The equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).
The given expression is c² - 64.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
1) The factorization of c² - 64 is as follows:
Now, factors of c² - 64 is c² - 8²=(c-8)(c+8)
2) 12y² -75 = 3 (4y²-25)
= 3((2y)²-5²)
= 3 (2y+5)(2y-5) (∵ a²-b²=(a-b)(a + b))
3) 9y²-36 = 9(y²-4)
= 9(y²-2²)
= 9(y-2)(y+2) (∵ a²-b²=(a-b)(a + b))
4) -x²+5x-4
= x²-5x+4
= x²-4x-x+4
= x(x-4)-1(x-4) (∵ a²-b²=(a-b)(a + b))
= (x-4)(x-1)
5) ab²-b
=b(ab-1)
Therefore, the equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
I think its a is one of them, im not completely sure tho
Step-by-step explanation:
An airplane covers 2 124 kilometres in 6 hours. How many minutes does it take to cover 1 770
kilometres?
Answer:
Step-by-step explanation:
It would take 300 minuets
Quadrilateral ABCD is similar to Quadrilateral WXYZ.
1) What is the scale factor using ABCD as the pre-image?
2) What is mZC?
3) What is mZZ?
4) What is AD?
Scale factor=
-10
m/XYZ =$7.47*
XY = 2.5 units
10
m B 5 units
N
0
B
Ws
A
WZ 3 units
D
m/CDA 75.96*
10
Answer:
Step-by-step explanation:
ur mom
WILL MARK BRAINLIEST drag and drop the discriptions into the box to correctly classify each pair of number angles each may be used more then once
Answer: 1 and 2 = vertical
3 and 4 = adjacent
Point value: 15
Please HELP!
Answer:
There are three terms in the given expression.
Step-by-step explanation:
First, a term is a single individual value on which mathematical operations occur in an algebraic expression. Essentially, terms are every part of an expression that is separated by any mathematical operation, such as PEMDAS. In the expression [tex]\frac{v}{3} -4*2[/tex], [tex]\frac{v}{3}[/tex], -4, and 2 are all terms. Therefore, there are three terms in the given equation.
Have a great day! Feel free to let me know if you have any more questions :)
Solve for x provide proofs pleaseee
Answer:
x = ~4.40 or [tex]\sqrt{19.37}[/tex]
Step-by-step explanation:
This is a right triangle, so we will use the Pythagorean Theorem.
The theorem goes as follows: [tex]a^2 + b^2 = c^2[/tex]
Let's set x as the a value in the theorem. Plug in 6.8 for b, and 8.1 for c.
[tex]x^2 + (6.8)^2 = (8.1)^2[/tex]
Then, simplify!
[tex]x^2 + 46.24 = 65.61[/tex]
Subtract 46.24 on both sides.
[tex]x^2 = 19.37[/tex]
Take the square root of both sides
[tex]x =\sqrt{19.37}[/tex]
Voila!
What is the simplified value of the expression
The simplified value of the expression is,
⇒ [tex]\frac{1}{\sqrt[5]{3} }[/tex]
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 expression is,
⇒ [tex]\frac{(\sqrt[3]{3} )^{3/5} }{(\sqrt[3]{3} )^{6/5} }[/tex]
Now, We can simplify by the rule of exponent as;
⇒ [tex]\frac{(\sqrt[3]{3} )^{3/5} }{(\sqrt[3]{3} )^{6/5} }[/tex]
⇒ [tex](\sqrt[3]{3} )^{3/5} }{(\sqrt[3]{3} )^{- (6/5)} }[/tex]
⇒ [tex](\sqrt[3]{3} )^{3/5 - 6/5[/tex]
⇒ [tex](\sqrt[3]{3} )^{-3/5[/tex]
⇒ [tex]\frac{1}{\sqrt[3]{3} ^{ 3/5} }[/tex]
⇒ [tex]\frac{1}{\sqrt[5]{3} }[/tex]
Thus, The simplified value of the expression is,
⇒ [tex]\frac{1}{\sqrt[5]{3} }[/tex]
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Ann borrowed $8000 at a rate of 15%, compounded annually. Assuming she makes no payments, how much will she owe after 6 years?
Answer:
Ann will owe $15,258.23 after 6 years, assuming she makes no payments.
What is Compound Interest ?
Compound interest is a method of calculating interest on a loan or investment, where interest is earned on both the initial principal amount and on any interest that has already been earned. In other words, interest is added to the principal, and then interest is calculated on the new total amount (the principal plus the previously earned interest). This results in the interest earned growing exponentially over time.
According t o given condition :
To calculate the amount Ann will owe after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
where:
A = the amount Ann will owe after 6 years
P = the initial principal amount borrowed, which is $8000 in this case
r = the annual interest rate as a decimal, which is 15% or 0.15
n = the number of times interest is compounded per year, which is once annually in this case
t = the number of years, which is 6 in this case
Plugging in these values, we get:
A =
A =
A = $15,258.23
Therefore, Ann will owe $15,258.23 after 6 years, assuming she makes no payments.
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Meginnis corporation's relevant range of activity is 3,000 units to 7,000 units. When it produces and sells 5,000 units, its average costs per unit are as follows:.
As per the concept of average, the cost of producing 6,000 units is $79,200.
The average, also known as the mean, is a mathematical representation of a set of data. It is calculated by adding all the values in the set and dividing the result by the number of values in the set.
When it comes to calculating the total amount of direct manufacturing cost incurred when 6,000 units are produced, it is important to use the average cost per unit. To do this, we need to multiply each average cost per unit by the number of units produced.
The total direct manufacturing cost incurred can be calculated as follows:
Direct materials = $5.20 * 6,000 = $31,200
Direct labor = $3.75 * 6,000 = $22,500
Variable manufacturing overhead = $1.65 * 6,000 = $9,900
Fixed manufacturing overhead = $2.60 * 6,000 = $15,600
The total direct manufacturing cost incurred is $79,200.
Complete Question:
Meginnis Corporation's relevant range of activity is 3,000 units to 7,000 units. When it produces and sells $5,000 units, its average costs per unit are as follows:
Average Cost per Unit
Direct materials $5.20
Direct labor $3.75
Variable manufacturing overhead $1.65
Fixed manufacturing overhead $2.60
Fixed selling expense $0.50
Fixed administrative expense $0.40
Sales commissions $1.50
Variable administrative expense $0.50
If 6,000 units are produced, the total amount of direct manufacturing cost incurred is closest to:
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I need some help with my homework
Answer:
c
Step-by-step explanation:
c
Answer:
A
Step-by-step explanation:
Triangle ABC is similar to triangle FGH. Given the following angle measures, find the missing angle measures.
m∠A = 22 degrees
m∠B = 75 degrees
Enter your answers as numbers only.
m∠F = _____ degrees
m∠G = _____ degrees
m∠H = _____ degrees
m∠C = _____ degrees
The missing angle measures are:
m∠F = 22 degrees
m∠G = 75 degrees
m∠H = m∠C = 83 degrees
m∠C = 83 degrees
The angle measuresSince triangles ABC and FGH are similar, their corresponding angles are equal. Therefore:m∠F = m∠A = 22 degrees
m∠G = m∠B = 75 degrees
m∠H = m∠C, since they are corresponding angles, but we still need to find the measure of m∠C.
To find m∠C, we can use the fact that the sum of the angles in a triangle is always 180 degrees. So:m∠A + m∠B + m∠C = 180 degrees
Substituting the given values, we get:22 degrees + 75 degrees + m∠C = 180 degrees
Simplifying, we get:m∠C = 180 degrees - 22 degrees - 75 degrees = 83 degrees
Therefore, the missing angle measures are:
m∠F = 22 degrees
m∠G = 75 degrees
m∠H = m∠C = 83 degrees
m∠C = 83 degrees
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Diane pays $3.84 for a bag of 16 tangerines.
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
Which function has a range limited to only negative numbers?
Answer:
F (x)=-x^2
Step-by-step explanation:
While shopping after her birthday, Annie bought 2 pairs of jeans and 3 shirts and spent $127. Her twin sister Hallie bought the same items consisting of 1 pair of jeans and 4 shirts and spent $116 how much does one pair of jeans cost and how much does a shirt cost
Answer:
The shirt costs $21
Step-by-step explanation:
2x + 3y = 127 ....eq 1
Her twin sister Hallie bought 1 pair of jeans and 4 shirts for $116.
So, x + 4y = 116 ....eq 2
Multiplying eq 2 by 2, we get :
2x + 8y = 232 ....eq 3
Subtracting eq 1 by eq 3, we get :
(2x + 8y) - (2x + 3y) = 232 - 127
5y = 105
Thus, y = 21
Putting this value of y in eq 2, we get :
x + 4(21) = 116
x = 116 - 84 = 32
Therefore, the cost of a pair of jeans = x = $32
And the cost of a shirt = $21
What is an equivalent expression for 27+3x
The equivalent expression is 81 + 9x
What is an algebraic expression?An algebraic expression is simply defined as an expression that is composed of terms, variables, coefficients, factors and constants.
They are also made up of arithmetic operations like subtraction, division, addition, multiplication, bracket and parentheses.
Equivalent expressions are defined as expressions with the same solution but which differs in the mode of their arrangement.
From the information given, we have that;
27+3x
Multiply the values by 3 each, we get;
81 + 9x
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What are the equations of the
asymptotes of the functions
f(x) =1/x-5 +3? What are the
domain and range?
Step-by-step explanation:
I am in class 7 If I know I tell you I am go to ask my teacher
Answer:
Domain:(−∞,5)∪(5,∞),{x|x≠5}
Range:(−∞,3)∪(3,∞),{y|y≠3}
Step-by-step explanation:
??????
find missing value
i rlly need help thanks
The missing value using concept of similar triangle ratio is; 35
How to find the length of similar triangles ?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Using the concept of similar triangles on the given diagram, we have;
p/(30 + 20) = 14/20
p = (14 * 50)/20
p = 35
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During the month of May, the sheriff's department issued 130 traffic tickets for speeding or failure to obey traffic signals. The fine for each speeding ticket
was $67.00, and each fine for failure to obey traffic signals was $67.00. The sheriff's department collected $8,710.00 in fines from these two offenses.
Which system of equations can be used to determine the number of speeding tickets given, x, and the number of tickets given for failure to obey traffic
signals, y?
Answer: The number of speeding tickets issued is represented by x and the number of tickets for failure to obey traffic signals is represented by y. The total number of tickets issued is 130, so we have:
x + y = 130
The total amount of money collected in fines is $8,710.00, so we have:
67x + 67y = 8710
These two equations form a system of linear equations that can be used to determine the number of speeding tickets, x, and the number of tickets for failure to obey traffic signals, y. To solve this system, we can use any of the methods for solving a system of linear equations, such as substitution, elimination, or matrices.
Step-by-step explanation:
Name at least two independent variables that could result in a change in a monthly electric bill
The two independent variables that could result in a change in a monthly electric bill will be Product physical dimensions and Machine operators' skill level.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
Independent variables are variables that do not depend on anything.
Dependent variables are variables that depend on the independent variables.
The independent variables in the electric bill are as follows:
Product physical dimensionsMachine operators' skill level.Non-production machines that use electricity, among other thingsThe two independent variables that could result in a change in a monthly electric bill will be Product physical dimensions and Machine operators' skill level.
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2/ac + 1/ab + 3/bc = ?
Answer:
Abc
Step-by-step explanation:
2b + c + 3a = Abc
a jet travels 470 miles in 5 hours at this rate how far could the jet fly in 8 hours
Jet could fly a distance of 752 miles in 8 hours if it travels at the same rate.
What is Speed?Speed is defined as the unit rate in terms of distance travelled and the time taken to travel the distance.
Speed has only magnitude and no direction and therefore is a scalar quantity.
Given that,
a jet travels 470 miles in 5 hours.
Distance travelled = 470 miles
Time taken to travel the distance = 5 hours
Speed of the jet = 470 miles / 5 hours = 94 miles per hour
Given that jet is travelling at the same rate. So the speed is constant.
We have to find the distance travelled in 8 hours.
Let d be the distance.
Speed = Distance / Time
Distance = Speed × Time
d = 94 × 8
d = 752 miles
Hence the distance travelled is 752 miles in 8 hours.
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During a seven-year period, the average housing prices (in thousands of dollars) for a year in Miami $M$M and Gainesville cap g$G$G are modeled by the equations
cap m is equal to 1 point 7 t cubed minus 6 point 5 t squared plus 212$M=1.7t^3-6.5t^2+212$M=1.7t3−6.5t2+212 and
cap g is equal to 1 point 6 t squared minus 14 t plus 165$G=1.6t^2-14t+165$G=1.6t2−14t+165 ,
where t is equal to 1$t=1$t=1 represents the first year.
a. Write a polynomial that represents the difference in housing prices.
Polynomial:
Question 2
b. What is the difference in housing prices in the fifth year?
$
The difference in housing prices in the fifth year is $7,125.
What is price?Price is the amount of money one has to pay for goods or services. It is also the return on an investment or the cost of borrowing money. Price is determined by the supply and demand of a product or service. It is also influenced by market forces such as competition, production costs, and availability of resources. Price is a key factor in determining the success of a business, as it can affect consumers' buying decisions and profitability.
$M(5) - G(5) = (1.7(5)³- 6.5(5)²+ 212) - (1.6(5)²- 14(5) + 165) = $7,125
Therefore, the difference in housing prices in the fifth year is $7,125.
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A construction worker places 60 bricks to make a wall. If he places 6 bricks in each column, how many columns are there?(1 point)
Answer:
10 columns
Step-by-step explanation:
[tex]\frac{60}{6}=10[/tex] columns
Write the number
five million four thousand three hundred
in standard form.
The required five million four thousand three hundred in standard form is 5,004,300.
What is a number system?A number system is described as a technique of composing to represent digits. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
In the question, we are asked to write the word of the number five million four thousand three hundred in standard form.
So,
five million four thousand three hundred = 5,004,300
Since
1 million = 1000, 000
1 thousand = 1000
1 hundred = 100
Thus, the required five million four thousand three hundred in standard form is 5,004,300.
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[TRUE or FALSE] finding a parametric description of the solution set of a linear system is the same as solving the system.
The statement is false. The solution set of a linear system can only be expressed using a parametric equation if the system has at least one solution.
Equation of this sort is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are specified as continuous and independent of other variables functions of the parameter Multiple parameters may be utilized as needed.For example, the following equation can be represented as a pair of equations in parametric form rather than the equation in Cartesian form: Parameterization, It effectively differentiates and integrates curves by converting a function into parametric form.
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ASAP!!! How do I solve this
Complete the equation of the circle that includes the points (-5,4), (3,4), and (3,0)
The equation of circle is ( x + 1 )² + ( y - 2 )² = 20
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the points on the circle be A ( -5 , 4 ) , B ( 3 , 4 ) and C ( 3 , 0 )
Now , the equation of the circle is of the form
ax + by + c = x² + y²
Substituting the values in the equation , we get
-5a + 4b + c = 41 be equation (1)
3a + 4b + c = 25 be equation (2)
3a + c = 9 be equation (3)
Subtracting equation (2) from equation (1) , we get
-8a = 16 be equation (4)
Divide by -8 on both sides of the equation , we get
a = -2
Substitute the value of a in equation (3) , we get
3 ( -2 ) + c = 9
-6 + c = 9
c = 15
Substitute the value of a and c in equation (2) , we get
-6 + 4b + 15 = 25
4b + 9 = 25
4b = 16
b = 4
So , the value of a , b and c are -2 , 4 and 15 respectively
Now , the equation of circle will be
-2x + 4y + 15 = x² + y²
On simplifying the equation , we get
x² + y² + 2x - 4y - 15 = 0
( x² + 2x + 1 ) - 20 + ( y² - 4y + 4 ) = 0
So , the equation will be
( x + 1 )² + ( y - 2 )² = 20
Hence , the equation of circle is ( x + 1 )² + ( y - 2 )² = 20
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How many solutions does the system of liner equations represented in the graph
Answer:
Infinite solutions
Step-by-step explanation:
There are an infinite number of solutions. If you have a system of linear equations, the solution for the system is the value that makes all of the equations true. For two variables and two equations, this is the point where the two graphs intersect.
which terms are used to describe events that have NO outcomes in COMMON?
Events that have no outcomes in common are said to be disjoint or mutually exclusive.
Two sets are known to be mutually exclusive when they have no common elements. Mutually exclusive events are those that cannot take place at the same moment.
If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero.
Set A = {2, 4, 6, 8, 10, 12, 14, 16}
Set B = {1, 3, 5, 7, 9, 11, 13, 15}
A and B do not have any numbers in common, so P (A ∩ B) = 0. Therefore, A and B are mutually exclusive.
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What is an equation of the line that passes through the point (5,-8) and is parallel to the line 5x-4y=16
Answer:
To find the equation of the line that passes through the point (5,-8) and is parallel to the line 5x-4y=16:
1. Identify the slope of the original line (m = 5/4).
2. Use the point-slope formula: y - (-8) = (5/4)(x - 5).
3. Simplify the equation.
4. The equation is y + 8 = 5/4(x - 5), or 5x - 4y = 16.
Superior segway tours gives sightseeing tours around chicago, illinois. it charges a one-time fee of $60, plus $28 per hour. what is the slope of this situation? a. 28 b. 32 c. 60d. 88
Answer:
the answer is (a) 28.
Step-by-step explanation:
The given situation can be represented by a linear equation of the form:
Cost = mx + b
where "m" is the slope (the rate of change of cost with respect to time), "x" is the number of hours of the tour, and "b" is the y-intercept (the cost when x = 0).
In this case, the y-intercept is $60, which represents the one-time fee. The cost increases by $28 per hour, so the slope is:
m = $28/hour
Therefore, the answer is (a) 28.