a man invested $6000 at 8% per annum simple interest for 5 years.
a).calculate the simple interest.
b).the total amount of money collected at the end of the 5 year period.​

Answer:

x = -2.5
x = 2

Step-by-step explanation:

Hello!

We can remove the denominators by multiplying everything by it.

Solve:

Let's make one side equal to 0.

Solve by factoring, and then the zero product property.

Multiply 2 and -10. You get -20. Think of two number that multiply to -20, and add to 1. If we think about the standard form of a quadratic, [tex]ax^2 + bx + c[/tex], think two numbers that equal "ac" and add up to "b".

Using the zero product property, set each factor to 0 and solve for x.

The two answers are x = -2.5, and x = 2.

Answer:

x = -5/2, 2

Step-by-step explanation:

Given:

[tex]\displaystyle \large{\dfrac{5}{x+3}+\dfrac{4}{x+2} = 2}[/tex]

With restriction that x-values cannot be -3 and -2 else it will turn the expression as in undefined.

First, multiply both sides by (x+3)(x+2) to get rid of the denominator.

[tex]\displaystyle \large{\dfrac{5}{x+3}\cdot (x+2)(x+3)+\dfrac{4}{x+2} \cdot (x+2)(x+3) = 2 \cdot (x+2)(x+3)}\\\\\displaystyle \large{5(x+2)+4(x+3) = 2(x+2)(x+3)}[/tex]

Simplify/Expand in:

[tex]\displaystyle \large{5x+10+4x+12 = 2(x^2+5x+6)}\\\\\displaystyle \large{9x+22=2x^2+10x+12}[/tex]

Arrange the terms or expression in quadratic equation:

[tex]\displaystyle \large{0=2x^2+10x+12-9x-22}\\\\\displaystyle \large{2x^2+x-10=0}[/tex]

Factor the expression:

[tex]\displaystyle \large{(2x+5)(x-2)=0}[/tex]

Solve like linear equation as we get:

[tex]\displaystyle \large{x=-\dfrac{5}{2}, 2}[/tex]

Since both x-values are not exact -2 or -3 - therefore, these values are valid. Hence, x = -5/2, 2

Answer:

multiply the probability of the first event by the second.

Step-by-step explanation:

Use the specific multiplication rule formula. Just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.

Answer:

[tex]\frac{1}{26} * \frac{1}{26} = \frac{1}{676} = .00148.[/tex]

Step-by-step explanation:

Multiply the probability of P by the probability of Q.

In which the probability of P is equal to [tex]\frac{R}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]

In which the probability of Q is equal to [tex]\frac{P}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]

There's a 1 in 676 chance that you'd randomly pick R, put the tile back in, and then pick P in a sack of 26 letters of the latin alphabet.

Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

[tex](\frac{1}{4}) ^{2}[/tex] can also be written as [tex](\frac{1}{4} )(\frac{1}{4} )[/tex]

So the answer is just [tex]\frac{1}{16}[/tex]

By taking a common factor, we will see that the equivalent expression is:

[tex]12*\sqrt[3]{6c}[/tex]

Here we start with the expression:

[tex]5*\sqrt[3]{6c} + 7*\sqrt[3]{6c}[/tex]

Notice that if we define:

[tex]\sqrt[3]{6c} = u[/tex]

We can rewrite our expression as:

[tex]5u + 7u[/tex]

Now we can take the common factor u to write:

[tex](5 + 7)u = 12u[/tex]

Now if we replace u y the cubic root, we will get:

[tex]12*\sqrt[3]{6c}[/tex]

So the correct option is the third one.

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The step of Talia that's incorrect.The step that is incorrect is: C. Step 3

The slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

Thus, we get:

Slope = rise/ run

Calculating the slope using two points on the line, (2, 5) and (1, 3), we have:

Slope (m) = (5 - 3)/(2 - 1)

Slope (m) = (2)/(1)

Slope (m) = 2

This shows that the ratio of the slope calculated by Talia was wrong. The step that is incorrect is: C. Step 3

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Let's consider the information at hand:

         ⇒ has some special property about its side length

             ⇒ look at the diagram I attached

Using the same ratios of side length as seen in the diagram:

  ⇒ we get the equation:

        [tex]\frac{1}{\frac{\sqrt{2} }{2} } =\frac{x}{3\sqrt{2} } \\\frac{\sqrt{2} }{2}*x=3\sqrt{2} \\\frac{x}{2}=3\\ x=3*2\\x=6[/tex]

Thus x = 6.

Answer: x = 6

Hope that helps!

If the volume of the aluminum brick will be 2218.5 cubic cm. Then the approximate density of the aluminum will be 8.9 grams per cubic cm.

Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.

The mass and density relation is given as

Density = mass/volume

A brick of aluminum weighs 19,745 grams and has the following dimensions: length 29 cm, height 15 cm, and width 51 mm.

Then the approximate density of the aluminum will be

The volume of the aluminum brick will be

V = 29 x 15 x 5.1

V = 2218.5 cubic cm

Then the density will be

D = 19,745 / 2218.5

D = 8.900 gram per cubic cm

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Answer: See attached

Step-by-step explanation:

   [] Since the inequality uses greater than (>) and not greater than or equal to (≥), the line will be dashed.

   [] The inequality is greater than (>) so we will shade above the line as values "above" are greater.

Answer:

here is what i got

Step-by-step explanation:

The probability that he would have done at least this well if he had no ESP is 0.99979

To determine the probability, we need to first find the probability of doing well with ESP.

The probability of having 20 correct answers out of 23 coin flips is:

[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]

Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:

[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]

There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.

Therefore, the probability of doing well with ESP is:

[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]

= 0.00021

The probability that he would have at least done well if he had no ESP is:

= 1 - 0.00021

= 0.99979

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Answer: C

Step-by-step explanation:

Complementary angles have measures that add to 180 degrees, so since angle EAD measures 20 degrees, we need an angle that measures 70 degrees. This is angle DAB.

Answer:

b = -8

Step-by-step explanation:

-2b + 9 =25

-9 = -9

-2b = 16

/-2 /-2

b = -8

Answer:

see explanation

Step-by-step explanation:

since the triangles are congruent, then corresponding angles are congruent.

∠ B = ∠ F

∠ FCE ≅ ∠ BDA

∠ EFC ≅ ∠ ABD

∠ FEC ≅ ∠ BAD

note that the order of letters in Δ ABD follows the same order as those in Δ BDA

Answer:

hope you can understand

[tex]\\ \rm\Rrightarrow \dfrac{1-cos^2\theta}{cos^2\theta}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{sin^2\theta}{cos^2\theta}[/tex]

[tex]\\ \rm\Rrightarrow tan^2\theta[/tex]

Option C

Answer:

Trigonometric identities

[tex]\large \begin{aligned}\cos^2 \theta + \sin^2 \theta & = 1\\\implies \quad \quad \sin^2 \theta & = 1 - \cos^2 \theta\\\\\tan \theta=\dfrac{\sin \theta}{\cos \theta} \end{aligned}[/tex]

Therefore, using the identities, the given expression can be simplified as follows:

[tex]\large\begin{aligned}\implies \dfrac{1- \cos^2 \theta}{\cos^2 \theta} & = \dfrac{\sin^2 \theta}{\cos^2 \theta}\\\\& = \tan^2 \theta\end{aligned}[/tex]

Answer:

[tex] \large {\boxed{ \sf{y = 2x + 5}}}[/tex]

Step-by-step explanation:

Suppose the slope of the line is k.

So,

[tex] \large {\bold {k = \frac{7 - ( - 1)}{1 - (3)} = \frac{7 + 1}{1 + 3} = \frac{8}{4} = 2 }}\\ [/tex]

So the line:

[tex] \large \bold{ \frac{y - 7}{x - 1} = k = 2 } \\ [/tex]

[tex] \: [/tex]

So,

[tex] \large \bold{y - 7 = 2(x - 1)}[/tex]

[tex]\large \bold{y - 7 = 2x - 2}[/tex]

[tex]\large \bold{y = 2x - 2 + 7}[/tex]

[tex]\large \bold{y = 2x + 5}[/tex]

[tex]{\rule{200pt}{4pt}}[/tex]

[tex] \large \bold{-N} \frak{unx-}[/tex]

The pair of rational numbers with their sum are matched.

The numbers in the form of p/q is called the rational number.

1. -2/a²b +2/ab² = ( -2ab² +2a²b) / a³b³

                          = 2(a-b)/a²b²

2. 1/2ab -1/4a²b² =( 4a²b² -2ab) / 8a³b³

                            = 2ab -1 /4a²b²

3. 2/a²b³ -2/ab = (2ab -2a²b³) / a³b⁴

                         = 2( 1- ab²) /a²b³

4. 1/ab³ -1/a²b = a²b - ab³ / a³b⁴

                       = (a - b²) / a²b³

Thus, all the rational numbers are matched with their sum.

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Answer:

10

Step-by-step explanation:

give brainliest please!

hope this helps :)

so these two angles add up to 180 degrees

7x -3 + 12x -7 = 180

7x+12x=180+7+3

19x=190

x=10

to check if this is true we can input 10 for x in each side.

7(10)-3 = 67

12(10)-7 = 113

113+67 = 180

Answer:

I don't know it

Step-by-step explanation:

try with an textbook you have

Answer:

C) [tex]3x^2-14x-5[/tex]

Step-by-step explanation:

[tex](5x^2-5x+1)-(2x^2+9x-6)\\\\5x^2-5x+1-2x^2-9x-6\\\\3x^2-14x-5[/tex]

The subtraction of the given expressions gives D. 3x² - 14x + 7.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given are two expressions.

5x² - 5x + 1 and 2x² + 9x - 6

We have to find the difference of the given expression.

(5x² - 5x + 1) - (2x² + 9x - 6)

= 5x² - 5x + 1 - 2x² - 9x + 6

Operating the like terms together,

= (5x² - 2x²) + (-5x - 9x) + (1 + 6)

= 3x² - 14x + 7

Hence the correct option is D.

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Answer: C i think.

Step-by-step explanation:

8 different trees multipled by s equal to 6 meters tall in total.

The purpose of using slang is mostly for social purposes such as:

Slangs is often used in the Sharing and keeping  of a constantly altering vocabulary aids.

It is used to show group solidarity and it is often used to include or exclude members.

The common sports slangs are:

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Answer:

cost of a doughnut is $0.75

cost of a cookie is $0.60

Step-by-step explanation:

As you wrote:
Let x = doughnuts

Let y = cookies

The first sentence of the problem (alexandra) can be written as:

[tex]2x + 3y = 3.30[/tex]

The second sentence of the equation (briana) can be written as:

[tex]5x + 2y = 4.95[/tex]

We must now solve for either [tex]x[/tex] or [tex]y[/tex] in this system of equations.

I will solve for [tex]x[/tex] in this example.

First we need to multiply the first equation by [tex]2[/tex] and the second equation by [tex]3[/tex]. This is so both equations have [tex]6y[/tex] as a term.

Equation 1:

[tex]2(2x + 3y) = (3.30)2\\4x + 6y = 6.60[/tex]

Equation 2:

[tex]3(5x + 2y) = (4.95)3\\15x+6y=14.85[/tex]

Now that both equations have [tex]6y[/tex] as a term, we can subtract Equation 1 from Equation 2. This will remove y from the equation and allow us to solve for x.

[tex](15x+6y) - (4x+6y) = (14.85) - (6.60)\\11x = 8.25\\\boxed{x = 0.75}[/tex]

We now know the cost of a doughnut is $0.75. Now we can solve for the cost of a cookie through substitution.

[tex]2x + 3y = 3.30\\2(0.75) + 3y = 3.30\\1.50 + 3y = 3.30\\3y = 1.80\\\boxed{y = 0.6}[/tex]

Now we know the cost of a cookie is $0.60.

These are the answers,

- Kan Academy Advance

The number of 1/3 cm-cubes that would fill the rectangular prism is approximately 20 cubes.

Volume = a³, where a is the side length.

Volume = lwh

Given the following:

Volume of the rectangular prism = (1/2)(1)(3/2)

Volume of the rectangular prism = (1/2)(1)(3/2) = 0.75 cm³

Volume of the cube = (⅓)³ = 0.037 cm³

Number of cubes that would fill the prism = 0.75/0.037 ≈ 20 cubes.

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The least expensive is the Stock Transportation charges $500 to cover the cost for the drivers plus $6 per student.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.

For example, if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.

If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Let the number of students the bus carries be x.

First Student charges $350 per bus. They will need 7 buses.

Therefore, the cost of the school hiring the bus is:

C = 7*350

C = 2450

The charge of per student

= 2450 / 260

= $ 9.4

Stock Transportation charges $500 to cover the cost for the drivers plus $6 per student.

C = 500 + 6*260

C = 500 + 1560

C = 2060

Switzer-Carty costs $7 for every student that they bus.

Therefore, the cost of the school hiring the bus is:

C = 7 * x

C = 7x

To bus 260 students, then, the cost will be:

C = 7 * 260

C = $1820

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[tex]\text{Given that,}\\\\~~~~~~~2x^4 +2y^4 +2z^4 = 144\\\\\implies 2(x^4+y^4 +z^4) = 144\\\\\implies x^4 +y^4 +z^4 = \dfrac{144}{2}\\\\\implies x^4 +y^4 +z^4 = 72\\\\\text{Mean} = \dfrac{x^4+y^4+z^4}{3}\\\\~~~~~~~~=\dfrac{72}{3}\\\\~~~~~~~~=24[/tex]

A straight line is represented by a linear equation given below.

The points are given as (1, 2) and (4, 4).

Start by calculating the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So, we have

[tex]m=\frac{4-2}{4-1} \\m=\frac{2}{3}[/tex]

The equation in slope-intercept form is then calculated as:

[tex]y=m(x-x_1)+y_1[/tex]

So, we have:

[tex]y=\frac{2}{3}(x-1)+2\\ \\y=\frac{2}{3}(x-4)+4\\[/tex]

Expand

[tex]y=\frac{2}{3}(x-1)+2\\ y=\frac{2}{3} x-\frac{2}{3}+2[/tex]

Take LCM

[tex]y=2/3x+4/3[/tex]

Multiply through by 3

3y=2x+4

So, the possible equations are:

.[tex]3y=2x+4\\y=\frac{2}{3}x+\frac{4}{3} \\y=\frac{2}{3}(x-1)+2\\y=\frac{2}{3}(x-4)+{4}[/tex]

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Answer:

B

C

E

Step-by-step explanation:

other dudes are  wrong

Inequalities help us to compare two unequal expressions. (-6, 3) is not the solution to the system of inequalities.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The graph of y ≥ −3x + 3 will be a solid line with the equation y=−3x + 3, this solid line signifies that the value on this line is also included in the solution. Since the symbol is '≥' therefore the area above the line will have the solutions.

The graph of y<(3/2)x -6 will be a dashed line with the equation y=(3/2)x - 6, this dashed line signifies that there is no solution on the line. since the inequality symbol is '<' therefore, the area under the dashed line will have all the solutions.

The area where both shaded areas meet is the area that will have all the possible solutions.

PartB:

y ≥ −3x + 3

3 ≥ -3(-6) + 3

3 ≥ 18 + 3

Since the above inequality is not satisfied, (-6, 3) is not the solution to the system of inequalities.

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Answer: C. y - 1 = 1/2(x-5)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = 1/2

y1 = 1

x1 = 5

y - 1 = 1/2(x-5)