Please help me. I really appreciate it if you answered. Thank you! <3

Mr. Brownwood invests a certain amount of money at 9% interest and $1,800 more than that amount in another account at 11% interest. At the end of one year, he earned a total of $818 in interest. How much money was invested in each account?

$3,500 at 9%;
$4,300 at 11%
$3,100 at 9%;
$4,900 at 11%
$3,400 at 9%;
$3,200 at 11%

Answer:

(x + 2)

Step-by-step explanation:

When we factor the expression x² - 8x - 20, we should get (x + 2)(x - 10).

Alternatively, we can use synthetic division or long division to get our answer.

Answer:

x + 2

Step-by-step explanation:

got it right edg '22

Answer:

C = pi * d

Step-by-step explanation:

C = 2 * pi *r

We can replace 2 * r with d since the diameter is twice the radius

C = pi * 2*r

C = pi * d

Answer:a

Step-by-step explanation:

Answer:

4 times

Step-by-step explanation:

1 quart is equivalent to 32 fluid ounces.

If each eruption consumes 8 fluid ounces of vinegar. Assuming that the amount of vinegar required per eruption is constant, the number of times Tanvi can make her volcano erupt is:

[tex]n=\frac{32}{8}\\n=4\ times[/tex]

Tanvi can make her volcano erupt 4 times  with 1 quart of vinegar.

Answer:

Step-by-step explanation:

Answer:

[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]

Step-by-step explanation:

[tex]$\left(\frac{1}{2}x+3y \right)^4=\left(\frac{x}{2}+3y \right)^4\\$[/tex]

Binomial Expansion Formula:

[tex]$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$[/tex], also [tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]

We have to solve [tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\sum_{k=0}^{4} \binom{4}{k} \left(3 y\right)^{4-k} \left(\frac{x}{2}\right)^k$[/tex]

Now we should calculate for [tex]k=0, k=1, k=2, k=3 \text{ and } k =4;[/tex]

First, for [tex]k=0[/tex]

[tex]$\binom{4}{0} \left(3 y\right)^{4-0} \left(\frac{x}{2}\right)^{0}=\frac{4!}{(4-0)! 0!}\left(3 y\right)^{4} \left(\frac{x}{2}\right)^{0}=\frac{4!}{4!}(81y^4)\cdot 1 =81 y^{4}$[/tex]

It is the same procedure for the other:

For [tex]k=1[/tex]

[tex]$\binom{4}{1} \left(3 y\right)^{4-1} \left(\frac{x}{2}\right)^{1}=54 x y^{3}$[/tex]

For [tex]k=2[/tex]

[tex]$\binom{4}{2} \left(3 y\right)^{4-2} \left(\frac{x}{2}\right)^{2}=\frac{27}{2} x^{2} y^{2}$[/tex]

For [tex]k=3[/tex]

[tex]$\binom{4}{3} \left(3 y\right)^{4-3} \left(\frac{x}{2}\right)^{3}=\frac{3}{2} x^{3} y$[/tex]

For [tex]k=4[/tex]

[tex]$\binom{4}{4} \left(3 y\right)^{4-4} \left(\frac{x}{2}\right)^{4}=\frac{x^{4}}{16}$[/tex]

You can perform the calculations, I will not type everything.

The answer is the sum of elements calculated.

Just organizing:

[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]

Answer:  [tex]\bold{\dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4}[/tex]

Step-by-step explanation:

                     Binomial Tree

n=0                         1

n=1                      1      1

n=2                  1    2     1

n=3               1    3    3     1

n=4            1    4    6    4    1

Using the Binomial Theorem

[tex]\bigg(\dfrac{1}{2}x+3y\bigg)^4\\\\\\=1\bigg(\dfrac{1}{2}x\bigg)^4(3y)^0\quad \rightarrow \quad \dfrac{1}{16}x^4\\\\+4\bigg(\dfrac{1}{2}x\bigg)^3(3y)^1\quad \rightarrow \quad \dfrac{3}{2}x^3y\\\\+6\bigg(\dfrac{1}{2}x\bigg)^2(3y)^2\quad \rightarrow \quad \dfrac{27}{2}x^2y^2\\\\+4\bigg(\dfrac{1}{2}x\bigg)^1(3y)^3\quad \rightarrow \quad 54xy^3\\\\+1\bigg(\dfrac{1}{2}x\bigg)^0(3y)^4\quad \rightarrow \quad 81y^4[/tex]

______________________

[tex]= \dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4[/tex]

Answer:

That is true, but there is no question being asked.

Answer:

3/4 teaspoons of pepper

Step-by-step explanation:

1/4 teaspoons : 3 potatoes = x teaspoons : 9 potatoes

(1/4)/3 = x/9

3x = 9 * 1/4

x = 3 * 1/4

x = 3/4

Answer: 3/4 teaspoons of pepper

Answer:

B

step-by-step explanation:

1/4 over 3 p/9

Answer:

X=1

Step-by-step explanation:

12x-14=-2

    +14 +14

12x=12

x=1

Answer:

x = 1

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 14 to both sides:

12x - 14 = -2

12x - 14 (+14) = -2 (+14)

12x = -2 + 14

12x = 12

Next, divide 12 from both sides:

(12x)/12 = (12)/12

x = 12/12

x = 1

x = 1 is your answer.

~

A=4[tex]\pi -8[/tex]

that is your answer :-)

Answer:

[tex]A = 4\pi - 8[/tex]

Step-by-step explanation:

ody

Answer:

Equation: f(x) = -x² + 3

Step-by-step explanation:

If we want to find the roots/solve for x, we can either graph the problem or use quadratic formula to find when f(x) = 0:

To get the equation of the graph, our parent function is: f(x) = a(x - h)² + k, or f(x) = x². Since we are reflecting over the x-axis with a vertical stretch and vertically moving up to (0, 3), we are modifying a and k only.

Answer:

230.59

Step-by-step explanation:

55 = 2.7sqrt(x) + 14

41 = 2.7sqrt(x)

15.185=sqrt(x)

x = 15.185^2

x=230.59

Answer:  (0, 0) & (3, √3)

Step-by-step explanation:

Since we need a distance of 2, I graphed y = √x and then drew a circle at center (2, 0) and radius of 2 to see where they intersect.

The coordinates of intersection can be determined by solving a system of equations.

Equation 1: y = √x

Equation 2: (x - 2)² + y² = 2²

I will use the Substitution method with Equation 2 to solve for x:

(x - 2)² + (√x)² = 2²        substituted y with √x

x² - 4x + 4 + x = 4           expanded binomial

x² - 3x + 4 = 4                 added like terms

x² - 3x = 0                       subtracted 4 from both sides

x(x - 3) = 0                       factored

x = 0     x - 3 = 0             applied Zero Product Property

            x = 3

Next, solve for y using Equation 1:

x = 0:    y = √0 = 0

x = 3:    y = √3

Coordinates of intersection are: (0, 0) & (3, √3)

Answer:

(0, 0) & (3, √3)

Step-by-step explanation:

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

[tex]((a, b), (c, d))\in R[/tex]

Where [tex]R[/tex] is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

1. First of all, let us check reflexive property:

Reflexive property means:

[tex]\forall a \in A \Rightarrow (a,a) \in R[/tex]

Here we need to prove:

[tex]\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R[/tex]

As per the given relation:

[tex]((a,b), (a,b) ) \Rightarrow ab =ab[/tex] which is true.

[tex]\therefore[/tex] R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

[tex]\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R[/tex]

Here we need to prove:

[tex]\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R[/tex]

As per the given relation:

[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = bc[/tex]

[tex]((c,d),(a,b)) \in R[/tex] means [tex]cb = da\ or\ ad =bc[/tex]

Hence true.

[tex]\therefore[/tex] R is symmetric.

3. R to be transitive, we need to prove:

[tex]if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R[/tex]

[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = cb[/tex].... (1)

[tex]((c,d), (e,f)) \in R[/tex] means [tex]fc = ed[/tex] ...... (2)

To prove:

To be [tex]((a,b), (e,f)) \in R[/tex] we need to prove: [tex]fa = be[/tex]

Multiply (1) with (2):

[tex]adcf = bcde\\\Rightarrow fa = be[/tex]

So, R is transitive as well.

Hence proved that R is an equivalence relation.

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

https://brainly.com/question/1503196

In an arithmetic sequence, consecutive terms differ by a fixed number d :

[tex]a_8=a_7+d[/tex]

[tex]a_9=a_8+d=a_7+2d[/tex]

[tex]a_{10}=a_9+d=a_7+3d[/tex]

and so on up to

[tex]a_{19}=a_7+12d[/tex]

Solve for d :

[tex]140=32+12d\implies12d=108\implies d=9[/tex]

Work backwards to find the first term in the sequence, and hence the n-th term:

[tex]a_6=a_7-d[/tex]

[tex]a_5=a_6-d=a_7-2d[/tex]

and so on down to

[tex]a_1=a_7-6d[/tex]

So the first term is

[tex]a_1=32-6\cdot9=-22[/tex]

which means the n-th term is

[tex]a_n=a_1+(n-1)d=-22+9(n-1)=9n-31[/tex]

[tex]S_n[/tex] denotes the n-th partial sum of the sequence, i.e. the sum of the first n terms. We want to find the number of terms such that this sum is 511:

[tex]\displaystyle S_n=\sum_{i=1}^na_i=\sum_{i=1}^n(9i-31)=511[/tex]

Distribute the summation and recall the formulas,

[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]

[tex]\implies S_n=\displaystyle9\sum_{i=1}^ni-31\sum_{i=1}^n1[/tex]

[tex]\implies511=9\cdot\dfrac{n(n+1)}2-31n[/tex]

[tex]\implies1022=9n^2-53n[/tex]

[tex]\implies9n^2-53n-1022=0[/tex]

[tex]\implies(n-14)(9n+73)=0[/tex]

[tex]\implies n=14\text{ or }n=-\dfrac{73}9[/tex]

n must be a positive integer, so we the sum is obtained from the first n = 14 terms.

Answer:

He will have enough paint to cover the tank with one layer of paint

Step-by-step explanation:

To calculate the area of the surface that has to be painted, we will have to calculate the lateral surface of the cylinder

Lateral surface of the cylinder is given by

A=2πrh

Where,

π=3.142

r=1.1/2m=

h=1.4m

A=2πrh

=2*3.142*1.1/2*1.4

=4.84m^2

He uses 250ml to cover 1m^2

To cover 4.84m^2, he will use

4.84m^2 × 250ml of paint

=1,210ml of paint is needed

He has 2 litres of paint

2litres =2000ml

Tublu has 2000ml of paint but needs 1210ml of paint

Therefore,

He has an excess of 2000-1210

=790ml

The answer is yes, he will have enough paint to cover the tank with one layer of paint.

Answer:

Please see attached picture for full solution.

Answer:

x = -3

Step-by-step explanation:

When asked to solve the equation for x, it mean that put x only on one side, and everything else on the other side. So....

x/3 - 1 = -2

x/3 = -1             ( add 1 on both side)

x = -3               (x3 on both side)

Answer:

V = 3534 cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

the radius is 7.5 and the height is 20

V = pi ( 7.5)^2 * 20

V =1125 pi cm^3

Using the pi button for pi

V =3534.291735 cm^3

Rounding to the nearest whole number

V = 3534 cm^3

Answer:

b)3534 cm^3

Step-by-step explanation:

To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.

Answer:

I think it is either 85 or 51 because the question was not specific

Step-by-step explanation:

I am not entirely sure if you mean Jose changed jobs or added a new job on top but i will do both.

34/2=17

17+34=51

OR

51+34=85

Answer:

51 miles.

Step-by-step explanation:

That would be 34 * 1 1/2

= 34 * 3/2

= 17 * 3

= 51 miles.

Answer: 6

Step-by-step explanation: I think..... this is a division sign, nvm... so 4 divided by 8/12 is basically 4 x 12/8 which is 48/8 simplified is/equals 6!

Answer:

6

Step-by-step explanation:

4 / 8/12 = 4 * 12/8 = 4 * 3/2 = 6

Answer:

I hope it's correct

Answer:

The car's average speed for the entire journey = 84.315 km/h

Step-by-step explanation:

Correct Question

A car travels the first 50km of its journey at an average speed of 25m/s and the next 120 km at an average speed of 80km/h. the car completes the last part of its journey at an average speed of 90km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.

Solution

Average speed is given as total distance travelled divided by total time taken.

So, we will compute the distance covered for each part of the journey and the corresponding time it takes to cover each of these distances.

- The car travels the 50 km first part of the journey at a speed of 25 m/s.

25 m/s = 90 km/h

We have the distance covered in the first part of the journey, now, we need the time taken to cover the distance.

Speed = (Distance/Time)

Time = (Distance/Speed)

Distance = 50 km, Speed = 90 km/h

Time = (50/90) = 0.5556 hr

- The next part, the car covers 120 km at a speed of 80 km/h

Time = (Distance/Speed) = (120/80) = 1.5 hr

- For the last part of the journey, the car travels with an average speed of 90 km/h for 35 minutes.

35 minutes = (35/60) hr = 0.5833 hr

Here, we need to calculate the distance covered for the last part.

Speed = (Distance/Time)

Distance = (Speed) × (Time) = 90 × 0.5833 = 52.5 km

Total distance covered = 50 + 120 + 52.5 = 222.5 km

Total time taken = 0.5556 + 1.5 + 0.5833 = 2.6389 hr

Average Speed = (222.5/2.6389) = 84.315 km/h

Hope this Helps!!!

Answer:

900L per minute

Step-by-step explanation:

1- 70 - 20 = 50

2- in this 50 min the 45000L has been drawned

3- 45000L / 50 = 900L

.. ..

Answer:

(2)They are perpendicular.

Step-by-step explanation:

Answer:

126 people

Step-by-step explanation:

9/5 is the ratio tea/coffee

let x be the one who preferred coffee and x+36 preferred tea

9/5=x+36/x

9x=5x+5(36)

9x-5x=180

4x=180

x=180/4=45

x=45 coffee

x+36=45+36=81

45+81=126

check : 81/45= 9/5

Answer:

A) 52.5 inches²

Step-by-step explanation:

The equation for the area of a trapezoid is a=1/2h(b1+b2). This basically means that you take the height of the trapezoid, multiply it by the top base plus the bottom base and divide that by 2. When you do this, you take 8.5 plus 6.5, which equals 15, and multiply that by 7 to get 105. After you get this, you divide it by 2 to get 52.5 inches².

Answer:

a) 12 (Simply divide 4800/5 to get 960.  Then divide 960/80 to get 12)

b) 2100 (Simply multiply 12 by 25 by 7)

Hope it helps <3

Answer:

30 people

Step-by-step explanation:

If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.

Answer:

Option A is the correct option.

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} - 2ab \: \cos \: c \: = {c}^{2} \\ a = 4 \\ b = 5 \\ c = 2 \\ \\ 2ab \: cos \: c = {a}^{2} + {b}^{2} - {c}^{2} \\ \: \: \: \: \: \: \: \: = {(4)}^{2} + {(5)}^{2} - {(2)}^{2} \\ \: \: \: \: \: \: \: \: = 16 + 25 - 4 \\ \: \: \: \: \: \: = 41 - 4 \\ \: \: \: \: \: \: = 37[/tex]

Hope this helps...

Good luck on your assignment...