Answer:
y = 2 ± √x is the inverse but it's not a function. (See note below for additional info)
Step-by-step explanation:
Given the quadratic function:
[tex] \displaystyle{y = {x}^{2} + 4x + 4}[/tex]
We can rewrite the function above using perfect square form:
[tex] \displaystyle{y = {(x + 2)}^{2} }[/tex]
Finding an inverse, we swap the terms of x and y:
[tex] \displaystyle{x = {(y + 2)}^{2} }[/tex]
Square root both sides, solving for y:
[tex] \displaystyle{ \sqrt{x }= \sqrt{ {(y + 2)}^{2}} } \\ \\ \displaystyle{ \sqrt{x }= \left| y+ 2\right| } \\ \\ \displaystyle{ \pm \sqrt{x }= y + 2}[/tex]
Subtract both sides by 2:
[tex] \displaystyle{ \pm \sqrt{x } - 2= y+ 2 - 2} \\ \\ \displaystyle{ \pm \sqrt{x } - 2= y} \\ \\ \displaystyle{y = 2 \pm \sqrt{x} }[/tex]
Therefore the inverse of y = x² + 4x + 4 is y = 2 ± √x.
Note: While it's possible to find the inverse of quadratic function, but the inverse version itself is not really a function. So if you want to go by definition or theorem, you can say there's no inverse function. Otherwise, the answer above is the solution.
Find the value of x.
Answer: x = 4
Step-by-step explanation:
Based on the given distances and angle measures, DE is congruent to XY, DF is congruent to ZX, and EF and ZY are congruent.
This means that:
[tex](4x-1)=15[/tex]
Simplify and solve for x.
[tex]4x-1=15\\4x=16\\x=4[/tex]
So, x = 4
Sara is saving her money in a piggy bank
and counts it each month. The graph
shows her monthly savings. Choose any
two points and draw a slope triangle.
Dilate the slope triangle along the graph
to determine whether the amount Sara
saves each month is constant.
Answer: It is not possible for me to draw a slope triangle or dilate it along the graph without more information about Sara's monthly savings.
To determine whether the amount Sara saves each month is constant, you can choose any two points on the graph and use them to calculate the slope of the line connecting them. If the slope is constant for all pairs of points, then the amount Sara saves each month is constant. If the slope is not constant, then the amount Sara saves each month is not constant.
To calculate the slope of the line connecting two points, you can use the following formula:
slope = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
You can then use the slope triangle to visualize the slope of the line connecting the two points. If you dilate the slope triangle along the graph and the slope remains constant, then the amount Sara saves each month is also constant.
Step-by-step explanation:
solue, giving all solutions between 0 and 360 degrees 8 (COS X)² - 10 COS X+3=0
Step-by-step explanation:
please refer to the sketch
After 9 years in an account with a 3.9% annual interest rate compounded continuously, an investment is worth a total of $17,757.16. What is the value of the principal investment? Around the answer to the nearest penny.
The value of the principal investment would be = $12,500.75
What is a principal investment?A principal investment is defined as the capital amount of money that is being deposited into an account with the purpose of receiving interest for a particular period of time.
The years of investment (t) = 9 years
The annual interest rate (r) = 3.9% = 3.9/100= 0.039
The total worth of the investment (A) = $17,757.16
Then, solve the equation for P
P = A / ert
P = 17,757.16 / e(0.039*9)
P = $12,500.75
Therefore, the principal amount that is needed which can be compounded continuously to get the total amount given = $12,500.75
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13. The line y = -2x +1 is reflected in the line y = 2. Write the equation of the image.
After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.
so the equation of the image is y = 2x + 1.
What is the line of reflection?A reflection over a line is a transformation in which each point of the initial figure (the pre-image) has an image that is on the opposite side of the reflection line from the original point and is situated at the same distance from the reflection line. The pre-size image's and shape are replicated in a reflection.
The line of reflection is typically expressed as y = m x + b y=mx+by, equals, m, x, plus, b. What need I do to draw the line of reflection? The starting points in the figure are all perpendicularly separated from the line of reflection by the same amount as the starting points in the image.
To reflect a line in the y-axis, we need to negate the slope of the line.
The line y = -2x +1 has a slope of -2 and y-intercept of 1.
After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.
so the equation of the image is y = 2x + 1.
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Here are the two sums
2/7 + 1/4 and 5/6 - 1/4
A. B
Which of the two sums is closer in value to 1/2?
You must show your working and state clearly whether the answer is A or B.
Note: Please use the “/“ key of your keyboard to enter the fractions (e.g. 2/7 as 2/7)
On solving the provided question, we can say that - the value of the fraction will be 1/4
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here,
x + x = 1/2
2x = 1/2
x = 1/4
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What are the dimensions of this shape in terms of the dimensions of the circle?
The diameter or radius of the circle is the dimension of a circle.
What is a circle?The circular line is drawn equidistant from the center point of a circle, which is a two-dimensional geometry object on a plane.
A geometrical rule states that the dimension of an object with n dimensions is n+1. For instance, a square is made up of line segments that are 1d and a cube is built up of squares that are 2d. The circle is therefore 2d or two-dimensional space since it is made up of 1d diameters.
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Answer:
The length of the parallelogram is half of the circumference of the circle, and its height is equal to the radius of the circle.
Step-by-step explanation:
Evaluate this problem
Answer:
78
Step-by-step explanation:
a + 8b = 6 + 8 x 9 = 6 + 72 = 78
Answer: 78
Step-by-step explanation:
value of a=6
value of b=9
a+8b= 6+8*9
as the 8 will be multiplied by 9
6+8*9= 6+72
6+72 = 78
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
B, C, E
Step-by-step explanation:
Let y = length.
Then, y - 5 = width.
area = length × width
area = y(y - 5)
area = 750
y(y - 5) = 750
y² - 5y = 750
A: y(y + 5) = 750
Since y = length, width must be y - 5, not y + 5, so A does not work.
B: y² - 5y = 750
This is what we got above, so this equation works.
C: 750 - y(y - 5) = 0
750 = y(y - 5)
750 = y² - 5y
This is the same as B and works.
D: y(y - 5) + 750 = 0
y(y - 5) = -750
The area cannot be -750, so this equation does not work.
E: (y + 25)(y - 30) = 0
y = -25 or y = 30
This also works.
Answer: B, C, E
Raina has to give medicine to her cat every morning for the next days. How many weeks is this?
Answer:
(number of days)/7
Step-by-step explanation:
1 week = 7 days
Divide the number of days by 7 to find the number of weeks.
-20 POINTS- Find the value of X
X=[?]
Answer:
x=1252x^2
I'm not sure if I'm 100% correct
Sorry.
What is the equation of the line that passes through the point (-4,-4) and has a
slope of -3/4?
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{3}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +4= -\cfrac{3}{4} (x +4) \\\\\\ y+4=-\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-7 \end{array}}[/tex]
Answer:
y = -3/4x - 7
Step-by-step explanation:
Given: slope = m = -3/4
Plug this value into the standard slope-intercept equation of y = mx + b.
y = -3/4x + b
To find b, we want to plug in a value that we know is on this line: in this case, point (-4, -4). Plug in the x and y values into the x and y of the standard equation.
-4 = -3/4(-4) + b
To find b, multiply the slope and the input of x(-4)
-4 = 3 + b
Now, subtract 3 from both sides to isolate b.
-7 = b
Plug this into your standard equation.
y = -3/4x - 7
This is your equation.
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i have been trying to figure this out for hours-
answer choices:
SSS
SAS
ASA
AAS
HL
Not Congruent
Answer: The answer is SAS
Find the slope of the line that passes through (4, 10) and (1, 11).
Answer:
-1/3
Step-by-step explanation:
72 ounces and 6 steaks = what rate and unit rate
Find the value of the lesser root of x squared -7x +12 =0
Answer:
3
Step-by-step explanation:
x² -7x + 12 =0
by factoring:
(x-4)(x-3) = 0
x = 4
x = 3
3<4
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
The spaceship will meet in how many hours?
The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.The intercept b represents the initial position.The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.x2(t) = 600 - 90t. (negative as they travel in opposite direction).They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?
Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.
The intercept b represents the initial position.
The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.
x2(t) = 600 - 90t. (negative as they travel in opposite direction).
They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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it takes 9 people 40 minutes to clean a hotel lobby. How many minutes would it take 4 people
Answer:
90 minutes
Step-by-step explanation:
9 people = 40 minutes
4 people = 40/4=10
10 * 9= 90
therefore 4 people will finish the work in 90 minutes
Can y’all pls help me solve this!!
Find a quartic function
The quartic equation y = x⁴ - x³ - 5 · x² - x - 6 has x = - 2 and x = 3 as its only real zeros. (Correct choice: C)
What quartic equation contains a given set of zeros?
Quartic equations are polynomials of grade 4, whose standard form is described below:
y = a · x⁴ + b · x³ + c · x² + d · x + e
Where a, b, c, d, e are real coefficients. A value of x is a zero of a polynomial when the result is equal to zero. The quickest way to find the polynomial is by evaluating each expression at x = - 2 and x = 3:
x = - 2
y = (- 2)⁴ - (- 2)³ - 5 · (- 2)² - (- 2) - 6
y = 16 + 8 - 20 + 2 - 6
y = 0
x = 3
y = 3⁴ - 3³ - 5 · 3² - 3 - 6
y = 81 - 27 - 45 - 3 - 6
y = 0
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4. What is the slope-intercept form of 9x + 3y = 15?
Oy=-3x+5
Oy=3x+5
Oy = 3x - 5
Oy=-3x - 5
The slope-intercept form of the equation 9x + 3y = 15 is y = -3x + 5.
What is slope-intercept form?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The given equation is 9x + 3y = 15.
Rearranging it to get in slope-intercept form -
⇒ 9x + 3y = 15
⇒ 3y = -9x + 15
Dividing LHS and RHS by 3 -
⇒ y = -3x + 5
Here, the equation is the slope-intercept form y = mx + c.
So, the slope is m = -3 in the equation.
Therefore, the slope-intercept form is y = -3x + 5.
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Rahul and his children went into a restaurant that sells hamburgers for $8 each and tacos for $4 each. Rahul has $80 to spend and must buy at least 11 hamburgers and tacos altogether. If x represents the number of hamburgers purchased and y represents the number of tacos purchased, write and solve a system of inequalities graphically and determine one possible solution.
x+y≥11 and 8x+4y=80 are system of inequalities and the number of tacos are two.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that Rahul and his children went into a restaurant that sells hamburgers for $8 each and
tacos for $4 each.
Rahul has $80 to spend and must buy at least 11 hamburgers and tacos altogether.
Let x represents the number of hamburgers purchased and y represents the number of tacos purchased,
x+y≥11...(1)
8x+4y=80..(2)
8(11-y)+4y=80
88-8y+4y=80
88-4y=80
8=4y
y≥2
Hence, x+y≥11 and 8x+4y=80 are system of inequalities and the number of tacos are two.
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#2 Lauren draws a still life picture of a vase of flowers using a scale where 1 inch= 3 inches. In her drawing, the vase is 6.75 inches tall. What is the actual height?
Answer:
20.25
Step-by-step explanation:
6.75 times by 3 is 20.25
Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand. How many acorns does frank have in the other hand?
The number of acorns that Frank have in the other hand will be 14.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.
Since Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand.
When Frank has 5 on one hand, the number of acorns that Frank have in the other hand will be:
= 10 + 9 - 5
= 14
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Complete question
Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand. Frank has 5 on one hand. How many acorns does frank have in the other hand
which equation represents the lime that is parallel to y=3 and passes through (-2,-8)?
A. x=-2
B. x=3
C. y=-8
D. y=3x -2
The line that parallels y = 1/2 x + 8 and goes through the point (-2, 2) is represented by the equation y = 1/2 x + 3.
What do you meant by x=-2 and x=3?
The entire time, the x-coordinate -2 is shown. A function is NOT what this is. A number is multiplied three times by itself to form a cube. The symbol for the cube of a number is x. 3.
To increase an integer to the third power is to cube it. A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.
A function, in general, is a relationship between two variables. In other words, the relationship x = y2 is not a function.
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50 POINTS! PLEASE HELP TT
A bag contains 1 red marble, 2 blue marbles, 3 yellow marbles, and 4 black marbles. A marble is randomly chosen from the bag, returned, and then another marble is chosen. What is the probablility that both marbles are blue?
Answer:
The probability that both marbles are blue is 1/25------------------------------------
Number of marbles:
Red = 1, blue = 2, yellow = 3, black = 4Total number:
1 + 2 + 3 + 4 = 10Probability of getting a blue marble:
P(blue) = number of blue / total numberP(blue) = 2/10 = 1/5Since the second marble is selected with replacement, the probability of the second blue marble is same, so the probability of two blue marbles is:
P(blue, blue) = 1/5*1/5 = 1/25[tex] \sf \: Probability _{(Blue)}=2/10×2/10 \\ \\ \sf Probability _{(Blue)}= \frac{1}{25} [/tex]
what is the slope for the equation?
Answer:
Slope: -1/2
Step-by-step explanation:
You can find the slope from this equation by adding 1/2 to each side of the equation since the way you find the slope of a line is by using: y = mx + b. The "m" must ALWAYS be on the right for it to be a valid slope equation, therefore, we have to use inverse operations for -1/2x to bring it to the right side.
Now, after we added 1/2x to each side, we get this equation:
-y = 1/2x + 3/4
We are not yet done since the y is accompanied by a negative 1, so, to isolate the variable, you use inverse operations once again and you get this equation:
y = -1/2x - 3/4
Therefore, the slope for this equation is -1/2.
Hope this helped! :D
What is the vertex of the function?
f(x) = 3(r - 2)2 + 4
Answer:
(2,4)
Step-by-step explanation:
The vertex of a parabola in the form of [tex]y=a(x-h)^2+k[/tex] is [tex](h,k)[/tex]. In this function, we have [tex](2,4)[/tex] as our vertex.
You buy 8.25 ounces of almonds and 7.5 ounces of cashews. You combine the nuts and divide them equally into 9 bags. How many ounces are in
each bag?
Options:
1.75 ounces
9.5 ounces
15.5 ounces
17.5 ounces
No. of many ounces are in each bag will be 1.75 ounces
What is the division of decimals?Unlike the division of natural numbers, the division of decimals is fairly straightforward. To divide decimal numbers by various sorts of numbers, such as whole numbers, decimal numbers, fractions, the powers of ten, etc., we can employ a variety of techniques. You may find answers to division of decimals quizzes and more practise problems in this article.
Dividing decimals is equivalent to dividing whole numbers, except when doing so, we take into account the decimal point as the final answer. The following are many options for splitting decimals:
Dividing by whole numbers with decimalsA decimal number divided by another decimal numberDecimal division using the powers of 10, specifically 10, 100, and 1000To be learn more about decimals refer to:
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Elijah is going to send some flowers to his wife. Kingwood Florist charges $1 per rose, plus
$20 for the vase. Anita's Flowers, in contrast, charges $3 per rose and $10 for the vase. If
Elijah orders the bouquet with a certain number of roses, the cost will be the same with
either flower shop. How many roses would there be?
Answer:
There will be 5 roses.
Step-by-step explanation:
Let r = the number of roses.
Total cost =
numberof Roses × price per rose AND cost of vase
Total at Kingwood's
= 1r + 20
Total at Anita's
= 3r + 10
We are looking for r (the number of roses) when the totals at either place are the same.
Set them equal to each other.
1r + 20 = 3r + 10
Subtract 1r.
20 = 2r + 10
Subtract 10.
10 = 2r
Divide by 2.
10/2 = r
5 = r
When Elijah buys 5 roses, the cost is the same at either florist.
Check:
at Kingwood's
= 1r + 20
= 1(5) + 20
=25
At Anita's
= 3r + 10
= 3(5) + 10
= 15 + 10
= 25
5 roses costs $25 at either florist.