Answer:
a
Step-by-step explanation:
52-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is two inches more than seven times the length of the first piece. Find the lengths of the pieces. The lengths of the first, the second, and the third pieces are in, in, and in respectively.
Answer:
First piece = a = 5 inches
Second piece = b = 10 inches
Third piece = c = 37 inches
Step-by-step explanation:
Let us represent:
First piece = a
Second piece = b
Third piece = c
52-inch piece of steel is cut into three pieces.
a + b + c = 52 inches
The second piece is twice as long as the first piece
= b = 2a
The third piece is two inches more than seven times the length of the first piece.
= c = 2 + 7(a)
Find the lengths of the pieces. The lengths of the first, the second, and the third pieces are in, in, and in respectively.
a + b + c = 52 inches
Substitute 2a for b
2 + 7a for c
a + 2a + 2 + 7a = 52
Collect like terms
10a = 52 - 2
10a = 50
a = 50/10
a = 5 inches.
b = 2a
b = (2 × 5)
b = 10 inches
c = 2 + 7a
= 2 + 7(5)
= 2 + 35
= 37 inches
In a video game, two characters follow paths represented by r = StartRoot 3 EndRoot + 2 cosine (theta) and r = 4 cos(θ), respectively. The characters travel at different speeds and could collide with each other. Which values of θ correspond to possible collision points? Check all that apply.
The point of collision is θ = π/6.
What are polar equations?A curve's polar equation is often stated with r as a function of θ and represented in polar coordinates.
The given equations are r = √3 + 2cosθ and r = 4cosθ.
The characters will collide at the intersection of these paths, the intersection of the two equations is given by:
√3 + 2cosθ = 4cosθ
4cosθ - 2cosθ = √3
2cosθ = √3
cosθ = √3/2
θ = cos⁻¹(√3/2)
θ = π/6
Hence, the point of collision is θ = π/6.
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help me please with geometry
Answer:
Step-by-step explaunfere:
The circumference of a circle is the distance around the outside of the circle. The diameter, and the circumference are the three defining aspects of every circle. Given the radius or diameter and pi you can calculate the circumference.
1- C ≈ 50.27 in
2- C ≈ 31.42 in
3- A ≈ 201.06
4- A ≈ 314.16
5- C = 14π = 43.982 ≈ 44 inches
π (Pi) times the Radius squared: A = π r2
or, when you know the Diameter: A = (π/4) × D2
or, when you know the Circumference: A = C2 / 4π
What is 38,050,000 expressed in scientific notation?
A. 0.3805 x 108
B. 3.805 x 107
C. 0.38 x 10-8
D. 3.805 x 108
Answer:
B. 3.805 x 10^7
Step-by-step explanation:
Choose the value that breaks this gem into 10 equal pieces
Answer:
the block with '10%'
The whole is 100% and 10% divided by 10 is 10%
In the following expression what are like terms?
2x−5y+8z−10+7y
The balance owed on your credit card triples from $700 to $2100 in 12 months. If the balance is growing linearly then it would take 45.4 months to reach $6000. If, on the other hand, the balance is growing exponentially, f(x)=700(1+0.096)x where x represents the number of months, what would the balance be after 45.4 months? Round your answer to the nearest cent.
Answer:
If the balance is growing exponentially the balance after 45.4 months will be $44,925.94.
Step-by-step explanation:
The exponential growth equation is:
[tex]f(x)=700(1+0.096)^{x}[/tex]
Compute the value of f (x) for x = 45.4 as follows:
[tex]f(x)=700(1+0.096)^{x}[/tex]
[tex]=700(1+0.096)^{45.4}\\\\=700\times (1.096)^{45.4}\\\\=700\times 64.1799181\\\\=44925.94267\\\\\approx 44925.94[/tex]
Thus, if the balance is growing exponentially the balance after 45.4 months will be $44,925.94.
Susan rides her bicycle 5 miles in 2/3 of an hour. At this rate, how many miles could she ride in 2 hours? Please help quick
Answer:
15 miles
Step-by-step explanation:
1 hour would be 7.5 miles an hour. So if you just add another one on then it'll be 15.
Given the formula for the arithmetic sequence, an = 6+ (n - 1)3, give the first 4 terms of the
sequence.
19
find the following:
[tex]a(n) = 6 + 3(n - 1)[/tex]
[tex]a(1) = 6 + 3(1 - 1)[/tex]
[tex]a(1) = 6 + 3 \times 0[/tex]
[tex]a(1) = 6 + 0[/tex]
[tex]a(1) = 6[/tex]
_________________________________
[tex]a(2) = 6 + 3(2 - 1)[/tex]
[tex]a(2) = 6 + 3 \times 1[/tex]
[tex]a(2) = 6 + 3 [/tex]
[tex]a(2) = 9[/tex]
_________________________________
[tex]a(3) = 6 + 3(3 - 1)[/tex]
[tex]a(3) = 6 + 3 \times 2[/tex]
[tex]a(3) = 6 + 6[/tex]
[tex]a(3) = 12[/tex]
_________________________________
[tex]a(4) = 6 + 3(4 - 1)[/tex]
[tex]a(4) = 6 + 3 \times 3[/tex]
[tex]a(4) = 6 + 9[/tex]
[tex]a(4) = 15[/tex]
I’m not sure if my answer is right, can someone help
slope of (-11,5) (-8,4)
kai is making 96 cupcakes for a schoolg event. how many more teaspoons of vanilla are needed to make all 96 cupcakes?
In order to answer this question, we need to know how many teaspoons of vanilla you need for each cupcake. Reply the teaspoon amount and I’ll be happy to help!
Please Help Me!!!! :)
Answer:
$28
Step-by-step explanation:
S = Shirt N = Shoes
N = S + 17
N is equal to 45
45 = S + 17
S = 28
which number line represents the solutions to absolute value of -2x=4
Answer:
poop
Step-by-step explanation:
desperate need of help please
Answer:
3/2
Step-by-step explanation:
Answer:
slope = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 14, - 18) and (x₂, y₂ ) = (- 10, - 12) ← 2 ordered pairs from the table
m = [tex]\frac{-12+18}{-10+14}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]
Match each word to the appropriate example using the expression 5a + 9b − 4.
is a coefficient.
is a constant.
There are
terms in the expression.
Answer:
5 and 9 are coefficients , -4 is a constant, and there are 3 terms in this expression.
Step-by-step explanation:
Sam will take four science tests this quarter. Her scores on three of the tests
are shown below.
Test 1
83%
Test 2
91%
Test 3
88%
Test 4
?
What does Sam need to score on the fourth test to ensure that she will have an
average of 90% for all four tests?
%
Answer:
98%.
Step-by-step explanation:
The following data were obtained from the question:
Test 1 (T₁) = 83%
Test 2 (T₂) = 91%
Test 3 (T₃) = 88%
Test 4 (T₄) =?
AVERAGE = 90%
We can obtain the score of 4th test by doing the following:
AVERAGE = (T₁ + T₂ + T₃ + T₄) /4
90 = (83 + 91 + 88 + T₄) /4
90 = (262 + T₄) /4
Cross multiply
90 × 4 = 262 + T₄
360 = 262 + T₄
Collect like terms
360 – 262 = T₄
T₄ = 98%
Therefore, Sam need to score 98% in the 4th test in order to have an average score of 90%.
In a trivia contest, players form teams and work together to earn as many points as possible for their team. Each team can have between 3 and 5 players. Each player can score up to 10 points in each round of the game. Elena and four of her friends decided to form a team and play a round.
Write an expression, an equation, or an inequality for each quantity described here. If you use a variable, specify what it represents.
1. the number of points that Elena's team earns in one round
2. the number of points Elena's team earns if each player misses one point
3. the number of players in a game if there are at least 3 teams
Answer:
(i) From 0 to 50.
(ii) From 3 to 5.
(iii) From 3R to 5R, where R=3,4,5,...
Step-by-step explanation:
Let N be the number of players in a team.
As each team can have numbers of player ranging from 3 to 5, so
[tex]3\leqN\leq5\cdots(i)[/tex]
Let P be the points scored by one player in one round of the game.
As each player can score up to 10 points in each round of the game, so
[tex]0\leq P \leq 10\cdots(ii)[/tex]
(1) There are 5 members in the team formed by Elena.
So, points earned by 5 players in 1 round = 5P
From equation (ii), the range is
[tex]0\leq 5P \leq 50[/tex]
Hence, the points earned by Elena's team is ranging from 0 to 50.
(2) If each played misses 1 point, then,
Points earned by 1 player in 1 round = 10-1=9
Hence, points earned by 5 players in 1 round = 9x5=45.
(3) Let R (an integer) denoted the number of teams.
As there are at least 3 teams in the game, so
[tex]R\geq3\cdots(iii)[/tex]
As the number of players in one team is N, so
the number of players in R team is NR, where R=3,4,5,...
Now, from equation (i)
[tex]3R\leqNR\leq5R[/tex]
Hence, if there are at least 3 teams, then the number of players is ranging from 3R to 5R.
For R=3, the number of players in the game is ranging from 3x3=9 to 5x3=15.
Someone answer my Algebra 2 question for 100 points! On my account
What conjecture can you make about the sum of the first 33 positive odd numbers?
Answer:
The number series 1, 3, 5, 7, 9, . . . . , 59. Therefore, 900 is the sum of first 30 odd numbers.
The conjecture we can make is C. The sum is equal to the no. of terms squared.
According to the given question we have been asked What conjecture can you make about the sum of the first 33 positive odd natural numbers.
We know that the sum of first 'n' odd natural numbers is n².
So, the sum of first 33 odd natural numbers is (33)² which is = 1089.
Let us prove this by AP.
First term(a₁) is = 1.
common difference(d) = 2.
No. of terms (n) = 33.
∴ aₙ = a₁ + (n-1)d
aₙ = 1 + (33-1)2
aₙ = 1 + 32(2).
aₙ = 1 + 64.
aₙ = 65.
∴ S₃₃ = 33/2×[ 2(1) + (33-1)2].
S₃₃ = 33/2×[ 2 + 64].
S₃₃ = 33/2×66.
S₃₃ = 33×33.
S₃₃ = 1089.
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Which graph represents this equation?
y = 1/2x^2 + 2x - 6
Answer:
C
Step-by-step explanation:
y = 1/2x^2 + 2x - 6
When, x = 0, y = - 6
you don't need to find another variable. Because in number C u can find a graph that has y= -6 when x =0.
The graph of the given equation is the graph C
What is a graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given is an equation, y = x²/2+2x-6, we need to identify the graph for the same,
y = x²/2+2x-6
Put x = 0,
y = -6
Point = (0, -6)
Put x = 2,
y = 2+4-6
y = 0
Point = (2, 0)
Put x = -6
y = 18-12-6
y = 0
Point = (-6, 0)
If we see all these points are lying in graph C, which means the graph C is satisfying the condition of the given equation,
Hence, the graph of the given equation is the graph C
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-3 1/6 divide (-1 4/9)
Answer:
2.19230769231
Step-by-step explanation:
turn that into a fraction use internet
What is the value of x in the figure below? In this diagram, ΔABD ~ ΔCAD.
Answer:
D
Step-by-step explanation:
The triangles CDA and ADB are similar, thus the ratios of corresponding sides are equal, that is
[tex]\frac{CD}{AD}[/tex] = [tex]\frac{DA}{DB}[/tex] , substitute values
[tex]\frac{13}{x}[/tex] = [tex]\frac{x}{3}[/tex] ( cross- multiply )
x² = 39 ( take square root of both sides )
x = [tex]\sqrt{39}[/tex] → D
Answer:
D is the answer
Step-by-step explanation:
What is the difference between: |x+3| = 10 & |x| + 3 = 10
Answer:
Step-by-step explanation:
|x+3| = 10 means the absolute value of x+3 equal 10, so the answer to that means x= -13 or x= 7 (i.e. |-13+3| = |-10| =10, |7+3| = |10| = 10)
|x| + 3 = 10 means the absolute value of just x, so the answer to that would be x= -7 or x= 7 (i.e. |-7|+3 = 7+3 = 10, |7|+3 = 7+3 = 10)
However, take everything I say with a grain of salt, because I struggle some with Absolute Value Equations as well.
I hope this helps give you an idea of what you're looking at, though :)
A business breaks even when the production costs are equal to the revenue. The expression 120+4x represents the cost of producing x items. The selling price is $5 for each item. Write an expression for the revenue generated by selling x items. How many items would you need to sell to break even? Write an equation and solve it.
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
The expression 120+4x represents the cost of producing x items. The selling price is $5 for each item.
The net income formula:
y= (5 - 4)x - 120
(5-4)= contribution margin per unit sold (x)
120= fixed costs
To calculate the break-even point in units, we need to use the following formula:
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 120 / 1
Break-even point in units= 120 units
Prove:
y= 1*120 - 120
y= 0
Nick and Linda are paid 52.25 for their work. Nick worked 1.5 hours, and Linda worked 4 hours. They split the money according to the amount of time each of them worked. How much is Nick's share of the money?
Answer:
5.00
Step-by-step explanation:
5.00
A bakery sells 8 lemon poppy muffins for every 1 bran muffin sold. Which table represents the relationship between lemon poppy and bran muffins?
A
\text{Lemon Poppy}Lemon Poppy \text{Bran}Bran
88 11
1616 99
3232 2525
B
\text{Lemon Poppy}Lemon Poppy \text{Bran}Bran
2424 33
2626 55
2828 77
C
\text{Lemon Poppy}Lemon Poppy \text{Bran}Bran
2424 33
4040 55
5656 77
D
\text{Lemon Poppy}Lemon Poppy \text{Bran}Bran
88 11
2424 44
4040 66
please answer the question im sturggling .
Answer:
A 1
Step-by-step explanation:
8x11=88
1x11=11
Which statement is modeled by 2p + 5 < 11
Group of answer choices
The sum of 5 and 2 times p is at least 11
5 added to the product of 2 and p is less than 11
2 times p plus 1 is at most 11
the product of 2 and p added to 5 is 11
Which of the binomials below is a factor of this Torinomial? X2 + 12x + 32
x2+12x+32
Factor out 2 from the expression
2(x+6x+16)
Collect like terms
2(7x+16)
Now we do the same thing only different way ok
x+6x
If a term doesn't have a coefficient , it is considered that the coefficient is 1
1x+6x
Collect like terms by adding their coefficients
(1+6)x
Add the numbers
7x
1+6=7
To add the numbers using a number line, start from zero.
Since 1 is positive, move the point 1 unit to the right.
Since 6 is positive, move the point 6 units to the right
The result is 7
Answer : 2(7x+16)
That's it . Hope it wasn't too hard to understand?
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Help me Plzzzzz!! ASAP!
