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.
what are the angle measurements of the triangle??
49y²+42y+9 please I need help, I promise to rate you as the brain lest when I get the exact answer am looking for
Answer:
[tex]\huge\boxed{\sf (7y+3)(7y+3)}[/tex]
Step-by-step explanation:
[tex]\sf = 49y^2+42y+9\\\\=(7y)^2+2(7y)(3)+(3)^2\\\\Using \ Formula \ a^2+2ab+b^2 = (a+b)^2\\\\= (7y+3)^2\\\\= (7y+3)(7y+3)\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Check For Understanding
CELL PHONES A Cell phone company is going to build three new towers in a nearby city. The city council has
released s map that shows where the towers will be built. On the map, the distance between towers A and B is 2
centimeters, the distance between towers B and C 3 centimeters, and the distance between towers A and C is 4
centimeters. A technician needs to visit the stes of the three towers, and he has outlined his travel route between
them on a map. The polygon formed by his travel route on the map will be similar to the polygon formed by the
technicians he drives to the three towers. If the actual distance between tower Band tower C is 600 meters, how
for was the technican have to travel to visit all three cell phone towers?
Answer:
Distance between A ----> B : 2 cm
B ---> C: 3 cm : 600 meters
A----> C: 4 cm
3:600 meters scaled
So its 200 meters per every 1 cm!
From A to B : 400 meters
From B to C : 600 meters
Frok C to A: 800 meters
Therefore we sum 400+600+800= 1800 meters
If KLM= NOP, find the perimeter of KLM.
Answer: 34 units
Step-by-step explanation:
I took the test
The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On
which day would you expect that number to be reached?
A)
8
B)
9
o
10
D
11
Answer:
c 10
Step-by-step explanation:
the number is increasing by 4. keep adding 4 until you reach 62, day 10
What is the rule when reflecting across the line y = x
Answer: switch the x and y values of the coordinates
(x, y) —> (y, x)
The second angle of a triangle is 3 times as large as the first angle. The third angle is 30 degrees more than the first angle. Find the measure of the angles.
Answer:
30-60-90 degrees
Step-by-step explanation:
1st angle: x
2nd angle: 3x
3rd angle: x+30
Sum of all angles must be 180 degrees
x + 3x + x + 30 = 180
5x + 30 = 180
5x = 150
x = 30
2 lines intersect to form angles 1 and 2.
Which equation represents the relationship between their measures?
mAngle1 + mAngle2 = 90°
mAngle1 + mAngle2 = 100°
mAngle1 + mAngle2 = 180°
mAngle1 + mAngle2 = 200°
Answer:
mAngle1 + mAngle2 = 180°
Step-by-step explanation:
This is the answer hope it helps
if u had a picture i could give further details
Hope this helped
Answer:
What if I told you I guessed
Step-by-step explanation:
but submitted and got it correct
...
its C:)2. What is the equation of the line that passes through the points (4,5) and
(8,3)?
Answer:
y = -1/2x + 7
Step-by-step explanation:
The slope is -1/2.
The y intercept is 7.
Plugging them into the format for the equation we have:
y = mx + b
(m = slope and b = y intercept)
y = -1/2x + 7
What is a rate? I will mark Brainiest
Answer:
A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. ... When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.
Step-by-step explanation:
amanda had to pay sales tax on a new iphone case she purchased last week. The iphone case was 35.00 and she pid 2.45 in taxes, what percent of the original price did she pay in taxes?
HELP
Answer:
7%
Step-by-step explanation:
[tex]\frac{2.45}{35} = \frac{x}{100}[/tex]
[tex]2.45*100[/tex] and [tex]35x[/tex]
[tex]\frac{245}{35} = \frac{35x}{35}[/tex]
[tex]245/35=7[/tex]
Flying to Havana with a tailwind a plane averaged 258 km/h. On the return trip the plane only
averaged 218 km/h while flying back into the same wind. Find the speed of the plane in still air
and the speed of the wind.
Brainlest if correct
Consider a function f(x) such that f(5x) =x-5/5x-1. Find f(x) and hence write down the domain of f(x).
Answer:
[tex]f(x) = \frac{x - 25}{5x - 5}[/tex]
Domain: [tex]x \ne 1[/tex]
Step-by-step explanation:
Given
[tex]f(5x) = \frac{x - 5}{5x - 1}[/tex]
Required
Determine f(x) and its domain
To determine f(x), we replace 5x with x in f(5x)
So, we have:
[tex]f(5x) = \frac{\frac{5x}{5} - 5}{5x - 1}[/tex]
[tex]f(x) = \frac{\frac{x}{5} - 5}{x - 1}[/tex]
Take LCM
[tex]f(x) = \frac{\frac{x - 25}{5}}{x - 1}[/tex]
[tex]f(x) = \frac{x - 25}{5} * \frac{1}{x-1}[/tex]
[tex]f(x) = \frac{x - 25}{5x - 5}[/tex]
To get the domain, we set the denominator as
[tex]5x - 5 \ne 0[/tex]
[tex]5x \ne 5[/tex]
[tex]x \ne 1[/tex]
Which ratio is equivalent to 2:3? A 8:12 B 9:10 C 10:9 D 12:8
Answer:
A 8:12
Step-by-step explanation:
If you multiply 2 and 3 by 4 you get 8:12
Answer:
The correct answer is A
is this table a function? why or why not?
A shoe store uses a 50% markup for all of the shoes it sells. What would be the selling
price of a pair of shoes that has a wholesale cost of $63?
4
Mathematical
9. PRACTICE Model Math The
table shows the lengths of four
trails at a horseback riding camp.
Estimate the total length of all the
trails.
Answer:
11
need more characters
What is the product of all constants $k$ such that the quadratic $x^2 + kx +15$ can be factored in the form $(x+a)(x+b)$, where $a$ and $b$ are integers?
YOU LITERIALLY ASKED THIS 7 TIMES ARE YOU OK?
is this still a problem you have?
if so ill solve it in one of the many other exact same threads.
6 x - 2 (x - 5) = 22
Answer:
x = 2.75
Step-by-step explanation:
6x - 2 (x - 5) = 22
6x -2x + 10 = 22
4x + 10 = 22
- 10 - 10
4x = 11
11/4 = 2.75
x = 2.75
Let me know if you need any more help!
Mildred has a bag of coins. The bag contains 10 dimes, 5 nickels, and 1 penny. She will randomly select 2 coins from the bag one at a time without replacement. What is the probability that Mildred will select a dime first and then a penny?
Answer:
Total possibilities = 16
Probability of a dime of the first draw is 10/16 = 5/8
Probability of a penny on the second draw = 1/15
Probability of both = 5/8 * 1/15 = 1/24
[tex]y > 3x + 9 y < 3x - 1[/tex]
please help is it infinite number of solutions, or no solution
Answer:
no solution
Step-by-step explanation:
Calculate the value of y
Answer:
157°
Step-by-step explanation:
(4x - 5)° = (x + 16)°.. (vertical angles)
4x - 5 = x + 16
4x - x = 16 + 5
3x = 21
x = 21/3
x = 7
(x + 16)° + y ° = 180°...(Linear pair angles)
(7 + 16)° + y° = 180°
23° + y° = 180°
y° = 180° - 23°
y° = 157°
please help! which sentence explains why the moon can be seen from the earth at night?
here are the options to choose from
Answer:
a
Step-by-step explanation:
Answer:
A - The Moon reflects light from the Sun.
Step-by-step explanation:
As the moon moves around the sun in a one month cycle, different parts of it are exposed to the sun. When it is exposed to the light from the Sun it is reflected and people on Earth could see it at night, and sometimes during the day as well.
I need help with this homework
4) Karen Waughtal invested some money at 5% annual simple interest
and $500 more than that amount at 8% annual simple interest. If her total
yearly interest was $300, how much was invested at each rate?
Answer:
15000
Step-by-step explanation:
write a statement that indicates that the triangles in each pair are congruent
Which pair of operations are not inverses?
a. Taking the square root of a number and squaring
b. Addition and subtraction
c. Multiplication and division
d. Squaring and division
help me due tomorrow at 4
if x+1/x = 5 find the value of x^3 +1/x^3. pls solve
Answer:
1) solve x+1/x = 5
[tex] \frac{x + 1}{x} = 5[/tex]
[tex]x + 1 = 5x[/tex]
[tex]x - 5x = - 1[/tex]
[tex] - 4x = - 1[/tex]
[tex]x = \frac{ -1}{ - 4} [/tex]
[tex]x = \frac{1}{4} [/tex]
2) solve x³+1/x³
[tex]x {}^{3} + \frac{1}{x {}^{3} } [/tex]
substitute x = 1/4 into the expression
[tex]( \frac{1}{4} ) {}^{3} + \frac{1}{( \frac{1}{4}) {}^{3} } [/tex]
[tex] \frac{1}{64} + \frac{1}{ \frac{1}{64} } [/tex]
[tex] \frac{1}{64} + \frac{64 \times 1}{1} [/tex]
[tex] \frac{1}{64} + 64[/tex]
[tex] \frac{4097}{64} \: or \: 64.02[/tex]