The discriminant of the given quadratic equation as in the task content can be evaluated by means of the formula; D = b²-4ac and it's value is; 13.
What is the discriminant of the quadratic equation as given in the task content?According to the task content, it follows that the quadratic equation whose discriminant is to be determined is; x²-5x+3=0.
By comparison with the standard form equation of a quadratic graph which goes thus; ax²+bx +c = 0, in which case, the determinant is given by the expression; b² - 4ac.
We can consequently evaluate the determinant of the quadratic equation in discuss as follows;
Determinant = b² -4ac = (-5)² - (4×1×3) = 25 - 12
Hence, the determinant in this case is; 13.
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3 bells ring at interval of 12,15 and 18 minutes.Respectively they all ring together at 6am,at what time will they ring together? again?
The least common multiple of two or more natural numbers is the least common multiple of all of them. This concept has historically been linked to natural numbers, but can be used for negative integers or complex numbers.
We calculate the least common multiple, by simultaneous decomposition, this method consists of extracting the common and non-common prime factors, therefore
The lcm of 12,15, 1812 - 15 - 18 | 2 6 - 15 - 9 | 2 3 - 15 - 9 | 3 1 - 5 - 3 | 3 1 - 5 - 1 | 5 1 - 1 - 1 |L.c.m.(12,15,18)= 2² × 3² × 5 = 180 min
The least common multiple of 12, 15, and 18 is 180.
Convert the minutes to hours, for this we apply the rule of 3:
x = 180 * 1 / 60 = 3 hrAs the bells all together ring at 6 am, so we add
6 a.m + 3 = 9Answer: The bells are rung together again at 9 in the morning.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]3x + y = - 4 \\ 3x + 0 = - 4 \\ 3x = - 4 \\ x = \frac{ - 4}{3} = - 1.333[/tex]
It has to be the last line in the second picture since it intersects the x axis at approximately x=-1.333[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \bm{Last \: option \: (D.)}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Write the equation in slope-intercept form. Then solve y.
▪ [tex]\small\longrightarrow \sf{3x-3x + y = −3x -4}[/tex]
▪ [tex]\small\longrightarrow \sf{y= -3x-4}[/tex]
Identify the x-intercept,
[tex]\small \sf \longrightarrow{3x + 0 = - 4}[/tex]
[tex]\small\longrightarrow \sf{3x=-4}[/tex]
[tex]\small\longrightarrow \sf{x = - \dfrac{4}{3} }[/tex]
[tex]\small\longrightarrow \sf{x = -1.33}[/tex]
The graph has the next properties:
[tex]\small\longrightarrow \sf{Slope: \: 3}[/tex]
[tex]\small\longrightarrow \sf{x-intercept: \: (-1.33,0)}[/tex]
[tex]\small\longrightarrow \sf{y-intercept: \: (0,4) }[/tex]
I need help with this please and thank you.
Answer: I believe the answer would be as follows:
8.431 grams
5.46 seconds
980 meters
900 miles
Step-by-step explanation:
it would first be which has the largest number after the decimal point, so if there’s three it goes first (0.12*3*). Then you would pick the one that is the smallest form of measurement, which would be meters in this case.
Hope this helped!
Use the drawing tool(s) to form the correct answers on the provided number line. plot the value(s) on the number line where this function is equal to zero: f(x) = (x 5)(x − 1).
Plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.
What is a parabola?A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.To plot the value(s) on the number line where the given function is equal to zero:
The equation is written as: y = (x+5)(x-1)
This is further written as:
(x+5)(x-1) = 0 and x+5 = 0x- 1 = 0Giving x = -5 and x = 1.The highest point occurs when x = 0, which is (5)(-1) = -5
Therefore, plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.
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The correct question is given below:
Use the drawing tool(s) to form the correct answers on the provided number line. plot the value(s) on the number line where this function is equal to zero: f(x) = (x + 5)(x − 1).
Which shows the following expression after the negative exponents have been eliminated?
Answer:
[tex]\frac{a^3b^4}{ab^2}[/tex] which is the last choice in the question
Step-by-step explanation:
Simplify
[tex]\frac{a^3b^{-2}}{ab^{-4}} = \frac{a^3}{a}\frac{b^{-2}}{b^{-4}}[/tex]
Using the fact that [tex]\frac{x^m}{x^n} =x^{m-n}[/tex]
We get
[tex]\frac{a^3}{a} = a^{3-1} = a^2[/tex]
[tex]\frac{b^{-2}}{b^{-4}} = b^{-2-(-4)} = b^2[/tex]
So
[tex]\frac{a^3b^{-2}}{ab^{-4}} =a^2b^2[/tex]
Multiplying numerator and denominator by [tex]ab^2[/tex] gives
[tex]a^2b^2 \frac{ab^2}{ab^2}[/tex]
= [tex]\frac{a^3b^4}{ab^2}[/tex] ANSWER
Hint:
We can eliminate first choice since negative exponents still remain
We can eliminate third choice because the expression has a minus sign which is not possible
That just leaves second and fourth choices to work with
The average of 15,19,23,41,and Z is 20. What is the value of x
The value of x from the given data is 2
Calculating the average of numbersMean is the ratio of sum of numbers to the total samples. Given the following data
15,19,23,41, and Z
The mean is calculated as
Mean = 15+19+23+41+z/5
Since the mean the of the data is given as 20. Substitute
20 = 15+19+23+41+z/5
Cross multiply
20*5 = 15+19+23+41+z
100 = 15+19+23+41+z
100 = 98 + z
z = 100- 98
z = 2
Hence the value of x from the given data is 2
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Which function represents the following graph?
X
The last one because the other ones only go to the positive side and not the negative too since the cube root
Use what you know about reflections of functions
to match the graph to the function rule.
The answers are :
y = 3ˣ ⇒ b
y = 3⁻ˣ ⇒ a
y = -3ˣ ⇒ c
For y = 3ˣ, we will get a graph that will increase exponentially in the direction of positive y-axis.
For y = 3⁻ˣ, we will get a graph that will decrease exponentially in the direction of positive x-axis.
For y = -3ˣ, we will get a graph that will decrease exponentially in the direction of negative y-axis.
What is the equation for the line of best fit on the scatter plot below?
Answer:
The correct answer is the third option: y = 4x - 20
Step-by-step explanation:
To solve this problem, we should first find two points that are located along our line of best fit. We can see that the points (25,80) and (15, 40) are both located along the line. Next, we can calculate the slope using these two points.
slope = rise/run = Δy/Δx = (80-40)/(25-15) = 40/10 = 4
Therefore, the slope of the line of best fit is 4.
To find the y intercept, we can use our equation for slope and plug in one of our points.
y = mx + b
y = 4x + b
40 = 4(15) + b
40 = 60 + b
b = -20
Therefore, the y intercept is -20.
If we put both our slope and y intercept into one equation, we get:
y = mx + b
y = 4x - 20
The correct answer is the third option.
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3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
I need to know how to solve it
The solution to the system of equations is x = 1, y = 10 and z = 4
How to solve the system of equations?The system of equations is given as:
3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
Multiply the second equation by 2
So, we have
4x - 2y + 6z = 8
Add this equation to the first equation
3x + 4x + 2y - 2y + 4z + 6z = 11 + 8
Evaluate the like terms
7x + 10z = 19
Multiply the second equation by 3
So, we have
6x - 3y + 9z = 12
Subtract this equation from the third equation
6x - 5x - 3y + 3y + 9z - 5z = 12 + 1
Evaluate the like terms
x + 4z = 13
Make x the subject
x = 13 - 4z
Substitute x = 13 - 4z in 7x + 10z = 19
7(13 - 4z) + 10z = 19
Expand
91 - 28z + 10z = 19
Evaluate the like terms
-18z = -72
Divide
z = 4
Substitute z = 4 in x = 13 - 4z
x = 13 - 4 * 4
Evaluate
x = 1
We have:
2x -y +3z = 4
This gives
2(1) - y + 3 * 4 = 4
Evaluate
2 - y + 12 = 4
This gives
y = 10
Hence, the solution to the system of equations is x = 1, y = 10 and z = 4
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peaches are 1.79 a pound at the grocery store.if kim bought 3.5 pounds of peaches how much did she spend?
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
-3
Step-by-step explanation:
(-3, -1), (-5, 5)
Each point is (x, y).
slope = (difference in y)/(difference in x)
slope = (-1 - 5)/(-3 - (-5)) = -6/(-3 + 5) = -6/2 = -3
The slope is -3
please i need help FAST
What is the area of the given triangle?
24 square units
12 square units
48 square units
17.2 square units
Answer: 12 square units
Step-by-step explanation: first you must count hom many units there are between points A and B, which is 4, and then count the points between B and C, which is 6.
Now that we have the units we do 6 x 4 = 24, however, you may be asking why we do not do 24 then, well if you were to be doing 6 x 4, you would be getting the area of a rectangle, and half of a rectangle is a triangle, so we have to do 24/2 which equals 12.
One large jar and five small jars can hold 26 ounces of jam. One large jar minus one small jar can hold 2 ounces of jam. Use the given matrix equation to solve for the number of ounces of jam that each jar can hold. Explain the steps that you took to solve this problem.
A matrix with 2 rows and 2 columns, where row 1 is 1 and 5 and row 2 is 1 and negative 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is l and row 2 is s, equals a matrix with 2 rows and 1 column, where row 1 is 26 and row 2 is 2.
Using a system of equations, it is found that one large jar holds 6 ounces and one small jar holds 4 ounces.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable l: Weight that a large jar holds.Variable s: Weight that a small jar holds.One large jar and five small jars can hold 26 ounces of jam, hence:
l + 5s = 26, which is the first equation in matrix form.
Then:
l = 26 - 5s.
One large jar minus one small jar can hold 2 ounces of jam, hence:
l - s = 2, which is the second equation in matrix form:
Then:
l = 2 + s = 26 - 5s
2 + s = 26 - 5s
6s = 24
s = 4.
l = 26 - 5s = 6.
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suppose sin(A) = 2/5. use the trig identity sin^2(A)+cos^2(A)=1 to find cos(A) in quadrant I. show all steps and round to ten-thousandth
In quadrant I, [tex]\cos(A)[/tex] is positive. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} = \dfrac{\sqrt{21}}5 \approx \boxed{0.9165}[/tex]
The table below shows the depth of water in a bathtub as it is being filled over time. The data can be modeled by a linear equation where x is the elapsed time in minutes and y is the depth of the water in inches. What does the y-intercept of the linear equation that models the data indicate?
In the linear equation, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.
What is the Y-intercept of a Linear equation?A linear equation is modelled in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept of the equation, which is the initial value of y when x is zero.
Using two pair of points from the table, say, (1, 3) and (2, 5), find the slope (m) of the linear equation:
Slope (m) = change in y / change in x = (5 - 3)/(2 - 1)
Slope (m) = 2/1
Slope (m) = 2
To find the y-intercept (b), substitute (x, y) = (1, 3) and m = 2 into y = mx + b
3 = 1(2) + b
3 = 2 + b
Subtract 2 from both sides
3 - 2 = 2 + b - 2
1 = b
b = 1
Thus, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.
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For Exercises 11-15, sketch the locus of points in a plane that satisfy the
given conditions.
14. equidistant from both points
A and B and points C and D
B C
A
O
D
15. equidistant from the sides of
LJKL and on OC
L
A locus is a set of a given point that satisfies certain/ stated conditions. This could be in the form of a curve, circle, or line. The required construction is wherewith attached to this answer.
Construction is a topic that requires following some steps to complete or solve a given question. This majorly requires the use of materials and instruments for drawing the expected figure.
A locus is a set of a given point that satisfies some given conditions. This could be in the form of a curve, circle, or line satisfying the required condition(s).
An equidistant locus is one that is at the same distance to a reference point or a line.
In question 14, the required locus should be at the same distance to points A, B, C, and D.
In question 15, the required locus should be at the same distance to sides KJ and KL. This should pass through point C.
The required construction is herewith attached to this answer.
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Given y = [tex]\frac{2x-5}{x^{2} -2}[/tex], find the value of [tex]\frac{dy}{dx}[/tex] at x = 2.
▪ [tex]\bold{\dfrac{2x-5}{x^{2} -2}}[/tex]
▪ [tex]\bold{\dfrac{dy}{dx}}[/tex]
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
» [tex] \tt{For \: \: y,}[/tex]
[tex]\longrightarrow\sf{y=v \dfrac{2x - 5}{ {x}^{2} - 2} }[/tex]
[tex]\longrightarrow\sf{\dfrac{dy}{dx} = \cfrac{ ( {x}^{2} - 2)(2) - (2x - 5)(2x)}{( {x}^{2} - {2}^{2} )}}[/tex]
[tex]\longrightarrow\sf{\cfrac{2 {x}^{2} - 4 - {4x}^{2} + 10x}{ ({x}^{2} - {2}^{2} )}}[/tex]
[tex]\longrightarrow{={ \boxed{\sf \cfrac{ - 2 {x}^{2} - 4 + 10x}{ ({x}^{2} - {2}^{2} )}}}}[/tex]
» [tex] \tt{At \: \: x = 2,}[/tex]
[tex]\longrightarrow\sf{ \dfrac{ - 2(2) {}^{2} + 10(2) - 4 }{( {2}^{2} - 2 {)}^{2} } }[/tex]
[tex]\longrightarrow\sf{\dfrac{ - 8 + 20 - 4}{4} }[/tex]
[tex]\longrightarrow\sf{ \dfrac{8}{4} }[/tex]
[tex]\longrightarrow{\sf = \boxed{\sf {2}}}[/tex] ✓
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
◆ The value of the given differential function at [tex]\sf{x=2}[/tex] is [tex]\sf{2.}[/tex]
Suppose we are given the following information.
Line 1 passes through (0, 6) and (6, 4).
Line 2 passes through (-1, -7) and (1, -1).
Are these lines parallel, perpendicular, or neither?
Group of answer choices
Since the product of the slope is -1, hence the lines are perpendicular
Parallel and Perpendicular linesTwo lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1
Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;
Slope = 4-6/6-0
Slope = -2/6
Slope = -1/3
Similarly for the coordinate points (-1, -7) and (1, -1).
Slope = -1+7/1+1
Slope of line 2 = 6/2
Slope = 3
Take the product of the slopes
Slope = -1/3 * 3
slope = -1
Since the product of the slope is -1, hence the lines are perpendicular
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A rectangular prism with a volume of 3x^3+16x^2+5x cubic units has a base area of x^2+5xsquare units. Find the height of the rectangular prism.
The height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.
Volume of rectangular prismVolume of the prism = 3x³ + 16x² + 5x cubic unitsBase area = x² + 5x square unitsVolume of a rectangular prism = Base area × height
Height = Volume of a rectangular prism ÷ Base area
3x³ + 16x² + 5x cubic units = (x² + 5x) square units × h
h = (3x³ + 16x² + 5x) cubic units ÷ (x² + 5x) square units
h = (3x³ + 16x² + 5x) / (x² + 5x) units
Therefore, the height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.
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What is the solution to the equation 1/x =x+3/2x^2?
Ox=-3
Ox= -3 and x = 0
O x = 0 and x = 3
O x = 3
The solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C
How to determine the equationIn solving for the values of 'x' we need to:
Simplify the expression, that is, make a quadratic equationSolve the quadratic equation formed by either fractorisation or completing the square methodsGiven the expression;
1/x =x+3/2x^2
Cross multiply
x ( x+ 3) = 2x² ( 1)
Expand the bracket
x² + 3x = 2x²
collect like terms and equate all the variables to zero, we have ;
2x² - x² - 3x = 0
We then subtract the like terms, we getv
x²- 3x = 0
Now, let's find the common factor
Factor out 'x':
x ( x - 3 ) = 0
Equate each of the factors to zero and find the value of 'x' for each
So,
x = 0
And
x - 3 = 0
x = 3
Thus, the solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C
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1
Select the correct answer.
Which expression is equivalent to x+y+x+y+ 3(y+5)?
OA. 2x+5y+5
OB. 2x+y+30
OC. 2x+ 5y + 15
OD. 2x+3y + 10
Calculate angles in a triangle
HELP
Answer:
angle a = [tex]\boxed{154}^{\circ}[/tex]
Step-by-step explanation:
The angles in a triangle add up to 180°.
∴ ∠a + 13° + 13° = 180°
⇒ ∠a + 26° = 180°
⇒ ∠a = 180° - 26°
⇒ ∠a = 154°
Answer:
Angle a equals= 154°
Step-by-step explanation:
you have two angles which add up to 26°
remember that triangle always adds up to 180°
so you calculate 180-26 and you get 154
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
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Graph. (Shade. Dashed line. Solid line?)
x+3y≥3
Answer:
Since the graph looks like this, I would say solid line
Which characteristic is necessary to create a table that compares two functions?
The characteristic that is necessary to create a table that compares two functions is D. Choose the same values for each functions .
What is the usefulness of table?The Mathematical tables can be regarded as the lists of numbers which is used in showing the results of a calculation and these can have varying arguments.
It should be noted that when necessary to creating a table that compares two functions it is important to Choose the same values for each functions .
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how do you solve this question?
The answers to the questions are as follows:
The value of the empty box in the diagram is 10The probability that the number is in AnB = 1/5How to solve the Venn diagramWe have E = {1, 3,5, 7, 9, 11, 13, 15, 17, 19}
A= { 3, 7, 9, 11, 15}
B = {5, 7, 11, 13}
We have A n B = numbers that are contained in both of the sets
= 7, 11
a.) We have to count the total number in the dataset. That is the total number of odd numbers that are less than 20.
Hence total numbers in the set = 10
b. The probability that the number is in set AnB
= 7, 11
= 2/10
= 1/5
We can conclude that the probability that the number is in A intersect B = 1/5
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Identify the equation for the line tangent to the circle x^2 + y^2 = 100 at the point (−6, 8).
The equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at the point (-6,8) is -6x+8y=100.
Given the equation of circle [tex]x^{2} +y^{2} =100[/tex]
and point at which the tangent meets the circle is (-6,8).
A tangent to a circle is basically a line at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of circle to the point P.
Linear equation looks like y=mx+c.
Tangent to a circle of equation [tex]x^{2} +y^{2} =a^{2}[/tex] at (z,t) is:
xz+ty=[tex]a^{2}[/tex].
We have to just put the values in the formula above to get the equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at (-6,8).
It will be as under:
x(-6)+y(8)=100
-6x+8y=100
Hence the equation of tangent to the circle at the point (-6,8) is -6x+8y=100.
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An ellipse has a center at the origin, a vertex along the major axis at (10, 0), and a focus at (8, 0).
Which equation represents this ellipse?
Answer:
In standard form x^2/64 + y^2/100 = 1
Step-by-step explanation:
The major axis is the y axis because 10 has a larger value than 8.
8x8 = 64
10 x10 = 100
Which rule describes the composition of transformations that maps ΔJKL to ΔJ"K"L"?
90 degree rotation about point 0 composition translation of 0 units x, negative 2 units y
Translation of 0 units x, negative 2 units y composition 90 degree rotation about point 0
90 degree rotation about point 0 composition translation of negative 2 units x, 0 units y
Translation of negative 2 units x, 0 units y composition 90 degree rotation about point 0
A rule which describes the transformations that maps ΔJKL to ΔJ"K"L" is: D. translation of -2 units x, 0 units y composition 90 degree rotation about point 0.
What is a transformation?A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on the diagram (see attachment), we can infer and logically deduce that a rule which describes the transformations that maps triangle JKL to triangle J"K"L" is a rotation of 90 degrees about the origin and then translated 2 units left.
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