The slope-intercept form of the equation 40x - y= 11 is?

The slope-intercept form of the equation 8x = 1/5y + 4 is?

The cat and the squirrel will meet again at the finish line after 10 minutes.

To calculate how long it takes for both animals to meet again at the goal, we must identify the useful information to solve this problem, the information is presented below.

According to the above, we must find a number that when divided by 5 and 2 gives us an integer. For example, 10 divided by 2 would give 5, that is, the cat would turn 2 times in this time. If we divide 10 into 2, they would give us 5, which means that the squirrel would go around 5 times in this time. So the answer would be 10 minutes.

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The kind of the graph represented by the points (-2, 9), (-1, 3), (0, 1), (1, 3), (2, 9) is a quadratic graph

From the question, we have the following parameters that can be used in our computation:

Set of ordered pairs

The set of ordered pairs is represented as

(-2, 9), (-1, 3), (0, 1), (1, 3), (2, 9)

Next, we represent the points as a table of values

This is represented as

x       y

-2     9

-1      3

0      1

1       3

2       9

From the above points, we can see that:

See that the absolute values of x have the same y value

The above illustration is an illustration of a quadratic graph

Hence, the points are quadratic graph

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Yes, the values in the table form a proportional relationship, with a constant of 8/3.

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

The constant then can be written as follows:

k = y/x.

This means that a data-set will only represent a proportional relationship if the division of y by x is constant for all coordinate pairs in the data-set.

The constant for each pair in the data-set given in the table is calculated as follows:

As the constant is equal for all coordinate pairs of the data-set, the table in fact represents a proportional relationship.

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Answer:

$62091.53

Step-by-step explanation:

Their starting money was 74561.49, so we add that with the interest she gained and her deposits. That comes out to 77442.40. Then we subtract her two withdrawals, and we get to $62,091.53.

The mathematical result applied to prove sin²Ф + cos² = 1 , is the Pythagorean theorem.

Any right triangle has an area equal to the sum of a sides of the squares which sides are the two legs (remember, the hypotenuse is the side opposite the right angle).

Consider the given triangle ABC, right angled at C.

Then,

AC² + BC² = AB²

Divide the equation by AB².

AC²/ AB² + BC²/ AB² = AB²/ AB²

(opposite/ hypotenuse)² + (adjacent/ hypotenuse)² = 1

Thus,

sin²Ф  = (opposite/ hypotenuse)²

cos² =  (adjacent/ hypotenuse)²

Then,

sin²Ф + cos² = 1

Thus, the mathematical result applied to prove sin²Ф + cos² = 1 , is the Pythagorean theorem.

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The solution to the given system of equations as given in the task content.is; x = 6 and y = 4.

It follows that the given system of equations is;

Y equals X minus 2X plus Y equals 10

y = x - 2

x + y = 10

By substituting y into the second equation; we have;

x + x - 2 = 10

2x = 10 + 2

2x = 12

x = 6

Since, y = x - 2;

y = 6 - 2

y = 4.

On this note, it follows that the solution to the system of equations is such that; x = 6 and y = 4.

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Using factorization, the algebraic expression 27d⁶ + 8g¹² is equal to (3d² + 2g⁴)(9d⁴ - 6d²g⁴ + 4g⁸)

Factorization, also known as factoring, is the process of breaking down a number or an algebraic expression into its prime factors. It is a mathematical process that helps to simplify complex algebraic equations and it is used in a variety of mathematical applications, including algebra, calculus, and number theory.

In this problem, we have an expression in which can be factored to produce two smaller expressions.

27d⁶ + 8g¹² = (3d² + 2g⁴)(9d⁴ - 6d²g⁴ + 4g⁸)

The expression 27d⁶ + 8g¹² is equal to (3d² + 2g⁴)(9d⁴ - 6d²g⁴ + 4g⁸)

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Answer: The number of pounds of blueberries were in each pie is 2.4

Given that,

mary bought 12 pounds of blueberries to make 5 pies.

Based on the above information, the calculation is as follows:

= 2.4

Answer:

4/5

Step-by-step explanation:

Answer:

Exact form: 4\5

Decimal form: 0.8

Step-by-step explanation:

1. 'Multiply' (-4\3) * (-3\5) = 12\15

2. 'Simplify' 12\15 = 4\5

The rocket will be at a height more than 100 feet for 10 seconds.

Quadratic equations are second degree equations involving a variable of the form [tex]ax^{2} + bx+c = 0[/tex].

We have the equation relating height and time as,

h(t) = -[tex]\frac{1}{2}[/tex] t² + 15 t

When height is 100 feet, equation becomes,

100 = -[tex]\frac{1}{2}[/tex] t² + 15 t

-[tex]\frac{1}{2}[/tex] t² + 15 t - 100 = 0

Multiplying throughout with -2, we get,

t² - 30t + 200 = 0

(t - 10) (t - 20) = 0

t - 10 = 0 or t - 20 = 0

t = 10 or t = 20

When rocket is at maximum height of 112.5 feet,

-[tex]\frac{1}{2}[/tex] t² + 15 t - 112.5 = 0

Multiplying throughout with -2, we get,

t² - 30t + 225 = 0

(t - 15) (t - 15) = 0

t - 15 = 0

t = 15

Hence the rocket reached at a height of 100 feet at t = 10 seconds and after 5 seconds it reached it's maximum height at t = 15 seconds and then the rocket goes down and again reached at a height of 100 m at t = 20 seconds. So the rocket is at height more than 100 m for 10 seconds.

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Answer:

7,001 meters is more than 7 kilometers. 1 kilometer is equal to 1000 meters, so 7 kilometers is equal to 7 x 1000 = 7000 meters. Therefore, 7,001 meters is greater than 7000 meters, or 7 kilometers.

Step-by-step explanation:

Due to the earth's rotation, a person would be traveling faster at the equator than they would at a position halfway from the equator to the North Pole. This is true.

The rotation of the planet Earth around its own axis and variations in the orientation of the rotation axis in space are referred to as Earth's rotation or Earth's spin. Earth rotates progradely in an easterly direction. The Earth rotates counter-clockwise when viewed from the northern polar star Polaris.

We cross the line separating day from night every day because the Earth is perpetually rotating. The length of our shadows is yet another pattern brought on by the Earth's rotation.

The circumference of the Earth is largest at the equator because of how the rotation of the Earth causes it to bulge there. In comparison to a location closer to the poles, the equator requires a person to travel a greater distance in a given amount of time. A person at the equator would therefore move more quickly than someone farther from the poles.

In conclusion, it is true.

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Due to the earth's rotation, a person would be traveling faster at the equator than they would at a position halfway from the equator to the North Pole.

True or false?

The period of the sinusoidal function is 4 s

The period of a sinusoidal function is the time it takes for the sinusoidal function to complete one cycle of revolution.

To find the period of the given sinusoidal function, we observe the graph. The period is the time at which the graph completes one cycle. Now, since the graph passes through the origin at x = 0 and completes one cycle at x = 4. So, the complete cycle is from x = 0 to x = 4.

Thus the period of the function is 4 s

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The consequences of this congruence are AB is parallel to CD( property of parallelogram)

∠ABD is congruent to ∠CDB( Angles opposite of equal sides are congruent)

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

We are given that ABCD is a parallelogram and [DB] is one of its diagonals.

In  Δs ABD and CDB

The Lines AB and CD are parallel

Therefore Angle B and Angle D are equal ; both angles are equal as they are alternate interior angles.

So An angle is always congruent to itself (Reflexive property of congruence)

Hence, the proved that Δs ABD and CDB are congruent.

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The measure of the given angle is given as 1.25 π radian the measure of the shaded portion is 40 π radian

The given figure is a circle to find the shaded portion we use the formula for area of sector in radian

Area of sector = (1/2) × r²θ

1.25 π radian = θ

8 = radius, r

Area of sector = (1 / 2) × 8² * 1.25 π radian

Area of sector =  (1 / 2) × 64 * 1.25 π radian

Area of sector =  (1 / 2) × 80 π radian

Area of sector =  40 π radian

The area of the sector the shaded portion is 40 π radian

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The probability that[tex]$QR \leq 100$[/tex] is equal to the ratio of the area of the region in which[tex]$QR \leq 100$[/tex] to the area of the region in which [tex]$0 \leq a \leq 75$ and $0 \leq b \leq 75$[/tex]. Therefore,[tex]$m + n$[/tex] is equal to the area of the region in which [tex]$0 \leq a \leq 75$ and $0 \leq b \leq 75$.[/tex]

The probability that

[tex]$QR \leq 100$[/tex]

is equal to the ratio of the area of the region in which

[tex]$QR \leq 100$[/tex]

to the area of the region in which

[tex]$0 \leq a \leq 75$[/tex]

[tex]$0 \leq b \leq 75$[/tex]

. To find this probability, we first need to find the area of the region in which

[tex]$0 \leq a \leq 75$ and $0 \leq b \leq 75$[/tex]

This region is a rectangle with sides of length[tex]$75$,[/tex] so its area is

[tex]$75^2$[/tex]. To find the area of the region in which

[tex]$QR \leq 100$[/tex],

we need to calculate the area of the triangle in which[tex]$QR$[/tex] is the hypotenuse.

This triangle has base [tex]$75$[/tex]and height [tex]$200$[/tex], so its area is [tex]$3750$[/tex]. Therefore, the desired probability is

[tex]$\frac{3750}{75^2}$, and $m + n[/tex]

[tex]= 75^2$.[/tex]

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If the Q and R are on the same side of the line OP and angle OQP and angle ORP are right triangles then the probability that QR ≤ 100 is 16/25 and the value of m+n is 41 .

The angles OQP and angle ORP are given as right angles that means

∠OQP = ∠ORP = 90° ,

In order to find the required probability we draw a semicircle having the diameter OP and points Q and R on the same side of the semicircle .

given that diameter  OP = 200 ,

So , the radius of the circle will be = 100 ,

Let QR = x ≤ 100 , From the figure ,

we can write ,

[tex]OQ = 200 \times Cos(a)[/tex] and [tex]PQ = 200 \times Sin(a)[/tex]

[tex]OR = 200 \times Cos(b)[/tex]  and  [tex]PR = 200 \times Sin(b)[/tex]

From the figure given below , we can conclude that the quadrilateral OQRP is a cyclic quadrilateral .

So , [tex]200x + (200 Cosa)\times(200 Sinb) = (200 Sina)\times(200 Cosb)[/tex]

we get , [tex]x = |200 Sin(a-b)| \leq 100[/tex] ,

| Sin(a-b)| ≤ 1/2 ;

which implies that |a-b| ≤ 30 ,

that means , -30 ≤ (a-b) ≤ 30 ,  

it is given that a and b are chosen independently and uniformly at random in interval (0,75).

which means , 0<a, b <75 .

The Probability that x ≤ 100 is = [tex]\frac{Favorable Area}{Total Area}[/tex]

=  [tex]\frac{75\times75-45\times45}{75 \times75}[/tex] = 1 - [tex]\frac{9}{25}[/tex] ,

On simplifying ,

we get

= 16/25 ,

and it is given that the probability is = m/n ,

So on comparing , we get that , m = 16 and n = 25 ,

and the value of m+n = 16+25 = 41 .

Therefore , the probability is 16/25 and the value of m+n is 41 .

The given question is incomplete , the complete question is

Two real numbers a and b are chosen independently and uniformly at random in the interval (0,75). Let O and P be two points on the plane with OP = 200. Let Q and R be on the same side of line OP such that the degree measures of angle POQ and angle POR are a and b respectively, and angle OQP and angle ORP are both right angles. The probability that QR ≤ 100 is equal to m/n , where m and n are relatively prime positive integers. Find m + n.

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Answer:

If the phone is on sale for 30% off, this means the phone has had 30% of its original price taken off to arrive at the new price of £128. To find the original price of the phone, we can use the equation:

Original price = Sale price / (1 - Discount percentage)

In this case:

Original price = 128 / (1 - 0.30)

When we calculate this we get:

Original price = 128 / 0.7

Original price = £183.33

So the phone cost £183.33 before the sale.

Step-by-step explanation:

First you simplify the fractions

17/12 × 1/2 × 3

17×1×3=51 and 12×2=24

51/24

Further simplifying after dividing the two numbers by 3 you get

17/8

Answer:

Step-by-step explanation:

If you are looking for an exact form, it will be 17/8

If you are looking for a decimal form, it will be 2.125.

If you are looking for a mixed number form, it will be 2 1/8

I hope this helps.

Answer:

Answer in image

Step-by-step explanation:

-Hope this helped

Answer:

Below

Step-by-step explanation:

742 mm  /  ( 760 mm / 1.013 x 10^5 Pa)  = 9.89 x 10^4 Pa

The sequence of rigid motion followed by a dilation with center (0, 0), that maps RSTU to VXYZ is described using option C as follows;

C. Reflection across the x-axis, translation 2 unit(s) left and 1 unit down, dilation with center (0, 0) and scale factor 0.5

A rigid transformation is one in which the distance between corresponding pairs of points in the pre-image is preserved in the image

The coordinates of a pair of points in RSTU are; R(6, 0), S(8, 4), and T(6, 8)

The coordinates of similar points in VXYZ are; V(1, -1), X(2, -3), and Y(1, -5)

Length of RS = √((8 - 6)² + (4 - 0)²) = 2·√5

Length of ST = √((8 - 6)² + (4 - 8)²) = 2·√5

Length of VX = √((2 - 1)² + (-3 - (-1))²) = √5

Length of XY = √((2 - 1)² + (-3 - (-5))²) = √5

Applying a reflection across the x-axis on the RSTU, we get;

R(6, 0) → R'(6, 0)

S(8, 4) → S'(8, -4)

T(6, 8) → T'(6, -8)

Applying a dilation of a scale factor of 0.5, we get;

R'(6, 0) → R'(6 × 0.5, 0 × 0.5) = R''(3, 0)

S'(8, -4) → S''(8 × 0.5, -4 × 0.5) = S''(4, -2)

T'(6, -8) → T''(6 × 0.5, -8 × 0.5) = T''(3, -4)

Applying a translation of 2 units left and 1 unit down to the R''S''T''U'', we get;

R''(3, 0) → V(3 - 2, 0 - 1) = V(1, -1)

S''(4, -2) → X(2 - 2, -2 - 1) = V(2, -3)

T''(3, -4) → Y(3 - 2, -4 -1) = Y(1, -5)

The coordinates of similar points in VXYZ are; V(1, -1), X(2, -3), and Y(1, -5)

Therefore; the sequence of rigid motion that maps RSTU to VXYZ is a reflection across the x-axis, a translation of 2 units to the left and 1 unit down followed by a dilation of 0.5 with the center of dilation at (0, 0)

The correct option that can be used is option C.

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The completed table that indicates the values of the specified exponential expressions is presented as follows;

[tex]\begin{array}{|c|c|cc|}\\2&1&\dfrac{1}{2} &\\&&&\\\dfrac{\left(3^7\cdot 4^7\right)\cdot \left(2\cdot 5\right)^{-3}\cdot \left(5^2\right)}{12^7\cdot 5^{-1}\cdot 2^{-4}} &\dfrac{\left(2\cdot 3\right)^{-1}\cdot 2^0}{\left(2\cdot 3\right)^{-1}} &\left(3^3\right)\cdot \left(4^0\right)^2\cdot \left(3\cdot 2\right)^{-3}\cdot \left(2^2\right) &\\ &&& \\&\dfrac{\left(2\cdot 3^{-2}\right)^3\cdot \left(5\cdot 3^2\right)^2}{\left(3^{-2}\right)\cdot \left(5\cdot 2\right)^2} & & \\\end{vmatrix}[/tex]

An exponential expression is a mathematical expression that consists of numbers and or variables that have index of numbers and or variables, validly combined together using mathematical operators.

The exponential expressions are;

First expression;

[tex]\dfrac{\left(2\cdot 3^{-2}\right)^3 \times \left(5\cdot 3^2\right)^2}{\left(3^{-2}\right)\cdot \left(5\cdot 2\right)^2}[/tex] = (2³ × 3⁻⁶) × (5² × 3⁴) ÷ ((3⁻²) × (5 × 2)²)

(2² × 3⁻⁶) × (5² × 3⁴) ÷ ((3⁻²) × (5² × 2²)) = 2⁽²⁻²⁾ × 3⁽⁻⁶⁺²⁺⁴⁾ × 5⁽²⁻²⁾

2⁽²⁻²⁾ × 3⁽⁻⁶⁺²⁺⁴⁾ × 5⁽²⁻²⁾ = 2⁰ × 3⁰ × 5⁰ = 1

Second expression;

(3³)×(4⁰)²×(3×2)⁻³(2²) = 3⁽³⁻³⁾ × (4⁰)² × 2⁽² ⁻ ³⁾ = 3⁰ × 4⁰ × 2⁻¹ = 1/2

(3³)×(4⁰)²×(3×2)⁻³(2²) = 1/2

Third expression;

(3⁷·4⁷) × (2·5)⁻³ × (5²) ÷ (12⁷ × 5⁻¹ × 2⁻⁴)

(3⁷·4⁷) × (2·5)⁻³ × (5²) ÷ (12⁷ × 5⁻¹ × 2⁻⁴) = (3×4)⁷ × (2⁽⁻³ ⁺ ⁴⁾) × 5⁽⁻³⁺¹⁺²⁾ ÷ 12⁷

12⁽⁷⁻⁷⁾ × (2⁽⁻³ ⁺ ⁴⁾) × 5⁽⁻³⁺¹⁺²⁾ = 12⁰ × 2 × 5⁰ = 2

Therefore;

(3⁷·4⁷) × (2·5)⁻³ × (5²) ÷ (12⁷ × 5⁻¹ × 2⁻⁴) = 2

Fourth expression;

(2·3)⁻¹ × 2⁰ ÷ (2 × 3)⁻¹

2⁽⁻¹⁺¹⁾ × 3⁽⁻¹⁺¹⁾ × 2⁰  = 2⁰ × 3⁰ × 2⁰ = 1 × 1 × 1 = 1

(2·3)⁻¹ × 2⁰ ÷ (2 × 3)⁻¹ = 1

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Answer:

a. x/24

b. (x+y)/24

c. y/12

Step-by-step explanation:

semimonthly = twice a month or 24 times a year (because 12 months * twice a month = 24 times)

a. as she was paid 24 times a year for x dollars last year,

24 semimonthly payments of d dollars = x

divide both sides by 24 to get d

x / 24 = d dollars per semimonthly payment

b. she is paid x + y dollars this year, so she is paid (x+y)/24 dollars for her semimonthly salary

c. she earns y additional dollars per year. divide by 12 (because 12 months = 1 year) to get one month's worth of additional dollars = y/12 dollars extra per month

Answer:

Step-by-step explanation:

Discontinuous points of the function f(x) occur at x = 0, x = 3, and x = -3.

Discontinuous is a term used to describe something that is not continuous. It can refer to physical objects, such as a line that is broken into two or more parts, or to abstract concepts, such as a set of data points that are not evenly spaced or connected. In mathematics, discontinuous functions have jumps or breakpoints where the graph of the function changes abruptly. For example, the graph of a discontinuous function might jump from one value to another, rather than smoothly transitioning between the two values. Discontinuous functions are often used to describe the behavior of certain physical systems, such as electrical circuits and mechanical systems.

At these points, the value of the function f(x) changes abruptly and does not follow the same pattern as other points.

For example, at x = 0, the value changes from 0 to (3-x)², and at x = 3, the value changes from 3 to 0. Similarly, at x = -3,

the value changes from -3 to 0. Thus, the discontinuous points of the function f(x) are 0, 3, and -3.

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Answer: The weight of each screwdrivers is 100 grams.

Step-by-step explanation: Solution:

Given,

wrench weight= 600 grams

weight of 1 screwdrivers =?

By the question

wrench weighs 3 times as much as 2 screwdrivers

So,

           2 screw drivers= 600g÷3

                                     = 200g

             1screw drivers = 200g÷2

                                      = 100grams

Therefore, one screwdriver weight is 100 grams.

Answer:

y < 4

Step-by-step explanation:

the broken horizontal line y = 4 means that y cannot equal 4

The shaded area below the line represents the solution, which is

y < 4

The correct answer is y<4.

Recall that the horizontal line has an equation of the type y=b, where b is the perpendicular distance from the x-axis. As the shaded region is below the line y=4, the inequality representing the region is y<4.

The length of the sides of triangle ABC are: 6, 8, and 12.

One of the conditions that two triangles are similar is their Three pairs of corresponding sides are proportional.

In the given problem, the ratio of the sides of triangle ABC is 3 : 4 : 6

Another triangle, let's say triangle DEF, is made with its vertices at midpoints of the sides of triangle ABC.

Hence, all three pairs of corresponding sides have the same proportion.

AB/DE = BC/EF = AC/DF = 1/2

Due to similarity, the ratio of the sides of triangle DEF is also 3 : 4 : 6.

ratio f sides : perimeter = 3 : 4 : 6 : 13

Since its perimeter is 13, it means that the length of sides of triangle DEF are: 3, 4, and 6

Length of the sides of triangle ABC = 2 x length of the sides of Δ DEF

Length of the sides of triangle ABC are: 6, 8, and 12.

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The limits of the functions (a) 1, (b) does not exist (c) 2, (d) does not exist, (e) -4 and (f) 3.

Limit of a function is defined as a value that the function tends to the output for the given input values.

(a) [tex]\lim_{x \to 2} [f(x)+g(x)][/tex] =  [tex]\lim_{x \to 2} f(x)[/tex] +  [tex]\lim_{x \to 2} g(x)[/tex]

[tex]\lim_{x \to 2} f(x)[/tex] is the value of y when x is approaching 2 from left and right.

[tex]\lim_{x \to 2} f(x)[/tex] = -1

Similarly,  [tex]\lim_{x \to 2} g(x)[/tex] = 2

[tex]\lim_{x \to 2} [f(x)+g(x)][/tex] = -1 + 2 = 1

(b)  [tex]\lim_{x \to 0} [f(x)-g(x)][/tex] =  [tex]\lim_{x \to 0} f(x)[/tex] -  [tex]\lim_{x \to 0} g(x)[/tex]

[tex]\lim_{x \to 0} f(x)[/tex] = 2

But  [tex]\lim_{x \to 0} g(x)[/tex] does not exist as the function g(x) has different limits 3 and 1 from left and right respectively as x approaches 0.

So [tex]\lim_{x \to 0} [f(x)-g(x)][/tex] does not exist.

(c)  [tex]\lim_{x \to -1} [f(x)g(x)][/tex] =  [tex]\lim_{x \to -1} f(x)[/tex] × [tex]\lim_{x \to -1} g(x)[/tex]

[tex]\lim_{x \to -1} f(x)[/tex] = 1

[tex]\lim_{x \to -1} g(x)[/tex] = 2

[tex]\lim_{x \to -1} [f(x)g(x)][/tex] = 1 × 2 = 2

(d)  [tex]\lim_{x \to 3} [f(x)/g(x)][/tex] =  [tex]\lim_{x \to 3} f(x)[/tex] /  [tex]\lim_{x \to 3} g(x)[/tex]

[tex]\lim_{x \to 3} f(x)[/tex] = 1

[tex]\lim_{x \to 3} g(x)[/tex] = 0

 [tex]\lim_{x \to 3} [f(x)/g(x)][/tex] = 1 / 0, not defined. So does not exist.

(e)  [tex]\lim_{x \to 2}[x^{2} f(x)][/tex] =  [tex]x^{2} \lim_{x \to 2} f(x)[/tex]

[tex]\lim_{x \to 2} f(x)[/tex] = -1

[tex]\lim_{x \to 2}[x^{2} f(x)][/tex] = (2)² × -1 = -4

(f) f(-1) = 1

[tex]\lim_{x \to -1} g(x)[/tex] = 2

f(-1) + [tex]\lim_{x \to -1} g(x)[/tex] = 1 + 2 = 3

Hence the values of the limits are given.

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