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is constructed so MP = and PN = y.
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K
D
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Complete part A of the proof.
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Part A: Prove a² = c.x
P
Below is the proof of the Pythagorean theorem, that a² + ² = c². The proof is divided into
three parts, where the title of each part indicates its main purpose.
Statement
ZNOM
ZOMN
C
AMNO AMOP
Pick ratio v
a² = c.x
Show the steps.l
ZOPM
PMO
y
[Show the steps.
Part B: Prove 6² = C. Y
b
#
N
Reason
All right angles are congruent.
Part C: Prove a² + b² = c²
Pick reason
Pick criterion ✓
Lengths of corresponding pairs of sides of similar triangles
have equal ratios. (3)
similarity
Multiply both sides by a 2. (4)
21
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Report a problem

The formula for the function obtained when the graph is shifted is f(x)=(x+7)^3+3.

Suppose the considered function whose graph is to be made is function f(x). The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.

They are together plotted on the point

(x,y) = (x, f(x))

This is why we usually write the functions as:

y = f(x)

Given;

f(x)=x^3 is shifted up 3 unit and to the left 7 units.

Now,

To shift upwards, we will add outside of the argument

To shift to the left, we will add inside of the argument

Therefore, the function will be f(x)=(x+7)^3+3

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The given statement exists true. A segment from the vertex of a triangle that is parallel to the other side.

The total of the lengths of any two segments must be greater than the length of the third segment in order to create a triangle. Any two sides of a triangle's lengths added together must be longer than the third side.

Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is seen in the above figure.

A segment from the vertex of a triangle that is parallel to the other side. This section could be found on the triangle, inside it, or outside it.

There are three medians for every triangle, just as there are three altitudes, angle bisectors, and perpendicular bisectors. The lines that connect a triangle's vertices to the middles of its two opposite sides are known as the medians. The centroid of the triangle is the location where the three medians intersect.

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True. Since all the three combinations of segments when added the sum is greater than the third side the given segments can form a triangle.

According to the Triangle Inequality Theorem, a triangle's two side lengths added together are always greater than its third side. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.

Given that the length of the three segments is:

AC = 9 units

CB = 4 units

BA = 11 units

According to the Triangle Inequality Theorem the sum of two sides of a triangle is always greater than third side. If this is true for all three combinations, then the triangle can be formed.

For the given segments:

AC + CB > BA

9 + 4 > 11

13 > 11 True

4 + 11> 9

True

9 + 11 > 4

Since all the three combinations when added the sum is greater than the third side the given segments can form a triangle.

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Answer:

12 root 3

Step-by-step explanation:

first, you can say that QRP is similar to PRS

with the ratios, you can say that

[tex]\frac{QR}{PR} = \frac{PR}{RS}\\[/tex]

by substituting values, you have

[tex]\frac{6}{PR} = \frac{PR}{18}\\[/tex]

[tex]PR^2=108[/tex]

[tex]PR=6\sqrt{3}[/tex]

using pythagorean theorem, you can determine that

[tex]PS^2=(6\sqrt{3})^2+18^2[/tex]

[tex]PS^2=432[/tex]

[tex]PS=\sqrt{432}=12\sqrt{3}[/tex]

Answer:

12√3

Step-by-step explanation:

cos∠RSP = 18/PS

cos∠PSQ = PS/24

∠RSP=∠PSQ     (the angle at S)

18/PS = PS/24

(PS)² = (18)(24) = 432

PS = √432 = 12√3

The exponential equation is P = 7000 * (1 + 0.08)ᵗ  and the nearest whole number.

What is the exponential equation?

In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures.

a. To write the exponential equation, let t be the number of years and let P be the amount of money in the account after t years. The exponential equation can be written as:

P = 7000 * (1 + 0.08)ᵗ

b. To solve for t, we need to find the number of years it takes for P to reach $30,100. We can set up an equation and solve for t:

30,100 = 7000 * (1 + 0.08)ᵗ

Dividing both sides by 7000:

30,100 / 7000 = (1 + 0.08)ᵗ

Taking the natural logarithm of both sides:

ln (30,100 / 7000) = t * ln (1 + 0.08)

Solving for t:

t = ln (30,100 / 7000) / ln (1 + 0.08)

Using a calculator, we get:

t = 21.1397

Rounding up to the nearest whole number, it will take Fred 22 years to have $30,100 for a new car.

Hence, the exponential equation is P = 7000 * (1 + 0.08)ᵗ  and the nearest whole number.

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Answer:

12

Step-by-step explanation:

The answer for your question is 12

Answer:

=12

Step-by-step explanation:

1(4×3)/3+ 8=

1(12)/3+8=

12/3 + 8=

4 + 8 = 12

I hope I help you in this ans and tq.

The percentage of the employees at the water slides are temporary​ is 88%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.

To find the percentage of the employees that are temporary

66/75 x 100/1

=88%

Hence, 88% is the percentage of the employees at the water slides are temporary​

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The value of the lesser integer is -9. The solution has been obtained by using algebra.

What is algebra?

In the area of mathematics known as algebra, abstract symbols rather than actual numbers are used to perform operations or manipulations.

Let the integer be 'x'.

We are given that when an integer is subtracted from 2 times the next consecutive integer, the difference is -7.

So, from this we can form the equation as

⇒2(x+1) - x = -7

⇒2x + 2 - x = -7

⇒x = -7 - 2

⇒x = -9

Hence, the value of the lesser integer is -9.

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Answer:The statement "The bank has the best decors and paintings in their branch" should not be one of Macky's reasons for choosing a bank. While the appearance of a bank branch may be important to some customers, it is not a primary factor in choosing a bank account. Macky should focus on more important factors such as interest rates, fees, customer service, and overall financial stability of the bank.

Step-by-step explanation:

The statement "The bank has the best decors and paintings in their branch" should not be one of Macky's reasons for choosing a bank. While the appearance of a bank branch may be important to some customers, it is not a primary factor in choosing a bank account. Macky should focus on more important factors such as interest rates, fees, customer service, and overall financial stability of the bank.

Answer:

4x² + 4x + 9 = 0 , has no real solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the solutions can be determined using the discriminant.

Δ = b² - 4ac

• if b² - 4ac > 0 , then real solutions

• if b² - 4ac = 0 , then real and equal solutions

• if b² - 4ac < 0 , then no real solutions

4x² + 4x + 9 = 0 ← in standard form

with a = 4, b = 4 , c = 9

b² - 4ac

= 4² - (4 × 4 × 9)

= 16 - 144

= - 128 ← no real solutions

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

- 4x² + 56x - 196 = 0 ← in standard form

with a = - 4 , b = 56 , c = - 196

b² - 4ac

= 56² - (4 × - 4 × - 196)

= 3136 - 3136

= 0 ← has real solutions

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

- 5x² - 10x + 10 = 0 ← in standard form

with a = - 5 , b = - 10 , c = 10

b² - 4ac

= (- 10)² - (4 × - 5 × 10)

= 100 - (- 200)

= 100 + 200

= 300 ← has real solutions

Step-by-step explanation:

4

Ws

The length of DE is  25. So correct option is (4).

In geometry, the term "parallel" refers to two lines that are equidistant from each other over their entire length and will never intersect, no matter how far they are extended. In other words, two parallel lines are parallel if they lie in the same plane and maintain the same distance between them at all times.

Since AB is parallel to DE and BD is perpendicular to both AB and DE, by alternate interior angles, we have:

angle BDA = angle DEC

Since BD is 7 and BC is 15, we have:

triangle BCD is a 7-15-17 right triangle (the Pythagorean theorem)

So, angle BDA = angle DEC = 90 - arctan(7/15) = arctan(15/7).

Also, since AB is parallel to DE, and BD is perpendicular to both AB and DE, we have:

angle ABD = angle CDE

So, by the vertical angles theorem, we have:

angle ABD = angle CDE = 90 degrees - arctan(15/7) = arctan(7/15)

Then, by the Pythagorean theorem, the length of DE can be found as:

[tex](DE)^{2}[/tex] = [tex](AB)^{2}[/tex] + [tex](BD)^{2}[/tex] = [tex]21^{2}[/tex] + [tex]7^{2}[/tex] = 441 + 49 = 490

So, DE = [tex]\sqrt{490}[/tex] = 2[tex]\sqrt{122}[/tex] = 2 * 11 = 22

Therefore, the length of DE is (4) 25.

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Answer:

im confused are you asking a question or telling us about something?

The algebraic expression for "the square of the difference of 10 and j less than the product of ten cubed" is  (10 - j)² < 10³.

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

The statement "the square of the difference of 10 and j less than the product of ten cubed" can be written as follow:

Step 1: Square the difference of 10 and j: (10 - j)²

Step 2: less than the product of ten cubed: (10 - j)² < 10³

Therefore, the algebraic expression is (10 - j)² < 10³

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Answer:

42

Step-by-step explanation:

If angle one equals 42, then angle 3 should too since they are the same angle.

hope it helps...

Answer: 30

Step-by-step explanation:

Vertical angles are congruent.

[tex]x+30=2x \implies x=30[/tex]

To calculate the amount of money that needs to be set aside today to purchase a new piece of equipment in 3 years, we need to find the future value of the equipment and calculate the present value of that future amount.

First, let's find the future value of the equipment:

The cost of the equipment is expected to increase by 3% per year, so after 3 years the cost will be:

$75,000 * (1 + 0.03)^3 = $78,225

Next, let's find the present value of that future amount:

The money is expected to earn 9% interest compounded annually, so to find the present value, we need to discount the future amount by the interest rate. We can use the formula:

PV = FV / (1 + r)^t

where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years.

Plugging in the values, we get:

PV = $78,225 / (1 + 0.09)^3 = $73,232.57

So, to purchase the equipment in 3 years, we need to set aside $73,232.57 today.

In standard position, 2.280° refers to an angle in the Cartesian plane with its beginning side on the positive x-axis and its terminal side establishing an angle of 2.280° with the positive x-axis counterclockwise.

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles. An angle is formed by joining two rays (half-lines) that have a shared terminal. The latter is referred to as the angle's vertex, while the rays are referred to as the angle's sides, legs, and arms.

Here,

The measure of 2.280° in standard position refers to an angle in the Cartesian plane, with its initial side on the positive x-axis and its terminal side making an angle of 2.280° with the positive x-axis in a counterclockwise direction.
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Answer:

A rate is two variables that relies on each other so a example would be a projectile and a cannon, in relation the cannon goes no where while the projectile is flying through the air

Step-by-step explanation:

The rule for the function is P(t) = 170 + 680t

Let's call Julia's final position after t hours as P.

If she drove at a constant speed v (in miles per hour), then the distance traveled can be given as:

P - P0 = vt

Given that she was 170 miles east from Denver after driving for a quarter of an hour (0.25 hours), we can write the first equation:

170 = v * 0.25

v = 680

This means that her speed was 680 miles per hour.

Using this speed, we can write the second equation:

P = 680 * t

100 = 680 * t

t = 100 / 680 = 0.147

Combining the two equations, we can find the function that gives Julia's position east from Denver after t hours as:

P(t) = P0 + v * t ----- P0 = 170 i.e. her initial position

P(t) = 170 + 680 * t

So, the rule for the function P(t) is:

P(t) = 170 + 680t

P^-1(16) is the inverse of the function P(t) at the value 16.

In other words, it gives us the time t after which Julia is 16 miles east from Denver.

To find its value, we can use the equation of the function P(t):

P(t) = 170 + 680 * t

16 = 170 + 680 * t

-154 = 680 * t

t = -154 / 680

Time cannot be negative.

So, it does not exist

P^-1(-141) is the inverse of the function P(t) at the value -141.

In other words, it gives us the time t after which Julia is 16 miles east from Denver.

So, we have

-141 = 170 + 680 * t

-311 = 680 * t

t = -311 / 680

Time cannot be negative.

So, it does not exist

We simply make t the subject in P(t)

So, we have

P^-1(t) = (t - 170) / 680

The graph is attached

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Based on the given trapeziums, each problem's answers are:

Let's discuss each problem we have:

1. The given trapezium is an isosceles trapezium, hence:

J = K = 7x  + 2

M = L = 25x - 14

Since trapezium is a part of parallelogram, then:

∠J + ∠K + ∠L + ∠M = 360°

2∠J + 2∠M = 360°

2(7x + 2) + 2(25x - 14) = 360°

14x + 4 + 50x - 28 = 360°

64x - 24 = 360°

64x = 384

x = 6

∠J = ∠K = 7x + 2

∠J = ∠K = 7(6) + 2 = 44°

∠M = ∠L = 25x - 14

∠M = ∠L = 25(6) - 14 = 136°

2. Since EFGH is an isosceles trapezoid, then:

EH = FG

4x - 27 = x + 9

3x = 36

x = 13

EG = FH

3y + 19 = 11y - 21

40 = 8y

y = 5

3. It was given that:

PQ = 27

SR = 39

WX?

WX is the mig segment, where:

Mid segment = (base + top) / 2

WX = (PQ + SR) /2

WX = (27 + 39) / 2

WX = 66/2

WX = 33

4. It was given that:

MN = 22

DC = 29

AB ?

MN is mid segment

MN = (AB + DC) / 2

22 = (AB + 29) / 2

44 = AB + 29

AB = 15

5. JK = 3x + 11

NP = 45

ML = 10x - 12

NP is mid segmet

NP = (JK + ML) / 2

45 = [(3x + 11) + (10x - 12)] / 2

90 = (3x + 11) + (10x - 12)

90 = 13x - 1

13x = 91

x = 7

ML = 10x - 12

ML = 10(7) - 12

ML = 58

6. BC = 19

GH = 9x - 3

FE = 5x + 1

GH is mid segment

GH = (BC + FE) / 2

(9x - 3) = (19 + (5x + 1)) / 2

18x - 6 = 19 + (5x + 1)

18x - 6 = 20 + 5x

13x = 26

x = 2

GH = 9x - 3

GH = 9(2) - 3

GH = 15

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Answer:

1. consistent independent
2. consistent dependent
3. inconsistent

Step-by-step explanation:

1. when we take the ratios of the two equations,
[tex]a_{1} : a_{2} \neq b_{1} :b_{2}[/tex]

2. when we take the ratios of the two equations,
[tex]a_{1} : a_{2} = b_{1} :b_{2} = c_{1} : c_{2}[/tex]

1. when we take the ratios of the two equations,
[tex]a_{1} : a_{2} = b_{1} :b_{2} \neq c{1} : c_{2}[/tex]

Step-by-step explanation:

4x + y = 8

x + 3y = 8

consistent independent

both equations are lines with different slope.

so, they intersect at one point.

that is the solution.

-4x + 6y = -2

2x - 3y = 1

consistent dependent

both equations are actually identical lines.

multiply the second equation by -2.

and you see the equality.

that means every point is a solution.

there are infinitely many solutions.

5x - 2y = 4

5x - 2y = 6

inconsistent

both equations are lines with identical slopes.

but with different y-intercepts.

they are parallel and never intersect.

there is no solution.

there is no (x, y) that their sum has 2

different results.

Step-by-step explanation:

To solve this problem, we'll use the exponential growth formula:

P(t) = P0 * e^(rt)

Where P(t) is the population after t years, P0 is the initial population (1543), r is the growth rate (0.038), and t is the number of years (5.2).

P(5.2) = 1543 * e^(0.038 * 5.2)

Using a calculator or natural logarithm rules:

P(5.2) = 1543 * e^0.199

P(5.2) = 1543 * 1.22

P(5.2) = 1887.46

So the population will be approximately 1887.46 after 5.2 years.

Answer: 1 3 4

Step-by-step explanation:

The value of function f ' (2) is, 7/4.

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

We have to given that;

The function is,

⇒ f (x) = 7/x

Now, We an solve as;

⇒ f ' (2) = lim h → 0 ( f (2 + h) -  f (2) / h )

⇒ f ' (2) = lim h → 0 ( 7 / (2 + h) - 7/2 / h )

⇒ f ' (2) = lim h → 0 ( 7/h (2 - 2 - h) / (2 + h)×2)

⇒ f ' (2) = lim h → 0 ( 7/h ( - h ) / 2 (2 + h) )

⇒ f ' (2) = lim h → 0 ( - 7 / 2 (2+ h))

⇒ f ' (2) = - 7/4

Thus, The value of function f ' (2) is, 7/4.

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Answer:    a = 2    f(x) = x^5

Step-by-step explanation:

The axis of symmetry for each function is given as follows:

Hence the rank from smallest to largest axis of symmetry is given as follows:

f(x), h(x), g(x).

The axis of symmetry of a quadratic function is given by the x-coordinate of the vertex of the quadratic function.

For function f(x), considering the vertex-form definition, the x-coordinate of the vertex is given as follows:

x = -4.

For function g(x), considering the standard definition, the x-coordinate of the vertex is given as follows:

x = -(-16)/2(4).

x = 16/4.

x = 4.

For function h(x), considering the graph of the function, the x-coordinate of the vertex is given as follows:

x = 1.

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Answer:

"w" (and any subsequent words) was ignored because we limit queries to 32 words.

w = 0.33 so, w lies before A, B, and C.

Option A is the correct answer.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

Average weight.

w = Sum of all the weight / 3

w = (0.5 + 0.3 + 0.2) / 3

w = 1/3

w = 0.33

Now,

A = 3, B = 6, and C = 7 on the number line.

0.33 lies before A, B, C

Thus,

w lies before A.

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The required solution is as follows,
(A) The value of the limit is -∞, as 7 is an odd number.
(b) Graf of the function has been shown.

Limit, which can be defined as every nearby value of a variable for a function that exists, is called limits

Here,
According to the question,
[tex]y = \lim_{x \to \ a} 1/[x-a]^n[/tex]

Put a = 2 and n = 7
[tex]y = \lim_{x \to \ 2} 1/[x-2]^7[/tex]

As n = 7 is odd, from the theorem,
y = -∞, as 7 is an odd number.

Thus, the required solution is as follows,
(A) The value of the limit is -∞, as 7 is an odd number.
(b) Graf of the function has been shown.

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