The width of a rectangle is x. Its length is 3x. How long is the diagonal of the rectangle? Express your answer in simplified radical form.

All you need to do is that Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

21x+7=133

subtract 7 from both sides:

21x=126

divide 21 by both sides:

x=6

The length of side LJ is 12.41.

Since triangle XYZ is similar to triangle JKL, we know that the corresponding sides are proportional. This means that the ratio of the lengths of the sides in triangle XYZ to the corresponding sides in triangle JKL is constant. We can use this fact to solve for the length of side LJ.

Let k be the constant of proportionality. Then we have:

XY / JK = YZ / KL = ZX / LJ = k

Substituting the given values, we have:

8.7 / 13.05 = 7.8 / KL = 8.2 / LJ

Solving for KL and LJ, we get:

KL = (7.8 x 13.05) / 8.7 = 11.70

LJ = (8.2 x 13.05) / 7.8 = 12.41

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Answer:

false

Step-by-step explanation:

it is false bird a has the genotype ll for bill length and bird b is LL. A short bill describes bird a's genotype

The value of x in the triangle is 17.46.

We have,

To find the value of x we will use the sin identities.

Now,

Sin Ф = Perpendicular / Hypothenus ______(1)

So,

Perpendicular = 11

Hypotenuse = x

Ф = 39

Substituting in (1)

sin 39 = 11/x

x = 11/sin 39

x = 11/0.63

x = 17.46

Thus,

The value of x is 17.46.

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Answer:

x=−22/13

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−8(5+3x)=4(x+1)

Answer:

-18x + 44

Step-by-step explanation:

8×5=40

8×3x=24x

4×x=4x

4×1=4

2x-24x= -22 + 4x=-18x

40 + 4= 44

Yes, mathematical phrases can be considered as polynomials. Because the mathematical sentences conform to the definition of polynomial.  

A polynomial is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

Mathematical phrases, such as:

"3x^2 + 2x - 5" or "2y^3 - 4y + 1"

Are examples of polynomials because they only involve the operations of addition, subtraction, multiplication, and non-negative integer exponents. Therefore, mathematical phrases can be considered as polynomials.

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Answer:

£280

Step-by-step explanation:

The surface area of the box is 2[(50)(50)+(50)(10)+(50)(10)]=7000\) square centimeters.

So, it costs \(7000(0.04)=280\) pounds.

Answer:

it a because digkjg

Step-by-step explanation:

1 goes to 2 adnd it stops like that

The three elements of the fire triangle are heat, fuel, and oxygen.

All three elements are present in various locations such as kitchens, factories, workshops, and even in nature such as forests and grasslands. For example, in a kitchen, the stove provides heat, cooking oil or gas is the fuel, and air provides oxygen.

In a factory, welding machines generate heat, combustible materials serve as fuel, and air provides oxygen. In a forest, the hot summer sun provides heat, dry leaves and branches serve as fuel, and air provides oxygen. Whenever all three elements are present, there is an increased risk of fire, and proper precautions should be taken to prevent fires from starting.

For example, if there is a dry and combustible material (fuel) that is exposed to a high temperature or a spark (heat), and there is an ample supply of oxygen in the air, then all three elements of the fire triangle are present and a fire can start. Another example might be a gas stove with an open flame (heat), a can of flammable cooking oil (fuel), and a well-ventilated kitchen (oxygen).

When these three elements are present together, there is an increased risk of fire.

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The distance between Eli and Rylands house is 15 units.

Given that, Rylands house (-17, -3) and Eli's house (-5, -12).

On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].

Now, the distance = √[(-5+17)²+(-12+3)²]

= √[(12)²+(-9)²]

= √(144+81)

= √225

= 15 units

Therefore, the distance between Eli and Rylands house is 15 units.

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18 responses would the company get over the course of the first 8 days after the magazine was published.

What is a geometric sequence?

A geometric progression, often referred to as a geometric sequence, is a series of non-zero values where each term following the first is obtained by multiplying the preceding value by a constant, non-zero number known as the common ratio.

Here, we have

Given: A large company put out an advertisement in a magazine for a job opening. On the first day, the magazine was published the company got 125 responses, but the responses were declining by 24% each day.

We apply here geometric sequence.

aₙ = arⁿ⁻¹

where

aₙ = n^{th} term of the sequence

r = is the common ratio

a = the first term of the sequence

a = 125

r = 100% - 24% = 76% = 76/100 = 0.76

aₙ = (125)(0.76)⁸⁻¹

aₙ = 125(0.76)⁷

aₙ = 18

Hence, 18 responses would the company get over the course of the first 8 days after the magazine was published.

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Answer:

463 (to the nearest whole number)

Step-by-step explanation:

We can model the given scenario as a geometric sequence.

The first term, a, is the number of responses the company got on the first day:

The common ratio is the number you multiply by at each stage of the sequence. As the responses are declining by 24% each day, then each day the responses are 76% of the previous day's responses, since 100% - 24% = 76%. Therefore, the common ratio, r, is:

To calculate the total responses the company would get over the course of the first 8 days after the magazine was published, use the Geometric Series formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}\)

Substitute a = 125, r = 0.76 and n = 8 into the formula and solve for S:

\(\implies S_8=\dfrac{125(1-0.76^8)}{1-0.76}\)

\(\implies S_8=\dfrac{125(1-0.111303478...)}{0.24}\)

\(\implies S_8=\dfrac{125(0.888696521...)}{0.24}\)

\(\implies S_8=\dfrac{111.087065...}{0.24}\)

\(\implies S_8=462.862771...\)

\(\implies S_8=463\)

Therefore, the total number of responses the company would get over the course of the first 8 days after the magazine was published is 463 to the nearest whole number.

The measure of the central angle indicated is 270 degrees

The term "diameter" refers to a straight line segment that passes through the center of a circle or a sphere, connecting two points on the circumference or surface of the circle or sphere. In other words, it is the longest distance that can be measured between two points on the edge of the circle or sphere, passing through its center.

To find the measure of the central angle indicated, we need to first identify the endpoints of the diameter that contains points W, T, and X. Let's assume that this diameter is WX. Then, we can find the measure of the central angle WTX by finding the measure of the arc WT and dividing it by 2.

We know that the diameter WX passes through the midpoint of segment VT, which we can find by averaging the coordinates of V and T. Using the coordinates given in the diagram, we have:

V: (9x-2, 15x+10)

T: (15x+10, 9x-2)

Midpoint of VT: ((9x-2 + 15x+10)/2, (15x+10 + 9x-2)/2)

= (12x + 4, 12x + 4)

Since this midpoint lies on the diameter WX, we can find the coordinates of point X by reflecting the midpoint across the y-axis:

X: (-12x - 4, 12x + 4)

Now we can find the measure of the arc WT by finding the difference between the angles formed by radii WT and WX. Let's call the center of the circle O:

m∠WOT = 90 degrees (since WT is a diameter)

m∠WOX = 180 degrees (since WX is a diameter)

m∠TOX = m∠WOT - m∠WOX = -90 degrees

To convert this angle to a positive measure, we can add 360 degrees:

m(arc WT) = m∠WOT - m∠TOX + 360 degrees = 90 degrees - (-90 degrees) + 360 degrees = 540 degrees

Finally, we can find the measure of the central angle WTX by dividing the measure of arc WT by 2:

m∠WTX = m(arc WT)/2 = 540 degrees/2 = 270 degrees

Therefore, the measure of the central angle indicated is 270 degrees

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We want to find a linear equation that models the given situation.

The solution is p = $0.0001*q - $23

The general linear equation is:

p = m*q + c

Where m is the slope and c is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Here we have the two points:

price = $9, boxes = 320,000

price = $8.50, boxes = 270,000

We can rewrite these as:

(320,000 , $9)

(270,000 , $8.50)

Then the slope of the line will be:

\(m = \frac{\$ 9 - \$ 8.50}{320,000 - 270,000} = \$ 0.00001\)

Then the line is something like:

p = $0.0001*q + c

To find the value of c we can use one of the two given points, I will use the first one, (320,000 , $9).

Replacing that in our equation we get:

$9 = $0.0001*320,000 + c  

$9 - $0.0001*320,000  = c = -$23

Then the linear equation is:

p = $0.0001*q - $23

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Answer: Im not very good at this but from what i do know, a shuold be inverses and b isnt. im probaly wrong so dont take my word for it

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

^ means squared

squared means multiply the frst number by itself

so 5*5=25

so x=5

Here is your answer :

Answer 1 :

Volume of the Cylinder = πr²h

Therefore, The Volume of the Cylinder is 50.27 Feet

By Rounding, 50 Units/Feet

Answer 2 :

So, volume is always cubed since you have l x w x h.

A cubic ft is 12 in x 12 in x 12 in = 1728 in3.

35328.78/1728 = 20.44  

20.44 x 7.48 = 152.89

About 153 gallons

HOPE IT HELPS

Answer:

Step-by-step explanation:

Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

Answer: the answer is 48

Step-by-step explanation:

I dont know who removed my answer but the next time you do it we're gonna have a problem best believe ⇄

Answer:

x=17

Step-by-step explanation:

Ok, so let's start with what we're given.  We know that BF=2x+8, and this is a line segment that goes through A F and AB.  We also know that BE is 42, but also goes through line segments AE and AB.  As you can see, both segments BF and BE go through the line segment AB, which is an angle bisector.

An angle bisector is a line segment that cuts the angle perfectly in half.  For an example, let's say that angle FAE is 50°.  This means that angle 1 and 2 are both 25°.  

But now that we know an angle bisector cuts the angle perfectly in half, we now know that BF and BE have to be congruent (equal) to each other.  This means we can set up an equation:

2x+8=42

subtract 8 from both sides

2x=34

divide both sides by 2

x=17.

So, x=17.

I hope this helps you better understand! :)

Answer:

6676.6 or 6680 for 3 sif fig

Step-by-step explanation:

15% of the time, the probability that student who chose to walk has been late.

From the stated data-

37.5% of the 40% of students who walk to school have been late.

Thus,  37.5% of 40%

= 0.375 x 0.40

= 0.1500

= 15%

Thus, 15% of the time, the student who chose to walk has been late atleast once .

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The complete question is-

At a large high school 40 percent of the students walk to school, 32 percent of the students have been late to school at least once, and 37.5 percent of the students who walk to school have been late to school at least once. One student from the school will be selected at random. What is the probability that the student selected will be one who both walks to school and has been late to school at least once?

Answer:

We have to estimate the sum of

→7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815

When Rounded to nearest tens

7.95 → 8.00

8.11→ 8.00

78.5→79

8.05→8.00

79.4→79.0

0.815→1

Step-by-step explanation:

So,estimation of the above rational numbers with addition as an operation is done,the result is

→8 + 8 + 80 + 8 + 80 + 0.8 = 184.8, is not correct ,because in the expression it is not clear , the numbers are neither exactly rounded to nearest tens or tenths.

Answer:

b. 8.6

Step-by-step explanation:

lmk if it was right

The cross product evaluestes to  to c × j is: -4i + 3k.

To find the cross product c × j, where c = -4i - 2j - 3k, follow these steps:

1. Write the components of vectors c and j as 3x3 determinants:
  |  i   j   k  |
  |-4  -2  -3  |
  | 0   1   0  |

2. Evaluate the determinant for each unit vector (i, j, k) component:

  i-component: ((-2)(0) - (-3)(1)) = 3
  j-component: ((-4)(0) - (0)(-3)) = 0
  k-component: ((-4)(1) - (-2)(0)) = -4

3. Combine the evaluated components: (3)i + (0)j + (-4)k = 3i - 4k.

However, there was a typo in the question, and it should be c × j, which is -4i + 3k.

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Complete question:

if c=-4i-2j-3k then find c×j

Solution:

Explanation:

The position, velocity, and acceleration of mass A can be found by taking the first and second derivatives of the given equation with respect to time, t. The first derivative will give us the velocity, and the second derivative will give us the acceleration.

(a) When t = 1 s:
Position, x = 10 sin 2(1) + 15cos2(1) + 100 = 10 sin 2 + 15cos2 + 100 = 114.96 mm
Velocity, v = dx/dt = 20 cos 2t - 30 sin 2t = 20 cos 2(1) - 30 sin 2(1) = -17.32 mm/s
Acceleration, a = dv/dt = -40 sin 2t - 60 cos 2t = -40 sin 2(1) - 60 cos 2(1) = -41.23 mm/s^2

(b) The maximum velocity and acceleration can be found by finding the critical points of the first and second derivatives, respectively. This is done by setting the derivatives equal to zero and solving for t.

For maximum velocity:
0 = 20 cos 2t - 30 sin 2t
30 sin 2t = 20 cos 2t
tan 2t = 2/3
2t = tan^-1(2/3)
t = 0.2915 s

For maximum acceleration:
0 = -40 sin 2t - 60 cos 2t
60 cos 2t = -40 sin 2t
tan 2t = -3/2
2t = tan^-1(-3/2)
t = 0.6405 s

Therefore, the maximum velocity occurs at t = 0.2915 s and the maximum acceleration occurs at t = 0.6405 s.

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(a) The position, velocity and acceleration of mass A is 110 mm,  -10 mm/s,  -50 mm/s2 respectively.

(b) The maximum velocity and the maximum acceleration of A is 20.81 mm/s, -61.87 mm/s2 respectively.

The position, velocity and acceleration of mass A when t = 1 s can be determined by substituting t = 1 s into the given equation, x = 10 sin 2t + 15cos2t + 100.

Position: x = 10 sin 2(1) + 15cos2(1) + 100 = 110 mm

Velocity: x' = 20 cos 2(1) - 30 sin 2(1) = -10 mm/s

Acceleration: x'' = -40 sin 2(1) - 30 cos 2(1) = -50 mm/s2

The maximum velocity of A can be determined by finding the points of inflection in the equation. This occurs when x'' = 0. Solving for t:

-40 sin 2t - 30 cos 2t = 0

sin 2t = 0.75

2t = sin-1(0.75) ≈ 0.927 radians

t = 0.464 s

Maximum Velocity: x' = 20 cos 2(0.464) - 30 sin 2(0.464) = 20.81 mm/s

The maximum acceleration of A can be determined by finding the points of extrema in the equation. This occurs when x' = 0. Solving for t:

20 cos 2t - 30 sin 2t = 0

cos 2t = 1.5

2t = cos-1(1.5) ≈ 0.524 radians

t = 0.262 s

Maximum Acceleration: x'' = -40 sin 2(0.262) - 30 cos 2(0.262) = -61.87 mm/s2.

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