Answers
The equation of the quadratic function g whose graph is shown above is g(x) = -(x + 4)² - 4
How to determine the factored form of a quadratic equation?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the vertex and other points, we can determine the value of a as follows:
g(x) = a(x - h)² + k
-13 = a(-7 + 4)² - 4
-13 = a(-3)² - 4
-13 + 4 = 9a
-9 = 9a
a = -1.
Therefore, the required quadratic function is given by:
g(x) = a(x - h)² + k
g(x) = y = -(x + 4)² - 4
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Related Questions
Help pleaseeeee I would appreciate it
Answers
The answers of the matrix of A after adding -5 times row 1 to row 3 of matrix is
1 -1 5 | -1
1 -1 -4 | 5
0 9 -25 | 4
What is a matrix in mathematics ?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
Matrices are useful for describing systems of linear or differential equations, as well as representing a linear application.
We perform the row operation and have:
1 -1 5 | -1
1 -1 -4 | 5
0 9 -25 | 4
The result after adding -5 times row 1 to row 3 of matrix is shown below:
1 -1 5 | -1
1 -1 -4 | 5
0 9 -25 | 4
In conclusion, in a matrix function, the input and the output values are matrices.
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Of the 22 students in a classroom, 10 are transfer students, 7 are nursing students, 4 are AAS students and 1 student is undecided. If 5 students are chosen randomly, with replacement, find the probability that at least one student is a transfer student.
Answers
The probability that a randomly chosen student is not a transfer student is 12/22, since there are 12 students who are not transfer students out of a total of 22 students. Therefore, the probability that none of the 5 students chosen are transfer students is:
(12/22)^5 = 0.068
To find the probability that at least one student is a transfer student, we can subtract this from 1:
1 - 0.068 = 0.932
Therefore, the probability that at least one student is a transfer student is 0.932.
Types of discontinuities
Identify and Classify the discontinuities in the function, please
Answers
The discontinuity at x = -2 is a removable discontinuity or a hole in the graph of the function.
To identify the discontinuities in the function f(x), we first need to find the values of x that make the denominator zero, since division by zero is undefined.
The denominator of f(x) is x² + x - 2, which can be factored as (x - 1)(x + 2). Therefore, the function f(x) is undefined at x = 1 and x = -2, since they would make the denominator zero.
Now we need to determine the type of discontinuity at these points.
At x = 1, the function f(x) approaches infinity as x approaches 1 from both sides of the graph.
At x = -2, the function f(x) has a hole in the graph.
This means that the function is undefined at x = -2, but if we "plug in" x = -2, we can factor the numerator and cancel out the common factor with the denominator, resulting in a new function that is continuous at x = -2. The new function is:
f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)
= [(x² - 1)(x² - 4)] / [(x - 1)(x + 2)]
= (x - 1)(x + 1)(x - 2), for x ≠ -2
Therefore, the discontinuity at x = -2 is a removable discontinuity or a hole in the graph.
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Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?
Answers
Carson can line up his textbooks on his bookshelf in 24 different ways
What is Permutation?
Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.
What is Combination?
The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.
According to the given information:
Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:
n! / (n - r)!
where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).
On substituting the values in the formula,
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.
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Jim bought a pair of shoes for $50 and laces for $1. If the sales tax is 7%, how much tax must he pay?
(a) $3.57
(c) $0.36
(b) $350
(d) $35.70
Answers
Jim must pay tax $3.57.
The correct answer is (a) $3.57.
To calculate the sales tax that Jim must pay, we need to find 7% of the total cost of the shoes and laces.
The total cost of the shoes and laces is $50 (shoes) + $1 (laces) = $51.
To calculate the sales tax, we multiply the total cost by the tax rate:
Sales tax = 7% of $51
[tex]= 0.07 \times $51[/tex]
= $3.57.
Therefore, Jim must pay $3.57 in sales tax.
The correct answer is (a) $3.57.
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divide to 7 digits after the decimal point. Do not round your answer 3.1 divided by 6
Answers
The value of 3.1 divided by 6 leaving 7 digits after the decimal point without rounding is 0.5166666
Evaluating the quotient expressionFrom the question, we have the following parameters that can be used in our computation:
3.1 divided by 6
When represented as an expression, we have
3.1 divided by 6 = 3.1/6
The above expression can be calculated using a calculator
Using a calculator, we have
3.1/6 = 0.51666666666
This means that
3.1 divided by 6 = 0.51666666666
Leaving 7 digits after the decimal point without rounding, we have
3.1 divided by 6 = 0.5166666
Hence, the value of 3.1 divided by 6 is 0.5166666
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La escuela de Hannah organizó una
donación de libros. Hay 150 estudiantes
en su escuela, que donaron b libros en
total. Hanna donó 3 veces el promedio
de libros que donó cada estudiante
Answers
According to the information, Hannah donated b/50 books in total.
How to calculate how many books did Hannah donate?First, we need to find the average number of books donated by each student. We can do this by dividing the total number of books donated by the number of students:
average number of books per student = b / 150Hannah donated 3 times this amount, so we can multiply the average by 3 to find how many books she donated:
Hannah's donation = 3 * (b / 150)Simplifying this expression, we get:
Hannah's donation = b / 50Therefore, Hannah donated b/50 books in total.
Note: This question is in Spanish. Here is the question in English:
Hannah's school organized a book donation. There are 150 students in her school who donated a total of b books. Hannah donated 3 times the average number of books donated by each student. How many books did Hannah donate?
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3+3=???
A: 3113
B: 33
C. 6 ( I did the math and never got this answer)
D. 9
please help !!!!!
Answers
Answer:
D
Step-by-step explanation:
gimme the points
cuz
scientific
Please help me I really don’t get this. ILL GOVE BRAINLIEST TO ANYONE PLEASD I GIVE 18 points
Answers
Answer: C, yes
Step-by-step explanation:
Again you have do the same thing to both sides
They added 1 to both sides
Answer is C , yes they are same
A rectangular classroom is 10m long and 4.6m wide. Make a scale drawing of the classroom using the following scales.
Answers
The scale drawing of the classroom have the dimensions of 10 centimeters by 4.6 centimeters
Making a scale drawing of the classroom using the scalesFrom the question, we have the following parameters that can be used in our computation:
Dimension of classroom = 10 meters by 4.6 meters
The scale of the drawing is given as
1 cm : 1 m
Using the above as a guide, we have the following:
Scale factor = 1 cm/1 m
So, we have
Scale factor = 1 cm per m
So, we have
Scale dimension of classroom = (10 meters by 4.6 meters) * 1 cm per m
Evaluate
Scale dimension of classroom = 10 centimeters by 4.6 centimeters
Hence, the scale drawing of the classroom have the dimensions of 10 centimeters by 4.6 centimeters
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Complete question
A rectangular classroom is 10 m long and 4.6 m wide. Make a scale drawing of the classroom using the following scales. 1 cm : 1 m
12 A quality control inspector at a plant has found the probability of randomly selecting a defective
battery from a batch of batteries being produced is 0.02. The probability of rain that day has been
projected to be 0.75. If these two events are independent, what is the probability that on that particular
day, it rains, and the inspector chooses a defective battery from the batch being produced?
(1) 0.77
(3) 0.015
(2) 0.5
(4) 0.95
Answers
Answer:
The answer is (3) 0.015.
Step-by-step explanation:
This is because to find the probability of finding both independent events happening at the same time, we must multiply them.
The independent events are:
- Randomly selecting a defective battery: 0.02
- Raining tomorrow: 0.75
0.02 x 0.75 = 0.015
Therefore, the answer is (3) 0.015.
Enter your answer in the box.
Answers
Answer:
- 63
Step-by-step explanation:
When x = 0, x - 1 = -1
f(x - 1) = f(-1) = 21 from the table
-3f(x-1) = -3 (21)
= -63
In how many distinct ways can the digits in the number 2,563,183,083 be arranged?
(If there are any zero digits then assume they can be placed in any position)
Answers
However, we need to account for the fact that three of the digits are 3s and two of the digits are 8s. To do this, we need to divide out the number of arrangements of those duplicates.
There are 3! = 6 ways to arrange the three 3s among themselves, and 2! = 2 ways to arrange the two 8s among themselves. So, we divide the total number of arrangements by these permutations of the duplicates:
10! / (3! * 2!) = 10 x 9 x 8 x 7 x 6 x 5 x 4 = 604,800
Therefore, there are 604,800 distinct ways to arrange the digits in the number 2,563,183,083, assuming that any zero digits can be placed in any position.
Jennifer deposits money into a bank account. The amount of money in her account is measured in dollars, and can be modelled by the function A(m)= 1750(1.025)^m, where m is the number of months since the initial deposit.
What is the percent change in Jennifer's account balance each month? Is it increasing or decreasing? Justify answer.
Answers
a) The percent change in Jennifer's account balance each month is 2.5%.
b) Based on the future value function, A(m)= 1750(1.025)^m, the account balance is increasing because the growth factor is 1.025 and not less than 1.
What is a growth function?A growth function is a mathematical equation that shows a constant rate in increase or growth in value of the dependent variable.
A growth function is modeled by a growth factor greater than 1 while a decay function shows a decay.
Percentage change = 2.5% (1.025 - 1)
2.5% = 2.5 ÷ 100 = 0.025
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If the ratio of a circle's circumference to the circle's area is 2/9, then find the circles area.
Answers
The area of the circle is 81π. Option A.
What is area of a circle?The area of a given circle is the amount of space that the circle will cover when considered in a 2 dimensional plane. It can be determined by;
area of a circle = πr^2
where r is the radius.
The circumference of a circle is the curved boundary of a circle. It can be determined by;
circumference of a circle = 2πr
where r is its radius.
From the given information in the question, we have a circle's circumference to the circle's area;
circumference/ area = 2/ 9
But,
circumference/ area = 2πr/ πr^2
= 2/ r
Then;
2/ r = 2/ 9
2r = 2*9
= 19
r = 18/ 2
r = 9
Thus,
area of the circle = πr^2
= π(9)^2
= 81π
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more aleks parallel and perpendicular lines
Answers
a. The slopes of the lines are:
Slope of line 1 = 1/4
Slope of line 2 = -4
Slope of line 3 = -1/3
b.
Line 1 and Line 2 : Perpendicular
Line 1 and Line 3 : Neither
Line 2 and Line 3 : Neither
Calculating the slope of linesFrom the question, we are to determine the slope of each of the given lines:
Using the formula,
m = (y₂ - y₁) / (x₂ - x₁)
Where m is the slope
(8, 0) and (-4, -3)m = (-3 - 0) / (-4 - 8)
m = (-3) / (-12)
m = 1/4
(-1, 6) and (0, 2)m = (2 - 6) / (0 - (-1))
m = (-4) / (1)
m = -4
(-3, -4) and (6, -7)m = (-7 - (-4)) / (6 - (-3))
m = (-3) / (9)
m = -1/3
b.
NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.
Thus,
Line 1 and Line 2 : Perpendicular
Line 1 and Line 3 : Neither
Line 2 and Line 3 : Neither
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Geometry
All I need is the letter that is correct. Don’t mind the ones I already circled
Answers
The translation of ABC by (Rx + Ry) is UVW and the rigid composition of XYZ to X'Y'Z' cannot be determined
Translation image of the triangleThe rule (Rx + Ry) represents a translation image of a shape, where R is a vector representing the direction and distance of the translation, and (x, y) are the coordinates of the original shape.
To apply this rule to a shape, we simply add the vector R to each point of the shape, which moves the shape in the direction and distance specified by R.
Using the above as a guide, we have the following the translation of ABC by (Rx + Ry) to be UVW
The rigid composition of XYZ to X'Y'Z'The triangle X'Y'Z' is not given in the figure
So, the rigid composition of XYZ to X'Y'Z' cannot be determined
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If Kayla has a 73% in her history class and she took a test 20% of her grade and got a 60 on it. What would her grade be?
Answers
Answer:
70.4%
Step-by-step explanation:
Assuming the test is the only graded assignment, and the remaining 80% of her grade is still at 73%, we can calculate Kayla's new overall grade as follows:
New overall grade = (0.80 x 73) + (0.20 x 60)
New overall grade = 58.4 + 12
New overall grade = 70.4
Therefore, Kayla's new overall grade is 70.4%
Answer:
70.4% or a C-.
Step-by-step explanation:
To calculate Kayla's new grade after taking the test, you need to first find out what percentage of her overall grade the test is worth. If the test is worth 20% of her grade, then the remaining 80% of her grade is based on other factors, such as homework, quizzes, and other tests.
To calculate Kayla's new grade, you can use the following formula:
New grade = (Current grade x Weight of current assignments) + (Grade on test x Weight of test)
Plugging in the numbers given in the problem, we get:
New grade = (0.73 x 0.80) + (0.60 x 0.20)
New grade = 0.584 + 0.12
New grade = 0.704
Therefore, Kayla's new grade after taking the test would be approximately 70.4%, or a C-.
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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What is the length of the side labeled x cm?
10.8
13.7
9.9
20.8
Answers
Answer:
B
Step-by-step explanation:
the answer is B because I know it
3. A room is 17 feet by 16 feet. Carpet for the room costs
$101 per square yard.
How much will it cost to carpet the room?
Question 1
Answers
Answer: First, let's convert the room's dimensions from feet to yards, since the carpet cost is given per square yard:
17 feet = 5.67 yards (rounded to two decimal places)
16 feet = 5.33 yards (rounded to two decimal places)
Next, we can calculate the area of the room in square yards by multiplying these values:
Area = 5.67 yards × 5.33 yards = 30.23 square yards (rounded to two decimal places)
Finally, we can multiply the area by the cost per square yard to get the total cost:
Total cost = 30.23 square yards × $101/square yard = $3,056.23 (rounded to two decimal places)
Therefore, it will cost $3,056.23 to carpet the room.
what is the expanded notation of -6⁷
Answers
Answer:
The expanded notation of -6⁷ means writing the number -6⁷ as a sum of its place values.
-6⁷ can be written as:
-6 × 6 × 6 × 6 × 6 × 6 × 6
or
-6 × (6 × 6 × 6 × 6 × 6 × 6)
or
-6 × 6⁶
In expanded notation form, it can be written as:
-6 × (6 × 6 × 6 × 6 × 6 × 6)
= -6 × (46656)
= -279936
Therefore, the expanded notation of -6⁷ is -279936.
Step-by-step explanation:
Starting from rest, an object travels at a constant speed of 150 cm/s (centimeters per second) along a straight line. If d is the total distance in cm that the object has traveled at time t seconds, then which of the following gives the equation expressing d as a function of t, and the total distance d in meters that the object has traveled at time t = 2 seconds?
Answers
The equation expressing d as a function of t can be found by using the formula for distance traveled with constant speed:
d = vt
where d is the distance, v is the constant speed, and t is the time elapsed.
In this case, the speed is 150 cm/s, so the equation is:
d = 150t
To find the total distance traveled in meters at t = 2 seconds, we need to first find the total distance traveled in centimeters at t = 2 seconds:
d = 150t
d = 150(2)
d = 300 cm
To convert to meters, we divide by 100:
d = 300/100
d = 3 meters
Therefore, at t = 2 seconds, the object has traveled a total distance of 3 meters.
Someone help i really need help with this
Answers
Step-by-step explanation:
we just need to find out how many percentage of the daily goal each day, so let's assume that $50 is 100% of the daily goal.
Need help! I HAVE 30 MIN! will pay for all work shown (ZELLE ONLY) Do all 3 please!
Answers
Answer: i gotchu
Step-by-step explanation:
1) Since the base of this function is greater than 1, this means its increasing exponentially (increases from left to right). So as x approaches positive infinity, y approaches positive infinity as well.
Domain (-∞,∞) Range (0,∞)
2) If the base changes to 1/9 the function would decrease. So as x approaches positive infinity, y approaches 0 (Check attached screenshot)
3) The "+5" raises the horizontal asymptote up 5 units. So the new equation for the horizontal asymptote is y=5.
The "x-2" shifts the x values to the right by 2 units.
u dont have to pay me, i literally just learned this like a month ago :)
HELP ME PLEASE!!!!!
Answers
Answer:
1. True
2.True
3.True
4.False
5.False
6.True
7.True
8.True
Step-by-step explanation:
1. The area of a rectangle is found by the formula A=bh.
2. There are 4 rectangles making up the lateral area of the prism. 2+3=5. 5*6=30, and multiply by 2 since there are two of the 2x6 and two of the 3x6 rectangles to get 60. The bases of the prism have an area of 6 square inches each.
60+12+12=84
3. 3*5=15
4. The base is not a square, so you cannot multiply by 4 to get the area of all the triangles. You can multiply by two, and also multiply 1/2(3)(4) by 2 to get the area of the other two triangles.
5. The base is a triangle. 1/2(3)(4)=6.
6. 2[1/2(3)(4)]=12. 2(8*5)=80. 3*8=24. 80+24+12=116
7. A cube has 6 identical sides, so you can find the area of one side and multiply by 6 to get the surface area of the cube.
8. 9^2=81. 81*6=486.
use compass and ruler to contruct bisector of the angle
Answers
Bisector of the angle is the line that divides the angle into two angles with the same measure. In the image attached, the bisector of the angle is represented by the green line.
Here, we have,
The next steps show you how to construct the bisector of the angle from a ruler and a compass.
Draw an arc using the vertex of the angle (O) as the center;
Mark the points A and B;
Draw an arc using the point (A) as the center;
Draw an arc, with the same radius, using the point (B) as the center. This arc should intersect the arc that you draw in the previous step.
Draw a line connecting the point C to the vertex O.
Finally, you have the bisector of the angle that is represented by the green line.
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For the following exercises, convert the angle measures to radians.
-236° (the exact answer) b) 601° (round to two decimal places)
Answers
The calculated values of the angle measures when converted to radians are 1.31π rad and 3.34π rad
Converting the angle measures to radians.To convert angles from degrees to radians, we multiply the number of degrees by π/180.
This means that
Angle = Degree measure * π/180
Using the above as a guide, we have the following:
Angle 236 = 236 * π/180
Evaluate the products
Angle 236 = 1.31π rad
Next, we repeat the same process for the second angle 601 degrees
Angle 601 = 601 * π/180
Evaluate the products
Angle 601 = 3.34π rad
Hence, the angles are 1.31π rad and 3.34π rad
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$5850 is invested at 6.5% compounded continuously. How long will it take for the balance to reach $11700? Round your answer to two decimal places.
Answers
Answer:10.66 years. Punch again to double check
Step-by-step explanation:
A=Pe^(rt)
11700=5850e^(.065t)
isolate the variable expression
2=e^(.065t) divide by 5850
ln2=lne^(.065t) take the natural log of both sides
ln2=.065t. Bring down the power, lne equals
t is about 10.66 years. Divide ln2 by .065
Evaluate log_10^3.
a) 100
b) 1, 000
c) 9
d) 3
Answers
log_b(x) = y if and only if b^y = x
In this case, we have log_10^3, which means that 10 is the base and 3 is the argument. We want to find the exponent y such that 10^y = 3.
However, there is no integer exponent that satisfies this equation, since 10^1 = 10 and 10^2 = 100 are both greater than 3, while 10^0 = 1 is less than 3.
Therefore, the value of log_10^3 is not an integer and cannot be expressed in the form of one of the answer choices. We can, however, approximate the value of log_10^3 as approximately 0.477, using a calculator or logarithm table.
