(Factoring Algebraic Expressions MC) Factor −4x2 + 12x. 4x(−x + 3) −4x(x + 3) x(4x + 12) 4(−x2 + 12x)
The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.
The given algebraic expression is -4x²+12x.
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The factorization of the given polynomial is
-4x²+12x
= 4x(-x+3)
The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.
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researchers want to decrease the margin of error by adjusting the confidence level. which confidence interval will have the smallest margin of error (moe)?
One-sided confidence interval which have the smallest margin of error.
Given that;
Researchers want to decrease the margin of error by adjusting the confidence level.
You cannot be completely certain of the true value of a parameter, such as the mean, if your confidence interval is too broad. However, there are a number of methods you may do to narrow a confidence interval and improve the accuracy of your estimate. The following characteristics have an impact on the confidence interval's width.
one-sided confidence interval:
The margin of error is lower for a one-sided confidence interval than a two-sided confidence interval. A one-sided interval, however, merely shows whether a parameter is larger or less than a cut-off number. A one-sided interval does not reveal anything regarding the parameter's value when viewed from the other direction. Therefore, only use a one-sided confidence interval to boost an estimate's precision when you are concerned that it will either be higher or lower than a cut-off value, but not both.
Hence, we use one-sided confidence interval which have the smallest margin of error.
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Linda has a shelf that is 56 over 5 inches wide. How many catalogs can Linda arrange on the shelf if each catalog is 4 over 5 of an inch thick?
Answer:
Last option: 31
Step-by-step explanation:
No. of catalogs that can be arranged
= (longest side of shelf ÷ longest side of catalog) × (shortest side of shelf ÷ shortest side of catalog)
= (56 ÷ 5) × (5 ÷ 4)
= 31
A textbook store sold a combined total of 382 chemistry and biology textbooks in a week. The number of biology textbooks sold was 58
less than the number of chemistry textbooks sold. How many textbooks of each type were sold?
Number of chemistry textbooks sold:
Number of biology textbooks sold:
Answer:
chemistry books is 220 and number of biology books is 220
Step-by-step explanation:
let y be biology books
let x be the number of chemistry books
x-58=y
equation 1 ) x+y=382
sub in x-58 for y
2. x+(x-58)=382
3. 2x-58= 382
4. 2x=382-58
5. 2x = 324
6. x/2 =324/2
7. x = 162
for x=y+58
y=162
x 220
220+162=382
y+x=382
Evaluate the numerical expression.
7.5 × 6.6 ÷ 0.6 − 15.3
Responses
A 67.2
B 97.8
C −32.25
D 197.25
The required numerical expression is evaluated as 67.2. Option A is correct.
Given that,
An expression is given 7.5 × 6.6 ÷ 0.6 − 15.3, we have to evaluate the given expression.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
= 7.5 × 6.6 ÷ 0.6 − 15.3
Simplify,
= 7.5 × 11 - 15.3
= 82.2 - 15.3
= 67.2
Thus, the required numerical expression is evaluated as 67.2. Option A is correct.
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a fence 4 feet tall runs parallel to a tall building at a distance of 4 feet from the building. what is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is 11.31 feet
Let L stand for the ladder's overall length.
Right angled triangle ΔAGB contains the following:
L² = h² +(x+4)²
( Since by using Pythagorean Theorem)
Triangles AGB and CDB also have similarities.
As a result, the corresponding sides' ratio is equal.
Hence, we have:
h/4 = (x+4)/x
h = 4(x+4)/x
As a result, when we enter the value of h in equation (1), we obtain:
L² = h² +(x+4)²
L² = (4(x+4)/x)² +(x+4)²
L² = (16(x+4)²/x²)+(x+4)²
L² = (x+4)²(16/x² + 1)
We now have to reduce L.
Therefore, we employ the differentiation method.
We distinguish in relation to x as follows:
L² = (x+4)²(16/x² + 1)
2L dL/dx =2(x+4)(16/x² + 1) + (x+4)² (-32/x³)
2L dL/dx =2(x+4){ (16/x² + 1) + (x+4) (-16/x³)
2L dL/dx =2(x+4){ (16/x² + 1 -16/x²-64/x³)
2L dL/dx =2(x+4){ (1-64/x³)
when the derivative is zero we have:
2(x+4){ (1-64/x³) = 0
x= -4 and x³ = 64 and x =∛64 = 4
But x can't be negative.
Hence, we have:
x = 4
After solving equation (2) with this value of x, we get the following result:
L² = (x+4)²(16/x² + 1)
L² = 128
L = 11.313 feet
Hence,
L = 11.313 feet
which on rounding to two decimal places is: 11.31 feet
As a result, the shortest ladder's length, measured from the ground to the building's wall over the fence, is 11.31 feet.
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Please help me, I need the answer asap
Find m<2
28
62
56
142
The given equation m<2 = 28⁰ so here in this case option A is correct .
What three characteristics do angles have?A transversal's corresponding angles are equal when it crosses two parallel lines.Angles that are vertically opposite are equal.All of the interior angles alternately are equal.Every other external angle is equivalent.On the same side of the transversal, the pair of internal angles is additional.Simplification:
<1 = <3
<1 = 5x + 8 ………………equation 1.
<3 = 12x – 20 ………………equation 2.
By angle property <1 = <3 [ given ]
and
<1 = <2 [ vertically opposite angles ]
We have some options so we can use it to get answer more quickly:
Put <1=28 and <3=28
And solve it for X.
28 = 5x + 8 Eq1
20=5x => x=4
28 = 12x - 20 Eq2
28 + 20 = 12x
48 = 12x
4 = x
X = 4
As <1 = <2 ( vertically opposite angles )
From the first equation <1 = <2 = 5x + 8 ......( equation 3)
Putting the value of x = 4 in (equation 3)
<2 = 5* 4+ 8
<2=28
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Using completing the square method to solve x^2-10x+25=0
The solution of the expression, [tex]x^{2} -10x+25 = 0[/tex], using completing the square method is [tex](x-5)^{2}[/tex].
According to the question,
We have the following expression:
[tex]x^{2} -10x+25 = 0[/tex]
Now, we will use completing the square method to solve this expression.
We will first try to convert the first and last term into perfect squares and rewrite the expression by splitting the middle term in multiplication of 2 and the squares .
[tex]x^{2}[/tex]-2*x*5+[tex]5^{2}[/tex] = 0
Now, we know that this expression fits in the identity:
[tex](a-b)^{2} = a^{2} +b^{2} -2ab[/tex]
In this case, we have a = x and b = 5
[tex](x-5)^{2}[/tex]
Hence, the solution of the expression, [tex]x^{2} -10x+25 = 0[/tex], using completing the square method is [tex](x-5)^{2}[/tex].
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What is the perimeter of a pentagon ABCDE with given vertices at A(4, -2), B(4, 10), C(7, 10), D(15, 4), E(7, -2)
Answer:
38 units
Step-by-step explanation:
You want the perimeter of pentagon ABCDE with vertices at A(4, -2), B(4, 10), C(7, 10), D(15, 4), E(7, -2).
PerimeterThe perimeter of a plane figure is the sum of the lengths of its sides.
Vertical, Horizontal sidesBy counting grid squares, or subtracting coordinates, you can find the lengths of the vertical and horizontal segments easily:
AB = 12, BC = 3, EA = 3
Diagonal sidesThe lengths of the diagonal segments can be found using the distance formula or your knowledge of Pythagorean triples. Counting grid squares (or subtracting coordinates), you see that each diagonal side has a vertical distance of 6 and a horizontal distance of 8. These correspond to twice the lengths of the sides in a 3-4-5 triangle, so you know the diagonal length is twice the hypotenuse: 2·5 = 10.
The Pythagorean theorem, or the distance formula, will tell you the same thing:
c² = a² +b² . . . . . . Pythagorean theorem for sides a, b, hypotenuse c
c = √(a² +b²)
diagonal length = √(6² +8²) = √100 = 10
Then the remaining two sides are ...
CD = 10, DE = 10
ApplicationThe perimeter is ...
perimeter = AB +BC +CD +DE +EA
= 12 +3 +10 +10 +3 = 38 . . . units
The perimeter of pentagon ABCDE is 38 units.
The image of ΔABC after a reflection across Line E G is ΔA'B'C'.
2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?
ΔBGC is right because Line EG is perpendicular-to CC'.
What is Reflection?A reflection image or reflection point is the mirror image of a figure in the axis or plane of reflection.
Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the other side of the line. This transformation is known as a reflection over line. The size and form of the image in a reflection are identical to those of the pre-image.
Given:
On the line of reflection will be the midpoints of the segments connecting a triangle vertex with its reflected image. The segment will be parallel to the reflection's line.
A triangle will be considered correct in this situation if it has a leg that is a part of the segment connecting the reflected points and a leg that is on the line of reflection. Such a triangle is the BGC.
Hence, BGC is right triangle.
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Answer: D
Step-by-step explanation: Trust
2
5. A square bathroom with side length 8m
needs tiling. One pack of tiles covers 10m².
How many packs do I need?
Answer:
6.4 packs (7 as integer)
Step-by-step explanation:
Area of the square: 8^2 = 64 m^2
64 : 10 = 6.4
8,40,200,...
Find the 10th term.
The sequence has the 10th term of 15625000
How to find the 10th term for the arithmetic sequence?The sequence is given as:
8,40,200,...
The above sequence has the following parameters
First term, a = 8
Common ratio, r = 5 i.e. 40/8 = 5
Number of terms , n = 10
This means that the sequence is a geometric sequence
The nth term of an geometric sequence is calculated as
f(n) = ar^(n - 1)
Substitute the known values in the above equation
So, we have the following equation
f(10) = 8 * 5^(10 - 1)
Evaluate
f(10) = 15625000
Hence, the 10th term for the sequence is 15625000
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Hi if someone can help me that would be great
The diagrams are shown in the solution.
What is a rectangle?A rectangle is a quadrilateral with all four interior angles 90°.
(1) The rectangle diagram of 1/2 × 5/6 can be drawn by converting the fractions into integers.
The dimension can be written as:
1/2 : 5/6
Multiply the ratio by 6:
3 : 5
Hence, the rectangle of 1/2 × 5/6 is proportional to 3×5.
The diagram is shown.
Similarly, the diagrams of other rectangles are shown.
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Find the values of the variables. Then find the side length of the square 
Answer:
x = 4y = 8side length = 4Step-by-step explanation:
You have a square with sides labeled (y-4), (3x-8), (2y-12), and you want to know the values of the variables as well as the side length.
SetupAll sides of the square are the same length. Equating two different y-expressions, we get ...
y -4 = 2y -12
We can use the solution to that to find x:
y -4 = 3x -8
SolutionAdding 12-y to the first of these equations gives us ...
8 = y
Using this value in the second equation, we have ...
8 -4 = 3x -8
12 = 3x . . . . . . add 8
4 = x . . . . . . . . divide by 3
The side length is ...
y -4 = 8 -4 = 4
The values of the variables are x = 4, y = 8, and the side length of the square is 4.
A health food store makes trail mix using dried fruit and nuts.the cost of the dried fruit is $2.50 per pound,and the cost of the nuts is $2.00 per pound .the total cost to make the trail mix is $225.if the total cost can be represented by the equation 2.5x +2y=225,what does the term 2.5x represent?
I need help:’)
The equation 2.5x + 2y = 225 represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
A health food business prepares trail mixes out of dried fruit and nuts. The dried fruit costs $2.50 per pound, while the nuts cost $2.00 per pound. The overall cost of making the trail mix is $225.
Let the quantity of the dried fruit is x,
And the quantity of nuts is y,
As per the given question, the equation would be as:
2.5x + 2y = 225
The above equation represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
Thus, 2.5x represents the cost of dried fruit when its quantity is x.
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A truck driver is driving from Nome, Alaska, I
Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs
check
the weather continuously to make sure the gas
his truck remains in liquid form. The
gas he uses freezes at -40° F and evaporates at 140° F.
Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form.
(2 points)
Part B: Describe the
graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to
the inequality represent. (4 points)
Part C: In January 1989, the temperature in Nome, Alaska, dropped to -49° F. Would the gas in
the driver's truck have
remained in liquid form so he could have
driven on this day? Why or why not? (4 points)
The inequality of the change of state of the gas in the driver's truck indicates;
Part A: The inequality that represents the temperature at which the gas in the truck will be in liquid form is; -40 ≤ T ≤ 140
Part B: The graph is a shaded region bounded by two solid vertical lines at t = -40 and t = 140
Part C: The gas will be frozen because the temperature is below the freezing point temperature of the gas.
What is an inequality?An inequality indicates the relationship between two expressions that are not equal
The temperature at which the gas freezes = -40 °F
Temperature at which the gas evaporates = 140 °F
Part A: The inequality that represents the temperature at which the gas in the truck will remain in liquid form, t is; -40 ≤ t ≤ 140
Part B: The description of the graph of the inequality is a region on the coordinate plane bounded by two solid vertical lines at x = -40 and x = 140, the region between the two solid vertical lines is shaded/.
Part C: The temperature of -49 °F obtained in January 1989 in Nome, Alaska is not in the feasible region of the graph of the inequality, therefore, the gas in the driver's truck will not remain in liquid form, and would freeze, such that the driver would not drive on the specified date.
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Convert this Slope Intercept Form equation into Standard Form. y=2x-12
Answer: -2x+y=-12
Step-by-step explanation:
After what I did this is what i got. Can't really explain it
Hope this helps :)
Solve for x.
9x3x36
0-6
O-4
O
4
6
Answer:
[tex]9x = 3x - 36 \\ 6x = - 36 \\ x = - 6[/tex]
hopefully this will u...^_^
#12 all parts please!!
Answer:
Step-by-step explanation:
a find the interpret the slope and the y-intercept of the graph
find the slope of (-4,-4), (-1, 14)
Answer:
6
Step-by-step explanation:
slope = m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
put values and find answer:
[tex]=\frac{14+4}{-1+4}[/tex]
= [tex]\frac{18}{3}[/tex]
= [tex]6[/tex]
Identify three segments parallel to AE using the figure shown. Assume lines and planes that appear to be parallel or perpendicular are parallel or perpendicular, respectively
From the figure, the lines parallel to AE are DH, CG, and EF.
What are parallel and perpendicular lines?Geometry is heavily reliant on parallel and perpendicular lines, and they can be easily distinguished thanks to a few unique qualities. If two lines never cross each other, are in the same plane, and are at the same distance from one another, then they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees.
If two straight lines are in the same plane and never intersect, they are said to be parallel lines.
So from the figure, we can see that the lines parallel to AE are DH, CG, and EF, as the lines are in the same plane.
As equidistant lines, they are always the same distance apart.
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PC=3x+7, can you find PC?
The value of PC is 40 when C is the circumcenter of triangle PQR.
Given that,
Consider the complete question is
C is the circumcenter of triangle PQR.
PC=3x-7
RC=5x-15 &
QC= 51-x
We have find the side PC.
A triangle's vertices are equidistance spaced from its circumcenter.
PC=RC=QC
RC=QC
5x-15= 51-x
5x+x= 51+15
6x=66
x=11
The value of x is 11.
We must determine PC's worth.
Substitute x=11 in the above equation.
PC= 3x+7
PC= 3(11)+7
PC=33+7
PC= 40
Therefore, The value of PC is 40 when C is the circumcenter of triangle PQR.
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On a math test student, Jake, has to identify all the coefficients and constants of the expression 9b+7+n. Jake says that 9 is a coefficient and 7 is a constant. Identify all the coefficients and constants of the expression. What error might Jake have made?
The coefficient(s) of the expression is/are _.
Answer:
The coefficient is 9 in 9b.
Step-by-step explanation:
A coefficient is a number before a variable.
Examples: 9 in 9b, 5 in 5y, 3 in 3x.
Practically anything before a variable is declared a coefficient.
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It helps a lot :)
6) There are 11 marbles in a bag. Two are yellow, five are pink and four are green. Suppose you pull out one
marble, record its color, put it back in the bag and then pull out another marble. Find the probability that
when selecting 3 marbles, you have selected a yellow first, green second and pink last.
The probability is 0.1.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.acc to our question-
total marbles= 11yellow marbles=2pink marbles=5green marbles=30.01 + 0.04 + 0.05Hence,The probability is 0.1.
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13) Mr. Harrington wants to buy a new TV for $500. He has a 10% off coupon and knows the tax
be 13.5%. How much money will he need to save to buy the TV?
a) $510.75
c) $450
b) $432.50
d) $567.50
Mr. Harrington will need $510.75 to buy the TV
The correct answer is an option (a)
In this question, Mr. Harrington wants to buy a new TV for $500
He has a 10% off coupon.
After applying this coupon, the cost of TV would be,
500 - (10 percent of $500)
= 500 -[ (10/100) * 500]
= 500 - 50
= 450
He knows the tax be 13.5%.
13.5 percent of 450 would be,
(13.5/100) * 450
= 60.75
So, the amount he will need to save to buy the TV,
$450 + $60.75 = $510.75
Therefore, Mr. Harrington will need $510.75 to buy the TV
The correct answer is an option (a)
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What is the absolute value of −9.4?
Answer:
9.4
Step-by-step explanation:
if the population were not approximately normal, would the confidence interval constructed in part (a) be valid?
No, to construct a confidence interval, the population should be is approximately normal.
The information about distribution of population is important in order to find out the sampling distribution. When we want to construct confidence interval, the accuracy of results depend on three conditions.
1. The data needs to be randomly selected.
2. The sampling distribution needs to be normally distributed
3. The observations must be independent.
So one of the conditions is to ensure that the population is normally distributed.
We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10
np ≥ 10
n(1 - p) ≥ 10
When the population follows normal distribution then a small number of samples will be adequate, on the other hand, if the population is skewed then we need a greater sample size to ensure normal sampling distribution.
Therefore, the population is approximately normal before constructing a confidence interval.
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Which number is a multiple of 4?
A.) 6
B.) 9
C.) 15
D.) 12
Answer:
D: 12
Step-by-step explanation:
multiples of 4: 4,8,12,16,20
12 is the only number that can be divided by 4 on the list
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Answer:
D. 12
Step-by-step explanation:
12 is a multiple of 4 because 4 goes into 12 (evenly, with no remainder).
That's what being a multiple means.
All the "answers" to 4 times table questions are multiples of 4. Here they are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...
Can't actually list them all because the list goes on forever.
Factor and solve f(x) = x³ + 8x² - 23x - 30 given the fact that f(3) = 0
The factored form of f(x) = x³ + 8x² - 23x - 30 is (x - 3)(x + 10)(x + 1).
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given a polynomial f(x) = x³ + 8x² - 23x - 30.
If f(3) = 0 then x - 3 is one of the factors of the polynomial f(x).
∴ f(x) = f₁(x)(x - 3), where f₁(x) is a quadratic equation we obtain it by long division or synthetic division.
f₁(x) = x² + 11x + 10.
Now, x² + 11x + 10 = 0.
x² + 10x + x + 10 = 0.
x(x +10) + 1(x + 10) = 0.
(x + 10)(x + 1) = 0.
x + 10 = 0 Or x = 1 = 0.
x = - 10 Or x = - 1.
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Daquin finished 30% of his homework in 27 minutes. How many minutes will it take him to finish the rest of his homework?.
In 27 minutes, Daquin completed 30% of his schoolwork. He must therefore finish another 70% of her homework.
We must multiply both sides of the equation by 3 to see how long it takes Daquin to finish 10% of the homework. It takes her 9 minutes.
We simply need to multiply our time estimate by seven to determine how long it will take her to complete the remaining 70% of her homework.
9 minutes are required for 10% of the homework.
63 minutes are required to complete 70% of the homework.
% finished equals 30%
Duration: 27 minutes
70% of the homework is still to be done.
Time required for the remaining task is 70/30 divided by 27 is equal to 63 minutes.
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