What is the axis of symmetry? What are the coordinates of the vertex?
y=x² +4x-11
Answers
Answer:
Step-by-step explanation:
The axis of symmetry of a parabolic function of the form y = ax^2 + bx + c is a vertical line that divides the graph of the function into two mirror images. The axis of symmetry of the function y = x^2 + 4x - 11 is the vertical line x = -2.
The vertex of a parabolic function is the highest or lowest point on the graph, depending on the direction of the parabola. The coordinates of the vertex can be found by completing the square.
To find the coordinates of the vertex of the function y = x^2 + 4x - 11, we can rewrite the function as follows:
y = (x^2 + 4x) - 11
= x^2 + 4x + (-11)
= (x^2 + 4x + 4) + (-11 + 4)
= (x + 2)^2 - 7
Related Questions
Can someone help me out with this questions please?!?!
Answers
The simplified form of inequality -3x - 1 ≥ 20 is x ≤ -7.
The correct option is option (A).
What is number line?A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.
The given inequality is,
-3x - 1 ≥ 20.
To find the right number line from the options
Solve the inequality,
Add 1 to both the sides,
-3x -1 + 1 ≥ 20 + 1
-3x ≥ 21
-x ≥ 21 / 3
-x ≥ 7
x ≤ -7
The value of x are less than or equal to -7. Implies that, in number line graph close circle.
The number line in option (A), is correct option.
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an outlier will have an effect on:
1) quartile III
2) the mean
3) the mode
4) the interquartile range
Answers
the mean
the mean is the average, having an outlier will make the average significantly higher or lower than accurate.
Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below.
Three lines of math. The first line, StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis. The second line, StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half EndFraction x minus x plus 4. The third line StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half EndFraction x plus 4.
StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half Endfraction x minus x plus 4.
StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half Endfraction x plus 4.
When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. results. What is the value of ?
–1
–negative StartFraction one-half EndFraction
0
StartFraction one-half EndFraction. BRAINIEST
Answers
When she subtracts 4 from both side of the equation, then she gets the value of x is 0.
What is expression?Expressions means the idea of expressing numbers using letters or alphabets without specifying their actual values, the expression is the statement consisting variable, numbers, and arithmetical operation.
Given that, Karissa begins to solve the equation,
1/2(x-14)+11 = 1/2x-(x-14)
1/2x-1/2(14)+11 = -1/2x-x+4
1/2x-7+11 = -1/2x+4
1/2x+4 = -1/2x+4
1/2x+1/2x = 4-4
x = 0
Hence, When she subtracts 4 from both sides, then x = 0
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I Agree With The Other Person
URGENT
pls answer soon
Answers
The measures of the angles are m ∠ 1 = 68°, m ∠ 2 = 126° and m ∠ 3 = 54°
What are parallel lines?Parallel lines are those straight lines that are always the same distance apart from each other. Parallel lines never meet, no matter how much they are extended.
Given is a figure, in which, lines d, e and lines f, g are parallel and h is a transversal.
In figure, (refer to figure attached)
ABC is a triangle,
Therefore, according to angle sum property of a triangle,
m ∠ 1 + 58° + 54° = 180°
m ∠ 1 = 180° - 112°
m ∠ 1 = 68°
Since, f║g
m ∠ 2 + 54° = 180° (consecutive angles between parallel line are supplementary)
m ∠ 2 = 126°
Similarly, d║e
m ∠ 2 + m ∠ 3 = 180°
m ∠ 3 = 180° - 126°
m ∠ 3 = 54°
Hence, The measures of the angles are m ∠ 1 = 68°, m ∠ 2 = 126° and m ∠ 3 = 54°
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In triangle xyz, m∠y = 38.25° and m∠z = 74.3°. determine the measure of the exterior angle to ∠x. 152.05° 112.55° 98.60° 62.05°
Answers
Applying the exterior angle theorem, the measure of the exterior angle to angle X is: B 112.55°.
How to Apply the Exterior Angle Theorem?In other to find the measure of the exterior angle to angle X, we have to recall the theorem known as the exterior angle theorem, which states that the measure of an exterior angle is equal to the two interior remote angles that are opposite to it.
In triangle XYZ, angle Y and Z are the remote interior angles. We are given the following:
Measure of angle Y = 38.25°
Measure of angle Z = 74.3°
Therefore:
The measure of the exterior angle to angle X = measure of angle Y + measure of angle Z
Substitute
The measure of the exterior angle to angle X = 38.25° + 74.3°
The measure of the exterior angle to angle X = 112.55°
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Which method could you use to eliminate one
of the variables from the following system of
equations?
4x - 6y = 18
3x + 4y = 5
A. Multiply the first equation by 2 and the second
equation by 3. Then add the equations.
B. Multiply the first equation by 3 and the second
equation by 4. Then add the equations.
C. Multiply the first equation by 4 and the second
equation by -6. Then add the equations.
D. Multiply the first equation by 5 and the second
equation by 18. Then add the equations.
Answers
Answer:
B
Step-by-step explanation:
To eliminate one of the variables from a system of equations, we can multiply one or both equations by constants and then add the equations together. In this case, the correct method to use is to multiply the first equation by 3 and the second equation by 4, and then add the equations together. This will eliminate the y-variable from the system of equations. Thus, the correct answer is option B: multiply the first equation by 3 and the second equation by 4, and then add the equations together.
The correct is option B (i.e.Multiply the first equation by 3 and the second
the equation by 4. Then add the equations.)
multiplying the first equation by 3 and the second equation by 4:
12x - 18y = 54
12x + 16y = 20
subtracting the first equation from the second equation:
( 12x - 18y = 54) - (12x + 16y = 20)
-2y = -34
y = 17
substituting y = 17 in the first equation:
4x - 6(17) = 18
4x = 106
x = 26.5
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The answers are
A. Statement: FDC≈FAB Reason: SAS
B. Statement FDC~FBA Reason: AA
C. Statement FDC≈FBA Reason: SAS
D. Statement FDC~FAB Reason: AA
Can I get an answer as well as how it makes sense?
Answers
Answer:
Step-by-step explanatihelpson:
is c hope it
If anyone can help me on the #14 please
4(4÷2+4)
Answers
Answer:24
Step-by-step explanation: 4(4÷2 + 4) = 24/1 = 24
Spelled result in words is twenty-four.
Divide: 4 / 2 = 2
Add: the result of step No. 1 + 4 = 2 + 4 = 6
Multiple: 4 * the result of step No. 2 = 4 * 6 = 24
This calculator adds two fractions. When fractions have the same denominators calculator simply adds the numerators and place the result over the common denominator. Then simplify the result to the lowest terms or a mixed number.
Answer:
24
Step-by-step explanation:
We have to solve this according to BODMAS Theorem.
That is,
B ⇒ Brackets
O ⇒ Of
D ⇒ Division
M ⇒ Multiplication
A ⇒ Addition
S ⇒ Subtraction
Let us solve it now.
4 ( 4 ÷ 2 + 4 )
4 ( 2 + 4 )
4 × 6
24
Is this statement true or false?
Answers
TRUE: The given condition is correct that m ≤ 10 and m > 4.
Explain the term inequality of the numbers?An inequality in mathematics depicts the relationship between these two values in an unbalanced algebraic expression. A sign of inequality can be used to show that one of the two variables is larger than, greater than or comparable to, less than, or equal to some other value.Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two parameters are not equal. But several inequalities are utilized to compare the numbers, either it is less than or higher than.For the given statement;
m ≤ 10 and m > 4, the number for the value of m be;
m = 5, 6, 7, 8, 9, 10.
Thus, the given condition is correct that m ≤ 10 and m > 4.
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if anyone can help me solve this i will give you 20 points!!
Answers
Answer:137
Step-by-step explanation:
watch your cholesterol: the mean serum cholesterol level for u.s. adults was 196 , with a standard deviation of 36 (the units are milligrams per deciliter). a simple random sample of 104 adults is chosen. use the ti-84 calculator. round the answers to four decimal places. what is the probability that the sample mean cholesterol level is greater than 205 ? the probability that the sample mean cholesterol level is greater than 205 is
Answers
The probability that the sample mean cholesterol level is greater than 205 is 0.62%.
To find the probability that the sample mean cholesterol level is greater than 205, we need to use the standard normal distribution and the formula for a normal distribution.
The sample mean cholesterol level, μ, is the population mean cholesterol level, 196, and the standard deviation of the sample mean, σ, is the standard deviation of the population divided by the square root of the sample size:
μ = 196
σ = 36 / √104 = 3.17
We want to find the probability that the sample mean cholesterol level is greater than 205, so we need to find the area under the curve of the standard normal distribution to the right of z = (205 - 196) / 3.17 = 2.5.
We can use the TI-84 calculator to find this probability by using the normal cdf function. In the function, we enter 2.5 as the lower bound and infinity as the upper bound to find the area under the curve to the right of z = 2.5.
The probability that the sample mean cholesterol level is greater than 205 is about 0.0062, or 0.62%.
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What is the percent of change of 3.25 centimeters to 2.95 centimeters
Answers
The percentage of change is 10.17%.
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
Given are the two measures 3.25 centimetres and 2.95 centimetres
The percentage change, of a quantity, is the ratio of the difference in the quantity to its initial value multiplied by 100.
Therefore, The percentage of change = [(3.25-2.95)/3.25]x100
= 0.3/3.25x100
= 10.17%
Hence, the percentage change = 10.17%
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at 2 p.m., two cars leave eagle river, wi, one headed east and one headed west. if the car traveling east averages 55 mph and the car traveling west averages 40 mph, when will the cars be 237.5 miles apart?
Answers
After 2.5 hours cars be 237.5 miles apart.
What is distance?
The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common usage can refer to a physical length or an estimation based on other factors.
First to write equation for each car
[tex]d_1=r_1t_1 (east bound)\\d_2 = r_2t_2 (west bound)[/tex]
They both start at the same time, and I will stop them both when they are 165 mi apart.
So, [tex]t_1=t_2[/tex] call just t.
⇒
[tex]d_1 = r_1t\\d_2=r_2t[/tex]
[tex]t = \frac{d_1}{r_1} \\t= \frac{d_2}{r_2}[/tex]
⇒
[tex]\frac{d_1}{r_1} = \frac{d_2}{r_2} \\d_1r_2 = d_2r_1[/tex] ..(1)
We also know that
[tex]d_1 + d_2 = 237.5[/tex]
[tex]d_2 = 237.5 - d_1[/tex]
[tex]r_1 = 55, r_2 = 40[/tex]
So, equation (1) becomes,
[tex]40d_1 = 55d_2[/tex]
Plug the value of [tex]d_2[/tex].
[tex]40d_1 = 55(237.5 - d_1)\\40d_1 = 13,062.5 - 55d_1\\40d_1 + 55d_1 = 13062.5\\95d_1 = 13062.5\\d_1 = 137.5[/tex]
[tex]d_1 = 137.5 mi[/tex]
Now,
[tex]t = \frac{d_1}{r_1} = \frac{137.5}{55} = 2.5[/tex]
Hence, after 2.5 hours cars be 237.5 miles apart.
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The radius of a circle is 5 feet. What is the length of an arc that subtends an angle of
radians?
3л/2
5 ft
Give the exact answer in simplest form.
feet
Answers
The radius of a circle is 5 feet, 23.55 feet is the length of an arc.
What is arc length?The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc.
The arc length formula may be used to get a circle's arc length from its radius and central angle.
The distance between two places in a curve's section is known as the arc length of a circle. Any portion of a circle's circumference is an arc. An arc's angle at any given location is the angle created by the two line segments connecting that point to the arc's endpoints.
Given that,
radius (r) = 5 feet
angle (θ) = 3π/2
Now as we know,
Arc length = radius x subtended angle in radians
or, Arc length = 5 feet x (3π/2 radians)
or, Arc length = 15π/2
or, Arc length = 23.55 feet
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A window company makes two square windowpanes. Windowpane A
has an area of 176 square inches. Windowpane B has an area of 275
square inches. How much longer is a side of Windowpane B than a
side of Windowpane A? Study the pictures.
Answers
Answer: 99.
If you take 275 and subtract it by 176, it should be 99, if I’m correct.
PLEASE HELLPPPP
The White Chuck Glacier is in the Cascade Range of western North America. In 1958 it covered 3.1 km?.
By 2002 it had lost about 70% of its area. What was the area of the glacier in 2002? Show your thinking.
Answers
Answer:
0.93 km
Step-by-step explanation:
The White Chuck Glacier lost 70% of its area between 1958 and 2002, which means that its area was reduced by 70/100 = <<70/100=0.7>>0.7.
Since the glacier-covered 3.1 km. in 1958, its area was reduced by 0.7 * 3.1 km? = <<0.7*3.1=2.17>>2.17 km.
Therefore, the area of the White Chuck Glacier in 2002 was 3.1 km. - 2.17 km? = <<3.1-2.17=0.93>>0.93 km.
the correlation between cost and distance is 0.791. describe the relationship between cost of damage and distance from the nearest fire station.
Answers
According to the question,
Given data,
The correlation between cost and distance is 0.791.
The farther the house is from a first station, the higher cost of damage tends to be.
the correlation between cost and distance
The largest single cost of liver transplantation is the cost of organ acquisition, with the variable portion of that amount being associated travel costs. We assessed the proportion of donors using ground, air, and jet transport and compared the transport costs of these three types of transport and their impact on organ procurement costs for transplant centers.
How is correlation measured?
The sample correlation coefficient r quantifies the strength of the relationship. Correlations are also tested for statistical significance.
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Please help me with my geometry work
Answers
In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. ,m∠2 = 40°.
What is a straight line?An unending, one-dimensional figure with no breadth is a straight line. It consists of an infinite number of points connected on either side of a point. A straight line has a 180° measurement.
Definition of angle bisector.In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. Alternatively said, it divides two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.
The graphic XYQ is the straight line, m∠3 = 40°, and m∠4 = 25°. YZ is the angle bisector of ∠s.
m∠2 = 40° the reason is YZ is the angle bisector of ∠s
∠s = m∠2 + m∠3
m∠2 = m∠3
therefore m∠2 = 40°
m∠1 + m∠2 + m∠3 + m∠4 = 180° the reason is XYQ is the straight line.
substitution of all values
m∠1 + 40° + 25° + 40° = 180°
m∠1 + 105° = 180°
m∠1 = 75° (straight line, substitution of all values )
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Ben has a barrel in his garden to collect rainwater. The barrel can hold less than 42 gallons of water. Which inequality represents this situation? Ow> 42 Ow< 42 w² 42 Ow≤ 42
Answers
Answer: The barrel can only hold less than 42 gallons of water, which means w<42.
pls help
write the equation that gives the proportional relationship of the graph
a. y=7x
b.y=35x
c.y=5x
d.y=1/7x
Answers
Answer:
y=7x
Step-by-step explanation:
10.
Manny took AABC and translated it according to (x,y)→(x+2,y-3).
What are the points of AA'B'C'?
Answers
the points of AA'B'C' is A'(4,0) B'(5,-1) C'(7,-2)
What are the points of AA'B'C'?Solution:
x, y = 0
(x + 2, y - 3) = 0
x + 2 = 0
x = -2
y - 3 = 0
y = 3
AABC
A(2,3) B(3,2) C(5,1)
A: (2,3) → (2+2,3-3) = (4,0)
B: (3,2) → (3+2,2-3) = (5,-1)
C: (5,1) → (5+2,1-3) = (7,-2)
AABC and A'B'C are equivalent. A student attempts to identify which of these straightforward transformations converted AABC into AA'B'C'. Points A and Bare are situated on sides CE and ED, respectively, in the CED as shown below. Given that AE = 3.75, AC = 5, EB = 4.5, and BD = 6, line segment AB is drawn. A"B"C" is a triangle congruent to ABC if T is the identity or a translation. A"B"C" is a triangle if T is a rotation by angle x but not a halfturn.To learn more about points refer to:
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can someone solve: Layla wants to build a wooden box with a volume of 454545 cubic centimeters.
She started with a width of 3\text{ cm}3 cm3, start text, space, c, m, end text and a height of 3\text{ cm}3 cm3, start text, space, c, m, end text.
How long should Layla make the box? if someone could kindly do so, please put an answer AND comment by copying and pasting the answer! omg tysm
Answers
Layla can make the box up to 5centimeter long.
How to calculate volume of a box?Rectangles have a volume that is equal to their length, breadth, and height. If your box is a cube or a rectangular prism, all you need to know is its size in terms of length, width, and height. Then, to calculate volume, multiply them all together.V = l x w x h
Measure the box's length. If you look up at your box from the bottom, the top appears to be a flat rectangle with the longest side being the height. This number should be noted as "length." If you measure one side in inches, you must measure them all in inches. Be sure to use the same measurement for each side.Next to the length, gauge the box's breadth. The box's other edge, adjacent to the length, is its breadth. The breadth is the side that forms a "L" with the length when you look at one side of the box. This measurement should be noted as "width." The side that is shorter is always the width.The box's height should be measured. The distance from the top of the box to the ground is the last side you haven't measured. This measurement should be noted as "height." Add the three sides together and multiply. Remember that the formula for volume is V = length x width x height, therefore to calculate volume, simply multiply the three sides by one another. Include the measurement units you used as well, so you don't misinterpret your results.Units should be added to your volume. Volume is a measurement, but if you don't know the system used to measure it, your result won't signify anything. Your form of measurement cubed is the proper way to write out volume.Here it is given that,
volume= 45cm³
width= 3cm
height=3cm
volume = width × height × length
45cm³=3cm×3cm×length
45cm³=9cm²×length
length=45cm³÷9cm²
=5cm.
Hence, Layla can make the box up to 5centimeter long.
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To find the mass in grams, ______ the number of kilograms by the unit rate, _____ grams per kilogram.
PLEASE HELP
Answers
Answer:
To find the mass in grams, multiply the number of kilograms by the unit rate, 1000 grams per kilogram.
Explanation:
For every kilogram, there are 1000 grams. So, if you have 12 kilograms, you have 12,000 grams.
This graph shows all the key characteristics of a particular polynomial function. Drag tiles to complete the function rule that could be represented by the graph
Answers
The function that can be represented by this graph is defined as follows:
f(x) = 2x³ + x - 3.
How to define the function?
The function is defined looking at the features of the graph.
The first feature which we look at is the y-intercept, as the graph of the function crosses the y-axis at y = -3, hence the function can be defined as follows:
f(x) = ax^n + x - 3.
The function has an inflection point, as it has a change in it's concavity, thus the function has a second derivative of the first degree, meaning that the function is of the third degree, that is:
n = 3.
The x-intercept is when the function crosses the x-axis, meaning that when x = 1, y = 0, then the leading coefficient a is obtained as follows:
0 = a + 1 - 3
a = 2.
Which means that the function rule can be given by:
f(x) = 2x³ + x - 3.
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What is the area of a rectangle with a height of t ^ 2 + 7t + 6 and a width of 2t + 1
Answers
The area of a rectangle with given length and width is 2t³+15t²+19t+6 square units.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Given that, length of a rectangle =t²+7t+6 and width of rectangle =2t+1.
Here, area of a rectangle = (t²+7t+6)×(2t+1)
= t²(2t+1)+7t(2t+1)+6(2t+1)
= 2t³+t²+14t²+7t+12t+6
= 2t³+15t²+19t+6 square units
Therefore, area of a rectangle is 2t³+15t²+19t+6 square units.
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a friend of yours who works in the it department of a bank tells you that tellers are allowed to log in to their terminals only from 9 a.m. to 5 p.m., monday through saturday. what is this restriction an example of?
Answers
Given restriction is an example of Time-of-day restrictions
The correct answer is an option (C)
In this question we have been given a friend tells you that tellers
are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday through Saturday.
We need to identify the type of restriction in this example.
We know that time-of-day restrictions are the restrictions that often used to limit the hours during which a user is allowed to log into or access a system.
This type of restrictions helps prevent unauthorized access outside that user's normal working hours .
Therefore, given restriction present in this example: Time-of-day restrictions
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The complete question is:
A friend of yours who works in the IT department of a bank tells you that tellers are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday
through Saturday. What is this restriction an example of?
A. User auditing
B. Least privilege
C. Time-of-day restrictions
D. Account verification
find the slope of the line thst passes through (10,2) and (1,3)
Answers
Answer: -7/1
Step-by-step explanation: When graphing both points and drawing a line through it, count how many times it goes up or down and then count how many times it goes left or right.
answer for ten points!
Answers
Answer:
try 1239128981441231241
Step-by-step explanation:
myra
Good luck and have a good day
Jacob is practicing the 100 meter dash. the data shows his time in seconds. 14, 13, 13.5, 16, 14 15.5, 14.5 Which box plot shows the data?
Answers
The box plot for given minimum, maximum, median, Q1 and Q3 is plotted below.
What is a box and whisker plot?A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.
The given data set is 14, 13, 13.5, 16, 14, 15.5, 14.5.
Order of data is 13, 13.5, 14, 14, 14.5, 15.5, 16.
Here, minimum is 13
Maximum is 16
Median is 14
Lower quartile range(Q1) is 13.5
Upper quartile range(Q3) is 15.5
Therefore, the box plot for given minimum, maximum, median, Q1 and Q3 is plotted below.
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how many 10-digit integers are there which are palindromes? be sure to describe the process you are using.
Answers
There are 90000 palindromes 10-digit numbers.
In this question we need to find the number of 10-digit integers are there which are palindromes.
We know that a palindrome is a number that reads the same forward and backward.
The numbers that remain same even if they are reversed.
For exa., 131, 5225
We can observe that for even digit palindromes first half should be equal second half in reversed order.
we can generalize it as variables:
abcdeedcba, for a not equal to 0
So if we know how many 5-digit numbers are there, all we have to do is reverse it and we will have our 10-digit palindrome number.
There are 10 digits in total (0 - 9)
Since the first digit cannot be zero we excluded it from our choice hence we have 1–9 i.e 9 choices for first place(hundred's place)
The second, third, fourth and fifth digit has all 10 choices.
So, in total there are 9 x 10 x 10 x 10 x 10= 90000 five digit numbers.
Therefore, the total 10-digit numbers which are palindromes = 90000
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