Write the equation of the line in fully simplified slope-intercept form.

Answer: b = 4f

Step-by-step explanation:

     Since every flashlight needs 4 batteries, every flashlight added (f) will be 4 more batteries needed total (b). With this information in mind, we can write the equation:

             b = 4f

Answer:

b = 4f

Step-by-step explanation:

4 batteries per flashlight

To find the percentage change, we have to divide

Step-by-step explanation:

To find the equivalent ratio for 13/20 in terms of m/n, we can set up the proportion:

13/20 = m/n

To solve for m/n, we can cross-multiply:

13n = 20m

Then, we can divide both sides by 13 to isolate m/n:

m/n = 20/13

So, the equivalent ratio for 13/20 in terms of m/n is 20/13.

Step-by-step explanation:

so, to find the % of successful free throws out of the total number of free throws, we only need to do the division as indicated by the ratio :

13/20 = 0.65

so, 0.65 parts of of the whole 1 were successful.

as % is expressed in parts of 100, we need to multiply this statement by 100 :

65 parts of the whole 100 were successful.

so, 65% were successful.

It mean the measure of the height, the apothem and the base of the triangle are change. It also mean, the circumference and the area of the triangle are change ,but the angle of the triangle did not change from the original triangle.

Dilatation is a process to change the size of the object whether it is to reduce or to enlarge it but did not change it shape. The follow methods use to in dilatation:

Learn more about dilatation here:

https://brainly.com/question/16888151

#SPJ4

Answer:

its b

Step-by-step explanation:

Answer:

The answer would be $67.2.

Step-by-step explanation: The answer would be $67.2. Take 80, divide it by 100 to get 1% of 80, 0.80. Now since you are taking 16% off the original price (100%), you multiply 0.80 (1%) by 84 (for 84% price), to get $67.2. This means, after the markdown, the 80$ item is now $67.2

The solution of given system equation can be calculated by using linear equation of two variable.

The correct option is \((3,\dfrac{1}{2})\).

Given:

The given system equation is,

\(x+2y=4\)

\(2x-2y=5\)

The linear equation of two variables defines as an equation where a, b and r are real numbers where a and b both are not equal to 0.

\(ax+by=r\)

Write the general linear equation of two variables.

\(a_1x+b_1y=r_1\\ a_2x+b_2y=r_2\)

Comparing the above 4 equations.

\(a_1=1, b_1=2, r_1=4\\ a_2=2, b_2=-2,r_2=5\)

Calculate the ratio of \(a_1\) and \(a_2\), \(b_1\) and \(b_2\).

\(\dfrac{a_1}{a_2}=\dfrac{1}{2}\\ \dfrac{b_1}{b_2}=\dfrac{2}{-2}=-1\)

From the above calculation, \(\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}\) the system of the equation has a unique solution.

Now, add the given equation,

\(3x=9\\ x=3\)

Substitute the value of \(x\) in above equation.

\(3+2y=4\\ y=\dfrac{1}{2}\)

Thus, the correct option is \((3,\dfrac{1}{2})\).

Learn more about linear equations here:

https://brainly.com/question/11897796

Answer:

B. (3, 1/2)

This is your answer!!!

Answer:30m²

Step-by-step explanation:

A = bh/2

b=5m

h=12m

A = (5x12)/2

   = 60/2

   = 30m²

The given equation is equivalent to Option D .

The mission option is

A. x+10= x+10

B. x+9 =x² + 20x + 100

C. x² +81 = x² + 100

D. x² + 81 = x² +20x + 100

An equation is a mathematical statement formed when two algebraic expression is equated by an equal sign .

An equation is given in the question

\(\rm \sqrt{x^2 + 81} = x +10\)

\(\rm {x^2 + 9^2} = (x +10)^2\)

\(\rm {x^2 + 81} = x^2 +20x + 100\)

Therefore the given equation is equivalent to Option D .

To know more about Equation

https://brainly.com/question/10413253

#SPJ1

The answer choice that represents a system of linear equations for the data in tables is: H. y = 2x + 1 (Equation 1) and y = 4x - 7 (Equation 2).

In mathematics, an equation is a statement that asserts the equality of two expressions. It typically contains one or more variables, which are placeholders for unknown values, and constants, which are known values. The goal in solving an equation is to find the values of the variables that satisfy the equation, that is, make it true. Equations can be linear or nonlinear, and they may involve one or more variables. Some common types of equations include polynomial equations, trigonometric equations, exponential equations, and logarithmic equations.

Here,

The values in the tables correspond to the points on the graph of the linear functions. By using any two points from each table, we can determine the slope and y-intercept of each function and write an equation in slope-intercept form. Then, we can write a system of linear equations by equating the two functions. The only answer choice that satisfies this is H.

To know more about equation,

https://brainly.com/question/28243079

#SPJ1

Answer:

x = 2.5y

Step-by-step explanation:

If a cow can give 5 gallons of milk after eating 2 pounds of grass.

Let's consider 'x' is the number of pounds of grass it eats and 'y' is the number of gallons of milk the cow gives.

Hence,

5y = 2x

We will simplify it to get what x equal to y by dividing 2 on both side we find,

x = 2.5y

x is equal to 2.5 y

By eating 1 pound of grass cow can give 2.5 gallons of milk.

Answer:

26xy

Step-by-step explanation:

#THANKMELATER

The simplified value is \(\frac{7a^{8}+12 }{21a^{5}}\).

What is a mathematical expression?

A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is \(\frac{a^{3}}{3}+\frac{4}{7a^{5}}\).

This can be simplified by cross-multiplying and adding.

\(\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{5}*a^{3}+4*3}{3*7a^{5}} \\=\frac{7a^{8}+12}{21a^{5}}\).

Therefore the simplified value of the given expression is :

\(\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{8}+12 }{21a^{5}}\)

To learn more about simplifying the expressions, refer to the link below:

https://brainly.com/question/723406

#SPJ1

Answer:

23

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Here you go, has to be 100 characters and did it quick

22 would be displayed by command print(magic(5)).

The statement print(magic(5)) would display the result of the magic function when called with an argument of 5.

The print function is a commonly used function in programming languages that allows you to display output to the console or terminal. It is used to output text, variables, or other data to the standard output device.

Substituting num = 5 into the function definition, we get:

x = num - 3 = 5 - 3 = 2

return x + 2 * 10 = 2 + 20 = 22

Therefore, print(magic(5)) would display 22.

Learn more about print function in code here:

https://brainly.com/question/31735421

#SPJ1

Step-by-step explanation:

To find the points of a parabola given the quadratic equation using substitution, follow these steps:

1. Write the quadratic equation in standard form: y = ax^2 + bx + c

2. Substitute the x-coordinate of the point you want to find into the equation.

3. Solve for the y-coordinate using algebraic operations.

4. Write the point as (x, y).

For example, let's say we have the quadratic equation y = 2x^2 - 4x + 3 and we want to find the point when x = 1.

1. The equation in standard form is y = 2x^2 - 4x + 3

2. We substitute x = 1: y = 2(1)^2 - 4(1) + 3

3. We solve for y: y = 2 - 4 + 3 = 1

4. The point is (1, 1)

Repeat the process for other x-values to find more points on the parabola.

A geometric series is a sequence of numbers formed by multiplying a constant, r (known as the common ratio), by each term of the preceding sequence.

It is as follows: S = a1 / (1 - r), where a1 is the first term and r is the common ratio. In the given series, the first term (a1) is 3, and the common ratio (r) is also 3. Thus: S = 3 / (1 - 3) = 3 / (-2) = -1.5, Since the sum of the series is a finite number (-1.5), we can conclude that the given geometric series is convergent. To determine whether a given geometric series is convergent or divergent, we need to examine its common ratio (r). If the absolute value of r is less than 1, then the series is convergent. If the absolute value of r is greater than or equal to 1, then the series is divergent. In this case, the common ratio is 3, which is greater than 1 in absolute value, so we know that the series is divergent. However, we can also use the formula for the sum of a geometric series to verify this. The formula is:

S = a1 / (1 - r),

where a1 is the first term and r is the common ratio.In this case, the first term (a1) is 3, and the common ratio (r) is also 3. Thus:

S = 3 / (1 - 3) = 3 / (-2) = -1.5

Since the sum of the series is negative and infinite, we can confirm that the given geometric series is divergent. Therefore, we can conclude that the geometric series [infinity]n=13n is divergent. By calculating the sum of the series using the formula for the sum of a geometric series, we determined that the given series is convergent with a sum of -1.5. However, by examining the common ratio and using the criteria for convergence/divergence of geometric series, we can see that the series is actually divergent. Therefore, we conclude that the series [infinity]n=13n is divergent.

To know more about geometric series :

brainly.com/question/13018577

#SPJ11

Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

To learn more about Central tendency, refer:

https://brainly.com/question/1288901

#SPJ4

Answer:

0.9962

Step-by-step explanation:

The z score shows the number of standard deviations by which the raw score is above or below the mean. If the raw score is above the mean then the z score is positive but if the raw score is less than the mean then the raw score is negative. The z score is given by:

\(z=\frac{x-\mu}{\sigma}\\ \\\mu=mean,\sigma=standard\ deviation, x=raw\ score\)

μ = 20.66°C, σ = 2°C

For x < Singapore temperature, i.e. x < 26

\(z=\frac{x-\mu}{\sigma} =\frac{26-20.66}{2}=2.67\)

From the normal distribution table P(x < 26) = P(z < 2.67) = 0.9962

Circuit diagram using only NOR gates: X = NOR = F(X,Y,Z), Y =NOR= F(X,Y,Z), Z = NOR = F(X,Y,Z)

a) To simplify the expression F(X,Y,Z) using Boolean algebra:

F(X,Y,Z) = (X + XY)(X + Y + Z) + (X + Y + XY)(XYZ)

Using the distributive law, we can rewrite the expression:

F(X,Y,Z) = X(X + Y + Z) + XY(X + Y + Z) + XYZ

Applying the absorption law, we have:

F(X,Y,Z) = X + XY + XYZ

The simplified expression is F(X,Y,Z) = X + XY + XYZ.

b) Circuit diagram using only NOR gates:

     _________

-----|         |

   X |    NOR  |-------

-----|___   ___|      |

      |  | |         |

      |  | |   ______|

      |  | |  |       |

      |  | |  |  NOR  |-----

      |  | |  |___   ___|

      |  | |      | |

    Y |__|_|______| |

                     |

                 ___|___

                |       |

              Z |  NOR  |

                |___   _|

                    |

                 F(X,Y,Z)

P4. (15 points)

a) Simplifying the expression F(A,B,C,D) using Boolean algebra:

F(A,B,C,D) = A(A + C)(AB

To learn more about “Circuit diagram” refer to the https://brainly.com/question/27084657

#SPJ11

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete. So, I will solve a general solution, instead.

Let (x,y) be the parent function

First transformation: 4 unit right translation

The rule to this is: \((x,y) \to (x + b,y)\)

Where b is the units of translation

i.e. \(b = 4\)

So, we have;

\((x,y) \to (x + 4,y)\)

Second transformation: Stretch by a factor of 5

The rule to this is: \((x,y) \to (x ,ay)\)

Where a is the units of translation

i.e. \(a = 5\)

So, we have;

\((x + 4,y) \to (x+4,5y)\)

Hence, the transformation from the parent function to the new function is:

\((x + 4,y) \to (x+4,5y)\)

The line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation , Option A is the correct answer.

When a quantity increases and the other quantity also increases , then those two quantities are said to be in direct variation.

It is asked in the question that which option depicts whether On a coordinate plane, a line goes through points (0, 0) and (1, 3) , represents a direct variation

As it is mentioned in the question that the line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation.

To know more about Direct Variation

https://brainly.com/question/14254277

#SPJ1

Answer:

a

Step-by-step explanation:

The solution to the inequality - 5.3 + x > 21 is x > 26.3

In mathematics, inequality refers to a relation which makes a non-equal comparison between two numbers or other mathematical expressions. In other words, it is a relationship between two expressions or values that are not equal to each other. It is used generally used to compare two numbers on the number line by their size.

In order to solve the given inequality - 5.3 + x > 21, add 5.3 both sides.

- 5.3 + x + 5.3 > 21 + 5.3

x > 26.3

The solution means that the value of x is greater than 26.3. The solution is graphed on a number line.

Learn more about Inequality:

https://brainly.com/question/25275758

#SPJ4

Answer:

y = -14x + 61

Step-by-step explanation:

y = mx + b

First, we can find the slope by reading the question and plugging in the slope of -14 into a slope-intercept formula.

y = (-14)x + b

Now, we need to find the "b" value. We can plug anything we want in for x and y here, but we want the equation for the line that passes through the the point (4,5). Plug in 4 into the x value and 5 into the y value, and solve for b.

5 = (-14)(4) + b

(Flip the equation, so we can solve for b.)

b = 5 - (-14) (4)

(Multiply.)

b = 5 - -56

(Substitute the double minus for a plus sign and add.)

b = 5 + 56

b = 61

Now, plug in your "b" value into our original equation.

FINAL ANSWER:

y = -14x + 61

Answer:

-5.4 C

Step-by-step explanation:

H) because if you create a number line, you'll see that -5 is less than -3 and positive 1.

Answer:

Mari used a thermometer to record temperatures of -3.4° Celsius and 1.6° Celsius.

Which temperature in degrees Celsius is less than both of the temperatures Mari recorded?

Step-by-step explanation:

The exterior angle property of a triangle

\( \Large\begin{gathered} {\underline{\boxed{ \rm {\red{y \: + \: 45 \degree \: = \: 100 \degree}}}}}\end{gathered}\)

Now , solving this liner equation

\({{ \large{ \purple{ \rm{{↬}}}}}} \rm \large \: \: \large \rm \: y \: + \: 45 \degree \: = \: 100 \degree\)

\({{ \large{ \purple{ \rm{{↬}}}}}} \rm \large \: \: \large \rm \: y \: = \: 100 \degree \: - \: 45 \degree \:\)

\({{ \large{ \purple{ \rm{{↬}}}}}} \rm \large \: \: \large \rm \: y \: = \: 55 \degree\)

Answer:

Your answer is Y = 55°.

Step-by-step explanation:

x = 180 - 100

x = 80

80+45 = 125

180-125 = 55

Hope this helps!

To complete the square for the equation \(x^2 + 8x + 32 = (x - h)^2 + 16\),

we need to choose h = -2.

To complete the square for the given equation

\(x^2 + 8x + 32 = (x - h)^2 + 16\),

we need to express the left-hand side of the equation in the form

\((x - p)^2 + q\), where p and q are constants.

We can start by expanding the right-hand side of the equation:

\((x - h)^2 + 16 = x^2 - 2hx + h^2 + 16\)

Now we can compare the coefficients of \(x^2\), x, and the constant term on both sides of the equation:

\(x^2 + 8x + 32 = (x - p)^2 + q\)

=> \(p^2 = 0\) (since the coefficient of \(x^2\) is 1 on both sides)

=> -2hp = 8 (since the coefficient of x is 8 on the left-hand side)

=> h = -2 (solving for h)

=> q = \(h^2 + 16\) = 20 (since the constant term on the right-hand side is 16)

For more questions on completing the square

https://brainly.com/question/1596209

#SPJ4

The complete question may be:

What value of h is needed to complete the square for the equation \(x^2+8 x+32=(x-h)^2+16\) ?

Answer:

y=1x-5

Step-by-step explanation:

Answer:

The equation for line one is y = -2x - 5

Answer:

Number of ways we can choose the four students who must ride in the car = 3060 ways

Step-by-step explanation:

This is a combination question.

The number of selections of "r" objects from the given "n" objects is denoted by;

C(n,r), and is given by;

C(n, r) = n!/[r!(n - r)!]

In this question, n = 18 and r = 4

Thus;

C(18, 4) = 18!/[4!(18 - 4)!]

C(18,4) = 3060

Number of ways we can choose the four students who must ride in the car = 3060 ways