Answer:
In this problem, we can assign X to the son’s age and Y to the father’s.
We know that a father is 3 times as old as his son.
Therefore, we can create the equation 3X=Y.
We must now create a second equation from the remaining information, being “In 12 years he will be twice as old as his son”. We know we can add 12 years, along with including 2X in the equation.
The equation that we can gather from this second piece of information will be Y=2X+12. This is because the father’s age, in 12 year’s time, will be twice that of the child.
Now we have our two equations:
Y=3X
Y=2X+12
Because both equations are set equal to the age of the father, we can use the substitution method to solve in terms of the son’s age, as follows:
3X = 2X+12
Now we subtract 2X from each side to isolate the variable:
X=12
The son’s age is therefore 12 years old. Should we plug that age back into our first equation, we get Y=3(12) or Y=36.
The father’s present age is 36, while the son’s present age is 12.
The current age of the father is 12, while the age of the son is 0.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let say,
X = age of sun
Y = age of father
Given that
A father's age now is three times the age that his son was 4 years ago
So,
Y = 3(X -4)
Y = 3X - 12
And In 12 years, the father will be twice as old as his son
Y + 12 = 2( X + 12 )
Y = 2X - 12
From booth equation
X = 0 and Y = -12 which is not practical so Y =12
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A book store is selling 4 books for $10 as parr of its clearance sale.Regina has $28 to spend.At this rate regina can purchase how many books?
Answer: 8 books (She will also keep with her a balance of $8)
Step-by-step explanation:
Total amount of money = $28
Cost of 4 books = $10
Sets of books able to be bought with the money = 28/10
= 2 (Reminder will be 8)
Amount of books able to be bought with the money = 2 × 4
= 8 books
Regina can purchase 11 books when she has $28 to spend.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.
For example 4/2 = 2
A bookstore is selling 4 books for $10 as part of its clearance sale. Regina has $28 to spend.
Let's represent the number of books Regina can purchase x.
The total price for x books at the clearance rate is 10/4x = $2.5x
Since Regina has 28 dollars to spend, she can purchase :
⇒ x = 28/2.5
Apply the division operation, and we get
⇒ x = 11.2 books.
Therefore, she can purchase 11 books.
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96 Children are on a school trip, there
are 7 seats in a mini bus. How many
mini bus are needed?
Solve for the value of r.
r =
Answer:
r=8
Step-by-step explanation:
45=6r-3
48=6r
r=8
If f(x) = x - 4 and g(x) = 3x + 5, find (f + g)(x).
A.4x+9
B.2x+9
C.2x-1
D.4x+1
Answer:
4x+1
Step-by-step explanation:
Ufbxkdjdnskkxkdd
Answer:
D. 4x + 1
Step-by-step explanation:
[tex](f+g)(x)=x-4+3x+5\\(f+g)(x)=4x+1[/tex]
[tex]B=(\frac{-3}{16} x^{2} y) . (4x^{4}y^{3})[/tex]
Answer:
[tex]B=-\frac{3}{4}x^6y^4[/tex]
Step-by-step explanation:
One is given the following equation:
[tex]B=(\frac{-3}{16}x^2y)(4x^4y^3)[/tex]
Multiply each term in one of the parenthesis by its like term in the other. Bear in mind, since all of the operations in this equation are multiplication, one doesn't have to multiply every single term by another in the parenthesis, one only has to multiply like terms to simplify.
[tex]B=(\frac{-3}{16}x^2y)(4x^4y^3)[/tex]
[tex]B=(\frac{-3}{16})(4)(x^2)(x^4)(y)(y^3)[/tex]
Simplify further, remember, when multiplying two terms with the same base, one can add their exponents to simplify,
[tex]B=(\frac{-3}{16})(4)(x^2)(x^4)(y)(y^3)[/tex]
[tex]B=(\frac{-3*4}{16})(x^2^+^4)(y^1^+^3)[/tex]
[tex]B=(\frac{-3*4}{16})(x^6)(y^4)[/tex]
Now simplify the fraction, remove like terms found in both the numerator and denominator. Remember, (4) is a factor of both (4) and (16):
[tex]B=(\frac{-3*4}{16})(x^6)(y^4)[/tex]
[tex]B=(-\frac{3}{4})(x^6)(y^4)[/tex]
[tex]B=-\frac{3}{4}x^6y^4[/tex]
1,2,3,5 and 7 are all common factors of two numbers. Write down the digit that the two numbers must end in? pls explain briefly
Answer:
9 or 11
Step-by-step explanation:
Please help with this question
Answer:
-3.662rad × 180/π = -209.8°
Step-by-step explanation:
Answer:
1 degree = .01745329 radians
1 radian = 57.2957877856 degrees
-209.8 degrees = .01745329 * -209.8 =
-3.66170024200 radians
Step-by-step explanation:
What is the image of the point (-1,3) after a rotation of 270° counterclockwise
about the origin?
Answer:
3,-1
Step-by-step explanation:
The image of the point (-1,3) after a rotation of 270° counterclockwise about the origin is (3, -1).
The given coordinate point is (-1, 3).
What is a rotation of 270° counterclockwise about the origin?When rotating a point 270 degrees counterclockwise about the origin our point A(x, y) becomes A'(y,-x). This means, we switch x and y and make x negative.
The point (-1, 3) is rotated 270° counterclockwise about the origin becomes (3, -1).
Therefore, the image of the point (-1,3) after a rotation of 270° counterclockwise about the origin is (3, -1).
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those are not the powers question from transformation of product and sum trigonometry
prove that : cos3A+cos5A+cos7A+cos15A= 4cos4Acos5Acos6A
Answer:
see explanation
Step-by-step explanation:
Using the sum to product identity
cosx + cosy = 2cos([tex]\frac{x+y}{2}[/tex] )cos( [tex]\frac{x-y}{2}[/tex] )
Consider left side
(cos5A +cos3A) + (cos15A + cos7A)
= 2cos([tex]\frac{5A+3A}{2}[/tex] )cos([tex]\frac{5A-3A}{2}[/tex] ) + 2cos( [tex]\frac{15A+7A}{2}[/tex]) cos( [tex]\frac{15A-7A}{2}[/tex] )
= 2cos([tex]\frac{8A}{2}[/tex]) cos([tex]\frac{2A}{2}[/tex]) + 2cos([tex]\frac{22A}{2}[/tex] )cos([tex]\frac{8A}{2}[/tex] )
= 2cos4AcosA + 2cos11A cos4A ← factor out 2cos4A from both terms
= 2cos4A( cos11A + cosA) ← repeat the process
= 2cos4A( 2cos([tex]\frac{11A+A}{2}[/tex] )cos([tex]\frac{11A-A}{2}[/tex] )
= 2cos4A(2cos([tex]\frac{12A}{2}[/tex])cos([tex]\frac{10A}{2}[/tex] )
= 2cos4A(2cos6A cos5A)
= 4cos4Acos5Acos6A
= right side , thus verified
The product of 7,x, and y is represented by the expression 7xy. If the value of x is negative, what
can be said about the value of y in order for the product to remain positive?
Answer:
In the expression of 7xy, if x is negative, then y must also be negative for the product to be positive.
Let me know if this helps!
Answer:
it must be negative
Step-by-step explanation:
7xy = a positive number
7 is positive.
x is a negative number.
y must be negative for 7xy to be positive.
(+) * (-) * (-) = +
The product of two negative numbers is positive.
On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 226 feet at an angle
of 39° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. Approximately how far does
the outfielder throw the ball?
Answer:
183.0 ft
Step-by-step explanation:
CAN SOMEONE PLS TELL ME DOMAIN AND RANGE
Answers:
Domain is (-4, 3]Range is (-5, 5]=====================================================
Explanation:
The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that [tex]-4 < x \le 3[/tex]. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).
The interval [tex]-4 < x \le 3[/tex] then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.
It says: x is between -4 and 3. It can't equal -4 but it can equal 3.
So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.
--------------------------------------------------
The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.
The range as a compound inequality is [tex]-5 < y \le 5[/tex]. This condenses into the shorthand of (-5, 5] which is the range in interval notation.
Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.
Answer:
Hello,
Step-by-step explanation:
Domain(f)= ]-4;3]={x€R | -4<x≤3}
Rang(f)=]-5;5]={y€R | -5< y ≤5}
not sure how to solve this
Answer:
x=11
Step-by-step explanation:
(x+7)×7=6×(6+15)
or, 7x+49=6×21
or, 7x=126-49
or, 7x=77
or, x=11
Steel chain costs $0.75 per foot from Company
X, which provides free shipping. The same
steel chain costs $1.20 per yard at Company Y,
which charges a $120.00 shipping fee for all
orders. How much more does Company
Y charge, in dollars, than company X for 300
feet of steel chains?
Answer:
Company Y charges 255 dollars more then Company X :)
Step-by-step explanation:
Company X: 0.75 * 300 = 225 + 0 shipping
Company Y: 1.20 * 300 = 360 + 120 shipping = 480
480 - 225 = 255
The constant value which is multiplied by each term in a geometric sequence to obtain the next term.
Answer: Geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio.
Step-by-step explanation:
Answer:
NOSEE EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Step-by-step explanation:
1. What is the sum of a + bº?
Answer:
the sum of angle a and angle b is 180 degrees as they make a linear pair.
Step-by-step explanation:
a+b = 180........(linear pair)
what fraction of these houses have seven rooms
Answer:
9/50
Step-by-step explanation:
18 % have 7 rooms
18 % means 18 out of 100
18/100
Divide top and bottom by 2
9/50
Which of the following numbers is between 0.08 and 0.4?
(A) 0.019
(B) 0.009
(C) 0.109
(D) 0.91
(E) 0.409
Answer:
C
Step-by-step explanation:
the numbers between 0.08 and 0.4 are:
0.09, 0.10, 0.11, 0.12, 0.13, 0.14, 0.15, .16, 0.17, 0.18, 0.19, 0.20, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39
I bolded the number closest to your answer choices, hope this helps!
The entrance fee to a local waterpark is $28 per person. At the waterpark, you can rent a raft for $2.50 per hour. Which expression is equivalent to
the amount it would cost Colton for h hours in the park if he rented a raft? �� 2.50h - 28
�� 2.50 (h - 28)
�� 2.50h + 28
�� 2.50 (h + 28)
Answer:
C
Step-by-step explanation:
The 28 is independent of the number of hours. Both B and D are incorrect.
You don't subtract the 28 from the total. That's part of the total. A is wrong.
The answer is C
I’m struggling, if someone can explain this please
Answer:
5
Step-by-step explanation:
6*3÷√9-1
=6*3÷3-1
=6*(3/3)-1
=6*1-1
=6-1
=5
Answer:
5
Step-by-step explanation:
We already know the square root of 9 is 3 because 3 times 3 equals 9
So now the equation is 6 * 3/3 - 1
3 divided by 3 is 1
6 * 1-1
6 times 1 is 6
6-1
You should get 5
Write the fraction as a decimal.
Answer:
0.5625
Step-by-step explanation:
9÷100=0 5625 in decimal mark me as a brainlist answer
Answer:
1.5625
Step-by-step explanation:
9/16=0.5625
therefore, 1.9/16=1.5625= 1.563
I need help please help
Answer:
m
Step-by-step explanation:
Answer:
Sin 73 = 0.956304756, Cos 17 = 0.956304756
Sin 18 = 0.3090169944, Cos 72 = 0.3090169944
This only works when the Sin angle and the Cos angle are complementary, meaning they add up to 90 degrees.
55+35=90
30+60=90
15+75=90
73+17=90
18+72=90
(Keep in mind the values for the Sin and Cos are approximations)
I hope this helped! :D
Jan has three times as many marbles as Liana. If Jan gives 3 of her marbles to Liana,
they will have the same number. How many marbles do they have between them?
(A) 18
(B) 6
(C) 8
(E) 16
Answer:
Step-by-step explanation:
I got 12 so not sure.
3x-3=x+3
2x=6
X=3
So 3x3 =9. +3. =12
plse help.....me
[tex]a - 3 + a - 5[/tex]
[tex]a-3+a-5=\\\\=a+a-3-5=\\\\=\boxed{2a-8}[/tex]
If the ratio of x+y to x-y is 2/5, what's the ratio of y to x ?
9514 1404 393
Answer:
y/x = -3/7
Step-by-step explanation:
Write the given relationship and solve for y/x.
(x +y)/(x -y) = 2/5
5(x +y) = 2(x -y) . . . . . multiply by 5(x-y)
5x +5y = 2x -2y . . . . . eliminate parentheses
7y = -3x . . . . . . . . . . . add 2y-5x
y/x = -3/7 . . . . . . . . divide by 7x
I’m so cool taht you should help me!
Answer:
See figure below.
Step-by-step explanation:
Start with each expression in the right column.
Combine like terms, and look for the answer in the left column.
See figure below.
Answer:
:4t+8=1-9t+7+6t+7t.
:-2t-9=2t-t-4-3t-5.
:-4t+8=-5t+8+t.
:2t-9=-t+3+3t-12.
Choose the composition of translations that maps the image ΔPQR onto ΔP′Q′R′.
Question 4 options:
(x,y) → (x + 6,y + 3)
(x,y) → (x – 6,y – 3)
(x,y) → (x + 6,y – 3)
(x,y) → (x – 6,y + 3)
Answer:
(x , y ) ---> (x + 6 , y - 3)
Step-by-step explanation:
(x , y ) ---> (x + 6 , y - 3)
P(-1 , 4) -----> P'(-1+6 , 4-3) = P'(5,1)
Comapre P and P' x-coordinate
-1 + a = 5
a = 5 +1 = 6
Q(-1, 2) ----->Q'(-1+6 , 2 -3)= Q'(5, -1)
R(3 , 1) ------> R'(3+6 , 1-3) = R'(9,-2)
the sum of a number and 3 divided by 9
Answer:
[tex]\frac{(x+3)}{9}[/tex]
Step-by-step explanation:
The graph below shows the solution set of which inequality?
[tex]\Large \boldsymbol{} \pmb {Answer: |x|<6}[/tex]
Step-by-step explanation :
[tex]\displaystyle \Large \boldsymbol{} |x|< 6 =>{ \left \{ {{\!\!\!x< 6} \atop {x> -6}} \right. } => \boxed{x \in (-6 ; 6 )} \ \ right[/tex]
Dino has 14 coins and 2 one-dollar bills. Which describes the relationship between the coins and the dollar bills?
