The diagonal of the rectangular solid that has l = 8, w = 4, h = 2, is calculated as: d = 2√21 units.
How to Find the Diagonal of a Rectangular Solid Shape?A rectangular solid has a length (l), height (h), and width (w). The diagonal of the rectangular solid, d, can be calculated using the given formula below:
Diagonal of rectangular solid (d) = √(l² + w² + h²).
Given the following dimensions of the rectangular box:
Length of the rectangular box = 8 unitsWidth of the rectangular box = 4 unitsHeight of the rectangular box = 2Substitute l = 8, w = 4,a nd h = 2 into the equation d = √(l² + w² + h²):
Diagonal of rectangular solid (d) = √(8² + 4² + 2²)
Diagonal of rectangular solid (d) = √(64 + 16 + 4)
Diagonal of rectangular solid (d) = √84
Simplify √84 further
Diagonal of rectangular solid (d) = √(4 × 21)
Diagonal of rectangular solid (d) = 2√21 units
Therefore, the rectangular solid has a diagonal that is: 2√21
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Find the slope and write an equation of the line which passes through the points.
A
(5,6) and (3,4)
The slope and equation of line with the coordinates (5,6) and (3,4) are 1 and y = x + 1 respectively.
How determine the slope of a line segment line?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point A(5,6)
x₁ = 5y₁ = 6Point B(3,4)
x₂ = 3y₂ = 4Slope m = ?
To determine the slope, plug the given coordinates into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 4 - 6 )/( 3 - 5 )
Slope m = ( -2 )/( -2 )
Slope m = ( -1 )/( -1 )
Slope m = 1/1
Slope m = 1
Next, use the the formula for the equation of line to determine the y-intercept 'b'.
y = mx + b
Plug in slope m = 1 and point (5,6)
6 = 1(5) + b
6 = 5 + b
b = 6 - 5
b = 1
Now that we have both the slope m ( 1 ) and y-intercept b ( 1 ), plug these values into y = mx + b to find the linear equation.
y = mx + b
y = 1x + 1
y = x + 1
Therefore, the slope is 1 and equation of line is y = x + 1.
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((50+50+50)*85)*0.9=
Answer:
(150*85)*0.9
=12750*0.9
=11475
Answer:
11475
Step-by-step explanation:
((50+50+50)*85)*0.9=
(150*85)*0.9=
12750*0.9=
11475
Work out the difference between the highest value and the lowest value in
the list below.
-55, 45, -30, 25, -90
Answer:
105
Step-by-step explanation:
Work out the difference between the highest value and the lowest value in
the list: -55, 45, -30, 25, -90
The lowest value will be the largest negative number in the list: -90
The highest value will be the largest positive number in the list: 45
the difference between -90 and 45:
-90 - 45 = 105
what is 130x1000 well I've been on this app and it has answered this question for me and and can for u to and can I know how this app has helped you with mathematics??
the answer to 130x1000 is
130,000
Jacob had $180 in his savings account at the beginning of summer vacation. over the next 12 weeks, he mowed lawns in his neighborhood earning $145 and spending $55 each week. he deposited all of his weekly profits to his savings account each week. when summer vacation is over, he plans to spend $180 per month. for how many months can he make withdrawals from his saving account until his balance is $0?
Jacob will need 7 months to spend all the money.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jacob had $180 in his savings account at the beginning of summer vacation. over the next 12 weeks, he mowed lawns in his neighborhood earning $145 and spending $55 each week. he deposited all of his weekly profits into his savings account each week. when summer vacation is over, he plans to spend $180 per month.
The number of months will be calculated as:-
Total money in the account = 180 + 12(145-55)
Total money in the account = $1260
Total months = 1260 / 180
Total months = 7 months
Therefore, Jacob will need 7 months to spend all the money.
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Is the following relation a function? x y −1 −2 2 3 3 1 6 −2 a Yes b No
Yes, the provided relation is, indeed, a function. Each x value has just one y value.
In the given table,
x y
-1 -2
2 3
3 1
6 -2
A relationship is a function if each x-value has its y-value.
In the relationship, each x-value has a unique and unique y-value. For example, a value of -1 is -2, a value of 2 is 3, a value of 3 is 1, and a value of 6 is -2.
Although the inclusion of (-1,-2) and (-3) suggests that this is not a one-to-one or infusion function of (6,-2).
As a result, the given relationship is a function. Each x-value has only one y-value.
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Graph the function f(x)=-3x+1.
Use the line tool and select two points to graph.
+Move Line
Undo
Redo
x Reset
The y-intercept is (0, 1).
Substituting [tex]x=-3[/tex] yields [tex]f(x)=-\frac{1}{3}(-3)+1=2[/tex].
So, draw the line through (0, 1) and (-3, 2).
Ramona wrote 14 letters to friends each month for n months in a row. Write an expression to show how many total letters Ramona wrote.
Answer:
let y represent number of months in a row and
let S represents sum of letters that have been sent in y number of months
This simply means that we can write equation:
14*y = S
For any number of months we express it in equation above and we get total number of letters she wrote.
Answer:
[tex]{ \sf{total = 14n \: \: letters}}[/tex]
Sarah has three sisters. lea is 4 less than 3 times the age of sarah. rachel is 3 years less than one-half sarah’s age. amanda is 1 year older than twice the age of sarah. if the sum of the ages of the four sisters is 46 years, how old is each sister?
Answer:
Sarah=x
Lea=3x-4
Rachel=1/2x-3
Amanda=2x+1
Sum=46
x+3x-4+1/2x-3+2x+1=46
6.5x-6=46
6.5x=52
x=52/6.5x
x=8
input x in each sister's age:
Sarah= 8 years
Lea = 3(8)-4=20 years
Rachel = 1/2(8)-3=1 year
Amanda = 2(8)+1=17years
Step-by-step explanation:
PLSSS HELP 20 POINTS I NEED IT BEFORE 12 PM SATURDAY
Graph each parabola and identify the axis of symmetry, focus, and directrix.
2x^2 − 8y=0
For given parabola 2x² - 8y = 0,
the axis of symmetry : y-axis
focus : (0, 1)
directrix : y = -1
In this question, we have been given an equation of parabola 2x² − 8y = 0
We need to graph the parabola and identify the axis of symmetry, focus, and directrix.
2x² - 8y = 0
2x² = 8y
x² = 8y/2
x² = 4y
The graph of the parabola x² = 4y is as shown below.
From this graph, the vertex is (0, 0)
We know that, for a parabola of the form x² = 4ay, the focus is (0, a) and directrix is y = -a
For the parabola x² = 4y, a = 1
So, the focus is (0, 1) and the directrix is y = -1
And the axis of symmetry for the parabola x² = 4y is the y-axis.
Therefore, for given parabola 2x² - 8y = 0,
the axis of symmetry : y-axis
focus : (0, 1)
directrix : y = -1
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The equation 270 = f + 6.50(30) represents the cost of printing the shirts at a second printing company. Find the solution to the equation and state what it represents in this situation
The solution to the equation is f = 75.
The initial charge or setup cost is represented by the intercept or f.
What is the slope-intercept function?The linear function is expressed using the slope of the line and the y-intercept in the slope-intercept form. Its form is y = mx+ b where the slope is m and the y-intercept is b.Given equation: 270 = f + 6.50(30)
We must identify the equation's solution and explain what it represents in this situation.
The equation above is written in the form of a slope-intercept function where 6.50 is the gradient or slope of the function and 30 equals the number of shirts. The total cost of printing is 270.
The equation 270 = f + 6.50(30) can be solved as follows:
270 = f + 6.50(30)
⇒ f = 270 - 195 = 75
Therefore, the initial charge or setup cost is represented by the intercept or f. As a result, the setup fee is 65.
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The difference of two and a number is 7.
2 + n = 7
2 - n = 7
n - 2 = 7
n + 2 = 7
Answer:
the answer for n is 5
Step-by-step explanation:
2 + n = 7
n = 7-2
n = 5
Show that (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0
Answer:
this equation is always trueStep-by-step explanation:
Show that (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0
(a−b)⋅(a+b)+(b−c)⋅(b+c)+(−a+c)⋅(a+c)=0
(a^2−b^2)+(b^2−c^2)+(−a^2+c^2)=0
(a^2−c^2)+(−a^2+c^2)=0
0=0
this equation is always true
[tex]\left(a-b\right)\left(a+b\right)+\left(b-c\right)\left(b+c\right)+\left(c-a\right)\left(c+a\right)=0[/tex]
[tex]\left(a-b\right)\left(a+b\right)+\left(b-c\right)\left(b+c\right)+\left(c-a\right)\left(c+a\right)-\left(b-c\right)\left(b+c\right)=0-\left(b-c\right)\left(b+c\right)[/tex]
[tex]\left(a-b\right)\left(a+b\right)+\left(c-a\right)\left(c+a\right)=-\left(b-c\right)\left(b+c\right)[/tex]
[tex]\left(a-b\right)\left(a+b\right)+\left(c-a\right)\left(c+a\right) = a^2-b^2+\left(c-a\right)\left(c+a\right) =a^2-b^2+c^2-a^2 =-b^2+c^2[/tex]
[tex]-\left(b-c\right)\left(b+c\right) =-\left(b^2-c^2\right) =-b^2-\left(-c^2\right) =-b^2+c^2[/tex]
[tex]-b^2+c^2=-b^2+c^2[/tex]
[tex]0=0[/tex]
It is always true because 0=0.
Question: 4 + 2x - 7(2)³
1. What is the variable?
2. What is the coefficient of the variable?
3. What is the term with the variable?
Answer:
1: x
A variable is a letter in an equation that represents an unknown value or a value that can change.
2: 2
A coefficient for a variable is the leading number in front of the variable. It tells you how many times the variable happens
3: 2x
A term is a multiplication or division statement separated by a +/- sign.
Hope that helps
Aldo spent $17.49 at the store. How much change will he receive if he pays with a $20 bill?
Answer:
he will receive $2.51
Step-by-step explanation:
In the diagram below, the numbers in each box is the sum of two numbers below it. Work out the missing numbers for boxes A and B.
The value of the missing number in box A is [tex]1\frac{1}{2}[/tex]
The value of the missing number in box B is [tex]7\frac{1}{4}[/tex]
What are the missing numbers?In order to determine the value of A, subtract [tex]1\frac{1}{4}[/tex] from [tex]2\frac{3}{4}[/tex]. Subtraction is the mathematical operation that is sued to determine the difference between two or more numbers
A = [tex]2\frac{3}{4}[/tex] - [tex]1\frac{1}{4}[/tex]
[tex]1\frac{3 - 1}{4}[/tex] = 1 [tex]\frac{2}{4}[/tex] = [tex]1\frac{1}{2}[/tex]
In order to determine the value of B, add [tex]4\frac{1}{2}[/tex] and [tex]2\frac{3}{4}[/tex] together. Addition is the process used to determine the sum of two or more numbers.
B = [tex]4\frac{1}{2}[/tex] + [tex]2\frac{3}{4}[/tex]
[tex]6\frac{2 + 3}{4}[/tex] = [tex]6\frac{5}{4}[/tex] = [tex]7\frac{1}{4}[/tex]
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How many miles is 100% of 44 miles?
Answer: 44 miles
Step-by-step explanation: any percentage can be written as a decimal. for example, 50% is 0.50 or 25% is 0.25. in this case, 100 percent is 1.00. now that we know what 100 percent is, we multiply 44 by 1.00(100%). my old math teacher told me that whenever you have something OF something, you multiply them togethor. in other words, of means times. this problem can be written 1.00 times 44.
Each box holds 48 pencils. The chart below shows the number of pencils in 1 box and 5 boxes.
Using a proportional relationship, we have that:
The table is completed as follows: x = 4, y = 192; x = 6, y = 288; x = 9; y = 432;6 boxes are not enough for 300 pencils, 7 are needed.What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is found with the multiplication of the input variable and the constant of proportionality k, as follows:
y = kx.
From the table in this problem, the constant is given as follows:
k = 240/5 = 48/1 = 48.
Hence the relationship is:
y = 48x.
Then:
When x = 4, y = 48(4) = 192.When x = 6, y = 48(6) = 288.When x = 9, y = 48(9) = 432.For 300 pencils, the number of boxes is given by:
48x = 300
x = 300/48
x = 6.25.
There are not decimal parts of a box, a complete box is needed, hence 7 boxes are needed, meaning that 6 boxes are not enough for 300 pencils.
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Find the approximate circumference of a circle with a radius of 75 yards.
O 942 yards
O 24 yards
O236 yards
O 471 yards
Any line segment that starts at the circle's center and ends at one of the circle's edges is known as a radius. The circumference is 471 yards
Do you need to know how to calculate a circle's circumference? Having trouble recalling the circumference formula?Do not worry; we have you covered. Simply enter the diameter into this formula, C=[tex]\pi[/tex]d, if you know it. Instead, did you receive the radius? No issue, just use the equation C=2[tex]\pi[/tex]r. For all the information you need on calculating a circle's circumference using its diameter or radius, keep reading. To make things simple, we even provide a circumference calculator.
To determine the circumference using the radius, use the formula C = 2[tex]\pi[/tex]r. The radius of the circle is denoted by "r" in this expression. Again, you can enter the number value of, which is a closer approximation of 3.14, into your calculator.
Any line segment that starts at the circle's center and ends at one of the circle's edges is known as a radius.
You might have noticed that this resembles the formula C = [tex]\pi[/tex]d. This is due to the fact that the diameter can be thought of as 2[tex]\pi[/tex]r because the radius is only half as long as the diameter.
Circumference= 2[tex]\pi[/tex]r
= 2*3.14*75 yards
= 471 yards
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r(x) = 4x² + 2x - c(x) = 10x + 25
(r-c) (x)
The most appropriate choice for function and subtraction of function will be given by-
(r-c)(x) = [tex]4x^2-8x-25[/tex]
What is function and subtraction of function?
A function from A to B is a rule that assigns to each element of A a unique element of B
A is the domain set and B is the co-domain set.
Subtraction of function
Suppose f(x) and g(x) are two functions. Then
(f - g)(x) = f(x) - g(x)
Here,
r(x) = [tex]4x^2 + 2x[/tex]
c(x) = [tex]10x+25[/tex]
(r-c)(x) = r(x) - c(x) = [tex](4x^2+2x)-(10x +25)[/tex]
= [tex]4x^2+2x -10x-25[/tex]
= [tex]4x^2-8x-25[/tex]
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CARD #7:
Rectangle BCDE will be dilated by
3
a scale factor of
2°
Gabe says the
rectangle will
be reduced.
Gabi says the
rectangle will
be enlarged.
Gabi is correct to say that the rectangle will be enlarged when it will be dilated by a scale factor of 3/2.
What does the scale factor determine?The image's size will depend on the scale factor, which is used to dilate a mathematical entity (compared to the original object).An expansion happens when the scaling factor's absolute value exceeds one.Compression happens when the scale factor's absolute value falls below one.When the scale factor's absolute value is 1, neither expansion nor compression takes place.As it is given that the rectangle BCDE is dilated by the scale factor of 3/2 which is more than 1, so the rectangle will expand or enlarge.
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The complete question is: "Rectangle BCDE will be dilated by a scale factor of 3/2.
Gabe says the rectangle will be reduced.
Gabi says the rectangle will be enlarged."
Hello is this correct
Answer:
Correct
Step-by-step explanation:
Surface area of a sphere = 4 pi r^2
diameter = 28 then r = 14 ft
4 (pi)(14^2) = 2463 ft^2
looks correct for your value of pi =3.14
What is the value of x (3x-10)° 152°
the 66th term of the arithmetic sequence - 10, 7, 24, ...
Answer:
the 66th term is 1095
Select all ratios equivalent to 4:16
5:8 3:12. 15:32
Answer:
3:12 is equivalent 4:16
Step-by-step explanation:
5:8 = 0.625
3:12 = 0.25
15:32 = 0.48...
and 4:16 is 0.25, equal to 3:12
:]
(Brainliest would help a lot) Tell me if this is incorrect!
0.21 / 1.008. Pls helppp
Step by step please
Pls help
Answer:
n= -3
Step-by-step explanation:
The solution is attached
f(x) = 4x²-3x, what is the value of f (2) ?
Answer:
Step-by-step explanation: : f(x) = 4x² + 3x – 7f(-2) = 4(-2)²+3(2)-7f(-2) =16+6-7 =32-7 = 25.
please help with 13 14 15 16
The domain and the range for the relations are given as follows:
13. Domain x ∈ R, range y ∈ R.14. Domain {x ∈ Z| -4 ≤ x ≤ 4 and x is even} , range y ∈ {y ∈ Z| -1 ≤ y ≤ 4}.15. Domain {x ∈ Z| -4 ≤ x ≤ 1} , range y ∈ {y ∈ Z| -4 ≤ y ≤ 1}.16. Domain x ∈ R, range y ∈ R.What are the domain and range of a function?The domain of a function is the set that contains all possible input values. Hence, in a graph, the domain is given by the values of x. The range of a function is the set that contains all possible output values. Hence, in a graph, the domain is given by the values of y.For items 13 and 16, the functions are continuous, hence it is over the real numbers, and both the domain and range are all real values.
For items 14 and 15, the functions are discrete, hence it is over the integer numbers, and the domain is composed by the values assumed by x and the range is composed by the values assumed by y.
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9x+y=11, -6x-y=-8
solve for x and y using system of elimination
Answer:
3
Step-by-step explanation:
9x+y=11 .....(1)
-6x-y=-8 ....(2)
Add equation 1 to equation 2
-6x+9x -y+y =-8+11
3x=3
Divide both sides by 3
3x/3=3/3