Write the expression as a number in scientific notation. quantity 8 times 10 squared end quantity times quantity 3.2 times 10 to the fifth power end quantity all divided by quantity 4 times 10 cubed 7.2 x 107 7.2 x 104 6.4 x 107 6.4 x 104

Answer:

Step-by-step explanation:

The principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

Given that, balance after 3 months = 22,275 and balance after 12 months = 18,900.

Average payment rate means, for any date of determination, the sum of the monthly payment rates for the prior three monthly periods divided by three.

Now, the difference of payment = 22,275 - 18,900

= $3,375

The difference of time = 12 - 3 = 9 months

So, the payment per month = 3,375 / 9

= $375 per month.

Now, 375 x 12 = $4,500

Principal amount = 4,500 + 18,900

= 23,400

Rate = 375 / 23400 × 100

= 0.016 × 100 = 1.60%

Therefore, the principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

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Answer:

the answer is 2 upon 10 ndnznnznznzjzjzj

The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth.

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

The distance between two points (x₁, y₁) and (x₂, y₂)  is given by ;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

So,

Distance between X(5,4) and Y(2,1)

[tex]d = \sqrt {\left( {5 - 2 } \right)^2 + \left( {4 - 1 } \right)^2 }[/tex]

d = √18 = 4.242640687

Roud to nearest tenth ⇒ 4.24 units.

Hence "The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth".

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The value of x if D bisects A and B is 6

The given parameters are

D bisects A and B.

Length AD = 2x - 2

Length DB = x + 4

This means that

AD =DB

So, we have

2x - 2= x + 4

Evaluate the like terms

x = 6

Hence, the value of x if D bisects A and B is 6

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Answer: number 1. 4 number2. 7

Step-by-step explanation:

I hope this helps!

The price of a rake and a shovel is $22 and $25 respectively.

Let's assume the price of a rake is x and the cost of a shovel is y.

Now, Theresa purchased 10 rakes and 15 shovels for $595.

10x + 15y = $595                                                                      -------------------(1)

Taking 5 common out from each side of the equation,

5( 2x + 3y) = 5( 119)

2x + 3y = 119                                                                             ------------------(2)

Brett purchased 8 rakes and 20 shovels for $676.

8x + 20y = $676                                                                       ------------------(3)

Multiply equation (2) by 4 and subtract from equation (3),

8x + 20y - ( 8x + 12y ) = 676 - 476

8x + 20y - 8x - 12y = 200

8y = 200

y = $25

Therefore,

10x + 15y = 595

10x + 15(25) = 595

10x + 375 = 595

10x = 595 - 375

10x = 220

x = $22

Hence, the price of a rake and shovel is $22 and $25 respectively.

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Answer:

8136366271773737i228882ywhw

Answer:

infinite number of solutions

Step-by-step explanation:

3(n + 11) - 5n = - 2(n - 12) + 9 ← distribute parenthesis on both sides

3n + 33 - 5n = - 2n + 24 + 9 , that is

- 2n + 33 = - 2n + 33

since the expressions on both sides are the same then any value of n will make the equation true.

thus the equation has an infinite number of solutions

Answer:

Any real value. Infinite no. of solutions.

Step-by-step explanation:

Let's open the bracket first. Multiply the term outside the bracket with each term inside the bracket.

[tex]\Rightarrow[/tex] 3(n+11)-5n = -2(n-12)+9

[tex]\Rightarrow[/tex] 3n + 33 - 5n = -2n + 24 + 9

Now simplify the n terms on both sides

[tex]\Rightarrow[/tex] -2n + 33 = -2n + 33

Here both LHS and RHS are same. And the terms gets canceled. Any real value of n satisfy the above equation.

The cost function will be of the form f(x) = x + 29.

A function have a set of dependent variable for the given or specified independent variable.

According to the given question Recycled​ CDs, Incorporated, offers a choice of 5 used CDs for ​29 dollars with each additional CD costing a dollar.

We have to write a function for purchasing 5 or more CDs where x represents the no. of CDs over 5.

Let f(x) represents the cost of CDs.

∴ f(x) = x + 29.

Here the constant 29 dollars represents the cost of 5 CDs and x represents no. of CD's over 5.Put x = 0 and the cost for 5 CDs will be 29 and for any more value of x we will get our desire result.

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Answer:

This will be a 30°-60°-90° triangle because the hypotenuse is 2 cm, which is twice the length of the shorter leg.

[tex]\cfrac{5}{6}\div 5\implies \cfrac{5}{6}\div \cfrac{5}{1}\implies \cfrac{5}{6}\cdot \cfrac{1}{5}\implies \cfrac{1}{6}\cdot \cfrac{5}{5}\implies \cfrac{1}{6}\cdot 1\implies \cfrac{1}{6}[/tex]

Answer:

13 cups of milk I think

Step-by-step explanation:

yes, actually it is possible. The mathematical expression f(x)=exp or ex denotes the exponential function.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function. The formula f(x)=2x is a straightforward example.

Hence, yes, actually it is possible.

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The missing values from area model will be  48, 240.

An area model is a rectangular diagram or model used in mathematics for problems involving multiplication and division, where the length and breadth of the rectangle are determined by the factors, quotient, and divisor.

Write the enlarged form of each component first. Next, sketch your model. To get the area of each smaller rectangle, multiply next. To determine the entire area, add those items last.

The area model will be -

                    60                        6

8                   480                      48

40                2400                    240

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An arithmetic sequence (AP) is a progression in which the difference (called the tolerance) between two consecutive terms in the passage/progression is constant.

Therefore, the expression for the nth term is,

an = a₁ + (n − 1) d

and in general

an = am + (n - m) d.

where d is the difference.

For an arithmetic series with initial term a₁ and difference between terms of d

an = a₁ + (n − 1) d

We are given some of the values,

d = 6 and

S8 = 440

So, we will put the values in the formula and calculate the desired value,

a1 = 440 = a1 + ( 8 - 1 ) * 6 = a1 + 42

a1 = 440 - 42 = 398.

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There are points P, M & Q collinear are not collinear because they didn't lie in the same line but they are coplanar.

Collinear points are defined as points that are along a straight line represented by a collinear. Because a straight line may be drawn continuously between any two points, they are always collinear. There can be a collinear relationship from three or more points, although it is not necessary.

We have given a line and a planar surface with points O, M, N, Q, P, S, and T.

Here three planes that intersect at point P which are PMN plane, PQM plane and QST plane.

Here three planes that intersect at point S which are STN plane, MNS plane and QST plane.

Here points P, M & Q collinear are not collinear because they didn't lie in the same line but they are coplanar.

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Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

And, . By using distance formula we have to write an expression for BC as,

⇒ [tex]D_{BC} = \sqrt{4a^2+b^2}[/tex]

Here,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

And, Write an expression for BC.

What is Isosceles triangle?

When two sides of a triangle are equal then the triangle is said to be isosceles triangle.

Now,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

For this we use distance formula and prove that the two sides of triangle are equal.

Distance between the points A (0, 0) and B (2a, b) is;

[tex]D_{AB} = \sqrt{(2a-0)^2 + (b-0)^2} = \sqrt{4a^2+b^2}[/tex]

And, Distance between the points B (2a, b) and C (4a, 0) is;

[tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

Hence, Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

c. By using distance formula we have to write an expression for BC as,

⇒ [tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

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Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Workers in an office of 90 staff were asked their favorite type of takeaway. The results are summarised in the table.

Take-away             Frequency            Angle

   Pizza                         29                       a

   Curry                          9                        b

Fish & chips                 24                        c

  Kebab                        16                        d

   Other                         12                       e

The angles on the pie chart are calculated by multiplying the table by 4. Then the angles will be

∠a = 4 x 29 = 116°

∠b = 4 x 9 = 36°

∠c = 4 x 24 = 96°

∠d = 4 x 16 = 64°

∠e = 4 x 12 = 48°

Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.

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The length of the side m are obtained using the theorem of Pythagoras and proportional triangles to give;

a) m ≈ 28.4

b) m ≈ 12.09

c) m ≈ 9.38

a) The given triangle, is a right triangle.

The length of the legs of the triangle are; 33 and 56.

According to Pythagorean theorem, the length of the hypotenuse side, l, is therefore;

l = √(33² + 56²) = 65

From the formula for the area of a triangle, we have;

Area of a triangle, A, equals half the base length multiplied by the height.

A = 0.5 × Base length × Height

For the right triangle, we have;

A = 0.5 × Leg 1 × Leg 2

Which gives;

A = 0.5 × 33 × 56 = 924

However;

A = 0.5 × l × m

Where;

l = The hypotenuse = The base length = 65

m = The height of the triangle

Which gives;

A = 0.5 × 65 × m = 924

m = 924/(0.5 × 65) ≈ 28.4

b) The side m is parallel the 14 units long side.

The proportion the side m divides a side of the triangle = 3 and 19

Given that the triangle formed by m is proportional to the larger triangle, we have;

m/14 = 19/(19+3)

c) From the proportionality of similar triangles, we have;

m/16 = 17/(14+15)

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35 mph= .58 of a mile per minute

21 miles in 30 minutes= .7 of a mile per minute

if you multiply by 60 to see the distance in the same amount of time:

rabbit: 35 mph

fox: 42

So the fox would run a greater distance in the time given. Hope this helps!

Option C: The value of m ∠3 is 30° (C).

As per the question, ∠4 and ∠5 form a linear pair. Therefore the sum of ∠4 and ∠5 is 180° so, so the sum of the remaining m∠1,m∠2, and m∠3 angles is 180°.

So, m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360° (as the total angle is 360°).

Now, m∠4 + m∠5 = 180°(∠4 and ∠5 form a linear pair). (∴ m∠1 + m∠2 + m∠3 = 180°). Now we will put the given values and will try to find out the value of x.

2x + (3x-20) + (x-4) = 180

[m ∠1 = 2 x, m ∠2 = 3 x-20, and m ∠3 = x-4]

or,

6x-24=180

or,

6x = 180+24

or,

6x = 204

or, x = 204/6

or. x = 34

As per the question we have to find out the value of m ∠3.

m ∠3 = 34° - 4° = 30° (as x = 30°)

So, m ∠3 is 30°.

If ∠4 and ∠ 5 form a linear pair. And, m ∠1=2 x, m ∠2=3 x-20, and m ∠3=x-4, the value of ∠3 is 30°. Therefore, Option C is the correct answer.

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Answer:

i just need a points thnkyuuuu

Answer:

x = 16

Step-by-step explanation:

16 and x have the same length.