Which line has a slope of LaTeX: \frac{1}{2}12and goes through the point (2, 4)?

Answer:

[tex]x^{4}[/tex] - 10x³ + 37x² - 60x + 36

Step-by-step explanation:

Given

(x - 3)²(x - 2)² ← expand each factor using FOIL

(x - 3)² = x² - 6x + 9

(x - 2)² = x² - 4x + 4

We now have the product

(x² - 6x + 9)(x² - 4x + 4)

Each term in the second factor is multiplied by each term in the first factor, that is

x²(x² - 4x + 4) - 6x(x² - 4x + 4) + 9(x² - 4x + 4) ← distribute each parenthesis

= [tex]x^{4}[/tex] - 4x³ + 4x² - 6x³ + 24x² - 24x + 9x² - 36x + 36

Collect like terms

= [tex]x^{4}[/tex] - 10x³ + 37x² - 60x + 36

Answer:

6

Step-by-step explanation:

362/60

362 is the miles per hour

60 is the minutes in an hour

Answer:

Step-by-step explanation:

(x+7)(x-5)

You need to find two numbers that multiply to make -35, but summed together make +2.  Thus +7 and -5 are your only options here.

Answer:

(x-5) (x+7)

Step-by-step explanation:

x^2 + 2x − 35

What two numbers multiply to -35 and add to 2

-5 *7 = -35

-5+7 =2

(x-5) (x+7)

Answer:

10

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

3x^2

Step-by-step explanation:

First lets simplify what is inside the square root

300x8

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

27x12

3 * 100 x^8

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

3 *9 x^12

The 3's cancel  and we know a^b/ a^c = a^(b-c)

100/9 x^ (8-12)

100/9 x^-4

sqrt( 100/9 x^-4)

Put the negative exponent in the denominator and make it positive

sqrt( 100 / (9x^4) )

We know that sqrt( a / b) = sqrt(a) / sqrt( b)

sqrt(100)

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

sqrt( 9x^4)

10

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

3x^2

Answer:

The measure of minor arc BC is 176°

Step-by-step explanation:

we know that

The semi-inscribed angle is half that of the arc it comprises.

so

∠B=(1/2)[minor arc BC]

substitute

88°=(1/2)[minor arc BC]

minor arc BC=176°

mayor arc BC=360°-176°=184°

Answer:

x= 0   x=2

Step-by-step explanation:

x^2 − 2x = 0

Factor out an x

x(x-2) =0

Using the zero product property

x =0  x-2 =0

x= 0   x=2

ANSWER

Commutative property of addition.

EXPLANATION

Let a,b be real numbers. The commutative property of addition states that,

[tex]a + b = b + a[/tex]

If we let a=-10 and b=6, then

[tex]-10+6=6+(-10)[/tex]

Therefore the given expression demonstrates the commutative property of addition.

The commutative property of addition tells us that, the order in which we add two real numbers does not affect the result.

Answer:

Jesse will spend 0.68$ for 1.3 lbs of lettuce. Jesse will spend about 0.46$ on a single head of lettuce.

Step-by-step explanation:

Answer:

$0.68 for 1.3 pounds of lettuce

$0.46

Step-by-step explanation:

Multiply .52 by 1.3 since its $0.52 per pound,

0.52*1.32 - 0.676

Since its money round to the nearest cent, so its $0.68

1 pound = 16 ounces

So first you have to find how much it costs for 1 ounce.

So divide 0.52 by 16

0.52/16 = 0.0325 for one ounce

Then multiply 0.0325 by 14 since its 14 ounces.

0.0325*14 = 0.455

Then round to the nearest cent since its money, so its $0.46

Answer:

A = 2000 e^(0.03 t)

The account will have $2255  after 4 years

Step-by-step explanation:

* Lets talk about the compound continuous interest

- Compound continuous interest can be calculated using the formula:

  A = P e^rt

# A = the future value of the investment, including interest

# P = the principal investment amount (the initial amount)

# r = the interest rate  

# t = the time the money is invested for

- The formula gives you the future value of an investment,  which is  

  compound continuous interest plus the  principal.  

- If you want to calculate the compound interest only, you need

 to deduct the principal from the result, So, your formula is:

 Compounded interest only = Pe^(rt)  - P

* Now lets solve the problem

-  Ira invests $2,000 in an account

∵ P = $ 2000

- That account has an interest rate of 3%

∵ r = 3/100 = 0.03

- It is compounded continuously

∵ The equation of the compounded continuously is A = P e^rt

∴ A = 2000 e^(0.03 t)

- We want to find the money in the account after 4 years

∵ t = 4

∴ A = 2000 e^(0.03 × 4) = $2254.99 ≅ $2255

* The account will have $2255  after 4 years

Answer:

The correct answer option is B. Point X.

Step-by-step explanation:

We are given a graph where two triangles, a fixed point X and an arc is shown and we are to determine the center of rotation in it.

Center of rotation is basically a fixed point on a plane or a graph about which and figure rotates. It acts like a pivot in a door.

So here. we can see that point X is the center of rotation about which the vertex of a triangle is rotated 90° counterclockwise, forming an arc.

Answer:

* The equation of the median of the trapezoid is 10x + 6y = 39

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) , (x2 , y2) is

  [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- The mid point of the line whose end point are (x1 , y1) , (x2 , y2) is

  [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

- The standard form of the linear equation is Ax + BC = C, where

  A , B , C are integers and A , B ≠ 0

- The median of a trapezoid is a segment that joins the midpoints of

 the nonparallel sides

- It has two properties:

# It is parallel to both bases

# Its length equals half the sum of the base lengths

* Lets solve the problem

- The trapezoid has vertices R (-1 , 5) , S (! , 8) , T (7 , -2) , U (2 , 0)

- Lets find the slope of the 4 sides two find which of them are the

 parallel bases and which of them are the non-parallel bases

# The side RS

∵ [tex]m_{RS}=\frac{8-5}{1 - (-1)}=\frac{3}{2}[/tex]

# The side ST

∵ [tex]m_{ST}=\frac{-2-8}{7-1}=\frac{-10}{6}=\frac{-5}{3}[/tex]

# The side TU

∵ [tex]m_{TU}=\frac{0-(-2)}{2-7}=\frac{2}{-5}=\frac{-2}{5}[/tex]

# The side UR

∵ [tex]m_{UR}=\frac{5-0}{-1-2}=\frac{5}{-3}=\frac{-5}{3}[/tex]

∵ The slope of ST = the slop UR

∴ ST// UR

∴ The parallel bases are ST and UR

∴ The nonparallel sides are RS and TU

- Lets find the midpoint of RS and TU to find the equation of the

 median of the trapezoid

∵ The median of a trapezoid is a segment that joins the midpoints of

   the nonparallel sides

∵ The midpoint of RS = [tex](\frac{-1+1}{2},\frac{5+8}{2})=(0,\frac{13}{2})[/tex]

∵ The median is parallel to both bases

∴ The slope of the median equal the slopes of the parallel bases = -5/3

∵ The form of the equation of a line is y = mx + c

∴ The equation of the median is y = -5/3 x + c

- To find c substitute x , y in the equation by the coordinates of the

  midpoint of RS  

∵ The mid point of Rs is (0 , 13/2)

∴ 13/2 = -5/3 (0) + c

∴ 13/2 = c

∴ The equation of the median is y = -5/3 x + 13/2

- Multiply the two sides by 6 to cancel the denominator

∴ The equation of the median is 6y = -10x + 39

- Add 10x to both sides

∴ The equation of the median is 10x + 6y = 39

* The equation of the median of the trapezoid is 10x + 6y = 39

Answer:

=36.0

Step-by-step explanation:

We use the sine rule to find the missing sides as follows;

Lets find the missing angle C by using the summation of interior angles in a triangle.

C=180-(44+48)

=88°

Then,

a/Sin A=c/Sin C

25/Sin 44=c/Sin 88

c=(25 Sin 88)/Sin 44

c=35.97

The side c=36.0 to the nearest tenth.

Answer:

36.0

Step-by-step explanation:

Natasha could have 9 red apples and 4 green apples, or 10 red apples and 3 green apples.

To determine the number of red and green apples Natasha could have, we need to consider the given information. Natasha has a total of 13 apples, and she has more red apples than green apples.

Let's assume that Natasha has r red apples and g green apples. We know that r + g = 13, since she has a total of 13 apples.

Given that she has more red apples than green apples, we can say that r > g.

Now, we need to find the possible values of r and g that satisfy these conditions. We can use trial and error to find the values that work:

Based on our analysis, Natasha could have either 9 red apples and 4 green apples, or 10 red apples and 3 green apples.

Answer:

There is no clear correlation between apple eaten per week and the times sick per year.

Step-by-step explanation:

The person who ate 7 apples got sick the same amount as the person who ate 0 apples did. When you graph the points, there's no clear correlation between the apples and the sick times

russin agree with other peson

Answer:

Step-by-step explanation:

The formal definition of a common difference is d = a_(n + 1) - a_n)

so

d = ?

a_(n+1) = a_2 = 14

a_n      = a_1 = 24

d = 14 - 24

d = - 10

-10

In the question, it is asking you to find the common difference between the numbers 24, 14, 4,...

In order to find the common difference between the numbers, we would nee to find the change between them.

In other words, we need to find out how much it's changing by between each number.

When you look at the sequence 24, 14, 4, you would know that it is decreasing each time. This means that the common difference would be a negative number.

Now, we need to figure out how much it is decreasing by.

When you subtract 24 and 14, [tex]24-14=10[/tex], you would get 10. When you subtract 24 by 10, you would get 14. So we know that the difference would be -10.

We can also check the next number. When you subtract 14 by 4, [tex]14-4=10[/tex], you would get 10. Then, when you subtract 14 by 10, you would get 4.

This means that the common difference of the sequence is -10

Answer:

The volume is 36 inches cubed.

Step-by-step explanation:

The volume of a rectangular prism is W*L*H.

You are given the H=3i, W=2 in, and L=6 in.

So now we plug into our formula for the volume of a rectangular prism which will result in 2*6*3=12*3=36.

The volume is 36 inches cubed.

Answer: [tex]36\ in^3[/tex]

Step-by-step explanation:

The volume of a rectangular prism can be calculated with this formula:

[tex]V=lwh[/tex]

Where "l" is the lenght, "w" is the width and "h" is the height.

In this case we know that this rectangular solid is 3 inches high, 6 inches long and 2 inches wide. Then:

[tex]h=3\ in\\l=6\ in\\w=2\ in[/tex]

Then, substituting these values into the formula, we get that its volume is:

[tex]V=(6\ in)(2\ in)(3\ in)\\\\V=36\ in^3[/tex]

Answer:

The correct options are A and B.

Step-by-step explanation:

Given information: ΔABC≅DEF

Corresponding parts of congruent triangle are congruent (CPCTC).

The corresponding angles of both triangles are congruent.

[tex]\angle A\cong \angle D[/tex]

[tex]\angle B\cong \angle E[/tex]

[tex]\angle C\cong \angle F[/tex]

The corresponding side of both triangles are congruent.

[tex]\angle AB\cong \angle DE[/tex]

[tex]\angle BC\cong \angle EF[/tex]

[tex]\angle AC\cong \angle DF[/tex]

Therefore the correct options are A and B.

The congruencies that are true are;

A. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DE}[/tex], and B. ∠C ≅ ∠F

The reason the selected options are correct is given as follows;

Known parameter;

ΔABC ≅ ΔDEF (Change of ~ to ≅ based on complete question accompanying screen grab as posted online)

CPCTC is the acronym for Congruent Parts of Congruent Triangles are Congruent

Required: To select the congruences that are true

Solution:

By observation, the height of ΔABC is equal to the height of ΔDEF, therefore;

∠C and ∠F are angles located in corresponding parts of both triangles

While the other options; ∠E and ∠C, ∠A and ∠E, [tex]\overline{AB}[/tex] and [tex]\overline{DF}[/tex], and [tex]\overline{AC}[/tex] and [tex]\overline{DE}[/tex] are not corresponding parts and they are therefore not congruent

The congruencies that are true are; A. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DE}[/tex], and B. ∠C ≅ ∠F

Learn more about CPCTC here:

https://brainly.com/question/1805755

Answer: 1/6

Step-by-step explanation: There are 9 marbles in total. There are 3 red marbles out of 9, and the fraction is 3/9, simplified to 1/3. Since the marble is not being replaced, there are now 8 marbles. 4 of the 8 marbles are blue. The fraction is 4/8, simplified to 1/2. Multiply the fractions.

1/3 x 1/2 = 1/6

There’s a 1/6 chance.

Answer:

i) sin(2x) = [tex]-\frac{\sqrt{3}}{2}[/tex]

ii) cot(x+360) = [tex]-\frac{\sqrt{3}}{3}[/tex]

iii) sin(x-180) = [tex]\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

sec(x) = 2

Since cos(x) is reciprocal of sec(x), this means:

cos(x) = [tex]\frac{1}{2}[/tex]

cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.

Part i)

sin(2x) can be simplified as:

sin(2x) = 2 sin(x) cos(x)

First we need to find the value of sin(x). According to Pythagorean identity:

[tex]sin^{2}(x)=1-cos^{2}(x)\\\\ sin(x)=\pm \sqrt{1-cos^{2}(x)}[/tex]

Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:

[tex]sin(x)=- \sqrt{1-cos^{2}(x)}\\\\ sin(x)=-\sqrt{1-(\frac{1}{2})^{2}}\\\\ sin(x)=-\frac{\sqrt{3}}{2}[/tex]

So,

[tex]sin(2x)=2 \times -\frac{\sqrt{3} }{2} \times \frac{1}{2}\\\\ sin(2x)=-\frac{\sqrt{3}}{2}[/tex]

Part ii)

We have to find cot(x + 360)

An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.

cot(x + 360) = cot(x)

[tex]cot(x) = \frac{cos(x)}{sin(x)}\\[/tex]

Using the values, we get:

[tex]cot(x)=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2} }\\\\ cot(x)=-\frac{\sqrt{3}}{3}[/tex]

Part iii)

We need to find the value of sin(x - 180)

sin(x - 180) = - sin(x)

Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.

So,

sin(x - 180) = [tex]-(-\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}[/tex]

Answer:

You can divide the numerator by the denomintor, then you move the decimal two places to the right.

Step-by-step explanation:

For example, say you want to turn 1/2 into a percent. You do 1 divided by 2. Which would give you 0.5. Next, you move the decimal two spaces to the right. All you have to do next is to add the percent sign. 50%

Answer:

Factored form...

Step-by-step explanation:

Foil out (x-4)(x+2)=16

First: x*x=[tex]x^{2}[/tex]

Outer: 2*x=2x

Inner: -4*x = -4x

Last: -4*2 = -8

Combine them all:

[tex]x^2+2x-4x-8=16[/tex]

Simplify:

[tex]x^2-2x-8=16\\x^2-2x-24=0[/tex]

What multiplies together to make -24 but adds together to make -2?

Lets list the factors of -24 to decide:

1 x -24

2 x -12

3 x -8

4 x -6

-6+4 = -2

Therefore...

[tex](x-6)(x+4)=0[/tex]

Answer:

3rd statement

Step-by-step explanation:

Lets go through the choices and see.

The first one says:

The equation x – 4 = 16 can be used to solve for a solution of the given equation.

If we solve this we get x=20. I just added 4 on both sides.

Is 20 a solution thr original equation? Let's check. We need to replace x with 20 in

(x – 4)(x + 2) = 16 to check.

(20-4)(20+2)=16

(16)(22)=16

16 times 22 is definitely not equal to 16 so the first statement is false.

Lets check option 2:

The standard form of the equation is

x2 – 2x – 8 = 0.

So lets put our equation in standard form and see:

(x – 4)(x + 2) = 16

Foil is what we will use:

First: x(x)=x^2

Inner: (-4)x=-4x

Outer: x(2)=2x

Last: -4(2)=-8

Add together to get: x^2-2x-8. We still have the equal 16 part.

So the equation is now x^2-2x-8=16. Subtracting 16 on both sides will put the equation in standard form. This gives us

x^2-2x-24=0. This is not the same as the standard form suggested by option 2 in our choices.

Checking option 3:

This says:

The factored form of the equation is

(x + 4)(x – 6) = 0.

So we already put our original equation in standard form. Lets factor our standard form and see if is the same as option 3 suggests.

To factor x^2-2x-24, we need to find two numbers that multiply to be -24 and add to be -2. These numbers are 4 and -6 because 4(-6)=-24 and 4+(-6)=-2. So the factored form of our equation is (x+4)(x-6)=0 which is what option 3 says. So option 3 is true.

Let's go ahead and check option 4: It says: One solution of the equation is x = –6. This is false because solving (x+4)(x-6)=0 gives us the solutions x=-4 and x=6. Neither one of those is -6. *

* I solved (x+4)(x-6)=0 by setting both factors equal to zero and solving them for x. Like so,

x+4=0 or x-6=0.

Answer:

reflected

Step-by-step explanation:

ΔXYZ was dilated, then reflected, to create ΔQAG.

Answer:

(x - 5)(x - 3)

Step-by-step explanation:

You need two numbers that multiply to 15 and add to 8. There aren't many numbers that will do that.

15 and 1 is one pair of numbers. They multiply to 15 but don't add to 8.

6 and 2 add to 8 but don't multiply to 15.

5 and 3. This in some form is your answer, but handle it carefully.

(x - 5)(x - 3)

The 5 and 3  both have to be minus.

Answer:

(x-3)(x-5)

Step-by-step explanation:

The expression is:

x2 - 8x+15

Break the middle term:

Coefficient of first term will be multiplied by constant

1*15 = 15

Now we have to find out which numbers will be multiplied to get 15

and also by adding those numbers we get the middle term:

3*5=15

3+5 = 8

Now break the middle term:

x^2-3x-5x+15

x(x-3)-5(x-3)

(x-5)(x-3)....

The factors are (x-5)(x-3)....

Answer: I need a picture off the pool and measurements.

Step-by-step explanation: I need this in order to figure out the problem and give you a helpful answer.

Answer:

Width or length

Step-by-step explanation:

Cavalieri's Principle states that in two solids with equal altitude, if the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal.

So, if Bailey's pool section is half her friend's pool, then the new volume would be half of the original.  To do that, she can half width or length

Answer:

I would recommend using algebraic methods.

Step-by-step explanation:

Of course, guess and check takes a long time and is not very time efficient. If you're graphing it by hand, it'll take time and get tedious, and using algebraic methods will probably give you the most accurate answer. If you have access to a graphing calculator or graphing website like Desmos, then I would suggest using the program to check the answers you got using the algebraic methods.

Hope this helped :)

Answer:

iii) Use algebraic methods

Step-by-step explanation:

There are various method of finding an accurate solution to a system of linear equations.

They are i) graphing method:  ii) algebraic method:  iii) Matrices method:

iv) determinant method:  v) guess method vi) Cramer's rule etc

Guess and check is not reliable because guess is possible only for integers or  numbers with 1 or 2 decimals. SOmetimes guess may give unreliable results.  And every time after the guess, checking and verifying will be time consuming and laborious

Graphing the lines may be accurate but writing tables for each line, choosing scales and drawing lines to find points of intersection may be time consuming.

Algebraic methods using are easy to understand, reliable, and less time consuming but 100% accuracy. There are a number of ways in algebraic method also such as substitution, elimination or cross

Answer:

15 - n/3 = 20

n = -15

Step-by-step explanation:

Decreased means subtract

15 -

quotient means divide

15 - n/3

Is means equals

15 - n/3 = 20

To solve subtract 15 from both sides

15-15 - n/3 = 20-15

-n/3 = 5

Multiply each side by -3

-3 * (-n/3) = 5*-3

n = -15

Answer:

h(x) = 6x² - 10x - 4

Step-by-step explanation:

f(x)g(x) = (2x - 4)(3x + 1)

Each term in the second factor is multiplied by each term in the first factor

2x(3x + 1) - 4(3x + 1) ← distribute both parenthesis

= 6x² + 2x - 12x - 4 ← collect like terms

= 6x² - 10x - 4

To find h(x), which is the product of f(x) and g(x), one must perform a binomial multiplication. The resulting function after simplification is h(x) = 6x² - 10x - 4.

The student is asking for the product of two functions, f(x) and g(x), defined as F(x)=2x-4 and G(x)=3x+1 respectively. To find the new function h(x), which is the result of multiplying f(x) and g(x) together, we use the following process:

h(x) = f(x) × g(x)

This translates into h(x) = (2x - 4)(3x + 1). We need to perform a binomial multiplication (also known as FOIL - First, Outside, Inside, Last) to combine these two expressions.

Applying binomial multiplication, we get:

Combining these terms, we get the final expression for h(x):

h(x) = 6x² + 2x - 12x - 4

Simplifying further:

h(x) = 6x² - 10x - 4

Answer:

Jamal is 12 and his mother is 36

Step-by-step explanation:

12 times 3 is going to be 36. Then after 12 years, Jamal will be 24 and Jamal's mother will be 36+12 which is 48. Comparing 24 to 48, 48 is double 24 which means that 48 is two times greater than 24, (putting it in terms of the question).

Answer:

Jamal is 12 and his mom is 36

Step-by-step explanation:

If Jamal is 12 right now and you multiply that by three, you get 36. But since he's going to be half of her age in 12 years. So if you add 12 to 12 you get 24 for Jamal and if you add 12 to 36 you get 48 for his mom. This makes her age exactly double Jamal's age.

Answer:

Step-by-step explanation:

The domain is (-5, infinity).  There's no graph for x ≤ -5.

The range is [2, infinity).

Answer:

C. The domain is [-k, ∞), and the range is [C, ∞).

Step-by-step explanation:

To be able to answer this question we first need to understand what exactly are the domain and range of a function. Domain and Range can be defined as the following,

Domain: are all the possible input values a function can recieve, displayed as the x-coordinates on a graph.

Range: are all the possible output values that a function can spit out, displayed as the y-coordinates on a graph.

With this understood, we can look at the graph and easily point out the domain and range as the following values.

Domain being [-5,∞) ..... closed bracket because the value is included

Range being [2, ∞) ..... infinity values always take an open parenthesis

Based on this information we can safely assume the answer is C. The domain is [-k, ∞), and the range is [C, ∞).

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.