What is the product?
(-2x- 9y2 )(-4x-3)

Answer: The difference cannot be found because the indices of the radicals are not the same.

Step-by-step explanation:

To find the difference you need to subtract the radicals. But it is important ot remember the following: To make the subtraction of radicals, the indices and the radicand must be the same.

In this case you have these radicals:

[tex]\sqrt[ {8ab}^{3} ]{{ac}^{2} }- \sqrt[ {14ab}^{3}]{{ac}^{2} }[/tex]

You can observe that the radicands are the same, but their indices are not the same.

Therefore, since the indices are different you cannot subtract these radicals.

Answer: [tex]\bold{64g^9h^6k^{12}}[/tex]

Step-by-step explanation:

[tex]\text{Apply the product rule:} (a^b)^c=a^{b*c}\\\\(4g^3h^2k^4)^3\\\\=4^{(1*3)}g^{(3*3)}h^{(2*3)}k^{(4*3)}\\\\=4^3g^9h^6k^{12}\\\\=64g^9h^6k^{12}[/tex]

Answer:

1/6

Step-by-step explanation:

there are 6 dresses altogether and 1 blue dress.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

We have been given that Maria has three red dresses, 2 white dresses, and one blue dress. We are asked to find the probability that Maria will wear a blue dress at her party.

[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]

We know that number of blue dresses is 1, so number of favorable outcomes is 1.

Total dresses = 3 Red dresses + 2 White dresses + 1 Blue dress = 6 dresses.

[tex]\text{Probability that Maria will wear a blue dress at her party}=\frac{1}{6}[/tex]

Therefore, our required probability is [tex]\frac{1}{6}[/tex].

Answer:

The statement is True

Step-by-step explanation:

The Isosceles Triangle Theorem states that;

If two sides of a triangle are congruent, then the angles opposite those sides are also congruent. The converse of this statement is;

if two angles are congruent, then sides opposite those angles are congruent.

Answer:

True.

Step-by-step explanation:

To start with , remember that congruent angles have the same degree of measurement. For example, in an isosceles triangle, the base angles are congruent angles because they both measure 45°

The base angles  theorem states that the sides next to congruent angles are equal.The statement is therefore True.If sides of the triangle are congruent, the opposite angles in the triangle are congruent .

Answer:

D. (-∞,4]

Step-by-step explanation:

The range is the y values

The lowest y values is negative infinity

The highest y values is 4

( - inf, 4]

We use the parentheses since we cannot get to negative infinity, the bracket since we reach 4

Answer:

The graph that represent direct variation in the attached figure

Step-by-step explanation:

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

The graph that represent direct variation in the attached figure

Answer:

option d

Step-by-step explanation:

Answer:  the answer would be -1/11

Step-by-step explanation: the reason being the slope of the green is a negative slope because it is going down ward not upwards therefore it is negative and because the the lines are parallel they are equal so the slope of both lines are -1/11

Answer:

-6

Step-by-step explanation:

The formula for finding the rate of change is:

[tex]Rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]

The interval is [1,5]

So, a = 1 and b=5

[tex]f(1) = 17 - (1)^2\\ =17-1\\=16\\f(5) = 17-(5)^2\\=17-25\\=-8[/tex]

Putting in the values

[tex]Rate\ of\ change = \frac{f(5)-f(1)}{5-1} \\=\frac{-8-16}{5-1}\\= \frac{-24}{4}\\ =-6[/tex]

The average rate of change is -6 ..

Answer:

-6

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Find out the total value of each option and see which one gives a total of $3.60

For A, 12 nickels + 12 dimes = 12 x $0.05  + 12 x $0.10 = $1.80 ≠ $3.60

For B, 24 nickels + 24 dimes = 24 x $0.05  + 24 x $0.10 = $3.60 (correct)

For C, 36 nickels + 36 dimes = 36 x $0.05  + 36 x $0.10 = $5.40 ≠ $3.60

For D, 48 nickels + 48 dimes = 48 x $0.05  + 48 x $0.10 = $7.20 ≠ $3.60

Answer:

For my opinion, the best option it B.

Answer:

[tex]\large\boxed{y=-\dfrac{3}{10}x+\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points from the graph (-5, 2) and (5, -1).

Substitute:

[tex]m=\dfrac{-1-2}{5-(-5)}=\dfrac{-3}{10}=-\dfrac{3}{10}[/tex]

We have the equation in form:

[tex]y=-\dfrac{3}{10}x+b[/tex]

Put the coordinates of the point (5, -1) to the equation:

[tex]-1=-\dfrac{3}{10}(5)+b[/tex]

[tex]-1=-\dfrac{3}{2}+b[/tex]

[tex]-\dfrac{2}{2}=-\dfrac{3}{2}+b[/tex]            add 3/2 to both sides

[tex]\dfrac{1}{2}=b\to b=\dfrac{1}{2}[/tex]

Answer:I think that in this problem you need a right angle with a circle in it

An answer is

  [tex]\displaystyle f\left(x\right)=\frac{\left(x+1\right)^3}{\left(x+2\right)^2\left(x-1\right)}[/tex]

Explanation:

Template:

  [tex]\displaystyle f(x) = a \cdot \frac{(\cdots) \cdots (\cdots)}{( \cdots )\cdots( \cdots )}[/tex]

There is a nonzero horizontal asymptote which is the line y = 1. This means two things: (1) the numerator and degree of the rational function have the same degree, and (2) the ratio of the leading coefficients for the numerator and denominator is 1.

The only x-intercept is at x = -1, and around that x-intercept it looks like a cubic graph, a transformed graph of [tex]y = x^3[/tex]; that is, the zero looks like it has a multiplicty of 3. So we should probably put [tex](x+1)^3[/tex] in the numerator.

We want the constant to be a = 1 because the ratio of the leading coefficients for the numerator and denominator is 1. If a was different than 1, then the horizontal asymptote would not be y = 1.

So right now, the function should look something like

  [tex]\displaystyle f(x) = \frac{(x+1)^3}{( \cdots )\cdots( \cdots )}.[/tex]

Observe that there are vertical asymptotes at x = -2 and x = 1. So we need the factors [tex](x+2)(x-1)[/tex] in the denominator. But clearly those two alone is just a degree-2 polynomial.

We want the numerator and denominator to have the same degree. Our numerator already has degree 3; we would therefore want to put an exponent of 2 on one of those factors so that the degree of the denominator is also 3.

A look at how the function behaves near the vertical asympotes gives us a clue.

Observe for x = -2,

Observe for x = 1,

We should probably put the exponent of 2 on the [tex](x+2)[/tex] factor. This should help preserve the function's sign to the left and right of x = -2 since squaring any real number always results in a positive result.

So now the function looks something like

  [tex]\displaystyle f(x) = \frac{(x+1)^3}{(x+2 )^2(x-1)}.[/tex]

If you look at the graph, we see that [tex]f(-3) = 2[/tex]. Sure enough

  [tex]\displaystyle f(-3) = \frac{(-3+1)^3}{(-3+2 )^2(-3-1)} = \frac{-8}{(1)(-4)} = 2.[/tex]

And checking the y-intercept, f(0),

  [tex]\displaystyle f(0) = \frac{(0+1)^3}{(0+2 )^2(0-1)} = \frac{1}{4(-1)} = -1/4 = -0.25.[/tex]

and checking one more point, f(2),

  [tex]\displaystyle f(2) = \frac{(2+1)^3}{(2+2 )^2(2-1)} = \frac{27}{(16)(1)} \approx 1.7[/tex]

So this function does seem to match up with the graph. You could try more test points to verify.

======

If you're extra paranoid, you can test the general sign of the graph. That is, evaluate f at one point inside each of the key intervals; it should match up with where the graph is. The intervals are divided up by the factors:

So we need to see if -2 < x < -1 matches up with the graph. We can pick -1.5 as the test point, then

  [tex]\displaystyle f(-1.5) = \frac{\left(-1.5+1\right)^3}{\left(-1.5+2\right)^2\left(-1.5-1\right)} = \frac{(-0.5)^3}{(0.5)^2(-2.5)} \\= (-0.5)^3 \cdot \frac{1}{(0.5)^2} \cdot \frac{1}{-2.5}[/tex]

We don't care about the exact value, just the sign of the result.

Since [tex](-0.5)^3[/tex] is negative, [tex](0.5)^2[/tex] is positive, and [tex](-2.5)[/tex] is negative, we really have a negative times a positive times a negative. Doing the first two multiplications first, (-) * (+) = (-) so we are left with a negative times a negative, which is positive. Therefore, f(-1.5) is positive.

Given.

6a - 5b

Plug in values.

6(-3) - 5(4) =

-18 - 20 =

-38

For this case we have the following expression:

[tex]6a-5b[/tex]

We must evaluate the expression when:

[tex]a = -3\\b = 4[/tex]

Then, replacing the values we have:[tex]6 (-3) -5 (4)[/tex]

Taking into account that according to the law of the signs of multiplication, it is fulfilled that:

[tex]+ * - = -[/tex]

So:

[tex]-18-20 =[/tex]

Equal signs are added and the same sign is placed:

-38

Answer:

-38

[tex] \frac{7}{8} \times 24 = 21 \\ [/tex]

You multiply 7/8 to the number of hours in a day which 24

Gerard's baby brother sleeps for 7/8 of the day, which equals 21 hours when calculated (7/8 * 24 hours).

Gerard's baby brother spends 7/8 of his day sleeping.

To calculate how many hours this is, we need to know how many hours there are in a full day.

A full day has 24 hours. So, we multiply 7/8 by 24 to find out the total hours spent sleeping.

Here's the step-by-step calculation:

Therefore, Gerard's baby brother sleeps for 21 hours a day.

Answer:

A. 68°

Step-by-step explanation:

sum of angles inside a triangle = 180°

75 + 37 + x = 180

x = 180 - 75 - 37

= 68°

The sum of angles inside a triangle is 180°. so option is A. 68°.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Given angles are; 75 and 37.

The sum of angles inside a triangle = 180°

75 + 37 + x = 180

x = 180 - 75 - 37

x = 68°

Learn more about the triangles;

https://brainly.com/question/2773823

#SPJ2

This is False

That is because the Arcs can only be congruent if the Chords are also Congruent

Answer:

FALSE

Step-by-step explanation:

let's bear in mind that perpendicular lines have negative reciprocal slopes...... hmmmm what's the slope of the given line anyway?

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-3)}{4-(-4)}\implies \cfrac{1+3}{4+4}\implies \cfrac{4}{8}\implies \cfrac{1}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]

so, we're really looking for a line whose slope is -2 and runs through (-4 , 3)

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-3)=-2[x-(-4)] \implies y+3=-2(x+4) \\\\\\ y+3=-2x-8\implies y=-2x-11[/tex]

Answer:

The answer is 6.

Step-by-step explanation:

Plug in:  f(-5)=|-5+1|

Because this an absolute problem -5 is positive within |x|

so therefore f(-5)= |6|

Answer: Number of pizzas would be less than 5 but not more than 50.

Step-by-step explanation:

Since we have given that

Number of pizzas so far = 25

His principal asked him to make at least 30 pizzas but no more than 75.

According to question, we have

30 ≤ x + 25 ≤ 75

First we subtract 25 from both the sides:

[tex]30-25\leq x \leq 75-25\\\\=5\leq x\leq 50[/tex]

Hence, number of pizzas would be less than 5 but not more than 50.

The solution to the compound inequality is 5  x 50.

The compound inequality given is 30 x 25  75, where x represents the number of additional pizzas Billy needs to make to satisfy the principal's request. To solve for x, we need to isolate x in the inequality.

First, we subtract 25 from all parts of the compound inequality to shift the 25 pizzas already made to the other side of the inequality. This gives us:

30 - 25 x + 25 - 25 75 - 25

Simplifying the inequality, we get:

5  x  50

This means that Billy needs to make at least 5 more pizzas to reach the minimum requirement of 30 pizzas (since 25 + 5 = 30) and no more than 50 additional pizzas to not exceed the maximum allowed number of 75 pizzas (since 25 + 50 = 75).

Therefore, the number of additional pizzas Billy should make is any integer value between 5 and 50, inclusive. This ensures that the total number of pizzas made will be within the principal's specified range of 30 to 75 pizzas."

Answer:

486 - 160l

Step-by-step explanation:

m = 90 - 32l

s = -48 + 18l

l = stationary

Combine like-terms, evaluate, then you will arrive at this crazy answer.

Answer:

Step-by-step explanation:

1 group = 10 students

x group = 240 students.

1/x = 10/240              Cross multiply

10x = 240                  Divide by 10

10x/10=240/10          Do the division

x = 24

its (8,6)

to get your x, you set what's in the absolute value to 0

so

x-8=0

then subtract 8 on both sides to get

x=8

then your y is just the number to the right of the absolute value so

y=6

Answer: Option B

(8, 6)

Step-by-step explanation:

By definition, for an absolute value function of the form

[tex]f (x) = | x-h | + k[/tex]

the vertex of f(x) will always be at the point

(h, k)

In this case we have the function of value ansoluto:

[tex]g(x) = |x - 8| + 6[/tex]

Therefore in this case

[tex]h=8\\k=6[/tex]

Finally the vertex of the function g(x) is: (8, 6)

The answer is the option B

Answer:

a = 3 ,  b = -2 ,  c = 0

Step-by-step explanation:

The given equation is:

1 = -2x + 3x^2 + 1

To find the correct substitution values of a, b and c. We need to convert t into the standard form first.

Standard form of a Quadratic equation is written as:

ax^2 + bx + c = 0        (where a is not equal to zero)

Converting the given equation into its standard form:

1 = -2x + 3x^2 + 1

-2x + 3x^2 + 1 - 1 = 0

3x^2 - 2x + 0 = 0  

OR 3x^2 - 2x = 0

According to the equation

a = 3 ,  b = -2 ,  c = 0

Answer:  15,600,000

Step-by-step explanation:

26 x 25 x 24 =15,600 combinations of letter with no repeats

10 x 10 x 10 = 1000 with repeating numbers

15,600 x 1000 = 15,600,000

The total number of possible license plates is 26*25*24*10*9*8.

The number of possible license plates with no repeated letters can be calculated by multiplying the number of choices for each position. Since no letter can be repeated, the choices for the first position would be 26 letters, then 25, and then 24 for the three positions. For the digits, there are 10 choices for each position.

So, the total number of possible license plates would be 26*25*24*10*9*8.

Answer:  5

Step-by-step explanation:

f(5) = 2 means that when x = 5, y = 2 --> (5, 2)

f⁻¹(2) is the inverse (when the x and y are swapped) --> when x = 2, y = 5

Answer:

1/2(x^3 - 1) or we could write it as (x^3 - 1) / 2.

Step-by-step explanation:

A number cubed is x^3. Difference of this and 1 is x^3 - 1.

Finall we have 1/2 of this:

= 1/2(x^3 - 1) or we could write it as (x^3 - 1) / 2.

Answer:

[tex]\frac{x^3-1}{2}[/tex]

Step-by-step explanation:

We must follow what the statement asks us, starting from the last thing and going forward from there.

A number cubed: [tex]x^3[/tex]

The difference of a number cubed and one: [tex]x^3-1[/tex]

And finally:

one-half of the difference of a number cubed and one, this would be one half of the expression we already found:

[tex]\frac{x^3-1}{2}[/tex]

For this case we can make a change of variable, to obtain a quadratic equation of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Making the change:[tex]u = 3x + 2[/tex]

Substituting the change we have:

[tex]u ^ 2 + 7u-8 = 0[/tex]

Thus, the correct option is:[tex]u ^ 2 + 7u-8 = 0[/tex]where [tex]u = 3x + 2[/tex]

Answer:

Option B

Answer:

second option: [tex]u^{2}+7u-8=0[/tex]

Step-by-step explanation:

We have the equation given:

[tex](3x+2)^{2}+7(3x+2)-8=0[/tex]

We can replace the variable in the quardatic equation.

So,

[tex]Putting\\u=3x+2[/tex]

Putting u in place of 3x+2 will give us:

[tex](u)^{2}+7(u)-8=0[/tex]

So the answer is:

[tex]u^{2}+7u-8=0[/tex]

So, the second option is correct ..

Answer:

A

Step-by-step explanation:

We can see that the slope is positive, which means that the x-term must be positive.

If you expand and simply both equations into the form y = mx + b, you will find that m is positive for A and negative for B, hence A is the correct answer.

The expression 81x⁴ - 1  can be factored completely by identifying it as a difference of squares. First, factor it into (9x² + 1)(9x² - 1) and then further factor (9x² - 1) into (3x + 1)(3x - 1). The final factored form is (9x² + 1)(3x + 1)(3x - 1).

We are given the expression 81x⁴ - 1 and need to factor it completely. This is a difference of squares, which can be written as:

The difference of squares formula is a²- b² = (a + b)(a - b). Applying this formula, we get:

Next, notice that 9x²- 1 is also a difference of squares:

Again using the difference of squares formula, we get:

Putting everything together, the complete factorization of 81x⁴ - 1 is:

Answer: Addition property of equality

Step-by-step explanation: You added the x to the other side, which is clearly using addition. Hope this help!