Draw a square and it diagonals. Guess the measures of these angles.

The person is overwieght as his BMI is 31.00 (approx)

What is Proportion?

In general, proportion refers to a part, share, or quantity assessed in comparison to a total. According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios or fractions are equivalent.

Solution:

Since, BMI is directly proportionate with weight and indirectly proportionate with square of height, we need to use a constant to make proportion to an equation.

According to the question,

BMI of a person who weighs 180 pounds and is 5 feet tall is 35.15.[tex]BMI = k*weight/height^{2}[/tex]

here, k is any constant value

35.15 = k*180/(60*60)

(35.15 * 3600)/180 = k

k = 703

Calculating BMI of a person weighing 210 pound and is 5 feet 9 inch tall.

First of all we need to convert 5 feet 9 inches into inches

5 feet = 60 inches

so, 5 feet 9 inch means 69 inches

BMI = 210*703/(69*69)

BMI = 31.00 (after rounding off)

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The differential equation is 8x-4 when the equation is (2x-3)(2x+1).

Given that,

The equation is (2x-3)(2x+1)

We have to find the differentiative equation.

Calculus differentiates the process of locating a function's derivatives. A derivative is the pace at which one function changes in relation to another. Sir Isaac Newton set the foundations for the laws of differential calculus. Numerous scientific disciplines make use of the limits and derivatives ideas. The essential ideas of calculus are differentiation and integration.

Differentiation is the rate at which one quantity changes in relation to another.

Take the equation

(2x-3)(2x+1)

We can do in two ways

1st way

Multiply

4x²+2x-6x-3

Subtraction

4x²-4x-3

Differentiation

8x-4

The equation is 8x-4.

2nd way

We have a formula in differentiation that is

u.v=uv'+vu'

Take u as 2x-3 and v as 2x+1

(2x-3)(2)+(2x+1)(2)

4x-6+4x+2

8x-4

Therefore, The differential equation is 8x-4 when the equation is (2x-3)(2x+1).

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Answers:

1st box:  [tex]\boldsymbol{90}[/tex]

2nd box:  [tex]\boldsymbol{90}[/tex]

3rd box:  [tex]\boldsymbol{\text{m}\angle 2 = \text{m}\angle 3}[/tex]

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

Explanation:

Complementary angles form a corner. Note that "complementary" and "corner" both start with "C" to help remember the rule.

By "corner", I refer to a 90 degree angle.

Since [tex]\angle 1\text{ and } \angle 2[/tex] are complementary, we know that [tex]\text{m}\angle 1+\text{m}\angle 2 = 90[/tex] simply by the definition of what it means to be complementary.

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

Through similar logic, [tex]\angle 1\text{ and } \angle 3[/tex] are complementary which means [tex]\text{m}\angle 1+\text{m}\angle3 = 90[/tex]

We can then equate the left hand sides (LHS) of both equations since both LHS expressions equal 90. This is an example of the substitution property in action.

That's how we end up with [tex]\text{m}\angle 1+\text{m}\angle 2 = \text{m}\angle 1+\text{m}\angle 3[/tex]

After this point, subtract [tex]\text{m}\angle1[/tex] from both sides to cancel them out. We'll be left with [tex]\text{m}\angle 2 = \text{m}\angle 3[/tex], which concludes with [tex]\angle 2 \cong \angle 3[/tex] to show the two angles are congruent.

Answer:

[tex]3a^4b^2-2a^2b+9a[/tex]

Step-by-step explanation:

Because multiplication is the inverse of division, we're able to split this fraction into three separate fractions, which will simplify nicely at the end:

[tex]\frac{21a^5b^3}{7ab}; \frac{-14a^3b^2}{7ab}; \frac{63a^2b}{7ab}[/tex]

We can start by simplifying each fraction since 21, -14, and 63 are all divisible by 7:

[tex]\frac{3a^5b^3}{ab}; \frac{-2a^3b^2}{ab}; \frac{63a^2b}{ab}[/tex]

Finally, when dividing quotients with exponents, we subtract the exponents and we put all of our answers back together since everything was multiplied by each other at the beginning of the problem:

[tex]3a^4b^2-2a^2b+9a[/tex]

Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.

Given that,

Luke asserts that since the shape is constant, two circles are always isometric.

We have to say is he accurate.

The answer is

No, an isometry keeps the size and shape intact.

Because a shape-preserving transformation (movement) in the plane or in space is called an isometric transformation (or isometry). The isometric transformations include translation, rotation, and combinations thereof, such as the glide, which combines a translation with a reflection.

Therefore, Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.

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The perimeter of the resulting hexagon is 60 meters.

In this problem we find the perimeter of a regular hexagon, which is dilated around its center. Regular hexagons are polygons with six sides of equal length. Dilations are rigid operations of the form:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

The perimeter is the sum of the side lengths of the hexagon and by dilation we find the following relationship between original and resulting perimeters (p, p'):

p' = k · p

If we know that p = 45 and k = 4 / 3, then the resulting perimeter is:

p' = (4 / 3) · (45)

p' = 60

The resulting hexagon has a perimeter of 60 meters.

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a. The smallest number of M & M's possible is 14.

b. The number of green is 24.

c. The ratio of green to yellow to red in 6: 15: 25.

a. When there are only green and yellow M & M's in the bag, the smallest number of M & M's possible will be:

= (2 × 2) + (2 × 5)

= 4 + 10

= 14

b. If there are 84 total green and yellow M & M's in the bag, the number of green will be:

= 2 / (2 + 5) × 84

= 2/7 × 84

= 24 green

c. If red M & M's were added to the bag in part b to get a total of 100, the ratio of green to yellow to red in simplest form will be:

= Green : Yello : Red

= 24 : 60 : 100

= 6 : 15 : 25

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Interest rate will cause his money to double in approximately 23 years is 3.13%.

Given:

Arnulfo deposited $55 into a savings account and interest is in semi annually.

For 23 years the interest payments will be = 23*2

= 46

Interest rate = 2*72 / 46

= 144/46

= 72/23

= 3.13%

Therefore Interest rate will cause his money to double in approximately 23 years is 3.13%.

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Answer:

A. Yes, they have the same slope and a different y-intercept.

Step-by-step explanation:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Rearrange 3x + y = 6 to y = mx + c form.

y = -3x + 6

Parallel lines have the same slope.

Since slope of both lines is -3, the lines are parallel.

Answer:

$67.50

Step-by-step explanation:

27(2) = 54

27/2 = 13.5

54+13.5 = 67.5

Answer:

67.5

explanation:

27/2= 13.5

5*13.5= 67.5

Answer:

a = -1
b = -9

Step-by-step explanation:

when x = -2 put -2 for x in the equation:

a(3- (-2)) = -2*(-2) + b and then solve
a(3+2) = 4+b
5a = 4+b

then look at the numbers in the box and try for which number this equation will work. when you put a = -1 and b = -9 you will see it is equal on both sides because each side is -5

Answer:

[tex]\boxed{\boxed{\sf s=\frac{1}{3}}\sf \:or\:\boxed{\sf s=0.33...}}[/tex]

Step-by-step explanation:

[tex]\sf 3\left(s+1\right)-8=6s\left(2-4\right)[/tex]

Expand ( Apply the Distributive Property):-

[tex]\sf 3s-5=-12s[/tex]

Add 5 to both sides:-

[tex]\sf 3s-5+5=-12s+5[/tex]

Simplify:-

[tex]\sf 3s=-12s+5[/tex]

Add 12s to both sides:-

[tex]\sf 3s+12s=-12s+5+12s[/tex]

Simplify:-

[tex]\sf 15s=5[/tex]

Divide both sides by 15:-

[tex]\sf \cfrac{15s}{15}=\cfrac{5}{15}[/tex]

Simplify:-

[tex]\sf s=\cfrac{1}{3}[/tex]

___________________

Hope this helps!

Have a great day! :)

The triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.

First, let us understand the SAS congruency theorem:

This one denotes Side - Angle - Side and it means that if 2 sides and one angle of a triangle are equal to the corresponding 2 sides and one angle of another triangle, then they are both congruent.

We are given:

SR and ST are straight lines.

side SX ≅ side SY

side XR ≅ side YT

So,

side SR ≅ side ST

In triangle RSY and triangle TSX;

side SR ≅ side ST (above proved)

∠RSY ≅ ∠TSX (Common)

side SY ≅ side SX (Given)

So, triangle RSY ≅ triangle TSX by SAS congruency theorem.

Thus, the triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.

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Answer:  Choice C

[tex]64m^3-32m^2+43m-15[/tex]

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

Explanation:

Multiply out the expressions using the distribution rule as shown below.

[tex](-8m+3)(-8m^2+m-5)\\\\n(-8m^2+m-5) \ \ \text{ ... see note1}\\\\-8m^2n+mn-5n\\\\-8m^2( n )+m( n )-5( n )\\\\-8m^2( -8m+3 )+m( -8m+3 )-5( -8m+3 ) \ \ \text{ ... see note2}\\\\( 64m^3-24m^2 )+( -8m^2+3m )+( 40m-15 )\\\\64m^3+(-24m^2-8m^2)+(3m+40m)-15 \\\\64m^3-32m^2+43m-15 \\\\[/tex]

I used the tool WolframAlpha to confirm the answer is correct. GeoGebra is another free tool that offers similar capabilities.

Footnotes:

Answer:

-32

Step-by-step explanation:

-(4)^2 - -2^4 = -16 - 16 = -32

Answer:

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

Use equation for continuous compound:

Plug in the values and calculate:

Answer:

$5,252.53 (nearest cent)

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=2900 \cdot e^{(0.054 \cdot 11)}[/tex]

[tex]\implies \sf A=2900 \cdot e^{0.594}[/tex]

[tex]\implies \sf A=2900 \cdot 1.81121882[/tex]

[tex]\implies \sf A=5252.53457...[/tex]

Therefore, assuming no deposits or withdrawals are made, the amount of money in the account after 11 years would be $5,252.53 (nearest cent).

Answer: 5x2x2x3x3 is the answer to your question

Answer:

1) 1 A. Yes B. Because the change in x and y is constant

2) 2 A. No B. Although the change in y is

constant, the change in x is not

3) 5. A. No B.Because the change in y is not constant

4) 4,5 A. yes B.Because the change in x and constant

Step-by-step explanation:

The GCF: 2x³y

answer: 2x³y2x³y(9y³+1)

The missing value of that makes the line that passes the given points have a slope of 0 is determined as: a. 15.

The slope (m) is defined as the rise of a line over its run. The formula for finding the slope (m) of a line is given as:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Given the points (-20, y) and (-11, 15) has a slope (m) of 0. Therefore, let:

(-20, y) = [tex](x_1, y_1)[/tex]

(-11, 15) = [tex](x_2, y_2)[/tex]

m = 0

Substitute the values into the slope formula:

0 = (15 - y) / (-11 -(-20))

0 = (15 - y) / 9

Multiply both sides by 9

0 = 15 - y

0 + y = 15 - y + y

y = 15

The answer is: a. 15.

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The given expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex].

What are Exponents?

What are the Laws of Exponents?

There are major seven Laws of Exponents as follows:

From the given question, we have the expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex]    -----(1)

Here, we can use the power of a power rule to simplify the expression.

The power of a power rule is of the form, [tex](a^{m} )^{n} =a^{m \times n}[/tex]

Solving expression (1) using the power of a power rule, we get

[tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-2 \times 3} }{(x^{6} y^{3} z)^{2 \times 3} }\\\implies [\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]

Therefore, the given expression is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]

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The equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.

Isaac made a 30-cup batch of potato salad, and now he is filling 2.5-cup

to-go containers to sell to customers.

Let y represent the number of cups of potato salad remaining,

And x represents the number of to-go containers Isaac has filled,

As per the given situation, we can write the equation as:

y = 30 - x  ....(i)

Substitute the value of x = 2.5 in the above equation,

y = 30 - 2.5

y = 27.5

Thus, the equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.

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Answer:

Step-by-step explanation:

Well let Krutica’s age = x

K = x,    G = x+5,    D = x-6

K+G+D = 86  

x + x+5 + x-6 = 86

3x = 87

x = 29

Gordon is the eldest of the few:

29 or x+5=

34 years old

Answer: Gordon is 34 years old

Answer:

B

Step-by-step explanation:

Answer:

A. 70.2

Step-by-step explanation:

solve your equation step-by-step.

842.412=x1

Step 1: Cross-multiply.

842.412=x1

(842.4)*(1)=x*(12)

842.4=12x

Step 2: Flip the equation.

12x=842.4

Step 3: Divide both sides by 12.

12x12=842.412

x=70.2

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Answer:

no, h=anything greater than 12

Step-by-step explanation

Answer:

No. It is false.

Step-by-step explanation:

h - 2 > 10; h = 12

Substitute 12 in place of h.

12 - 2 >? 10

Simplify.

10 >? 10

10 is NOT > 10

10 is not greater than 10. 10 is equal to 10. If the symbol had the "or equal to" underline under it, then it would be true. See image.

Answer:

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

Answer:

3y + 4.1

Step-by-step explanation:

You can't add unlike terms, so you collect like terms:

9y - 6y + 4.1

= 3y + 4.1

The correct option A. 1, is the value of the variable 's' for which the solution of the expression is greatest .

For the given question,

The expression is-

(s + 6) ÷ s

Use the options;

A : s = 1

= (s + 6) ÷ s

= (1 + 6) ÷ 1

= 7

B : s = 2

= (s + 6) ÷ s

= (2 + 6) ÷ 2

= 4

C : s = 3

= (s + 6) ÷ s

= (3 + 6) ÷ 3

= 3

D : s = 4

= (s + 6) ÷ 4

= (4 + 6) ÷ 4

= 2.5

Thus, the value of the variable 's' for which the solution of the expression is greatest is 1.

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