GEOMETRY The length of a rectangle is twice the
width. Find the area, if the perimeter is 60 centimeters.
Draw a picture, define a variable, write an equation, and
solve the problem.

The egg production in 2000 is predicted to be 64.6 billions eggs

y = mx + c

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

m = (60.3 - 51.7 ) / ( 4 - 0 )

m = 8.6 / 4

m = 2.15

y - y1 = m ( x - x1 )

y - 51.7 = 2.15 ( x - 0 )

y - 51.7 = 2.15

y = 2.15x + 51.7

year 2000 is equivalent to x = 6

y = mx + c

plugging in x = 6 gives

y =  2.15 * 6 + 51.7

y = 64.6 billions eggs

The egg production in 2000 is predicted to be 64.6 billions eggs

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 In the equation of the given parabola the values of the vertex, focus and directrix are as follows:

  The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

  In this case we have an expression given by:

x = - 4y²

   We must find the canonical equation:

-4(y - 0)² = 1(x - 0)

(x - 0) = -4 (y - 0)²

has the form

(y - k)² = 4p(x - h)

  This means that the vertex of this parabola is

v = (h, k)

v = (0,0)

  To know the focus we must know the value of "p".

4p = -1/4

p = -1/16

f = (0, -1/16)

d = x = 1/16

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The solution of the given linear equation in one variable 5(3w - 2) -7= 23  is at w = 8/3.

According to the given question.

We have a linear equation in one variable 5(3w - 2) - 7 = 23.

As we know that, as we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 5(3w -2) = 23 is given by

5(3w - 2) -7= 23

⇒ 15w - 10 -7 = 23  ( by distributive rule)

⇒ 15w -7-10 = 23

⇒ 15w -17 = 23

⇒ 15w = 23 + 17     ( adding 17 both the sides)

⇒ 15w = 40

⇒ w = 40/15

⇒ w = 8/3

Hence, the solution of the given linear equation in one variable 5(3w - 2) -7= 23  is at w = 8/3.

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Answer:Your answer is X>7

Step-by-step explanation:

Form:

x>7

Interval Notation:

(7,∞)

   The equation that defines the parabola with vertex at the origin and directrix at x = -5/2 is

x = y²/10

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

The canonical equation of a parabola is given by

(x - h)² = 4p(y - k)

The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

v = (0, 0)

d = (-2.5, 0) them the focus is on the right so the parabola is of the form X = Y².

(y - 0)² = 4p(x - 0)

If the directrix is x = -5/2 then the focus will be:

f = (0 + p, 0)

0 + p = 2.5

p = 0 + 2.5

p= 2.5

(y - 0)² = 4*2.5(x - 0)

(Y)² = 10(X)

x = y²/10

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The solution of the system as an ordered triple (x, y, z) is; (2, 1, 1.25).

The cost of a bouquet of 12 daisies is; $15

Let the cost of roses be x

Let the cost of carnations be y

Let the cost of Daisies be z

Thus, we have the three simultaneous equations as;

12x + 8y + 8z = 42   ------(1)

8x + 6y + 10z = 34.5   ------(2)

10x + 10y + 6z = 37.5    ------(3)

Using online simultaneous equation calculator gives us the values as;

x = 2; y = 1; z = 1.25

Thus, the solution of the system as an ordered triple (x, y, z) is; (2, 1, 1.25).

The cost of a bouquet of 12 daisies is;

Cost = 12 * 1.25 = $15

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The output is always an even integer for every input. Odd numbers end in the digits 1, 3, 5, 7 while even numbers conclude in the numerals 0, 2, 4, 6, 8.

Let us consider an input = number (n) × even number.

So, the output is definitely an even number.

The output is always an even integer for every input. Odd numbers end in the digits 1, 3, 5, 7 while even numbers conclude in the numerals 0, 2, 4, 6, 8. In this instance, we can multiply any x number by any even integer to obtain an even number.

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2.42 km was steve's peak speed in kilometers per hour.

Describe speed -

Given speed is 67.1 cm/s

we know that 1 cm = 10-² m

            and  1 m = 10-³ km

∴   1 cm = 10-5 ∴m

also          1 sec = 1/3600 hr

∴   67.1 cm/s  = [tex]\frac{67.1 * 10^{-5 km} }{\frac{1 hr}{3600 } }[/tex]

or  67.1 cm/s  =  2. 4156 km/hr  or 2.42 km

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Answer:4

Step-by-step explanation: 2x2 = 4 just as u said

To ensure that the car has enough petrol of a trip, we get that it should have 52.58 liters of petrol.

We are given that:

For 27 liters of petrol, we can drive a car for 95 km.

SO, by using the unitary method, we get that:

for 1 km of journey, the liters of petrol that we need is = 27 / 95 liters.

1 km = 27 / 95 liters

For 185 km, we get that:

185 km = 27 / 95 × 185 liters

185 km = 52.58 liters.

Therefore, to ensure that the car has enough petrol of a trip, we get that it should have 52.58 liters of petrol.

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The monthly payment for Jake borrowing $41,000 for 5 years at a 3% APR is $736.72.

Monthly payments are equal periodic payments made to offset an outstanding liability.

The monthly payments are the compounded principal (Principal + Compound Interest amount) divided by the number of periods.

The  monthly payments can be computed using an online finance calculator as follows:

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 3%

PV (Present Value) = $41,000

FV (Future Value) = $0

Results:

Monthly Payment (PMT) = $736.72

Sum of all periodic payments= $44,203.20

Total Interest = $3,203.20

Thus, Jake who borrowed $41,000 for 5 years at a 3% APR needs to make a monthly payment of $736.72 to settle the principal and the compounded interest.

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Using the given information, the equation of the circle with center located at point (1 , -2) and passes through the point (0 , 1) is (x - 1)^2 + (y + 2)^2 = 10.

Using the distance formula, get the radius of the circle by solving for the distance between the center (1 , -2) and the point (0 , 1).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(0 - 1)^2 + (1 - -2)^2

radius= √1 + 9

radius = √10

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (1 , -2)

r = √10

(x - 1)^2 + (y - -2)^2 = (√10)^2

(x - 1)^2 + (y + 2)^2 = 10

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The hypothesis is the phrase following the word if = " 2 x+6=10"

The conclusion is the phrase following the word then = " x=2"

A specific, verifiable prediction of what the researcher(s) believe the study's results will be is known as a hypothesis (plural: hypothese). It is stated at the outset of the investigation.

Most often, this entails speculating on a potential correlation between two variables: the independent variable (what the researcher modifies) and the dependent variable (what the research measures).

The null hypothesis and the alternative hypothesis (known as the experimental hypothesis when the technique of examination is an experiment) are traditionally written as two separate forms of the hypothesis in research.

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Jupiter is closer to the sun with 17. 3 × 10^ -2 kilometers

A ratio can be defined as the comparison of two numbers or elements indicating their sizes in relation to each other.

It also explains how many times a number contains another.

From the information given, we have;

To determine the distance Jupiter is from the sun than Neptune, we have to divide the distance for Jupiter by Neptune

= 7. 78 × 10^8/ 4. 5 × 10^9

= 0. 173

= 17. 3 × 10^ -2 kilometers

Thus, Jupiter is closer to the sun with 17. 3 × 10^ -2 kilometers

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A variable is a place where values are kept. The number of students in Shawn's school with at least one sibling is 367.

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically denote a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

Let the number of students be x, then

25/32 = x/470

simplifying the above equation, we get

25(470) = 32x

32x = 11750

Dividing both sides of the equation by 32, we get

32x / 32 = 11750 / 32

x = 367

The value of x = 367.

Therefore, at least one sibling is present among 367 kids at his school.

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18 lines of symmetry the dome have, after excluding the spire of the dome.

36 ÷ 2 = 18

3 row × 36 windows per row, total windows = 108. 36 of them connects a window with the window across to form 1 line of symmetry.

If two additional identical parts that are arranged in an orderly fashion can be divided from a shape, it is said to be symmetrical. As an illustration, if you are instructed to cut out a "heart" from a piece of paper, you need just fold the paper, draw one-half of the heart at the fold, and then cut it out to discover that the second half exactly matches the first half.

Asymmetrical and symmetrical balances are the two types of balance. The two parts of the thing are precisely identical and balanced in symmetrical balance. The two parts of an asymmetrical balance are not similar; rather, separate things are arranged such that they appear to be balanced.

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Answer:

V = E - F + 2.

Step-by-step explanation:

V − E + F = 2

Add E to both sides

V + F = E + 2

Subtract F from both sides:

V = E - F + 2.

Line segments are congruent if they have the same length.

∠ ACB ≅ ∠ ABC

Segments of the same length are said to be congruent. Collinear points are those that share a line. A mathematical assertion that can be validated is known as a theorem. A point that separates a segment into two congruent segments is the segment's midpoint.

Line sections are harmonious assuming that they have a similar length. You can utilize tick imprints to demonstrate harmonious line sections. In the triangle underneath, line fragments Stomach muscle and BC are harmonious.

Harmonious portions are sections that have a similar length. ≅ Focuses that lie on a similar line are called collinear. A hypothesis is a numerical explanation that can be demonstrated. The midpoint of a section is a point that separates the portion into two harmonious fragments.

Therefore, ∠ ACB ≅ ∠ ABC

The complete question is:

a. Name two unmarked congruent segments.

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The expressions which does not represent one of the section is 4 ÷ 12 and 4 × 12

The correct answer options is option B and C

Algebra is a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

The expression to represent one of the sections = Quantity of decorative fence border ÷ Number of sections

= 12 ÷ 4

= 12 / 4

Therefore, the expressions which does not represent one of the section is 4 ÷ 12 and 4 × 12

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(a) The equation connecting y and x is y = 21 × 1 / x .

(b) The value of y when x = 21 is  1 .

(a) It is given that y is inversely proportional to x which means that it can be written as y ∝ 1 /x   an hence y = k × 1 /x    ......(1) where "k " is proportionality constant .

Putting y = 7 and x = 9 in equation (1) , we get

    7 = k × 1 / 3

    k = 7 ×  3

    k = 21

Hence , equation connecting y and x is y = 21 × 1 / x       ....(2)

(b) Putting x = 21 in equation (2) , we get

        y =  21 × 1 / 21

        y = 1

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Answer:

no

Step-by-step explanation:

(x, y) (7, 1)

x = 7

y = 1

plug these numbers into y = x + 6

1 = 7 + 6

1 = 13

false

so, no

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Answer:

(1,12)

Step-by-step explanation:

in a graph we know that 5 is equal to 10 so the answer is 1,12

The orthocenter of the ΔABC is ( -1,5 ).

In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.

Given the  co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

To find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y = mx + b

where m is the slope and b is the y-intercept.

Using the formula of slope given [tex]$m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]  , we will find the slope of AB and BC.

Now, slope of AB is m = (7-3/-1 + 3)  

i.e. m = (4/2) = 2

Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,

y = mx + b

1 = 2 × (-1) + b

i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is m=(3-7/3+1)  i.e. m=-4/4 i.e. m--1

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is [tex]m*2=-1[/tex]  i.e. m = -1/2

So, slope of line perpendicular to BC is  i.e.[tex]m*-1=-1[/tex] i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB m=-1/2 i.e.  and the point opposite to AB

i.e. C(3, 3), we get,

y = mx + b

i.e. [tex]3=-1/2*3+b[/tex]  

i.e. b = 9/2

So, the equation of line perpendicular to AB is

[tex]y=-x/2+9/2[/tex]

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC

i.e. A( -3,3 ), we get,

y = mx + b

i.e. 3 = 1 × -3 + b

i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of (x, y).

As, we have y = x + 6 and  y = -x/2 + 9/2

This gives, y = -x/2 + 9/2 → x + 6

y = -x/2 + 9/2

simplifying the above equation, we get

2x + 12 = -x + 9

3x = -3

x = -1.

So, y = x + 6

simplifying the above equation, we get

y = -1 + 6

y = 5.

The value of x = -1 and y = 5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

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The  triangle formed by joining three points on the graph is isosceles triangle

To find out the type we need to find the length of each side which can be found out with distance formula =√[tex](x2-x1)^{2}[/tex]+[tex](y2-y1)\^{2}[/tex] ) provided in the coordinate geometry

so, the length of side PQ of triangle PQR = √[tex](4-2)^{2}[/tex])+[tex](2-5) ^{2}[/tex])

   = √[tex]2^{2}[/tex] +[tex](-3)^{2}[/tex]

                          = √4+9

                           = √13 units

So, the length of side QR of triangle PQR =  √[tex](7-4)^{2}[/tex]+[tex](4-2)^{2}[/tex] )

   = √[tex]3^{2}[/tex] + [tex]2^{2}[/tex]

                          = √(9+4)

                           = √13 units

So, the length of side PR of triangle PQR = √([tex](7-2)^{2}[/tex]+[tex](4-5)^{2}[/tex] )

   = √([tex]5^{2}[/tex] + [tex](-1)^{2}[/tex] )

                          = √(25+1)

                           = √26 units

As the two sides of triangle are equal so this triangle formed by joining three points on the graph is isosceles triangle

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Answer:

It would be b. and c. and d.

Step-by-step explanation:

Answer:

Your answer is 20

Step-by-step explanation:

Ok so AB= 25

BC= 15

We need to find AC And the Pythagorean theorem says a²+b²=c²

Since we only got C and B were gonna do subtraction

So 25²-15²= 400

And 400 square rooted is 20

Hope this helps :33333

The slope is -A/B and y-intercept is C/B in the line (A/D)x + (B/D)y = C/D

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x.

We also refer to this tan as the line's slope

We know that the equation for slope(m) and y - intercept(c) of a line is given by :

y = mx + c

Here the equation is give as (A/D)x + (B/D)y = C/D, lets simply

⇒ (A/D)x + (B/D)y = C/D

⇒ B(y)/D = C/D -(A/D)x

⇒ [tex]\frac{B(y)}{D}[/tex] = [tex]\frac{C -A(x)}{D}[/tex]

⇒ B(y) = C - A(x)

⇒ y = [tex]\frac{C -A(x)}{B}[/tex]

⇒ y = [tex]\frac{ -A}{B}x + \frac{C }{B}[/tex]

Here, slope is -A/B and y-intercept is C/B

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