A ′ B ′ C ′ triangle, A, prime, B, prime, C, prime is the image of △ A B C △ABCtriangle, A, B, C under a rotation about the origin, ( 0 , 0 ) (0,0)left parenthesis, 0, comma, 0, right parenthesis.

Observe that

[tex]x^2 + 3x + 1 = (x^2 + 4x + 4) - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - (x + 2) - 1[/tex]

so that

[tex]P(x+2) = (x+2)^2 - (x+2) - 1 \implies P(x) = x^2 - x - 1[/tex]

Then

[tex]P(x - 1) = (x-1)^2 - (x-1) - 1 \\\\ ~~~~~~~~ = (x^2 - 2x + 1) - (x - 1) - 1 \\\\ ~~~~~~~~ = \boxed{x^2 - 3x + 1}[/tex]

Alternatively, we can avoid find [tex]P(x)[/tex] altogether and instead first write [tex]x-1[/tex] in terms of [tex]x+2[/tex] :

[tex]x - 1 = (x - 1) + 2 - 2 = (x + 2) - 1 - 2 = (x + 2) - 3[/tex]

Then

[tex]P(x - 1) = P((x + 2) - 3) \\\\ ~~~~~~~~ = (x - 3)^2 + 3 (x - 3) + 1 \\\\ ~~~~~~~~ = x^2 - 3x + 1[/tex]

Answer:

28 legs are on the ground

The interest that Marcos will get is 50000.

The following can be deduced from the information given:

Principal = 50000

Interest rate = 12.5%

Time = 8 years

The simple interest will be:

= (PRT/100)

= (50000 × 12.5 × 8)/100

= 50000

The amount that will be obtained after 8 years will be:

= Principal + Interest

= 50000 + 50000

= 10000

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Answer:

The interest that Marcos will get is 50000.

1st transformation: A vertical translation of the figure down by 8 units

2nd transformation: Shows a reflection on both axis and vertical translation up the plane by 8 units

Transformation is a way of changing the position of an object on an xy-plane.

For the translation

(x, y)-> (x, y-8)

It shows a vertical translation of the figure down by 8 units while the translation;

(x, y - 8) -> (-x, -y)

shows a reflection on both axis and vertical translation up the plane by 8 units

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Answer:

8

Step-by-step explanation:

The equation of the parabola can be represented as

[tex]y = a(x + 1)(x - 5)[/tex]

for some constant a.

Since the coefficient of x² is 2, a = 2, so

[tex]y = 2(x + 1)(x - 5) \\ \\ y = 2( {x}^{2} - 4x + 5) \\ \\ y = 2 {x}^{2} - 8x + 10[/tex]

So, the answer is 8.

Answer:

C

Step-by-step explanation:

you can only work 40 or less hours per week but you must earn greater then or equal to $323.

Answer: -4/15

Step-by-step explanation: Since the base denominator is the same, all we have to do is add the numerators (the denominators stay the same.)

-9 + 5 = -4 which is -4/15.

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Answer:

The order of operations is Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

Step-by-step explanation:

The order of operations is PEMDAS.

P: Parenthesis

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

An easy way to remember PEMDAS is, please excuse my dear aunt sally.

Hope this helps!

If not, I am sorry.

The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.

Answer:

The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.

Step-by-step explanation:

The distance between points M and N according to the task content is; 9.8 meters.

From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints of KL and JL respectively.

Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;

NM/19.6 = 7.4/(2×7.4)

NM = 19.6/2 = 9.8 meters.

This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.

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Answer: 9.8 meters

Step-by-step explanation:  Trust Me!! I got the answer correct on Edge.

Q:  What is the distance between points M and N?

A:  9.8 meters  

Answer:

it might be greater i think

Answer:

x=180 - 25

x=155

x+ 169=180

x=180-169

x=11

Angle x of the triangle PQR is 53 degrees.

Angle x is gotten by alternate angle relationship.

Line AB is parallel to line CD

Therefore,

AB║CD

Hence,

62 + x = 115(alternate angles)

62 - 62 + x = 115 - 62

x = 53°

We got the angle x degrees from alternate angle relationship.

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Answer:

x = 50

Step-by-step explanation:

Angle <BPR and angle <PRD are supplementary angles so their sum is equal to 180

m<BPR + 115 = 180 subtract 115 from both sides

m<BPR = 65

angles:

<APQ, x, and <BPR form a straight line and so their sum is equal to 180

65 + x + 65 = 180 add like terms

130 + x = 180 subtract 130 from both sides

x = 50

The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the markup, since the store sells the cell phone for $315, hence:

(315 - 140)/140 * 100% = x

x = 125%

The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.

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Using proportions, considering the given ratio, it is found that 9090 grapes were there.

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

The ratio of bananas to grapes of 3:101 means that out of 104 fruits, 3 are bananas and 101 are grapes. Hence the rule of three is given as follows:

3 bananas - 101 grapes

270 bananas - n grapes.

Applying cross multiplication:

3n = 101 x 270

n = 101 x 270/3

n = 9090.

9090 grapes were there.

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Answer:

Arithmetic sequence

Step-by-step explanation:

The given sequence is arithmetic because it is increases gradually by 5

so the answer is "an arithmetic" and "difference" is equal to "5"

Answer:

<PQR is 130 degrees

Step-by-step explanation:

When it says the line bisects the angle, that means the two smaller angles are equal to each other.

Therefore 3x+5 = 2x+25

Now rearrange to get x.

3x-2x=25-5

x=20

Now plug the x back into both phrases and them together to get the final answer for <PQR.

20 * 3 + 5 = 65

20 * 2 + 25 = 65

65*2 = 130

The true statement is Line MK is the perpendicular bisector of LN and ML is ≅  MN.

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given:

Δ LMN and Δ LKN are connected at side LN.

As per the information,

Line MK is the perpendicular bisector of LN. and ML ≅  MN.

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Answer: b and d

Step-by-step explanation:

Answer: x > -1, see attached.

Step-by-step explanation:

To solve the inequality, we will isolate the x-variable.

Given:

    3x - 19 > -22

Add 19 to both sides:

    3x > -3

Divide both sides by 3:

    x > -1

To graph, we will use an open circle since it is only greater than and not equal to. Then, we will place this circle on -1. Lastly, we will shade to the right of -1, since it is greater than -1.

Answer:

0y^2 + 2z^3 + 3y^3

Step-by-step explanation:

The simplified form of the expression is 0y²+2z³ + 3y³

The given expression is -1/3y² + 2/3 z³ +1/3y² +3y³+4/3z³.

In the expression y, z are the variables.

Combine the like terms:

(-1/3+1/3)y²+(2/3+4/3)z³ + 3y³

Simplify each term:

0y²+2z³ + 3y³

Hence, the simplified form of the expression is 0y²+2z³ + 3y³

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You have the correct answer. Apply a 180 degree rotation around the point (0,2)

Reason:

We'll connect corners between figures A and B.

Draw a line from the upper right corner of figure A to the lower left corner of figure B. This line is in red (see diagram below).

Draw another line from the lower right corner to the upper left corner. This line is in blue.

The red and blue lines intersect at the center of rotation (0,2)

The line segments constructed consist of endpoints of "before" and "after". For instance, the upper right corner in figure A rotates to the lower left corner of figure B. This happens because of the 180 degree rotation.

Note: You can do this rotation either clockwise or counterclockwise, and you would get the same result.

Answer:

-28

Step-by-step explanation:

x/4= -7

4* x/4= -7*4

x= -28

Answer:

(a) 1

(b) 1/2

(c) 1/2

Step-by-step explanation:

[tex]x^2 + y^2 = 5/8 (1)\\\frac{4}{3}xy = \frac{1}{4} (2)\\\\\textrm {From (2) by multiplying both sides by 3/4 we get}\\\\xy = \frac{3}{16} (3)\\\textrm{We know that } (x + y)^2 = x^2 + 2xy + y^2 \\\textrm{Adding 2xy to the LHS and RHS of equation 1 gisues us }\\x^2 + y^2 + 2xy = \frac{5}{8} + 2 * \frac{3}{16} = \frac{5}{8} + \frac{3}{8} = \frac{8}{8} = 1[/tex]

[tex](x + y)^2 = 1 == > x+y = \sqrt{1} = 1\\\\(x - y)^2 = x^2 -2xy + y^2\\\\\textrm{Subtracting 2xy from both sides of Equation 1}\\x^2 + y^2 - 2xy = \frac{5}{8} - 2*\frac{3}{16} = \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \\x-y = \sqrt{\frac{1}{4}} = \frac{1}{2}\\\\x^2 - y^2 = (x+y)(x-y) = 1 . \frac{1}{2} = \frac{1}{2}[/tex]

The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5

The equation of a line can be represented as follows:

y = mx + b

where

Therefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4

Hence,

perpendicular lines follows the rule below:

m₁m₂ = -1

Hence,

5x - 3y = 4

5x - 4 = 3y

y = 5/ 3 x - 4 / 3

m₁ = 5 / 3

5/3 m₂ = -1

m₂ = - 3 / 5

Hence,

using (-4, 5)

5 = - 3 / 5 (-4) + b

5 = 12 / 5 + b

b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5

Therefore,

y = -3 / 5 x + 13 / 5

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Answer:

  3x +5y = 13

Step-by-step explanation:

The equation of a perpendicular line through a given point can be obtained by swapping the x- and y-coefficients of the original line's equation, and negating one of them. The constant in the equation needs to be chosen so the equation will be true at the given point.

Swapping the coefficients of the given equation, we have ...

  3x -5y = c . . . . . for some constant c

Negating the y-coefficient gives a perpendicular line:

  3x +5y = c

We want the equation to be true for (x, y) = (-4, 5), so the constant needs to be ...

  3x +5y = 3(-4) +5(5) = -12 +25 = 13

The equation of the perpendicular line is ...

  3x +5y = 13

__

Additional comment

This process works for equations given in any form. If you start with point-slope form or slope-intercept form, some manipulation of the result may be required to get to the form you want. Standard-form or general-form equations are the easiest to apply this method to.

Note that equations in standard form want to have a positive leading coefficient. That is why we chose to change the sign of the y-coefficient, rather than the x-coefficient.

The amount Cindy should increase in each dimension of the scaled model is 12 m.  

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

We have:

The scaled model of the container has dimensions 2m by 4m by 6m.

Volume of the scaled model = 2×4×6 = 48 cubic m

Let x be the amount by which each dimension is increased.

(2 + x)(4 + x)(6 + x) = 84(48)

[tex]\rm 48+44x+12x^2+x^3=4032[/tex]

[tex]\rm x^3+12x^2+44x-3984=0[/tex]

[tex]\rm x-12=0\quad \mathrm{or}\quad \:x^2+24x+332=0[/tex]

The quadratic equation has no real solution so,

x = 12 m

Thus, the amount Cindy should increase in each dimension of the scaled model is 12 m.  

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The probability that the team will win the sport is 77%.

Given that an area kicker in pro football incorporates a 77% probability of creating a field goal over 40 yards and every attempt field goal is independent.

Probability is how something is likely to happen. The probability of a happening is calculated by the probability formula by simply dividing the favorable number of outcomes by the overall number of possible outcomes.

So, his team will win the sport if he makes a goal otherwise loses.

Therefore, the Probability that his team will win the sport P[E] =P[making a field goal]

P[E]=77%

Hence, the probability that the team will win the sport when making a field goal is 77%.

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The value of x in the straight line shown in the attached diagram is 64°

An equation is an expression that shows the relationship between two or more variables and numbers.

From the image:

x + 26 + 90 = 180° (sum of angles in a straight line)

hence:

x + 116 = 180

x = 64°

The value of x in the straight line shown in the attached diagram is 64°

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[tex] \sf{\red{Answer}}[/tex]

[tex]\sf{m = \frac{1}{2} }[/tex]

[tex] \sf{\purple{Explanation}}[/tex]

[tex] \sf{m = \frac{y_{2}- y_{1}}{m_{2} - m_{1}} }[/tex]

[tex] \sf{m = \frac{9- 3}{7- ( - 5)} }[/tex]

[tex]\sf{m = \frac{6}{7 + 5} }[/tex]

[tex]\sf{m = \frac{6}{12} }[/tex]

[tex]\sf{m = \frac{1}{2} }[/tex]