Writing Linear Equations

Answer:

[tex]x=\frac{324}{5}[/tex]

Step-by-step explanation:

Given the following question:

[tex]\sqrt{5x} -7-3=8[/tex]

To find the answer we are going to use inverse of operations to isolate the variable x, doing this we can then find the value of the variable and then have our answer.

[tex]\sqrt{5x} -7-3=8[/tex]
[tex]-7-3=-10[/tex]
[tex]\sqrt{5x} -10=8[/tex]
[tex]-10+10=0[/tex]
[tex]8+10=18[/tex]
[tex]\sqrt{5x} =18[/tex]
[tex]\sqrt{5x} =5[/tex]
[tex]18\times18=324[/tex]
[tex]5x=324[/tex]
[tex]5x\div5=x[/tex]
[tex]324\div5=x=\frac{324}{5}[/tex]
[tex]x=\frac{324}{5}[/tex]

Your answer is "x = 324/5."

Hope this helps.

Answer:

Its perimeter is 23 units

Step-by-step explanation:

The perimeter of any figure is the sum of the lengths of its outline sides

The rule of the distance between two points is:

In the given figure ABCD:

Its perimeter = AB + BC + CD + DE + EA

→ Find the length of each side using the rule above

A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1), E = (2, -4)

→ Substitute them in the rule above to find the lengths of its sides

[tex]AB=\sqrt{(-1--4)^{2}+(2--2)^{2}}=\sqrt{(-1+4)^{2}+(2+2)^{2}}\\\\=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}[/tex]

∴ AB = 5

[tex]BC=\sqrt{(2--1)^{2}+(2-2)^{2}}=\sqrt{(2+1)^{2}+(0)^{2}}\\\\=\sqrt{(3)^{2}+0}=\sqrt{9+0}=\sqrt{9}[/tex]

∴ BC = 3

[tex]CD=\sqrt{(5-2)^{2}+(-1-2)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}\\\\=\sqrt{9+9}=\sqrt{18}[/tex]

∴ CD = [tex]\sqrt{18}[/tex]

[tex]DE=\sqrt{(2-5)^{2}+(-4--1)^{2}}=\sqrt{(-3)^{2}+(-4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}[/tex]

∴ DE = [tex]\sqrt{18}[/tex]

[tex]EA=\sqrt{(-4-2)^{2}+(-2--4)^{2}}=\sqrt{(-6)^{2}+(-2+4)^{2}}\\\\=\sqrt{(-6)^{2}+(2)^{2}}=\sqrt{36+4}=\sqrt{40}[/tex]

∴ EA = [tex]\sqrt{40}[/tex]

→ Add them to find the perimeter of the figure ABCDE

∴ Its perimeter = 5 + 3 + [tex]\sqrt{18}[/tex] + [tex]\sqrt{18}[/tex] +[tex]\sqrt{40}[/tex] ≅ 22.8098

→ Round it to the whole number

∴ Its perimeter = 23 units

Answer:

y = (-1/3)x + 4

Step-by-step explanation:

m = rise/run =    y2 - y1         3 - 4        -1

                         -----------   =   -------- = ----

                          x2 - x1          3 - 0       3

y = mx + b

y = (-1/3)x + b

Pick either coordinate. For this, I'll pick (0, 4)

4 = (-1/3)(0) + b

4 = b

y = (-1/3)x + 4

If you are certain about M = (-5/6), then replace (-1/3) with (-5/6)

I hope this helps!

The perpendicular bisector of the diameter divides the diameter into two equal parts i.e. the radius

From the diagram of the circle, we have two diameters, each of which have two endpoints.

This means that there are four endpoints in the figure.

Next, we connect adjacent endpoints on the diagram

When the endpoints are connected, the shape formed is a square

See attachment for the sketch

Read more about constructions at:

https://brainly.com/question/1686819

6.0x74=444

4.5x80=360

5.1 x 78 = 397.8

1.9 x 70=133

Answer:

(1+1)+1=3 therefore 3×10¹

Answer: 3 times 10 to the power of just 0

Step-by-step explanation:

(1+1) + 1 is 3

So now we must put the number 3 in standard form...

The answer for this would be 3 times 10 to the power of 0

Answer:

$121.25

Step-by-step explanation:

97 X 1.25 = 121.25

Answer: 1.2y+5

If 1+4 =5 and 2.1y-0.9y=1.2y then 1+2.1y-0.9y+4 = 1.2y+5

Answer: It changes the slope from positive to negative.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given relationships allow us to write a system of equations in the speeds of the wind and plane.

Let w and p represent the speeds of the wind and the plane, respectively. We know speed is the ratio of distance to time, so ...

  p -w = 6300 km/(7 h) = 900 km/h

  p +w = 8400 km/(6 h) = 1400 km/h

__

Adding these two equations gives ...

  2p = 2300 km/h

  p = 1150 km/h . . . . . . divide by 2

Subtracting the first equation from the second gives ...

  2w = 500 km/h

  w = 250 km/h

The speed of the plane in still air is 1150 km per hour; the speed of the wind is 250 km per hour.

Answer: x=-3

Step-by-step explanation:

In this question, they simply want you to find a pair of x and y-coordinates that would be valid in this equation.

We can take a random number for x, like, say, 3.

y = 2x + 6

y = 2(3) + 6

y = 6 + 6

y = 12

Since giving the value of 3 to x results in y being 12, we can safely say that the coordinates (3, 12) would be valid in this equation. Therefore:

(12) = 2(3) + 6

Let me know if you need me to explain anything.

- Breezyツ

Answer: -122

Step-by-step explanation:

-234+112=-122 hope that helps!

Answer:

-122

Step-by-step explanation:

Answer:

D. 0.05

Step-by-step explanation:

5 x 10 = 50

50 as a decimal

0.5

9514 1404 393

Answer:

Step-by-step explanation:

The given inequality is in vertex form:

  y = a(x -h)^2 +k . . . . . . has vertex (h, k)

so the vertex can be read from the given expression.

  y > (x +2)^2 -1   ⇒   (h, k) = (-2, -1) . . . the vertex

The leading coefficient (+1) is positive so the parabola opens upward.

__

The y > ( ) tells you the boundary line is dashed (is not part of the solution). It also tells you the shading is above the curve, hence inside the parabola.

The two offered points (0, 0), (2, -3) are NOT part of the solution set.

Answer:

A. X =8

Step-by-step explanation:

5/X=12.5/20

cross multiply

12.5X = 20*5

12.5X=100

X=100/12.5

X=8

Answer:

Q4 part d

Q5 part c

Step-by-step explanation:

Answer:

[tex]y(x)=\frac{5}{3\pi}-\frac{5\pi}{27+3\pi^2}e^{-3x}-\frac{15}{9\pi+\pi^3}cos(\pi x)-\frac{5}{9+\pi^2}sin(\pi x)[/tex]

Step-by-step explanation:

[tex]y''+3y'+2y=5sin(\pi x),\: y(0)=y'(0)=0\\\\\mathcal{L}\{y''\}+3\mathcal{L}\{y'\}+2\mathcal{L}\{y\}=\mathcal{L}\{5sin(\pi x)\}\\\\s^2Y(s)-sy(0)-y'(0)+3[sY(s)-y(0)]+2Y(s)=\frac{5\pi}{s^2+\pi^2}\\\\s^2Y(s)+3sY(s)=\frac{5\pi}{s^2+\pi^2}\\ \\(s^2+3s)Y(s)=\frac{5\pi}{s^2+\pi^2}\\ \\Y(s)=\frac{5\pi}{(s^2+\pi^2)(s^2+3s)}\\ \\Y(s)=\frac{5\pi}{s(s+3)(s^2+\pi^2)}[/tex]

Perform the partial fraction decomposition

[tex]\frac{5 \pi}{s \left(s + 3\right) \left(s^{2} + \pi^{2}\right)}=\frac{A}{s}+\frac{B}{s + 3}+\frac{C s + D}{s^{2} + \pi^{2}}\\5\pi=s \left(s + 3\right) \left(C s + D\right) + s \left(s^{2} + \pi^{2}\right) B + \left(s + 3\right) \left(s^{2} + \pi^{2}\right) A\\\\5 \pi=s^{3} A + s^{3} B + s^{3} C + 3 s^{2} A + 3 s^{2} C + s^{2} D + \pi^{2} s A + \pi^{2} s B + 3 s D + 3 \pi^{2} A\\\\5\pi=s^3(A+B+C)+s^2(3A+3C+D)+s(\pi^2A+\pi^2B+3D)+3\pi^2A[/tex]

Solve for each constant

[tex]\begin{cases} A + B + C = 0\\3 A + 3 C + D = 0\\\pi^{2} A + \pi^{2} B + 3 D = 0\\3 \pi^{2} A = 5 \pi \end{cases}[/tex]

[tex]3\pi^2A=5\pi\\A=\frac{5}{3\pi}[/tex]

[tex]A+B+C=0\\3A+3B+3C=0\\(3A+3B+3C=0)-(3A+3C+D=0)\\3B-D=0\\3B=D[/tex]

[tex]\pi^2A+\pi^2B+3D=0\\\pi^2(\frac{5}{3\pi})+\pi^2B+3(3B)=0\\\frac{5\pi}{3}+\pi^2B+9B=0\\ B(\pi^2+9)=-\frac{5\pi}{3}\\B=-\frac{5\pi}{3(\pi^2+9)}\\B=-\frac{5\pi}{3\pi^2+27}[/tex]

[tex]3B=D\\3(-\frac{5\pi}{3\pi^2+27})=D\\-\frac{5\pi}{\pi^2+9}=D[/tex]

[tex]A+B+C=0\\\frac{5}{3\pi}-\frac{5\pi}{3\pi^2+27}+C=0\\\frac{15\pi^2+135}{3\pi(3\pi^2+27)}-\frac{15\pi^2}{(3\pi)(3\pi^2+27)}+C=0\\\frac{135}{9\pi^3+81\pi}+C=0\\\frac{15}{\pi^3+9\pi}+C=0\\C=-\frac{15}{\pi^3+9\pi}[/tex]

Take the inverse transform and solve for the IVP

[tex]Y(s)=\frac{\frac{5}{3 \pi}}{s}+\frac{- \frac{5 \pi}{27 + 3 \pi^{2}}}{s + 3}+\frac{- \frac{15 s}{9 \pi + \pi^{3}} - \frac{5 \pi}{9 + \pi^{2}}}{s^{2} + \pi^{2}}\\\\Y(s)=\frac{\frac{5}{3 \pi}}{s}-\frac{\frac{5 \pi}{27 + 3 \pi^{2}}}{s + 3}-\frac{ \frac{15 s}{9 \pi + \pi^{3}}}{s^{2} + \pi^{2}}-\frac{\frac{5\pi}{9+\pi^2} }{s^2+\pi^2}\\ \\y(x)=\frac{5}{3\pi}-\frac{5\pi}{27+3\pi^2}e^{-3x}-\frac{15}{9\pi+\pi^3}cos(\pi x)-\frac{5}{9+\pi^2}sin(\pi x)[/tex]

Answer: No solution

Step-by-step explanation:

Subtracting x from both sides, we get 5=45, which is false.

The sequence of transformations involves reflection, translation, dilation and reflection

The question is incomplete;

So, I will give a general explanation

For the two rectangles are similar shapes, then the corresponding sides of the shapes must be similar.

If the rectangles do not have the same size, then the scale ratio of the sides of the rectangles must be the same

if the rectangles have the same size, then the rectangles must fit perfectly on one another

Read more about transformation at:

https://brainly.com/question/4289712

Answer:

See Below.

Step-by-step explanation:

  Statements:                                              Reasons:

1) [tex]\angle 4\cong \angle 3; c\parallel d[/tex]                                           Given

2) [tex]\angle 1\cong \angle 3[/tex]                                                 Alternate Interior Angles Theorem

3) [tex]\bf{\angle 4 \cong \angle 1}[/tex]                                                 Transitive Property of Congruence

4) [tex]\angle 1\cong \angle 2[/tex]                                                 Vertical Angles Theorem

5) [tex]\bf{\angle 4\cong \angle 2}[/tex]                                                 Transitive Property of Congruence

And we’re done!

Answer:

Kyle has 25 postcards

Step-by-step explanation:

Joanna has 45 postcards in her collection, which is 180% of the number of postcards of Kyle.

If the number of postcards of Kyle is K, and the number of postcards of Joanna is J, then:

J=180% K

Recall a percentage can be expressed in decimal by dividing by 100:

J=180/100*K

To find the value of K, we solve the above equation:

K=100/180*J

Since J=45:

K=100/180*45=25

Kyle has 25 postcards

Answer:

Stem  Leaf

5          4 6

6          2 5 6

7          0 2 2 4

8          5 5 8 8 8

9          0 1 2 7 9

Step-by-step explanation:

That is how the stem and leaf plot will look like

Hope this helps

There are three section here

First section is the event of only E, the second is the event of only F, and the third is the event of the overlap of E and F

E or F means the total unit of events. Which is (only E)+(only F)-(E and F)

Using substitution we get 45=20+45-(E and F)

solving the equation

E and F=65-45

E and F=20

Therefore, P(E and F) is 20

I hope this helps, if you have any questions please ask!

Answer:

Club A charges $4 per car and club B charges $4 also

Step-by-step explanation:

Answer:

Yes,

Step-by-step explanation:

Club A charges $4 per car and club B charges $4 also

Answer:

snacks, the reason being that it can be anything

Step-by-step explanation:

Answer:

Donuts

Step-by-step explanation:

The donuts are specifically tastier than the options mentioned

Answer:

I am sure it's 2

Step-by-step explanation:

Source: Trust me bro

Answer:

The answer is 2 because 1 plus 1 is like having 2 things

Answer:

option 1

Because not all of them are equal lengths

Answer:

line 2.

Step-by-step explanation:

the correct way is provided in the attachment (under the green line). Note, only positive value (it is the length of the side) can be considered as answer.