what contribution to geometry is attributed to the work of rene descartes

Step-by-step explanation:

length = the original length

width = the original width

length = width + 10 or

width = length - 10

(length + 4) × (width + 8) = 135

A

now we are using the first equation in the second to solve then for length :

(length + 4) × (length - 10 + 8) = 135

(length + 4) × (length - 2) = 135

length² - 2×length + 4×length - 8 = 135

length² + 2×length = 143 or

length² + 2×length - 143 = 0

this is the equation to model the scenario.

solving in general such a quadratic equation :

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = length

a = 1

b = 2

c = -143

length = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =

= (-2 ± sqrt(4 + 572))/2 =

= (-2 ± sqrt(576))/2 =

= (-2 ± 24)/2 = (-1 ± 12)

length1 = -1 + 12 = 11

length2 = -1 - 12 = -13

a negative solution for a length is not applicable, so,

length = 11

width = length - 10 = 11 - 10 = 1

B

the expanded length = 11 + 4 = 15

the expanded width = 1 + 8 = 9

the expanded perimeter is then

2×15 + 2×9 = 30 + 18 = 48

Answer:

16

Step-by-step explanation:

i hope this help you

The correct answer is option D.The point 1.6 with bar will be lies between 1 and 2.

The image of the question is attached with the answer below:-

The number line is the line on which real numbers are marked with the same interval between them. Number lines are used to mark any point of the real number on the line.

We can see in the image that A, B, C and D points are marked on the number line. The line is marked with real numbers that are integers.1.6 bar number will lie between 1 and 2 numbers.

Therefore the correct answer is option D.The point 1.6 with a bar will be lies between 1 and 2.

To know more about Number line follow

https://brainly.com/question/24644930

#SPJ1

Answer:

D

Step-by-step explanation:

The number of seeds in 2 ounce package is 6.7 × 10⁷ seeds

From the question, we are to determine the number of seeds in 2 ounce package

From the given information,

An orchid seed weighs 3.2 × 10⁻⁸ ounces

If an orchid seed weighs 3.2 × 10⁻⁸ ounces

Then,

2 ounce package will contain [tex]\frac{2}{3\times 10^{-8} }[/tex] seeds

= 0.67 × 10⁸

= 6.7 × 10⁷ seeds

Hence, the number of seeds in 2 ounce package is 6.7 × 10⁷ seeds

Learn more on Calculating quantity here: https://brainly.com/question/11262670

#SPJ1

Answer: I think

Step-by-step explanation:Let the coordinate of the point be (x,y,z). Since the point is located 3 units behind the YZ− plane, 4 units to the right of XZ− plane and 5 units above the XY−plane ,x=−3,y=4 and z=5 Hence, coordinates of the required points are (−3,4,5)

Abby can make 5 complete groups with 9 extra bonus coupons.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here, Abby has total number of coupons = 159

        Number of coupons in a group = 30

Total number of groups = Total Coupons / coupons in a group

                                         = 159 / 30

                                         = 5.3

Thus, Abby can make 5 complete groups with 9 extra bonus coupons.

Learn more about Division from:

https://brainly.com/question/2273245

#SPJ1

Given the charges for a football and the tax rate, the total price to purchase a football is $23.6698.

Given that;

First, we calculate the tax price on the football.

Tax price = Tax rate × Charges for the football

Tax price = 6% × $22.33

Pax price = 0.06 × $22.33

Tax price = $1.3398

Now, total price to purchase football will be;

Total price = Charges for a football + Tax price

Total price = $22.33 + $1.3398

Total price = $23.6698

Given the charges for a football and the tax rate, the total price to purchase a football is $23.6698.

Learn more about tax here: https://brainly.com/question/16423331

#SPJ1

The trip would have taken 6 hours.

(300 mi) / (50 mi/h) = 6 h

Answer:

76°

Step-by-step explanation:

The 2 base angles are equal so

52+52+vertex angle=180° (Angle Sum Property)

104+ vertex angle=180°

vertex angle= 180-104

vertex angle=76°

cos²(x) = 3 sin²(x)

1 - sin²(x) = 3 sin²(x)

1 = 4 sin²(x)

1/4 = sin²(x)

± √(1/4) = sin(x)

± 1/2 = sin(x)

sin(x) = 1/2   or   sin(x) = -1/2

[x = arcsin(1/2) + 2nπ   or   x = π - arcsin(1/2) + 2nπ]

… … … or   [x = arcsin(-1/2) + 2nπ   or   x = π - arcsin(-1/2) + 2nπ]

(where n is any integer)

[x = π/6 + 2nπ   or   x = 5π/6 + 2nπ]

… … … or   [x = -π/6 + 2nπ   or   x = 7π/6 + 2nπ]

Answer:

last option

Step-by-step explanation:

hope it helps

One way to determine the factors of x³ + 5x² - 6x - 30 by grouping is shown by option D. x² (x + 5) - 6(x + 5).

Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.

Given a cubic polynomial,

x³ + 5x² - 6x - 30

Taking the first two terms together and the other two terms together,

(x³ + 5x²) + (- 6x - 30)

Taking x² common from first and -6 common from second,

x² (x + 5) - 6(x + 5)

Hence the correct option is D.

Learn more about Polynomials here :

https://brainly.com/question/28315959

#SPJ7

Answer:

Step-by-step explanation:

Method

Inversely in this sentence means

y = k/x    

So you first step is to find the value of k. You do that by setting up an inverse relationship with y = 2 , x = 5

2 = k/5                     Multiply both sides by 5

2*5 = 5*k/5

10 = k

Now you are able to answer the question.

y = 10/x

3= 10/x                      Multiply both sides by x

3*x = x * 10/x

3x = 10                      Divide both sides by 3

3x/3 = 10/3

x = 3.33 or x = 3 1/3

Answer

x = 3.33 or x = 3  1/3

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{4}{x}~~ = ~~\cfrac{x}{9}\implies 36=x^2\implies \sqrt{36}=x\implies 6=x[/tex]

The results for the matching between function and its period are:

If a given function presents repetitions, you can define the period as the smallest part of this repetition. As an example of periodic functions, you have: sin(x) and cos(x).

[tex]\mathrm{Period\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}[/tex]

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}[/tex]

The period of sin(x) and cos(x) is 2π.

For solving this question, you should analyze each option to find its period.

1) Option 1

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi }{\frac{1}{2} }=4\pi[/tex]

Thus, the option 1 matches with the letter D.

2) Option 2

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{4} =\frac{\pi }{2}[/tex]

Thus, the option 2 matches with the letter A.

3) Option 3

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{2} =\pi[/tex]

Thus, the option 3 matches with the letter C.

4) Option 4

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{8} =\frac{\pi }{4}[/tex]

Thus, the option 4 matches with the letter B.

Read more about the period of a trigonometric function here:

https://brainly.com/question/9718162

#SPJ1

Answer:

10.5

Step-by-step explanation:

quick math

The height in meters of a lava rock that falls for 5 seconds is; 122.5 m.

We are told that the height is modelled by the equation;

y = ¹/₂gt²

where;

y represents the height.

g is 9.8 m/s²

t represents the falling time of the lava rocks.

Thus, at t = 5, we have;

y(5) = ¹/₂(9.8)(5)²

y(5) = 122.5 m

Read more about quadratic equations at; https://brainly.com/question/1214333

#SPJ1

Answer:

D / 242

Step-by-step explanation:

hope this helps!

Answer:

[tex]y=\dfrac{1}{2}(x+5)^2-3[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

Parent function

[tex]y=-x^2[/tex]

Reflected in the x-axis

[tex]-f(x) \implies y=-(-x^2)\implies y=x^2[/tex]

Compressed vertically by a factor of 1/2

Multiply the whole function by the given scale factor:

[tex]\dfrac{1}{2}f(x)\implies y=\dfrac{1}{2}x^2[/tex]

Translated 3 units down

Subtract 3 from the whole function:

[tex]f(x)-3 \implies y=\dfrac{1}{2}x^2-3[/tex]

Translated 5 units left

Add 5 to the variable of the function:

[tex]f(x+5) \implies y=\dfrac{1}{2}(x+5)^2-3[/tex]

To sketch the parabola

Vertex = [tex](-5, -3)[/tex]

Axis of symmetry:  [tex]x = -5[/tex]

Plot points:

[tex]x=-9 \implies \dfrac{1}{2}(-9+5)^2-3=5 \implies (-9,5)[/tex]

[tex]x=-7 \implies \dfrac{1}{2}(-7+5)^2-3=-1 \implies (-7,-1)[/tex]

[tex]x=-3 \implies \dfrac{1}{2}(-3+5)^2-3=-1 \implies (-3,-1)[/tex]

[tex]x=-1 \implies \dfrac{1}{2}(-1+5)^2-3=5 \implies (-1,5)[/tex]

Answer & explanation:

A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question.

Pls, choose me as brainliest!

Answer:

Quadrilateral:  shape with 4 sides

Perpendicular means at right angles.  Therefore, draw two sides at a right angles to each other.  Mark this with a right angle symbol.

Draw 2 sides that are parallel.  Mark these with arrows.

Please see attached diagrams.

[tex] \sqrt{8 \: + \: 2 \sqrt{15} } [/tex]

[tex] \sqrt{( \sqrt{3 } \: + \: \sqrt{5} ) ^{2} } [/tex]

[tex] \boxed{ \bold{\sqrt{3} \: + \: \sqrt{5} }}[/tex]

Answer:

14) x = 30°

15) x = 50°

Step-by-step explanation:

14) 60 + x = 90

     x = 90 - 60

     x = 30°

15) 130 + x = 180

     x = 180 - 130

     x = 50°

Hope this helps

Step-by-step explanation:

Is first image we are given a right angle and we know that right angle = 90°

So,

60 + x = 90

x = 90 - 60 = 30°

x = 30°

In the second image we are given a straight line and we know that on the 180° angle is a straight line.

so,

130 + x = 180

x = 180 - 130

x = 50°

Answer:

a) v>4.5

b) w<6.5

a) 0.3 recurring

b) 5/11

Answer:

The answer to the equation is B.

Step-by-step explanation:

Answer:

i took the test and its B

Step-by-step explanation:

The average rate of change of the function over the interval [-1, 2] is: C. 2.5.

The average rate of change over an interval of a function is: f(b) - f(a) / b - a.

Given the interval  [-1, 2]:

a = -1; f(a) = -5

b = 2; f(b) = 2.5

Average rate of change = (2.5 - (-5)) / (2 - (-1)) = 7.5/3

Average rate of change = 2.5 (option C).

Learn more about average rate of change on:

https://brainly.com/question/11627203

#SPJ1

Answer:y=5x+1

Step-by-step explanation:the y intercept is the y value when x=0 which we can read off as run. Slope =rise/run=(change in y value)/(change in x value) for any two points.

Answer:

yes they do

Step-by-step explanation:

they share a ray