If the area of AABC is 288in², and if DB = 15in, and CD = 9in, what is the length of AD

The required simplified solution of the given expression is given as ±√10.

Given that,
To determine the simplified solution of x² = 10, by factorization.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
x² = 10
Taking square root on both sides,
x = ±√10

Thus, the required simplified solution of the given expression is given as ±√10.

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Answer:

s=1

Step-by-step explanation:

Slope formula is

Δy/Δx

Substitute in:

7-6/s-10=-1/9

cross multiply

7-6=-1/9s+10(1/9)

7-6=-1/9s+10/9

1-10/9=-1/9s

-1/9=-1/9s

divide both sides by -1/9

thus:

1=s

s=1

(check by plugging back in)

7-6/1-10=-1/9

Answer:

B

Step-by-step explanation:

In a positive correlation, an increase in the independent variable has a corresponding increase in the dependent variable.

What is correlation?

Correlation is a statistical measure that expresses the extent to which two variables are linearly related. We know a positive correlation—when the correlation coefficient is greater than 0 signifies that both variables move in the same direction. Also, A positive correlation exists when one variable decreases as the other variable decreases or one variable increases while the other increases.

I would appreciate it if you mark my answer as brainliest.

Answer: x = 140°

Step-by-step explanation:

The sum of all interior angles in a pentagon is 540°.

Since you have every other angle except for one, you can subtract them from the total:

540°-120°-118°-89°-73° = 140°

Therefore the x angle is equal to 140°.

The correct option is, Mickey should have added –4 and 2 when combining the coefficients of the x terms.

Given,

The expression;  2x² - 4x - 9 - x² + 2x + 3

We have to simplify the expression;

To group and arrange an expression in such a way that it is easier to understand and solve is to simplify the expression.

We first group and find like terms and then add and cancel out

2x²-x²- 4x+2x - 9+ 3

=x²-2x-6

Mickey did not add the coefficients -4 and +2 for x terms in the expression, instead it looked like he added 4+2 as the coefficients

Therefore the correct option is

Mickey should have added –4 and 2 when combining the coefficients of the x terms.

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Answer: 21.5 hrs

Step-by-step explanation:

40 - 18.5 = 21.5 hours left

Answer:

21.5

Step-by-step explanation:

hope it helps

Answer:

B=4

Hope that helps! :)

The probability of being more than 135 false-positive result is equal to 0.0853.

As given in the question,

Probability of false positive 'p' = 1/125

                                                   = 0.008

Number of people tested 'sample size n' = 15,000

Mean 'μ' = np

              = 15000 × 0.008

              = 120

Standard deviation 'σ' = √n × p × ( 1 - p )

                                    = √15000 × 0.008 × ( 1 - 0.008)

                                    =√ 15000 × 0.008 × 0.992

                                    = √119.04

                                    = 10.9

z = (X - μ) /σ

Approximate probability of being more than 135 false-positive results

= P( X > 135)

= P[( X - μ )/σ > ( 135 - μ)/σ

= P ( z > (135 - 120)/ 10.9)

= P ( z > 1.37)

= 1 - P ( z ≤ 1.37)

= 1 - 0.9147  

= 0.0853 ( from z table)

Therefore, probability of being more than 135 false-positive results is equal to 0.0853.

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Answer:

y= 1/4x+5

Step-by-step explanation:

y=mx+c

to calculate gradient: change in y/change in x

-3/-12 = 0.25

y = 1/4x+c

4 * 1/4 = 1

6-1 = 5

c= 5

Totally:
y= 1/4x+5

Answer:

the first one 792 ft²

Step-by-step explanation:

you do length times width times height = lxwxh

The base of the triangle is 15 meters.

Here, we are given that the height of a triangle is 5 m longer than the base.

Let the height of the triangle be h

Then, the base of the triangle will be = h - 5

Further, we are given that area of the triangle = 150 meter square

We know that area of a triangle = 1/2 × base × height

⇒ 150 = 1/2 × h × (h-5)

150 × 2 = h(h-5)

300 = [tex]h^{2}[/tex] - 5h

[tex]h^{2}[/tex] - 5h - 300 = 0

Now, we solve the above quadratic equation by splitting the middle term.

[tex]h^{2}[/tex] + 15h - 20h - 300 = 0

h( h + 15) - 20( h + 15) = 0

(h - 20) (h + 15) = 0

Thus, h = 20 or -15

But since height cannot be negative, h = 20

⇒ base = h - 5

= 20 - 5

= 15 meters

Thus, the base of the triangle is 15 meters.

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The probability that at least one person will receive the correct letter is 2/3.

Given data,

Let's say that the letter matching to the envelope is A, B, and C.

Each envelope has exactly one letter inside it once the letters are randomly placed inside.

Aa, Bb, Cc, Aa, Bc, Cb, Ab, Ba, Cc, Ab, Bc, Ca, Ac, Bb, Ca, Ac, Ba, Cb, are all possible combinations.

Thus, the total number of scenarios is 6 (n(S)).

A=(Aa, Bb, Cc), (Aa, Bc, Cb), (Ac, Bb, Ca), (Ab, Ba, Cc), n(A)=4

let A be an event that at least one letter is in its right envelope.

So,

The probability that at least one letter is in the right envelope P(A) = n(S) / n(A) = 4 / 6

= 2 / 3

​

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0.01 N of work is to be done to move the chopsticks to a distance of 0.01 m

0.02m far the tips of the chopsticks move.

What is work done?

Every time a force pushes something over a distance, work is done. By multiplying the force by the distance moved in the force's direction, you may determine the energy transferred, or work done. Energy transmitted equals work done, which is force times the distance travelled in the force's direction.

1. WD = F×d

      = 1×0.01

      = 0.01 N

2. d = WD/F

   = 0.01/(0⋅5)

   = 0.02m

0.02m far the tips of the chopsticks move.

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Step-by-step explanation:

4x - 9 ≥ 17

4x ≥ 17 + 9

4x ≥ 26

4x/4 ≥ 26/4

x ≥ 13/2

x ≥ 6.5

Answer:

Below

Step-by-step explanation:

YES  function  because there is only ONE value of Y for each value of X

Answer:

k = [tex]\frac{fr^2}{90}[/tex]

Step-by-step explanation:

f = k [tex]\frac{90}{r^2}[/tex] ( multiply both sides by r² to clear the fraction )

fr² = 90k ( divide both sides by 90 )

[tex]\frac{fr^2}{90}[/tex] = k

when sample size increases, everything else remaining the same, the width of a confidence interval decreases.

The sample size is defined as the the number of observations or participants included in a study.

The confidence interval is defined as the mean of the estimate plus and minus the variation in that estimate. That means when you do the test multiple times, then the value may be vary from the estimated value. The confidence interval is the range of those values.

So when the sample size increases the width of the confidence interval decreases

Hence, when sample size increases, everything else remaining the same, the width of a confidence interval decreases.

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Its phase is 60 degrees and π/3 radian

From the question, we have

Each complete cycle measures 360 degrees.

So, 1/6 cycle = 1/6 × 360° = 60°

Each complete cycle measures 2π radian.

So, 1/6 cycle = 1/6 × 2π = π/3 radian

Multiplication:

In mathematics, multiplying two or more numbers yields the product of the numbers. One of the basic mathematical operations is one that we commonly perform. The most obvious example is using multiplication tables. Mathematicians multiply two integers to illustrate the process of repeatedly adding one number to another. The types of numbers that can be included include natural numbers, fractions, integers, whole numbers, and others. When M is multiplied by n, it either adds or subtracts from itself 'n' times.

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A company received 15 funding applications and want to select 8 of them to be funded. The number of different lists of successful applications is 6,435

Suppose we have n objects in total and we want to select r objects among total objects, the number of ways they can be selected is given by the combination formula:

ⁿCr = n! / [r! (n-r)!]

Data from the problem:

n = total applications = 15

r = number of selected applications = 8

Hence, the number of different lists of successful applications is:

¹⁵C₈ = 15! / [8! (15-8)!]

       = 15! / [8! 7!]

       = 6,435

Thus, the number of different lists can be selected is 6,435

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Answer:

[tex]3( - 7x - 3) + 4x = - (x - 3)[/tex]

[tex] - 21x - 9 + 4x = - x + 3[/tex]

[tex] - 21x + 4x + x = 9 + 3[/tex]

[tex] - 16x = 12[/tex]

[tex] - 16 \div ( - 16x = 12)[/tex]

[tex]x = - \frac{3}{4} [/tex]

Step-by-step explanation:

it is negative 3/4 not positive 3/4

The correct statement that regarding the angles of triangle is option (C)  m∠C > m∠A > m∠B

The value of p ≥ 3

Consider the value p = 3

The length of the side AB = 4p - 1

= 4×3 - 1

= 12 - 1

= 11 units

The length of side BC = 3p

= 3×3

= 9 units

The length of the side AC = p + 4

= 3 + 4

= 7 units

Then length of AB > length of BC > length of AC

The angles opposite to the side AB, BC and AC are m∠C , m∠A and m∠B

Then  m∠C > m∠A > m∠B

Hence, the correct statement that regarding the angles of triangle is option (C)  m∠C > m∠A > m∠B

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First, we have to recognize that if the current number of girls in the class is a 15% increase from last year, then this year's number is 115% of last year's number.  

With that, we can set up a proportion comparing last year to this year, in both percentages and numbers:

     [tex]\dfrac{100}{115} = \dfrac{x}{15}[/tex]

Note that both numerators are last year's values and the denominators are this year's values.

If we multiply both sides by 15, we have that x ≈ 13.043478260869565.  Since we're dealing with whole people, we'd say that there were 13 girls in the class last year.

Jessica bought [tex]2\frac{1}{4}[/tex] yards of fabric more than Derek.

According to the question,

We have the following information:

Jessica bought 5 yards of fabric, plus 20% extra fabric. Derek bought 3 yards of fabric, plus 25% extra.

Now, we will find first the extra fabric they both bought:

For Jessica, we have:

20% of 5

20*5/100

1 yard

Now, the total fabric Jessica has:

5+1

6 yards

For Derek, we have:

25% of 3

25*3/100

3/4 yards

Now, the total fabric Derek has:

3 + 3/4

Taking 4 as the least common factor and adding the fractions:

15/4 yards

Now, we will subtract the fabric Derek has from the fabric Jessica has:

6 - 15/4

(24-15)/4

9/4

Converting this into mixed fraction:

[tex]2\frac{1}{4}[/tex] yards

Hence, the correct option is B.

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The solution of the expression is 2√5x(√2-1).

From the question, we have

√5x ( √8x² - 2√x)

= √5x ( 2√2x - 2√x)

= √5x(√2-1)(2√x)

= 2√5x(√2-1).

The solution of the expression is 2√5x(√2-1).

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer: ITS D

Step-by-step explanation:

2x sqrt 10x - 2x sqrt 5

Answer:

1/4

Step-by-step explanation:

3/4 divided by 3=1/4

According to the Centroid Ratio Theorem , we have:

                    x = 37 , DG = 22,

                   AG = 44  and AD = 66

Centroid Ratio Theorem:

The Centroid ratio theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid point of the side.

according to the centroid ratio theorem, we have,

                        AG = 2/3 (AD)       ----------------------------- (1)

                        AG = x + 7

                        DG = x - 15

                        AD = x + 7 + x- 15 = 2x - 8

Putting the values in equation (1)

     x + 7 = 2/3 (2x - 8)

⇒ 3(x + 7) = 2( 2x - 8)

⇒3x + 21 = 4x - 16

⇒ -x = -37

⇒ x = 37

Putting the value of x= 37

DG = 37 - 15 = 22

AG = 37 +7 = 44

AD= 2×37 - 8 = 66

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The solution to the linear equation is (-1, 3).

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.

2x + y = 1 …… (1)

3x - y = -6 …… (2)

To solve the linear equations in two variables

By adding both the equations

5x = -5

x = -1

Substitute the value of x in equation (1)

2 (-1) + y = 1

-2 + y = 1

y = 1 + 2 = 3

y = 3

Therefore, the solution to the linear equation is (-1, 3).

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We need to multiply equation 2 with 3 and result is x = 1.25. The cost of one apple and one banana is $1.25 and $0.75 respectively.

Forming the equation using given variables x and y. Firstly writing the equation based on Lydia's items.

5x + 3y = 8.50 : Equation 1

Now writing the equation based on Ari's items.

3x + 2y = 5.25 : Equation 2

Now we need to equate one variable to find the other variable. So, multiplying equation 1 with 2 and equation 2 with 3.

10x + 6y = 17 : Equation 3

9x + 6y = 15.75 : Equation 4

Subtracting equation 4 from equation 3. We get the result -

x = 1.25

Keep the value of x in equation 1 to find the value of y

5×1.25 + 3y = 8.50

6.25 + 3y = 8.50

3y = 8.50 - 6.25

3y = 2.25

y = 2.25/3

y = 0.75

Thus, the cost of one apple is $1.25 and cost of one banana is $0.75.

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The complete question is -

lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. this system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas. 5x 3y = 8.5 3x 2y = 5.25 if you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination? complete the multiplication and add the equations. what is the result? what is the price per pound of apples? what is the price per pound of bananas?