By substitute values in formula for volume of cuboid we get;
x² + 12x – 220 = 0
What is mean by Volume?
Volume of cuboid is defined as the amount of space occupied by the sides of cuboid in three-dimensional space.
Given that;
A cuboid with a volume of 924 cm' has dimensions,
4 cm, (x + 1) cm and (x + 11) cm.
Since, Volume of cuboid = Length x width x height
After substitute we get;
Volume of cuboid = 4 × (x + 1) × (x + 11)
924 = 4 (x² + 11x + x + 11)
924 = 4 (x² + 12x + 11)
Divide 4 both side;
231 = x² + 12x + 11
x² + 12x + 11 - 231 = 0
x² + 12x - 220 = 0
Thus, By the formula of volume of cuboid we get;
x² + 12x - 220 = 0
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Lynette is making candles for her online store the wholesale cost of the materials for one candle is $5.35 if she sells a candle for $12 what is the percent markup round to the nearest percent
The percent markup is 124.30%.
The wholesale cost of one candle is $5.35
The selling price of the candle is $12
The profit she earns = 12 - 5.35
= $6.65
Here we have to find the percent markup.
The formula for the percent markup =( profit/ wholesale cost )× 100
Markup percent = 6.65 / 5.35 × 100
= 1.24299 × 100
= 124. 30%
Therefore the markup percentage is 124.30%.
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Three times the first of two numbers decreased by the second number equals 9. Twice the first number increased by the second number equals 11. Find the two numbers
As per the given condition for the system of equation, the two numbers are equal to 4 and 3.
As given in the question,
To begin with the solution, let the two unknown numbers be x and y. Now, translating the two mathematical statements into system of equations,
When three times the first of two numbers decreased by the second number equals 9.
3 x - y = 9 ____(1)
Twice the first number increased by the second number equals 11,
2 x + y = 11 ____(2)
By solving resultant system of equations we get,
3 x - y = 9
2 x + y = 11
5x = 20 (by adding the two equations)
=> x = 4
Substituting the value of x in second equation,
y = 11 - 2x
= 11 - 2(4)
= 11 - 8 = 3
Therefore, as per given condition for the system of equation, the two numbers are equal to 4 and 3.
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The following is the prime factorization of which composite number?
22.3².5
120
60
20
180
The prime factorization given as 2².3².5 is for the number D. 180.
What are prime numbers?It should be noted that prime numbers are numbers that can only be divided by itself and one. This include 2, 3, 5, 7, etc
A composite number is one that can be generated by multiplying two smaller positive numbers. It is a positive integer with at least one divisor other than 1 and itself. Prime factorization is defined as the process of determining a number's prime factors so that the original number is evenly divisible by these factors.
In this case, it should be noted that we are given the expression as 2². 3². 5. It simply means that we have to multiply them to get the original number.
This will be:
= 2² × 3² × 5
= 4 × 9 × 5
= 180
Therefore, the number is 180.
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P(6 or 7 or diamond or club) =
Answer:
The answer is 17/52. Explanation: The number of diamond cards is 13, and the number of '6' cards is 4 Picking one diamond out of 13 is 13C1
Step-by-step explanation:
Use the picture shown to solve for inequalities in two triangles
GIVEN
Two triangles ABC and ACD where two corresponding sides of the two triangles are equal.
SOLUTION
The two triangles have equal sides such that:
[tex]\begin{gathered} AB=AD \\ and \\ AC=AC \end{gathered}[/tex]By this, the length of the remaining sides BC and DC are related such that the side opposite the greater angle has the greater length.
Since [tex]BC>DC[/tex]Substitute known values into the inequality:
[tex]\begin{gathered} DC=11x-33 \\ BC=77 \\ \therefore \\ 77>11x-33 \end{gathered}[/tex]Solving the inequality:
[tex]\:x<10[/tex]Recall that the side DC has to be greater than 0. Therefore:
[tex]\begin{gathered} 11x-33>0 \\ \therefore \\ x>3 \end{gathered}[/tex]Combining both solutions:
[tex]3ANSWERA school is arranging chairs in rows for an assembly. $11$ chairs make a complete row, and right now there are $110$ chairs total. The school wants to have as few empty seats as possible, but all rows of chairs must be complete. If $70$ students will attend the assembly, how many chairs should be removed?
Answer:
40
Step-by-step explanation:
Write the domain and range of the function using interval notation.
The domain of the function using interval notation is 4 ≤ y < 8 and the range of the function using interval notation is 4 ≤ y < 6.
What is a domain?A domain simply refers to the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
By critically observing this graph of a function shown, we can reasonably infer and logically deduce the following:
Domain = (4, 8).Range = (4, 6).In interval notation, the domain of this function can be rewritten as 4 ≤ y < 8. In interval notation, the range of this function can be rewritten as 4 ≤ y < 6.
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The price of an item has been reduced by 60%. The original price was $65. What is the price of the item now?
Answer:
$26
Step-by-step explanation:
65 x 60% = 39
65 - 39 = 26
Which of these strategies would eliminate a variable in the system of equations?
2x + 3y = -5
2x - 3y = 10
Choose all answers that apply:
Answer:
jhhuibhhhiihhuuuuuuuuuuuuuuuuuuuuuuuu
Line 1: m = 4/5
Line 2: m = -5/4
Are the lines parallel, perpendicular, or neither?
neither
perpendicular
parallel
The point (-13, 24) is on the graph of y = f(x). Find the corresponding point on the graph of y= g(x), where g(x) = 1/4f(x)
Answer:
(−12,2)
Step-by-step explanation:
1:
Dividing the function by 2 divides all the y-values by 2 as well. So to get the new point, we will take the y-value
(4) and divide it by 2 to get 2
.
Therefore, the new point is
(−12,2)
2:
Subtracting 2 from the input of the function makes all of the x-values increase by 2 (in order to compensate for the subtraction). We will need to add 2 to the x-value
(−12) to get −10
.
Therefore, the new point is
(-10,4)
3:
Making the input of the function negative will multiply every x-value by
−
1
. To get the new point, we will take the x-value
(−12) and multiply it by −1 to get 12.
Therefore, the new point is
(12,4)
4:
Multiplying the input of the function by 4 makes all of the x-values be divided by 4 (in order to compensate for the multiplication). We will need to divide the x-value
(−12) by 4 to get −3
.
Therefore, the new point is
(−3,4)
5:
Multiplying the whole function by
4
increases all y-values by a factor of
4
, so the new y-value will be
4
times the original value
(4), or 16.
Therefore, the new point is
(−12,16)
6:
Multiplying the whole function by
−1
also multiplies every y-value by
−1
, so the new y-value will be
−1
times the original value
(4), or −4.
Therefore, the new point is
(−12,−4)
Prove the second property one pair of congruent legs is true (prove segment DA is congruent to CB)
Answer
he trapeziunm is an isosceles trapezoid since there are pairs of congruent base angles ADC and BCD
Lines AB and DC are the bases'
To proof that
[tex]\bar{AD}\cong\bar{BC}[/tex]WDraw perpendicular line segments from A to P and from B to Q which are perpendicular to line DC
∠APD =∠BQC (Right angle)
That is ∠D ≅ ∠C
Now the perpendiculars AP and BQ are congruent
By AAS Property, triangles APD and BQC are congruent and this implies that the hypotenuses AD and BC are congruent.
Therefore the legs AD and BC are congruent.
which of thr following options is an equivalent function too f(x)=2(5)2x
Although part of your question is missing, you might be referring to this full question: Which of the following options is an equivalent function to f(x) = 2(5)^2x? choices:
f(x) = 50^x
f(x) = 100^x
f(x) = 2(25)^x
f(x) = 4(25)^x
The equivalent function too expression is f(x)= 2(25)ˣ. Thus option c is correct.
The expression of function f(x) given, f(x)=2(5)²ˣ.
Functions are said to be equal if they have same domain or codomain such that f(x) = g(x). Thus, the two functions are equal functions.
∴ The function after solving expression is,
f(x)= 2×(5²)ˣ
f(x)= 2×(25)ˣ
Hence, the correct equivalent function is f(x)= 2(25)ˣ.
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Write the equation of the line in point-slope form that passes through the given point with the given slope. (,)open 1 comma 5 close; =−m equals negative 3
The equation of the line in point slope form that passes through (1,5) and slope = -3 , is y = -3x+6 .
The equation of line in point slope form passing through the points (x₁,y₁) and slope =m is given by the formula
(y-y₁)=m(x-x₁)
In the question ,
it is given that
the line passes through the point (1,5) and has a slope m = -3.
so the values become x₁=1 and y₁=5 and m = -3
Substituting the values in the formula for equation of line , we get
(y-5)=(-3)(x-1)
y-5= -3x + 1
y = -3x + 1 + 5
y = -3x+6
Therefore , the equation of the line in point slope form that passes through (1,5) and slope = -3 , is y = -3x+6 .
The given question is incomplete , the complete question is
Write the equation of the line in point-slope form that passes through the point (1,5) with slope = -3.
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IS this a function or no (ALGEBRA
We can see that the same input is mapped into two different outputs, so this is not a function.
Is this a function?A relation maps elements called inputs into another elements called outputs.
Such that a relation is a function if each input is mapped into only one output.
The notation used is (input, output).
So, here we can see the points:
(4, 12) and (4, 15).
The input 4 is being mapped into two different outputs, thus, this is not a function.
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I want the answer for this question pls...
Simplify 72h ÷ 9h
Answer:
8
Step-by-step explanation:
[tex] \frac{72h}{9h} = 8[/tex]
The h is common in the numerator and the denominator, so it cancels out. We are left with 72/9 = 8.
please I need to know number 2 :)
Answer: [tex]-4 < m \le -3[/tex]
=========================================================
Reason:
If m = -4, then f(x) = m becomes f(x) = -4. This yields the single solution x = -4
How do we get this solution? Start at -4 on the y axis. Move horizontally until reaching the curve. You should arrive at (-4,-4) which is the lowest point of this curve. Then move upward until reaching the x axis to arrive at x = -4
All of this says that the input x = -4 leads to the output y = f(x) = -4
---------------
We've gone over m = -4 leading to one solution, so that's out of the question since we want two solutions.
But if m = -3 for instance, then notice how tracing a horizontal line to the curve arrives at two locations instead of one. We arrive at x = -2 and x = -5 as the solutions to f(x) = -3
All of these solutions mentioned are negative which fits the criteria we're after. If m is in the interval from -4 to -3, excluding -4 but including -3, then we'll have f(x) = m with two negative solutions for x.
Evaluate the integral.
[tex]\pi\int\limits^{\frac{3\pi}{4}}_{\frac{\pi}{6}} {sin^4x+4sin^2x} \, dx[/tex]
By using trigonometric formulas and integration rules, we conclude that the integral is approximately equal to - 7.764 units.
How to determine the value of a definite integral
In this problem we must determine the solution to a definite integral of trigonometric equations, which requires the use of trigonometric formula and integration rules to be found. The integral can be simplified by using the following formulas:
sin⁴ x = (1 / 8) · (3 - 4 · cos 2x + cos 4x)
sin² x = (1 /2) · (1 - cos 2x)
Then, the integral is simplified into this form:
[tex]I = \pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} \sin^{4} x \,dx + 4\pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} \sin^{2} x \,dx[/tex]
[tex]I = \frac{\pi}{8} \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} (3 - 4\cdot \cos 2x + \cos 4x) \,dx + 4\pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} (1 - \cos 2x) \,dx[/tex]
[tex]I = \frac{3\pi}{8}\cdot x - \frac{\pi}{4} \cdot \sin 2x + \frac {\pi}{32}\cdot \sin 4x - 4\pi \cdot x - 2\pi\cdot \sin 2x[/tex], for x ∈ [π / 6, 3π / 4]
And the definite integral is:
I = 2.159 + 1.466 - 0.085 - 23.028 + 11.724
I = - 7.764
The definite integral of f(x) = sin⁴ x + 4 · sin² x for x ∈ [π / 6, 3π / 4] is approximately equal to - 7.764.
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Please help, it's due today!
Answer:
Output= -31
Step-by-step explanation:
f(x)= -3x²+8x-3
Therefore, f(-2)= -3(-2)²+8(-2)-3
= -3×4 -16 -3
= -12-16-3
= -31
14) Solve. Which number will be an ordered pair for the solution of y = 6x + 1; (2,__) a) 13 b) 11 c) 8 d) 3
14) y = 6x + 1
( 2, y)
if x = 2 as stated in the coordinate, then y = 6(2) + 1 = 12 + 1 = 13
y =13
The ordered
Which values are solutions to the inequality below? √x≤=7 check all that apply: A.48 B. 14 C. 51 D. -15 E. 2 F. NO SOLUTION
The correct options are (A) and (B).
Because
[tex]\begin{gathered} \sqrt[]{48}<7 \\ \text{and } \\ \sqrt[]{14}<7 \end{gathered}[/tex]a) What is the difference between a 90º counterclockwise rotation and a 90º clockwise rotation?
b) If you use the letter C, what letter will each of those rotations look like...
...a 90º counterclockwise rotation?
...a 90º clockwise rotation?
Answer: answer to A: Clockwise rotations clockwise, while counterclockwise rotations rotate in the opposite direction
Answer to B: i have no idea but i hope the first one helps
Step-by-step explanation:
If 3x. (6x) ≤ 9, which of the following inequalities must be true?
Answer:
if x=0than 3×0×(6×0)_< 9
What is the slope of the line perpendicular to the line represented by the equation 2x+2y=-12
The slope of the line perpendicular to the line given by equation 2x+2y=-12 is found as 1.
What is the definition of line slope?The slope of a line measures its steepness as well as direction.The slope of a line is defined as the change throughout y coordinate in relation to the transitions in x coordinate.The net change in y coordinates is Δy, while the net change in x coordinates is Δx.So m represents the change in y coordinate in relation to a shift in x coordinate.The slope can be calculated using the following formula:
m = Δy/Δx
Where, m is the slope.
The equation of the line is; 2x+2y=-12
Write the equation in slope-intercept form.
2x + 2y = -12
Divide by 2.
x + y = -6
y = -x - 6
Slope m₁ = -1 and y-intercept = -6.
As, both line are perpendicular.
Thus,
m₁ x m₂ = -1
m₂ = -1/m₁
Put the value.
m₂ = -1/(-1)
m₂ = 1
The slope of the perpendicular line is found as 1.
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1. Select all the conditions for which it is possible to construct a triangle.
A 60°, 80°, and 80°
B) 4cm, 5cm, and 6CM
C)4 cm, 5 cm, and 15 cm
D)4cm, 5 cm, and 50°
E)30°, 60°, and 3 cm
The conditions for which it is possible to construct triangles are:
(D) 4cm, 5 cm, and 50°.(E) 30°, 60°, and 3 cm.What are triangles?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. Three straight sides and three angles make up the two-dimensional shape of a triangle. Three sides, three vertices, and three angles make up a triangle. A triangle's three interior angles are always added up to 180 degrees. A triangle's two longest sides added together are always longer than its third side. The six different kinds of triangles are right, obtuse, acute, equilateral, scalene, and isosceles.So, the condition for which it is possible to construct a triangle:
(A) 60°, 80°, and 80°:
Not possible as the sum of angles is greater than 180°.(B) 4cm, 5cm, and 6cm:
Not possible as the square of the 2 shorter sides is greater than the square of the longest side.(C) 4 cm, 5 cm, and 15 cm:
Not possible as the square of the 2 shorter sides is greater than the square of the longest side.(D) 4cm, 5 cm, and 50°:
Yes, it is possible to construct a triangle.(E) 30°, 60°, and 3 cm:
Yes, it is possible to construct a triangle.
Therefore, the conditions for which it is possible to construct triangles are:
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is it a compound interest problem, a saving annuity problem, a payout annuity problem, or a loan problem ?
a. Marcy received an inheritance of 20000, and invested it at 6% interest. She is going to use it for college, withdrawing money for tuition and expenses each quarter. How much can she take out each quarter if she has 3 years of school ?
1. The scenario represents a payout annuity.
2. Marcy can withdraw $1,833.60 per quarter until after 3 years when the inheritance will be exhausted.
What is a periodic withdrawal of a sum lump?A periodic withdrawal is the opposite of a periodic payment.
In a periodic withdrawal, the investor withdraws a constant amount from the investment that earns interest until it is exhausted.
A periodic withdrawal is the same as a payout annuity, which involves periodic receipts from the invested capital.
Using an online finance calculator, we can compute the quarterly withdrawals as follows:
N (# of periods) = 12 quarters (3 x 4)
I/Y (Interest per year) = 6%
PV (Present Value) = $20,000
FV (Future Value) = $0
Results:
Withdrawals = $-1,833.60
Sum of all periodic payments = $-22,003.20
Total Interest $2,003.20
Thus, in this payout annuity, Marcy can withdraw $1,833.60 quarterly for 3 years.
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Need help with this !!!!
The equation of the line in slope intercept form is y = -7x/2 - 5.
What is termed as the slope intercept form?A straight line's slope-intercept form is y = mx + b. In the equation y = mx + b for a straight line, m is known as the slope and b is known as the y-intercept. where y = mx+by = how much further up or down the line is,x = how far along the line is it,b = value of y when x equals 0 andm = indicates how steep this same line is.This is calculated using m = (distinction in y coordinates)/ (difference in x coordinates).For the given question,
The graph of the straight line is given.
Select two points which lies on the line.
(x₁, y₁) = (0, -5)
(x₂, y₂) = (-2, 2)
Find the slope using the formula.
m = (y₂ - y₁)/(x₂ - x₁)
m = (2 + 5)/(-2 - 0)
m = -7/2
The equation of the line in slope intercept form is given as;
y - y₁ = m(x - x₁)
Put the values.
y + 5 = (-7/2)(x - 0)
y = -7x/2 - 5
Thus the equation of the line in slope intercept form is y = -7x/2 - 5.
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Write your answer as a fraction or mixed number in simplest form. 4 6/7 ÷ 9
The value of the given expression in simplest form is 34/63.
Mixed fraction
It is a form of a fraction which is defined as the ones having a fraction and a whole number.
Example: 2(1/7), where 2 is a whole number and 1/7 is a fraction.
To convert 2(1/7) into improper fraction , we will multiply 7 and 2 and then add 1 to it to get the numerator part and 7 will be the denominator of the fraction that is 15/7.
Given expression:
4(6/7) ÷ 9
We have to find the value of the given expression in simplest form.
We can write the mixed fraction 4(6/7) as 34/7
(34/7) ÷ 9
(34/7)*(1/9) = (34*1)/(7*9) = 34/63
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Ela enjoys scuba diving. On one particular trip she was diving at a rate of 5 ½ ft per
minute. If Ela started at the surface, how far below the surface was she after 6 minutes?
(Hint: below sea level is a negative value)
Answer:
30 1/2
Step-by-step explanation:
Which equation represents the proportional relationship displayed in the table?
x: 4, 9, 11, 14
y: 32, 72, 88, 112
A. y = 8x
B. y = 8x + 4
C. y = 1/8x
Answer:
A. y = 8x
Step-by-step explanation:
y = 8x
From first term
32 = 8(4)
32=32
Correct