Step-by-step explanation:
n^2 - n -56 = 0
n^2 -8n +7n-56 = 0
n(n-8) +7(n-8) = 0
(n+7)(n-8) = 0
n = (-7,8)
option B
In one week, a printing center made 1,233 copie of a 26 page article. The printing center alo printed 658 copie of a 12 page eay. How many page did the printing center print during the week?
As per given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.
As given in the question,
Number of copies of 26 pages article print by printing center is equal to 1,233 copies
Number of copies of 12 page article print by printing center is equal to 658 copies
Total number of pages print by printing center during this one week is equal to
= ( 1233 × 26 ) + ( 658 × 12 )
= 32,058 + 7896
=39,954 pages
Therefore, for the given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.
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An elevator travles 310 feet in 10 seconds. at that speed, how far can this elevaor travles in 12 seconds? explain your reasoning.
Explanation:
We can do cross multiplying through ratios:
310 feet / 10 secs = x feet / 12 secs
10x = 310 * 12
10x = 3720
x = 372 feet
OR
Divide 310 feet and 10 secs to get 31 feet in 1 sec
Multiply 31 ft and 1 sec to get 372 ft in 12 secs
Gustavo has been waiting to purchase an acoustic guitar. This week, the guitar is on sale for 34 of the original price. With the sale, Gustavo paid $90, without tax, for the guitar. Write an equation to find the original price p of the guitar.
The original price of the guitar is $120
From the question, we have
guitar is on sale for 3/4 of the original price (p).
3/4*p = $90
p = (90*4)/3
p= $120
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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hello can someone help me pls
1. The number of sides of the polygon is of: 12 sides.
2. The missing exterior angles are of: α = 48.5º.
3. The size of the exterior angle is of 20º, hence the polygon has 18 sides.
What is the relation between the measure of the exterior angles and the number of sides of a regular polygon?A regular polygon is a polygon in which all the sides have the same length.
The relation between the measure of the exterior angles of a regular polygon and the number of sides is given as follows:
Measure of each angle = 360º/number of sides.
For item a, the measure of each angle is of 24º, hence the number of sides is obtained as follows:
24º = 360º/number of sides.
24n = 360
n = 360/24
n = 12 sides.
The sum of the measures of the external angles of a polygon is always of 360º.
Hence, for item 2, the missing angles are obtained as follows:
2α + 90 + 55 + 40 + 78 = 360
2α + 263 = 360
2α = 97
α = 97/2
α = 48.5º.
An interior angle and it's exterior angle are supplementary, hence, for item 13, the measure of the exterior angle is of:
Exterior angle = 180º - 160º = 20º.
Then the number of sides of the polygon is obtained as follows:
20n = 360
n = 360/20
n = 18 sides.
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f(x)=5/x-1
g(x)=4-2x
Calculate fg(x)
Answer:
Step-by-step explanation:
define function fg(x) :
Fg(x) = f(g(x))
= [tex]\frac{5}{x}[/tex] (4-2x)-1
= [tex]\frac{20}{x}[/tex] - [tex]\frac{10x}{x}[/tex] - 1
= 20 - 10x -1
= 20 - 1 - 10x
= 19 - 10x
£2448is invested in an account at rate of compound interest. One year after the investment there is £2496.96 in the account. How much is in the account 4years after the investment.
The amount after four years is £2649.79 .
What is the amount after four years?Now we know that we need to obtain the rate for the compounding of the money and we need to recall that for the amount, we have;
A = P(1 +r/n)^nt
A = amount
P = principal
r = rate
n = number of times compounded
t = time
For one year in which the interest is compounded annually;
2496.96 = 2448(1 + r)^1
2496.96/ 2448 = (1 + r)
1.02 = 1 + r
r = 1.02 - 1
r = 0.02 or 2%
Now after four years;
A = 2448(1 + 0.02)^4
A = £2649.79
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2x + 21/5 = 3 Solve for x.
Simplify your answer as much as possible.
Answer:
x= -3/5
Step-by-step explanation:
2x+21/5=3
2x+21/5-21/5=3-21/5 (subtract 21/5 from both sides)
2x=3-21/5 (L.C.M=5)
2x= 15-21/5
2x= -6/5
2x/2=-6/5/2 (divide both sides by 2)
x= -6/5x1/2 (reciprocal)
x= -6/10
simplify:
x= -3/5
i = prt ; p = $2,000, r = 3%, and t = 2 yr.
Evaluate the expression using the given values.
Please and Thank you
The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.
Given that,
p = $2,000, r = 3%, and t = 2 yr.
We have to find the i when i=prt.
Here,
i is interest amount.
p is principal amount.
r is rate of interest per year.
t is time period.
So,
Formula for finding interest amount is
i=prt
So,
i=2000(3/100)(2)
i=20×3×2
i=120
Therefore, The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.
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Consider a causal continuous time LTI system whose input x(t) and output y(t) are related by the following differential equation d/dt y(t) + 4y(t) = x(t) Find the Fourier series representation of the output y(t) for each of the following inputs: A. x(t) = cos(3 pi T) B. x(t) = sin(3 pi t) + cos(6 pi t+pi/4)
The Fourier series representation of the output y(t) is;
(a) y(t) = 0.097 cos(3πt - 67)
(b) y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)
Given;
A causal continuous-time LTI system whose input x(t) and output y(t) are related by the following differential equation;
[tex]\frac{d}{dt}y(t) + 4y(t) = x(t)[/tex]
By taking Laplace's Transform;
sY(s) + 4Y(s) = X(s)
Y(s)/X(s) = H(s) = 1/(s + 4)
(a) When input x(t) = cos3πt
∵ ω = 3π
H(jω) = 1/(jω + 4)
H(jω₁) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.097
∠H(jω) = -tan⁻¹(ω/4) = -67° = Ф₁
y(t) = H(jω₁)*cos(3πt + Ф₁)
→ y(t) = 0.097 cos(3πt - 67)
(b) When input x(t) = sin3πt + cos(6πt + π/4)
∵ ω = 6π
H(jω) = 1/(jω + 4)
H(jω₂) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.051
∠H(jω) = -tan⁻¹(ω/4) = -78° = Ф₂
y(t) = H(jω₁) * sin(3πt + Ф₁) + H(jω₂) * cos(6πt + π/4 + Ф₂)
→ y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)
The Fourier series representation of the output y(t) is;
y(t) = 0.097 cos(3πt - 67)
y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)
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HELP ME SOMEONE PLEASEE
Find the quotient. 5/4 1 1/2=
Find the value of x.
x(x+4)
148⁰
the answer is 148 the reason is two angle interception
Step-by-step explanation:
The angle on top of x(x+4) is equal to 148.
The angle at x(x+4) = 180 -148 = 32
[tex]x(x + 4) = 32 \\ {x}^{2} + 4x = 32 \\ {x}^{2} + 4x - 32 = 0 \\ (x - 4)(x + 8) = 0[/tex]
x-4=0
x=4
x+8=0
x=-8
If the geometric mean of 10 and x is 30, what is the value of x?
Step-by-step explanation:
10 + x = 30
or, x = 30 - 10
x = 20
Latrell jogs around a lake. Each lap around the lake is 4/3 mi. Latrell jogs a total of 7 mi. How many laps around the lake does Latrell jog? Write your answer as a whole number of laps, plus a fraction of a lap. You can use the model to help. Latrell jogs ? Whole laps, plus ? of a lap
Answer:
5 whole laps + 1/4 of a lap. Or, 5.25 laps
Step-by-step explanation:
We can solve this 2 ways.
First, we can continuous add 4/3rds to itself until we reach 7 miles.
4/3 + 4/3 = 2 2/3
+ 4/3 = 4
+ 4/3 = 5 1/3
+ 4/3 = 6 2/3
Then you see that we are almost at 7. We have 1/3 left until we reach 7. 1/3 is 0.25% of 4/3, so its only 25% of a lap. That plsu the 5 other laps we did would equal 5.25 laps.
An easier way is 7 divided by (4/3), which is 5.25.
Good Luck! Hope this helps.
f(x) = x^2. What is g(x)?
Answer:
B. -x^2-2
Step-by-step explanation:
-x^2 would max out at 0, so you need to shift it down by 2 (hence the -2) to have the correct function.
Hope this helped!
What is the slope of the line on the graph?
Need help.
help please this is confusing will will give brainiest
Answer:
Slope = - 2
Explanation step by step:
Please help me with this question.
Answer:
7x + 4,
8y - 3 > 13,
8a,
9 < 5x - 1
Step-by-step explanation:
Hello!
For this question it's important to know what form an expression takes, which is essentially a group of "things" (such as x, y, and numbers) that don't necessarily equal anything else, that would be an equation
In other words, an expression is a mathematical statement that does not include an = sign.
suppose this player attempts 10 shots in a game and makes only 3 of them. does this provide convincing evidence that she is less than a 47% shooter?
No, because it is plausible that she would make 3 or fewer shots by chance alone.
What is convincing evidence?
The proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent.
if our test statistic is: positive and greater than the critical value, then we have sufficient evidence to reject the null hypothesis and accept the alternative hypothesis. positive and lower than or equal to the critical value, we must accept the null hypothesis.
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If you go out to eat with 3 friends and your meal was $72.50.
The sales tax is 6.75% sales tax and you tip the waiter 15%.
How much is the total bill?
The total bill that will be paid by the friends is $88.27.
How to calculate the total bill?Cost of meal = $72.50
Sales tax = 6.75%
The amount on tax will be:
= 6.75% × $72.50
= $4.89
Tip = 15% × $72.50
Tip = $10.88
The total bill will be:
= Cost of bill + Tax + Tip
= $72.50 + $4.89 + $10.88
= $88.27
The cost is $88.27.
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Matt's bus ride to school is 3 minutes more than 1/4 the time of Rick's bus ride. Write an equation to model this situation and graph it
An equation to model this situation is M = t/3 + 3, which is shown in the graph attached below.
How to write an equation to model this situation?In order to solve this word problem, we would assign variables to the amount of time taken by Rick's bus ride and Matt's bus ride to school, and then translate the word problem into algebraic equation as follows:
Let the variable t represent the amount of time taken by Rick's bus ride. Let the variable M represent the amount of time taken by Matt's bus ride.Therefore, translating the word problem into an algebraic equation, we have the following;
M = 1/4(t) + 3
M = t/3 + 3
Based on the graph (see attachment) which models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride, we can logically deduce that the slope of the graph is 1/4 and the y-intercept is equal to 3.
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HELP ALOT OF POINTSSS
Evaluate the expression if a=−12, b=34, and c=−23.
−||6c−16b||+1
-691 is the value of the expression −||6c−16b||+1 when a=−12, b=34, and c=−23.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is −||6c−16b||+1
The values of c is minus twenty three, the value a is minus twelve and the value of b is thirty four.
−||6c−16b||+1
-||6(-23)-16(34)||+1
-||-138--55||+1
-||-692||+1
-692+1
=-691
Hence -691 is the value of the expression −||6c−16b||+1 when a=−12, b=34, and c=−23.
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What are all the common factors of 15,45,90
(Pls help me I got till 5:10)
Which expression gives the volume of a sphere with radius 7?
O A.
(7³)
OB. 4 (7²)
O C.
(7²)
O D. 4 (7³)
The required expression is
(4/3)π(7)³
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
We are given to select the correct expression that gives the volume of a sphere with a radius of 7 units.
We know that,
the VOLUME of a sphere with radius 'r' units is given by
V=(4/3)πr³
Here, the radius of the given sphere is
r = 7 units.
Therefore, the volume of the sphere will be
V=(4/3)π(7)³
Thus, the required expression is
(4/3)π(7)³
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Find the slope of the line shown on the graph to the right.
Answer: [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
The two points found on the graph are:
(x₁, y₁) = (2, 4)(x₂, y₂) = (-1, -3)The slope can be calculated as:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-3-4}{-1-2} =\frac{-7}{-3} =\frac{7}{3}[/tex]
NEED HELP PLEASEEEEEEEE
Answer:
1/2
Step-by-step explanation:
Because the y is going up by 0.5 which in a fraction form is 1/2 and it isn't negative 1/2 because the number is growing and is not decreasing.
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
1) Find the difference between and y
5 - 0 = 55.5 - 1 = 4.56 - 2 = 46.5 - 3 = 3.52) Find the pattern between the numbers
As we can see there is a pattern of subtract [tex]\frac{1}{2}[/tex] between every number
To find this just subtract each number by the other
5 - 4.5 = 0.54.5 - 4 = 0.54 - 3.5 = 0.5As 0.5 is equal to [tex]\frac{1}{2}[/tex] the answer to the solution would be [tex]\frac{1}{2}[/tex]
Hope this helps, have a great day!!
54g of AI react completely with 409.2g of ZnCI2 to form 196.2 of Zn metal. How many grams of AICI3 are formed
By the use of the law of conservation of mass, the mass of the aluminum chloride is 267 g.
What is the mass of the aluminum chloride formed?We know that a chemical reaction occurs when there is the combination of two or more substances such that a new substances is formed. We have to put down the reaction equation in this case and we have;
[tex]4Al(s) + 3ZnCl_{2} (aq) ---- > 2Al_{2} Cl_{3}(aq) +3 Zn(s)[/tex]
Using the law of the combination of mass, the total mass of the reactants must be equal to the total mass of the products; Let the mass of the aluminum chloride formed be x
54 + 409.2 = 196.2 + x
x = (54 + 409.2) - 196.2
x = 267 g
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Which graph represents this function?
f(X)=√X+1
Question
A store has 9 packages of candles. Each package has 4 candles.
Which equation can be used to solve for the total number of candles?
What is the area of the base, B, of the prism?
Area of the base 'B' of a given rectangular prism is equal to 12 ft².
As given in the question,
For the given rectangular prism ,
Shape of the base is rectangle,
Length of the base of a rectangular prism = 4 ft
Width of the base of a rectangular prism = 3ft
Area of the base of a rectangular prism is given by
= ( length of the base ) × ( Width of the base)
Substitute the value of length and width of the base of the rectangular prism we get,
= ( 4 × 3 ) ft²
= 12 ft²
Therefore, area of the base 'B' of given rectangular prism is equal to 12 ft².
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Answer:
Step-by-step explanation:
Which theorem or postulate could be used to prove the congruence of the triangles?
The third congruent side is not included the side of angles thus it will be congruent by the AAS rule thus option (B) is correct.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
In other meaning, if you can copy a figure then that copy and the original figure will be congruent.
As per the given two triangles,
The two angles are congruent.
The sides which are congruent in both triangles are not the common side of angles or not included in the side of angles thus it will be AAS congruency.
Hence "The third congruent side is not included the side of angles thus it will be congruent by the AAS rule".
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