A test of a new car results in 370 miles on 10 gallons of gas. How far could you drive on 65 gallons of gas?
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9514 1404 393

Answer:

  CX = 15√2 inches

  BC = 15√3 inches

  AC = 15√6 inches

Step-by-step explanation:

In this geometry, all of the triangles are similar:

  ΔABC ~ ΔACX ~ ΔCBX

Corresponding segments are proportional in similar triangles, so we have ...

  AX/CX = CX/BX = (long leg)/(short leg)

Filling in the numbers, we get

  30/CX = CX/15

  CX² = 15×30

  CX = 15√2 . . . . . exact length of the altitude (inches)

__

Similarly, we can form proportions with the legs:

  AB/BC = CB/BX

  BC² = (BX)(AB) = (45)(15)

  BC = 15√3 . . . inches

and

  AC/AB = AX/AC

  AC² = (AX)(AB) = (30)(45)

  AC = 15√6 . . . inches

_____

Additional comment

You may notice that each of the segments we're interested in is the root of a product involving segments of the hypotenuse. This "root of a product" is called the geometric mean. Here, the three geometric mean relations are ...

  altitude = geometric mean of hypotenuse segments

  short side = geometric mean of short segment and whole hypotenuse

  long side = geometric mean of long segment and whole hypotenuse

__

Strictly speaking the geometric mean is the n-th root of the product of n items. Here, there are only 2 items, so it is the square root of their product.

Answer:

76cm²

Step-by-step explanation:

SA=2lw+2lh+2hw

length=4cm

width=2cm

height=5cm

= 2(4×2+4×5+5×2)

=8+20+10

=2×38

=76cm²

Answer:

9.95 for 30oz

Step-by-step explanation:

30/9.95 = 3.02

12/3.5 = 3.43

Answer: 450 minutes

Step-by-step explanation: First you find 7 hours to minutes by multiplying 7 by 60. You will get 420. Then, add 420 and 30 because a half of an hour is 30 minutes. Your final answer will be 420 minutes!

Your welcome!

Good night!

8x -5 = 4x+7

8x - 4x = 7 + 5

4x = 12

x = 3

Answer:

6:100 or 3:50

Step-by-step explanation:

8ft 4 in = 100 inches

Step-by-step explanation:

Given

x = 3g + 2

Making g as a subject then

3g = x - 2

g = ( x - 2 ) / 3

Hope it will help :)❤

Answer:

g=(x-2)/3

Step-by-step explanation:

Step-by-step explanation:

Blank #1 STQ

Blank #2 SSS (Side-Side-Side)

Answer:

142.72

Step-by-step explanation:

In the question it states that the number in the hundreds place should be twice the number in the hundredth place.

142.72

1 is in the hundreds place. Now the value in the hundredth place should be twice the value of 1. When it say twice it says 2 times the number. 1 time 2 = 2 which would make the answer true.

Hope this helps, thank you :) !!

Answer:

3x - 5 = 3x + (-5)

Step-by-step explanation:

Answer:

gggggggg

Step-by-step explanation:

Step-by-step explanation:

triangle c two sides measure length 6cm

Answer:

x=16

Step-by-step explanation:

Answer:

p = 19 and q = 71

hope it helps

thanks

Answer:

1086.3 cm²

Step-by-step explanation:

surface are of sphere = πD²

SA = (3.14)(18.6 cm)^2

SA = 1086.3 cm²

Answer:

14.3 yds.

Step-by-step explanation:

c=√a^2 +b^2

c=√14^2 +3^2

c=√=196+9

c=14.31782106327

c=14.3 yds.

Answer:

XZ = 14.32 yd

Step-by-step explanation:

Use the Pythagorean theorem

14^2 + 3^2 = XZ^2

196 + 9 = XZ^2

XZ^2 = 205

XZ = 14.32 yd

Answer:

The data is symmetric.

The IQR is 30.

Step-by-step explanation:

Answer:

The data is symmetric.

The IQR is 30.

Answer:

Substitute the given value for the  

✔ variable

.

Use the  

✔ order of operations

to simplify.

First, complete the  

✔ multiplication

inside the parentheses.

Next, complete the  

✔ addition

inside the parentheses.

Last, complete the subtraction.

The value is  

✔ 1

.

Step-by-step explanation:

Answer:Evaluate (3n + 2) – 10 when n = 3.

First, evaluate within the parentheses. Then evaluate exponents. Next multiply and divide from left to right. Then, add and subtract from left to right.

Evaluate the expression for the given value of the variable and use the drop-down menus to complete the statements.

Substitute the given value for the

✔ variable

.

Use the

✔ order of operations

to simplify.

First, complete the

✔ multiplication

inside the parentheses.

Next, complete the

✔ addition

inside the parentheses.

Last, complete the subtraction.

The value is

✔ 1

.

Step-by-step explanation:

Answer:

A. 106

B. 25

Step-by-step explanation:

A. 33 times 2 = 66

66 Plus the 40 for the membership

66 + 40 = 106

B. 90 - 40 = 50  (40 from the membership)

50 divided by 2 = 25

9514 1404 393

Answer:

  -28/45

Step-by-step explanation:

Step 1, the sign

When the fractions have an odd number of minus signs (1, not 0 or 2), the result will be negative. This knowledge lets you ignore the sign while you do the rest of the arithmetic. The appropriate sign is applied to the final numbers.

Step 2, the formula

The ratio (a/b)÷(c/d) is (ad)/(bc). There are several ways you can get there:

⇒ "invert and multiply" or "swap dot"

  [tex]\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\,\cdot\,\dfrac{d}{c}=\dfrac{ad}{bc} \quad\text{division is multiplication by the reciprocal}[/tex]

⇒ "numerators of a common denominator"

  [tex]\dfrac{\left(\dfrac{a}{b}\right)}{\left(\dfrac{c}{d}\right)}=\dfrac{\left(\dfrac{ad}{bd}\right)}{\left(\dfrac{bc}{bd}\right)}=\dfrac{ad}{bc}[/tex]

⇒ "swapped denominators of a common numerator"

  [tex]\dfrac{\left(\dfrac{a}{b}\right)}{\left(\dfrac{c}{d}\right)}=\dfrac{\left(\dfrac{ac}{bc}\right)}{\left(\dfrac{ac}{ad}\right)}=\dfrac{ad}{bc}[/tex]

The use of common numerators or common denominators is most often seen when the numerator or denominator of one fraction is a multiple of that in the other fraction. Example: (2/3)÷(1/6) = (4/6)÷(1/6) = 4/1 = 4

Step 3, reduce the result

Any of these fractions is reduced by cancelling common factors from numerator and denominator. Your fractions here don't have any common factors, so there is nothing to cancel.

_____

Your product is ...

  (4/9) ÷ (-5/7) = -(4·7)/(9·5) = -28/45

Step-by-step explanation:

angle ABC= angle ACB= 37° --------- because AB=AC

angle ACB+ angle ACD=180°

37+angle ACD=180

angle ACD=143°

Answer:

143 is the answer

Step-by-step explanation:

Answer:

Discount of Original Price = Discounted Price

20% of $30 =  $24

30% of $24 = 16.8

40% of $35 = $21

Explanation:

0.2 x 30 = 6

30 - 6 = 24

0.3 x 24 = 7.2

24 - 7.2 = 16.8

0.4 x 35 = 14

35 - 14 = 21

Answer:

6x-7

Step-by-step explanation:

Answer:

[tex]6x - 7[/tex]

Step-by-step explanation:

1) Simplify 2-1 to 1.

[tex]5 \times 1 + 2(3x - 6)[/tex]

2) Simplify 5 × 1 to 5.

[tex]5 + 2(3x - 6)[/tex]

3) Expand by distributing terms

[tex]5 + 6x - 12[/tex]

4) Collect like terms.

[tex]6x + (5 - 12)[/tex]

5) Simplify.

[tex]6x - 7[/tex]

So, therefor, the answer is 6x - 7.

Answer:

y=1/3x-7

Step-by-step explanation:

Answer:

6,9

Step-by-step explanation:

Got it right on edg

The ordered pair which is also on the graph is (6, 9).

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

Suzy is shopping at a book sale.

We can see from the table that when books( x) is 2 then the value of y is 3.

Similarly, x = 4 then y = 6

then we can say that the value of y is the addition of half of the value of x in itself.

So, according to the number pattern;

if we take x = 6

Then 6 + 3 = 9

y = 9

Thus, The ordered pair which is also on the graph is (6, 9).

Learn more about a number pattern:

brainly.com/question/14471389

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