Answer:
The car will travel 1980 meters in 15 minutes.
Hence, option 'D' is true.
Step-by-step explanation:
Given that a car travels 300 meters in the first minute, so
a₁ = 300Each minute after, the car travels 120 meters. , so the sequence becomes
a₁, a₂, a₃, a₄, a₅, ...
300, 420, 540, 660, 780, ...
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
[tex]20-300=120,\:\quad \:540-420=120,\:\quad \:660-540=120,\:\quad \:780-660=120[/tex]
The difference between all the adjacent terms is the same and equal to [tex]d=120[/tex]
now, we have
a₁ = 300d = 120so substituting a₁ = 300 and d = 120 in the nth term of the sequence
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=120\left(n-1\right)+300[/tex]
[tex]a_n=120n+180[/tex]
Thus, the nth term of the sequence is:
[tex]a_n=120n+180[/tex]
Determining the distance the car travels in 15 minutes
As we have already determined the nth term of the sequence such as
[tex]a_n=120n+180[/tex]
now substituting n = 15
[tex]a_{15}=120\left(15\right)+180[/tex]
[tex]a_{15}=1800+180[/tex]
[tex]a_{15}=1980[/tex]
Therefore, the car will travel 1980 meters in 15 minutes.
Hence, option 'D' is true.
What sre three decimal forms of 21.5
Answer:
21.5
Step-by-step explanation:
6. 3x2 – 2x = 5
Quadratic formula
Answer:
The solution to the quadratic equation be:
[tex]x=\frac{5}{3},\:x=-1[/tex]
Step-by-step explanation:
Given the expression
3x² – 2x = 5
Solving with the quadratic formula
[tex]3x^2-2x=5[/tex]
subtract 5 from both sides
[tex]3x^2-2x-5=5-5[/tex]
Simplify
[tex]3x^2-2x-5=0[/tex]
For a quadratic equation of the form ax²+bx+c=0
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
For a = 3, b = -2, c = -5
[tex]x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-5\right)}}{2\cdot \:3}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-2\right)\pm \:8}{2\cdot \:3}[/tex]
Separate the solutions
[tex]x_1=\frac{-\left(-2\right)+8}{2\cdot \:3},\:x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}[/tex]
solving
[tex]x_1=\frac{-\left(-2\right)+8}{2\cdot \:3}[/tex]
[tex]=\frac{2+8}{2\cdot \:3}[/tex]
[tex]=\frac{10}{6}[/tex]
[tex]=\frac{5}{3}[/tex]
also solving
[tex]x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}[/tex]
[tex]=\frac{2-8}{2\cdot \:3}[/tex]
[tex]=\frac{-6}{2\cdot \:3}[/tex]
[tex]=\frac{-6}{6}[/tex]
[tex]=-\frac{6}{6}[/tex]
[tex]=-1[/tex]
Therefore, the solution to the quadratic equation be:
[tex]x=\frac{5}{3},\:x=-1[/tex]
Dianna made several loaves of bread yesterday. Each loaf required cups of flour. All together, she used cups of flour. How many loaves did Diana make? 3 loaves 4 loaves 5 loaves 7 loaves
Answer:
5 loaves
Step-by-step explanation:
Dianna made several loaves of bread yesterday. Each loaf required 2 2/3 cups of flour. All together, she used 13 1/3 cups of flour. How many loaves did Dianna make?
Flour per loaf = 2 2/3 Cups of flour
Total cups of flour used = 13 1/3 cups
How many loaves did Dianna make?
Number of loaves Dianna makes = Total cups of flour used / Flour per loaf
= 13 1/3 ÷ 2 2/3
= 40/3 ÷ 8/3
= 40/3 × 3/8
= (40*3) / (3*8)
= 120 / 24
= 5 loaves
Number of loaves Dianna makes = 5
Answer:
for me and my lazy people 5
Step-by-step explanation:
3. What is the slope of the table shown? Cars Washed Number Money ($) 5 40 10 80 15 120 20 160
Six pears and eight lemons is $5.00. Five pears and four lemons cost $4.70.
Answer:
There is not enough info for me to answer this.
Two red and two blocks are placed into a bag you take one of the blocks out of the bag what is the probability the block is not blue
Question:
Two red and two blue blocks....
Answer:
[tex]P(Not\ Blue) = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]Red = 2[/tex]
[tex]Blue = 2[/tex]
Required
Probability of not selecting blue
First, we calculate the probability of selecting blue
[tex]P(Blue) = \frac{Blue}{Total}[/tex]
[tex]P(Blue) = \frac{2}{2+2}[/tex]
[tex]P(Blue) = \frac{2}{4}[/tex]
[tex]P(Blue) = \frac{1}{2}[/tex]
In probability:
Opposite probabilities sum up to 1 i.e.
[tex]P(Blue) + P(Not\ Blue) = 1[/tex]
This gives
[tex]\frac{1}{2} + P(Not\ Blue) = 1[/tex]
[tex]P(Not\ Blue) = 1 - \frac{1}{2}[/tex]
[tex]P(Not\ Blue) = \frac{2-1}{2}[/tex]
[tex]P(Not\ Blue) = \frac{1}{2}[/tex]
Answer:
the answer would be 1/2 .,
Need help pls pls!!!!
Find the measure of one interior angle in a octagon. Round to the nearest tenth if necessary.
A drink is made by pouring one part of squash to four parts
of water. If there is a total of 500 ml, how much of it is
squash?
As per linear equation, there are 100 ml of squash in that drink.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, 'A' is a coefficient and 'B' is constant".
Let, the part of squash in the drink is = x ml.
Therefore, the part of water in the drink = 4x ml.
Now, (x + 4x) = 500
⇒ 5x = 500
⇒ x = 100
Therefore, the part of squash is 100 ml.
Learn more about linear equation here: https://brainly.com/question/11352342
#SPJ2
what is the nth ternm of this sequence -4,1,6,11,16,
a 5n-4
b -4n+5
c -9n
d 5n-9
Answer:
d. 5n-9Step-by-step explanation:
Given sequence:
-4, 1, 6, 11, 16, ...It is an AP with:
The first term is a = -4Common difference is d = 5Nth term of this sequence is:
aₙ = a + (n - 1)daₙ = - 4 + 5(n - 1) = -4 + 5n - 5 = 5n - 9Correct option is d.
Answer:
d. (5n-9)Step-by-step explanation:
First term = -4Common difference = 1-(-4)=1+4=5Formula used: L =a+(n-1)dwhere, L is the last term;
a is the first term ;
n is the number of terms;
and d is the common difference.
L = -4+(n-1)5= -4+5n-5 = 5n-9Therefore, the last term is (5n-9).
Which fraction equals a repeating decimal? select
A. 18 over 81. Yes or No
B. 11 over 88. Yes or No
Answer:
a. yes
b. no
Step-by-step explanation:
im pretty sure this is right hope this helps
PLEASE ANSWER ASAP !!!!!!
Answer:
-2
Step-by-step explanation:
h(-5) is the x value so -2 would be the y value
Out of 25 students interviewed, 21 students said they believe in the Loch
Ness monster. Represent this portion as a fraction, decimal, and percent.
Answer:
Fraction it's 21/25 Decimal it's 0.84 Percent is 84%
Step-by-step explanation:
Ben has exactly the right number of cubes, each of the sides 5 cm, to make a solid cube of side 1 m. He places the smaller cubes side by side to form a single row. How long is this row?
Answer: just multiply width by length
Step-by-step explanation:
Marton finds a shirt on sale for 10% off at the department store. the original price was $20 marton also must pay the sales tax of 8,5%
When you divide the number of permutations of 11 objects taken 3 at a time by 3!, you will get the number of combinations of 11 objects taken 3 at a time.
Answer:
Yes
Step-by-step explanation:
Permutation :
nPr = n! ÷ (n - r)!
nCr = n! ÷ (n-r)!r!
11 objects taken 3 at a time :
11P3 = 11! ÷ (11 - 3)!
11P3 = 11! / 8!
11P3 = (11 * 10 * 9 )
11P3 = 990
Dividing by 3!
3! = 3*2*1 = 6
= 990 / 6
= 165
For combination :
11C3 = 11! ÷ 8!3!
11C3 = (11 * 10 * 9) / (3 * 2 * 1)
11C3 = 990 / 6
11C3
help me please, i dont understand
Answer:
119°
Step-by-step explanation:
So its saying if angle 4 is 119 degrees what is angle 1
Arthur sets off at 9am. Arthur's journey north will take 2 hours and 35 minutes, but the train makes a stop for 45 minutes at Crewe. What time will he eventually arrive at his destination?
Answer:
I believe the answer to be 12:20 p.m.
Step-by-step explanation:
2 hours and 35 minutes + the 45 minute stop = 3 hours and 20 minutes.
From 9:00 am, 3 hours is 12:00, plus the 20 minutes left over.
Answer:
12:20 PM
Step-by-step explanation:
Simply add 35 and 45, which would give you 80. Since you know that there can only be 60 minutes in an hour, you just subtract 60 from 80, which will give you 20. all those 60 minutes (or an hour) to the 32 hours you already have. Now you have 3 hours. Now add the 20 minutes we have left over and then you have an answer of 3 hours and 20 minutes. Now add 3 hours and 20 minutes to 9 AM and you get an answer of 12:20 PM.
A motor racing circuit has length 5 5/6 miles. A straight section of the circuit has 1 1/4 miles. What fraction of the circuit is the straight section? Give the answer in its simplest form
Answer:
3/14
Step-by-step explanation:
1 1/4 can be written as 5/4
5 5/6 can be written as 35/6
so divide (5/4)/(35/6)
= (5/4)*(6/35)
=(1/4)*(6/7)
=6/28
simplified = 3/14
Draw the graph of y = x^3+3 for values of x between –3 and 3.
Use your graph to estimate the value of y when x = -2.5.
Answer:
Substitute different values of x in y=3x and get corresponding y coordinates.
Substitute different values of x in y=3x and get corresponding y coordinates.Such as (0,0),(1,3),(2,6),(−1,−3),(−2,−6)
Substitute different values of x in y=3x and get corresponding y coordinates.Such as (0,0),(1,3),(2,6),(−1,−3),(−2,−6)Now, when x=−2 then y=−6 .
[tex]r = \frac{a { }^{2} + 2a - 7 }{ \sqrt{a} } [/tex]
differentiate this using the quotient rule
Answer:
[tex]\frac{dr}{da} = \frac{3a^2 + 2a + 7}{2a^{\frac{3}{2} }}[/tex]
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Expand by FOIL (First Outside Inside Last)Terms/Coefficients/DegreesAlgebra II
Exponential Rule: [tex]x^{-m}= \frac{1}{x^m}[/tex]Exponential Rule: [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]Calculus
Derivatives
Derivative Notation
The derivative of a constant is equal to 0
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Quotient Rule: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]r = \frac{a^2+2a-7}{\sqrt{a}}[/tex]
Step 2: Rewrite
[tex]r = \frac{a^2+2a-7}{a^{\frac{1}{2} }}[/tex]
Step 3: Differentiate
Quotient Rule [Basic Power: [tex]\frac{dr}{da} = \frac{a^{\frac{1}{2} }(2a^{2-1} + 2a^{1-1}) - \frac{1}{2}a^{\frac{1}{2} - 1 }(a^2 + 2a + 7)}{(a^{\frac{1}{2} })^2}[/tex]Simplify: [tex]\frac{dr}{da} = \frac{a^{\frac{1}{2} }(2a + 2) - \frac{1}{2}a^{-\frac{1}{2}}(a^2 + 2a + 7)}{a}[/tex]Simplify: [tex]\frac{dr}{da} = \frac{2}{2} \cdot \frac{a^{\frac{1}{2} }(2a + 2) - \frac{1}{2}a^{-\frac{1}{2}}(a^2 + 2a + 7)}{a}[/tex]Multiply: [tex]\frac{dr}{da} = \frac{2a^{\frac{1}{2} }(2a + 2) - a^{-\frac{1}{2}}(a^2 + 2a + 7)}{2a}[/tex]Factor: [tex]\frac{dr}{da} = \frac{a^{-\frac{1}{2}}[2a(2a + 2) - (a^2 + 2a + 7)]}{2a}[/tex][Brackets] Distribute: [tex]\frac{dr}{da} = \frac{a^{-\frac{1}{2}}[4a^2 + 4a - a^2 - 2a - 7]}{2a}[/tex][Brackets] Combine Like Terms: [tex]\frac{dr}{da} = \frac{a^{-\frac{1}{2}}[3a^2 + 2a - 7]}{2a}[/tex]Simplify: [tex]\frac{dr}{da} = \frac{3a^2 + 2a + 7}{2a^{\frac{3}{2} }}[/tex]HELP ME WILL GIVE BRAINLY
Answer:
C
Step-by-step explanation:
Answer:4/6 is the Awnser
Step-by-step explanation:hope this helps
ONE HUNDRED POINTS
Complete the proof.
Below is a drag and drop geometric proof. Complete the proof in your notebook.
Choose from these possible answers:
Answer:
I'm sorry I dont really know this but maybe you have to find the simiular parts then put em together as EX: AB. EF. GE. CF.
Step-by-step explanation:
.....Sorry I couldn't help
Create an equivalent fraction to 6/14. Explain your reasoning
Answer:
3/7
Step-by-step explanation:
3/7 is 6/14 simplified
A cell phone that regular costs $780 is on sale for 15% off. What is the total cost of the phone if you have to pay 5.5% sales tax? Round to the nearest cent.
Answer:
$700
Step-by-step explanation:
Step one:
Given data
Regular cost of cell phone= $780
discount = 15%
tax = 5.5%
Step two
Let us compute the discounted amount
= 15/100*780
=0.15*780
=$117
hence the selling price is
=780-117
=$663
Also, the tax-deductible is
=5.5/100*663
=0.055*663
=$36.465
The total cost of the phone will be
=663+36.465
=699.465
=$700 to the nearest cent
Joakim is icing 30 cupcakes. He spreads mint icing on 1 5of the cupcakes and chocolate on 1 2of the remaining cupcakes. The rest will get vanilla icing. How many cupcakes have vanilla icing?
Answer: 12
Step-by-step explanation:
From the question, we are informed that Joakim is icing 30 cupcakes and that he spreads mint icing on 1/5 of the cupcakes. This means that he spreads 1/5 × 30 = 6 cupcakes.
After spreading 6 cupcakes, he will have: 30 - 6 = 24 cupcakes left. We are told that he spreads chocolate on 1/2 of the remaining. This means that he spreads chocolate on 1/2 × 24 = 12 cupcakes.
Therefore, he will have 12 left
= 24 - 12
= 12
Therefore, the rest that'll get vanilla icing will be 12 cupcakes
2 - (y +2) = 3y
solve for y
Answer:
y=0
Step-by-step explanation:
hope this is correct!! c:
Which is the graph of y =[x] -2?
Answer:
In the graph of y = x2, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point. We can graph a parabola with a different vertex.
Find the measure of the missing angle.
a.163°
b.90°
c.63°
d.73°
Answer:
d
Step-by-step explanation:
90-17=73
Solve the following inequality. 2 (P + 1) > 7+P
