Why do you think the acceleration due to gravity is represented by a negative number?

Answer:

Step-by-step explanation:

Look at the picture.

Mark points (0, 2) and (8, -4) in the coordinate system.

Plot the line going through these points.

Read the coordinates of the intersection of the line (solution).

The solution of the system of linear equation is (4,-1) and this can be determined by using the arithmetic operations.

Given :

Equations  ---  y = x - 5   --- (1)

                       [tex]\rm y = -\dfrac{3}{4}x+2[/tex]    --- (2)

The system of linear equations can be determined by substituting the value of y in terms of x in another equation in order to determine the value of 'x' and by finding the value of 'x', the value of 'y' can also be determined.

Substitute the value of 'y' in equation (2) that is:

[tex]\rm x-5 = -\dfrac{3}{4}x+2[/tex]

Further, simplify the above equation.

[tex]4x - 20 = -3x +8[/tex]

7x = 28

x = 4

Now, substitute the value of 'x' in equation (1) that is:

y = 4 - 5

y = -1

So, the solution of the system of linear equation is (4,-1).

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Step-by-step explanation:

recall in a linear equation expressed in the form

y = mx + b,

m represents the slope or the rate of change in the value of y for a unit change in the value of x

b represents the y-intercept (i.e the value of y when x = 0)

If you compare these definitions to what was given in the question, the rate of  change in snowfall is given as 1/2 inches per hour. This is equivalent to the m value in our general equation above. Hence we can say that the rate of change in snowfall is equal to the slope of the graph.

The question also states that before the snow even started to fall (i.e when x=0 hours), there was already 8 inches on the ground. This is equivalent to the value of b in our general equation above. Hence we can say that the y-intercept is representative of the 8 inches that was already on the ground when the snow started falling.

Answer:

-12x+54

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{In order for you to simplify, you need to}[/tex] [tex]\huge\text{ distribute}[/tex]

[tex]\huge\text{The formula is: a(b + c) = a(b) + a(c) = ab + ac}[/tex]

[tex]\huge\text{Simplify: -6(2x - 9)}[/tex]

[tex]\huge\text{-6(2x) = -12x}\\\huge\text{-6(-9) = 54}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: -12x + 54}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

Part 1)  [tex]x=11[/tex]

Part 2)  [tex]k=57.2[/tex]  

Part 3)  [tex]y=9.2[/tex]

Part 4)  [tex]x=2.375[/tex]

Part 5) [tex]y=3.3[/tex]

Part 6)  [tex]k=6.7[/tex]

Part 7)  [tex]k=115.2[/tex]

Part 8)  [tex]y=1.4[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Part 1) y varies inversely with x. If y = 3 and k (the constant of variation) = 33, what is x?

we have

[tex]y*x=k[/tex]

[tex]y=3[/tex]

[tex]k=33[/tex]

substitute and solve for x

[tex]3*x=33[/tex]

Divide by 3 both sides

[tex]x=33/3[/tex]

[tex]x=11[/tex]

Part 2) y varies inversely with x. When y = 11, x = 5.2. What is the value of k, the constant of inverse variation?

we have

[tex]y*x=k[/tex]

[tex]y=11[/tex]

[tex]x=5.2[/tex]

substitute and solve for k

[tex]11*5.2=k[/tex]

[tex]k=57.2[/tex]  

Part 3) y varies inversely with x, and k (the constant of variation) = 72. What is the value of y when x = 7.8?

we have

[tex]y*x=k[/tex]

[tex]x=7.8[/tex]

[tex]k=72[/tex]

substitute and solve for y

[tex]y*7.8=72[/tex]

Divide by 7.8 both sides

[tex]y=72/7.8[/tex]

[tex]y=9.2[/tex]

Part 4) y varies inversely with x. If y = 8 and k (the constant of variation) = 19, what is x?

we have

[tex]y*x=k[/tex]

[tex]y=8[/tex]

[tex]k=19[/tex]

substitute and solve for x

[tex]8*x=19[/tex]

Divide by 8 both sides

[tex]x=19/8[/tex]

[tex]x=2.375[/tex]

Part 5) y varies inversely with x, and k (the constant of variation) = 23. What is the value of y when x = 7?

we have

[tex]y*x=k[/tex]

[tex]x=7[/tex]

[tex]k=23[/tex]

substitute and solve for y

[tex]y*7=23[/tex]

Divide by 7 both sides

[tex]y=23/7[/tex]

[tex]y=3.3[/tex]

Part 6) y varies inversely with x. When y = 6.7, x = 1. What is the value of k, the constant of inverse variation?

we have

[tex]y*x=k[/tex]

[tex]y=6.7[/tex]

[tex]x=1[/tex]

substitute and solve for k

[tex]6.7*1=k[/tex]

[tex]k=6.7[/tex]

Part 7) y varies inversely with x. When y = 9.6, x = 12. What is the value of k, the constant of inverse variation?

we have

[tex]y*x=k[/tex]

[tex]y=9.6[/tex]

[tex]x=12[/tex]

substitute and solve for k

[tex]9.6*12=k[/tex]

[tex]k=115.2[/tex]

Part 8) y varies inversely with x, and k (the constant of variation) = 5.6. What is the value of y when x = 4?

we have

[tex]y*x=k[/tex]

[tex]x=4[/tex]

[tex]k=5.6[/tex]

substitute and solve for y

[tex]y*4=5.6[/tex]

Divide by 4 both sides

[tex]y=5.6/4[/tex]

[tex]y=1.4[/tex]

Answer:

x= -4 and x=-2

Step-by-step explanation:

Using a graphing calculator (See picture attached) we find that the solution to the equation are the x-values at which the graph of the function intercepts the x-axis. It ocurrs at x= -4 and x=-2.

Given that exact roots were found, there's no need to state the consecutive integers between which the roots are located.

Answer:

the answer is 15

Step-by-step explanation:

Answer:

a = 162

Step-by-step explanation:

9 = 1/27 a +3

Subtract 3 from each side

9-3 = 1/27 a +3-3

6 = 1/27 a

Multiply each side by 27

6*27 = 1/27 a *27

162 = a

Answer:

a = 162.

Step-by-step explanation:

1/27 a + 3 = 9

1/27 a = 9 - 3 = 6

Multiply both sides by 27:

a = 6 * 27

a =  162.

Answer:

The simplified form of √100 is 10

Step-by-step explanation:

We have given√100

We know that if we multiply 10 two times than it will give us 100 as  an answer

So,

√100 =√10*10

√100 = 10

The simplified form of √100 is 10....

Answer:

The 5 all the way to the left

325,251.58

Step-by-step explanation:

The 8 is in the hundredths place

The 5 is in the tenths place

The 1 is in the ones place

The 5 is in the tens place

The 2 is in the hundreds place

The 5 is in the thousands place

The 2 is in the ten-thousands place

The 3 is in the hundred-thousands place

Hope This Helped :}

Neither of the given numbers (325,25 and 1.58) have a thousands place. This would typically be represented by the digit to the left of the hundreds place.

The student has asked about the thousands place in a pair of numbers. Looking at the numbers provided (325,25 and 1.58), neither of these numbers actually have a thousand place digit. In a number, the thousands place digit is the digit to the left of the hundreds place. For example, in the number 6528, which is from an arithmetic operation given in the reference information (6527.23 + 2 = 6528.23), the 6 represents 6 thousands, or 6000.

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The value of x will be equal to 3.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

We know that the  exterior angles are equal to the opposite interior angles

So the equation would be:

25x  +  57  +  x   =   45x

26x  +  57   =   45x

57  =   19x

x    =    3

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Answer:

2313

Step-by-step explanation:

A = P(1+r)^t

where A is the final amount, P is the initial amount, r is the rate, and t is time.

Here, P = 1000, r = 0.15, and t = 6.

A = 1000(1.15)^6

A ≈ 2313

Step-by-step explanation:

Population after n days is given by

              [tex]P_n=P_0(1+r)^n[/tex]

Initial population, P₀ = 1000

Increase rate, r = 15 % = 0.15

Number of days, n = 6

Substituting

             [tex]P_n=P_0(1+r)^n\\\\P_6=1000(1+0.15)^6\\\\P_6=1000(1.15)^6\\\\P_6=1000\times 2.313\\\\P_6=2313[/tex]

Number of bacteria after 6 days = 2313

Answer:

  x = {-8/3, 7/2}

Step-by-step explanation:

To use the zero product property, you need the equation in the form of a product that is equal to zero. We can get that by subtracting 56 and factoring the resulting equation.

  6x^2 -5x -56 = 0

  (3x +8)(2x -7) = 0

The zero product property tells us this product is zero only when the factors are zero:

  3x +8 = 0   ⇒   x = -8/3

  2x -7 = 0   ⇒   x = 7/2

The solution is x = {-8/3, 7/2}.

_____

Comment on factoring

Consider the product ...

  (ax +b)(cx +d) = (ac)x^2 +(ad +bc)x +(bd)

Now consider the product of first and last term coefficients compared to the coefficient of the middle term:

  acbd = (ad)(bc)  vs.  ad+bc

We see that the coefficient of the middle term is the sum of two of the factors of the first·last product. This means we want factors of 6·(-56) that have a sum of -5.

  6(-56) = -(2^4)(3)(7) . . . . has 20 divisors.

We're looking for factors that are nearly equal. The clue is given by simplifying the above factoring:

  = -(16)(21) = (16)(-21) . . . . the sum of these factors is -5, as we need.

Again considering the first-last product and the middle coefficient, we see that we can choose ...

  ad = -21, bc = 16; ac = 6, so a=3, c=2, and ...

  (a, b, c, d) = (3, 8, 2, -7)

These values give us the factors we used above.

Note this process gets easier with practice and familiarity with multiplication tables.

Answer:

30

Step-by-step explanation:

[tex]\sin^{-1}(\theta)[/tex] is going to output a number in between [tex]\frac{-\pi}{2}[/tex] and [tex]\frac{\pi}{2}[/tex].

Luckily you are looking for [tex]\theta[/tex] in the 1st quadrant which is contained in the given interval above, so the answer just comes down to what the calculator returns from entering [tex]\sin^{-1}(\frac{1}{2})[/tex] in your calculator.

You may also use the unit circle.  sine value refers to the y-coordinate on there.

So you are looking for when the y-coordinate is 1/2 in the fist quadrant which is at 30 degrees.

Answer:

C   2x^2 + 3/2x -5

Step-by-step explanation:

f(x)=x/2-2

g(x)=2x^2+x-3

(f+g) (x)=x/2-2+2x^2+x-3

Combine like terms

           2x^2 + 3/2x -5

Both of these are linear equations with different y-intercepts and different slopes.

Let's analyze the lines:

y = 2x:

This is a linear equation with a slope of 2 and a y-intercept at the origin (0,0). This means that for every unit increase in x, y increases by 2. The graph is a straight line that passes through the origin.

y = 2 - x:

This is also a linear equation, but with a slope of -1 and a y-intercept at (0,2). This means that for every unit increase in x, y decreases by 1. The graph is a straight line that intersects the y-axis at the point (0,2).

Now, let's consider their relationship:

Both equations are linear, so their graphs are straight lines.

Therefore, the graphs of these two equations are lines with different slopes. The line represented by y = 2x slopes upwards, while the line represented by y = 2 - x slopes downwards.

[tex]\huge{\boxed{1}}[/tex]

This statement can be represented as [tex]2*\frac{3}{6}[/tex], since the quotient is the answer to a division problem.

Divide. [tex]2*\frac{1}{2}[/tex]

Multiply. [tex]2*\frac{1}{2}=\frac{2}{1}*\frac{1}{2}=\frac{2*1}{1*2}=\frac{2}{2}[/tex]

Simplify.  When the numerator and denominator are the same, the fraction is equal to 1. [tex]\frac{2}{2}=1[/tex]

Answer:

Mary has 72 breads and Sue has 72 breads....Total they have 144 breads.

Step-by-step explanation:

Let the bread of Sue be x and Mary be y.

y=x

Later , Sue has x- 54 breads and Mary has y+ 54 breads.

As per question,

y+54=7(x-54)

y+54= 7x-378

y+54=7y- 378

6y= 378+54

y=432/6

y=72

2(5x+4)+3(2x-1)

Use the distributive property for both sets of parenthesis:

2(5x+4) = 2*5x + 2*4 = 10x+8

3(2x-1) = 3*2x - 3*1 = 6x-3

Now you have:

10x+8 + 6x-3

Now combine like terms:

10x + 6x = 16x

8-3 = 5

The final answer is 16x+5

Algebraic expression includes at least one unknown variable and at least one mathematics operation. The simplified way to represent the given equation is [tex]16x+5[/tex].

The given algebraic expression is,

[tex]2(5x+4)+3(2x-1)[/tex]

An algebraic expression is the mathematical expression of variable which is the combination of variables, coefficients of variables and constants.Algebraic expression includes at least one unknown variable and at least one mathematics operation.

Let [tex]f(x)[/tex] is equal to the given expression. Thus,

[tex]f(x) =2(5x+4)+3(2x-1)[/tex]

The above equation consist one unknown variable x.

Solve the equation using the BODMOS rule. According to the BODMOS to solve a equation first open its bracket. Thus,

[tex]f(x) =2(5x+4)+3(2x-1)[/tex]

[tex]f(x) =10x+8+6x-3[/tex]

Arrange the equation with same power of the variables,

[tex]f(x) =10x+6x+8-3[/tex]

[tex]f(x) =16x+5[/tex]

Hence the simplified way to represent the given equation is [tex]16x+5[/tex].

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Answer:

Step-by-step explanation:

because :

when : x = 2        y = 3(2)-4 =6-4 =2   non 3

Answer:

2 and 7/25

Step-by-step explanation:

Trust me dude.

let's firstly convert the mixed fractions to improper fractions, also recall PEMDAS, multiplication is done before any additions or subtractions.

[tex]\bf \stackrel{mixed}{1\frac{1}{5}}\implies \cfrac{1\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{6}{5}}~\hfill \stackrel{mixed}{2\frac{2}{5}}\implies \cfrac{2\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\mathbb{P~E~M~D~A~S}}{\cfrac{6}{5}\cdot \cfrac{12}{5}-\cfrac{3}{5}}\implies \cfrac{6\cdot 12}{5\cdot 5}-\cfrac{3}{5}\implies \cfrac{72}{25}-\cfrac{3}{5}\implies \stackrel{\textit{using the LCD of 25}}{\cfrac{(1)72~~-~~(5)3}{25}} \\\\\\ \cfrac{72-15}{25}\implies \cfrac{57}{25}\implies 2\frac{7}{25}[/tex]

Answer:

28.57142857% decrease

Step-by-step explanation:

To find the percentage decrease in speed, take the original speed minus the new speed over the original speed.  Then multiply by 100%

original speed = 70   new speed =50

percent decrease = (70-50)/70 *100%

                              = 20/70 *100%

                              =28.57142857%

Answer:

9(sqrt)2 (B)

Step-by-step explanation:

1. 18(sqrt)2/2=12.727

2. 9(sqrt)2=12.727

3. 12.727=12.727

They match! So the final answer is B

Hope this helps :)

your question is incomplete. please read below to find the missing content.

A. 9 cm

B. 9[tex]\sqrt{2}[/tex] cm

C. 18 cm

D. 18[tex]\sqrt{2}[/tex] cm

The answer is option B. 9[tex]\sqrt{2}[/tex] cm

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios.

Calculations:-

given length=18 cm (hypoteneuse)

angle = 45°

⇒sin 45°=perpendicular/hypoteneuse

⇒1/[tex]\sqrt{2}[/tex]=perpendicular/hypoteneuse

⇒perpendicular =1/[tex]\sqrt{2}[/tex]*hypoteneuse

⇒perpendicular = 18/[tex]\sqrt{2}[/tex] = 12.727

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Answer: 72

Step-by-step explanation:

Answer:

none

Step-by-step explanation:

Hi, I hope this helps, I'm in high school LOL.

Use these, they help to figure this out:

a + b > c

b is the longest side, or hypotenuse. c would be the base.

We have to make sure that c is less than what a + b is.

Plug the numbers in:

2.7 + 4.8 > 8.6

4.8 plus 2.7 is 7.5 cm.

So, 7.5 > 8.6

Obviously, 7.5 is less than 8.6 so 7.5 > 8.6 does not work at all.

That tells you that no triangles can be formed. So, it's none.

Answer:

The answer is 183.

When you estimate that it is 200.

So the answer is (C) 200

Step-by-step explanation:

The explanation is shown in the picture.

The answer is 183.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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[tex]\large\boxed{\$4}[/tex]

In this question, we're trying to find how much Voldemort had to pay for the ice cream.

To answer this question, we need to gather some important information that was provided in the question.

Important information:

With the information above, we can solve the problem.

The easiest way to solve this problem is to multiply. We would multiply 6.6 and 0.60 in order to see how much did Voldemort had to pay.

[tex]6.6*0.60=3.96[/tex]

When you multiply, you should get 3.96

This means that Voldemort payed $3.96 for the ice cream.

But we need to round it to the nearest dollar.

When you round it, you should get $4

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]hypotenuse^2=leg^2+leg^2[/tex]

We have

[tex]leg=AC=36,\ leg=AB=15, hypotenuse=BC[/tex]

Substitute:

[tex]BC^2=36^2+15^2\\\\BC^2=1296+225\\\\BC^2=1521\to BC=\sqrt{1521}\\\\BC=39[/tex]

Answer:

39

Step-by-step explanation:

3.1.3

Answer:

Part 1) The smallest x-intercept is x=-1

Part 2) The largest x-intercept is x=6

Part 3) The y-intercept is y=-6

Part 4) The vertex is the point (2.5,-12.25)

Part 5) The equation of the line of symmetry is x=2.5

Step-by-step explanation:

we have

[tex]f(x)=x^{2}-5x-6[/tex]

step 1

Find the x-intercepts

we know that

The x-intercept is the value of x when the value of the function is equal to zero

so

equate the function to zero

[tex]x^{2}-5x-6=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-5x-6=0[/tex]

so

[tex]a=1\\b=-5\\c=-6[/tex]

substitute in the formula

[tex]x=\frac{-(-5)(+/-)\sqrt{-5^{2}-4(1)(-6)}} {2(1)}[/tex]

[tex]x=\frac{5(+/-)\sqrt{49}} {2}[/tex]

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

[tex]x=\frac{5(+)7} {2}=6[/tex]

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

therefore

The x-intercepts are

x=-1 and x=6

The smallest x-intercept is x=-1

The largest x-intercept is x=6

step 2

Find the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]f(0)=(0)^{2}-5(0)-6[/tex]

[tex]f(0)=-6[/tex]

therefore

The y-intercept is y=-6

step 3

Find the vertex

we know that

The equation of a vertical parabola into vertex form is equal to

[tex]f(x)=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex

Convert the function into vertex form

[tex]f(x)=x^{2}-5x-6[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)+6=(x^{2}-5x)[/tex]

Complete the square, Remember to balance the equation by adding the same constants to each side

[tex]f(x)+6+2.5^{2}=(x^{2}-5x+2.5^{2})[/tex]

[tex]f(x)+12.25=(x^{2}-5x+6.25)[/tex]

Rewrite as perfect squares

[tex]f(x)+12.25=(x-2.5)^{2}[/tex]

[tex]f(x)=(x-2.5)^{2}-12.25[/tex]

The vertex is the point (2.5,-12.25)

step 4

Find the equation of the line of symmetry

we know that

In a vertical parabola the equation of the line of symmetry is equal to the x-coordinate of the vertex

we have

vertex (2.5,-12.25)

The x-coordinate of the vertex is 2.5

therefore

The equation of the line of symmetry is x=2.5

Answer:

f(x) = -5x + 250

Step-by-step explanation:

* Lets  explain how to solve the problem

- In week 10 the manufacturer fixed 200 cars

- In week 15, the manufacturer fixed 175 cars

- the reduction in the number of cars each week is linear

- The form of the linear equation is y = mx + c, where m is the slope of

 the line which represent the equation and c is the y-intercept

- The slope of the line m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

  where (x1 , y1) and (x2 , y2) are two points on the line

* Lets solve the problem

- Assume that the weeks' number is x and the cars' number is y

∴ (10 , 200) and (15 , 175) are two points on the line which represent

  the linear equation between the cars' numbers and the weeks

  numbers

∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)

∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175

- Use the rule of the slope above to find m

∴ [tex]m=\frac{175-200}{15-10}=\frac{-25}{5}=-5[/tex]

- Substitute the value of x in the form of the linear equation above

∴ y = -5x + c

- To find c substitute x and y by one the coordinates of one of the

  two points

∵ x = 10 when y = 200

∴ 200 = -5(10) + c

∴ 200 = -50 + c

- Add 50 to both sides

∴ 250 = c

- Substitute the value of c by 250

∴ y = -5x + 250, where the number of cars seen each week is y and

  x is the number of the week

∵ f(x) = y

∴ f(x) = -5x + 250

Answer:

B f(x) = −5x + 250

Step-by-step explanation:

Step-by-step explanation:

The answer is attached.

Probability helps us to know the chances of an event occurring. The given symbols can be matched with their description as shown below.

Probability helps us to know the chances of an event occurring.

The given symbols can be matched with their description as shown below, therefore,

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