Help me out on this, ASAP!!! (Geometry)

Write formal proofs using the HL Theorm.

Answer:

8(3j - 2).

Step-by-step explanation:

24j-16

GCF = 8

so the answer is

8(3j - 2).

The remaining amount after 4 years is 1.25 kg

The half life of a function is represented as:

[tex]A = A_o * (1/2)^{t/h}[/tex]

Where

Ao represents the initial amount

So, we have:

[tex]A = 5 * (1/2)^{t/2}[/tex]

In 4 years, t = 4.

So, we have:

[tex]A = 5 * (1/2)^{4/2}[/tex]

This gives

[tex]A = 5 * (1/2)^2[/tex]

Evaluate the expression

A = 1.25

Hence, the remaining amount after 4 years is 1.25 kg

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The value of the probability P(A and B) is 0.12

The given parameters are

P(A) = 0.40

P(B) = 0.30

Given that the events are independent events;, we have:

P(A and B) = P(A) * P(B)

So, we have:

P(A and B) = 0.40 * 0.30

Evaluate

P(A and B) = 0.12

Hence, the value of the probability P(A and B) is 0.12

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Answer:

7

Step-by-step explanation:

given a polynomial divide by (x - a) then the remainder is f(a)

here f(x) is divided by (x - 5) , so remainder is

f(5) = 2(5)³ - 12(5)² + 11(5) + 2

     = 2(125) - 12(25) + 55 + 2

     = 250 - 300 + 57

     = - 50 + 57

    = 7

The tiles to match the descriptions are;

Hull house - Neighbourhood assistance.

Muckrakers - Investigative journalists.

Protestants - Temperance movement.

Women's suffrage - Nineteenth amendment.

The Progressive Era, which encompassed the years between the 1890s and the 1920s in US history, was one of intense social and political reform with the goal of advancing the creation of a better society.

Case 1: The settlement home that welcomed newly arrived European immigrants to the United States in 1889 is known as Hull House. There were also social, educational, and artistic initiatives for immigrants in this building.

Case 2: Muckrakers A name used to describe a group of North American journalists in the early 20th century who made public criticisms of: government corruption, abuse of labor is destructive to society and is committed by influential people or institutions of the time.

Case 3: Third, the term "Protestantism" is used to describe a variety of 16th-century religious movements. Because the Catholic Church had a different understanding of the Bible's holy texts, this movement was distinguished by its break with it.

Case 4: The 19th Amendment to the United States Constitution, which was adopted in June 1919, guaranteed every American woman the right to vote.

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The complete question is-

Think about what you learned about the events during the Progressive time period. Drag and drop the tiles to match the

descriptions                        

Tiles;

Hull House

Muckrakers

Protestants

Women's Suffrage

Pairs;

Investigative journalists

Temperance Movement

Neighbourhood assistance

Nineteenth Amendment

The value of the given expression (a + b/2)/a - bx² = 219.5/(76 - 287x²).

An expression is the combination of variables, coefficients, and constants that are separated by an arithmetic operator(+, -, ...).

The given expression is

(a + b/2)/a - bx²

It is given that a = 76 and b = 287

On substituting,

(a + b/2)/a - bx² = (76 + 287/2)/76 - 287x²

⇒ (76 + 143.5)/76 - 287x²

⇒ 219.5/(76 - 287x²)

Therefore, the given expression for the values a = 76 and b = 287 is 219.5/(76 - 287x²).

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Answer:

Step-by-step explanation:

Two triangles are similar but not congruent if they have three congruent angles but the side lengths are not equal.

What is the congruency of triangles?

To show how can the triangles be proven similar by the SSS similarity theorem:

The two triangles can be shown to be similar given that the ratios of the corresponding sides ΔWUV and ΔYXZ are constant

Reason:

Known parameters are:

ΔWUV and ΔXZY are shown:

∠VUW ≅ ∠YXZ

∠UWV ≅ ∠XZY

∠UVW ≅ ∠ZYX

Length of side VW = 60

Length of side VU = 50

Length of side UW = 40

Length of side  ZY = 48

Length of side  YX = 40

Length of side  XZ = 32

The ratio of the sides are:

[tex]\frac{VW}{ZY} =\frac{60}{48} =\frac{5}{4} \\\frac{VU}{YX} =\frac{50}{40} =\frac{5}{4} \\\frac{UW}{XZ} =\frac{40}{32} =\frac{5}{4}[/tex]

Therefore, given that  the angles of ΔWUV and ΔXZY are all congruent, and the sides of triangle ΔWUV and ΔXZY have a constant proportion, we have that the two triangles are congruent by the Side-Side-Side SSS congruency theorem,  and we have:

ΔWUV ~ ΔYXZ given that ΔYXZ is a scaled drawing of ΔWUV.

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The complete question is given here:

Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.

How can the triangles be proven similar by the SSS similarity theorem?

The cost of one gizmo is $18.

The cost of one thingamajigs is $9

3g + 6t = 102 equation 1

5g + 11t = 179  equation 2

Where:

Multiply equation 1 by 5 and equation 2 by 3

15g + 30t = 510 equation 3

15g + 33t = 537 equation 4

Subtract equation 3 from equation 4

3t = 27

t = 27 / 3

t = $9

Substitute for t in equation 1

3g + 6(9) = 102

3g + 54 = 102

3g = 102 - 54

3g = 48

g = 48 / 3

g = $18

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Answer:

1.5, -1.5

Step-by-step explanation:

Using the quadratic formula, you should have a plus, and minus solution. These should be your answers.

Answer:

-2

Step-by-step explanation:

The slope of a line is rise/run

So, just see how much the line rises/how much the line runs

In this case, the line rises 2 units for every -1 unit it runs

So, the slope is -2

The value of the given expression; f(x) = 4 - 2x, for f(3r -1) as required in the task content is; f(3r-1) = 6 - 6r.

Since it follows from the task content that the given function is defined by the expression;

f(x) = 4 - 2x.

To evaluate the function f(x) = 4 - 2x, for f(3r -1); we must substitute 3r -1 for x in the equation as follows;

f(3r -1) = 4 - 2(3r-1)

f(3r-1) = 6 - 6r.

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Using a proportional relationship, the scaled distances, in sheets of toilet paper, are given as follows:

The real distances are missing, and they are given in the table at the end of the answer.

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

In the case of an inverse relationship, we have that:

y = k/x.

k is the constant of proportionality for both cases.

For this problem, the constant for the Scaled Distances as a function of the Real Distances is given as follows:

k = 5/149.6 = 7.6/227.9 = 0.03334795963.

Hence, the relationship for the Scaled Distances is given by:

S = 0.03334795963R

In which R is the real distance.

Then the scaled distances for the planets are given as follows:

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Answer:

edmentum/plato hope this can help someone :)

Step-by-step explanation:

Answer:

Should be 3.9

Step-by-step explanation:

prove me wrong

When the balloon, rising at 10 ft/sec, rises to 100 feet, the rate of change of the angle of elevation is 0.05 rad/sec

The rate at which the balloon rises = 10 ft/sec

Horizontal distance of the balloon from the observer, d = 100 feet

Therefore;

[tex] \frac{dy}{dt} = 10[/tex]

The angle of elevation can be presented as follows;

[tex] tan(\theta) = \frac{y}{100} [/tex]

[tex] y = 100 \times tan(\theta) [/tex]

Therefore;

[tex] \frac{dy}{dt} = \mathbf{ 100\cdot sec^2 \frac{d \theta}{dt}} [/tex]

Which gives;

[tex] \frac{d \theta}{dt}= \frac{ \frac{d y}{dt}}{100} \times cos^2 \theta [/tex]

[tex] \mathbf{ \frac{d \theta}{dt}} = \frac{ 10}{100} \times cos^2 \theta [/tex]

When the balloon is 100 ft. from the ground, we have;

Therefore;

[tex] \frac{d \theta}{dt}= \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 [/tex]

[tex] \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 = \frac{ 1}{20} [/tex]

Which gives;

[tex] \frac{d \theta}{dt}=\frac{ 1}{20} = 0.05 [/tex]

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Answer:

(D). 6.

Step-by-step explanation:

The number of parts = 1 + 10 = 11.

So 10/11 of the alloy is copper and 1/11 is aluminium.

So the answer is 1/11 * 66

= 66/11= 6 pound,s

Solving a system of equations we can see that:

First, let's define the variables:

With the given information we can write 3 equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

Then we need to solve a system of equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

We can first replace the first equation into the third to get:

(3/4)*V + V + K = $386.4

And rewrite the second to get:

k = V + $18

And replace that in the other equation:

(3/4)*V + V + V + $18 = $386.4

Now we can solve this for V:

V*(1 + 1 + 3/4) = $386.4 - $18

V*(11/4) = $368.40

V = (4/11)*$368.40 = $133.96

Now that we know the value of V, we can replace it in:

K = V + $18 = $133.96 + $18 = $151.96

A = (3/4)*V = (3/4)*$133.96 = $100.47

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The solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is y=[tex]-x^{2} +1[/tex].

Given a differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex].

We are required to find the solution of the differential equation when y(0)=1.

dy/dx=[tex]2xy/(x^{2} -1)[/tex]

Taking y to left side and dx to right side.

1/y dy=2x/[tex](x^{2} -1)[/tex] dx

Integrating both sides.

[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]----------1

log y=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]

Solving right side.

[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]

let [tex]x^{2} -1[/tex]=z

differentiating both sides with respect to x.

2x=dz/dx

2x dx=dz

Put 2x dx=dz in 1.

[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {1/z } \, dz[/tex]

log y=log z+log c

Put z=[tex]x^{2} -1[/tex]

log y=log([tex]x^{2} -1[/tex])+log c

log y=log [{[tex]x^{2} -1[/tex])c]

y=([tex]x^{2} -1[/tex])c------------2

Put x=0 and y=1

1=(0-1)c

1=-c

c=-1

Put c=-1 in 2 to get the solution.

y=-1([tex]x^{2} -1[/tex])

y=[tex]-x^{2} +1[/tex]

Hence the solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is

y=[tex]-x^{2} +1[/tex].

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Answer:

See below

Step-by-step explanation:

To pay the loan off more quickly.

To pay less overall interest.

Often get a lower interest rate for a shorter term loan.

3a) The coordinate of R after dilation is; R' = (-6, 21)

3b) The coordinate of T after dilation is; T' = (1, 3)

5) A dilation by a scale factor of 2 followed by a translation right 1 up 3.

3a) We are given the coordinates of the rectangle as;

Q(-2, -1), R(-2, 7), S(4, 7), T(4, -1)

Now, we are told that R(-2, 7) is dilated about the origin with a scale factor of 3. Thus;

R' = (-2 *3), (3 * 7)

R' = (-6, 21)

3b) We are now told that T(4, -1) is dilated by a scale factor of 1/2 with R as center of origin. R has a coordinate of (-2, 7). Thus;

Coordinate of T' = (-2, 7) + ¹/₂((4, -1) - (-2, 7))

Coordinate of T' = (-2, 7) + ¹/₂(6, -8)

Coordinate of T' = (-2, 7) + (3, -4)

Coordinate of T' =  (1, 3)

5) We can see that LN is 2 units while L'N' is 4 units and so we can say scale factor in the transformation of ΔLMN to ΔL'M'N' is 2.

Now, if we apply scale factor of 2 to coordinates of N before transformation, we will have; 2(3, 1) = (6, 2)

Comparing to N' which is (5, 5) we can say that it was shifted up by 3 units and right by 1 unit.

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The sum of the numbers is 7.69 * 10^6

The expression is given as:

(1.54 times 10 superscript 6 baseline) (6.15 times 10 superscript 6 baseline)

Rewrite properly

(1.54 * 10^6) + (6.15 * 10^6)

Factor out 10^6

(1.54 + 6.15) * 10^6

Evaluate the sum

7.69 * 10^6

Hence, the sum of the numbers is 7.69 * 10^6

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Answer:

a

Step-by-step explanation:

Find the sum. Express the answer in scientific notation.

(1.54 times 10 Superscript 6 Baseline) + (6.15 times 10 Superscript 6 Baseline)

7.69 times 10 Superscript 6

9.471 times 10 Superscript 6

7.69 times 10 Superscript 12

9.471 times 10 Superscript 12

Answer:

  √5 is irrational

Step-by-step explanation:

A rational number is one that can be written exactly as an integer or ratio of integers. Written as a decimal number, it will have a finite number of digits, or a repeating decimal fraction.

Usually, a number that can only be expressed exactly using a symbol will be irrational. For square roots, any root of an integer other than a perfect square will be irrational.

The integer 5 is not a perfect square. It is between the squares 2²=4 and 3²=9. The square root of 5 is irrational.

__

Additional comment

A reduced fraction whose denominator has factors other than 2 or 5 will translate to a repeating decimal. The number of repeating digits may be as many as 1 less than the denominator. For example, 1/19 has an 18-digit repeating decimal equivalent.

The solution to the system of equations is (8, -4)

The system of equations is given as;

y = -1/4x - 2

y = 3/8x - 7

See attachment for the graph of the equations

From the attached graph, we have the point of intersection to be

(x, y) = (8, -4)

Hence, the solution to the system of equations is (8, -4)

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The correct option is D: G(x) = -5x².

The equation of G(x) will be -5x² after vertically stretching and flipping.

A function change called a stretch or compression makes a graph bigger or narrower without moving it horizontally or vertically.

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The complete question is -

The graph of F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x). If F(x) = x², which of the following could be the equation of G(x)?

A: G(x) = -1/5x²

B: G(x) = 5x²

C: G(x) = 1/5x²

D: G(x) = -5x²

Range of values of the variable p is  [tex]0\leq p\leq \frac{10}{3}[/tex]

Step-by-step explanation:

From general quadratic equation [tex]ax^{2} +bx+c[/tex], for imaginary case-

[tex]D\leq 0\\b^2-4ac\leq 0[/tex]

In given question, [tex]a= p+2[/tex], [tex]b=2p[/tex], [tex]c= 5-p[/tex]

using above condition-

[tex]b^2-4ac = 4p^2-4(2p)(5-p)\leq 0\\4p^2 - 40p+8p^2\leq 0\\12p^2-40p\leq 0\\4p(3p-10)\leq 0[/tex]

Here, [tex]4p\leq 0, p\leq 0[/tex]

and

[tex]3p-10\leq 0\\p\leq \frac{10}{3}[/tex]

Therefore, range of values of the variable p is  [tex]0\leq p\leq \frac{10}{3}[/tex].

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Option B is correct. 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet. This can be obtained by using the formula of density.

Given that there are 22 goldfishes,

mass of tank = 22 goldfishes

volume of tank = 56 cubic feet

                      = 22/56

                      = 0.39 goldfish per cubic feet

Hence 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet.

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Answer: 0.39 goldfish

Step-by-step explanation:

[tex]8 \: cars = 120 \: dollars \\ 1 \: car = \frac{120}{8} = 15 \: dollars[/tex]

[tex]m(c) = 15c[/tex]

Answer:

d: m=15c

Step-by-step explanation:

Usually (not always), variable y depends on variable x.

Since in this question, the amount of money Paul can earn changes based on the number of cars he washes, y is the amount of money, and x is the number of cars he washes.

This can be represented as: 120 = 8 times ___

___ is the amount of money Paul earns by cleaning 1 car.

___ is 120 divided by 8, which is 15.

--> Paul earns $15 by cleaning each car.

The new equation will be m = 15c

Answer:

answer is 121/9

Step-by-step explanation:

13.4444444444 (decimal form)

121/9 (improper fraction form)

13 4/9 (mixed fraction form)

Answer:

  P = 160/A

Step-by-step explanation:

For P to vary inversely with A, we must have P be proportional to the reciprocal of A. The constant of proportionality is given.

Two quantities are directly proportional if there is a constant of proportionality (k) that multiplies one of them to give the value of the other:

  y = kx

They are inversely proportional if the inverse of one of them can be multiplied by a constant of proportionality to give the value of the other:

  y = k(1/x) = k/x

In this problem, the variables P and A are said to be inversely proportional. That means the equation that relates them will be of the form ...

  P = k/A

You are given such a form with k=160, which is an appropriate value for the relation given by the problem. All you need to do is fill in the variable:

  P = 160/A

Answer:

y =  x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (0, - 2 )

m = [tex]\frac{-2-2}{0-4}[/tex] = [tex]\frac{-4}{-4}[/tex] = 1

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = x - 2 ← equation of line