9. Construct a right triangle CHA at H and such that : a) HC = 4 cm; HA = 6 cm. b) AC = 5 cm; HA = 4 cm. c) A = 40°; HA = 8 cm.​

the equation for line will be y = (5/4)x + 13.

What is the slope of line?

Determine the slope of the line using the slope formula given two line-side coordinates. The formula m=(y2-y1)/ describes the slope as the proportion of the change in y values to the change in x values (x2-x1). The coordinates of the first point represent x1 and y1 respectively. At x2, y2, and their respective locations are the second points. It doesn't matter which point you choose to rank as the first and which as the second.

Knowing that formula two, which is used to determine the slope of a line connecting two points, is

The line passes through (-4, 8) so,

8 = (5/4)(-4) + c

8 = -5 + c

c = 13

c = 13

The equation of a line is y = (5/4)x + 13

Hence the equation for line will be y = (5/4)x + 13.

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Statement: 5(x+6)=x+38 is x=2

We are given the equation 5(x+6)=x+38. We can solve this equation by isolating x on one side of the equation. To do this, we will first subtract x from both sides of the equation. This will leave us with 5x+30=38. We can then subtract 30 from both sides of the equation to isolate the x terms. This leaves us with 5x=8. We can then divide both sides of the equation by 5 to isolate x. This gives us x=2.

Therefore, if 5(x+6)=x+38, then x=2.

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The Given Statement is  true reason is the value in the left-hand side is equal to the value in the right-hand side. it shows proof that 5(x+6) = x+38 for x =2.

Here we have to understand what is an equation because in question we have given an equation.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

2x - 5 and 13 are expressions in this case.

These two expressions are joined together by the sign "=".

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

Here we have given an equation

5(x+6) = x+38  we have to proof for x = 2.

LHS 5(x+6) = 5(2+6) = 5*8 = 40

RHS x+38 = 2+38 = 40

So the given statement is true because LHS = RHS.

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The tangent to the graph f,  f(x) = [tex]5x^4[/tex]/4 + 15/4.

When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals.

Given:

f '(x) = 5x³

and, line: 5x + y= 0

We integrate to get f(x) = ∫5x³ dx = [tex]5x^4[/tex]/4 + C.

As, tangent line is y = - 5x,

then f'(x) = 5x³ = - 5, x³ = -1 and x = -1 is x-coordinate of tangent point.

So, the y-coordinate of tangent point is

f(-1) = 5[tex](-1)^4[/tex]/4  + C

      = 5/4 + C.

and, the equation of tangent line is

y - 5/4 - C = - 5(x + 1)

y = - 5x - 15/4 + C.

Thus,  -15/4 + C = 0,

C = 15/4 and f(x) = [tex]5x^4[/tex]/4 + 15/4

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Answer: Pablo 45   josh 15  Melissa 6

Step-by-step explanation: 15 • 3 + 15 + 6 = 66

Answer:

Step-by-step explanation:

Solve the problem 4p-32=p+7

4p - 32 = p + 7

3p = 39

p = 39 : 3

p = 13

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

4 x 13 - 32 = 13 + 7

20 = 20

The equation of the circle with a radius of 12 and a center at (11, -9) is

x² + y² - 22x + 18y + 58 = 0

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is given as πr²

We have,

Equation of a circle:

(x - h)² + (y - k)² = r²

Where (h. k) is the center of the circle and r is the radius of the circle.

Now,

The radius of the circle = 12

Center of the circle = (11, -9) = (h, k)

Now,

(x - h)² + (y - k)² = r²

(x - 11)² + (y + 9)² = 12²

(x - 11)² + (y + 9)² = 144

x² - 22x + 121 + y² + 18y + 81 = 144

x² + y² - 22x + 18y = 144 - 121 - 81

x² + y² - 22x + 18y + 58 = 0

Thus,

x² + y² - 22x + 18y + 58 = 0 is the equation of the circle.

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Monique can make 5 Vase with 4 Daisies and 5 Roses in each.

The greatest number among all the common factors of the given numbers is the HCF (Highest Common Factor) of two numbers.

For example, the HCF of 12 and 36 is 12 because 12 is the highest common factor of 12 and 36.

Given:

Daisies = 20

Roses = 25

Monique obviously wants to use all the flowers so she does not any left over. She needs to find a number which divides into 20 and 25,

So, the HCF of 16 and 24, which is 5.

Factors of 20 = 2, 4, 5, 10, 20.

Factors of 25 = 5, 25

So, She will be able to make 5 bouquets.

and, Each bouquet will have 4 Daisies and  5 Roses.

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The Complete Table that missing in the table is

Flower Type Number

Daisies 20

Roses 25

Point (80, 185) represents the location of the beetle 5 seconds after starting.

An equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables. When necessary, more than one parameter can be used. For instance, the equation y = x2 can be expressed as a pair of equations in parametric form, x = t and y = t2, rather than the Cartesian form of y = x2. Parameterization, which transforms a function into a parametric form, greatly improves the efficiency of differentiating and integrating curves.

The parametric equations for the path of the beetle are:

x(t) = 28t

y(t) = 84t + 10

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Answer:

it’s not 80,185 I got it wrong on edge

Step-by-step explanation:

ugh

Use identity:

Modify it as follows:

Substitute a = p, b = 1/p and evaluate:

Proved

========================================================

Explanation:

When working on complicated problems, it's best to break things down as much as possible.

Toby knows how to work with 2 terms, so let's start with that.

Ignore the 8^2 for now.

Focus on the first 2 exponential terms 8^7 and 8^3.

Multiply them to get: 8^7*8^3 = 8^(7+3) = 8^10

Which Toby should know how to do. The general rule is

a^b*a^c = a^(b+c)

Add the exponents but only when the bases are the same.

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

This means

8^7* 8^3*8^2

is the same as

8^10*8^2

Then apply that rule again to get

8^10*8^2 = 8^(10+2) = 8^12

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

So overall, 8^7*8^3*8^2 = 8^12

In other words, we add the exponents to get 7+3+2 = 12 as the final exponent. The base stays at 8 the entire time.

The reasons for each statement about the given triangle are as follows:

Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.

Given, A triangle PWZ in that base ∠1 and ∠2 are same and the distance between W and Z from X and Y are the same where XY is the base of another triangle inside the ΔPWZ.

For ΔPWZ

We know PWZ is an isosceles triangle since its two angles are the same.

thus another ΔPXY is on the same base of ΔPWZ and also at the same distance from its point Hence, these triangles are congruent triangles.

Looking at that perspective, we can say that ∠1 and ∠2 are pairs of alternate angles and are congruent.

∠1 ≅ ∠2

The same with ∠3 and ∠4.

∠3 ≅ ∠4

Therefore, As a result, according to the ASA Theorem, the Triangles are congruent. The two angles and the side they encompass are comparable.

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Using the diameter given, the volume of the sphere is 14137.17cm³

The volume of a sphere is a measurement of how much space it takes up. It is calculated using the following formula and represents the volume of the sphere:

v = 4/3 * π * r³

Where: r is the radius of the sphere, which is the distance from the sphere's center to its surface, and π is a mathematical constant roughly equal to 3.14.

The formula is based on the observation that a sphere's volume is two thirds that of a cylinder with the same radius and height.

The volume of a sphere is directly proportional to the cube of the radius, which is a crucial point to remember.

In the problem, the diameter given is 30cm, we can calculate the radius from this.

radius = diameter / 2

radius = 30 / 2

radius = 15cm

We can plug in the values to calculate the volume of this sphere;

v = 4/3πr³

v = 4/3(3.14)(15)³

v = 14137.17cm³

The volume is 14137.17cm³

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Answer:

91

Step-by-step explanation:

89+89+89+92+x / 5= 90

359+x / 5= 90 (multiply by 5 both sides)

359+x =450 (subtract 359 from both sides)

X= 91

Answer:

Step-by-step explanation:

16 = 20% of x

20% = 1/5

So...

16 = 1/5 of x

16 = 1/5*x

Multiply both sides by 5...

80 = x

There are 80 questions on the test.

Please mark brainliest.

If variation in a process results from common causes alone, the process is said to be in statistical control.

When talking about control charts, being in-control means your process is exhibiting common cause variation and is predictable.

Variation due to the inherent variability in a system of operation is called. special or assignable causes.

Industrial control systems are used by a discipline known as industrial process control in continuous manufacturing processes to produce at a level of consistency, economy, and safety that is impossible to achieve exclusively through manual human control. Process control systems make guarantee that industrial activities are carried out efficiently, dependably, and with as little fluctuation as is practical. They are installed in industrial settings to guarantee throughput, quality, yield, and energy efficiency. Ensure that work is done profitably and safely according to established procedures.

Therefore,

If variation in a process results from common causes alone, the process is said to be in statistical control.

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Answer:

[tex]0.15*x \leq 4.5\\x \leq 30\\Where\ x \ represents\ the\ amount\ of\ candy[/tex]

Step-by-step explanation:

Divide the amount we have by the price of the sweets, and write it into an inequality.

The inequality symbol represents that the total price of all the sweets we want to buy cannot be larger than our budget.

Using Pythagoras theorem, the hypothenuse is equal 4 units

Pythagoras theorem states that in a right triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be expressed as a²+ b² = c², where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.

The length of the third side is the hypothenuse and we can use Pythagoras theorem to find that.

a²+ b² = c²

3² + (√7)² = c²

9 + 7 = c²

c² = 16

Taking the square root of both sides;

c = √16

c = 4

The third side is 4 units

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The third side which is a hypotenuse of the right angle triangle have the length equal to 4.

We shall represent the length of the third side with x, so that by Pythagoras rule we evaluate for the hypotenuse as follows:

x² = 3² + (√7)² {note that: (√7)² = √7 × √7 = 7}

x² = 9 + 7

x² = 16 {square root of both sides}

x = √16

x = 4.

Hence the length of the hypotenuse is equal to 4 by proper application of the Pythagoras rule.

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Households with negative or zero net worth may have high credit card debt due to financial distress, using credit to cover everyday expenses, or difficulty managing finances.

Financial distress: Households with negative net worth may be in financial distress and may be relying on credit cards to cover their basic expenses. This can lead to high levels of credit card debt as they continue to use their credit cards to pay for necessities such as food, housing, and utilities.

Financing everyday expenses: Households with zero net worth may also have high levels of credit card debt if they are using their credit cards to finance their everyday expenses. This can happen if they do not have sufficient income to cover their expenses, or if they have high levels of fixed expenses such as mortgage or rent payments.

Difficulty managing finances: Households with negative or zero net worth may also have a harder time managing their finances and may be more prone to making financial mistakes such as missing credit card payments or making late payments. This can lead to higher levels of credit card debt as they incur late fees and interest charges.

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Households with net worth in the negative or zero have the highest average credit card debt due to the lack of other financing options available to them.

The reason why households with net worth in the negative or zero have the highest average credit card debt is likely due to the fact that they have less access to other financing options and thus rely more heavily on credit cards. When a household has no net worth, they are unable to turn to other sources of borrowing such as home equity loans or personal loans, as they have no equity to borrow against. Therefore, they are more likely to use credit cards to cover unexpected expenses or emergency needs. In addition, households with zero or negative net worth may have lower income and less access to savings, causing them to rely heavily on credit cards for daily expenses.

To illustrate this concept, let’s assume that there are two households with different levels of net worth. Household A has a net worth of $10,000 and Household B has a net worth of -$2,000. Both households have monthly expenses of $1,000 and an income of $2,000. Household A has more financial flexibility because they can turn to other sources of borrowing to cover their expenses, such as home equity loans or personal loans. Household B, however, is unable to borrow against their negative net worth and must rely solely on credit cards to cover their monthly expenses. This makes them more likely to accumulate higher levels of credit card debt due to their limited access to other financing options.

Therefore, it is evident that households with net worth in the negative or zero have the highest average credit card debt due to the lack of other financing options available to them.

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The cylinder has a height of 18 in, a base radius of 7 in, and a volume of 2769.5 in³.

A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been a solid in three dimensions. In elementary geometry, it is regarded as a prism with a circle as its basis.

V = πr²h is the formula for computing a cylinder's volume.

where ;

Replace the specified arguments to obtain:

V = π(7)² * 18

V = 2769.5 in³

Therefore, the cylinder's volume, which has a base radius of 7 inches and a height of 18 inches, is 2769.5 in³.

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Answer:

x = 30

Step-by-step explanation:

3x + 1 + 89 = 180

3x + 90 = 180

3x = 90

x = 30

3(30) + 1 = 91

91 + 89 = 180

Answer:

Step-by-step explanation:

3x + 1 + 89 = 180

3x = 180 - 1 - 89

3x = 90

x = 90 : 3

x = 30°

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

3 x 30 + 1 + 89 = 180

90 + 90 = 180

180 = 180

The expression is a polynomial expression that has 3 terms

The constant is 1/10

the leading coefficient is 1

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable.

A polynomial with an exponent of 1 is, for instance, 2x + 5.

The given polynomial is written as -x + 1/10 + x⁴

x⁴ - x + 1/10

the number of terms are 3

the constant term is 1/10

the leading coefficient is the coefficient of x⁴ which is 1

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About 13 gallons. Paid $2.76 per gallon rounded

12.762 rounded up is about 13. After tge decimal look at the 7, then 6 next to it. Anything 5 or higher round up. 4 or lower, round down.

Same rules with the amount per gallon.

The best sampling method, among these four, will be ¹²C₂ × ¹⁰C₁.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

Three pupils will be chosen from a class of 12 girls and 10 males to sit on a school advisory council. Here are four distinct approaches to choosing.

The total number of students is given as,

Total = 12 + 10 = 22

Then the best sampling method, among these four will be given as,

¹²C₃ × ¹⁰C₀, ¹²C₂ × ¹⁰C₁, ¹²C₁ × ¹⁰C₂, ¹²C₀ × ¹⁰C₃

The best sampling method, among these four, will be ¹²C₂ × ¹⁰C₁.

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To draw a line segment, Gather your drawing materials and decide on the starting and ending points of your line segment. Place your pen or pencil on the starting point and use a ruler to guide it to the ending point, drawing a continuous, straight line and Lift the pen or pencil from the paper to complete the line segment.

To draw a line segment, follow these steps:

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Answer:

56.25

Step-by-step explanation:

Answer:

-20x^2 -6x

Step-by-step explanation:

I don't want to explain the whole thing, but here's a pic.

The area of the enclosed region is 83.4 square units.

To calculate the integral, first determine the limits, which will be the points where both curves meet.

The area will be integrated with respect to y.

In respect to y:

[tex]2x + y^{2}[/tex] = 24

[tex]2x[/tex] = 24 - [tex]y^{2}[/tex]

[tex]x[/tex] = 12 - [tex]\frac{y^{2} }{2}[/tex]

Finding limits:

y = 12 - [tex]\frac{y^{2} }{2}[/tex]

12 - [tex]\frac{y^{2} }{2}[/tex] - y = 0

Multiply by 2 to facilitate calculations:

24 - [tex]y^{2}[/tex] - 2y = 0

Resolving quadratic equation:

- [tex]y^{2}[/tex] -2y + 24 = 0

- ([tex]y^{2}[/tex] + 2y - 24 ) = 0

Divide both sides the same factor,

[tex]y^{2}[/tex] + 2y - 24  = 0

Use Quadratic formula,

y = (-b ± [tex]\sqrt (b^{2} -4ac)[/tex] ) / 2a

y = (-2 ± [tex]\sqrt{2^{2}-4*1*(-24) }[/tex] ) / 2*1

y = (-2 ± [tex]\sqrt{4+96}[/tex] ) / 2

y = (-2 ± [tex]\sqrt{100}[/tex] ) / 2

y = (-2 ± 10 ) / 2

y = (-2 + 10 ) /2  ,     y = (-2 - 10 ) /2  

y = 8/2  ,                  y = -12/2

y = 4   ,                     y = -6

y = 4 and y = -6

Then, integral to calculate area will be with limits -6<y<4:

A = [tex]\int\limits^[/tex] 12 - [tex]\frac{y^{2} }{2}[/tex] - y dy

A = 12y - [tex]\frac{y^{3} }{6}[/tex] - [tex]\frac{y^{2} }{2}[/tex]

A = 12*4 - [tex]\frac{4^{3} }{6}[/tex] - [tex]\frac{4^{2} }{2}[/tex] - [12(-6) - [tex]\frac{-6^{3} }{6}[/tex] - [tex]\frac{-6^{2} }{2}[/tex] ]

A = 48 - 10.6 - 8 - [ -72 + 36 - 18 ]

A = 48 - 10.6 - 8 + 72 - 36 + 18

A = 83.4

Therefore,

The area of the enclosed region is 83.4 square units.

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The general form of an exponential decay function is f(a) = P . (1 - r)ᵃ, hence a function is an exponential decay if the factor (1 - r) is less than 1.

The general exponential decay function can be written as:

f(a) = P . (1 - r)ᵃ

Where:

P = initial quantity

f(a) = remaining quantity at time a

a = time period

r  = decay rate

(1 - r) = decay factor

On the other hand, the general exponential growth function can be written as:

f(a) = P . (1 + r)ᵃ

Hence, the difference between decay function and growth function is: the factor in decay faction is less than 1, while in growth function, the factor is greater than 1.

Example:

f(a) = 6 . (0.25)ᵃ

This is an exponential decay function because the factor is less than 1, that is 0.25

f(a) = 10 . (3)ᵃ

This is not an exponential decay function, but a growth function,  because the factor is greater than 1, that is 3

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People hate their jobs, want to get away from them, and hate having to be responsible, claims Theory X. People are independent and appreciate having obligations placed on them, claims Theory Y.

Theories of human labor motivation and management include Theory X and Theory Y.

They were invented by Douglas McGregor in the 1950s while he was a faculty member at the MIT Sloan School of Management, and they underwent further development in the 1960s.

Consider work a natural part of life, and come up with creative solutions for workplace issues.

According to Theory X, individuals despise their jobs, desire to escape them, and detest having to be accountable.

According to Theory Y, people are self-driven and enjoy having responsibilities placed on them.

Therefore, people hate their jobs, want to get away from them, and hate having to be responsible, claims Theory X. People are independent and appreciate having obligations placed on them, claims Theory Y.

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the sum of 4.06 x 10¹⁹ and 5.034 x 10¹⁷ is 4.11034 x 10¹⁹ (option b)

to add 4.06 x 10¹⁹ and 5.034 x10¹⁷ following steps are to be followed

4.06 x 10¹⁹ can be written as 406x10¹⁷

taking 10¹⁷ common from 406x10¹⁷ and 5.034 x10¹⁷ (406x10¹⁷ +5.034 x10¹⁷)  it will be 411.034 x 10¹⁷

or we can write it as 4.11034 x 10¹⁹

therefore, the sum of 4.06 x 10¹⁹ and 5.034 x 10¹⁷ is 4.11034 x 10¹⁹

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