consequently, the square root of the  [tex]\sqrt{25}[/tex] is 5 and  square root of  [tex]\sqrt{4}[/tex]  is 2 . The square root and nth root .

The square root or nth root is represented by the radical sign. Square roots are a component of root expressions. There is a radical's radicand—a number or word that appears. Radicals like 7 and 2y+1 serve as examples. Additional terms that describe radicals include: Radical equations are those equations that include radicals. A "root expression" is the phrase used to describe the expression contained within the square root. To demonstrate radical representations, consider the numbers 2, 372, 2x+7, and 41p. The phrase "root expression" refers to the expression contained within the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.

given

square root of (a)  [tex]\sqrt{25}[/tex] because 5 is the square root, square root of

as b ) square root of  [tex]\sqrt{4}[/tex]   s2's square root

Consequently, the square root of the  [tex]\sqrt{25}[/tex] is 5 and  square root of  [tex]\sqrt{4}[/tex]  is 2 .

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The results suggest that the lead concentrations in the medicine samples are relatively low, as all of the values are below 20 mg/g. However, it would be necessary to compare these values to a standard, such as the acceptable limit of lead in medicine set by a regulatory body, in order to determine if the medicine is considered safe.

The decimal values of the listed amounts suggest that the measurements were precise, as they are all reported to one decimal place. It means that the measurement was done with a precision of 0.1. In addition to that, the measurements are consistent and close to each other, which also indicates that the measurements were precise.

It's important to keep in mind that precision and accuracy are different things. Precision refers to the degree of reproducibility of a measurement, while accuracy refers to the degree of closeness of a measurement to the true value. In this case, the measurements are precise but it's not specified if the measurements are accurate or not.

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Answer:

No it is not

Step-by-step explanation:

In an additive relationship, two quantities can be expressed as related to each other through addition. It can be written as y = x + a, where y is related to x through the addition of a constant, “a”.

In this scenario, the "a" is not constant

1+2=3, 5+3=8, and 9+4=13

the number is increasing by one each time

Answer:

y= 60+ 2x  and if he spent 19.5 hours then he would pay $99 for that month

Step-by-step explanation:

$60 PER MONTH + $2 per hour of boxing classes

X represents the total hours he had the boxing classes

equation: y= 60+ 2x

if he spent 19.5 hours in boxing class

plug in 19.5 hours to X

99 = 60+ 2(19.5)   = 60 + 39

Answer:

A

Step-by-step explanation:

Answer: y = (3/4)x - (7/4).

Step-by-step explanation:

Subtract 3x from both sides of the equation. Divide both sides of the equation by -4. Simplify. We get that solving 3x - 4y = 7 for y gives y = (3/4)x - (7/4).

f(x) = √x   ⇒   f(x) = -√(x -a) +b . . . . . . matches choice B

Function is the relationship between the input or domain and the output. A relation is a function if and only if there exists one value in the range for every domain value. A function is written as f x , where x is the input value. The general form of a function is y = f x

Function transformations

To move the domain from [0, ∞) to [a, ∞) requires the function be translated 'a' units to the right. That transformation is accomplished by replacing x with (x-a) in the function definition.

To move the range from [0, ∞) to [b, ∞) requires the function be translated upward by 'b' units. This is accomplished by adding 'b' to every function value.

Therefore, the range of the function will be (-∞,b] i.e. y ≤ b.

Hence, the required function is  f(x) = √x   ⇒   f(x) = - √(x -a) +b . . . . . . matches choice B

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The function to represent the arithmetic sequence is y = 0.17x + 0.71, and an envelop weighing 8 ounces cost $2.07

An equation is an expression that shows the relationship between variables and numbers.

An arithmetic sequence is in the form:

[tex]a_n=a_1+(n-1)d\\\\where\ a_1=first\ term,d=common\ difference[/tex]

Let y represent the price to send an envelop of x ounces. The arithmetic sequence is:

y = a₁ + (x - 1)d

Given that the first ounce is 88 cents($0.88), hence a₁ = 0.88. Eadh additional ounce is 17 cents (0.17), hence d = 0.17. Therefore:

y = 0.88 + (x - 1)(0.17)

y = 0.17x + 0.71

For a cost of $2.07:

2.07 = 0.17x + 0.71

x = 8 ounces

The function to represent the arithmetic sequence is y = 0.17x + 0.71

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Answer:

Fraction of fruit or vegetable cans = 13/28

Step-by-step explanation:

The fraction of the cans that are either fruit or vegetables is the sum of the fractions of the cans that are fruit and the cans that are vegetables. Since the fractions are for mutually exclusive categories, we can add the fractions of cans of fruit and the cans of vegetables to find the total fraction of cans that are either fruit or vegetables.

Fraction of fruit cans: 6/7

Fraction of vegetable cans: 1/4

Therefore,

Fraction of fruit or vegetable cans = 6/7 + 1/4 = (6 + 7)/(7*4) =13/28

Therefore , the solution of the given problem of set A when A= {5, 6, 7, 8, ..., 35}.

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.

Here,

The set A contains integers between 5 and 35, inclusive. So, the cardinality of set A is the number of integers between 5 and 35, which is 35-5+1 = 31.

b. A when A= {xEZ: -2 ≤ x ≤ 90}.

The set A contains all integers between -2 and 90, inclusive. So, the cardinality of set A is the number of integers between -2 and 90, which is 90-(-2)+1 = 93.

c. An B| when A= {x EN: x ≤ 31} and B = {x EN: x is prime}

The set A contains all the natural numbers less than or equal to 31. The set B contains all the prime numbers less than or equal to 31. There are 15 prime numbers less than or equal to 31: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. So, the cardinality of set B is 15.

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Solving the provided question, we can say that Not exponential growth or decay (no exponent) G(x)=1.3(x)

The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially.

The base of the exponentiation is the strongest indicator of whether an equation exhibits an exponential growth or decline.

It will be an exponential growth if the base is greater than 1.

It will be an exponential decay if the base is less than 1.

There won't be any exponential growth or decay if the function's exponent is zero.

Therefore: Decay exponential (base less than 1:

W = 9/8(3/5)t

f(t) = (3/4)t

L = 4.2(0.6)t

Exponential Growth (base larger than 1:

L = 0.25(12)t

W = 0.5(2.1)t

f(t) = 2/3(6)t

Not exponential growth or decay (no exponent):

G(x)=1.3(x)

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The value of the z is 6√6 units. The triangles follow similar triangle property.

What are similar triangles?

Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.

Consider △BDC and △ABC:

∠C = ∠C

∠ABC = ∠BDC = right angle

If two angles of a triangle are equal to two angles of another triangle, then third angle of the triangles also equal.

∠BAC =∠DBC

According to A-A-A rule △BDC and △ABC are similar to each other.

Thus the ratio of corresponding sides is also equal.

Therefore:

AB/BD = BC/DC = AC/ BC

Consider the last two ratios:

BC/DC = AC/ BC

z/12 = z/18

z² = 12 × 18

z² = 6×2×6×3

z = 6√6

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You can hold qualified investments like cash, stocks, bonds, mutual funds in a TFSA and can withdraw contributions as well as the interest, capital gains, and dividends earned in the account at any time1, without paying taxes

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The perimeter of Δ BUG with sides BG = 105, BU = 16 and UG = 30 is 151 units.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

It is given that ΔTOP ~ ΔBUG.

The lengths of sides of ΔTOP is - TO = 16, TP = 20, OP = 30.

The length of one side of ΔBUG is BG = 105.

Since ΔTOP is same as ΔBUG, so sides BU and UG will same as sides TO and OP respectively.

So, BU = 16 and UG = 30.

The formula for the perimeter of a triangle is -

P = a + b + c

Where, P is the perimeter and a, b, c are the sides of the triangle.

For ΔBUG -

P = BU + BG + UG

P = 16 + 105 + 30

P = 151

Therefore, the perimeter of ΔBUG = 151 units.

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