Simplify. Rewrite the expression in the form 3^n3 n 3, start superscript, n, end superscript. 3^4\cdot 3^2=3 4 ⋅3 2 =3, start superscript, 4, end superscript, dot, 3, squared, equals

Answer:

[tex](-\infty, -1)\ \cup\ (0, 2)[/tex]

Step-by-step explanation:

So if you expand out the two binomials (k-2)(k+1), you'll get: [tex]k^2+k-2k-2[/tex]. which simplifies to: [tex]k^2-k-2[/tex]. Multiplying this by the k gives you: [tex]k^3-k^2-2k[/tex]. As you can see the degree is odd, this means that this polynomial will have two opposite end behaviors. And as you can see the leading coefficient is positive, meaning that this function will go towards positive infinity as k goes towards positive infinity. Also we if look at the original equation given, it's in factored form, with the zeroes as k=0, k=2, and k=-1. So given this we can draw a simple graph to see when the value of the equation is negative. If you look at the graph I drew you'll see that it's negative from (-infinity, -1) and then negative from (0, 2)

Answer:

9

Step-by-step explanation:

So first step is to subtract [tex]3x^2+4x[/tex] from [tex]7x^2+x+9[/tex]. In setting this up you get the following expression

[tex](7x^2+x+9)-(3x^2+4x)[/tex]

Distribute the negative

[tex]7x^2+x+9-3x^2-4x[/tex]

Group like terms

[tex](7x^2-3x^2)+(x-4x)+9[/tex]

Simplify:

[tex]4x^2-3x+9[/tex]

Now subtract [tex]4x^2-3x[/tex]. In setting this up you get the following expression

[tex](4x^2-3x+9)-(4x^2-3x)[/tex]

Distribute the negative:

[tex]4x^2-3x+9-4x^2+3x[/tex]

Group like terms

[tex](4x^2-4x^2) + (-3x+3x) + 9[/tex]

Simplify:

[tex]9[/tex]

The attached graph represents the graph of [tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]

The inequality is given as:

[tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]

The above inequality represents a conic section.

The inequality symbol <= implies that, we make use of a closed line on the graph.

Next, we plot the graph using a graphing tool

See attachment for the graph of [tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]

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Complete question

Which graph represents [tex]\frac{(x - 2)^2}{16} = \frac{(y + 1)^2}{9}[/tex]?

Answer:

C

Step-by-step explanation:

Got it right on Edge

Answer:

15,746,400

Step-by-step explanation:

This is an example of an exponential function.

1. The function is: [tex]800 * 3^{x}[/tex]

2. We can plug the number of hours into the equation.

3. population = 800 * [tex]3^{9}[/tex]

4. population = 15,746,400

The percent by volume of the resulting solution is 10L by 93 percent

The resulting solution = sum of the volumes of both solutions

Resulting solution = 6L × 33 percent + 4L × 60 percent

Resulting solution = 10 L × 93 percent

This is so because both solutions add up to form the resulting solution

Thus, the percent by volume of the resulting solution is 10L by 93 percent

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The angle z is equal to 110° by vertically opposite angles. Hence, the correct option will be C. z = 110°.

The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Given;

The one angle is given as 110°.

So, angle z will be equal to 110° by vertically opposite angles.

Hence, the correct option will be C. z = 110°.

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Answer:

16 to the power of 5

y to the power of 4

(7a) to the power of 3 or 7 times a to the power of 3

David paid $22 for the beanie baby.

Profit and loss formulas are used to calculate the profit or loss that has been incurred by selling a particular product. They are mainly used in business and financial transactions to depict how much profit or loss a trader has incurred from any particular deal.

Let the cost which  David pay for the beanie baby be x and y be the price at which Jessica bought the beanie baby

Profit formula :

Profit = Selling price (S.P.) - Cost price (C.P.)

So using the profit formula

$6 = $25 - y

$19 = y

Now using the same equation for David

-$3 = $19 - x

$22 = x.

Thus David paid $22 for the beanie baby.

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Answer:

The solution set in interval form is [tex]$\left[\frac{-4}{3}, 4\right]$[/tex].

Step-by-step explanation:

It is given in the question an inequality as [tex]$|3 x-4| \leq 8$[/tex].

It is required to determine the solution of the inequality.

To determine the solution of the inequality, solve the inequality [tex]$3 x-4 \leq 8$[/tex] and, [tex]$-8 \leq 3 x-4$[/tex].

Step 1 of 2

Solve the inequality [tex]$3 x-4 \leq 8$[/tex]

[tex]$$\begin{aligned}&3 x-4 \leq 8 \\&3 x-4+4 \leq 8+4 \\&3 x \leq 12 \\&x \leq 4\end{aligned}$$[/tex]

Solve the inequality [tex]$-8 \leq 3 x-4$[/tex].

[tex]$$\begin{aligned}&-8+4 \leq 3 x-4+4 \\&-4 \leq 3 x \\&-\frac{4}{3} \leq x \\&x \geq-\frac{4}{3}\end{aligned}$$[/tex]

Step 2 of 2

The common solution from the above two solutions is x less than 4 and [tex]$x \geq-\frac{4}{3}$[/tex]. The solution set in terms of interval is [tex]$\left[\frac{-4}{3}, 4\right]$[/tex].

Answer:

1.19x = 12

Step-by-step explanation:

To write an equation, we multiply the cost of each song by the number of songs, x

1.19 * x

This is equal to the total amount he is allowed to spend

1.19x = 12

Answer:

D

Step-by-step explanation:

If Doug can download new songs for $1.19 each, then he will be able to download 12 songs.

Step-by-step explanation:

There cannot be such a question because the difference of half of the big number and the small number will automatically be zero, but we can find it with the equation I circled on the paper I gave you. achievements

Answer:

Step-by-step explanation:

6. The rate of change is essentially the slope. But in other words, it's how much the y changes as x increases by 1. If this rate of change is 0, that means the y-value is constant, while the x can be any real number. It can be generally given in the formula: y=b, which comes from simplifying the slope-intercept form: y=(0)x+b = b. You can also derive the same thing for a point-slope form: y-a = 0(x-b)=0 so y=a. In both cases, y is equal to some constant value. So graphing this makes a horizontal line.

7. To define a parallel line, you need the same slope, and a different y-intercept, which is under the assumption that the line has a slope that is definable. If the slope is definable, you'll have the equation: y=mx+b, where m is the same as the other line. Then you plug in the known values as x and y, to solve for b, which is the y-intercept. Now if the line is a vertical line, a parallel line can be defined as: x=a, where a doesn't equal the constant, the other vertical line is equal to. To make it pass through some point (c, d). Then you would simply set x=c, since the x is the only thing that matters, since the y-value is all real numbers, so it will eventually have the y-value d somewhere on the line.

8. To define a perpendicular line, you get the reciprocal of the slope and change the sign. So if the slope is: [tex]\frac{a}{b}[/tex] then it becomes [tex]-\frac{b}{a}[/tex] and vice versa depending on the sign. In this example, let's just say m=a/b, then the perpendicular slope would be -b/a. You can then plug this into the slope-intercept formula: [tex]y=-\frac{b}{a}+c[/tex] where c is the y-intercept. Then you plug in the known point as (x, y) and solve for c, the y-intercept. Now let's say for example that you have a vertical line: x=a. In this case you can see the slope as: [tex]\frac{1}{0}[/tex][tex]\frac{y_2-y_1}{a-a}[/tex]. Of course this isn't definable, but if you take the reciprocal you get something that is: [tex]-\frac{0}{y_2-y_1}[/tex] which will always evaluate to 0. This means you get a horizontal line, since the slope is 0. This means if you have a vertical line, any horizontal line should be perpendicular, which makes sense, since it should form a 90 degree angle when they intersect, because they're straight lines. To make sure that horizontal line passes through the point (b, c), you simply set the y equal to c. So y=c, will pass through (b, c), since the c is constant, and the x can equal anything so somewhere on the line it will intersect (b, c). But let's say we had a horizontal line, the reciprocal can be defined as: [tex]\frac{a-a}{x_2-x_1}[/tex] where a is the y constant. If you take the reciprocal, then you have a-a in the denominator, which gives you an undefined slope, because the perpendicular line to a horizontal line, is a vertical line. To ensure this perpendicular line passes through the point (b, c). You simply set x equal to b. so that x=b.

#6

if m is 0

Hence line is parallel to x axis

#7

parallel lines have equal slopes

so we can use the point slope form of line to find the equation

#2

Same process like no 7 but

slope of perpendicular line is negative reciprocal of given line's slope

I think the answered is ×=20

The logarithmic expression of 4^(1/2) = 2 is [tex]\log_4(2) = \frac 12[/tex]

The expression is given as:

4^(1/2) = 2

Take the logarithm of both sides

log(4^(1/2)) = log(2)

Apply the change of base rule

1/2log(4) = log(2)

Divide both sides by log(4)

1/2 = log(2)/log(4)

Change the base

[tex]\frac 12 =\log_4(2)[/tex]

Rewrite as:

[tex]\log_4(2) = \frac 12[/tex]

Hence, the logarithmic expression of 4^(1/2) = 2 is [tex]\log_4(2) = \frac 12[/tex]

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Answer:

f(x)=x²-3x-10

Step-by-step explanation:

[tex]f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5[/tex]

therefore the zeros of the equation are x₁=-2,x₂=5

The system of equations has (d) 0 real solutions

The system of equations is given as:

y = x^2+1

y=x

Substitute y=x in y = x^2+1

x = x^2+1

This gives

x^2 - x + 1 = 0

Calculate the discriminant using:

d = b^2 - 4ac

So, we have:

d = (-1)^2 - 4 * 1 * 1

Evaluate

d = -3

Because the discriminant is negative, the equation has no real solution

Hence, the system of equations has (d) 0 real solutions

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The equation of the straight line is y = -1/6(x - 10) + 4

The equation is given as:

y = 2x + 6

Linear equations are represented as:

y = mx + c

Where:

Slope = m

So, we have:

m = 6

The slopes of perpendicular lines are represented as:

n = -1/m

So, we have:

n = -1/6

The equation is then represented as:

y = n(x - x1) + y1

This gives

y = -1/6(x - 10) + 4

Hence, the equation of the straight line is y = -1/6(x - 10) + 4

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Answer:

c.) 38

Step-by-step explanation:

[tex]\sum\limits_{n=3}^6 a_n[/tex]   means "summation of the all the elements starting from the 3rd element to the 6th element".

The 3rd element in the series is 14, and the 6th element is 5; we have to add these and all the elements between them together.

∴    [tex]\sum\limits_{n=3}^6 a_n[/tex]    =  14 + 11 + 8 + 5

                   = 38

Step-by-step explanation:

I assume

SR = 2x + 23

RQ = x + 21

if that is true, then the situation is completely simple :

14 = (2x + 23) + (x + 21) = 3x + 44

3x = -30

x = -10

SR = 2×-10 + 23 = -20 + 23 = 3

RQ = -10 + 21 = 11

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = -10 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \qquad \tt \rightarrow \: SR + RQ = SQ[/tex]

[tex]\qquad \tt \rightarrow \: 2x + 23 + x + 21 = 14[/tex]

[tex]\qquad \tt \rightarrow \: 3x + 44 = 14[/tex]

[tex]\qquad \tt \rightarrow \: 3x = 14 - 44[/tex]

[tex]\qquad \tt \rightarrow \: 3x = - 30[/tex]

[tex]\qquad \tt \rightarrow \: x = - 10[/tex]

Now,

[tex] \qquad \tt \rightarrow \: SR = 2x + 23 [/tex]

[tex] \qquad \tt \rightarrow \: SR = 2(-10) + 23 [/tex]

[tex] \qquad \tt \rightarrow \: SR =-20+ 23 [/tex]

[tex] \qquad \tt \rightarrow \: SR = 3 \:\: units [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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

Which ordered pairs make the equation [tex]\bf{3x+2y=-7}[/tex] true? Select all that apply. 3 options are given

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

We can tell which ordered pairs make equations true by plugging in the coordinates.

[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;ONE}[/tex]

[tex]\bf{3(3)+2(-8)=-7}[/tex] | simplify

[tex]\bf{9-16=-7}[/tex] |simplify

[tex]\bf{-7\equiv-7}[/tex] | this one checks

[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;TWO}[/tex]

[tex]\bf{3(-2)+2(-1)=-7}[/tex] | simplify

[tex]\bf{-6-2=-7}[/tex] | simplify

[tex]\bf{-8\neq-7}[/tex] | this one does not check

[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;THREE}[/tex]

[tex]\bf{3(1)+2(-4)=-7}[/tex] | simplify

[tex]\bf{3-8=-7}[/tex] | simplify

[tex]\bf{-5\ne-7}[/tex] | this one does not check

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

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

              [tex]\bf{=The\;First\;Option[/tex]

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

Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

The scatter plot is a manner in which data is presented as dots on a cartesian axes, The line of best fit is a description of the data that is presented in the scatter plot.

Hence, Marta is incorrect because Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

Missing parts;

Marta believes that the equation of the line of best fit for the scatterplot below is y=-5/9x+23/9. Which statement best summarizes why Marta is likely incorrect?

Marta’s equation has a positive y-intercept, but the scatterplot suggests a negative y-intercept.

Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

Marta’s equation has a negative slope, but the scatterplot suggests a negative y-intercept.

Marta’s equation has a negative slope, but the scatterplot shows a positive correlation.

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[tex]\huge\boxed{192\ \text{in}^2}[/tex]

There are three parts to this figure: a rectangle and two triangles that are congruent.

We'll add together the area for each to get the total area.

We'll start by finding the area of the rectangle. We don't know its length, so we need to find the bases of the triangles and add them together.

We know that [tex]a^2+b^2=c^2[/tex]. Substitute and solve for [tex]a[/tex]:

[tex]\begin{aligned}a^2+6^2&=10^2\\a^2+36&=100\\a^2+36-36&=100-36\\a^2&=64\\\sqrt{a^2}&=\sqrt{64}\\a&=8\end{aligned}[/tex]

Now, double this to get the total length of the rectangle, which is [tex]16[/tex] inches.

The area of the rectangle is equal to its length times its height:

[tex]16\cdot9=\underline{144}[/tex]

Now, we'll find the area of one of the triangles and double it since they're congruent.

The area of a triangle is one-half of its base times its height, which we then double.

[tex]2\left(\frac{1}{2}\cdot b\cdot h\right)[/tex]

The [tex]2[/tex] and the [tex]\frac{1}{2}[/tex] cancel each other out.

[tex]b\cdot h[/tex]

Substitute and solve:

[tex]8\cdot6=\underline{48}[/tex]

Finally, add the rectangle's area to the two triangles' area.

[tex]144+48=\boxed{192}[/tex]

The solution is x=3/4

How can we solve given equation?

First, we will solve like terms. Then shift constant to other side and keep x on the same side to get the value of x.

We can solve given equation as shown below:

5/2-3x-5+4x=-7/4

(5-10)/2+x=-7/4

-5/2+x=-7/4

x=5/2-7/4

x= (10-7)/4

x=3/4

Hence, the solution is x=3/4.

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Answer:

[tex]6[/tex]

Step-by-step explanation:

The gist of modular arithmetic in a nutshell: the numbers [tex]a[/tex] and [tex]b[/tex] are considered to be congruent by their modulus [tex]m[/tex] if [tex]m[/tex] is a divisor of their difference.

In mathematics: [tex]a \equiv_{m} b \Leftrightarrow (a - b) \vdots m[/tex]

Exemplifying this: [tex]6 \equiv_{7} -1[/tex] because [tex]6 - (-1) = 6 + 1 = 7[/tex], [tex]7 \vdots 7[/tex].

Let us have following equivalences: [tex]a \equiv_{m} b[/tex] and [tex]c \equiv_{m} d[/tex], then:  [tex](a - b) \vdots m[/tex] and [tex](c - d) \vdots m[/tex] by definition.

Properties:

1. [tex]a + c \equiv_{m} b + d \Leftrightarrow ((a + c) - (b + d)) \vdots m \Leftrightarrow (a + c - b - d) \vdots m \Leftrightarrow ((a - b) + (c - d)) \vdots m[/tex].

2. [tex]a - c \equiv_{m} b - d \Leftrightarrow ((a - c) - (b - d)) \vdots m \Leftrightarrow (a - c - b + d) \vdots m \Leftrightarrow ((a - b) - (c - d)) \vdots m[/tex].

3. [tex]ac \equiv_{m} bd \Leftrightarrow (ac - bd) \vdots m \Leftrightarrow (ac - bc - bd + bc) \vdots m \Leftrightarrow (c(a - b) + b(c - d)) \vdots m[/tex].

4. What if we have [tex]a \equiv_{m} b[/tex] twice? If we abide by property 3, we can come to the conclusion that [tex]a^2 \equiv_m b^2[/tex]. It is fair enough that there is room for the equivalence [tex]a^n \equiv_{m} b^n[/tex].

[tex]3^{51} = (3^3)^\frac{51}{3} = 27^{17} \equiv_{7} (-1)^{17} \equiv_{7} -1 \equiv_{7} 6[/tex].

We used property 4.

Keep in mind that any remainder cannot be a negative number.

Therefore, the remainder equals [tex]6[/tex].

Answer:

18 and 72

Step-by-step explanation:

the smaller part can be assigned as x while the larger will be 4x. Both numbers need to add up to 90, giving the equation: 4x+x = 90

Solve:

4x+x = 90

5x = 90

x = 18

4x = 72

The inverse operations used after the distributive property is B. subtraction then division.

The equation given goes thus:

5(x + 6) = 50.

5x + 30 = 50

5x = 20.

x = 4

Therefore, the inverse operations used after the distributive property is subtraction then division.

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The table below is a quadratic function.

A quadratic function is an Algebraic function with the power of its variable as 2.

This function normally has three algebraic terms, the x-square term, the x-term and the constant term.

Analysis:

The X-column values increases from -2 to 1, while the f(x) column which is the y-column increase from -9, until it gets to 1, where the value falls to -5.

A typical behavior of an inverted-v curve which is a quadratic curve.

If it were a linear function, as x values increase, y value would either keep increasing or decreasing, it does not change its orientation.

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Using the Central Limit Theorem, the standard deviation of the sampling distribution of sample means would be of 0.86.

It states that the standard deviation of the sampling distribution of sample means is given by:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\sigma = 6.8, n = 63[/tex].

Hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]s = \frac{6.8}{\sqrt{63}}[/tex]

s = 0.86.

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The angle of y in the triangle is 30 degrees.

∠O = 180 - 30 - 70 (angles in a triangle)

∠O = 180 - 100(angles in a triangle)

∠O = 80°

Using vertically opposite angle principle and sum of angle in a triangle,

80 + y + 70 = 180

180 - 150 = y

y = 30 degrees

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