Answers
We are given the following expression
[tex]\frac{x^2}{x-5}-\frac{8}{x-2}[/tex]Let us re-write the expression as a ratio of polynomials p(x)/q(x)
First of all, find the least common multiple (LCM) of the denominators.
The LCM of the denominators is given by
[tex](x-5)(x-2)[/tex]Now, adjust the fractions based on the LCM
[tex]\begin{gathered} \frac{x^2}{x-5}\times\frac{(x-2)}{(x-2)}=\frac{x^2(x-2)}{(x-5)(x-2)} \\ \frac{8^{}}{x-2}\times\frac{(x-5)}{(x-5)}=\frac{8(x-5)}{(x-2)(x-5)} \end{gathered}[/tex]So, the expression becomes
[tex]\frac{x^2(x-2)}{(x-5)(x-2)}-\frac{8(x-5)}{(x-2)(x-5)}[/tex]Now, apply the fraction rule
[tex]\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex][tex]\frac{x^2(x-2)}{(x-5)(x-2)}-\frac{8(x-5)}{(x-2)(x-5)}=\frac{x^2(x-2)-8(x-5)}{(x-5)(x-2)}[/tex]Finally, expand the products in the numerator
[tex]\frac{x^2(x-2)-8(x-5)}{(x-5)(x-2)}=\frac{x^3-2x^2-8x+40}{(x-5)(x-2)}[/tex]Therefore, the given expression as a ratio of polynomials p(x)/q(x) is
[tex]\frac{x^3-2x^2-8x+40}{(x-5)(x-2)}[/tex]Related Questions
Two rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded) if AB = BE = 2 and AD = ED = 4.
Answers
The area of the overlapping region is of: 6.25 units squared.
Area of a rectangleThe area of a rectangle of length l and width w is given by the multiplication of the dimensions, as follows:
A = lw.
The dimensions of the right triangle as follows:
Leg x.Leg 2.Hence the remaining leg on the overlapping region is:
4 - x, as AD = 4.
By symmetry, the other dimension of the overlapping region is also of:
4 - x.
Being also the hypotenuse of the right triangles.
The value of x can be found applying the Pythagorean Theorem as follows:
x² + 2² = (4 - x)²
x² + 4 = 16 - 8x + x²
8x = 12
x = 1.5.
Then the two dimensions of the shaded region are:
4 - 1.5 = 2.5.
Meaning that the area is of:
A = 2.5 x 2.5 = 6.25 units squared.
Missing information
The figure is missing and is given by the image at the end of the answer.
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Hello I would like to know what is the answer to the question 3/4x 3 < 6
Answers
I'll send a pic of the problem
Answers
Weare given a graph that relates the number of strawberries to the number of containers in pairs (x, y)
being x the number of containers, and y the number of strawberries.
The points of the graph read:
(3. 57)
(5, 95)
(7, 133)
(9, 171)
and we are asked to find the proportionality between those values.
We then calculate the slope that joins the points, using for example the first two pairs:
slope = (y2 - y1) / (x2 - x1)
in our case:
slope = (95 - 57) / (5 - 3) = 38 / 2 = 19
we check this same type of calculation with another pair of points to see if it holds true as well:
slope = (171 - 133) / (9 - 7) = 38 / 2 = 19
So we can answer that the proportionality is 19 strawberries per container.
Susan is putting 11 colored lightbulbs into the string of lights that are three blue light bulbs to yellow light bulbs and six orange light bulb how many distinct orders of lightbulbs are there is two lightbulbs of the same color are considered identical(not distinct)
Answers
Using combinations, the number of ways is 36,036.
How to find a number of ways?Combinations are a method of calculating the total outcomes of an event where the order of the outcomes is irrelevant. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations, where n represents the total number of items and r represents the number of items chosen at a time.How many distinct orders of light bulbs are there?
Since we have given thatNumber of white light bulbs = 5Number of orange light bulbs = 6Number of blue light bulbs = 2Total number of light bulbs = 13So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.
Therefore, using combinations, the number of ways is 36,036.
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rag the red and blue dots along the x-axis and y-axis to graph 10x - 7y=40
Answers
We were given the equation:
[tex]10x-7y=40[/tex]We will proceed to graph this equation as shown below:
[tex]\begin{gathered} 10x-7y=40 \\ \text{Make ''y'' the subject of the equation, we have:} \\ \text{Subtract ''10x'' from both sides, we have:} \\ -7y=-10x+40 \\ \text{Divide through each term by ''-7'' to obtain the equation in terms of ''y'', we have:} \\ y=\frac{-10}{-7}x+\frac{40}{-7} \\ y=\frac{10}{7}x-\frac{40}{7}_{} \\ \\ y=\frac{10}{7}x-\frac{40}{7}_{} \\ when\colon x=-7 \\ y=\frac{10}{7}(-7)-\frac{40}{7} \\ y=-10-\frac{40}{7} \\ y=-\frac{110}{7} \\ \\ when\colon x=0 \\ y=\frac{10}{7}(0)-\frac{40}{7} \\ y=-\frac{40}{7} \\ \\ when\colon x=7 \\ y=\frac{10}{7}(7)-\frac{40}{7} \\ y=10-\frac{40}{7} \\ y=\frac{30}{7} \end{gathered}[/tex]We will proceed to plot these ordered pairs on a graph, we have:
May I please get help with this. I have tried multiple times but still could not get the correct answer or at least answer to them
Answers
SOLUTION:
Step 1:
In this question, we have the following:
Step 2:
The details of the solution are as follows:
Parallelogram:
a) Two pairs of parallel sides: Yes
b) Only one pair of parallel sides: NO
c) Four right angles: NO
d) All sides congruentnt: NO
Rectangles:
a) Two pairs of parallel sides: Yes
b) Only one pair of parallel sides: NO
c) Four right angles: Yes
d) All sides congruentnt: NO
Trapezoid:
a) Two pairs of parallel sides: NO
b) Only one pair of parallel sides: NO
c) Four right angles: NO
d) All sides congruentnt: NO
Find the equation for thefollowing parabola.Vertex (0,0)Focus (2, 0)A. 2x^2 = yB. y^2 = 8x2C. X^2 = ByD. y^2 = 8x
Answers
To answer this question we need the equation of a parabola that uses the distance from the focus to the vertex.
This formula is,
[tex]4p(y-k)=(x-h)^2[/tex]where,
p is the distance from the focus to the vertex, and the point (h,k) is the vertex.
[tex]\begin{gathered} \text{focus (2,0)} \\ \text{Threrefore} \\ p=2 \end{gathered}[/tex][tex]\begin{gathered} \text{vertex (0 , 0)} \\ \text{Therefore,} \\ h=0 \\ k=0 \end{gathered}[/tex]Let us now substitute the data into the equation of the parabola,
[tex]\begin{gathered} 4\times2(y-0)=(x-0)^2 \\ 4\times2(y)=x^2 \\ 8y=x^2 \end{gathered}[/tex]Hence, the equation for the parabola is, x² = 8y.
Option C is the correct answer.
Adam is working in a lab testing bacteria populations. After starting out with a population of 390 bacteria, he observes the change in population and notices that the population quadruples every 20 minutes.Step 2 of 2 : Find the population after 1 hour. Round to the nearest bacterium.
Answers
The given information is:
The starting population of bacteria is 390.
The population quadruples every 20 minutes.
To find the equation of the population in terms of minutes, we can apply the following formula:
[tex]P(t)=P_0\cdot4^{(\frac{t}{20})}[/tex]Where P0 is the starting population, the number 4 is because the population quadruples every 20 minutes (the 20 in the power is given by this), it is equal to 4 times the initial number, and t is the time in minutes.
If we replace the known values, we obtain:
[tex]P(t)=390\cdot4^{(\frac{t}{20})}[/tex]To find the population after 1 hour, we need to convert 1 hour to minutes, and it is equal to 60 minutes, then we need to replace t=60 in the formula and solve:
[tex]\begin{gathered} P(60)=390\cdot4^{(\frac{60}{20})} \\ P(60)=390\cdot4^3 \\ P(60)=390\cdot64 \\ P(60)=24960\text{ bacterias} \end{gathered}[/tex]Thus, after 1 hour there are 24960 bacterias.
Find the a) domain, b) x-intercept and c) y - intercept: 1) f(x) = 3x-12 2x+4 2x+9 2) f(x) = x²-16 3) f(x) = x2-9
Answers
Answer
Check Explanation
Explanation
Before we start answering, we should first explain what these terms stand for
- Domain
The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists. It is the region around the x-axis that the graph of the function spans.
- x-intercept
The x-intercept refers to the value of x when the value of y or f(x) = 0, that is, the value of x at which the graph of the function crosses the x-axis. To obtain this, we just solve for x when y or f(x) = 0
- y-intercept
The y-intercept refers to the value of y or f(x) when the value of x = 0, that is, the value of y when it crosses the y-axis. To obtain this, we just substitute 0 for x and solve for f(x)
We can now solve
[tex]f(x)=\frac{3x-12}{2x+4}[/tex]- For the domain, we can tell that x can take on any real number value and provide an answer for f(x) except the point where the denominator of this is equal to 0. At the point where the denominator is 0, f(x) will tend to infinity.
2x + 4 = 0
2x = -4
Divide both sides by 2
(2x/2) = (-4/2)
x = -2
So, the domain of this function is all real number values for x except x = -2
- For the x-intercept, we just solve for x when f(x) = 0
[tex]\begin{gathered} f(x)=\frac{3x-12}{2x+4} \\ \text{when f(x) = 0} \\ 0=\frac{3x-12}{2x+4} \\ \text{Cross multiply} \\ 3x-12=0\times(2x+4) \\ 3x-12=0 \\ 3x=12 \\ \text{Divide both sides by 3} \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]The x-intercept = 4.
In coordinate form, the x-intercept is (4, 0)
- For the y-intercept, we just solve for f(x) when x = 0
[tex]\begin{gathered} f(x)=\frac{3x-12}{2x+4} \\ \text{when x = 0} \\ f(x=0)=\frac{3(0)-12}{2(0)+4} \\ f(x)=\frac{0-12}{0+4}=\frac{-12}{4}=-3 \end{gathered}[/tex]The y-intercept = -3
In coordinate form, the y-intercept is (0, -3)
For the second question
[tex]f(x)=\frac{2x+9}{x-3}[/tex]- The domain will be all real number values of x except when (x - 3) = 0
x - 3 = 0
x = 3
The domain will be all real number values of x except when x = 3.
- For the x-intercept, we just solve for x when f(x) = 0
[tex]\begin{gathered} f(x)=\frac{2x+9}{x-3} \\ when\text{ f(x) = 0} \\ 0=\frac{2x+9}{x-3} \\ \text{Cross multiply} \\ 2x+9=0 \\ 2x=-9 \\ x=-4.5 \end{gathered}[/tex]The x-intercept = -4.5
In coordinate form, the x-intercept = (-4.5, 0)
- For the y-intercept, we solve for f(x) when x = 0
[tex]\begin{gathered} f(x)=\frac{2x+9}{x-3} \\ \text{when x = 0} \\ f(x=0)=\frac{0+9}{0-3}=\frac{9}{-3}=-3 \end{gathered}[/tex]The y-intercept = -3
In coordinate form, the y-intercept is (0, -3)
For the third question
[tex]f(x)=\frac{x^2-16}{x^2-9}[/tex]- For the domain, we first solve for when x² - 9 = 0
x² - 9 = 0
x² = 9
x = ±√9
x = ±3
x = +3 or -3
The domain of this function is all real number values of x except when x = +3 and x = -3
- For the x-intercept, we solve for x when f(x) = 0
[tex]\begin{gathered} f(x)=\frac{x^2-16}{x^2-9} \\ \text{when f(x) = 0} \\ 0=\frac{x^2-16}{x^2-9} \\ \text{Cross multiply} \\ x^2-16=0 \\ x^2=16 \\ x=\pm\sqrt[]{16} \\ x=\pm4 \\ x=+4_{} \\ or\text{ x = -4} \end{gathered}[/tex]The x-intercepts are at -4 and +4.
In coordinate form, the x-intercept are (-4, 0) and (4, 0)
- For the y-intercept, we solve for f(x) when x = 0
[tex]\begin{gathered} f(x)=\frac{x^2-16}{x^2-9} \\ \text{when x = 0} \\ f(x)=\frac{0-16}{0^{}-9}=\frac{-16}{-9}=1.7778 \end{gathered}[/tex]The y-intercept = (16/9) = 1.7778
In coordinate form, the y-intercept is (0, 1.7778)
Hope this Helps!!!
Consider the following statement:
If Paul is older than Bill and Fred is younger than Bill, then Bill's age is between Paul's and Fred's.
Write the Given statement
Answers
Paul is the oldest and Fred is the youngest of the three.
What is mean by younger?Younger is a comparative adjective that generally indicates more youthful.
Similar to old, elder simply indicates older in age. It is a comparative version of old.
Given that x is a natural number, let Bill's age equal x years.
Paul's age is thus calculated as (x + a) Years, where an is any positive integer.
Fred is also younger than Bill.
So, Fred's age is equal to x - k, where k is any positive integer.
As a result, if we arranged Fred, Bill, and Paul's ages, they would be
Bill, Fred, and Paul
x-k < x < x+a
As a result, we can conclude that Paul is the oldest and Fred is the youngest of the three.
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Triangle KLM has KL = 28, KM = 28, and LM = 21. What is the area of the triangle?The area of AKLM is about(Simplify your answer. Round to one decimal place as needed.)
Answers
Area = (b * h)/2, b = 21 bu we don't know h, s we have to calculate it
To calculate the height "h" we can use pythagoras with a triangle rectangle with base = 21/2 = 10.5 and hypothenuse = 28, so the height "h" is:
28² = h² + 10.5² ==> h² = 28² - 10.5² = 784 - 110.25 = 673.75
h² = 673.75
h = 25.96
Now that we have the height, the Area of the triangle = (b * h)/2 = (21 * 25.96)/2 = 272.5
Answer:
272.5
A savings account has $2000 in it, earns no interest, andreceives a deposit of $150 per month.What type of growth characterizes the account's change invalue?
Answers
SOLUTION
The question can be written in equation form as:
help mee pleaseeeeeeeeeeeeee
Answers
Step-by-step explanation:
this simply means to put first 5, then 9 and then 12 in place of the x in the function and calculate the 3 results.
a.
after 5 years it is worth
V(5) = -1500×5 + 21000 = -7500 + 21000 = $13,500
b.
after 9 years it is worth
V(9) = -1500×9 + 21000 = -13500 + 21000 = $7,500
c.
V(12) = $3000
means that after 12 years the car is worth only $3000.
let's check
V(12) = -1500×12 + 21000 = -18000 + 21000 = $3000.
correct.
drag and drop the matching inequality from the left into the box on the right
Answers
The first problem is modeled by the following inequality:
[tex]40+5x\ge95-4x[/tex]The second problem is represented by
[tex]95+4x<40+5x[/tex]The third problem is represented by
[tex]95-4x<40+5x[/tex]Observe that, "spending" refers to subtraction, "earnings" refers to addition. Also, the variables represent time. Additionally, "less than" is expressed as "<", "as much as or more than" is expressed as >=.
A toy car that is 0.5 ft long is used to model the actions of an actual car that is 15 ft long. Which ratio shows the relationship between the sizes of the model and the actual car? A. 2:5 B. 5:2 C. 30:1 D. 1:30
Answers
A toy car that is 0.5 ft long is used to model the actions of an actual car that is 15 ft long. Which ratio shows the relationship between the sizes of the model and the actual car?
A. 2:5
B. 5:2
C. 30:1
D. 1:30
_____________________
0.5 ft the toy car: 15 the actual car
0.5*2 =1
15 *2 = 30
1: 30
_____________________________________
The ratio1:30 shows the relationship between the sizes of the model and the actual car
____________
Do you have any questions regarding the solution?
graph a line that is parallel to the given line. determine the slope of the given line and the one you graphed in simplest form. click and drag on the graph to draw a line. Click and drag to plot a parallel line. The line will change colors when a parallel or perpendicular line is drawn accurately.
Answers
Choosing two points of the line given ( Lg ):
• A( ,0, -4, )
,• B( -,1.5, 0, )
Procedure:
0. Finding the slope ( ,m ,) of ,Lg:
[tex]m_{Lg}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m_{Lg}=\frac{0_{}-(-4)_{}}{-1.5_{}-0_{}}=\frac{4}{-1.5}=-\frac{8}{3}[/tex][tex]m_{Lg}=-\frac{8}{3}[/tex]Also, based on point (0, -4), we can determine the intersection in y - axis ( b = -4). Therefore, the equation of the line given is:
[tex]y=mx+b[/tex][tex]y=-\frac{8}{3}x-4[/tex]To determine the parallel slope ( mp ), we know that parallel lines have the same slope:
[tex]m_p=m_{Lg}=-\frac{8}{3}[/tex]For the new graph, you would have to choose a different parameter b, all the equation would be the same except b. Choosing b = 3 as an example:
[tex]y=-\frac{8}{3}x+3[/tex]Answer:
• Original slope: -8/3
,• Parallel slope: -8/3
For each equation in the table, give the slope of the graph.
Answers
Solving the Question
Linear equations are typically organized like this: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
When the equation is like [tex]y=b[/tex], it means that it is a horizontal line and the slope is 0.
When the equation is like [tex]x=d[/tex], it is a vertical line and the slope is undefined.
AnswerFirst equation: 0
Second equation: undefined
Third equation: [tex]\dfrac{4}{5}[/tex]
Mai is filling her fish tank water flows into the tank at a constant rate. 2.&- 0.5 1.6 time (minutes) water (gallons) 0.5 0.8 1 x1.6 1.6 x1.6 4.8 25 G 3 40 1) How many gallons of water will be in the fish tank after 3 minutes? Explain or show your reasoning. 2) How long will it take to fill the tank with 40 gallons of water? Explain or show your reasoning. 3) What is the constant of proportionality? What does it tell us about this situation?
Answers
Given
x = 0.5; y = 0.8
The constant of proportionality has to be calculated to estimate the other values.
The constant of proportionality "k" determines the relation of x and y, which can be represented as: y = kx.
So, in this exercise,
[tex]\begin{gathered} 0.8=k\cdot0.5 \\ \frac{0.8}{0.5}=k \\ k=1.6 \end{gathered}[/tex]y = 1.6y
(1) From this, we can estimate the value of y when x = 3.
[tex]\begin{gathered} y=1.6\cdot3 \\ y=4.8\text{gallons} \end{gathered}[/tex](2) If we want how long it will take to fill the tank with 40 gallons:
[tex]\begin{gathered} 40=1.6\cdot x \\ \frac{40}{1.6}=x \\ 25=x \end{gathered}[/tex]It will take 25 minutes.
(3) Finally, the constant of proportionality is 1.6 (as calculated above).
It tells us that the ratio between the gallons water of water and time. In other words, it tells us that for each 1 minute, 1.6 gallons are filled.
The figure below shows a rectangular court. 74 ft (a) Use the calculator to find the area and perimeter of the court. Make sure to include the correct units. Area: 93 ft Perimeter: (b) The court will have a wood floor. Which measure would be used in finding the amount of wood needed? Perimeter O Area (c) A strip of tape will be placed around the court. Which measure would be used in finding the amount of tape needed? Perimeter O Area ft X ft² Ś ft³ ?
Answers
Given a rectangle with sides "a" and "b":
The area of the rectangle is:
[tex]A=ab[/tex]The perimeter of the rectangle is:
[tex]P=2a+2b[/tex]Given the sides of the rectangle:
a = 74 ft
b = 93 ft
(a)
The area of the rectangle is:
[tex]\begin{gathered} A=74ft*93ft \\ A=6882ft^2 \end{gathered}[/tex]The perimeter of the rectangle is:
[tex]\begin{gathered} P=2*74ft+2*93ft \\ P=148ft+186 \\ P=334ft \end{gathered}[/tex](b) The wood will cover all the area of the court, then the area must the used.
(c) The tape will be placed around the court, then the perimeter must be used.
Answer:
(a)
(b)
(c) Perimeter
Which statement about the graph below is true?
Answers
Answer:
a. The relation is a function because every input has an output.
Step-by-step explanation:
a relation in which for every input there is exactly one output (for every x there is just one y)
quizlet
Answer:
A. The relation is a function because every input has an input
Step-by-step explanation:
A relation is a function as long as there are not multiple outputs for one input. It's okay if there are multiple inputs for one output, like we can see here with points (-6, 1) and (2, 1).
Another way to test if a graphed relation is a function is the vertical line test. Draw vertical lines at multiple spots on the graph and if any of the vertical lines touches 2 points, the graphed relation is not a function.
:)
the coordinates of two points on a line are (-4,8) and (2,2). Find the slope of the line.
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the coordinates of two points on a line are (-4,8) and (2,2). Find the slope of the line.
Applying the formula to calculate the slope
we have
m=(2-8)/(2+4)
m=-6/6
m=-1
slope is -1Write an absolute value inequality that represents all real numbers more than 4 units away from x
Answers
We have to write as inequality the following
"All real numbers more than 4 units away from x""4 units away from x" means four units plus x. So, the expression would be
[tex]|x|>4[/tex]Where x represents real numbers.
This expression is referring to all real numbers more than 4 units and less than -4 units because according to the property of absolute values for inequalities, we have
[tex]|x|>x-4\rightarrow x>x-4,or,x<-(x-4)[/tex]This is represented in the following graph to see it better
For x=1
[tex]\begin{gathered} |1|>x-4\rightarrow1>1-4,or,1<-(1-4) \\ 1>-3 \\ 1<3 \end{gathered}[/tex]Both results are true.
To find this absolute value inequality we used the following property
[tex]|x|>a\rightarrow a>b,or,a<-b[/tex]Where the absolute value inequality has "more than" we rewrite the expression in two inequalities.
What is the equation of a line with slope 7/12 and y-intercept -3?
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
Given that m = 7/12 and c = - 3, the equation of the line would be
y = 7x/12 - 3
Since January 1, 1960, the population of Slim Chance has been described by the formula P = 27000(0.95)^t, where P is the population of the city t years after the start of 1960. At what rate was the population changingon January 1, 19702?numerical rate of change= ___ people per year
Answers
We have to calculate the rate of change of the population P(t) at January 1, 1970 (t = 10).
The expression for P(t) is:
[tex]P(t)=27000\cdot0.95^t[/tex]The rate of change will be given by the first derivative of P(t):
[tex]\frac{dP}{dt}=27000\cdot\ln (0.95)\cdot0.95^t[/tex]Then, we can calculate the value of the rate of change when t = 10, by replacing t with 10 in the last expression. We then will get:
[tex]\begin{gathered} \frac{dP}{dt}(100)=27000\cdot\ln (0.95)\cdot0.95^{10} \\ \frac{dP}{dt}(100)\approx27000\cdot(-0.0513)\cdot0.5987 \\ \frac{dP}{dt}(100)\approx-829 \end{gathered}[/tex]The population, on January 1st 1970, is decreasing at a rate of 829 people per year.
Answer: numerical rate of change= -829 people per year
A 9-foot roll of waxed paper costs $4.95. What is the price per yard ?
Answers
Answer:
$0.55 per yard
Step-by-step explanation:
a 9 foot roll is 4.95 so you divide the cost by the amount to get the unit rate which is $0.55 per yard
use matrices D, E, and F to find each sum or product
Answers
Problem
Solution
5. E-D
Procedure
-3-2 =-5
-4-1=-5
0-7=-7
1-5=-4
2-3=-1
6- (-4)=10
And the answer would be:
-5 -5
-7 -4
-1 10
6. 3F
Procedure
3* -2=-6
3 *5 = 15
3* 1= 3
3*3 = 9
3*14=12
3 * -6= -18
And the answer would be:
-6 15 3
9 12 -18
propriate symbols and/or words in your submissionSolve for the indicated measure.5. R = 19°, ZB = 56°, find mZT.6. R = 19, ZB'S 56°, find mZS.7. R = 19°, ZB = 56°, find mZC.8. True or false?AABC = AZXY9. Are the two triangles congruent?Yes or no?10. Use the image below to complete the proof.Identify the parts that are congruent by the given reason in the proof.STATEMENTS REASONSAB = DC GivenAB || DC Given2.Alternate Interior Angles TheoremReflexive Property of CongruenceSAS Congruence Theorem3.4.
Answers
ok
The sum of the internal angles in a triangle equals 180°
R + B = T = 180
Substitution
19 + 56 + T = 180
T = 180 - 19 - 56
T = 105°
Result:
T = 105°
You have two spinners each with three sections of equal size labeled with numbers 1,2,3. You spin both and observe the numbers. Let x be the sum of the two numbers. Find the probability distribution for X.
Answers
From the given problem with two spinners with three sections of equal size labeled as 1, 2, and 3.
Spinner 1 : 1 2 3
Spinner 2 : 1 2 3
The sum is as follows :
1+1 = 2
1+2 = 3
1+3 = 4
2+1 = 3
2+2 = 4
2+3 = 5
3+1 = 4
3+2 = 5
3+3 = 6
There are 9 total outcomes
There are (1) 2,
(2) 3's
(3) 4's
(2) 5's
and
(1) 6
and their corresponding probability can be calculated by :
[tex]\text{probability}=\frac{\text{ quantity}}{\text{ total quantity}}[/tex]Probability of 2 = 1/9
Probability of 3 = 2/9
Probability of 4 = 3/9 or 1/3
Probability of 5 = 2/9
Probability of 6 = 1/9
Construct the probability distribution :
To check if your probability distribution is correct.
The sum of P(X) must be equal to 1
1/9 + 2/9 + 1/3 + 2/9 + 1/9 = 1
Therefore the distribution is correct.
slope= 2; point on the line (-2,1) in slope intercept form I know y=m*x+b but all I know is 2 would be m
Answers
y=2x+5
1) Since we were told the slope is m=2, one point on the line (-2,1), and the slope-intercept form is:
[tex]y=mx+b[/tex]2) The next step is to find the value of "b", the y-intercept. So, let's pick that point, the slope, and plug them into the Slope-Intercept form:
[tex]\begin{gathered} y=mx+b,m=2,(-2,1) \\ 1=2(-2)+b \\ 1=-4+b \\ 1+4=b \\ b=5 \end{gathered}[/tex]3) Now that we know the y-intercept (b), we can write the function's rule as
[tex]y=2x+5[/tex]Solve for x and then give the m
Answers
x = 38
Step-by-step explanation:
(x + 6) + (3x - 16) + x = sum of angles in a triangle
(x + 6) + (3x - 16) + x = 180
(x + 3x + x ) + (6 - 16) = 180
5x +(-10) = 180
5x - 10 = 180
5x = 180 + 10
5x = 190
5x/5 = 190/5
x = 38
Answer:
x = 38 and m∠M = 98
Step-by-step explanation:
Angles in any triangle will always add up to 180 :
So angle O + Angle N + Angle M = 180
(x+6)+(3x-16)+(x) = 180
Simplify:
5x-10 = 180
Add 10 to both sides :
5x = 190
Divide both sides by 5 :
x = 38
Angle M will therefore
= 3(38) - 16
= 114 - 16
= 98
Hope this helped and have a good day
