Answer:
The value of positive integers are 21.22 and 12.11
Step-by-step explanation:
Given as :
The sum of squares of two integer = 698
Let The one positive integer be x
And The other positive integer be y
According to question
one positive integer = 3 less than twice the other positive integer
So, x = 2 × y - 3
I.e x = 2 y - 3
And x² + y² = 698
So, Put the value of x
I.e ( 2 y - 3 )² + y² = 698
or, 4 y² + 9 - 12 y + y² = 698
Or, 5 y² - 3 y - 698 = 0
Now solving this quadratic equation
y = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
Or, y = [tex]\frac{3\pm \sqrt{-3^{2}-4\times 5\times -698}}{2\times 5}[/tex]
Or, y = [tex]\frac{3\pm \sqrt{13969}}{10}[/tex]
Or, y = [tex]\frac{3\pm 118.19}{10}[/tex]
∴ y = 12.11 , - 11.51
So , The value of y = 12.11
And the value of x = 2 × 12.11 - 3
I.e x = 21.22
Hence The value of positive integers are 21.22 and 12.11 Answer
To find the two integers, we can set up two equations based on the given information. By substituting the value of x from the first equation into the second equation, we can solve for y. Then, substituting the value of y back into the first equation, we can find the value of x.
Explanation:To solve this problem, we can set up two equations based on the given information. Let's say the first integer is x and the second integer is y. We are given that x is 3 less than twice y, so we can write the equation: x = 2y - 3. We also know that the sum of their squares is 698, so the equation becomes x^2 + y^2 = 698. Now we can substitute the value of x from the first equation into the second equation and solve for y.
Substituting x = 2y - 3 into the equation x^2 + y^2 = 698, we get (2y - 3)^2 + y^2 = 698. Expanding this equation, we get 4y^2 - 12y + 9 + y^2 = 698. Combining like terms, we have 5y^2 - 12y + 9 = 698. Rearranging this equation and simplifying, we get 5y^2 - 12y - 689 = 0. Now we can solve this quadratic equation to find the value of y.
Using the quadratic formula, y = (-(-12) ± sqrt((-12)^2 - 4(5)(-689))) / (2(5)). Simplifying the equation further, we have y = (12 ± sqrt(144 + 13780)) / 10. Taking the positive value, y = (12 + sqrt(13924)) / 10. Evaluating this expression, we find y ≈ 9.7394. Now we can substitute this value back into the first equation to find x.
Using x = 2y - 3, we have x = 2(9.7394) - 3. Simplifying this equation, we get x ≈ 16.4788. Therefore, the two integers are approximately 16.4788 and 9.7394.
Which graph best represents the function f(x) = (x - 1)(x + 3)(x – 3)?
Answer:
The graph you posted was Incorrect! An easy way you can check is like this:
Insert the function "f(x) = (x - 1)(x + 3)(x – 3)" into desmos, you get this which should perfectly match the function shown.
The graph that represents the function is attached to the answer.
What is a Graph?The graph is a mathematical representation of the relation between two objects.
It helps in determining the function that fits best for the data obtained.
A function is a mathematical statement that defines a relationship between a dependent and an independent variable.
A function always has a defined range and domain, domain is all the value a function can have as input and range is all the value that a function can give as output.
The function is f(x) = (x-1)(x+3)(x-3)
The graph for the function will be determined by plotting,
The graph is plotted and attached with the answer.
The parent function is a cubic function, which is also plotted along with the function graph.
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Supposed charity received a donation of $23.9 million. If this represents 54% of the charity donated funds what is the total amount of its donated funds? round your answer to the nearest million dollars.
Total amount of funds is $44.26 million.
Step-by-step explanation:
Given,
Donation received = $23.9 million
As it represents 54% of charity.
Let,
Total amount = x
Therefore,
54% of x = 23.9 million
[tex]\frac{54}{100}*x=23.9\\0.54x=23.9[/tex]
Dividing both sides by 0.54
[tex]\frac{0.54x}{0.54}=\frac{23.9}{0.54}\\x=\$44.26\ millions[/tex]
Total amount of funds is $44.26 million.
Keywords: percentage, division
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10. A square picture has a 1-inch frame around it. If the
area of the frame alone is 80 in.2, what is the area of the
picture?
Answer:
361 sq, inches.
Step-by-step explanation:
Let us assume that the dimensions of the square picture are P in × P in.
So, the area of the picture alone is, A = P²
Now, if the photo has a frame of 1 inch wide, then the dimensions of the photo with frame are (P + 2) in × (P + 2) in.
So, the area of the photo with frame is A' = (P + 2)(P + 2) = (P + 2)²
Now, the area of the frame alone is 80 sq. inches.
Hence, A' - A = 80
⇒ (P + 2)² - P² = 80
⇒ 4P + 4 = 80
⇒ 4P = 76
⇒ P = 19 inches.
So, the area of the picture is = 19² = 361 sq. inches. (Answer)
361 sq, inches.
Step-by-step explanation:
Haley wrote the expression 24m – 6n. Kensi wrote an expression equivalent to Haley’s. Which expression could Kensi have written? 2(6m – 4n) 4(6m – 6n) 6(4m – n) 12(2m – 2n)
Answer:
C) 6(4m-n)
Step-by-step explanation:
Because 6(4m-n)=24m-6n.
Consider this function. f(x) = 2x - 2 Which graph represents the inverse of function f?
Answer:
W
Step-by-step explanation:
If its the graphs I got then yeah
The Graph that represents the inverse of function f is attached below.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
We have been given a function of x as; f(x) = 2x - 2
If function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
y = 2x - 2
x = 2y - 2
x + 2 = 2y
y = (x + 2)/2
It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f' function here.
To Graph the inverse, Simply use a graphing calculator and the correct graph is attached below.
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12. What is the equation of a line perpendicular to the x-axis that passes through the point (-2,-4)? What is the slope of
this line?
what answer?
Answer: the vertical line with the equation "x=-2"
Step-by-step explanation:
if you are perpendicular to the x axis, you will be looking for vertical lines that pass through (-2,-4)
the vertical line with the equation "x=-2" will pass though the point because (-2,-4) has an x coordinate of -2
Sheldon needs to buy 8 gallons of coleslaw for a family reunions the table shows the prices for different size of two brands of coleslaw use the table for exercises 11 and 12
-3x+12y=24 What is the Y intercept
Answer:
(0,2)
Step-by-step explanation:
y-intercept: when x = 0
-3(0) + 12y = 24
12y = 24
y = 2
what is the probability that a randomly-selected driver fatality who was female was less than 16 years old the probability that a randomly-selected driver fatality who was female was less than 16 years old is approximately _____.
Answer:
0.19%
Step-by-step explanation:
To know what is the probability that a female who is less than 16 in involved in a driver fatality, we have to compare the cases of fatalities for females who are less than 16 years old, with the total cases of fatalities, commited by all kind of persons. Then, to know the proportion of the population of driver fatalities represented by female who are less than 16, we divide the amount of cases that happend under the characteristics mentioned (females <16) and the total amount of fatalities: [tex]\frac{100}{Total_{fatalities}} =\frac{100}{141+100+4970+2331+11009+....} =\frac{100}{52693}=0.0019=0.19\%[/tex], which is the probability that a randomly-selected driver fatality were commited by a females who is less than 16.
the ratio of potatoes to turnips is 1:1 if there are are 473 potatoes how many turnips are there
Answer:
473 turnips
Step-by-step explanation:
well if its 1 to 1 that means how ever meany you have of one you will have the same exact amount of the other food
473x1 = 473x1
Final answer:
To find the number of turnips, set up a proportion using the given ratio and cross multiply to solve for the number of turnips.
Explanation:
To find the number of turnips, we can set up a proportion using the given ratio:
Number of potatoes / Number of turnips = Ratio of potatoes to turnips.
Since the ratio of potatoes to turnips is 1:1, the proportion will be:
473 / Number of turnips = 1 / 1.
To solve for the number of turnips, cross multiply:
473 * 1 = Number of turnips * 1.
Number of turnips = 473.
Therefore, there are 473 turnips in this scenario.
I am a two-digit even number. I am
a multiple of 5. My tens digit is 8
more than my units digit.
answer this for me please and quick!!
Answer:
24.3
Step-by-step explanation:
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation. What are the values a, b, and c in the following quadratic equation? −5x2 − 9x + 12 = 0
A:a = −9, b = 12, c = 0
B: a = −5, b = −9, c = 12
C: a = 5, b = 9, c = 12
D:a = 9, b = 12, c = 0
Answer:
B
Step-by-step explanation
Answer:
Option B. a = −5, b = −9, c = 12
Step-by-step explanation:
The general form of the quadratic equation is as following
ax² + bx + c = 0
Where a, b and c are constants.
And the given equation is −5x2 − 9x + 12 = 0
Comparing the given equation to the general form
ax² + bx + c = 0
−5x2 − 9x + 12 = 0
So, a = -5 , b = -9 and c = 12
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
So, the answer is option B: a = −5, b = −9, c = 12
3) 8p + 7q= 43
2p-7=-q
I need to solve using substitution. thanks.
Answer:
p=1, q=5. (1, 5).
Step-by-step explanation:
8p+7q=43
2p-7=-q
------------------
q=-2p+7=7-2p
8p+7(7-2p)=43
8p+49-14p=43
8p-14p=43-49
-6p=-6
6p=6
p=6/6=1
2(1)-7=-q
2-7=-5=-q
q=5
Can someone actually answer this question please QUICK
A+b=c>4
b=7
a= 2
what is c?
Answer:
9
Step-by-step explanation:
The value of c is found by adding a (2) and b (7) together, which equals 9.
Explanation:The question a + b = c is asking for the value of c when a is 2 and b is 7. To find c, we simply add the values of a and b together. In mathematics, this is known as solving for the unknown variable.
In this case:
a + b = c
2 + 7 = c
c = 9
Therefore, the value of c when a is 2 and b is 7 is 9.
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F(x)= 5x^2+6, g(x)= 7x find (f o g)(x), find (g o f)(x), find f(g(-4)), fine g(f(5))
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x^2+6\\g(x) = 7x[/tex]
So
[tex](f o g)(x) = 5(7x)^2+6\\= 5(49x^2)+6\\=245x^2+6\\(g o f)(x) = 7(5x^2+6)\\= 35x^2+42\\(fog(x))=245x^2+6f(g(-4)) = 245(-4)^2+6 \\=245(16)+6\\=3920+6\\=3926\\g(f(x)) = 35x^2+42\\g(f(5)) = 35(5)^2+42\\=35(25)+42\\=875+42\\=917[/tex]
Hence,
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Keywords: functions, Function composition
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What is CD?
6 units
12 units
18 units
24 units
Answer: 18 units
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
6 times 2 = 12
12+6=18
Factor the expression into an equivalent form. ab^2 - b
Answer:
ab² - b = b(ab -1)
Step-by-step explanation:
The variable b is common to both terms here. Thus,
ab² - b = b(ab -1)
Nancy is taking inventory in the pharmacy to make sure there is enough eye medication in the pharmacy. She counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in stock. Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes. Calculate how many boxes of each Nancy needs to order.
Answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy.
Step-by-step explanation:
Nancy counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in the stock.
So, there is a need to order (15 - 10) = 5 boxes of travoprost.
Again, Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes.
So, there is a need to order (12 - 3) = 9 boxes of latanoprost.
Therefore, Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy. (Answer)
Final answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost to fulfill the pharmacy's minimal stock requirement.
Explanation:
Nancy needs to order more boxes of eye medication to meet the pharmacy's minimal stock levels. For travoprost, the pharmacy requires 15 boxes but currently has only 10 boxes. So, Nancy needs to order:
15 boxes (required amount) - 10 boxes (current amount) = 5 boxes of travoprost.
For latanoprost, the pharmacy needs 12 boxes, but only has 3 boxes in stock, meaning Nancy needs to order:
12 boxes (required amount) - 3 boxes (current amount) = 9 boxes of latanoprost.
Given the equation square root of quantity 3x plus 6 end quantity equals 3, solve for x and identify if it is an extraneous solution. 1; solution is extraneous 1; solution is not extraneous 3; solution is extraneous 3; solution is not extraneous
Answer:
1; solution is not extraneous
Step-by-step explanation:
the value 3=3 is true, meaning its not extraneous and also I got it correct on the test
The value of x is 1, and the solution is not extraneous.
Given that,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
We have to determine,
The value of x and identify if it is an extraneous solution.
According to the question,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
To find the value of the x following all the steps given below.
Squaring both the sides to solve the equation,
[tex]\sqrt{3x+6 } = 3\\\\(\sqrt{3x + 6 })^2= 3^2\\\\3x + 6 = 9\\\\3x = 9-6\\\\3x = 3\\\\x = \dfrac{1}{1}\\\\x = 1[/tex]
An extraneous solution is a root of a transformed equation that is not a root of the original equation.
Therefore, The solution is not extraneous.
Hence, The value of x is 1, and the solution is not extraneous.
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When a 49 pound weight is attached to a spring, the spring stretches 7 inches. Assume that the length of the spring y varies directly
with the weight attached x. Write and solve a direct variation equation to
find the length of the spring when a 63 pound weight is attached.
PLEASE ANSWER NOW
Stephen, Paul & Bridget share some money in the ratio 3 : 4 : 2. In total, Stephen and Bridget receive £50. How much does Paul get?
Answer:
The money receive by Paul is [tex]\pounds 40[/tex].
Step-by-step explanation:
Given as :
The ratio of share of money among three people as
Stephen : Paul : Bridget = 3 : 4 : 2
The total money receive by Stephen and Bridget = [tex]\pounds 50[/tex]
Let The money receive by Stephen = 3 x
Let The money receive by Paul = 4 x
Let The money receive by Bridget = 2 x
Now, According to question
The total money receive by Stephen and Bridget = [tex]\pounds 50[/tex]
I.e 3 x + 2 x = [tex]\pounds 50[/tex]
i.e 5 x = [tex]\pounds 50[/tex]
∴ x = [tex]\frac{\pounds 50}{5}[/tex]
x = [tex]\pounds 10[/tex]
So, The money receive by Stephen = 3 × [tex]\pounds 10[/tex] = [tex]\pounds 30[/tex]
Let The money receive by Paul = 4 × [tex]\pounds 10[/tex] = [tex]\pounds 40[/tex]
Let The money receive by Bridget = 2 × [tex]\pounds 10[/tex] = [tex]\pounds 20[/tex]
Hence The money receive by Paul is [tex]\pounds 40[/tex]. Answer
Choose a system of equations with the same solution as the following system:
6x + 2y = −6
3x − 4y = −18
---------------------
A: 8x + 4y = −4
17x + 2y = −28
B: 12x + 4y = 12
21x + 2y = −36
C: 6x + 8y = −36
15x + 6y = −60
D: 6x + y = 15
15x − y = −9
Answer
______________
The same solution of the given system of equations will be same as the solution of below system of equations;
⇒ 8x + 4y = −4
17x + 2y = −28
Option A is true.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The System of equation is,
6x + 2y = - 6 ..(i)
3x - 4y = - 18 ..(ii)
Now,
Solve the given system of equation as;
The System of equation is,
6x + 2y = - 6 ..(i)
3x - 4y = - 18 ..(ii)
By equation (i);
6x + 2y = - 6
2(3x + y) = - 6
3x + y = - 3 ..(iii)
Subtract equation (ii) from (iii), we get;
3x - 4y - (3x + y) = - 18 - (-3)
3x - 4y - 3x - y = - 18 + 3
- 5y = - 15
y = 3
And, By equation (i), we get;
6x + 2y = - 6
6x + 2 × 3 = - 6
6x + 6 = - 6
6x = - 6 - 6
6x = - 12
x = - 2
Thus, The solution of given system of equation are;
x = - 2 and y = 3
Now,
Substitute the value of x and y in all the given options and find the same solution of given system of equation as;
A: 8x + 4y = −4
17x + 2y = −28
Substitute the value of x = - 2 and y = 3;
8x + 4y = −4
8 × - 2 + 4 × 3 = - 4
- 16 + 12 = - 4
- 4 = - 4
17x + 2y = −28
17 × - 2 + 2 × 3 = - 28
- 34 + 6 = - 28
- 28 = - 28
Thus, This system of equation has same solution.
Therefore, The same solution of the given system of equations will be same as the solution of below system of equations;
⇒ 8x + 4y = −4
17x + 2y = −28
Option A is true.
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y = 3x - 1
12x – 4y = 12
Answer:
8 and 23
Step-by-step explanation:
let the 1st equation be i and 2nd be ii
now putting the value of x in eqn ii, we get
12x -4×(3x-1) = 12
12x-12x+4=12
x=12-4
x=8
again,
y=3×8-1
y=23
Katelynn earned $1240 in two weeks at the recreation
center during a trap shooting tournament. She earned
$480 the first week and the rest the second week.
Write an algebraic equation to model the situation.
x = 1240-y can be used to model the situation where x is the amount earned in second week.
Step-by-step explanation:
Given,
Total amount earned = D = $1240
Amount earned in first week = y = $480
Let,
x be the amount earned in second week.
Therefore,
Total amount earned = Amount earned in 1st week + 2nd week amount
D = x + y
1240 = x + y
Solving for x;
[tex]x= 1240- y [/tex]
x = 1240-y can be used to model the situation where x is the amount earned in second week.
Keywords: linear equation, subtraction
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Help Please !!!
Will mark the brainliest.
Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.
Answer:
The mirror is 20/3 of feet, which is about 6.7 feet, from the basketball goal.
Explanation:
The figure attached represents the situation.
The triangle on the left and the triangle on the right are similar triangles because they are right triangles and the marked angles are congruent.
The distance between the mirror and the basketball goal is represented by the unknown x.
By similarity:
[tex]10/6=x/4[/tex]Solving:
[tex]x=40\times 10/6=40/6=20/3[/tex]Thus, the mirror is 20/3 of feet, which is about 6.7 feet, from the basketball goal.
In the world balloons the ratio of wolves to consonant is
Answer:
The ratio of consonants to is 4:3. 4 consonants and 3 wolves.
Which graph shows the solution set to this inequality? 4x < 12
Answer:
x=1,2
Step-by-step explanation:
we show that 4x is <12
if x=1,,,4x=4*1=4
if x=2,,,4x=4*2=8
if x=3,,,4x= 4*3=12
so 1 &2 is right ans
Help me find the value of the missing variable
Answer:
Its isosceles, so the the 2 sides other than st are equal. 2x+6=3x-6
Moves to one side. 12=x
x=12
Step-by-step explanation:
x=12
Step-by-step explanation:
You know that angles T and S are equal, meaning the lengths of the lines TV and SV are also equal. That means 2x+6=3x-6. You transfer the xs and get 6=x-6. You undo the negative 6, receiving 12=x.
Help!!
Kerry has a bag containing white and yellow marbles. Kerry randomly selects one marble from the bag, records the result, and returns the marble to the bag. The results of the first 65 selections are shown below.
- A white marble was selected 41 times
- A yellow marble was selected 24 times.
Based on these results what is the probability that the next marble Kerry selects will be white?
A. 41%
B. 50%
C. 59%
D. 63%
The probability that the next marble Kerry selects will be white is; D: 63%
Probability of Selection
The results of Kerry randomly selecting one marble from the bag out of 65 selections are;
White marble = 41Yellow Marble = 24Now, these numbers of marbles represents the amount of times the respective colors are gotten for every 65 selections. Thus;
P(next marble that Kerry selects will be white) = 41/65 * 100
P(next marble that Kerry selects will be white) ≈ 63%
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