Q9.
Solve the simultaneous equations
7x – 2y = 34
3x + 5y = -3
Show clear algebraic working.

Answer:

  a. f = 17.5/c

  b. 8.75 N

Step-by-step explanation:

Inverse variation means one variable is proportional to the inverse of the other. The equation for that is ...

  f = k(1/c) . . . . . . force (f) is proportional to the inverse of distance (c)

We find the value of k using data given for a specific instance.

  3.5 N = k(1/(5 cm)) . . . . use the given values

  17.5 N·cm = k . . . . . . multiply by the denominator

Then the equation of interest is ...

  f = 17.5/c . . . . . . . where c is in cm, and f is in newtons

__

Using the above equation, we find the force to be ...

  f = 17.5/2 = 8.75 . . . . newtons

_____

Additional comment

We often look at several different kinds of proportionality:

and there are combinations of these, such as ...

You may have noticed that when x and y are inversely proportional, their product is a constant. y = k/x  ⇒  xy = k

__

We have left off the units of k in the problem above. Sometimes it is a good idea to retain them, or to pay close attention to what they are. This can avoid using the wrong measures for the variables.

  f = (17.5 N·cm)/(2 cm) = 8.75 N . . . . . units of cm cancel

Step-by-step explanation:

1.

so 90 km on 17 liters.

that is a 90/17 ratio (or proportion).

that means it runs 90/17 km on 1 liter.

and therefore (90/17)×20 on 20 liters.

90×20/17 = 105.8823529... km

2.

the ratio is 66/22 based on the RPMs.

66/22 = 3/1 = 3

so, the larger gear has then 3×6 = 18 teeth.

3.

the ratio is 150/75 based on the RPMs.

the circumference of a circle is

2×pi×r

so, it is a linear relationship with the radius r (and therefore the diameter d).

so, the diameter of the larger pulley is 2×10 = 20 in

4.

the ratio here is 18/6.

18/6 = 3/1 = 3.

again, this relates to the circumference, which is a linear relationship with the radius or diameter.

the smaller gear has then 72/3 = 24 teeth.

5.

the ratio is 2/3.

so, the larger pulley has 3450×2/3 RPM.

= 2,300 RPM

6.

2.5 kg cost 110.

that is a 2.5/110 ratio :

and that means we get 2.5/110 kg for one unit of money.

and therefore we get 80 × 2.5/110 kg for 80 units of money.

80 × 2.5/110 = 8 × 2.5/11 = 20/11 = 1.818181818... kg

Answer:

The width would be 64 cm

Step-by-step explanation:

Because the equation to find area is length times height

Since you have the area and the length, divide the area by the length to find the width

I hope this helps!

The notation A = {0,1, 2} is an illustration of sets

The set A do not have isolated points

An isolated point is an element of a set that belongs to a set A and any neighboring sets N, such that the set N do not contain other elements of set A

The set A is given as:

A = {0,1, 2}

The elements of the set A do not exists in other sets

So, we can say that set A do not have isolated points

Read more about sets at:

https://brainly.com/question/1563195

Answer:

200000×2

=R400 000 and minus 50000

=300000

Answer:

A=1

4πd2=1

4·π·122≈113.09734

Step-by-step explanation:

Answer:

113.04 feet :)

Step-by-step explanation:

First we divide 12 by 2 to find the radius!

12/2 = 6

Now we can solve!!

3.14(6^2)

3.14(36)

113.04

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

basketballs = 210 footballs = 70

Step-by-step explanation:

footballs =b

basketballs= 3b

if there ate 140 fewer footballs than basketballs it means that the difference between basketballs and footballs sold is 140

hence 3b - b = 140

2b= 140

b= 70

hence footballs are 70

while basketballs are 70×3 = 210

Answer:

16

Step-by-step explanation:

12 divided by 2 x 3 - (7 - 5)

6 x 3 - 2

18 - 2

16

Answer:

answer 16

Step-by-step explanation:

12 ÷ 2 x 3 - ( 7 - 5 ) is it right?
---------------------------------------------

Solving from left to right

12 ÷ 2 x 3 - ( 7 - 5 )
6 x 3 - (+2)
18 - 2

16

3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]31+22-50[/tex]

____________________________________________

Calculate

[tex]53-50[/tex]

____________________________________________

Calculate the sum or difference

[tex]3[/tex]

I hope this helps you

:)

Answer:

7k + 6

Steps:

Subtract the numbers 20+6k-14k+k

6+6k+k

Combine the terms:

6+6k+k

6+7k

Rearange terms:

6+7k

7k+6

I assume the base of S is the disk centered at the origin, or x² + y² ≤ r². Solving for y gives two solutions corresponding to the upper and lower halves of the circular boundary,

[tex]x^2+y^2 = r^2 \implies y = \pm \sqrt{r^2-x^2}[/tex]

and the vertical distance between them - i.e. the side length of each cross section - is

[tex]\sqrt{r^2-x^2} - \left(-\sqrt{r^2-x^2}\right) = 2\sqrt{r^2-x^2}[/tex]

Then the volume of each square cross section 4 (r² - x²) ∆x, and the volume of S is

[tex]\displaystyle \int_{-r}^r 4(r^2-x^2) \, dx[/tex]

By symmetry, this is the same as

[tex]\displaystyle 8 \int_0^r (r^2-x^2) \, dx[/tex]

which gives a volume of

[tex]\displaystyle 8 \int_0^r (r^2-x^2) \, dx = 8 \left(r^3 - \frac{r^3}3\right) = \boxed{\frac{16r^3}3}[/tex]

Answer:

x = 3.25 Each diagonal = 34.25. Step-by-step explanation: LMNP is a rectangle and it has diagonals LN and MP. Now, given that LN = 13x - 8 and MP = 9x + 5 Now, we know that the two diagonals of a rectangle are of the same length. So, LN = MP   ⇒ 13x - 8 = 9x + 5 ⇒ 4x = 13 ⇒ x = 3.25 (Answer) Therefore, the each diagonal is of (13 × 3.25 - 8) = 35.25 length. (Answer)

Read more at Answer.Ya.Guru – https://answer-ya.com/questions/4694576-lmnp-is-a-rectangle-find-the-value-of-x-and-the-length-of-each.html

Step-by-step explanation:

Answer:

Can you provide an Attachment?

Step-by-step explanation:

^^

Answer:

12

Step-by-step explanation:

Answer:

24 cubic units

Step-by-step explanation:

Count the front layer by fours because there are 3 rows of 4 and 3 rows of 4 on the other side.So count by 4's on the front layer then the back layer.

Answer:

3

Step-by-step explanation:

3x - 1 < 8

Solve this inequality like a two-step equation.

Add 1 to both sides to cancel the -1.

3x - 1 < 8

3x < 9    Divide both sides by 3 to cancel the 3 in 3x.

x < 3

Find the absolute value (distance the number is from 0).

Absolute value = 3

I hope this helps and please mark me as brainliest!

Answer:

that's a computer I'm sorry di ko po Alam

Step-by-step explanation:

ty sa points

Answer:

40

Step-by-step explanation:

Answer:

A triangular prism is a three-dimensional shape having two triangular bases and three rectangular sides.

Answer:

10

Step-by-step explanation:

On the chart, it says "Number of hostel rooms: 10". The rest of the data is useless and is just there to confuse you.

Answer:

f(x) = x² - 4x + 2 or f(x) = (x - 2)²

Step-by-step explanation:

What is the value of "a"?

So, our quadratic equation will be :

Answer:

f(x)=(x-2)^2

Step-by-step explanation:

They deleted my first answer, the one you marked brainliest :/

Promise this is correct, but i don't know how to explain it. The person above me did it wonderfully though. Hope this helped <3, Have a great day!

Answer: 4 pounds

Step-by-step explanation:

      First, we will see how much the coffee cost by subtracting what was left by the total gift card.

             $90 - $59.64 = $30.36

      Now, we will divide how much the coffee cost by how much one pound costs. This will give us how many pounds she bought, and the answer to your problem

             $30.36 / $7.59 = 4

                 She bought four pounds of coffee.

In Cartesian coordinates, the volume is

[tex]\displaystyle \iiint_R \mathrm dV[/tex]

where R is the set

[tex]R = \left\{(x,y,z) \, : \, -4\le x\le4 \text{ and } -\sqrt{16-x^2} \le y \le \sqrt{16-x^2} \text{ and }\right. \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~\left.-\sqrt{16-x^2-y^2} \le z \le \sqrt{16-x^2-y^2} \right\}[/tex]

Converting to spherical coordinates, we take

[tex]\begin{cases}x=\rho\cos(\theta)\sin(\phi) \\ y=\rho\sin(\theta)\sin(\phi) \\ z = \rho\cos(\phi)\end{cases}[/tex]

and we can compute the Jacobian to find

[tex]dV = dx\,dy\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]

and the set R transforms to

[tex]R' = \left\{(\rho,\theta,\phi) \,:\, 0\le \rho\le4 \text{ and }0\le\theta\le2\pi \text{ and } 0\le\phi\le\pi\right\}[/tex]

The new integral and hence the volume is then

[tex]\displaystyle \iiint_R \mathrm dV = \iiint_{R'} \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi \\\\ = \boxed{\int_0^\pi \int_0^{2\pi} \int_0^4 \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi}[/tex]

Answer:

C. 4

Step-by-step explanation:

Each side of the Square pyramid is congruent

Answer: c which is 4 sides

Step-by-step explanation: the square pyramid has 4 sides which are having equal sides so they are congruent . Hope it helps . Please give brainliest .

Multiply 80 by number of copies sold and add to her salary:

P = 80N + 1700

Now replace N with 26:

P = 80(26) + 1700

P = 3,780

Answer:

P=1,700+80n

Total Pay if Yoko sells 26 Copies; 3,780

Hope This Helps! :) Please Mark Brainliest!

The radioactive sponteanous decay of the parent nucleus gives rise to the daughter nucleus.

Radioactivity refers to the sponteanous decay of a substance. We have the formula;

N(t) = Noe^-kt

Where;

N(t) = amount of radioactive material left after time t

No = amount of radioactive material initially present

k = decay constant

t = time taken

Let us now solve the questions individually;

a)

No = 20 pounds

N(t) = ?

k = 0.0231

t = 10 years

N(t) = 20e^-(0.0231 * 10)

N(t) = 16 pounds

b)

No =  80 pounds

N(t) = ?

k = 0.0248

t =  75 years

N(t) =80e^-(0.0248 * 75)

N(t) = 12.45 pounds

Learn more about radioactivity: https://brainly.com/question/15289741?