Using the Rule of 72, how long would it take for Anthony to double his investment of $5,000 in a
money market account that earns 7% per year?

Answer:

I think it's B.

Step-by-step explanation:

Answer:

82

Step-by-step explanation:

because diagonals are equal in quadrilater

Answer:

(3,2)

Step-by-step explanation:

Setting up equation so we can use substitution method

x - y = 1 , x + 3y = 9

step 1 set first equation equal to x by adding y to both sides so we can use the substitution method to solve the system of equations.

x = y + 1 , x + 3y = 9

now we can plug in ( or substitute hence substitution method ) the first equation into the second

Solving for y using the substitution method

x + 3y = 9

plug in x = y + 1

y + 1 + 3y = 9

combine like terms

4y + 1 = 9

subtract 1 from both sides

4y = 8

divide both sides by 4

y = 2

Now to find the value of x we plug in the value of y into one of the equations and solve for x.

Solving for x

x - y = 1

y = 2

x - 2 = 1

add 2 to both sides

x = 3

The solution would be (3,2)

Answer:

x = 3 and y = 2 or (3,2) in coordinate form

Step-by-step explanation:

Given:

[tex]\displaystyle \large{\begin{cases} x-y=1 \\ x+3y=9 \end{cases}}[/tex]

Solve by elimination of x-terms by multiplying either one of equations with -1:

For this, I choose to multiply -1 in first equation:

[tex]\displaystyle \large{\begin{cases} -1(x-y=1) \\ x+3y=9 \end{cases}}\\\displaystyle \large{\begin{cases} -x+y=-1 \\ x+3y=9 \end{cases}}[/tex]

Then add both equations:

[tex]\displaystyle \large{-x+x+y+3y=-1+9}\\\displaystyle \large{4y=8}[/tex]

Divide both sides:

[tex]\displaystyle \large{\dfrac{4y}{4} = \dfrac{8}{4}}\\\displaystyle \large{y=2}[/tex]

Next, substitute y = 2 in one of equations to solve for x:

For this, I choose to substitute y = 2 in the first equation:

[tex]\displaystyle \large{x-y=1}[/tex]

Substitute y = 2 in:

[tex]\displaystyle \large{x-2=1}[/tex]

Add both sides by 2:

[tex]\displaystyle \large{x-2+2=1+2}\\\displaystyle \large{x=3}[/tex]

Hence, the solution is x = 3 and y = 2 or you can write as in coordinate form (3,2)

__________________________________________________________

First method is elimination method, I’ll demonstrate another method which is by using matrices to find the solutions.

Given:

[tex]\displaystyle \large{\begin{cases} x-y=1 \\ x+3y=9 \end{cases}}[/tex]

Write the system of equations in matrices form:

[tex]\displaystyle \large{\left[\begin{array}{ccc}1&-1\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}1\\9\end{array}\right]}[/tex]

Let:

[tex]\displaystyle \large{A=\left[\begin{array}{ccc}1&-1\\1&3\end{array}\right] }\\\displaystyle \large{X=\left[\begin{array}{ccc}x\\y\end{array}\right] \\\displaystyle \large{B = \left[\begin{array}{ccc}1\\9\end{array}\right] }[/tex]

From [tex]\displaystyle \large{AX=B \to X=A^{-1}B}[/tex] where:

[tex]\displaystyle \large{A^{-1}=\dfrac{1}{\det A} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right] = \dfrac{1}{ad-bc} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right] }[/tex]

Find [tex]\displaystyle \large{\det A}[/tex]:

[tex]\displaystyle \large{\det A = ad-bc = 3+1=4}[/tex]

Therefore:

[tex]\displaystyle \large{A^{-1} = \dfrac{1}{4}\left[\begin{array}{ccc}3&1\\-1&1\end{array}\right]}\\\therefore \displaystyle \large{X = \dfrac{1}{4}\left[\begin{array}{ccc}3&1\\-1&1\end{array}\right] \left[\begin{array}{ccc}1\\9\end{array}\right]}[/tex]

Evaluate the matrices:

[tex]\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}3(1)+1(9)\\-1(1)+1(9)\end{array}\right] }\\\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}3+9\\-1+9\end{array}\right] }\\\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}12\\8\end{array}\right]}\\\displaystyle \large{X= \left[\begin{array}{ccc}3\\2\end{array}\right] }\\\therefore \displaystyle \large{\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}3\\2\end{array}\right]}[/tex]

Therefore, the solution is x = 3 and y = 2

Answer:

This is hard

Step-by-step explanation:

I'm so sorry I can't do it

Answer:

[tex]\frac{69}{20}[/tex]

Step-by-step explanation:

[tex]\frac{3}{7} -\frac{11}{4} +\frac{16}{5} +\frac{18}{7}[/tex]

= [tex]\frac{3}{7} +\frac{18}{7}-\frac{11}{4} +\frac{16}{5}[/tex]

= [tex]\frac{21}{7} -\frac{11}{4} +\frac{16}{5}[/tex] As both denominators have 7 you can add their numerators

=[tex]\frac{21}{7} -(-\frac{9}{20})[/tex]     L.C.M

=[tex]\frac{21}{7} +\frac{9}{20}[/tex]   L.C.M

=[tex]\frac{69}{20}[/tex]

Answer:

  19

Step-by-step explanation:

The triangle inequality tells you the possible values of x are ...

  24 -10 < x < 24 +10

  14 < x < 34

There are 19 integer values of x in this range.

Answer:

Ray.

Step-by-step explanation:

Lines have no endpoints, while rays have 1 endpoint (:

Answer:

n=5

Step-by-step explanation:

So I'm not sure how to write the equation, but i do know that each term has five added from the previous one, hope that help a little bit!

Answer:

Depends on the question or if it specifically says to.

Step-by-step explanation:

For finding the volume of cylinders and spheres use the pi symbol or just say "use 3.14 for pi"

Answer:

its 10

Step-by-step explanation:

The reason its 10 is because it shows more 10 then any number

Answer:

71.98

[tex]d=2\sqrt{ \frac{A}{\pi }} = 2 * \sqrt{\frac{4069.44}{\pi }}[/tex] ≈ 71.98175 rounded to hundred-thousandths

Answer:

x = 5

Step-by-step explanation:

Tangents from a specific point are equal in length.

3x - 7 = 18 - 2x

5x - 7 = 18

5x = 25

x = 5

Answer:

12

Step-by-step explanation:

End points of [tex]\overline{RS}[/tex] are:

[tex]R (4, \:-8)\implies x_1 = 4,\: y_1=-8[/tex]

[tex]S (25, \:-1)\implies x_2 = 25,\: y_2=-1[/tex]

Point T divides [tex]\overline{RS}[/tex] in the ratio 4 : 3

[tex]\implies m = 4,\: n= 3[/tex]

Now, by section formula:

[tex]T=\bigg(\frac{mx_2+nx_1}{m+n},\:\:\frac{my_2+ny_1}{m+n}\bigg)[/tex]

Plugging in the values of [tex]x_1 ,\: y_1, \:x_2,\: y_2\:\&\: m, \: n[/tex] in the above formula, we find:

[tex]T=\bigg(\frac{4(25)+3(4)}{4+3},\:\:\frac{4(-1)+3(-8)}{4+3}\bigg)[/tex]

[tex]\implies T=\bigg(\frac{100+12}{7},\:\:\frac{-4-24}{7}\bigg)[/tex]

[tex]\implies T=\bigg(\frac{112}{7},\:\:\frac{-28}{7}\bigg)[/tex]

[tex]\implies T=(16,\:\:-4)[/tex]

Sum of the coordinates of T = 16 + (-4) = 16 - 4 = 12

Answer:

1.9998 inches = radius

Step-by-step explanation:

V=(4/3)πr³

33.5 = (4/3)πx³

33.5 * 3/4 = (4/3)πx³(3/4)

25.125 / π = (πx³) / π

[tex]\sqrt[3]{7.998}[/tex] = [tex]\sqrt[3]{x^3}[/tex]

1.9998 = x

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Since it's a Trapezoid with its non - parallel sides equal to one another,

[tex]\qquad \sf  \dashrightarrow \:\angle A + \angle P = 180[/tex]

[ By forming co - interior angle pair ]

[tex]\qquad \sf  \dashrightarrow \:\angle A +100 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \:\angle A = 180 - 100[/tex]

[tex]\qquad \sf  \dashrightarrow \:\angle A = 80 [/tex]

Now, similarly,

[tex]\qquad \sf  \dashrightarrow \:\angle A + \angle R = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle R + 80 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle R = 100[/tex]

Similarly,

[tex]\qquad \sf  \dashrightarrow \angle K + \angle R = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \angle K + 100 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \angle K = 80[/tex]

Consecutive angles are supplementary

Opposite angles are equal

Opposite angles are equal again

Step-by-step explanation:

it is a combination of a cone and half a sphere.

the volume of a cone is

ground area × height / 3

the ground area is a circle, so we have

pi×r²×h/3

in our case

pi×(10/2)²×12/3 = pi×5²×4 = pi×25×4 = 100pi

the volume of a sphere is

4/3 × pi×r³

and half a sphere is then

4/3 / 2 × pi×r³ = 4/6 × pi×r³ = 2/3 × pi×r³

in our case

2/3 × pi×5³ =2/3 × pi×125 = 250/3 × pi

together we get

100pi + 250/3 × pi = 300/3 × pi + 250/3 × pi =

= 550/3 × pi = 575.9586532... cm³ ≈ 576 cm³

if we use 3.14 for pi we get

575.6666666... cm³ ≈ 576 cm³

The volume of 3 of shipping containers 267.75 cubic yards.

We need to find the volume of one shipping container and then multiply it by 3 to find the volume of three shipping containers.
Find the volume of one shipping container.
Volume = Base Area × Height
Volume = 25.5 square yards × 3.5 yards
Calculate the volume.
Volume = 89.25 cubic yards
Find the volume of three shipping containers.
Total Volume = Volume × Number of Containers
Total Volume = 89.25 cubic yards × 3
Calculate the total volume.
Total Volume = 267.75 cubic yards.

For similar question on volume.

https://brainly.com/question/12410983

#SPJ11

Hello there!

In order to solve this inequality, we should first use the distributive property:-

3(a-4)≥4(a+5)

3a-12≥4a+20

Now, add 12 to both sides:-

3a≥4a+32

Subtract 4a from both sides:-

3a-4a≥32

-a≥32

Divide both sides by -1:-

a≤-32

The inequality sign changed because we divided both sides by a negative number.

[tex]\mathcal{NOTE:-}[/tex]

I hope everything is clear; however, if you need any explanation or clarification, don't hesitate to let me know, and I will comment or edit my answer. Good luck and have a great rest of your day! :)

Answer:

The first table

Step-by-step explanation:

If you create a fraction x/y, you will see all of the answers reduce down to -1/4. The other tables don't reduce to the same values.

Answer:

  43°

Step-by-step explanation:

Triangle ADM is a right triangle with legs AD=4 cm and DM=√18 cm. The angle at M is the angle of interest. It can be found using the inverse tangent function.

  Tan = Opposite/Adjacent

  tan(∠AMD) = AD/MD = 4/√18

  ∠AMD = arctan(4/√18) ≈ 43.31°

The angle the plane makes is about 43°.

Answer:

the measure of the angle that the plane ABC makes with the base of the prism = 43 degree (to the nearest degree)

Step-by-step explanation:

We notice that the plane ABC and the base of the prism intersect along the line BC

And as the plane (ADM) is perpendicular to the line BC

then the angle between the plane ABC and the base of the prism is the angle AMD

Let θ be the measure of the angle AMD

[tex]\begin{aligned}\tan (\theta) &=\frac{A D}{M D} \\&=\frac{4}{\sqrt{18}}\end{aligned}[/tex]

[tex]\begin{aligned}\Rightarrow \theta &=\tan ^{-1}\left(\frac{4}{\sqrt{18}}\right) \\&=43,31385 \ldots\end{aligned}[/tex]

The line of best fit of the traffic study is a line through a scatterplot of data points which shows the relationship between the points.

Your information is incomplete as the table isn't given. Therefore, an overview will be given.

The least square methods is used by statisticians to arrive at the geometric equation for the line. A straight line will simply result from a simple regression of two or more independent variables.

A regression that has to do with multiple related variables lead to a curved line. The line of best fit is an important output of regression analysis.

A regression that has two independent variables will have a formula with:

y = c + b1x1 + b2x2

where,

c = constant

b1 = first regression coefficient

x1 = first independent variable

b2 = second regression coefficient

x2 = second independent variable.

In conclusion, the line of best fit expresses the relationship in a scatterplot of the data points.

Learn more about line of best fit on:

https://brainly.com/question/21241382

Answer:

[tex]\pi[/tex] is infinite. 3.14 only has three numbers.

Step-by-step explanation:

so [tex]\pi[/tex] multiplied by any number (except 0) will have infinite numbers

Answer:

See below ↓

Step-by-step explanation:

When multiplying a number by 3.14, which is the simplified version of pi, it will give a constant term. But, when multiplying by π, the actual value is equal to 22/7, and it is a non-terminating decimal. Therefore, when you multiply any number with 3.14, it will be slightly lesser than when you multiply with π.

Answer:

A

Step-by-step explanation:

my brain says so?

Answer:

The zeros are -5, -1, 0, 4, 5.

Step-by-step explanation:

x(x2 – 25)(x2 – 3x – 4) = 0

x(x - 5)(x + 5)(x + 1)(x - 4) = 0

so either x or the other 4 factors can be 0 :

x = 0, x - 5 = 0, x + 5 = 0, x + 1 = 0 or x - 4= 0, giving:-

x = 0, 5, -5, -1, 4.

just more and more of these.

⇒ ANSWER :   x = 0, x = 5, x = -5, x = 4 and x = -1

EQUATION GIVEN: g(x) = x(x2 – 25)(x2 – 3x – 4)

1) factorize the equation

g(x)=x(x-5)(x+5)(x²-3x-4)

2) expand the equation

g(x)=x(x-5)(x+5)(x²+x-4x-4)

3) factorize

g(x)=x(x-5)(x+5)(x(x+1)-4(x+1))

4) factor out x+1

g(x)=x(x-5)(x+5)(x-4)(x-1)

5) equate to 0

x(x-5)(x+5)(x-4)(x+1)=0

6) solve for x

x = 0, x = 5, x = -5, x = 4, x = -1

Pain.

Answer:

-8

Step-by-step explanation:

Hey there!

(1/2)(10) - (-12) - 25

= 1/2(10) - (-12) - 25

= 5 - (-12) - 25

= 5 + 12 - 25

= 17 - 25

= -8

Therefore, your answer is: -8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

4250

Step-by-step explanation:

0.13 = 13%

1000×0.13=130
130×25= 3250 + 1000 = 4250

What I did:

You have to turn the percent to a decimal first

Then multiply the decimal by the first investment amount (1000)

then multiply that by the years that you have before retirement
You add that amount plus the 1000 you have started with

q=w/ 3-7

q(3-7)= w

hope this helps :)

Answer:

w = 3q + 21

Step-by-step explanation:

assuming you mean

q = [tex]\frac{w}{3}[/tex] - 7 ( add 7 to both sides )

q + 7 = [tex]\frac{w}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

3(q + 7) = w , that is

w = 3q + 21

Answer:

The median is 8.1

Step-by-step explanation:

You add up all the numbers and divide it by how much numbers there are.

1) Add. 1 + 7+ 16 + 18 + 40 = 81

2) Count. There are 10 numbers.

3) Divide 81/10

4) 8.1

The median is 8.1

Answer:

Pythagorean Theorem used for finding the missing side length for a triangle the formula is a^2 + b^2 = c^2
a= base
b= height
c= the diagonal side a.k.a. hypotenuse

Answer:

u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye

Step-by-step explanation: