Step-by-step explanation:
x^4-9x^2-8x^2+72
x^2(x^2-9)-8(x^2-9)
(x^2-8)(x^2-9)
(x^2-8)(x+3)(x-3)
How many solutions does 5x 2 7x 4 0 have?
The given equation gives two solution. We can find solution by using quadratic formula or discriminant.
How do you find the number of solutions?A linear equation in two variables is an equation of the form ax + by + c = 0 where a, b, c ∈ R. So a and b ≠ 0. When we consider a system of linear equations we can find the number of solutions by comparing the coefficients of the variables of the equations.
How do you find how many solutions are in a quadratic equation?
if the discriminant is positive. Then the quadratic equation has two solutions.
if the discriminant is equal. Then the quadratic equation has one solution.
if the discriminant is negative. Then the quadratic equation has no solution.
Here we have
a=5 b=-7 c=4
Disc= [tex]b^2[/tex]-4ac
Disc= [tex](-7)^2[/tex]-4(5)(4)
Disc= 49+80
=129
Disc >0 it has two solutions.
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Complete question is: How many solutions are there for 5x^2+7x-4=0?
a) 0
b) 1
c) 2
d) 3
PLEASE HELP!!! WILL AWARD BRAINLIEST!!!
Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions.
Top data set labeled males, minimum at 1, Q1 at 3, median at 11, Q3 at 14, maximum at 21, and an outlier at 30.
Bottom data set labeled females, minimum at 0, Q1 at 15, Median at 18, Q3 at 21.
Part A: Estimate the IQR for the males' data. (2 points)
Part B: Estimate the difference between the median values of each data set. (2 points)
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)
Part D: Provide a possible reason for the outlier in the data set. (2 points)
Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions
The estimated IQR for the males dataset is 24 , the estimated difference between median value of each dataset is 14.
What is median ?
The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution in statistics and probability theory. It can be regarded as "the middle" value for a set of data.
When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.
In a collection of numbers, the median is the value in the middle. A series of numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest in order to find the median value.
A. IQR for male dataset
The IQR is calculated as follows:
IQR = Q3 - Q1
=
For the male's data:
IQR = Q3 - Q1
= 25 - 1
= 24
Hence, the IQR of the male dataset is 24.
B. Difference in median values
We have:
median = 20 ----- Male dataset
median = 6 ----- Female dataset
So, the difference (d) is:
d = 20 - 6
= 14
Hence, the difference in median of both dataset is 14.
C. Best measure of center
The female box plot has an outlier. This means that the measure of center to use for the female dataset is the median.
The male box plot has no outlier; this means that the mean can be used as a measure of center for the male box plot
D. Reason for outlier
There are several reasons that could cause an outlier in a dataset. One of the reasons is human error during data entry.
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How many 1/3 ounce cups can be taken from a 30 ounce box of cereal?
Answer:
90 cups
Step-by-step explanation:
Number of cups needed = 30 / (1/3) cups
= 90 cups
Thought process:
1 cup -> 1/3 ounce
3 cups -> 1 ounce
? cups -> 30 ounce
Hence, ? = 30 x 3
= 90
How to read linear equations?
To read a linear equation, first, identify the constants and the variable, then determine the coefficient of the variable.
A linear equation is an equation that contains two variables and can be written in the form of ax + b = 0, where 'a' and 'b' are constants and 'x' is the variable. This coefficient will indicate how the variable is related to the constants. Then, solve the equation by isolating the variable to determine its value.
To read a linear equation, start by identifying the constants and the variable. The constant is the numerical value that is not connected to the variable. For example, in the equation "2x + 4 = 0", the constants are '2' and '4'. The variable is the letter that represents the values that can change. In this equation, the variable is 'x'.
Next, determine the coefficient of the variable. The coefficient is the numerical value in front of the variable. It represents how the variable is related to the constants. In this example, the coefficient of 'x' is '2'. This means that the value of 'x' will be twice as much as the constants.
Once the constants, variables, and coefficients have been identified, the equation can be solved.
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Alex has five cups of strawberries. He wants to use 1 3/4 cups of strawberries for a fruit salad and 3 1/2 cups for jam. Does Alex have enough strawberries to make both recipes? Solve this problem any way you choose. Grade 5
Alex has five cups of strawberries and wants to use 1 3/4 cups of strawberries for a fruit salad and 3 1/2 cups for jam. Alex has enough strawberries to make both recipes.
To check if Alex has enough strawberries, we add the amount of strawberries needed for the fruit salad (1 3/4 cups) and the amount needed for the jam (3 1/2 cups)
1 3/4 cups + 3 1/5 cups
= 1 + 3/4 + 3 + 1/5
Multiplying 3/4 with 5/5 and 1/5 with 4/4 to make denominator equal
= 1 + 15/20 + 3 + 4/20
= 4 + 19/20
= 4 19/20 cups
4 19/20 is less than 5 cups. So Alex has enough strawberries for both recipes.
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How do you find the legs of a 45 45 90 triangle given the hypotenuse?
The value of the legs of the triangle would be hypotenuse/√2.
You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).
That is perpendicular=hypotenuse/√2
Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)
That is base=hypotenuse/√2
Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.
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Please help me with these two questions
The expression for area of the rectangles are obtained as x² + 10x + 21 and x² - 9x + 8 respectively. The correct options for both parts are (C) and (B) respectively.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The dimension of both the rectangles are given as,
First rectangle : (x + 3) and (x + 7)
Second rectangle : (x - 1) and (x - 8)
Since, the area of a rectangle is product of its dimensions.
It can be obtained as,
Area of first rectangle is given as,
⇒ (x + 3) × (x + 7)
⇒ x² + 10x + 21
Area of second rectangle is given as,
⇒ (x - 1) × (x - 8)
⇒ x² - 9x + 8
Hence, the area of both the rectangles are obtained as x² + 10x + 21 and x² - 9x + 8 respectively.
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Why are 3 4 5 and 5 12 13 Pythagorean triples?
A Pythagorean triple is a set of three positive integers a, b, and c that satisfies the equation a2 + b2 = c2.
In this case, the triple is (3, 4, 5) and (5, 12, 13).
The equation for the first triple is 32 + 42 = 52.
3² = 9
4² = 16
9 + 16 = 25
25 = 25
The equation for the second triple is 52 + 122 = 132.
5² = 25
12² = 144
25 + 144 = 169
169 = 169
Therefore, both sets of numbers are Pythagorean triples because they both satisfy the equation a2 + b2 = c2.
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Distribute and then combine the like terms to simplify each expression.
8f - 6 (-5 - 7f)
please help
Answer: We start by distributing the -6 to the terms inside the parentheses:
8f - 6(-5) - 6(7f)
Then we simplify each term inside the parentheses:
8f + 30 + 42f
Now we combine like terms:
8f + 30 + 42f = 50f + 30
So the simplified expression is 50f + 30
Step-by-step explanation:
P=-3w+9 solve for w
Pls help
Isolating for a variable: rearranging an equation so that a variable is on its own. This is done by performing inverse operations until a variable is isolated.
[tex]P-9=-3w+9-9[/tex]
[tex]p-9=-3w[/tex]
[tex]\frac{p-9}{-3}=\frac{-3w}{-3}[/tex]
[tex]-\frac{P-9}{3} =w[/tex]
PLS HELP WILL MARK BRAINEST
Answer:
Step-by-step explanation:
Answer is choice A
Both functions are decreasing at a rate of -2. You can find this by finding the slope.
When two lines intersect the vertically opposite angles so formed are Class 7?
When two lines intersect the vertically opposite angles so formed are equal in measure.
When two lines intersect each other, then the opposite angles, created due to the intersection are called vertical angles or vertically opposite angles.
We can see in the figure two lines intersect each other at a point. Therefore the two pairs of vertically opposite angles are ∠1 and ∠3, ∠2 and ∠4.
From the figure, ∠1 + ∠2 = 180° [Linear pair] eqn(1)
∠2 + ∠3 = 180° [Linear pair] eqn(2)
From eqn(1) and eqn(2), we get
∠1 + ∠2 = ∠2 + ∠3
∴ ∠1 = ∠3
Similarly, we can prove ∠2 = ∠4 also.
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HELP PLEASE!!!!!!!!!!!!!!!
Answer:
Its the second image
Step-by-step explanation:
what are the coordinates of the center of the center and the length of the radius of the circle whose equation is x^2 y^2
The coordinates of the center of the circle and the radius length of the specified circle are (-3,2) and 6 units, respectively.
What is circle?A circle is a shape formed by all points in a plane that are at a particular distance from the center. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant. A circle is a closed two-dimensional object in which the set of all the points in the plane is equidistant from a particular point called "centre". The line of reflection symmetry is formed by every line that travels through the circle. It also features rotational symmetry around the center for all angles.
Here,
x²+6x+9-9+y²-4y+4-4=23
(x+3)²-9+(y-2)²-4=23
(x+3)²+(y-2)²=36
(x+3)²+(y-2)²=6²
center=(-3,2)
radius=6
The coordinates of the center of the center and the length of the radius of the given circle is (-3,2) and 6 units.
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His coordinate grid shows where Alberto's school is located. Each unit represents one block. Alberto's house is at (3, 4). The library is located at the reflection of (3, 4) across the y-axis. Use absolute value to find the distances from Alberto's house to the school and from Alberto's house to the library
The distance from Alberto's house to the school is 4 units and from Alberto's house to the library is 6 units
Consider the following diagram.
From given coordinate grid we can observe that Alberto's school is located at point (-1, 4)
Alberto's house is at (3, 4).
And the library is located at the reflection of (3, 4) across the y-axis.
This means, the libarary is located at point (-3, 4)
We know that the absolute value is nothing but the distance between a number and zero on a number line.
The distance from Alberto's house to the school would be,
= distance between points (3, 4) and (-1, 4)
= |3 - (-1)|
= |3 + 1|
= |4|
= 4 units
And the distance between Alberto's house to the library would be,
= distance between points (3, 4) and (-3, 4)
= |3 - (-3)|
= |3 + 3|
= |6|
= 6 units
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The complete question is:
This coordinate grid shows where Alberto’s school is located. Each unit represents one block. Alberto's house is at (3, 4). The library is located at the reflection of (3, 4) across the y-axis. What are the coordinates of the library?
How do you find the shorter leg of a 30 60 90 triangle?
The short leg of a 30-60-90 triangle is 1/2 the length of the hypotenuse. 30-60-90 triangle is the half of an equilateral triangle.
Right triangles with 30-60-90 interior angles are called special right triangles.
A 30-60-90-degree triangle is a special right triangle and its side lengths are always consistent with each other. The ratio of the sides follows the 30-60-90 triangle ratio: 1: 2: [tex]\sqrt{3}[/tex] .
Short side (opposite the 30° angle) = x
Hypotenuse (opposite the 90° angle) = 2x
Long side (opposite the 60° angle) = x√3
30-60-90 Triangle Theorem:
These three properties can be examined by the 30-60-90 triangle theorem and are unique to these special right triangles:
The hypotenuse (the triangle's longest side) is twice the length of the short leg.The length of the longer leg is the√3 times of the shorter leg.If we know the length of any one side of a 30-60-90 triangle, we can find the missing side lengths.Read more about the right triangle :
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Working as a team, 8 mathletes solve 20 problems in 10 minutes. At this rate, how many mathletes solve 30 problems in 5 minutes
Step-by-step explanation:
the given ratio is
8 / 20/10 = 8 / 2 = 4
for x mathletes we need to keep the same ratio :
x / 30/5 = 4
x / 6 = 4
x = 4×6 = 24
24 mathletes.
The scattered plot below shows the relationship between the total calories a meal has and the number of calories from fat.
If a meal has 300 calories from fat, how many total calories would you expect it to have?
Total 400 calories is expected to have a meal has 300 calories from fat the relationship between the total calories a meal has and the number of calories from fat .
what is scatterplot ?A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they can display the degree of connection, if any, between values of observable quantities or events (called variables). There are points on a scatter (XY) plot that depict the connection between two sets of data. The sample illustrates the weight and height of one person for each dot. Data points are plotted on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another. The values of the columns selected on the X and Y axes determine where each row in the data table is represented by a marker, whose position.
given
300 calories from fat
total = 100 + 100 + 200
= 400 calories
Total 400 calories is expected to have a meal has 300 calories from fat the relationship between the total calories a meal has and the number of calories from fat .
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just need help with #7. A cube has an edge length given by the variable “s” as shown. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s^2 volume= s^3 Find the ratio of the surface area to the volume in simplest terms of “s”.
Surface Area : Volume = 6 : s
What is cube ?A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
Surface Area of a Cube = 6a² in a square units
Volume of cube = a³ cubic units
where a is the side length of the cube.
Given length of the cube = s
Surface Area of cube A = 6s²
Volume of cube V = s³
Ratio between Surface Area and volume:
Surface Area / Volume = 6s² / s³
Surface Area / Volume = 6 / s
Surface Area : Volume = 6 : s
Hence the ratio between Surface area and volume of cube is 6 : s.
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In our class there are 40 boys. 22 students are girls write a ratio comparing girls to boys
Answer:
Its 22:40
Step-by-step explanation:
Answer: 22:40
Pretty simple
Step-by-step explanation:
The rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRYYYYYYYYYYY
The area of the floor in the scale drawing is 60 inches²
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Actual rectangular floor.
Length = 24 feet
Width = 40 feet
Scale rectangular floor.
Length = 6 inches
Width = 40/4 = 10 inches
The area of the scale rectangular floor.
= Length x Width
= 6 x 10
= 60 icnhes²
Thus.,
The area of the floor is 60 inches².
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Find three consecutive numbers such that the sum of twice the first, three times the second and four times the third togetherbmakes 191.
Answer:
find 3 consecutive numbers such that twice the first , 3 times the second and 4 times the third together make 191 ?
Let n-1,n and n+1 be three consecutive numbers.
Given
2(n-1)+3n+4(n+1)=191
2n-2+3n+4n+4=191
9n+2=191
9n = 189
n = 21
So, n-1=20 and n+1=22
So the answer is 20,21,22
[tex] \huge \bold{\color{red}{ANSWER}}[/tex]
[tex]\pmb { \orange{Given }:} \sf{ Three \: Consecutive \: numbers}[/tex]
[tex]\pmb{\orange{To find}: } \sf{Least \: of \: the \: numbers}[/tex]
[tex]\pmb{\orange{Solution}: }[/tex]
[tex]\sf{Let \: the \: three \: consecutive \: numbers \: be }[/tex]
[tex] \sf\red x, \red {x+1}, \red{x+2}[/tex]
[tex]\sf{Twice \: the \: number = 2\red x}[/tex]
[tex]\sf{3 \: times \: the \: Second \: number = 3(\red{ x+1})}[/tex]
[tex]\sf{4 \: times \: the \: third \: number= 4(\red {x+2})}[/tex]
☆ according to question
[tex] \pmb{2\red x + 3(\red{x+1})+4(\red{x+2})= 191}[/tex]
[tex] \pmb{2\red{x} + 3\red{x}+3+4\red{x}+8= 191}[/tex]
[tex] \pmb{9\red{x}=191-11 = 180}[/tex]
[tex] \pmb{\red{x}=20}[/tex]
[tex] \sf{∴the \: three \: Consecutive \: numbers \: are} [/tex]
[tex] \pmb{\pink{20}, \pink{21}, \pink{22}}[/tex]
_________________......
[tex] \purple{ \pmb{LearningLifeII}}[/tex]
a smallercircle passes through the center of, and is tanget to a larger cirlc the area of the smaller circle is 9 square units. What is teh area of the larger circle in square units
36 square units make up the larger circle's surface area.
We can use the fact that the smaller circle is tangent to the larger circle and passes through its center to find the area of the larger circle. Since the radius of the smaller circle is tangent to the larger circle, the radius of the larger circle is double the radius of the smaller circle.
Let's call the radius of the smaller circle "r" and the radius of the larger circle "R". We know that R = 2r.
We know that the area of a circle is given by the formula A = πr^2.
We know that the area of the smaller circle is 9 square units, we can use this formula to find the radius:
A = πr^2 => r^2 = 9/π => r = sqrt(9/π)
Now we can use the formula of the area of a circle with R-value to get the area of the larger circle:
A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36
So the area of the larger circle is 36 square units
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10. Find the degree of the monomial. 7m^6n^5
11
6
7
5
Answer:
(a) 11
Step-by-step explanation:
You want the degree of the monomial 7m^6n^5.
DegreeThe degree of a monomial is the sum of the exponents of its variables.
m has an exponent of 6
n has an exponent of 5
The degree is 6+5 = 11.
please help: find m∠BCF
Step-by-step explanation:
so, clearly, the triangles BCF and DCF are congruent.
that makes the line CF a bisector of the kite figure.
and so, both angles are identical halves of the total angle at C.
therefore,
3x + 13 = 13x - 7
13 = 10x - 7
20 = 10x
x = 20/10 = 2
Solve the system of equations using subtraction.
2x-6y = -2 - 2y
-6x - 4y = -38 -2x
Answer:
y=7/2 and x=6
Step-by-step explanation:
2x−6y=−2y−2 can be turned into x=2y−1.
Now you can substitute the equations.
−6x−4y=−2x−38
−6(2y−1)−4y=−2(2y−1)−38
Then you can simplify.
−12y+6=−36
−12y=−42
y=7/2
Then you can substitute y to find x.
x=2y−1
x=2(7/2)-1
x=6
And then our answers are y=7/2 and x=6.
Hope this helped! :)
Law of sines: Which measures are accurate regarding triangle JKL? Check all that apply. M∠K = 84° m∠K = 94° k ≈ 3. 7 units k ≈ 4. 6 units KL ≈ 2. 5 units KL ≈ 3. 2 units
The median's class interval is 20 hours and 30 minutes. And the average number of hours is thought to be 26.17.
Who defines median?The median is the exact middle value of a dataset after it has been sorted. A measure of central tendency is the distance between the bottom 50% of data and the top 50% of values. The methods for determining the median will vary depending on whether you have an odd or even number of data points.
the class interval that have median.
total is frequency is as -
∑f = 30
median class of corresponds to half of the value
∑th is the value
i.e. 15th value.
least cumulative frequency higher than or equal to 15 is obtained by accumulating frequencies starting at the top.
[tex]2+8+9=19[/tex]
So, corresponds to the class interval = [tex]20 < h\leq 30.[/tex]
Hence, median class is [tex]20 < h\leq 30.[/tex]
Since this is a grouped data we use the midpoint
The median:-
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Suppose y varies directly with x, and y = 6.5 when x = 1.3. What direct variation equation relates x and y ?
Select one:
a.
y = − 5x
b.
y = x / 5
c.
y = 5x
d.
y = 1.5x
Answer:
c
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 6.5 when x = 1.3
6.5 = 1.3k ( divide both sides by 1.3 )
5 = k
y = 5x ← equation of variation
Piper has a coin collection. She keeps 12 of the coins in her box, which is 2% of the collection. How many total coins are in her collection?
The total number of coins Piper has in her collection is 100 coins.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Piper has a coin collection. She keeps 12 of the coins in her box, which is 2% of the collection.
Let, The total number f coins in the box be 'x'.
Therefore, 2% of 'x' is 12 which can be numerically expressed as,
(2/100)×x = 12.
0.02x = 12.
x = 2/0.02.
x = 100.
So, She has 100 coins in her box.
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what is 8 1/4 divided by d=2/11
When 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the statement -
"8[tex]\frac{1}{4}[/tex] divided by 2/11"
We can write it as -
x = {8[tex]\frac{1}{4}[/tex]} ÷ {2/11}
x = 33/4 x 11/2
x = 363/8
x = 45[tex]\frac{3}{8}[/tex]
Therefore, when 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].
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