X=-3±2√2
Solve for x

1. Solve s in the second equation:

2. Substitute the s in the first equation by the value you get in the previous step:

3. Solve t:

4. Use the value of t to solve s:

The minimum additional information needed in order to be able to state that the triangles are congruent by AAS is . Option A

[tex]\angle A B C=\angle A D C[/tex]

This is further explained below.

Generally, The triangles are said to be congruent if they satisfy the AAS (Angle-Angle-Side) condition, which states that if two angles and a non-included side in one triangle are congruent to two angles and the equivalent non-included side in another triangle, then the triangles are congruent.

In conclusion, The following pieces of knowledge are the bare minimum that is required in order to be able to make the assertion that the triangles are congruent according to AAS:

[tex]\angle A B C=\angle A D C[/tex]

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Answer: 4√2-0.5

Step-by-step explanation:

[tex]\sqrt{(2\sqrt{2}-3)^2 } +|2\sqrt{2}+5|-|-2.5|=\\\\|2\sqrt{2}-3|+(2\sqrt{2}+5)-(2.5 )=\\\\2\sqrt{2}-3+2\sqrt{2}+5-2.5 =\\\\4\sqrt{2} -0.5[/tex]

At time 1.75 seconds the ball is in the 51 feet high.

What is substitution method?

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

Given that;

The height of the football could be describe by the model,

h = - 16t² + 56t + 2   ..... (i)

Where, h describes the height of the ball in feet.

and t is the time in seconds after the ball was kicked.

Now,

At height 51 feet, the time is calculated as;

Substitute h = 51 in equation (i), we get;

h = - 16t² + 56t + 2  

51 = - 16t² + 56t + 2  

16t² - 56t - 2 + 51 = 0

16t² - 56t + 49 = 0

Solve for t by using quadratic formula;

t = - (-56) ± √(-56)² - 4 × 16 × 49 / 2 × 16

t = 56 ± √3,136 - 3,136 / 32

t = 56 ± 0 / 32

t = 56 / 32

t = 1.75 seconds

Thus, At time 1.75 seconds the ball is in the 51 feet high.

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Answer:

7.63 x 10⁷

Step-by-step explanation:

To convert to scientific notation you have to move the decimal place to where there is only one number in front of it. In this cause the number in front is 7. You have to maintain the same number of significant figures which in this case was 3 then multiply by 10 to the exponent of how many times you moved the decimal place.

Answer:

=76.3×10⁶

Step-by-step explanation:

=76,300,000÷1,000,000

=76.3×10⁶

The equation have infinitely many solution when n is equal to -15.41.

A linear equation in one variable is an equation which has a maximum of one variable of order 1. It is of the form ax + b = 0, where x is the variable. This equation has only one solution.

Given equation is;

24( mx + n ) = 3x + 17

where; m and n are real numbers.

Part 1.  If m = 14 and n = 13 then

Putting the value of m and n in the equation we get;

= 24( 14.x + 13 ) = 3x + 17

=  336x + 312 = 3x + 17

=  336x - 3x = 17- 312

=  333x = -295

x = 0.886

Hence,  x = 0.886  the equation having one solution .

part 2.  if m = 18 then to find n .

put m = 18 in the given equation;

= 24(18.(0.886) + n ) = 3(0.886) + 17

= 24(15.94) + 24n = 2.658 + 17

= 382.56 + 24n = 19.658

= 24n = 19.658 - 382.56

n = -15.41

Hence, The equation have infinitely many solution when n is equal to -15.41.

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The complete question is;

PART A: Rosie writes the equation 24(mx+n)=3x+17, where m and n are real numbers.

If m=14 and n=13, does the equation have one solution, infinitely many solutions, or no solutions? Explain your answer.

Step-by-step explanation:

Q.1

6×sqrt(27) + 11×sqrt(75) =

= 6×sqrt(3×9) + 11×sqrt(3×25) =

= 3×6×sqrt(3) + 5×11×sqrt(3) =

= 18×sqrt(3) + 55×sqrt(3) = 73×sqrt(3)

Q.2

53×sqrt(5) × (-103×sqrt(50)) =

= 53×-103 × sqrt(5)×sqrt(50) =

= -5459 × sqrt(5×50) = -5459 × sqrt(250) =

= -5459 × sqrt(10×25) = -5459 × 5×sqrt(10) =

= -27,295 × sqrt(10)

Q.3

1/4 + 1/2 rational (as both terms are rational)

sqrt3 + 4 irrational (as sqrt(3) is not rational)

sqrt4 + 7 rational (sqrt(4) = 2, 2+7 = 9)

2 x sqrt9 rational (sqrt(9) = 3, 2×3 = 6)

7 x sqrt6 irrational (sqrt(6) is not rational)

4x2sqrt3 irrational (sqrt(3) is not rational)

3. 7 x (1/3) rational (all terms are rational)

7 x sqrt81 rational (sqrt(81) = 9, 7×9 = 63)

Uniform line movement.

The uniform rectilinear movement is the movement that maintains a variation of the distance with respect to time always constant, since the acceleration is zero.

If we know that Wilson travels 53.7 miles in 1.6 hours, we determine the average speed from the following equation:

Speed = distance / time

Speed = 53.7 miles / 1.6 hours

Speed = 33.5625 miles/hour

V = 33.6 miles/hour

The average speed that Wilson travels is: V = 33.6 miles/hour.

Answer:

52% of them are girls

Step-by-step explanation:

The associative property can be applied to addition and multiplication.

When more than two numbers are added together or multiplied, the outcome is always the same, regardless of how the numbers are arranged. This is known as the associative property.

For example,

2 × (7 × 6) = (2 × 7) × 6

2 + (7 + 6) = (2 + 7) + 6

Associative Addition Property

The associative feature of addition states that the total sum of the numbers will not change no matter how they are arranged. This may be stated as follows:

(x + y) + (z + y) = x

Associative Multiplication Property

The idea behind the associative property for multiplication is that no matter how the numbers are arranged, the result will always be the same. This may be stated as follows:

P = (q)/(r) = (q)/(r)

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An expression which can be used to find the total number of squares below (see attachment) is: B. 7 × 5

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In this exercise, you're required to determine the total number of squares that are shown in the image attached below. By critically observing the image, we can reasonably and logically deduce that there are five (5) categories of squares and each of them comprises seven (7) squares.

Therefore, the total number of squares can be calculated by using this expression:

Total number of squares = 7 × 5

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Answer:

x=21

Step-by-step explanation:

6-1/3x=-1

-6        -6

-1/3x=-7

__     __

-1/3    -1/3

x=21

Hello!

Let's solve:

 [tex]\text{Copy down the equation}\\6-\dfrac{x}{3}=-1 \\\\\text{Move 'x/3' to the right side and '-1 to the other side}\\6+1=\dfrac{x}{3}\\ 7=\dfrac{x}{3} \\\\\text{Multiply 3 to both sides}\\7*3=3*\frac{x}{3} \\x = 21[/tex]

Answer: x = 21

Hope that helps!

Answer:

y = 7

eight grade math comes back to haunt me

The situation that is best represented by an exponential distribution is given by the following option:

Tafadzwa runs between 10 and 16 laps every day. his times get slower as he gets tired, but his daily average is 48.2 s per lap. what is the probability that his mean lap time tomorrow will be less than 45 s?.

The exponential probability distribution, with mean m, is described by the following mass function:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

From this, we get that the exponential distribution is used when we want to study the time between events in a distribution, and only the first option in this problem gives it.

As for the other options, the distributions are as follows:

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The average rate for the entire walk of hiker is 3.75 miles per hour by the concept of average speed.

The instantaneous speed is the upper limit of the average speed as the duration of the time interval approaches zero. An object's average speed during a certain period of time is equal to its distance traveled over that period divided by its duration. Speed and velocity are distinct concepts.

The whole distance traveled divided by the total time results in the average rate for the entire walk, expressed in miles per hour.

Given that:

Distance A = 12.8 miles

Distance B = 17.2 miles

Total distance = Distance A + Distance B

Total distance= 12.8 + 17.2

Total distance= 30 miles

Time A = 9:00 a.m. to noon = 3 hours

Time B = 1:00 p.m. to 6:00 p.m. = 5 hours

Total time = Time A + Time B

Total time= 3 + 5

Total time= 8 hours

Average rate = Total distance/Total time

Average rate= 30 miles/8 hours

Average rate= 3.75 miles per hour

Therefore, the average rate for the entire walk of hiker is 3.75 miles per hour.

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Here, we are given;

P(A)=0.6

P(B)=0.42

P(B/A)=0.63

We have to find;

Now,

This is the formula for finding conditional probability.

From here,we can see that we have values of P(B/A) and P(A) and we can easily find P(Aand B) from here.

Since P(A)>0 so we can use this formula.

Therefore,

Using the given information, the fraction is 3/8

From the question, we are to determine the fraction

Let the numerator of the fraction be x and the denominator be y

From the given information,

"if the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2, the result is 2"

That is,

4x/(y -2) = 2

and

" If the numerator of the fraction is increased by 15 and 2 is subtracted from the double of the denominator, the result is 9/7"

That is,

(x + 15)/(2y - 2) = 9/7

From the first equation,

4x/(y -2) = 2

4x = 2(y-2)

4x = 2y - 4

4x + 4 = 2y

y = 2x + 2 ----------- (3)

From the second equation,

(x + 15)/(2y - 2) = 9/7

7(x + 15) = 9(2y - 2)

7x + 105 = 18y - 18

Substitute equation (3)

7x + 105 = 18(2x + 2) - 18

7x + 105 = 36x + 36 - 18

105 - 36 + 18 = 36x - 7x

87 = 29x

x = 87/29

x = 3

Substitute the value of x into equation (3)

y = 2x + 2

y = 2(3) + 2

y = 6 + 2

y = 8

Thus, the number is 3/8

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Answer:x=16

Step-by-step explanation:

just divide both sides by negative 1

If the coordinates of the vertex of a parabola are known [tex]V(p,k)[/tex], the equation for that parabola can be written by the following formula;7

Now let's find the vertex of the given equation.

We've found our vertex.

Let's substitute the unknowns in the formula I've given.

Let's expand the expression and find the coefficient p.

Finally;

[tex]q=\frac{7}{4}[/tex]

[tex]p=2[/tex]

When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative

What is the explanation?

U(2, 7) → U'(-7, 2)

V(10, 7) → V'(-7, 10)

W(2, 3) → W'(-3, 2)

Step-by-step explanation:

From the picture attached,

Coordinates of the vertices of the given triangle,

U → (2, 7)

V → (10. 7)

W → (2, 3)

Since rule for the coordinates of a point P(x, y) after a rotation of 90° counterclockwise about the origin is,

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The graph for given values is below -

The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.

For the graph,

the value of y for x = 1,

y = -6.3 or 13/2

(1,-6.5)

For x= 2,

y = -7

(2,-7)

For x = 4,

y = -8

(4, -8)

With respect to the given line which is y = -1/2x - 6

the coordinates are following -

(1,-6.5), (2,-7), (4, -8)

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The earned amount by Dale in 3 years is: 15 dollars.

How to calculate the amount?

To calculate the annually amount based on the principal money is by using simple interest method. This interest was given by the bank. And it is calculated by multiplying the principal amount, rate and time and divided by 100.

According to the question, the given amount parameters for the simple interest calculation is as follows:

Principal amount: $100

Rate of interest: 5%

Time(years): 3 years

Using standard simple interest formula, we get:

S.I. = (P x R x T)/100

S.I. = (100 x 5 x 3)/100 = 15 dollars

Hence, the earned amount by Dale in 3 years is: 15 dollars

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Answer:

One, Buff Billy's, has a joining cost of $80 and charges $25 a month. The other, Shredded Eddie's, has no joining cost but charges $35 a ...

Step-by-step explanation:

Julia must sell 21 tacos to meet the requirement .

Given: Price of each taco = $ 3.75

Price of each burrito = $ 6

Total amount of money she needs to earn = $ 330

Also the number of burritos sold= 42.

So the total amount earned on selling these burritos= 42× 6 = $ 252

And as it is given that total money she needs to earn is $ 330 .

so required money= $ 330- $ 252

=$ 78

Thus the total number of tacos she needs to sell = 78/ price of 1 taco

= 78/ 3.75

= 20.8 ≈ 21

Thus Julia must sell 21 tacos to meet the requirement .

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We know that the equation of a line is given by

y = mx + b, where m and b are numbers:

m is the slope of the line and b is the y intercept.

In this case we have the equation:

6 - 2y = - 6

We clear y so we can identify m and b

6 - 2y = -6​

6 = -6​ + 2y

6 + 6​ = 2y

12 = 2y

12/2 = y

6 = y

In this case

y = 6

Then m=0 and b = 6

The interest for the first payment is $30.00

Interest is how much is paid for the use of money.

Therefore, you  take a $4,500 loan to pay for trip to the Amazon rainforest to photograph wild animals.

The  loan's interest rate is 8% for 1 year.

Therefore, the interest for the first payment can be calculated as follows:

Interest for the first payment = 8% of 4500 × 1 / 12

Interest for the first payment = 8 / 100 × 4500 × 1 / 12

Interest for the first payment = 8 × 45 × 1 / 12

Interest for the first payment = 360 / 12

Interest for the first payment = $30

Therefore,

interest = $30

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A. P( 2∪3∪6 ) = 1/2

B. P( 1∪2∪3∪4∪5 ) = 9/16

The probability of an occurrence e can be written as P (e), and its equation is as follows:

P (e) = Number of favorable outcomes / Total number of outcomes

This can only be used with a straightforward event.

The probability will also be influenced by other factors, whether they are imposed or a result of the event's inherent characteristics.

Using a six-sided die,

A) First, in order to gather as much information as possible from the question, we concentrate on the probabilities provided P(1∪4∪5)=1/2 and P(2∪3∪5)=1/2 and we need to use P(5)=7/16.

It's crucial to remember that while using a dice, receiving two values on the same roll is impossible. Due to this and the likelihood of certain circumstances:

P(1∪4∪5) = P(1) + P(4) + P(5) - P(1∩4)(= 0) - P(4∩5)(= 0) - P(1∩5)(= 0) + P(1∩4∩5)(= 0)

P(1∪4∪5)=P(1) + P(4) + P(5)

1/2 = P(1) + P(4) + 7/16

P(1)+P(4)=1/16

If we do the same with P(2∪3∪5), we get:

P(2) + P(3) = 1/16

Now that we have this new knowledge, we can determine P(6):

P(6) = 1 - P(1∪2∪3∪4∪5)

P(6) = 1 - [P(1) + P(2) + P(3) + P(4) + P(5)] -- (There is no chance that two of these will occur simultaneously.)

P(6) = 1 - (1/16 + 1/16 + 7/16)

P(6) = 1 - 9/16

P(6) = 7/16

And with it, we can find P(2∪3∪6):

P(2∪3∪6) = P(2) + P(3) + P(6)

P(2∪3∪6) = 1/16 + 7/16

P(2∪3∪6) = 8/16 = 1/2

B) Keep in mind that the probability you need to know if you wish to roll anything other than a 6 is P(1∪2∪3∪4∪5)" but we found that in part A

P(1∪2∪3∪4∪5) = 9/16

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Answer:

3

Step-by-step explanation:

3=1/3^27

Step-by-step explanation:

3 is the answer , you can do it with a calculator