Given the general form: F( x )= a(x^2)+bx+cConvert it to vertex form (also known as standard form) by putting the values for a,h and k into the correct boxes.F(x)=a(x-h)^2+kIdentify the vertex(x,y)General form: F( x )=1 x^2+6 x +-1 Vertex form: F( x )= Answer for part 1 and coordinate 1 (x- Answer for part 1 and coordinate 2 )^2 +Answer for part 1 and coordinate 3Vertex: (Answer for part 2 and coordinate 1,Answer for part 2 and coordinate 2)
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1) In order to convert from the standard version to the vertex form we'll need to find the vertex of that parabola:
[tex]f(x)=x^2+6x-1[/tex]We can find the vertex, using these formulas:
[tex]\begin{gathered} x=h=-\frac{b}{2a}=\frac{-6}{2}=-3 \\ k=(-3)^2+6(-3)-1=9-18-1=9-19=-10 \\ V(-3,-10) \end{gathered}[/tex]So this is the vertex of that parabola at point (-3,-10)
2) Now, note that the coefficient a = 1, and with the vertex, we can now rewrite that equation into the vertex form:
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=(x-(-3))^2+(-10) \\ y=(x+3)^2-10 \end{gathered}[/tex]
Related Questions
Answer To this question so that we can move onto the next question so that we can get done with all this homework so we can go play
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We need to transform a number that is written in scientific notation to the standard notation. For that we have to move the dot to the right, because the exponent of the power is positive, every time we do that we will subtract one from the exponent. When there is no more dot we will add zeros. This is done below:
[tex]\begin{gathered} 2.07\cdot10^5 \\ 20.7\cdot10^4 \\ 207\cdot10^3 \\ 2070\cdot10^2 \\ 20700\cdot10 \\ 207000 \end{gathered}[/tex]The correct answer is 207,000.
A circle has a center at (4, -7) and a radius of 4 units. What is the equation of this circle?
O (4)² + (y + 7)² = 16
O (x + 4)² + (y + 7)² = 4²
O(x-4)² + (y - 7)² = 16
O(x + 4)² + (y - 7)² = 4²
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the equation for the circle with radius, r = 4 units and center =(4,-7)
will be (x-4)² + (y+7)² = (4)².
When the center and radius of a circle are known, how do you determine its equation?
Use the formula (x-a) ² + (y-b) ² = r ² to determine a circle's equation when you are aware of its radius and center. Here, stands for the circle's center, and is its radius. This equation is essentially a variant way of writing the general equation for a circle.
In this question,
we are given the center of our circle to be,
(4,-7) ≈ (a,b)
thus we are given,
a = 4
and b = -7
and we are given the radius to be 4units
substituting these values in the above equation,
(x-4)² + (y-(-7))² = (4)²
= (x-4)² + (y+7)² = (4)²
Hence the equation for the circle with radius, r = 4 units and center =(4,-7)
will be (x-4)² + (y+7)² = (4)².
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Select the correct figures
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The correct answer is the figure
Please answer this question with an explanation. Thank you. :)
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The rate is positive because she is withdrawing funds from her account. So, Option C is the correct option.
What is the rate of change?The momentum of a variable is represented by the rate of change, which is used to mathematically describe the percentage change in value over a defined period of time.
How do you calculate the slope's rate of change?The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.Jessica's savings account balance is plotted against the number of months.
Rate of withdrawal from her account is given as:
Amount in Savings account/Number of months
= 1000/10
= 100 dollars/month
Therefore, Jessica is withdrawing 100 dollars per month from her savings account.
As a result, the rate is positive because she is taking money out from her account. Option C is thus the right option.
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A shirt costs ₹(a2 –ab -b2 ) , a pair of trousers cost ₹(2a2 +8ab-2b2 ) and a pair of shoes cost ₹(a2 –3ab+4b2 ) .After collecting these three items from the store, Ranjan paid ₹(2a+b )2 .What balance will Ranjan receive from the cashier ?
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The balance Ranjan will receive from the cashier is ₹ 0
How to determine the balanceBased on the information given, we have that;
shirt costs ₹(a² –ab -b² ) pair of trousers cost ₹(2a² +8ab-2b² ) pair of shoes cost ₹(a² –3ab + 4b² ) Ranjan paid ₹(2a+b )2Now, expand the bracket for the payment, we have;
(2a+b )²
(2a +b) (2a + b)
Multiply through
4a² + 2ab + 2ab + b²
Add like terms
4a² + 4ab + b²
Now, let's add the amount for the items bought
a² –ab -b² + 2a² +8ab-2b² + a² –3ab + 4b²
add like terms
4a² + 4ab + b²
Now, subtract the amounts
4a² + 4ab + b² - 4a² + 4ab + b²
₹ 0
Hence, the balance is ₹ 0
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Describe in extension each of the following sets:a) A is the set of positive integers less than 8.C) C is the set of digits of the number 12353888D) D is the set of courses you are enrolled in.
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a. All positive integers are greater than 0,
we can express this as a set which positive integers less than 8, A = {1, 2, 3, 4, 5, 6, 7}.
This is a Finite Set.
b. The number 12353888 has a set of digits, 1, 2, 3, 5 and 8 and can be expressed as C = {1, 2, 3, 5, 8}
This is also a Finite Set.
c. The set of courses you are enrolled depends on the number of courses. We can express this as
D = {course1, course2, course3, ...}
This is Universal Set.
Jena's income is $3800 a month, and she plans to budget 13 of her income for savings and 16 of her income for groceries.
What fraction of her income does she plan to spend each month on these two items together?
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The fraction of Jena's income does she plan to spend each month on these two items together is 1/2
The fraction of her income does she plan to spend each month on the two itemsJena's income for the month = $3800Fraction of Jena's income for savings = 1/3Fraction of Jena's income for groceries = 1/6Amount of Jena's income spent on savings = 1/3 × $3800
= 1266.666666666666
Approximately,
= $1,266.67
Amount of Jena's income spent on groceries = 1/6 × $3800
= 633.3333333333333
Approximately,
= $633.33
Amount spent on the two items = $1,266.67 + $633.33
= $1900
Fraction of Jena's income spent on the two items = 1/3 + 1/6
= (2+1) / 6
= 3/6
= 1/2
So therefore, Jena spent 1/2 of her income on savings and groceries.
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A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was $1,253.07, and the tax rate in the area is 7.1%, what was the pre-tax subtotal?
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To answer this question, we can proceed as follows:
1. We have that the after-tax total was $1,253.07.
2. We have that the tax rate in the area is 7.1%.
3. Then to find the pre-tax subtotal, we can proceed as follows:
[tex]7.1\%=\frac{7.1}{100}=0.071[/tex]Therefore, we have:
[tex]x+0.071x=1253.07[/tex]4. Finally, we need to add the like terms as follows:
[tex]1.071x=1253.07[/tex]And using technology, we can divide both sides by 1.071:
[tex]\begin{gathered} \frac{1.071}{1.071}x=\frac{1253.07}{1.071} \\ \\ x=1170 \\ \end{gathered}[/tex]Therefore, the pre-tax subtotal is $1,170.
A table is on sale for $589, which is 24% less than the regular price.
What is the regular price?
Answers
$589 + $141.36 = $730.36
Regular price was $730.36
The slope of a line which passes through the vertex and the y-y− intercept of the quadratic equation x^2 + 10x - 5x
2
+10x−5 is
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The slope of the line passing through the y intercept and the vertex of the quadratic x²+10x-5 is 5.
The provided quadratic equation is,
y = x²+10x-5
The vertex of a quadratic equation,
(-b/2a, -D/4a)
Where,
a = 1,
b = 10,
c = -5,
D = (b²-4ac)
D = (10²-4(-5)(1))
D = 100+20
D = 120,
Putting all the values to find the vertex of the equation,
(-10/2,-120/4)
(-5,-30)
So, the vertex are now known,
To find the y intercept, putting x = 0 and solving the equation for y,
y = (0)²+10(0)-5
y = -5
The y intercept is,
(0,-5)
If there are two points on the line, let say (a,b) and (c,d), then the slope of the line is,
M = (d-b)/(c-a)
Now, we know two points,(-5,-30) and (0,-5).
We can now find the slope of line,
M = (-5+30)/(0+5)
M = 25/5
M = 5
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please hurry. I need help on all three questions. please show working clearly.
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Evaluate 14xy if x=−23 and y=35 . Write your answer as a fraction in simplest form.
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Answer: -11270
Step-by-step explanation:
14xy = -11270 x=-23 y=35
14(-23)(35) = -11270
The table below represents the snacks that Sidney and Erica purchased at the movies last month. Write a system of equations to determine the price of each candy and each drink.
Answers
SOLUTION:
Case: System of equations
Given: A table of value of snacks and drinks for Sidney and Erica
Required: Write a system of equations to determine the price of each candy and each drink.
Method:
Step 1: Assume the price of snacks be represented by s and drinks by d
Step 2: Equation for Sidney
[tex]\begin{gathered} 2s+1d=13.50 \\ 2s+d=13.50.........equation(1) \end{gathered}[/tex]Step 3: Equation for Erica
[tex]\begin{gathered} 3s+1d=12.85 \\ 3s+d=12.85.......equatiion(2) \end{gathered}[/tex]Final answer:
The system of equations is:
[tex]\begin{gathered} 2s+d=13.50 \\ 3s+d=12.85 \end{gathered}[/tex]Which of the following best describes AD?17D17сA. MedianB. AltitudeC. Perpendicular bisectorD. Angle bisector
Answers
The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side thus bisecting that side.
Hence, Median best describes the line.
Option A is the correct option,
solve the triangle. round to the nearest tenth A B 16 14 С
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According the question
Side AC of the triangle = 16
Side BC = 14
The opposite side of the triangle is AC = 14
The adjacent side of the triangle is BC = 16
Using SOH CAH TOA
[tex]\begin{gathered} \text{Tan }\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \text{Tan }\theta\text{ = }\frac{14}{16} \\ \text{Tan }\theta\text{ = 0.875} \\ \theta\text{ = arc tan of 0.875} \\ \theta=tan^{-1}(0.875) \\ \theta\text{ = 41. 18 degre}es \\ To\text{ the nearest tenth} \\ \theta\text{ = 41.2 degre}es \end{gathered}[/tex]please look at screenshots
Answers
When the linear correlation coefficient is 1 there is a perfect positive linear relation between the two variables. Scatter diagram would contain points that all lie on a line with a positive slop.
What is coefficient coorelation?A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.
A correlation coefficient is a metric that expresses a correlation, or a statistical link between two variables, in numerical terms. Two columns of a specific data set of observations, sometimes referred to as a sample, or two parts of a multivariate random variable with a known distribution may serve as the variables.
The strength and direction of the linear links between two sets of variables are evaluated using correlation coefficients. Use Pearson's correlation coefficient if both variables are regularly distributed; otherwise, use Spearman's correlation coefficient.
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Please help which best explains an effect of the Diaspora on Jewish people?
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The BEST explanation of the effect of the Diaspora on Jewish people is d) They developed new rituals to accommodate the loss of the Temple.
What new rituals were developed by the Diaspora Jews?Some of the new rituals developed by the Diaspora Jews included:
Accommodating plenty of other cultures from different geographies.Utilizing the Torah to represent the symbol of God.Elevation of prayer and deeds of lovingkindness as ways to connect to God instead of the Temple.The Diaspora did not affect the Jewish people by dividing their homeland, making the destroyed Temple of Jerusalem the center of their religiosity, or making Rabbis insignificant.
Thus, the Diaspora affected the Jewish people in Option D.
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Question Completion with Answer Options:a) Their homeland was divided into Israel and Judah.
b) The Temple of Jerusalem became the center of religious activity.
c) Rabbis no longer served as significant religious leaders.
d) They developed new rituals to accommodate the loss of the Temple.
I need help on this also could you check if the first 3 questions are correct
Answers
We have two parallel lines intersected by other line.
We have to relate the angles.
We will take the angle with measure 17° as reference (red angle).
The angle <1 has a measure that is supplementary to the red angle, as <1 is supplementary to the <4, which is a corresponding angle to the red angle.
[tex]m\angle1=180-17=163\degree[/tex]It has no direct relationship with the red angle.
The angle <2 is supplementary to <1, so it will have the same measure as the red angle (m<2 = 17°).
The relationship with the red angle is that they are alternate exterior angles.
Angle <3 has no direct relationship with the red angle. As it is vertical with <1 it has the same measure (m<3 = 163°) and is supplementary to the red angle.
Angle <4 and the red angle are corresponding angles.
They have the same measure, so they are congruent.
Angle <5 and the red angle form a linear pair, so they are supplementary. The measure of <5 is then m<5 = 163°.
Angle <6 and the red angle are vertical angles, so they have the same measure.
Angle <7 and the red angle form a linear pair, so they are supplementary. The measure of <7 is then m<7 = 163°.
Answer:
Angle <1:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <2:
Measure = 17°
Relationship: Alternate exterior and congruent.
Angle <3:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <4:
Measure = 17°
Relationship: Corresponding and congruent.
Angle <5:
Measure = 163°
Relationship: Linear pair and supplementary.
Angle <6:
Measure = 17°
Relationship: Vertical and congruent.
Angle <7:
Measure = 163°
Relationship: Linear pair and supplementary.
Translate to a system of equations and solve:Priam has a collection of nickels and quarters, with a total value of $9.30. The number of nickels is six less than three times the number of quarters. How many nickels and how many quarters does he have?
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The value of a nickel is 5 cents
The value of the quarter is 25 cents
Since Priam has a total of 9.30 dollars = 930 cents, then
[tex]5n+25q=930[/tex]Simplify the equation by dividing all terms by 5
[tex]\begin{gathered} \frac{5n}{5}+\frac{25q}{5}=\frac{930}{5} \\ n+5q=186\rightarrow(1) \end{gathered}[/tex]Since he has 6 nickels less than 3 times the quarters, then
[tex]n=3q-6\rightarrow(2)[/tex]Substitute n in equation (1) by equation (2)
[tex](3q-6)+5q=186[/tex]Add the like terms on the left side
[tex]\begin{gathered} (3q+5q)-6=186 \\ 8q-6=186 \end{gathered}[/tex]Add 6 to both sides
[tex]\begin{gathered} 8q-6+6=186+6 \\ 8q=192 \end{gathered}[/tex]Divide both sides by 8
[tex]\begin{gathered} \frac{8q}{8}=\frac{192}{8} \\ q=24 \end{gathered}[/tex]The number of quarters is 24
Substitute q by 24 in equation 2 to find n
[tex]\begin{gathered} n=3(24)-6 \\ n=72-6 \\ n=66 \end{gathered}[/tex]The number of nickels is 66
He has 66 nickels and 24 quarters
you deposit $3,300 in account with an annual interest of 3.3% for 20 years. what is the amount of money you'll have at the end of the 20 years?
Answers
Given data:
The given principal is P=$3,300.
The given rate of interest is r=3.3%.
The given time is t=20 years.
The expression for the final amount of money is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=(3,300)+\frac{3,300\times3.3\times20}{100} \\ =3,300+2,178 \\ =5,478 \end{gathered}[/tex]Thus, the final amount after 20 years is 5,478.
Can somebody please help me right now??? i’m stuck and i need help with this bad
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Answer:
Step-by-step explanation:
The answer is B!
[tex]k(x) = 3(2) {}^{x} - 8[/tex]. Is the function linear, quadratic, exponential or neither?
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An exponential function is defined as a function of the form:
[tex]f(x)=a(b)\placeholder{⬚}^x+c[/tex]where a, b and c are constants.
We notice that the function given has this form, therefore the function given is an exponential function.
Find the image of D (0, -2) after the composition of translations
(x, y) → (x+10, y − 8) and (x, y) → (x − 7, y + 15).
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The ordered pair that represents the image of the point after the transformation is (3, 5)
How to determine the transformation of the point?The ordered pair of the point is given as
D = (0, 2)
The above point is an ordered pair on a coordinate plane
The sequence of transformations of the points is given as
(x, y) → (x+10, y − 8) and (x, y) → (x − 7, y + 15).
When the above transformations are applied on the point, we have:
So, we have the following equation
(x, y) → (x + 10 - 7, y − 8 + 15)
Evaluate the sum and the difference
So, we have the following equation
(x, y) → (x + 3, y + 7)
Recall that
D = (0, -2)
So, we have
D' = (0 + 3, -2 + 7)
Evaluate
D' = (3, 5)
Hence, the image of point D is (3, 5)
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What’s the slope I need help
Answers
Answer:
-8/3
Step-by-step explanation:
You want the slope of the line shown in the graph.
Slope from point coordinatesWhether counting grid squares on the graph, or using the slope formula, it is convenient to choose two points on the grid where the line crosses the intersection of grid lines.
It appears, the line passes through grid points (1, 4) and (4, -4). Using the slope formula, we find the slope of the line to be ...
m = (y2 -y1)/(x2 -x1)
m = (-4 -4)/(4 -1) = -8/3
The slope of the line is -8/3.
Counting grid squaresThe slope is the ratio of "rise" to "run" for the line. From the two points we see where the line crosses grid intersections, we have a "rise" of -1 from y=4 to y=-4, and a "run" of 3 from x=1 to x=4.
rise/run = -8/3 = slope of the line
In the expression below, what operation should be done first?
4 + 8 ÷ 2
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Answer:
Division
Step-by-step explanation:
Using the tool PEMDAS, you will see the order that you must complete an equation in, P=Parenthesis E=Exponents M=Multiplication D=Division Addition S=Subtraction
can someone please help me find the value of x to this equation
Answers
SOLUTION
This is a right-triangle problem.
We will use the SOHCAHTOA principle.
In this triangle, we will relate the opposite side and the hypotenuse side to get the value of x. That will be the CAH relationship.
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \cos \theta=\frac{5}{18} \\ \cos \theta=0.27778 \\ \theta=\cos ^{-1}(0.27778) \\ \theta=73.872^o \\ \theta=73.87^o \end{gathered}[/tex]The final answer is 73.87 degrees.
solve x=y+4, where x=3
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if x=3 we get
[tex]3=y+4\rightarrow y=3-4=-1[/tex] work out the sale has been decreased
20% of 120
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The current amount of the sale is 96
How to find the current amount of the sale ?The sale is 120
It was decreased by 20%
20/100 × 120
= 0.2 × 120
= 24
The amount of the current sale is
120-24
= 96
Hence the amount of the current sale which is calculated by subtracting 24 from 120 is 96
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a salad dressing recipe calls for 3/4 cup of olive oil for every 1/2 cup of vinegar is needed for 2 cups of olive oil?
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the answer is 1 1/4 cups of vinegar
Step-by-step explanati
Find the slope between the points with coordinates
(-2,3) and (4, 5).
Answers
Answer:
1/3 or 2/6
Step-by-step explanation:
you just plug the coordinates into a calculator and look at the rise over run.