The final answer is the combination of both solutions x = 3,− 3.
What are quadratic in math?
A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Latin word meaning square, is where the word "quadratic" originates.Use the quadratic formula to find the solutions
x = - b + √b² - 4ac / 2a
Substitute the values
a = 1, b = 0, and c = − 9 into the quadratic formula and solve for x.
x = 0 + √ 0² - 4 . ( 1 . 9 ) / 2. 1
Simplify
The final answer is the combination of both solutions.
x = 3,− 3
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State whether the sentence is true or false. If false, replace the underlined term to make a true sentence.
Geometric probability involves a geometric measure such as length or area.
True, Geometric probability involves a geometric measure such as length or area.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.True, Geometric probability involves a geometric measure such as length or area.
Also, genuineness of the second statement does not give any information whether the first statement is true or not.
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The speed of an average garden snail is estimated to be 8.056 x 10 miles per second. Write the speed in standard fo miles per second
The speed written in standard form is 0.000008056 miles per second.
How to write the speed in standard miles per second?
Here we know that the average speed of a garden snail is:
8.056 x 10⁻⁶ miles per second.
Notice that it is written in scientific notation and we want to write this in standard form, so we just need to expand the product.
Notice that the exponent is -6, this means that we need to "move" the decimal point 6 times to the left, so we will get:
S = 8.056 x 10⁻⁶ miles per second.
S = 0.000008056 miles per second.
That is the speed written in standard form.
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70 POINTS! 1st photo. What is the equation of the line of symmetry (or the point of symmetry if there is one) for the image?
2nd photo. List the equation(s) of the line of symmetry or the point(s) of symmetry for the image. Be sure to include all equations and/or points of symmetry.
3rd photo. Classify this graph by the following functions as even, odd or neither. Be sure to include your work to justify your classification. SHOW YOUR WORK.
1) The line of symmetry is; Vertical Line x = 0
2) The line of symmetry is; Vertical line x = 4 and horizontal line y = -4
3) The line of symmetry is; Vertical Line x = 3
What is the Line of Symmetry?
1) A line of symmetry is a line that divides a figure into two parts such that each part is the mirror image of the other.
From the given image, we can see that the line of symmetry here is a vertical line at x = 0. This is because that is the half way point of the object such that when mirrored, it produces the exact same image.
2) The line of symmetry here for the given object is;
x = 4 and y = -4
3) The line of symmetry here for the given parabola curve is;
x = 3
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6 millimeters into miles
The globe has a diameter of 22 inches. What is the volume of the globe?
A. 1520.5 in³
B. 1741.4 in³
C. 5575.3 in³
D. 6014.8 in³
The volume of the globe is (c) 5575.3 cubic inches.
It is given in the question that the diameter of the globe is 22 inches.
We have to find the volume of the globe.
We know that a globe is spherical in shape and the volume of a sphere is given by:-
[tex]\frac{4}{3} \pi r^3[/tex]
Where, r is the radius of the sphere
We know that,
Diameter/2 = Radius
Hence, we can write
22/2 = radius
Radius of the globe = 11 inches
Hence, volume of the globe is given by :-
(4/3) * (22/7) *11*11*11 = (88/21) *1331 = 5575.3 cubic inches.
The answer is (c)
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can someone help me solve this pls "write an equation of the line passing through the points (4,12) and (-1,-13)"
Use the given rule to write the 4th, 5th, 6th, and 7th terms of each sequence. an = n+1/ n+2
The fourth, fifth, sixth, and seventh term of the sequence an = n+1/ n+2 are 5/6, 6/7, 7/8, and 8/9.
According to the given question.
We have a rule for finding the terms of a sequence i.e.
an = n+1/ n+2.
Therefore,
The fourth term of the sequence is given by
[tex]a_{4}[/tex] = 4 + 1/ 4 + 2 = 5/6
The fifth term of the sequence is given by
[tex]a_{5}[/tex] = 5 + 1/5 + 2 = 6/7
The sixth term of the sequence is given by
[tex]a_{6}[/tex] = 6 + 1/(6 + 2) = 7/8
And, the seventh term of the sequence is given by
[tex]x_{7}[/tex] = 7 + 1/( 7 + 2) = 8/9
Hence, the fourth, fifth, sixth, and seventh term of the sequence an = n+1/ n+2 are 5/6, 6/7, 7/8, and 8/9.
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Rachel lives in state without income tax. Each month, she pays $307 in federal income tax
and $206 in other taxes. Her pay after taxes is $2,040. What are Rachel's monthly earnings?
Step-by-step explanation:
u simply add 307 and 206 to 2,040 giving u 2553
E W
4. What is the slope of the line
that contains
the points (13, -2) and (3, -2)?
Answer:
Step-by-step explanation:
Point slope form y-y₁ = m(x-x₁)
-2 - (-2) = m(3 - 13)
0 = m(-10)
m/slope = 0
-5q - 7/4 + 8q < 5/8; q = 5/6 what's the answer?(And step-by-step please)
Can someone help?!! This is Due TOMORROW!!!!!!
According to the question, the given simplification based inequality equation can be solved by substituting the values to the standard equation.
Given expression = [tex]-5q-\frac{7}{4} +8q < \frac{5}{8}[/tex]
Substituting the value of the variable 'q' as (5/6) and solving the left hand side expression:
Therefore, the expression can be re-written as:
Required expression = [tex]-5(\frac{5}{6} )-\frac{7}{4} +8(\frac{5}{6} )=\frac{15}{6}-\frac{7}{4} =\frac{3}{4}[/tex]
The calculated left hand side value is (3/4) which is greater than the right hand side value as (5/8).
[tex]\frac{3}{4} > \neq \frac{5}{8}[/tex]
Hence, the given inequality fraction expression is greater than the given value.
What is an inequality equation?
Inequality equation are those expression which some variables which are least in nature. They can be solved with the help of algebraic expressions using addition, subtraction, multiplication and division.
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(-5,-1)(-4,-2)(-2,-2)(-10,-1) Translate the trapezoid 3 units down. Then reflect on the x-axis.
Answer:
(-5, 4)
(-4, 5)
(-2, 5)
(-10, 4)
Step-by-step explanation:
Given points:
(-5, -1)(-4, -2)(-2, -2)(-10, -1)To translate a point 3 units down, subtract 3 from its y-coordinate.
To reflect a point across the x-axis, the y-coordinate becomes its additive inverse.
Therefore, the mapping rule is:
[tex](x,y) \rightarrow (x, -(y-3))[/tex]
Translated points:
(-5, -1) → (-5, -(-1-3)) = (-5, 4)(-4, -2) → (-4, -(-2-3)) = (-4, 5)(-2, -2) → (-2, -(-2-3)) = (-2, 5)(-10, -1) → (-10, -(-1-3)) = (-10, 4)Learn more about translations here:
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Show your work given the rule of (x,y)—->(x-7.5,y+6.8)
Original coordinate (5,3)
Show your work given the rule of (x, y)—->(x-7.5,y+6.8)
Original coordinate (5,3)
The output coordinate is if the input coordinate is (5,3) is (-2.5,9.8).
Given that,
(x, y)—->(x-7.5,y+6.8)
Given original coordinate are (5,3).
We substitute the original coordinate in the given point (x, y).
A location on a grid, also known as a coordinate plane, is identified by coordinates, a pair of numbers (also known as Cartesian coordinates), or sometimes a letter and a number. The two axes that make up a coordinate plane are the horizontal x axis and the vertical y axis (vertical).
Put x=5 and y=3 in (x, y)
We get
[tex]=(5-7.5, 3+6.8)\\=(-2.5, 9.8)\\[/tex]
Therefore, The output coordinate is if the input coordinate (5,3) is (-2.5,9.8).
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The sum of a and 10 is twice as large as b, where both a and b are integers. If the sum of a and b is divisible by 4, which of the following CANNOT be the value of b?
A) 6
B) 8
C) 10
D) 14
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
Determine whether the following statement is sometimes, always, or never true. Explain.
The orthocenter of a right triangle is located at the vertex of the right angle.
The statement that the orthocenter of a right triangle is located at the vertex of the right angle is always true.
The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.
You can see in the image, there is a right-angled triangle ABC right angled at B. When we draw perpendiculars from each of vertices of the triangle, they intersect at the vertex of the right angle. Hence, we can say that the orthocenter of a triangle is always located at the vertex of the right angle.
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What is the solution of 4(x-5)+x=8 x-10-x ?
The value of x using the given equation is -5.
Define the solution of an equation.
A solution of an equation is defined as the set of all possible values of unknown variables that will make the equality hold.
Solving for the value of x
Given the equation, 4(x - 5) + x = 8x - 10 - x
4x - 20 + x = 8x - 10 - x
5x - 20 = 7x - 10
Rearranging the equation, we get,
7x - 10 - 5x + 20 = 0
2x + 10 = 0
x = -10 / 2
x = -5
Hence, the value of x on solving given equation is -5.
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What’s the inverse??
Answer: The inverse is b.
Step-by-step explanation:
Solve-2x - 7> 5x+14.
Ο A. * < -3
OB. x>-5
O C. x < -5
OD. x>-3
Answer:
D.
[tex]x > - 3[/tex]
Step-by-step explanation:
[tex] - 2x - 7 > 5x + 14 \\ - 2x - 5x < 14 + 7 \\ - 7x < 21 \\ x < \frac{21}{ - 7} \\ x > - 3[/tex]
A quadratic function is shown on the graph.
a downward opening parabola beginning with open circle at negative 3 comma negative 7 increasing to a vertex at 0 comma 2 and then decreasing to a closed circle at 2 comma negative 2
What is the range of the function?
{y | −7 < y ≤ 2}
{y | −7 ≤ y ≤ 2}
{x | −3 ≤ x ≤ 2}
{x | −3 < x ≤ 2}
The range of the quadratic function represented with the given parameters is {y | −7 < y ≤ 2}
What is the range of a function?The range of a function is the set of output values of the graph. This in other words mean the range of a function is the set of y values of the graph.
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the range of the function?From the question, we have the following parameters:
The parabola opens downwardVertex = (0, 2)Open circle points = (-3, -7) and (2, -2)Write out the vertex
So, we have
Vertex = (0, 2)
Remove the x value
y = 2
From the question, we have
The parabola opens downward
This means that the vertex is a maximum
So, the range is
y ≤ 2
Rewrite properly as
{y | −7 < y ≤ 2}
Hence, the range of the quadratic function is {y | −7 < y ≤ 2}
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Answer:
Answer is A :)
Step-by-step explanation:
Find the product of (1 3/4-2.4).[0.5.(2/5 plus 2.6)
The product of (1 3/4-2.4).[0.5.(2/5 plus 2.6) is 2.75.
How to calculate the product?It should be noted that we are to find the product of (1 3/4-2.4).[0.5.(2/5 plus 2.6).
This will be:
= (1 3/4-2.4).[0.5.(2/5 plus 2.6)
= (1.75 - 0.5) × [0.5(0.4 + 2.6)]
= 1.25 × 0.5(3)
= 1.25 + 1.5
= 2.75
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A high school has 40 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players
weighing less than or equal to 246 pounds?
There are 91% of players weighing less than or equal to 246 pounds that the players' weights are given in the box plot.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that the box plot
Here, the total number of players = 40
And the minimum weight of players = 152 pounds
Third quartile (Q₃) = 246
In the box plot, approximately 10 of the 11 coverage intervals occur between 152 and 254.
So the approximate percentage of students that weigh 246 kg or less would be
⇒ (10 / 11)×100
⇒ 90.90
Therefore, there are 91% of players weigh less than or equal to 246 pounds.
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Find the perimeter and area of rectangle ABCD if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, if
necessary.
area
cm
perimeter
cm
A(-2,7)
DI-4,3)
C(2,0)
B(4,4)
According to the question, ABCD is a rectangle with different coordinate values and they are as follows: A(-2,7); B(4,4); C(2,0); D(-4,3), The perimeter will be 14cm.
Using the standard definition of the perimeter that is perimeter is the sum of all the sides.
Therefore,
Perimeter = Sum of all the sides
Perimeter = -2+7+4+4+2+0-4+3 = 14 cm
And using the standard formula of the area that is the multiplication of length and width.
Now,
Area = (4)(4) = 16 cm
Hence, the calculated area = 16 cm^2 and calculated perimeter = 14 cm.
What is the area and perimeter of a rectangle?
The perimeter of a rectangle can be calculated by adding all the four lengths from all the sides. Similarly, to know the area of the rectangle by multiplying length and width.
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Circle J has a radius of 10 units, ®K has a radius of 8 units, and BC = 5.4 units. Find the measure.
AB
Circle J has a radius of 10 units and BC = 5.4 units then the measure of AB is 14.6 units.
What is meant by the radius of a circle?A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length. The name is derived from the Latin radius, which means both rays and spoke of a chariot wheel.
The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.
Since AC is the diameter of circle J and the radius is 10, AC = 2(10) or 20 units.
AB + BC = AC
Where the value of BC = 5.4, we get
substitute the value of BC in the above equation, then we get
AB + 5.4 = 20
subtract 5.4 from both sides
AB + 5.4 - 5.4 = 20 - 5.4
simplifying the above equation,
AB = 14.6
Therefore, the measure of AB is 14.6 units.
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Austin makes $10 an hour working as a cashier at a bookstore. His employer requires him to work at least 10 hours per week and his current school schedule limits him to a maximum of 25 hours per week.
1. Write an equation that represents Austin's gross pay where x represents the number of hours he works per week and f(x) (as in functions) represents his gross pay.
2. What is the domain and range in this situation?
The linear function is:
f(x) = $10*x
Where the domain is: [10, 25]
And the range is: [$100, $250]
How to write the equation that models Austin's gross pay?Here we know that x represents the number of hours that he works per week, and we also know that he wins $10 per hour, then if he works x hours, the amount that he wins is x times $10, so the equation is just:
f(x) = $10*x
Now we also want to get the domain and range for this function. We know that he needs to work at least 10 hours and at maximum of 25 hours, so we have the restrictions:
10 ≤ x ≤25
So the domain is D: [10, 25]
To find the range we evaluate in the values of the domain, the minimum of the range is f(10) = $10*10 = $100
The maximum of the range is f(25) = $10*25 = $250
Then the range is R: [$100, $250]
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the constant of proportionality between the number of fiction book (f) and the number of nonfiction books (n) in library 15/22. There are 3498 nonfiction books in library. How many fiction books are in the library?
The total number of fiction books are 2385.
What is constant of proportionality?
The constant of proportionality is the ratio of two proportional values at a constant value is known as the constant of proportionality. When either their ratio or product results in a constant, two variables' values are said to be proportionally related. The ratio between the two stated quantities determines the value of the proportionality constant.
Given that,
Let the total number of fiction books be f and nonfiction books be n.
The constant of proportionality between the number of fiction book(f) and the number of non-fiction books(n) in a library is 15/22 .
f/n= 15/22
Also, the total number of nonfiction books is 3498.
Therefore,
f/3498 = 15/22,
f= 15/22 x 3498,
f= 15 x 159,
f= 2385.
Hence, the total number of fiction books in the library are 2385.
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A box of packaged snacks contains 6 individual bags and costs $5.40. Each individual bag contains 18 crackers. What is the cost per cracker?
Answer:
$0.05
Step-by-step explanation:
First, find the total amount of crackers and the total cost.
Crackers: 6*18=108 crackers
$5.40/108=0.05
$0.05
Perform the indicated operation.
2 3/8 x 5 3/4
Answer:
1st convert mixed numbers
19/18 x 23/4
2nd multiply fractions
437/32
Answer: 437/32
Jacob rides his bike up a large hill. If he is moving at 15 mph at the bottom and slows to 3 mph 2.75 minutes later when he gets to the top, what is the acceleration?
Please show work! Also please answer quick, I have other work to do. Thank you!
The acceleration when he gets to the top is -0.0325 m/s²
Calculating accelerationFrom the question, we are to determine the acceleration when Jacob gets to the top
Using one of the equations of motion, we have that
v = u + at
Where v is the final velocity
u is the initial velocity
a is the acceleration
and t is the time
From the given information,
u = 15 mph = 6.7 m/s
v = 3 mph = 1.34 m/s
t = 2.75 minutes = 165 seconds
Then,
1.34 = 6.7 + a×165
1.34 - 6.7 = 165a
-5.36 = 165a
a = -5.36/165
a = -0.0325 m/s²
NOTE: Negative sign indicates deceleration
Hence, the acceleration when he gets to the top is -0.0325 m/s².
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Compare the following numbers using division. Which of the statements below
expresses the relationship between the numbers?
100 and 25
100 ÷ 25 = 4
25 is four times as large as 100.
100 is four times as large as 25.
100 is one-quarter as large as 25.
O100 is four more than 25.
Answer: 100 is four times as large as 25.
Step-by-step explanation:
[tex]100 \div25=4[/tex]
Hence, 100 is four times as large as 25.
Answer:
The answer is 100 is four times as large as 25
Step-by-step explanation:
Division compares numbers by telling you how many times larger the first number is then the second number. In this problem, 100/25=4.
Put another way, 25 x 4 = 100. Therefore,100 is four times as large as 25
Use the spinner to find the probability. If the spinner lands on a line it is spun again.
P (pointer not landing on green)
Probability of spinner pointer not landing on green is equal to 2/3 if the spinner lands on a line it is spun again.
As given in the question,
Total colors in the spinner is equal to 6
Each color is 2 times
Total number of colored region =6
Number of green region = 2
Probability of pointer landing on green color P(G)= 2 /6
Probability of pointer not landing on green P(G') = 1- P(G)
= 1- (2/6)
= 2/3
Therefore, probability of spinner pointer not landing on green is equal to 2/3, if the spinner lands on a line it is spun again.
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Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V = ²h
Write the formula to calculate the height, h.
(0) 101
√O
h =
Vo 4
+
X
11
v
V
IV
TL
α β εθ
λμ ρ
8
sin cos tan sin costan.
csc sec cot log log In
||
0
I
to m
N2
The formula for calculating the Hight of the cone as follows h = 3(V/(πr²))
Is a cone's volume one-third that of a cylinder?Thus, the volume of a cone is one-third that of a cylinder with the same base radius and height.
Is a cone three times the size of a cylinder?Cone and cylinder volumes are related in exactly the same manner as pyramid and prism volumes are related. If the heights of a cone and then a cylinder are the same, the volume of the cylinder equals three times that of the cone.
According to the given data:The volume, V, formula of a cone with radius, r, and height, h.
The volume of the cone using the formula:
V = 1/2πr²h
h = 3(V/(πr²))
The formula for calculating the Hight of the cone as follows h = 3(V/(πr²)).
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