Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1).

Answer:

  M/6 = G/5

Step-by-step explanation:

We are given a relation between the numbers of students in two different groups. That relation can be used to write an equation.

If we consider M&M buyers to be 6 in a group, then the number of those groups is ...

  M/6

Similarly, the number of groups who bought gum will be ...

  G/5

where there are 5 gum-buyers in each group.

The problem statement tells us that for each group of one kind, there is a matching group of the other kind. That is, the numbers of groups are equal:

  M/6 = G/5

Answer: Option (3)

Step-by-step explanation:

[tex]|-2x|=4\\\\|2x|=4\\\\|x|=2\\\\x=\pm 2[/tex]

The number line represents the solutions to  |-2x| = 4 is Number line C.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have Equation: |-2x| = 4

We know the value inside the mod is always positive.

So, 2x = ±4

x= ±4/2

x= ±2

Thus, the required number line is C.

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Step-by-step explanation:

it is 8+1 people (8 students and 1 teacher).

a.

how many seating arrangements are possible ?

start with any of the 9 seats. there are 9 possibilities who will sit in that chair.

the next seat has then only 8 possibilities left. the next one 7. the next b one 6. and so on.

so, all possibilities are

9×8×7×6×...×1 = 9! = 362,880

b.

if the teacher is fixed to a specific seat, then this position is constant in all seating arrangements.

that means for the variable part we have only 8 people remaining.

and that gives us now only

8! = 40,320

possibilities

c.

how many combinations are there for the triplets, when they sit together, to arrange their internal sitting sequence ?

3! = 6

and we need to block these 6 combinations for each of the freely selectable seats as starting seat for such a block of 3.

to visualize this, let's give each seat an identifier.

we have the seats s1, s2, s3, ... s8, s9.

for all the combinations of these 9 seats, we need to eliminate the 6 combinations, where the triplets sit on s1, s2, s3.

and then the 6 combinations, where they sit at s2, s3, s4.

and then at s3, s4, s5. then at s4, s5, s6. ... s8, s9, s1. and s9, s1, s2.

it is not clear if b. still applies here (and the teacher has a fixed seat), or if we are back to the general a. scenario.

if we have again all 9 people picking their seats freely, and we only block the triplets from sitting together, then we need to block these 6 combinations for each of the 9 seats (as visualized above) giving us

9! / (9×3!) = 362,880 / 54 = 6,720 remaining possibilities.

if we have again the teacher blocking one fixed seat, then we need to block the 6 triplets combinations theoretically for each of the 8 remaining seats as above.

but : the teacher is now a separator disabling some of these blocks of 3.

e.g. let's say the teacher's seat is s9. then the teacher automatically separates the triplets in otherwise "illegal" blocks of 3.

s7, s8, s1 is now a valid seat combination for the triplets (because there is the fixed s9 in between).

the same for s8, s1, s2.

so, we need to eliminate the 6 combinations not for all 8 starting seats, but only for 6.

and that gives us

8! / (6×3!) = 40,320 / 36 = 1,120 remaining possibilities.

Answer:

required expression = 11x-5

Step-by-step explanation:

We have information about the following things :

Since units digit is 5 less than the tens digit, then the unit digit will become

x-5

Now we have these two things:

Now let us look at some two digit numbers like 29 , 43 and 78

in 29, tens digit is 2 and units digit is 9

29 is formed by multiplying the tens digit by 10 and multiplying the units digit by 1 like this : 29 = (2×10) + (9×1)

Similarly;

43 = (4×10) + (3×1)

78 = (7×10)+(8×1)

Now to get out two digit number from the question, we similarly need to multiply the tens digit with 10 and units digit with 1 and add them like this:

tens digit : x

Units digit : x-5

Hence the number is (x × 10) + [(x-5)×1] = 10x + x-5 = 11x-5

hence the required algebraic expression is 11x-5

Answer:

Step-by-step explanation:

So in this example we'll be using the difference of squares which essentially states that: [tex](a-b)(a+b)=a^2-b^2[/tex] or another way to think of it would be: [tex]a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})[/tex]. So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:

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

Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:

[tex]x^4-4 = (x^2-2)(x^2+2)[/tex]

So completely factored form is: [tex](x^2-2)(x^2+4)(x^4+4)[/tex]

I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because [tex]x^2+4 = x^2-(-4)[/tex]. and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: [tex]x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i)[/tex] just something that might be useful in some cases.

We can factor this into [tex](x^{4}+4)(x^{4} -4)[/tex].

This is because we use  difference of two squares where [tex]x^{2} -y^{2} = (x+y)(x-y)[/tex]

So we rewrite x^8-16 to x^8-4^2.

This can then be written to the equation I put at the start.

p.s. The reason its [tex]x^{4}[/tex] is because [tex]x^{4} * x^{4} = x^{8}[/tex]
(P.S.S I just found that the other helper did it fully so I stopped here, read his, its correct)

The two ways that can be used to find the area of a trapezoid include:

It should be noted that a trapezoid simply means a four sided shape that has parallel sides.

To find the area of the shape goes thus:

Find the length of each base.

Find the height of the trapezoid.

Substitute the values into the formula: A = (a + b) × h/2

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Answer:

let's playthe games questiontag

5x>25

x>5

Hope it helps!

Answer:

Negative

Step-by-step explanation:

When you move the decimal place to the right, the exponent in scientific notation is negative. In other words, when you are converting a number smaller than 1 into scientific notation, the exponent will be negative. In this case, because you are moving the decimal place to the right 3 places, the new number would be 4.430 x 10⁻³ cm.

When you move the decimal place to the left, the exponent in scientific notation is positive.

Based on the data given, the length of line segment AC is 2.29

Based on the given data:

The triangle ABC is an isosceles triangle.

The line segment AC is the hypotenuse of the the triangle ACD.

The length of AD = 3/2

[tex]AC = \sqrt{(\sqrt{3)^{2}} + (\frac{3}{2})^{2}}= 2.29[/tex]

In conclusion, the length of  AC is 2.29

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For finding the inverse of a function you have to write it as an ecuation.

[tex]y = 4x + 7[/tex]

Invert the values of x and y.

[tex]x = 4y + 7[/tex]

Our objetive now in this new equation is to clear y. First, subtract 7 in both sides of the equation.

[tex]x - 7 = 4y[/tex]

Then, divide both sides by 4.

[tex] \frac{x - 7}{4} = y[/tex]

Finally, invert the values of x and y again and put the equation like a function.

[tex] {f}^{ - 1} (x) = \frac{x - 7}{4} [/tex]

This is correct because f(x) = x is the axis of symmetry for both functions (green one).

Angles are complementary

Answer:

A and C are complementarty

sinC=cos90-C

Step-by-step explanation:

Just took the exam on a pex

good luck homedawg

The key features of the graph include the fact the graphs are periodic.

It should be noted that a graph is a diagram that represents ban interrelations between variables.

The tan graph is simply the visual representation of the tangent function for a range of angles.

In this case, the graphs have been attached and it can be seen that the tan graph repeats every 180° and is not a continuous curve.

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Answer: it is a ratio of vertical alignment w.r.t horizontal alignment

Step-by-step explanation:

The main difference is that graph of tan(x) is the ratio of sin(x)/cos(x) that is it is a ratio of vertical alignment w.r.t horizontal alignment whereas graph of x^3 is not trigonometric but algebraic in nature as ( x×x×x).

The end behavior is that as the value of x increases the value of function increases.

A) We want to completely factor; f(x) = 2x² - x - 10

⇒ f(x) = 2x² - 5x + 4x - 10

⇒ 2x(x + 2) - 5(x + 2)

⇒ (2x - 5)(x + 2)

B) The x-intercept occurs at y = 0. Thus;

(2x - 5)(x + 2) = 0

x  =5/2  and x = -2

C) f(x) = 2x² - x - 10

Thus, the end behavior is that as the value of x increases the value of function increases.

D) The graph steps has been attached

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Answer:26

Step-by-step explanation:

Answer:

102cm^3

Step-by-step explanation:

Answer:

210 ways

Step-by-step explanation:

7 P 3 = 210  ways

or    7 C 3 = 35     choices of 3 posters which can bearrranged in 6 different ways     6 * 35 = 210 ways

It is a. True that educators should teach children how to properly use yardsticks to measure.

A yardstick is a standard long tool used to measure lengths.  It contains three feet, 36 inches, or 0.9144 meters.

Since it is three times the length of a standard ruler of 12 inches, it is recommended for teaching children.

Thus, truly, educators should teach children how to properly use yardsticks to measure.

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The amount of the portions can be made with one case will be 399.25 ounces.

Conversion means to convert the same thing into different units.

You buy tomatoes in 25 pounds (11.34 kg) cases.

We know that 1 pound (0.45 kg) is equal to 16 ounces (0.45 kg).

Then the number of the ounces in 25 pounds (11.34 kg) will be

⇒ 25 x 16

Multiply the numbers, then the expression will be

⇒ 400 ounces (11.33 kg)

In 25 pounds of tomatoes, there will be 400 ounces.

One portion of salad requires 0.75 ounces (0.02 kg) of tomatoes.

Then the amount of the portions can be made with one case will be

⇒ 400 – 0.75

⇒ 399.25 ounces

Thus, the amount of the portions can be made with one case will be 399.25 ounces.

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The expression πr² = 6477 can be used to solve for the radius of the sphere.

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]

Area of sphere A = 6477 square inches

A = 4πr²

A = 6477

4πr² = 6477

πr² = 6477

Thus, the expression πr² = 6477 can be used to solve for the radius of the sphere.

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Answer:

b. 4.5 cm

a. 42 mm is the answer

Answer:

[tex]25x^2-10x+4[/tex]

Step-by-step explanation:

You can use the quadratic formula to determine if a quadratic equation has real or imaginary solutions. The quadratic formula is: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]. What really matters in this case is the discriminant, which is the stuff under the radical which is: [tex]b^2-4ac[/tex]. This is because the solutions are only imaginary, if the discriminant is negative, because then you would be taking the square root of a negative number. So let's look through each example:

[tex]25x^2+20x-4[/tex]; a=25, b=20, c-4: [tex]20^2-4(25)(-4) = 800[/tex]. By examining this one example, it's important to note, if you have one negative number as a or c, then it cancels out the negative sign in the -4, and it becomes positive. So let's look at examples where a or c doesn't equal a negative number OR both a and c equal negative, that way they cancel out and over -4ac is still negative.

[tex]25x^2-10x+4[/tex]; a=25, b=-10, c=4. In this case both a and c are positive so -4ac will remain negative. This gives you: [tex](-10)^2-4(25)(4) = 100-400 = -300[/tex]. So this has a negative discriminant meaning it will have no real solution but rather imaginary solutions

The coordinates represents a possible collision point of the objects according to equations r = 4cos(θ) and r = –1/ 2cos(θ)  cos(∅) are (-2,2π/3).

Given Equations  r = 4cos(θ) and r = –1 2cos(θ).

We have to find the coordinates of collision.

The first object is moving around the screen r = 4cos(θ).

The second object is moving around the screen r = –1 /2cos(θ).

According to question

Coordinate can be found out by equating both the equations.

4cos(θ) =–1 /2cos(θ)

2cos(θ)=-1

cos(θ)=-1/2

θ=[tex]cos^{-1} (1/2)[/tex]

=120°

θ=-2π/3

Therefore the two equations are equal when

θ=2π/3

we have

r=4 cos(2π/3)=-2

and r=-1+2 cos(2π/3)

r=-2

Hence the coordinates that represent the collision point are (-2,2π/3).

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Answer: Option A on EDGE

Just took test

Step-by-step explanation:

Answer: A. (3x² + 4x-7)(x) + (3x² + 4x-7)(-2)

Step-by-step explanation:

The expressions are equivalent by the distributive property.

Using relations in a right triangle, it is found that:

cos(A) = 3/5 = 0.6.

The relations in a right triangle are given as follows:

In this triangle:

Hence:

cos(A) = 30/50 = 3/5 = 0.6.

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Answer:

Additive = -10x^2+70x

Multiplicative = 1/10x(x−7)

Step-by-step explanation:

The multiplicative inverse of a number is the reciprocal of that number. Since 10(x^2−7x)⋅ 1/10x(x−7)=1 , then 1/10x(x−7)  is the multiplicative inverse of  10(x^2−7x) .

Since  10(x^2−7x)−10x^2+70x=0 , then −10x^2+70x

is the additive inverse of 10(x^2−7x).

The table that represents a linear function is y=3,7,11,15

For a table to represent a linear function, the table must have a constant rate of change i.e. a common difference

From the list of options, we have:

y=3,7,11,15

The difference between each y value is 4

i.e. 7 - 3 = 11 - 7 = 15 - 11 = 4

Hence, the table that represents a linear function is y=3,7,11,15

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Determine the slope of a line that is parallel to the equation [tex]\bf{3x+6y=18}[/tex].

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

First we should divide the whole equation by 6,

[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}}[/tex] | simplify

[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x

[tex]\bf{y=-\dfrac{1}{2}x+3[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=Slope-\dfrac{1}{2}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Answer:

[tex]volume=558.9[/tex]

Step-by-step explanation:

find the volume of the cone and the hemisphere and add them together

cone:

[tex]Vcone=\pi r^{2} \frac{h}{3} \\\\V=\pi (5.3)^2(\frac{8.4}{3} )\\V=\pi (28.09)(2.8)\\V=247.09\pi \\V=247.1[/tex]

hemisphere:

[tex]Vhemisphere=\frac{2\pi r^3}{3} \\V=\frac{2\pi (5.3)^3}{3} \\V=\frac{2\pi (148.877)}{3} \\V=\frac{297.754\pi }{3} \\V=\frac{935.421}{3}\\ V=311.8[/tex]

add the volumes together:

[tex]Vol=247.1+311.8\\Vol=558.9[/tex]

Answer:

[tex] \frac{2}{15} {cm}^{2} [/tex]

Step-by-step explanation:

Area of Rectangle = Length x Breadth

=

[tex] \frac{1}{5} \times \frac{2}{3} \\ = \frac{2}{15} {cm}^{2} [/tex]