Answers
Answer:
\((-1, -16)\)
Step-by-step explanation:
First, we can expand the right side of this equation.
\(y=(x + 5)(x-3)\)
\(y = x^2 -3x + 5x - 15\)
\(y = x^2 + 2x - 15\)
Then, we can move the 15 to the left side.
\(y + 15 = x^2 + 2x\)
Now, the equation is in a form where we can complete the square for x. Remember that anything we add to one side, we also have to add to the other side.
\(y + 15 + (2/2)^2 = x^2 + 2x + (2/2)^2\)
\(y + 16 = x^2 + 2x + 1\)
\(y + 16 = (x+1)^2\)
Finally, we can move the 16 to the right side.
\(\boxed{y = (x+1)^2 - 16}\)
The equation of the parabola is now in vertex form:
\(y = (x - h)^2 + k\),
where \((h,k)\) is the vertex of the parabola.
In the equation we just solved for (\(y = (x+1)^2 - 16\)), we can identify the following:
\(h = -1\)\(k = -16\)Therefore, the vertex of the parabola is:
\(\boxed{(-1, -16)}\)
Related Questions
Select each angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z
Answers
The angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z are
180 degrees
540 degrees
900 degrees
How to find the angle of rotationThe transformation rule for an angle of 180 degrees is simply a reflection or a flip. This means that any object or figure that undergoes this transformation will be flipped over a line or axis.
The rule is (x, y) will become (-x, -y)
Where 540 degrees = 360 + 180
where 900 degrees = 360 + 360 + 180
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Solve for x. Round to the nearest tenth, if necessary.
56
Z
43°
x
M
Answers
60.2 is the value of x in Trigonometric ratios
What are the trigonometric ratios?
Trigonometric ratios are used to describe the side ratios of a right triangle. The sine (sin), the cosine (cos), and the tangent are three popular trigonometric ratios (tan).
Greek is the language of measuring, "metric," and "trigon" is the language of triangles. It is possible to measure a right triangle specifically using its trigonometric ratios.
43 degree as reference angle
using tan rule
tan 43 = opposite / adjacent
0.93 = x / 56
x = 56/0.93
x = 60.21
x = 60.2
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help here's a pic on the problem
Answers
The linear function that shows the proportional relationship between the distance and time is d = 100t
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,
'm' is the slope of the line'b' is the y-intercept of the line'x' is the independent variable'y' (or f(x)) is the dependent variableFrom the table given, we can find the slope of the function by using the formula
m = y₂ - y₁ / x₂ - x₁
m = 300 - 200 / 3 - 2
m = 100
To find the y - intercept,
y = mx + c
300 = 100(3) + c
300 = 300 + c
c = 300 - 300
c = 0
The equation that shows the relationship is
d = 100t
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Is there a proportional relationship between number of sandwiches and the cost of the order? Explain how you know.
(In the picture are my answers so you guys can see them, but what I need to know is if they are proportional or not, and why.)
(20 points)
Answers
Answer:
CMER BOOOOOOOOOOOOOOOOOOOOOO
Step-by-step explanation:
Select the number that round to 387.4 when rounded to the nearest tenth.
A. 387.461
B. 387.344
C. 387.309
D. 387.352
E. 387.779
Answers
Answer:
D
Step-by-step explanation:
When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"
If you think my answer is the best, please mark it as the Brainliest.
Thank you! :))
AB is the line segment, M is the midpoint of AB. A is (-4,5) and M is (5, -1), what are the coordinates of B?
Answers
\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -4}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(5~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=5\implies x-4=10\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=-1\implies y+5=-2\implies \boxed{y=-7}\)
7. Suppose random samples of 48 are taken from a distribution that is skewed right. The sampling distribution will be which of the following?
Answer choices:
Skewed left
Skewed right
Non-normal
Normal
Answers
Answer:
Step-by-step explanation:
The Central Limit Theorem states that as sample size increases, the sampling distribution of the sample mean becomes approximately normal, regardless of the shape of the population distribution, as long as the sample size is sufficiently large (usually n > 30).
In this case, the sample size is 48, which is larger than 30, so we can expect the sampling distribution of the sample mean to be approximately normal, even if the population distribution is skewed right. Therefore, the answer is "Normal".
Due in a MINUTE!!! Need help!
Answers
Answer:
GH = 15
Step-by-step explanation:
In a trapezoid, the length of the median is one-half the sum of the lengths of the bases. Therefore:
\(9x - 3 = \frac{1}{2} (19 + 5x + 1)\)
\(18x - 6 = 5x + 20\)
\(13x = 26\)
\(x = 2\)
\(9(2) - 3 = 18 - 3 = 15\)
tony hit a baseball into the air with an initial upward velocity of 48 feet per second. The height h in feet of the ball above the ground can be modeled by h=-16t^2+48t+2. find the time it takes the ball to reach 38 feet above the ground
Answers
Answer:
H=-6t^2+38t+1
Step-by-step explanation:
rotate the figure 90 degrees clockwise then translate 4 units left
Answers
Answer:
If I am not mistaken, the new figure will be here (view attachment, bright blue figure is the new transformation)
Answer:
For each of the following equations determine the output values Corresponding to the input value
(-2;-1;0;1;2;3)
Finn has $60 in a savings account. The interest rate is 10% per year and is not compounded. How much interest will he earn in 1 year?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
Answer:
6$
Step-by-step explanation:
Answer:
I = $ 6.00
Step-by-step explanation:
Equation:
I = Prt
Calculation:
First, converting R percent to r a decimal
r = R/100 = 10%/100 = 0.1 per year,
then, solving our equation
I = 60 × 0.1 × 1 = 6
I = $ 6.00
The simple interest accumulated
on a principal of $ 60.00
at a rate of 10% per year
for 1 years is $ 6.00.
Hope its correct
Mr garcia purchased a property 3 years ago for $155,750.00.The market has growth rate of 3.75% compounded monthly. What is the current value of the property?
Answers
Mr. Garcia purchased a property 3 years ago for $155,750.00
So, number of years = 3 and Initial amount = $155,750.00
The market has a growth rate of 3.75% compounded monthly.
So, interest rate = 3.75% and the number of times compounded in a year = 12
What is the current value of the property?
Recall that the compound interest formula is given by
\(A=P(1+\frac{r}{n})^{nt}\)Where
A = Future value (current value in this case)
P = Principle value (initial value = $155,750.00)
r = interest rate (growth rate in this case)
t = number of years (3 years in this case)
n = number of times compounding is done in a year (monthly means n = 12)
Let us substitute the given values into the above formula
\(\begin{gathered} A=155,750(1+\frac{0.0375}{12})^{12\cdot3} \\ A=155,750(1+0.003125)^{36} \\ A=155,750(1.003125)^{36} \\ A=155,750(1.11887) \\ A=\$174,264.00 \end{gathered}\)Therefore, the current value of the property is $174,264.00
Solve for X. PLEASE HELP
Answers
Answer:
xxtentacion for life
Step-by-step explanation:
9 + 7 = 8 + x
16 = 8 + x
x = 8
3. What is the slope of the line through the points (2, 5) and (6, 13)?
Answers
Answer:
m = 2
Step-by-step explanation:
\(m=\frac{rise}{run}=\frac{13-5}{6-2}=\frac{8}{4}=\boxed{2}\)
Hope this helps.
6 * 10x^{-3}/8*10x^{-6}
Answers
The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4 × 10³
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
6 × 10⁻³ / 8 × 10⁻⁶
Simplifying the expression
6 × 10⁻³ / 8 × 10⁻⁶
This can be written as
6/8 × 10⁻³/10⁻⁶
Reduce the fraction
3/4 × 10⁻³/10⁻⁶
Apply the division law of indices
3/4 × 10⁻³ ⁻ ⁽⁻⁶⁾
3/4 × 10⁻³ ⁺ ⁶
3/4 × 10³
Hence, the value is 3/4 × 10³
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Each of the four sets a1, a2, a3, and a4 contains four elements. the intersection of every i of these four sets (2 < i < 4) consisters of 5 - i elements. What is a1 U a2 U a3 U a4?
Answers
Answer:
the new year was patrick's year and the second time she had the target audience in her career as an 34696468 )/684₩¥€=÷×+)^^*,?^&££)ktuioon
Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065. New equipment is being tested in an attempt to improve quality by reducing variation. A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.047 . Use a 0.05 significance level to test the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.065. Does the new equipment appear to be effective in reducing the variation of weights?
Answers
Answer:
Yes, the new equipment appear to be effective in reducing the variation of weights.
Step-by-step explanation:
We are given that Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065.
A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.047.
Let \(\sigma\) = standard deviation of weights of new equipment.
SO, Null Hypothesis, \(H_0\) : \(\sigma \geq\) 0.065 {means that the new equipment have weights with a standard deviation more than or equal to 0.065}
Alternate Hypothesis, \(H_A\) : \(\sigma\) < 0.065 {means that the new equipment have weights with a standard deviation less than 0.065}
The test statistics that would be used here One-sample chi-square test statistics;
T.S. = \(\frac{(n-1)s^{2} }{\sigma^{2} }\) ~ \(\chi^{2}__n_-_1\)
where, s = sample standard deviation = 0.047
n = sample of quarters = 25
So, the test statistics = \(\frac{(25-1)\times 0.047^{2} }{0.065^{2} }\) ~ \(\chi^{2}__2_4\)
= 12.55
The value of chi-square test statistics is 12.55.
Now, at 0.05 significance level the chi-square table gives critical value of 13.85 at 24 degree of freedom for left-tailed test.
Since our test statistic is less than the critical value of chi-square as 12.55 < 13.85, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the new equipment have weights with a standard deviation less than 0.065.
What is the answer of this triangle congruence question.
Answers
The value of x in the triangles are 9.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The triangles are congruent.
That means, their corresponding angles are also congruent.
In ΔJKL,
the sum of all the angles of the triangle is 180°.
So,
x²-2x + x + 29 + 3x + 52 = 180
x² + 2x - 99 = 0
Solving the quadratic equation,
x² +11x - 9x - 99 = 0.
x (x + 11) -9 (x + 11) = 0
x = 9 and x = -11
Here, we take x = 9.
Therefore, the value of x is 9.
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●
Jamie went out to her grandfather's farm.
Her grandfather has pigs and chickens on his farm.
She noticed that there were a total of 26 heads and
68 feet among them. How many chickens and how
many pigs did her grandfather have?
Answers
Answer:
8 pigs
Step-by-step explanation:
Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.
Suppose all animals are chickens.
Total no. of feet = 26 chickens × 2 feet
= 52 feet
Difference in total no. of feet = 68 feet - 52 feet
= 16 feet
Difference in no. of feet each animal has
= 4 feet (a pig) - 2 feet (a chicken)
= 2 feet
∴ No. of pigs = 16 feet ÷ 2 feet
= 8 pigs
The conditional statement below is true. If possible, write the biconditional statement.
If 2x = 18, then x = 9.
Answers
The biconditional statement for the given conditional statement would be:
2x = 18 if and only if x = 9.
The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".
To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.
If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.
Based on this, we can write the biconditional statement:
2x = 18 if and only if x = 9.
The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.
In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.
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I need help again
I am
Sorry
Answers
Answer:
x = 171.16 - 5.8
x = 165.36
please give me brainlist
Step-by-step explanation:
Answer:
165.36 is Pete's height
Step-by-step explanation
You have to subtract 5.8 by 171.16 and that will be Pete's height.
Solve the inequality for w.
w+7<20
Simplify your answer as much as possible.
0
Answers
Answer:
w<13
Step-by-step explanation:
Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.
Answer:
w < 1`3
Step-by-step explanation:
Isolate the variable w on one side of the inequality sign.
w+7<20
w<20 - 7
w<13.
i
You are given the difference of the numbers of boys and girls in a class and the ratio of boys to girls. How many boys
and how many girls are in the class?
4 more girls; 9 for every 13
There are
boys and
girls in the class.
Answers
Answer:
Maybe they are all 13s th am sure
Simplify. Write your answers without exponents.
Answers
Answer:
1st one is: 1/125
2nd one is: 1/16
Find the slope of the line that contains the points (1, 6) and (10, -9)
Answers
Answer:
-15/9
Step-by-step explanation:
The slope is the steepness of the line. To find it, you divide how far up it goes by how far across it goes. This equals the diagonal incline. To find it with points, you find the difference between the y values and divide that by the difference in the x values!
-9-6=-15
10-1=9
-15/9=-15/9
This slope means that for every nine units the line goes across, it goes down 15 units!
Have a wonderful day :D
7. Alexis has 145 stickers. She wants to divide the stickers evenly among 5 of her friends. How
many stickers will each friend get?
Write your answer in the box.
stickers.
8. There are 2,472 seats in the school auditorium. The seats are divided into 6 equal sections.
How many seats are in each section? Write your answer in the box.
seats
Explain how you found your answer. Show your work.
Answers
Answer: 7: 29 stickers for each friend
8: 412 seats in each section
Step-by-step explanation:
We will have to divide 145 (stickers) by 5 (friends) to get 29
We will have to divide 2472 by 6 to get 412
7.) 145 ÷ 5 = 29 → Each friend will get 29 stickers
8.) 2,472 ÷ 6 = 412 → There are 412 seats in each second.
I divided for both problems using the long division method and multiplied which is the inverse operation, to check my work.
how do I solve this screen shot
Answers
Answer:
add me as a friend and give me thanks
Step-by-step explanation:
the answer is A for sure
Simplify: 4 1/2
÷ 2:
Answers
Answer:
9/4 = 2 1/4
Step-by-step explanation:
Solve the system of equations by using elimination. Write the solution as an ordered pair.
4x−3y=35x+6y=7
Answers
Step by step
Our equations are
4x -3y = 3 ➡️ equation 1
5x + 6y = 7 ➡️ equation 2
Using elimination method we need to change one equation so one variable can be eliminated and then solve
I will multiply all terms in equation 1 by 2
2 ( 4x -3y = 3)
8x -6y = 6 ➡️ equation 1
5x + 6y = 7 ➡️ equation 2
So you see we can eliminate -6y and +6y by adding the like terms in the equations
13x = 13
Divide both sides by 13 to solve for x
13/13 x = 13/13
x = 1
Now substitute the value of x = 1 into equation 2
5x + 6y = 7 ➡️ equation 2
5(1) + 6y = 7
5 + 6y = 7
Subtract 5 from both sides to isolate variable
5 -5 + 6y = 7 -5
Simplify
6y = 2
Divide both sides by 6 to solve for y
6/6 y = 2/6
Simplify
y = 1/3
I graphed it to check my work, solution is correct
Write an equation of the line, in point-slope form, that passes through the two given points. points: (-3.18), (12.-12)
Answers
Answer:
y=-2x+12
Step-by-step explanation:
Count how much the y raises for each x through division for the slop, and then plug that in to the x on either one of the pairs to get the number, and then add or subtract whatever the actual y is to get the y intercept.