The rational expression written using the least common denominator [tex]\frac{x+1}{4x^{2} }+\frac{x+1}{x^{2} }\\[/tex] is [tex]\frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }[/tex].
What is a rational expression?The ratio of two polynomials is displayed in rational expressions. It indicates that the denominator and numerator are polynomials. It is an algebraic expression that has a ratio and an unknown variable, just like a fraction. Although we can simplify this kind of equation with the aid of a calculator.
Because one is divided by the other, just like a ratio, it is a "rational expression."
The polynomial that we divide by cannot be zero, as a reminder.
The least common denominator for [tex]4x^{2}[/tex] and [tex]x^{2}[/tex] is calculated to be [tex]4x^{2}[/tex].
Thus, the required rational expression is [tex]\frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }[/tex].
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Solving Quadratic Inequalities
Nathan is a product manager for a home security company. Through testing and focus groups, he has modeled the equation P = -(x - 32)2 + 1000 to represent the profit (in thousands) of the price x for a new home security camera. Find the prices in dollars at which Nathan can make a profit of at least $471, 000. Show your work as it is done in the lesson content and include units of measurement.. HINT: Use 471 as part of the inequality you set up, not 471,000.
The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the profit (P) in thousands for security camera with price of x, hence for a profit of at least $471, 000:
-(x - 32)² + 1000 ≥ 471
-(x² - 64x + 1024) + 1000 ≥ 471
-x² + 64x - 1024 + 1000 - 471 ≥ 0
-x² + 64x - 495 ≥ 0
x = 55 or x = 9
The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9
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A table has an area of x² + 12x + 35. Find the possible dimensions of the table.
Answer:
x + 7 and x + 5 are possible dimensions
Step-by-step explanation:
x² + 12x + 35 ← factor the quadratic
consider the product of the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)
the factors are + 7 and + 5 , since
7 × 5 = + 35 and 7 + 5 = + 12 , then
x² + 12x + 35 = (x + 7)(x + 5) ← in factored form
now the area A = length × breadth , that is
A = x² + 12x + 35 = (x + 7)(x + 5) , then
length = x + 7 or x + 5
breadth = x + 5 or x + 7
Which expression is equivalent to -1/6y+1/3?
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression that is equivalent to -(1/6)y + 1/3 is,
-(1/6)y + 1/3
Take 1/6 common from both first and the last term,
1/6 (-y + 2)
Hence, the correct option is C.
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Which linear function represents the line given by the point-slope equation y-8=(x-4)?
A) f(x) = x +4
B) f(x) = x+6
C) f(x)=x-10
D) f(x)=x-12
The answer is (A) f(x) = x+4.
write an equation in slope- intercepty form of the line that passes through the point (5,9) with slope 7
A total of 316 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?
Step-by-step explanation:
ATTACHED IS THE SOLUTION!Answer:
Adults: 79 tickets
Students: 237 tickets
Step-by-step explanation:
a + b = 316 Eq. 1
b = 3a Eq. 2
a = adults
b = students
Replacing Eq. 2 in Eq. 1
a + 3a= 316
4a = 316
a = 316/4
a = 79
from the Eq. 2
b = 3a
b = 3*79
b = 237
Check:
from the Eq. 1
a + b = 316
79 + 237 = 316
8. Jess walked for 45 minutes at 3 km/h and then ran for half an hour at x km/h. At the end
of that time she was 6 km from the starting point. Find the value of x.
Answer:
x = 7.5 km/h
Step-by-step explanation:
• First calculate the distance covered by walking at 3 km/h for 45 minutes ( 0.75 h):
distance = speed × time
= 3 × 0.75
= 2.25 km
• Therefore, she covered 2.25 km of the total journey by walking. Since she was 6 km from the starting point at the end of the entire journey, we can calculate the distance remaining, which she had to run:
distance she had to run = 6 - 2.25
= 3.75 km
• Now we can calculate the speed of the 30 minute (0.5 h) run:
speed = distance ÷ time
= 3.75 ÷ 0.5
= 7.5 km/h
This means that she ran at 7.5 km/h for half an hour.
∴ x = 7.5
10 + (-8) - 2
Answer the equation
Answer:
0
Step-by-step explanation:
[tex]10 + ( - 8) - 2 \\ = 1 0 - 8 - 2 \\ = 2 - 2 \\ = 0[/tex]
Answer: 0
Step-by-step explanation: -8+-2 is -10 and -10+10 is 0
Find the coordinates of the intersection of the diagonals of the parallelogram with the vertices W(−2, 5), X(2, 5), Y(4, 0),
and Z(0, 0)
.
Using the midpoint formula, the coordinates of the intersection of the diagonals of the parallelogram is: (1, 2.5).
What are Diagonals of a Parallelogram?The diagonals of a parallelogram bisect each other, therefore, the coordinates of their intersection can be determined using the midpoint formula, which is: [tex]M(\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].
A diagonal is XZ.
X(2, 5) = (x1, y1)
Z(0, 0) = (x2, y2)
Plug in the values
[tex]M(\frac{0 + 2}{2}, \frac{0 + 5}{2})[/tex]
= (1, 2.5).
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If f(x) = x..........
Answer:
b.) 0
Explanation:
⇒ f(g(-1))
go from right to left while solving such function questions.
⇒ f(-1 + 2)
⇒ f(1)
⇒ (1)² -2(1) + 1
⇒ 0
Step-by-step explanation:
[tex]f(x) = {x}^{2} - 2x + 1[/tex]
[tex]f(x) = {(x - 1)}^{2} [/tex]
[tex]g(x) = x + 2[/tex]
[tex] \: [/tex]
[tex] = f(g( - 1))[/tex]
[tex] = {(x - 1)}^{2} [/tex]
[tex] = {((x + 2) - 1)}^{2} [/tex]
[tex] = {(( - 1 + 2) - 1)}^{2} [/tex]
[tex] = {(1 - 1)}^{2} [/tex]
[tex] = {0}^{2} [/tex]
[tex] = 0[/tex]
The answer is B.
A small town's population, P, can be modeled by the equation P (t) = 45,000(2.66), where t is the time in years. Is the statement below true of false. The rate of population growth each year is 166% O True O False
A function assigns the values. The statement "The rate of population growth each year is 166%" is true.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function of the population for the town is [tex]P (t) = 45,000(2.66)^t[/tex], where t is the time in years. Comparing the given function to the general function of the population,
P(x) = a(1+b)ˣ
Then, the value of b will be 166%.
Hence, the statement "The rate of population growth each year is 166%" is true.
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In the diagram of AABC shown below, DE || BC.
B
A
3) 3
4) 15
E
If AB= 10, AD = 8, and AE = 12, what is the
length of EC?
1) 6
2) 2
C
dd or create
k as done
nments
As
to Susan Guha
Answer:
3
Step-by-step explanation:
AD/AB = AE/AC
8/10 = 12/AC
AC = 12(10/8)=15
EC = 15 - 12 = 3
CHECK
n =
Solve the equation.
−4(n − 6)= 12
[tex] - 4(n - 6) = 12 \\ (n - 6) = \frac{12}{ - 4} \\ n - 6 = - 3 \\ n = - 3 + 6 \\ n = 3[/tex]
If you rolled two dice, what is the probability
Give
that you would roll a sum of 5?
your answer as a simplified fraction. Enter
the
number that belongs in the green box.
second
first
1 2
3 456
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
§
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3
6,4 6,5 6,6
Answer:
Probability of rolling a sum of 5 is 1/9.
There are 36 different combinations because 6(first roll)*6(second roll) = 36. The only possible combinations are {1,4},{2,3}{2,3}and{4,1}
4/36 = 1/9
You have learned how to divide polynomials in three different ways: by factoring, by long division, and by synthetic division. Explain in words and with mathematical representations how you would divide this polynomial in each of the three ways:
a) Factoring:
b) Long division:
c) Synthetic division:
d) Now, explain a connection you can see for each pair of methods. How does factoring relate to long division? How does long division relate to synthetic division? How does synthetic division relate to factoring?
The way to solve the polynomial using the methods is given below.
How to explain the polynomial?Polynomial by factoring:
An example is (t² + 5t + 4) / +t + 4)
= (t + 1)(t + 4)/(t + 4)
= t + 1.
Dividing polynomial by long division:
Divide the first term of the dividend by the first term of the divisor.
Put this as the first term in the quotient.
Subtract to create a new polynomial.
Continue until you can't divide anymore.
Dividing polynomial by synthesic division:
Step 1: Set up the synthetic division.
Step 2: Bring down the leading coefficient to the bottom row.
Step 3: Multiply c by the value just written on the bottom row.
Step 4: Add the column created in step 3.
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Willey’s Grill & Restaurant Corporation wholesales ovens and ranges to restaurants throughout the Southwest. Willey’s Grill & Restaurant, which had 335,000 shares of common stock outstanding, declared a 2-for-1 stock split. This information has been collected in the Microsoft Excel Online file. Open the spreadsheet, perform the required analysis, and input your answers in the questions below.
a. The number of shares outstanding after the stock split by Willey’s Grill & Restaurant Corporation is 670,000 (335,000 x 2).
b. If the common stock had a market price of $510 per share before the stock split, the approximate market price per share after the split is $255 ($510/2).
What is a stock split?A stock split is a way that a corporation increases the number of its shares by increasing or decreasing the number of shares outstanding.
When a stock split increases the number of outstanding shares, the market price reduces proportionately.
Question Completion:a. What will be the number of shares outstanding after the split? Round your answer to the nearest whole number.
b. If the common stock had a market price of $510 per share before the stock split, what would be an approximate market price per share after the split? Round your answer to the nearest dollar.
Thus, the stock split increased the outstanding shares to 670,000 while reducing the market price to $255.
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What is the value of h(a) when a = 2 in the
piecewise function
3a + 2
4a +5
3
h(a) =
when a > 3
when a = 3
when a <3
=========================================================
Explanation:
This is the given piecewise function
[tex]h(a) = \begin{cases}3a+2 \text{ when } a > 3\\4a+5 \text{ when } a = 3\\3 \text{ when } a < 3\\\end{cases}[/tex]
We can rewrite things like this
[tex]\text{when } a > 3, \ \ h(a) = 3a+2\\\text{when } a = 3, \ \ h(a) = 4a+5\\\text{when }a < 3, \ \ h(a) = 3\\[/tex]
I personally prefer this format better because it mentions the inputs first, and that leads to which function definition we go for.
The input a = 2 fits the description of [tex]a < 3[/tex] since [tex]2 < 3[/tex] is a true statement. Therefore we go for the third line and can see that [tex]h(a) = 3[/tex] becomes [tex]h(2) = 3[/tex]
-----------
As another example, if we had the input a = 7, then we'd go for the first line (since 7 > 3) and get
h(a) = 3a+2
h(7) = 3(7)+2
h(7) = 23
please help
f (5) = x2
Answer:
25
Step-by-step explanation:
f(5)=x2
=25
The information below explains the transformations and translations of a logarithmic function. What is the equation for this function?
Shift 4 units left
Shift 3 units up
Vertical Compress by 1/3
Horizontal stretch by 3
Fill in the table below for the information of the function f(x) = log[-(x – 5)] + 4
Function
Log[-(x - 5)] + 4
Domain
Range
Interval of Increase/Decrease
Equation of Asymptote
The transformed function is y = 1/3(log(x/3 + 4)) + 1
How to transform the logarithmic function?The parent logarithmic function is
y = log(x)
When shifted left by 4 units, we have:
y = log(x + 4)
When shifted up by 3 units, we have:
y = log(x + 4) + 3
When compressed vertically by 1/3, we have:
y = 1/3(log(x + 4) + 3)
This gives
y = 1/3(log(x + 4)) + 1
When stretched horizontally by 3, we have:
y = 1/3(log(x/3 + 4)) + 1
Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1
The transformation of function f(x)We have:
f(x) = log[-(x – 5)] + 4
Set the radicand greater than 0
-(x - 5) > 0
Divide by -1
x - 5 < 0
Add 5 to both sides
x < 5 -- this represents the domain
A logarithmic function can output any real number.
So, the range is [tex]-\infty < f(x) < \infty[/tex]
In the domain, we have:
x < 5
This means that the interval of decrease is [tex]-\infty < x < 5[/tex]
Rewrite as an equation
x = 5 --- this represents the equation of asymptote
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Which relation is also a function?
O {(1,0), (2,2), (1,3)}
O {(1, 2), (1, 4), (2, 6) }
○ {(2, 1), (2, 2), (2, 3) }
○ { (0, 0), (4, 0), (6, 0) }
Answer: Option 4
Step-by-step explanation:
Each value of x maps onto one value of y, meaning the relation is a function.
The graph of y = |2x – 2| – 4 is shown. On a coordinate plane, an angled line opens up. It approaches the grid line at (negative 4, 6), crosses the x-axis at (negative 1, 0), the y-axis at (0, negative 2), has a vertex of (1, 4), and crosses the x-axis at (3, 0). Which statement about the graph is accurate? An x-intercept of the graph is (0, 3). The graph has two y-intercepts. A y-intercept of the graph is (0, –2). The graph has no x-intercepts.
76.89 sjsbs austere. Sisson whenever. Ebenezer oe eie h rur fuf 8r r earned e 3epoe9 r rur 8e e aonwowne e7 rjr or
Use the function below to find F(3).
Answer: B
Step-by-step explanation:
Plug in x for 3. Then solve.
4*(1/3)^3
4*1/9
4/9
Which of the following segments is a radius of OK?
M
K
OA. KM
B. MR
C. RT
D. MT
SUB
Answer:
A. KM
Step-by-step explanation:
A circle is named by its center. Circle K has its center at point K.
A radius is a line segment that extends from the center of the circle to a point on the circle. Point K must be one end of any radius.
ApplicationSegment KM is a radius.
Segments between points on the circle are chords. The other named segments in the answer choices are all chords of the circle.
Given that sin(90-x)°=0.8. where x is an acute angle.Find without using calculator or mathematical table the value of tan x
By using trigonometric properties, we will see that:
tan(x) = 3/4.
How to find the value of tan(x)?
Remember that the sine of the difference is:
sin(a - b) = sin(a)*cos(b) - sin(b)*cos(a).
Here we have:
sin(90° -x ) = 0.8
Expanding the sine:
sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°)
We know that:
sin(90°) = 1 and cos(90°) = 0, then:
sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°) = cos(x).
Then we have:
cos(x) = 0.8
And we want to find the tangent of x, which is:
[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]
We already know that cos(x) = 0.8
Now, remember that:
[tex]sin(x)^2 + cos^2(x) = 1\\\\sin(x) = \sqrt{1 - cos^2(x)} \\[/tex]
Because x is an acute angle, sin(x) > 0, that is why we choose the positive root.
Replacing cos(x) we get:
[tex]sin(x) = \sqrt{1 - 0.8^2} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6[/tex]
Then the tangent of x is:
[tex]tan(x) = \frac{0.6}{0.8} = \frac{6}{10}*\frac{10}{8} = 6/8 = 3/4[/tex]
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The table below shows which hand is favored by each person from a sample of 100 people (50 male and 50 female). Use the information in the table to answer the following questions
Determine the probability that a randomly selected person from the sample will be female or left-handed.
The probability that a randomly selected person from the sample will be female or left-handed will be 0.05.
What is the probability?Probability is synonymous with possibility. It is concerned with the occurrence of a random event.
Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.
Given data;
Total number of sample,n(S) = 100 person
No of female or left-handed is,n(E) =5
P(E) is the probability that a randomly selected person from the sample will be female or left-handed
The probability that a randomly selected person from the sample will be female or left-handed is found as;
P(E) = n(E)/n(S)
P(E) = 5 / 100
P(E) = 0.05
Hence the probability that a randomly selected person from the sample will be female or left-handed will be 0.05.
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The sum of product of two and nine and product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers.
The sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression can be written as,
[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)[/tex]
The result of the above expression will be,
[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)\\\\=\dfrac{18+72}{9} \times (10)\\\\[/tex]
= (90/9) × 10
= 10 × 10
= 100
Hence, the sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.
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Evaluate x² + 4x + 1 when x = -3
Answer: -2
Step-by-step explanation:
We can combine the fundamentals of mental math and the brain to calculate the problem when x is -2. You wake up noticing x is -2 and you instantly know the answer and solved in less than a second.
Which expression is equivalent to (3x² + 4x-7)(x-2)?
OA. (3x2 + 4x-7)(x) + (3x² + 4x-7)(-2)
OB. 2x(3x² + 4x-7)
OC. x(3x² + 4x-7) - 2
OD. x(3x² + 4x-7)+2(3x² + 4x-7)
Answer: A
Step-by-step explanation:
The expressions are equivalent by the distributive property.
the cone shaped game piece is made of metal with a mass of 9.2g/cm3 what is the mass of the game piece
The volume of the piece of the metal Gina is found to be 22.82 cubic cm.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of cube or cuboid.
Given the density of the metal = 9.2g/cm3
Given the mass of the piece of the metal = 210 g
Assuming the volume of a piece of metal to be V
The expression for the density is shown below:-
Density = Mass / Volume
9.2 = 210 / V
V = 210 / 9
V = 22.82 cubic cm.
Therefore the volume of the piece of the metal Gina is found to be 22.82 cubic cm.
The complete question is given below:-
Gina was given an irregularly shaped piece of metal and was told that the density of the metal was 10 g/cm3. She measured the mass of the piece to be 210 g. What was the volume of the piece of metal Gina was given?
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Use the function below to find F(4).
Answer:
A. 81
Step-by-step explanation:
F(x)=[tex]3^{x}[/tex]
if x=4, then F(4) = [tex]3^{4}[/tex] = 3×3×3×3=81