Examine the following table of points, which are all on a certain line.


x y

−2 4

0 2

1 1

3 −1



What is the slope of this line? Enter your answer as a number, like this: 42, or, if the slope is undefined, enter the lowercase letter "u".

Answer:

Let's solve for x.

4x−2y=20

Step 1: Add 2y to both sides.

4x−2y+2y=20+2y

4x=2y+20

Step 2: Divide both sides by 4.

4x/4

=  2y+20/4

x=  1/2y+5

Answer: x=  1/2y+5

Answer:

[tex]\large\boxed{y=-(x+5)^2+4}[/tex]

Step-by-step explanation:

[tex]\text{The vertex form of an quadratic equation}\\\\f(x)=ax^2+bx+c=a(x-h)^2+k\\\\h=\dfrac{-b}{2a}\\\\k=f(k)=\dfrac{-(b^2-4ac)}{4a}\\=================================[/tex]

[tex]\text{We have:}\\\\y=-x^2-10x-21\\\\a=-1,\ b=-10,\ c=-21\\\\h=\dfrac{-(-10)}{2(-1)}=\dfrac{10}{-2}=-5\\\\k=f(-5)=-(-5)^2-10(-5)-21=-25+50-21=4\\\\y=-(x-(-5))^2+4=-(x+5)^2+4[/tex]

Final answer:

The vertex form of the quadratic equation  [tex]y = -x^2 - 10x - 21[/tex]is  [tex]y = -(x + 5)^2 + 4[/tex], with the vertex being (-5, 4).

Explanation:

To find the vertex form of the quadratic equation  [tex]y = -x^2 - 10x - 21[/tex], we need to complete the square. Here's a step-by-step guide:

Start with the given quadratic equation:  [tex]y = -x^2 - 10x - 21.[/tex]

Factor out the coefficient of the  [tex]x^2[/tex]term from the first two terms:  [tex]y = -(x^2 + 10x) - 21.[/tex]

Find the number that completes the square for the expression [tex]x^2 + 10x.[/tex]This is  [tex](10/2)^2 = 25.[/tex]

Add and subtract this number inside the parentheses, then group the perfect square and the constant terms: y = -[tex](x^2 + 10x + 25 - 25) - 21.[/tex]

Rewrite the equation, recognizing the perfect square trinomial:  [tex]y = -[(x + 5)^2 - 25] - 21.[/tex]

Combine the constant terms: [tex]y = -(x + 5)^2 + 4.[/tex]

The vertex form of the equation is  [tex]y = -(x + 5)^2 + 4[/tex], where the vertex of the parabola is (-5, 4).

Reflection across y-axis

Imagine folding the paper in half with the y-axis being the crease. the triangles would line up perfectly

The resulting transformation is a combination of rotation and translation.

The resulting R'ST' is an example of a Rotation and Translation.

In a rotation, an object is turned or twisted around a fixed point. In this case, R'ST' is rotated around a specific point.

A translation refers to the sliding of an object in a particular direction.

In this case, R'ST' is also shifted or translated in a specific direction.

Therefore, the resulting transformation is a combination of rotation and translation.

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The answer is:

The second option:

[tex]Volumen_{max}=(8-2x)(6-2x)*x[/tex]

From the statement, we know the dimensions of the box, and the length of the sides to be cut (x).

So,

Working with the length of the box:

Let be 8 the length of the cardboard for the length of the box, so, if we cut out the side of length "x", we have:

[tex]Length=(8-(x+x))=(8-2x)[/tex]

Now,

Working with the width of the box:

Let be 6 the length of the cardboard for the width of the box, so, if we cut out the side of length "x", we have:

[tex]Length=(6-(x+x))=(6-2x)[/tex]

Now that we already know the length and the width of the box, we must remember that the bottom of the box will have the same length "x", so, the greatest possible volume of the cardboard box will be:

[tex]Volumen_{max}=Length*Width*Bottom=(8-2x)(6-2x)*x[/tex]

Have a nice day!

Answer: The second option!

Step-by-step explanation:

Answer:

hopes this helps

Step-by-step explanation:

this is a tricky one here

40x X 22= $880

second week

40x X 29=1,160

Answer: Our equation becomes,

[tex]y=22x\ ;\ x\leq 40\\\\and\\\\y=29(x+40)\ ;\ x>40[/tex]

Step-by-step explanation:

Let the number of hours she works for be 'x'.

Let the number of dollars she will be paid in week be 'y'.

Cost per hour for first 40 hours = $22

Cost per hour for over 40 hours = $29

We need to model the piece-wise equation for her total pay in week.

So, our equation becomes,

[tex]y=22x\ ;\ x\leq 40\\\\and\\\\y=29(x+40)\ ;\ x>40[/tex]

ANSWER

{x|x<0} and {x|x>0}

EXPLANATION

If the two inequalities have an intersection,then it has a solution.

If the two inequalities have no intersection, then there is no solution.

The inequality {x|x<0} and {x|x>0} has no intersection, there is no solution.

The inequalities

{x|x≤0} and {x|x≥0},

{x|x≤0} or {x|x≥0}

both have intersection, therefore have solutions.

Answer:

D

Step-by-step explanation:

This graph shows two vertical asymptotes, one at x = +3, the other at x = 4.  Thus, we omit the first two answer choices.  Next, we substitute 0 for x and determine the y value in Answer Choice C:  F(0) = 0.  Does the graph go through (0, 0)?  Yes, it does.  Next, evaluate F at x = 3.5 (halfway between x =  3 and x = 4); that is, evaluate function D at x = 3.5.  Does the y value come out to be -4 as shown in the graph?  Yes, it does.    So D is the correct function to match this graph.

Considering the vertical asymptotes of the function, and it's behavior, it is found that the rational function graphed below is given by:

D. [tex]f(x) = \frac{1}{(x - 3)(x - 4)}[/tex]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

In this problem:

Thus, the correct option is:

D. [tex]f(x) = \frac{1}{(x - 3)(x - 4)}[/tex]

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Answer:

3 /2

Explanation:

If two lines are perpendicular , when you multiply the gradients together you get -1

The slope of a line is 2/3 What is the slope of a line that is perpendicular to this line?

Answer:

-3/2

-$1.71

To find the average of a set of numbers, you add them all together and divide by the amount of numbers.

Start by adding the numbers together to get -8.55.

Since they are 5 numbers, divide -8.55 by 5 to get -1.71.

So, the average daily change of the stock’s value is -$1.71.

Answer:

75

Step-by-step explanation:

Henry started with 20 convertibles and 5 trucks.

His aunt bought him x miniature trucks.

Now, his convertibles represent 1/5 of his collection.  How many trucks did her aunt buy?

So, if his convertible represent 1/5 of his collection now, that means his collection is 5 times larger than the number of convertibles.  We know he has 20 convertibles... so the collection now counts 100 (5 * 20) items.

Out of 100 items, we remove the 20 convertibles to get a total of 80 trucks.

Then we subtract the initial 5 trucks... so, his aunt bought him 75 trucks.

His aunt bought 75 trucks

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem!

Let :

Number of Additional Miniature Trucks from Henry's Aunt = X

Initial Number of Convertibles = 20

Initial Number of Trucks = 5

Henry's aunt bought him some more miniature trucks,Henry found that one-fifth of his collection consisted of convertible.

[tex]\frac{1}{5}( 20 + 5 + x ) = 20[/tex]

[tex]\frac{1}{5}( 25 + x ) = 20[/tex]

[tex]( 25 + x ) = 20 \div \frac{1}{5}[/tex]

[tex]25 + x = 20 \times \frac{5}{1}[/tex]

[tex]25 + x = \frac{20 \times 5}{1}[/tex]

[tex]25 + x = \frac{100}{1}[/tex]

[tex]25 + x = 100[/tex]

[tex]x = 100 - 25[/tex]

[tex]x = \boxed {75 ~ \texttt{trucks}}[/tex]

Henry's aunt bought him 75 trucks

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent

Answer: 64.7

Step-by-step explanation: 258.8 divided by 4

Answer:

The equation of the line is y = 4x

Step-by-step explanation:

* Lets revise how to form an equation of a line from its slope and

 a point on the line

- The equation of a line is written as y = mx + b where m is the

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

- The line intersect the y-axis at point (0 , b)

* Lets solve the problem

- The line has slope = 4

- The line passes through the point (2 , 8)

∵ The slope = 4

∵ m is the slope of the line in the equation

∴ m = 4

- Substitute the value of m in the equation

∵ y = mx + b

∴ y = 4x + b

- To find the value of b substitute the x-coordinate and the

  y-coordinate of the point instead of x and y of the equation

∵ The point (2 , 8) lies on the line

∵ y = 4x + b

- Put x = 2 and y = 8 in the equation to find b

∴ 8 = 4(2) + b ⇒ simplify

∴ 8 = 8 + b ⇒ subtract 8 from both sides

∴ 0 = b

- That means the y-intercept = 0 and the line passing through

  the origin point

∴ y = 4x + 0

* The equation of the line is y = 4x

You could express 48+32 by doing 50 + 30 because your adding 2 to the 48 and subtracting 2 from the 32 so that’s not how you could express that.

You could express it by using negatives.

-1(-48-32)

-1(-80)

80

The orginal was:

48+32

=80

Answer: (4 x 5)÷(2 + 8)

Step-by-step explanation:

The product is multiplied so the product of 4 and 5 is 20

The sum is adding so the sum of 2 and 8 is 10

Then it wants you to divide them. The 4 * 5 and 2 + 8 are in parenthesis because they are done first.

Answer:

2460 square units

Step-by-step explanation:

Calculate the surface area of the Rectangular Pyramid, calculate the surface area of the Square Prism [Cube], then you add them up.

Answer:

25

Step-by-step explanation:

Pythagorean theorem :

a² + b² = c²

Substitute the values:

24² + 7² = x² (c = x)

576 + 49 = x²

625 = x²

x = √625

x = 25

Answer:

Step-by-step explanation:

This explains step by step

Hope this helps! <3 -K

Answer:

Their people deserved to determine their own political futures.

Step-by-step explanation:

Answer:

Wilson believed that in conquered empires their people deserved to determine their own political futures

Step-by-step explanation:

Wilson was convinced that democracy was gaining ground allover the world so he declared that he believed "just government must rest upon the consent of the governed" during his taking over  of office. he worked with the secretary of state Bryan to sign 22 bilateral treaties to agreed to cooling periods

conquered Latin American states were granted freedom to conduct there own affairs without American interference during this period

The answer is 90 elves.

Here's how to find it

100 giants = 100/160 or 5/8

3/8 is left for the elves

3/8 x 240 = 90

Divide 1800 by 1/5 and then add the answer to 1800 (4/5) so you get a whole: then double.

I hope this helps. Good luck, I was in the same boat not too long ago.

The square root of 44 is 6.633249581

If you were going to round to the nearest whole number, it would be seven.

Hope that helps!

The value square root of 44 is 6.63 thus nearest integer of the square root of 44​ will be 7.

To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.

In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we keep it as it is.

As per the given,

The square root of 44​ = √44

√44 = 6.633249581

Since 6 > 5 so it will round up to the nearest integer.

6.633249581 → 7

Hence "The value square root of 44 is 6.63 thus nearest integer of the square root of 44​ will be 7".

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Answer:

one solution : x = -1

Step-by-step explanation:

look this solution :

The solutions of the given rational equation are negative one and three.

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

The rational equation is given below.

[tex]\rm \dfrac{1}{x-4} + \dfrac{x}{x-2} = \dfrac{2}{x^2-6x+8}[/tex]

By solving the equation, then we have

[tex]\begin{aligned} \dfrac{1}{x-4} + \dfrac{x}{x-2} &= \dfrac{2}{x^2-6x+8}\\\\ \dfrac{x- 2 + x(x - 4)}{(x-4)(x - 2)} &= \dfrac{2}{x^2-6x+8}\\\\\dfrac{x^2 -4x + x - 2}{x^2 - 6x + 8} &= \dfrac{2}{x^2-6x+8}\\\\x^2 - 3x - 2 &= 2\\\\x^2 - 3x - 4 &= 0\end[/tex]

Then the solution of the equation will be

          x² - 3x - 4 = 0

    x² - 4x + x - 4 = 0

x(x - 4) + 1 (x - 4) = 0

       (x - 4)(x + 1) = 0

                       x = -1, 4

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The answer is 125° = x because the exterior angle is 55°, from adding up all the exterior angles to ensure they add up to 360°. Then, you would have to use the Supplementary Angeles Theorem to find the obtuse measure beside that 55° exterior angle: 55 + m<x = 180. This is how you get 125° = m<x. You understand?

Answer:

B

Step-by-step explanation:

Two pairs of consecutive sides are congruent, so it can't be C.

At least one pair of opposite sides are parallel, so it can't be A.

The quadrilateral can't be inscribed in a circle, so it can't be D.

Therefore, the quadrilateral is a rhombus.  Answer B.

Given : f(x) = 5x² - 7(4x + 3)

Now,

f(3) = 5 × 3² - 7(4 × 3 + 3)

= 5 × 9 - 7(12 + 3)

= 45 - 7 × 15

= 45 - 105

= - 60

Hence,

f(3) = - 60

To find f(3) for the function f(x) = 5x² - 7(4x + 3), we substitute 3 into the function and simplify to get f(3) = -60.

To evaluate f(3) for the function f(x) = 5x² - 7(4x + 3), we need to substitute the value of 3 into the function:

f(3) = 5(3)² - 7(4(3) + 3)

Now we simplify the expression step by step:

The final result is:

f(3) = 45 - 105 = -60.

Answer: [tex]1.38\frac{g}{cm^3}[/tex]

Step-by-step explanation:

You need to remember the formula for calculate the density:

[tex]density=\frac{mass}{volume}[/tex]

In this case:

[tex]density_{(rock)}=\frac{mass_{(rock)}}{Volume_{(rock)}}[/tex]

You know that:

[tex]mass_{(rock)}=15.5g[/tex]

And when it is placed in a graduated cylinder, the volume is displaced from 25.0 mL to 36.2 mL.

Then, the volume of the rock is:

[tex]Volume_{(rock)}=36.2mL-25.0mL=11.2mL[/tex]

Since [tex]1mL=1cm^3[/tex], you can rewrite the volume as:

[tex]Volume_{(rock)}=11.2cm^3[/tex]

Substituting values into the formula, you get that the density of the rock is:

[tex]density_{(rock)}=\frac{15.5g}{11.2cm^3}=1.38\frac{g}{cm^3}[/tex]

Answer:

The answer is 22.5

Step-by-step explanation:

The person who answered above me said it was 0.375, but that was in hours. 0.375 hours in min = 22.5.

The person who answered above me is not wrong, it is just that it was in hours.

Welcome! :)

Ava and Kelly will be 3/4 mile apart after 22.5 minutes of running at their respective speeds of 6 mph for Ava and 8 mph for Kelly.

To determine when Ava and Kelly will be 3/4 mile apart in a road race, we must calculate the difference in distance they cover over the same time frame. Ava runs at 6 miles per hour (mph) and Kelly runs at 8 miles per hour (mph). The difference in their speeds is 2 mph (8 mph - 6 mph).

We need to calculate the time it takes for this difference in speed to result in a gap of 3/4 miles. Since speed is distance divided by time, we can use the formula:
Time = Distance / Speed. Substituting the values we have, we get:
Time = (3/4) miles / 2 mph. When we calculate this, we find the time to be 3/8 hours, or 22.5 minutes.

Therefore, Ava and Kelly will be 3/4 mile apart after 22.5 minutes of running at their respective average speeds.

ANSWER

(–4.5, 4.25)

EXPLANATION

The first equation is

[tex]y = - \frac{5}{2}x - 7[/tex]

This function is in the slope-intercept form

The second equation is:

x + 2y = 4

2y =-x+ 4

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

The graph of the two functions are shown in the attachment.

The point of intersection represents the solution to the system of equations they represent.

The solution is

(–4.5, 4.25)

2. and 3. are already in slope intercept form.

1. y=4x-2

4. y=3x-2