The length of a rectangular parking area is two times the width. The perimeter is 90 ydFind the length and width of the parking area.

Answer:

down

Step-by-step explanation:

c) 6 and 8

a) 7 and 1

b) 5 and 4

Step-by-step explanation:

320 = 80 × 4

80 = 8 × 10

4 = 2 × 2

10 = 5 × 2

bold one's are answer.

hope this helps you.

Divide both systems:

y=4(4)^x

y=4^x+1

========================================================

Explanation:

Going from the first term to the second, we add on -2

Then going from the second term to the third, we add on +2

This inconsistency (-2 vs +2) means we don't have a common difference, and therefore the sequence is not arithmetic.

------------

Now let's divide each term by their previous term

term2/term1 = 0/2 = 0

term3/term2 = 2/0 = undefined

We can stop here and conclude that we don't have a common ratio either, so this sequence is not geometric.

------------

Side note: The subsequence 0,2,4,6,... is arithmetic with common difference d = 2 because we add 2 to each term. It's that first 2 in the original sequence that breaks everything.

Let

[tex]I(a) = \displaystyle \int_0^\infty \frac{\sqrt x \arctan(ax)}{1+x^2} \, dx[/tex]

Differentiate with respect to a :

[tex]I'(a) = \displaystyle a \int_0^\infty \frac{x^{\frac32}}{(1+x^2)(1+a^2x^2)} \, dx[/tex]

Substitute y = √x :

[tex]I'(a) = \displaystyle 2a \int_0^\infty \frac{y^4}{(1+y)(1+a^2y)} \, dy[/tex]

Polynomial division yields

[tex]\dfrac{y^4}{(1+y)(1+a^2y)} \\\\ = \dfrac1{a^2}y^2 - \left(\dfrac1{a^2} + \dfrac1{a^4}\right)y + \dfrac1{a^2} + \dfrac1{a^4} + \dfrac1{a^6} - \dfrac{\left(1+\frac1{a^2} + \frac1{a^4} + \frac1{a^6}\right)y + \frac1{a^2} + \frac1{a^4} + \frac1{a^6}}{(1+y)(1+a^2y)}[/tex]

Computing I'(a) isn't so difficult from here. You'd find (assuming a ≥ 0)

[tex]I'(a) = \displaystyle \frac\pi{\sqrt2\left(\sqrt a + a + a^{\frac32} + a^2\right)}[/tex]

Integrate both sides with respect to a. On the right side, substituting b = √a yields

[tex]\displaystyle \int \frac{da}{\sqrt a + a + a^{\frac32} + a^2} = \int \frac{2b}{b + b^2 + b^3 + b^4} \, db \\\\ = 2 \int \frac{db}{1 + b + b^2 + b^3} \\\\ = 2 \int \frac{db}{(1+b)(1+b^2)} \\\\ = \int \left(\frac1{1+b} + \frac{1-b}{(1+b^2)}\right) \, db \\\\ = \frac14 \left(2 \arctan(b) + 2 \ln(1 + b) - \ln(1 + b^2)\right) + C \\\\ = \frac14 \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right) + C[/tex]

Noting that a = 0 makes the integral I(a) vanish, we have

[tex]0 = \dfrac14 \left(2 \arctan(\sqrt0) + 2\ln(1 + \sqrt0) - \ln(1 + 0)\right) + C \implies C = 0[/tex]

and so

[tex]\displaystyle I(a) = \frac\pi{4\sqrt2} \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right)[/tex]

We recover the integral we want with a = 1, which gives a value of

[tex]\displaystyle \int_0^\infty \frac{\sqrt x \arctan(x)}{1 + x^2} \, dx = \boxed{\frac{\pi^2 + 2\pi\ln(2)}{4\sqrt2}}[/tex]

Answer:

(b) NO

Step-by-step explanation:

It must have the square to to be a right angle

Answer:

A: It is obtuse

B: It is a right angle

Step-by-step explanation:

A: Angle RST equals 110*, if it is greater than 90*, it is obtuse

B: Right Angles are 90*, so this is simple, you subtract RST by UST, so 110-20=90

Answer:

Step-by-step explanation:

First Choice

Answer:

[tex]x=\frac{5+\sqrt{15}}{2},\:x=\frac{5-\sqrt{15}}{2}[/tex]

Step-by-step explanation:

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\mathrm{For\:}\quad a=2,\:b=-10,\:c=5[/tex]

[tex]x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:2\cdot \:5}}{2\cdot \:2}[/tex]

[tex]\sqrt{\left(-10\right)^2-4\cdot \:2\cdot \:5}[/tex]

Apply exponent rule: (-a)^n=a^n, if n is even

[tex]\left(-10\right)^2=10^2[/tex]

[tex]=\sqrt{10^2-4\cdot \:2\cdot \:5}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2\cdot \:5=40[/tex]

[tex]=\sqrt{10^2-40}[/tex]

[tex]10^2=100[/tex]

[tex]=\sqrt{100-40}[/tex]

[tex]\mathrm{Subtract\:the\:numbers:}\:100-40=60[/tex]

[tex]=\sqrt{60}[/tex]

[tex]60\:\mathrm{divides\:by}\:2\quad \:60=30\cdot \:2[/tex]

[tex]=2\cdot \:30[/tex]

[tex]30\:\mathrm{divides\:by}\:2\quad \:30=15\cdot \:2[/tex]

[tex]=2\cdot \:2\cdot \:15[/tex]

[tex]15\:\mathrm{divides\:by}\:3\quad \:15=5\cdot \:3[/tex]

[tex]=2\cdot \:2\cdot \:3\cdot \:5[/tex]

[tex]2,\:3,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex]

[tex]=2\cdot \:2\cdot \:3\cdot \:5[/tex]

[tex]=2^2\cdot \:3\cdot \:5[/tex]

[tex]=\sqrt{2^2\cdot \:3\cdot \:5}[/tex]

Apply Radical Rule:

[tex]=\sqrt{2^2}\sqrt{3\cdot \:5}[/tex]

Apply Radical Rule:

[tex]\sqrt{2^2}=2[/tex]

[tex]=2\sqrt{3\cdot \:5}[/tex]

[tex]\mathrm{Refine}[/tex]

[tex]=2\sqrt{15}[/tex]

[tex]x_{1,\:2}=\frac{-\left(-10\right)\pm \:2\sqrt{15}}{2\cdot \:2}[/tex]

[tex]\mathrm{Separate\:the\:solutions}[/tex]

[tex]x_1=\frac{-\left(-10\right)+2\sqrt{15}}{2\cdot \:2},\:x_2=\frac{-\left(-10\right)-2\sqrt{15}}{2\cdot \:2}[/tex]

[tex]\frac{-\left(-10\right)+2\sqrt{15}}{2\cdot \:2}[/tex]

Apply Rule -(-a)=a

[tex]=\frac{10+2\sqrt{15}}{2\cdot \:2}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4[/tex]

[tex]=\frac{10+2\sqrt{15}}{4}[/tex]

[tex]=\frac{2\left(5+\sqrt{15}\right)}{4}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:2[/tex]

[tex]=\frac{5+\sqrt{15}}{2}[/tex]

[tex]\frac{-\left(-10\right)-2\sqrt{15}}{2\cdot \:2}[/tex]

[tex]=\frac{10-2\sqrt{15}}{2\cdot \:2}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4[/tex]

[tex]=\frac{10-2\sqrt{15}}{4}[/tex]

[tex]=\frac{2\left(5-\sqrt{15}\right)}{4}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:2[/tex]

[tex]=\frac{5-\sqrt{15}}{2}[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]

[tex]x=\frac{5+\sqrt{15}}{2},\:x=\frac{5-\sqrt{15}}{2}[/tex]

Answer:

3

Step-by-step explanation:

Answer:

what are you trying to solve?

Answer:

5/6

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

All of the answers either increase or reduce to 8/10 except 5/6

Hope this helps! Please mark as brainliest answer if correct.

Stay safe, God bless, and happy studying!

Answer:

4/5

Step-by-step explanation:

There are 10 tiles total, and E and I are vowels. This makes 2/10 of the tiles tiles. The other 8/10 are not vowels.

8/10 can be simplified down to 4/5.

There is a 4/5 probability of picking a letter that is not a vowel.

Answer:

12

Step-by-step explanation:

Given :-

Two numbers => 48 and 60

To Find :-

HCF of 48 and 60

Solving :-

Prime factorize the numbers.

48 = 2⁴ x 3

60 = 2² x 3 x 5

Solution :-

HCF (48, 60) = 2² x 3 = 12

To find out the box number the boxes, extract the same number of balls as the number of the box, calculate the total weight.

Considering you can only weigh the balls extracted once and you need to find the box with balls that are 1-kilo lighter; here are the steps you can follow:

The total weight using this method would be 6,300 kg which is the result of adding 30 kg (first box) + 60 kg (second box)... However, since there is a box with lighter balls the total weight will be less.

Let's imagine the weight is 6,290, this means there are 10 fewer kilos and therefore the box with the lighter balls is box 10 since this is the box number from which 10 balls were extracted.

Learn more about weight in: https://brainly.com/question/10069252

Answer:

alternate angled

Step-by-step explanation:

add up to 180

Answer:

x+y=12

Step-by-step explanation:

Standard form is ax+by=c

Given, y-8 = -(x-4)

y-8=-x+4

x+y=4+8

x+y=12

Answer:

x + y = 12

Step-by-step explanation:

Standard form is Ax+By=C

so the goal is to get the y and the x on the same side without and negatives or fractions on that side.

y - 8 = - (x - 4)  first, start by simplifying

y - 8 = -x +4  next, because it is negative, we are going to add x to -x on the right side to get it to cancel out and we'll add x to y on the left side

x + y - 8 = 4  now we need to get rid of that eight so we'll add 8 to -8 so it cancels out and we'll add 8 to 4

x + y = 12 now it is in standard form

Answer:

Uh how to use segmant tool

Step-by-step explanation:

not there

Answer: The correct equation should be 0.2+5.8=6

Step-by-step explanation: First of all let's look at the equation without the decimal ".8". So, it would be 2+5 which equals 7. Since the sum is greater, adding a decimal will make the sum larger than 6. 2+5.8=7.8, therefore the correct equation being 0.2+5.8=6. Hopes this makes sense and helps!

Answer:

The answer is True.

Step-by-step explanation:

The earliest civilizations developed between 4000 and 3000 BCE, when the rise of agriculture and trade allowed people to have surplus food and economic stability.

Hope this helps you!

The profit that Jude made during the party was £3700.

Profit is the difference between revenue and cost. It is given by:

Profit = Revenue - Cost

From the question:

The total cost = 300 + 2500 + 500 + (1 * 400 people) = £3700

Revenue = 400 ticket * £16 = £6400

Profit = Revenue - Cost = £6400 - £3700

The profit that Jude made during the party was £3700.

Find out more on profit at: https://brainly.com/question/23103804

Answer:

x less than or equal to -2

9514 1404 393

Answer:

Step-by-step explanation:

The point-slope form of the equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Comparing this to the equation you have, you see that you have a "point-slope form" equation with m=7 and (h, k) = (4, 2).

__

The standard form of an equation for a line is ...

  ax +by = c

where a, b, c are mutually prime integers and a > 0.

Putting your equation into standard form would make it look like ...

  7x - y = 26

Your equation is not in correct standard form.

_____

see https://brainly.com/question/18537811 for more information

Answer:

x=40

Step-by-step explanation:

The angles of both expressions (4x-28) and (3x+12) are congruent (alternating exterior angles). So, you can set up the equation 4x-28 = 3x+12 because both expressions are equivalent, so it makes sense. Then solve for x.

4x - 28 = 3x + 12

x - 28 = 12

x = 40

Answer:3500

Step-by-step explanation:

9514 1404 393

Answer:

  congruent

Step-by-step explanation:

Angles supplementary to the same angle are congruent.

__

Here, angles 1 and 3 are both supplementary to angle 2, so ...

  angle 1 and angle 3 are congruent

A function is a relation in which there is only one y-value for every x-value.

If we given an input of 3 for x, for example, we would only get one output for y, like 1, for example.

If we look at the table, we can see that the x-value of 3 gives us two outputs: 7 and 9.

Therefore, this relation is not a function.

Answer:

X = 11/36

Step-by-step explanation:

First, find the common denominator of the fractions and convert them.

(4/9) x 4 = 16/36

(3/4) x 9 = 27/36

X + 16/36 = 27/36

Now you can solve for X

X = 11/36

The fraction cannot be simplified