Answer:
Step-by-step explanation:
gerald=2x
guy=x
gill= aproximately 0.3x
2x+x+0.3x=99
2.3x=99
x=43.04
The age of the guy is 29.72 years, the age Gerald is 59.44 years and the age of gill is 9.8 years.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given data in the question,
The equation according to the given statement will be,
The age of Gerald is 2x,
The age of the guy is x and the age of the gill is 0.33x.
So, the equation will be,
x + 2x + 0.33x = 99
3.33x = 99
x = 99/3.33
x = 29.72
Age of Gerald, 2x = 2(29.72) = 59.44 years.
Age of guy, x = 29.72 years and,
Age of gill, 0.33x = 0.33(29.72) = 9.8 years.
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How are the roots of a quadratic equation and the zeroes of a quadratic relation related?
The roots of a quadratic equation and the zeroes of a quadratic equation are related in the following form: [tex]\sum\limits_{i= 0}^{2} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{2} (x-r_{j}) = 0[/tex].
What do represent the roots of a quadratic equation?Polynomials are algebraic entities that satisfy the following condition:
[tex]p(x) = \sum\limits_{i= 0}^{n} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{n} (x-r_{j})[/tex] (1)
Where:
x - Independent variablen - Grade[tex]c_{i}[/tex] - i-th Coefficient[tex]r_{j}[/tex] - j-th RootIf we have that [tex]p(x) = 0[/tex], then there are n values of x such that the equation is satisfied and those values are called zeroes. For the case of a quadratic equation, there are two zeroes.
[tex]\sum\limits_{i= 0}^{2} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{2} (x-r_{j}) = 0[/tex] (2)
Please note that the right part of (2) contains the roots of the polynomial and (2) represents a relationship based on the closure properties for algebraic fields.
Therefore, the roots of a quadratic equation and the zeroes of a quadratic equation are related in the following form: [tex]\sum\limits_{i= 0}^{2} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{2} (x-r_{j}) = 0[/tex].
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Evaluate lim x²-1 x/x^2+3x-4
Nandyan na po
Step-by-step explanation:
I hope I helpWhat is the volume of Prism B if the volume of Prism A is 1120 in??
Answer:
140 in³
Step-by-step explanation:
The ratio of volumes of similar objects is proportional to the cube of the ratio of the linear dimensions.
__
Here, prism B is half the height of prism A, so will have (1/2)³ = 1/8 of the volume of prism A:
Vb = (1/8)×Va
Vb = (1/8)×(1120 in³) = 140 in³
The volume of Prism B is 140 cubic inches.
if a number is added by 2 the answer is10 find the number
Krista Kellman has an opportunity to purchase a government security that will pay $200,000 in 5 years.
How many solutions are there to the equation below?
x²=9
A. 9
B. 0
C. 4
D. 2
E. 3
F. 1
Answer: D) 2
Step-by-step explanation:
x² = 9 means what number times itself is equal to 9
We know that 3×3=9 so that is already one solution, but there is another
-3×-3 is also equal to 9
A negative number times a negative number results in a positive number so -3 is another solution.
That gives us two solutions
Answer:
D; only 2
Step-by-step explanation:
Solve for x over the real numbers:
x^2 = 9
Take the square root of both sides:
Answer: x = 3 or x = -3
rewrite 4+2/3x=3/4 so it does not have fractions.
Answer:
48 + 8x = 9
Step-by-step explanation:
4 + [tex]\frac{2}{3}[/tex] x = [tex]\frac{3}{4}[/tex]
multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions
48 + 8x = 9
write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.
x-2
________
x^2+11x+28
Answer:
A/(x+7) +B/(x+4)
Step-by-step explanation:
The denominators of the partial fraction expansion are the factors of the denominator of the rational function.
__
Here, the rational function's denominator can be factored as ...
x² +11x +28 = (x +7)(x +4)
Then the form of the decomposition is ...
[tex]\dfrac{x-2}{x^2+11x+28}=\boxed{\dfrac{A}{x+7}+\dfrac{B}{x+4}}[/tex]
_____
Additional comment
Here, A=3. B=-2.
If the factors of the denominator have multiplicity greater than 1, then there is a fraction with each power of that factor up to the multiplicity. For example, if there is a factor (x+4)³, then the decomposition would include fractions A/(x+4) +B/(x+4)² +C/(x+4)³.
What is 8,838 rounded to the nearest ten
Answer:
8840
Step-by-step explanation:
Answer:
8,840
Step-by-step explanation:
solve for x ~
[tex]x {}^{2} - 5x + 6 = 0[/tex]
thankyou ~
[tex]x^2 -5x +6 =0\\\\\implies x^2 -3x -2x +6 = 0\\\\\implies x(x-3) -2(x-3) =0\\\\\implies (x-3)(x-2)=0\\\\\implies x =3, ~ x = 2[/tex]
Answer:
The value of x = 2 or 3
Step-by-step explanation:
By factorisation ,
=> x² - 5x + 6 =0
=> x² - 3x - 2x + 6 = 0
=> x ( x-3 ) -2 ( x-3 ) = 0
=> (x-2) (x-3) = 0
so, the value of x = 3 or 2
A sector of a circle has a central angle of 45 ∘ . Find the area of the sector if the radius of the circle is 18 cm. cm2
Answer:
1,090
Step-by-step explanation:
Which of the following numerical expressions results in a positive number?
A (-12) - (-21) - 10
B (-12) - (-21)
C 12 - 21
D (-21) – (-12)
NEED AN ANSWER RIGHT NOW I HAVE ALMOST NO TIME PLEASE
The zeros of a quadratic relationship are 3 and 7. The optimal value is -3. Is the optimal value a maximum or minimum? Explain.
TYSM IF SOMEONE HELPS
Answer:
Minimum
Step-by-step explanation:
The zeros of a quadratic equation are the points at which the parabola intersects the x-axis.
[tex]\sf x=3 \implies x-3=0[/tex]
[tex]\sf x=7 \implies x-7=0[/tex]
[tex]\sf \implies y=a(x-3)(x-7)[/tex] (for some constant a)
[tex]\sf \implies y=ax^2-10ax+21a[/tex]
The optimal value is the y-coordinate of the vertex.
[tex]\sf \implies vertex=(x,-3)[/tex]
The x-coordinate of the vertex is the midpoint of the zeros:
[tex]\sf x=\dfrac{7-3}{2}+3=5[/tex]
[tex]\sf \implies vertex=(5,-3)[/tex]
Therefore, the vertex will be in Quadrant IV and so the parabola opens upwards into Quadrant I.
So the optimal value is a MINIMUM since the vertex is the minimum point of the curve.
Additional Information to create the equation of the quadratic
Vertex form of quadratic equation: [tex]\sf y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
[tex]\sf \implies y=a(x-5)^2-3[/tex]
[tex]\sf \implies y=ax^2-10ax+25a-3[/tex]
To find the value of a, compare the constants of both equations:
[tex]\sf 21a=25a-3[/tex]
[tex]\sf \implies -4a=-3[/tex]
[tex]\sf \implies a=\dfrac34[/tex]
So the final equation is:
[tex]\sf factor \ form \implies y=\dfrac34(x-3)(x-7)[/tex]
[tex]\sf standard \ form\implies y=\dfrac34x^2-\dfrac{15}{2}x+\dfrac{63}{4}[/tex]
[tex]\sf vertex \ form \implies y=\dfrac34(x-5)^2-3[/tex]
Please help EDGINUITY 2022
3/11 x 4/9 fraction multiplication
pls help
Answer:
[tex] \frac{1}{9} [/tex]
Step-by-step explanation:
[tex] \frac{3}{11} \times \frac{4}{9} [/tex]
[tex] \frac{12}{108} [/tex]
[tex] \frac{1}{9} [/tex]
Which of the following means less than or to?
A.not less than
B.at most
C.at least
D.mininum
Answer:
B. At most
Gives a maximum that it can be.
Function g is represented by the table. x -1 0 1 2 3 4 g(x) 24 6 0 -2 Which statement correctly compares the two functions? A. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. C. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞.
The statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Function g is represented by the table.
x -1 0 1 2 3 4 g(x) 24 6 0 -2The line plotted with these data is shown below where y represent the g(x).
In this line,
X-intercept approaches negative infinity (-∞) to positive infinity (∞).Y-intercept approaches -2.426 to 24.86.Thus, the statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
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Identify the rational function whose graph is given below. Note the x-intercept of the graph is x=4 and the y-intercept of the graph is y=−3. The graph has one vertical asymptote at x=2
Using the vertical asymptote of the function, it is found that it is given by:
[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the x-intercept of the graph is x=4, hence the numerator is a(x - 4).
The graph has one vertical asymptote at x=2, hence the denominator is x - 2.
Hence:
[tex]f(x) = \frac{a(x - 4)}{x - 2}[/tex]
The y-intercept of the graph is y=−3, hence:
[tex]-3 = \frac{a(0 - 4)}{0 - 2}[/tex]
[tex]-4a = 6[/tex]
[tex]a = -1.5[/tex]
Thus, the function is:
[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]
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Evaluate Grace's new budget.
ОА. Her new budget should have money in every budget category, including debts and medical expenses
OB. Her new budget should have money in medical expenses because she does not know what medical problems she will
encounter in the future.
OC. Her new budget is fine because debts and medical expenses were not needed last month.
OD. Her new budget should have money in debts so that she can afford to go into debt if she has medical expenses.
A recipe for a batch of 3 dozen chocolate chip cookies calls for 3 cups of flour, one cup of sugar, and 2 cups of chocolate chips. how much of each ingredient should be used to make 2 dozen cookies
Answer:
2 cups of flour
2/3 cup of sugar
1 1/3 cups of chocolate chips
Step-by-step explanation:
3 dozen chocolate chip cookies
3 cups of flour
1 cup of sugar
2 cups of chocolate chips
The recipe is for 3 dozen cookies as stated above.
If you make 2 dozen cookies, then you are making 2/3 of the recipe since 2 is 2/3 of 3.
That means you need 2/3 of all the ingredients.
2/3 × 3 dozen chocolate chip cookies
2/3 × 3 cups of flour
2/3 × 1 cup of sugar
2/3 × 2 cups of chocolate chips
We simplify the amounts to:
2 dozen chocolate chip cookies
2 cups of flour
2/3 cup of sugar
1 1/3 cups of chocolate chips
Can I please get help I don’t know how to use the numbers on the front
HELP ASAP will get brainly user !!!
Answer:
46
Step-by-step explanation:
p=6,q=12.
Put the numbers where the letters are.
7x6+12/3
46
Hope this helps!
Answer:
[tex]beinggreat78~here~to~help~you~learn![/tex]
When doing short equations like this, you want to use P.E.M.D.A.S. That just means you want to use parentheses first, exponents second, multiply third, divide fourth, add fifth, and subtract last. In this case, since there are no parentheses, or subtraction, or exponents, we cross those three out, and make multiplication our top priority. But, what exactly does seven p mean? p is an assigned, substituted number. Sometimes people will use p instead of x as subs, but it really does not matter. So now that we have enough information, let's start.
[tex]7p=7 * number(In~this~case,~6)[/tex]
[tex]7 * 6 = 42[/tex]
The next step is to divide q(12) by three. Before adding, you want to divide, because it is your second-top-priority.
[tex]\frac{q}{3} = \frac{12}{3}~which~is~4[/tex]
Lastly, add the quotient and the product together.
[tex]7p(42) + \frac{q}{3} (4) = 46[/tex]
And we are done! The result is 46, so that means your answer is D! Yay!
What have we learned while doing this problem?
We have learned how to multiply and divide in order of operations while dealing with substitution.rena divides a square into 8 equal part. what unit fraction should she write as a label for each parts?
If rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.
What is Fraction?A fraction represents a part of a whole.
Given that rena divides a square into 8 equal part.
A division is a process of splitting a specific amount into equal parts.
Let the whole square is divided into eight equal parts.
Which can be represented by 1/8.
Where the numerator 1 represents the whole and eight represents the parts.
The unit fraction for each part is 1/8 because the square is divided into 8 equal parts.
This means each part is one eighth of the whole.
Hence, if rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.
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surface area.... again
Answer:
1848 square inches
Step-by-step explanation:
surface area is the combined area of all the outside surfaces.
area of triangle is base x height / 2
There are two, so no need to divide
18 x 12 = 216
Area of rectangle is base x height
15 x 34 + 15 x 34 + 18 x 34 = 1632
Then add
216 + 1632 = 1848
The perimeter of a rectangle is 120 meters and the length is 20 meters longer than the width. Find the dimensions of the rectangle. Let x = the length and y = the
2+2y = 12)
width. The corresponding modeling system is 2x + 2y =120 x-y = 20
Solve the system graphically
The dimension of the rectangle is 40meters by 20meters
What is the perimeter of a figure?The perimeter of a figure is the sum of all the external sides of the figure
The formula for calculating the perimeter of rectangle = 2(l+w)
If the length is 20 meters longer than the width, then;
l = 20 + w
Substitute
120 = 2(20+2w)
60 = 20 + 2w
30 = 10 + w
w = 20 meters
Since l = 20 + w
l = 20 + 20
l = 40 meters
Hence the dimension of the rectangle is 40meters by 20meters
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A study of 110 students who had been awarded University scholarship showed that 40 worked part time jobs, 29 made the dean's list the previous semester and 16 both worked a part time job and made the dean's list the previous semester. What is the probability that a student worked a part time job or made the dean's list.
Answer:
i dont understand i need pic
18. Cancellation refers to the procedure for
A. reducing fractions to make multiplying easier.
B. inverting the divisor in a division problem.
C. changing a mixed number to an improper fraction.
D. finding the lowest common denominator for a group of fractions.
The correct option regarding the operation of cancellation in a fraction is given by:
A. reducing fractions to make multiplying easier.
What is an example of cancellation in a fraction?It happens when two fractions are multiplying each other, and terms are simplified to make the multiplication easier. For example:
[tex]\frac{2}{3} \times \frac{6}{4} = \frac{6}{3} \times \frac{2}{4} = 2 \times \frac{1}{2} = 1[/tex]
The terms 2 and 4, and 3 and 6, were canceled. Hence option A is correct.
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He decided to bike from his home to the library to return some books. Ell biked 110 miles when he remembered that he had left a book at home, so he biked back home to get it. After getting the book from home, he biked to the library. What was the total distance, in miles, en had biked when he finally reached the library Show your work. miles Answer
Answer:
2 2/10 miles
but on the part where he realized he forgot his books was he at the library already when he realized cuz if not them it's more than 2 2/10
Jupiter takes 4332 earth days to orbit the sun mercury orbits the sun in 88 earth days. How many complete orbits will mercury make until Jupiter completes one
Answer:
At this distance, Jupiter takes 11.8618 Earth years to complete a single orbit of the Sun. In other words, a single Jovian year lasts the equivalent of 4,332.59 Earth days.
Step-by-step explanation:
that the best i can do !!!!
A new board game comes with a deck of 20 cards: 5 red, 3 blue, 2 orange, and 10 green.
After the deck is shuffled, the player is to choose the top card and note its color, replace
the card, shuffle the deck again, and then choose the top card again and note its color.
What is the probability that both cards selected are blue?
A.3%
B.2.25%
C.9%
D.6.25%
Answer:
B
Step-by-step explanation:
3/20x3/20=
15/100x15/100