Answers
Hello !
56)
[tex]5 {x}^{2} + 8x = - 1 \\ 5 {x}^{2} + 8x + 1 = 0[/tex]
[tex]\Delta = {b}^{2} - 4ac \\ = {8}^{2} - 4 \times 5 \times 1 \\ = 64 - 20 \\ = 44[/tex]
The value of the discriminant is 44.
57) ∆>0 : there are two solutions.
58)
[tex]x_1 = \frac{ - b + \sqrt{\Delta} }{2a} \\ = \frac{ - 8 + \sqrt{44} }{2 \times 5} \\ = \frac{ \sqrt{11} - 4 }{5} [/tex]
[tex] x_2 = \frac{ - b - \sqrt{\Delta} }{2a} \\ = \frac{ - 8 - \sqrt{44} }{2 \times 5} \\ = \frac{ - \sqrt{11} - 4 }{5} [/tex]
Have a nice day
56. 44
57. 2
58. Image attached.
First, let's simplify some things. Let's make this a quadratic equation.
Moving the -1 (by adding 1 to both sides) gives us 5x^2 + 8x + 1 = 0. Note that this is the standard form of a quadratic, which is ax^2 + bx + c = 0.
Now, the discriminant. The discriminant is helpful because it tells us if we have 2 real solutions, 1 real solution, or if this equation is imaginary and thus impossible to solve using elementary techniques. If the discriminant is greater (>) than 0, then it has 2 solutions. If the discriminant equals (=) 0, it has 1 solution. If the discriminant is less than (<) 0, then it is imaginary.
The discriminant of a quadratic equation is defined as b^2 - 4ac (from the quadratic formula.) We just plug in b, a and c. b will be 8, a will be 5, and c will be 1. Now we just solve. (8)^2 - 4 * 5 * 1 = 64 - 20 = 44. Since 44 is greater than 0, we have 2 solutions for this. 44 is the discriminant. (Answer to 56.) We also have 2 solutions (answer to 57.)
Now, I'll solve the quadratic equation using the quadratic formula. I'll attach my work in an image (answer to 58.)
Hope this helped!
Related Questions
-3x + 2y = 9
x - 3y = 4
Answers
Answer:
(-5, -3)
Step-by-step explanation:
Isolate x:
x - 3y = 4
x = 3y + 4
Substitute to get y:
-3x + 2y = 9
-3(3y + 4) + 2y = 9
-9y - 12 + 2y = 9
-7y = 21
y = -3
Substitute to get x:
x = 3y + 4
= 3(-3) + 4
-9 + 4
= -5
NEED HELP ASAP
there should be a picture giving you info
Answers
Answer:
to find this radius you need to square the area and divide it by pi or 3.14 if your using Alex
A local hospital currently has 184 male patients. If the ratio of male to female patients is 4:3, how many female patients are there in the hospital?
Answers
There are 138 female patients in the hospital.
Solving word problems involving ratios.The solution to the word problem involving ratios in the given problem can be determined as follows.
From the given information:
The total number of people in the hospital = male + female
= 184 + x(unknown)
If the ratio of male to female is 4: 3. The total ratio is 4+3 = 7The ratio of males in the hospital is:
[tex]\mathbf{184= \dfrac{4}{7} \times x }[/tex]
[tex]\mathbf{184\times 7= 4 x }[/tex]
x = 322
The number of female patients in the hospital can now be computed as:
[tex]\mathbf{=\dfrac{3}{7}\times 322}[/tex]
= 138 female patients
Check:
The total number of people in the hospital is:
= 184 + 138
= 322 patients
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Find the range of the function f(n) = n² - 2n for the domain (1, 3, 5).
Range:
Answers
Answer: {-1, 3, 15}
Step-by-step explanation:
[tex]f(1)=-1\\\\f(3)=3\\\\f(5)=15[/tex]
So, the range is {-1, 3, 15}.
A company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. The cost of labor to manufacture a mountain bike is $90, and the cost of labor to manufacture a trail bike is $30. During a week in which the company has budgeted $1,600 for materials and $2,700 for labor, how many mountain bikes does the company plan to manufacture?
Answers
An equation is formed when two equal expressions. The company is planning to produce 25 mountain bikes and 15 trail bikes.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of mountain bikes produced by the company be x, while the number of trail bikes produced by the company is y.
The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. Also, the budget of the company is $1,600. Therefore,
1600 = 40x + 40y
x + y = 40
y = 40-x
The cost of labour to manufacture a mountain bike is $90, and the cost of labour to manufacture a trail bike is $30. Also, the budget for labour is $2,700.
2700 = 90x + 30y
2700 = 90x + 30(40-x)
2700 = 90x + 1200 - 30x
1500 = 60x
x = 25
Substitute the value of x,
y = 40 - x
y = 15
Hence, the company is planning to produce 25 mountain bikes and 15 trail bikes.
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Nadia says the hypotenuse of this right triangle has a length of 73 because the pythagorean theorem states that (28 45) squared = 73 squared. 3 squares are positioned to form a right triangle. the small square is labeled 28, medium square is 45, and large square is not labeled. which best describes nadia’s solution?
Answers
Both the options that Nadia gives are wrong about the length of hypotenuse.
Given length of hypotenuse is 73 and options which are :
1) Because the pythagoras theorem states that [tex]28^{2} +45^{2}[/tex] squared = 73 squared.
2) 3 squares are positioned to form a right triangle.
We have to choose the correct option which shows the calculation of length of hypotenuse.
Pythagoras theorem says that in a right angled triangle the square of hypotenuse of triangle is equal to sum of the square of base and square of perpendicular.
[tex]H^{2} =P^{2} +B^{2}[/tex]
First option says that [tex]28^{2} +45^{2} =73^{2}[/tex]
784+2025=5329
2809≠5329
so it is wrong.
Second option says that the length of hypotenuse is the sum of three squares but we have seen that the square of the length of hypotenuse is equal to sum of two square one is the square of base and the square of perpendicular.
Hence both the options are incorrect about the length of hypotenuse.
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Answer:
C
Step-by-step explanation:
A high school baseball player has a 0.229 batting average. in one game, he gets 5 at bat. what is the probability he will get at least 2 hits in the game? round your answer to four places.
Answers
The probability he will get at least 2 hits in the game is 0.470
GivenThe batting average is 0.229
In one game he gets 5 at bat
To find the probability he will get at least 2 hits we use binomial distribution.
What is Binomial distribution?The binomial distribution is also a Frequency distribution used for the possible no. of successful outcomes in a given no. of trials in each of which there is the same probability of success.
So we have
n = 5
p = 0.299
q = 1 - p
= 0.701
[tex]P(X) = nC_{x} p^x q^(n-x)[/tex]
P(at least 2 hits in the game) = 1 - P(less than 2 hits)
= 1 - P(0) - P(1)
[tex]= 1 - 0.701^5 - 5C1 x 0.299 x 0.701^4[/tex]
= 1 - 0.169 - 0.361
= 0.470
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This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the
candy bar. If AD = 2.5 cm, what is the smallest diameter of wrapper that will fit the candy bar?
Answers
TheThe smallest diameter of wrapper that will fit the candy bar is 5cm.
Smallest diameterGiven:
AD = DC
AC = AD + DC
Segment AD = 2.5cm
Hence:
AC = AD + AD (AD = DC)
AC = 2AD
Where:
AD=2.5
So,
AC = 2(2.5cm)
AC = 5cm
Therefore the smallest diameter of wrapper that will fit the candy bar is 5cm.
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Answer: 5cm.
Step-by-step explanation:
MD writes an order for Lortab Elixir 5mg by mouth as needed for pain every 4 hours. Pharmacy dispenses you with 7.5mg/15ml. How many tablespoons will you administer per dose?
Answers
Following the prescription, You will need to administer a 0.7 tablespoon per dose.
Determining the number of tablespoons by using equivalent expressions?We can determine the number of tablespoons that are administered by using equivalent expressions.
From the standard conversion rate, we know that:
1 ml = 0.067628 tbsp15 ml = 1.01442 tbspUsing equivalent expressions:
7.5 mg/1.01442 tbsp = 5 mg/x tbsp
x = (1.01442 × 5)/7.5 tbsp
x = 0.67 tbsp
x = 0.7 tbsp per dose.
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A metallurgist has one alloy containing 45% copper and another containing 69% copper. How many pounds of each alloy must be use to make 42 pounds of a third alloy containing 66% copper
Answers
5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the amount of 45% copper and y represent the amount of 66% copper needed to make 42 pounds of a third alloy containing 66% copper. Hence:
x + y = 42 (1)
Also:
0.45x + 0.69y = 42(0.66) (2)
This gives:
x = 5.25, y = 36.75
5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper
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Graph the line that passes through the two points. Then find the slope of the line. (2,9), (4, 18)
Answers
The slope of the line is 4.5
How to determine the slope?The points are given as:
(2,9) and (4, 18)
The slope (m) is calculated using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (18 - 9)/(4 -2)
Evaluate
m = 4.5
Hence, the slope of the line is 4.5
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What is the value of g(f(x)) when x=-2 if f(x)=x3
Answers
Answer:
The answer would be A: -15
At Hinsdale College, students are employed by the college library to re-shelve books.
The students claim that a 15-minute coffee break every hour would relive boredom and
increase the average number of books re-shelved per hour. To test the student's claim,
the following data were gathered on a random sample of seven student employees.
Over a period of one week, each student worked a normal schedule without coffee
breaks. Then, during the next week, the students were allowed coffee breaks.
Unknown to the students, a member of the library staff secretly recorded the average
number of books shelved per hour and computed the averages with and without the
coffee break system. The results are below. Test the claim that the students shelve
more books when they have a coffee break, use a 0.05 level of significance.
Student 1 2 3 4 5 6 7
Without
Coffee
breaks
75 63 82 53 79 96 73
With
Coffee
Breaks
90 72 95 50 85 110 89
Answers
The p value is less, therefore one should reject the null hypothesis.
How to illustrate the information?From the information given, the test statistic will be:
t = (10 - 0)/(6.733/✓7)
t = 3.930.
The degree of freedom will be:
= 7 - 1 = 6
Using the table, the p value will be 0.0039.
Since the p value is less than 0.05 one should reject the null hypothesis.
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f(x)=3√x + 7. Find the inverse of f(x).
Answers
step 1- switch x and y
step 2- isolate y, and get to (x-7)/3=sqrty
step 3- square each side to get rid of the square root and isolate y
step 4- f(x)=(x^2-14x+49)/9
Answer:
[tex]f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=3\sqrt{x}+7[/tex]
To find the inverse of the function
Swap f(x) for y:
[tex]\implies y=3 \sqrt{x}+7[/tex]
Subtract 7 from both sides:
[tex]\implies y-7=3 \sqrt{x}+7-7[/tex]
[tex]\implies y-7=3\sqrt{x}[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3\sqrt{x}}{3}=\dfrac{y-7}{3}[/tex]
[tex]\implies \sqrt{x}=\dfrac{y-7}{3}[/tex]
Square both sides:
[tex]\implies \left(\sqrt{x}\right)^2=\left(\dfrac{y-7}{3}\right)^2[/tex]
[tex]\implies x=\left(\dfrac{y-7}{3}\right)^2[/tex]
Swap the x for [tex]f^{-1}(x)[/tex] and y for x:
[tex]\implies f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]
5. Lucinda is a babysitter. Her hourly rate is $5.00. fin one week, she baby sat 13 hours and
received tips of $14.50. How much did she earn?
Answers
$65 + $14.50 = $79.50
I’m so confused please help
Answers
Answer:
976cm squared
Step-by-step explanation:
that's all I could do .hope it helps. in case of any questions please ask.
The Robinsons family drove for 4000 miles. This was the
distance the Jones family drove. How many miles did the Jones
family drive?
Answers
Answer:1333.3 Contiuous
Step-by-step explanation:
.
4000/3,=1333.3x1,=1333.3
I'm not sure
Solve the quadratic equation by using the quadratic formula. If the solutions are not real, enter NA.
2x2−7x+1=0
Enter the exact answers.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter.
Enclose numerators and denominators in parentheses. Remember that (a−b)/1+n is not the same as (a−b)/(1+n) .
Answers
By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.
How to find the roots of quadratic equation by quadratic formula
For polynomials of the form a · x² + b · x + c = 0, the two roots can be found analytically by quadratic formula, whose expression is described below:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
If we know that a = 2, b = - 7 and c = 1, then the roots of the polynomial are:
x = 7/4 ± (1/4) · √41
x = (7 ± √41) / 4
By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.
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factor equation step by step.
Answers
Answer:
no solution
Step-by-step explanation:
use grouping method:
f(x) = x^2 - 4x + 2
factor it:
when we try to factor the above equation, we see that there is no ordered pair in which the numbers multiple to -4 and add to 2, so there is no solution
14 ) Mark Achin sells 3,600 electric motors each year . The cost of these is $ 200 each , and demand is constant throughout the year . The cost of placing an order is $ 40 , while the holding cost is $ 20 per unit per year . There are 360 working days per year and the lead - time is 5 days . What is his economic order quantity in units ? A ) 100 B ) 200 C ) 60 D 120
Answers
Mark Achin's economic order quantity in units is D. 120 units.
What is economic order quantity?The economic order quantity (EOQ) is the optimal order quantity that minimizes the total costs (ordering, receiving, and holding inventory).
The formula for the economic order quantity is the square root of [2(setup costs)(demand rate)] / holding costs.
Data and Calculations:Annual demand = 3,600
Cost price per unit = $200
Ordering cost = $40
Holding cost per unit = $20
Working days per year = 360
Lead time = 5 days
Economic order quantity (EOQ) = square root of: [2(setup costs)(demand rate)] / holding costs.
= square root of (2 x $40 x 3,600)/$20
= 120
Thus, Mark Achin's economic order quantity in units is D. 120 units.
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put the events in order of what is most likely to happen, to least likely to happen. If you were to win a million dollars for winning one of these events, which would you pick to play? Use probability to explain your answers
Answers
Answer:
no man you should reconsider the question again
try typing again i guess its wrong
Step-by-step explanation:
no man you should reconsider the question again
try typing again i guess its wrong
winning a lottery would be correct one i guess
which shows a correct step in using substitution to slove the system of equation y=2x-1 4x+y=2
Answers
The solution using correct step of substitution in the equation y=2x-1 4x+y=2 is x = 1/2 and y = 0
Simultaneous equationy = 2x - 1
4x + y = 2
Substitute the value of y in equation (1) into (2)4x + y = 2
4x + (2x - 1) = 2
4x + 2x - 1 = 2
6x - 1 = 2
6x = 2 + 1
6x = 3
x = 3/6
x = 1/2
substitute the value of x into equation (1)y = 2x - 1
y = 2(1/2) - 1
= 2/2 - 1
= 1 - 1
y = 0
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Factor by Grouping.
25x^2-20x-12
Answers
Answer:
ac = -300-20 = -30 +10(5x +2)(5x +(-6))Step-by-step explanation:
The sequence of required answers provides a step-by-step solution to the problem.
Factors of acIn the given trinomial, we identify the coefficients as ...
ax² +bx +c = 25x² -20x -12 ⇒ a=25; b=-20; c=-12
Then the ac product is ...
ac = (25)(-12) = -300
The factor pairs that make this product can be listed as ...
-300 = (-300)(1) = (-150)(2) = (-100)(3) = (-75)(4) = (-60)(5) = (-50)(6) = (-30)(10) = (-25)(12) = (-20)(15) . . . . (only pairs with a negative sum are listed)
The sums of these pairs are -299, -148, -97, -71, -55, -44, -20, -13, -5.
The factors of the ac product that add to -20 are -30 and 10.
Factor by groupingThese factors are used to rewrite the -20x term as a sum.
25x² -20x -12 = 25x² -30x +10x -12
Grouping these terms in pairs, we can identify common factors:
= (25x² -30x) +(10x -12)
= 5x(5x -6) +2(5x -6)
= (5x +2)(5x +(-6))
Perform the operation and simplify
Answers
Answer:
[tex]\frac{(x-2)(x+4)}{x+2}[/tex]
Step-by-step explanation:
[tex]\frac{(x+4)^2}{x+2} :\frac{(x+2)(x+4)}{(x+2)(x-2)} =\frac{(x+4)^2(x+2)(x-2)}{(x+2)(x+2)(x+4)}=\frac{(x-2)(x+4)}{x+2} .[/tex]
If 3 times a certain number is increased by 4 the result is 28. What is the number?
If x is "the number," which of the following equations could be used to solve for the number?
3 x + 4 = 28
3 x = 4 + 28
3( x + 4) = 28
Answers
Answer:3x+4=28
Step-by-step explanation:
the second one would equal 3x=32
And the third one would equal 3x+12=28 which isn’t right either
M=−8r
2
+11r−6
T=−7r
2
−9r+14
M
+
T
=
M+T=M, plus, T, equals
Your answer should be a polynomial in standard form.
Answers
M + T in standard form polynomial is -15r² + 2r + 8
How to represent polynomial in standard form?Polynomial in standard is when all its terms are arranged by decreasing order of degree.
Therefore,
M = - 8r²+ 11r - 6
T = -7r² - 9r + 14
M + T = - 8r²+ 11r - 6 + (-7r² - 9r + 14)
M + T = - 8r²+ 11r - 6 - 7r² - 9r + 14
combine like terms
M + T = - 8r² - 7r² + 11r - 9r - 6 + 14
In standard form, the polynomial is represented as follows;
M + T = -15r² + 2r + 8
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3. Which graph represents the solution to 13k-21> 7?
Answers
Answer: Option (2)
Step-by-step explanation:
[tex]|3k-2| > 7[/tex] means [tex]3k-2 < -7[/tex] or [tex]3k-2 > 7[/tex].
Solving each of these cases gives [tex]k < -\frac{5}{3}[/tex] or [tex]k > 3[/tex].
So, the answer is Option (2).
What is addition and subtraction
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{What is addition \& subtraction?}[/tex]
[tex]\huge\textbf{What is addition?}[/tex]
[tex]\bullet\large\textbf{ Well, \underline{addition} simply means when you're ADDING}\\\large\textbf{2 or more numbers from each other to get the result of}\\\large\textbf{a number.}[/tex]
[tex]\huge\textbf{Random notes}[/tex]
[tex]\star\large\textbf{ Usually, you start working with addition when you're in}\\\large\textbf{pre-kindergarten (pre-k also known as head-start)}\\\\\star\large\textbf{ When, you're adding you are going upward.}\\\\\star\large\textbf{ Addition sometimes come after you learn how to count}\\\large\textbf{the basic numbers and so forth because adding never}\\\large\textbf{ends if you really think about.}[/tex]
[tex]\huge\textbf{Example:}[/tex]
[tex]\heartsuit\large\textbf{ 2 \boxed{\bf +} 5 = 7}\\\\\\\heartsuit\large\textbf{ You got the result of 7 because you started at 2 \& went}\\\larg\textbf{up 5 spaces to your right on your number and you landed}\\\large\textbf{on 7.}[/tex]
[tex]\huge\textbf{What is subtraction?}[/tex]
[tex]\bullet\large\textbf{ Well, subtraction simply means you're taking away. Often}\\\large\textbf{people call it take aways.}[/tex]
[tex]\huge\textbf{Random notes:}[/tex]
[tex]\star\large\textbf{ Usually, you start working with subtraction when you're}\\\large\textbf{in pre-kindergarten (pre-k also known as headstart)}\\\\\star\large\textbf{When you're subtracting you are doing downward.}\\\\\star\large\textbf{You focus more on subtraction when you're counting}\\\large\textbf{backwards.}[/tex]
[tex]\huge\textbf{Example:}[/tex]
[tex]\heartsuit\large\textbf{ 7 \boxed{\bf -} 5 = 2 }\\\\\\\heartsuit\large\textbf{ 7 \boxed{\bf -} 2 = 5}\\\\\\\heartsuit\large\textbf{ For equation \#1. you begin at 7 and go BACK 5 spaces}\\\large\textbf{and you should have landed on 2.}\\\\\\\heartsuit\large\textbf{ For equation \#2. you begin at 7 \& go BACK 2 spaces}\\\large\textbf{and you should have landed on 5.}[/tex]
[tex]\huge\textsf{KEEP IN MIND:}[/tex]
[tex]\circ\large\textsf{ Addition OPPOSITE is subtraction \& subtraction OPPOSITE is}\\\large\textsf{addition.}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitirite1040:)}[/tex]
What is the following quotient?
2
√13+√11
O√13-2√11
√13+√11
6
O
113 + √11
12
O
● √13 - √11
Answers
[tex]\frac{2}{\sqrt{13}+\sqrt{11}} \times \frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\\\=\frac{2\sqrt{13}-2\sqrt{11}}{13-11}\\\\=\boxed{\sqrt{13}-\sqrt{11}}[/tex]
The solution is: our final quotient is: (√13 - √11).
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Explanation
Since we have radicals in the denominator, we need to rationalize our expression.
To do it we just need to multiply both numerator and denominator by the conjugate of the denominator.
Remember that the conjugate of a binomial is the same binomial with the sing in between changed.
given that,
2/ (√13 + √11)
Now, we can simplify the denominator:
multiplying by (√13 - √11)
we get,
2 * (√13 - √11) / (√13 + √11)* (√13 - √11)
The only radical that we can simplify in the numerator is , which simplifies to:
2 (√13 - √11) / 13 - 11
= 2(√13 - √11) /2
= (√13 - √11)
So, our final quotient is: (√13 - √11)
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which statement is true about finding the midpoint between two points located on a horizontal or vertical line ?
A . When finding the midpoint between two points on a vertical line, keep the y-coordinate and find the average of the x-coordinate
B . When finding the midpoint between two points on vertical line, keep x-coordinate and find the average of the y-coordinates
C . When finding the midpoint between two points on a horizontal line, the x-coordinate is always 0 and the y-coordinates are averaged
D. When finding the midpoint between two points on a horizontal line , the y-coordinate is always zero and the x-coordinates are averaged
Answers
Answer: B. When finding the midpoint between two points on a vertical line, keep the x-coordinate and find the average of the y-coordinates