Magda utilizó una cuadrícula de 1 cm de lado para dibujar la figura sombreada, usando triángulos
rectángulos.

The equation of the parabola given in the graph is:

(x - 5)² = -8(y + 4).

The equation of a quadratic function, of vertex (h,k), is given by:

a(y - k) = (x - h)²

In which a = 4p is the leading coefficient.

In this problem, the vertex is at point (5,-4), hence h = 5, k = -4, and the equation is:

a(y + 4) = (x - 5)²

The focus is at y = -6, which means that p = -6 - (-4) = -2, hence the leading coefficient is:

a = 4p = 4(-2) = -8

Hence the equation is:

(x - 5)² = -8(y + 4).

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Answer:

2nd option, x > 1.10

Step-by-step explanation:

[tex]7e^{2x}-5 > 58[/tex]

Add 5 to both sides,

[tex]7e^{2x}-5+5 > 58 +5\\7e^{2x} > 63[/tex]

Divided both sides by 7,

[tex]\frac{7e^{2x}}{7} > \frac{63}{7}[/tex]

[tex]e^{2x} > 9[/tex]

Apply Exponent Rule,

[tex]2x > 2ln(3)[/tex]

[tex]\frac{2x}{2} > \frac{2ln(3)}{2}[/tex]

x > ln(3) or x > 1.09861

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First of all, your question should be: Factor completely 2xy – 6mn – 3my + 4nx, and not Factorize completely 2xy – 6mn – 3m + 4nx. This noted, we proceed to the solution, which is:

2xy – 6mn – 3my + 4nx

→ y(2x – 3m) + 2n(–3m + 2x)

→ (2x – 3m) (y + 2n)

.: Final answer: (2x – 3m) (y + 2n)

(2x – 3m) (y + 2n) is the factorized form of  2xy -6mn - 3m + 4nx

Two or more expressions with an Equal sign is called as Equation.

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

The given expression is 2xy – 6mn – 3my + 4nx

Two times of xy minus six times of mn minus three times of m y plus four times of nx

2xy – 6mn – 3my + 4nx

By using commutative property arrange the terms

2xy –3my– 6mn+ 4nx

Take y as common from first two terms and 2n as common in last two terms

y(2x – 3m) + 2n(–3m + 2x)

(2x – 3m) (y + 2n)

Hence, (2x – 3m) (y + 2n) is the factorized form of  2xy -6mn - 3m + 4nx

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Answer:

Center is at (0,0)

Step-by-step explanation:

An equation of ellipse in standard form is:

[tex]\displaystyle{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2} = 1[/tex]

Where center is at point (h,k)

From the equation of [tex]\displaystyle{x^2+5y^2-45=0}[/tex]. First, we add 45 both sides:

[tex]\displaystyle{x^2+5y^2-45+45=0+45}\\\\\displaystyle{x^2+5y^2=45}[/tex]

Convert into the standard form with RHS (Right-Hand Side) equal to 1 by dividing both sides by 45:

[tex]\displaystyle{\dfrac{x^2}{45}+\dfrac{5y^2}{45}=\dfrac{45}{45}}\\\\\displaystyle{\dfrac{x^2}{45}+\dfrac{y^2}{9}=1}[/tex]

Therefore, the center of ellipse is at (0,0) since there are no values of h and k.

They will both have the same amount in the bank after 10 weeks

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, we have

Nancy

Initial = 400

Rate = 10

So, the equation is

y = 400 + 10x

700

Initial = 700

Spending = 20

So, the equation is

y = 700 - 20x

When they both have the same amount of money in the bank, we have

700 - 20x = 400 + 10x

Evaluate the like terms

30x = 300

Divide by 30

x = 10

Hence, they will both have the same amount in the bank after 10 weeks

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Answer: 7 pigeons sitting on the branches,  5 pigeons under the tree

=12 in total

Step-by-step explanation:

Upper branch has x pigeons, lower has y.

Top branch said: "If one of you flies up to us our number will be double yours":

Well, if one of the bottom branch flies up, the top branch will have x+1 birds and the bottom will have (y−1). The top will have double the bottom, so:

x+1=2(y−1)

Top branch said: "If one of us flies down to you, our numbers will be equal":

Now, the top branch will have x−1 and the bottom y+1. The numbers should be equal:

x−1=y+1

The value of the given trigonometry function is 2√15/15

Half angles are trigonometric identities used to express sine, cosine and tangent of half angles.

For instance the value of cos theta is expressed as shown below;

cosФ = cos(Ф/2+Ф/2)

cosФ = cos²Ф/2-sin²Ф/2
cosФ = cos²Ф/2-(1-cos²Ф/2)
cosФ  = 1 - 2cos²Ф/2

Given the following parameters

cosФ = -7/15

Substitute

cosФ  = 1 - 2cos²Ф/2

-7/15  = 1 - 2cos²Ф/2

-2cos²Ф/2 = -7/15 - 1

-2cos²Ф/2 = -8/15

cos²Ф/2 = 4/15
cosФ/2 = 2/√15

Rationalize

2/√15 * √15/√15

2√15/15

Hence the value of the given trigonometry function is 2√15/15

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A graph which shows the image of ABCD is: A. on a coordinate plane, parallelogram A'B'C'D' has points (-2, 5), (0, 3), (0, -1.2), (-2, 1).

A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on transformation of parallelogram ABCD, we can infer and logically deduce that a graph which shows the image of ABCD is that on a coordinate plane, with parallelogram A'B'C'D' having points (-2, 5), (0, 3), (0, -1.2), (-2, 1) as shown in the image attached below.

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The coordinates of point r(-8,0).

The coordinates of the point r(x,y) which divides the line segment joining the points p([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and q([tex]x_{2}[/tex],[tex]y_{2}[/tex]) internally in the ratio :[tex]m_{1}[/tex][tex]m_{2}[/tex] are

[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]

Given that,

Two end points on the line q(-14,0) and s(2,0). point r(x,y) is the partition of the line segment from q to s in a ratio 3:5

[tex]m_{1}[/tex] = 3 and [tex]m_{2}[/tex] = 5

By using the midpoint formula

[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]

[tex]\left(\frac{3(2)+ 5(-14) }{3+5 } ,\frac{3(0)+ 5(0) }{3+5 }\Rifgt)[/tex]

[tex]\left(\frac{-64}{8 } ,\frac{0 }{8 }\Rifgt)[/tex]

[tex]\left(-8 ,0\Rifgt)[/tex]

Hence, The coordinates of point r(-8,0).

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The height of the second square base prism is 50 cm.

The volume of the first square base prism is represented as follows:

v = ha²

where

Therefore, the height of the prism is 10 cm.

v = 10a²

Hence, the volume of the initial prism is 5 times the volume. Therefore,

v = 5(10a²)

v = 50a²

Therefore,

50a² = ha²

divide both sides by a²

50a² / a² = ha² / a²

50 = h

h = 50  cm

Therefore, the height of the second square base prism is 50 cm.

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Answer:

Step-by-step explanation:

Solution

There are 36 possible ways to combine two dice. The ones you are interested in, are in the table below

Numbers less that 5 are   with their probabilities

Number    Probability    How done.

2                   1/36           1 + 1

3                   2/36          2 + 1      1 + 2

4                   3/36           2 + 2     1 +3    3 + 1

Total             6/36           1/6

Greater than 7

Number        Probability  How done

8                    5/36           6+2    2+6   5 +3    3+5     4 + 4

9                    4/36            6+3     3 + 6     5+4    4+ 5  

10                   3/36            6+4    4 +6      5 + 5

11                    2/36             5+6      6 + 5

12                   1 /36             6 + 6

Total              15/36            

Answer

15/36 + 1/6 = 15/36 + 6/36 = 21/36

Final Answer: 7/12

Answer:

$591.10

Step-by-step explanation:

First, add up $475.88 and $609.00 together. Then, subtract it from $1675.88. They need $591.10 more for their vacation.

Total parrot=40

Caught=8

Fraction

#2

Out of 40 parrots 8 are ringed

Parrots per one ringed=40/8=5

Total ringed before=32

Total no of parrots

There are 160 parrots

Answer:

[tex]\sf 1) \quad \dfrac{1}{5}[/tex]

[tex]\sf 2) \quad 160\:parrots[/tex]

Step-by-step explanation:

Given information:

Therefore, the fraction of ringed parrots from the second catch is:

[tex]\implies \sf \dfrac{ringed\:parrots}{total\:caught\:parrots}= \dfrac{8}{40}=\dfrac{1 \times 8}{5 \times 8}=\dfrac{1}{5}[/tex]

If she caught and ringed 32 parrots in her first catch, but only 1/5 of the parrots caught in the second catch were ringed, then 32 parrots represents 1/5 of the total number of parrots.  To find the total number of parrots, simply multiply the total number of ringed parrots by 5:

[tex]\implies \sf \textsf{Total number of parrots}=32 \times 5 = 160[/tex]

Answer:

Robert bought 13 colored pencils and 2 pencils

Step-by-step explanation:

13 x 0.60 = 7.8
2 x 0.45 = 0.9

7.8 + 0.9 = 8.70

13 colored pencils are $7.80

2 pencils are $0.9

15 total is $8.70

Option C is correct (y + z = 6) ⋅ −3

What is a linear equation in math?

As per the statement -

A student is trying to solve the system of two equations given below:

Equation P:   y + z = 6              ....[1]

Equation Q:  3y + 4z = 1           ....[2]

Multiply the equation [1] by -3 to both sides we have;

-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)

Add equation [2] and [3] to eliminate the y-term;

z = -17

Therefore, the  possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3

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The complete question is -

A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?

(y + z = 6) ⋅ 4

(3y + 4z = 1) ⋅ 4

(y + z = 6) ⋅ −3

(3y + 4z = 1) ⋅ 3

Answer:

x = 4, y = 1

Step-by-step explanation:

y = (1/4)x  

2x + 4y = 12

replace y with something x

2x + 4(1/4)x = 12

3x = 12

x = 4

so y = 1

160 cubes required to completely pack the prism without any gap or overlap

The dimensions of the rectangular prism are given as:

Length = 1 1/3

Width = 5/6

Height = 2/3

The volume is

Volume = Length * Width * Height

This gives

Volume = 1 1/3 * 5/6 * 2/3

Evaluate the product

Volume = 20/27

The side length of the cube is

L = 1/6

The volume of the cube is

V = (1/6)^3

Evaluate

V = 1/216

The number of cubes required to completely pack the prism without any gap or overlap is

n =  (20/27) / (1/216)

Evaluate

n =  160

Hence, 160 cubes required to completely pack the prism without any gap or overlap

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For the first representation, the equation is : y = 3x-5.

For the second representation, the equation is : y = -12x+2.

For the third representation, the equation is : y = 5/4x-5.

For the fourth representation, the equation is: y = -6x+3.

Analyze the representations given in the question, in order to find its corresponding equation.

According to the question,

For the first representation, y=1 when x=2, y=-2 when x=1 and y=4 when x=3. On substituting these values of x and y in the given equations, we get that y = 3x-5.

Similarly, for the second representation, we get, y = -12x+2.

For the third representation, we get, y = 5/4x-5.

For the fourth representation, we get, y = -6x+3.

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your question is not clear

Based on the calculations, the coordinates of the mid-point of BC are (1, 4).

First of all, we would determine the initial y-coordinate by substituting the value of x into the equation of line that is given:

At the origin x₁ = 0, we have:

y = 2x + 1

y₁ = 2(0) + 1

y₁ = 2 + 1

y₁ = 3.

When x₂ = 2, we have:

y = 2x + 1

y₂ = 2(2) + 1

y₂ = 4 + 1

y₂ = 5.

In order to determine the midpoint of a line segment with two (2) coordinates or endpoints, we would add each point together and divide by two (2).

Midpoint on x-coordinate is given by:

Midpoint = (x₁ + x₂)/2

Midpoint = (0 + 2)/2

Midpoint = 2/2

Midpoint = 1.

Midpoint on y-coordinate is given by:

Midpoint = (y₁ + y₂)/2

Midpoint = (3 + 5)/2

Midpoint = 8/2

Midpoint = 4.

Therefore, the coordinates of the mid-point of BC are (1, 4).

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A sample statistic becomes more accurate as the sample size increases due to the law of large numbers.(option C)

The law of large numbers is a theorem in statistics that states that as the number of experiments increases, the sample mean becomes closer to the theoretical mean. The law of large numbers was first proved by Jacob Bernoulli.

For example, if you carry out an experiment to determine how many students in the US attend high school and the only person you ask tells you he does not attend high school. If you conclude the experiment based on the response of that one person, it is likely that you would conclude that on average, people in the US do not attend high school. If you ask more people, it is likely that your opinion would change and you could come to the conclusion that majority of US citizens attend high school.

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75  is  the least positive integers which , when subtracted 7300 would make a result a perfect square

So normally the least positive integer of all the numbers is the number 1 but when you talk about least positive integer, often times you are talking about the special function called the ceiling function

The smallest of the numbers in the set {1, 2, 3, …} is 1.

So, the number 1 is the smallest positive integer.

7300

If we Take Square root of 7300 we have to subtract 75 from 7300 to get a perfect square.

7300-75=7225

(85)^2=7225

75 to be subtracted

√7300 ≥ 85

Perfect Square = 85² =  7225     or (7300-7225 = 75)

75  is  the least positive integers which , when subtracted 7300 would make a result a perfect square

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Answer:

B

Step-by-step explanation:

The beginning temperature is -12 and then it rises 5 degrees each hour at the end of the game it is 32 degrees.

Answer:

below

Step-by-step explanation:

2) 10², the second power of ten

3) 10⁴, the fourth power of ten

4) 1000

5) 400

6) 90,000

7) 10

8) 100,000

9) 50

10) 7000

11) 8

12) 24 x 10⁴

13) 93,000,000

Answer + Step-by-step explanation:

The maximum height is; 180 ft and the Total time in the air is 12 seconds

We are given the equation that represents the height of the rocket as;

d = 60t - 5t²

Taking the derivative of the formula gives us;

d' = 60 - 10t.  

-10t represents the acceleration.  The 60 represents the initial velocity.

Set 60 - 10t = 0 and solve for t to get;

t = 60/10 = 6seconds.  

That's when the maximum height occurs. Plug that value of t into the original quadratic equation to get the maximum height.

d(6) = 60t - 5t²

d(6) = 60(6) - 5(6²)

d(6) = 180

So,  maximum height is about 180 ft.  

Thus, total time in air = 2 * 6 = 12 seconds

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Answer:

you better give me brainliest

65/79

Step-by-step explanation:

number if boys =79-14 = 65

p of selecting a boy >> 65/79

can't cancel out so leave your answer like that

The numeric values from the function are given by:

The function is:

f(x) = 4 - 2x + 6x².

When x = a:

f(a) = 4 - 2a + 6a².

When x = a + h:

f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.

For the last question

[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h

Hence:

[f(a + h) - f(a)]/h = 12a + 6h - 2.

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Answer:

35

Step-by-step explanation:

Angle QRS is an inscribed angle, so measure of angle QRS is half the measure of the intercepted arc, arc SPQ. Therefore arc SPQ is 125*2 = 250 degrees, and arc QRS is 360 - 250 = 110 degrees.

Angle QPS is an inscribed angle, and arc QRS is its intercepted arc. Therefore angle QPS is 110/2 = 55 degrees. Since PS is the radius of the circle, angle PQS, the angle inscribed in the semicircle, is 90 degrees. Since interior angles of the triangle QPS add up to 180 degrees, angle QSP is 180 - 90 - 55 = 35 degrees.

Angles QSP and UST are vertical angles, and by the vertical angles theorem, they are congruent. Therefore x = 35.