The model represents a polynomial and its factors. An algebra tile configuration. 4 tiles are in the Factor 1 spot: 1 is labeled x and 3 are labeled negative. 2 tiles are in the Factor 2 spot: 1 is labeled x and 1 is labeled negative. 8 tiles are in the Product spot: 1 is labeled x squared, 4 are labeled negative x, and 3 are labeled. Which equation is represented by the model? x2 â€" 2x â€" 3 = (x â€" 3)(x 1) x2 â€" 4x 3 = (x â€" 3)(x â€" 1) x2 2x 3 = (x 3)(x â€" 1) x2 4x â€" 3 = (x 3)(x 1).
Answers
The model is a representation of the polynomial factors using algebraic
tiles.
The equation represented by the model is the option;
\(\underline{x^2 - 4 \cdot x + 3 = (x - 3) \cdot (x - 1)}\)Reasons:
The parameters of the model of the polynomial and the factors of the
polynomial are;
The number of factors of the polynomial = 2
Number of tiles in the factor 1 spot = 4 tiles, including;
1 of the four tiles is labelled x
3 of the four tiles is labelled -ve
Therefore;
A factor of the polynomial is x-tile, -tile, -tile, -tile = (x tile - 3 tiles) = (x - 3)
Number of tiles in the factor 2 spot = 2 tiles which are;1 of the two tiles is labelled x
1 of the two tiles is labelled -ve
Which gives;
A factor of the polynomial is x, -tile = (x-tile - 1 tile) = (x - 1)
Number of tiles in the Product spot = 8 tilesThe 8 tiles are as follows;
1 of the 8 tiles is labelled x²
4 of the 8 tiles are labelled -x
3 of the 8 tiles are labelled +
Which gives;
The product of the polynomial is; (x²-tile - 4·x-tiles + 3-tiles) = (x² - 4·x + 3)
Multiplying the factors gives;
(x - 3) × (x - 1) = x² - 3·x - x + 4 = x² - 4·x + 3
The correct option is therefore;
\(\underline{x^2 - 4 \cdot x + 3 = (x - 3)\cdot (x - 1)}\)The question options are;
x² - 2·x - 3 = (x - 3)·(x + 1)
x² - 4·x + 3 = (x - 3)·(x - 1)
x² + 2·x + 3 = (x + 3)·(x - 1)
x² + 4·x - 3 = (x + 3)·(x + 1)
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Related Questions
7. Mr. Bob the Builder drew a map of a school. There are 16 inches between the cafe
teacher's lounge on the map, and 208 feet between the cafeteria and teacher's lounge in real life.
What scale is being used?
Answers
The scale being used in Mr. Bob the Builder's map is 1 inch on the map corresponds to 156 inches in real life.
Using the given measurements, we can create a proportion to determine Mr. Bob the Builder's map's scale:
In real life, 16 inches on the map equal 208 feet.
Let's use the same measurement for the units. It is convenient to use the same unit of measurement on both sides of the proportion because we are attempting to establish the scale. How about we convert 208 feet to inches:
1 foot equals 12 inches; 208 feet equals 208 times 12 inches, or 2496 inches. Now we know the ratio:
We can cross-multiply to solve for the scale factor: 16 inches (on the map) x 2496 inches (in real life).
16 * 1 = 2496 * x
16 = 2496x
x = 16/2496
Improving on the part:
x = 1/156, so Mr. Bob the Builder's map uses a scale where one inch on the map is equivalent to 156 inches in real life.
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In the cofinite topology on the infinite set X
, any two non-empty open sets have a non-empty intersection. This should be reasonably clear: if U
and V
are non-empty and open and U∩V
is empty, then
X=X−(U∩V)=(X−U)∪(X−V).
But now the infinite set X
is a union of two finite sets, a contradiction.
Now, in a metric space, do ALL pairs of non-empty open sets always have non-empty intersection?
Answers
The answer to the question is false, not all pairs of non-empty open sets always have a non-empty intersection in a metric space.
In general, we cannot guarantee that every pair of non-empty open sets in a metric space has a non-empty intersection. Consider, for example, the real line R equipped with the Euclidean metric. The intervals (-1, 0) and (0, 1) are both open and non-empty, but they have an empty intersection. In the standard topology on the real line, we can find many pairs of non-empty open sets that have an empty intersection.
A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.
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The communications department hired Marilyn Curtis at an annual salary of $154,950. Advertising costs were $2,247.50. Interviewing expenses were: Marilyn Curtis, $1,647.43; Tom Hart, $996.94. The agency fee is 20% of the first year's salary. What was the total cost of hiring Marilyn?
Answers
Answer:
The total cost of hiring Marilyn Curtis would be $189,978.13----------------------
First, we need to calculate the agency fee, which is 20% of Marilyn's annual salary:
Agency fee = 20% of $154950 = 0.2 * $154950 = $30990Next, we add up all the expenses:
Salary = $154950 Advertising costs = $2247.50 Interviewing expenses = $1647.43 + $996.94 = $2644.37 Agency fee = $30990Total cost is the sum of the four:
$154950 + $2247.50 + $2644.37 + $30990 = $189,978.13Aaron invested $7,500 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 8 years?
Answers
Answer:
\text{Compounded Continuously:}
Compounded Continuously:
A=Pe^{rt}
A=Pe
rt
P=7500\hspace{35px}r=0.015\hspace{35px}t=8
P=7500r=0.015t=8
Given values
A=7500e^{0.015(8)}
A=7500e
0.015(8)
Plug in
A=7500e^{0.12}
A=7500e
0.12
Multiply
A=8456.22638685
A=8456.22638685
Use calculator (with e button)
A\approx 8500
A≈8500
Round to nearest hundred dollars
Step-by-step explanation:
The amount of money to the nearest hundred dollars that would be in the account after 8 years is $60,900.
What is the future value of the account?The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate7500 x e^0.015 x 8 = $60,900
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if the probability of a machine producing a defective part is 0.05, what is the probability of finding exactly 4 defective parts from a sample of 100? (assume that the process follows a binomial distribution.)
Answers
There is a probability of 22% that exactly 4 defective parts will be found in a sample of 100.
Probability of a machine producing a defective part is 0.05,
p = 0.05
q = 1 - p = 1 - 0.05 = 0.95
n = 100
P(x) = ⁿCₓ pˣqⁿ⁻ˣ
x = 4
P(4) = ¹⁰⁰C₄(0.05)⁴(0.95)⁹⁶
P(4) = 0.215569
= 0.2156
0.2156 is the probability of finding exactly 4 defective parts from a sample of 100.
The probability of defective parts is the likelihood that a part will be defective. This can be due to a variety of factors, such as poor quality control, incorrect manufacturing process, or use of sub-standard materials. A high probability of defective parts can lead to serious problems, such as faulty products, safety hazards, and financial losses.
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A ladder leans against the side of the house. The length of the ladder is 17 feet. The base of the ladder is 8 feet from the house. How far off the ground is the top of the ladder?
Answers
Answer:
17² - 8² = 225
√225=15
Step-by-step explanation:
a = x
b = 8
c = 17
a² + b² = c²
b² = c² - a²
the circumference of a circle is 25.12 meter. What is the diameter of this circle?
Use 3.14 for pi
Answers
We are looking for R first, so
=
——
2
r= 25.12
————
2(3.14)
r= 25.12
———-
6.28
r= 4
diameter= r(2)
4(2)= 8
THE DIAMETER OF THE CIRCLE IS 8
Answer:
Step-by-step explanation:
8 sqaure feet
Please answer this question now
Answers
Answer:
112°
Step-by-step explanation:
By inscribed angle theorem:
\( m\widehat {BCD} = 2\times m\angle BAD\\
\therefore m\widehat {BCD} = 2\times 129\degree \\
\therefore m\widehat {BCD} = 258\degree\\\\
\because m\widehat{CD} = m\widehat {BCD}-m\widehat{BC} \\
\therefore m\widehat{CD} = 258\degree - 146\degree \\
\huge \red {\boxed {\therefore m\widehat{CD} = 112\degree}} \)
Can you help please thank you
Answers
Answer:
usYou use numbers in money and in constructenine numbers in evrything.
Step-by-step explanation:
A radioactive compound with mass 320 grams decays at a rate of 27% per hour. Which equation represents how many grams of the compound will remain after 7 hours?
Answers
Answer:
320 grams ÷ 27% = 8.3 grams
Step-by-step explanation:
mark brainliest plss
What is the height of the tree?
Answers
Answer: 12 ft
Step-by-step explanation:
Answer:
\(\huge\boxed{12 \ \text{ft}}\)
Step-by-step explanation:
We can see that the yard stick and the tree are forming triangles with the ground.
We also given that these are similar figures. Therefore, the ratio between both their corresponding sides will be the same for every side.
AKA:
Since the yardstick has a 6ft leg, but the tree has a 24ft leg, the tree will be equally proportional to the yardstick.
What's the scale factor that we use to get from the yardstick to the tree?
We have 24 to 6.
\(24 \div 6 = 4\)
So the scale factor is 4.
Therefore, if we multiply the yardstick height by 4, we will get the height of the tree.
\(3 \cdot 4 = 12\)
So the tree is 12 feet tall.
Hope this helped!
3.6 + 8.3 find the sum plz need help
Answers
Answer:
11.9
Step-by-step explanation:
just add the two numbers :)
Answer:
the answer 11.9
Step-by-step explanation:
add by lining up the decimals
P(Y1−3>Y2)=P(Y1>Y2+3). Why does the two integrations evaluate to different values?
Answers
The bounds of integration in the second integration are different from the first integration. Specifically, the second integration includes the region where Y1−Y2≤3, which was excluded in the first integration. This is why the two integrations evaluate to different values.
The two integrations evaluate to different values because the bounds of integration are different.
When we write P(Y1−3>Y2), we are considering the event that Y1 is greater than Y2+3. This can be represented as the region in the Y1-Y2 plane where Y1−Y2>3, as shown below:
To find the probability of this event, we need to integrate the joint density function of Y1 and Y2 over this region:
P(Y1−3>Y2) = ∫∫_{y1-y2>3} f(y1,y2) dy1 dy2
On the other hand, when we write P(Y1>Y2+3), we are considering the event that Y1 is greater than Y2+3. This can be represented as the region in the Y1-Y2 plane where Y1>Y2+3, as shown below:
To find the probability of this event, we need to integrate the joint density function of Y1 and Y2 over this region:
P(Y1>Y2+3) = ∫∫_{y1>y2+3} f(y1,y2) dy1 dy2
The bounds of integration in the second integration are different from the first integration. Specifically, the second integration includes the region where Y1−Y2≤3, which was excluded in the first integration. This is why the two integrations evaluate to different values.
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What is the volume of the pyramid?
12 in
8 in
10 in
120 in
320 in
480 in
960 in
Answers
Answer:
B. 320 inches cubed
Step-by-step explanation:
A pyramid's volume is denoted by: V = (1/3) * B * h, where B is the base area and h is the height.
Here, the base is a rectangle with dimensions 10 inches by 8 inches. The area of a rectangle is denoted by: A = lw, where l is the length and w is the width. The length is 8 and the width is 10, so plug these in:
A = lw
A = 8 * 10 = 80
So, we know that B = 80.
We are also given that the height is h = 12, so plug these values into the volume formula:
V = (1/3) * B * h
V = (1/3) * 80 * 12 = 320
The answer is thus B.
Answer:b
Step-by-step explanation:
If there is a point on the grid and its (6,4) and its asking to rotate it 90 degrees clockwise what is the answer ?
Answers
In each of the following situations, state whether it is a correctly stated hypothesis
testing problem and why?
1. H0: = 25, H1: ≠ 25
2. H0: > 10, H1: = 10
3. H0: x = 50, H1: x ≠ 50
4. H0: p = 0.1, H1: p = 0.5
5. H0: = 30, H1: > 30
Answers
1. Correctly stated hypothesis testing problem: H0: μ = 25, H1: μ ≠ 25 (two-tailed test).
2. Incorrectly stated hypothesis testing problem: H0: μ > 10, H1: μ = 10 (null hypothesis should have an equal sign).
3. Correctly stated hypothesis testing problem: H0: x = 50, H1: x ≠ 50 (two-tailed test).
4. Correctly stated hypothesis testing problem: H0: p = 0.1, H1: p = 0.5 (two-tailed test).
5. Correctly stated hypothesis testing problem: H0: μ = 30, H1: μ > 30 (one-tailed test).
1. H0: μ = 25, H1: μ ≠ 25
This is a correctly stated hypothesis testing problem. H0 represents the null hypothesis, which states that the population mean (μ) is equal to 25. H1 represents the alternative hypothesis, which states that the population mean is not equal to 25.
The use of the symbol "≠" indicates a two-tailed test, where we are interested in determining whether the population mean is significantly different from 25 in either direction.
2. H0: μ > 10, H1: μ = 10
This is not a correctly stated hypothesis testing problem. The null hypothesis (H0) should always represent the hypothesis of no effect or no difference, while the alternative hypothesis (H1) should represent the hypothesis we are trying to establish.
In this case, the null hypothesis suggests that the population mean (μ) is greater than 10, while the alternative hypothesis states that the population mean is equal to 10. This formulation is incorrect because the null hypothesis should always have an equal sign (e.g., =, ≤, or ≥) and the alternative hypothesis should have an inequality sign (e.g., ≠, <, or >).
3. H0: x = 50, H1: x ≠ 50
This is a correctly stated hypothesis testing problem. Here, H0 represents the null hypothesis that the sample mean (x) is equal to 50. H1 represents the alternative hypothesis, stating that the sample mean is not equal to 50.
The symbol "≠" indicates a two-tailed test, where we are interested in determining whether the sample mean is significantly different from 50 in either direction.
4. H0: p = 0.1, H1: p = 0.5
This is a correctly stated hypothesis testing problem. H0 represents the null hypothesis that the population proportion (p) is equal to 0.1. H1 represents the alternative hypothesis, stating that the population proportion is equal to 0.5.
The use of the equal sign (=) in both hypotheses indicates that this is a two-tailed test, seeking to determine whether the population proportion significantly differs from 0.1 in either direction.
5. H0: μ = 30, H1: μ > 30
This is a correctly stated hypothesis testing problem. H0 represents the null hypothesis that the population mean (μ) is equal to 30. H1 represents the alternative hypothesis, stating that the population mean is greater than 30. The symbol ">" indicates a one-tailed test, where we are interested in determining whether the population mean is significantly larger than 30.
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is figure pqrstu a translation, reflection, or rotation? Explain your reasoning
PLEASE HELP ME
Answers
Answer: I'd say reflection
Answer:
It is a reflection
Step-by-step explanation:
In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
A vase contains 60 marbles, all of which are red or orange. if the ratio of red marbles to orange ones is 1:5, what is the total number of red marbles in the vase?
Answers
The total number of red marbles in the vase are 10.
What is the ratio?A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.
The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.
Now, according to the question;
Let 'x' be the red marbles in the vase.
Let 'y' be the orange marbles in the vase.
The total number of marbles in the vase are 60
x + y = 60 (equation 1)
The ratio of red marbles to orange ones is 1:5.
Thus, x/y = 1/5
cross multiplying;
5x = y
or y = 5x
substitute the value of y in equation 1;
x + y = 60 (equation 1)
x + 5x = 60
6x = 60
x = 10 (red marbles)
Thus, the number of red marbles in the vase are 10.
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A right rectangular prism is 2.75 in by 4 in by 16.5 in. what is the total surface area of the prism? 244.75 in2 222.75 in2 122.375 in2 112.75 in2
Answers
If the right rectangular prism is 2.75in by 4in by 16.5in, then the total surface area of the prism is (a) 244.75 in².
We know that the total surface area of a right rectangular prism is given by the formula ⇒ 2lw + 2lh + 2wh
Where ⇒ l, w, and h are length, width, and height of rectangular prism, respectively.
The dimensions of the rectangular prism is 2.75in by 4in by 16.5in,
Substituting the values of length , width and height , we get:
⇒ 2×2.75×4 + 2×2.75×16.5 + 2×4×16.5,
⇒ 22 + 90.75 + 132
⇒ 244.75
Therefore, the total surface area of the prism is 244.75 in²,the correct option is (a).
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The given question is incomplete, the complete question is
A right rectangular prism is 2.75 in by 4 in by 16.5 in. What is the total surface area of the prism?
(a) 244.75 in²
(b) 222.75 in²
(c) 122.375 in²
(d) 112.75 in²
A 14 ounce energy drink contains 10 1/2 teaspoons of sugar.How much sugar is in one ounce of the drink?
A.3/4 teaspoon
B.1 1/3 teaspoons
C.1 1/2 teaspoons
D.3 1/2 teaspoons
Answers
(PLS HURRY!) On Melissa's 6th birthday, she gets a 2000$ CD that earns 6% interest, compounded. If the CD matures on her 14th birthday, how much money will be available?
Answers
Using compound interest formula when the CD matures on Melissa's 14th birthday, there will be $3187.69 available.
What is Compound Interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Use the formula for compound interest to calculate the amount of money that will be available when the CD matures -
\(A = P(1 + r/n)^(nt)\)
Where A is the amount of money available when the CD matures, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, the initial principal is $2000, the interest rate is 6%, and the CD will be held for 8 years (from Melissa's 6th to 14th birthday).
It is not given how many times per year the interest is compounded, so assume it is compounded annually.
Using these values in the formula -
\(A = $2000(1 + 0.06/1)^(1*8)A = $2000(1.06)^8A = $3187.69\)
Therefore, the value is obtained as $3187.69.
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four percent of the customers of a mortgage company default on their payments. a sample of 20 customers is selected. what is the probability that exactly two customers in the sample will default on their payments?
Answers
Using the Binomial probability distribution,
The probability that exactly two customers in the sample will default on their payments is 0.31..
We have given that,
4% of total customers a mortgage company default on their payments .
The probability of success i.e number of customers default on their payments (p) = 4%
= 0.04
The probability of failure (q) = 1-p = 1-0.04 = 0.06
Total number of customers in sample (n) = 20
we have to find out the probability that exactly two customers in the sample will default on their payments.
Using the Binomial probability distribution,
P(X=x)= ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾
the required probability is P(X= 2 )
Now, P(X= 2) = ²⁰C₂(0.04)²(0.06)¹⁸
=> P(X=2) = 190 × 0.0016 × 1.0155 = 0.31
Hence, the required probability is 0.31
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Elenas parents added $5. 50 of her account. She now has less than $20 of her balance
Answers
Elena's starting balance was $14.50. After her parents added $5.50, her new balance was $20.00. By subtracting $20 from her new balance, we can determine that she now has less than $20 remaining in her account.
The starting balance of Elena's account was $14.50. After her parents added $5.50, her new balance is $20.00. This can be expressed in the following equation:
14.50 + 5.50 = 20.00
To find out how much less than $20 she has, we can subtract $20 from her new balance amount:
20.00 - 20.00 = 0.00
Therefore, Elena has less than $20 remaining in her account.
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Simple geometry equation
Answers
Answer:
106 or 4x+18
Step-by-step explanation:
Since Ray QR is a bisector you can determine that PRQ and QRS are equal angles (def. of a bisector). Then, what I chose to do is graph them and find where they intercept which was 22. We now know 22 is x so we can substitute it into the equation and solve to deterine that our answer is 106.
x+ 31 = 3x-13
-x. -x
31=2x-13
+13.. +13
44-=2x
—. .—
2. 2
22= x
Which is greater, 11/16 or 24/32?
Answers
24/32=0.75
0.75 is greater than 0.6875 so 24/32 is greater than 11/16
Answer:
24/32
Step-by-step explanation:
24/32 is the answer because:
1) We should first try to see if we can find a common denominator so it is easier to compare and find the larger number
2) The common denominator is 32 because 16 multiplied by 2 is 32 and 11 multiplied by 2 is 22. The new fraction is 22/32
3) Finally, compare 22/32 and 24/32, we know that 24 is bigger than 22. Therefore, 24/32 is greater than 11/16
Hope this helps!
It is the assumption of staff at NSA that 96% of students will graduate on time. Last year 150 out of 154 students graduated on time. What is the p-value and z-score of the graduation rate at NSA?
a. p = .625, z = .73
b. p = .73, z = .625
c. p = .96, z = 1.976
d. p = 1.10, z =0.986
Is the staff at NSA correct in assuming that 96% of NSA students will graduate on time?
Yes
No
Answers
please help me
the denominator only
Answers
Answer:
6/51/33/1013/549/201/15Step-by-step explanation:
You cannot subtract JUST a denominator. The subtraction sign is lower down because of the odd printing just like the equal signs.
1. The first thing you have to do is change this from a mixed fraction into an improper fraction in order to subtract. This becomes:
12/5 -6/5 (This is done by multiplying the large number by the denominator and adding it to the exsisiting numerator)12-6=6 therefore the answer is 6/52. This one requires you to multiply your denominator so that it is the same for both fractions. The least common denominator (LCD) for these fractions is 12
7/12-1/4(3) (Because 3x4 is 12 which is the LCD)7/12-3/12 = 4/12 (this can be simplified)1/33. This is fairly straight-forward the denominators already match so just subtract the numerators
6/10-3/10= 3/104. Because we have a full number we must make it into a fraction in order to subtract it and also turn the mixed fraction into an improper fraction
We'll start with the mixed because we've done that before multiplying 4 by 5. Add to that 20 the 2 from the original fraction to get 22/ 5For the full number use the denominator of the number to determine the fraction. Multiply the full number by the denominator (5) to get 35 and place a 5 underneath and call it a day.Therefore: 35/5-22/5=13/55. This problem requires multiple steps the first would be to make improper fractions then get a LCD and then of course subtract.
(6x8)+2=48+2=50 --> 50/8(5x3)+4=15+4=19 --> 19/5LCD 5:5,15,20,25,30,40 & LCD 8: 8,16,24,32,40 LCD=40(50/8)x5-(19/5)x8 = 250/40-152/40 = 98/40 This can be simplified49/206. For this we will use another LCD.
LCD 3: 3,6,9,12,15 LCD 5: 5,10,15 LCD=15(2/3)x5-(3/5)x3 = 10/15-9/15 = 1/15what percent of 74 is 86
Answers
Answer:
about %55
Step-by-step explanation:
You can find the answer by dividing the percent number by the whole number:
74/86 ≈ %55
A choir teacher is dividing 12 sopranos and 9 altos into singing groups. He wants each group to have the same combination of sopranos and altos, with no singers left over. What is the greatest number of groups he can make?
Answers
Answer:
3 groups
Step-by-step explanation:
Sopranos = 12
Altos = 9
Find the highest common factor of 12 and 9
12 = 1, 2, 3, 4, 6, 12
9 = 1, 3, 9
The highest common factor of 12 and 9 is 3
Therefore, the choir teacher can only have 3 groups
12 sopranos / 3 groups
= 4 sopranos per group
9 Altos / 3 groups
= 3 altos per group
Each of the 3 groups Will have 4 sopranos and 3 altos each
which statement is not guaranteed to be true
Answers
Answer:
Diagonal AC is NOT perpendicular to diagonal BD
Step-by-step explanation: