A stone fell from the top of a cliff into the ocean.
In the air, it had an average speed of 16 m/s. In the water, it had an average speed of 3 m/s before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds.
How long did the stone fall in the air and how long did it fall in the water?

Answer:   Hence the dimension of triangle are 15, 15 and 23.

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram attached.

Suppose two congruent sides of triangle are : x

Suppose the base of the triangle : y

As per question, the base of the triangle is seven less than two times the congruent sides lengths.

So,

[tex]y = 2x-7[/tex]  .......................(1)

Now the perimeter of triangle is given as : 53

It means

[tex]x+x+y=53[/tex]

[tex]2x+y=53[/tex]  .......................(2)

Plugging the value of y from equation (1) in equation (2)

[tex]2x+2x-7=53[/tex]

[tex]4x-7=53[/tex]

[tex]4x=60[/tex]

[tex]x=15[/tex]

Plugging the value of x in equation (1)

[tex]y=2\times (15)-7[/tex]

[tex]y=23[/tex]

Hence the dimension of triangle are 15, 15 and 23.    :   Answer

Hope it will help :)

Answer:

The two numbers are 10 and 7.

Step-by-step explanation:

Given:

The two numbers whose difference is three, when the larger number is decreased by three times the smaller number the result is -11.

Now, find the two numbers.

Let the larger number be [tex]x[/tex].

Let the smaller number be [tex]y[/tex].

As given, the two numbers whose difference is three:

[tex]x-y=3[/tex]

[tex]x=3+y[/tex]

So, the value of [tex]x=3+y[/tex].

According to question:

[tex]x-3y=-11[/tex]

Putting the value of [tex]x[/tex] we get:

[tex]3+y-3y=-11[/tex]

[tex]3-2y=-11[/tex]

Moving variables on one side and the number on the other we get:

[tex]3+11=2y[/tex]

[tex]14=2y[/tex]

Dividing both sides by 2 we get:

[tex]7=y[/tex]

The smaller number = 7.

Now, putting the value of [tex]y[/tex] in the equation [tex]x-y=3[/tex]:

[tex]x-y=3[/tex]

[tex]x-7=3[/tex]

Adding both sides by 7 we get:

[tex]x=10.[/tex]

The larger number = 10.

Therefore, the two numbers are 10 and 7.

Answer:

the answer is c, 5 stages

Answer:

discriminant=D=0

Step-by-step explanation:

given, 9x^2-18x+9=0...............(1)

equ (1) divided by 9

x^2-2x+1=0

discriminant=D=b^2-4ac

where, b=-2, a=1, c=1

D=(-2)^2-[tex]4\times 1\times 1[/tex]

D=4-4=0

D=0

hence discriminant=D=0  answer

Answer:

[tex]\large\boxed{(1+2x^3)^2=4x^6+4x^3+1}[/tex]

Step-by-step explanation:

[tex](1+2x^3)^2\\\\\bold{METHOD\ 1:}\\\\(1+2x^3)^2=(1+2x^3)(1+2x^3)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(1)(1)+(1)(2x^3)+(2x^3)(1)+(2x^3)(2x^3)\\\\=1+2x^3+2x^3+4x^6\qquad\text{combine like terms}\\\\=1+4x^3+4x^6[/tex]

[tex]\bold{METHOD\ 2:}\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(1+2x^3)^2=1^2+2(1)(2x^3)+(2x^3)^2\\\\=1+4x^3+2^2(x^3)^2\\\\=1+4x^3+4x^6[/tex]

Answer:

y = 4/7x + 2 ( slop-intercept form)

Step-by-step explanation:

Answer:

The slope-intercept form of the given equation is,

[tex]y = \frac{4x}{7}-2[/tex]

Step-by-step explanation:

The given equation of the line is,

- 4x + 7y = - 14

Adding '4x' on both sides of the above equation, we get

   - 4x + 7y + 4x = - 14 + 4x

⇒ 7y = 4x - 14

Now, dividing both sides of the above equation by '7', we get

       7y ÷ 7 = (4x - 14) ÷ 7

[tex]\implies y = \frac{4x}{7}-\frac{14}{7}[/tex]

[tex]\implies y = \frac{4x}{7} - 2[/tex]

This is the required equation of the line in slope-intercept form.

There are 6 balloons in small bouquet and 21 balloons in large bouquet.

Step-by-step explanation:

Let,

Number of balloons in small balloon bouquet = x

Number of balloons in large balloon bouquet = y

According to given statement;

2x+3y=75    Eqn 1

2x+y=33      Eqn 2

Subtracting Eqn 2 from Eqn 1

[tex](2x+3y)-(2x+y)=75-33\\2x+3y-2x-y=42\\2y=42[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{42}{2}\\y=21[/tex]

Putting y=21 in Eqn 2

[tex]2x+21=33\\2x=33-21\\2x=12[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{12}{2}\\x=6[/tex]

There are 6 balloons in small bouquet and 21 balloons in large bouquet.

Keywords: linear equation, subtraction

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Final answer:

In solving the system of linear equations, we determined that a small balloon bouquet contains 6 balloons and a large balloon bouquet contains 21 balloons.

Explanation:

Solving a System of Equations

Let's denote the number of balloons in a small bouquet as s and in a large bouquet as l. The given problem provides us with two equations based on the information about the graduation party and Father's Day celebration:

For the graduation party: 2s + 3l = 75

For the Father's Day celebration: 2s + l = 33

Now we solve this system of linear equations to find the values of s and l. Subtracting the second equation from the first gives us:

2s + 3l - (2s + l) = 75 - 33

Which simplifies to:

2l = 42

Dividing by 2 gives us:

l = 21

Now we can plug in the value of l into any of the original equations to find the value of s. Let's use the Father's Day equation:

2s + 21 = 33

Subtracting 21 from both sides gives us:

2s = 12

Finally, dividing by 2 gives us:

s = 6

Therefore, a small balloon bouquet contains 6 balloons and a large balloon bouquet contains 21 balloons.

Answer:

x = 3

Step-by-step explanation:

Since all 3 sides of the triangle are congruent then the triangle is equilateral

The 3 angles are congruent and equal to 60°, thus

25x - 15 = 60 ( add 15 to both sides )

25x = 75 ( divide both sides by 25 )

x = 3

Answer:

-4, -0.5, 1

that's the answer

Answer:-4, -0.5, 1

Step-by-step explanation:

Answer:

Equation: y = 15x.

:)

Answer:

y = 15x

Step-by-step explanation:

The question asked,  what equation shows the line through the data points.  And it stated the equation needed to be in the form y = kx

Where

y represents the vertical axis

x represents the horizontal axis

k = constant

K is the constant interval and can be use to get the next points

y = kx

viewing the most visible points from the graph , let use the point where total saved is 90(y axis) and the time in weeks (x axis) is 6, the constant K can be gotten.

y = 90

x = 6

y = kx

90 = 6k

divide both sides by 6

k = 90/6

k = 15

Therefore,

y = 15x

Answer:

A real number encompasses all numbers, whether it be irrational (irrational numbers go on forever) like pi or the square root of 5, an integer like a negative, a decimal, a fraction, 0, a whole number, a natural number etc.

Step-by-step explanation:

A real number encompasses all numbers, whether it be irrational (irrational numbers go on forever) like pi or the square root of 5, an integer like a negative, a decimal, a fraction, 0, a whole number, a natural number etc. (This doesn't include imaginary numbers however, like the square root of -1.)

Answer:

Step-by-step explanation:

A real number is a number that can be found on a number line. Numbers we use everyday. Real numbers include : natural numbers, whole numbers, integers, fractions, rational numbers, and irrational numbers. They do not include imaginary numbers, numbers that cannot be quantified, such as square root of -1.

The equation in standard form is x + 2y = 8

Solution:

Given that we have to write the given equation in standard form

The equation given is:

[tex]y = \frac{-1}{2}x + 4[/tex]

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers. When we shift the variable terms to the left side of the equation and everything else to the right side, we get the standard form.

[tex]y = \frac{-1}{2}x + 4\\\\y = \frac{-x}{2} + 4\\\\y =\frac{-x + 8}{2}\\\\2y = -x + 8[/tex]

Keep the variables on one side and constant term on other side

x + 2y = 8

Thus the above equation is in standard form of Ax + By = C

Answer:

x+2y=8

Step-by-step explanation:

Answer:

Therefore the equation of the line through ( -7 , 5 ) and ( -5 , 9) is

Linear Relationship i.e [tex]y-5=2(x+7)[/tex]

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( -7, 5 )  

point B( x₂ , y₂) ≡ (-5, 9)  

To Find:

Equation of Line AB =?

Solution:

Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula

[tex](y - y_{1} )=(\frac{y_{2}-y_{1} }{x_{2}-x_{1} })\times(x-x_{1}) \\[/tex]

Substituting the given values in a above equation we get

[tex](y-(5))=(\frac{9-(5)}{-5--7})\times (x--7)\\ \\(y-5)=\frac{4}{2}(x+7)\\\\y-5=2(x+7)...............\textrm{which is the required equation of the line AB}[/tex]

Therefore the equation of the line through ( -7 , 5 ) and ( -5 , 9 ) is

Linear Relationship i.e [tex]y-5=2(x+7)[/tex]

Answer: $4

Step-by-step explanation:

2d + 14 = 22

subtract 14

2d = 8

divide by 2

d = $4

each bag of Doritos costs $4

Elizabeth spent a total of $8 on 2 large bags of Doritos after spending $14 on soda, which means each bag costs $4.

To determine the price of each bag of Doritos, we need to subtract the amount spent on soda from the total amount spent. Elizabeth spent $14 on soda and had a total of $22 in expenses. So, the money spent on Doritos is the difference between the total amount and the soda amount.

Amount spent on Doritos = Total amount - Amount spent on soda

Amount spent on Doritos = $22 - $14

Amount spent on Doritos = $8

Since Elizabeth bought 2 large bags of Doritos, we can find the price per bag by dividing the total amount spent on Doritos by 2.

Price per bag of Doritos = Total spent on Doritos / Number of bags

Price per bag of Doritos = $8 / 2

Price per bag of Doritos = $4 per bag

Therefore, each large bag of Doritos costs $4.

Answer:

x=2 and y = 2

Step-by-step explanation:

Im going to use GeoGebra for graphing the 2 lines. I always find it helpful to move y to side of the equation and the rest of the equation to another side. This is the slope intercept equation by the way. We get our equations as y = -2x+6 and y= 2x-2.

You can find that the common point is (2,2) between the lines.

Answer:

Step-by-step explanation:

2/3 = 8/x+6

2 * ( x+6) = 8 * 3

2x + 2 * 6 = 24

2x + 12 = 24

2x = 24 -12

2x = 12

x = 12/2

x = 6

Answer:

I took the test and its B

Step-by-step explanation:

Also the person above me has got it covered so im gonna avoid confusion and not explain

Answer:

b

Step-by-step explanation:

Answer:

The library is 6 blocks away to the left of Alberto's place

Step-by-step explanation:

There's missing information on this question.

Suppose the point here is to find the distance.

A reflection across the y-axis makes the y-axis as the symmetry axis.

1) Each unit represents one block and they share the same y-coordinate (4).

2) We have to subtract the absolute value of x-coordinate.

So,

[tex]|-3-(3)|=|6|=6[/tex]

The library is 6 blocks away to the left of Alberto's place.

Answer:

12.8

Step-by-step explanation:

Answer:

[tex]x^{6}[/tex] - 8

Step-by-step explanation:

A difference of cubes has the form

a³ - b³

Note that [tex]x^{6}[/tex] is a perfect cube, that is [tex](x^2)^{3}[/tex], but

[tex]x^{8}[/tex] is not

8 is a perfect cube, that is 2³ , but 6 is not

Thus

[tex]x^{6}[/tex] - 8 ← is a difference of cubes

= [tex](x^2)^{3}[/tex] - 2³

The expression which is a difference of cubes is B. x⁶ - 8.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Difference of cubes is termed for those expressions which can be written as the difference of terms which are cubes of some numbers or expressions.

Here,

From, x⁶ - 6, we cannot write 6 as a cube of any number.

So this is not the option.

From x⁶ - 8,

x⁶ can be written as (x²)³ using power of a power rule.

x⁶ - 8 = (x²)³ - (2)³

Hence the expression is x⁶ - 8.

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The equivalent expression to the value 16 is 2 × 8.

The equivalent expression to the value 16 is 2 × 8.

This is because 16 can be written as the product of 2 and 8.

Therefore, the expression 2 × 8 is equivalent to the value 16.

Answer:

Step-by-step explanation:

Answer:

y=5/4x-5

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-(-5)=5/4(x-0)

y+5=5/4(x)

y+5=5/4x

y=5/4x-5

Answer:

The interest rate is 8% simple interest.

Step-by-step explanation:

Let the investment of $555 is getting r% simple interest for 6 years to become the balance of $821.4.

So, from the equation of the simple interest we can write

[tex]821.4 = 555(1 + \frac{6r}{100})[/tex]

⇒ [tex](1 + \frac{6r}{100}) = 1.48[/tex]

⇒ [tex]\frac{6r}{100} = 0.48[/tex]

⇒ r = 8%

Therefore, the interest rate is 8% simple interest. ( Answer )

Answer:D

Step-by-step explanation:

From the inequality, y= -75 or Less, the next whole number less than -75 is -76

Answer:

Y=74

Step-by-step explanation:

Answer: The answer is below with explanations.

Step-by-step explanation:

In the binomial expansion of (x+y)^10, each term is calculated using the binomial coefficient formula. The expansion is [tex]x^10 + 10x^9y + 45x^8y^2 + 120x^7y^3 + 210x^6y^4 + 252x^5y^5 + 210x^4y^6 + 120x^3y^7 + 45x^2y^8 + 10xy^9 + y^10[/tex].

To expand the expression (x+y)^10 using the binomial theorem, we need to find the coefficients of each term. The general formula for the binomial expansion is: [tex](a+b)^n = C(n,0)a^n*b^0 + C(n,1)a^(n-1)*b^1 + ... + C(n,n)a^0*b^n[/tex], where C(n,k) represents the binomial coefficient. In this case, a=x, b=y, and n=10. Using the binomial coefficient formula, we can find the coefficients for each term:

[tex]C(10,0)*x^10*y^0 + C(10,1)*x^9*y^1 + C(10,2)*x^8*y^2 + ... + C(10,10)*x^0*y^10[/tex].

By calculating the binomial coefficients, the binomial expansion of (x+y)^10 is:

[tex]x^10 + 10x^9y + 45x^8y^2 + 120x^7y^3 + 210x^6y^4 + 252x^5y^5 + 210x^4y^6 + 120x^3y^7 + 45x^2y^8 + 10xy^9 + y^10[/tex].

Answer:n=10, 5n=50

Step-by-step explanation:

an=50

n=50/a

n=50/5=10

5n=5×10=50

Answer:

Step-by-step explanation:

an = 50

a +(n-1)d = 50

5 + (n-1)*3 = 50

(n-1)*3 = 50 - 5 = 45

n-1 = 45/3

n-1 = 15

n=15+1 = 16

n = 16

Answer:

9x+5m-3

Step-by-step explanation:

3x-10+5m+6x+7

3x+6x+5m-10+7

9x+5m-3

The value of the solution to the system of equations are, (10, - 20)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

System of equations are,

y = -5x + 30  .. (i)

x = 10

Now, We can find the solution as;

Plug x = 10 in equation (i);

y = - 5x + 30

y = - 5 × 10 + 30

y = - 50 + 30

y = - 20

Thus, The value of the solution to the system of equations are, (10, - 20)

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Answer:

(-4 1/8)

Step-by-step explanation:

-6 1/4 - (-2 1/8)          The subtraction cancels out the subtraction.

-6 1/4 + 2 1/8            

-6 + 2 = -4                 The whole numbers are independent in this case.

1/4 + 1/8                     Find the least common multiple

Multiples:

4| 4_8_12

8| 8_16

8 is the least common multiple

4 goes into 8 twice so multiply the top and bottom by 2

4 * 2 = 8              1 * 2 = 2

-2/8 + 1/8 = -1/8

add that to -4