The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.
what is a quadratic equation?
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.
where a, b, and c are constant terms and x is the unknown variable.
Here I am using the factoring method to solve a quadratic equation.
Given quadratic equation is
[tex]2x^2 - 5x -12 = 0.[/tex]
By comparing the General form of the quadratic equation we will get
a = 2, b = -5 and c = -12.
2x^2 - (8-3)x - 12 = 0.
2x^2 - 8x + 3x -12 = 0.
2x(x-4) + 3(x-4) = 0
(x - 4) (2x + 3) = 0.
x - 4 = 0 or 2x + 3 = 0
x = 4 or x = -3/2
Given Question is incomplete complete question here:
What are the solutions of the quadratic equation 2x^2-5x-12 = 0?
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simplify 2√12+3√48-√75
Answer:
11√12
Step-by-step explanation:
√12 = 2√3
2√12
= 2 * 2√3
= 4√3
√48 = 4√3
3√48
= 3 * 4√12
= 12√12
√75 = 5√3
2√12 + 3√48 - √75
= 4√3 + 12√12 - 5√12
= 16√12 - 5√12
= 11√12
Answer: My answer is 11√3
Step-by-step explanation:
Pull terms out from under the radical, assuming positive real numbers.
Exact Form:
11√3
Decimal Form:
19.05255888…
what is the vertex and solutions for y=x^2+5x-7 and y=-x^2+3x+8
The vertex for the given equation [tex]y=x^2+5x-7 is (-2.5,-4.25)[/tex] and the solution to the equation is x = -5,7/1. Similarly , the vertex for the given equation [tex]y=-x^2+3x+8\ is\ (-3/2,1/4)[/tex] and the solution to the equation is [tex]x = -2,4[/tex].
What is parabola?The graph of a quadratic function is a symmetrical, U-shaped geometric form known as a parabola. It is the collection of all points that are equally spaced apart from a fixed point (referred to as the focus) and a fixed straight line (called the directrix).
What is vertex of a parabola?A parabola's vertex is the location where its symmetry line and parabola intersect.
The vertex of a parabola is the highest or lowest point on the graph of the parabola. In the case of a parabola in the form of [tex]y = ax^2 + bx + c[/tex], the vertex is the point (h, k), where:
[tex]h = -b / 2a\\k = f(h) = a(h^2) + bh + c[/tex]
For the first equation: [tex]y = x^2 + 5x - 7[/tex]
The vertex would be:
[tex]h = -b/2a = -5/2 = -2.5\\k = f(h) = a(h^2) + bh + c = (1)((-2.5)^2) + (5)(-2.5) - 7 = 6.25 - 12.5 - 7 = -4.25[/tex]
So the vertex is [tex](-2.5,-4.25)[/tex]
For the second equation:[tex]y = -x^2 + 3x + 8[/tex]
The vertex would be:
[tex]h = -b/2a = -3/2(1) = -3/2\\k = f(h) = a(h^2) + bh + c = (-1)((-3/2)^2) + (3)(-3/2) + 8 = -9/4 + -9/2 + 8 = 1/4[/tex]
So the vertex is [tex](-3/2,1/4)[/tex]
To find the solutions or roots of the equation, you can set the equation equal to zero and solve for x.
[tex]y = x^2 + 5x - 7 = 0\\x^2 + 5x - 7 = 0\\x^2 + 5x - 7 + 7 = 0 + 7\\x^2 + 5x = 7\\x(x+5) = 7\\x = -5,7/1\\y = -x^2 + 3x + 8 = 0\\x^2 - 3x - 8 = 0\\(x-4)(x+2) = 0\\x = -2,4[/tex]
Solutions for first equation are x = -5 and x = 7/1 and for the second equation are x = -2 and x = 4
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someone helpp me plsss
Answer: 2i+5
Step-by-step explanation: so (-2+14i)-(-7+12i)
Multiply (-1) to 7 and -12
Then: -2+14i+7-12i
Common numbers: (7-2) and 14i-12i
Then you get 2i+5
Reflect shape A in the line y = -x.
Answer:
pentagon
Step-by-step explanation:
pentagon...................................
If the scale of a map is 1:32000 then what will be the actual distance of 20 cm on the map?
Therefore, By using the formula actual distance = (Map distance) x (Scale ratio) the actual distance of 20 cm on the map of 1:32000 is 0.000625 km or 625 meters.
Define Scale ratio.A ratio scale is a numerical scale with a genuine zero and uniform distances between adjacent points. The Kelvin scale is an illustration of a ratio scale. The actual zero point exists on a Kelvin scale.
What are adjacent points?Two locations that are close to one another are said to be adjacent points.
A scale of 1:32000 means that one unit of measurement on the map represents 32000 units of the same measurement in the real world.
To calculate the actual distance of 20 cm on the map,
We know,
Actual distance = (Map distance) x (Scale ratio)
Actual distance = (20 cm) x (1/32000)
Actual distance= 20/32000
Actual distance = 0.000625 km or 625 meters.
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The ratio of the number of model cars that jim owns to the number of model cars Terrence owns is 8:6. Terrence owns 36 model cars
Part A
How many model cars does Jim own?
___
Part B
How will the ratio change if Jim and Terrence each sell ten of their model cars?
O The new ratio would stay the same
O The new ratio would be 4:3
O The new ratio would be 23:29
O The new ratio would be 19:13
When Jim's model car ownership is compared to Terrence's model car ownership, the ratio is 8:6, Jim possesses 48 model vehicles.
what is equation ?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, according to the definition given by the term in its most basic form. When two terms are placed on each side of an equal sign, a simple equation is used to show their relationship. The four mathematical operations of addition, subtraction, multiplication, and division may be used singly or in combination in simple equations.
given
You are aware that Jim and Terrence both own four model automobiles in comparison to three owned by Jim.
Let's assume that Jim owns Jim has the following number of model cars, then you can answer the task as follows:
4/3 = x/36
x = (4* 36)/ 3
x = 48
Therefore, Jims owns 48 model cars.
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Lori's bookcase has 5 mystery novels and 8 romance novels. She randomly picks out 2 mysteries and 3 romances. How many different sets of 5 novels could Lori pick out?
Answer:
I would say 6 sets
Step-by-step explanation:
Mystery = 5 | Romance = 8
0 5
1 4
2 3
3 2
4 1
5 0
each time she picks out 5 novels. There is only 5 mystery novels so you cant go past that
....but that's just me personally
Answer:
Step-by-step explanation:
560
what is h over 7.5 = 3.2
Answer:
h = 24
Step-by-step explanation:
h ÷ 7.5 = 3.2
Multiply both sides by 7.5
h = 3.2 × 7.5
h = 24
Which shows that the set of irrational numbers under addition is not closed?
3+3
π + π
π +3
3π + (−3π)
The option that shows that the set of irrational numbers under addition is not closed is B. π + π.
What is an irrational number?All real numbers that are not rational numbers are referred to as irrational numbers in mathematics. In other words, it is impossible to express an irrational number as the ratio of two integers. The collection of real numbers known as irrational numbers, where p and q are integers, are those that cannot be expressed as fractions, such as p/q.
The example of "π + π" shows that the set of irrational numbers under addition is not closed, because the result of adding two irrational numbers (π + π) is an irrational number (2π) which is not included in the set of irrational numbers.
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Graph the line that passes through the points (9, 4) and (9, 1) and
determine the equation of the line.
Answer:
x = 9
Step-by-step explanation:
The equation is y = mx + b
m = The slope
b = y-intercept
The slope here is undefined, and there is no y-intercept, so the equation is
x = 9
The total number of laps anitia swims, d, is proportional to the total timethat she swims, t, at constant pace, r. Which of the following equations best represents this situation.?
360 multiplied by 420
the answer is 151200
Help me. The question is giving me problems help.
D/3
The real world situation that can be modelled with the given expression can be modelled as shown below.
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 expression as -
D/3
A real world situation that can be modelled with this expression can be written as follows -
Amanda has a total of {D} bananas. She divides the bananas into 3 of her childrens equally. Write an expression that would represent the amount of bananas recieved by each of her child.
Therefore, the real world situation that can be modelled with the given expression can be modelled as shown above.
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please help quickly
If UY=13p-1 and VX=20p-95 than what is UY
Viewing the given triangle, the information given helped to determine side UY to be 90
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
WX and WY, XV and YU
The solution is worked out using sides WX and XV, WY and YU
WX / WY = XV / YU
WX / WY = 1/2 since it is a mid segment
1 / 2 = (20p - 95) / (13p - 1)
13p - 1 = 2 * (20p - 95)
13p - 1 = 40p - 190
190 - 1 = 40p - 13p
189 = 27p
p = 7
solving for UY
= 13p - 1
= 13 * 7 - 1
= 90
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Simplify algebraic expression
Answer:
1
Step-by-step explanation:
To start, we will substitute 8 in for w. So, we get:
[tex]5 - \frac{32}{8}[/tex]
Then, we simplify our fraction, giving us:
5 - 4
Then, 5 - 4 = 1. So our answer is 1.
Hope this helped!
Answer:
5 - (32/w) = 1
Step-by-step explanation:
Given expression,
→ 5 - (32/w)
Now we have to use,
→ w = 8
Let's solve the expression,
→ 5 - (32/w)
→ 5 - (32/8)
→ 5 - (4)
→ 5 - 4
→ 1 => final value
Therefore, the answer is 1.
You are conducting a survey on the number of pets per household in your region. From a sample with n = 40, the mean number of pets per household is 2 pets and the standard deviation is 1 pet. Using chebyshev's theorem, determine at least how many of the households have 0 to 4 pets
At least 30 of the households have 0 to 4 pets.
What is Chebyshev's theorem?
The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied to this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.
Here,
we have a sample size of n = 40.
The mean number of pets per household is 2 and the standard deviation is 1.
We need to determine at least how many of the households have 0 to 4 pets.
By using Chebyshev’s inequality rule with k = 2(that is ) then,
= 100(1- (1/k²))%
= 100 (1- (1/2²))%
= 100 (1- (1/4))%
= 75%
The corresponding number of households is the percentage multiplied by the sample size.
= 75% × 40 = 30
Hence, at least 30 of the households have 0 to 4 pets.
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DIG DEEPER! A cube is removed from a rectangular prism. Find the surface area of the figure after removing the cube.
A rectangular prism with length 9 feet, width 8 feet, and height 5 feet. A cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet.
The surface area is ______ square feet
The surface area of the figure after a cubic hollow runs to the height of the rectangular prism is 364 square feet.
The surface area is 364 square feet.
Find the surface area of the rectangular prism.
To do this, use the formula for the surface area of a rectangular prism:
(2 x length x width) + (2 x width x height) + (2 x length x height)
In this case, the length is 9 feet, the width is 8 feet, and the height is 5 feet. Plugging these values into the formula gives:
= (2 × 9 × 5) + (2 × 8 × 5) + (2 × 9 × 8)
= 314 square feet
When a cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet, 2 cubic faces is removed and 4 cubic faces added to the surface area of the resultant solid. So
surface area = 314 - 2×5² + 4×5²
= 314 + 2×5²
= 314 + 50
= 364 square feet
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What is the relationship between multiplying and factoring?
You multiply numbers or expressions to produce a
[Select]
numbers or [Select]
produce it.
✓. You factor a product into the
✓that were multiplied to
Polynomial factoring is the opposite of polynomial multiplication. A polynomial's leftover will be 0 if it is divided by its factors after factoring.
What do "multiply" and "factor" mean?A multiple is a number that is the result of multiplying the provided number by other numbers, as opposed to a factor, which divides the given number perfectly without leaving a remainder.
What connection exists between the factor theorem and the division of polynomials?When a polynomial f(x) is divided by (x - c), and (x - c) is a factor of the polynomial f(x), the remainder of the division is simply equal to 0. Therefore, if the remainder of a division like the ones mentioned above equals zero.
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2) Julie wants to purchase swim lessons for her son. There are four different stores that offer swim lessons. Based on the lowest cost per minute, which store has the BEST deal ?
Store A: $25 for a 45 minute lesson, Store B: $30 for a 1 hour lesson, Store C: $45 for a 1.5 hour lesson, and Store D: $80 for three 1 hour lessons
Store C offers the best deal
Based on the lowest cost per minute, Store C has the best deal. It charges $45 for a 1.5 hour lesson, which works out to $0.30 per minute. The other stores charge more per minute: Store A charges $0.56 per minute, Store B charges $0.50 per minute, and Store D charges $0.40 per minute for each of the three 1 hour lessons.
Store A has the highest cost that is $0.56 per minute
Next Store B comes in the 2nd place which costs around $0.50 per minute.
After that Store D charges at the rate of $0.40 per minute.
Store C offers the best deal which is $0.30 per minute.
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How do you solve a 2 step equation 7th grade?
The Two steps equation in mathematics can be solved within exactly two steps by performing operation on both sides of the equation .
What is a Two Step Equation ?
The Two Step Equation can be defined as the equations that can be solved exactly within two steps.
When solving the two step equation, we have to perform the operation on both sides of equals to sign.
To solve the equation we need to perform same operation on both sides of equation.
For Example ⇒ Solve [tex]3x+3=12[/tex] ;
Step1 : we Subtract 3 from both sides to isolate the variable x.
⇒ [tex]3x + 3 - 3 = 12 - 3[/tex]
⇒ [tex]3x = 9[/tex]
Step2 : We Divide both the sides of equation by 3 and solve for x.
⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]
⇒ [tex]x = 3[/tex] ;
Therefore , the given equation is solved in two steps .
The given question is incomplete , the complete question is
How do you solve a 2 step equation ?
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A right pyramid has a square base with perimeter 24 inches. Its apex is 9 inches from each of the other vertices. What is the height of the pyramid from its peak to the center of its square base, in inches
If the square base with perimeter 24 inches then the height of the right pyramid be 8.485 - inches.
What is meant by right pyramid?A right pyramid is one whose apex is located exactly above the centroid of the base. As a result, a right pyramid is a special instance of a regular pyramid.
It is referred to as the right pyramid if the pyramid's apex lies immediately above the base's center. If not, the pyramid is known as the oblique pyramid.
A right-triangular pyramid is a three-dimensional object that has a base that is a right-angle triangle and extends up to a single point.
Right pyramids have apex points that are immediately above the centroid of their base. Oblique pyramids are referred to as non right pyramids. An implied right pyramid is a regular pyramid since it has a regular polygon base.
24 / 4 = 6 inches - the edge length of the square base
9² = 3² + Height²
simplifying the above equation, we get
Height² = 9² - 3²
Height² = 72 take the square root of both sides
Height = ~8.485 - inches - the height of the pyramid.
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If the square base with perimeter 24 inches then the height of the right pyramid be 8.485 - inches.
What is meant by right pyramid?The centroid of the base is exactly where the top of a right pyramid sits. Consequently, a right pyramid is a unique example of a standard pyramid.
If the top of the pyramid sits directly above the centre of the base, it is referred to as the right pyramid. If not, the structure is referred to as an oblique pyramid.
A right-triangular pyramid is a three-dimensional object with a base that rises to a single point from a right-angle triangle.
Apex points of right pyramids are located directly above the centroid of their base. Non-right pyramids are another name for oblique pyramids. Given that its base is a regular polygon, an implied right pyramid is a typical pyramid.
24 / 4 = 6 inches - the edge length of the square base
9² = 3² + Height²
simplifying the above equation, we get
Height² = 9² - 3²
Height² = 72 take the square root of both sides
Height = ~8.485 - inches - the height of the pyramid.
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Put one pair of bracket into this calculation to make it correct.
7 x 5 - 2 + 3 = 42
The equation becomes true if we put brackets in the following way:
7x(5 - 2 + 3) = 42
Where do we need to put the bracket?Here we have the expression:
7x5 - 2 + 3 = 42
And we want to find where we need to put brackets in such a way that the equation becomes true.
If we solve the equation as it is, we will get:
7x5 - 2 + 3 = 42
35 - 2 + 3 = 42
36 = 42
Now, let's return to the equation:
7x5 - 2 + 3 = 42
If we put one pair of brackets that includes from the 5 to the 3, we will get:
7x(5 - 2 + 3) = 42
7x(4) = 42
42 = 42
So the equation becomes true.
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Triangle BAC was rotated 90° clockwise and dilated at a scale factor of 2 from the origin to create triangle XYZ. Based on these transformations, which statement is true?
<Z=<A
<B=<Y
<A=<X
<C=<Z
We know that a 90-degree clockwise rotation is the same as a 270-degree counterclockwise rotation, which means that the coordinates of each point in the original triangle BAC will be flipped across the x-axis, and then rotate 270 degrees.
We also know that a dilation at a scale factor of 2 means that the coordinates of each point are multiplied by 2.
Based on these transformations, the statement that is true is <C=<Z
In triangle BAC, point C has the same coordinates as point Z in triangle XYZ.
This because, the original point C is transformed by rotating 90 degrees counterclockwise and scaling by a factor of 2, This result in point C moving to the position of point Z.
The rest of the statements are not true based on this rotation and dilation because the coordinates of points A, B, and Y will be different from the original triangle BAC.
Write an exponential function f so that the slope of a line from the point (0, f(0)) to the point (2, f(2)) is equal to 12.
The exponential function f so that the slope of a line from the point (0, f(0)) to the point (2, f(2)) is equal to 12 is defined as follows:
f(x) = 5^x.
How to define the exponential function?The general format of an exponential function is given as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.The slope of a line, given two points, is given by the division of the change in the output by the change in the input of these two points.
Considering that the slope of points (0, f(0)) and (2, f(2)) is equals to 12, we have that:
[f(2) - f(0)]/(2 - 0) = 12
f(2) - f(0) = 24.
One case that satisfies this involves these two following points.
(0,1) -> f(0) = 1.(2,25) -> f(2) = 25.Hence the parameter a is given as follows:
a = 1.
When x = 2, y = 25, meaning that the parameter b is calculated as follows:
b² = 25
b = 5.
Hence the exponential function is:
f(x) = 5^x.
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How do you calculate undefined FG?
To calculate undefined FG, subtract the original gravity (OG) from the final gravity (FG) of the beer. This will give you the amount of sugar that has been fermented and, therefore, the amount of alcohol produced. The formula is:
Undefined FG = OG – FG
In order to calculate the undefined FG of a beer, the original gravity (OG) and the final gravity (FG) of the beer must first be determined. The OG is a measure of the sugar content of the wort before fermentation, while the FG is a measure of the sugar content of the beer after fermentation. To calculate the undefined FG, the OG is then subtracted from the FG. This calculation provides the amount of sugar that has been fermented by the yeast, and therefore the amount of alcohol produced. This calculation is important for brewers, as it provides a quick and easy way to determine the ABV of a beer. In addition, the undefined FG can be used as a measure of the fermentation efficiency of the yeast, as a higher undefined FG indicates that more sugar has been fermented than a lower undefined FG. Understanding the undefined FG of a beer can help brewers make informed decisions about their brewing process and the quality of their beers.
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Samera placed the congruent sides of these two triangles together to form a quadrilateral.
2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.
Which statements are true of the quadrilateral she constructed? Select three options.
It is a rectangle.
It is a trapezoid.
It has only one right angle.
It has two right angles.
It has two sides that are parallel.
The correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.
What is a trapezoid?A quadrilateral with at least one pair of parallel sides is called a trapezoid.
Given that, Samara placed the congruent sides of these two triangles together to form a quadrilateral.
2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.
If we construct such quadrilateral, we will get a trapezoid with one angle a right angle.
Hence, the correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.
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Answers:
1. B its a trapezoid
2. D it has two right angles
3. E it has 2 sides that are parallel
Step-by-step explanation:
solve x^2-4x=0 by factoring
[tex]\huge\text{Hey there!}}[/tex]
[tex]\mathsf{x^2 - 4x = 0}[/tex]
[tex]\text{Factor the LEFT side of your given equation to make it easier to solve}[/tex]
[tex]\mathsf{x(x - 4) = 0}[/tex]
[tex]\text{Set the factors to equal to the number 0}[/tex]
[tex]\mathsf{x - 4 = 0\ \& \ x = 0}[/tex]
[tex]\text{Simplify find and you should be able to have your answer to the given equation}[/tex]
[tex]\mathsf{x = 4 \ \& \ x = 0}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 4\ or \ x = 0}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
x-5 that is the answer na
Matthew's total points scored in basketball this season were 168 points. He scored 147 of those points in the regular season and the rest were scored in his only playoff game. What percent of his total points did he score in the playoff game?
Answer:
12.5%
Step-by-step explanation:
He scored [tex]168-147=21[/tex] points in the playoff game.
This is equal to [tex]\frac{21}{168}(100)=12.5\%[/tex].
Maria is using a coordinate plane with the axes labeled only with integers. She says that the point (-0. 5, 2) cannot be plotted because halves are not numbered on the x-axis. Write a note to explain how to plot the point.
Someone pls help?
Therefore , As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).
Definition of a scatter plot.Several dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).
Here,
Maria You've erred, you know that. You don't understand the points at all. The attachment can be used to your advantage.
The property of rational numbers, according to which there are an endless number of terminating decimals between any two terminating decimals, must be used in order to plot any terminating decimal on the coordinate plane.
On the X axis, indicate -0.5 between 0 and -1.
Mark integer 2 on the Y axis in a similar manner.
Draw a line perpendicular to the Y axis, passing through (-0.5,0), and a line perpendicular to the X axis, passing through (0,2).
These two lines must cross at the specified position (-0.5,2).
As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).
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