write the equation of the line that passes through the point (-4,-2) and is parallel to the line y= 1/4x + 3

Explanation:

In a function, each x-value has one y-value.

___

That is the definition of a relation that is a function.

Final answer:

Each x-value in a function has exactly one corresponding y-value. Functions map elements of the domain to unique elements in the range, which can be represented graphically and must pass the vertical line test. The derivative in calculus, such as dy/dx, reflects the rate of change between these variables.

Explanation:

In a function, each x-value has one corresponding y-value. This is a foundational concept in mathematics that defines a relationship whereby each input (or x-value) in the function produces exactly one output (or y-value). Essentially, a function maps each element of the domain to exactly one element in the range.

An example of a function is y = f(x), which could represent a linear function like y = 3x + 2. In this case, for every x-value, there is a specific y-value determined by the function's formula. So if x were 1, then y = 3(1) + 2 = 5. The graphical representation of a function, such as its curve or line on a coordinate plane, must pass the vertical line test. That means if you draw a vertical line through any point on the graph, it should intersect the graph at no more than one point, confirming that each x-value has only one y-value.

Understanding functions is pivotal in different areas of mathematics, including calculus where the derivative of a function represents the rate of change of the y-value with respect to the x-value. In the case of the linear function y = 6+3x, the derivative dy/dx is constant at 3, implying that for every unit increase in x, y will increase by 3 units.

Answer : The dimensions ​of table runner will be, 20 inch length and 4 inch width.

Step-by-step explanation :

Let the width of table runner be, x

and, the length of table runner will be, 5x

Given:

Area of table runner = [tex]80inch^2[/tex]

As we know that:

Area of rectangle = Length × Width

[tex]80inch^2=(5x)\times (x)[/tex]

[tex]80inch^2=5x^2[/tex]

[tex]x=4inch[/tex]

The width of table runner = x = 4 inch

The length of table runner = 5x = 5(4) inch = 20 inch

Therefore, the dimensions ​of table runner will be, 20 inch length and 4 inch width.

Answer:

The length of the edge of the cube = 4 inches

Step-by-step explanation:

* Lets describe the cube

- It has 6 faces all of them are squares

- It has 8 vertices

- It has 12 equal edges

∵ The volume of any formal solid = area of the base × height

∵ The base of the cube is a square

∴ Area base = L × L = L² ⇒ L is the length of the edge of it

∵ All edges are equal in length

∴ Its height = L

∴ The volume of the cube = L² × L = L³

* Now we have the volume and we want to find the

 length of the edges

∵ Its volume = 64 inches³

∴ 64 = L³

* Take cube root to the both sides

∴ ∛64 = ∛(L³)

∴ L = 4 inches

* The length of the edge of the cube = 4 inches

The length of the edges of the cube is 4 inches.

Given that the volume V  is 64 cubic inches, we can set up the equation:

[tex]\[ a^3 = 64 \][/tex]

To solve for a , we take the cube root of both sides:

[tex]\[ a = \sqrt[3]{64} \][/tex]

The cube root of 64 is 4, since [tex]\( 4^3 = 4 \times 4 \times 4 = 64 \).[/tex]

Therefore, the length of the edges of the cube is 4 inches.

Answer:

  9.4 ft

Step-by-step explanation:

The formula for the circumference of a circle is ...

  C = πd . . . . . where d represents the diameter

Putting your numbers into this equation gives ...

  C = 3.14·(3 ft) = 9.42 ft

Rounding as required gives the length of fence as 9.4 ft.

To find the length of fencing needed for a circular flower bed, use the formula C = π * d, where C is the circumference and d is the diameter of the circle.

To find the length of fencing needed to go around a circular flower bed, we need to calculate the circumference of the circle. The circumference can be found using the formula C = π * d, where π is approximately 3.14 and d is the diameter of the circle. In this case, the diameter of the flower bed is 3 feet, so the circumference is 3.14 * 3 = 9.42 feet.

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Answer:

Your answer is

x = -4, 6 or (b)

Have a nice day and please mark me as brainliest!! (:|

~abelxoconda

The solution of the equation for the value of x will be (-4,6).

The polynomial equation with the degree of two will be termed as the quadratic equation or the highest power of the variable is 2 in the quadratic equation.

The given equation is:-

=x²-2x-24

Now we will split the equation

=x²-6x+4x-24

=x(x-6)+4(x-6)

=(x-6)(x-4)

Hence the value of x will be -4 and 6.

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Answer:

Robert is 7 years old and Maria is 14 years old.

Step-by-step explanation:

You can use 2 variables: m and r and write 2 equations:

m = r +7

m + 2 = 4( r -3)

So 3 * r = 21 or r= 7

Maria and Robert are currently with present ages as 14 and 7 years old, respectively.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It demonstrates that the expressions on the left and right sides are connected in the same way.

An equation has components like as coefficients, variables, operators, constants, terms, expressions, and the equal to sign. The "=" sign and terms on both sides are required when generating an equation.

The information is ,

Let's say the equation looks like this: A

Right now, A is valued at

Let Maria's age be x.

Let Robert's age be y.

Maria now has a 7-year age gap with Robert.

Hence, the equation x = 7 plus y (1)

Also, in two years she will be four times Robert's age from the previous three years.

The equation is (x + 2) = 4 (y - 3). (2)

We obtain (7 + y + 2) = 4y - 12 y + 9 = 4y - 12 after simplifying.

We obtain 3y = 21 by subtracting y and adding 12 on both sides.

We obtain y = 7 years old by dividing both sides by 3.

Robert is therefore 7 years old.

And , x = 14 years old

And , the age of Maria is 14 years old

As a result, Maria and Robert are currently 14 and 7 years old, respectively.

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Answer:

The correct answer is 2 23/63

Step-by-step explanation:

To determine how much the plant grew, start by subtracting the starting whole number value from the ending whole number value.

4 - 1 = 3

Now do the same with the fractions. Use common denominators.

2/9 - 6/7

14/63 - 54/63

-40/63

Now add the two numbers together.

3 - 40/63 = 2 23/63

Answer:

(2, 5)

Step-by-step explanation:

Dilating 3, means that the values were multiplied by 3.  To find their original location, divide the x and y values of the new point by 3...

(6/3, 15/3) = (2, 5)

In a dilation with a factor of 3, to find the original coordinates from the dilated point (6,15), we divide each coordinate by the dilation factor. The original point A was at (2,5).

In mathematics, dilation is a geometric transformation that resizes a figure, maintaining its shape but changing its size. It involves multiplying the coordinates of each point in the figure by a constant scale factor. If the scale factor is greater than 1, the figure expands, while a scale factor between 0 and 1 results in a reduction. Dilation is commonly used in geometry to study similarity between shapes, where corresponding angles remain equal, and corresponding sides are proportional. It plays a crucial role in various mathematical concepts and applications, such as transformations, similarity, and geometric modeling.

In a dilation, the points move closer or farther away from a certain point, called the center of dilation, by a certain factor. In this case, the dilation factor is given as 3, so the original point is gained by dividing the coordinates of the image by the dilation factor. The image of point A is given as (6,15). To find the original point A, we divide both coordinates by the dilation factor.

So, the original location of point A is (2,5).

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Answer:

The two consecutive positive integers are 7 and 8

Step-by-step explanation:

Let

x ----> the first positive integer

x+1 ----> the second consecutive positive integer

we know that

[tex]x^{2} -17=4(x+1)[/tex]

Solve for x

[tex]x^{2} -17=4x+4\\ \\x^{2}-4x-21=0[/tex]

Solve the quadratic equation by graphing

The solution is x=7

see the attached figure

Find the value of x+1

x+1=7+1=8

therefore

The two consecutive positive integers are 7 and 8

To find two consecutive positive integers, we can set up an equation and solve for the values of x and x + 1.

Let's assume the first positive integer is x. Since we need to find two consecutive positive integers, the second positive integer would be x + 1. According to the given condition, the square of the first decreased by 17 should be equal to 4 times the second. This can be written as:

x^2 - 17 = 4(x + 1)

Now, we can solve this equation to find the values of x and x + 1.

x^2 - 17 = 4x + 4

x^2 - 4x - 21 = 0

By factoring or using the quadratic formula, we can find the solutions for x. Once we have the values of x, we can calculate x + 1 to find the two consecutive positive integers.

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Answer:

the answer is C.Peter walks at a rate of 13/4 miles per hour.  hope this was helpful

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Final answer:

To find the exponential function that passes through (-3, 80) and (-1, 20), we use the general form y = abˣ. By solving a system of equations using these points, we find that the exponential function is y = 40*2ˣ.

Explanation:

To write an exponential function that passes through the points (-3, 80) and (-1, 20), we can use the general form of an exponential function, which is y = abˣ. Here, a and b are constants we need to find. Given two points, we can set up a system of equations to solve for a and b.

Using the first point (-3, 80):
80 = a*b⁻³

Using the second point (-1, 20):
20 = a*b⁻¹

Dividing the second equation by the first gives us:
b2 = 4 which simplifies to b = 2 or b = -2. However, in exponential functions, b is positive, so we choose b = 2.
Substituting b = 2 into the second equation gives a = 40. Thus, the exponential function is y = 40*2ˣ.

Answer:

Step-by-step explanation:

The range is the difference between the highest and the lowest values in a set of data.  The interquartile range, the IQR, is what's "inside" the box in a box plot, which consists of the difference between the central measures, which are the first and the third quartiles.

Range is the difference between the maximum and minimum values in a dataset, while the Interquartile Range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3), representing the spread of the middle 50% of the data.

It is calculated by subtracting the minimum value from the maximum value.

For example, if the highest score in a test is 95 and the lowest score is 55,

the range is 95 - 55 = 40.

To find the IQR, we first need to determine the first quartile (Q1) and the third quartile (Q3).

Q1 is the median of the lower half of the data, while Q3 is the median of the upper half.

The IQR is then calculated by subtracting Q1 from Q3.

For example, in a dataset:

If Q1 = 70 and Q3 = 90, then

IQR = 90 - 70 = 20.

The IQR is useful in identifying potential outliers and understanding the spread of the central data.

Answer:

y = 2/3 x -2

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

We need to solve for y

2x-3y = 6

Subtract 2x from each side

2x-2x-3y=-2x+6

-3y = -2x+6

Divide  by -3

-3y/-3 = -2/-3x+6 /-3

y = 2/3 x -2

The slope is 2/3 and the y intercept is -2

Answer:

5/18

Step-by-step explanation:

The desired fraction can be found by dividing the fraction of distance by the fraction of hours:

(1/6 distance)/(3/5 hour) = (1/6·5/3) distance/hour = 5/18 distance/hour

Then 5/18 of the distance can be covered in one hour.

Answer:

5/18

Step-by-step explanation:

Answer: 14 gallons

Step-by-step explanation:

Let's call the total gallons of gas Abdul's tank can hold x.

Then, based on the information given in the problem, you can write the following expression:

[tex]\frac{1}{5}x+7=\frac{7}{10}x[/tex]

Therefore, when you solve for x, you obtain the following result:

[tex]\frac{1}{5}x+7=\frac{7}{10}x\\\\\frac{1}{5}x-\frac{7}{10}x=-7\\\\-\frac{1}{2}x=-7\\\\-x=(-7)(2)\\x=14[/tex]

Answer:

  15.7 cm

Step-by-step explanation:

The length (s) of an arc of a circle of radius r with a central angle of θ radians is ...

  s = rθ

Here, the radius is given as 7.9 cm, and the arc of interest is the supplement of 66.4°, so is ...

  θ = π·(1 - 66.4/180) ≈ 1.9827 . . . . radians

Then the arc length is ...

  s = (7.9 cm)·(1.9827) ≈ 15.7 cm

Answer:

  1/96

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

Then ...

[tex]6^{-1}\cdot 4^{-2}=\dfrac{1}{6}\cdot\dfrac{1}{4^{2}}=\dfrac{1}{6\cdot 16}=\dfrac{1}{96}[/tex]

A sample must be a group of people who are the target of the survey question

Answer:

The correct option is 1.

Step-by-step explanation:

The set of all observations is known as populate set.

A sample is a small subset of population set that is the representative of the entire population. The sample must have sufficient size and it should include all population.

A sample must be a group of people who are the target of the survey question. This statement is true.

Therefore the correct option is 1.

A sample should have different characteristics than the population. This statement is false.

A sample must be very small. This statement is false.

A sample should include only boys or only girls.  This statement is false.

Therefore options 2, 3 and 4 are incorrect.

Answer:

  $491.37

Step-by-step explanation:

The appropriate formula for the future value of a single investment is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested (389), r is the annual rate (0.039), n is the number of compoundings per year (12), and t is the number of years (6).

Putting the given numbers into the formula, you get ...

  A = 389·(1 +.039/12)^(12·6) = 389·1.00325^72 ≈ 491.37

The total in the account after 6 years will be $491.37.

Answer:

The acute angles of the rhombus are 80°; the obtuse angles are 100°.

Step-by-step explanation:

Since each diagonal bisects the angle of the rhombus, the given conditions are the same as saying the angles of the rhombus are in the ratio 4:5. Adjacent angles add to 180°, and the sum of the ratio units is 4+5=9. So each ratio unit stands for 180°/9=20° of angle, and the angles are ...

80° : 100°

The angles of the rhombus are 80° and 100°.

Answer:

a) The other root is -2

   The coefficient c = -106

b) q = 35

c) c = -8.75

Step-by-step explanation:

* Lets study the general form of the quadratic equation

* ax² + bx + c = 0

- Their roots are x1 and and x2

- The sum of them = -b/a ⇒ x1 + x2 = -b/a

- The product of them = c/a ⇒ (x1)(x2) = c/a

a) * Assume that the roots of the equation 10x² - 33x + c = 0

     are m and n

∵ m + n = -b/a

∵ a = 10 and b = -33

∴ m + n = -(-33)/10 = 3.3

∵ m = 5.3

∴ 5.3 + n = 3.3 ⇒ n = 3.3 - 5.5 = -2

∴ n = -2

* The other root is -2

∵ m × n = c/a

∵ m = 5.3 , n = -2 , a = 10

∴ (5.3)(-2) = c/10

∴ -10.6 = c/10 ⇒ Multiply both sides by 10

∴ c = -106

* The coefficient c = -106

b) * Assume that the roots of the equation x² - 12x + q = 0

     are m and n

∵ The difference between the roots is 2

∴ m - n = 2 ⇒ (1)

∵ From the equation m + n = -b/a

∵ a = 1 , b = -12

∴ m + n = -(-12)/1 = 12

∴ m + n = 12 ⇒ (2)

* Lets solve the two equation

- Add the two equation to eliminate n

∴ 2m = 14 ⇒ divide both sides by 2

∴ m = 7

* Substitute the value of m in (1) or (2)

∴ 7 - n = 2 ⇒ 7 - 2 = n ⇒ 5 = n

∴ n = 5

∵ mn = c/a

∵ c = q , a = 1

∴ mn = q/1 = q

∴ q = 7 × 5 = 35

* q = 35

c) * Assume that the roots of the equation x² + x + c = 0

     are m and n

∵ The difference between the roots is 6

∴ m - n = 6 ⇒ (1)

∵ From the equation m + n = -b/a

∵ a = 1 , b = 1

∴ m + n = -(1)/1 = -1

∴ m + n = -1 ⇒ (2)

* Lets solve the two equation

- Add the two equation to eliminate n

∴ 2m = 5 ⇒ divide both sides by 2

∴ m = 2.5

* Substitute the value of m in (1) or (2)

∴ 2.5 + n = -1 ⇒ n = -1 - 2.5 = -3.5

∴ n = -3.5

∵ mn = c/a

∵ c = c , a = 1

∴ mn = c/1 = c

∴ c = 2.5 × (-3.5) = -8.75

* c = -8.75

➷ Find the total data in the first row:

90 + 30 = 120

Now divide each of these values by the total:

(30/120) = 0.25

(90/120) = 0.75

It would be 0.25 in the first box and 0.75 in the second.

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Answer:

Group1 .18

Group2 = .54

Step-by-step explanation:

To find the relative frequency, you divide the number by the total number

The total number is 30+90+14+32 = 166

Category 1 Group 1 has 30 in it

The relative frequency is 30/166 = .180722892 = .18

Category 1 Group 2 has 90 in it

The relative frequency is 90/166 =.542168675=.54

Vertex is at (-1,-7), because the |x+1| moves the graph left 1 and -7 moves the graph down 7.

Answer:

the second answer is a

Step-by-step explanation:

edge 2020

Answer:

[tex]a^{2b}=x^{2}[/tex]

Step-by-step explanation:

we know that

[tex]a^{b}=x[/tex] ----> equation A

Find the value of [tex]a^{2b}[/tex]

Remember that

[tex]a^{2b}=(a^{b})^{2}[/tex]

[tex](a^{b})^{2}[/tex] ----> equation B

substitute equation A in the equation B

[tex](a^{b})^{2}=x^{2}[/tex]

therefore

[tex]a^{2b}=x^{2}[/tex]

Answer:

  $111

Step-by-step explanation:

The bank balance is ...

  $700 × (1 + 0.05) = $735

The cost of the computer is ...

  $750 × (1 -0.20) × (1 +0.04) = $624

The remaining bank balance after paying for the computer is ...

  $735 -624 = $111

_____

When you add a percentage, you effectively multiply by the sum of 1 and that percentage. The same is true if the amount "added" is negative (as for a discounted price).

  (original amount) + (percentage)×(original amount)

Use the distributive property to factor out the original amount:

 = (original amount)×(1 + percentage)

Answer:

A ) subtract the second equation from the first equation

Step-by-step explanation:

2x + 3y = 7

2x - 4y = -5

subtracting the second equation from the first equation we get,

7y = 12

y=12/7

This is the correct option

Answer:

A ) subtract the second equation from the first equation

Step-by-step explanation:

Let's consider the following system of equations.

2x + 3y = 7

2x = 4y - 5

If we subtract the second equation from the first equation, we get:

2x + 3y - 2x = 7 - (4y - 5)

3y = 7 - 4y + 5

7y = 12

y = 12/7

Then, we can use any of the original equations and solve for x.

2x = 4y - 5

2x = 4(12/7) - 5

x = 13/14

The equations for the two machines are y = 5x and y = 8x, which represent their respective production rates. Over an 8 hour period, the first machine produces 40 miles of ribbon and the second produces 64 miles, resulting in a difference of 24 miles.

The two machines described in the question produce ribbon at different rates, which can be represented with two linear equations in slope-intercept form (y = mx + b) where m is the rate of production (slope) and b is the initial amount of ribbon (y-intercept, in this case 0 as the machine starts with no ribbon).

The first machine can produce 5 miles of ribbon in an hour, so its rate is 5 miles/hour. This gives the equation y = 5x.

The second machine can produce 8 miles of ribbon in an hour, leading to the equation y = 8x.

In an 8 hour period, the first machine will produce y = 5*8 = 40 miles of ribbon, while the second machine will produce y = 8*8 = 64 miles of ribbon. The difference is 64 - 40 = 24 miles.

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The first machine will make 40 miles of ribbon in 8 hours, and the second machine will make 64 miles of ribbon. The difference in length for an 8-hour period between the two machines is 24 miles.

To graph the length of ribbon each machine will make in 8 hours, we can start by determining the length each machine can make in one hour.

The first machine can make 5 miles of ribbon in an hour, so in 8 hours, it will make 8 times 5 = 40 miles of ribbon.

The second machine can make 8 miles of ribbon in an hour, so in 8 hours, it will make 8 times 8 = 64 miles of ribbon.

The slope-intercept form of an equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept. For the first machine, the equation would be y = 5x + 0, and for the second machine, the equation would be y = 8x + 0.

The difference in length between the two machines for an 8-hour period is 64 - 40 = 24 miles.

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so calculate the Volume of the water that is already in the tank

so l x w x h

4 x 18 x 12

=864cm^3 is in the tank

find the total volume of the tank:

6 x 18 x 12

=1296cm^3

and subtract the current from the total to find what you need:

1296cm^3 - 864cm^3

= 432 cm^3

you can also find how much you need by using the remaining 2cm from the height (6-4=2) and use the volume formula with 2 substituted as the height and you’ll get the same answer

The amount of water needed to fill the tank is 432 cm³.

Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.

Volume of cuboid = lwh

The tank is filled with water to a height of 4 centimeters.

The dimension of the tank is width is 18 cm, length is 12 cm, and height 6 cm.

So, the Volume of water present in the tank

= l x w x h

= 4 x 18 x 12

= 864 cm³

Now, the total Volume of tank

= 6 x 18 x 12

= 1296 cm³

So, the amount of water needed to fill the tank

= 1296 - 864

= 432 cm³

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Answer:

The altitude of the plane is 8 miles

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

tan(72°)=h/x

h=xtan(72°) -----> equation A

In the right triangle ABD

tan(55°)=h/(x+3)

h=(x+3)tan(55°) -----> equation B

equate equation A and equation B and solve for x

xtan(72°)=(x+3)tan(55°)

xtan(72°)-xtan(55°)=3tan(55°)

x[tan(72°)-tan(55°)]=3tan(55°)

x=3tan(55°)/[tan(72°)-tan(55°)]

Find the value of h

h=xtan(72°)

h=[3tan(55°)*tan(72°)]/[tan(72°)-tan(55°)]

h=8 miles

Answer:

8.0 is the right answer

Step-by-step explanation:

ur welcommmme ;)

He should have 27.5 left I'm 100% sure