The expression 25x^2 - 40xy + 16y^2 can be factored as (5x - 4y)(5x - 4y).
Factorization is defined as the process of breaking down a number or polynomial into factors that when multiplied will give the same value.
The expression 25x^2 - 40xy + 16y^2 resembles the form
ax^2 + bxy + cy^2 which has factors (mx + ny)(ox + py).
Factoring polynomial expression like 25x^2 - 40xy + 16y^2 can be done by grouping method shown earlier.
Find the two pairs of numbers whose products are 25 and 16.
Taking 5 and 5, and 4 and 4 as the pair of numbers.
(5x - 4y)(5x - 4y)
Checking the product of this factors:
(5x -4y)(5x - 4y)
25x^2 - 20xy - 20xy + 16y^2
25x^2 - 40xy + 16y^2
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please just solve this, I'm confused.
The quotient of each of the expressions are:
a. 1⅖ / -1/5 = -7
b. -0.4 ÷ 0.25 = 1.6
c. 7/8 ÷ -3/4 = -7/6
d. 0.7 ÷ -1 1/6 = -0.6
How to Find the Quotient?Quotient is the result you get after dividing one quantity by another. For example, the quotient of a and b is a/b.
Find the given quotient as shown below:
a. 1⅖ / -1/5
Convert mixed fraction to improper fraction
7/5 / -1/5
Change the division sign to multiplication and turn the fraction upside down
7/5 × (-5/1)
= -(7 × 5)/(5 × 1)
= -(7 × 1)/(1 × 1)
= -7/1
= -7
b. -0.4 ÷ 0.25
-0.4/0.25
= 1.6
c. 7/8 ÷ -3/4
Change the division sign to multiplication and turn the fraction upside down
7/8 × -4/3
= -(7/8 × 4/3)
= -(7 × 4)/(8 × 3)
= -(7 × 1)/(2 × 3)
= -7/6
d. 0.7 ÷ -1 1/6
0.7 ÷ -7/6
Change the division sign to multiplication and turn the fraction upside down
0.7 × -6/7
0.1 × -6/1
= 0.1 × -6
= -0.6
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prove that triangles abc and def are congruent
Answer:
Below.
Step-by-step explanation:
In Δ ABC m < B = 180 - (50+70) = 60 degrees.
in Δ DEF m < D = 180- ( 60 + 70) = 50 degrees.
BC = DE ( both are 10 cm).
m < A = m < F ( both 70 and directly opposite BC and DE)
m < C = m < D (corresponding angles and both = 50 degree)
Therefore, Δ's ABC and DEF are congruent by AAS.
A four-foot tree was planted. It will grow 2.5 feet each year. The relationships between x, the number of years since the tree has been planted, and y, the projected height of the tree is a linear relationship.
Write an equation to represent this relationship.
The relation between these two variables can be represented by the linear equation:
y = 4ft + 2.5ft*x
How to write an equation that represents this relationship?We know that the original height of the tree was 4 ft, and it grows 2.5 feet each year.
Then if we define the variables:
y = height.
x = number of years.
The relation between these two variables can be represented by the linear equation:
y = 4ft + 2.5ft*x
This linear equation relates the height of the tree as a function of the number of years since it was planted.
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Answer:
y = 4ft + 2.5ft*x
Step-by-step explanation:
In an inverse variation,y = 4when x = 2.Write an inverse variatione quation thats hows there relationship between x and y . Write the equation using a decimal or an integer.
When y = 4 and x = 2, the inverse variation equation is y = 8/x
What is inverse variation?Inverse variation is variation in which the relationship between two variables is an inverse one. That is, while one variable increases, the other decreases.
How to write an inverse variation equation that shows there relationship between x and y.Given that in an inverse variation, y = 4 when x = 2. Since y and x have an inverse relationship, we have that
y ∝ 1/x, this implies that
⇒ y = k/x where k = constant of proportionality
Now, given that in an inverse variation, y = 4 when x = 2. Substituting the values of y and x into the equation, we have that
y = k/x
4 = k/2
k = 4 × 2
k = 8
So, susbstituting k = 8 into the equation for y, we have
y = k/x
y = 8/x
So, the inverse variation equation is y = 8/x
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A floor 5m by 20m is covered by square tiles
The number of tiles is mathematically given as
x=2500Tiles
This is further explained below.
How many tiles are needed??Generally, the equation for the Area of the floor is mathematically given as
A= 20*5
A = 100m^2
Where
20*20=400cm
Therefore no tiles needed is
x=100*10000/400
x=2500Tiles
In conclusion, the number of tiles is
x=2500Tiles
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CQ
\A floor 5m by 20m is covered by square tiles of side 20cm. How many tiles are needed?
Consider the equation |4x + 20 = 6x. Without calculating how do you know that x=-2 is an
extraneous solution?
Without calculating you would that x=-2 is an extraneous solution because an absolute value inequality usually two possible solutions.
Solution of absolute value inequalities
An absolute value inequality is an expression with absolute functions as well as inequality signs. This type of inequality usually have two solutions.
The given equation
|4x + 20| = 6x
The solution to the absolute value inequality above is calculated as follows;
4x + 20 = 6x ------ (1)
-4x - 20 = 6x ------ (2)
from equation (1) above, the value of x is calculated as follows;
2x = 20
x = 20/2 = 10
from equation (1) above, the value of x is calculated as follows;
-10x = 20
-x = 20/10
-x = 2
x = -2
Thus, without calculating you would that x=-2 is an extraneous solution because an absolute value inequality usually two possible solutions.
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Triangle PQR, with vertices P(-9,-7), Q(-4,-8), and R(-5,-5), is drawn on the
coordinate grid below.
-10
P
R
-3
T
ch
9
5
9
-10
What is the area in square units of triangle POR2
Answer:7
Step-by-step explanation:
Triangle fits inside of a rectangle (A=15).
If the rectangle is drawn around the triangle, three other right triangles are formed outside of it. Find the area of each right triangle (4, 1.5, and 2.5), add those together, and subtract from the area of the rectangle.
(15 - 8 = 7)
you conduct a survey of your small town about having a townwide gargae sale. of those surveyed, 56% are in favor and 44% are opposed. the actual percent could be 5% more or 5% less than the acquired results. write an absolute value equation for the least and greatest percentages that could be opposed. use x for the variable.
In the given statement is:
You conduct a survey of your small town about having a town wide gargae sale. of those surveyed, 56% are in favor and 44% are opposed. the actual percent could be 5% more or 5% less than the acquired results.
Using the absolute value function, we have that:
A. The least percentage is of 39% and the greatest is of 49%.
B. Since the greatest percentage is below 50%, the statement conflicts with the survey data.
What is the absolute value function?
The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin.
For this problem, the difference between the percentage of opposed and 44% can be of at most 5%, hence the absolute value equation is:
|x - 44| = 5.
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A hose fills a tank at a rate of 24 gallons per minute.
What is the rate in quarts per second?
Enter your answer in the box.
Answer:
1.6 qt/s
Step-by-step explanation:
You want the fill rate of 24 gal/min converted to quarts per second.
Units conversionTo convert units, multiply by a factor that has units you want and cancels units you don't want. The numerator value and the denominator value of the conversion factor should be equal:
4 qt = 1 gal
1 min = 60 s
Your conversion is ...
[tex]\dfrac{24\text{ gal}}{\text{min}}=\dfrac{24\text{ gal}}{\text{min}}\times\dfrac{4\text{ qt}}{1\text{ gal}}\times\dfrac{1\text{ min}}{60\text{ s}}=\dfrac{24\cdot4}{60}\,\dfrac{\text{qt}}{\text{s}}=\boxed{1.6\text{ qt/s}}[/tex]
Yall I'm really struggling can you help me out
The quotient 49/109 ÷ 28/37 represents a quotient expression. This is because 49/109 is the dividend and the number 28/37 is the divisor. The quotient of 49/109 ÷ 28/37 is 259/436
How to complete the blanks?The quotient expression is given as
49/109 ÷ 28/37
The above expression is a quotient expression such that
Dividend = 49/109 Divisor = 28/37To calculate the quotient, we start by rewriting the expression as a product
So, we have:
49/109 ÷ 28/37 = 49/109 * 37/28
Divide 49 and 28 by 7
So, we have
49/109 ÷ 28/37 = 7/109 * 37/4
Multiply the numerator and the denominator
So, we have
49/109 ÷ 28/37 = 259/436
Hence, the complete statement is
The quotient 49/109 ÷ 28/37 represents a quotient expression. This is because 49/109 is the dividend and the number 28/37 is the divisor. The quotient of 49/109 ÷ 28/37 is 259/436
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Cara used 4 1/6 sheets of construction paper to make 1/6 of her poster borad project. At that rate, how many sheets will she use for the whole project?
Based on the number of sheets of construction paper that Cara uses to make 1/6 of her project, the number of sheets for the whole project would be 25 sheets
How to find the number of sheets needed?Cara will use 4¹/₆ sheets of construction paper for 1/6 of her poster board project so to find the sheets needed for the whole project, use direct proportion.
4¹/₆ sheets of construction paper : 1/6 of project
x sheets of construction paper : 1
1/6 × x = 4¹/₆
1/6x = 4¹/₆
x = 4¹/₆ ÷ 1/6
x = 25/6 x 6/1
x = 25 sheets
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Graph the result of the following transformation.
f(x) + 6
Step-by-step explanation:
I cannot draw here but f(x) + y simply means everything moves up by 6 units.
the line is parallel to the original line and goes now through the points (0, 4) and (1, 8).
Show work please and thank you.
Step-by-step explanation:
2 things to remember :
the sum of all angles in a triangle is ashtrays 180°.
the sum of all angles around a point on one side of a line is also always 180° (because that represents a half-circle).
let's call the 3rd angle in the triangle "innerQ".
so,
180 = (4x + 13) + 19 + innerQ
180 = (7x + 2) + innerQ
as innerQ is also the supplementary angle of 7x + 2.
because of that, we can now say
(4x + 13) + 19 + innerQ = (7x + 2) + innerQ
4x + 13 + 19 = 7x + 2
4x + 32 = 7x + 2
30 = 3x
x = 10
so, the angle S = 4×10 + 13 = 40 + 13 = 53°
Identify the horizontal asymptote of f(x) = 4 x over 7.
y = 0
y = 4 over 7
y = 7 over 4
No horizontal asymptote
Answer:
Step-by-step explanation:
This is a straight line with positive gradient 4/7
There is no horizontal asymptote.
Tell what point is located at each ordered pair.
1. (3,-2)
4. (-7,-8).
2. (2,3)
5. (-4,4)
3. (-5,5)
6. (-5,0)
Write a polynomial function with rational coefficients and the given roots.
-i, 4 i
The polynomial function is x²- 3xi + 4
What are polynomial functions ?In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear PolynomialQuadratic PolynomialSome examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
roots are -i , 4i
Thus the factors are :
(x - (-i) ) ( x - (4i) )
=> ( x + i )( x - 4i )
=> x²- 4xi + xi - 4i²
=> x²- 3xi + 4 ( as i² = -1)
Thus polynomial function for given roots is x²- 3xi + 4
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I don't know the answer
Answer:
21
Step-by-step explanation:
→ Substitute in the values
3³ + 11 × 2 - ( 4 × 7 )
→ Simplify
27 + 22 - 28
→ Evaluate
21
what is the inverse of (x) = [tex]\sqrt{x+9}[/tex] x[tex]\geq[/tex] -9
f−1(x)=(x−9)2, x≥9
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals left parenthesis x minus 9 right parenthesis squared, , , x is greater than or equal to 9
f−1(x)=−(x−9)2, x≤9
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative left parenthesis x minus 9 right parenthesis squared, , , x is less than or equal to 9
f−1(x)=x2−9, x≥0
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals x squared minus 9, , , x is greater than or equal to 0
f−1(x)=x2−9, x≤0
The inverse of [tex]f[/tex], denoted [tex]f^{-1}[/tex], is such that
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Given [tex]f(x)=\sqrt{x+9}[/tex], we have
[tex]f\left(f^{-1}(x)\right) = \sqrt{f^{-1}(x) + 9} = x[/tex]
Solve for [tex]x[/tex].
[tex]\sqrt{f^{-1}(x) + 9} = x[/tex]
[tex]\left(\sqrt{f^{-1}(x) + 9}\right)^2 = x^2[/tex]
[tex]f^{-1}(x) + 9 = x^2[/tex]
[tex]f^{-1}(x) = x^2 - 9[/tex]
Note that [tex]f(x)\ge0[/tex], so we must also have [tex]f\left(f^{-1}(x)\right) = x \ge 0[/tex]. This makes the third choice the correct one.
What are the slope of the two lines?
ABC=40 and Bd is angle bisector of ABC what is Y= ?
The measure of angle ABD is 20 degrees and this can be determined by using the properties of the angle bisector.
Given :
ABC = 40 and BD is the angle bisector of angle ABC.
The following steps can be used in order to determine the angle ABD:
Step 1 - According to the given data, BD is the angle bisector of angle ABC.
Step 2 - An angle bisector bisects the angle into two equal parts.
Step 3 - So, the measure of angle ABD is calculated as:
So, the measure of angle ABD is 20 degrees.
What is 2m to the 4th power times 5m to the second power
Answer:
hope this helps if this is what you meant
10m6
Step-by-step explanation:
=2*m4*5*m2
=10*m6
=10m6
How do you solve this −6x−16<2x
Answer:
x >-2
Step-by-step explanation:
subtract 2x from both sides
-6x - 16 - 2x < 0
subtract 2x from 6x
-8x - 16 < 0
add 16 to both sides
-8x < 16
divide by -8
x> -2
Help me with my problem please I NEED HELP!!!!!!!
The second
The correct answer is N ∈ line MN
The third
The correct answer is P ∉ line MN
The fourth
The correct answer is B ∉ line MN
How to interpret the symbolsThe symbols are interpreted as follows
∈ is interpreted as "is a member of"∉ is interpreted as "is not a member of"Given data
line MN
How to describe the location with respect to line MNThe first
It is already given that is M ∈ line MN
point M can be located in line MN
The second
The correct answer is N ∈ line MN
point N can be located in line MN
The third
The correct answer is P ∉ line MN
point P cannot be located in line MN it is off the line
The fourth
The correct answer is B ∉ line MN
point B cannot be located in line MN it is off the line
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What is the x value of the solution to the system shown?
2y = 2x + 12
2-y=4
Answer:
[tex]x = -8[/tex]
Step-by-step explanation:
[tex]\begin{cases}2y = 2x + 12\\2-y = 4\end{cases}[/tex]
It would be easier to start with the second equation.
[tex]2 - y = 4 \text{ // Add y and subtract 4}\\\to 2 - y - 4 = 4 - y - 4\\\to -2 = y[/tex]
From here, we can substitute [tex]y = -2[/tex] into the first equation, to solve for [tex]x[/tex].
[tex]2(-2) = 2x + 12\\\to -4 = 2x + 12 \text{ // Subtract 12 on both sides}\\\to -4 - 12 = 2x + 12 - 12\\\to -16 = 2x \text{ // Divide by 2}\\\to -\frac{16}2 = \frac{2x}2\\\to -8 = x[/tex]
17. Callie's cat lost 41/2 pounds before having
surgery. Two weeks after having surgery, her
cat gained 2 7/8 pounds. What was the total
change in weight of Callie's cat?
The total change in the weight of Callie's cat will be - 1 5/8 pounds.
Callie's cat lost weight = 4 1/2 pounds
Lost = 9 / 2 pounds
Cat gained the weight = 2 7/8 pounds
Gained = 23 / 8 pounds
Net change = - 9 / 2 pounds + 23 / 8 pounds
= - 36 / 8 pounds + 23 / 8 pounds
= - 13 / 8 pounds
= - 1 5/8 pounds
She lost the net weight of 1 5/8 pounds.
Therefore, the total change in the weight of Callie's cat will be - 1 5/8 pounds.
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P = IV
●
Here is what you know about the baseball field parking lot situation.
There are 9 lamp posts connected to this circuit.
Each lamp post has a 400 watt lamp installed.
The circuit is 120-volt and 20-amp.
Here is what you don't know, but can figure out:
How many watts does 9
lampposts require?
How many lamposts could this
circuit handle? HELP
Answer:
1M
Step-by-step explanation:
HOPE ITS HELP!! PLEASE STAY ALIVE!! :D
19 1/5 - 11 1/11?????????
let's firstly convert the mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{19\frac{1}{5}}\implies \cfrac{19\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{96}{5}} ~\hfill \stackrel{mixed}{11\frac{1}{11}}\implies \cfrac{11\cdot 11+1}{11}\implies \stackrel{improper}{\cfrac{122}{11}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{96}{5}~~ - ~~\cfrac{122}{11}\implies \stackrel{\textit{using the LCD of 55}}{\cfrac{(11)96~~ - ~~(5)122}{55}}\implies \cfrac{1056~~ - ~~610}{55} \\\\\\ \cfrac{446}{55}\implies {\LARGE \begin{array}{llll} 8\frac{6}{55} \end{array}}[/tex]
The equation shown has a missing value. Answer parts a through c.
In linear equation, the missing value is a 16.
According to the statement
We have to find that the value of the linear equation.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
It is given that:
The equation shown includes a missing value.
-2(2x - ?) + 1 = 17 - 4x
Applying the distributive property:
-4x + ? + 1 = 17 - 4x
? + 1 = 17
There aren't any values that the equation has only 1 solution or unique solutions.
For no solution the missing value are often anything except 16
? + 1 = 17
? = 17 - 1
? = 16
Thus, there aren't any values that the equation has just one solution for no solution the missing value are often anything except 16.
So,In linear equation, the missing value is a 16.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
The equation shown has a missing value. -2(2x-?)+1=17-4x. For what missing value(s), if any, does the equation have exactly one solution?For what missing value(s), if any does the equation have no solution?
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Kinsley went rock climbing at Red River Gorge. At noon, she was at an elevation of 76 feet. Then, she climbed 28 feet higher to reach the peak.
What was Kinsley's elevation at the peak?
Answer:
Step-by-step explanation:
28 + 76=
104
Her elevation is 104 at the peak.
pleaseeee help
round to the nearest decimal point
Answer:
the answer is 43.1
Step-by-step explanation:
because i searched it up