the division of fractions follows the stes
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]Applying this into the expression given
[tex]\frac{3\cdot(a-9)}{9\cdot(a^2-81)}[/tex]simplify the coefficients by decomposing 9 into a product and cancelling the common factors
[tex]\frac{3\cdot(a-9)}{3\cdot3\cdot(a^2-81)}[/tex]simplify
[tex]\frac{a-9}{3\cdot(a^2-81)}[/tex]In the denominators there is a difference of squares that can be rewriten as a product, in which by definition the difference of square is described as
[tex]a^2-b^2=(a+b)\cdot(a-b)[/tex]In the denominator of the expression we can see that a is squared and that 81 has an exact root which is 9, reason why we can write this as a difference of squares, it should look like this:
simplify the expression
[tex]\frac{1}{3\cdot(a+9)}[/tex]distribute the 3
[tex]\frac{1}{3a+27}[/tex]EASY) write and equation for x then solve for x
Answer:
[tex]\large\boxed{\tt x = 23^{\circ}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are given 2 \underline{Linear Pairs}. We are asked to form an equation, and to solve for x.}[/tex]
[tex]\large\underline{\textsf{What are Linear Pairs?}}[/tex]
[tex]\textsf{Linear Pairs are 2 Adjacent Angles that form a 180}^{\circ} \ \textsf{angle, or add up to 180}^{\circ}.[/tex]
[tex]\textsf{For our problem, these 2 angles given to us are Linear Pairs, which equal 180}^{\circ}[/tex]
[tex]\textsf{when added together. Let's create an equation to find x.}[/tex]
[tex]\large\boxed{\tt 180^{\circ}=93^{\circ} + (3x+18)^{\circ}}[/tex]
[tex]\textsf{Now, let's solve for x by using the \underline{Properties of Equality}.}[/tex]
[tex]\large\underline{\textsf{What are the Properties of Equality?}}[/tex]
[tex]\textsf{The Properties of Equality are Properties that allow us to manipulate equations.}[/tex]
[tex]\textsf{There are 9 properties of equality that we can use, each allowing us to simplify}[/tex]
[tex]\textsf{one side of an equation. These properties are mainly used to find missing variables.}[/tex]
[tex]\textsf{Let's solve for x by using the Properties of Equality.}[/tex]
[tex]\large\underline{\textsf{Solving for x;}}[/tex]
[tex]\tt 180^{\circ} = 93^{\circ} + 3x^{\circ}+18^{\circ}.[/tex]
[tex]\textsf{Let's first Combine Like Terms.}[/tex]
[tex]\tt 180^{\circ} = \boxed{\tt 93^{\circ}} + 3x^{\circ}+\boxed{\tt 18^{\circ}}[/tex]
[tex]\tt 180^{\circ} = 111^{\circ} + 3x^{\circ}[/tex]
[tex]\textsf{Now, let's use the Subtraction Property of Equality which states that if 2 same}[/tex]
[tex]\textsf{numbers are subtracted from both sides of the equation, then both expressions}[/tex]
[tex]\textsf{still equal each other. Let's subtract 111 from both sides of the equation.}[/tex]
[tex]\tt 180^{\circ} - 111^{\circ} = 111^{\circ} - 111^{\circ} + 3x^{\circ}[/tex]
[tex]\tt 69^{\circ} = 3x^{\circ}[/tex]
[tex]\textsf{Let's use the Division Property of Equality, which is similar to subtraction but it's}[/tex]
[tex]\textsf{for division. Divide each side of the equation by 3.}[/tex]
[tex]\tt \frac{69^{\circ}}{3} = \frac{3x^{\circ}}{3}[/tex]
[tex]\large\boxed{\tt x = 23^{\circ}}[/tex]
Class Period Sequencing on a Coordinate Plano Instruction: Using the coordinate plane, graph the sequence of transformations, record the coordinates for each transformation, and write the general rule (algebraio expression). Please graph each image a different color on the coordinate plane
Note that:
The first quadrant of a graph belongs to the negative x - axis, and the positive y-axis
Since it is stated that the points of the preimage belong to the first quadrant, we can reasonably selects the values of Points A, B, C, and D that obey this instruction.
1) Coordinates of the preimage in the first quadrant
Let us selects arbitrary coordinates that belong to the first guadrant for the points:
A(-1, 2), that is, x = -1, y = 2
B(-1, 6), that is, x = -1, y = 6
C(-3, 2), that is, x = -3, y = 2
D(-3, 6), that is, x = -3, y = 6
2) Coordinates of the image after translating the object by 7 units left (i.e x -7) and 3 units up (i.e y + 3)
[tex]\begin{gathered} \text{Transformation rule:} \\ T_{}} \end{gathered}[/tex]The preimage is translated 7 units left and 3 units up. The coordinates of the points become:
A' (-1-7, 2+3)
A' (-8, 5)
B' (-1-7, 6 + 3)
B'(-8, 9)
C'(-3-7, 2+3)
C'(-10, 5)
D'(-3-7, 6+3)
D'(-10, 9)
Hello Blessing, can you see the solution here?
Are you still there?
Which of the functions below have period 2π? Check all that apply.
We need to select all the functions from the options that have a period of 2π.
If a function has period P, the function f(x) repeats its values every time x is a multiple of P.
Thus, by analyzing the graph of periodic functions, we can determine their period.
Observe the graphs of the following functions:
Notice that the functions y = tan x and y = cot x have period π.
And the functions y = csc x and y = sec x have period 2π.
Therefore, the functions that have period 2π are:
A. y = csc x
B. y = sec x
The front of a big wave is approaching a beach at a constant speed of 11.6ms-! When it is 30 m away from a boy on the beach, the wave starts decelerating at a constant rate of 1.6 ms-2 and the boy walks away from the sea at a constant speed of 2 ms-! Show that the wave will not reach the boy and find the minimum distance between the boy and the wave.
Answer:
minimum distance between the boy and the wave is 1.2 m
Step-by-step explanation:
Use v = u + at, with v as 0, to find how long it takes for the wave to decelerate to 0 m/s.
0 = 11.6 - 1.6t
t = 7.25s
Then find how far the wave has traveled by substituting in s = ut + 1/2 at²
s = 11.6 * 7.25 + 1/2(-1.6)(7.25²)
s = 42.05m
Find out how far the he has traveled in the same time
s = vt + 30 (since he was 30m ahead)
s = 2*7.25 + 30
s = 44.5m
The boy has traveled a greater distance so the wave does not reach by the time it decelerates to 0m/s
Find the time at which the wave reaches a speed of 2m/s.
v = u + at
2 = 11.6 - 1.6t
t = 6s
Now find the distance traveled by the wave in that time
s = ut + 1/2 at²
s = (11.6*6) + 1/2(-1.6)(6²)
s = 40.8m
Now find the distance traveled by the boy in that same time
s = vt + 30
s = 2*6 + 30
s = 42m
Find the difference, which is the minimum separation
42 - 40.8 = 1.2m
Students in 6 classes, displayed below, ate the same ratio of cheese pizza slices to pepperoni pizza slices. Complete the following table, which represents the number of slices of pizza students in each class ate.
Slices of Cheese Pizza 2 , 6, 8, 5 ½, 3 1/3, 3/5 Slices of Pepperoni Pizza 5, 15, 20, 13 ¾, 8 1/3, 1 ½ Total Slices of Pizza 7, 21, 28, 19 ¼, 11 2/3, 2 1/10
I’m not quite sure how to prove this geometric proof.
For the given question, we will prove ABCD is a parallelogram
The proof will be as follows:
Statements Reason
1. AB ≅ CD Given
2. AB // CD Given
3. CB ≅ AD Given
4. CB // AD Given
5. ABCD is a parallelogram Parallegram theorem
Solve the system by substitution. x = -8y-x + y = 18 Submit Answer
We have a system of linear equations:
[tex]\begin{gathered} x=-8y \\ -x+y=18 \end{gathered}[/tex]We have to solve by substitution. This is the most appropiate method a s we already have one of the variables in function of the other.
Then, we can replace x in the second equation as:
[tex]\begin{gathered} -x+y=18 \\ -(-8y)+y=18 \\ 8y+y=18 \\ 9y=18 \\ y=\frac{18}{9} \\ y=2 \end{gathered}[/tex]With the value of y, we can calculate x from the first equation:
[tex]x=-8y=-8\cdot2=-16[/tex]Answer: x=-16 and y=2
=4(+) solve for d, how do I love for this equation?
Hi I need help with this is it A. B. C. D. And the last multiple choice question says - The cost of 4 adult tickets equals the cost of 3 children’s tickets
Given that:
x = number of adult tickets.
y = number of children's tickets.
And the ordered par (4, 3).
Since an ordered pair is represented by (x, y):
x = 4 = number of adult tickets.
y = 3 = number of children's tickets.
Answer: A. Ms. Monti bought 4 adults tickets and 3 children's tickets.
what is 3.141 3 2/3 π √3 3.111111111 listed from least to greatest
First, let's put the numbers that are not in the decimal form in this form:
[tex]undefined[/tex]make 8/3 a mixed number
Given data:
The given nnumber is 8/3.
The given number is lie between 2 and 3 , more close to 3.
Here, each division is one unit and the dot represent the number which is lies bewteen 2 and 3.
17 in which graph does the shaded region represent the solution to the inequalityU2 Linear inequalities in Two Variable
We have the following inequality
[tex]x-y\le1[/tex]and its graph is
=
Find the interest on the following loan. Assume 365 days in a year.
$35,500 at 10.25% for 151 days
The interest that would be paid on the loan is $1,505.35.
What is the interest?
Interest is the amount that a debtor has to pay the creditor for use of her funds. The interest that is paid on a loan depends on the interest rate, duration of the loan and the amount borrowed.
Th amount of interest can be determined using the simple interest formula.
Interest = loan amount x interest rate x duration of the loan
Interest = $35,500 x 10.25% x (151 / 365)
Interest = $35,500 x 0.1025 x 0.41370
Interest = $1,505.35
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Martina deposited $4,000 into an account with 5.1% interest compounded semi-annually. assuming that no no withdrawals are made how much will she have in the account after 9 years?
Martina deposited $4,000 into an account with 5.1% interest compounded semi-annually. assuming that no no withdrawals are made how much will she have in the account after 9 years?
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
P=$4,000
r=5.1%=5.1/100=0.051
n=2
t=9 years
substitute in the formula
[tex]\begin{gathered} A=4,000(1+\frac{0.051}{2})^{2\cdot9} \\ A=\$6,293.64 \end{gathered}[/tex]the answer is $6,293.64Below is the graph of y = f(x).Translate it to make it the graph of y=f(x) - 2.
Answer:
Hold the point (2,1) and drag it down until it is at the point (2, -1).
Explanation:
Given the graph of y=f(x).
If we have:
[tex]y=f(x)-2[/tex]This is a Vertical Translation Down by 2 units.
This means we shift the graph of y=f(x) down by 2 units.
From the graph:
In y=f(x), we have a point (2,1).
[tex](2,1)\to(2,1-2)=(2,-1)[/tex]Hold the point and drag it down until it is at the point (2, -1).
55. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside?ע86Seaside. 42-8 642468xLandviewOceanfront6-8A. about 8 milesB. about 10 milesC. about 50 milesD. about 40 miles
Given:
The coordinates of the Oceanfront, (x1, y1)=(3, -2).
The coordinates of the Seaside, (x2, y2)=(-2,4).
The distance between the points corresponding to Oceanfront and Seaside is,
[tex]\begin{gathered} D=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ =\sqrt[]{(-2-3)^2+(4-(-2)^2} \\ =\sqrt[]{(-5)^2+6^2} \\ =\sqrt[]{25+36} \\ =\sqrt[]{61} \end{gathered}[/tex]It is given that one unit represents 5 miles.
So, the actual distance between Oceanfront and Seaside is,
[tex]\begin{gathered} d=5D \\ =5\times\sqrt[]{61} \\ \cong40\text{ miles} \end{gathered}[/tex]Therefore, actual distance between Oceanfront and Seaside is about 40 miles.
compute the finance charge, at 3% for one month on average daily balance of $268.42
Finance charge = average daily balance * interest rate * time period
Given:
average daily balance of $268.42
interest = 3% = 0.03
Time period = 1 month
so,
Finance charge = 268.42 * 0.03 * 1 = $8.0526
so, the answer is option B) $8.05
what do you see around you that weighs about 1 kilogram (you may not answer, " 1 kilogram packet of sugar etc. "!)
It is described as being the mass of a certain platinum-iridium prototype that is held at the International Bureau of Weights and Measures. One liter of pure water's bulk (10-3 cubic meters) served as its original definition.
A mass of 1 kilogram weighs roughly 2.20 pounds at Earth's surface (lb).
The fundamental mass unit in the metric system is the kilogram (kg). Since it was initially designed to be exactly equal, a kilogram is very nearly equivalent to the mass of.
What is a kilogram, and what does it look like?
kilograms is definedThe fundamental metric mass unit, which is equivalent to 1,000 grams (2.2 pounds). 1. 1. The Systeme International d'Unités defines a kilogram as a unit of measurement .
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||| GEOMETRY Area of a piecewise rectangular figure Find the area of the figure. (Sides meet at right angles.) ہے 5 cm 8 cm 3 cm 3 cm 8 cm 0 2 cm
Given: A piecewise rectangular figure is given.
Required: To determine the area of the given figure.
Explanation: The area of the given figure can be determined by splitting the figure into two squares as shown below:
Now the figure is divided into a square with an edge of 3 cm and a rectangle of 8 cm by 5 cm.
And the area of the square is
[tex](edge)^2[/tex]And the area of a rectangle is the product of length by breadth.
Hence, the area of the figure is-
[tex]\begin{gathered} A=(8\times5)^+(3)^2 \\ =40+9 \\ =49\text{ cm}^2 \end{gathered}[/tex]Final Answer: The area of the figure is 49 square centimeters.
In the United States, the relative risk of a woman getting multiple sclerosis (MS) compared to a man is 2.82.
Complete the sentence by selecting the best choice:
Compared to men, ____________ proportion of women get MS.
a. the same
b. a smaller
c. a larger
The percentage of women who get MS is 0.59%. What percentage of men get MS?
Compared to men,b. a smaller proportion of women get MS.
MS, resulting in nerve damage disrupts conversation between the mind and the body, more than one sclerosis causes many specific signs and symptoms, which include imaginative and prescient loss, pain, fatigue, and impaired coordination.
The signs, severity, and duration can vary from person to man or woman. a few people may be symptom-unfastened most of their lives, at the same time as others can have excessive continual signs that by no means go away. Physical therapy and medicinal drugs that suppress the immune machine can assist with signs and gradual disorder development.
Multiple sclerosis can weaken the muscle tissues that manage the lungs. Such breathing problems are the essential reason for sickness and demise in people in the very last stages of MS. Spasticity or growth in stiffness and resistance as a muscle is moved can impair motion and motive aches and other issues.
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A particular disease is tested for results determine that it occurs in about 1 of every 425 Black males and every 102,000 non black males. Find the empirical probability that a randomly selected black male will have this disease
The empirical probability would be:
(number of males that tested positive)/(total number of black males tested)
1/425 (Based on the information given)
The answer is 1/425 or 0.00235(written as a decimal)
Drag the tiles to complete the composition of the functions described
g(x) = x - 3
h(x) = 3x + 1
To find g(h(x)), you have to replace x = h(x) into g(x), as follows:
g(h(x)) = (3x + 1) - 3
g(h(x)) = 3x + (1 - 3)
g(h(x)) = 3x - 2
To find h(h(x)), you have to replace x = h(x) into h(x), as follows:
h(h(x)) = 3(3x + 1) + 1
h(h(x)) = 3(3x) + 3(1) + 1
h(h(x)) = 9x + 3 + 1
h(h(x)) = 9x + 4
Expand and simplify 3(x+2) + 4(2x+1)
Answer:
11x+10
Step-by-step explanation:
Distribute the GCF:
3(x+2) = 3x+6
4(2x+1) = 8x+4
(3x+6)+(8x+4)
Add the expressions:
(3x+6)+(8x+4) = 11x+10
Hope that helps
2.
3.
James has 28 marbles. He puts them into 4 bags.
He puts the same number of marbles in each bag.
How many marbles are in each bag?
Answer:
Wendy has 36 books. She has a bookshelf with 6 shelves
on it. If Wendy puts the same number of books on each
shelf, how many will be on each shelf?
Answer:
Pat is having a picnic for her family. She has 42 cookies.
There are 7 people in her family. If each person gets the
same number of cookies, how many cookies will each
person get?
Answer:
Answer:
Step-by-step explanation:
1. 7
2. 6
3. 6
Translate the following statement into a mathematical equation:Three times a number, minus four, is five.4 - 3 w = 53 w - 4 = 53(4 - w) = 53( w - 4) = 5
ANSWER:
2nd option: 3 w - 4 = 5
STEP-BY-STEP EXPLANATION:
Let w be the number to create the equation, triple is multiplied by 3 w then subtract 4 is equal to 5, we have the following result:
[tex]3w-4=5[/tex]Therefore, the correct answer is the 2nd option: 3 w - 4 = 5
Recall that two angles are complementary if the sum of their measures is 90°.
angles if one angle is eight times the other angle.
Find the measures of two complementary
Larger angle = L°
Answer:
See below
Step-by-step explanation:
L + 1/8 L = 90
L = 90 / ( 9/8) = 80° smaller = 10 degrees
12 cos^2 ( x ) − sin ( x ) − 6 = 0
The solutions to the trigonometric equation 12cos²(x) - sin(x) - 6 = 0 are given as follows:
x = 42º and x = 228º.
What is the solution to the trigonometric equation?The equation is given as follows:
12cos²(x) - sin(x) - 6 = 0
The following identity is applied:
sin²(x) + cos²(x) = 1.
Hence:
cos²(x) = 1 - sin²(x).
Replacing this identity into the equation, we have that:
12(1 - sin²(x)) - sin(x) - 6 = 0
12 - 12sin²(x) - sin(x) - 6 = 0
12sin²(x) + sin(x) - 6 = 0.
The following transformation is applied:
y = sin(x).
Hence the equation is:
12y² + y - 6 = 0.
Which, using a calculator, has the solutions given by:
y = -3/4, y = 2/3.
Then the solutions for the variable x are given as follows:
sin(x) = -3/4 -> x = arcsin(-3/4) = 228º.sin(x) = 2/3 -> x = arcsin(2/3) = 42º.Missing informationThis problem is incomplete and could not be found on any search engine, hence we are going to suppose that it asks for the solutions to the equation.
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You have $25 to purchase apps on your cell phone. Each app you want costs $3.99. Describe the number of apps you can purchase.
Answer:
6 apps
Step-by-step explanation:
Comment
The trick to this question is that you must stay under $25 dollars. Make a rough estimate to the answer. Suppose each a[[ costs 4 dollars.
Then the total number you can but is 25/4 = 6.25 spps. But you can't buy 1/4 of an app, so the answer must be 6.
To be just a bit formal
1 app costs 3.99 dollars
6 apps cost 3.99 * 6 = 23.94 dollars.
What happens if you try and buy the 7th app?
7 apps cost 3.99 * 7 = 27.93 which is over 25.
You cannot by 7 apps.
You can only buy 6 apps.
Find the quotient. 1 8 = 1 3 8+1 1 8 = 1 3 (Type a whole number or a fraction.) Fnter your a the answer box and then click Check Answer
In order to calculate the result of this division, first let's convert the mixed number 1 1/3 into a fraction:
[tex]1\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}_{}_{}[/tex]Now, calculating the division, we have:
[tex]\frac{8}{\frac{4}{3}}=8\cdot\frac{3}{4}=2\cdot3=6[/tex]So the result is 6.
2012Active12310TIME REMAINING52:12Five students, Adriana, Ben, Chandra, Diana, and.Ernesto, would each like one of the four spots at theregional science fair. Their names are placed in a hat, and four names are chosen at random to decide whoattends the fair.What is the theoretical probability that Chandra will be chosen as one of the science fair participants?25%60%75%80%
1) Fo
Adriana
Ben
Chandra
Diana
Ernesto
