Mary, Hans, and Alan have a total of $54 in their wallets. Mary has $10 more than Hans. Alan has 2 times what Mary has. How much do they have in their
wallets

Answer:

2x + 4y = 28

-2y = x + 28

Step-by-step explanation:

Looking at the graph, we can see that the lines do not intersect. Therefore, they do not have a shared solution. We need to find the system of equations that does not have a solution.

1) Let's try to solve the third system given (counting from the top). To solve with the substitution method, we need to isolate one variable in one of the equations. I chose to isolate y in -2y = x + 28:

[tex]-2y = x + 28\\y = \frac{-1}{2}x -14[/tex]

2) Now that we've isolated the y in that equation, substitute what y equals in that equation for the y in the other equation. So, substitute [tex]\frac{-1}{2}x-14[/tex] for y in 2x + 4y = 28 and simplify:

[tex]2x + 4(\frac{-1}{2}x - 14) = 28\\2x - 2x- 64 = 28\\-64 = 28[/tex]

In a normal situation, the x's would not cancel out, and we would be able to isolate x to get the x-value of the solution. However, in this case, they have, and we ended up with a false statement, as -64 does not equal 28. Whenever this happens, it means the system does not have a solution. Therefore, the third option would represent the system in the graph.

The given graph shows the simultaneous relationship of equations 2x + 4y = 28 and  -2y = x + 28. Option C is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
From the graph, the two lines represents the simultaneous relationship,
Where,

The slope of the both lines is,
m = -1/2

And y-intercept of both lines is,
C₁ = 7 and C₂ = - 14

Now,
equations  of the lines are,
y = -x/2 + 7 and y = -x/2 - 14
x + 2y = 14  and x + 2y = -28
or
2x + 4y = 28  - - - - -  -(1) and  -2y = x + 28 - - - - - - -(2)

Now,
From equation 2 substitute y in equation 1
2x + 4[-x - 28]/2= 28
2x - 2x - 56 = 28
-56 = 28
So the lines are parallel and has no solution.

Thus, the given graph shows the simultaneous relationship of equations 2x + 4y = 28 and  -2y = x + 28. Option C is correct.

Learn more about simultaneous equations here:

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Answer:

[tex]x^2+11x+24[/tex]

Step-by-step explanation:

The area of a rectangle is given by [tex]l\cdot w[/tex]. Plugging in our given values, we get:

[tex]A=(x+3)(x+8)=x^2+8x+3x+24=\fbox{$x^2+11x+24$}[/tex].

This is a polynomial in standard form [tex]\checkmark[/tex]

Answer:

x^2 + 11x + 24

Step-by-step explanation:

x times x is x^2

x times 8 is 8x

x times 3 is 3 x

8 times 3 is 24

add it all together and its x^2 + 11x + 24

Step-by-step explanation:

Area of Sector

= θ/360° * πr² (degrees) or 0.5r²θ (radians)

Question 11:

Question 12:

Question 13:

Question 14:

Question 15:

Question 16:

here is the answers!

Area of Sector

= θ/360° * πr² (degrees) or 0.5r²θ (radians)

Question 11:

(88°)/360° * π(19)² = 277.23ft².

Question 12:

(260°)/360° * π(11)² = 274.54mi².

Question 13:

0.5(6.2)²(7π/12) = 35.22km².

Question 14:

0.5(7.1)²(5π/3) = 131.97cm².

Question 15:

(215°)/360° * π(4.5)² = 37.99yd².

Question 16:

0.5(21.4)²(13π/18) = 519.54m².

Answer:

4x + (-2) = -2x+6

Step-by-step explanation:

im not gonna explain a diagram but it won't let me submit.

Answer:

i think the rubber ducky in the bath died on the celling so she was happy and then there was a puddle of tears on the ground so thats why u should never go to school

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given a circle with a partially shaded region. First, we need to determine the area of the whole circle. To do this, we need the measurement of the radius of the circle:

Use the Pythagorean theorem to solve for the other leg of the right triangle inside the circle:

5^2 = 3^2 + x^2

x = 4

The radius is 4 + 1 cm = 5 cm

So the area of the circle is A = pi*r^2

A = 3.14 * (5)^2  

A = 25pi cm^2

To solve for the area of the shaded region:

Ashaded = Acircle - Atriangles

we need to solve for the area of the triangles:

A = 1/2 *b*h

A = 1/2 *6 * 5

A = 15 cm^2

Atriangles = 2 * 15  

Atriangles = 30 cm^2

Ashaded = 25pi - 30

Answer:

34 lies in between 5 and 6

5^2=25, 6^2=36, so sqrt(34) lies between 5 and 6

Answer

how much more is the cost of tickets than the cost of parking pass

Step-by-step explanation:\

i think, sorry if im wrong but its kinda hard to understand what you typed.

Answer:

A: No the tickets won't cost more than $1500.

B: 90 more dollars.

6 season tickets cost $720

D: 2 parking tickets will cost $60

Answer:

1,36  2,18  3,12  4,9 and 6,6

Step-by-step explanation:

If you multiply them, they equal 36

What is the question?

Step-by-step explanation:

Answer:

so you need to find the cost of one pen, which ever is cheaper pick that one

Answer:

the anser is 22.10

Step-by-step explanation:

you have to round to the nearest ten. here is a tip 4 or down round down 5 or up round up now you are good to go! and also to find me if you need help

Answer:

154.8 is you answer

Step-by-step explanation:

Answer:

171.38 - 15% plus tax= 171.23

Hope this helped!

Step-by-step explanation:

Sum of interior angles in a polygon

= 180°(n - 2), where n is the number of sides.

Hence a convex polygon with 6 sides

=> 180°(6 - 2) = 720°.

Answer:

x=-3

Step-by-step explanation:

rearrange terms

distribute

subtract the numbers

subtract 1 from both sides of the equation

simplify

Answer:

Step-by-step explanation:

Here you go mate

Step 1

7(1-8x)-6=169  Equation/Question

Step 2

7(1-8x)-6=169  Simplify

-56x+1=169

Step 3

-56x+1=169  Subtract 1

-56x=168

Step 4

-56x=168  Divide both sides

Answer

x=-3

Answer:

32

Step-by-step explanation:

We can either add all the terms.

2+6=8

2,8

8+6=14

2,8,14

14+6=20

2,8,14,20

20+6=6

2,8,14,20,26

26+6=32

2,8,14,20,26,32

The Sixth term is 32

or We can multiply 6 times 5 (30) and add 2, which would give us 32.

The reasoning behind this is that we are adding six five times (so six times five) and we are also adding the first term (2).

Answer:

Step-by-step explanation:

(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]

Suppose [tex]5x^4 + 1 = f[/tex]

by differentiation;

[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]

Suppose n = 3

Then, the integral

[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]

[tex]= \int e^f \ \dfrac{df}{20}[/tex]

[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]

[tex]= \dfrac{1}{20} e^f + C[/tex]

recall that [tex]f = 5x^4 + 1[/tex]

Then;

[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]

(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]

suppose; [tex]\dfrac{1}{x^3} = f[/tex]

[tex]x^3 = f[/tex]

[tex]\implies -3x^{-4} \ dx = df[/tex]

[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]

If n = u, then the integration is:

[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]

[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]

Since;  [tex]x^3 = f[/tex]

Then;

[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]

(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]

Suppose  [tex]x^2 + 8x - 4 = f[/tex]

Then, by differentiation of both sides

[tex](2x + 8) \ dx = df[/tex]

[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]

Suppose n = 4 in integration, then:

[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]

By substitution;

[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]

[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]

[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]

The suitable substitutions of n are 3,4,4 respectively.

The process of finding integrals is called integration.

a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

Suppose

[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]

So, we need n=3 for easy integration.

[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]

[tex]I=\frac{e^{t} }{20}[/tex]

[tex]I = e^{5x^{4}+1 }/20 +c[/tex]

b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]

n=4 is needed for easy integration.

I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]

c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]

n=4 is needed for easy integration.

[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]

Hence, the suitable substitutions of n are 3,4,4 respectively.

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Answer:

$455 for seven nights

Step-by-step explanation:

260/4= 65

65 is the cost for 1 night

65*7=455

Answer:

$455

Step-by-step explanation:

260 divided by 4 will give you how much for one night so then multiply that answer by 7 and you have your answer.

Answer:

a = 14 m/min²

Step-by-step explanation:

The displacement of bike is given by :

[tex]s(t)=t^3-2t^2+3[/tex]

Velocity, [tex]v=\dfrac{ds(t)}{dt}[/tex]

Finding velocity of the bike.

[tex]v=\dfrac{d}{dt}(t^3-2t^2+3)\\\\=3t^2-4t[/tex]

Acceleration, [tex]a=\dfrac{dv(t)}{dt}[/tex]

[tex]a=\dfrac{d}{dt}(3t^2-4t)\\\\=6t-4[/tex]

At t = 3 minutes,

a = 6(3) - 4

= 18-4

= 14 m/min²

So, the bike's acceleration after 3 minutes is 14 m/min².

Answer:

look it up

Step-by-step explanation:

Answer:

Step-by-step explanation:

The two base angles in each triangle are equal. (The triangle is isoceles and the property used is angles opposite equal sides are equal).

Now the tricky part. The peak angles are also equal. That's because both peak angles are made equal by Peak angle + 2*base angle = 180

Peak angle = 180 - 2*base angle

Therefore the triangles are congruent by SAS.  

I suppose you could get them equal by taking one of the base angles (all 4 are equal to each other) and the peak angles and claim equality by ASA, but it seems a little bit tortuous to me.

Answer:

1.32%

2.24%

3. 12%

4.35%

5. 6%

6. 30%

7. 65%

8. 200%

9. 125%

10. 300%

Help full?

6/2 or 3/0 I dont know if this is right I'm really not sure but the sums look right except for the fact that you can simplify down to 3/0 overall I think its ok

Step-by-step explanation:

39+24+33 = 96

11+13+8 = 32

96/32 simplified down = 6/2 = 3/0

Step-by-step explanation:

if something is plentiful, possession of it will not increase your power. A resource need to be perceived as scarce to create dependency.

Answer:

someone game me that same question but sadly i wasn't able to get the answer sorry for the inconvience

Step-by-step explanation:

Answer:

3. 2nd degree. Leading term:

[tex] {3x}^{2} [/tex]

Leading coefficient: 3x

Part 1:

[tex] {2x}^{2} + 11x + 15[/tex]

Part 2:

[tex] {3x}^{2} - x - 2[/tex]

Part 3:

[tex] - {x}^{2} + 12x + 17[/tex]

(Part 3 should be correct, double check it, I think it cancels out the minuses in the part 2 equation?)

P.S. I forgot to solve the equations on this and the first page, don't forget that and I can leave another answer for those if you need!

Answer:

I think its true but im not sure

Step-by-step explanation:

Answer:

1. 90

2. 61

3. 29

4. 61

Step-by-step explanation:

1 is a 90 degree angle. Triangles = 180 degrees