A car company sells a scale model to of the size of one of its cars.
Complete the following table.
Scale Model
Real Car
2
Area of windscreen (cm)
135
V25
[3]
3
Volume of storage space (cm)
408000

Answer:

5040

Step-by-step explanation:

The given series is :

24 + 48 + 72 + 96 +...+ 480

The first term, a= 24

Common difference, d = 24

The last term, [tex]a_n=480[/tex]

Let there are n terms in the AP.

So,

[tex]a_n=a+(n-1)d\\\\480=24+(n-1)24\\\\480=24+24n-24\\\\n=20[/tex]

There are 20 terms in the series. The sum of 20 terms is :

[tex]S_{20}=\dfrac{n}{2}(2a+(n-1)d))\\\\=\dfrac{20}{2}\times (2(24)+19(24))\\\\=5040[/tex]

So, the sum of the given arithmetic series is equal to 5040.

Answer:

Step-by-step explanation:

(x+4)^2.(x+4)^2

= x^4 +16x^3+96x^2+256x+256

Answer:

A

Step-by-step explanation:

If lines are parallel and intersected by another line then there are 2 alternating angles between them.

Answer: 1 pigeon is $320

1 love bird is $80

Step-by-step explanation:

Let the cost for 1 love bird be represented by x

Let the cost for 1 pigeon be represented by y.

Since John bought 8 birds and 6 pigeons for $2400. This will be:

8x + 6y = 2400 ...... i

If he had bought 1 more pigeon and 2 fewer birds, he would have paid $200 more. This will be:

6x + 7y = 2600 ...... ii

8x + 6y = 2400 ...... i

6x + 7y = 2600 ...... ii

Multiply equation i by 6

Multiply equation ii by 8

48x + 36y = 14400 ...... iii

48x + 56y = 20800 ...... iv

Subtract iii from iv

20y = 6400

y = 6400/20

y = 320

1 pigeon is $320

From equation i

8x + 6y = 2400

8x + 6(320) = 2400

8x + 1920 = 2400

8x = 2400 - 1920

8x = 480

x = 480/8

x = 60

1 love bird is $80

Answer:

D. (10, 2)

Step-by-step explanation:

A' = [ 2(3)-(-4) ; 2]

=> (6+4 ; 2)

=> (10, 2)

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

sqrt(100) is 10

Replace x and y with their values:

Sqrt (2 -14(-7))

Multiply 14 and -7

Sqrt(2 - -98)

Add

Sqrt(100)

Simplify to get 10

Answer = 10

Answer:

5.5 = AB

Step-by-step explanation:

take 62 degree as reference angle

using cos rule

cos 62 = adjacent / hypotenuse

0.46 = AB / 12

0.46*12 = AB

5.52 = AB

5.5 = AB

The length of side AB in the given right angle triangle of hypotenuse  12 cm is  5.7 cm.

A triangle with one angle at [tex]90^o[/tex] is called right angle triangle.

Given that:

Hypotenuse = 12 cm

[tex]\theta = 62^o[/tex]

The length of side AB in the given right angle triangle is calculated as:

Using trigonometric function,

[tex]\cos\theta = \dfrac{base}{hypotenuse}[/tex]

Let, the value of base be x

Substitute the values in the given formula:

[tex]\cos 62^o = \dfrac{x}{12}[/tex]

Using the trigonometric table, the value of [tex]\cos 62^o[/tex] is 0.4694

[tex]0.4694 \times 12[/tex]= x

x= 5.6328

x = 5.7

Thus, the length of side AB to 1 decimal place is 5.7 cm

Learn more about trigonometric function here:

https://brainly.com/question/25618616

#SPJ7

Answer:

4cm

Step-by-step explanation:

first find the length of the side of one square

the length of the rectangle will be twice the width

let y represent the width

area of a rectangle=length x width

2cm²=2yxy

2cm²=2y²

2cm²/2=2y²/2

1cm²=y²

1√cm²=√y²

1cm=y

perimeter of a square=4xside

4x1cm

4cm

Answer:

1

----------

x+1

Step-by-step explanation:

2x+12

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

2x^2 + 14x+12

Factor

2(x+6)

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

2(x^2+7x+6)

2(x+6)

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

2(x+6)(x+1)

Cancel like terms

1

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

(x+1)

Answer:

the midpoint of it is 8,-6

Step-by-step explanation:

rhgsr egh

Answer:

6.75

Step-by-step explanation:

that is the answer by the way

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:2}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]x + 11 + 8x = 29[/tex]

[tex]➺ \: x + 8x = 29 - 11[/tex]

[tex]➺ \: 9x = 18[/tex]

[tex]➺ \: x = \frac{18}{9} [/tex]

[tex]➺ \: x = 2[/tex]

Therefore, the value of [tex]x[/tex] is 2.

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

[tex]x + 11 + 8x = 29[/tex]

[tex]➺ \: 2 + 11 + 8(2) = 29[/tex]

[tex]➺ \: 2 + 11 + 16 = 29[/tex]

[tex]➺ \: 29 = 29[/tex]

➺ L. H. S. = R. H. S

Hence verified.

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35\:ヅ}}}}}[/tex]

Answer:

p = 1.4

Step-by-step explanation:

The ratio of sides is the same

p/4.2 = 1.7/5.1

multiply both sides by 4.2

p = 1.7/5.1 * 4.2

p = 1.4

===========================================================

Explanation:

JK = LM because opposite sides of a parallelogram are the same length.

Side LM is p units long, where p is a placeholder for a number.

To determine what number replaces p, we can form the proportion shown below

BC/KL = CD/LM

Refer to the drawing below. I've circled the corresponding pieces. Note the color coding. Other equations are possible.

-----------

So,

BC/KL = CD/LM

(5.1)/(1.7) = (4.2)/p

5.1p = 1.7*4.2 ....................... cross multiply

5.1p = 7.14

p = (7.14)/(5.1)

p = 1.4

Answer:

4/33

Step-by-step explanation:

do the normal steps to conversion

Step-by-step explanation:

Given that,

The length of a carton, h = 9 cm

Width, b = 13 cm

height, h = 24 cm

I drink one-third of the fruit juice, then two third will be left. So, the volume is :

[tex]V=\dfrac{2}{3}\times lbh\\\\V=\dfrac{2}{3}\times 9\times 24\times 13\\\\V=1872\ cm^3[/tex]

Since, 1 L = 1000 cm³

1872 cm³ = 1.8 L

or

= 1800 mL

Hence, this is the required solution.

Answer:

35m^2

Step-by-step explanation:

4×2.5=10 10×2=20

3×2.5=7.5 7.5×2=15

20+15=35

Hope this helps! :)

Answer:

150°

Step-by-step explanation:

2x+x+90=180

3x=90

x=30

z= 180-x = 180-30 = 150°

Answer:

A:He is trying to find the diameter

B: 3.14*14=43.96

C: 3.14*14^2=615.44

Hope This Helps!!!

Answer:

8. B

9. B

Step-by-step explanation:

add all sides to get perimeter

multiply sections of the area to get area (length times width)

Given:

The expression is:

[tex]6\div 8[/tex]

To find:

The value of the given expression by using the long division method.

Solution:

We have,

[tex]6\div 8[/tex]

Here, dividend is 6 and divisor is 8.

Since 6<8, therefore we will use the decimal in dividend and quotient as shown below:

[tex]\underline{\quad 8\quad}|\overline{\quad 6.00\quad }|\underline{\quad 0.75\quad }[/tex]

         [tex]\underline{\quad 56\quad }[/tex]

               [tex]40[/tex]                  (After subtraction)

           [tex]\underline{\quad 40\quad }[/tex]

             [tex]\underline{\quad 0\quad }[/tex]               (After subtraction)

Therefore, the value of the given expression is 0.75.

Answer:

a. 8 / 10

Step-by-step explanation:

0.8 = 8 / 10

Answer:

8/10

Step-by-step explanation:

0.8

The number is in the tenths place

The denominator is 10

8/10

Answer:

Step-by-step explanation:

Middle point of AB

x(m) = (6+1)/2 = 7/2

y(m) = (7+4)/2 = 11/2

slope of the line that contains AB

(4-7)/(6-1) = -3/5

eqaution of the perpendicular bisector

y-11/2 = 5/3(x-7/2)

y = 5/3x -35/6 + 11/2

y = 5/3x + (-35 + 33)/6

y = 5/3x -1/3

Middle point of AC

x(m) = (1+5)/2 = 3

y(m) = (7+5)/2 = 6

Slope of the line that contains AC

(5-7)/(5-1) = -1/2

equation of the perpendicular bisector

y-6 = 2(x-3)

y = 2x -6 + 6

y = 2x

Point of intersection

y= 5/3x -1/3

y = 2x

2x = 5/3x - 1/3

6x = 5x - 1

x = -1

y = -2

P(-1,-2)

Answer:

(1,7)

Step-by-step explanation:

Given:

A(1,7)

B(6,4)

C(5,5)

Solution:

Mid point of AB = M((1+6)/2,(7+4)/2) = M(3.5,5.5)

Slope of AB = (4-7)/(6-1) = -3/5

Perpendicular bisector of AB:

L1: y -  11/2 = -(3/5)(x-7/2) ............(1)

Mid point of AC, m= N((1+5)/2,(7+5)/2) = N(3,6)

Slope of AC, n = (5-7)/(5-1) = -2/4 = -1/2

perpendicular bisector of AC:

L2: y-6 = -(1/2)(x-3) ..........."(2)

To find the point of intersection,

(1)-(2)

-5.5 - (-6) = -(3/5)x +12/5 + x/2 - 3/2

1/2 = -x/10 + 6/10

x/10 = 1/10

x = 1

substitute x in (1)

y = 3/2+11/2 =7

Therefore Point of intersection is (1,7)

Answer:

see below

Step-by-step explanation:

R:B = 8:3

5 ratio marbles is 35 (to make ration 3:3)

1 ratio=7

He originally had 56 red marbles and 21 blue (77 total)

Now he has 21 Red and 21 Blue (42 total)

Answer:

1. 194

2. 189

Step-by-step explanation:

1. 991 - 797 = 194

2. 826 - 637 = 189

Answer:

1. 194 people increased.

2. Edith has 189 stamps more than Parick.

Step-by-step explanation:

1. 991 - 797 = 194

2. 826 - 637 = 189

Answer:

X=3

Y=1

Step-by-step explanation:

Vertex A forms dilation F

Answer:

30

So the two sectors add to the full length:

JK + IJ = IK

x+6 + 9 = 2x

Rearrange:

x=15

So the numerical length:

2x

2*15

30

Well, If the area of ABC is 20cm², Then the area of ABS would be 10cm² and the area of ACS would also be 10cm². You basically are just cutting the ABC in half. I hope this helps!

Answer:

a) 400

b)160,000

Step-by-step explanation:

times 20 by 20 hence 20² for a. you get 400, for b, just do 400² which gets you 160,000.

If its wrong im so sorry

Answer:

a) x^2 + y^2

b) 9-xy

Step-by-step explanation:

Here, we want to write the algebraic statements as expressions;

a) The sum of the squares of x and y

The square of x is x^2

The square of y is y^2

The sum of the squares is x^2 + y^2

ii) Product of x and y subtracted from 9

The product of x and y is x * y = xy

Subtracting these from 9, we have;

9-xy

Answer:

x

Step-by-step explanation: