The formula for the value of discriminant in a quadratic equation in the form ax^2 + bx + c = 0 is :
[tex]d=b^2-4ac[/tex]Where d is the discriminant and
a, b, c are the coefficients in the quadratic equation.
From the given problem,
[tex]ax^2+bx+c=0\Rightarrow-2x^2+6x-3=0^{}[/tex]a = -2, b = 6 and c = -3
Using the formula above,
[tex]\begin{gathered} d=b^2-4ac \\ d=6^2-4(-2)(-3) \\ d=36-24 \\ d=12 \end{gathered}[/tex]Note that if the discriminant is greater than 0, the number of real solution is 2.
The answer is
discriminant = 12
Number of real solutions = 2
Answer:
[tex]2[/tex]
[tex]x[/tex]
Joseph and his children went into a movie theater where they sell bags of popcorn for $7.50 each and pretzels for $4.75 each. Joseph has 595 to spend and must buy no less than 16 bags of popcorn and pretzels altogether. If z represents the number of bags of popcorn purchased and y represents the number of pretzels purchased, write and solve a sstem of inequalities graphically and determine one possible solution.
We will have the following system of inequalities:
[tex]\begin{cases}z+y\ge16 \\ 7.50z+4.75y\le595\end{cases}[/tex]This graphically is:
So, the solutions will be located at the intersection of both graphs. So, one possible solution is:
5 bags of popcorn and 15 bags of pretzels. This solution can be seen in the following graph:
If sin0 =0.5974, then theta is
To find the angle Θ, find the sine inverse of 0.5974 with a calculator or mathematical table for sine
That is,
[tex]\begin{gathered} \theta=\sin ^{-1}(0.5974) \\ \theta=36.68^0\text{ (to the nearest tenth)} \end{gathered}[/tex]The answer is: Θ=36.68⁰
the dimensions of the rectangular prism shown are given in centimeters
The volume of the prism = Length x breadth x height
= 4cm x 1.4cm x 3cm = 16.8 cm^3
I
3. How many pictures would you draw for biking if
each = 5 students?
Answer:
You can draw a car for five students
I need help with all those questions in the image!
Answer:
The rate of change of elevation tends to a constant value.
Explanation:
The average rate of change of e(x) on the interval [a, b] defined as
[tex]m_{\text{avg}}=\frac{e(b)-e(a)}{b-a}[/tex]which explicitly we can write as
[tex]m_{\text{avg}}=\frac{\sqrt[]{b-10}-\sqrt[]{a-10}}{b-a}[/tex]Now, the question is, what happens to m_avg as we increase b while keeping a fixed?
As b becomes large then √b -10 becomes √b and b - a becomes b (since a is comparatively small); therefore, m_avg becomes
[tex]m_{\text{avg}}=\frac{\sqrt[]{b-10}-\sqrt[]{a-10}}{b-a}\Rightarrow\frac{\sqrt[]{b}-\sqrt[]{a-10}}{b}\Rightarrow\frac{\sqrt[]{b}}{b}[/tex][tex]\Rightarrow m_{\text{avg}}=\frac{\sqrt[]{b}}{b}[/tex]which for any fixed value of b is a constant.
The same behaviour can be extrapolated by looking at the graph of e(x).
As can be seen from the graph, as x increases, the slope of the function becomes flatter and flatter, meaning it tends to be a constant. In other words, for large values of x, you can approximate the slope of the function by a straight line.
Select the correct answer from each drop-down menu.The graph of the function /(=)foin(a) + I is shown. What are the key features of this function?y
Given:
[tex]f(x)=\frac{5}{4}sin(x)+1[/tex]Required:
We need to find the maximum, minimum, range, and interval of the increasing function.
Explanation:
We know that the maximum value of the function occurs whenever sinx=1.
Substitue sin(x)=1 in the given equation to find the maximum value.
[tex]The\text{ maximum}=\frac{5}{4}(1)+1[/tex][tex]The\text{ maximum}=\frac{5}{4}+\frac{4}{4}[/tex][tex]The\text{ maximum}=\frac{9}{4}[/tex][tex]The\text{ maximum}=2.25[/tex]We know that the minimum value of the function occurs whenever sinx=-1.
Substitue sin(x)=-1 in the given equation to find the maximum value.
[tex]The\text{ minimum=}\frac{5}{4}(-1)+1[/tex][tex]The\text{ minimum=}\frac{-5}{4}+\frac{4}{4}[/tex][tex]The\text{ minimum=}\frac{-1}{4}[/tex][tex]The\text{ minimum=-0.25}\frac{}{}[/tex][tex]\text{ Consider the interval }(0,\frac{\pi}{4})[/tex]if the value of y is increasing on increasing the value of x, then the function is known as an increasing function
The given function is increasing to the maximum value when the value of x is increasing.
The values of the given function are increasing in the given interval.
[tex]In\text{ the interval \lparen0,}\frac{\pi}{4})\text{ the function is increasing.}[/tex]We know that the range of the function lies between the minimum and maximum values.
[tex]Range=[-0.25,2.25][/tex]Final answer:
[tex]The\text{ maximum}=2.25[/tex][tex]The\text{ minimum=-0.25}\frac{}{}[/tex][tex]In\text{ the interval \lparen0,}\frac{\pi}{4})\text{ the function is increasing.}[/tex][tex]Range=[-0.25,2.25][/tex]name three fractions that are equivalent to 2/5
what are all the possible rational roots of x^2+x-6
The root of x^2 + x - 6 is the values of x when y = 0
x^2 + x - 6 = 0
Factorize it into two factors
Since the last sign is (-), so the brackets of the factors have different sign
Wr need two numbers their product = 6 and their
Solve for
x: 5/6x+7=1
Answer:
x=2/3
Step-by-step explanation:
5/(6x+1) * 6x+1 = 1 * (6x+1)
5=6x+1
5-1=6x+1-1
6x=4
6x/6=4/6
x=2/3
Ken is building a deck. He determined that he needs 25 blocks that cost $7.97 each and 48 deck boards that cost $14.00 each. How much will Ken pay for these items?
Ken will pay $ 871.25 for these items
Explanation
to find the total cost we need add the cost of the blocks to the cost of the total boards, so
Step 1
find the total cost of the blocks
a) when having the cost per unit and the amount, we just need to do a multiplication, so
[tex]\begin{gathered} total\text{ cost= rate*amount} \\ replace \\ tota\text{l cost of the blocks= 7.97}\frac{\text{ \$}}{block}*25\text{ Blocks} \\ tota\text{l cost of the blocks= \$ 199.25} \end{gathered}[/tex]Step 2
now, the total cost of the boards:
[tex]\begin{gathered} total\text{ cost= rate*amount} \\ replace \\ tota\text{l cost of the boards= 14}\frac{\text{ \$}}{board}*4\text{8 boards} \\ tota\text{l cost of the boards= \$ 672} \end{gathered}[/tex]Step 3
finally, add the costs to find the total
[tex]\begin{gathered} total\text{ cost= \$199.25+672} \\ total\text{ cost= 871.25} \end{gathered}[/tex]therefore, Ken will pay $ 871.25 for these items
I hope this helps you
x - 9 f(x) = { for x +-4 for x = -4 -4 Find f(-4)
You have the following piece function:
f(x) = -x-9 for x≠-4
-4 for x=-4
as you can notice in the previous piece function, there is a unique value of f(x) when x=-4, and such value is f(-4) = -4
I need help with exercise 8-3 I already did 15. So I need the rest
STEP 1: we create a table of values for y and x as shown below;
For each value of x, we get a corresponding value for y;
[tex]\begin{gathered} y=x^{2^{}}-2x-15 \\ \text{When x=-4} \\ y=(-4)^2-2(-4)-15=9 \end{gathered}[/tex]We continue with this process till when x = 6
[tex]\begin{gathered} \text{When x=-3} \\ y=(-3)^2-2(-3)-15=0 \\ \text{When x=-2} \\ y=(-2)^2-2(-2)-15=-7 \\ \text{When x=-1} \\ y=(-1)^2-2(-1)-15=-12 \\ \text{When x=0} \\ y=(0)^2-2(0)-15=-15 \\ \text{When x=1} \\ y=(1)^2-2(1)-15=-16 \\ \text{When x=2} \\ y=(2)^2-2(2)-15=-15 \\ \text{When x=3} \\ y=(3)^2-2(3)-15=-12 \\ \text{When x=4} \\ y=(4)^2-2(4)-15=-7 \\ \text{When x=5} \\ y=(5)^2-2(5)-15=0 \\ \text{When x=6} \\ y=(6)^2-2(6)-15=9 \\ \end{gathered}[/tex]In the figure below, m ZIKL = 143° and mZ1 =499, Find m2, M 2 1 2 K
In this case, we have a segment line KM that divides the angle [tex]\begin{gathered} m<\text{JKL}=m<1+m<2 \\ \end{gathered}[/tex]As we know, m[tex]\begin{gathered} m<1+m<2=m<\text{JKL} \\ 49\~+m<2=m<\text{JKL}+m<2=143\~ \end{gathered}[/tex]And subtracting 49 from both sides, we get:
[tex]undefined[/tex]Find the domain of the logarithmic function and then graph the function. y= In (4x - 5) Find the domain of the function.
Domain = ( 5/4 , ∞)
Explanations:The logarithm function is given as:
y = ln (4x - 5)
the domain of the functions is a set of all the values of x that makes the function true (defined)
Note that the natural logarithm of a negative number is undefined. This means that the natural logarithm (ln) is only defined for positive numbers
This means that in y = ln (4x - 5), 4x -5 has to be greater than zero for the function to be defined.
Set 4x - 5 > 0
4x > 5
x > 5 / 4
Therefore, the domain of the function is a set of values greater than 5/4
Domain = ( 5/4 , ∞)What is 4 notes that are important to the concept of. Absolute Value and the Additive
This problem is about absolute value.
Four important notes to remember are:
• Absolute value is the modulus of a number, that is, includes only the number without any signs.
• The absolute value of a number can be positive, when the number is positive, that is
[tex]|x|=x[/tex]• The absolute value can be negative if the number is negative
[tex]|x|=-x[/tex]• The absolute value of zero is zero.
[tex]|0|=0[/tex]There you have it, those are 4 important notes to keep in mind about absolute value.
On the other hand, "the additive" would refer to a wide variety of subjects, so, there's a word missing to complete the question.
To start solving the system, Elena wrote:4x + y = 14x + 8y = 36And then she wrote:4x + y =14x + 8y = 36 --7y=-351. What were Elena's first two moves? What might be possible reasons for those moves?
Looking at the equations after Elena started solving the system, we can see that the second equation is different.
Each coefficient is 4 times greater the old coefficiets. That means equation B was multiplied by 4. She did this step to make both equations have the term 4x.
Then, in the next step, she subtracted the equations. Since both equations have 4x, subtracting the equations would cancel this term, then she can solve the result for y.
Therefore, in this step, she Subtracted the equations, this way she can cancel out the variable x.
find the value of x for which m parallels nthe value of x for which m paralles n is......
If m and n are parallel, then: 4x - 33 = 3x + 8
Soving for x:
4x - 33 = 3x + 8
4x - 3x = 8 + 33 = 41
x = 41
Answer:
41
Do the points on the linehave a constant ratio of they-coordinate to the x-co-ordinate for any point onthe line except the y-inter-cept? Explain your answer.
-2×+5y=-13×+2y=11[tex] - 2 \times + 5y = - 1[/tex]
nealmiyasmith20, this is the solution:
-2× + 5y= -1
3× + 2y= 11
___________
Step 1: Isolating x on the first equation:
-2× + 5y= -1
-2x = - 1 - 5y
Dividing by -2 at both sides:
-2x/-2 = -1/-2 - 5y/-2
x = 1/2 + 5y/2
______________________
Step 2: Substituting x and solving for y on the second equation:
3× + 2y = 11
3 ( 1/2 + 5y/2) + 2y = 11
3/2 + 15y/2 + 2y = 11
19y/2 = 11 -3/2
19y/2 = 19/2
Multiplying by 2/19 at boths sides:
19y/2 *2/19 = 19/2 * 2/19
y = 1
___________________
Step 3: Substituting y and solving for x on the first equation:
-2× + 5y = -1
-2x + 5 * 1 = -1
-2x + 5 = -1
-2x = -1 - 5
-2x = -6
Dividing by -2 at both sides:
-2x/-2 = -6/-2
x = 3
Step 4: Proving that x = 3 and y = 1 are correct on the second equation:
3× + 2y = 11
3 * 3 + 2 * 1 = 11
9 + 2 = 11
11 = 11
We proved that x = 3 and y = 1 are correct
jewel brought home four gallons of milk how many quarts is four gallon
Here, we want to know the number of quarts that are in 4 gallons
Mathematically;
1 quart = 0.25 gallons
This means that ;
4 quarts = 1 gallon
Hence, 4 gallons = 4 * 4 quarts
= 16 quarts
There are 16 quarts in 4 gallons
Please help with the question below (please try to answer in max 10/15 minutes).Jasmine can run 4 5/6 miles in 2/3 of an Hour. How many miles can she run in 1 hour?Simplify completely
Explanation
We are given the following:
[tex]Jasmine\text{ }can\text{ }run\text{ }4\frac{5}{6}\text{ }miles\text{ }in\text{ }\frac{2}{3}\text{ }of\text{ }an\text{ }hour[/tex]We are required to determine how many miles she can run in 1 hour.
This is achieved thus:
[tex]\begin{gathered} 4\frac{5}{6}miles\Rightarrow\frac{2}{3}hour \\ \therefore1hour\Rightarrow4\frac{5}{6}\div\frac{2}{3} \\ =\frac{29}{6}\div\frac{2}{3} \\ =\frac{29}{6}\times\frac{3}{2} \\ =\frac{29}{2}\times\frac{1}{2} \\ =\frac{29}{4} \\ =7\frac{1}{4} \end{gathered}[/tex]Hence, the answer is:
[tex]7\frac{1}{4}\text{ }miles[/tex]Order of operations was it evaluated correctly? 5^(2) + 1^(2) = 6(2) = 36EXPLAIN your reasoning. Thank you
The answer to the operation is as follows:
5^(2) + 1^(2) = 5*5 + 1*1 = 25 + 1 = 26.
Here, we have to remember PEMDAS. First, we solve parentheses, then exponents (or exponentiation operations); then, multiplications, divisions, and, after all this, addition and subtractions.
In the above operation, we solve first the raising of 5 to 2, then 1 raised to 2. We sum the result of both operations. So the value of 36 is not correct. The correct value is 26.
n Studies / 22FYF013/ Chapter 2: Statistics STACK statistics pr
The numbers of days work missed by 20 workers in one year (ordered by size) we
[0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 8, 55]
Calculate the mean and median. Enter your answers to 1 d.p.
Mean =
Median =
Please answer all parts of the question
The mean and median of the given data set are 5.55 and 4.
What are the mean and median?A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint. Identifying the median The data points should be arranged from smallest to largest. The median is the middle data point in the list if the number of data points is odd. The median is the average of the two middle data points in the list if the number of data points is even.So, the data is:
[0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 8, 55](A) Mean of data:
Sum of all terms/number of terms111/205.55(B) Median of data:
The data set has even terms.Average of two middle terms:4 + 4 / 28/24Therefore, the mean and median of the given data set are 5.55 and 4.
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Suppose you deposited $13000 in a saving account in which interest is compounded continuously. It takes 14 years to double your money in this account.(1) What is the annual rate of interest? (Round your answer to one decimal place.) % Tries 0/99(2) How much will you have in this account after 26 years? (Round your answer to two decimal places.) dollars Tries 0/99
Remember that
The formula to calculate continuously compounded interest is equal to
[tex]A=P\left(e\right)^{\left\{rt\right\}}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is the Number of Time Periods
e is the mathematical constant number
In this problem, we have that
Part 1
P=$13,000
A=$26,000
t=14 years
substitute given values
[tex]\begin{gathered} 26,000=13,000\left(e\right)^{\left\{14r\right\}} \\ solve\text{ for r} \\ 2=e^{14r} \\ apply\text{ ln on both sides} \\ ln(2)=lne^{14r} \\ ln(2)=14r \\ r=\frac{ln(2)}{14} \\ \\ r=0.0495 \\ r=4.95\% \\ r=5\% \end{gathered}[/tex]Part 2
we have
P=$13,000
r=5%=0.05
t=26 years
substitute in the formula
[tex]\begin{gathered} A=13,000(e)^{\operatorname{\{}0.05*26\operatorname{\}}} \\ A=\$47,700.86 \end{gathered}[/tex]A recipe book shows measurement conversions for pints to cups. It shows that 1.5 pints equals 3 cups and 2.5 pints equals 5 cups.
Write an equation that shows the proportional relationship between pints and cups where p represents pints and n represents cups.
p equals 3 over 1.5 times n
n equals 1.5 over 3 times p
p = 0.5n
n = 0.5p
The equation that shows the proportional relationship between pints and cups where p represents pints and n represents cups is p = 0.5n
How to calculate the value?From the information, the recipe book shows measurement conversions for pints to cups. It shows that 1.5 pints equals 3 cups and 2.5 pints equals 5 cups.
p = pints
n = cups.
Therefore, the equation will be illustrated as
1.5 = 3k
where k = constant of proportionality
Divide
k = 1.5/3
k = 0.5
Therefore, the equation is p = 0.5n.
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Terrance says that (5, 4) is a point on the line of y-4=1/2(x-5). He says it’s impossible to find another point on the line because the equation is in point-slope form. Explain Terrance’s error.
Terrance’s error is that he limits the solution of the equation to one ordered pair
How to determine the error in Terrance’s claim?The equation is given as
y - 4 = 1/2(x - 5)
The solution is given as
(5, 4)
The above solution is true
This is so because; when x = 5, the value of y is 4
i.e.
y - 4 = 1/2(5 - 5)
y - 4 = 0
y = 4
Next, we set x to another value (say x = 9)
So, we have
y - 4 = 1/2(5 - 9)
y - 4 = -2
y = 6
This means that the equation can have another solution
In this case, it is (9, 6)
Hence, one ordered pair cannot be the solution to the equation
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Simplify.
(4.17x−1.32)+(−7.6x+3.54)
Responses
−3.43x+2.22
negatvie 3.43 x plus 2.22
7.71x−8.92
7.71 x minus 8.92
11.77x + 4.86
11.77, x, + 4.86
2.85x−4.06
The value of the expression (4.17x−1.32)+(−7.6x+3.54) is A. −3.43x+2.22 or negatvie 3.43 x plus 2.22
What are expressions?Expressions are used in Mathematics to illustrate the relationship between the variables.
The expression is given as:
(4.17x−1.32)+(−7.6x+3.54)
Open the parentheses and collect like terms
4.17x - 7.6x - 1.32 + 3.54
-3.43x + 2.22
Therefore, the correct option is A.
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Which expression is equivalent to 5 + 9z+ 6 + 4z?
Answer: 13z + 11
Step-by-step explanation:
5 + 9z + 6 + 4z
a) Add.
5 + 6 = 11
b) Combine like terms.
9z + 4z = 13z
11 + 13z
c) Reorder.
13z + 11
Fencing costs $25.80 per yard. How much does it cost to enclose two adjacent rectangular pastures as shown?
In the metric system, 1 gran is the mass of 1 milliliter of water. So, a 2-liter bottle of water has a mass of 2 kilograms. A gallon of water weighs about 8 pounds. What is the mass of a gallon of water to the nearest tenth of a kilogram?Parts A-D
We know that:
[tex]1\text{ lb }\to0.45\text{ kg}[/tex]A)
Using the conversion law, we can calculate the conversion factor as a fraction:
[tex]\frac{0.45\text{ kg}}{1\text{ lb}}=\frac{9\text{ kg}}{20\text{ lb}}[/tex]B)
Now, we multiplicate 8 pounds by the conversion factor:
[tex]\frac{9\text{ kg}}{20\text{ lb}}\cdot8\text{ lb }\approx3.6\text{ kg}[/tex]C)
The pound units cancel, resulting in an answer given in kilograms.
D)
When you choose a conversion factor, the unit you are converting to is the first quantity in the rate.
