If the middle term of a quadratic trinomial is negative and the last term is negative, then
the sum of the factors for the middle term must be __

Equation of a Line

The slope-intercept form of a line is:

y = mx + b

Where m is the slope.

We are given the equation of a line:

24x - 2y = 38

Subtracting 24x:

-2y = -24x + 38

Dividing by -2:

y = (-24/-2)x + 38/(-2)

Operating:

y = 12x - 19

We can see that b = 12, thus the slope of the graph is 12

Answer:

D. 12

The area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

Since kite ABCD is divided into two triangles by its diagonals, we can find the area of the kite by finding the sum of the areas of these two triangles.

Let AC and BD be the diagonals of the kite, intersecting at point E. Then triangle ABE and triangle CDE are the two triangles formed by the diagonals.

The area of a triangle can be found using the formula: Area = (base x height) / 2

For triangle ABE, the base is AB and the height is the distance from E to the line containing AB. Similarly, for triangle CDE, the base is CD and the height is the distance from E to the line containing CD.

Since the diagonals of a kite are perpendicular and bisect each other, the distance from E to the line containing AB is the same as the distance from E to the line containing CD.

Therefore, the heights of the two triangles are equal.

So, we can find the area of ABCD as follows:

Area of ABCD = Area of triangle ABE + Area of triangle CDE

= (AB x height)/2 + (CD x height)/2

= (AB + CD) x height / 2

Therefore, the area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

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The statement that is not necessarily correct is ΔTRS ≅ ΔVUW. So, correct option is D.

The given information states that two triangles are congruent based on the corresponding parts, RS ≅ UV, RT ≅ UW and ∠R ≅ ∠U.

To determine which statement is not necessarily correct, we need to use the congruence criteria that are sufficient to prove the congruence of triangles. These criteria are:

SSS (Side-Side-Side): If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

ASA (Angle-Side-Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Using the given information, we can apply the SAS criterion to show that ΔRST ≅ ΔUVW. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (a) ΔRST ≅ ΔUVW is correct.

Now, we can use the SAS criterion again to show that ΔSTR ≅ ΔVWU. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (b) ΔSTR ≅ ΔVWU is also correct.

We can also use the SAS criterion to show that ΔTRS ≅ ΔVWU. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (c) ΔTRS ≅ ΔVWU is correct.

However, we cannot use any of the above criteria to show that ΔTRS ≅ ΔVUW. This is because we do not know that TU ≅ VW. Therefore, the statement (d) ΔTRS ≅ ΔVUW is not necessarily correct.

So, correct option is D.

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Answer:

c) 3

Step-by-step explanation:

1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Answer:

(879,120)÷(56709072) ×(-659340)=-10221.274

Step-by-step explanation:

we use bedmas rules when it comes to long solving questions.

Answer:

(-2, 3)

Step-by-step explanation:

5/2(3/4x + 1/3y = -1/2)

1/2x - 5/6y = -7/2

15/8x + 5/6y = -5/4

19/8x = -19/4

x = -2

1/2(-2) - 5/6y = -7/2

-1 -5/6y = -7/2

-5/6y = -5/2

y = 3

Therefore, if the person works 54 hours, they would make $1,163.04. Rounded to 2 decimal places, the answer is $1,163.00.

The decimal system employs ten decimal digits, a decimal mark, and a minus sign ("-") for negative quantities when writing numbers. The decimal digits are 0 through 9, with the dot (".") serving as the decimal separator in many (mainly English-speaking) nations and the comma (",") in others.

The fractional portion of the number is represented by the place value that follows the decimal. The number 0.56, for instance, is composed of 5 tenths and 6 hundredths.

We can use proportionality to solve this problem. If the person works 25 hours and makes $539, then their hourly rate is:

$539 ÷ 25 hours = $21.56 per hour

They would make if they work 54 hours, we can multiply their hourly rate by the number of hours worked:

$21.56 per hour × 54 hours = $1,163.04

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Answer:

3 ( 3 x + 1 ) ( 3 x − 1 )

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

the ratio of the 2 numbers = 3 : 4 = 3x : 4x ( x is a multiplier ) , then

3(3x) + 2(4x) = 68 , that is

9x + 8x = 68

17x = 68 ( divide both sides by 17 )

x = 4

smaller number = 3x = 3 × 4 = 12

Answer:

5 hours

Step-by-step explanation:

Variable x = number of hours

Step 1: set up equations

Cwicky Cleaners: 100 + 20x

No Mo Mess: 50 + 30x

Step 2: to find the same hours equal the two equations

100 + 20x = 50 + 30x

Isolate the variable (x)

100 - 50 = 30x - 20x

50 = 10x

50 ÷ 10 = x

5 = x

Step 3: Check your work

Plug in 5 for x on both sides and equal equations together

100 + 20(5) = 50 + 30(5)

100 + 100 = 50 + 150

200 = 200

If they equal each other, then the answer is correct.

This answer is correct.

Answer:

16 miles

Step-by-step explanation:

let the number of miles driven be = x

Company A = Company B

8 + 0.10x = 0.60x

8 = 0.50x

x = 16

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Answer:

x = 4

Step-by-step explanation:

-x + 6 = 0.5x

1.5x = 6

x = 4

1)13/4: Rational (a fraction)

2)√17: Irrational (square root of a non-perfect square)

3)3π: Irrational (product of a rational number and an irrational number)

4)0.1 (1 bar): Rational (repeating decimal)

5)-√2: Irrational (negative square root of a non-perfect square)

6)√24: Irrational (square root of a non-perfect square)

7) -√49: Rational (negative square root of a perfect square)

1)13/4: Rational - This number is a fraction, and any number that can be expressed as a fraction is considered rational. In this case, 13/4 can be simplified to 3.25, which is a rational number.

2)√17: Irrational - The square root of 17 cannot be expressed as a simple fraction or terminating decimal. It is an irrational number, meaning it cannot be expressed as a ratio of two integers.

3)3π: Irrational - π (pi) is an irrational number, and when multiplied by a rational number like 3, the result is still an irrational number. Therefore, 3π is an irrational number.

4)0.1 (1 bar): Rational - This number is a repeating decimal, indicated by the bar over the 1. Although it does not have a finite representation, it can be expressed as the fraction 1/9, which makes it rational.

5)-√2: Irrational - Similar to √17, the square root of 2 is also an irrational number. Multiplying it by -1 does not change its nature, so -√2 remains an irrational number.

6)√24: Irrational - The square root of 24 is an irrational number because it cannot be expressed as a simple fraction or terminating decimal. It can be simplified to √(4 × 6), which further simplifies to 2√6, where √6 is an irrational number.

7)-√49: Rational - The square root of 49 is 7, which is a rational number. Multiplying it by -1 does not change its nature, so -√49 remains a rational number.

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The complete question is :

Select whether the following numbers are rational or irrational.

1. 13/4

2. \sqrt{17}

3. 3 π

4. 0.1 (1 bar)

5. - \sqrt{2}

6. \sqrt{24}

7. - \sqrt{49

9514 1404 393

Explanation:

In general, a system of equations has a solution that satisfies all of the equations. That is, the solution set is the intersection (and) of the solution sets of the individual equations in the system. Equations involving the absolute value function are no different.

That being said, you need to consider the meaning of an equation involving the absolute value function.

The function itself is piecewise defined:

  \(\displaystyle |x|=\left\{ {x, x\ge0} \atop {-x, x<0}} \right.\)

So, any equation involving the absolute value function automatically resolves to two equations, each with its own condition on the function value.

__

Example 1:

  |x+1| > 3

is equivalent to the two disjoint conditional equations ...

  (x +1) > 3  and  (x +1) ≥ 0 . . . . OR

  -(x +1) > 3  and  (x +1) < 0

the first of these has the solution x > 2; the second of these has the solution x < -4. The solution set of this equation is the OR of the two solution sets:

  x < -4  or  x > 2

__

Example 2:

  |x +1| < 3

is equivalent to the two disjoint conditional equations ...

  (x +1) < 3  and  (x +1) ≥ 0 . . . . OR

  -(x +1) < 3  and  (x +1) < 0

The first of these has the solution -1 ≤ x < 2, and the second of these has the solution -4 < x < -1. Again, the solution set of this equation is the OR of the two solution sets. However, we find we can write that union as a single compound inequality:

  -4 < x < 2

__

When an absolute value equation involves more than one absolute value function, then the equation will probably resolve into multiple equations, each defined on its own domain. Sometimes keeping those domains straight can be tedious.

Above, we have considered inequalities. If you have an equation, you need to consider that it will likely resolve to two equations. The solution set will be the OR of the solutions to those two equations.

Example 3:

  |x +1| = 3

is equivalent to the two conditional equations ...

  (x +1) = 3  and  (x +1) ≥ 0 . . . . OR

  -(x +1) = 3  and  (x +1) < 0

The first of these has the solution x = 2; the second has the solution x = -4. The solution set is the OR of these two solutions:

  x = -4  or  x = 2

__

The "and" condition restricts the domain of each of the individual pieces of the equation. The "or" condition applies to the collection of solutions that may exist in each of those restricted domains.

Answer:

Real numbers = 39 and 9

Step-by-step explanation:

The standard form of a quadratic equation is ax² + bx + c = 0

Given the following data;

a = 1

b = -43

c = 306

Quadratic equation formula is;

\( x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} \)

Substituting into the equation, we have;

\( x = \frac {-(-43) \; \pm \sqrt {43^{2} - 4*1*306}}{2*1} \)

\( x = \frac {43 \pm \sqrt {1849 - 1224}}{2} \)

\( x = \frac {43 \pm \sqrt {625}}{2} \)

\( x = \frac {43 \pm 25}{2} \)

\( x_{1} = \frac {43 + 25}{2} \)

\( x_{1} = \frac {68}{2} \)

\( x_{1} = 39 \)

\( x_{2} = \frac {43 - 25}{2} \)

\( x_{2} = \frac {18}{2} \)

\( x_{2} = 9 \)

Therefore, the two real numbers are 39 and 9.

The quadratic equation now becomes;

x² - 43x + 306 = (x - 39)(x - 9) = 0

6) The solution of the system of linear equations is (x, y, z) = (2, 5, 3).

11) The average depth of the water is 0.35 kilometers.

12) The dollar value of the deposit after 10 years is $ 1205.85.

13) Three horses need a consumption of 930 pounds of hay for the month of July.

14) The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.

15) Anna has a mean time of 7.39 minutes.

In this question we must analyze and resolve on algebraic equations such as linear equations or conic sections. 6) We must use algebra properties to solve on the system of linear equations. First, we clear x in the first equation:

x = y - z

Then, we apply it in the two remaining equations:

- 5 · (y - z) + 3 · y - 2 · z = - 1

2 · (y - z) - y + 4 · z = 11

- 2 · y + 3 · z = - 1

y + 2 · z = 11

Second, we clear y in the second expression and we substitute into the first expression:

y = 11 - 2 · z

- 2 · (11 - 2 · z) + 3 · z = -1

- 22 + 7 · z = - 1

z = 3

y = 5

x = 2

The solution of the system of linear equations is (x, y, z) = (2, 5, 3).

11) There is a function of the speed of a tsunami in terms of the average depth of the water. The former variable is known and we need to clear d in the formula to find the missing value:

145 = 356 · √d

d = (145 / 356)²

d = 0.345 km

The average depth of the water is 0.35 kilometers.

12) The compound interest model is shown below:

C' = C · (1 + r / 100)ˣ      (1)

Where:

If we know that C = 500, r = 4.5 and x = 20, then the resulting capital after 10 years is:

C' = 500 · (1 + 4.5 / 100)²⁰

C' = 1205.85

The dollar value of the deposit after 10 years is $ 1205.85.

13) The situations indicates a direct variation as the amount of hay is directly proportional to the number of days. Hence, we have the following linear model for the hay consumption of one horse:

y = m · x        (2)

y = 10 · x

Where:

The total consumption of three horses during July is equal to the product of the number of horses and consumed hay by one horse during one month:

y' = 3 · [10 · (31)]

y' = 930

Three horses need a consumption of 930 pounds of hay for the month of July.

14) There is the general equation of the circumference and we must transform it into its vertex form to find information about the radius. This can done by algebraic procedures:

x² + y² + 8 · y + 8 · y + 28 = 0

(x² + 8 · y) + (y² + 8 · y) = - 28

(x² + 8 · y + 16) + (y² + 8 · y + 16) = 4

(x + 4)² + (y + 4)² = 2²

The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.

15) We need to sum all the times described in the table and divide it by the number of data to find the mean time for a 1-kilometer race:

x = (7.25 + 7.40 + 7.20 + 7.10 + 8.00 + 8.10 + 6.75 + 7.35 + 7.25 + 7.45) / 10

x = 7.39

Anna has a mean time of 7.39 minutes.

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Amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

Let amount of one tin of paint = x

Let the total amount Mr. Chong  having = y

On buying 18 tins of paint, he will need another $80. This can we mathematically represented as,

18x = y + 80            

On rearranging this equation can be written as,

18x - y = 80                                         equation 1

On buying 10 tins of paint, he will will have $32 left. This can we mathematically represented as,

10x = y - 32

On rearranging this equation can be written as,

-10x + y = 32                                      equation 2

On adding equation 1 and equation 2, we get

18x - y -10x + y = 80 + 32

8x = 112

x = (112/8) = 14

On substituting x = 14 in equation 2 , we get

-140 + y = 32

y = 172

So, amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

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The probability that a randomly chosen return shows an adjusted gross income of $50,000 or more is 33.2%.

For mutually exclusive events, use the following addition rule:

        P(A or B) = P(A) +P(B)

The corresponding probabilities is :

   P( income > $50000) = P( >50)

= P(50 - 90) +P( 100 - 499) +P( ≥ 500)

= 0.215 + 0.100 +0.006

= 0.321

Therefore, the probability of a random selection returning is

P( income > 50000) = 0.321

Now ,

P( income ≥ 50000 and ≥ 100000 ) = P( > 100000)

= 0.100 + 0.006

= 0.106

The Probability Condition is:

   P(A/B) = P(A and B) / P(B)

Therefore,

P( ≥ $100000 / $ $50000)

=   P( ≥ $100000 and $ $50000)/ P( ≥ $50000)

= 0.106/ 0.321

≈ 0.3302

= 33.2%

Therefore, the conditional probability of earning at least $50000 and more is 33.2%

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Answer:

6x+24

Step-by-step explanation:

The expression 6x+24 is equivalent to 3x+14+3x+10

3x+14+3x+10

3x+3x+14+10

6x+24

Hope this helps ;) ❤❤❤

Answer:

6x + 24

Step-by-step explanation:

Step 1:

3x + 14 + 3x + 10

Step 2:

6x + 14 + 10

Answer:

6x + 24

Hope This Helps :)

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

wow that's pretty lit

Answer:what the heck are you trying to say?

Step-by-step explanation:

The required equation function j which is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

As we can see in the graph the functions j and f are similar but the graph of j is 2 units left of f. So, function f(x) has a domain of real number greater than equal to zero, while as the function j is 2 units left of f then its equation is given as  \(j(x)= (x+2)^{1/2}\)  where the domain of j is all real numbers greater then or equal to -2.

Thus, the equation of function j is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

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In the question the graph is missing, a graph has been added on behalf of the incomplete question.

Answer:

8

Step-by-step explanation:

The given set to us is ,

=> A = { 2 , 3 , 4 }

And ,

=> n(A) = 3

The Total number of subsets of a set A with n number of elements is given by ,

=> n(subsets) = 2ⁿ .

=> n( subsets) = 2³

=> n ( subsets ) = 8

Answer:

2 3 4 5

Step-by-step explanation:

1/2*-2+3 = 2

1/2*0+3 = 3

1/2*2+3 = 4

1/2*4+3 = 5

Answer:

0.2941 M

Step-by-step explanation:

Formula for molarity is;

M = number of moles(n)/volume of solution(v)

We are given;

n = 0.5 moles

Volume = 1700 mL = 1700 × 10^(-3) L

Thus;

M = 0.5/(1700 × 10^(-3))

M = 0.2941 M

The total surface area to paint is 22000 sq. ft.

Surface area is the measurement of the outer surface of an object. It is often used to calculate the area of a three-dimensional object, such as a cube, cylinder, or sphere, and is also used to calculate the area of the faces of a solid object. Surface area is measured in square units such as square centimeters (cm2), square meters (m2), or square inches (in2).

Surface Area = 2(lw + lh + wh)

Surface Area = 2((100' x 50') + (100' x 40') + (50' x 40'))

Surface Area = 2(5000' + 4000' + 2000')

Surface Area = 2(11000')

Surface Area = 22000 sq. ft.

Answer: The total surface area to paint is 22000 sq. ft.

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Answer:

210 seconds

Step-by-step explanation:

LCM of 5,6 and 7