Answer:
SA(surface area) of the rectangular prism is 1,510 in inches
Step-by-step explanation:
SA=2(lh+lw+hw)
2inch=24ft
lh=264
lw=336
wh=154
755*2=1,510
There are 5 consecutive even integers with a sum of –80. What is the greatest of these integers?
The greatest even integers that the 5 consecutive number has a sum of - 80 is - 12.
How to find the greatest even integers?Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.
Therefore, even integers are integers that are even.
There are 5 consecutive even integers with a sum of –80.
let
x = first integers
Therefore,
x + x + 2 + x + 4 + x + 6 + x + 8 = - 80
5x + 20 = - 80
5x = -80 - 20
5x = - 100
divide both sides by 5
x = - 100 / 5
x = -20
Therefore,
greatest integer = - 20 + 8 = - 12
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Jeanne has 3 7/8 yards of fabric. The table shows the amount of fabric she needs for different items. How many pairs of shorts can she make?
Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric.
What do you mean by ratio?
The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
The total amount of fabric = 3 7/8 yards = 31/8 yards.
Amount of fabric needed to make 1 pair of shorts = 1 1/4 = 5/4 yards.
The number of shorts that can be made = 31/8 ÷ 5/4
⇒ 3.1 so it will be 3 because no relevance of decimal shorts.
Hence "Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric".
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Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt.
A: $69
B: $90
C: $420
D: $1,080
Oliver has to pay an amount of B: $90 with simple interest.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business.
The bank offered him an interest rate of 12% for 6 months.
P = $1500, r= 12% and t = 6 months or 1/2 or 0.5 years.
∴ SI = (1500×12×0.5)/100.
SI = 15×6.
SI = $90.
The amount of simple interest Oliver has to pay is $90.
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Solve the inequality statement:
2v+1> 7
v > 3
v > 4
v < 3
v < 4
Answer:
v>3
Step-by-step explanation:
2v>7-1
2v>6
v>6/2
v>3
A real estate company balances the books for its business on the first day of each month. It hopes to sell houses
every other day of the month. The average number of houses, S, the company sells each day, t, is represented by the inverse of the function S^-1 = t^2+4t-12/t^2-9t+14
-
Which equation represents the average sales each day for the real estate company?
The inverse function is given as s⁻¹ = [tex]\frac{t^2+4t-12}{t^2-9t+14}[/tex] and the equation represents the average sales each day for the real estate company would be [tex]s^{-1}=\frac{t+6}{t-7}[/tex].
What is an equivalent expression?
The equivalent is the expression that is in different forms but is equal to the same value.
A real estate company balances the books for its business on the first day of each month.
It hopes to sell houses every other day of the month.
The average number of houses, S, the company sells each day, t is represented by the inverse of the function given below.
[tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}[/tex]
Then the inverse function can be written as
[tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}\\\\s^{-1}=\frac{t^2+6t-2t-12}{t^2-7t-2t+14}\\\\s^{-1}=\frac{(t+6)(t-2)}{(t-7)(t-2)}\\\\s^{-1}=\frac{t+6}{t-7}[/tex]
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Answer:
C. [tex]S=\frac{7t+6}{t-1}[/tex]
Step-by-step explanation:
I got it right on the exam.
First, take the equation and inverse it, replace and t with y and the y with t
[tex]y=\frac{t^{2}+4t-12}{t^{2}-9t+14} \\\\t=\frac{y^{2} +4y-12}{y^{2}-9y+14}[/tex]
Then, factor both the top and bottom
[tex]t=\frac{(y+6)(y-2)}{(y-7)(y-2)}[/tex]
You see that there is a duplicate of the (y-2) in the numerator and denominator, so they cancel out,
[tex]t=\frac{(y+6)}{(y-7)}[/tex]
Now you can start getting the y alone to make an equation,
[tex]t(y-7)=\frac{(y+6)}{(y-7)} (y-7)\\t(y-7)=(y+6)[/tex]
[tex]ty-7t=y+6\\ty-7t-y+7t=y+6-y+7t\\ty-y=7t-6\\y(t-1)=7t-6\\\frac{y(t-1)}{(t-1)} =\frac{7t-6}{t-1} \\y=\frac{7t-6}{t-1}[/tex]
Which of the coordinate pairs below are separated by a vertical
distance of greater than 6 units? Select all that apply.
A) (5.1, -3.3) and (5.1, 3.4)
B) (-1, 2.6) and (-1, -4.2)
C) (3.7, 2.2) and (3.7, -3.4)
D) (6, 1.5) and (6, -2)
Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.
Given that,
The coordinate pairs separated by a vertical distance of greater than 6 units is to be determined.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
here,
(A)
Since the x coordinate is the same in all the pairs, distance on the y axis can only be calculated.
(5.1, -3.3) and (5.1, 3.4)
y = 3.4 - (-3.3)
y = 6.7
Similarly distance,
(B) y = 6.8
(C) y = 5.6
(D) y = 3.5
Thus, Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.
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M a t h (look at image)
Answer:
241
Step-by-step explanation:
9 x 12 = 108 m (area of square)
19 x 14 = 266 / 2 = 133 (area of triangle)
108 + 133 = 241
Find the length of the missing side in the following examples. Round answers to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:[tex]x2{12}5\\ =18[/tex]
Alfred begins collecting model cars. He buys 3 new model cars every week. Is the number of cars he owns proportional to the number of weeks that have passed since he started his collection?
The relationship between the number of weeks and cars are proportional since they are dependent on each other.
ProportionRatio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
In this question, Alfred, buy three car each week. As the number of weeks increase, so is the number of his car increasing at definite proportions.
This implies that we can set an equation to represent the number of cars Alfred will have after certain number of weeks.
Let;
x = number of weeksy = number of carsy = 3x
At week 10, Alfred will have
y = 3(10) = 30 cars
After 10 weeks, Alfred will have 30 cars
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The linear equation y = negative 2 x + 4 is represented on the graph below.
On a coordinate plane, a line goes through (0, 4) and (2, 0).
A second linear equation is represented by the data in the table.
x
y
–4
–3
0
–1
2
0
6
2
What is the solution to the system of equations?
(2, 0)
(0, 4)
(0, –1)
(4, –4)
The solution to the system of equations will be;
⇒ (2, 0)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The first equation is,
y = - 2x + 4
And, A line goes through (0, 4) and (2, 0).
Now,
For the second linear equation;
The coordinates are,
(-4, -3) (0, -1) , (2, 0) , (6, 2)
Hence, The equation of line passes through the points (-4, -3) and (0, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - (-3)) / (0 - (-4))
m = 2 / 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - (-3)= 1/2 (x - (-4))
⇒ y + 3 = 1/2 (x + 4)
⇒ y = 1/2x + 2 - 3
⇒ y = 1/2x - 1
Now, We find the value of system of equations;
y = - 2x + 4
y = 1/2x - 1
Solve both above equation, we get;
1/2x - 1 = - 2x + 4
1/2x + 2x = 4 + 1
5/2x = 5
x = 2
And, y = 1/2 (2) - 1 = 0
Thus, The solution to the system of equations will be;
⇒ (2, 0)
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Answer:
A
Step-by-step explanation:
pasagot po nito
(A) 4, 9, 14, 19, 24, …
Give the next two terms:
Give an expression for the nth term:
Find the 30th term:
(B) 8, 10, 12, 14, 16, …
Give the next two terms:
Give an expression for the nth term:
Find the 30th term:
(C) 1, 8, 15, 22, 29, …
Give the next two terms:
Give an expression for the nth term:
Find the 20th term:
For each of the arithmetic sequences, we have that:
a)
The next two terms are 29 and 34.The expression for the nth term is of: [tex]a_n = 4 + 5(n - 1)[/tex].The 30th term is: 149.b)
The next two terms are 18 and 20.The expression for the nth term is of: [tex]a_n = 8 + 2(n - 1)[/tex].The 30th term is: 66.c)
The next two terms are 36 and 43.The expression for the nth term is of: [tex]a_n = 1 + 7(n - 1)[/tex].The 20th term is: 134.What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
For the sequences in this problem, we have that:
The first terms are, respectively, 4, 8 and 1.The common ratios are, respectively, 5, 2 and 7.Then the general rule is applied to find the nth term of the sequence, while the next two terms are found adding the common ratio.
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12 mushrooms $3 How much for one
Answer:
4
Step-by-step explanation:
12÷3=4
Write the point-slope form of the equation of the line that passes through the origin and has a slope of 2. a. using variables, write out the formula for the point-slope form of the equation. b. identify the values for m, x1, and y1. c. fill these values into the point-slope form of the equation from part (a), and simplify as needed. use the box provided to submit all of your calculations and final answers.
The point slope form of the equation is = P2 = (11, 2)
What is point slope?The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation. Several techniques include:Form of point slopeForm of a slope-interceptTwo-point form for interceptingacc to our question-
Since m = and P1 = (2, -1) then x1 = 2 and y1 = -1. 1y – y1 = m (x – x1)y – (-1) = (x – 2)y + 1 = (x – 2)3 (y + 1) = 1(x – 2)3y + 3 = x – 25 = x – 3y or x – 3y = 5(This the standard formula of the line)Step 2: Calculate P2.Select any valueyou with for x or y and substitute it into the equation found instep 1. For this example y will equal 2.x – 3y = 5x – 3(2) = 5x – 6 = 6x = 11learn more about slope click here:
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I NEED SOME HELP URGENT
solve for the missin lengths in the sets of sumilar figures below.
The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units
Similar triangles:Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
When two triangles ΔABC and ΔXYZ are similar then
AB/XY = BC/YZ = AC/XZ
Here we have
ΔABC and ΔOPQ which are similar and right-angled triangles
As we know in a right-angled triangle
=> Hyp² = side² + side²
From ΔABC,
AB² = AC² + BC²
=> AB² = 6² + 4²
=> AB² = 100 = 10²
=> AB = 10 units
Since ΔABC and ΔOPQ are similar
=> AB/OP = BC/OQ = AC/PQ
=> 10/OP = 4/ f = 6/ 6
Take 10/OP = 6/ 6
=> 6(10) = 6(OP)
=> OP = 10 units
4/ f = 6/ 6
=> f = 4 units
Therefore,
The Missing Lengths are AB = 10 units, OP = 10 units and f = 4 units
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A box is filled with black (B), white (W), red (R), green (G), and prink (P) phone cases. A phone case is selected at random. what is the sample space for this experiment? A) S={B,W,R,G,P} B) S={B,W,R} C) S={G,P} D) S={B,R,G,P}
Use the formula A = nr² to find the area of a circle.
PLEASE HELP
The area of a circle is 12πx-60π unit².
How to use the formula to find the area of a circle?By examining the given figure, there are two circles i.e the small circular hole and the bigger circle. Since the small is a hole then we have to subtract its area from the area of the bigger circle.
Given:
radius of small circle(r₂) = x+2
radius of bigger circle(r₁) = x+8
The formula of Area(A) = πr²
Area of the figure = A₁ - A₂
= πr₁² - πr₂²
= π(x+8)²- π(x+2)²
= π(x²+16x+64) - π(x²+4x+4)
= x²π+16πx+64π - x²π-4πx-4π
= 12πx-60π unit squared
Therefore, the area of the circle is 12πx-60π unit squared. So the 2nd option is the answer.
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write another subtraction problem involving two negatie number that has a positive difference. then write another subtraction problem involving two negative numbers that has a negative difference.
Answer:
Two negatives, positive answer:
-3 - (-4) = 1
Two negatives, negative answer:
-45 - (-1) = -44
"15 fish per fish tank" translated expression
Answer:
15/x
Step-by-step explanation:
x = fish tank
Of the students at Milton Middle School, 112 are girls. If 40% of the students are girls, how many total students are there at Milton Middle school
Angie is baking blueberry pies to sell at her bakery. She starts with 3 7/10 cartons of blueberries, of which she uses 1/3 for the first batch of pies. How many cartons of blueberries does Angie use for the first batch of pies?
Answer:
1 carton
Step-by-step explanation:
3 (7/10)= 21/10
1/3 of 21/10= 7/10
7/10=1 carton
a closed right circular cylinder is to have a volume of 128pi cubic inches. find the radius r and height h of the cylinder with minimal surface area
∛128 is the radius r and height h of the cylinder with minimal surface area .
What is Surface Area?
The term "area" refers to the area occupied by a flat, two-dimensional surface. In square units, it is calculated. A three-dimensional object's surface area is the space it takes up when viewed from the outside.V = πr²n
128π = πr²n
n = 128/r²
s = 2πrn + 2πr²
s = 2πr 128/r² + 2πr²
s = 256π/r + 2πr²
ds/dt = - 256π/r² + 2πr
d²s/dt² = -256/(-2) r³ + 2π
d²s/dt² = 128/r³ + 2π
for maxima or minima
ds/dt = 0
- 256 π/r² + 2πr = 0
256 = 2r³
r = ∛128
d²s/dt² = 128/(∛128)³ + 2π
= 2π + 1
d²s/dt² > 0
so surface area is minimum
a + r = ∛128
n = 128(∛128)²
n = ∛128
r = ∛128 , n= ∛128
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→
Enter a formula using k to connect the two
variables.
y is proportional to x³
Directly proportional to x.
What is propotionality?In algebra, proportionality is the equality of two ratios. A and B are in the same ratio as C and D in the formula a/b = c/d. When one of a proportion's four quantities is unknown, a proportion is often built up to resolve the word problem. By multiplying one numerator by the opposing denominator and equating the result to that of the other numerator and denominator, the equation can be solved. Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.Acc to our question-
If two variables' ratios (yx)(x and y) have the same value as a constant (k=yx)therefore the ratio's variable (y) in the numerator is the sum of the other variable and the constant (y=k:x).With a proportionality constant of k, it is claimed that y is directly proportional to x in this instance.Hence,Directly proportional to x.
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23.45+1.9-5.78-2.6 ?
Answer:
16.97
Step-by-step explanation:
Y intercept = -1 and goes through the point (3,8)
The equation of a line for y-intercept and the coordinate point is y=3x-1.
Given that, y-intercept is -1 and the line passes through the point (3, 8).
What is a y-intercept?In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
Put, c=-1 and (x, y)=(3, 8) in y = mx+c, we get
8=m(3)-1
⇒ 3m=9
⇒ m=3
Substitute c=-1 and m=3 in y = mx+c, we get
y=3x-1
Therefore, the equation of a line for y-intercept and the coordinate point is y=3x-1.
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On September 1st there are 5 bacteria in a jar. The population of bacteria doubles each day. How
much bacteria will be there at the end of the month
If its a 28 day month then 671088640
29 days 1342177280
30 days 2684354560
and 31 days 5368709120
/what is y-5x=3 solve for Y
Answer:
y=3+5x
Step-by-step explanation:
Add 5x to both sides.
What is the equation of the line that passes through the point (−2,−7) and has a slope of 6?
The equation of the line in slope intercept form is y = 6x + 5
How to determine the equation of the line?The given parameters are
Slope, m = 6
Points, (x₁, y₁) = (-2, -7)
A linear equation can be represented as
y = slope * x + y-intercept
i.e.
y = m(x - x₁) + y₁
Substitute the known values in the above equation
So, we have the following equation
y = 6(x + 2) - 7
Expand
y = 6x + 12 - 7
Evaluate the like terms
y = 6x + 5
Hence. the linear equation is y = 6x + 5
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how long does it take lena to compress the accordion completely and then stretch it back out to a length of 50\text{ cm}50 cm50, start text, space, c, m, end text?
It takes Lena to compress the accordion completely and then stretch it back out to a length of 50cm.
It takes Lena 4.1 seconds to compress the accordion completely and then stretch it back out to a length of 50cm.
I am assuming the function without a T: [tex]A(t) = 25_{cos}(t)+65[/tex]
The function is graphed in the figure attached, and the blue line is [tex]y = 50cm[/tex].
From the graph we see that the accordion is completely stretched (has minimum length) at [tex]t = \pi[/tex] seconds, and stretches back to 50cm at [tex]t = 4.069s[/tex]; therefore, it takes Lena 4.069 seconds to stretch the accordion back again, which to the nearest tenth of a second is 4.1s.
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Answer: 1.3s
Step-by-step explanation:
If you're solving for [tex]A(t)=25cos( \pi t)+65\\[/tex]
show your work using standard athgorithm
Use the properties of exponents to rewrite this expression.
(204)
a0a5
What is the value of the rewritten expression when a = -5?
The rewritten expression will be 4a³ and the value of this expression is -500.
Given in the question:
(2a⁴)² / a⁰a⁵
We know that
(xy)ⁿ = xⁿ × yⁿ ... (i)
We can use equation (i) for the next step of our given expression.
In the case of the numerator:
(2a⁴)² = 2² × a⁸ = 4a⁸
Now, we know, any number to the power of zero is 1.
So, for the denominator, we get:
a⁰a⁵ = 1 × a⁵ = a⁵
We know,
pˣ / pʸ = y ⁽ˣ⁻ʸ⁾ ... (ii)
Using this equation, we can further simplify the given expression:
⇒ 4a⁸ / a⁵
⇒ 4 a⁽⁸ ⁻ ⁵⁾
⇒ 4 a ³ ... (iii)
Now, in the second part of the question, we need to find the value of the expression.
Given a = -5
Putting this value in equation (iii) we get:
4 a ³
⇒ 4 (-5) ³
⇒ 4 × (-125)
⇒ -500
Hence, the simplified expression is 4 a ³ and the value of the simplified equation is -500.
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