Use the graph to write the explicit rule of the arithmetic sequence.

Answer:

8.9

Step-by-step explanation:

9.0-0.1= 8.9

which is one-tenth less than 9

The total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.

In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred as the common ratio.

In the question:

Let 'x' be the miles that Rowan runs in 1st week.

Xn for the nth week.

x1 = 15 (given)

x2 = 15*(1 + 3%) = 15*1.03

Xn = 15*(1 + 3%0ⁿ⁻¹ = 15*(1.03ⁿ⁻¹)

Let 'S' be the total miles.

S = x1 + x2+ .....+ xn

S = 15 + 15 *1.03 + 15*1.03² + ...+ 15*1.03⁹

On solving the series:

S = 15 × 1.(1.03¹⁰ - 1)/0.03

S = 57.31

S = 58

Thus, the total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.

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Answer:

$7.49

Step-by-step explanation:

49.99-42.50=7.49

Answer:

60 pages

Step-by-step explanation:

64 + 56 = 120

180-120 = 60 pages

Answer: Let's use the variables x and y to represent the number of small boxes and large boxes shipped, respectively.

The system of equations that could be used to determine the number of each type of box is:

x + y = 21 (equation 1)

7x + 14y = 252 (equation 2)

In equation 1, the left side represents the total number of boxes shipped, which is the sum of the number of small boxes (x) and the number of large boxes (y). The right side of the equation represents the total number of boxes shipped, which is given as 21.

In equation 2, the left side represents the total volume of paper shipped, which is the sum of the volume of all the small boxes (7 cubic feet per box) and the volume of all the large boxes (14 cubic feet per box), multiplied by the number of boxes shipped. The right side of the equation represents the total volume of paper shipped, which is given as 252 cubic feet.

These two equations can be used to solve for x and y, which represent the number of small boxes and large boxes shipped, respectively.

Step-by-step explanation:

The polynomial expressions are P(x) = x(x - 5)(x - 2), P(x) = (x + 3)(x + 5)(x - 3)(x + 1), P(x) = (x + 5)(x² - 4x + 5) and P(x) = (x + 5)(x² + 4)

Zeros (1): 0, 5, 2

This means that

Roots: x = 0, x = 5 and x = 2

The equation can be represented as

P(x) = (x - root)

So, we have

P(x) = (x - 0)(x - 5)(x - 2)

Evaluate

P(x) = x(x - 5)(x - 2)

Zeros (2): 0, 5, 2

Here, we have

Roots: x = -3, x = -5, x = 3 and x = -1

Using the form in (a), we have

P(x) = (x + 3)(x + 5)(x - 3)(x + 1)

Zeros (3): 0, 5, 2

Here, we have

Roots: x = -5, x = 2 + i

Using the form used abov]e, we have

P(x) = (x + 5)(x - 2 - i)(x - 2 + i)

Expand

P(x) = (x + 5)((x - 2)² + 1)

So, we have

P(x) = (x + 5)(x² - 4x + 5)

Zeros (4): -1 and 2i

Here, we have

Roots: x = -1, x = 2i

Using the form used abov]e, we have

P(x) = (x + 1)(x - 2i)(x + 2i)

Expand

P(x) = (x + 5)(x² + 4)

Zeros (5):2 mult.2, -4

The zeros here are not clear

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Answer:

2.51

Step-by-step explanation:

Layla goes out to lunch. The bill, before tax and tip, was $16.90. A sales tax of 6% was added on. Layla tipped 14% on the amount after the sales tax was added. How much tip did she leave? Round to the nearest cent.

Find the amount after sales tax was added:

Find the amount after sales tax was added:

bill

+

sales tax

=

bill+sales tax=

100

%

+

6

%

100%+6%

=

=

106

%

106%

amount after tax

=

amount after tax=

106

%

of

bill

106% of bill

=

=

1.06

×

$

16.90

1.06×$16.90

106% = 1.06

=

=

$

17.914

$17.914

Click to see alternative method

Find the tip:

Find the tip:

tip

=

tip=

14

%

of

amount after tax

14% of amount after tax

=

=

0.14

×

$

17.914

0.14×$17.914

14% = 0.14

=

=

$

2.50796

$2.50796

≈

≈

$

2.51

$2.51

Round to the nearest cent

Layla left a $2.51 tip.

Layla left a $2.51 tip.

Answer:4. (a) BMN = 75°(b) AMP = 105°Explanation:Given that ABC is an isosceles triangle with base BC, and ABC = 75°. Also, BC = MB = PM and MN || BC.(a) To find BMN, we can use the fact that MN || BC. This means that ∠BMN = ∠ABC = 75°. Therefore, BMN = 75°.(b) To find AMP, we can use the fact that BC = MB = PM. This means that triangle BMP is an isosceles triangle with base MP. Since BMN = 75°, we can find ∠BMP by using the fact that the sum of the angles in a triangle is 180°:∠BMP = (180° - 75°)/2 = 52.5°Now, we can find AMP by using the fact that the sum of the angles in a triangle is 180°:AMP = 180° - 75° - 52.5° = 52.5°Therefore, AMP = 105°.

(a) The angle BMN is 30°.

(b) The angle AMP is 15°.

The total angle of a triangle is 180°.

We have an isosceles triangle ABC with base BC and ∠ABC is 75°. We construct point M on AC and N, P on AB. It makes BC = MB = PM and MN || BC.

Since ABC is an isosceles triangle, ∠ACB is also 75°. See the picture attached!

Since BC = MB, the triangle MBC is isosceles with base MC. So, BMC is 75°.

The angles of triangle MBC will sum up to 180°. So,

∠MBC = 180 - (75 + 75) = 30°

The angle BMN and MBC is alternate interior angles, so

∠BMN = ∠MBC = 30°

Now, we have ∠NBM = 75 - 30 = 45°. Since MB = PM, it makes BMP an isosceles triangle. The angle BPM will be the same with PBM. It is 45°.

The angle PMN will be

= 180 - (45 + 45 + 30)

= 60°

The angle CMB, BMN, NMP, and AMP are supplementary. So, the angle AMP is

= 180 - (75 + 30 + 60)

= 15°

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Different triangles with the same areas include:

Right angle triangle: base = 6, height = 4

Acute triangle: base = 8, height = 3

Obtuse triangle: base = 16, height = 1.5

To create a right angle triangle, an acute triangle, and an obtuse triangle that all have the same area, we can use the following dimensions:

Right triangle: base = 6, height = 4

Acute triangle: base = 8, height = 3

Obtuse triangle: base = 16, height = 1.5

We can calculate the area of each triangle using the formula A = 1/2 (base x height):

Right triangle: A = 1/2 (6 x 4) = 12

Acute triangle: A = 1/2 (8 x 3) = 12

Obtuse triangle: A = 1/2 (16 x 1.5) = 12

Therefore, we can see that all three triangles have the same area, which is 12 square units. We know this because they all have the same base-to-height ratios, which means they have the same "steepness" or "slope". This means that the area of each triangle is proportional to its base and height, and since they all have the same ratio of base to height, they will all have the same area.

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Answer: the number that goes beneath the radical symbol is 17

The theorem you mentioned is known as Meusnier's theorem. The edge of regression of the polar developable of a space curve is the locus of the center of spherical curvatures.

It states that the locus of the center of spherical curvature of a space curve is the edge of regression of the polar developable of the curve. In other words, the center of curvature of a curve at any point lies on the edge of regression of the polar developable curve.

This theorem is used to describe the curvature of a curve in three-dimensional space. It is named after the French mathematician Jean Baptiste Meusnier, who first discovered it in 1776.

In mathematical terms, the theorem can be expressed as follows:

Let C be a space curve with curvature k and torsion T. Let P be a point on C and N be the normal vector at P. Then, the center of curvature of C at P is given by:

O = P + (1/k)N

The edge of regression of the polar developable of C is the locus of the point O as P varies along C.

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The reciprocal of 5/11 is: 11/5

The reciprocal of 20 is: since 20=20/1 so the reciprocal is 1/20

Answer: 11/5, 1/20

Step-by-step explanation:

The reciprocal of a value is the numerator and denominator of that value switched.

When you look at 5/11, we see that 5 is the numerator and 11 is the denominator. The reciprocal(switch numerator and denominator) is 11/5.

The reciprocal of 20 can be tricky because it isn't written with a denominator. But we know intuitively that 20 is also equal to 20/1.

Therefore we apply the same steps as in the first instance and we get that the reciprocal of 20/1 is 1/20.

The correct statement is f(x)=33(1.32)^(x). .

The original statement is false because it does not accurately represent the increase in the number of weekly flu tests. The original statement suggests that the number of tests decreases by 32% each week, which is not the case.

To accurately represent the increase in the number of weekly flu tests, we need to use the growth factor of 1.32, which is equivalent to 100% + 32%. This means that the number of weekly flu tests increases by 32% each week, as stated in the problem.

Therefore, the correct statement is f(x)=33(1.32)^(x).

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Triangle AXC is congruent to triangle AYB by the SAS Congruence Criteria.

In geometry, two triangles are said to be congruent if they have the same shape and size. More specifically, two triangles are congruent if all three sides and all three angles of one triangle are equal to the corresponding sides and angles of the other triangle. When two triangles are congruent, they can be superimposed on top of each other, and all corresponding parts of the triangles will match exactly.

There are several ways to prove that two triangles are congruent, including using the side-angle-side (SAS) theorem, the angle-side-angle (ASA) theorem, the side-side-side (SSS) theorem, and the hypotenuse-leg (HL) theorem.

Given that |AB|=|CD| and triangle ABC is isosceles.

We need to prove that triangle AXC = triangle AYB.

To do so, we will use the Side-Angle-Side (SAS) Congruence Criteria.

AC = BC (Given)

∠ACX = ∠BCY (Vertical Angles)

∠CAX = ∠CBY (Base Angles of Isosceles Triangle)

Therefore, triangle AXC is congruent to triangle AYB by the SAS Congruence Criteria.

Hence, proved.

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Answer:

Refer to pic...........

The area of the trapezoid is 65.16 metres squared.

The area of a trapezoid can be found as follows:

area of a trapezoid = 1 / 2 (a + b)h

where

Therefore,

a = 5metres

b = 13.1 metres

h = 7.2 metres

Hence,

area of a trapezoid = 1 / 2 (5 + 13.1) 7.2

area of a trapezoid = 1 / 2 (18.1)7.2

area of a trapezoid = 130.32 / 2

Therefore,

area of a trapezoid = 65.16 metres squared

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Answer: six hundred nine thousandths

Step-by-step explanation:

The two alleles that have the highest probability of being inherited together are A. G and k.

Alleles that are physically close to each other on a chromosome have a higher probability of being inherited together, a phenomenon known as linkage. The closer two alleles are to each other on a chromosome, the less likely it is that they will be separated by a recombination event during meiosis.

The degree of linkage between two alleles is determined by their relative physical distance on the chromosome. The closer two alleles are, the higher the probability that they will be inherited together.

G and k are the closest alleles to each other on the genetic map and so have a higher probability of being inherited together.

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The distance between Jason's school and his house is 8 miles.

What is the Cartesian system?

Any point can be located using a Cartesian coordinate system or coordinate system, and that point can be plotted as an ordered pair (x, y) known as Coordinates. The origin, symbolized by the letter "O," is the point where the two number lines intersect. The horizontal number line is known as the X-axis, and the vertical number line is known as the Y-axis.

Given that the coordinates of Jason's house is (-4,-5). The coordinates of his school is  (-10,-11).

The formula distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

Here, x₁ = -4, y₁ = -5,x₂= -10, y₂ = -11

The distance between points is

√[(-10-(-4))² + (-11 - (-5))²]

=√(6² + 6²)

= √(36+36)

= √72

= 6√2

= 8.48

≈ 8 miles

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The properties of logarithms, we can expand each expression and rewrite it as a sum, difference, or product of logs. This makes it easier to simplify and solve the expression.

The properties of logarithms can be used to expand each logarithm as much as possible. These properties include the product property, the quotient property, and the power property. Using these properties, we can rewrite each expression as a sum, difference, or product of logs.

15. log(z^19*x^13*19​)
= log(z^19) + log(x^13) + log(19)
= 19*log(z) + 13*log(x) + log(19)

16. ln(b^−4*0*a^−2​)
= ln(b^-4) + ln(0) + ln(a^-2)
= -4*ln(b) + ln(0) + -2*ln(a)

17. log(x^3*y^-4​)
= log(x^3) + log(y^-4)
= 3*log(x) + -4*log(y)

18. ln(y^1*−y*y​​)
= ln(y^1) + ln(-y) + ln(y)
= 1*ln(y) + ln(-y) + ln(y)

By using the properties of logarithms, we can expand each expression and rewrite it as a sum, difference, or product of logs. This makes it easier to simplify and solve the expression.

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By evaluating the function in j = 1, we conclude that each bottle costs 80 cents.

We know that the total cost in dollars can be represented by the linear equation:

C(j) = 0.8*j

Where C is the cost, and j is the number of juice bottles bought.

Then to get the cost of each bottle, we can evaluate the function in 1, which means buying only one.

C(1) = 0.8*1 = 0.8

So each bottle costs $0.80 (or 80 cents).

In mathematics, a function is a relationship between a set of inputs and a set of possible outputs, such that each input is associated with a unique output. Functions are represented by mathematical expressions or equations that specify how the input values are transformed into output values. For example, the function f(x) = x^2 takes an input value x and produces an output value equal to x squared.

Functions play a crucial role in many areas of mathematics, science, and engineering. They can be used to model complex systems, analyze data, and solve problems. Functions are also used in computer programming, where they are used to encapsulate a specific set of operations that can be reused throughout a program.

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The average rate of change of f(x) for the given values of h are:
When h=0.2, the average rate of change of f(x) is 112.84.
When h=0.1, the average rate of change of f(x) is 206.41.
When h=0.01, the average rate of change of f(x) is 1850.5601.
When h=−0.01, the average rate of change of f(x) is -1807.5399.
When h=−0.1, the average rate of change of f(x) is -171.39.
When h=−0.2, the average rate of change of f(x) is -80.76.

To calculate the average rate of change of f(x) for the given values of h, we need to substitute the values of h into the difference quotient and simplify.

When h=0.2:
f(3+0.2)−f(3)/0.2 = [(3.2^3−15(3.2)) - (3^3−15(3))]/0.2 = (32.768 - 10.2) - (27 - 45)/0.2 = 22.568/0.2 = 112.84

When h=0.1:
f(3+0.1)−f(3)/0.1 = [(3.1^3−15(3.1)) - (3^3−15(3))]/0.1 = (29.791 - 9.15) - (27 - 45)/0.1 = 20.641/0.1 = 206.41

When h=0.01:
f(3+0.01)−f(3)/0.01 = [(3.01^3−15(3.01)) - (3^3−15(3))]/0.01 = (27.270601 - 8.765) - (27 - 45)/0.01 = 18.505601/0.01 = 1850.5601

When h=−0.01:
f(3+(-0.01))−f(3)/(-0.01) = [(2.99^3−15(2.99)) - (3^3−15(3))]/(-0.01) = (26.730399 - 8.655) - (27 - 45)/(-0.01) = 18.075399/(-0.01) = -1807.5399

When h=−0.1:
f(3+(-0.1))−f(3)/(-0.1) = [(2.9^3−15(2.9)) - (3^3−15(3))]/(-0.1) = (24.389 - 8.25) - (27 - 45)/(-0.1) = 17.139/(-0.1) = -171.39

When h=−0.2:
f(3+(-0.2))−f(3)/(-0.2) = [(2.8^3−15(2.8)) - (3^3−15(3))]/(-0.2) = (21.952 - 7.8) - (27 - 45)/(-0.2) = 16.152/(-0.2) = -80.76

Therefore, the average rate of change of f(x) for the given values of h are:
When h=0.2, value is 112.84.
When h=0.1, value is 206.41.
When h=0.01, value is 1850.5601.
When h=−0.01, value is -1807.5399.
When h=−0.1, value is -171.39.
When h=−0.2, value is -80.76.

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The first set is countable, the second set is also countable. The third set is also countable.

(a) The set {x∈R:2 is countable because it is finite.
(b) The set {x∈Q:∣x∣≥2} is countable because it is a subset of the rational numbers, which are countable.
(c) The set {x∈Q:∣x∣<4} is countable because it is a subset of the rational numbers, which are countable.

In Maths, sets are referred as a collection of well-defined objects or elements. A set is usually represented by a capital letter symbol and the total number of elements in the finite set is basically represented as the cardinal number of a set in a curly bracket.

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rank(A) = 1

Given that A = $\left[\begin{array}{cc}a & b \\ a & b\end{array}\right]$, where $a \neq 0$.Let's find the rank of A:Rank(A) = number of leading 1's in the row echelon form of A.= $\left[\begin{array}{cc}a & b \\ a & b\end{array}\right]$=> $\left[\begin{array}{cc}a & b \\ 0 & 0\end{array}\right]$There are two leading 1's in row 1. Hence, rank(A) = 1.Now, let's find the basis of the null space of A:Null space of A is the set of all solutions to the equation $Ax=0$.So, $Ax$ = $\left[\begin{array}{cc}a & b \\ a & b\end{array}\right]$ $\left[\begin{array}{c}x \\ y\end{array}\right]$= $\left[\begin{array}{c}ax+by \\ ax+by\end{array}\right]$= $\left[\begin{array}{c}(a+b)x \\ (a+b)y\end{array}\right]$= $\left[\begin{array}{c}0 \\ 0\end{array}\right]$=> (a + b) x = 0 and (a + b) y = 0=> $x = \frac{-b}{a}y$=> $\left[\begin{array}{c}x \\ y\end{array}\right]$= $\left[\begin{array}{c}\frac{-b}{a}y \\ y\end{array}\right]$= $y \left[\begin{array}{c}\frac{-b}{a} \\ 1\end{array}\right]$=> Null space of A = $\{y \left[\begin{array}{c}\frac{-b}{a} \\ 1\end{array}\right] | y \in R \}$Let's take a = 1, b = 2. So, the null space of A = $\{y \left[\begin{array}{c}-2 \\ 1\end{array}\right] | y \in R \}$Therefore, the basis of the null space of A = $\left[\begin{array}{c}-2 \\ 1\end{array}\right]$Now, let's find the basis of the row space of A:Row space of A is the span of the rows of A.=> Row space of A = span $\left\{\left[\begin{array}{cc}a & b\end{array}\right]\right\}$Since rank(A) = 1, there is only 1 non-zero row. Therefore, a basis of the row space of A is $\left\{\left[\begin{array}{cc}a & b\end{array}\right]\right\}$.

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The solution is, the triangle ABC and DBC are congruent, by the Side-Angle-Side Triangle Congruence Theorem.  

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

As we can seen from the given figure that two triangles are given.

The triangles ABC and BDC are :

AB = CD

AC = BD

BC = BC

Hence using the SSS theorem of the triangle, the triangle ABC and DBC are congruent, Thus the angle A  is equal to angle D.

Hence the option D and E are correct. i.e. congruent by the Side-Angle-Side Triangle Congruence Theorem.  

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(a)  The future value of the investment if interest is compounded semiannually is $24,840.28.

(b) The future value of the investment if interest is compounded quarterly is $25,025.68.

(c) The future value of the investment is $185.40 greater when the interest is compounded quarterly.

The future value of an investment can be calculated using the formula FV = P(1 + r/n)^(nt), where FV is the future value, P is the principal amount deposited, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the investment is held.

If the interest is compounded semiannually, then n = 2. Plugging in the given values, we get:

FV = 18000(1 + 0.04/2)^(2*9)

FV = 18000(1.02)^18

FV = $24,840.28

So the future value of the investment if interest is compounded semiannually is $24,840.28.

If the interest is compounded quarterly, then n = 4. Plugging in the given values, we get:

FV = 18000(1 + 0.04/4)^(4*9)

FV = 18000(1.01)^36

FV = $25,025.68

So the future value of the investment if interest is compounded quarterly is $25,025.68.

To find out how much greater the future value of the investment is when the interest is compounded quarterly, we can subtract the future value when interest is compounded semiannually from the future value when interest is compounded quarterly:

$25,025.68 - $24,840.28 = $185.40

So the future value of the investment is $185.40 greater when the interest is compounded quarterly.

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The value of x will be 6° according to the remaining angles values in the diagram.

What is a Triangle?

With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.

How are the sum of triangles calculated in a triangle?

In a triangle, the total interior angles are supplementary. In other words, the sum of a triangle's inner angle measurements is 180°. Hence, we can write the triangle sum theorem's formula as A + B + C = 180° for the triangle ABC.

Now according to the question

                          => 40+110+8x-18=180 (Theorem)

                          => 150+8x-18=180

                          => 8x=180-150+18

                          => 8x=48

                          => x=6°

The  value of x will be : 6°

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The measure of the angle x is 50 degrees

In order to determine the value measure of the angle at the center, we need to know that;

The angle subtended by an arc at the center is said to be twice the angle subtended at the circumference.

In other words, we can say that the angle at the center is double the angle at the circumference.

This is represented as;

x = 2x

Such that '2x' is the angle at the circumference

From the image shown, we have that;

x = 2(25)

multiply the value

x = 50 degrees

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