There are 6 people in Jacob’s family. Jacob’s sister is 5 years younger than he is. He has twin brothers who are 3 years older than he is. His mom is 3 times Jacob’s age, and his dad is 4 years older than his mom. The total of all the ages of all his family members is 165 years. How old is Jacob? Define a variable, write an equation, and solve the problem.
Answer:
Jacob is [tex]16[/tex] years old.
Step-by-step explanation:
Let the age of Jacob be [tex]x[/tex] years.
Jacob’s sister is [tex]5[/tex] years younger than he is.
So, the age of Jacob's sister be [tex]x-5[/tex] years.
Jacob's twin brothers are [tex]3[/tex] years older than he is.
So, the age of each of the twin brother be [tex]x+3[/tex] years.
Jacob's mom is [tex]3[/tex] times his age.
So, the age of Jacob's mom be [tex]3x[/tex] years.
Jacob's dad is [tex]4[/tex] years older than his mom.
So, the age of Jacob's dad be [tex]3x+4[/tex] years.
Now, the total of all the ages of all his family members is [tex]165[/tex] years.
So, [tex]x+x-5+x+3+x+3+3x+3x+4=165[/tex]
[tex]\Rightarrow 10x+5=165[/tex]
[tex]\Rightarrow 10x=165-5[/tex]
[tex]\Rightarrow 10x=160[/tex]
[tex]\Rightarrow x=\frac{160}{10}[/tex]
[tex]\Rightarrow x=16[/tex]
Hence, Jacob is [tex]16[/tex] years old.
Noah and his dad went out to lunch thier meal cost $34.56 Noah dad left a 15% tip on the table what is the amount of the tip he left for the meal what is the amount of lunch including tip
The farmer down the street has an orchard with both orange and grapefruit trees. Over the weekend, she collected 49 oranges and 84 grapefruits. She wanted to make baskets to sell at the local farmer's market with an equal number of oranges and grapefruits in each basket. What is the greatest number of baskets she can make.
Number of baskets she can make with an equal number of fruits in each basket?
Number of oranges in each basket?
Number of grapefruits in each basket?
Answer:
30 baskets
Step-by-step explanation:
Find the gfc of 150 and 240, you'll find that it is 30
The unit price of a shirt is $12. The cost, c, of n shirts is represented by the equation c = 12n. Select the value that belongs in the highlighted box.
$2
$3
$18
$48
$60
$72
Write an equation of a line with slope -3/2 and x-intercept (4,0)
Answer:
An equation of a line with slope -3/2 and x-intercept (4,0) will be:
[tex]y\:=\:-\frac{3}{2}x\:+\:6[/tex]
Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
m is the slopeb is the y-interceptGiven
Slope m = -3/2x-intercept (4, 0)now substitute m = -3/2 and the point (4, 0) in the slope-intercept form of line equation
[tex]y = mx+b[/tex]
[tex]0\:=\:-\frac{3}{2}\left(4\right)\:+\:b\:\:\:\:\:[/tex]
[tex]-6+b=0[/tex]
Add 6 to both sides
[tex]-6+b+6=0+6[/tex]
Simplify
[tex]b=6[/tex]
Thus, the y-intercept b = 6
now substitute m = -3/2 and b = 6 in the slope-intercept form of line equation
[tex]y = mx+b[/tex]
[tex]y\:=\:-\frac{3}{2}x\:+\:6[/tex]
Therefore, an equation of a line with slope -3/2 and x-intercept (4,0) will be:
[tex]y\:=\:-\frac{3}{2}x\:+\:6[/tex]
and no boxes were removed, all the boxes in the warehouse were arranged in stacks of 14 boxes each, with no boxes left over. How many boxes were in the warehouse before the 60 additional boxes arrived
Answer:
360 boxes
Step-by-step explanation:
The number of boxes in the warehouse before 60 boxes were added is;
n = 12k .... equation 1
where k is the constant of the number of stacks and n is the number of boxes.
The number of boxes after the 60 boxes were added is;
n + 60 = 14k ... equation 2
substitute the value of n in equation 2 for equation 1:
12k + 60 = 14k
60 = 14k - 12k
60 = 2k
k = 60 / 2 = 30
The number of boxes in the warehouse before 60 boxes was added is;
n = 12 * 30 = 360
(8, -1) and slope m= -3 for slope intercept
Answer:
Slope-intercept Form: [tex]y = -3x + 16[/tex]
Step-by-step explanation:
Point-slope: [tex]y- y_1 = m (x - x_1)[/tex]
[tex]y + 1 = -3(x - 8)\\y \frac{+8}{-8} = -3x + \frac{+24}{-8} \\y = -3x + 16[/tex]
What percent of the students ride on the bus ?
2х + 3 +7+ 1 = simply the expression
Answer:
2x + 11
Step-by-step explanation:
2x stays by itself and the integers combine. (3+7+1 = 11)
Answer:
2x + 11
Step-by-step explanation:
you just add the 7 + 3 + 1 = 11
2x + 11
Use the Distributive Property to expand the algebraic expression. -5 (-3b - 2c)
Answer:
-5(-3b) - (-5(2c)
Step-by-step explanation:
you flip a coin 10 times in a row. every single time it comes up heads. on the 11th flip, is it more likely to be heads, tails, or are heads and tails equally likely
Answer:
1/2
Step-by-step explanation:
It will be either heads of tails equally likely.
It’s still 1/2. Flipping a coin is an independent event. In other words, the outcome of the next flip is uninfluenced by what has happened previously. It’s as if it were the first time you ever flipped the coin. The probability is unaltered.
Can somebody please help me please!!!!
A. 28.26cm
B. 37.68cm
C. 18.84cm
D. 56.52cm
Answer:
Option D
Step-by-step explanation:
circumference: 2pi x r
r = 9 (6 + 12)/ 2
2 x pi x 9
= 18 pi cm^2 = 56.55 cm^2
Answer:
D. 56.52 cm
Step-by-step explanation:
Circumference = 2*pi*r
Based on the picture, we can see the largest circle has a diameter of 18 cm. (12 + 6)
The radius of the largest circle is half of it's diameter: 18/2 = 9 cm
Now put in the numbers for the circumference equation:
Circumference = 2 * pi * 9 (9 is the radius)
Circumference = 56.5 cm
Is the function in the table linear or nonlinear Why
Answer:
linear
Step-by-step explanation:
it goes thru the (0,0) orgin
The total cost to go horseback riding is x dollars per hour plus a 2 fee for renting a helmet which expressions represent the cost in dollars
Answer:
I believe its x. I'm not fully understanding the question as you have it worded odd. Maybe help me understand so that I can further help you?
Step-by-step explanation:
??
Find the slope
1. (4,7) (-2,-5)
2. (-10,8) (-5,4)
3. (1,2) (3,9)
Answer:
1. m= 2
2. m= -4/5
3. m= 7/2
Step-by-step explanation:
Jane read 3/8 of a book for 6 days. How many books did she read?
Answer:
2 and a half books.
Step-by-step explanation:
3/8×6=?
I simplified it by dividing 8 and 6 with 2 to get:
3/4×3=9/4
in whole numbers it will be, 2 and a half books
Brianna has a sheet of paper that is 4 feet long. She cuts the length of paper into halves and then cuts the length of each of these pieces into fourths. How many pieces does she have? How many inches long is each piece?
Answer:
she has 8 and the length 6 inches
Step-by-step explanation:
have a great day
Please answer any one them thank you so much
Answer:
is this alegebra? if so im failing in it.
Step-by-step explanation:
because im bad at alegebra
Answer:
left to right:
4a + 12
6a - 36
12c+6
10d + 30
40e + 64
48f - 72
14g - 20
66h - 36
22 + 14i
90j - 27
27k - 30
65m - 143
Step-by-step explanation:
I really hope this helped
a circular railroad-crossing sigh has a radius of 15 inches. which measurement is closest to the area of the sigh in square inches?
Answer:
30
Step-by-step explanation:
A rental car company charges $68.64 per day to rent a car and $0.12 for every mile driven. Jaxon wants to rent a car, knowing that: • He plans to drive 500 miles. • He has at most $210 to spend. What is the maximum number of days that Jaxon can rent the car while staying within his budget?
Answer:
2 days
Step-by-step explanation:
According to the problem, calculations of given data are as follows,
Rental charges per day = $68.64
Rental per mile = $0.12
Total miles = 500
Total spend = $210
Let number of days = X
So, we can find number of days by using following equation,
($68.64 × X ) + ( $0.12 × 500) = $210
$68.64 X + $60 = $210
$68.64 X = $210 - $60
$68.64 X = $150
X = $150 ÷ $68.64
X = 2.18 or 2 Days
y=5x+7 and passes through (4,3)
the answer is y=5x-17
How do you get the -17?
Answer:
i do not no i do not no
Step-by-step explanation:
Dianna made several loaves of bread yesterday. Each loaf required 2 and two-thirds cups of flour. Altogether, she used 13 and one-third cups of flour. How many loaves did Dianna make?
3 loaves
4 loaves
5 loaves
7 loaves
Answer:
5
Step-by-step explanation:
2[tex]\frac{2}{3}[/tex]x=13[tex]\frac{1}{3}[/tex][tex]\frac{8}{3}[/tex]x=[tex]\frac{40}{3}[/tex]x=5A farmer estimated that there were 25 gallons of water left in the tank. If this is an understatement by 16%, how much water was actually left in the tank
Answer:
29.76 is ur answer
Step-by-step explanation:
Ethan was able to save ₱220.00 in 5 days, spending only ₱25.50 of the allowance given him daily. How much allowance is he given a day?
Answer:
44 pounds daily
Step-by-step explanation:
Step one:
Given data
Ethan was able to save ₱220.00 in 5 days
He only spends ₱25.50 of the allowance given him daily
Required
His daily allowance
Step two:
if in 5 days he saves 220 pounds
then in 1 day he will save
=220/5
=44 pounds
Write a unit rate for the following situation. $54 for 3 every guests
Answer:
Step-by-step explanation:
It's 18 dollars per guest with 54:3
What i 9X3? what is the correct answer
The simplification of the given expression 9 x 3 is equal to 27.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is to determine the product of two or more numbers. If an event can occur in m different ways and if following it, that a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We don not write symbols like of currency generally, and understand it from context. Also, sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together.
We are given the number as 9 x 3
WE can see that the number is multiple of 3
Therefore by using simplification we get;9 x 3 = 27
Hence, the answer is 27.
Learn more about multiplications;
https://brainly.com/question/14059007#SPJ2
Find the ratio of the volume of the triangular prism
to the volume of the cuboid.
Give your answer in its simplest form.
Answer:
triangular prism
0.5 X 5 X 4 X 9 = 90 cubed cm
cuboid
6 X 5 X 20 = 600 cubed cm
triangular prism : cuboid
90:600
now simplify
both are divisible by 30
3:20
this cannot be simplified further
answer = 3:20
What is the measure of AngleEDH? 10° 40° 50° 90°
Answer:
50
Step-by-step explanation:
The scale factor from a small triangle ABC to a large triangle XYZ is 5. How many times larger will the perimeter of triangle XYZ be than
the area of triangle ABC?
Answer:
Answer below :)
Step-by-step explanation:
Hi there!
Question 4 - the answer will be 5. Since the scale factor is 5, we would (hypothetically) multiply the area by 5 to get the new area of XYZ, so area XYZ is 5 times the area of ABC.
Question 5 - A.
First we multiply 45 by 12 to find the amount in inches. This is 540. Now, we divide that by 6 to get 90. This is our scale factor in inches, but the answers only show the scale in feet, so we have to convert. Divide 90 by 12 to get 7.5.
I hope this helps!