A man borrows $200 000 to buy a sports car. He is charged a simple interest of
2.88% per annum. If the loan is for 7 years, find the
(a) interest payable
(b) amount of each repayment if the total sum is to repaid in 84 equal
installments.

This is a problem using the Pythagorean theorem.

The square of the length required is 122 + 122 + 302 = 1188

The length is the square root of this number; I will leave it to you to extract the square root.

Answer:

34.47

Step-by-step explanation:

Answer: 1 U.S.dollar  = 0.85 euro.

1 euro = 1.18 dollars.

Step-by-step explanation:

The given equation: [tex]E=\dfrac{17}{20}D[/tex]

, where 'E' is the amount of euros that has the same value as 'D' U.S. Dollars.

At D= 1,

[tex]E=\dfrac{17}{20}=0.85\text{ euro}[/tex]

i.e. 1 U.S.dollar  = 0.85 euro.

At E= 1 , we have

[tex]1=\dfrac{17}{20}D\\\\\Rightarrow\ D= 20/17\approx1.18\text{ dollars}[/tex]

Hence, 1 euro = 1.18 dollars.

4(1-3x) + 7x -8

Use distributive property:

4 -12x + 7x -8

Now combine like terms:

-5x -4

Answer:

[tex]-5x-4[/tex]

Step-by-step explanation:

With the expression [tex]4(1-3x) + 7x - 8[/tex], we can simplify it down by applying the distributive property, then combining like terms.

[tex]4(1-3x)+7x-8\\\\4-12x+7x-8\\\\4-5x-8\\\\-5x-4[/tex]

Hope this helped!

Answer:

Assuming you mean "American History V World History"

American History tends to focus on the history of the United States, beginning largely with the colonial era and tracking forwards towards the present. It's largely a national history. World History, on the other hand, is far more encompassing, both geographically as well as temporally.

Assuming you mean "Global History V World History"

World history encompasses a history that is not necessarily completely interconnected through globalization, while global history examines this specific history of inter-connectivity. World History examines the individual histories of different locations around the world, whereas Global History examines how those locations are connected.

Answer:

World history encompasses a history that is not necessarily completely interconnected through globalization, while global history examines this specific history of interconnectivity. ... Furthermore, the fluid nature of what world and global histories mean ensures a number of disagreements with these definitions.

Answer:

The correct option is;

45°

Step-by-step explanation:

By angle sum theorem, we have that the sum of angles in a triangle = 180°

Therefore, we have;

When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;

The third angle + 60° + 75° = 180°

Which gives;

The third angle  = 180°- 60° - 75° = 180°- 135° = 45°

The measurement of the third angle by the angle sum theorem will be 45°

The correct option is ∠third angle = 45°.

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]

[tex] \mathrm{dividing \: a \: negative \: and \: a \: positive \: equals \: a \: negative \:. \: ( - ) \div ( + ) = ( - )}[/tex]

[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]

[tex] \mathrm{dividing \: is \: equivalent \: to \: multiplying \: with \: the \: reciprocal}[/tex]

[tex] \mathrm{ - \frac{4}{5} \times \frac{1}{2} }[/tex]

[tex] \mathrm{reduce \: the \: numbers \: with \: G.C.F \: 2}[/tex]

[tex] \mathrm{ - \frac{2}{5} }[/tex]

Hope I helped!

Best regards!

The quotient of  -4 /5 divide 2 would be equal to -2/5 in simplified form.

Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.

We have been given that  -4 /5 divide 2

Thus, we have to divide the terms as;

-4 /5   ÷ 2

Therefore,  -4 /5 x 1/ 2

-2/5

Hence, the quotient of  -4 /5 divide 2 would be equal to -2/5 in simplified form.

Learn more about the quotient;

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Answer:

2.79 * 10^4

Step-by-step explanation:

6.4 x 10^3+ 1.4 x 10^4+ 7.5 x 10^3

The exponents need to be the same

6.4 x 10^3+ 14 x 10^3+ 7.5 x 10^3

Add the numbers

6.4 + 14+ 7.5 =27.9

Multiply by the exponent

27.9 * 10 ^3

But this is not in scientific notation

Move the decimal one place to the left and add one to the exponent

2.79 * 10^4

Answer:

Step-by-step explanation:

Answer:

Sequence a) Pattern: (-2) -9, -11, -13, -15, -17

Sequence b) Pattern: (-5) -15, -20, -25, -30, -35

Sequence c) Pattern: (-6) -13, -19, -25, -31, -37

Hope this helps!

Hi there! Hopefully this helps!

-------------------------------------------------------------------------------------------------------------

A (Subtracting by 2): -9, -11, -13, -15, -17.

B(Subtracting by 5): -15, -20, 25, -30, -35

C(Subtracting by 6): -13, -19, -25, -31, -37

Answer:

The number of seedlings the three boys planted together is 560 seedlings

Step-by-step explanation:

The possible information in the question are;

Percentage of the seedlings planted by Ali = 40%

Percentage of the seedling planted by Ben = 45%

The percentage of the seedling planted by Cliff = The rest of the seedling

The number of seedling planted by Cliff = 84 siblings

Therefore, the percentage of the seedling planted by Cliff = 100% - 45% - 40% = 15%

Given that Cliff planted 15% of the seedlings, we have;

15% of seedlings Cliff planted = 84

Let X = the total number of seedlings

15/100 × X = 0.15×X = 84

X = 84/0.15 = 560

The total number of seedlings = The number of seedlings the three boys planted together = 560 seedlings.

Answer:

8

Step-by-step explanation:

If f and g are inverse functions , they undo each other

f(g(8))= 8 when  f and g are inverses

Answer:

8

Step-by-step explanation:

I have no further information so this is the only answer.

Answer:

[tex]slope=\frac{1}{2}[/tex]

Step-by-step explanation:

Use the following equation:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change of the x-axis, otherwise known as the slope.

Insert the values:

[tex](1_{x1},2_{y1})\\(5_{x2},4_{y2})[/tex]

[tex]\frac{4-2}{5-1}=\frac{2}{4} =\frac{1}{2}[/tex]

The slope is [tex]\frac{1}{2}[/tex].

:Done

Answer:

1/2

Step-by-step explanation:

The formula for slope is: y1-y2/x1-x2

The points given are: (x-coordinate, y-coordinate)

In the formula:

y1 is the y-coordinate of the first point

y2 is the y-coordinate of the second point

x1 is the x-coordinate of the first point

x2 is the x-coordinate of the second point

This said, we can plug our points in.

2-4/1-5

Subtract.

-2/-4

Simplify.

-1/-2

The negatives will cancel each other out.

1/2

The slope of the line that cuts through the points (1,2) and (5,4) is 1/2.

Answer:

f(x) = 4x² + 48x + 149

Step-by-step explanation:

f(x) = 4(x + 6)² + 5

The above expression can be written as: f(x) = ax² + bx + c, by doing the following:

1. Expand (x + 6)²

(x + 6)² = (x + 6)(x + 6)

(x + 6)(x + 6)

x(x + 6) + 6(x +6)

x² + 6x + 6x + 36

x² + 12x + 36

(x + 6)² = x² + 12x + 36

2. Substitute x² + 12x + 36 for (x + 6)² in

f(x) = 4(x + 6)² + 5

This is illustrated below:

f(x) = 4(x + 6)² + 5

(x + 6)² = x² + 12x + 36

f(x) = 4(x² + 12x + 36) + 5

Clear bracket

f(x) = 4x² + 48x + 144 + 5

f(x) = 4x² + 48x + 149

Therefore, the standard of the function:

f(x) = 4(x + 6)² + 5

is

f(x) = 4x² + 48x + 149

Answer:

5.95

Step-by-step explanation:

that is because 96 is rounded too 100

so its 5.9500 = 5.95

Answer:

5.950

Step-by-step explanation:

5.9496

ones . tenths  hundredths  thousandths  ten thousandths

5       .  9              4                     9                   6

We are rounding to the thousandths place

so we look at the ten thousandths place

6 > 5 so we round up the the thousandths place

9 will go up so that forces the hundreds place up

4 becomes 5 in the hundreds place

5.950

Answer:

D + E = F + H

Step-by-step explanation:

We have to identify the two pairs from the give table which have the same result.

These pairs show the relation as A + B = C + D

We take a pair of expressions given in options (D) and (E)

By adding them,

D + E = (-4 + 9i) + (6 - 6i)

         = 2 + 3i

Similarly we add the expressions given in options (F) and (H),

F + H = (-9 + 15i) + (11 - 12i)

         = 2 + 3i

Therefore, D + E = F + H will be the answer.

Answer:

18.18 min

Step-by-step explanation:

The complete question is

On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?

The initial temperature of the engine [tex]T_{1}[/tex] = -18 F

rate of increase in temperature r = 5.4 F/min

Final temperature [tex]T_{2}[/tex]  = 80 F

Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F

time taken to reach this 80 F will be = ΔT/r

where ΔT is the difference in temperature

r is the rate of change of temperature

time taken = 98/5.4 = 18.18 min

Answer:

Area of the triangle = 98.1 km²

Step-by-step explanation:

In the given triangle WXV,

m∠W + m∠X + m∠V = 180°

m∠W + 119° + 34° = 180°

m∠W = 180° - 153°

m∠W = 27°

By applying Sine rule in the given triangle,

[tex]\frac{\text{SInW}}{\text{XV}}=\frac{\text{SinX}}{\text{WV}}[/tex]

[tex]\frac{\text{SIn27}}{\text{XV}}=\frac{\text{Sin119}}{26}[/tex]

[tex]XV=\frac{26\times (\text{Sin27})}{\text{Sin119}}[/tex]

XV = 13.496 km

Area of the ΔWXV = [tex]\frac{1}{2}(\text{WV})(\text{XV})(\text{SinV})[/tex]

                               = [tex]\frac{1}{2}(26)(13.496)(0.55919)[/tex]

                               = 98.109

                               ≈ 98.1 km²

Answer:

The equation would be a quadratic trinomial

Step-by-step explanation:

Step 1: Expand the equation to remove the brackets

0 = 8x² + 3x - 12x² + 1

Step 2: Collect like terms

0 = -4x² + 3x + 1

Step 3: Count number of terms

0 = -4x² + 3x + 1

1 2 3

Therefore there are 3 terms and this is a quadratic equation making the answer B, a quadratic trinomial

Answer:

3 1/6 cups of flour.

Step-by-step explanation

[tex]_5C_3\cdot _4C_2=\dfrac{5!}{3!2!}\cdot\dfrac{4!}{2!2!}=\dfrac{4\cdot5}{2}\cdot\dfrac{3\cdot4}{2}=2\cdot5\cdot3\cdot2=60[/tex]

Answer:

[tex]\large \boxed{\mathrm{A. \ 60}}[/tex]

Step-by-step explanation:

[tex]\displaystyle nC_r=\frac{n!}{r!(n-r)!}[/tex]

[tex]5C_3 \times 4C_2[/tex]

[tex]\displaystyle \frac{5!}{3!(5-3)!} \times \frac{4!}{2!(4-2)!}=10 \times 6 = 60[/tex]

Answer:

Step-by-step explanation:

a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...

  m = -1/(5/6) = -6/5

Then the point-slope form of the desired line through (-3, 6) can be written as ...

  y = m(x -h) +k . . . . . line with slope m through (h, k)

  y = (-6/5)(x +3) +6

  y = -6/5x +12/5 . . . equation of line B

__

b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.

When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...

  d = |ax +by +c|/√(a² +b²)

The equation of line A can be written in general form as ...

  y = 5/6x -5/2

  6y = 5x -15

  5x -6y -15 = 0

Then the distance from P to the line is ...

  d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61

The length of segment PX is (66√61)/61.

__

c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...

  y = 5/6x -5/2

  y = -6/5x +12/5

Equating y-values gives ...

  5/6x -5/2 = -6/5x +12/5

Adding 6/5x +5/2 gives ...

  x(5/6+6/5) = 12/5 +5/2

  x(61/30) = 49/10

  x = (49/10)(30/61) = 147/61

  y = 5/6(147/61) -5/2 = -30/61

Then the point of intersection of the lines is X = (147/61, -30/61).

So, the midpoint of PX is ...

  M = (P +X)/2

  M = ((-3, 6) +(147/61, -30/61))/2

  M = (-18/61, 168/61)

Answer:

-20

Step-by-step explanation:

First thing you do is set up your equation:

y-17= -37

+17   +17        Next you add 17 to both sides

-------------        Follow your integer rules

y= -20

We can check this by putting it back into the solution

-20-17= -37  Integer Rules

                     You use KCC aka Keep Change Change

= -20+ -17= -37

Answer:

14

Step-by-step explanation:

Answer:

The answer is D. 5

Step-by-step explanation:

14-(-3)^2=

14-9=5

The value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.

We have the following function of [tex]a[/tex] -

f(a) = 14 - [tex]a^{2}[/tex]

We have to determine the value of this function at a = -3.

The value of f(x) = 2x - 3  at x = 3 can be calculated as follows -

f(3) = 2 x 3 - 3 = 6 - 3 = 3

According to the question -

f(a) = 14 - [tex]a^{2}[/tex]

Now, the value of the function f(a) can be calculated as follows -

f(- 3) = 14 - [tex](-3)^{2}[/tex]

f(- 3) = 14 - 9

f(- 3) = 5

Hence, the value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.

To solve more questions on evaluating expressions, visit the link below -

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Answer:

x = 6

Step-by-step explanation:

x + 4 = 10

x = 10 - 4

x = 6

hope it helps

Answer:

E. -2, 4

Step-by-step explanation:

If the zeroes of a function are given as [tex]\alpha, \beta[/tex], then the function can be written as:

[tex](x-\alpha)(x-\beta) = 0[/tex]

Here, we are given that zeros of [tex]f(x)[/tex] are x=-1 and x=2.

As per above, we can write the function [tex]f(x)[/tex] as:

[tex](x- (-1))(x-2) = 0\\\Rightarrow (x+1)(x-2)=0[/tex]

So, [tex]f(x) =(x+1) (x-2)[/tex]

To find:

Zeroes of [tex]f(\frac{x}2)[/tex].

Solution:

We have found that [tex]f(x) =(x+1) (x-2)[/tex]

Replacing [tex]x[/tex] with [tex]\frac{x}2[/tex]:

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

Now, Let us put it equal to 0 to find the zeroes.

[tex]f(\frac{x}2) =(\frac{x}2+1) (\frac{x}2-2) = 0\\\Rightarrow (\frac{x}2+1) = 0 \ OR\ (\frac{x}2-2) =0\\\Rightarrow \frac{x}{2} = -1\ OR\ \frac{x}{2}=2\\\Rightarrow \bold{x =-2, 4}[/tex]

So, the zeroes are -2, 4.

Answer:

C

Step-by-step explanation:

Definitely not a! To square a number you multiply it by itself. for example, if you were squaring 3, you would do 3x3.

Not b either! You will have to take the SQUARE ROOT of the number!

C is the right answer, as I said for a.

D is wrong! The perfect square 49 has a sqrt (square root) of 7. That is NOT even, so d cannot be true.

C is the only true statement. Also, if this is right, can I get branliest answer? Thx :)

Answer:

£13496.80

Step-by-step explanation:

We can ignore the £ sign for now, that is just units.

If we decrease a number by 4.5%, we will have to find [tex]100-4.5=95.5[/tex]% of 14132.77.

We can easily do this by setting up a proportion.

[tex]\frac{x}{14132.77} = \frac{95.5}{100}[/tex]

Multiply 14132.77 by 95.5:

[tex]14132.77\cdot95.5=1349679.535[/tex]

Divide by 100:

[tex]1349679.535\div100=13496.79535[/tex]

Rounding this to two decimal places, it simplifies to 13496.80.

Hope this helped!

Answer:

15.6

Step-by-step explanation:

We can take this equilateral triangle and split it in half to form a 30-60-90 triangle. This will have base of 3, and height of 3[tex]\sqrt{3}[/tex]. The area of this is

1/2 ( 3 )( 3[tex]\sqrt{3}[/tex] ), but the 1/2 cancels since we have 2 halves of the triangle, and so the area is 9.

[tex]\sqrt{3}[/tex] is approx. 1.732, so multiplying this by 9, our answer is 15.6

Answer:

15.6 inches squared.

Step-by-step explanation:

According to the diagram below, the formula for the area of an equilateral triangle is the square root of 3 times the side length squared divided by 4.

The side length is 6. So, the area of the triangle is...

[tex]\frac{\sqrt{3} * 6^2}{4}[/tex]

= [tex]\frac{6^2 * \sqrt{3}}{4}[/tex]

= [tex]\frac{36\sqrt{3}}{4}[/tex]

= [tex]9\sqrt{3}[/tex]

= 9 * 1.732050808

= 15.58845727, which is about 15.6 inches squared.

Hope this helps!

dac=90-(30+45)

=90-75

=15

hope it helps

It is complementary

Answer:

it is complementary angle.

15degrees

Step-by-step explanation:

complementary angle is when the sum of angles is equal to 90degrees.

45+30+<DAC=90

75+<DAC=90

<DAC=90-75

<DAC=15 degrees.