The factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
Given expression:
= 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex]
divide by 18 .
= 4[tex]a^{9} b^{3}[/tex] - [tex]a^{7} b^{5}[/tex]
divide by [tex]a^{7}[/tex]
= 4[tex]a^{2}b^{3}[/tex] - [tex]b^{5}[/tex]
divide by [tex]b^{3}[/tex]
= 4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]
= 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
Therefore the factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
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Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 28.45°. What is the measure of ∠P?
28.45°
75.775°
121.55°
151.55°
Step-by-step explanation:
the sum of all angles in a triangle is ALWAYS 180°.
and by using the word "congruent" : for angles that only means they are equally large.
we know the third angle.
so,
180 = P + Q + R = 2×P + 28.45
(because P = Q)
2×P = 151.55
P = Q = 151.55 / 2 = 75.775°
Need help
The equation of the line L1 is y = 3x - 2
The equation of the line L2 is 3y - 9x + 5 = 0
Show that these two lines are parallel
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 24 grams. The jeweler made a total of 16 bracelets and necklaces using 258 grams of gold. Determine the number of bracelets made and the number of necklaces made.
Answer:
Bracelets: 7 Necklaces: 9
Step-by-step explanation:
b+n=16
6n+24n=258
b=-n+16
6(-n+16)+24n=258
-6n+96+24n=258
18n=162
n=9
6n+24(9)=258
6n+216=258
6n=42
n=7
B stands for bracelets
N stands for necklaces
what is the unit rate for $44 in 4 days
Answer:11
Step-by-step explanation: 44 divided into 4 is 11.
Answer:
The answer would be 11
Step-by-step explanation:
Because, 44 divided by 4 = 11
write another subtraction problem involving two negatie number that has a positive difference. then write another subtraction problem involving two negative numbers that has a negative difference.
Answer:
Two negatives, positive answer:
-3 - (-4) = 1
Two negatives, negative answer:
-45 - (-1) = -44
0.25 in standard form
Answer:
2.5 × 10^-1
step-by-step explanation:
To get to standard form, you must move the decimal to the right one place so the number before it is not a 0. Because you move the decimal, you must add the second part of the equation so that the value does not change.
Answer:
02.5 but the 0 at the beginning isn't significant so 2.5
Step-by-step explanation:
because to find the standard form you move the decimal point so that there is only one non-zero digit in front of the decimal point.
Three friends go grocery shopping together and buy apples. Logan buys 4
pays $7.00. Lin buys 6 lb and pays $10.50. Chita buys 2 lb
pounds (lb) and
and pays
$3.50.
Identify the graph and unit price that represent the cost of the apples.
The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.
What is the slope of a line?
The slope of a line is the tangent of the angle that the line makes with the positive direction of the x-axis. It signifies the rise in the y-variable for a unit change in the x-variable.
If the line passes through the points (x, y) and (x, y), then the slope of the line, m = (y - y)/(x - x).
(2, 3) representing the purchase by Logan,
(5, 7.5) representing the purchase by Lin,
(3, 4.5) representing the purchase by Chita.
The unit price can be calculated by the slope of the line;
m = (7.5 - 4.5)/(5 - 3) = 3/2 = 1.5.
Hence, The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.
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Find the measures of each numbered angle:
∠A=5x−12 ∘ start color #11accd, angle, A, equals, 5, x, minus, 12, degrees, end color #11accd \qquad \green{\angle B=2x + 24^\circ}∠B=2x+24 ∘
The solution to the variable x is 12 and the measure of ∠B is 48°.
How to solve congruent angles?∠A = 5x−12°
∠B = 2x+24°
Angle A and Angle B are congruent angles.
Congruent angles are angles with the same or equal measures.
So,
∠A = ∠B
5x - 12 = 2x + 24
collect like terms5x - 2x = 24 + 12
3x = 36
divide both sides by 3
x = 36/3
x = 12
So therefore,
∠A = 5x−12°
= 5(12) - 12
= 60 - 12
= 48°
∠B = 2x+24°
= 2(12) + 24
= 24 + 24
= 48°
Therefore, since ∠A and ∠B are congruent, the measure of ∠A and ∠B is 48° respectively.
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degree and real roots of (x-3)(x+1)(x-1)=0
Step-by-step explanation:
at first multiply the factors
[tex] ({x}^{2 } + x \: - 3x \: - 3)(x - 1) = 0[/tex]
[tex] {x}^{3} - {x}^{2} - 3 {x}^{2} - \: 3x - {x}^{2} - x \: + 3x + 3 = 0[/tex]
[tex] {x}^{3} - 5 {x}^{2} - x + 3 = 0[/tex]
Here we see the highest power is 3 so the degree of the equation is 3
As for the real roots, the factors each as in (x-1), (x-3) & (x+1) can be considered zero each to find the real roots because for the value of x to be zero any of the multiplied factors must be zero.
either, x-1=0
=> x = 1
or, x+1=0
=> x = -1
or, x-3=0
=> x = 3
real roots of x are: 1, -1 and 3
Which relation is a function?
The relation that is a function in the option is graph C.
What is a function?A function relates an input to an output.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
In a simpler term, a function relates each element of a set with exactly one element of another set (possibly the same set).
In a function, the x value is exactly related to a single y value, exactly, means that a function is single valued. It will not give back 2 or more results for the same input.
Therefore, the only graph that follows the rule of a function is graph C.
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The ratio 20mins to 1 hour can be written in the form 1:n find the value of n.
Answer:
1:3
n=3
Step-by-step explanation:
1 hour = 60 minutes
20:60
20÷20=1
60÷20=3
1:3
clint's cowboy shop buys horse feed for $\$10$ per cubic meter ($\text{m}^3$). clint's customers don't like the metric system, so they'll only buy horse feed by the cubic foot. how many cents should clint charge for a cubic foot ($\text{ft}^3$), if he wants to sell the horse feed for twice the price he bought it at?
In linear equation, 57 cents per cubic foot should clint charge for a cubic foot .
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18.cubic meter = [3.28 ft ]^3 ≈ 35.29 cubic feet
So,
price [ in cents] / 35.29 cubic feet = 2000 / 35.29 ≈ 57 cents per cubic foot
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write a function that will standardize a multivariate normal sample for arbitrary n and d. that is, transform the sample so that the sample mean vector is zero and sample covariance is the identity matrix. to check your results, generate multivariate normal samples and print the sample mean vector and covariance matrix before and after standardization.
The function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
According to a multivariate normal distribution with mean vector m and variance-covariance matrix M, then this random vector, X , will have the joint density function as shown:
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
where, |M| denotes the determinant of the variance-covariance matrix M and M^(-1) is just the inverse of the variance-covariance matrix M.
Hence, the function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
The equation of the parabola
f(x) = [tex]7x^2[/tex]
The standard vertex form of a parabola is
y = [tex]a(x-h)^2[/tex] + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) = [tex]7x^2[/tex]
The value of a = 7
Substitute the values in the vertex form of a parabola
y = [tex]7(x-3)^2[/tex] + 5
Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
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Omar is hiring a painting company to paint the interior of his house. The table represents prices the painting company quoted Omar.
Write a two-variable linear equation to represent the total cost, c, given the square feet, s, of the house.
A: c=2.25s+1347.85
B: c=2.25s+2847.85
C: c=2.25s+4047.85
D: c=2.25s+7654.60
The linear equation to represent the total cost c = 2.25s + 1,347.85.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
Using slope
slope= ( 5847. 75 - 4074 . 85)/( 2000- 1200)
slope= 1800 - 800
slope= 2.25
and, slope- intercept form
c - 4047.85 = 2.25 ( s- 1200)
c - 4047.85 = 2.25s - 2700
c = 2.25s - 2700 + 4047.85
c = 2.25s + 1,347.85
Hence, linear equation to represent the total cost c = 2.25s + 1,347.85.
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Caleb solved this equation and recorded his work.
7.4x + 4.1(2x − 4) = −2.3(x − 6) − 21.6
1. 7.4x + 8.2x − 16.4 = −2.3x + 13.8 − 21.6
2. 15.6x − 16.4 = −2.3x + 35.4
3. 17.9x − 16.4 = 35.4
4. 17.9x = 51.8
5. x ≈ 2.89
When Caleb verified his solution, it didn’t work. What mistake did he make?
In step 1, the distributive property was not used properly on the right side of the equation.
In step 2, the like terms were not combined properly on the right side of the equation.
In step 3, the addition property of equality was not used properly to isolate the variable term.
In step 5, the division property of equality was not used properly to solve for x.
hurry pls :,)
Answer:
the mistake was in subtracting 21.6 from 13.8
Step-by-step explanation:
the answer was suppose to be -7.8 and not 35.4
Answer:
the mistake was in subtracting 21.6 from 13.8
Step-by-step explanation
the answer was suppose to be -7.8 and not 35.4
Which pairs of triangles are similar? check all that apply. â–³abc ~ â–³def â–³def ~ â–³ghi â–³ghi ~ â–³abc â–³ghi ~ â–³jkl â–³jkl ~ â–³abc
The similar pairs of triangles are given as follows:
DEF and HGI.JKL and ABC:What are similar triangles?Similar triangles are two triangles that have the same angle measures.
For these triangles, considering the relations between angles such as sine/cosine/tangent, or the law of sines, the side lengths have to be proportional.
Considering the need for proportional side lengths, the similar triangles in this problem are given as follows:
DEG and HGI: as the proportion between the side lengths of each triangle is of 1.5.JKL and ABC: as the proportion between the side lengths of each triangle is of 0.5.The other triangles are not similar as there are no proportional relationships that can be established from the side lengths of these triangles.
Missing InformationThe problem is given by the image at the end of the answer.
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Complete the equation so that it has no solution.
-15x + 4x + 2-x=__x+3
Equation -15x + 4x + 2-x= -12x+3 has no solution.
Define equation.A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities. The x + 4 = 12 equation states that the left and right sides of the equation are equal. A assertion that "this equals that" is what constitutes an equation.
Given,
Equation:
-15x + 4x + 2 - x = _x +3
For no solution, value of x on both sides should be equal,
So,
-15x + 4x - x
-12x
Value of x will be -12.
Equation -15x + 4x + 2-x= -12x+3 has no solution.
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(b) Expand and simplify.
(2x - 5) (x - 3)
help me pls
[tex] = 2x(x - 3) - 5(x - 3) \\ = 2 {x}^{2} - 6x - 5x + 15 \\ = 2 {x}^{2} - 11x + 15 [/tex]
ATTACHED IS THE SOLUTION
i count in equal steps my first number is -2 my fifth number is 26 whats my third number
The required third number will be 12 when numbers are in the A.P.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The given data as
first number = - 2
fifth number = 26
Assume that the given numbers are in the A.P.
The formula to find the general term of an arithmetic sequence is,
Tₙ = a₁ + (n-1)d ...(i)
Substitute the value of n = 5 and a₁ = -2 in the above formula
T₅ = a₁ + (5-1)d
26 = -2 + 4d
4d = 28
d = 7
For finding the third term (number):
T₃ = -2 + (3-1)7
T₃ = -2 + (2)7
T₃ = -2 + 14
T₃ = 12
Therefore, the required third number will be 12 when numbers are in the A.P.
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Write 22 as a percentage of 58
Give your answer correct to the nearest whole number.
Answer:
38%
Step-by-step explanation:
22 ÷ 58 = 0.3793...
Ans × 100 = 37.93%
As a whole number = 38%
Explain c-a, when c = 7 and a=6
Answer:
1
Step-by-step explanation:
7-6=1
Answer:
c-a
replace x with 7 and a with 6
rewrite: 7-6
7-6 = 1
Answer: 1
A train leaves a station heading east. after traveling east for 33 miles, the train leaves 56 miles south. How far is the train from the station?
Answer
23
45
65
89
If a train leaves a station heading east. after traveling east for 33 miles, the train leaves 56 miles south. The distance of the train from the station is C. 65.
How to find the distance?Using Pythagoreans theorem formula to find the distance
d² = a² + b²
Where:
d = distance =?
a= east for 33 miles
b = 56 miles south
Let plug in the formula
d = √33² + 56²
d = √ 1089 + 3136
d = √4225
d = 65 miles
Therefore the correct option is C.
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She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 41 seconds at a speed of 4.9 feet per second.
She then ascends for 49 seconds at a speed of 3.2 feet per second.
After this 90-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at 3.6 feet per second?
The scientist will take 23 seconds to get back to the sea level.
Let us calculate the distance covered by the scientist at the given speeds and at the specified times.
She travels down for 41 seconds at speed of 4.9 feet per second.
Distance travelled = 41 × 4.9 = 200.9 feet
Elevation = -200.9 feet
She then goes up for 49 seconds at speed of 3.2 feet per second.
Distance travelled = 49 × 3.2 = 156.8 feet
Elevation = -222.9 + 156.8 = -44.1
So she is at a depth of 44.1 feet below the sea level.
Time taken = 44.1 / 3.6 = 12.25 seconds
Therefore it will take her about 12.25 seconds to go back to the sea level.
The average surface level of one or more of the Earth's coastal bodies of water is known as mean sea level (MSL), which can be used to calculate heights like elevation.
There are several terminologies that describe the ebb and flow of the relationship between sea level and dry land.
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As the diameter (d) of a circle increases in size, the circumference (C)
increases Likewise, as the diameter decreases in size, so does the circumference,
The constant of variation between Cand dist. Describe the kind of variation
between eireumference and diameter Write the equation.
PLEASE HELP!
629 students at a school each pay £6 to go on a school trip. How much money do they pay in total?
Show all your working.
Answer:
£3,774
Step-by-step explanation:
629 students at a school each pay £6 to go on a school trip. How much money do they pay in total?
629 * £6 = £3,774
Answer:
no of students= 629
amount paid each =£6
amount paid by all the students =no of students × amount paid each
:: 629
× 6
£3774
76.43 divide 3.4
Please Answer
Answer:
22.479411764705882352941176470588
Step-by-step explanation:
76.43/3.4
=22.479411764705882352941176470588
a javalina rancher wants to enclose a rectangular area and then divide it into 5 pens with fencing parallel to one side of the rectangle. there are 580 feet of fencing available to complete the job. what is the largest possible total area of the 5 pens?
When there is 580 feet of fencing available to complete the job, the largest possible total area of the 5 pens is 7008.33 feet.
What is an area?The quantity area expresses the extent of a region on a plane or curved surface.
STEP 1: We know that,
A=x y
The perimeter equals 580feet.
The equation is,
580=6x+2y
Step 2: Solving y terns with x,
y=-3x+290
This information will assist us in obtaining our Area equation in terms of a single variable (just in terms of x).
Step 3: Using the x-y relationship discovered in Step 2, write your Area equation in terms of x only. You should obtain
A=x y
A=x(-3x+290)
A=-3x²+290x
Step 4: Derive the area equation, A' = -6x+290
Step 5: Set A' = 0
-6x+290=0
x=290/6
x=48.33
Step 6: Find y by substituting 48.33 in x in the perimeter equation then,
y=-3(48.33)+290
y=145.01
Step 7: A=x y
A=(48.33)(145.01)
A=7008.33 feet
The largest possible total area of the 5 pens is 7008.33 feet
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Write an absolute value equation representing all numbers x whose distance from 5 is 5 units
The absolute value equation representing all numbers x whose distance from 5 is equal to 5 units is written as:
|x - 5| = 5
How to write the absolute value equation?An absolute value equation where the variable is x can be written as:
|x - a| = b
This means that the distance between x and a is equal to b.
So if we want to write an equation where the distance between x and 5 is equal to 5, then we can replace:
a = 5
b = 5
And the absolute value equation will be:
|x - 5| = 5
This is what we wanted to get.
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