The length of a rectangle is 5 m longer than its width.
If the perimeter of the rectangle is 70 m, find its length and width.
length: m
width: m

The probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.

In the given question we have to find the probability of first tile is less than 15 and the second tile is even or greater than 25.

Tiles numbered 1 through 20 are placed in a box.

Tiles numbered 11 through 30 are placed in a second box.

One tile is randomly drawn from each box.

Now finding the probability of first tile is less than 15.

Since in first box tile is numbered as 1 to 20.

So the outcomes of less than 15 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

So favourable outcome = 14

Total number of tile = 20

So the probability = 14/20 = 70%

Now finding the probability of second tile is even or greater than 25.

Since in second box tile is numbered as 11 to 30.

So the outcomes of even or greater than 25 = 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 29, 30

So favourable outcome = 12

Total number of tile = 20

So the probability = 12/20 = 60%

Hence, the probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.

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The right question

"Tiles numbered 1 through 20 are placed in a box. Tiles numbered 11 through 30 are placed in a second box. One tile is randomly drawn from each box. Find each probability. The first tile is less than 15 and the second tile is even or greater than 25."

Answer:

D or C

Step-by-step explanation:

[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=\stackrel{width}{base}\\ h=height\\[-0.5em] \hrulefill\\ A=247\\ b=19 \end{cases}\implies 247=\cfrac{1}{2}(19)h \\\\\\ 494=19h\implies \cfrac{494}{19}=h\implies 26=h[/tex]

The length of the side a = 9.43 cm and b = 12.04 cm

Consider the first triangle

The hypotenuse of the triangle = a

The base of the triangle = 5 cm

The length of the vertical side = 8 cm

Apply the Pythagorean theorem here

[tex]a= \sqrt{8^2+5^2}[/tex]

Find the square of the terms

a = [tex]\sqrt{64+25}[/tex]

a = [tex]\sqrt{89}[/tex]

a = 9.43 cm

Consider the second triangle

The hypotenuse of the triangle = 17 cm

The base of the triangle = 12 cm

The length of vertical side = y cm

Apply the Pythagorean theorem

b = [tex]\sqrt{17^2-12^2}[/tex]

b = [tex]\sqrt{289-144}[/tex]

b = [tex]\sqrt{145}[/tex]

b = 12.04 cm

Hence, the length of the side a = 9.43 cm and b = 12.04 cm

The complete question is

Work out the lengths of sides a and b give your answer to the 1st decimal

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The solution for this system of equations. 12x+ 15y = 34 -6x+ 5y = 3

is (x,y) =(2/3, 8/5)

Given a system of equations,

12x + 15y = 34  ------(1)

-6x + 5y = 3 ------(2),

To solve this we use the elimination method

In the elimination method, you either add or subtract the equations to get an equation in one variable.

Equation (1) + 2 × Equation (2),

We get,

(12x+15y=34)+(-12x+10y=6)

⇒ 15y+10y=34+6

⇒ 25y=40

⇒ y=40/25

⇒ y=8/5

From equation (2),

⇒  -6x+5(y)=6

⇒  -6x+5(8/5)=6

⇒  -6x+8=6

⇒  -6x=-2

⇒ x=2/3

Hence the solution for this system of equations. 12x 15y = 34 -6x 5y = 3

is (x,y =(2/3, 8/5)

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The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.

What ordered pair is a solution to the system of linear equations?

An equation is said to linear when it is in ax+ by = c form where a , b and c are real numbers . System of linear equation consist of a set of two or more equation with same variables. such as ,

a₁ x + b₁ y = c₁

a₂ x + b₂ y = c₂

A solution to a linear system is an ordered pair (x ,y) that solves both the equations .

To check that an ordered pair is a solution ,we have to substitute the corresponding values of our variables (x ,y) into our equations and see if they satisfy both the equations.

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The sine and cosine functions with the ordered pairs A(1,4) and B(0,-4) are given as follows:

Both the sine and the cosine functions have similar definitions, given as follows:

The meaning of the coefficients of the functions are presented as follows:

The functions vary between -4 and 4, hence the amplitude is given as follows:

a = 4.

This is the standard oscillation for a trigonometric function with amplitude 4, between -4 and 4, hence the vertical shift is of:

d = 0.

The difference between the x-coordinates of the maximum and the minimum value is half the period, hence the period is of 2 x 1 = 2, and the coefficient b is:

2π/b = 2

b = π.

The cosine function has no phase shift, it just is inverted, as it should assume a value of 4 at x = 0, hence the definition is:

g(x) = -4cos(πx).

The sine function has a phase shift, as it should assume a value of -4 at -π/2, not π/2, hence it is shifted shift π/2 units, hence the definition is:

f(x) = 4sin(π(x + π/2)).

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The polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

The polynomial having the highest power of 3 is called the cubic polynomial.

Given that the roots 2, -3, and 4 that has to pass through the point (1, 10).

The polynomial will be written as,

Y = (x-2)(x+3)(x-4)

Y = x³+x²-6x-4x²-4x=24

Y = x³-3x²-10x+24

Therefore, the polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.

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The equation of the polynomial equation P(x) = (x + 3)²(x - 5)²

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zero 5 is 2

The equation of the polynomial is then calculated as

P(x) = (x - zero)^multiplicity

So, we have

P(x) = (x - (-3))² * (x - 5)²

This gives

P(x) = (x + 3)²(x - 5)²

Hence, the equation is P(x) = (x + 3)²(x - 5)²

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Possible question

Form a polynomial with real coefficients having the given degree and zeros.

Degree​ 4; ​

Zeros: -3 and 5 with multiplicity 2

The distance between the two cities, Ottawa and Toronto, as determined by Greg and Max is 280.37 miles.

What is a Speedometer?

What is Distance?

How is Distance Calculated?

The distance between two locations can be calculated using the formula,
d = s x t,------ (1)

where [tex]d[/tex] is the distance travelled, [tex]s[/tex] is the average speed, and [tex]t[/tex] is the total time.

In the given question, it is given that Greg and Max travel from Ottawa to Toronto with an average speed of 40 mph and 30 mph for the return trip.

So, [tex]s_{1}=40 mph[/tex] and [tex]s_{2}=35mph[/tex].

The total travelling time for the round trip, T = 15h  ------(2)

Let the distance from Ottawa to Toronto be x.

From (1), we get that, the formula for the time taken is,

[tex]t=\frac{d}{s}[/tex]

So, the time taken to travel from Ottawa to Toronto,

[tex]t_{1} =\frac{d}{s_{1} } \\\implies t_{1} =\frac{x}{40}[/tex]      ------- (3)

And, the time taken for the return trip (back from Toronto to Ottawa),

[tex]t_{2} =\frac{d}{s_{2} } \\\implies t_{2} =\frac{x}{35}[/tex]      --------(4)

Here, the total time travelled from the round trip is equal to the sum of the time taken to travel from Ottawa to Toronto and back from Toronto to Ottawa.

T = t_1 + t_2------(5)

Substituting the values of (2), (3), and (4) in (5), we get

15 = x/40 + x/35
--> 15 = 0.0535x

Simplifying,

x = 15/0.0535
--> x = 280.37 miles

Therefore, the distance between the two cities as determined by Greg and Max is equal to 280.37 miles.

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SSS should be used to show that the triangles are congruent.

What is the congruent triangle?

Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.

From the given images of the triangles, it is clear that the the legs of the triangles are equal to each other.

If two legs of two triangles are equal, then the bases are equal to each other.

Thus to prove that the triangles are congruent to each other, apply SSS  postulate.

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n(x) is a vertical dilation of scale factor 4 followed by a translation of 2 units upwards of the parent linear function.

The parent linear function is:

f(x)= x

And the function n(x) is:

n(x) = 4x + 2

If first we apply a vertical dilation of scale factor 4 to the parent linear function, we will get:

n(x) = 4*f(x)

And if now we apply a translation of 2 units upwards, then we get:

n(x) =4*f(x) + 2

Replacing f(x) by x we get:

n(x) = 4*x + 2

And we returned to n(x), so these are the transformations that define our function in terms to the parent function.

And the slope 4 means that each month 4 books are added, the y-intercept 2 means that she starts with 2 books.

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The possible heights of the parallelogram are 2/3 and 3

So, the correct option is A and C

The given expression:

area of a parallelogram, A = 12 square unit

a side of the parallelogram,  = 18 units

another side of the parallelogram = 6 units

let,

the height of the parallelogram, h

The area of a parallelogram is given as;

Area = base (b) x height (h)

height (h) = Area/base(b)

From the given sides, the possible heights of the parallelogram are calculated as follows;

if the base, b = 18 units

height(h) =  12/18

              = 2/3

Also, if the base, b = 6 units

height(h) =  12/6

              = 2

Therefore, the possible heights of the parallelogram are 2/3 and 2

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Step-by-step explanation:

55/12

hope this helps:)

The distance Manatee will swim in 5 hours is 25 miles.

Distance can be defined as the length between two points.

To calculate the distance manatee can swim in 16 hours, we use the equation below

Make y₂ the subject of the equation

Where:

Substitute these values into equation 2

Hence, manatee can swim a distance of 25 miles.

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Complete question: A manatee can swim an average of 10 miles every 2 hours how far can it swim in 5 hours. Assume the distance y in miles is proportional to the number of hours x the manatee swam.

Answer:

Area = 1/2 * base * height

Area = 1/2 * 155 * 175

Area = 13,563.75

Answer:

I think 28.6

Step-by-step explanation:

the second and last one

The answer is  

AEB and IAE

DEA and CED

[tex]\boldsymbol{\sf{Your\:exersice \to \dfrac{1}{x+9}+\dfrac{1}{5}=\dfrac{1}{4} }}[/tex]

Variable x cannot be equal to −9 as division by zero is undefined. Multiply both sides of the equation by 20(x+9), the lowest common denominator of x+9,5,4.

[tex]\boldsymbol{\sf{20+20(x+9)\times\left(\dfrac{1}{5}\right)=5(x+9) }}[/tex]

Multiply 5 and 1/5 to get 4.

[tex]\boldsymbol{\sf{20+4(x+9)=5(x+9)}}[/tex]

Use the distributive property to multiply 4 by x+9.

[tex]\boldsymbol{\sf{20+4x+36=5(x+9)}}[/tex]

Add 20 and 36 to get 56.

[tex]\boldsymbol{\sf{56+4x=5(x+9)}}[/tex]

Use the distributive property to multiply 5 by x+9.

[tex]\boldsymbol{\sf{56+4x=5x+45}}[/tex]

Subtract 5x on both sides.

[tex]\boldsymbol{\sf{56+4x-5x=45}}[/tex]

Combine 4x and −5x to get −x.

[tex]\boldsymbol{\sf{56-x=45}}[/tex]

Subtract 56 from both sides.

[tex]\boldsymbol{\sf{-x=45-56}}[/tex]

Subtract 56 from 45 to get −11.

[tex]\boldsymbol{\sf{-x=-11}}[/tex]

Multiply both sides by −1.

[tex]\boldsymbol{\sf{x=11}}[/tex]

Answer:

m∠X=75.75

Step-by-step explanation:

A triangle's angles combine to 180 degrees. Subtract 62.45+41.8 from 180.

The measure of the exterior angle of the triangle is given by ∠A = 104.25°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ΔXYZ

Let the measure of the exterior angle be m∠A

Now , the measures of the angles of the triangle are

The measure of angle ∠Y = 62.45°

The measure of angle ∠Z = 41.8°

The measure of angle ∠X = m∠X

Now , for a triangle , the sum of the interior angles = 180°

So ,

m∠X + m∠Y + m∠Z = 180°

Substituting the values in the equation , we get

m∠X + 62.45° + 41.8° = 180°

Subtracting 104.25 on both sides of the equation , we get

m∠X = 75.75°

Now , the measure of angle exterior to m∠X be ∠A = 180° - m∠X

The measure of m∠A = 180° - 75.75°

The measure of m∠A = 104.25°

Therefore , the measure of ∠A = 104.25°

Hence , the exterior angle of the triangle is ∠A = 104.25°

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1/16 is the ratio of a blue and unbarred parrot as offspring

Dihybrid cross is a cross between two individuals with two observed traits that are controlled by two distinct genes. The idea of a dihybrid cross came from Gregor Mendel when he observed pea plants that were either yellow or green and either round or wrinkled. Crossing of two heterozygous individuals will result in predictable ratios for both genotype and phenotype in the offspring. The expected phenotypic ratio of crossing heterozygous parents would be  Deviations from these expected ratios may indicate that the two traits are linked or that one or both traits has a non-Mendelian mode of inheritance.

When two heterozygous parents for color (Gg) and barring (Bb) are crossed, each parent's genotype is GgBb. Each parent produces four gametes, such as GB, Gb, gB, and gb. As a result, the total number of offspring will be 16, as each parent produces four gametes. Nine will be G B_, three will be G bb, three will be ggB_, and one will be ggbb.

Therefore, 1/16 is the ratio of a blue and unbarred parrot as offspring

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Answer:

Step-by-step explanation:

Between 9 and 10.

Why?

Because sq of 9 is 81 and sq of 10 is 100 which gives us the gesture that sq.rt of 84 is between 9&10.  

Hence, Two integers are 9 and 10.

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Coordinate of circumcenter of the given triangle = (3, 2)

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of circumcenter be (x , y)

Distance of Circumcenter from (4,2) =

[tex]\sqrt{(x - 4)^2 + (y-2)^2[/tex]

Distance of Circumcenter from (3, 3) =

[tex]\sqrt{(x - 3)^2 + (y-3)^2[/tex]

Distance of Circumcenter from (2,2) =

[tex]\sqrt{(x - 2)^2 + (y-2)^2[/tex]

By the problem,

[tex]\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\[/tex]..... (1)

Again,

[tex]\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\[/tex]...... (2)

Adding (1) and (2)

[tex]2x = 6\\x = \frac{6}{2}\\x = 3[/tex]

Putting the value of x in (1),

3 + y = 5

y = 5 - 3

y  = 2

Coordinate of circumcenter = (3, 2)

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6629\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A=6629\left(1+\frac{0.1}{1}\right)^{1\cdot 4} \implies A \approx 9705.52~\hfill \underset{earned~interest}{\stackrel{9705.52~~ - ~~6629}{\approx\text{\LARGE 3076.52 }}}[/tex]

The graph is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.as stated

The term "range" refers to every potential value in a graph's output.

The result of range is seen in the y coordinate, and the range of potential values is given here.

0 ≤ y ≤ 5

The term "domain" refers to every conceivable value in a graph's input.

The x coordinate is the input, and the extent of potential values is

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Explanation:

Each component has 1/3 as the probability of failure.

1 - 1/3 = 2/3 is the probability a particular component works.

Each component is independent of one another, allowing us to multiply the probabilities: (2/3)*(2/3)*(2/3) = 8/27

8/27 is the probability that all three components work simultaneously, and it's the probability that the machine works.

1 - 8/27 = 19/27 represents the probability that at least one component fails, and hence causes the entire machine to fail also.

19/27 = 0.7037 = 70.37% approximately. It appears this machine fails pretty often.

Answer: C: 62

Step-by-step explanation: -7 + -12 = -19

-19 + 81 = 62