Which function has a range of y < 3?
y=3(2)x
y=2(3)x
y=-(2)x +3
y = (2)x - 3

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:

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:

-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:

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.

                              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:

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

[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:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=\dfrac{1}{2}x-4&(1)\\y=-2x-9&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\\dfrac{1}{2}x-4=-2x-9\qquad\text{multiply both sides by 2}\\\\x-8=-4x-18\qquad\text{add 8 to both sides}\\\\x=-4x-10\qquad\text{add 4x to both sides}\\\\5x=-10\qquad\text{divide both sides by 5}\\\\x=-2\\\\\text{put it to (2):}\\\\y=-2(-2)-9\\\\y=4-9\\\\y=-5[/tex]

Answer:

D

Step-by-step explanation:

7(1–k)

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

= 7–7k

Answer:

There are 18 nickel coins and 27 dime coins

Step-by-step explanation:

Remember that

1 nickel=$0.05

1 dime=$0.10

Let

x ----> the number of nickel coins

y ---> the number of dime coins

we know that

x+y=45

x=45-y -----> equation A

0.05x+0.10y=3.60

Multiply by 100 both sides

5x+10y=360 ----> equation B

Solve the system by substitution

Substitute equation A in equation B and solve for y

5(45-y)+10y=360

225-5y+10y=360

5y=360-225

5y=135

y=27

Find the value of x

x=45-27= 18

therefore

There are 18 nickel coins and 27 dime coins

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:

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.

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:

Step-by-step explanation:

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

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

m - slope

b - y-intercept → (0, b).

The formula of a slope:

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

We have the points A(0, -4) → b = -4 and B(6, 2).

Calculate the slope:

[tex]m=\dfrac{2-(-4)}{6-0}=\dfrac{6}{6}=1[/tex]

Put the value of m and of b to the equation:

[tex]y=1x-4[/tex]         add 4 to both sides

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

Answer:

a=-2

b=4

c=-3

Step-by-step explanation:

You just compare -2x^2+4x-3=0 to

                              ax^2+bx+c=0

There is really no work here.

For this case we have that by definition, a quadratic equation is of the form:

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

The roots are given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

We have the following equation:

[tex]-2x ^ 2 + 4x-3 = 0[/tex]

So:

[tex]a = -2\\b = 4\\c = -3[/tex]

Answer:

[tex]a = -2\\b = 4\\c = -3[/tex]

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:

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:

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:

-0.1715

Step-by-step explanation:

Answer:

[tex]y-3=-5(x-6)[/tex]

Step-by-step explanation:

we know that

The equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-5[/tex]

[tex](x1,y1)=(6,3)[/tex]

substitute

[tex]y-3=-5(x-6)[/tex] ----> equation of the line into point-slope form

Answer:

5 gallons and 3 quarts

Step-by-step explanation:

There are 4 quarts in a gallon so 23/4=5 gallons and 3 quarts

Answer:

5 gal and 3 qt.

Step-by-step explanation:

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.

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:

(3, 1)

Step-by-step explanation:

x = y + 2

y = -2x + 7

y = -2(y +2) +7

y = -2y -4 +7

y + 2y = 3

3y = 3

y = 3/3

y = 1

x = y +2

x = 1 +2

x = 3

The value of x is 1/3 and y is -5/3. using substitution method

solving this we will get the valve of Y if x is given.

CALCULATION:-

Y=x-2 -----(1)

y=-2x+7 ---------(2)

putting the value of y in the equation (2)

x-2= -2x+7

x+2x=7+2

3x=9

x=9/3

x=1/9

putting the value of X in equation(1)

 Y=x-2 -----(1)

y=1/3-2

y=-5/6  

Learn more about linear equations here:https://brainly.com/question/2972832

#SPJ2

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:

D. 804.2

Step-by-step explanation:

The area equation is πr^2 so

16^2 = 256

256 × π (or 3.14) = 803.84

which is ≈ 804.2

Please mark brainliest. :)

UWU have a nice day!

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:

[tex]\$2,161.1[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\P=\$4,500\\ r=0.04\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$4,500(1+\frac{0.04}{1})^{1*10}[/tex]  

[tex]A=\$4,500(1.04)^{10}[/tex]

[tex]A=\$6,661.10[/tex]    

Find the interest

[tex]I=A-P[/tex]

[tex]I=\$6,661.10-\$4,500=\$2,161.1[/tex]

Answer:

2161.10

Step-by-step explanation: