Line AB contains points A (3, −2) and B (1, 8). The slope of line AB is

−5
negative 1 over 5
1 over 5
5

Answer:

x-axis only.

Step-by-step explanation:

2x = 5y2 - 3

Convert to vertex form:

x = 5/2 y^2 - 3/2

This is a parabola  with axis of symmetry  y = 0. The vertex is at (-3/2, 0) and it opens to the right.

The axis of symmetry is the x-axis ( y = 0).

The equation 2x = 5y2 - 3 is only symmetric with respect to the x-axis but not the y-axis or the origin.

To test an equation for symmetry with respect to the x-axis, you would replace 'y' with '-y' and see if the equation remains the same. For symmetry with respect to the y-axis, you'd replace 'x' with '-x'. For origin symmetry, you would replace 'x' with '-x' and 'y' with '-y'

Applying this to your equation, 2x = 5y2 - 3:

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Answer:

55

Step-by-step explanation:

Assuming she deposited the same amount each month.

Total ÷ Months = Amount Deposited Each Month

1,320 ÷ 24 = 55

Answer:

x=-1

Step-by-step explanation:

2x -2= -4

2x = -2

x = -1

Answer:

-1

Step-by-step explanation:

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I hope this answer helps! :D

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Answer:

5.6

Step-by-step explanation:

If there is 70 percent of chocolate milk in the fridge and she holds 0.125 in each canister and divide and get 5.6 then turn that back into a fraction which should be easy.

Ana can fill exactly 5 full glasses of chocolate milk with her 7/10 of a liter, as each glass holds 1/8 of a liter. The calculation involves simple fraction division and the realization that 56/10 simplifies to 5 3/5, indicating the number of full glasses.

The question is about determining how many glasses of chocolate milk Ana can fill from the amount she has in her refrigerator. Since each glass holds 1/8 of a liter and Ana has 7/10 of a liter of chocolate milk, we need to calculate how many 1/8 liter portions make up 7/10 of a liter. To find this, we can set up a division:

[tex]\(\frac{7/10}{1/8}\)[/tex].

To divide fractions, we multiply by the reciprocal of the divisor:

[tex]\(\frac{7/10}{1} \times \frac{8}{1}\) = \(\frac{56}{10}\).[/tex]

Now we simplify the resulting fraction:

[tex]\(\frac{56}{10}\)[/tex] simplifies to [tex]\(5 \frac{3}{5}\)[/tex].

So, Ana can fill 5 full glasses of chocolate milk and will have some milk left over.

Answer:

Part 1) The expression is [tex]24n[/tex]

Part 2) The value is [tex]115.2[/tex]

Step-by-step explanation:

Part 1) Find the expression

Let

n -----> the number

we know that

The algebraic expression of the phrase "The product of 24 and a number"  is equal to multiply the number by 24

so

[tex]24n[/tex]

Part 2) Find the value of the product when n=4.8  

substitute the value of n in the algebraic expression

[tex]24(4.8)=115.2[/tex]

Answer: It's C i got it right on edge

Step-by-step explanation:

Answer:

The solution is the point (-12,8)

Step-by-step explanation:

we have

-x-y=4 ----> equation A

x+2y=4 ----> equation B

Adds equation A and equation B and solve for y

-x-y=4

x+2y=4

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

-y+2y=4+4

y=8

Find the value of x

x+2y=4

x+2(8)=4

x=4-16

x=-12

therefore

The solution is the point (-12,8)

Answer:

The positive difference between the a values is 0.5

Step-by-step explanation:

we know that

Both parabolas cross the x axis at (-4,0) and (6,0)

so

The general equation is

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

Find the value of a in the first parabola

The y-intercept is (0,-12)

so

For [tex]x=0, y=-12[/tex]

substitute

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

[tex]-12=a(0+4)(0-6)[/tex]

[tex]-12=a(-24)[/tex]

[tex]a=0.5[/tex]

Find the value of a in the second parabola

The y-intercept is (0,-24)

so

For [tex]x=0, y=-24[/tex]

substitute

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

[tex]-24=a(0+4)(0-6)[/tex]

[tex]-24=a(-24)[/tex]

[tex]a=1[/tex]

Find the positive difference between the a values for the two functions

so

[tex]1-0.5=0.5[/tex]

0.5

Step-by-step explanation:

Answer:

the answer is -14

Step-by-step explanation:

3x - 2y

3(2)-2(10)

6-20

6+-20

-14

The value of 3x - 2y when x = 2 and y = 10 is -14

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. f(x) < 0

Interval of the domain where the graph is below the x-axis

because the negative regions of a function compromises those intervals where the function lies below the x-axis

2. x-intercept

Location on graph where output is zero

because when we find x-intercept we put y=0

3. y-intercept

Location on graph where input is zero

because when we find y-intercept we put x=0

4. f(x) > 0

Interval of the domain where the graph is above the x-axis

because the positive regions of a function compromises those intervals where the function lies above the x-axis

Answer:

x ≈ 56.7°

Step-by-step explanation:

Since the triangle is right use the sine ratio to solve for x

sin x° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{66}{79}[/tex], hence

x = [tex]sin^{-1}[/tex] ( [tex]\frac{66}{79}[/tex] ) ≈ 56.7°

Answer:

x = 56.7

Step-by-step explanation:

Answer:

(a+2) Is your answer

Step-by-step explanation:

You could try synthetic division, but it's pretty complicated (not to mention for much harder problems), so you should try factoring this. What two numbers multiply up to 10 and add up to 7? Using trial and error, we would find these two numbers to be 2 and 5. Therefore, it factors into (a+5)(a+2).

Answer:

2

Step-by-step explanation:

Answer:

Option A and C are correct

Step-by-step explanation:

A polynomial is defined as an algebraic expression that consists of variables and constants involving operations of addition, subtraction, multiplication and non-negative exponents.

A. 4x^2+9x+12 is a polynomial

B. 3-√2x is not a polynomial

C. 15x^4 is a polynomial

D. 6x^2+2/x is not a polynomial

So, Option A and C are correct.

Answer: Option A and Option C

Step-by-step explanation:

Polynomials always have the following form:

[tex]ax ^ n + bx ^{n-1} + cx^{n-2} +...+ d[/tex]

Where a, b, c, and d are constant and are real numbers

The exponents of the variable x are always greater than or equal to zero.

Then identify among the options the expressions that have these characteristics

The answer are:

Option A.

[tex]4x^2 +9x+12[/tex]

Option C.

[tex]15x^4[/tex]

Check the picture below.

bearing in mind that ⌈some expression⌉ means "ceil" or the ceil() function, which means any number in between one integer and the next, "ceils" or gets bumped up to the next integer.

namely for example, for y = ⌈x⌉ will yield

y(0.5) = 1

y(0.7) = 1

y(0.0000001) = 1

y(3.0000001) = 4

y(-2.000001) = -2

y(-5.00001) = -5

and so on

the same is true btw for the y = ⌊x⌋ or the "floor" floor() function, but it "floors" or drops down instead.

y(0.5) = 0

y(3.9999999) = 3

y(-5.0000001) = -6

and so on.

in this case is y = 4⌈x⌉, so any values in between each integer for "x" gets bumped up.

The graph which represents the given function is first graph.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given a function,

f(x)=4[x]

The step function [x] is defined as the piecewise constant function which has a countable or finite number of pieces.

Here a step function is multiplied to 4.

The correct graph which represents the step function is first graph.

Hence the correct option is A.

Learn more about Step Functions here :

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Answer:

4309

Step-by-step explanation:

initial 8000

1st year 8000(1-.06)=8000(.94)

2nd year 8000(.94)^2

...

10 year 8000(.94)^10 approx 4309

Answer:

Events D and C are mutually exclusive.

Step-by-step explanation:

Two events D and C are mutually exclusive if

[tex]Pr(D\cup C)=Pr(D)+Pr(C)[/tex]

Find these probabilities. In a standard deck of 52 playing cards there are 13 diamond cards and 13 club cards.

The probabilty of chosing diamond is

[tex]Pr(D)=\dfrac{13}{52}=\dfrac{1}{4}[/tex]

The probabilty of chosing club is

[tex]Pr(C)=\dfrac{13}{52}=\dfrac{1}{4}[/tex]

The probabilty of chosing diamond or club is

[tex]Pr(D\cup C)=\dfrac{13+13}{52}=\dfrac{1}{2}[/tex]

Since

[tex]\dfrac{1}{2}=\dfrac{1}{4}+\dfrac{1}{4},[/tex]

events D and C are mutually exclusive.

Final answer:

In the context of a standard deck of 52 playing cards, the events representing diamonds (D) and clubs (C) are mutually exclusive events because a single card cannot be both a diamond and a club at the same time.

Explanation:

The question asks about the concept of mutually exclusive events in probability, using the context of a standard deck of playing cards. In a standard deck, there are four suits: spades, hearts, diamonds, and clubs. Diamonds (D) and clubs (C) are two different suits of cards, and so they are mutually exclusive events because the same card cannot be both a diamond and a club at the same time.

In reference to a standard deck of 52 cards which contains clubs, diamonds, hearts, and spades, each suit has 13 cards - A (ace), 2 through 10, J (jack), Q (queen), and K (king). Therefore, seeing as how a card from a deck cannot belong to two different suits, D and C are mutually exclusive events; there is no overlap between these two groups of cards.

Answer:

Step-by-step explanation:

The correct answer is the second one. The function g(x) is increasing "faster" than f(x), and this is true of exponential functions in general. This should make sense if you're familiar with the concept of limits at infinity.

vertical multiplication [tex]x^{2} -x +1\\x.x^{2} -2x-2[/tex]

is C.[tex]x^{2} -x^4-x^3-4x^{2} -2[/tex]

Vertical multiplication

Vertical Multiplication. Set up the vertical multiplication by stacking the factors vertically and lining up the digits by place value. Although multiplication is commutative (order is not important) we want to place the number with more digits on top.

The angles opposite each other when two lines cross. They are always equal. In this example a° and b° are vertical angles. "Vertical" refers to the vertex (where they cross), NOT up/down. They are also called vertically opposite angles.

To learn more about vertical multiplication, refer

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Answer:

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=5x-2,\ g(x)=2x+1\\\\\text{Substitute:}\\\\(f-g)(x)=(5x-2)-(2x+1)\\\\=5x-2-2x-1\qquad\text{combine like terms}\\\\=(5x-2x)+(-2-1)\\\\=3x-3[/tex]

Answer:

A. 12-12

Step-by-step explanation:

Becuase if the temperature was originally 12°C then it decreases by 12° then it will be 12-12

Answer:

A.)  12 - 12.

Step-by-step explanation:

Given  : From 12:00 midnight to 6:00 am, the  temperature decreased by 12°C. If the original temperature was 12°C.

To find :  which expression can be used to represent this situation.

Solution : We have given

At 12 : 00 midnight temperature = 12 °C.

At 6 : 00 am temperature decreased  by 12 °C.

So, Final temperature  = 12 °C - 12 °C.

Therefore, A.)  12 - 12.

Step-by-step explanation:

let w be the cost of a bottle of water and p be the cost of a bag of pretzels

"2 bottles of water and 3 bags of pretzels is $7.05" can be written as

2w + 3p = 7.05    ------------- eq.1

"The cost of a bag of pretzels is $1.35" can be written as

p = 1.35 ------------- eq 2

Together, eq 1 and eq 2 make up your system of equations

To solve, take eq 2 and substitute this value int eq 1

2w + 3 (1.35) = 7.05

2w + 4.05 = 7.05

2w = 7.05 - 4.05

2w = 3

w = 1.5

Hence the cost of a bottle of water is $1.50

Answer: the cost of one bottle of water is $1.5 and the cost of one bag of pretzels is $1.35.

Step-by-step explanation: Let's call "b" the cost of a bottle of water and "p" the cost of a bag of pretzels, in the first equation of the system, we need to express the total prize of 2 bottles of water and 3 bags of pretzels, so it would be:

2b+3p=$7.05

The second equation will express the cost of a bag of pretzels:

p=$1.35

Now, to solve the system we replace the second equation into the first one:

2b+3($1.35)=$7.05

2b=$7.05-$4.05

2b=$3

b=$1.5

So the cost of one bottle of water is $1.5 and the cost of one bag of pretzels is $1.35.

By factorising a function, you can find the value of x-intercepts by substituting f(x)=0

By plotting a graph, you can check the values of x-intercepts

A function graph can be used to verify if a function is factored correctly by comparing the x-intercepts on the graph to the solutions of the factored function.

A function graph can be used to help verify that a function is factored correctly by examining its x-intercepts. When a function is factored correctly, the x-intercepts represent the values of x for which the function equals zero. In other words, they are the solutions to the equation f(x) = 0. By plotting the function and identifying the x-intercepts on the graph, we can compare them to the solutions of the factored function to determine if they match.

For example, let's say we have a function f(x) = (x+2)(x-3). The factored form suggests that the x-intercepts should occur at x = -2 and x = 3. By graphing the function and observing where it crosses the x-axis, we can confirm if these values are indeed the x-intercepts.

If the x-intercepts on the graph match the solutions of the factored function, it indicates that the function is correctly factored. However, if they do not match, it suggests an error in the factoring process.

[tex]\bf \cfrac{18x^4+27x^3-36x^2}{9x^2}\implies \stackrel{\textit{distributing the denominator}}{\cfrac{18x^4}{9x^2}+\cfrac{27x^3}{9x^2}-\cfrac{36x^2}{9x^2}} \\\\\\ \cfrac{18x^4x^{-2}}{9}+\cfrac{27x^3x^{-2}}{9}-\cfrac{36x^2x^{-2}}{9}\implies \cfrac{18x^{4-2}}{9}+\cfrac{27x^{3-2}}{9}-\cfrac{36x^2x^{-2}}{9} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 2x^2+3x-4~\hfill[/tex]

Answer:

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Step-by-step explanation:

Answer: OPTION C.

Step-by-step explanation:

Given the expression [tex]\frac{4x^4y^3}{-8x^2y }[/tex] you  need to remember a property called "Quotient of powers property". This property states the following:

[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]

Therefore, in order to reduce the given expression to lowest terms, it is necessary to apply this property. Once you apply it, you get:

[tex]\frac{4x^4y^3}{-8x^2y}=-\frac{x^{(4-2)}y^{(3-1)}}{2}=-\frac{1}{2}x^{2}y^{2}[/tex]

Answer:

2  2/3

Step-by-step explanation:

I'm going to change it to a multiplication problem by flipping the fraction after the division sign: 4/6  *    12/3

I'm going to reduce the fractions:  2/3   *  4

I'm going to write 4 as 4/1           : 2/3   * 4/1

Multiply straight across on top and straight across on bottom:   8/3

How many times does 3 go into 8:    2

The remainder of that is 2

So 8/3 can be written as    2  2/3  which really just means 2+2/3

Answer:

[tex] 2 \frac{2}{3} [/tex]

Step-by-step explanation:

To divide by a fraction multiply by the reciprocal of that fraction (flip the fraction you are dividing by and multiply)

[tex] \frac{4}{6} \times \frac{12}{3} [/tex]

Reduce the fractions and multiply:

[tex] \frac{4}{1} \times \frac{2}{3} = \frac{4 \times 2}{1 \times 3} = \frac{8}{3} [/tex]

8/3 equals 2 2/3.

Hope this helps!

ANSWER

[tex](4 + 9i)(7 - 4i) = 64 + 47i [/tex]

EXPLANATION

The given complex number expression is:

[tex](4 + 9i)(7 - 4i)[/tex]

We expand using the distributive property to get;

[tex](4 + 9i)(7 - 4i) = 4(7 - 4i) + 9i(7 - 4i)[/tex]

[tex](4 + 9i)(7 - 4i) = 28- 16i + 63i - 36 {i}^{2} [/tex]

Recall that,

[tex] {i}^{2} = - 1[/tex]

Our expression now simplifies to:

[tex](4 + 9i)(7 - 4i) = 28 + 47i + 36 [/tex]

[tex](4 + 9i)(7 - 4i) = 64 + 47i [/tex]

Answer: [tex]64+47i[/tex]

Step-by-step explanation:

Given the Complex numbers multiplication:

[tex](4+9i)(7-4i)[/tex]

You need to follow these steps:

1. Apply Distributive property:

[tex](4+9i)(7-4i)=(4)(7)+(4)(-4i)+(9i)(7)+(9i)(-4i)=28-16i+63i-36i^2[/tex]

2. You need to remember that:

[tex]i=\sqrt{-1}\\\\i^2=-1[/tex]

Then, you need to substitute [tex]i^2=-1[/tex]:

 [tex]28-16i+63i-36(-1)=28-16i+63i+36[/tex]

3. Finally, add the like terms:

[tex]64+47i[/tex]

Answer:

A. (2,7/2)

Step-by-step explanation:

The midpoint formula is (x1+x2/2 , y1+y2/2).

So just plug the numbers into that formula and you get the answer.