in 2009 a total of R36 000 was invested in two accounts. One account earned 7% annual interest and the other earned 9% .The total annual earned was R2 920 .How much was invested in each accounts?​

Answer:

length=0.65 mi

length in yr= 0.65x1760=1144

The length of the jogging track is 0.65 miles.

To convert the length of the jogging track from yards (yd) to miles (mi), use the ratio between yards and miles.

1 mile = 1760 yards

Now, set up the equation to convert the length:

Length in miles (mi) = Length in yards (yd) / Conversion ratio

Length in miles (mi) = 1144 yd / 1760 yd/mi

Now, perform the calculation:

Length in miles (mi) = 1144 / 1760 ≈ 0.65 miles (rounded to the nearest hundredth)

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Answer:

y = 1.25r

Step-by-step explanation:

1.25 x r(the pounds brought) = y(the money spent)

The inverse function value in degrees will be 45°. Option C is correct.

Assuming function 'f' is a one-to-one and onto function which is a need for inverses to exist. The inverse of the considered function is. f⁻¹(x).

The given function is;

f(x)=sin⁻¹(1/2)

The given function is arranged is;

x=sin⁻¹(1/2)

The given function in terms of  sin;

sinx=1/2

Putting the values in terms of sin we get;

sinx=sin30°

x=30°

The inverse function value in degrees will be 45°.

Hence,option C is correct.

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Answer:

no 2³ = 8

Step-by-step explanation:

2³ = 2 times 2 times 2 which = 8

The solution of the function [tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex] is - cos t - ¹/₄cos 2t + c.

An indefinite integral is a function that practices the antiderivative of another function.

It can be visually represented as an integral symbol, a function, and then a dx at the end.

The given function is;

[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex]

Multiply by sint in the function and simplify;

[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt[/tex]

Use trigonometric formulas for double angles:

[tex]\rm 2sintcost =sin2t\\\\sin t cost =\dfrac{1}{2} sin2t[/tex]

Substitute the values in the function

[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt}\\\\ \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\[/tex]

And now we integrate this trigonometric form.

[tex]\rm \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\ \int{sin(t) dt } +\dfrac{1}{2}\int{sin(2t)\, dt}\\\\-cost -\dfrac{1}{2} \times \dfrac{1 \times -cos2t}{2}\\\\-cost -\dfrac{{1 \times -cos2t}}{4}+c[/tex]

Hence, the solution of the given function is - cos t - ¹/₄cos 2t + c.

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Answer:

10 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (8, 5 ) and (x₂, y₂ ) = (- 2, 5 )

d = [tex]\sqrt{(-2-8)^2+(5-5)^2}[/tex]

   = [tex]\sqrt{(-10)^2+0^2}[/tex]

   = [tex]\sqrt{100}[/tex]

   = 10

Answer:

[tex]1.47 \times {10}^{4} [/tex]

Step-by-step explanation:

Answer:

x = -2, -8.

Step-by-step explanation:

x =[(-b +/- √(b^2 - 4ac)] / 2a

x^2 + 10x + 16 = 0

Here a = 1, b = 10 and c = 16, so substituting in the formula:

x = [-10 +/- √(10^2 - 4*1*16)] / 2

= (-10 +/- √36)/2

= (-10 +/- 6)/2

= -4/2, -16/2

= -2, -8.

Answer:

x = - 8 , x = - 2

Step-by-step explanation:

x² + 10x + 16 = 0

with a = 1, b = 10 , c = 16

then using the given quadratic formula

x = [tex]\frac{-10+/-\sqrt{10^2-(4(1)(16)} }{2}[/tex]

  = [tex]\frac{-10+/-\sqrt{100-64} }{2}[/tex]

  = [tex]\frac{-10+/-\sqrt{36} }{2}[/tex]

  = [tex]\frac{-10+/- 6}{2}[/tex]

then

x = [tex]\frac{-10-6}{2}[/tex] = [tex]\frac{-16}{2}[/tex] = - 8

x = [tex]\frac{-10+6}{2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

Answer:

x = 50° y = 130°

Step-by-step explanation:

x and 50° are vertically opposite angles and are congruent , then

x = 50°

y and 50° are adjacent angles and sum to 180° , then

y + 50° = 180° ( subtract 50° from both sides )

y = 130°

Step-by-step explanation:

15÷3=5

There are 5 equal groups of 3

8÷4=2

There are 4 equal groups of 2

18÷6=2

There are 3 equal groups of 3

45÷5=9

There are 9 equal groups of 5.

The quadratic function that models the data given in the table is 203.8x² - 26.6x + 8.6

A quadratic function is an equation that usually has a single variable and it is raised to the power of 2.

A quadratic function has the form : ax² + bx + c = 0

Where: a, b,c are known numbers and x is unknown

Given the quadratic function: 185x²+ 1.

Given the quadratic function: 203.8x² - 26.6x + 8.6

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The perimeter of the quadrilateral is the sum of the side lenths, and the perimeter is 72 units

The given parameters are:

AP = 10

EO = 12

The perimeter of the quadrilateral is calculated using:

Perimeter = 2 * (EO + 2AP) + 4

So, we have

Perimeter = 2 * (10 + 2 * 12) + 4

Evaluate

Perimeter = 72

Hence, the perimeter of the quadrilateral is 72 units

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Answer: MQ=16, QL=32

Step-by-step explanation:

The centroid splits the median in a 2:1 ratio.

The measure of MQ and QL are 16 and 32 respectively.

Centroid is the point on the median which divides it in the ratio 2:1.

The ratio of lengths QL and MQ will be 2:1.

[tex]\frac{QL}{MQ}=\frac{2}{1}\\QL=2MQ[/tex]

It is known that ML is the sum of MQ and QL.

MQ+QL=ML

Substitute QL=2MQ and ML=48 into the obtained equation.

MQ+2MQ=48

3MQ=48

MQ=16

Substitute MQ=16 into QL=2MQ

QL=2(16)

=32

Thus, the lengths are MQ=16 and QL=32.

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1) Diagonals of a rectangle bisect each other, so AW=13.

2) Since diagonals of a rectangle are congruent, AC=BD. Then, since diagonals of a rectangle bisect each other, DW=13.

3) Diagonals of a rectangle are congruent, so BD=26.

4) Opposite sides of a rectangle are congruent, so AD=10.

5) Using the Pythagorean theorem, BA=24.

Answer:

It's 44 in²

Remember the diagonal formula, whereas there is p and q for the diagonals.

[tex]A = \frac{pq}{2} = \frac{11*8}{2} = 44~in.[/tex]

Answer:

Area of rhombus  = 44 square inches

Step-by-step explanation:

[tex]\sf \boxed{Area \ of \ rhombus = \dfrac{d_1*d_2}{2}}[/tex]

[tex]\sf \text{Here, $d_1$ and $d_2$ are the diagonals}[/tex]

                             [tex]\sf = \dfrac{11 *8}{2}\\\\ = 11*4\\\\ = 44 \ in^{2}[/tex]

The different mathematical operations that have as a result 54 are 9x6,  8x9 - 18, 5x5 + 29, and 27x2.

This refers to calculating values using addition, multiplication, division, etc.

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Answer:

D. 159

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

For a circle:

   Area = pi r^2   =   3.14 * 1.6^2 = 8.04 units^2

   Circumf = pi * d   = pi * 2r = 3.14 * (2 * 1.6) = 10.05 units

Answer:

There are now 6.5 ounces in the new bag.

Step-by-step explanation:

To solve this question, take 30% of 5 and add it to the original amount of 5

30% = 0.30

5 * 0.30 = 1.5

5 + 1.5 = 6.5 ounces of candy.

Hope this helps!

Answer: 5/24

Step-by-step explanation:

7/8 = 21/24      2/3= 16/24

21/24 - 16/24 = 5/24

Option B is correct after applying the property of integer exponent and simplification.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have:

[tex]=\rm (x.x^{-3}.y^{\dfrac{1}{3}})^2[/tex]

[tex]=\rm (x^{-2}.y^{\dfrac{1}{3}})^2\\\\=\rm (x^{-4}.y^{\dfrac{2}{3}})\\\\=\rm \dfrac{y^{\dfrac{2}{3}}}{x^{4}}\\\\[/tex]

Thus, option B is correct after applying the property of integer exponent and simplification.

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Answer:

1.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

That means the chance of getting blue = 12/20

12/20 = 6/10

6/10 = 3/5

also, 3/5 = 60%, or .60