This is the original expression x(x + 1) = [tex]x^{2}[/tex] + x that we started with, so we can be confident that our factorization is correct.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
To factorize an expression means to write it as a product of factors. In this case, we want to write [tex]x^{2}[/tex] + x as a product of factors. One way to do this is to look for common factors that we can take out of both terms in the expression.
In this case, the only common factor in both [tex]x^{2}[/tex] and x is x itself. Therefore, we can take out an x from both terms to get:
x(x + 1)
This is the fully factorized form of the expression [tex]x^{2}[/tex] + x. It shows that [tex]x^{2}[/tex] + x can be written as a product of two factors: x and (x + 1).
We can verify that this is correct by multiplying out the two factors:
x(x + 1) = [tex]x^{2}[/tex] + x
Therefore, This is the original expression x(x + 1) = [tex]x^{2}[/tex] + x that we started with, so we can be confident that our factorization is correct.
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a grab bag contains 2 football cards and 8 basketball cards. an experiment consists of taking one card out of the bag, replacing it, and then selecting another card. what is the probability of selecting a football card and then a basketball card? express your answer as a decimal.
The probability of selecting a football card and then a basketball card is 0.16 or 16%. The probability of selecting a football card and then a basketball card can be calculated by multiplying the probability of selecting a football card on the first draw and the probability of selecting a basketball card on the second draw.
Since the first card is replaced before the second draw, the probability of selecting a football card or a basketball card remains the same on both draws.
The probability of selecting a football card on the first draw is 2/10, or 0.2, since there are 2 football cards in a total of 10 cards in the bag. The probability of selecting a basketball card on the second draw is 8/10, or 0.8, since there are 8 basketball cards left after the first draw.
Therefore, the probability of selecting a football card and then a basketball card can be calculated as follows:
P(Football and Basketball) = P(Football on 1st draw) x P(Basketball on 2nd draw)
= (2/10) x (8/10)
= 0.16
So, the probability of selecting a football card and then a basketball card is 0.16 or 16%.
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Find the perimeter of a polygon. Assume that lines which appear to be tangent are tangent A. 32.1 B. 39 C. 45.2 D. 59.7
Check the picture below.
The regular price of a cell phone is $150 during a weekend sell all cell phones were 35% off how much will Colin save if he buys his cell phone during the sale
Answer:
Step-by-step explanation:
cost of the phone = 150
sale is 35% off
Multiply the original cost $150.00 time the percent off as a decimal.
35% = . 35 (drop the sign and move the decimal two places left.)
150 X .35 = 52.50 off the price
He will save $52.50 off the cell phone during the sale.
Answer of the second question with explanation.
1 + 1/(1 + 1/(1 - 1/2)) =
What is the sum of 12 - 5i and -3 + 4i? a. -16 + 63ib. 9 - i c. 9 - 9i d. 15 - 9i
Answer: 9 - i
Step-by-step explanation:
The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)
We have to give that,
The sum of numbers 12 - 5i and - 3 + 4i.
Now, we can find the sum of complex numbers as,
(12 - 5i) + (- 3 + 4i)
12 - 5i - 3 + 4i
Combine like terms,
12 - 3 - 5i + 4i
9 - i
Therefore, The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)
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Which sign makes the statement true?
-2/5 ? -4/10
< > =
The fractions [tex]\frac{-2}{5}[/tex] and the fraction [tex]\frac{-4}{10}[/tex] , both are equal [tex]\frac{-2}{5} =\frac{-4}{10}[/tex], which means the "=" sign makes the statement true.
What are inequality signs?A mathematical relationship between two expressions is called inequality, and it is expressed using one of the following:
"less than or equal to": [tex]\leq[/tex]
"greater than" :>
"greater than or equal to" : [tex]\geq[/tex]
"less than": <
"not equal to": [tex]\neq[/tex]
To compare the fraction, make the denominator of both fractions the same.
Given:
Fraction 1 = [tex]\frac{-2}{5}[/tex]
Fraction 2 = [tex]\frac{-4}{10}[/tex]
To make the same denominator we can multiply by 2 to the numerator and denominator of the fraction 1.
[tex]\frac{-2}{5} =\frac{-2 * 2}{ 5*2}[/tex]
[tex]\frac{-2}{5} =\frac{-4}{10}[/tex]
Hence from the above calculation, the given fractions are equal.
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4 consecutive odd integers with a sum of 3048
Answer:
The integers you seek are:
759, 761, 763, 765
since
759 + 761 + 763 + 765 = 3048.
Hope this helps!
a quality control expert at life batteries wants to test their new batteries. the design engineer claims they have a variance of 8100 with a mean life of 1192 minutes. if the claim is true, in a sample of 72 batteries, what is the probability that the mean battery life would be greater than 1173.8 minutes? round your answer to four decimal places.
The probability that the mean battery life would be greater than 1173.8 minutes is 0.9588
We can solve this problem using the central limit theorem, which tells us that the distribution of sample means from a population with a known variance becomes approximately normal as the sample size increases.
The standard error of the mean can be calculated as
SE = σ / sqrt(n)
where σ is the population standard deviation, n is the sample size
Here, we are given that the population variance is 8100, so the population standard deviation is the square root of 8100, which is 90.
SE = 90 / sqrt(72) = 10.6066
Next, we need to standardize the sample mean using the z-score formula
z = (X - μ) / SE
where X is the sample mean, μ is the population mean.
Here, the population mean is given as 1192 minutes and the sample mean we are interested in is 1173.8 minutes.
z = (1173.8 - 1192) / 10.6066 = -1.7356
We want to find the probability that the sample mean is greater than 1173.8 minutes. Since we have a negative z-score, we need to find the area to the right of this value on a standard normal distribution. We can use a z-table or a calculator to find this probability.
Using a standard normal distribution table, we find that the area to the right of z = -1.7356 is 0.9588.
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a group of friends pooled their money and purchased a winning raffle ticket. the $480 prize was split equally among x winners. what expression represents the amount of prize money each winner received?
The amοunt οf prize mοney each winner received can be represented by the expressiοn: $480 / x
What is Linear Equatiοn?A linear equatiοn is a mathematical equatiοn that represents a straight line when graphed, and is in the fοrm οf y = mx + b, where m represents the slοpe οf the line and b represents the y-intercept.
The amοunt οf prize mοney each winner received can be represented by the expressiοn:
$480 / x
This is because the prize mοney οf $480 was split equally amοng x winners, sο dividing the tοtal prize mοney by the number οf winners (x) gives the amοunt each winner received. This expressiοn calculates the quοtient οf $480 divided by the number οf winners (x), resulting in the amοunt οf prize mοney each winner received.
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solve each system by substitution
The solution to the system of equations is p = 4 and q = 2
What do you mean by Substitution method ?The substitution method is a way to solve a system of linear equations. In this method, we solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. This produces a new equation with one variable, which we can then solve for its value. Once we know the value of one variable, we can substitute it back into one of the original equations to find the value of the other variable.
To solve the system of equations using the method of substitution, we need to solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. We can start by solving the second equation for p:
p + 2q = 8
p = 8 - 2q
Now we can substitute this expression for p in the first equation:
2p - 3q = 2
2(8 - 2q) - 3q = 2
16 - 4q - 3q = 2
16 - 7q = 2
-7q = -14
q = 2
We can now substitute q = 2 into the expression we found for p:
p = 8 - 2q
p = 8 - 2(2)
p = 4
Therefore, the solution to the system of equations is p = 4 and q = 2.
correct question Solve the equations 2p – 3q = 2 and p + 2q = 8, using the method of substitution.
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A tourist from Mexico is vacationing in the U.S. One day, he notices that gasoline costs 2.97 dollars per gallon. On that same day, 1 peso is worth 0.053 dollars. How much does the gas cost in pesos per liter?
Answer: 3.71
Step-by-step explanation:
Donna drove 522 miles in 9 hours. At the same rate, how many miles would she drive in 11 hours?
Answer:
522/9=58
11-9=2
58*2=116
522+116=638
Step-by-step explanation:
Answer:
638
Step-by-step explanation:
help me please last question until 10/10
Assuming the black and red squares are equally likely and there is no bias in the coin, the probability that it will land heads up on a black square is 1/2, or 50%.
What is probability and why will it be 1/2?Probability is a branch of mathematics that studies the likelihood of a random event occurring. When a coin is tossed into the air, for example, the possible outcomes are Head and Tail.
We will have a probability of 50%; this is because there are two equally likely outcomes when flipping a coin - heads or tails - and each square on the checkerboard has an equal chance of being landed on.
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how do i solve this problem
The coordinates of the image of the triangle and the rules that can be used to transform the triangle are;
1. A' is located at (-3, 3)
B' is located at (-2, -1)
C' is located at (2, 1)
Second part; The rules are;
(x, y) → (x + 5, -y)
(x, y) → (5·x, 5·y)
What is a transformation of a geometric figure?A transformation of a figure is the reorientation of the figure to change the size and position of the figure.
1. The coordinates of the triangle ABC following the transformation (x, y) → (-x, y) are;
A(3, 3) (x, y) → (-x, y) A'(-3, 3)
B(2, -1) (x, y) → (-x, y) B'(-2, -1)
C(-2, 1) (x, y) → (-x, y) C'(2, 1)
2. The coordinates of the vertices of the triangle are; (1, 1), (4, 1), and (0, 4)
Translating the triangle five units right, we get;
(1 + 5, 1) = (6, 1), (4 + 5, 1) = (9, 1), and (0 + 5, 4) = (5, 4)
The coordinates of the triangle following a translation 5 units right are therefore; (6, 1), (9, 1), and (5, 4)
The coordinates of the image of the point (x, y) following a reflection across the x-axis is the point (x, -y), therefore;'
The coordinates of the image of the triangle obtained from the previous transformation following a reflection across the x-axis is therefore;
(6, 1) reflection across the x-axis → (6, -1)
(9, 1) reflection across the x-axis → (9, -1)
(5, 4) reflection across the x-axis → (5, -4)
A rule that takes the triangle to a congruent triangle right five units and reflected over the x-axis is therefore;
(x, y) → (x + 5, -y)The transformation of a triangle by a dilation by a scale factor of five, such that the triangle is five times larger can be obtained by the expression for a dilation transformation as follows;
(x, y) → (a·x, a·y)
Therefore, we get;
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find m<7 if m<8 =110
180º-110º = 70º
m∠7 = 70°
which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test? which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test? the sample size is greater than 30. the number of categories is less than 10% of the number of observations. the expected count is the same for each category. the population distribution is approximately normal. the expected count for each category is at least 5.
The condition that must be satisfied to use a chi-square goodness-of-fit test is D. The expected count for each category is at least 5.
A chi-square goodness-of-fit test is a statistical test used to determine whether the observed frequencies of categorical data match the expected frequencies. This test is often used to analyze categorical data, such as determining if the distribution of colors in a bag of candies matches the expected proportions.
The reason behind this condition is that the chi-square test is based on the assumption that the data follow a specific distribution. When the expected count for each category is less than 5, the test might not accurately represent the true distribution, and the results may be misleading. By having an expected count of at least 5 in each category, the test can better approximate the true distribution and provide more reliable results. Therefore, option D is correct.
The Question was Incomplete, Find the full content below :
which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test?
A. The sample size is greater than 30.
B. The number of categories is less than 10% of the number of observations.
C. The expected count is the same for each category. the population distribution is approximately normal.
D. The expected count for each category is at least 5.
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what changes the width of a confidence interval? a marketing director wants a 95% confidence interval for the mean cost of running shoes. she randomly
The width of the confidence interval increases as the sample size increases and decreases as the confidence interval decreases. The confidence interval decreases as the sample size increases and increases as the confidence level increases.
Sample size is defined as the number of observations used to determine
an estimate of a particular population. The size of the model is drawn by people. Sampling is the process of selecting a group of individuals from a population to estimate the characteristics of the entire population. Select the number of establishments in a population group for analysis.
The sample size increases with the square of the standard deviation and decreases with the square of the difference between the mean under the alternative hypothesis and the mean under the null hypothesis.
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Solve for x.
[tex]\left[\begin{array}{ccc}5&2\\3&x\\\end{array}\right] =x^2[/tex]
[tex]\begin{bmatrix} 5&2\\ 3&x \end{bmatrix}~~ = ~~x^2\implies \stackrel{ \textit{determinant of a }2\times 2 ~matrix}{(5)(x)~~ - ~~(3)(2)}~~ = ~~x^2\implies 5x-6=x^2 \\\\\\ 0=x^2-5x+6\implies 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}[/tex]
−3x − 8y = 20
−5x + y = 19
Answer:
x = -4,
y = -1
Step-by-step explanation:
{-3x - 8y = 20,
{-5x + y = 19;
Make x or y the subject from either the 1st or the 2nd equation (I chose to make x the subject from the 2nd equation, because after division, the numbers can be written as a finite decimal fraction):
-5x = 19 - y / : (-5)
x = -3,8 + 0,2y
Replace x in the 1st equation with its value from the 2nd one (the underlined expression):
-3(-3,8 + 0,2y) - 8y = 20
Multiply every term inside the bracket by the term on the outside:
11,4 - 0,6y - 8y = 20
Collect like terms and add them together:
-8,6y = 20 - 11,4
-8,6y = 8,6 / : (-8,6)
y = -1
y = -1x = -3,8 + 0,2 × (-1) = -4
Pls help fast, I need the answer soon
(Also pls tell me how to actually do it!)
Write 3a^2b^3c^5/8x^4y^3z using no denominator. (fraction line is necessary. Use x for multiplication between numbers.)
(Whatever is in the picture already is required!)
Answer:
0.375 × a² × b³ × c⁵ ÷ x⁴ ÷ y³ ÷ z
Step-by-step explanation:
First, we can represent 3/8 in decimal form:
0.375
Next, we can show the numerator using multiplication:
0.375 × a² × b³ × c⁵
Then, we can individually divide by each factor in the denominator using the principle:
[tex]\dfrac{A}{B \times C} = A \div (B \times C) = A \div B \div C[/tex]
0.375 × a² × b³ × c⁵ ÷ x⁴ ÷ y³ ÷ z
I need some help pretty please
Answer:
[tex]y - ( - 20) = 9(x - ( - 2))[/tex]
[tex]y + 20 = 9(x + 2)[/tex]
Step-by-step explanation:
[tex]m = \frac{79 - ( - 20)}{9 - ( - 2)} = \frac{99}{11} = 9[/tex]
[tex]y - ( - 20) = 9(x - ( - 2))[/tex]
[tex]y + 20 = 9(x + 2)[/tex]
If a bird flies at a rate of 28 miles in 2 hrs, how many miles does it travel in 40 minutes?
Answer: 9 and 1/3
Step-by-step explanation:
First of all, you have to find the unit rate. So 28 divided by 2 = 14.
The bird flies at a unit rate of 14 miles in 1 hour.
Next, we need to find out what fraction of an hour is 40 minutes.
How many minutes in an hour? 60... so 40 would be 40/60 of an hour or 4/6 or 2/3 of an hour.
Next, remember the formula D=rt which is distance= rate multiplied by time
We can use this formula here: 14 times 2/3 = 9 and 1/3
suppose that the distance a car travels varies directly with the amount of gasoline it uses. a certain car uses 28 gallons of gasoline to travel 924 miles. how many miles can the car travel if it has 19 gallons of gasoline? miles
The distance a car travels varies directly with the amount of gasoline it uses. If a car uses 28 gallons of gasoline to travel 924 miles, the car can travel 627 miles with 19 gallons of gasoline.
We can set up a proportion to solve the problem:
distance / gasoline = constant
Let's use x to represent the distance the car can travel with 19 gallons of gasoline:
924 / 28 = x / 19
Simplifying and solving for x:
x = (924 / 28) * 19 = 627 miles
Therefore, the car can travel 627 miles with 19 gallons of gasoline.
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In cyclic quadrilateral PQRS,
[tex]\frac{\ \textless \ P}{3} =\frac{\ \textless \ Q}{4} =\frac{\ \textless \ R}{5}[/tex]
Find the largest angle in quadrilateral PQRS, in degrees. ("<" =angle and the answer isn't 120)
The largest angle in quadrilateral PQRS is angle R with a measure of 150 degrees.
what is quadrilateral?
A quadrilateral is a four-sided polygon, which is a two-dimensional closed shape with straight sides. In other words, a quadrilateral is a geometric figure that has four sides, four vertices, and four angles. The sum of the interior angles of a quadrilateral is always equal to 360 degrees. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.
From the given information, we have:
angle P = 3p
angle Q = 4q
angle R = 5r
Since PQRS is a cyclic quadrilateral, the sum of opposite angles is equal to 180 degrees. Therefore, we have:
angle P + angle R = 180 degrees
3p + 5r = 180 degrees
Similarly, we have:
angle Q + angle S = 180 degrees
4q + S = 180 degrees
S = 180 - 4q
To find the largest angle, we need to find the largest angle measure among angles P, Q, R, and S.
Let's substitute the expression for S in terms of q into the equation for angle Q and simplify:
angle Q = 4q
angle Q + angle S = 180 degrees
4q + (180 - 4q) = 180 degrees
4q - 4q + 180 = 180 degrees
180 = 180 degrees
This equation is true, but it does not provide any information about the largest angle in PQRS.
Let's now substitute the expressions for angles P, Q, and R in terms of p and r into the equation for angle P + angle R = 180 degrees:
3p + 5r = 180 degrees
We want to find the largest angle, so we need to find the largest value of p or r that satisfies this equation. One way to do this is to try different values of p and r that satisfy the equation and see which one yields the largest value for angle P or angle R.
Let's try p = 10 and r = 30:
3p + 5r = 3(10) + 5(30) = 150
This satisfies the equation, so we can calculate angle P and angle R:
angle P = 3p = 30 degrees
angle R = 5r = 150 degrees
Therefore, the largest angle in quadrilateral PQRS is angle R with a measure of 150 degrees.
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Pls answer fast!!! Whoever gets it correct first gets a brainly!!!!
Answer: B
Step-by-step explanation:
The answer is 9x^2 + 14xy -19y^2
PLS HELPPPPPPPPPP i need this completed today
The given measure of ∠ DEC = 80 degrees
How to solve for the angleWe have the following details
m ∠BAC = 46 degrees
m ∠ CBA = 54 degrees
We are to find the measure of angle DEC
This is a question that shows us two similar triangles
We have ∠BAC = DCE
∠ CBA = ∠ EDC
then ∠ DEC = ∠ BCA
The angle sum propertyThe measure of the angles that are in a triangle is given as 180 degrees
we have ∠BAC + ∠ CBA + ∠ BCA = 180
46 + 54 + ∠ BCA = 180 degrees
∠ BCA = 180 - 100
∠ BCA = 80 degrees
We know that corresponding angles are equal when we have parallel lines
since ∠ DEC = ∠ BCA
∠ DEC = 80 degrees
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Please help me answer the equation of the area of triangles as attached below.
Answer:15
You multiply 6 and 5. That equals 30 then divide the 30 by 2 and that equals 15
Which value is NOT greater than [-4.2] A [-4.2]
B [3.5]
C [4.1]
D [-4.5]
The value that is NOT greater than [-4.2] is D. [-4.5]
The values [-4.2], [3.5], and [4.1] are all greater than [-4.5]. To determine which value is the greatest, we can use a number line or compare the numbers directly. On a number line, we can see that [-4.5] is located to the left of [-4.2], [3.5], and [4.1]. This means that [-4.2], [3.5], and [4.1] are all greater than [-4.5].
Alternatively, we can compare the values directly. We know that -4.5 is less than -4.2 since -4.5 is farther to the left on the number line. We also know that 3.5 and 4.1 are positive values, which are greater than any negative value. Therefore, the answer is [-4.5] is not greater than [-4.2]. Hence, option D is correct.
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help im clueless i wasn't at school the day we learned this
Answer:
for the firsts ones :
1. 12 x 2 x 5
2. 4 x 11 x 2,25
3. 6.5 x 22.6 x 10
Step-by-step explanation:
100000+1X2 222+222+22222222222x111111111111111111111+222222222222222222
So, 100000+1X2 + 222+222+22222222222x111111111111111111111+222222222222222222 = 24,691,458,024,691,358,024,691,826
What does an expression mean?
It is preferable to use moving integer variables, which can be rising, decreasing, or blocking, rather than estimates that are generated at random. They could only assist one another by exchanging resources, knowledge, or answers to problems. A declaration of truth equation may include the justifications, components, and mathematical comments for strategies like extra disapproval, production, and mixture.
Let's solve this equation step by step:
100000+1X2
This is a simple expression which involves addition and multiplication.
100000+1X2 = 100000 + 2 (since 1X2 equals 2)
Therefore, 100000+1X2 = 100002
222+222+22222222222x111111111111111111111
This expression involves addition and multiplication as well.
We need to multiply 22222222222 by 111111111111111111111 first, and then add 222+222 to the result.
22222222222 x 111111111111111111111 = 24,691,358,024,691,358,024,691,358
222+222 = 444
So, 222+222+22222222222x111111111111111111111 = 24,691,358,024,691,358,024,691,802
222222222222222222
This is a simple number.
So, 100000+1X2 + 222+222+22222222222x111111111111111111111+222222222222222222 = 24,691,458,024,691,358,024,691,826
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