The expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped. What is the distance the object falls during each time?
10 seconds

Answer:

x = -14

Step-by-step explanation:

Solve:

7x - 28 = 2(4x - 7)

7x - 28 = 8x - 14

Substrate 8x from both sides.

7x - 28 - 8x = 8x - 14 - 8x

-x - 28 = -14

Add 28 to both sides.

-x - 28 + 28 = -14 + 28

-x = 14

Divide both sides by -1.

-x/-1 = 14/-1

x = -14

Therefore x = -14

Answer: not possible

Step-by-step explanation:

I think you're doing quadratics and if that's the case probably go and rework the problem because that doesn't work.

I believe it's 3ײ - 6x - 7.56

Sorry if this isn't helpful!

The other option would be -6x + 3ײ-7.56 (but this is the problem in a simplified form and not when it is evaluated).

The population of Somerville is approximately 35047 after a depreciation of of 3% every year .

Depreciation is economics refers to two different aspects of the same idea: first, the actual decline in an asset's fair value as it is used and worn, such as the annual decline in value of factory equipment; and second, the allocation in accounting statements of the asset's original cost to the periods during which it is used.

Here depreciation is the gradual decline in population each year in the town.

The rate of depreciation or decline is the percentage amount of population that decreases every year.

The formula used to calculate depreciation is given by:

[tex]A=P(1-r)^t[/tex]

Given the rate of depreciation as 3%.

Population at present = 38400

Population after 3 years:

= 38400 (1 - 0.03 )³

= 38400 ( 0.97 )³

= 35046.6432

≈ 35047

Hence the population after 3 years will be approximately 35047.

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Answer: =35047

Step-by-step explanation:

The measures of the indicated angles are

m ∠EFH = 59.5°

m ∠GFH = 59.5°

From the question, we are to determine measures of the indicated angles

The angles are ∠EFH and ∠GFH

From the given information,

FH bisects ∠EFG

Since FH bisects ∠EFG,

Then,

m ∠EFH  = m ∠GFH

and

m ∠EFH  + m ∠GFH = m ∠EFG

Then,

We can write that

m ∠EFH  + m ∠EFH = m ∠EFG

2 × m ∠EFH = m ∠EFG

2 × m ∠EFH = 119°

m ∠EFH = 119°/2

m ∠EFH = 59.5°

Thus,

m ∠GFH = 59.5°

Hence, the measures of the indicated angles are

m ∠EFH = 59.5°

m ∠GFH = 59.5°

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Answer:

lol

Step-by-step explanation:

L O LDJDDHDHDHDHFFHFVDVDVDBSSBDBDBDBD

The triangle is an isosceles triangle with sides XY and XZ equal to [tex]\sqrt{29}[/tex] units and side YZ as 4 units.

Given that:-

Coordinates of X = (7,6)

Coordinates of Y = (5,1)

Coordinates of Z = (9,1)

We have to find the measures of the sides of ΔXYZ and classify the triangle by its sides.

Using distance formula, we can find the measure of the sides of the triangle.

Distance formula for the line segment with points (a,b) and (c,d):-

[tex]\sqrt{(d-b)^2+(c-a)^2}[/tex]

Hence,

XY = [tex]\sqrt{(1-6)^2+(5-7)^2} =\sqrt{25+4} =\sqrt{29}[/tex] units.

YZ = [tex]\sqrt{(1-1)^2+(9-5)^2} =\sqrt{0+16} =\sqrt{16}[/tex] = 4 units.

XZ = [tex]\sqrt{(1-6)^2+(9-7)^2} =\sqrt{25+4} =\sqrt{29}[/tex] units.

Here,

XY = XZ, hence it is an isosceles triangle.

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Answer: The answer is x = 6.5

The point of intersection for the function is  (2, 2)

Considering to the line passing through the points (0,6) and (3,0)  to be f(x).Therefore the slope intercept of the function is

m = 0-6/3-0 = -2

So, the functions F(x) in the slope-intercept form f(x)= -2x+6  ......1

interchanging the variable x to y and y to  x

=> x =-2y + 6

=> 2y = -x + 6

=> y= -0.5x + 3

let  f⁻¹(x)= y

f⁻¹(x) =-0.5x+3   ......2

Solving the equation  1 and 2, we get

=> -0.5x + 3 = -2x + 6

=> 2x - 0.5x = 6 - 3

=> 1.5x = 3

=> x = 2

Substituting the values of x in the function  we get,

f( x) = -2(2) + 6 = 2

Thus, the outcome is (2,2)

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The total number of matches played will be 46. matches.

From the information, there are 24 baseball teams in a league each team plays two matches against each of the other teams.

The total number of matches that will be played will be:

= (24 - 1) × 2

= 23 × 2

= 46 matches.

Therefore, the total number of matches played will be 46. matches.

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  For numbers 5 and 45 the value of the geometric mean of these numbers is

Gm (5, 45) = 15

   The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:

Gm (a,b) = √ab

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

Gm (5, 45) = √5×45

Gm (5, 45) = √225  ;    In this case the square root is direct-

Gm (5, 45) = 15

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The result of the expression [tex]y^{2}+3[/tex]  for the variable y= [tex]\sqrt{7}[/tex] is 10

Given,

The algebraic expression = [tex]y^{2}+3[/tex]

The value of y = [tex]\sqrt{7}[/tex]

Substitute the values in the expression

[tex]y^{2}+3=(\sqrt{7} )^{2}+3[/tex]

=7+3

=10

Hence, the  result of the expression [tex]y^{2}+3[/tex]  for the variable y= [tex]\sqrt{7}[/tex] is 10

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Answer:

11/11 is an improper fraction.

Step-by-step explanation:

In order for a fraction to be considered "Proper" a < b, when a/b. Meaning that the numetator must be less than the denominator.

In the case for 11/11, it does not follow these qualifications.

Hope this helps!

Answer:

they would need a 98 on the next math test.

Answer:

decimal is the number system of 10base .

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

Work Shown:

[tex]SA = 2\pi r^2 + 2\pi r h\\\\SA \approx 2*3.14*15^2 + 2*3.14*15*40\\\\SA \approx 5181\\\\[/tex]

The cylinder has a surface area of about 5181 square feet.

Side notes:

Answer:

Step-by-step explanation:

3768 feet. Is this right?

Answer:

Step-by-step explanation: First row, first column 500 * 7 = 3500

1st row , second column 7 * 60 = 420

1st row, third column 7 * 3 = 21

Do similary for the others

2nd row, 40,000                  4800                  240

3rd row , 100000                  12000                6000

Answer:

[tex]\large\text{ \quad \quad \quad \quad 500 \quad \quad\;\;\;60 \quad \quad \;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{3500} &\boxed{420} & \boxed{21}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{40000} & \boxed{4800} & \boxed{240}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{100000} & \boxed{12000} & \boxed{600}\\\cline{2-4} \end{array}[/tex]

Step-by-step explanation:

For each box, multiply the number of the row by the number of the column:

[tex]\large\text{ \quad \quad \quad \quad \quad 500 \quad \quad \quad\;\;60 \quad \quad \quad \;\;\;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{7 \times 500} &\boxed{7 \times 60} & \boxed{ 7 \times 3}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{80 \times 500} & \boxed{80 \times 60} & \boxed{80 \times 3}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{200 \times 500} & \boxed{200 \times 60} & \boxed{200 \times 3}\\\cline{2-4} \end{array}[/tex]

When multiplying numbers ending in zeros (multiples of 10, 100, etc.), first multiply the numbers as if they didn't have zeros, then add all the zeros to the final answer.

For example:

200 × 500 has a total of 4 zeros.

Multiply 2 × 5 = 10

Then add 4 zeros: 10 0000

Therefore, 200 × 500 = 100000

Final Solution

[tex]\large\text{ \quad \quad \quad \quad 500 \quad \quad\;\;\;60 \quad \quad \;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{3500} &\boxed{420} & \boxed{21}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{40000} & \boxed{4800} & \boxed{240}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{100000} & \boxed{12000} & \boxed{600}\\\cline{2-4} \end{array}[/tex]

The explicit formula for give sequence an = n² + 1:

An arithmetic sequence has the explicit formula a = a + (n - 1)d, and each term of the series may be calculated without knowing the values of the previous terms. The nth term in an arithmetic, geometric, or harmonic series is usually the explicit formula.

a1 = (1) + 1 = 2

a2 = 2.2 + 1 = 5

a3 = 3.3 + 1 = 10

a4 = 4.4 + 1 = 17

a5 = 5.5 + 1 = 26

and so on.

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Answer:

12 oranges

Step-by-step explanation:

The ratio is K/L where K = Kudi's oranges and L = Ludi's oranges

K/L = 2/3

To find the number of oranges that Kudi has, divide the numerator by the sum of numerator and denominator.Then multiply by total number of oranges

For Ladi, divide the denominator by the sum of numerator and denominator. Then multiply by total number of oranges

[tex]K = 20\cdot \dfrac{2}{2+3} = 20 \cdot \dfrac{2}{5} = 8 \; \mathrm {oranges}\\\\L = 20\cdot \dfrac{3}{2+3} = 20 \cdot \dfrac{3}{5} = 12 \; \mathrm {oranges}[/tex]

So answer is Ladi has 12 oranges

The relationship between the ∠4 and ∠5 is that both are consecutive interior angles

Given,

The angles =∠4 and ∠5

Here, ∠4 and ∠5 are interior angles.

Both are lies on the opposite sides of the transversal.

So, ∠4 and ∠5 are consecutive interior angles

Hence, The relationship between the ∠4 and ∠5 is that both are consecutive interior angles

The complete question is :

Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠4 and ∠5

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The explicit formula of arthmetic sequence is [tex]a_{n}[/tex] = a + (n-1)d

Here is an explicit formula of the sequences 62, 59, 56, and 53...

  [tex]a_{n}[/tex] = 62 + (n-1)(-3)

In the formula, n is any term number and [tex]a_{n}[/tex] is the nth term.

This formula allows us to simply plug on the number of the term we are interested in, and we will get the value of that term.

In order to find the fifth term, for example, we need to plug n = 6

     [tex]a_{6}[/tex] = 62 + (6-1)(-3) = 62 + 5× -3

      = 62- 15

      = 47

In this way, we can find any term by using the explicit formula of an arithmetic sequence.

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After solving each system, -6 = 3x - 6y, 4x = 4 + 5y, the values of x and y are calculated to be 6 and 4 respectively.

The two equations,  -6 = 3x - 6y, and 4x = 4 + 5y can be considered as linear equations as the highest power of the variables in these equations is one.

By rearranging the first equation, the value of x can be found to be,

-6 = 3x - 6y

3x = 6y - 6

x = 6y - 6 / 3

Putting the calculated value of x in the second equation,

4x = 4 + 5y

4(6y - 6 / 3) = 4 + 5y

24y - 24 / 3 = 4 + 5y

24y - 24 = 3 ( 4 + 5y)

24y - 24 = 12 + 15y

Rearranging,

24y - 15y = 12 + 24

9y = 36

y = 36 / 9

y = 4

To solve for x, put y = 4 in the first equation as follows,

-6 = 3x - 6y

-6 = 3x - 6(4)

-6 = 3x - 24

Rearranging,

24 - 6 = 3x

18 = 3x

x = 18/3

x = 6

Thus the value of x and y in these systems are calculated to be 6 and 4 respectively.

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Answer:

y = 1

if you need answer of x

x = 2

Step-by-step explanation:

Let's solve your system by substitution.

4x+2y=10;3x+5y=11

Step: Solve4x+2y=10for x:

4x+2y=10

4x+2y+−2y=10+−2y(Add -2y to both sides)

4x=−2y+10

4x/4 = −2y+10/4

(Divide both sides by 4)

x= −1/2y+5/2

Step: Substitute −1/2y+5\2 for x in3x+5y=11:

3x+5y=11

3(−1/2y+5/2)+5y=11

7/2y+15/2=11(Simplify both sides of the equation)

7/2y+15/2+−15/2=11+/−152

(Add (-15)/2 to both sides)

7/2y=7/2

7/2y/7/2 = 7/2/7/2

(Divide both sides by 7/2)

y=1

Step: Substitute1for y in x= −1/2y+5/2:

x=−1/2y+5/2

x=−1/2(1)+5/2

x=2(Simplify both sides of the equation)

According to the given statement

The area of Colorado is 67.43 times greater than the area of Rhode Island

Area is typically thought of as a specific instance of volume for two-dimensional regions. By applying axioms, one can define area as the relationship between a set of real numbers and a collection of particular plane figures.

Area is a mathematical concept that describes the size of a region on a planar or curved surface. The area of an open surface or the border of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

According to the given values;

The area of Rhode Island = 43.07 billion square feet.

The area of Colorado = 2.9045 trillion square feet.

43.07 billion =43,070,000,000

2.945 trillion =2,9045,000,000,00

Now we have to find how many times as great is the area of Colorado than the area of Rhode Island.

For this ,we divide area of Colorado by area of Rhode Island.

=2,9045,000,000,00/43,070,000,000

=67.43

So, the area of Colorado is 67.43 times greater than the area of Rhode Island.

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The equation of the circle with radius 6 and center at (0 , 0) is x^2 + y^2 = 36.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = 6

(x - 0)^2 + (y - 0)^2 = 6^2

x^2 + y^2 = 36

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The value of the function at an input of 50 will be 36.95.

Since the pressure at the surface is 14.7 psi, a function to represent water pressure will be:

= 14.7 + (0.445 × p)

where p is the increase in pressure for each foot

= 14.7 + 0.445p

Therefore when the input is 50, the amount will be:

= 14.7 + 0.445p

= 14.7 + 0.445(50)

= 14.7 + 22.25

= 36.95

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The operator *= is called  multiple assignment operator.

The operator is given as

*=

Take for instance, we have the following statement in Python

a *= b

The meaning of the above statement is

a = a * b

Assume the following values for the variables

a = 6 and b = 3

The value of the operation a *= b would be

a *= b --- given expression

a = a * b --- expanded expression

a = 6 * 3 ---- when the values are substituted

a = 18 --- the result

This implies that the operator represents an assignment and a multiply operator

Hence, the operator *= is called  multiple assignment operator.

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