Solve the set of simultaneous equations graphically. Use a scale of 1cm = 1 unit on both axes.
y=4+x
y=1+3x ; 0≤x≤6

Step-by-step explanation:

the first step in my opinion would be find the norm(s) in this scenario.

100 pounds is a good norming weight.

the speed of these 100 pounds with a 10 HP motor is

50ft/30sec = 5/3 ft/s

so, then let's ask next what size of motor is needed to lift the same 100 pounds 40 ft in 40 seconds

40ft/40sec = 1 ft/s

to get the same speed as in the first case the motor need to be weaker (to move slower). and that goes by the same factor as the ratio between the 2 speeds :

5/3×f = 1

f = 3/5

10 HP × f = 10 × 3/5 = 30/5 = 6 HP

so, it takes a 6 HP motor to lift these same 100 pounds 40 ft in 40 seconds.

and now, how strong must the motor be to lift 800 pounds (= 8 times the original 100 pounds) with the same speed ?

well, 8 times

8×6 = 48 HP

so, it would take a 48 horsepower motor to lift 800 pounds 40 ft in 40 seconds.

the equation would then be

HP = p/100 × 6 = 6p/100 = 3p/50

HP = horsepower

p = pounds

the rest I cannot really answer, as I don't know your class and it's contents.

I hope I covered the topics of your class with that solution.

Answer:

492.99

Step-by-step explanation: x = amount invested at 12%

y = amount invested at 9%

---

x + y = 20287

0.12x = 0.09y + 492.99

---

put the system of linear equations into standard form

---

x + y = 20287

0.12x - 0.09y = 492.99

The amount invested at 14% is $4144 and the amount invested at 12% is $9894.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

Investment at 14%= $14,038

Investment at 12%= $984.34

Now,

Let x be the amount invested at 14% and y be the amount invested at 12%. Then we have:

x + y = 14038 (total amount invested)

0.14x - 0.12y = 984.34 (difference in interest)

We can solve this system of equations by substitution or elimination. For example, by elimination, we can multiply the first equation by 0.12 and subtract it from the second equation to get:

0.02x = 82.88

x = 4144

Then we can plug x into the first equation and get:

y = 14038 - 4144

y = 9894

Therefore, the simple interest will be $4144 and $9894.

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Answer:

8:10

Step-by-step explanation:

8 parts for brown sugar and 10 parts flour.

In simplest, 4:5 (divide 8 and 10 by 2)

Answer:

x=1.2

Step-by-step explanation:

2(5x-4)=4

distribute 2 to 5x and -4

10x-8=4

add 8 to negative 8 and 4

10x=12

now divide both sides by 10

10x/10= 12/10

x=1.2

The value of x for the logarithmic expression will be x=1.2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is log2(5x-4)=4. The value of x will be calculated as,

2(5x-4)=4

Distribute 2 to 5x and -4,

10x-8=4

Add 8 to negative 8 and 4,

10x=12

Now divide both sides by 10,

10x/10= 12/10

x=1.2

Therefore, the value of x for the logarithmic expression will be x=1.2.

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Answer:

32 large lemonades

Step-by-step explanation:

4 gallons = 512 ounces

512 ounces / 16 ounces

= 32 large lemonades.

It has a positive slope.

when it starts at the bottom left like that and goes up it is positive. :)

Answer:

|279|

Step-by-step explanation:

so when ur doing absolute value you js need distance so lets work with the problem, if ur 279 feet below water u would need to get to zero feet below sea level (ground lvl) to do so how many feet towards ground lvl would u go? (279 clearly) so the distance from how many feet under u are to the ground lvl is ur absolute value.

Tbh in school they over complicate it if u need an absolute number from a negative number like -279 (as it is in the problem) you would js make it a positive (if its positive 279 u js say the absolute value is 279)

(also the absolute value is the distance between the number and zero so yh u can put that)

Answer:

3rd option

Step-by-step explanation:

The angle opposite the shortest side is the smallest

The angle opposite the longest side is the largest

Shortest side is AC with ∠ B opposite , thus smallest

Longest side is AB with ∠ C opposite, thus largest

Then order of angles from least to greatest is

∠ B , ∠ A , ∠ C

Answer:

3/4 is in it's simplest form

Step-by-step explanation:

3/4 cannot be simplified any more, so it is at it's simplest form

Answer:

36

Step-by-step explanation:

First, you subtract 4 by 36 which is 32. Then, divide 32 by 8 which equals 4 therefore the answer is 36.

Answer:

y = -1/4x + 2

Step-by-step explanation:

using the slope-intercept form (y=mx+b) m is the slope of the line which is -1/4 because it is decreasing and b is the y-intercept of the line which is 2

Answer:

32

Step-by-step explanation:

Answer:

1/2, or 0.5

Step-by-step explanation:

Answer:

She would have written 6 2/3 pages.

Step-by-step explanation:

2 2/3 pages = 1 hour

6 2/3 pages = 2 1/2 hours

If 2 angles are formed on a line, then they make a supplementary / linear pair of angles, i.e, both the angles form 180°.

Here,

Angle A = 80°

Angle B = x°

So,

Angle A + Angle B = 180°

80° + x° = 180°

x° = 180° - 80°

x° = 100°

=》 Angle B = 100°

_____

Hope it helps ⚜

Answer:

median is a hight of a triangle

Answer:

[tex]3(5x + 4) = 3 \times 5x + 3 \times 4 \\ = 15x + 12 [/tex]

Answer:

15x+12

Step-by-step explanation:multiply 5x + 4 by 3 hence answer is 15x +12

Answer:

x > -1

Step-by-step explanation:

-10 < x - 9

Add 9 to each side

-10+9 < x - 9+9

-1 < x

x > -1

Answer:

Step-by-step explanation:

- 10 < x - 9

- 10 + 9 < x - 9 + 9

- 1 < x

x > - 1

Answer:

3 in 75,341 = the hundreth place.  3 in 293,467 = the thousandth place.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Substitute n = 9 into the nth term rule

A(9) = - 15 + 2(9 - 1) = - 15 + 2(8) = - 15 + 16 = 1 → A

Answer:

60

Step-by-step explanation:

edge

Answer:

10%

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is a parrallelogram, the two lines are Parallel to each other meaning they will never cross each other

The given xy- plane is a parallelogram.

A plane figure is called a parallelogram when it have four sides, in which opposite sides are parallel to each other and each side is equal in length to its opposite side.

If [tex](x_{1},y_{1} })[/tex] and [tex](x_{2},y_{2})[/tex] are the two points then the distance between these points is given by

[tex]d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1} ) ^{2} }[/tex]

Where, d is the distance between two points.

According to the given question

We have a plane figure PSTO

And the coordinates of points P, S, T, and O are (a, b), (a + c, b), (c, 0) and (0,0) respectively.

Now, the length of the sides by distance formula

PS = [tex]\sqrt{(a-a-c)^{2}+(b-b)^{2} }[/tex]

PS = [tex]\sqrt{c^{2}+0 }[/tex]

PS = c

Similarly,

ST =[tex]\sqrt{(a+c-c)^{2}+(b-0)^{2} }[/tex]

ST = [tex]\sqrt{a^{2} +b^{2} }[/tex]

TO = [tex]\sqrt{(c-0)^{2}+(0-0)^{2} }[/tex]

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

TO = c

And, PO = [tex]\sqrt{(a-0)^{2}+(b-0)^{2} }[/tex]

PO = [tex]\sqrt{a^{2} +b^{2} }[/tex]

From the above calculation we found that

PS = TO

PO = ST

⇒ Length of the  opposite sides of the plane figure are equals.

And from the given figure we can see that the opposite sides are also parallel to each other.

Therefore, the given xy- plane is a parallelogram.

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Answer:

1. 27

2. 48

3. 40

Step-by-step explanation:

3 to the power of 2 is 9 (3×3)

9×3=27. (8-5=3)

6 to the power of 2 is 36 (6×6)

36+12=48. (4×3=12)

42-2=40

Answer:

1.  8^7

2. 2^2

Step-by-step explanation:

I am not sure about these

4. 6.32066568875585e+24

5. 1.0853858230617127e+182

6. Infinity

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