Step 1: Set up a table.
Algebra Age Problems
Step 2: Fill in the table with information given in the question.
John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now?
Let x be Peter’s age now. Add 5 to get the ages in 5 yrs.
Algebra Age Problems
Write the new relationship in an equation using the ages in 5 yrs.
In 5 years, John will be three times as old as Alice.
2x + 5 = 3(x – 5 + 5)
2x + 5 = 3x
Isolate variable x
x = 5
Answer: Peter is now 5 years old.
A sketch of a rectangular patio is shown below. A concrete triangular section is planned for an outdoor fireplace. What is the area of the concrete section, in square units? A rectangle has a width of 69. A segment is drawn from the top left corner down to a point on the bottom side, creating a right triangle. The segment, which is the hypotenuse of the triangle, is 115 units long. From the segment to the bottom left corner is 100 units. A. 517.5 square units B. 1,587 square units C. 3,174 square units D. 7,935 square units
Answer:
3,174
Step-by-step explanation:
Answer: 3,174
Step-by-step explanation:
115^2-69^2= sqrt8464=92
100+92=whole leg=192
192*69=13248= whole area
69*92=6348
6348/2
=3174
A group of people went to a coffee shop.
Each person chose a drink and a treat.
number of people who chose coffee: number of people who chose tea = 1:4
Of those who chose coffee,
number of people who chose a muffin number of people who chose a tart = 2:7
Of those who chose tea,
number of people who chose a muffin : number of people who chose a tart = 5:1
What fraction of the people chose a tart?
Answer:
Fraction of the people chose a tart = [tex]\frac{13}{45}[/tex]
Step-by-step explanation:
Given - A group of people went to a coffee shop. Each person chose a
drink and a treat. number of people who chose coffee: number of
people who chose tea = 1:4. Of those who chose coffee, number of
people who chose a muffin number of people who chose a tart =
2:7. Of those who chose tea, number of people who chose a muffin
: number of people who chose a tart = 5:1.
To find - What fraction of the people chose a tart?
Proof -
Let the Total number of People went to a coffee shop = 5x
Now,
As given, number of people who chose coffee: number of people who chose tea = 1:4
⇒Total number of people who chooses coffee = [tex]\frac{1}{5}.5x[/tex] = x
Total number of people who chooses tea = [tex]\frac{4}{5}.5x[/tex] = 4x
Now,
As given,
Of those who choose coffee, number of people who chose a muffin number of people who chose a tart = 2:7
⇒Total number of people who choose muffin after coffee = [tex]\frac{2}{9}x[/tex]
Total number of people who choose tart after coffee = [tex]\frac{7}{9}x[/tex]
Also,
Given that
Of those who chose tea, number of people who chose a muffin : number of people who chose a tart = 5:1
⇒Total number of people who choose muffin after tea = [tex]\frac{5}{6}.4x = \frac{20}{6}x[/tex]
Total number of people who choose tart after tea = [tex]\frac{1}{6}.4x = \frac{4}{6}x[/tex]
∴ we get
Total number of people who chooses tart = Total number of people who choose tart after coffee + Total number of people who choose tart after tea
⇒Total number of people who chooses tart = [tex]\frac{7}{9}x[/tex] + [tex]\frac{4}{6}x[/tex]
= [tex]\frac{7}{9}x + \frac{2}{3}x[/tex]
= [tex]\frac{7x + 6x}{9}[/tex]
= [tex]\frac{13}{9}x[/tex]
⇒Total number of people who chooses tart = [tex]\frac{13}{9}x[/tex]
Now,
Fraction of the people chose a tart = [tex]\frac{People choose tart}{Total people}[/tex]
= [tex]\frac{\frac{13}{9}x }{5x}[/tex]
= [tex]\frac{13}{45}[/tex]
⇒Fraction of the people chose a tart = [tex]\frac{13}{45}[/tex]
A box of pencils is 5 1/4 inches wide. Seven pencils, laid side by side, take up 2 5/8 inches of the width. How many inches of the width of the box is not taken up by pencils?
Answer:
Step-by-step explanation:
5.25 - 2.625 = 2.625 inches
Plss help......ASAP!!
Answer:1-12.5 feet, 2-10 feet, 3-13.75 feet, 4-8.125 feet,5-25 feet, 6-20 feet
Step-by-step explanation: All you have to do is break down the scale factor to 1:2.5 and multiply each measurement by 2.5.
Please help. Image below.
Answer:
a) 78
b) 1275.....
Step-by-step explanation:
.............
Activity 1: Put me in the Box!
Direction: Determine the hypothesis and the conclusion of the given statement
the hypothesis in Box A and the conclusion in Box B.
1. Vertical angles are congruent
2. Bats are mammals that can fly.
3. You are a good citizen when you obey rules and regulations.
4. A number is divisible by 10 if its last digit is a 0.
5. 3x + 6 = 21, because x = 5
Step-by-step explanation:
To find - Determine the hypothesis and the conclusion of the given
statement the hypothesis in Box A and the conclusion in Box B.
1. Vertical angles are congruent
2. Bats are mammals that can fly.
3. You are a good citizen when you obey rules and regulations.
4. A number is divisible by 10 if its last digit is a 0.
5. 3x + 6 = 21, because x = 5
Proof -
Firstly we will write the conditional statements , so that we can easily find the hypothesis and the conclusion of the given statement.
1.)
Given statement - Vertical angles are congruent
Conditional statement - If two angles are vertical , then they are congruent.
Hypothesis - Two angles are vertical
Conclusions - They are congruent.
2.)
Given statement - Bats are mammals that can fly
Conditional statement - If bats are mammals , then they can fly.
Hypothesis - Bats are mammals
Conclusions - They can fly.
3.)
Given statement - You are a good citizen when you obey rules and regulations.
Conditional statement - If you are a good citizen , then you obey rules and regulations.
Hypothesis - You are a good citizen
Conclusions - You obey rules and regulations.
4.)
Given statement - A number is divisible by 10 if its last digit is a 0.
Conditional statement - If a number is divisible by 10, then its last digit is a 0.
Hypothesis - A number is divisible by 10
Conclusions - Its last digit is 0.
5.)
Given statement - 3x + 6 = 21, because x = 5
Conditional statement - If 3x + 6 = 21, then x = 5
Hypothesis - 3x + 6 = 21
Conclusions - x = 5
24. $5.24 + 23¢ + 2¢ (53)
Answer:
$5.49
Step-by-step explanation:
Rewrite 23¢ and 2¢ as $0.23 and $0.02, and then combine them: $0.25. Now add this result to $5.24. We get $5.49
In 2003 a gallon of gas cost $1.75. The cost has risen $0.17 each year since then
Write an equation to represent the cost of gas (in gallons) as a function of years.
What would the cost of a gallon of gas be in 16 years?
Answer:
x + m × y
$4.47
Step-by-step explanation:
The equation and computation is shown below:
Let us assume the cost of gallon be x
Increase each year be m
And, the number of years be y
So, the equation is
= x + m × y
The cost of gallon of gas in 16 years is
= $1.75 + $0.17 × 16
= $1.75 + $2.72
= $4.47
Mai says that equations A and B have the same solution.
Equation A: –3(x + 7) = 24
Equation B:x + 7 = -8
Explain why this is true?
Answer:
Step-by-step explanation:
Equation A:
-3(x + 7) = 24
=> -3x -21 = 24
=> -3x = 45
=> x = -15
Equation B:
x + 7 = -8
=> x = -15
Find an equation in point-slope for the line having the slope m m = - 6 and containing the point (8,6)
Answer:
y-6 = -6(x-8)
Step-by-step explanation:
Here, we want to get the equation of the line in point-slope form
The point slope form is;
y-y1 = m(x-x1)
(x1,y1) represents the slope
We have this as ;
y-6 = -6(x-8)
A number between 10 and 20 is both a foctor of 60 and
a multiple of 6.
What is the number?
Answer:
12
Step-by-step explanation:
List out factors of 60 =
1 x 60 = 60
2 x 30 = 60
3 x 20 = 60
4 x 15 = 60
5 x 12 = 60
6 x 10 = 60
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 are factors of 60.
List out multiples of 6 from 10 to 20.
12 and 18.
Since 12 is seen on one of the factors of 60 and a multiple of 6 between 10 and 20, the answer is 12.
complete the square
x²+8x
pls help lots of points and brainlist
Answer:
( x + 4 ) ²-16
Step-by-step explanation:
when i multiply it by 6 and subtract 29, the answer is 37.
what is my number?
Let the required number be "x"
According to the statement:
x(6) - 29 = 37
6x - 29 = 37
6x = 37 + 29
6x = 66
x = 66/6
x = 11
Therefore, the required number is 11.
when i multiply it by 6 and subtract 29, the answer is 37.
what is my number?
SOLUTION:▶️Let the required number be x.
According to the question the equation will form like:
▶️6x - 29 = 37
▶️6x = 37+29 (transposing x to RHS)
▶️6x = 66
▶️x = 66/6 (transposing 6 to RHS)
▶️x = 11
VARIFICATION:According to the question :
▶(️11×6) - 29
▶️ 66 - 29
▶️37
Hence varified..
ANSWER:11
What is the value of ry' when x = 5 and y = 10?
Answer:
135
Step-by-step explanation:
Answer:
1250
Step-by-step explanation:
X^3 • Y^1
Since X=5 & Y=10,
Substitute
5^3 •10^1
simplify
5*5*5*10=1250
pls hurry will give brainliesttt
Answer:
It's on the line x
Step-by-step explanation:
Draw the line over it
I will mark you brainiest if right
Sarah buys a car for £32,000. It depreciates at a rate of 2% per year. How many years will it take to be worth less than £30,000?
Answer:
no f ing clue
Step-by-step explanation:
sym
Point A (2, -3) is translating five units to the left and 4 units up. What is thenew point? *
(-3, 1)
(-5, 4)
(7, 1)
(-3,-7)
(a)
Find the hypotenuse, c, of the triangle.
4
B
12
Figure not drawn to scale
Answer:
[tex]\sqrt{160}[/tex]
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2} \\4^{2} +12^{2} =c^{2} \\16+144=c^{2} \\160=c^{2}\\\sqrt{160}=\sqrt{c^{2} }[/tex]
Hope this helps
pls help me with this question
Answer:
height = 12 feet
Step-by-step explanation:
r (radius of circle) = 7 ft
pi = 3.14 (in this context)
v = 1/3 * [tex]πr^{2}[/tex] (or pi * radius squared) * h
r squared = 49 ft
v = 1/3 3.14 * 49 * h
v = 1/3 153.86 * h
3v = 153.86 * h
v = 196π
v = 615.44
3v = 1,846.32
1,846.32 = 153.86 * h
h = 12 ft.
Complete the
following patt
using the formula belowo:
Question 2: lf 2,5,8,11,14......is a sequence, Find:
8 th
• 11 th
15 th
• 22 th
• 18 th
Answer:
8th: 23
11th: 32
15th: 44
22nd: 65
18th: 53
Step-by-step explanation:
The pattern is adding 3 each time:
2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65
Hope it helps!
Felipe and Makayla each tried to solve the same equation for x.
Original equation: 2x + 6= 3x - 8
The result of Makayla’s first
step was 6 = x - 8
Describe the first step Makayla made to the equation.
34.2 was rounded to one decimal place. What is the upper and lower bound?
Answer:
lower=34.15 upper=34.25
Step-by-step explanation:
I am stuck with the above question, please help
Answer:
D
Step-by-step explanation:
Two lines are parallel if they have the same slope.
the given equation is in the form
y=mx+b
where
m=-5/2
b=-7
m is the slope. You can see this by noting that if you increase x by 1 you increase y by m.
So, in this case, you are looking for a line with slope of -5/2.
You can solve each of the choice equations for y to see which one has the right slope.
A: y=(2/5)x-6 no good
B: y=-(2/5)x-1 no good
C: y=(5/2)x-4 no good
D: y=-(5/2)x-4 GOOD
between which two integers that Square Root of 11 Lie?
Answer:
3 and 4
Step-by-step explanation:
Answer:
3 and 4
Step-by-step explanation:
HELP ASAP!!
Find the length of side a
Answer:
d. 8
Step-by-step explanation:
by Pythagoras theorem:
(Hypo)² = (Perp)² + (Base)²
(Perp)²= (Hypo)² - (Base)²
= 10 × 10 - 6 × 6
= 100 -36
=(underroot) 64
= 8
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
[tex] \large \boxed{v > - 1}[/tex]
Step-by-step explanation:
Given the Inequality:
[tex] \large{ \frac{1}{3} (v -2) < v}[/tex]
Step 1
Multiply the fraction or 1/3 in the expression.[tex]\large{ \frac{1}{3} v - \frac{2}{3} < v}[/tex]
Step 2
Multiply the whole Inequality by 3 to get rid of the denominator.[tex] \frac{1}{3} v(3) - \frac{2}{3} (3) < 3(v) \\ v - 2 < 3v[/tex]
Step 3
Solve the Inequality for v-term by making v as the subject.[tex] - 2 < 3v - v \\ - 2 < 2v \\ \frac{ - 2}{2} < v \\ - 1 < v \\ v > - 1[/tex]
Hope this helps! If you have any questions that are related to the answer, feel free to use "Comment" feature!
Which expression is equivalent to 1/7 divided by 2/5
Answer:
is C
1/7 • 5/2
have a nice day!
Which is a better buy, 5 for $4.25 or 8 for $6.88?
Answer:
5 for $4.25
Step-by-step explanation:
First you find how much of one each cost
4.25 divided by 5 = 0.85
6.88 divided by 8 = 0.86
The one for 5 for $4.25 is one cent less
one cent is still money
HELLLLPPPPPP PLEASEEEEEEE
Answer:
(19,520-1,478) * 8
Step-by-step explanation:
PLS HURRY WILL GIVE BRAINLIEST
Answer:
C. y= 6x-5
Step-by-step explanation:
Given Information :
Slope (m) = 6
y-intercept (b) = -5
Equation of a line :
y=mx+b
Where :
m = slope
b = y-intercept
So , with the given the information , the equation is :
[tex]y = 6x - 5[/tex]
