What is the following quotient

Answer:

x=-1 or x=3

Step-by-step explanation:

This is a quadratic equation

You can use the graph tool to visualize the x-intercepts on the graph as attached below.

x=-1 or x=3

For this case we must find the x-intersepts values of the following equation:

 [tex]y = -4x ^ 2 + 8x + 12[/tex]

Doing y = 0 we have:

[tex]0 = -4x ^ 2 + 8x + 12[/tex]

Dividing between -4 on both sides of the equation:

[tex]x ^ 2-2x-3 = 0[/tex]

We factor, we look for two numbers that when multiplied by -3 and when added by -2. These are -3 and 1:

[tex]-3 + 1 = -2\\-3 * 1 = -3\\(x-3) (x + 1) = 0[/tex]

Thus, the x-intercepts values are:

[tex]x_ {1} = 3\\x_ {2} = - 1[/tex]

Answer:

[tex]x_ {1} = 3\\x_ {2} = - 1[/tex]

Answer:

C) not isomeric because side lengths not same

Step-by-step explanation:

Isometric means that the lengths are preserved after rotation or transformation.

As we can see in the given figures that the lengths of sides of the original figure and transformed figure are are not same which means the lengths are not preserved.

So the correct answer is:

C) not isomeric because side lengths not same ..

Option: C is the correct answer.

C)   Not isomeric because side lengths not same.

Isometry--

It is a transformation which preserves the length of  the original figure i.e. it is a distance preserving transformation.

Two figures are said to be isometric if they are congruent.

By looking at the figure displaying the transformation we observe that the size of the original figure is changed.

i.e. the figure is dilated by a scale factor of 2 , since each of the sides of the polygon which is a trapezoid is increased by a factor of 2.

Hence, the transformation is not an isometry.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+2y=14\\-x+y=5&\text{\underline{multiply both sides by 2}}\end{array}\right\\\\\boxed{\underline{+\left\{\begin{array}{ccc}2x+2y=14\\-2x+2y=10\end{array}\right}}\qquad\text{add both sides of the equations}\\.\qquad\qquad4y=24\qquad\text{divide both sides by 4}\\.\qquad\qquad y=6\\\\\text{put the value of y to the second equation:}\\\\-x+6=5\qquad\text{subtract 6 from both sides}\\-x=-1\qquad\text{change the signs}\\x=1[/tex]

Answer: Its Multiplication property of Equality

Step-by-step explanation: Just did the test

Answer:

Option D is correct.

Step-by-step explanation:

We need to find that how many quarts are there in 583.7 liters.

From conversion table we geet,

1 quart = 0.95 liters

=> 1 liters = 1/0.95 quarts

=> 1 liters = 1.0526 quarts

I liter has 1.0526 quarts then 583.7 liters will have:

583.7 liters = 1.0526*583.7 quarts

583.7 liters = 614,4 quarts.

So, Option D There are 614.4 quarts in 583.7 liters. is correct.

Answer:

d

Step-by-step explanation:

Answer:

x^2

Step-by-step explanation:

given:

x^3-1/x+2

As the denominator is linear function and the highest power in numerator is x^3

So the first term in quotient is going to be x^2 to cancel first term of numerator i.e x^3!

Answer:

x^2

Step-by-step explanation:

given:

x^3-1/x+2

As the denominator is linear function and the highest power in numerator is x^3

So the first term in quotient is going to be x^2 to cancel first term of numerator i.e x^3!

The ratio you need to find is goals : games

In this case you have...

9 goals

12 games

Plug this into the ratio goal : games

9 : 12

This ratio can be further reduced to...

3 : 4

What this means in words:

A hockey player will make 3 goals for every 4 games

Hope this helped!

~Just a girl in love with Shawn Mendes

Equivalent expressions are expressions of equal values.

[tex]\mathbf{x^2 - 50x + 9}[/tex] and [tex]\mathbf{ -(-x^2 + 50x - 9)}[/tex] are equivalent expressions for the opposite of [tex]\mathbf{-x^2 + 50x - 9}[/tex]

The expression is given as:

[tex]\mathbf{f(x) = -x^2 + 50x - 9}[/tex]

To calculate the opposite, we simply negate the signs of the expression.

So, we have:

[tex]\mathbf{-f(x) = -(-x^2 + 50x - 9)}[/tex]

Expand

[tex]\mathbf{-f(x) = x^2 - 50x + 9}[/tex]

The above highlights mean that:

[tex]\mathbf{x^2 - 50x + 9}[/tex] and [tex]\mathbf{ -(-x^2 + 50x - 9)}[/tex] are equivalent expressions for the opposite of [tex]\mathbf{-x^2 + 50x - 9}[/tex]

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Final answer:

To find equivalent expressions for the opposite of the polynomial [tex]-x^2+50x-9[/tex], we change the signs of all terms to get [tex]x^2-50x+9[/tex]. Equivalent expressions may be generated by distributing a factor such as [tex](-1)(-x^2+50x-9)[/tex], but the polynomial does not factor nicely over the integers for other simplifications.

Explanation:

To find two equivalent expressions for the opposite of the polynomial [tex]-x^2+50x-9[/tex], we start by taking the opposite of the given polynomial. The opposite (or negative) of a polynomial consists of changing the sign of each term. Therefore, the opposite of the given polynomial is [tex]x^2 - 50x + 9.[/tex]

An equivalent expression can be obtained by factoring, if possible, or by using other algebraic manipulations. However, in this case, [tex]x^2 - 50x + 9[/tex] does not factor nicely over the integers. To get an equivalent expression, we can express it in different forms, such as:

Another way to express an equivalent polynomial is to add and subtract the same value within the expression, which maintains its equality.

Answer:

b) [tex]12x^2-48x+21[/tex] ; all real numbers

Step-by-step explanation:

f and g are polynomials and polynomials have domain all real numbers.

This is because when you input any number there will always be a existing output. There are no restrictions on what you can plug into a polynomial.

So the answer is either b or c.

[tex](f \times g)(x)=f(x) \times g(x)[/tex]

[tex](f \times g)(x)=(-2x+7) \times (-6x+3)[/tex]

[tex]f \times g)(x)=(-2x+7)(-6x+3)[/tex]

Let's use foil!

First: [tex]-2x(-6x)=12x^2[/tex]

Outer: [tex]-2x(3)=-6x[/tex]

Inner:  [tex]7(-6x)=-42x[/tex]

Last:  [tex]7(3)=21[/tex]

-----------------------------Add like terms:

[tex]12x^2-48x+21[/tex]

The answer is b.

Answer:

A standard deck of 52 playing cards contains four of each numbered card 2–10 and four each of aces, kings, queens, and jacks. Two cards are chosen from the deck at random.

Which expression represents the probability of drawing a king and a queen?

StartFraction (4 P 1) (3 P 1) Over 52 P 2 EndFraction

StartFraction (4 C 1) (3 C 1) Over 52 C 2 EndFraction

StartFraction (4 P 1) (4 P 1) Over 52 P 2 EndFraction

StartFraction (4 C 1) (4 C 1) Over 52 C 2 EndFraction

it is D

Step-by-step explanation:

The probability of drawing a king and a queen is 1/169.

Given,

A standard deck of 52 playing cards contains four of each numbered card 2–10 and four each of aces, kings, queens, and jacks.

Two cards are chosen from the deck at random.

We need to find which expression represents the probability of drawing a king and a queen.

A combination is used when we want to determine the number of possible arrangements in a collection of items where the order of the selection does not matter.

The formula is given by:

[tex]^nC_r[/tex] = n! / r! ( n-r)!

We have,

52 playing cards

4 kings and 4 queens.

This means we have

The probability of drawing a king and a queen is:

= probability of drawing a king x probability of drawing a queen

= ^4C_1 / ^52C_1 x  ^4C_1 / ^52C_1

= 4 / 52 x 4 / 52

= 1/13 x 1/13

= 1/169

Thus the probability of drawing a king and a queen is 1/169.

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Answer:

[tex]y'=\frac{y^2-xy\ln(y)}{x^2-xy\ln(x)}[/tex]

Step-by-step explanation:

Take natural log of both sides first.

[tex]x^y=y^x[/tex]

[tex]\ln(x^y)=\ln(y^x)[/tex]

Taking the natural log of both sides allows you to bring down the powers.

[tex]y\ln(x)=x\ln(y)[/tex]

I'm going to differentiate both sides using the power rule.

[tex](y)'(\ln(x))+(\ln(x))'y=(x)'(\ln(y))+(\ln(y))'x[/tex]

Now recall (ln(x))'=(x)'/x=1/x while (ln(y))'=(y)'/y=y'/y.

[tex]y'(\ln(x))+\frac{1}{x}y=1(\ln(y))+\frac{y'}{y}x[/tex]

Simplifying a bit:

[tex]y' \ln(x)+\frac{y}{x}=\ln(y)+\frac{y'}{y}x[/tex]

Now going to gather my terms with y' on one side while gathering other terms without y' on the opposing side.

Subtracting y'ln(x) and ln(y) on both sides gives:

[tex]\frac{y}{x}-\ln(y)=-y'\ln(x)+\frac{y'}{y}x[/tex]

Now I'm going to factor out the y' on the right hand side:

[tex]\frac{y}{x}-\ln(y)=(-\ln(x)+\frac{x}{y})y'[/tex]

Now we get to get y' by itself by dividing both sides by (-ln(x)+x/y):

[tex]\frac{\frac{y}{x}-\ln(y)}{-\ln(x)+\frac{x}{y}}=y'[/tex]

Now this looks nasty to write mini-fractions inside a bigger fraction.

So we are going to multiply top and bottom by xy giving us:

[tex]\frac{y^2-yx\ln(y)}{-xy\ln(x)+x^2}=y'[/tex]

[tex]y'=\frac{y^2-xy\ln(y)}{x^2-xy\ln(x)}[/tex]

The derivative of the implicit function [tex]x^y = y^x[/tex] is [tex]\[\frac{dy}{dx} = \frac{\ln(y) - \frac{y}{x}}{\ln(x) - \frac{x}{y}}\][/tex].

To find the derivative of the implicit function defined by [tex]\( x^y = y^x \),[/tex] follow these steps:

        [tex]\ln(x^y) = \ln(y^x)[/tex]

        y ln(x) = x ln(y)

Differentiate both sides with respect to x. Use implicit differentiation where y is considered a function of x:

        [tex]\[ \frac{d}{dx}[y \ln(x)] = \frac{dy}{dx} \ln(x) + y \cdot \frac{1}{x} \][/tex]

        [tex]\[ \frac{d}{dx}[x \ln(y)] = \ln(y) + x \cdot \frac{1}{y} \cdot \frac{dy}{dx} \][/tex]

        [tex]\[ \frac{dy}{dx} \ln(x) + \frac{y}{x} = \ln(y) + \frac{x}{y} \cdot \frac{dy}{dx} \][/tex]

Solve for [tex]\( \frac{dy}{dx} \):[/tex]

        [tex]\[ \frac{dy}{dx} \ln(x) - \frac{x}{y} \cdot \frac{dy}{dx} = \ln(y) - \frac{y}{x} \][/tex]

        [tex]\[ \frac{dy}{dx} \left(\ln(x) - \frac{x}{y}\right) = \ln(y) - \frac{y}{x} \][/tex]

        [tex]\[ \frac{dy}{dx} = \frac{\ln(y) - \frac{y}{x}}{\ln(x) - \frac{x}{y}} \][/tex]

Answer:

Step-by-step explanation:

The input-output table can be made by putting value of x and finding the value of f(x)

f(x) = 3x^2-x+4

f(0) = 3(0)^2-0+4 = 0-0+4 = 4

f(1) = 3(1)^2-1+4 = 3-1+4 = 2+4 =6

f(2) = 3(2)^2-2+4 = 3(4)-2+4 = 12-2+4 = 10+4 = 14

f(3) = 3(3)^2-3+4 = 3(9)-3+4 = 27-3+4 = 24+4 = 28

So put value of x and find f(x) and fill the input-output table.

x  f(x)

0   4

1    6

2   14

3    28

Answer:

Piston displacement = 84.8

Step-by-step explanation:

We will find the volume of the cylinder in order to find the piston displacement.

Here, (bore = diameter, so r = diameter/2) (height = stroke)

Volume = [tex] \pi r^2h[/tex] [tex]=3.14\times1.5^2\times 3[/tex] = 21.2 cubic units

Since the engine has 4 cylinders, so we will multiply the piston displacement by 4 to get:

Piston displacement = [tex]21.2 \times 4[/tex] = 84.8

The total piston displacement for a 4-cylinder engine with a bore and stroke of 3 inches can be calculated using the formula: pi/4 * bore^2 * stroke * number of cylinders. For this example, it is approximately 113.097 cubic inches.

To calculate the total piston displacement, we use the formula for the displacement of a single cylinder, which is pi/4 * bore^2 * stroke * number of cylinders.

In this scenario, the bore and stroke are both 3 inches and it's a 4-cylinder engine. Therefore, we plug in these values into the formula.

So, the total displacement is pi/4 * (3inch)^2 * 3inch * 4. This calculates to approximately 113.097 cubic inches.

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Answer:

10.2 kilograms

Step-by-step explanation:

You do the equation,  1.4kg+5kg+3.8kg​ and that is = to 10.2 kg

Hope that helped you :)

Good luck :))

Answer: 11.2 kg

Step-by-step explanation: Add the weights.

1.4+5+3.8=11.2

The total weight is 11.2 kg.

thats easy it is 4

Hope this helps:)

Answer: I believe the answer is B.

Although, if the answer to this question isn't B, it should defiantly be C.

Answer:

The correct option is B.

Step-by-step explanation:

The graph of f(x) is g(x) is given.

Graph of both functions intersect each other at a point. Before the point of intersection g(x)>f(x) and after the point of intersection g(x)<f(x).

The graph of f(x) will eventually exceed the graph of g(x). Therefore the correct option is B.

Function g(x)<f(x) for the large value of x, So option A is incorrect.

From the given graph it is clear that the y-intercept of f(x) is 0.2 and y-intercept of g(x) is 2.

So, option C and D are incorrect.

Answer:

79.67479675 %

Step-by-step explanation:

To find the percentage take the correct amount over the total amount, then multiply by 100

98/123 * 100

79.67479675 %

Answer:

the answer is 79.64%

Step-by-step explanation:

A/B=P/100

98/123=p/100

9800/123=123p/123

p=79.64%

Answer:

Josh has 29 coins.

Step-by-step explanation:

Let Terry have x coins then Josh has x + 12 coins.

Together they have x + x + 12 coins so we can form the equation:

x + x + 12 = 46

2x + 12 = 46

2x = 46 - 12 = 34

x = 17, so Terry has 17 coins and Josh has 17 + 12 = 29 coins.

Answer:

The answer is C

Step-by-step explanation:

Use the method of elimination

First rearrange the first equation to look like the second

[tex]2x + 3y = 17 \\ 4x + 6y = 34 \\ - 4x - 6y = - 34[/tex]

Next add the two equations together eliminating the y term.

[tex] - 4x - 6y = - 34 \\ 3x + 6y = 30 \\ \\ - x = - 4 \\ x = 4[/tex]

There's only one answer with x = 4 so you're done. To go further, substitute x = 4 into the second equation and solve for y

[tex]3x + 6y = 30 \\ 3 \times 4 + 6y = 30 \\ 12 + 6y = 30 \\ 6y = 18 \\ y = 3[/tex]

Answer:

c

Step-by-step explanation:

Answer: There were 7 groups.

Step-by-step explanation:

43 + 13 = 56

56/8 = 7

Answer: 7 groups.

Step-by-step explanation: Add the new and the only players.

43+13=56

Divide this number by 8.

56/8=7

There are 7 groups.

We found the values of the function f(x) at points 1 and 3 and compared them. It's found that the value of f(1) is significantly larger than the value of f(3), hence the third statement is true.

To answer your question, we need to substitute 1 and 3 into the function f(x)=-2x^2+3x+10, respectively. So:

For f(1), we get -2*1^2 + 3*1 + 10 = -2 + 3 + 10 = 11.

For f(3), we get -2*3^2 + 3*3 + 10 = -18 + 9 + 10 = 1.

Therefore, we can clearly see that the value of f(1) is larger than the value of f(3), meaning the third statement is true.

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For this case we must find the solutions of the following equation:

[tex]4x ^ 2-x + 9 = 0[/tex]

We apply the cudratic formula:

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

Where:

[tex]a = 4\\b = -1\\c = 9[/tex]

Substituting:

[tex]x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (4) (9)}} {2 (4)}\\x = \frac {1 \pm \sqrt {1-144}} {8}\\x = \frac {1 \pm \sqrt {-143}} {8}[/tex]

Thus, the complex roots are:

[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]

Answer:

[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]

Answer:

the two expressions are equivalent.

Step-by-step explanation:

We know that f(x)= 3x-7 and g(x)= -2x+5, therefore:

f(x) - (-g(x)) = 3x-7 - ( +2x-5) = 3x - 7 - 2x + 5 = x -2

f(x) + g(x) = 3x-7 -2x + 5 = x - 2

Therefore,  f(x) - (-g(x)) is equivalent to f(x) + g(x).

Another way to check that the two expressions are equivalent is by solving the parenthesis:

f(x) - (-g(x)) →  f(x) + g(x)

Therefore, the two expressions are equivalent.

The system of equation will have one solution.

The correct answer is an option (B)

It is a collection of one or more linear equation involving the same variable.

For given question,

Two equations have negative reciprocal slope .

Which means if one equation have slope = m

then slope of other equation will be = -1/m

This means, both the lines are perpendicular to each other , hence both the lines must be intersecting each other at one point.

In system of equation , the solution of the two equation is the point where they intersect .

Since, both the lines are intersecting at one point . Hence, it will have only one solution.

Therefore, the correct answer is an option b) the system will have one solution

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Answer: 1.25

Step-by-step explanation:

x=2/1.6

x=1.25

Answer:

x = 1.25

Step-by-step explanation:

Divide 1.6 on both sides to isolate x. 2 ÷ 1.6 = 1.25, so x = 1.25

Answer:

8000

Step-by-step explanation:

The value of 8 in this number is 80, so you multiply that by to get 8000.

I am joyous to assist you.

Answer:

24 students

Step-by-step explanation:

So we started with 32 cups of juice.

Kahled drunk 2 cups so (32-2)=30 cups is left.

If x represents the number of students he receive juice and each student gets the same amount of juice which is 1.25 cups, then we have the equation

1.25x=30 to solve for x.

Divide both sides by 1.25:

x=30/1.25

x=24

24 students receive juice

Answer:

y=-5x-58

Step-by-step explanation:

The equation of a line in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

Perpendicular lines have opposite reciprocal slopes.

Anyways we need to find the slope of the line going through (10,6) and (5,5).

To find the slope, we are going to line up the points vertically and subtract vertically, then put 2nd difference over 1st difference. Like so:

 (  10   ,   6)

- (   5   ,   5)

------------------

    5         1

So the slope of the line through (10,6) and (5,5) is 1/5.

The slope of a line that is perpendicular will be the opposite reciprocal of 1/5.

The opposite reciprocal of 1/5 is -5.

The line we are looking for is y=-5x+b where we need to find the y-intercept b.

y=-5x+b goes through (-10,-8)

So we can use (x,y)=(-10,-8) to find b in y=-5x+b.

y=-5x+b with (x,y)=(-10,-8)

-8=-5(-10)+b

-8=50+b

Subtract 50 on both sides:

-8-50=b

-58=b

So the equation is y=-5x-58

Answer:

A

Step-by-step explanation:

A translation of 6 units down means subtract 6 from the original y- coordinates while the x- coordinates remain unchanged, that is

(4, 2 ) → (4, 2 - 6 ) → (4, - 4 )

(- 2, 2 ) → (- 2, 2 - 6 ) → (- 2, - 4 )

Answer:

Step-by-step explanation:

[tex]f(x)=\left\{\begin{array}{ccc}x+4&if&-4\leq x<3\\2x-1&if&3\leq x<6\end{array}\right\\\\\text{The domain of a function is a set of x's}.\\\\\text{We have}\\\\-4\leq x<3\to x\in[-4,\ 3)\\3\leq x<6\to x\in[3,\ 6)\\\\\text{The domain:}\ [-4,\ 3)\ \cup\ [3,\ 6)=[-4,\ 6)[/tex]

Answer:

C (X,Y)->(X-4,×-5) I would say bro