Answers
The equation is (x+1)²-4.
Here the graph is in the form parabola, where the parabola is basically a graph for a quadratic function which is a curve in such an order that a point on it is equidistant from a fixed point called the focus of the parabola, and a fixed line called the directrix of the parabola. The general formula for a parabola is: y = a(x-h)² + k , where (h,k) signifies the vertex whereas the standard equation of a parabola is y² = 4ax.
For the given graph the vertex is (h,k)=(-1,-4)
so the equation for the parabola is
=>y= a(x+1)^²-4 .......1
Since we can see the parabola intercept at the x-axis at point (1,0), putting those in the above equation :
=>0=a(1+1)^2-4
=>4=a(2)^2
=>a=1
So, substituting the value of an in equation 1, we get
=>y= (x+1)^2-4
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Related Questions
PLS HELP ( geometry) and please explain the steps tyy
Answers
Answer: The line parallel to y = -2x + 5 that passes through the point(1,1)
Has the same slope, m but a different y intercept (0,b)
So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b
y = mx + b
m = -2
1 = -2(1) + b
1 = -2 + b
Add 2 to both sides of the equation to solve for b
1 + 2 = b
3 = b
The line is
y = -2x + 3
Step-by-step explanation:
Need help answering the following polynomial
Answers
The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
The given expression is [tex]-x^{2}-\frac{1}{6}[/tex].
We have to complete the given sentence;
The expression represents a ........... polynomial with ........terms. The constant term is .........., the leading term is..........., and the leading coefficient is .................... .
we first complete the given sentence then we explain the sentence.
The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
Firstly about Quadratic Polynomial
When the highest degree term in a second-degree polynomial equals to 2, the polynomial is said to be quadratic.
Now about Constant Term
A number that is constant and does not have any variables in an algebraic expression is a constant term.
Now about Leading Coefficient
The numbers placed in front of the variable with the biggest exponent are known as leading coefficients.
Hence, the expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
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What is the degree of the second term in this polynomial
Answers
The degree of the second term in the polynomial;
[tex]5x^{27}+5x^{19}+9x^9[/tex]is 19
Sue traveled 96 miles in 12 hours. A unit rate to describe Sue's travel is 8 miles per hour. What is another unit rate in this situation?
Answers
Answer:
Sue travels 8 miles per hour.
Step-by-step explanation:
Write the correct inequality for the following statement and then solve for the given number of
yards.
You have found a used car and your parents have agreed to pay the first
$750 for you. You have a summer job mowing yards for $25 per yard.
Write and inequality that will calculate the number of yards (y) you will
have to mow to get to at least the cost (C) of the car.
If the car cost a total of $4500 how many yards will you have to mow?
Answers
The inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car is 25y + 750 ≥ C.
If the car costs a total of $4500 number of yards you will have to mow is 150 yards at least.
What is inequality in math?In mathematics, a statement of an order relationship between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to) is called an Inequality.
Given:
Price of the car paid by your parents = $750
You have a summer job mowing yards for $25 per yard.
We have to determine an inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car.
So, the required inequality is
25y + 750 ≥ C
Now, the Cost of the car given is $4500.
Substituting this in the inequality to find the number of yards,
25y + 750 ≥ 4500
Subtracting 750 from both sides
25y ≥ 3750
Dividing both sides by 25,
y ≥ 150
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Write the number positioned at point D.
Answers
(The intervals are in 0.25)
A regular polygon is shown.
15 sided regular polygon
Determine the measure of one of its angles.
156°
168°
2,340°
2,700°
Answers
The measure of the given polygon's angle is 2340°
Polygons are two-dimensional closed objects in geometrical mathematics where n number of line segments cross each other to generate n number of vertices. A triangle is a polygon with three sides, for instance.
In an n-sided polygon, there are n inner angles.
The total of all interior angle measurements in a polygon is always constant and is denoted by the notation "n" for the number of sides in the polygon.
the formula is ;
Sₙ = ( n - 2 ) 180°
Here in question n is given as 15
Thus Sₙ = ( n - 2 ) 180° becomes
Sₙ = ( 15 - 2) 180
13 × 180
= 2340 °
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Answer:
it is really A 156 i took the test and got an 100%
Step-by-step explanation:
QuestRecently, More Money 4U offered an annuity that pays 6.6% compounded monthly. If $1,504 is deposited into this annuity every month, how much is in the account after 11 years? How much of this is interest?Type the amount in the account: $(Round to the nearest dollar.)
Answers
ANSWER
Amount = $3102.75
Interest = $1598.75
EXPLANATION
The annuity pays 6.6% compounded monthly.
The formula for an Amount compounded at a rate of r after t years is given as:
[tex]A\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]where P = principal (amount deposited) = $1,504
r = rate = 6.6% = 0.066
n = 12 (12 months in a year)
t = number of years = 11 years
Therefore, the amount in the account after 11 years is:
[tex]A\text{ = 1504(1 +}\frac{0.066}{12})^{12\cdot\text{ 11}}[/tex][tex]\begin{gathered} A=1504(1+0.0055)^{132} \\ A\text{ = 1504(}1.0055)^{132} \\ A\text{ = 1504 }\cdot\text{ 2.063} \\ A\text{ = \$3102.75} \end{gathered}[/tex]That's the amount in the account after 11 years.
This means that the amount of interest after 11 years is the amount after 11 years minus the amount that was there initially:
Interest = 3102.75 - 1504
Interest = $1598.75
A bag with 10 marbles has 3 yellow marbles, 2 blue marbles, and 5 red marbles. A marble is chosen from the bag at random. What is the probability that it is yellow or blue? Write your answer as a fraction in simplest form.
Answers
Which of the following is an example of the associative property of multiplication?7 . (3 . 5) = (7 . 3) . 507. (3+5) = 21 + 357.(3.5) = 7 . (5. 3)0.1=1
Answers
The associative property of multiplication states that you can choose any pair of numbers to multiply first when there are more than two numbers being multiplied. This doesn't change the final result:
a . b . c = (a . b) . c = a . (b . c)
So, we see an example of such property in the first option:
7 . (3 . 5) = (7 . 3) . 5
Let's check this is indeed true:
7 . (3 . 5) = 7 . 15 = 105
(7 . 3) . 5 = 21 * 5 = 105
Therefore, the first option is correct.
Notice that the second option uses the distributive property of multiplication over addition:
a . (b + c) = a . b + a . c
The third uses the commutative property of multiplication:
a . b = b . a
The fourth is wrong since zero multiplied by any number is zero, not one:
0 . a = 0, for all values of a.
15) What is the range of the following set of points: {(3, 4), (7,-2), (11, -8)}? Al{-8, -2,3,7,11} B {3,7, 11} C{-8, -2,4} D{-19, -9,1}
Answers
The range is the set of y-values of the points given.
The points given are:
{(3, 4), (7,-2), (11, -8)}
The range would be:
4, -2, and -8
Range = {4,-2,-8}
Option C
Each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. How could one express the number of ways those textbooks could be distributed among the students?
Answers
The way that expresses the number of ways those textbooks could be distributed among the students is ⁵C₂.
What is combination?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr
Combination formula will be:
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
In this case, each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. This will be illustrated as ⁵C₂.
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There are ten ways (which are ⁵C₂ = 10) to distribute those textbooks could be among the students in this situation.
What is the Combination?Combinations indicate the choosing of items from a predetermined list of items.
The combination is given by the relation, ⁿCₓ = n!/{x!(n-x)!}
The quantity is given by n. and x is equal to how many objects are taken at once.
Each of the five students in this situation wants to purchase a specific textbook, but there are only 2 books available.
The expression for the number of possible distributions of such textbooks among the students is
⇒ ⁵C₂
⇒ 10
Hence, there are ten ways to distribute those textbooks could be among the students.
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Triangle XWY is transformed to produce triangle URL. Select all the transformations that would guarantee triangles XWY and URL are congruent.
O reflection, then a translation
O dilation, then a reflection a
O rotation, then a dilation a
O translation, then a rotation.
O rotation, then a reflection
Answers
The correct transformations are;
1. Reflection, then a translation
2. Rotation, then a reflection
3. Translation, then a rotation.
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
Triangle XWY is transformed to produce triangle URL.
Now,
The images arise from transformation should remain the same with respect to the size or shape.
So, we get;
The correct transformations are;
1. Reflection, then a translation
2. Rotation, then a reflection
3. Translation, then a rotation.
Thus, The correct transformations are;
1. Reflection, then a translation
2. Rotation, then a reflection
3. Translation, then a rotation.
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There are two numbers whose sum is 50. Three times the first is 5 more than twice the second. What are the numbers?
Answers
The two numbers whose sum is 50 and three times the first is 5 more than twice the second are 21 and 29.
What do you mean by sum?
A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
Let the two numbers be X and Y.
There are two condition given in the question through which we can form a system of equation containing two equations.
First condition: The sum of the numbers is 50.
Therefore,
X + Y = 50
Second Condition: Three times the first is 5 more than twice the second
Therefore,
3X = 2Y + 5
We get the system of equation:
X + Y = 50
3X = 2Y + 5
Solving this system of equation
3X - 5 = 2(50 - X)
3X - 5 = 100 - 2X
X = 105/5
X = 21
Putting the value of X in one of the equation:
Y = 50 - X
Y = 50 - 21
Y = 29
Therefore, two numbers are 21 and 29
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What what solid is generated when the semi circle is rotated about the line
Answers
Sphere solid is generated when the semicircle is rotated about the line.
Given,
The semi circle is rotated about the line.
To find the what solid is generated?
Now, According to the question:
We know that when a semicircle is rotated about any line then the three dimensional figure or a solid that is formed on this rotation transformation is Sphere.
Hence, Sphere solid is generated when the semicircle is rotated about the line.
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write an equation of a line m= -7 b= -11
Answers
Answer:
y= -7x-11
Step-by-step explanation:
m= -7 (gradient)
b= -11 (y-intercept)
write in the form of y=mx+b
y=-7x-11
f(2x)
13
-5
2
-3
What is x?
Answers
The solution for the given equivalent equation f(2x) is 10.
What is equation?
In mathematics, the term equation can be defined as the two algebraic expression which are equal to each other. This method is used to calculate the values of the parameters in the problems.
According to the question, the given equivalent equation is as follows:
Equivalent equation: f(2x) = 3x + 3 = x + 13
By using the addition-subtraction property, to generate the equivalent equations.
3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5
Now, f(2x) = 2x = 10
Hence, the solution for the given equivalent equation is 10.
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The correct equation is: f(2x) = 3x + 3 = x + 13
Question at position 3
Write the expression as a sum and/or difference of logarithms with all variables to the first degree
[tex]ln\sqrt{8t^{4} v^{2}[/tex]
Answers
The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]
Given,
Write the expression as a sum and/or difference of logarithms with all variables to the first degree.
[tex]In\sqrt{8t^4v^2}[/tex]
Convert to exponential form
= [tex]In(8t^4v^2)^\frac{1}{2}[/tex]
Simplify using exponent rule with same exponent [tex](ab)^n = a^n . b^n[/tex]
= [tex]In (8^\frac{1}{2} . (t^4)^\frac{1}{2}(v^2)^\frac{1}{2} )[/tex]
Apply laws of logarithms to simplify the expression.
= [tex]In 8^\frac{1}{2} + In(t^4)^\frac{1}{2} + In(v^2)^\frac{1}{2}[/tex]
Express the logarithm of a power of an expression as the power times the logarithm of the expression.
= [tex]\frac{1}{2} . In8 + In(t^4)^\frac{1}{2} + In(v^2)\frac{1}{2}[/tex]
=[tex]\frac{1}{2} . In8 + \frac{1}{2} . In(t^4) + \frac{1}{2} .In(v^2)[/tex]
Multiply the monomials
[tex]\frac{In8}{2} + \frac{1}{2} . 4 . In t + \frac{1}{2} . 2 . In v[/tex]
= [tex]\frac{In8}{2} + 2 . In t + \frac{1}{2} . 2 . In v[/tex]
= [tex]\frac{In8}{2} + 2 . In t + In v[/tex]
Hence, The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]
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8 Write the equation of the line in standard form, point-slope form, and slope-intercept form. 4 -2 DELL
Answers
step 1
Find the slope
we need two points
take the points (0,3) and (1,0)
m=(0-3)/(1-0)
m=-3
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-3
b=3
substitute
y=-3x+3step 3
Find the equation of the line in point slope form
y-y1=m(x-x1)
we have
m=-3
point (0,3)
y-3=-3(x-0)
y-3=-3xstep 4
standard form
AX+By=C
we have
y=-3x+3
3x+y=3 -----> standard formHi, can you help me with this Exercise , please!
Answers
The weekly cost C of producing x units in a manufacturing process is given by
[tex]C(x)=60x+750[/tex]The number of units x produced in t hours is given by
[tex]x(t)=50t[/tex](a) The composite function C(x(t)) is given by
[tex]\begin{gathered} C(x)=60x+750 \\ C(x(t))=60(50t)+750 \\ C(x(t))=3000t+750 \end{gathered}[/tex]The function C(x(t)) gives us the cost of production for t hours.
(b) The number of units produced in 4 hours is given by
[tex]\begin{gathered} x(t)=50t \\ x(t)=50(4) \\ x(t)=200 \end{gathered}[/tex]200 units will be produced in 4 hours.
(c) Let us graph the function C(x(t)) = 3000t + 750 to find the value of t for which the cost increases to $15,000
As you can see, the value of t is 4.75 hours when the cost is $15,000.
Therefore, 4.75 hours must elapse until the cost increases to $15,000.
Help me please, it’s due in 10 minutes!
Answers
Answer: x<2 or (−∞,2)
Step-by-step explanation:
A line intersects the points
(-2, 9) and (3, -11).
m = -4
Write an equation in point-slope form
using the point (-2, 9).
y - [?] =(x-)
Answers
Answer: (3,11)
Step-by-step explanation:
I need help with this practice problem The subject is trigonometry It asks to graph the function If you can ❗️ use Desmos to graph
Answers
We will have the following:
7. Each set of numbers below represents the lengths of three line segments.
Which set represents line segments that could be connected to form a triangle:
A. (1, 2, 3)
B. (3, 4, 5)
C. (1, 10, 100)
D. (1, 2, 5)
E. (1, 3, 4)
F. (1, 20, 100)
Please don't just give a letter choice as an answer. There are more questions like this one and I'd like to understand how to do it : )
Answers
Answer:
B: (3, 4, 5)
Step-by-step explanation:
You want to know which segment lengths could be used to form a triangle.
Triangle inequalityThe triangle inequality requires the sum of the two short sides of a triangle exceed the length of the longest side.
A: 1+2 = 3 . . . not a triangle
B: 3+4 > 5 . . . forms a triangle
C: 1+10 < 100 . . . not a triangle
D: 1+2 < 5 . . . not a triangle
E: 1+3 = 4 . . . not a triangle
F: 1+20 < 100 . . . not a triangle
__
Additional comment
The above expression of the triangle inequality seems to be the one most commonly used in algebra and geometry courses.
The triangle inequality can also be seen to be expressed as ...
a + b ≥ c . . . . . . where a, b, c are side lengths in any order
The "equal to" case allows triangles of zero height. (They look like a line segment.) Using that formulation, triples A and E in your answer list will also be considered to form a "triangle."
Find three number in arithmetic progression whose sun is 21 and product is 315
Answers
Answer:
Step-by-step explanation:
It should be option D
Reason
The correct answer to the 3 numbers with a sum of 21 is 6,7,8 but those 3 numbers don’t make a product of 315
8,9,10 sum is 27 product is 720
2,3,4 sum is 9 product is 24
11,12,13 sum is 36 product is 1716
5,6,7 sum is 18 product is 210
So none of these will fit that criteria
You can find the sum of 3 numbers with equation
x+ x+1 + x+2 = 21
3x + 3 = 21
3x = 18
x = 6
x +1 = 7
x + 2 = 8
Can someone please help me with this problem? I’ll give brainliest
Answers
Answer:
Step-by-step explanation:
gee girls generation
what is ST? I've included a photo of the problem
Answers
Answer
ST = 14
According to the diagram
UV = VW
ST = UT
UT = VT - UV
UV = 14 and VT = 29
UT = 29 - 14
UT = 15
SInce UT = ST, Therefore, ST = 14
Use the graph below for this question: graph of parabola going through negative 3, negative 1 and 5, negative 1. What is the average rate of change from x = −3 to x = 5? (1 point) A) −1
B) 0
C) 1
D) 8
Answers
The average rate of change of the function at the interval x = -3 to x = 5 has a value of (b) 0
How to calculate the average rate of change f?From the question, we have the following points
Parabola going through (-3, -1) and (5, -1).
Also from the question, the interval is given as
x = −3 to x = 5
This interval can also be represented as
(a, b) = (-3, 5)
The points in the question can be expressed as
f(a) = f(-3) = -1
f(b) = f(5) = -1
The value of the average rate of change of the graph at the interval is then calculated as
Rate = [f(b) - f(a)]/[b - a]
Substitute the known values in the above equation
So, we have the following equation
Rate = [f(5) - f(-3)]/[5 + 3]
So, we have the following equation
Rate = [-1 + 1]/[5 + 3]
Evaluate the above quotient
Rate = 0
Hence, the average rate of change of function f is (b) 0
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what is the price of a line jacket at discount Heaven?
Answers
The price of the lined jacket at discount heaven is 32.
To find the price of the lined jacket at the house of denim we use the rule of three.
[tex]\begin{gathered} 35.25\rightarrow100 \\ x\rightarrow10 \end{gathered}[/tex]Then the discount is:
[tex]x=\frac{10\cdot35.25}{100}=3.525[/tex]Hence, the price of the lined jacket at house of denim is:
[tex]35.25-\text{3}.525=31.725=\text{31}.73[/tex]Therefore, the price of the lined jacket at house of denin is $31.73.
Please Help . I'm Running Out Of Time!
Answers
-5/4 can be shown as -1 1/4, and plotted on the number line as the first quarter tick past -1. Its opposite, 1 1/4, is the same way, the first quarter tick past 1.
Answer: On the plot line 5/4 is 5 tic marks passed 0 so -5/4 would be 6 tic marks before. Hope this helps
If this is wrong I am deeply sorry.