Describe the translation from AB to A’B’

Answer:

x + 7y = 34

Step-by-step explanation:

the altitude through C meets the opposite side AB at right angles

calculate the slope of AB using the slope formula

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

with (x₁, y₁ ) = A (2, - 4 ) and (x₂, y₂ ) = B (3, 3 )

[tex]m_{AB}[/tex] = [tex]\frac{3-(-4)}{3-2}[/tex] = [tex]\frac{3+4}{1}[/tex] = [tex]\frac{7}{1}[/tex] = 7

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{7}[/tex] , then

y = - [tex]\frac{1}{7}[/tex] x + c ← partial equation of the altitude

to find c substitute C (- 1, 5 ) into the partial equation

5 = [tex]\frac{1}{7}[/tex] + c ⇒ c = 5 - [tex]\frac{1}{7}[/tex] = [tex]\frac{35}{7}[/tex] - [tex]\frac{1}{7}[/tex] = [tex]\frac{34}{7}[/tex]

y = - [tex]\frac{1}{7}[/tex] x + [tex]\frac{34}{7}[/tex] ( multiply through by 7 )

7y = - x + 34 ( add x to both sides )

x + 7y = 34 ← equation of altitude in standard form

The augmented matrices for each system are given as follows:

1.

[ -9 4 | 1 ]

[ 7 0 | 14]

2.

[ -5 6 | 1 ]

[ 5 -2 | 9]

For a system of n variables, the first n columns of the matrix are composed by the coefficients of the variable of the system.

The two systems in this problem have variables x and y, hence:

Then the last column is composed by the values on the right side of the equations, that is, the results of the operations.

The second equation of the first system is:

7x - 9 = 5 -> 7x + 0y = 14 (this format is needed to build the augment matrix.

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The solution is x ≤ -2 or x ≥ 10.

The inequalities are given in two parts which can be combined to form a single inequality as follows,

13 ≤ -5x + 3 or -47 ≥ -5x + 3

⇒ 13 ≤ -5x + 3 ≤ -47

Let's solve this.

First subtract 3 from all terms,

⇒ 10 ≤ -5x ≤ -50

Divide by 5 on all terms,

⇒ 2 ≤ -x ≤ -10

Multiply with (-1) on all terms, but then the inequality gets reversed as,

⇒ -2 ≥ x ≥ 10

We can now split the inequalities into two to make sense,

⇒ x ≤ -2 or x ≥ 10.

This solution can be graphed on a number line by darkening a line on the number line from 10, extended to the right of it. Then darken the line from -2, extend it to the left side.

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Answer: 1.one cup

2. 2 cups of each

Step-by-step explanation:

The initial number of bacteria in a culture is found as 200.

Using the model P = P₀e^(kt),

Where:

P(t) = the amount of bacteria at time t = 2000.

P₀ = initial amount at time t = 0

r = growth rate

t = time (number of periods)

k is the growth constant.

For t = 3 hours.

400 =P₀e^(k*3)    ......eq 1

2000 = P₀e^(k*10)   ......eq 2

Re writing eq 1.

400 = P₀e^(k*3)

as (400/P₀) = [e^k]^3,

Solve for e^k,

∛(400/P₀) = e^k

For eq 2.

2000 = P₀e^(k*10)

Rewrite it as;

(2000/P) = [e^k]^10.  

Substituting ∛(400/P₀) for e^k, we obtain:              

(2000/P₀) =  (400/P₀ )^(10/3)

Solved for P.  

Raise sides by the power of 3, we get:

(2000/P₀)^3 = (400/P₀)^10.

Therefore,

2000^3/  P₀^3  =  400^10/P₀^10

Solve,

2000^3/ 1 =  400^10/P₀^7

Taking reciprocal.

Solving

P₀^7 = 400^10/2000^3

P₀^7 = 1.31 x 10¹⁶

Take the 7th root of both sides;

P₀ = 200.67

Thus, the initial number of bacteria in a culture is found as 200.

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Answer: 20

Step-by-step explanation:

130+60= 190

60 ÷ 3 = 20

Answer:

its 16

Step-by-step explanation:

Answer:

FG = 16

Step-by-step explanation:

the angle between EF ( y- axis) and EH (x- axis) is right

thus the 4 angles in EFGH are right angles meaning the figure is a square.

the sides of a square are congruent , so

GH = FG , that is

3x + 1 = x + 11 ( subtract x from both sides )

2x + 1 = 11 ( subtract 1 from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Then

FG = x + 11 = 5 + 11 = 16

13 + √85/3 is the perimeter of triangle .

Explain what a triangle is.

The points P ( - 3 , -8 ) Q ( - 3, - 1) R ( -9,-8)

Distance between PQ = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

                                      = [tex]\sqrt{( - 1 + 8)^{2} + ( -3 + 3)^{2} }[/tex]

                                      = [tex]\sqrt{( -7 )^{2} +0 }[/tex]

                                       = √49  ⇒ 7

Distance between QR = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

                                     = [tex]\sqrt{( -9 + 3 )^{2} + ( -8 + 1)^{2} }[/tex]

                                     = [tex]\sqrt{(- 6)^{2} + ( - 7)^{2} }[/tex]

                                     = [tex]\sqrt{36 + 49}[/tex]

                                   = √85

Distance between RP = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

                                     = [tex]\sqrt{( - 3 + 9)^{2} + ( -8 + 8)^{2} }[/tex]

                                     = [tex]\sqrt{(6)^{2} }[/tex]

                                     = √36

                                    = 6

perimeter = PQ + QR+RP/3

                = 7 + √85 + 6/3

              = 13 + √85/3

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Answer:

10.9 feet

Step-by-step explanation:

its Pythagoras but reversed. So instead of a squared plus b squared equals c squared its (c squared)-(a squared) equals (b squared)

so (12x12) - (5x5) = 119

square root of 119 is 10.9

sorry im replying on phone i cant do exponents and stuff

The solution of the expression (3/5)v + 3 = (2/5)v - 4 would be v = - 35 which is the correct answer would be option (A).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have to determine the solution of three-fifths times v plus 3 equals two-fifths times v minus 4.

Translate the phrase into an algebraic expression:

⇒ (3/5)v + 3 = (2/5)v - 4

Rearrange the likewise terms and apply arithmetic operations,

⇒ (3/5)v - (2/5)v  = - 3 - 4

⇒ (1/5)v = - 7

⇒ v =  - 7 × 5

⇒ v = - 35

Therefore, the solution of the expression (3/5)v + 3 = (2/5)v - 4 would be v = - 35.

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Answer:

2.6

Step-by-step explanation:

cause it is 2.6299999999

2.629 to the nearest tenth is 2.6.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

Given:

A decimal number,

2.629.

Here, 2 is the whole number component and 0.629 is the fractional component part.

To round the number to the nearest tenth:

The number in tenth place is 6.

And the value right next to 6 is 2.

6 > 2.

So, the number will stay the same.

2.629 = 2.63

Then 2.63 = 2.6 to the nearest tenth.

Therefore, 2.6 is the required decimal.

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Answer:

Step-by-step explanation:

Total number of gifts = Sum of all gifts given to each guest

                                    = (Number of guests) * (Number of gifts per guest)

By making the number of gifts per guest the subject of the formula:

Number of gifts per guest = Total number of gifts/Number of guest

But:

Total number of gifts = 32

Number of guests = 8

Number of gifts per guest = Total number of gifts/Number of guest

                                              =32/8

Solutions are given below:

1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14

2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]

3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)

4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2

What is a solution?

Solutions are given below:

1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14

2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]

3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)

4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2

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Answer:37.5

Step-by-step explanation:

so basically a square has four sides so 150 divided by 4

Answer:

1- 1/9

Step-by-step explanation:

[tex]p(5 then 10) = \frac{4}{9} \times \frac{2}{8} [/tex]

[tex]p(5 then 10) = \frac{1}{9} [/tex]

Assuming without replacement

Answer:

-1

Step-by-step explanation:

-8+10÷(-2)

2÷(-2)

-1

The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, then the mass of one the bodies is

[tex]m_{1} = 1.88(10)^{-7}[/tex]

The amount of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, a chair, your bed, a football, a glass, and even air. The mass of a thing determines whether it is light or heavy.

Given that : The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m

F=[tex]G\frac{m_{1} .m_{2} }{r^{2} }[/tex]

[tex]m_{1} =\frac{F.r^{2} }{Gm_{2} }\\ m_{1} =\frac{745.(70.3)^{2} }{6.7(10)^{-11}.2050 }\\\\[/tex]

[tex]m_{1} =\frac{26881.3(10^{7} )}{13735}[/tex]

[tex]m_{1} = 1.88(10)^{-7}[/tex]

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Answer:

See below

Step-by-step explanation:

To find pole height

for a right triangle

sin 38 = opposite leg / hypotenuse = height /15 m

sin 38 = height / 15

15 sin 38 = height = 9.2 meters

To find rope DC

  Use pythagorean theorem ( you have leg1 = height and leg 2 = 10.7)

     DC ^2 = 9.2^2  + 10.7^2

     DC = 14.1 m

Hello!

What is the standard form of the parabola:

 [tex]\hookrightarrow y=(x-h)^2+k[/tex]

          => h: x-coordinate of vertex

          => k: y-coordinate of vertex

Since our vertex is (1,-8)

 [tex]\hookrightarrow \text{Our equation is }y=(x-1)^2}-8[/tex]  <== Answer

Hope that helps!

1) We can solve this problem by setting up a System of Linear Equations. So, based on this text, we can write out the following equations:

Note that the first equation relates itself to the total cost, and the second one to the amount of blend.

2) Now, we can solve this system of Linear Equations by the Elimination Method. Let's multiply the second equation by -5.65 so that we can add them both and eliminate "a"

Now, we can plug into the second equation b=90 and then solve it for a:

Thus, the answer is:

Answer:

Let the length be x. The breadth be y Area=xy. On reducing breadth by 4 new breadth will be (y-4). X(y-4)=xy-240. Xy-4x=xy-240. -4x=-240. X=60. Hence rectangle is 60cm long

Step-by-step explanation:

hope it will help

∠1 and ∠8 are supplementary angles,  ∠5 and ∠6 are Congruent, ∠6 and ∠8  are Congruent .

Supplementary angles are those angles that sum up to 180 degrees. Two or more angles that are identical to each other are referred to as Congruent angles.

We are provided with the figure shown in the question. We need to name the angles provided or need to tell the relation between two angles.

∠1 and ∠8 are supplementary angles as there sum is 180°.

∠1 + ∠8 = 180°

So, angle ∠1 and ∠8 are supplementary.

∠5 and ∠6 are Congruent as they  are identical to each other.

∠5 = ∠6

∠6 and ∠8  are Congruent as they  are identical to each other.

∠6 = ∠8

Thus, we can conclude that ∠1 and ∠8 are supplementary angles, ∠6 and ∠8  are Congruent , ∠5 and ∠6 are Congruent.

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If [tex]$f(x)=4^x$[/tex] and [tex]$g(x)=4^{x+1}-3$[/tex] be the two functions then Horizontal translation 1 units right.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Let [tex]$f(x)=4^x$[/tex] and [tex]$g(x)=4^{x+1}-3$[/tex]

We can see that in place x , we have x + 1

so, f(x) exists shifted right side by 1 unit

and we can see that 2 exists added to y-value

so, it exists shifted upside by 2 units

horizontal translation 1 unit right

vertical translation 2 units up

Therefore, the correct answer is option e) Horizontal translation 1 units right.

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Answer:

The answer is 18^4

Step-by-step explanation:

Its the answer

The height of the pyramid = BC = 14 units

It is a three-dimensional shape that has a polygonal base and flat triangular faces which joins at the apex at the top of the pyramid.

We have,

Base edge length = 14 units

From the figure below,

The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units so,

We get,

AC = CD = AD = 14 units _____(1)

All sides in an equilateral triangle are equal.

In the right triangle ABC,

tan 45° = BC / AC

tan 45° = 1

1 = BC / AC _____(2)

From (1) and (2) we get,

1 = BC / 14

BC = 14 units

The height of the pyramid = BC = 14 units

Thus,

The height of the pyramid is 14 units.

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Answer: C 14 UNITS

Step-by-step explanation:

Answer:

y=2(x−3)

Step-by-step explanation:

Bette needs 8 jumbo cans of frosting to frost 280 cupcakes.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Bette used 3 jumbo cans of frosting to frost 105 cupcakes for the cupcake challenge at her school and 5 jumbo cans of frosting to frost an additional 175 cupcakes which are given in the question.

Let x jumbo cans of frosting would she need to frost 280 cupcakes

As per the given question, we can write the ratio as

3 jumbo cans of frosting : 105 cupcakes = x jumbo cans of frosting : 280 cupcakes

⇒ 3/105 = x/280

⇒ x = ( 280 × 3 )/ 105

⇒ x = 8

Therefore, she needs 8 jumbo cans of frosting to frost 280 cupcakes.

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Answer:

see explanation

Step-by-step explanation:

given a quadratic in standard form

y = ax² + bx + c (a ≠ 0 )

• if a > o then curve opens up

• if a < 0 then curve opens down

for y = - 2x² + 4x ← in standard form with a = - 2, b = 4 and c = 0

here a = - 2 < 0 so curve opens down

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

the axis of symmetry is a vertical line passing through the vertex

the x- coordinate of the vertex, which is also the equation of the axis of symmetry is

x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{4}{-4}[/tex] = 1

equation of axis of symmetry is x = 1

substitute x = 1 into the equation for y- coordinate of vertex

y = - 2(1)² + 4(1) = - 2 + 4 = 2

vertex = (1, 2 )

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

to find the zeros let y = o , that is

- 2x² + 4x = 0 ← factor out - 2x from each term

- 2x(x - 2) = 0

equate each factor to zero and solve for x

- 2x = 0 ⇒ x = 0

x - 2 = 0 ⇒ x = 2

the zeros are x = 0 and x = 2

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

since the graph opens down then it has a maximum value

this is the y- coordinate of the vertex

thus maximum at y = 2

Answer:

AC=KM

AB=KL

BC=LM

Step-by-step explanation:

Answer:

AC=MK

AB=KL

BC=LM

This are corresponding sides