The equation that models the balance y after x months will be: y = -115x + 1600.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Zachary purchased a computer for $1600 on a payment plan.
Then two months after he purchased the computer, his balance was $1255. Three months after his balance was $1140.
Initial cost = 1600
Difference in balance = 1,255 - 1,140 = 115
Number of months used = 3 months - 2 months = 1 month1
Therefore, the equation that models the balance b after m months will be:
= - (115/1)x + 1600
y = - 115x + 1600
Hence, The equation that models the balance y after x months will be: y = -115x + 1600.
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Which equation represents a line that has a slope of 1/3 and passes through point (-2, 1)?
y=1/3x-1
Y=1/3x+5/3
Y=1/3x-5/3
Y=1/3x+1
Considering the definition of a line, the equation of the line that passes through the point (-2, 1) and has a slope of 1/3 is y= 1/3x + 5/3.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Line in this caseIn this case, you know:
The line has a slope of 1/3.The line passes through the point (-2, 1).Substituting the value of the slope m, you get:
y= 1/3x + b
Replacing the value of the point in previous expression, the value of the ordinate to the origin b can be obtained:
1= 1/3× (-2) + b
1= - 2/3 + b
1 + 2/3= b
5/3= b
Finally, the equation of the line is y= 1/3x + 5/3.
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how do you know that 2 to the power of 3 x 3 is not a common multiple
Answer:
512
Step-by-step explanation:
A common multiple is defined as a whole number, a shared multiple of each set of numbers. The multiples common to two or more numbers are called the common multiples of those numbers.
OML I just gave u the answer do I need to put this in simple terms for you since u don't understand - 2 to the power of 3 x 3 is 512 and that is not a whole number a common multiple is defined as a whole number and for 512 to be an integer it has to be a whole number. UNDERSTAND NOW???
Calculate the eighth term in the sequence 512, 256,128, ...
Answer:
4
Step-by-step explanation:
You want the 8th term of the geometric sequence 512, 256, 128, ....
Explicit formulaThe formula for the n-th term of a geometric sequence is ...
an = a1×r^(n-1)
where a1 is the first term (512), and r is the common ratio (1/2).
Then the 8th term is ...
a8 = 512(1/2)^(8-1) = 512/128 = 4
The eighth term of the sequence is 4.
Mike staples 10 sheets of paper together to make a packet.
He makes fewer than 8 packets. He uses all of the paper. How
many sheets of paper could Mike have used? Explain how you
know.
Answer:
70
Step-by-step explanation:
8 - 1 = 7
7 x 10 = 70
He used 70 sheets.
factorise 6x^2+11x+4
Answer:
(2x+1)(3x+4)
Step-by-step explanation:
6x² + 11x + 4
multiply the first and last term
i.e (6x²)(4) = 24x²
find two terms that multiplies to give 24x² and when added would give 11x
¶ 8x and 3x
Therefore; 6x² + 11x + 4
6x² + 8x + 3x + 4
2x(3x + 4) + 1(3x + 4)
Answer; (2x + 1)(3x + 4)
imagine it as a degree:
We get the expression with the powers as
a) x⁻³.x⁵= x²
b) m⁻³:m⁶= m⁻⁹
c) a⁻⁷.a⁻²= a⁻⁹
d) (m⁻³)⁻²= m⁶
Given that,
We have to find the power of the expressions.
a) x⁻³.x⁵
Bases are equal so powers must be added.
x⁻³⁺⁵
x²
b) m⁻³:m⁶
It is in ratio that means
m⁻³/m⁶
We can take the m⁶ to numerator
m⁻³.m⁻⁶
Bases are equal so powers must be added.
m⁻³⁻⁶
m⁻⁹
c) a⁻⁷.a⁻²
Bases are equal so powers must be added.
a⁻⁷⁻²
a⁻⁹
d) (m⁻³)⁻²
Powers are multiplied
m⁶
Therefore, We get the expression with the powers as
a) x⁻³.x⁵= x²
b) m⁻³:m⁶= m⁻⁹
c) a⁻⁷.a⁻²= a⁻⁹
d) (m⁻³)⁻²= m⁶
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This is due tomorrow, please help!
Mr. Phone stayed in a hotel room for 2 nights that cost $210. The hotel room tax rate is 12% what is the total cost for the hotel room?
Answer:
$235.20
Step-by-step explanation:
the tax :
[tex] \frac{12}{100} \times 210 = 25.20[/tex]
total cost :
$210 + $25.20 = $235.20
what ticket price would maximize revenue?
As per the concept of system of linear equations, the maximum revenue of this basket ball match is $3.4
Linear equation:
Linear equation refers the one variable is an equation in which there is only one variable present. And it is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.
Given,
A baseball team plays in a stadium that holds 66000 spectators. With the ticket price at $10 the average attendance has been 28000. When the price dropped to $7, the average attendance rose to 33000. Assume that attendance is linearly related to ticket price.
Here we need to find the ticket price would maximize revenue.
In order to find the ticket price for the maximum revenue,
We have to identify the details from the given question,
Total seating capacity = 66,000
When ticket price $10 then the attendance 28,000
When ticket price $7 then the attendance 33,000
Let us consider the x be the maximum revenue ticket price.
Now, to solve this we have to find the slope for the equation,
That is,
=> m = (33000 - 28000)/(7 - 10)
=> m = 5000/-3
=> m = -5000/3
=> m = 1666.6
Then the revenue equation is written as,
=> y = (10 - x) * (28,000 + 1666.6x)
=> y = 280000-11334x-1666.6x²
If we plot the this function into the graph, then we get the graph like the following.
Therefore, the solution of the graph is 3.4.
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*PRE-CALC URGENT + 100 POINTS*
A jumping spider's movement is modeled by a parabola. The spider makes a single
jump from the origin and reaches a maximum height of 20 mm halfway across a horizontal distance of 160 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
Answer:
A. (x - 80)² = -320(y = 20)
B. Focus: (80, -60)
Directrix: y = 100
Axis of symmetry: x = 80
Step-by-step explanation:
Part AIf the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:
x-intercepts = (0, 0) and (160, 0)Vertex = (80, 20)Standard form of a parabola with a vertical axis of symmetry:
[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]
If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.
[tex]\textsf{Vertex}=(h, k)[/tex][tex]\textsf{Focus}=(h,k+p)[/tex][tex]\textsf{Directrix}:y=(k-p)[/tex][tex]\textsf{Axis of symmetry}:x=h[/tex]Substitute one of the x-intercepts and the vertex into the formula and solve for p:
[tex]\implies (0-80)^2=4p(0-20)[/tex]
[tex]\implies (-80)^2=4p(-20)[/tex]
[tex]\implies 6400=-80p[/tex]
[tex]\implies p=-80[/tex]
Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:
[tex]\implies (x-80)^2=4(-80)(y-20)[/tex]
[tex]\implies (x-80)^2=-320(y-20)[/tex]
Part BGiven:
h = 80k = 20p = -80[tex]\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}[/tex]
Then has a recipe for a marinade recipe says to mix 3/8 cup olive oil 1/4 cup soy sauce and 1/8 cup lime juice how much olive oil does he need to make 9 cups of the marinade show your work
You have to multiply 3/8 by 9 and then you get your answer which is 3.375
J. Lo’s Clothiers has forecast credit sales for the fourth quarter of the year: September (actual) $ 70,000 Fourth Quarter October $ 60,000 November 55,000 December 80,000 Experience has shown that 30 percent of sales are collected in the month of sale, 60 percent are collected in the following month, and 10 percent are never collected. Prepare a schedule of cash receipts for J. Lo’s Clothiers covering the fourth quarter (October through December)
The preparation of a schedule of cash receipts for J. Lo's Clothiers covering the fourth quarter from October through December is as follows:
Fourth Quarter Cash Receipts October November December
Month of sale (30%) $18,000 $16,500 $24,000
Following month (60%) 42,000 36,000 33,000
Total cash receipts $60,000 $52,500 $57,000
What is a schedule of cash receipts?A cash receipts schedule is a financial document that specifies how a business expects to collect cash from its credit sales customers based on the sales budget.
The cash collection formula can be established using the company's past collection patterns.
September
Credit Sales (actual) $ 70,000
Fourth Quarter October November December
Credit Sales $60,000 $55,000 $80,000
Cash Receipts:
Month of sale (30%) $18,000 $16,500 $24,000
Following month (60%) 42,000 36,000 33,000
Total cash receipts $60,000 $52,500 $57,000
Cash receipts in October = $60,000 ($60,000 x 30% + $70,000 x 60%)
Cash receipts in November = $52,500 ($55,000 x 30% + $60,000 x 60%)
Cash receipts in December = $57,000 ($80,000 x 30% + $55,000 x 60%)
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A paper company needs to ship papre to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weight 35 ponds and each large box of paper wight 60 pounds. There were 7 more small boxes shipped than large boxes and the total wight of all boxes was 815 ponds. Write a system of equations that could be used to determine the number of small boxes shipped and the number boxes shipped.
Setting up a system of equation, the number of small boxes shipped is 13 and large box shipped is 6
System of EquationSystem of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
Let;
x = small boxy = large boxWe can represent this using equations;
35x + 60y = 815 ...eq(i)
x = 7 + y ... eq(ii)
Solving equation (i) and (ii)
x = 13, y = 6
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Answer the question in the picture
The area of the semicircle is A = 1187.9 cm².
What is the area of a circle?The area of a circle with a radius of r is A = πr².
Given that, the diameter of the semicircle is 55 cm.
The radius of the semicircle is,
r = 55/2
The area of a semicircle is given by,
A = (1/2)πr²
Substitute the values,
A = (1/2)π(55/2)²
A = 1187.9
Hence, the area of the semicircle is A = 1187.9 cm².
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what the slopes and y intercepts for both of these?
Answer:
First graph: slope = [tex]\frac{2}{3}[/tex] & y-intercept = (0, -1). Second graph: slope = 2 & y-intercept = (0,2)Step-by-step explanation:
They're both linear graphs, so they both follow the formula y = mx + b.
The y-intercept is when the graph crosses the y-intercept, so when x = 0.
First graph:
(x, y₁) = (0, -1)(x₂, y₂) = (-3, -3)Slope(m): [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-3-(-1)}{-3-0} =\frac{-2}{-3} =\frac{2}{3}[/tex]
y-intercept(b): (0, -1)
Second graph:
(x, y₁) = (0, 2)(x₂, y₂) = (-3, -4)Slope(m): [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-4-2}{-3-0} =\frac{-6}{-3} =2\\[/tex]
y-intercept(b): (0, 2)
Find the average rate of change of f(x) = -x² + 3x + 1 from x=2 to x = 5.
Simplify your answer as much as possible.
Answer:
The average rate of change is: -4
Step-by-step explanation:
So to solve this we just need to plug our numbers into the formula. We are using the formula f(b) - f(a)b - a where “a” and “b” are our numbers. So we are given the intervals x=2 and x=5. When we see that we can rewrite it as (2,0) and (5,0). This is because when it is telling us just “x” we know “y” (the second number in the parentheses) is 0. So just plugging in the numbers we get: (-(5)2+3(5)+1)-(-(2)2+3(2)+1)(5 - 2). Solving it we get -4.
In AGHI, h = 300 inches, ZG=30° and H=29°. Find the
length of i, to the nearest inch.
The length of i will be 531.3 inch when h is 300 inch and ∠G is 30° and ∠H is 29°.
What is angle?When two straight lines or rays intersect at a shared terminal, an angle is generated. An angle's vertex is the common point of contact. The difference in direction between two lines or surfaces is defined as an angle. Angles are expressed in degrees. From a same point, the two hands draw separate sets of lines. Angle refers to these groups of lines that originate from a common point. Every minute, the two hands create various angles. In real life, one example of an angle is a clock.
Here,
∠I=180-(30+29)
=180-59
∠I=121°
h/sin H=i/sin I
300/sin 29=i/sin 121
i=300*sin 121/sin 29
i=531.3 inch
When h is 300 inches, G is 30 degrees, and H is 29 degrees, the length of I is 531.3 inches.
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What is the value of 4n+ 7 when n
-
2?
Answer:
Either 15 or -1 see below
Step-by-step explanation:
I am not sure if you menat n = 2 or n = -2
n= 2
4n + 7 Subtitute in 2 for n
4(2) + 7
8 + 7
15
n = -2
4n + 7y
4(-2) + 7
-8 + 7
-1
A species of bacteria has a population of 80 at noon. It double every 8 hours. The function that models the growth of the population, P, at any hour, t, is
P(t) = 80(28) 8 a. Why is the exponent ?
b. Why is the base 2?
c. Why is the multiplier 80?
d. Determine the population at noon the next day.
e. Determine the time at which the population first exceeds 60 Thousand.
Answer:123
Step-by-step explanation:
31231231232131
75°
64°
2
The measure of the exterior angle of the triangle is
Answer:
exterior angle = 139°
step-by-step explaination:(I'm using "X" instead of "2")
to find the exterior angle, find the interior angle first and then use the straight line.
interior angle = 180° therefore,
75° + 64° + X = 180
139° + X = 180°
X = 180° - 139°
X = 41° (not the answer)
a straight line = 180°
X = 41°
Y - the exterior angle
41° + Y = 180°
Y = 180° + 41°
Y = 139°
hope this is clear :)
WHAT IS THE ANSWER PLEASE HELP ME
Answer:
option 4
Step-by-step explanation:
Use distributive property: a(b +c) = (a*b) + (a*c).
Multiply each term of (-x - 5) by (-3).
-3( -x - 5) = ( -3* -x) + (-3*-5)
= ( 3x ) + ( 15)
= 3x + 15
⇒Note I am going to solve them step by step for you to understand.
1.
[tex]3(x)+3(5)=3x+5\\3x+15=3x+5\\3x-3x=5-15\\no\\solution[/tex]
since 0≠-10
2.
[tex]-3(x)-3(-5)=-3x-15\\-3x+15=-3x-15\\-3x+3x=-15-15\\0\neq -30\\no\\solution[/tex]
3.
[tex]3(-x)+3(5)=8-x\\-3x+15=8-x\\\\-3x+x=8-15\\-2x=-7\\\frac{-2x}{-2} =\frac{-7}{-2} \\x=\frac{7}{2}[/tex]
4.
[tex]-3(-x)-3(-5)=3x+15\\3x+15=3x+15\\3x-3x=15-15\\0=0\\[/tex]
Note there is no certain value for x as any value you insert as x can make the whole equation true.
No solution is the answer for Q4
John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubedJohn painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)John painted his most famous work, in his country, in 1930 on composition board with perimeter 104.09
in. If the rectangular painting is 5.72
in. taller than it is wide, find the dimensions of the painting.
Question content area bottom
Part 1
What is the width? enter your response here
▼
in. squared
in. cubed
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
The dimensions of the rectangular paint of perimeter 104.09 inches are given as follows:
Height: 28.88 inches.Width: 23.16 inches.How to obtain the perimeter of a rectangle?The perimeter of any polygon, including a rectangle, is given by the sum of all the lengths of the outer edges of the figure.
Hence, for a rectangle of height h and width w, the perimeter is given by twice the sum of these dimensions, hence it is given as follows:
P = 2(h + w).
In this problem, the perimeter has the value given as follows:
P = 104.09 inches.
Hence:
2(h + w) = 104.09
h + w = 104.09/2
h + w = 52.045 inches.
The painting is 5.72 inches taller than it is wide, hence:
h = 5.72 + w.
Then the height is obtained as follows:
5.72 + w + w = 52.045
2w = (52.045 - 5.72)
w = (52.045 - 5.72)/2
w = 23.16 inches.
Then the height of the rectangular painting is given as follows:
h = 5.72 + w = 5.72 + 23.16 = 28.88 inches.
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Solve the inequality3/2 w ≤1/2.
Assume the $26,000 Treasury bill, 5% for 13 weeks. Calculate the effective rate of interest.
Note: Use calendar year. Round your answer to the nearest hundredth percent.
Effective rate of interest
Simple interest of $325 was accrued on a principal of $26,000.00 for a period of 0.25 years (13 weeks) at a rate of 5% per year, bringing the total amount due to $26,325.00 (principal plus interest).
What is simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay additional interest on the interest that has already accrued.
Here,
A = $26,325.00
I = A - P = $325.00
A is equal to P(1 + rt).
The first step is to convert R percent to r a decimal, which is equal to R/100 = 5%/100 = 0.05 per year.
For ease, let's convert time to years: 13 weeks / 52 weeks / year = 0.25 years.
How to resolve our equation
A = 26000(1 + (0.05 × 0.25)) = $26,325.00
Simple interest accrued on a principal of $26,000.00 at a rate of 5% per year for 0.25 years (13 weeks) totaling $26,325.00 (principal plus interest).
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Can someone help please? Very much appreciated
Answer:
Coefficient is 7, variable is z
Step-by-step explanation:
Find the points on the graph for the function f (x) =x²-8x/7x+12 at the value f(x) = 3.
The points on the graph of the given function at the value f(x)=3 would be x=5.0971 and x=1.5695.
What is a graph of a function?
A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f could also be defined as the graph of the equation y = f(x).
The given function is
[tex]f(x)=\frac{8-x}{x^2-7x+12}\\\\\[/tex]
Now we put f(x) = 3, we get
[tex]3=\frac{8-x}{x^2-7x+12}\\\\\\\3x^2-21x+36=8-x\\3x^2-20x+24=0\\[/tex]
Solving we get
x=5.09717
x=1.5695
So the points on the graph of the given function at the value f(x)=3 would be x=5.0971 and x=1.5695.
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Give g(x)=4x-4 , solve for x when g (x) =0
Answer:
x = 1
Step-by-step explanation:
Given:
g(x) = 4x - 4
To Find:
x when g(x) = 0
[tex] \rm \implies 4x - 4 = 0 \\ \\ \rm \implies 4x - 4 + 4 = 0 + 4 \\ \\ \rm \implies 4x = 4 \\ \\ \rm \implies \cancel{\frac{4}{4}} x = \cancel{ \frac{4}{4} } \\ \\ \rm \implies x = 1[/tex]
Look at this graph:
10
9
8
7
9
S
4
لیا ۔
N
L
0
1 2 3 4 5 6 7 8 9 10
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
For the given graph , slope of the line is equal to ( 1 / 2 ).
As given in the question,
Form the given graph,
Scale is given by,
On x-axis each unit of the graph represent 1 unit.
On y- axis each unit of the graph represent 1 unit.
Consider two coordinates from the line of the graph,
( x₁ , y₁ ) = ( 1, 2 )
( x₂ , y₂ ) = ( 3, 3 )
Slope of the line = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substitute the value in the formula of the slope we get,
Slope of the line = ( 3 - 2 ) / ( 3 - 1 )
⇒ Slope of the line = 1 / 2
Therefore, for the given graph , slope of the line is equal to ( 1 / 2 ).
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Determine which integer makes the inequality 6(n − 5) < 3(n + 4) true.
S:{11}
S:{14}
S:{30}
S:{42}
Answer:
S: {11}
Step-by-step explanation:
Hello!
Solve the inequality for n by isolating the variable.
Solve for n 6(n − 5) < 3(n + 4) 6n - 30 < 3n + 123n - 30 < 123n < 42n < 14The solution for n is all values less than 14, so 11 would work.
in a chocolate factory a machine takes a 1 kg block of chocolate. It then divides it into rectangles each weight 10g
The number of division that will take place when the chocolate factory a machine takes a 1 kg block of chocolate is 100.
How to calculate the value?From the information, in the chocolate factory a machine takes a 1 kg block of chocolate and then divides it into rectangles each weight 10g.
It is important to note that:
1000 grams = 1 kilograms
Therefore, since the chocolate is divided into 10g, this will be:
= Total grams / 10 gram
= 1000g / 10g
= 100
Therefore, there will be 100 division.
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Complete question
In a chocolate factory a machine takes a 1 kg block of chocolate. It then divides it into rectangles each weight 10g. How many division will take place?
5. Mrs. Hans bought a house for $35,000 ten years ago. If she sells it this year for $119,000, what percent profit will she make?
Answer:
340%
Step-by-step explanation:
119000/35000