The Factors of x² - 5x + 6 are (x-3) (x-2)
Step 1: Add the constant term to the first term's coefficient. i.e (6 x 1) = 6
Step 2:Find the two factors of 6 whose total matches the middle term's coefficient., i.e -5.
Thus, the factors are -3 and -2 as,
-3 × (-2) = 6 (Product)
-3 + (-2) = -5 (Sum)
The polynomial may be expressed as follows after dividing the middle term by the two components, -3 and -2:
x² - 3x - 2x + 6 = 0
⇒ x(x-3) -2(x-3) = 0
⇒ (x-3)(x-2) = 0
Thus, the Factors of x² - 5x + 6 are (x-3) (x-2).
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Find the area of the figure given to the right. Round to the nearest whole number.
Looking at the figure, we can tell that the top is a triangle and the base is a trapezium. To find the area of the figure, we would find the sum of the triangle and the trapezium.
Recall, the formula for finding the area of a triangle is expressed as
Area = 1/2 x base x height
Looking at the triangle,
base = 9 + 9 = 18
height = 3
Thus, Area = 1/2 x 18 x 3 = 27
Again, the formula for finding the area of a trapezium is expressed as
Area = 1/2(a + b)h
where
h is the height of the trapezium
a and b are the lengths of the parallel sides
Looking at the trapezium,
a = 9 + 9 = 18
b = 13.4 + 13.4 = 26.8
h = 12
Area = 1/2(18 + 26.8)12
Area = 268.8
rounding to the nearest whole number,
Area = 269 squared ft
Transform the quadratic equation into a perfect square equation by completing the square.x² + 4x +2=0
Solution:
Given:
[tex]x^2+4x+2=0[/tex]Line segments AB and CD arecongruent. Their coordinatesare AC-11, -3), B(-2,5), C(7,1)and D(x, 9). Find the value of x.
We have the following points:
A(-11, -3) and B(-2,5)
The distance between AB is:
[tex]\left(|-11--2|,|-3-5|\right)=(9,8)[/tex]C(7,1) and D(x, 9)
[tex]\begin{gathered} 7-x=9 \\ x=-9+7 \\ x=-2 \end{gathered}[/tex]the value of x is -2
Determine an equation of the line that is perpendicular to the tangent to the graph y=1/x at x=2 and intersects at the point of tangency.
ANSWER
[tex]y=4x-\frac{15}{2}[/tex]EXPLANATION
Two lines are perpendicular if they have opposite reciprocal slopes. So, to find the line, first, we have to find the slope of the line tangent to the graph of y = 1/x at x = 2. To do so, we have to find the derivative of the function and evaluate it at x = 2. That is the slope of the tangent line at that point.
The derivative of the function is,
[tex]y^{\prime}=\left(\frac{1}{x}\right)^{\prime}=(x^{-1})^{\prime}=-1\cdot x^{-1-1}=-1x^{-2}=-\frac{1}{x^2}[/tex]So, the slope of the tangent line at x = 2 is,
[tex]y^{\prime}(2)=-\frac{1}{2^2}=-\frac{1}{4}[/tex]Therefore, the slope of the perpendicular line is the opposite reciprocal,
[tex]m=-\frac{1}{y^{\prime}(2)}=-\frac{1}{-\frac{1}{4}}=4[/tex]So we have that the perpendicular line we are looking for is,
[tex]y=4x+b[/tex]We have to find the y-intercept, b. We know that this perpendicular line intersects the graph at the tangency point, so with that point, we will find b.
The x-coordinate of the tangency point is x = 2, and the y-coordinate is,
[tex]y(2)=\frac{1}{2}[/tex]Substitute (x, y) with (2, 1/2) in the equation of the line to find b,
[tex]\begin{gathered} \frac{1}{2}=4\cdot2+b \\ \\ \frac{1}{2}=8+b \end{gathered}[/tex]Subtract 8 from both sides,
[tex]b=\frac{1}{2}-8=\frac{1-8\cdot2}{2}=\frac{1-16}{2}=-\frac{15}{2}[/tex]Hence, the equation of the line perpendicular to the tangent of the graph at x = 2 passing through the tangency point is,
[tex]y=4x-\frac{15}{2}[/tex]cos(θ)= 1/6Trig: use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function.a. Sin (θ)b. Tan (θ)c. Sec (θ)d. Csc (90° -θ)
a. Sin (θ) = √35 / 6
b. Tan (θ) = Tan θ = √35
c. Sec (θ) = 6
d. Csc (90° -θ) = 6
Explanations:Note that according to trigonometric identities:
cos θ = Adjacent / Hypotenuse
From the question:
cos θ = 1/6
Comparing this with the given trigonometric identity:
Adjacent, A = 1
Hypotenuse, H = 6
Let us look for the opposite, O
Using the pythagora's theorem
H² = A² + O²
6² = 1² + O²
36 = 1 + O²
36 - 1 = O²
O² = 35
O = √35
Therefore, Opposite = √35
a) Sin θ = Opposite / Hypotenuse
Sin θ = √35 / 6
b) Tan θ = Opposite / Adjacent
Tan θ = √35 / 1
Tan θ = √35
c) Sec θ = 1 / cos θ
Sec θ = 1 ÷ 1/6
Sec θ = 1 x 6
Sec θ = 6
d) Csc ( 90 - θ) = Sec θ
Since Sec θ = 6
Csc ( 90 - θ) = 6
If x is 5 more than y, and y is 3 less than z, what is the value of x when z=3
Answer: X=5
Step-by-step explanation: If x is 5 more than y, and y is 3 less than z. Well we already know z=3 so z=3 - 3 less than Y=0. Making Y=0, and if x is five more than Y, 5+0=5. Making x=5
Consider the following sequence: 7,14,28,56,... find a19
We have the sequence:
[tex]\begin{gathered} a_1=7, \\ a_2=14, \\ a_3=28, \\ a_4=56, \\ \ldots \end{gathered}[/tex]We rewrite the sequence as:
[tex]\begin{gathered} a_1=7\cdot1=7\cdot2^0=7\cdot2^{1-1}, \\ a_2=7\cdot2=7\cdot2^1=7\cdot2^{2-1}, \\ a_3=7\cdot4=7\cdot2^2=7\cdot2^{3-1}, \\ a_4=7\cdot8=7\cdot2^3=7\cdot2^{4-1}, \\ \ldots \end{gathered}[/tex]From the previous equations, we see that the general term is given by:
[tex]a_n=7\cdot2^{n-1}.[/tex]Replacing n = 19, we get:
[tex]a_{19}=7\cdot2^{19-1}=7\cdot2^{18}=7\cdot262144=1835008.[/tex]Answer
[tex]a_{19}=7\cdot2^{18}=1835008[/tex]If f(x) = 1/x which equation describes the graphed function?
y = f(x+2) -1 is the equation which describes the graphed function.
What is translation?Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same. In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered.
Given,
When F crosses the x-axis when it is negative.
-1 indicates a 1 unit down translation.
So, the equation will be y = f(x+2) -1.
y = f(x+2) -1 is the equation which describes the graphed function.
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Help Me Please!!
Thank you
Answer: 1/2
Step-by-step explanation:
1) Find the equation of sin of angle K
Sine is opposite/hypotenuse.
Opposite of K = 5.
the hypotenuse of K = 10
You then get 5/10
2) Simplify the fraction
5/10 = 1/2
Don is 6 feet tall. At a given time of day, he measures his shadow to be 13 feet long. At the same time, he measures the shadow length of a nearby tree to be 52 feet. How tall is the tree?
Answer:
24
Step-by-step explanation:
We will use the proportional concept to solve it.
So, 6/13 = x/52
x = 6*4
x = 24
So, height of tree is 24 feet
Express the interval in using inequality notation
(-4,-1)
Expression of the given interval (-4,-1) in inequality notation is -4< x <-1.
As given,
Given interval:
( -4 , -1 )
Let us consider x variable belongs to given interval x ∈ ( -4 , -1 ).
Given interval ( -4 , -1 ) is open interval.In open interval when we plot it on the real number line , we are not including upper limit and the lower limit of the given interval.-4 and -1 are exclusive values for the given variable.Symbol representing open interval is sign of < or >.Interval (-4,-1) in inequality notation is given by -4 < x < -1.All values are included between -4 and -1 except -4 and -1.Therefore, the expression of the given interval (-4,-1) in inequality notation is -4 < x < -1.
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Assume that a sample is used to estimate a population mean μ . Find the 99.5% confidence interval for a sample of size 867 with a mean of 60.2 and a standard deviation of 21.9. Enter your answer as a tri-linear inequality accurate to 3 decimal places.
Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.
What is a confidence interval?
Add & deduct the error margin from the sample mean to get this confidence interval.The confidence interval's top and lower limits are represented by this result.Mean, x= 60.2
sample size, n= 867
standard deviation=21.9
population mean m as a tri-linear inequality is given by,
The t value for a 99.5% Confidence interval because the sigma is unknown.
From Inverse t Distribution Calculator, the Confidence interval is 0.995 and the degree of freedom is 867-1=866
One-sided t-Score: 1.8125
We can now determine the standard error E:
E=1.8125(21.9/√867)=1.348
We can now create the confidence interval by:
x - E < m< x + E
60.2-1.348< m <60.2+1.348
58.852< m<61.548
Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.
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5. Noah orders an extra-large pizza. It costs $12.49 for the pizza plus $1.50for each topping. He orders an extra-large pizza with t toppings that costsa total of d dollars. Select ALL of the equations that represent therelationship between the number of toppings t and total cost d of the pizzawith t toppings."12.49 + t = 012.49 + 1.501 - 012.49 +1.500 t12.49 = d + 1.500t = (d. 12.49) / 1.5t=d12.49/1.5
The cost of 12.49 is fixed, while the extra cost for toppings is 1.5 per topping.
If we have a total of t topping, the cost of the toppings will by 1.50t, adding the fixed cost, we will have the total cost, which should be equal to d. so we have the equation:
[tex]d=12.49+1.50t[/tex]Now, we can manipulate the equation to check which ones are equivalent to it.
As we can see, the first one is missing the 1.50, so it is not equivalent.
The second have the 1.50, it is just inverted:
[tex]12.49+1.50t=d[/tex]So, it is equivalent.
The third had the t and d switched, so it is not equivalent.
The fourth get the 1.50t to the other side, but don't change the sign accordingly, so it is not equivalent.
The fifth solved for t let's do that:
[tex]\begin{gathered} 12.49+1.50t=d \\ 1.5t=d-12.49 \\ t=\frac{(d-12.49)}{1.5} \end{gathered}[/tex]So, it is equivalent.
The sixth don;t distribute the denominator correctly, so it is not equivalent.
So, the alternatives that are equivalent are:
[tex]\begin{gathered} 12.49+1.50t=d \\ t=(d-12.49)/1.5 \end{gathered}[/tex]The second and fifth.
find the volume of the following rectangular prism Round to the nearest tenth if necessary.
Consider that the volume of a rectangular prism is given by the following formula:
V = l·h·w
l: length = 4 cm
w: width = 5.1 cm
h: height = 9 cm
replace the previous values of the parameters into the formula for V:
V = (4 cm)(5.1 cm)(9 cm)
V = 183.6 cm³
Hence, the volume of the rectangular prism is 183.6 cm³
Convert0.0032% in fraction
STEP-BY-STEP EXPLANATION:
What to do? Convert percentage to fraction
Given parameter
0.0032%
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
It would be, Yes, No, Yes, Yes.
Hope this helps!
Please help me I beg you I love you!
1) [tex]\overline{AB} \cong \overline{CD}[/tex] (given)
2) [tex]\angle BAC \cong \angle ACD[/tex] (given)
3) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)
[tex]\triangle ABC \cong \triangle CDA[/tex] (SAS)
hwlp
Marcus has twice as many CD's as Kristen. Sherry has 12 more than Kristen. Together they have 100 CD's. How many does each person have?
Marcus have 44 CDs, Sherry have 34 CDs and Kristen have 22 CDs.
Let us assume that Kristen has x numbers of CD's.
According to the provided situation,
Marcus have twice the number of CDs as Kristen.
Number of CDs of Marcus = 2x
The number of CDs of Sherry is 12 more than the CDs of Kristen
Number of CDs of of Sherry = 12 + x
Total number of CDs combined are 100.
So, we can write,
x + 2x + (12 + x) = 100
4x + 12 = 100
Any equation with the highest degree of variable as one, just like the above equation is called Linear Equation.
Further solving the Equation,
4x + 12 = 100
4x = 88
x = 22
The number of CDs that Kristen has is 22.
The number of CDs that Marcus have is 2(22).
The number of CDs Marcus gas is 44.
The number of CDs Sherry has is (12 + x) which is equal to 34.
The number of CDs Kristen, Marcus and Sherry have is 22, 44 and 34 respectively.
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Which of the following is the correct mathematical expression for:
Double a number and then increase it by five
2x+5
2x-5
1/2x+5
1/2x-5
What is the position vector of the midpoint of the line PQ if P has coordinates(-13,-4,6) and Q has coordinates (0,4,11)?OA. ( 130 - 17)B.(-13,0,1)c. (2.0.1D. (-2,0. - 1)
The general formula to find the midpoint of a line in a 3D space is given by
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2})[/tex]In this case, we have
[tex]M=(\frac{-13+0}{2},\frac{-4+4}{2},\frac{6+11}{2})=(\frac{-13}{2},0,\frac{17}{2})[/tex]So the position vector of the midpoint of the line PQ is
[tex]M=(-\frac{13}{2},0,\frac{17}{2})[/tex]which is option B.
What is the surface area of the cube below?
A. 96 units²
B. 120 units²
C. 64 units²
D. 80 units²
Answer:
A. 96 U2
Step-by-step explanation:
The cube has 6 faces
Multiply by 6 the area of one face
Surface area = 6 (4)(4) = 96 units2
Hope this helps
Can you please help me
Area of Sector.
The area of a sector is given by the formula below:
[tex]\begin{gathered} \text{Area =}\frac{\theta}{360}\times\pi r^2 \\ \text{where }\theta=148\text{ ; r=6m ; }\pi=\frac{22}{7} \end{gathered}[/tex]Substituting these values into the formula above, we get
[tex]\begin{gathered} \text{Area of the shaded sector = }\frac{148}{360}\times\frac{22}{7}\times6^2 \\ \text{ } \\ \text{ = }\frac{148\times22}{70}\text{ = }46.514\text{ }\approx46.5m^2 \end{gathered}[/tex]Thus, the correct answer is 46.5 square meters.
Use the following cell phone airport data speeds (Mbps) from a particular network. Find P70
Note that the data is in ascendinhg order.
We shall find the position of the pth percentile as follows;
[tex]\begin{gathered} i=\frac{p}{100}\times n \\ \text{Where } \\ p=70,n=50\text{ (number of data)} \end{gathered}[/tex]We now have;
[tex]\begin{gathered} i=\frac{70}{100}\times50 \\ i=35 \end{gathered}[/tex]In the 34th and 35th position we have;
[tex]\begin{gathered} \text{The 35th percentile is;} \\ (\frac{5.4+5.7}{2}) \\ =(\frac{11.1}{2}) \\ =5.55 \end{gathered}[/tex]ANSWER:
[tex]P_{70}=5.55\text{Mbps}[/tex]What’s the domain of F(x)=|x|, g(x)=x+9 find domain for f o g
The domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The function f(x):
f(x) = |x|
The domain of the function is:
x ∈ R
g(x) = x + 9
The domain of the function:
x ∈ R
f o g = f(g(x)) = |x + 9|
The domain of the function f o g is x ∈ R
Thus, the domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.
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Find all value of x for which:
a. f(x) > g(x)
b.f(x) < g(x)
Answer: a. (-10, 0) u(12, infinity)
b. (negative infinity, -10) u(0, 12)
All of this is assuming that the ends of both functions are continuing in the direction it's going shown in the graph.
Step-by-step explanation:
f(x) and g(x) basically means the y value. So when f(x) is greater than g(x), it's saying the y value for the f(x) line is greater than the y value for g(x). This happens when x = -10 till x = 0 and x = 12 till forever going right.
Side note: (-10, 0) is a way to write the domain, with the first number meaning the start and the second number meaning the end.
We know that line ad is congruent to line BC and that angle 1 is congruent to angle 2. Which of the three theorems (ASA, SAS or SSS) would be used to justify that triangle ABC is congruent to triangle CDA? Explain your choice
The theorem that would be used to justify that triangles ABC and CDA are congruent is: SAS.
How to Apply the SAS Congruence Theorem?If we can show that the two sides and one included angle in one triangle is congruent to the two corresponding sides and an included angle in another triangle, then we can state that the two triangles are congruent to each other by the SAS congruence theorem.
Triangles ABC and CDA have the following:
Side AD is congruent to side BC [one pair of congruent sides]
Side AC is congruent to side CA based on the reflexive property [one pair of congruent sides]
Angle 1 is congruent to angle 2 [one pair of included congruent angle]
Therefore, the above information satisfies the SAS congruence theorem. Therefore, they are congruent triangles based on the SAS. The theorem that justifies why they are congruent is therefore SAS.
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May I please get help with this. For I am confused as to how i can get the correct answers as I’ve tried may times
The new coordinates are (-1, 7), (-3, 3) and (-8, 5)
Explanation:To get the new coordinates after the translation, we will first find the initial coordinates of the three vertices
The three vertices: (3, 3), (1, -1) and (-4, 1)
A translation of 4 units to the left:
[tex]\begin{gathered} \text{suntract 4 units form the x coordinates:} \\ (3,\text{ 3): (3-4, 3) = (-1, 3)} \\ (1,\text{ -1): (1-4},\text{ -1) = (-3, -1)} \\ (-4,\text{ 1): (-4 -4, 1) = (-8, 1)} \end{gathered}[/tex]A translation of 4 units up:
[tex]\begin{gathered} \text{Add 4 units to y coordinates} \\ (-1,\text{ 3): (-}1,\text{ 3 + 4) = (-1, 7)} \\ (-3,\text{ -1): (-3, -1+4) = (-3, 3)} \\ (-8,\text{ 1): }(-8,\text{ 1+ 4) = (-8, 5)} \end{gathered}[/tex]Plotting the points:
Issay's school plans to add one of three new elective classes next year:
teen leadership, fashion design, or robotics. Issay wants to know which
class the students at his school want most. He plans to survey a sample
of the population. Will each approach result in a sample that is
representative of the population? Explain.
Be
Yes, the probability approaches each time will result in getting a sample that is representative of the population of that group class.
Why does the entire sample need to be an absolute representative of the population?If you are going on and properly conducting the specific research on a specific population, you will totally want to make sure that your taken sample of that population is absolutely representative.
If in any case your sample is a kind of representative of your total population, you will be able to confidently take up and generalize the results of your study to that of the population.
How to determine if a sample is absolutely representative of the population?In order to be a representative sample, the sample of the group must represent the total population as a whole.
For instance, if the researcher’s population of absolute interest has 60% of people of total ages 18-25 and 40% of the total people ages from about 26-40, then the representative sample must also absolutely reflect this ratio.
Is there the single one way of ensuring that a sample is absolutely representative of the population?The best way of ensuring a representative sample is to have a complete list (i.e., sampling frame) of all the elements in the present population and know that each and every element (e.g., people or present households) on the list that has a nonzero chance (but then it is not necessarily required to be an equal chance) of being included in the entire sample.
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find the value of the misssing variables im pretty sure the answer is either a or c
the sum of the internal angles of the 4-sided polygon is 360, therefore
[tex]\begin{gathered} m\angle D+m\angle G+m\angle F+m\angle E=360 \\ m\angle D+m\angle G+64+119=360 \\ m\angle D+m\angle G+183=360 \\ m\angle D+m\angle G+183-183=360-183 \\ m\angle D+m\angle G=177 \end{gathered}[/tex]then
[tex]m\angle D=y=116[/tex][tex]m\angle G=z=61[/tex]answer: a. y = 116° and z = 61°
In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.3
inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d)
below.
(a) Find the probability that a study participant has a height that is less than 68 inches.
The probability that the study participant selected at random is less than 68 inches tall is
There is a 0.0530 percent probability that the randomly chosen study participant will be shorter than 68 inches.
The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
We have been given that
μ = 68.3
σ = 4.0
Find the probability that a study participant has a height that is less than 68 inches.
We are supposed to find P(x<68)
x = 68
z = (x - μ) / σ
z = (68 - 68.3) / 4
z = -0.3 / 4
z = -0.075
Use z table :
So, P(z<-0.0725)=0.0530
So, The probability that the study participant selected at random is less than 68 inches tall is 0.0530
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