Juan is three times as old as Gabe and Gabe is six years older than Catherine. If the sum of their ages is 149, how old is each person? Define a variable, write an equation, solve the equation, and answer in a complete sentence. (Remember to clearly show your work on your work page.)
Answer:
Juan = 93 years.
Gabe = 31 years.
Catherine = 25 years.
Step-by-step explanation:
Let the age of Juan = J
Let the age of Gabe = G
Let the age of Catherine = C
Translating the word problem into an algebraic equation, we have;
[tex] J = 3G[/tex] ..........equation 1
[tex] G = C + 6 [/tex] ........equation 2
[tex] J + G + C = 149 [/tex] ........equation 3
We would solve the linear equations by using the substitution method;
Substituting equation 2 into equation 1;
[tex] J = 3(C + 6)[/tex]
[tex] J = 3C + 18[/tex] ........equation 4
Substituting equation 2 and equation 4 into equation 3;
[tex] (3C + 18) + (C + 6) + C = 149 [/tex]
Simplifying the equation, we have;
[tex] 5C + 24 = 149[/tex]
[tex] 5C = 149 - 24[/tex]
[tex] 5C = 125[/tex]
[tex] C = \frac {125}{5}[/tex]
C = 25 years.
To find G; from equation 2
[tex] G = C + 6[/tex]
Substituting the value of "C" into equation 2, we have;
[tex] G = 25 + 6[/tex]
G = 31 years.
To find J; from equation 1
[tex] J = 3G [/tex]
Substituting the value of "G" into equation 1, we have;
[tex] J = 3 * 31[/tex]
J = 93 years.
Therefore, Juan is 93 years old, Gabe is 31 years old and Catherine is 25 years old.
Find the total cost of buying a product that cost $12 if it is 25% off. DO NOT PUT A $. Only numbers.
Answer:
the answer will be 9 dollars
Explanation:
The discount of 25% off means you save 0.25*12 = 3 dollars, meaning the final cost is 12-3 = 9 dollars.
Or you can think of it like this: if you save 25%, then you still pay the remaining 75%. So 0.75*12 = 9 dollars is the total cost.
Mary used one big bag of flour. She baked four loaves of bread. Then, she used the remaining flour to make 48 muffins. How much flour was in the bag when Mary began? Plz help!!!! I have 20 minutes left
Answer is 11.
Step-by-step explanation:
Maria used two loaves of bread , One loaf is equal=2 1/4 cups so two becomes 2 ×2 1/4= 9/2
Maria makes the remaing 48 muffins of the flour left so,
One muffin is equal 3 1/4 cups so two becomes 2×3 1/4=13/2
Add both of them
9/2+13/2=11
9. The diameter of the Earth is 7899.83 miles from the North Pole to the South Pole and 7926.41 miles from opposite points at the equator.
a. Find the approximate surface area of Earth using each measure.
b. About 75% of Earth's surface is covered by water. Find the surface area of water on Earth, using the diameter of the Earth is 7926.41 miles from opposite points at the equator.
Answer:
We could think of the Earth as a sphere, where the diameter of this sphere will the mean diameter between the measure from the North pole to the Soth pole and the measure from opposite points of the equator.
Remember that the mean between two numbers A and B is:
Mean = (A + B)/2
In this case, the mean diameter will be:
D = (7,899.83mi + 7,926.41mi)/2 = 7,913.115 mi
And we know that the surface of a sphere of diameter D is:
S = 4*pi*(D/2)^2
Where pi = 3.14
Then the surface of the Earth will be something like:
S = 4*3.14*(7,913.115mi/2)^2 = 196,618,601.47 mi^2
b) We know that 75% of the Earth's surface is water, now we will use the diameter 7,926.41 mi to compute the surface.
First, the total surface of the Earth will be:
S = 4*3.14*(7,926.41mi/2)^2 = 197,279,843.03 mi^2
And 75% of this is water, then the total water surface is 0.75 times that area, this is:
water surface = 0.75*197,279,843.03 mi^2 = 147,959,882.27 mi^2
Maria tenia 6.500kg de patatas. Las envaso en sacos de 25kg y los puso a la venta a 30$ cada uno. Vendio la mitad de los sacos a ese precio y el resto los vendio todos a 2$ menos cada saco. ¿ Cuanto dinero obtuvo?
Responder:
$ 7540
Explicación paso a paso:
Dado que:
Kilogramos totales de papa = 6500
Número de kilogramos por paquete = 25
Precio por paquete = $ 30
La mitad se vendió a $ 30
El resto se vende a ($ 30 - $ 2)
Número total de paquetes de 25 kg:
6500 kg / 25 kg = 260 paquetes
Por lo tanto, paquete total = 260 paquetes
La mitad se vende a $ 30:
(260/2) * 30
130 * $ 30 = $ 3900
Resto vendido a $ 28:
(260 - 130) * $ 28
130 * $ 28 = $ 3640
Cantidad total realizada:
$ (3640 + 3900) = $ 7540
Given that log x = 3 and log y = 5, find log (x^2)(y^2)- log xy
Step-by-step explanation:
logx²y² - logxy
= log(x²y²/xy)
= logxy
= logx + logy
= (3) + (5)
= 8.
The value of logx²y² - logxy when log x = 3 and log y = 5 is 8.
What is a logarithm?The logarithm is the opposite of exponentiation as a function. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b.
Given:
log x = 3 and log y = 5
logx²y² - logxy
Calculate the above expression as shown below,
logx²y² - logxy = log x²y² / xy
logx²y² - logxy = log xy
logx²y² - logxy = logx + logy
logx²y² - logxy = 3 + 5
logx²y² - logxy = 8
Therefore, the value of logx²y² - logxy when log x = 3 and log y = 5 is 8.
To know more about logarithms:
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Find the circumference of the given circle use 3.14 pie and 7 in diameter
Answer:
43.98
Step-by-step explanation:
2piR
BTW the 7 is the radius not the diameter
Calculator Item 2 is unpinned. Click to pin. Mrs. Pitts wrote the volume formula as "V=1/3 Bh. What does "B" represent? A: The radius of the base B: The circumference of the base C: The diameter of the base. D: The area of the base.
Answer:
D: The area of the base.
Step-by-step explanation:
The volume of a triangular based pyramid is represented by the formula given that the question as:
V = 1/3BH
where B = Base area of the triangular based pyramid
H = Height of the triangular based pyramid.
Hence, option D is correct
B = The area of the base.
Determine if lines JK and LM are parallel, perpendicular or neither. J(-10, -7) K(-4, 1) L(-3, 2) M(-6, -2)
Answer:
i think it is neither
Step-by-step explanation:
Whats the slope of (6,0) and (2,-2)
Given f of x equals 6 1 minus x , what is the value of f of negative 6 ?
Answer:
answer will be 67
Step-by-step explanation:
f(x) = 61 - x
x = -6
hence we substitute the value of x in f(x)
f(-6) = 61 - (-6)
= 61 + 6
= 67
The value of the function f(x) = 6(1 - x) at x = -6 will be given 42.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The function is given below.
f(x) = 6(1 - x)
The value of the function at x = -6 will be given as,
f(-6) = 6[1 - (-6)]
Simplify the equation, then we have
f(-6) = 6[1 - (-6)]
f(-6) = 6(1 + 6)
f(-6) = 6 × 7
f(-6) = 42
The value of the function f(x) = 6(1 - x) at x = -6 will be given 42.
More about the function link is given below.
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Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: A(3,6) B(11,10)
Line 2: C(-4, 2) D(6, 16)
Parallel, Perpendicular, or Neither:
Answer:
Line 1 : A. Neither B. Parallel__________ Line 2: A. Perpendicular B. Parallel
Step-by-step explanation:
Sorry this was hard to make a picture of it in my head. *Exhausted face* ._.
Raquel is at an arcade. She bought 8 tickets, and each game requires 2 tickets. -Write two equivalent expressions that gives the number of tickets Maddy has left in terms of x, the number of games she has already played.
Answer:
raquel can only play 4 games
so 2x4=x=8
or 8 divided by 4 is x=2
Step-by-step explanation:
tell me your opinions on the following image
Answer:
gorgeous
Step-by-step explanation:
Answer:
i am disturbed.
Step-by-step explanation:
this image is disturbing to me, because he is staring at you in your sleep too
I need some help with this.
Answer:
b is 16 d is 13
Step-by-step explanation:
ok is a baby girl that can I be happy
On a bank account of $1,600, how much yearly interest will be paid
if the rate is 5%?
Answer:
Step-by-step explanation:
if in the bank account is 1600 dollars
the rate is 5%
1600*5%=80 dollars
Evaluate f(x) = 4 - 5x for f(-2)
*
Answer: the answer would be X E R
Step-by-step explanation:
e - i = 5
e + 3i = 9
e value =
i value =
What is the answer
Answer:
e value = 6
i value = 1
Step-by-step explanation:
The system of equation are;
e - i = 5...(1)
e + 3·i = 9...(2)
Making e the subject of equations (1) and substituting the value of e equation (2) gives;
From equation (1), e - i = 5, we have, e = 5 + i
Substituting the value of e in equation (2), e + 3·i = 9 gives;
e + 3·i = (5 + i) + 3·i = 5 + 4·i = 9
4·i = 9 - 5 = 4
i = 4/4 = 1
i = 1
From e = 5 + i, we have;
e = 5 + i = 5 + 1 = 6
e = 6
Therefore;
e value = 6
i value = 1
I needs help please and tank chu
9514 1404 393
Answer:
C {2, 4, 9, 16}
Step-by-step explanation:
The domain is the list of numbers at the tails of the arrows.
The range is the list of numbers at the heads of the arrows: {2, 4, 9, 16}.
If the relative frequencies are 0.48 and 0.52, which
conclusion is most likely supported by the data?
O There is likely an association between the
categorical variables because the relative
frequencies are similar in value.
O An association cannot be determined between the
categorical variables because the relative
frequencies are similar in value.
O An association cannot be determined between the
categorical variables because the relative
frequencies are not similar in value.
O There is likely an association between the
categorical variables because the relative
frequencies are both close to 0.50.
Answer:The Last One
Step-by-step explanation:
Option (B) an association cannot be determined between the categorical variables because the relative frequencies are similar in value is the correct answer.
What is relative frequency?The relative frequency of an event is defined as the number of times that the event occurs during experimental trials, divided by the total number of trials conducted. The sum of all relative frequencies will be one.
For the given situation,
The relative frequencies are 0.48 and 0.52.
A two-way frequency table can be used to show, analyze, and examine the relationships that exists between two categorical variables.
The two relative frequencies have the values that are similar to (close to) each other. So, there will be no association between the categorical values.
Hence we can conclude that option (B) an association cannot be determined between the categorical variables because the relative frequencies are similar in value is the correct answer.
Learn more about relative frequencies here
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can someone help with the equation(s)?
Answer:
Ok this is multiplication so its 30.25
Step-by-step explanation:
5.50 X 5.50 = 30.25
How are coordinate planes the same ????
22 points if u can answer
Answer: Its a trick question
Step-by-step explanation:
I did this yesterday
Answer:
They are the same because they all have an X-axis and a Y-axis
Step-by-step explanation:
sorry if im wrong lol
What is the slope of the line that passes through the following points:
(4,-3), (-5,10)
Answer:
13/-9
Step-by-step explanation:
5,680÷80=
WITH REMAINDER
NO CALCULATOR IT WILL NOT WORK
Answer:
71
Step-by-step explanation:
i used my calculator :D
Which number represents 50% of 74?
35
37
38
39
Answer: 37!!!
Step-by-step explanation:
1. 50% equals .5 in decimal form.
When converting a percentage to decimal, divide by 100 or move the decimal point to the left twice.
2. The word of means multiply so we multiply .5 by 74.
3. We get 37!
hope this helped, brainliest plsss :))))
I was the first one!
Help pls I am in 4th and my sister is at school so she can't help pls I was sick when we learned this I need like a couple more and then I can do the rest :(
Answer:
3/20
Step-by-step explanation:
you multiply 1/4 and 2/5 to get the answer
Please find the value of the x so that the function has the given value
f(x) = (-4/5)x+7 ; f(x) = 29
Can someone help me please
Answer:
D
Step-by-step explanation:
The answes D kiddo cuz
10 x 3 = 30 and 17 x 3 = 51
this one alsooooooooo
Answer:
the answer is cd
Step-by-step explanation:
Randall graphed the equation y=-2x+3 as follows:
Did Randall correctly graph the equation?
A. Yes he correctly graphed the equation B. No he graphed the line with a slope of 2 instead of -2 C. No, Randall graphed the line with a slope of -1/2 instead of -2 D. No, Randall graphed an x-intercept of (3,0) instead of y-intercept (0,3)
Answer:
C.
Step-by-step explanation:
Hope I could help :)))