ANSWER :
The answer is B. y = (x + 4)^2 + 9
EXPLANATION :
From the problem, we have :
[tex]y=x^2+8x+25[/tex]Group the terms in which the constant term and the terms with variables are separated.
[tex]y=(x^2+8x)+(25)[/tex]add and subtract a variable m to the parenthesis to maintain equivalency.
[tex]y=(x^2+8x+m)+(25-m)[/tex]Calculate the value of m using b^2/4a^2 with a = 1 and b = 8
[tex]m=\frac{b^2}{4a^2}=\frac{8^2}{4(1^2)}=16[/tex]Then :
[tex]\begin{gathered} y=(x^2+8x+16)+(25-16) \\ y=(x^2+8x+16)+(9) \end{gathered}[/tex]The first parenthesis will be a perfect square trinomial.
Factor and simplify :
[tex]\begin{gathered} y=(x^2+8x+16)+9 \\ y=(x+4)^2+9 \end{gathered}[/tex]1. What is the center of the hyperbola?
(y+3)^2/9 − (x−2)^2/2 = 1
Enter your answer by filling in the boxes.
The center of the hyperbola given as (y + 3)²/9 − (x − 2)²/2 = 1 is (2, -3)
How to determine the center of the hyperbola?From the question, the equation of the hyperbola is given as
(y + 3)²/9 − (x − 2)²/2 = 1
As a general representation, a hyperbola is represented as
(y - k)²/a² − (x − h)²/b² = 1
From the above general representation, the coordinates of the center of the hyperbola is
Center = (h, k)
By comparing the equations (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1, we have the following representstion
(h, k) = (2, -3)
This means that
Center = (2, -3)
Hence, the center is (2, -3)
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Answer:
(2,-3) See question 10
Step-by-step explanation:
15:4y2 – 30:23 + 4554The quotient of517is7. When this quotient is divided bythe result is 3-35-5I3y – 25y2 + 3
We are given the following expression:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}[/tex]To determine the quotient of the expression we will factor the numerator. To do that we take the Greatest Common Multiple of the denominator.
The denominator is the following expression:
[tex]15x^4y^2-30x^2y^3+45xy[/tex]To get the greatest common multiple we need to determine the multiples of the coefficients first.
For 15 we have:
[tex]factors\text{ 15= 1, 3, 5, 15}[/tex]For 30 we have:
[tex]\text{factors 30 = }1,2,3,5,6,10,15,30[/tex]For 45 we have:
[tex]\text{factors 45 =}1,3,5,9,15,45[/tex]We notice that the factors that are repeated for each of the numbers are:
[tex]\text{repeated = 1,3,5,15}[/tex]The greatest of the repeated factors is 15, therefore, the greatest common factor is 15.
Now, we take the variables that are repeated in the expression and we take the ones with smaller exponents. The variables repeated are:
[tex]xy[/tex]Of these, the ones with smaller exponents are:
[tex]xy[/tex]Now, combining the two parts we get that the greatest common factor of the denominator is:
[tex]15xy[/tex]We take out that factor and re arrange the expression, like this:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}=\frac{15xy(x^3y-2xy^2+3)}{5xy}[/tex]Now, we cancel out the "xy" and simplify 15/5:
[tex]\frac{15xy(x^3y-2xy^2+3)}{5xy}=3(x^3y-2xy^2+3)[/tex]And thus we get the quotient.
We notice that the quotient is multiplied by 3, therefore, if we divide by 3:
[tex]\frac{3(x^3y-2xy^2+3)}{3}[/tex]We can cancel out the 3 and we get:
[tex]\frac{3(x^3y-2xy^2+3)}{3}=x^3y-2xy^2+3[/tex]Therefore, the quotient is divided by 3.
Dr. Choi just started an experiment. He will collect data for days. How many hours is this?
The data collected in [n] days is collected in 24n hours.
What is the SI unit of time?
The SI unit of time is Seconds. In 1 second, there are (1/60) minutes.
Given is Dr. Choi who just started an experiment and he will collect data for days.
Assume that he collects the data for [n] number of days. In one day, we have 24 hours. Therefore, in [n] number of days, there will be total of 24n hours.
Therefore, the data collected in [n] days is collected in 24n hours.
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17) g(x)= x³ + 4x²
f(x) = 3x + 1
Find g(x) + f(x)
Answer:
x³ + 4x² + 3x + 1
Step-by-step explanation:
fg(x) + f(x)
= x³ + 4x² + 3x + 1
6V
6V
I
I₁
R₁ =
6Ω
IT
B₁
1₂
R₂
352
B₂
Series or parallel?
m
VT=
V Branches
1₁ =
1₂=
IT =
RT =
P =
Answer:
12
Step-by-step explanation:
The Smiths have decided to put a paved walkway of uniform width around their swimming pool. The pool is a rectangular pool that measures 12 feet by 20 feet. The area of the walkway will be 60 square feet. Find the width of the walkway.
***NOTE*** This is a Quadratic Word Problem, so please the Quadratic Method!! Extra 20 BRAINLIST will be reward if work is shown step by step CORRECTLY!!
Answer:
Step-by-step explanation:
12 times 2 =24 60 into 10 so i think it will be 6
Assume the TV warranty or replacement times for TV sets are normally distributed with a mean of 9.2 years and a standard deviation of 1.1 years. Find the probability that a randomly selected TV will have a replacement time of less than 6 years.
Firstly, let's draw a picture of the distribution:
Graphically, we want to calculate the blue area. To put it differently, we want to calculate
[tex]P(X<6).[/tex]To do this, we need to find the z-score associated with 6. We can calculate it by
[tex]\begin{gathered} z=\frac{6-\mu}{\sigma}\Rightarrow\begin{cases}\mu=\operatorname{mean} \\ \sigma=\text{standard deviation}\end{cases}, \\ \\ z=\frac{6-\mu}{\sigma}=\frac{6-9.2}{1.1}\approx-2.91. \end{gathered}[/tex]Now, we must check our favorite z-score table and look for the probability associated with the z-score we just found. It's 0.0018.
AnswerThe probability that a randomly selected TV will have a warranty of less than 6 years is 0.0018.
The following shape consists of a rectangle and a triangle. Determine its area.
Answer:
72 cm²
Step-by-step explanation:
You want the area of a shape consisting of a rectangle and a triangle. The rectangle is 7 cm long and 8 cm high. The triangle has a base of 8 cm and a height of 4 cm.
AreaThe area of the rectangle is ...
A = bh
A = (8 cm)(7 cm) = 56 cm²
The area of the triangle is ...
A = 1/2bh
A = 1/2(8 cm)(4 cm) = 16 cm²
Total areaThe total area is the sum of the areas of the parts:
total area = rectangle area + triangle area
= (56 cm²) +(16 cm²) = 72 cm²
The area of the shape is 72 cm².
__
Additional comment
You can see from the area formula that the area of a triangle is half the area of its enclosing rectangle. That is, the 4 cm high triangle on the right side of the figure effectively adds the area of a 2 cm wide rectangle with the same base.
The figure's area is equivalent to that of a rectangle 7+(4/2) = 9 cm wide and 8 cm high: (9 cm)(8 cm) = 72 cm², as above.
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PLEASE HELP ME!!!!!!!
Answer: 31
Step-by-step explanation:
The numbers are increasing by 1, then 2, then 3, ...
In other words, the second difference is 1.
So, the next number is likely [tex]24+7=31[/tex].
What is the measure of C?
Please show your work if you want to be brainiest!
The measure of ∠C in the given triangle is 58°.
According to the question,
We have the following information:
ACD is a triangle where we have BD as an altitude on the side AC.
Now, we know that the altitude on any side makes an angle of 90° or in other words, it can be said that it makes a right angle.
Now, we have two right-angled triangle: ABD and CBD.
We have ∠ADB = 32°.
Now, ∠CDB will also be equal to 32° because the altitude bisects the angle (in two equal parts).
We know that the sum of the three angles in a triangle is 180°.
In ΔCBD, we have:
∠B + ∠C + ∠CDB = 180°
90° + ∠C + 32° = 180°
∠C + 122° = 180°
∠C = (180-122)°
(Moving 122 from the left hand side to right hand side will result in the change of sign.)
∠C = 58°
Hence, the measurement of ∠C in the given triangle is 58°.
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Select the correct answer.
Which of the following represents a function?
B. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
C. x -5 -1 9 8 -1
y 1 7 23 17 1
The relation which represents a function is the mapping diagram.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value).
In this scenario, the same x-value of the given ordered pairs (3, 2) and (3, 4) have the different output variable (y-value) and as such does not represent a function. Similarly, the table of values has the same x-value (-1) which outputs different numerical values.
Based on the ordered pairs and table shown above, we can reasonably and logically deduce that it is only the mapping diagram that represents a function.
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Your family used 27.5 gallons of gas to drive 654.5 miles. how many miles did you drive for each gallon?
Answer:
total distance = 654.5
Total gas used = 27.5
Distance per gallon = 654.5 ÷ 27.5 = 23.8
We drove 23.8 miles for each gallon of gas
If p and q are integers and pq +p is an odd number, which of the following numbers must be even?
1-p
2-q
3- pq-3
4- p^2
Answer:Answer: number 2 is correct
Determine the last possible degree of the polynomial function shown
We are asked to determine the degree of the polynomial given its graph. To do that we can count the number of bumps in the graph. We notice that it has 4 bumps:
This type of behavior is usual of polynomials of degree 5.
May I please get help with this. I have tried multiple times to get the correct answer for this but still could not seem to get the right one.
Answer:
42
Explanation:
Recall that two triangles are said to be similar if their corresponding angles are congruent and their corresponding sides are in equal proportion.
Given that triangles ABC and XYZ are similar, to be able to determine missing side length, we have to set up proportions as seen below;
[tex]\begin{gathered} \frac{AB}{XY}=\frac{AC}{XZ} \\ \frac{30}{5}=\frac{AC}{7} \end{gathered}[/tex]Let's cross multiply;
[tex]\begin{gathered} 5\cdot AC=30\cdot7 \\ 5AC=210 \end{gathered}[/tex]Let's divide both sides of the equation by 5;
[tex]\begin{gathered} \frac{5AC}{5}=\frac{210}{5} \\ AC=42 \end{gathered}[/tex]So the missing side length is 42
Can Some one help PLEASEE
The variable x is 9 and the two adjacent angles have measures of 117° and 63°, respectively.
How to find the variable associated to the measure of two angles in a parallelogram
Parallelograms are quadrilaterals with two pairs of parallel sides of equal length. According to Euclidean geometry, the measures of two adjacent angles in a parallelogram are supplementary. Thus,
13 · x + 7 · x = 180°
Now we clear the variable x:
20 · x = 180°
x = 9
And the missing angles are:
13 · 9 = 117°
7 · 9 = 63°
The value of the variable x is 9 and the measures of the two adjacent angles are 117° and 63°, respectively.
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Let g(x) be the transformation of f(x) = IxI so that the vertex is at (-1, -3). Identify the rule for g(x) and its graph.
EXPLANATION
Since the vertex is at (-1, -3), the only appropriate option is to translate the function one unit to the left, and again translating 3 units down, with the following form:
g(x) = |x+1| - 3
Therefore, the solution is the last option.
Find an equation for the line that passes through the points (3, -4) and (-3, -1).
Answer:
That is my own idea and I hope it is very helpful
Question 12
I just want the answer :)
Given the information marked on each figure below, select all classifications that must be true.
Note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determining your answers.
If necessary, you may learn what the markings on a figure indicate.
1. Quadrilateral.
The quadrilateral is not necessarily a parallelogram since the diagonals don't necessarily bisect each other.2. Rectangle.
The quadrilateral is a parallelogram because there is one pair of congruent and parallel sides.The parallelogram is a rectangle because there is one right angle.3. Parallelogram.
The quadrilateral is a parallelogram because there is one pair of congruent and parallel sides.Linear ApplicationThe function V(x) = 20.6 +2.2x gives the value (in thousands of dollars) of an investmentafter a months.Interpret the Slope in this situation.The value of this investment is decreasing✓at a rate ofdollars per year V
SOLUTION:
Case: Interpreting slopes from linear equations
Method:
V(x) = 20.6 + 2.2x
Compared to
y = mx + b
Where m is the slope and it is being interpreted as the rise for every single run on the line graph.
As it applies,
V(x) = 20.6 + 2.2x
m = 2.2 thousand ie. 2200
It is interpreted as the amount the value increases by each month.
Final answer:
The value of this investment is increasing at a rate of $2200 each month
Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Which choice represents the sample space, S, for this event?
S = {PQR}
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
S = {PQ, PR, QR}
S = {PQ, QP, PR, RP, QR, RQ}
The resulting sample space of the given situation is S = {PQ, QP, PR, RP, QR, RQ}
Sample space:
Sample space refers the collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.
Given,
Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Here we need to find the sample space for the event.
Let us consider,
P represents Patty
Q represents Quinlan
R represents Rashad
And through the question we have know that, the teacher drawn two card at a time,
So we have consider that the teacher is going to draw out of the hat one first, without replacement, and then draw another one.
The first chosen one will be the president, and that could be P, Q or R, Now, the chosen second one is the Vice president, and already one has already being drawn, that could only be two fellows.
Therefore, the total of likely outcomes is PQ,QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.
So, the resulting sample space is
S = {PQ, QP, PR, RP, QR, RQ}
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PLEASE HELP ME FIND X
Answer:
28°
Step-by-step explanation:
AB and CD are straight lines, all angles in a straight line add up to 180
Lines a and b are parallel. Line c is perpendicular to line a. Must it also be perpendicular to line b? Explain your thinking.
Line c is also perpendicular to line a.
Suppose that c and b are perpendicular. This implies that:
option 1) b and a are the same line or,
option 2) b is parallel to a
Since we know that a and b are different lines, hence, the option 2 is the correct.
A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of careconomy luxury The charge E dollars) to rent an economy car is given by the function E = 15.95 + 0.60M where M is the number of miles drivenThe charge (dollars) to rent a luxury car is given by the function L = 18.20 + 1.25M be how much more it costs to rent a luxury car than an economy car (in dollars)an equation relating C to Simplify your answer as much as possible
C=34.15+0.65M
ExplanationGiven
[tex]\begin{gathered} E=15.95+0.60M \\ L=18.20+1.25\text{ M} \\ where \\ E\text{ is the cost to rental an Economy car} \\ Lis\text{ the total cost to rental an Luxury car} \\ M\text{ is the number of miles traveled} \end{gathered}[/tex]so
to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ \end{gathered}[/tex]so, replace and simplify
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ C=18.20+1.25M-(15.95+0.60M) \\ C=18.20+1.25M-15.95-0.60M \\ C=34.15+0.65M \end{gathered}[/tex]therefore, the answer is
C=34.15+0.65M
I hope this helps you
C=34.15+0.65M
ExplanationGiven
[tex]\begin{gathered} E=15.95+0.60M \\ L=18.20+1.25\text{ M} \\ where \\ E\text{ is the cost to rental an Economy car} \\ Lis\text{ the total cost to rental an Luxury car} \\ M\text{ is the number of miles traveled} \end{gathered}[/tex]so
to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ \end{gathered}[/tex]so, replace and simplify
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ C=18.20+1.25M-(15.95+0.60M) \\ C=18.20+1.25M-15.95-0.60M \\ C=34.15+0.65M \end{gathered}[/tex]therefore, the answer is
C=34.15+0.65M
I hope this helps you
23 - x < 23(1 + 7x)
What does x equal???
[tex]23 - x < 23 + 161x \\ - x - 161x < 23 - 23 \\ - 162x < 0 \\ \frac{ - 162x}{ - 162} < \frac{0}{ - 162} \\ x > 0[/tex]
without given any restriction x is all the numbers greater than 0.
NOTE THAT THE SIGNS >< CHANGE DIRECTION WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
Either Table A or Table B shows a proportional relationship.
Plot the points from the table that shows a proportional relationship.
Table A shows a proportional relationship
What is proportional relationship?
When the value of independent variable changes the value of dependent variable changes. that means if the value independent variables is increase the value of dependent variable will also be increased.
In the figure we are given 2 tables
We plot both the curve on the graph we get
Table A shows a linear relationship where are Table b Does not shows a proportional relationship
Hence Table A shows a proportional relationship
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Answer:
Step-by-step explanation:
suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of inches and a standard deviation of inches. what proportion of woodlice have antenna lengths that are more than inches? round your answer to at least four decimal places.
Proportion = 0.2119
P (X is less than or equal to 0.18) = P [(X-μ)/ sigma is less than or equal to (0.18-0.22)/ 0.05] = P(Z is less than or equal to -0.80). Using z-table proportion = 0.2119
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Nicole made $91 for 7 hours of work. At the same rate, how much would she make for 11 hours of work?
3y=x-6 in standard form
Answer: x-3y=6
Step-by-step explanation:
so first subtract x to get -x+3y = -6 because standford is ax+by = c
and then multiply by -1 since x has to be positive
x-3y = 6 That is your answer
1. What is the value of 18 + (-7) – (-5)
Answer:
16
Step-by-step explanation:
Two negatives make a positive:
18-7+5
Solve the problem left to right:
18-7=11
11+5=16
