-0.81 has negative direction and o.81 is the magnitude, 0.40 has positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude
What is Vector?A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.
-0.81
Minus zero point eight one has negative direction and o.81 is the magnitude
0.40
zero point four zero has positive direction and 0.40 is the magnitude
0.15
Zero point one five has positive direction and 0.15 is the magnitude
-0.08
Minus zero point zero eight has negative direction and 0.08 is the magnitude
0.29
Zero point two nine has positive direction and 0.29 is the magnitude
Hence -0.81 has negative negative direction and o.81 is the magnitude, 0.40 has positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude
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please help with the first one
Answer:
y = x +5
Step-by-step explanation:
The equation of a parallel line will have the same x- and y-coefficients, but a different constant. You need to find the constant that makes the line go through the given point.
ApplicationThe given line is y = x +1. The equation you're looking for is
y = x +c . . . . . . for some new constant c
We want this equation to be true for (x, y) = (-2, 3). Putting these values into the equation, we can solve for c.
3 = -2 +c
5 = c . . . . . . add 2
The desired equation is y = x +5.
An unknown radioactive element decays into non-radioactive substances. In 340
days the radioactivity of a sample decreases by 61 percent.
(a) What is the half-life of the element?
half-life: ? (days)
(b) How long will it take for a sample of 100 mg to decay to 81 mg?
time needed: ? (days)
(a) The half-life of the unknown radioactive element is 250.28 days.
(b) The time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.
Half life of the unknown radioactive elementN(t) = N₀(0.5)^t/h
where;
t is time of decayh is half lifeN₀ is initial massN(t) remaining mass at time, tin 340 days; N(340) = N₀(0.39);
1 - 0.61 = 0.39
N(340) = N₀(0.5)^340/h
N(340)/N₀ = 0.5^340/h
0.39 = 0.5^340/h
log(0.39) = 340/h x log(0.5)
log(0.39) /log(0.5) = 340/h
1.358 = 340/h
h = 340/1.358
h = 250.28 days
Time taken for the sample to decay 81 mg81 = 100(0.5)^t/250.28
81/100 = (0.5)^t/250.28
0.81 = (0.5)^t/250.28
log(0.81) = t/250.28 x log(0.5)
log(0.81) / log(0.5) = t/250.28
0.304 = t/250.28
0.304(250.28) = t
76.1 days = t
Thus, the half-life of the unknown radioactive element is 250.28 days and the time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.
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So confused please help me thank u
The coefficient of 2(3)(6)Q is
The coefficient of 2(3)(6)Q is 2(3)(6)
How to determine the coefficient?The expression is given as:
2(3)(6)Q
For an expression
AQ
Where A is a number or product of numbers and Q is a variable
The number A represents the coefficient
By comparing:
AQ and 2(3)(6)Q
We have
A = 2(3)(6)
Hence, the coefficient of 2(3)(6)Q is 2(3)(6)
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A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 45% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 35% pure antifreeze, how many gallons of each brand of antifreeze must be used?
The gallons of the first brand of antifreeze should be 60 gallons.
The gallons of the second brand of antifreeze should be 90 gallons.
What are the linear equations that represent the question?0.2f + 0.45s = 52.50 (0.35 x 150) equation 1
f + s = 150 equation 2
Where:
f = gallons of the first antifreezes = gallons of the second antifreezehow many gallons of each brand of antifreeze must be used?
Multiply equation 2 by 0.2
0.2f + 0.2s = 30 equation 3
Subtract equation 3 from equation 2
0.25s = 22.50
s = 22.50 / 0.25
s = 90
f = 150 - 90 = 60 gallons
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Please help me with the first question!
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]
( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )
[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]
[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]
[tex]\qquad❖ \: \sf \:6x = 168[/tex]
[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]
Next,
[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]
( x = 28° )
[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
Lamar, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $10, and paint and canvas for each painting costs $45; he will sell each painting for $50. Once Lamar sells a certain number of his paintings, he will be breaking even. How many paintings will that be?
Answer:
2
Step-by-step explanation:
If he sells and makes x paintings, his expenses will he 10+45x and his revenue will be 50x.
50x = 45x + 105x = 10x = 2The break-even point is the point at which total cost and total income are equal. For breakeven, Lamar needs to sell 2 paintings.
What is breakeven?In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even."
Let the number of paintings that Lamar makes and sells at the break-even point be represented by x.
Given that Lamar bought some brushes for $10, and paint and canvas for each painting cost $45. Therefore, the total cost of making x number of paintings is,
Total cost of x painting = $10 + $45(x)
Also, the selling price of each painting is $50. Therefore, the revenue generated from x paintings is,
Revenue generated = $50(x)
Further, at the breakeven point, the total cost of production of any product is equal to the revenue generated by the product. Therefore, we can write,
Total cost of x painting = Revenue generated
$10 + $45(x) = $50(x)
10 + 45x = 50x
10 = 50x - 45x
10 = 5x
x = 10/5
x = 2
Hence, For breakeven Lamar needs to sell 2 paintings.
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What is the length of S?
Answer:
S = √( 1009)
Step-by-step explanation:
S = √( h² + 1/2)²)
S = √(28² + 15²)
S = √( 1009)
Hope this helps u!
[tex] \: \: \: \: \: \: \: \: \: \: \: n\\ evaluate \: \: \: \: \: Σ \: (nCi)\\ \: \: \: \: \: \: \: \: \: \: \: \: i = 0[/tex]
Evaluate the summation
Assuming you mean
[tex]\displaystyle \sum_{i=0}^n {}_nC_{i}[/tex]
where
[tex]{}_n C_i = \dbinom ni = \dfrac{n!}{i! (n-i)!}[/tex]
we have by the binomial theorem
[tex]\displaystyle (1 + 1)^n = \sum_{i=0}^n {}_nC_{i} \cdot 1^i \cdot 1^{n-i}[/tex]
so that the given sum has a value of [tex]\boxed{2^n}[/tex].
Suppose that the base salary of a salesperson is $30,000 per year. The salesperson gets an additional $50 for every sale. Let x represents the number of sales. How can we model the scenario with a linear function? How many items does the salesperson need to sell to earn $50,000
Answer:
See below
Step-by-step explanation:
Salary (y) = 30 000 + 50 x
y = 30 000 + 50x where x is the number of sales
How many sales for 50 000 ?
50 000 = 30 000 + 50 x
20 000 = 50 x
x = 400 sales
I. Model Problems
A linear model is a linear equation that represents a real-world
scenario. You can write the equation for a linear model in the same way
you would write the slope-intercept equation of a line. The y-intercept
of a linear model is the quantity that does not depend on x. The slope is
the quantity that changes at a constant rate as x changes. The change
must be at a constant rate in order for the equation to be a linear model.
Example 1 A machine salesperson earns a base salary of $40,000 plus
a commission of $300 for every machine he sells. Write an equation
that shows the total amount of income the salesperson earns, if he sells
x machines in a year.
The y-intercept is $40,000; the salesperson earns a $40,000 salary in a
year and that amount does not depend on x.
The slope is $300 because the salesperson’s income increases by $300
for each machine he sells.
Answer: The linear model representing the salesperson’s total income
is y = $300x + $40,000.
Linear models can be used to solve problems.
Example 2 The linear model that shows the total income for the
salesperson in example 1 is y = 300x + 40,000. (a) What would be the
salesperson’s income if he sold 150 machines? (b) How many
machines would the salesperson need to sell to earn a $100,000
income?
(a) If the salesperson were to sell 150 machines, let x = 150 in the linear
model; 300(150) + 40,000 = 85,000.
Answer: His income would be $85,000.
(b) To find the number of machines he needs to sell to earn a $100,000
income, let y = 100,000 and solve for x:
Questions are in the pictures
The values of h and r to maximize the volume are r = 4 and h = 2
The formula for h in terms of rFrom the question, we have the following equation
2r + 2h = 12
Divide through by 2
r + h = 6
Subtract r from both sides of the equation
h = 6 - r
Hence, the formula for h in terms of r is h = 6 - r
Formulate a function V(r)The volume of a cylinder is
V = πr²h
Substitute h = 6 - r in the above equation
V = πr²(6 - r)
Hence, the function V(r) is V = πr²(6 - r)
The single critical pointV = πr²(6 - r)
Expand
V = 6πr² - πr³
Integrate
V' = 12πr - 3πr²
Set to 0
12πr - 3πr² = 0
Divide through by 3π
4r - r² = 0
Factor out r
r(4 - r) = 0
Divide through by 4
4 - r = 0
Solve for r
r = 4
Hence, the single critical point on the interval [0. 6] is r = 4
Prove that the critical point is a global maximumWe have:
V = πr²(6 - r)
and
V' = 12πr - 3πr²
Determine the second derivative
V'' = 12π - 6πr
Set r = 4
V'' = 12π - 6π* 4
Evaluate the product
V'' = 12π - 24π
Evaluate the difference
V'' = -12π
Because V'' is negative, then the single critical point is a global maximum
The values of h and r to maximize the volumeWe have
r = 4 and h = 6 - r
Substitute r = 4 in h = 6 - r
h = 6 - 4
Evaluate
h = 2
Hence, the values of h and r to maximize the volume are r = 4 and h = 2
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An object is launched directly in the air at a speed of 64 feet per second from a platform located 16 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+64t+16, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Considering the vertex of the quadratic equation, the maximum height that the object will reach is of 80 feet.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the equation is:
f(t) = -16t² + 64t + 16.
Hence the coefficients are:
a = -16, b = 64, c = 16.
The maximum value is found as follows:
[tex]y_v = -\frac{64^2 - 4(-16)(16)}{4(-16)} = 80[/tex]
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Identify the coefficient -7x2 y4
The answer is -7.
The coefficient is the part of the variable that does not change with respect to the variable.
Hence, in the monomial -7x²y⁴, the coefficient is -7.
find all the zeros in y=x^2+2x-24
Answer:
x = 4 and x = 6
Step-by-step explanation:
A box contains 13 green marbles and 13 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without replacement, another white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.
[tex]\textbf{Answer:\ \ \large\boxed{\frac{12}{25} }\ or\ 0.4800}[/tex]
Step-by-step explanation:
[tex]\large\boxed{13\ green\ marbles\ and\ 13\ white\ marbles}[/tex]
After a white marble is chosen:
[tex]\large\boxed{13\ green\ marbles\ and\ 12\ white\ marbles}[/tex]
Now there are 25 (13 + 12) total marbles.
Without replacing the white marble we chose already, what is the probability of choosing another white marble?
Well, now there are 12 white marbles to choose from, out of a total of 25 marbles. This means our probability is:
[tex]\large\boxed{\frac{12}{25} }[/tex]
This in decimal form is:
0.4800
Select the common ratio and the 4th term of the geometric series: 9, -6,4...
The given geometric sequence has the common ratio, r = -2/3, and the value of the 4th term, a₄ = -8/3.
A geometric sequence is a special series where every term is the product of the previous term and a common ratio.
The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.
In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........
The first term of the sequence, a = 9.
The second term of the sequence, a₂ = -6.
By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:
a₂ = a.r²⁻¹.
Substituting the values, we get:
-6 = 9(r²⁻¹),
or, r²⁻¹ = -6/9,
or, r = -2/3.
Thus, the common ratio of the given geometric sequence is -2/3.
The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:
a₄ = a.r⁴⁻¹ = a.r³.
Substituting the values, we get:
a₄ = 9(-2/3)³,
or, a₄ = 9.(-8/27),
or, a₄ = -8/3.
Thus, the 4th term of the given geometric sequence is -8/3.
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Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y= cos 2 (x+y/2) cos (x-y/2) .
The trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
In the question, we are asked to derive the trigonometric identity, cos x + cos y = 2 cos (x + y/2) cos (x - y/2), using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
We are given the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
Substituting a = x + y/2 and b = x - y/2 in this, we get:
cos (x + y/2) cos (x - y/2) = 1/2[cos (x + y/2 + x - y/2) + cos (x + y/2 - x - y/2)],
or, cos (x + y/2) cos (x - y/2) = 1/2[ cos (2x/2) + cos (2y/2) ],
or, 2 cos (x + y/2) cos (x - y/2) = cos x + cos y, which on inter-changing the sides, gives us:
cos x + cos y = 2 cos (x + y/2) cos (x - y/2), which is the required trigonometric identity.
Thus, the trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].
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The provided question is incorrect. The correct question is:
"Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y = 2 cos (x + y/2) cos (x - y/2) ."
Allison went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar and each bottle of juice has 20 grams of sugar. Allison purchased a total of 11 bottles of juice and soda which collectively contain 445 grams of sugar. Write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. Define the variables that you use to write the system.
Using a system of equations, it is found that Allison bought 2 bottles of juice and 9 bottles of soda.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are:
Variable x: bottles of juice purchased.Variable y: bottles of soda purchased.Allison purchased a total of 11 bottles of juice, hence:
x + y = 11 -> x = 11 - y.
These 11 bottles contain 445 grams of sugar, hence, considering the amounts of each bottle, we have that:
20x + 45y = 445
Since x = 11 - y:
20(11 - y) + 45y = 445
25y = 225
y = 225/25
y = 9.
x = 11 - y = 11 - 9 = 2.
She bought 2 bottles of juice and 9 bottles of soda.
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Two jets leave an air base at the same time and travel in opposite directions. One jet travels 80 mi/h faster than the other. If the two jets are 11392 miles apart after 8 hours, what is the rate of each jet?
Jet 1 moves with a speed of 672 mi/h, while jet 2 moves with a speed of 672 mi/h + 80mi = 752 mi/h.
How to get the rate of each jet?
Let's say that the rate (or speed) of the slower jet is R, then the rate of the faster jet is:
R + 80mi/h
Now, if we step on any of the two jets (such that we view it as if it doesn't move) the other jet will move with a speed equal to:
S = R + R + 80mi/h
We know that after 8 hours, the to jets are 11,392 mi apart, then we know that:
(R + R + 80mi/h)*8h = 11,392 mi
Now we can solve that for R:
2*R + 80mi/h = 11,392 mi/8h = 1,424 mi/h
R = 1,424 mi/h - 80mi/h)/2 = 672 mi/h
So Jet 1 moves with a speed of 672 mi/h, while jet 2 moves with a speed of 672 mi/h + 80mi = 752 mi/h.
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What is the value of 11!
Answer:
39916800
Step-by-step explanation:
1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer:
22.34021442
Step-by-step explanation:
22.34021442
One company estimates same-day delivery as more than three less than half the total number of miles. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)? Note that the graphs have miles for the independent variable on the x-axis, and the y-axis is a unit of time dependent on the number of miles.
By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.
How to determine the graph?Based on the information provided about this company with respect to its delivery and total number of miles to be covered, we would assign variables as follows:
Let y represent same-day delivery.Let x be the total number of miles.Next, we would translate the word problem into an algebraic equation by using an inequality:
y > x/2 - 3
Also, we would determine the intercepts as follows:
When x = 0, we have;
y = 0/2 - 3
y = -3.
y-intercept = (0, -3).
For the x-intercept, we have:
When y = 0, we have;
0 = x/2 - 3
x/2 = 3
x = 6.
x-intercept = (6, 0).
By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.
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Answer:
c
Step-by-step explanation:
c is the answer
A rectangular park had a dirt path across its diagonal that was yards long. The diagonal and the long side of the park formed an angle that measured . A person walked along the sidewalks outside the park, from the start to the end of the path, as shown by the arrows. The diagonal dirt path that cuts across the rectangular park and the sidewalks outside the park form a right triangle. The dirt path is the hypotenuse and it is labeled 100 yards. The start of the sidewalk is adjacent to the 30-degree angle, and it is labeled X. The end of the path is opposite the 30-degree angle, and it is labeled Y. Which expression shows the distance that he walked?
Trigonometry functions are functions that relate two sides of a given triangle with one of its included angles.
The expression that shows the distance that he walked = x + y + 100
= 87 + 50 + 100
= 237 yards
Trigonometry functions are functions that relate two sides of a given triangle with one of its included angles. The required function may be a sine function, a cosine function, or a tangent function.
Such that;
Sin θ = [tex]\frac{Opposite}{Hypotenuse}[/tex]Cos θ = [tex]\frac{Adjacent}{Hypotenuse}[/tex]Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]The given question can be solved by applying the appropriate trigonometric function.
So that to determine the value of x, we have:
Cos θ = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Cos 30 = [tex]\frac{x}{100}[/tex]
⇒ x = 100 cos 30
= 100 x 0.866
x = 86.60
Thus, the start of the sidewalk is approximately 87 yards.
To determine the value of sidewalk y, we have:
Sin θ = [tex]\frac{Opposite}{Hypotenuse}[/tex]
Sin 30 = [tex]\frac{y}{100}[/tex]
⇒ y = 100 x Sin 30
= 100 x 0.5
y = 50
Thus the sidewalk which represents the end of the path is 50 yards.
Therefore, the total distance that he walked = 100 + 87 + 50
= 237 yards
The expression that shows the distance that he walked = x + y + 100
= 87 + 50 + 100
= 237 yards
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A certain cellular phone plan charges $31.00 per month plus $0.14 for each minute of usage. The monthly charge is given by the formula monthly charge=0.14x+31, where x represents the number of minutes of usage per month. What is the charge for a month with 340 minutes of usage? Write your answer to two decimal places as money is traditionally written.
Answer:
$78.60
Step-by-step explanation:
0.14x + 31 = 0.14*340 + 31 = 78.6
Choose the equation that
matches the graph.
a. (1/2)x-4
b. y = 4x-1
C.
y = (1/1)
(¹²) ² − 4
-
d.
e.
x-4
y = (1/1)
y = 4x + 1
y = 4x+1
Answer: d
Step-by-step explanation:
The graph is increasing, so the base must be more than 1.
Eliminate a and c.Also, the y-intercept is 2.
Eliminate b and e.This leaves d.
PLEASE HELP AS SOON AS POSSIBLE
A quadrilateral PQRS is a parallelogram. PQ and RS are opposite sides then the answer of this particular question is , x = 4, the parallelogram PQRS is a rhombus, QR = 31, The opposite angles are congruent. Thus, more than one answer is correct.
According to the question,
PQ = 7x+12; RS = 5x -20 and QR = 31
Solving PQ and RS we get x = 4. Thus, PQ = 40 and RS = 40.
A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent. A quadrilateral that has all sides equal and opposite sides parallel is called Rhombus.
Thus, the parallelogram PQRS is a rhombus.
Hence, a quadrilateral PQRS is a parallelogram. PQ and RS are opposite sides then the answer of this particular question is , x = 4, the parallelogram PQRS is a rhombus, QR = 31, The opposite angles are congruent. Thus, more than one answer is correct.
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A teacher records the number of students present in her 1st period class each day. This count is a ___________ random variable.
A. Discrete
B. Countable
C. Continuous
D. Finite
This count is a discrete random variable (option A).
What is a discrete random variable?A discrete random variable is a variable that contains integers that can only be a limited number of possible values. A discrete random variable is can contain only a finite set of numbers .
An example of discrete random variable is the number of students in the first period class. It is impossible for the number of students in the class to go on indefinitely.
Discrete random variable has the following properties:
It is finiteIt is numericIt is countableIt contains non-negative integers.A continous random variable is a variable that has an infinite number.
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A baker uses 3 cups (c) of flour to bake 2 loaves of bread. If 1 pound (lb) of flour is equivalent to 3 c, how many loaves of bread can the baker make with a 10 lb-bag of flour? 3 (Round the answer to the nearest whole number.)
The number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.
Number of loavesRatio of flour to loaves of bread = 3 cups : 2 loaves
1 pound (lb) of flour = 3 cups of flour10 pounds (lb) of flour = 30 cups of flourNumber of loaves of bread can the baker make with a 10 lb-bag of flour
Equate the ratio of flour to loaves of bread3 : 2 = 30 : x
3/2 = 30/x
3 × x = 2 × 30
3x = 60
x = 60/3
x = 20 loaves of bread
Therefore, the number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.
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Add: 5/7 + 9/11 + 21/77
Answer:
Step-by-step explanation:
You want to begin by making each fraction have the same common denominator. The LCF (least common factor) is 77. So, knowing this, we can now multiply the fractions that need to have a denominator of 77.
1. 5/7*11/11=55/77
2. 9/11 * 7/7 =63/77
Now we can add
55/77 + 63/77 + 21/77 = 139/77 or 1.805194805
Melissa is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Melissa has been adding money. Suppose that x and y are related by the equation y = 550+20x.
Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of money in the account?
What was the starting amount of money in the account?
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