Write a quadratic equation with 7 and 2/5 as its roots. Write the equation in the form ax2 + bx+c= 0, where a, b, and c are integers.
Answers
As given by the question
There are given that the roots: 7 and 2/5.
Now,
Since the roots are integers, we can write the equation in the given form using a = 1.
Then,
b is the opposite of the sum of the roots
So,
[tex]\begin{gathered} b=-((7)+(\frac{2}{5})) \\ b=-(\frac{35+2}{5}) \\ b=-\frac{37}{5} \end{gathered}[/tex]And
c is the products of the roots
So,
[tex]\begin{gathered} c=7\times\frac{2}{5} \\ c=\frac{14}{5} \end{gathered}[/tex]Now,
The desired quadratic equation is:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x^2-\frac{37}{5}x+\frac{14}{5}=0 \\ 5x^2-37x+14=0 \end{gathered}[/tex]Hence, the correct option is A.
Related Questions
How do you multiply 6x 1 1/3?
Answers
To multiply a mixed number, first, we have to convert it into a fraction as follows:
[tex]1\frac{1}{3}=\frac{1\cdot3+1}{3}=\frac{4}{3}[/tex]Now, we need to multiply 6 by 4/3, as follows:
[tex]6\cdot1\frac{1}{3}=6\cdot\frac{4}{3}=\frac{6\cdot4}{3}=\frac{24}{3}=8[/tex]Which function could represent the height in feet, h, of a soccer ball t seconds after being kicked from an initial height of 1 foot?
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Let h is the height of the ball after t seconds
The acceleration upward = -32 feet/sec.^2
This situation must be represented by a quadratic function
The form of the function is:
[tex]h=ut+\frac{1}{2}at^2+h_0[/tex]u is the initial velocity
a is the acceleration of gravity
t is the time
h0 is the initial height
From the given, the initial height is 1 foot
The acceleration of gravity is a constant value -32 ft/s^2
The initial velocity is unknown
Let us substitute the values given in the function
[tex]\begin{gathered} h=ut+\frac{1}{2}(-32)t^2+1 \\ h=ut-16t^2+1 \end{gathered}[/tex]Let us arrange the terms from greatest power of t
[tex]h=-16t^2+ut+1[/tex]We have only 1 function in the choices similar to our function
[tex]h=-16t^2+25t+1[/tex]The answer is the second choice
The price of hamburger increased from .50 cent to .60 cent. What is the percent increase
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The hamburguer was .50 cent and increased to 0.60 cent. Let's calculate the percent increase:
The percent increase may be calculated using the formula:
percent increase = [(final value - initial value)/initial value]*100
So:
[tex]\begin{gathered} \frac{0.6-0.5}{0.5}\cdot100= \\ \frac{0.1}{0.5}\cdot100= \\ 0.2\cdot100=20 \end{gathered}[/tex]So, the percent increase was 20%
Determine the degree of the polynomial 2w with exponent of 2+ 2w:
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The degree of the polynomial is 2, because the degree of a polynomial is defined as the same as the greater exponent on the polynomial.
In this case, w² is the greater, then the degree is 2.
convert the following into a decimal you must include the decimal in your answer and round to the nearest thousands)3/8
Answers
3/8 = 0.375
Explanations:The given fraction is 3/8
Using the long division method to convert 3/8 to decimal
Therefore, 3/8 = 0.375
(X^2+8x+12)/(x+2) que
Answers
Given:
[tex]\frac{x^2+8x+12}{x+2}[/tex]Let's divide the polynomials.
To divide, let's factorize the polynomial in the numerator.
Factorize using the AC method.
Find a pair of numbers whose product is 12 and whose sum is 8.
Thus, we have the numbers:
2 and 6
The factors of the polynomial in the numerator are:
(x+2) and (x+6)
We have:
[tex]\frac{(x+2)(x+6)}{x+2}[/tex]Now, cancel the common factors:
Therefore, the quotient after dividing the polynomials is = x + 6
ANSWER:
[tex]x+6[/tex]Which equation represents a circle centered at (3.5) and passing through the point (-2.91?OA (+3)2 + (y + 5)² = 17OB. (-3)²+(y-5)² = 17OC. (x+3)²+(y+ 5)² = 41OD. (-3)2 + (y-5)² = 41ResetNext
Answers
ANSWER
[tex](x-3)^2+(y-5)^2=41[/tex]EXPLANATION
Given;
[tex]\begin{gathered} center=(3,5) \\ points=(-2,9) \end{gathered}[/tex][tex]\begin{gathered} (x-a)^2+(y-b)^2=(r)^2 \\ (x-3)^2+(y-5)^2=(\sqrt{41})^2 \\ \end{gathered}[/tex]using trig to find a side
Answers
we have that
tan(16)=NO/OM -------> by opposite side divided by the hypotenuse
solve for NO
NO=OM*tan(16)
x=16*tan(16)
x=4.6 ftThe net of a rectangular prism is shown below. The surface area of each is labeled
Answers
Given:
Area of box I = 48 cm²
Area of box 2 = 24 cm²
Area of box 3 = 48 cm²
Area of box 4 = 24 cm²
Area of box 5 = 72 cm²
Area of box 6 = 72 cm²
• Let's find the values which represent the dimensions of the prism.
Let L represent the length.
Let w represent the width
Let h represent the height.
Now, to find the surface area of a rectangular prism apply the formula:
A = 2(wL + Lh + wh)
Now, given each rectangular face, we have:
Area of length and width, Lw = 72 cm²
Area of length and height, Lh = 48 cm²
Area of width and height, wh = 24 cm²
Now to find the dimensions, we have:
[tex]\begin{gathered} \frac{Lh}{wh}=\frac{48}{24} \\ \\ \frac{L}{w}=2 \\ \\ L=2w \end{gathered}[/tex]Now, substitute 2w for L in Lw:
[tex]\begin{gathered} Lw=72 \\ \\ 2w(w)=72 \\ \\ 2w^2=72 \\ \\ w^2=\frac{72}{2} \\ \\ w^2=36 \\ \\ \text{ take the square root of both sides:} \\ \sqrt{w^2}=\sqrt{36} \\ \\ w=6 \end{gathered}[/tex]Therefore, the width is 6 cm.
Now, substitute 6 for w in wh:
[tex]\begin{gathered} wh=24 \\ \\ 6*h=24 \\ \\ Divide\text{ both terms by:} \\ \frac{6*h}{6}=\frac{24}{6} \\ \\ h=4 \end{gathered}[/tex]Now, substitute 4 for h in Lh:
[tex]\begin{gathered} Lh=48 \\ \\ L*4=48 \\ \\ \text{ Divide both sides by 4:} \\ \frac{L*4}{4}=\frac{48}{4} \\ \\ L=12 \end{gathered}[/tex]Therefore, the values which represent the dimensions are:
4, 6, 12
ANSWER:
4, 6, 12
Name all the sets of numbers to which real number belongs: 6.5
Answers
Given the number 6.5
The number belongs to:
1) Rational Numbers because it can be written as a/b
Pls look at Question and answer pls If it’s a compound then you will need to choose if it’s conjunctional, disjunction, conditional, or biconditional
Answers
Three statements are given. It is required to determine if the statements are simple or compound, and if it's compound, it is required to choose which type.
Recall that a simple statement is a statement containing no connectives like 'or', 'and', and so on.
Recall also that a compound statement is a combination of two or more simple statements which are joined by connectives.
Compound statements joined by 'or' are called disjunctions, while those joined by 'and' are called conjunctions.
Compound statements with 'if-then' are called conditional, while the ones with 'if and only if' are called biconditional.
a) The first statement is: My cousins each have some sort of engineering degree.
Since the statement is not joined by any connectives, it is a simple statement.
b) The second statement is: My eyes are bad or this print is tiny.
Since it is a combination of two simple statements joined by the connective 'or', then, it is a compound statement, which is a disjunction.
c) The third statement is: The cat will come to you if and only if you set well.
Since it is a combination of two simple statements joined by the connective 'if and only if ', it follows that it is a compound statement and it is a biconditional.
You travel 5 hours and 50 minutes. If you drove at an average of 41 mph, how much distance you traveled?
Answers
First, let's convert those 50 minutes into hours:
This way,
[tex]x=\frac{50\cdot1}{60}\Rightarrow x=0.83[/tex]I would have driven for 5.83 hours.
Using this, and the average pace (46 miles in one hour),
We get that:
[tex]x=\frac{46\cdot5.83}{1}\Rightarrow x=268.18[/tex]I would have traveled 268.18 miles
A Use the information given to answer the question. A student works at a job in order to save money to buy a desktop computer. • The student works 80 hours each month. • The desktop computer costs $850. Part B If the student has already saved $150 and plans to save an additional $100 each week, the function g(w) = 100w + 150 represents the total amount of money, in dollars, saved after w weeks. What is the value of g(5)?
Answers
The function given is:
[tex]g\mleft(w\mright)=100w+150[/tex]Where
w represents the week
g(w) represents the total money
We want to fing g(5).
This means, put "5" into the function g.
Put "5" in place of "w" in the function g.
Shown below:
[tex]\begin{gathered} g(w)=100w+150 \\ g(5)=100(5)+150 \\ g(5)=500+150 \\ g(5)=650 \end{gathered}[/tex]When graphing an inequality in slope-intercept form, which of the folowing indicates that you have to shade ABOVE the boundary line? Select ALL that apply.
Answers
Explanation
When graphing an inequality in slope-intercept form, we are asked to find which of the folowing indicates that you have to shade ABOVE the boundary line. This can be seen below.
The symbols
[tex]>\text{ and }\ge[/tex]Indicates that one should shade above the boundary line, The only difference is that the boundary line is broken in the case of greater than and unbroken in the case of greater than or equal to.
Answer:
[tex]>\text{ and }\ge[/tex]
Sketch the right triangle and find the length of the side not given if necessary approximate the light to the nearest thousandth
Answers
Let's take a look at our triangle:
Using the pythagorean theorem, we'll have that:
[tex]h^2=12^2+16^2[/tex]Solving for h,
[tex]\begin{gathered} h^2=12^2+16^2 \\ \rightarrow h=\sqrt[]{12^2+16^2} \\ \rightarrow h=\sqrt[]{400} \\ \\ \Rightarrow h=20 \end{gathered}[/tex]This way, we can conlcude that the missing side measures 20 units.
Can someone please help me solve the following?Please put numbers on graph
Answers
Given:
The equation of the hyperbola is given as,
[tex]\frac{y^2}{25}-\frac{x^2}{4}=1........(1)^{}[/tex]The objective is to graph the equation of the hyperbola.
Explanation:
The general equation of hyperbola open in the vertical axis of up and down is,
[tex]\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1\text{ . . . . . . . .(2)}[/tex]Here, (h,k) represents the center of the hyperbola.
The focal length can be calculated as,
[tex]c=\sqrt[]{a^2+b^2}\text{ . . . . (3)}[/tex]On plugging the values of a and b in equation (3),
[tex]\begin{gathered} c=\sqrt[]{5^2+2^2} \\ =\sqrt[]{25+4} \\ =\sqrt[]{29} \end{gathered}[/tex]The foci can be calculated as,
[tex]\begin{gathered} F(h,k\pm c)=F(0,0\pm\sqrt[]{29}) \\ =F(0,\pm\sqrt[]{29}) \end{gathered}[/tex]The vertices can be calculated as,
[tex]\begin{gathered} V(h,k\pm a)=V(0,0\pm5) \\ =V(0,\pm5) \end{gathered}[/tex]To obtain graph:
The graph of the given hyperbola can be obtained as,
Hence, the graph of the given hyperbola is obtained.
Suppose that E and F are independent P(E) = 0.8 and P(F) = 0.4What is P(E and F)?
Answers
Answer:
P(E and F) = 0.32
Explanation:
Given that E and F are independent, then
P(E and F) is the multiplication of P(E) and P(F).
P(E) = 0.8, and P(F) = 0.4
P(E and F) = 0.8 * 0.4 = 0.32
RecommendationsSkill plansMathLE Language artsScienceSocial studiesDE TX StandaAlgebra 10.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! Go toWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.Students in a poetry class are writing poems for their portfolios. The teacher wants them towrite stanzas with certain numbers of lines each. Dan wrote 7 short stanzas and 6 longstanzas, for a total of 140 lines. Jim wrote 7 short stanzas and 2 long stanzas, for a total of84 lines. How many lines do the two sizes of stanzas contain?The short stanzas containlines and the long ones containlines.Submit
Answers
Answer:
Short stanzas contains 8 lines
Long stanzas contains 14 lines
Explanations:
Let the number of short stanzas be "x"
Let the number of long stanzas be "y"
If Dan wrote 7 short stanzas and 6 long stanzas, for a total of 140 lines, this is expressed mathematically as:
7x + 6y = 140 ............................ 1
Similarly, if Jim wrote 7 short stanzas and 2 long stanzas, for a total of
84 lines, this is expressed as:
7x + 2y = 84 ......................... 2
Solve both equations simultaneously using elimination method
7x + 6y = 140 ............................ 1
7x + 2y = 84 ......................... 2
Subtract both equations
6y - 2y = 140 - 84
4y = 56
y = 56/4
y = 14
Substitute y = 14 into equaton 1.
Recall that 7x + 6y = 140
7x + 6(14) = 140
7x + 84 = 140
7x = 140 - 84
7x = 56
x = 56/7
x = 8
This shows that the short stanzas contains 8 lines and the long ones contains 14 lines
i need help with this question parts c d and e
Answers
ANSWER :
c. None
d. 0
e. (-1, 0)
EXPLANATION :
c. Values of x in which f(x) = -2
From the illustration, the graph does not pass through the y = -2
So there's NO values of x that will give f(x) = -2
d. Values of x in which f(x) = -3
From the illustration, when x = 0, f(x) will be -3
So the value of x is 0
e. x-intercepts are the points in which the graph intersects the x-axis.
In this case, the graph intersects at point (-1, 0)
There were 55.5 million people enrolled in Medicare in 2015. In 2009, there were 46.6million enrolled. Which value best represents the unit rate of change (slope) in millions per year?a)-1.48b) 1.48c) 19.1%d) -0.674
Answers
Let the number of people enrolled in Medicare be represented by y
Let the year be represented by x
So that,
[tex]\begin{gathered} (x_1,y_1)=(2015,55.5\text{ million)} \\ (x_2,y_2)=(2009,46.6\text{ million)} \end{gathered}[/tex]The unit rate of change (slope) in millions per year can be calculated by:
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ \text{Hence,} \\ slope=\frac{46.6million_{}-55.5million_{}}{2009_{}-2015_{}} \\ slope=\frac{-8.9}{-6} \\ slope=1.48 \\ \end{gathered}[/tex]Therefore, the unit rate of change in millions per year is 1.48 [Option B]
Find an equation of the line that has a slope of -1 and a y intercept of 2. Write your answer in the formy = mx + b.
Answers
Based on the information the equation would be:
y = -1x + 2
m=slope
b= y-intercept
Which of the following numbers is irrational? (A)-1.325 (B)√8 (C)2 (D)4
Answers
Answer:
(B)√8
Explanation:
Irrational numbers are numbers which when converted to decimal can be written indefinitely without repeating.
Irrational Numbers are numbers that cannot be written as a terminating or repeating decimal.
Examples of Irrational Numbers are:
[tex]\sqrt{2},\text{ }\pi,\text{ }\frac{22}{7},\text{ }\sqrt{5}\text{, etc.}[/tex]From the given options, the number which is irrational is √8.
Compare f(-4) and g(-4)f(-4) is >, <, or = to g(-4)
Answers
The answer is f(-4)
EXPLANATION
When we check the value of -4 for both functions on the graph
f(-4) gives 3
g(-4) gives a number slightly greater than 1
Therefore f(-4)>g(-4)
2 2. 8 friends are going on a camping trip. 5 friends own a sleeping bag. How many friends need a sleeping bag? + Il8-5=3
Answers
If 8 friends go camping and only 5 friends have sleeping bag
Then of the 8 friends, the number that need a sleeping bag would be
= 8 - 5
= 3
Hence 3 friends will be in need of a sleeping bag
solve the equation1/4p-2/5=3/4p+7P=
Answers
Solve:
[tex]\frac{1}{4}p-\frac{2}{5}=\frac{3}{4}p+7[/tex]The LCM of the denominators is 4*5 = 20. So we multiply each term by 20 to eliminate denominators:
[tex]20\cdot\frac{1}{4}p-20\cdot\frac{2}{5}=20\cdot\frac{3}{4}p+20\cdot7[/tex]Operating:
[tex]5p-8=15p+140[/tex]Adding 8 and subtracting 15p:
[tex]5p-15p=8+140[/tex]Simplifying:
[tex]-10p=148[/tex]Dividing by -10:
[tex]p=\frac{148}{-10}[/tex]Simplifying:
[tex]p=-\frac{74}{5}[/tex]Which of the following represents the LCM of 98 ab^ 3 and 231 a^ 3 ?
Answers
The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.
Solution by using the division method:
This method consists of grouping by separating the numbers that will be decomposed on the right side by commas while on the left side we put the prime numbers that divide any of the numbers on the right side. We starting with the lowest prime numbers, divide all the row of numbers by a prime number that is evenly divisible into 'at least one' of the numbers. We stop when it is no longer possible to divide (the the last row of results is all 1's). See below how it works step-by-step.
2 | 98, 231
3 | 49, 231
7 | 49, 77
7 | 7, 11
11 | 1, 11
1 | 1, 1
The LCM is the product of the prime numbers in the first column, so:
LCM = 2 . 3 . 7 . 7 . 11 = 3234
Solution by listing multiples:
This method consists of listing the multiples of all the numbers that we want to find the LCM. Multiples of a number are calculated by multiplying that number by the natural numbers 2, 3, 4, ..., etc. See below:
* The multiples of 98 are 98, 196, 294, 392, 490, 588, ..., 3234
* The multiples of 231 are 231, 462, 693, 924, 1155, ..., 3234
Because 3234 is the first number to appear on both lists of multiples, 3234 is the LCM of 98 and 231.
Hence the answer is The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.
To learn more about LCM click here https://brainly.com/question/233244
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if -x - 3y = 2 and -8x + 10y = 9 are true equations, what would would be the value of -9x + 7y?
Answers
To find the value we add both equations:
[tex]\begin{gathered} (-x-3y)+(-8x+10y)=2+9 \\ -9x+7y=11 \end{gathered}[/tex]Therefore the value of the expression given is 11.
solve the following equation for x..[tex]5x { }^{2} = 180[/tex]
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The square root of 36 has 2 results, one positive and one negative.
[tex]\begin{gathered} x=\sqrt[]{36} \\ x=\pm6 \\ or \\ x_1=6\text{ and }x_2=-6\text{ } \end{gathered}[/tex]the ratio of the cost price to selling price is 8:9 . If the cost price of the power generator is 8500 what is the selling price?
Answers
Please give me the correct answer.Please decide if these 4 statements is a function or not a function.
Answers
As according to given statement:
1). Each school has one principal so as there is a relation between school and principal so it is a function.
2). Each student has a unique student ID number: so as there are so many students and they allhave different unique student ID's so there is a function.
3). Shoe manufacturers make different type of shoes : so as there is relation but we can't describe a function between them.
4). Each month of the year has a total amount of rainfall measured in inches:
So it is a function between month and the rainfall measured in inches.