The correct factorization are as follows:
(a) x² + x = x(x + 1)
(b) 3x-9x² = 3x(1 - 3x)
(c) 7x³ - 35x = 7x(x^2 - 5)
(d) 4x³ + 24x² = 4x^2(x + 6)
What do you mean by "factorization"?
The most crucial step in factorization is to identify the terms points of commonality. Divide each term by the common factor between them, then multiply the result by the entire expression to maintain the value.
One of the key techniques for reducing an algebraic or quadratic equation to a simple form is factorization. Thus, one should be familiar with factorisation formulas in order to simplify the complex problem.
Additionally, you can always multiply your response to see if you end up with the same result as your starting point.
Step by step solution:
(a): x² + x, [Here both terms have 'x' in common]
=x( (x²/x) + (x/x) )
= x(x+1)
(b): 3x - 9x², [Here both terms have '3x' in common]
=3x( (3x/3x) - (9x²/3x) )
= 3x(1-3x)
(c): 7x³ - 35x, [here both terms have '7x' in common]
=7x( (7x³/7x) - (35x/7x) )
= 7x(x²-5)
(d): 4x³+ 24x² [here both terms have 4x² in common]
=4x²( (4x³/4x²) + (24x²/4x²) )
= 4x²(x+6)
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8. Given DF bisects LEDF, find n and then find FG. The diagram is not drawn to scale.
2 points
Show your work to find FG
Show your work to find n
GIVING 20 POINTS!!
The measure of length of FG is 105 units.
What is bisection?
To determine the roots of a polynomial problem, utilise the bisection method. It splits and separates the interval in which the equation's root is located. The continuous functions intermediate theorem serves as the method's guiding premise.
From the given diagram, since Line DF bisects angle EDG, then -
EF = FG
Given the following parameters -
EF = 9n - 3
FG = 8n + 9
Equating both expressions -
9n - 3 = 8n + 9
9n - 8n = 9 + 3
n = 12
Get the measure of FG -
FG = 8n + 9
FG = 8(12) + 9
FG = 96 + 9
FG = 105
Hence, the line FG measures as 105 units.
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Benji's flight from Chicago to San Jose took 0.5 hour longer than his return flight from San Jose
to Chicago. If Benji's flight from Chicago to San Jose was 4.5 hours long, how long was his return
flight, in hours?
Choose 1 answer:
A
3.5
B 4
C 4.5
D
assroom
5
The time taken for his return flight, in hours could be 4 hours.
What is time ?
Time is defined as the sequence of events that occurs which can be from past through present or to future.
Given,
Benji's flight from Chicago to San Jose took 0.5 hour longer than his return flight from San Jose to Chicago.
If Benji's flight from Chicago to San Jose was 4.5 hours long
let,
chicago to san jose = san jose to chicago+0.5
4.5 - 0.5 = san jose to chicago
san jose to chicago = 4 hours
Hence, How long was his return flight, in hours is 4 hours.
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How do you represent a number line on a class 7?
Draw a line and locate the origin '0', mark the positive numbers on the right and the negative number on the left of '0' at an equal distance.
A number line is a horizontal straight line in which the integers are placed in equal intervals. All the numbers can be represented in a number line. This line can be extended indefinitely at both ends.
A number line is a graphical representation of numbers on a straight line. It is used for comparing and ordering numbers. It can be used for representing any real number that includes every whole number and natural number.
Draw a line and locate the point ‘0’. This point is known as the origin. If the given number is positive, draw it on the right side of the origin. If it is a negative number, draw it on the left side of zero. Divide each unit into the values equal to the denominator of the given fraction.
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50 points + brainliest PLS HELP ME ASAP. All I need is a right answer and a clear solution. Ty in advance! :)
(anyone who gives absurd answers will be reported right away)
Dimensions of the parallelogram are:
Base is b = 2 ft, Side is a = 5 ft, Height is h = 4 ft.Its perimeter is:
P = 2(2 + 5) = 2(7) = 14 ftIts area is:
A = bh = 2*4 = 8 ft²When the scale factor is 2Perimeter is 2 times greater:
P = 2*14 = 28 ftArea is 2*2 = 4 times greater:
A = 4*8 = 32 ft²When the scale factor is 3Perimeter is 3 times greater:
P = 3*14 = 42 ftArea is 3*3 = 9 times greater:
A = 9*8 = 72 ft²When the scale factor is 1/2Perimeter is 2 times smaller:
P = 14/2 = 7 ftArea is 2*2 = 4 times smaller:
A = 8/4 = 2 ft²Which expression can be used to represent the
volume of this prism?
6 × 11 units³
78°F
Sunny
O 48 x 3 units³
O 14 x 3 units³
O 8x9 units³
H
а
1
i
8 units
1
1
2
3
3 units
6 units
4
5
Volume of prism is given by V= base area × height cubic unit. The expression 48 × 3 unit³ can be used to represent the volume of the prism.
What is prism?Prism is a three-dimensional geometrical figure having identical two ends. A prism has flat faces, similar bases and equal cross sections. A prism is normally bounded by plane faces.
What is volume of prism?
Volume of prism is calculated by the product of base area and height of the prism. At first, we need to calculate the base area and then height is multiplied with it.
Prisms are different types such as triangular prism, rectangular prism, pentagonal prism and hexagonal prism so depending on the figure area for the base is different. As a result, different shaped prism has different formula for volume calculation.
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Why is the sine of an acute angle less than one?
The sine of an acute angle is less than one because it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio is always less than one.
To what does sin equate?
In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.
It's also the same reason why the cosine of an acute angle is always less than one because it is the ratio of the adjacent side of the angle to the hypotenuse.
It's important to note that this is only true for acute angles, angles smaller than 90 degrees.
For obtuse angles, greater than 90 degrees, the sine and cosine values are greater than one.
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A solid right prism $ABCDEF$ has a height of $16,$ as shown. Also, its bases are equilateral triangles with side length $12.$ Points $X,$ $Y,$ and $Z$ are the midpoints of edges $AC,$ $BC,$ and $DC,$ respectively. A part of the prism above is sliced off with a straight cut through points $X,$ $Y,$ and $Z.$ Determine the surface area of solid $CXYZ,$ the part that was sliced off.
A solid right prism ABCDEF has a height of 16. A part of the prism is sliced off with a straight cut through points X, Y, and Z. CXYZ is a triangular pyramid and its surface area is 48 + 9√3 + 3√91 or 92.2
The situation can be depicted in the attached picture. CXYZ is a triangular pyramid.
The surface area of CXYZ is equal to:
area CXYZ = area ΔCXY + area ΔCYZ + area ΔCXZ + area ΔXYZ
ΔABC and ΔCXY are congruent, hence ΔCXY is a equilateral triangles with its sides are 1/2 those of ΔABC.
CX = CY = XY = 1/2 x 12 = 6
To find the area of ΔCXY, find its height first.
√3/2 = h/6
h = 3√3
Area ΔCXY = 1/2 x 3√3 x 6 = 9√3
ΔCXZ is a right triangle at C. Hence,
Area ΔCXZ = 1/2 x CX x CZ
= 1/2 x 6 x 8 = 24
ΔCYZ = ΔCXZ
Hence,
Area ΔCYZ = 24
To find the area of ΔXYZ, find XZ first using the Pythagorean Theorem.
XZ² = CX² + XZ² (XZ = 8, since Z is midpoint of CD)
XZ² = 6² + 8²
XZ² = 10²
XZ = 10
Find the height of ΔXYZ
h = √(10² - 3² )
h = √91
Therefore,
Area ΔXYZ = 1/2 x XY x h
= 1/2 x 6 x √91 =3√91
Finally,
area CXYZ = area ΔCXY + area ΔCYZ + area ΔCXZ + area ΔXYZ
= 9√3 + 24 + 24 + 3√91
= 48 + 9√3 + 3√91
= 92.2
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sutton is listing the prime factorazation for 220 what is the last factor she needs 2 square root of 5
Answer:
4.472135955
Step-by-step explanation:
a circular fish pond has a diameter of 14 m the pond is surrrounding by a concrete path 1.75 meters wide. Find the ponds area. take pi as 22/7
Area of the pond is 86.625 m²
What is the area formula to a circle?The following formulae can be used to determine a circle's area: Area is equal to r2, where r stands for radius. Area is equal to (/4) d2, where d stands for diameter.The region encircled by a circle of radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.Pi () is a unique mathematical constant that expresses the relationship between a circle's circumference and diameter.Given data :
Diameter of the pond = 14m
Radius of the inner circle (pond), r = 7 m
Width of the concrete path = 1.75m
Radius of outer circle (Including pond + Path), R = 7 + 1.75 = 8.75 m
Area of the path = Area of the outer circle − Area of the inner circle.
= πR² - πr²
= 22 / 7 x ( 8.75 + 7) ( 8.75 − 7 )
= 86.625 m²
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Question 3 of 10
If f(x) = 7x-6, which of the following is the inverse of f(x)?
O A. f-1(x) = x76
f−¹(x) = x=7
X-7
6
B.
O C. f-1(x) = x+7
D. f¹(x) = x+6
7
SUBMIT
Therefore, the solution of the given problem of function comes out to be [tex]f^{-1}[/tex] = x+ 6 /7.
Describe function.Mathematics includes the study of numbers, equations and associated structures, forms and the environments in which they occur, quantities and their changes, and spatial relationships. A function is an association between such a set of inputs, each of which has an output. Simply described, a function is an association between the inputs and outputs in which each input results in a single, distinct result. Each operation has a domain and a scope, which are also referred to as codomains.
Here ,
In our case, f(x) = y = 7x-6.
The following procedures must be taken in order to determine the inverse function of the given function:
First, x and y must be switched, thus
x= 7y-6
We must add 6 to both sides in order to solve for y in the following step.
x+6=7y
7 divided by both sides, that is
y = x+ 6 /7
Therefore, the solution of the given problem of function comes out to be
[tex]f^{-1}[/tex] = x+ 6 /7.
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A distribution of exam scores has mean 60 and standard deviation 18. If each score is doubled, and then 5 is subtracted from that result, what will be the mean and standard deviation, respectively, of the new scores
If each score is doubled, and then 5 is subtracted from that result, then the mean and standard deviation will be 115 and 36 respectively.
What will be the mean and standard deviation?A huge group of test results has a mean of 60 and a standard deviation of 18. If each score is doubled and then 5 is deducted from the result, the mean and standard deviation are “ mean = 115; standard deviation = 36”. Mean = 2 x 60 -5 = 120 -5 = 115
2 x 18 = 36 standard deviation
The mean is the average and is calculated as the sum of all the results from the example divided by the total number of events.
The standard deviation (SD) is a statistic used to assess the degree of variation or dispersion in a set of data values.
A low standard deviation indicates that the information points slant toward being near the mean of the set, whereas an exclusive expectation deviation or a high standard deviation indicates that the information points tilt toward being near the mean of the set.
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plane flew from Red Deer to Winnipeg, a flying distance of 1260 km. On the return journey, due to a strong head wind, the plane travelled 1200 km in the same time it took to complete the outward journey. On the outward journey, the plane was able to maintain an average speed 20 km/hr greater than on the return journey. Calculate the average speed of the plane from Winnipeg to Red Deer.
The average speed of the plane from Winnipeg to Red Deer is 400 km/h
What is average speed?Average speed is total distance travelled over total time taken.
What is the average speed of the plane from Winnipeg to Red Deer?Since a plane flew from Red Deer to Winnipeg, a flying distance of 1260 km. On the return journey, due to a strong head wind, the plane travelled 1200 km in the same time it took to complete the outward journey. On the outward journey, the plane was able to maintain an average speed 20 km/hr greater than on the return journey.
Let
v = speed of plane on outward journey , v' = speed of plane return journey and t = time of travelSince the plane travels 1260 km on the outward journey, we have that
1260 = vt (1)
Also, the plane travels 1200 km on the inward journey, we have that
1200 = v't (2)
Since the plane was able to maintain an average speed 20 km/hr greater than on the return journey, we have that
v = v' + 20 (3)
Substituting equation (3) into (1), we have that
1260 = (v' + 20)t (4)
The required equations are
1260 = v't + 20t (4)
1200 = v't (2)
Subtracting equations, (2) from (4), we have that
1260 = v't + 20t (4)
-
1200 = v't (2)
60 = 20t
t = 60/20
t = 3 h
From equation (2), we have that the average speed
v' = 1200/t
Substituting t = 3 into the equation, we have that
v' = 1200/3
v' = 400 km/h
So, the average speed is 400 km/h
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Help me solve this please
Answer:
Step-by-step explanation:
The four options just swap the order, and you should choose them all
What is the solution to the equation 9(x + 2) = 27?
A. x = 2.5
B. x = 0.5
C. x = −0.5
D. x = −3.5
find the real solutions to the equation 3,888=3h^4
Answer:
[tex]h=\pm6[/tex]
Step-by-step explanation:
[tex]3h^4=3888\\h^4=1296\\h=\pm6[/tex]
Jill had -$100 in her bank account in March. Jill then added $75 to her account in April.
What was the change in Jill's bank account for March and April combined?
How much did she have in her account at the end of April?
please help me !!
literally struggling right now !!
•35 POINTS• (it’s not SAS)
1.SSS
2.ASA
3.SAA
Answer:
SAA
Step-by-step explanation:
SU is a midsegment of QRT
If QR=-5v+96 and SU = 19v-38 than what is the value of X
Answer:
v = 4
Step-by-step explanation:
⭐What is the midsegment of a triangle?
a segment that runs from the midpoints of two opposite sides⭐What are some properties of the midsegment?
the midsegment is 1/2 of the length of the baseThus, we have to make an equation using the properties of the midsegment to solve for v.
Working:
[tex]SU = \frac{1}{2}(QR)[/tex]
[tex]19v - 38 = \frac{1}{2}(-5v + 96)[/tex]
[tex]38v - 76 = -5v + 96[/tex] . . . . . multiply both sides by 2 to get rid of the fraction
[tex]43v = 172[/tex] . . . . . add 5v and 76 to both sides
∴ [tex]v = 4[/tex] . . . . . . . . . divide both sides by 43 to isolate v
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A local boys club sold 196 bags of mulch and made a total of $357. It sold two types of mulch: hardwood for $2.00 a bag and pine bark for $1.75 a bag. How many bags of each kind of mulch did it sell?
Total 56 bags of hardwood and 140 bags of pine bark bags are sold.
In the given question, a local boys club sold 196 bags of mulch and made a total of $357.
It sold two types of mulch: hardwood for $2.00 a bag and pine bark for $1.75 a bag.
We have to find how many bags of each kind of mulch did it sell.
Let total number of x bags of hardwood sell.
Let total number of y bags of pine bark sell.
Now the equation should be
2x + 1.75y = 357............................(1)
Total number of bags sold 196.
So x + y = 196............................(2)
From the equation 2 the value of x = 196-y. Now putting the value of x in equation 1.
2(196 - y) + 1.75y = 357
392 - 2y + 1.75y = 357
392 - 0.25y = 357
Subtract 392 on both side, we get
-0.25y = -35
Divide by -0.25 on both side, we get
y = 140
Now putting the value of y in x = 196-y
x = 196 - 140
x = 56
Hence, 56 bags of hardwood and 140 bags of pine bark bags are sold.
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-97.54 es racional o irracional
Respuesta: Racional
Explicación:
El número es racional ya que podemos representarlo como una fracción de enteros.
Más específicamente, -97.54 = -9754/100
-----------------------------------------------------------------------------
Translation to English:
Answer: Rational
Explanation:
The number is rational since we can represent it as a fraction of integers.
More specifically, -97.54 = -9754/100
asmine is filling a small fish tank with water. The fish tank is in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in. What is the volume of this fish tank
The volume of the fish tank in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in is 90π cubic inches.
Therefore the answer is 90π in³.
Recognize that the fish tank is in the shape of a right circular cylinder.
Remember that the formula for the volume of a cylinder is
V = πr^2h
where r is the radius and h is the height.
Plug in the given values for the radius (r = 3 inches) and the height (h = 10 inches) into the formula.
Perform the calculation:
πr^2h
= π(3^2)(10)
= π×9×10
= 90π cubic inches
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It costs $0. 50 per square yard to waterproof canvas. What will it cost to waterproof a canvas truck cover that is 15' x 24'
It will cost $10.00 to waterproof a canvas truck cover that is 15' x 24'.
To find this, we need to first convert the dimensions of the canvas truck cover from feet to yards, since the cost is given per square yard. 15' x 24' = 180 sq ft. 1 sq yard is equal to 9 sq ft, so 180 sq ft/9 sq ft/yard = 20 sq yard. Then we multiply the square yards by the cost per square yard to find the total cost:
20 sq yard x $0.50/sq yard = $10.00.It's important to note that the measurements of the canvas truck cover are given in feet and the cost is given per square yard. It's important to convert it to square yards to match the unit of measurement and calculate the cost.
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What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?
The equation of a parabola that intersects the x-axis at points (-1, 0) and
(3, 0) is y = x² - 2x - 3.
What is a parabola?
An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola.
Since the parabola intersects x-axis at points (-1,0) and (3,0), the parabola has its axis parallel to y-axis.
The general equation for such parabola is,
y = ax² + bx + c
The roots of the quadratic equation is found when y = 0
We know that when y = 0, x = -1 , 3
So (x+1) (x - 3) = 0
Solving the above equation we can find the equation of parabola
x² - 3x + x -3 = y
Therefore y = x² - 2x- 3 is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0).
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Brian buys bananas from the grocery store each week. Last week he bought 5 pounds of bananas and paid $2.95. If he buys 8 pounds of bananas this week, how much will he pay?
help me i been stuck for like a good 20 min
[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]
notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.
Similar Figures / Proportion (Level 1)
Triangle OPQ is similar to triangle RST. Find the measure of side ST. Round your
answer to the nearest tenth.
Rounded to the nearest tenth, the measure of side ST is 8.0.
How to find measure of sides?In order to find the measure of side ST, you will need to use the concept of similarity. If two triangles are similar, then their corresponding sides are in proportion. If we let x be the measure of side ST, then we can set up a proportion using the given information:
[tex]OP/PQ = ST/RQ[/tex]
We also know that
[tex]OP/PQ = 2/3[/tex]
and
[tex]RQ = 12[/tex]
So we can substitute these values into the proportion and solve for x:
[tex](2/3) = ST/12[/tex]
[tex]ST = (2/3) * 12[/tex]
[tex]ST = 8[/tex]
Rounded to the nearest tenth, the measure of side ST is 8.0.
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What is a 3 variable equation called?
Equations with three variables that are linear. Ax + by + cz = r is referred to as a linear equation in three variables.
what is linear equation ?A linear equation is one that has the form y=mx+b in algebra. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
equations with three variables that are linear. Ax + by + cz = r is referred to as a linear equation in three variables if all four variables—a, b, c, and r—are real values and not equal to 0.
(The x, y, and z are the "three variables"). The coefficients of the equation are designated by the numerals a, b, and c.
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Question content area top
Part 1
A computer store buys a computer system at a cost of $. The selling price was first at , but then the store advertised a markdown on the system. Answer parts a and b.
Question content area bottom
Part 1
a. Find the current sale price.
The sale price is $
enter your response here.
(Round to the nearest cent as needed.)
Part 2
b. Members of the store's loyalty club get an additional % off their computer purchases. How much do club members pay for the computer with their discount?
The price for club members is $
enter your response here.
(Round to the nearest cent as needed.)
a. The current sale price for the computer system is given as follows: $618.4.
b. The amount paid by the club members, with the discount, is given as follows: $587.48.
How to obtain the prices?The prices are found applying the proportions, which are the decimal equivalent of the percentages relative to each discount.
The selling price is of:
$773.
The markdown is of 20%, hence the current sale price is 100 - 20 = 80% of the selling price, hence:
0.8 x 773 = $618.4.
Club members get an additional discount, of 5%, meaning that they pay 95% of $618.4, and the amount is obtained as follows:
0.95 x 618.4 = $587.48.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Thirty percent of the balloons used to decorate a party are red and the rest are yellow. If one-quarter of the yellow balloons have strings and there are a total of 40 balloons, how many of the yellow balloons do not have strings
62.5 of the yellow balloons lack strings. The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the probability.
What is the probability formula?The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood. The formula is: Probability of an Event P(E) = (Number of Favorable Outcomes) (Sample space).
The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood.
A sample is created in this way, and using the data collected, the calculation can be done. The formula for calculating probabilities is probability = Favorable instances / Possible cases x 100, given as a percent.
25/40 * 100 = 0.625*100 = 62.5.
62.5 of the yellow balloons lack strings.
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