solve by completing the square: x^2-10x+8=0

Answer:

l

Step-by-step explanation:

There are infinitely many combinations of trucks and sedans that could have passed through the toll booth to collect a total of $128 in 2 hours.

Let's assume the number of trucks that passed through the toll booth in the 2-hour period is represented by 't', and the number of sedans is represented by 's'.

According to the given information, the toll collector received $8 for each truck and $3 for each sedan. We can write two equations based on the total amount collected and solve them simultaneously.

The total amount collected from the trucks:

Amount from trucks = $8 × number of trucks = 8t

The total amount collected from the sedans:

Amount from sedans = $3 × number of sedans = 3s

We are also given that the toll collector collected a total of $128 in 2 hours. So we can write the equation:

Amount from trucks + Amount from sedans = $128

8t + 3s = 128

Now, we need to solve the above two equations simultaneously to find the values of 't' and 's'.

To solve these equations, we can use a method called substitution. Let's solve for 't' in terms of 's' using the first equation:

8t = 128 - 3s

t = (128 - 3s)/8

Now we substitute this value of 't' in the second equation:

8(128 - 3s)/8 + 3s = 128

128 - 3s + 3s = 128

128 = 128

We see that both 's' and 't' have been eliminated from the equation, and we are left with 128 = 128. This means the value of 's' can be any number, as long as it satisfies the equation.

Therefore, there are infinitely many combinations of trucks and sedans that could have passed through the toll booth to collect a total of $128 in 2 hours.

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First add all the numbers in the data:

15.8 + 14.9 + 16.7 + 17.6 + 13.4 = 78.4

Divide by how many numbers are in the data set there is 5 so:

78.4 ÷ 5 = 15.7

The mean is 15.7

390-35=355

355-10w

355/10=35.5

355-10(35.5)

35 and a 1/2 weeks

36 weeks to have the full amount needed

Answer:

36th weeks

Step-by-step explanation:

Kelsey has saved $35 to buy a video game worth $390.

She plans to save additional $10 per week.

Let w represents number of week.

Let s represents total saving in w weeks.

Addition saving per week = $10

In w weeks saving  = 10w

Previous saving amount = $35

Total saving in w week, s = 35 + 10w

Expression which represents total saving in w weeks

s = 35 + 10w

Now find number of weeks to save $390

So, put s=390 and solve for w

35 + 10w = 390

        10w = 390 - 35

           w = 355÷10

          w = 35.5

Hence, Kelsey will save $390 in 36th weeks.

Answer(a):

We have been given two functions f(x)=100+3x and g(x)=8x.

Now we need to decide which one of them is cost function and which one is the revenue function.

We know that production usually involves fixed cost for operating the production so usually that is of the form y=mx+b.

Hence f(x)=100+3x is the cost function

Answer(b):

Then g(x)=8x is the revenue function.

Answer(c):

We know that profit function is the difference of revenue and cost

Profit = Revenue - Cost

P(x)= g(x) - f(x) =8x-(100+3x)

P(x)= 8x-100-3x

P(x)= 5x-100

Hence P(x)= 5x-100 is the profit function.

Answer(d):

P(x)= 5x-100 is the profit function.

Answers:

Angle A = 104 degrees

Angle B = 76 degrees

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

Supplementary angles add to 180 degrees.

A+B = 180

(3x-7)+(2x+2) = 180

5x-5 = 180

5x-5+5 = 180+5 ... add 5 to both sides

5x = 185

5x/5 = 185/5 .... divide both sides by 5

x = 37

Use x =37 to find

Angle A = 3x-7 = 3*37-7 = 111-7 = 104 degrees

Angle B = 2x+2 = 2*37+2 = 74+2 = 76 degrees

As a check: A+B = 104+76 = 180 so that helps confirm the answer

The measure of supplementary angle ∠A is 107 degrees and the measure of supplementary angle ∠B is 76 degrees. We get these values by setting up an equation based on the fact that the sum of the measures of two supplementary angles is 180 degrees, solving for x, and then substituting x back into the original equations.

In this problem, we're asked to find the values of the supplementary angles ∠A and ∠B. The measure of a supplementary angle is based on the concept that the sum of the measures of two supplementary angles is 180 degrees. We can form an equation since we know m∠A + m∠B = 180°. This translates to (3x – 7)° + (2x + 2)° = 180°. To solve the equation, consolidate like terms, so 5x - 5 = 180. Add 5 to both sides of the equation to find that 5x = 185. Dividing both sides of the equation by 5, we find that x = 37. Substitute x = 37 back into the original equations for m∠A and m∠B to find m∠A = 3*37 - 7 = 107 degrees, and m∠B = 2*37 + 2 = 76 degrees.

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Hey there!!

The measure of the unlabeled angle is ( x + y - 5 ) due to the vertically opposite angles.

We also know 2x = y due to vertically opposite angles

If we add up all the angles, we get 360 degrees.

Hence,  

y + 2x + x + y - 5 + x + y - 5 = 360

4x + 3y - 10 = 360

Add 10 on both sides

4x + 3y = 370

We know 2x = y

Hence,

4x + 3y = 370 can be broken down as ,

4x + y + y + y = 370

4x + 2x + 2x + 2x = 370

10x = 370

x = 370 / 10

x = 37

The unknown angle = x + y - 5

x + 2x - 5

3x - 5

3 ( 37 ) - 5

111 - 5

106

Hence, the unknown angle is 106°

Hope my answer helps!!

Answer:

y + 6 = (x -3)^2

Step-by-step explanation:

Let's use the general form of the vertex equation of a quadratic:  y - k = a(x - h)^2.

Subst. 10 for y, 7 for x, -6 for k and 3 for h.  Then, 10 + 6 = a(7 - 3)^2, or

16 = a(4)^2, or 16 = a(16).  Thus, a = 1, and the equation of this particular parabola is:

y + 6 = (x -3)^2

Given a quadratic function with a vertex at (3,-6) and a point (7,10), by substituting the values into the equation, we find that another point on the graph is (4,-5).

The vertex form of a quadratic function is [tex]\(y = a(x - h)^2 + k\)[/tex], where (h, k) is the vertex of the parabola. In this case, the vertex is (3, -6), so the equation is [tex]\(y = a(x - 3)^2 - 6\).[/tex]

You're also given a point on the graph, which is (7, 10). You can use this point to find the value of a.

Substitute the point's coordinates into the equation and solve for a:

[tex]\(10 = a(7 - 3)^2 - 6\)[/tex]

[tex]\(10 = a(4^2) - 6\)[/tex]

10 = 16a - 6

Now, isolate a:

16a = 10 + 6

16a = 16

a = 1

Now that you know a = 1, you can use this information to find another point on the graph. Simply plug in a different value for x into the equation. Let's choose x = 4 for example:

[tex]\(y = 1(4 - 3)^2 - 6\)[/tex]

y = 1(1) - 6

y = 1 - 6

y = -5

So, another point on the graph is (4, -5).

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The standard for of this equation is x – y = 0

Firstly, options A and D are not in standard form, so they are not options.

To decided between B and C, we choose a point on the line and see if it works. For example, we'll use (2, 2).

x – y = 0

2 - 2 = 0

0 = 0

This is true for option C. Therefore, it is correct.

Answer:

C.

Step-by-step explanation:

Edgen 2023

x^2-2=7

Subtract 7 from both sides

x^2-2-7=7-7

x^2-9=0

x^2-3^2=0

Using a^2-b^2=(a+b)(a-b)

Where a=x and b=3

(x-3)(x+3)

Answer:

7

Step-by-step explanation:

assign the amount of weeks to x. then we write the equation 160+3x=195-2x which is 7

The equation that can be used to find the number of weeks it will take them to weigh the same amount is 160 + 3w = 195 - 2w , and it will take them 7 weeks to weigh the same amount.

Let's take w as the weight,

Nick's weight after w weeks: 160 + 3w

Adam's weight after w weeks: 195 - 2w

Since they will weigh the same after w weeks, you can set up the equation:

160 + 3w = 195 - 2w

Now, solve for w:

Combine like terms:

3w + 2w = 195 - 160

5w = 35

Divide both sides by 5 to isolate w:

w = 35 / 5

w = 7

So, it will take them 7 weeks to weigh the same amount.

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The answer to your question is,

5/7.

-Mabel <3

the answer is $29 dollars! ! ! ! ! !  

The overall change to theo's account was that he deposited 29$ to the account. Hope this helps :)

The direct variation equation that is satisfied by this ordered pair is y = 6/5x

In order to find this, we start with the base equation for direct variation. We then plug in and solve for k.

y = kx

6 = k5

6/5 = k

And now we can use that to model all future direct variations with this.

y = 6/5x

If you mean -17 times -6 then the answer is a positive 102

You get 1 9/10. You can change 0.38 to 38/100 which simplifies to 19/50. Then u can change 15 1/3 to an improper fraction. You get 46/3. Then multiply 19/50 by 46/3 and you get 19/10 which simplifies to 1 9/10.

we are given

[tex]y=cos^{-1}(x-\pi)[/tex]

Since, we have to find inverse function

step-1:

Set y=f(x)

It is already there

step-2:

Switch x and y

[tex]x=cos^{-1}(y-\pi)[/tex]

step-3: Solve for y

We can take cos on both sides

[tex]cos(x)=cos(cos^{-1}(y-\pi))[/tex]

we can simplify it

[tex]cos(x)=y-\pi[/tex]

now, we can solve for y

[tex]cos(x)+\pi=y-\pi+\pi[/tex]

[tex]cos(x)+\pi=y[/tex]

[tex]y=\pi +cos(x)[/tex]..............Answer

Answer:

The answer is C

Step-by-step explanation:

Coordinates of C: (-5,-1)

Coordinates of D: (0,3)

Distance formula:

[tex]d = \sqrt({x2 - x1)^2 + (y2 - y1)^2}[/tex]

--> [tex]\sqrt{(0 - (-5))^2 + (3 - (-1))^2}[/tex]

---> [tex]\sqrt{5^2 + 4^2}[/tex]

----> [tex]\sqrt{25 + 16} = \sqrt{41}[/tex]

The distance rounded to the nearest tenth is 6.40 units.

Answer:

this box will show you the answer

Step-by-step explanation:

Thank Natalie222 for the answer its  6x10 not 6x3 :3

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{y})\qquad(\stackrel{x_2}{-11}~,~\stackrel{y_2}{8})\\\\\\slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-y}{-11-(-3)}~~=~~\stackrel{m}{-2}\\\\\\\cfrac{8-y}{-11+3}=-2\implies \cfrac{8-y}{-8}=-2\implies 8-y=16\implies -8=y[/tex]

8, 15 - 7 = 8 thats correct

Joanne can distribute her campaign materials to 4 classrooms. Each classroom would get 5 flyers and 4 buttons.

The subject of this question is Mathematics, specifically it deals with the topic of finding the greatest common divisor (GCD). In this scenario, Joanne has 20 flyers and 16 buttons she wants to distribute evenly amongst classrooms. The greatest number of classrooms she can distribute materials to is found by determining the GCD of 20 (the number of flyers) and 16 (the number of buttons). The GCD of 20 and 16 is 4. Therefore, Joanne can distribute her campaign materials to a maximum of 4 classrooms without any materials being left over. It is important to note that, in each classroom, there would be 5 (20/4) flyers and 4 (16/4) buttons.

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The vertical angles theorem states that vertical angles are congruent to each other. Since angles E and F are vertical angles, this means you can make them equal to each other in an equation.

m∠E = m∠F

17x + 1 = 20x - 14

Subtract 20x from both sides.

-3x + 1 = -14

Subtract 1 from both sides.

-3x = -15

Divide both sides by -3.

x = 5

Substitute 5 for x in m∠F (20x - 14).

20(5) - 14 = 86

m∠F = 86°

the vertex is (-6,-28). let me know if i'm wrong

Its helpful because it gives you the number to put in and to find the unit rate

Tables aid in constructing equations by facilitating the organization and visualization of mathematical data. This makes it easier to apply given parameters to equations and to understand their behavior. For instance, an equilibrium state can be visually represented in a table.

A table is incredibly helpful when constructing equations because it aids in the organization and visualization of mathematical data. Through the usage of tables, one can clearly list and categorize known values that might be used in an equation, thereby making it easier to identify what needs to be solved. For instance, if you're given multiple variables and constants in a word problem, a table can be used to order these parameters systematically so they can be more easily applied into constructing equations.

Similarly, tables contribute to expressing equations visually as they can illustrate changes in variable values, which can further assist in understanding the behavior of the equation. An equilibrium state, for instance, can be clearly italicized in a table to visually represent the point where an equation balances, which would be harder to see in text form.

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We know that

triangles ADE and ABC are similar triangles

so, the ratios of their sides must be same

now, we will find value of sides

we are given

AD=12

DB=6

AE=14

EC=7

[tex]AB=AD+DB[/tex]

now, we can plug values

[tex]AB=12+6[/tex]

[tex]AB=18[/tex]

so, we can get ratio

[tex]\frac{DE}{BC} =\frac{AD}{AB}[/tex]

now, we can plug values

[tex]\frac{DE}{BC} =\frac{12}{18}[/tex]

So, the ratio in simplest form is

[tex]\frac{DE}{BC} =\frac{2}{3}[/tex]..............Answer

you will

have 14 rings

you will have 14 rings, because you have ten fingers, and ten plus 4 is 14.

hope it helps.

24 rounds to 25 and 80 stays the same