Richard owned n cows.
Ellis had exactly 4 times as many cows as Richard.
Richard buys 13 extra cows.
Ellis sells 9 of his cows.
Ellis still has more cows than Richard.
Form an inequality, in terms of n.
Solve the inequality to find the least value of n.
You must show all your working.

Step-by-step explanation:

1. ∠EBC = x (Theorem One: The angle at the centre of the circle is twice the angle at the circumference subtended on the same arc. You already have this one labelled)

2. ∠FCD = x (F rule / corresponding angles are equal)

3. ∠CAE = x (Theorem Two: Angles at the circumference subtended by the same arc are congruent)

4. ∠BED = ∠DCF = ∠FCD = x (Theorem Fifteen: The exterior angle of a cyclic quadrilateral is congruent to the interior opposite angle)

5. ∠CDF = ∠BED = x (F rule / corresponding angles are equal)

6. ∠CAE = ∠OAE = ∠OEA = x  (CAE and OAE are the same angles, OF and OA are radii, thus they must both be equivalent in magnitude, therefore making the triangle ΔAOE isosceles. Base angles of an isosceles triangle are always equal, since we knew ∠OAE from '3.' was x, we found that ∠OEA was also x)

Answer:

3. 15 outcomes

5. 72 outcomes

Step-by-step explanation:

5 x 3 = 15

(2 x 3) x 12 = 72

2 x 3 = 6

6 x 12 = 72

Check the picture below.

[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{600\times 600}{360000}\\ h=300 \end{cases}\implies V=\cfrac{(360000)(300)}{3}\implies V=36000000~ft^3[/tex]

Answer:

It is c

Step-by-step explanation:

When you fold it up, it makes a box just like the solid figure.

Have an amazing day!

PLEASE RATE!!

Answer:

Step-by-step explanation:

let us first model the amount that Jaime and Jon will charge

let the total amount be y and let the number of hours be x

Jaime will charge

y=30+4x------1

Jone will charge

y=50x-----2

equating 1 and 2 we can solve for x which is the number of months Jaime and Jon will charge the same price

50x=30+40x

50x-40x=30

10x=30

divide both sides by 10 we have

x=30/10

x=3

Answer: The coefficients are: 16ab, 5c, and 2w. The terms are: 16ab, 5c, 8, 21, 2w, H, W, and L. The constants are: 8 and 21. And the variables are: H, W, and L.

Answer:

463.70 or 500.45

Answer:

2.2360679775

Step-by-step explanation:

Answer:

2.2360679775

Step-by-step explanation:

Answer:

height of pyramid = 3 cm

height of prism = 9 cm

Step-by-step explanation:

Square Pyramid

surface area of 4 triangular sides of the pyramid = [tex]2a\sqrt{\dfrac{a^2}{4}+h^2}[/tex]

(where [tex]a[/tex] is the base edge and [tex]h[/tex] is the height)

Given [tex]a[/tex] = 8 cm

[tex]\implies \textsf{SA}=2\cdot8\sqrt{\dfrac{8^2}{4}+h^2}[/tex]

            [tex]=16\sqrt{16+h^2}[/tex]

Square Prism

surface area of square prism with one base = [tex]a^2+4ah[/tex]

(where [tex]a[/tex] is the base edge and [tex]h[/tex] is the height)

Given [tex]a[/tex] = 8 cm and [tex]h[/tex] = 3h

[tex]\implies \textsf{SA}=8^2+4\cdot 8\cdot 3h[/tex]

Total surface area

total SA = SA of pyramid + SA of square prism

Given total SA = 432 cm²

[tex]\implies 432=16\sqrt{16+h^2}+64+96h[/tex]

[tex]\implies 368=16\sqrt{16+h^2}+96h[/tex]

[tex]\implies 368=16(\sqrt{16+h^2}+6h)[/tex]

[tex]\implies 23=\sqrt{16+h^2}+6h[/tex]

[tex]\implies 23-6h=\sqrt{16+h^2}[/tex]

[tex]\implies (23-6h)^2=16+h^2[/tex]

[tex]\implies 529-276h+36h^2=16+h^2[/tex]

[tex]\implies 35h^2-276h+513=0[/tex]

[tex]\implies (h-3)(35h-171)=0[/tex]

[tex]\implies h=3, h=\dfrac{171}{35}[/tex]

Inputting both values of [tex]h[/tex] into the equations for SA:

when [tex]h = 3[/tex]:

[tex]\textsf{pyramid}=16\sqrt{16+3^2}=80 \ \sf cm^2[/tex]

[tex]\textsf{square prism}=64+96(3)=352 \ \sf cm^2[/tex]

[tex]\textsf{total SA}=80+352=432 \ \sf cm^2[/tex]

when [tex]h=\dfrac{171}{35}[/tex]:

[tex]\textsf{pyramid}=16\sqrt{16+(\frac{171}{35})^2}=101.0285714... \sf cm^2[/tex]

[tex]\textsf{square prism}=64+96(\frac{171}{35})=533.0285714... \ \sf cm^2[/tex]

[tex]\textsf{total SA}=101.0285714...+533.0285714... =634.0571428... \ \sf cm^2[/tex]

Therefore, h = 3 only (since the total area is 432 cm²)

⇒ height of pyramid = 3 cm

⇒ height of prism = 3h = 3 × 3 = 9 cm

Answer:

100

Step-by-step explanation:

Lets solve this the easiest way possible :)

120/6 = 20

Now since they sold 5/6 of these copies, lets multiply the 20 by 5 to figure out how much they sold.

20 x 5 = 100

They sold 100 copies :)

Hope this helps!!!

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

100

Step-by-step explanation:

5     120

-----   ------

6          1

=

600

-------   =  100

6

Answer:

(a) [tex]A=1600(1+\frac{0.0375}{12})^{12t}[/tex]

     (where [tex]A[/tex] is the account balance and [tex]t[/tex] is the time in years)

(b) $1,929.40

Step-by-step explanation:

Compound interest formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

Substituting these values into the formula:

[tex]\implies A=1600(1+\frac{0.0375}{12})^{12t}[/tex]

(where [tex]A[/tex] is the account balance and [tex]t[/tex] is the time in years)

Part (b)

Substitute [tex]t=5[/tex] into the equation created in part (a):

[tex]\implies A=1600(1+\frac{0.0375}{12})^{12\cdot 5}[/tex]

[tex]\implies A=1600(1.003125)^{60}[/tex]

[tex]\implies A=1929.404236...[/tex]

[tex]\implies A=1929.40[/tex]

Therefore, her account balance after 5 years will be $1,929.40

Answer:

It would be $45.00.

Step-by-step explanation:

50 divided by 10 would be 5. Subtract that from 50 to get 45.

Answer:

$45.00

Step-by-step explanation:

If an item cost $50 and the discount is 10% then:

Convert 10% to a decimal

10/100 = .1

.1 * $50 = $5

The discount is $5, subtract the discount from the original amount.

$50 - $5 = $45

The item would cost $45.00 after the discount.

Answer:

I got you :)

Step-by-step explanation:

F(x)=2x-10

Ok, so when you need to know f(4) you plug in 4 for x

f(4)=2(4)-10

2x4 = 8

8-10= -2

f(4)= -2

Hope this helps!

Hi! Hope you're enjoying your day!

In order to solve this, all we have to do is plug in the value of x.

So we're given that

f(x)=2x-10

So f of x is equal to 2 times x minus 10.

Thus

f of 4 is equal to 2 times 4 minus 10 (it can be simplified, right?) :)

f(4)=8-10

f(4)=-2

Hence, the answer is

[tex]\boxed{\boxed{\bold{f(4)=-2}}}[/tex]

Hope everything is clear.

If you have any questions, please ask.

#LearningIsFun

[tex]\rule{200}{2}[/tex]

Answer:

All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle

Step-by-step explanation:

Answer:it’s the third answer choice

Step-by-step explanation:

Answer: C) Draw segment TU and point R on segment TU.

The construction he set up so far is pretty much almost done. If he draws a ray through points T and U (with T as the endpoint), then ray TU combines with ray TS to get angle STU. This angle is congruent to angle BCD.

The point R is introduced so that we call this angle STR instead of angle STU, but it's the same basic idea. You could also replace "ray" with "line" or "line segment" to get the same basic construction of copying an angle.

Answer:

Dear Friend here is your answer.

Answer:

2m-8+1=2m-7

Step-by-step explanation:

Step-by-step explanation:

-2 (4a + 4b) + 5a > -35

-8a -8b + 5a > -35

-3a -8b > -35

for a

-3a > -35 + 8b

a < -35 + 8b ÷ -3

a < 35 - 8b ÷ 3

for b

-3a - 8b > -35

-8b > -35 + 3a

b < -35 + 3a ÷ -8

b < 35 - 3a ÷ 8

we can see that the triangle is isosceles since it has 2 equal sides

so that means 2 equal angles then :

x + 17 = 4x - 34

3x = 51

x = 17

or

the sum of 3 triangles angles = 180

6x + 10 + x + 17 + 4x - 34 = 180

11x = 187

x = 17

Answer:

Step-by-step explanation:

(6x+10)+(x+17)+(4x+34)=180

11x+61=180

11x+61-161=180-61

11x=119

11x/11=119/11

x=10 9/119

Answer:

9 /89

Step-by-step explanation:

Answer:

140 squirrels

Step-by-step explanation:

first week, there are 5 squirrels.

second week, there are 8 squirrels.

third week, there are 11 squirrels.

let's calculate the amount of squirrels at the end of 28 weeks. from the statement given, an addition of 3 squirrels for every week.

by cross multiply method:

5 squirrels = 1 week

x squirrels = 28 weeks

x = 28 x 5

x = 140 squirrels.

so you will have an amount of 140 squirrels after 28 weeks.

Answer:

can't solve this

Step-by-step explanation:

Answer:

4. F

5.C

6.G

7.D

8.A

9.E

10.B

Step-by-step explanation:

Answer:

(f+g)(x) > 3 for all values of x

Answer:

0.00000001

Step-by-step explanation:

Answer:

0.000000001

Step-by-step explanation:

Answer:

Ok, suppose that there are M Petri dishes, where M is an integer number.

If there are N students in the class, then the number of Petri dishes that each student gets is:

# = M/N.

(always that N divides M)

If not, we will have a remainder, R,  of Petri dishes such that:

M ≥ N

R < N

This means that:

The total number of Petri dishes must be equal or larger than the number of students.

If M is larger than N, and N does not divide M, then the remainder of the quotient will be smaller than N.

Now with this, you can replace the numbers and do the math.

"The more students that decide to do the bacteria experiment, the fewer the number of Petri dishes each student gets."

You can easily see this because the equation for the number of Petri dishes that each student gets is:

# = M/N.

Here, N is in the denominator, then if the number of students in the class increases, the denominator in the operation increases, which means that the quotient will be smaller.

Answer:

0.00000049

I believe this is right if not I apologize