Answer:
d = 7
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Give a₁₀ = 67 and a₁ = 4 , then
a₁ + 9d = 67
4 + 9d = 67 ( subtract 4 from both sides )
9d = 63 ( divide both sides by 9 )
d = 7
The distance required for a car to stop is directly proportional to the
square of its velocity. If a car can stop in 112.5 meters at 15 kilometers
per hour, how many meters are needed to stop at 25 kilometers per hour?
Answer:
312.5 m
Step-by-step explanation:
let distance be d and velocity be v , then
d = kv² ← k is the constant of variation
To find k use the condition d = 112.5, v= 15
112.5 = k × 15² = 225k ( divide both sides by 225 )
0.5 = k
d = 0.5v² ← equation of variation
When v = 25 , then
d = 0.5 × 25² = 0.5 × 625 = 312.5 m
Can i get some help :
Answer:
the second
Step-by-step explanation:
Answer:
0.9 + n = 5.2
Step-by-step explanation:
what is 3x + 4y = 10
6x - 4y = 8
Answer:
x=2
y=1
Step-by-step explanation:
9x+0=18
so it's x=2
6=4y=10
so y=1
The equation of a line is y = 12x - 3. Write the equation of a line parallel to this line.
Answer:
y=12x+3
Step-by-step explanation:
when parallel the slopes need to be the same but the y-intercept has to change
I need help with this question can someone plss help me!!
Answer:
Step-by-step explanation:
compare. 2 1/4 and 3 /14
Answer:
[tex]\frac{1}{4}[/tex] is larger than [tex]\frac{3}{14}[/tex]
[tex]\frac{1*14}{4*14}[/tex] = [tex]\frac{14}{56}[/tex]
[tex]\frac{3*4}{14*4}[/tex] = [tex]\frac{12}{56}[/tex]
i cant tell if it is [tex]\frac{1}{4}[/tex] or 2 [tex]\frac{1}{4}[/tex]
but if it is 2 [tex]\frac{1}{4}[/tex] that mean this is a mixed number
and [tex]\frac{3}{14}[/tex] is a proper fraction
Sally is making 15 individual blueberry cheesecakes. How many pounds of blueberries will be in each cheesecake if 514 pounds of blueberries are divided equally among them?
Answer:
About 35 or 34.27 if you round to the tenths spot.
Step-by-step explanation:
514 divided by 15 is 34.27 once rounded.
Lillian read 43 pages in 1 1/3 hours. At what rate, in pages per hour, did she read?
Answer:
hi
Step-by-step explanation:
Answer:
She reads one page in 1.40
Ryan and Taylor are both saving money to buy new video game equipment. Ryan's savings plan can be modeled by the function s= 15m + 50 where m represents the number of months since Ryan started his plan, and s represents the amount of money saved in dollars. The table shown represents Taylor's savings plan.
Taylor's Savings Plan --- In the file (Picture).
a. Ryans rate of change is_________Taylor's rate of change.
b. Ryans starting balance is _________Taylor's starting balance.
a. Ryan's rate of change is $15 per month;
Taylor's rate of change is $20 per month
b. Ryan's starting balance is $50;
Taylor's starting balance is $25.
Recall:
A linear function is modelled by the equation, y = mx + b, where m is the rate of change and b is the initial value (starting value).Rate of change = change in y/change in xRyan's Savings Plan Function:
s = 15m + 50
Thus, the starting value (starting balance) modelled by this function is $50
The slope/rate of change is $15 per month
Taylor's Savings Plan:
Given the table, the starting value will be the amount saved (initial value) at 0 number of months.
Therefore, Taylor's starting balance is: $25Using (0, 25) and (1, 45) find the rate of change:
Rate of change = (45 - 25)/(1-0) = 20/1 = $20In summary:
a. Ryan's rate of change is $15 per month;
Taylor's rate of change is $20 per month
b. Ryan's starting balance is $50;
Taylor's starting balance is $25.
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The lines represented by the equations y=x+5 and 2y-2x=10 are
The equations representing the lines, y=x+5 and 2y-2x=10, have the same slope, therefore the lines are parallel.
Recall:
Two lines that are parallel will have the same slope value.Two lines that are perpendicular to each other will have slopes that are negative reciprocal of each other.Equation representing a line in slope-intercept form is: y = mx + b, where m is the slope.Given:
y = x + 5
2y - 2x = 10
The slope of y = x + 5 is 1.
Rewrite 2y - 2x = 10 in slope-intercept form to determine its slope.
2y - 2x = 10
2y = 2x + 10
Divide both sides by 2y = x + 5
Thus, the slope of y = x + 5 (2y - 2x = 10) is also 1.
The equations representing the lines, y=x+5 and 2y-2x=10, have the same slope, therefore the lines are parallel.
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Please find the area...
In your own words, describe how to find the GCF for a set of numbers. Use the numbers 24 and 32 as an example. (PLS HELP ILL GIVE 100 points and brainlest also no links please, thanks)
Answer:
8Step-by-step explanation:
You need to factorize each number in the set:
24 = 2*2*2*332 = 2*2*2*2*2Common factors of both numbers are:
2*2*2 = 8GCF(24, 32) = 8
The total number of gallons of water in a tank, w, after t minutes is given in this table and the plot.
What is an equation showing the relationship between w and t?
Enter your answer by filling in the box to complete the equation.
w =
The equation showing the relationship between w and t is [tex]w = 4t[/tex]
From the table, we have the following points:
(0,0) and (1,4)
Start by calculating the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{4 -0}{1 -0}[/tex]
Simplify the numerator and the denominator
[tex]m = \frac{4}{1}[/tex]
Divide 4 by 1
[tex]m = 4[/tex]
The equation is then calculated as:
[tex]w = m(t - t_1) + w_1[/tex]
This gives
[tex]w = 4(t - 0) + 0[/tex]
Simplify
[tex]w = 4t[/tex]
Hence, the equation is [tex]w = 4t[/tex]
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Carol has some dimes and quarters. If she has 31 coins worth a total of $4.30, how many of each type of coin does she have?
Answer:
23 Dimes and 8 Quarter.
Step-by-step explanation:
Important info:
31 Coins worth a total of $4.30
Note:
Dimes = .10
Quarters = .25
10 Dimes = 1.00
4 Quarter = 1.00
Question to Answer:
How many of each type of coin does she have?
Solution:
Lets get rid of the .30 cent in $4.30 so
.30 = 3 Dimes
Now $4.00,
4.00-1.00 of quarter
=
3.00 and 4 quarter..
Right now we have 3 Dimes and 4 Quarter = $1.30.
And that 7 Coins worth of $1.30.
3.00-2.00= 1.00 and 20 Dimes so now we have
23 Dimes and 4 Quarter.
And that add up to 27.
1.00-1.00 of Quarter = 4 Quarter.
so 31 worth a total of $4.30.
So that's 23 Dimes and 8 Quarter.
Check Work:
23 Dimes = $2.30 and 8 Quarter = $2.00
$2.30 + $2.00 = 4.30
Hence, The Correct Answer is 23 Dimes and 8 Quarter.
~[ RevyBreeze }~
Is 6 a factor of the number 56 yes or no?
Answer:
No it is not a factor of 56
Answer:
No
Step-by-step explanation:
6,12,18,24,30,36,42,48,54,60
An arts academy requires there to be 4 teachers for every 100 students and 5 tutors for every 60 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 144 standents?
Answer: 25 students per teacher and 12 students per tutor. They need 2.4 tutors for the school
Simplify.
(7⁴)²
(EXPONENT FORM ONLY)
an airplane on autopilot took 5 hours to travel 3,475 kilometers, what is the unit rate?
I need to know how to get the roots for example what is the root of 2 root 5
Answer:
Square roots are when you multiply the same number by itself like for example, the square root of 5 is 25, because 5*5=25
Step-by-step explanation:
The value of the root of 2√5 is approximately 2.116.
Here, we have,
To find the root of a number, you can use the concept of radicals.
The "root" refers to the inverse operation of raising a number to a power. For example, the square root (√) is the most common root, and it represents finding a number that, when squared, gives the original number.
To find the root of a number, such as the square root (√), you can use the following notation:
√(2 * √(5))
In this case, we have the square root of (2 times the square root of 5).
To simplify this expression further, we can break it down step by step:
Step 1: Simplify the square root of 5:
√(5) = 2.236 (approximately)
Step 2: Substitute the simplified value back into the original expression:
√(2 * 2.236)
Step 3: Simplify the expression:
√(4.472) = 2.116 (approximately)
Therefore, the root of 2√5 is approximately 2.116.
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If t=100, find 2t + 1
need help
a rectangular garden is 50m long and 45 m broad A path 2m wide is. running inside the garden . Calculate the cost of gravelling the path at rs 40 per square meter.....
Answer:
Rs. 14560
Hope you could get an idea from here.
Doubt clarification - use comment section.
In rectangle ABCD
L=50mB=45m[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]
[tex]\\ \sf{:}\longrightarrow Area=50(45)[/tex]
[tex]\\ \sf{:}\longrightarrow Area=2250m^2[/tex]
In rectangle PQRS
L=50-2=48mB=45-2=43m[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]
[tex]\\ \sf{:}\longrightarrow Area=48(43)[/tex]
[tex]\\ \sf{:}\longrightarrow Area=2064m^2[/tex]
Now
[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=Area_{(ABCD)}-Area_{(PQRS)}[/tex]
[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=2250-2064=186m^2[/tex]
Cost:-
[tex]\\ \sf{:}\longrightarrow 186(40)[/tex]
[tex]\\ \sf{:}\longrightarrow Rs 7440[/tex]
67-7x(12-3)
Evaluate
Answer:
67-63x
Step-by-step explanation:
help please???????????
Answer:
The answer is C. (a + -a = 0 )
Step-by-step explanation:
"The additive inverse of a number a is the number that, when added to a, yields zero"
My question is in the attachment.
Answer:
5 and 25
Step-by-step explanation:
let the son's age be x then the father's age is x + 20
In 5 years
son = x + 5 and father = x + 20 + 5 = x + 25
Then
x + 25 = 3(x + 5) ← father is three times as old as son
x + 25 = 3x + 15 ( subtract x from both sides )
25 = 2x + 15 ( subtract 15 from both sides )
10 = 2x ( divide both sides by 2 )
5 = x and x + 20 = 5 + 20 = 25
si=on is 5 and father is 25
Answer:
The son is 5 and the father is 25.
Step-by-step explanation:
We can do this using Algebra.
Let the son be x years old.
Then the father's age is x + 20 years.
After 5 years the father's age is x + 25 and the son is x + 5 years.
So we can write the equation:
x + 25 = 3(x + 5)
x + 25 = 3x + 15
25 - 15 = 3x - x
10 = 2x
x = 5.
So the father's present age is 20 + 5 = 25 and the son is 5 years old.
help me pls... ....
Step-by-step explanation:
A1
1 yard = 3 feet
1 foot = 12 inches
therefore,
100 yards = 100×3×12 inches = 3600 inches
A2
again, 1 yard = 3 feet
8 ft = 8/3 = 2.67 yards = 2 2/3 yards
A3
1 gallon = 8 pints
A4
1 liter = 1000 milliliters (remember, "mili" means 1/1000).
therefore,
2.2 liters = 2.2×1000 = 2200 milliliters
A5
again, 1 liter = 1000 milliliters
therefore
1 milliliter = 1/1000 liter
670 milliliters = 670 × 1/1000 liter = 670/1000 liter =
= 0.67 liter
B1
1 kg (kilogram) = 1000 grams ("kilo" means 1000).
we have 3 layers.
each layer weighs (cake plus icing)
1/2 kg + 100 g = 500 g + 100 g = 600 g
3 layers then weigh
3×600 g = 1800 g
the additional candle weighs 250 g.
so, the total is
1800 g + 250 g = 2050 g = 2.05 kg
B2
area is 110 m².
1 m = 100 cm ("centi" means 1/100).
and 1 m² is then 100×100 = 10000 cm².
so, the area in cm² is
110 × 10000 = 1,100,000 cm²
the top area of one brick = 10 × 20 = 200 cm²
so, we need
1,100,000 / 200 = 11,000 / 2 = 5500 bricks
A motorcycle can travel 60 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 40 km? [1 mile = 1. 6 km] 0. 04 0. 08 0. 20 0. 42.
The motorcycle needs to travel 40 km, 0.42 gallons of fuel.
Given that,
A motorcycle can travel 60 miles per gallon.
We have to find,
How many gallons of fuel will the motorcycle need to travel 40 km?
According to the question,
The motorcycle travel 60 miles per gallon,
The motorcycle travels 40 km,
To convert it into kilometers 60 miles per gallon.
[tex]\rm 1 \ mile = 1.6\ k.m.\\\\60 \ miles \times 1.6 \ k.m. = 96 \ k.m.[/tex]
Therefore,
The gallons of fuel will the motorcycle need to travel 40 km is,
[tex]= \dfrac{96}{40}\\\\= 0.42[/tex]
Hence, The motorcycle needs to travel 40 km, 0.42 gallons of fuel.
For more details refer to the link given below.
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If l || m, find the value of x
Answer: 9
Step-by-step explanation:
Answer:
9!
Step-by-step explanation:
f(x) = -4(x+2) what is f(4)
Answer:
-24
Step-by-step explanation:
f(4)= -4(x+2)
f(4)= -4(6)
f(4)= -24
Answer:
F(x)=-4(x+2)
0=-4-8
4x=-8
X=-2
So,-2×2
-4
Step-by-step explanation:
Have a great day!
The sum of -14 and a number is positive. Identify a possible value for that number
Explain your selection
Answer:
15
Step-by-step explanation:
Since, we need a number that if added to -14, it'll give a positive result. The first number is gonna be 15, . Because, it's the first number that can give a positive number if summed up with -14.
Choose the linear equations.
Answer:
y = [tex]\frac{3}{3}[/tex]x - 5
y = 2x + 5
Step-by-step explanation:
In linear equations, both variables x and y must have the exponent of 1 (i.e. they cannot have a small number at the top-right). And they cannot be in the exponents (i.e. cannot be the small number at the top-right).
