Write in Expanded form
(-3x)^4
Use parenthesis to indicate multiplication

Answer:

Kate’s photo get 14 likes

Step-by-step explanation:

Let

x ----> Kate's likes

y ---> Ali's likes

we know that

y=42 likes ----> equation A

y=3x ----> equation B

Solve by substitution

Substitute equation A in equation B and solve for x

42=3x

Divide by 3 both sides

x=42/3

x=14 likes

Kate's photo got 14 likes.

The student is dealing with a basic algebra problem that involves setting up and solving an equation. To find out how many likes Kate's photo got, we can let x represent the number of likes on Kate's photo. Given that Ali's photo got 42 likes, which is three times as many as Kate's photo, we can write the equation as:

3x = 42

To find x, we divide both sides of the equation by 3:

x = 42 / 3

x = 14

Therefore, Kate's photo got 14 likes.

Answer:

[tex]A=5, B=0,C=3[/tex]

Step-by-step explanation:

The partial fraction decomposition is given as:

[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{A}{x+3}+\frac{Bx+C}{x^2+9}[/tex]

We collect LCD on the RHS to obtain;

[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{A(x^2+9)+(x+3)(Bx+C)}{(x+3)(x^2+9)}[/tex]

We expand the parenthesis in the numerator of the fraction on the RHS.

[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{Ax^2+9A+Bx^2+(3B+C)x+3C}{(x+3)(x^2+9)}[/tex]

This implies that:

[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{(A+B)x^2+(3B+C)x+3C+9A}{(x+3)(x^2+9)}[/tex]

This is now an identity. Since the denominators are equal, the numerators must also be equal.

[tex]5x^2+3x+54=(A+B)x^2+(3B+C)x+3C+9A[/tex]

We compare coefficients of the quadratic terms to get:

[tex]A+B=5\implies B=5-A...(1)[/tex]

Also the coefficients of the linear terms will give us:

[tex]3B+C=3...(2)[/tex]

The constant terms also gives us;

[tex]3C+9A=54...(3)[/tex]

Put equation (1) in to equations (2) and (3).

[tex]3(5-A)+C=3\implies C=3A-12...(4)[/tex]

[tex]3C+9A=54...(5)[/tex]

Put equation (4) into (5).

[tex]3(3A-12)+9A=54[/tex]

[tex]9A-36+9A=54[/tex]

[tex]9A+9A=54+36[/tex]

[tex]18A=90[/tex]

[tex]A=\frac{90}{18} =5[/tex]

Do backward substitution to get:

[tex]C=3(5)-12=3[/tex]

[tex]B=5-5=0[/tex]

[tex]\therefore A=5, B=0,C=3[/tex]

The constants A, B, and C in the partial fraction decomposition are determined to be A = 5, B = 0, and C = 3.

To find the values of A, B, and C in the partial fraction decomposition of the rational function

Therefore, the number of adul, follow these steps:

Answer:

13 = m

Step-by-step explanation:

I do not know what that nine is doing there, but you just simply evaluate to arrive at your answer.

[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y=-\cfrac{3}{4}x+6[/tex]

Answer:

D y= -2 (x-8)2 -3

Step-by-step explanation:

The equation of the new parabola will be y = -2(x + 2)² + 1. Then the correct option is A.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation of the parabola is given below.

y = -2(x - 3)² + 4

If this parabola is shifted 5 units to the left and 3 units down. Then replace x with x + 5 and subtract 3 from the equation.

Then the equation of the new parabola will be given as,

y = -2(x + 5 - 3)² + 4 - 3

y = -2(x + 2)² + 1

The condition of the new parabola will be y = - 2(x + 2)² + 1. Then, at that point, the right choice is A.

More about the equation of the parabola link is given below.

https://brainly.com/question/20333425

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Answer:

-15

Step-by-step explanation:

Note that it says x = -9. Plug in -9 for all x inside the expression and solve.

(x² + 9)/(x + 3) = (-9² + 9)/(-9 + 3)

Solve. First, solve the parenthesis, then divide:

(-9² + 9) = (81 + 9) = 90

(-9 + 3) = (3 - 9) = -6

Divide:

(90)/(-6) = -15

-15 is your answer.

~

Step-by-step answer with explanations:

Recall that a coordinate pair such as (5,-1) has two components.

The first (5, -1) means that the point is situated at x=5.

The second (5, -1) means that the point is situated at y=-1.

Now, a horizontal line through (5,-1) means that ALL points on the line have y-coordinate equal to -1, so that any point with y=-1 will lie on this horizontal line.  An example would be (-2,-1).

A vertical line through (5, -1) means that ALL points on the line have x-coordinate equal to 5, so that any point with x=5 will lie on this vertical line.  An example would be (5,4).

Answer:

its D

Step-by-step explanation:

ur welcome =)

Answer:

Table 3 and 4

Step-by-step explanation:

Let us understand the coordinates symmetry of the graphs of quadratic equations.

In a quadratic equation, we have a polynomial in x with degree 2. Hence the result in y or P(x) do get repeated as polynomial contains [tex]x^2[/tex] in it.

Thus by analysing the tables we see that in table 3 , y= -10 gets repeated and in table 4 , y =4 and y=-4 repeated. Hence they are the graph of a quadratic polynomial

Answer:

8,640 ft^2

Step-by-step explanation:

There are 144 square inches per square foot, therefore 144x60=8,640 ft^2

                              108

                              /     \

                            12     9

                           /  \      /  \

                         4   3    3   3

                        / \

                      2   2

             2y                     5

             / \                     /  \

           2   y                 1    5

<Hope this helps!>

Step-by-step explanation:

all work is pictured and shown

Answer: 317.93

Step-by-step explanation:

317.93371 when rounded off to nearest hundred, we get 317.93.

Rounding off is the method by which a decimal integer is reduced to its nearest closer value of the next number . After the decimal point, if the value is greater than 5 we increment the numerical value by 1 and if the value is less than 5 we keep the numerical value intact.

The given value is 317.93371 .

Rounding off to nearest hundred means that we will get the rounded off value up to two decimal places.

We can see that the third decimal place is 3 which means that the second decimal place of the number will be kept intact.

Rounded off value is -  317.93 .

Thus, 317.93371 when rounded off to nearest hundred, we get 317.93.

To learn more about rounding off, refer -

https://brainly.com/question/48768

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Answer:

Option C. approaches but does not cross.

Step-by-step explanation:

In Maths, an asymptote is a line that the graph (a drawing that shows two sets of related amounts) of a function (e.g. x=1/x) approaches but does not cross (or intersect). The image below illustrates such concept.

Answer:    C. Approaches but does not cross

Step-by-step explanation:  Basically an asymptote is a line that approaches a given curve which is graph of a function, but it never touches, cross or intersect in any finite. Asymptote can be any line, horizontal, vertical, inclined, which approaches the function graph. Theoretically, according to mathematical principles,  the function graph line is approaching to a asymptote at infinity, and therefore the asymptotes are suitable as the type of guide to complete the graph of the function.

Answer:

You MUST use parentheses around denominator 8+x, or ANY denominator that consist of more than a single number of variable. 

Also, don't use lower case and upper case interchangeably. 

In algebra, x and X are different, as are y and Y. 

f(x) = y = 3x/(8+x) 

Switch x and y, solve for y: 

x = 3y/(8+y) 

x(8+y) = 3y 

8x+xy = 3y 

8x = 3y−xy 

8x = y(3−x) 

y = f⁻¹(x) = 8x/(3−x)

I hope this helps, love 

Step-by-step explanation:

Answer:

In the explanation

Step-by-step explanation:

Going to start with the sum identities

sin(x+y)=sin(x)cos(y)+sin(y)cos(x)

cos(x+y)=cos(x)cos(y)-sin(x)sin(y)

sin(x)cos(x+y)=sin(x)cos(x)cos(y)-sin(x)sin(x)sin(y)

cos(x)sin(x+y)=cos(x)sin(x)cos(y)+cos(x)sin(y)cos(x)

Now we are going to take the line there and subtract the line before it from it.

I do also notice that column 1 have cos(y)cos(x)sin(x) in common while column 2 has sin(y) in common.

cos(x)sin(x+y)-sin(x)cos(x+y)

=0+sin(y)[cos^2(x)+sin^2(x)]

=sin(y)(1)

=sin(y)

Answer:

It is an identity, the proof is in the explanation

Step-by-step explanation:

csc(A)-cot(A)=tan(A/2)

I'm going to start with right hand side

tan(A/2)=(1-cos(a))/(sin(a))                half angle identity

tan(A/2)=1/sin(a)-cos(a)/sin(a)         separate fraction

tan(A/2)=csc(a)-cot(a)                     reciprocal and quotient identities

Answer:

0.16

Step-by-step explanation:

81 is 1 standard deviation below the mean.  According to the empirical rule, 68% of data lies within 1 standard deviation of the mean; here the equivalent statement would be that half of that, or 34%, lies within 1 standard deviation below the mean.  Half of the area under the standard normal curve, less this 0.34, is the probability that the random variable is below 1 standard deviation beneath the mean.  That comes to 0.16.

On a calculator, you might enter the command normalcdf(-100,81,85,4); on my old TI-83 Plus I get 0.1587, which rounds off to 0.16.

Final answer:

The z-score of -1 corresponds to a probability of approximately 0.1587, therefore P(x < 81) is approximately 0.1587, or 15.87%.

Explanation:

To find the probability that a normally distributed random variable x is less than 81, P(x < 81), when the mean μ is 85 and the standard deviation σ is 4, we need to use the properties of the normal distribution.

First, we convert the raw score of 81 into a z-score. The formula for calculating a z-score is:

[tex]z = (x - μ) / σ[/tex]

For x = 81, the z-score would be:

z = (81 - 85) / 4

z = -1

Next, we use a standard normal distribution table, a calculator, or software to find the probability that correlates with this z-score. The table lists probabilities to the left of z-scores.

The z-score of -1 corresponds to a probability of approximately 0.1587, therefore P(x < 81) is approximately 0.1587, or 15.87%.

Answer:

Option A and B

Step-by-step explanation:

sides of the triangle have been given as 15, 15.8, 30 units.

angles of the same triangle has been given as 70°, 80°, [180-(70+80)] or 30°.

Here we see all sides and all the angles of the given triangle have different measures ( all the three sides and angles are different )

By the definition of scalene triangle the given triangle will be scalene.

Since all three angles of the triangle are acute angles (less than 90°).

Therefore, Option A and B are correct.

Step-by-step explanation:

Volume of a cylinder is:

V = π r² h

where r is the radius (half the diameter) and h is the height.

Here, r = 3 and h = 9.

V = π (3)² (9)

V = 81π

Answer:

Undefined

Step-by-step explanation:

You can deduce the solution in two ways: if the slope of m is zero, it is horizontal. So, n is vertical because it must be perpendicular to n. Vertical lines have undefined slope.

Alternatively, if the slope of line m is k, the slope of a perpendicular line n is -1/k. So, if k=0, you can't compute -1/0.

Answer:

-5,-4,-3

Step-by-step explanation:

Let n be an integer.

The next integer would have to be n+1.

The integer before n would have to be n-1.

So the numbers in order are n-1, n , n+1

The sum of the first 2 equals 3 times the third:

n-1     +     n                      =     3(n+1)

2n-1                                 =      3(n+1)

2n-1=3n+3

Subtract 2n on both sides

    -1=n+3

Subract 3 on both sides

    -4=n

If n=-4

then n-1=-5

and n+1=-3

So the three numbers are -5,-4,-3 .

Answer:

-0.1715

Step-by-step explanation:

False.

This is not a function because for something to be a function each x value can only have one y value. In this case two of the points have a value of 1 and their y are different, making them NOT a function

(1, 3)

(1, 2)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

14.4 in

Step-by-step explanation:

2160/ 150= 14.4

Answer:

Both the lines would have the same slope since they are parallel. The lines would not however have the same y-intercept.

Step-by-step explanation:

This is because in order for lines to be parallel the lines must have the same slope, otherwise they would meet at some point. They would not have the same y-intercept because if both the y-intercept and the slope were the same it would be the same line.

Answer:

Both lines are parallel, so they have the same slope. However, the y-intercepts of the lines are not the same. For the lines to be parallel, the slopes of the lines must be the same. If both the y-intercept and slope are the same, they are the same line, so they do not have the same y-intercept.

Hi! Let's go over the meanings of each term to find our answer.

Domain of an exponential parent function - the set of all real values of x that will give real values for y in the given function

Range of an exponential parent function - the set of all real values of y that you can get by plugging real numbers into x in the same function

Now we have our answers! All we had to do was go over the meanings, or definitions.

Hope this helps!

- Kylie

Answer:

The domain of exponential parent function is all real values and range is real positive numbers [tex]y>0[/tex].

Step-by-step explanation:

We are asked to find the domain and range of exponential parent function.

We know that an exponential parent function is in form [tex]f(x)=b^x[/tex], where b is the base of function.

We can see from parent exponential function that as x approaches to very large values of x, the value of y increases with no bounds.

As x approaches negative infinity, y approaches to zero.

We know that the domain of a parent exponential function is all real values of x that is [tex](-\infty,\infty)[/tex] in interval notation.

The range of a parent exponential function is positive real numbers that is [tex]y>0[/tex].

Answer:

[tex]\large\boxed{Q1.\ 80\ cm^3}\\\boxed{Q2.\ 45\ in^3}\\\boxed{Q3.\ 48\ m^3}\\\boxed{Q4.\ A,\ D}\\\boxed{Q5.\ 96\ in^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a rectangular prism:}\\\\V=lwh\\\\l-length\\w-width\\h-height[/tex]

[tex]\bold{Q1}\\\\l=10\ cm,\ w=4\ cm,\ h=2\ cm\\\\V=(10)(4)(2)=80\ cm^3\\\\\bold{Q2.}\\\\l=5\ in,\ w=3\ in,\ h=3\ in\\\\V=(5)(3)(3)=45\ in^3\\\\\bold{Q3.}\\\\l=4\ m,\ w=2\ m,\ h=6\ m\\\\V=(4)(2)(6)=48\ m^3\\\\\bold{Q4.}\\\\V=120\ ft^3\\\\\bold{A:(5)(4)(6)=120}\\B:\ (7)(7)(6)=294\\C:\ (3)(6)(4)=72\\\bold{D:\ (10)(3)(4)=120}\\\\\bold{Q5.}\\\\l=8\ in,\ w=4\ in,\ h=3\ in\\\\V=(8)(4)(3)=96\ in^3[/tex]

Answer:

x = [tex]\frac{C-By}{A}[/tex]

Step-by-step explanation:

Given

Ax + By = C ( isolate the term in x by subtracting By from both sides )

Ax = C - By ( divide both sides by A )

x = [tex]\frac{C-By}{A}[/tex]

Answer:

Step-by-step explanation:

Solve Ax+By=C for x.:

Ax= - By+C

case 1 : A≠0       x = (- B/A)y+C/A

case 2 : A=0

you have : 0x = - By+C

B=0 :  ox = C     C = 0  infinity of x      C≠0  no solutions

Answer:

x + y = 330

9x + 16y = 4650

Step-by-step explanation:

Given that x = children and y = adults, we can say that x + y = 330.

Since the total amount of money collect from both children and adults was $4650, we can say that 9x + 16y = 4650.

So the system that represents the situation is:

x + y = 330

9x + 16y = 4650

Answer:

Answer:

x + y = 330

9x + 16y = 4650

Step-by-step explanation:

Given that x = children and y = adults, we can say that x + y = 330.

Since the total amount of money collect from both children and adults was $4650, we can say that 9x + 16y = 4650.

So the system that represents the situation is:

x + y = 330

9x + 16y = 4650

Answer:

[tex]e^{ln(12)}=12[/tex]

Step-by-step explanation:

I suppose your intended expression is;

[tex]e^{ln(12)}[/tex]

The exponential function, e, and the natural logarithm function, ln, are inverses of each other;

[tex]e^{lnx}=x\\\\lne^{x}=x[/tex]

Therefore, our expression becomes;

[tex]e^{ln(12)}=12[/tex]

Answer:

D

Step-by-step explanation:

7(1–k)

= 1(7) -k(7)  -------------> distributive property

= 7–7k