Answers
The values of k for the different quadratic equation solutions are as follows
a the equation 2x² - x + 3k = 0 has two distinct real roots
k < 1/24b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots
k = 3/5ci the equation -x² + 3x + (k + 1) = 0 has real roots
k > -3.25d the equation 3kx² - 3x + 2 = 0 has no real solutions
k < ± 1.633How to solve quadratic equations to get different answersQuadratic equations of the form ax² + bx + c = 0 is solved using the formula
[tex]-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex] OR [tex]-b-\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
The equation b² - 4ac is called the discriminant and it is used as follows
To solve the equation and get two real roots: 2x² - x + 3k = 0
b² - 4ac > 0substituting the values gives
(-1)² - 4 * 2 * 3k > 0
1 - 24k > 0
1 > 24k
divide through by coefficient of k
k < 1/24
To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0
b² - 4ac = 0substituting the values gives
(-2)² - 4 * 5 * (2k - 1) = 0
4 - 40k + 20 = 0
-40k = -24
divide through by coefficient of k
k = 3/5
To solve the equation and get real roots -x² + 3x + (k + 1) = 0
b² - 4ac > 0substituting the values gives
(3)² - 4 * -1 * (k+1) > 0
9 + 4k + 4> 0
4k > -13
divide through by coefficient of k
k > -3.25
To solve the equation and get no real solutions 3kx² - 3x + 2 = 0
b² - 4ac < 0substituting the values gives
(-3)² - 4 * 3k * 2 < 0
9 - 24k² > 0
9 > 24k²
divide through by coefficient of k²
k² < 24/9
k < ± 1.633
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Answer:
ax² + bx + c = 0 is solved using the formula
Step-by-step explanation:
Related Questions
What type of transformation is illustrated in the picture below? A. rotationB. translation
Answers
Rotation simply means turning around a centre . From the diagram above the vehicle rotated in a clockwise fashion.
The equation of a line is x + 4y = 15.What is the y-intercept of the line? −151515/44/15
Answers
Given:
[tex]x+4y=15[/tex][tex]4y=-x+15[/tex][tex]y=-\frac{1}{4}x+\frac{15}{4}[/tex][tex]\text{The general equation is }[/tex][tex]y=mx+c[/tex]c is the y-intercept
[tex]y-\text{intercept (c)= }\frac{15}{4}[/tex]please look at screenshots
Answers
Answer:
c
Step-by-step explanation:
it not linear relationship
What is the value of 7 + z ÷ 2, when z = 10?
Answers
Answer:
12
Step-by-step explanation:
7 + z ÷ 2 ,z=10(bodmas , division is the first)
7 + 10 ÷2
7 + 5
12
Answer:
12
Step-by-step explanation:
Substitute 10 for z
7+10 ÷ 2
divide first
7+5=
12
which expression is equivalent to (4^2)^-2?
Answers
Answer:
[tex](4^2)^{-2}=\frac{1}{x^4}[/tex]Explanation: We need to simplify the given expression to get an equvilant expression: The given is as follows.
[tex](4^2)^{-2}[/tex]Simplification:
Using the following exponent property:
[tex](x^a)^{-b}=x^{a\times(-b)}^{}=x^{-ab}^{}=\frac{1}{x^{ab}}[/tex]The equvilant expression we get is:
[tex](4^2)^{-2}=x^{2\times-2}=x^{-4}=\frac{1}{x^4}[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
This data shows the height of 10 trees, in metres, after 5 years’ growth.
2.1
2.5
2.2
2.4
2.2
2.7
2.4
2.3
1.9
2.6
Calculate the median, showing your answer to two decimal places and remembering to include units with your answer.
Answers
The median of the given data would be 2.35 meters.
What is the median of data?The median is defined as the value range. To get it, arrange the numbers in ascending order from smallest to largest, then hide one number on either end until you reach the center.
The given set of data as:
{2.1, 2.5, 2.2, 2.4, 2.2, 2.7, 2.4, 2.3, 1.9, 2.6}
Arrange the data in ascending order.
1.9, 2.1, 2.2, 2.2, 2.3, 2.4, 2.4, 2.5, 2.6, 2.7
Since the number of elements in the data set is 10.
Median = [(n/2)th term + ((n/2) + 1)th term]/2
Median = [(10/2)th term + ((10/2) + 1)th term]/2
Median = [5th term + 6th term]/2
Median = [2.3 + 2.4]/2
Median = 4.7/2
Median = 2.35
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Marques works in a department store selling clothing. He makes a guaranteed salary of $200 per week, but is paid a commission on top of his base salary equal to 10% of his total sales for the week. How much would Marques make in a week in which he made $750 in sales? How much would Marques make in a week if he made x dollars in sales?
Answers
Base salary = $200 per week
Commission = 10% of total sales for that week
In a certain week, he makes sale of = $750
So, commission for that week = 10% of $750 = 10/100 x $750 = $75
In that particular week, Marques earned = base salary + commission = $200 + $75 = $275
For a week, in which he makes x dollars in sales,
Commission = 10% of x = 10/100 x (x) = $x/10
Total earning for that week = base salary + commission = $200 + $x/10
What are Commissions?The payment for goods or services sold in the form of commissions is a type of variable pay. Salesperson motivation and reward frequently involve commissions. Incentives like commissions might be used to promote particular sales techniques. When offering substantial reductions, for instance, commissions might be cut. Alternatively, commissions could go up when a company sells a certain product it wishes to advertise. A sales incentive program's framework, which may comprise one or more commission programs, governs how commissions are normally administered.The principal-agent problem is often solved by businesses by calculating payments as a proportion of revenue in an effort to better align employee interests with those of the business.Creating incentives that take account of an agent's performance is one of the most popular ways to try and balance principal and agent interests. The different forms of compensation systems, such as fixed salaries, straight commissions, or a mix of both, have a wide range of variations.To learn more about Commissions, refer to:
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Write a quadratic function in standard form whose graph has the given characteristics.
Answers
The quadratic function in standard form that passes through (-2, 0), (4, 18), and (10, 0) is y = (- 1/2) x² + 4x + 10.
Given that, (-2, 0), (4, 18) and (10, 0).
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
Now, the equation passes through (- 2, 0)
y = ax² + bx + c
0 = 4a - 2b + c ----------------(1)
The equation passes through (4, 18)
y = ax² + bx + c
18 = 16a + 4b + c ----------------(2)
The equation passes through (10, 0)
y = ax² + bx + c
0 = 100a + 10b + c ----------------(3)
Using the Gauss elimination method to solve the system of equations we get,
a = -1/2, b = 4, and c = 10
The quadratic equation will be:
y = ax² + bx + c
y = (- 1/2) x² + 4x + 10
Therefore, a quadratic function in standard form with the given characteristics is y = (- 1/2) x² + 4x + 10.
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Determine if triangle EFG and triangle HIJ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Answers
Given the triangles EFG and HIJ, you can identify that:
[tex]EG=19\text{ }[/tex][tex]EF=18[/tex][tex]\begin{gathered} FG=16\text{ } \\ \\ \text{ }HI=90 \\ \\ IJ=80 \end{gathered}[/tex][tex]\begin{gathered} m\angle F=67\text{ \degree} \\ \\ m\angle I=67\text{ \degree} \end{gathered}[/tex]By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.
In this case, you can identify that you know two pairs of corresponding sides. Then, you can find in they are in proportion. Set up that:
[tex]\frac{EF}{HI}=\frac{FG}{IJ}[/tex]Substituting values and simplifying, you get:
[tex]\begin{gathered} \frac{18}{90}=\frac{16}{80} \\ \\ \frac{1}{5}=\frac{1}{5} \end{gathered}[/tex]Notice that they are in proportion.
You can also identify that the corresponding angles F and I are congruent because they have equal measure.
Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).
Hence, the answer is: Third option.
What is the magnitude of -5 + 121?
Answers
Question:
Solution:
For a complex number z = x + yi, we define the magnitude, |z|, as follows:
[tex]|\text{ z |=}\sqrt[]{x^2+y^2}[/tex]thus, according to this, we can conclude that the magnitude of the given complex number is:
[tex]|\text{ z |=}\sqrt[]{(-5)^2+(12)^2}\text{ = 13}[/tex]so that, the correct answer is:
[tex]13[/tex]
Consider the following equation. State any restrictions on the variable, if they exist.
Answers
In equation like this one, the restriction happens when there are variables in the denominator. Since the denominator can't be equal to zero, when we have a variable in the denominator, we have to find the restrictions to the variable.
However, in this case, no denominator have variables in it.
So, in this case, there is no restriction for the values of x.
fx) -2 x 14 11 3 5 5 4 -8 Determine the Solution utilizing the Table of Values* (1 Point)
Answers
The domain x with the value of 5 according to the table has a range value of -8.
A. -8
Miles has 327 action figures and 4 shoeboxes to store them in.Does miles have enough shoe boxes? ,if not, how many action figures are left over?
Answers
Step 1:
Concept
To find out if Miles has enough shoeboxes to fit all 327 of his action figures, we first need to find the amount of action figures his current amount of shoeboxes can store. We can do this by multiplying the amount of shoeboxes Miles has by the amount of action figures each shoebox can hold.
Step 2:
Shoe boxes can contain 80
Total = 4 x 80 = 320
Step 3
There will be 7 left
Left over = 7
Help I’m completely lost on this I have no clue what I’m doing. I’ve tried 3 times
Answers
Answer:
Explanation:
Given the equation:
[tex]undefined[/tex]What was done to the linear parent function, f(x) = x, to get the functiong(x) = ?A. Horizontally compressed by a factor of 6B. Vertically stretched by a factor of 6C. Vertically compressed by a factor of 6D. Shifted unit up
Answers
Given
Two functions
[tex]\begin{gathered} f(x)=x \\ g(x)=\frac{1}{6}x \end{gathered}[/tex]Procedure
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.
A gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. How many different gift-wrapping options are available at this store?
Answers
14*12*8=1344
1344 options
Rewrite y = a (2)¹/3 in the form y = a(1+r) or y = a(1-r)'. Round each value to the nearest hundredth, if necessary. Then state the growth or decay rate.yoThe rate is about %.This is a rate.
Answers
we have the equation
[tex]y=a(2)^{\frac{t}{3}}[/tex]Rewrite the given equation
[tex]\begin{gathered} y=a(2^{\frac{1}{3}})^t \\ y=a(1.26)^t \\ y=a(1+0.26)^t \end{gathered}[/tex]the base of the exponential function is b=1.26
1.26 > 1
that means
is an exponential growth function
1+r=1.26
r=1.26-1
r=0.26
therefore
The rate is about 26%This is a growth rateWhat is the correct answer
Answers
In transversal lines, All angles are equal and parallel, so TV ║ WY are parallel lines .
What are transversal lines?
A line that crosses two lines in the same plane at two different geometric locations is referred to as a transversal. Different sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.A line that crosses other lines is known as a transversal. When transversals intersect parallel lines, such as the two railroad tracks, we often operate with them.∠TUX ≅ ∠UXY ( Alternate angle)
∠SUV ≅ ∠TUX ( Vertically angle)
∠UXY ≅ ∠SUV ( Interior angle )
TV ║ WY ( All angles are equal and parallel, so TV ║ WY
are parallel lines .
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f(x)=x^2-8, g(x)=17-x
(f/g)(-4)=?
Answers
The quotient between the two functions evaluated in -4 is equal to 8/21.
How to find the quotient?
Here we have the two functions:
f(x) = x^2 - 8
g(x) = 17 - x
And we want to find:
(f/g)(-4)
That can be rewritten as:
f(-4)/g(-4)
By evaluating the two functions we get:
f(-4) = (-4)^2 - 8 = 16- 8 = 8
g(-4) = 17 - (-4) = 17 + 4 = 21
replacing that in the quotient we get
f(-4)/g(-4) = 8/21
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please help with this practice question asap
Answers
The slope of the line passing through the points (4, -5), (-4, -5) is m = 0.
What do we mean by a slope?The slope of a line can be used to gauge how steep it is.Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).Every time the equation of a line is written as y = mx + b, the slope-intercept form of the equation is used.The slope of the line is shown by M.B is the value of b at the location of the y-intercept (0, b).For instance, y = 3x - 7 has a slope and y-intercept of 3 and 0, respectively.So, the slope of (4, -5) (-4, -5):
The slope formula: m = y₂ - y₁/x₂ - x₁Now, substitute the values in the formula and find the slope as follows:
m = y₂ - y₁/x₂ - x₁m = (-5) - (-5)/(-4) - 4m = -5 + 5/-4 - 4m = 0/-8m = 0Therefore, the slope of the line passing through the points (4, -5), (-4, -5) is
m = 0.
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The science club took a survey to see how many hours each member in the club worked on a science project. The table below
shows the results of the survey.
Students Hours
Greta
16
Juan
14
Mika
20
Paulo
18
Su-Lin
16
Tanika
31
Darnell
13
Wesley
24
What is the mean (average) number of hours the students worked on the science project?
OA. 21
OB. 19
OC. 20
18
Answers
Answer: 19
Step-by-step explanation:
To find an average, you take each of your values, add them, and then divide by the numbers of values you have. There were 8 students interviewed, so your total numbers of values is 8.
Addition: 16 + 14 + 20 + 18 + 16 + 31 + 13 + 24 = 152
Division: 152 ÷ 8 = 19
Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 9x^4 − 35x^2 − 4(x − 2)
Answers
[tex]9x^4-35x^2-4[/tex]
Lets divide this polynomial by x - 2
9x^4 0x³ -35x² 0x -4 | x - 2
-9x^4 +18x³ | 9x³
18x³ -35x² 0x -4 | x - 2
-18x³ 36x² | 9x³ + 18x²
x² 0x -4 | x - 2
-x² +2x |9x³ + 18x² + x
2x -4 |x - 2
-2x + 4 |9x³ + 18x² + x +2
0
Since there is no rest for the division, x - 2 is a factor of the given polynomial:
[tex]9x^4-35x^2-4=(x-2)\cdot(9x^3+18x^2+x+2)[/tex]Washing his dad's car alone, Matt takes 6 hours. If his dad helps him, then it takes 2 hours. How long does it take Matt's dad to wash the car by himself?
Answers
If it takes 6 hours for Matt to wash the car, then he washes at a rate of 1/6 cars per hour:
[tex]\begin{gathered} \frac{1}{x}=6 \\ x=\frac{1}{6} \end{gathered}[/tex]Let y be the time in which Matt's dad washes the car and state an equation that describes the situation in which Matt and his dad wash the car together:
[tex]\begin{gathered} \frac{1}{6}+\frac{1}{y}=2 \\ \frac{1}{y}=2-\frac{1}{6} \\ \frac{1}{y}=\frac{11}{6} \\ y=\frac{6}{11} \end{gathered}[/tex]It means that he washes the car in 6/11 hours (approximately 0.54hours).
7.) A jug of egg nog sells for $5.12One jug holds(128 ounces. What is the unit priceper ounce?
Answers
To find the unit price per ounce, we just need to divide the total price by the total amount of egg nog(in ounces). The total price is $5.12 and the amount of egg nog is 128 ounces, therefore, the unit price per ounce is
[tex]\frac{5.12}{128}=0.04[/tex]$0.04.
The length of a rectangle is 3 more than the width. Find the length of the rectangle if the perimeter is 98 in.A.47.5 inB.24.5 inC.26 in.D.23 in.
Answers
Answer
Length of the rectangle = 26 inches
Explanation
Let the length of a rectangle be L
Let the width of the rectangle be W
The length of the rectangle is 3 more than the width.
L = W + 3
But we are provided with the perimeter of the rectangle.
The perimeter of a figure is the sum of the dimensions of its exterior.
For a rectangle,
Perimeter = 2 (L + W)
For this question,
Perimeter = 98 inches
L = W + 3
W = ?
Perimeter = 2 (L + W)
98 = 2 (W + 3 + W)
98 = 2 (2W + 3)
98 = 4W + 6
4W + 6 = 98
4W = 98 - 6
4W = 92
Divide both sides by 4
(4W/4) = (92/4)
W = 23 inches
L = W + 3 = 23 + 3 = 26 inches
Hope this Helps!!!
Use intercepts to graph the line described by the equation.4y =5x +20
Answers
We have to graph the equation 4y=5x+20 using the intercepts.
First we are going to find the y-intercept of the line, to do this we have to remember that the line intercepts the y-axis when x=0. Plugging this value of x in the equation we have
[tex]\begin{gathered} 4y=5(0)+20 \\ 4y=20 \\ y=\frac{20}{4} \\ y=5 \end{gathered}[/tex]Hence the y-intercept is 5. This represents the point (0,5).
Now we draw this point on the graph:
Now we have to find the x-intercept of the line, this happens when y=0. Plugging this value of y in the equation we have that
[tex]\begin{gathered} 4(0)=5x+20 \\ 0=5x+20 \\ 5x=-20 \\ x=-\frac{20}{5} \\ x=-4 \end{gathered}[/tex]Then, the x-intercept is -4. This represents the point (-4,0).
Drawing this point on the graph we have.
Now we only connect the points with a straight line:
That's the graph of the line that we find with the intercepts.
Need to study for finals need help on this problem on my study guide find the measure of each angle calculate the length of each side
Answers
Answer:
[tex]\begin{gathered} m\angle B\text{ = 28}\degree \\ AB\text{ = 9.75} \\ BC\text{ = 7.7} \end{gathered}[/tex]Explanation:
Here, we want to calculate the measure of each of the missing angles and sides
We have one missing angle and 2 missing sides
a) Let us get the angle at B
Mathematically, the sum of angles in a triangle is 180 degrees
Thus:
[tex]\begin{gathered} 90\text{ + 62 + B = 180} \\ B\text{ = 180-90-62} \\ B\text{ = 28}\degree \end{gathered}[/tex]b) Let us get the measure of AB
We can use the appropriate trigonometric ratio here
The side that measures 6 is an opposite to the angle B
Since AB is the hypotenuse (the side facing the right angle and the longest side of in the triangle), we use sine
Sine is the ratio of the opposite and the hypotenuse
Mathematically:
[tex]\begin{gathered} sin\text{ 38 = }\frac{6}{AB} \\ \\ AB\text{ =}\frac{6}{sin\text{ 38}} \\ \\ AB\text{ = 9.75} \end{gathered}[/tex]c) side BC
We can use tan to get this
Tan is the ratio of the opposite to the adjacent side
The opposite side here is the side AC, while the adjacent is BC
Thus, we have it that:
[tex]\begin{gathered} Tan\text{ 38 = }\frac{6}{BC} \\ \\ BC\text{ = }\frac{6}{Tan\text{ 38}} \\ \\ BC\text{ = 7.7} \end{gathered}[/tex]Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
randomly chosing a number from the even number between 10 and 20 nclusive
Answers
For the given experiment, the sample space has 6 elements which are:
{10, 12, 14, 16, 18, 20}
How to identify the sample space?
For any experiment with different outputs (each output with a defined probability).
We define the sample space as the set of all the possible outcomes of the experiment.
Now, the experiment here is:
"randomly choosing a number from the even number between 10 and 20 inclusive"
So the possible outcomes are all the even numbers on the interval [10, 20]
Then the sample space of the experiment is:
{10, 12, 14, 16, 18, 20}
It has 6 elements.
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I need help on this question
Answers
DA bisects EB
then
DC is congruent with AC
EC is congruent with BC
and
ED is congruent with AB