Write a ratio to represent the scale used in the drawing.

By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.

In this question we know the lengths of two sides of the right triangle. By Pythagorean theorem we get the length of the missing side:

a² + b² = c²

b² = c² - a²

b = √(c² - a²)

b = √(37² - 12²)

b = 35

By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.

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Step-by-step explanation:

find the greatest number which divides 225 and 1029 leaving remainder of 5 in each case

Answer:

D

Step-by-step explanation:

Sequence A is increasing using + 6

Sequence B is decreasing using - 6

Sequence C is decreasing using - 6

Sequence D is increasing using x 3

D is the odd one out

Using proportions, they must win 22 games to maintain to the ratio of wins to losses.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the next 28 games, we have that:

To keep the same proportion, we have that:

[tex]\frac{33}{42} = \frac{33 + x}{70}[/tex]

Applying cross multiplication:

42(33 + x) = 33 x 70

Simplifying by 14:

3(33 + x) = 33 x 5

3x = 33 x 5 - 33 x 3

3x = 33 x 2

3x = 66

x = 66/3

x = 22.

They must win 22 games to maintain to the ratio of wins to losses.

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(In c) * 1/c = 0.0604 is the change in the function.

According to the statement

y = (In x)^2 on interval [1,4]

By mean value theorem

we use this formula to find a change f '(c)= [f(b) - f(a)] / (b - a)

Let it f(y) = (In x)^2

Now, f(4) = (In 4)^2

f(4) = (0.602)^2

f(4) = 0.3624

and

f(1) = (In 1)^2

f(1) = (0)^2

f(1) = 0

Now, f'(c) = 2 (In c) * 1/c

Substitute all these values in a formula

2 (In c) * 1/c = 0.3624 - 0 / 4 - 1

2 (In c) * 1/c = 0.3624/3

2 (In c) * 1/c = 0.1208

(In c) * 1/c = 0.0604

So, (In c) * 1/c = 0.0604 is the change in the function.

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Answer: 3

Step-by-step explanation:

[tex]\frac{3-0}{1-0}=3[/tex]

The equation is in direct variation and have constant of variation is 2.

According to the statement

we have given equation is 3x - 6y = 0 and find that the equation is direct variation of not.

Direct variation is the mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other.

So, to find the direct variation equate the given equation equal to zero and solve it.

So, 3x - 6y = 0

3x=6y

or

x/ y=2 or x=2⋅y

here x is directly proportional to the y by 2 times.

∴x∝y

So, this equation in direct variations and constant of variation is 2.

From above this is clear that the equation is in direct variation and have constant of variation is 2.

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From ratio concept, the greater number number is 32 .

A ratio exists as an ordered pair of numbers a and b, written a / b where b does not equivalent to 0. A proportion exists in an equation in which two ratios stand set equal to each other. For example, if there exists 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there exist 3 girls)

Let the greater number be x .

The ratio given is 3:8 .

Thus, by the concept of ratio -

⇒ 3/8 = 12/x

⇒ x = (8/3 * 12)

∴  x = 32

Therefore, from ratio concept, the greater number number is 32 .

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Answer:

Step-by-step explanation:

Let  [tex]x_{n}[/tex] represent the nth term in the sequence. Then  [tex]x_{n-1}[/tex] represents the previous term

The first term, [tex]x_{1}[/tex] = -7

Each consecutive term is obtained by adding 4 to the previous term.

So the recursive relation is
[tex]\left \{ {{x_{1}= -7} \atop {x_{n}= x_{n-1} + 4}} \right.[/tex]

Answer:

You will need 187 80 pounds bags of concrete.

Step-by-step explanation:

12x14x(2/3) x 0.6 = 186.666 or 187

Based on the triangle midsegment theorem, the midsegments and the sides they are parallel to are:

MP is parallel to XY

PZ is parallel to WX

MZ is parallel to WY

The segment that connects the midpoints of two sides of a triangle is referred to as the midsegment of the triangle. All triangles possess three midsegments. According to the triangle midsegment theorem, the third side of the triangle that is directly opposite the midsegment is twice the size of the midsegment and it is parallel to it.

In the diagram showing triangle WXY with midpoints at points M, Z, and P, the midsegments are:

MP which is parallel to XY, also, MP = 1/2(XY)

PZ which is parallel to WX, also, PZ = 1/2(WX)

MZ which is parallel to WY. also, MZ = 1/2(WY)

Thus, the midsegments and the sides they are parallel to are:

MP is parallel to XY

PZ is parallel to WX

MZ is parallel to WY

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The sum of the first five terms is 11/2

The series is given as:

1/2, -1,2,-4…

Calculate the common ratio of the series using

r = -4/2

Evaluate

r = -2

The sum is then calculated as:

[tex]S_n = a\frac{1 - r^n}{1 - r}[/tex]

This gives

[tex]S_n = \frac{1}{2} * \frac{(1 - (-2)^5}{1 + 2}[/tex]

Evaluate

[tex]S_n = \frac{1}{2} * \frac{33)}{3}[/tex]

Evaluate

[tex]S_n =\frac{11}{2}[/tex]

Hence, the sum of the first five terms is 11/2

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The formula to find the height of the Cylinder is; h = V/(πr²) and at V = 45π and r = 3, we have; h = 5

We are given the formula for volume of a cylinder as;

V = πr²h

where;

h is height

r is radius

To make h the subject, let us divide both sides by  πr² to get;

V/(πr²) = h

At V = 45π and r = 3, we have;

h = 45π/(πr²)

h = 45/3²

h = 5

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Answer:

60

Step-by-step explanation:

140-80=60

The maximum amount of water that can be used by each house on a daily basis is 100 liters.

4,500 = 500 + 40x

4,500 - 500 = 40x

4,000 = 40x

x = 4,000 / 40

x = 100 liters

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True

Personally, when I see the line underneath the equality sign, I know I've got to draw a dotted line. That's how I remember the difference between drawing a solid / dotted line.

Hope this helps!

Answer:

The water costs $1.90, the chips are $.95 and the milk is $3.80.

Step-by-step explanation:

Let m = milk

Let w = water

Let c = chips

2m+6w+7c =25.65      w = 2c     m = w + 1.90

For the first equation, substitute w for 2C and m for w + 1.90 to get:

2(w+1.90) +6(2c) + 7c = 25.65

2w+3.8+12c+7c=25.65

2w+19c = 21.85

Now substitute 2c for w:

2(2c)+19c =21.85

4c + 19c = 21.85

23c = 21.85

c = .95  Now that we know the cost of the chips we can use that to find the water and the milk for the original equations that we wrote at the top.

w = 2c

w=2(.95) = 1.90

m = w + 1.90 = 1.90+1.90 = 3.80

The value of x is 78

Given:

[tex]\frac{m}{FCD}=x+48\\\\ \frac{m}{BCD} =x+17\\\\\frac{m}{BCD} =95^0[/tex]

From the given equations, two of them are exactly equivalent

The equivalent equations are compared below

x  +  17   =  95

x  =  95  -  17

x  =  78

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The slope of restaurant B is twice that of restaurant A

The tables of values are given as

           X(Bill)     Y(Tip)                          X(Bill)        Y(Tip)

Rest A     10           1                  Rest B      25            5    

Rest A     20          2                 Rest B      50            10

Rest A     30          3                 Rest B      75             15

The slopes are calculated using

Slope = (y2 - y1)/(x2 - x1)

Using the table of values, we have:

Rest A = (2 - 1)/(20 - 10)

Rest A = 0.1

Rest B = (10 - 5)/(50 - 25)

Rest B = 0.2

By comparing the slopes, we have:

Rest B = 2 * Rest A

This implies that the slope of restaurant B is twice that of restaurant A

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Answer:

slope intercept form: y = mx + b

6x - 4y = 24

4y = 6x - 24

y = 3/2x - 6

slope: 3/2

y intercept: - 6

Answer:

y = 3/2 x -6

The slope is 3/2 and the y intercept is -6

Step-by-step explanation:

6x-4y = 24

The slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

We need to solve the equation for y

6x-4y =24

Subtract 6x from each side

6x-4y-6x =-6x+24

-4y = -6x+24

Divide each side by -4

-4y/-4 = -6x/-4  + 24/-4

y = 3/2 x -6

The slope is 3/2 and the y intercept is -6

Answer:

x = 10

Step-by-step explanation:

∆RSE ~ ∆FGE

SE/ GE = RE/ FE

45/ 12x-3 = 55/ 143

3/ 3(4x - 1) = 11/ 143

11(4x-1) = 429

44x-11 = 429

44x = 440

x =10

Answer:

[tex] \frac{2}{3} [/tex]

Step-by-step explanation:

=18÷[7+2{7+2(7-6)}+2]

=18÷[7+2{7+2×1}+2]

=18÷[7+2×9+2]

=18÷[7+18+2]

=18÷27

=[tex] \frac{18}{27} [/tex]

=9 two is 18 and 9 three is 27

So,

=[tex] \frac{2}{3} [/tex]

answer: 200, 2 hundred, two hundred

The values of x and y that can represent the equation is illustrated.

The equation given us 32 = xy + 16

The table will be:

x. y

4. 4

16. 1

2. 8

32. 0.5

For example, when x and y are 4. This will be:

= xy + 16

= (4 × 4) + 16

= 32

Other values of x and y will also give 32.

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The inverse statement is:

¬q ⇒ ¬p

Which is true.

Here we have the biconditional statement:

A number is negative if and only if it is less than zero.

Where:

So we can write the statement as:

p ⇔ q

The inverse statement is:

if not q, then not p.

or

¬q ⇒ ¬p

Replacing p and q, we have:

"if a number is not less than zero, then the number is not negative".

This is true, if the number is not less than zero, then the number is 0 or larger, so that number is not negative.

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Answer:

D.

∼p↔∼q

and

G.

The inverse of the statement is true.

Step-by-step explanation:

Answer:

7.5. hours

Step-by-step explanation:

Trust me

12 men will take 3.34 hours to build a similar storeroom if they work at the same rate.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that it took 8 hours for 5 men to build a storeroom. The time required by 12 men to do the same work will be calculated as below:-

Time taken by one man  = 8 x 5 = 40 hours

Time is taken by 12 men will be = 40 / 12 = 3.34 hours

Therefore, 12 men will take 3.34 hours to build a similar storeroom if they work at the same rate.

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Based on our examination of the y-intercepts, we can deduce that the y-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)

The value of the function at the point where the value of x is equal to zero is known as the y-intercept.

f(x)=-6(1.05)^x

Considering x

x=0

f(0)=-6(1.05)^0

f(0)=-6(1)

f(0)=-6

Therefore, the y-intercept is point (0,-6)

Generally, the equation for the function of the y-intercept of g(x) is  mathematically given as

From table

at x=0

The y-intercept is the point (0,-3)

Based on our examination of the y-intercepts, we can deduce that the ty-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)

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Answer:

the product is 1.32057606543E32