Find the solutions to the equation below.
Check all that apply.
2x2 + 7x + 3 = 0
A. X= 4
B. X=-3
C. X= 7
D D. x= 3
O E. X = 2
F. X=-1/2
2x²+7x+3=0
2x²+(1+6)x+3=0
2x²+1x+6x+3=0
x(2x+1)+3(2x+1)=0
(2x+1)(x+3)=0
2x+1=0. x+3=0
2x=-1. x=-3
x=-1/2
3. Resuelve las siguientes multiplicaciones de fracciones. Observa el ejemplo
450* -} - - 150
255 -
292
2 *
-2942
876-73
12
10
?? * 1 -
17
3
* * * *
Answer:
idnnnvnvnvnv
Step-by-step explanation:
hahnndndndnd
Find [a * b] for the following pairs of vectors
We have to calculate the a x b for the following vectors.
We will have the following vector as result of a x b:
\(a\times b=\begin{bmatrix}i & j & k \\ a_x & a_y & a_z \\ b_x & b_y & b_z \\ \end{bmatrix}=(a_y\cdot b_z-a_z\cdot b_y)\cdot i+(a_z\cdot b_x-a_x\cdot b_z)\cdot j+(a_x\cdot b_y-a_y\cdot b_x)\cdot k\)The resulting vector will be perpendicular to both a and b.
i) If a = (0,7,0) and b = (2,-4,7), we can calculate c as:
\(\begin{gathered} c=a\times b \\ c=(a_y\cdot b_z-a_z\cdot b_y)\cdot i+(a_z\cdot b_x-a_x\cdot b_z)\cdot j+(a_x\cdot b_y-a_y\cdot b_x)\cdot k \\ c=(7\cdot7-0\cdot(-4))\cdot i+(0\cdot2-0\cdot7)\cdot j+(0\cdot(-4)-7\cdot2)\cdot k \\ c=49\cdot i+0\cdot j+(-14)\cdot k \\ c=(49,0,-14) \end{gathered}\)ii) If a = 4*i+7*k = (4, 0, 7) and b = -6*i + 2*j = (-6, 2, 0), then c will be:
\(\begin{gathered} c=a\times b \\ c=(a_y\cdot b_z-a_z\cdot b_y)\cdot i+(a_z\cdot b_x-a_x\cdot b_z)\cdot j+(a_x\cdot b_y-a_y\cdot b_x)\cdot k \\ c=(0\cdot0-7\cdot2)\cdot i+(7\cdot(-6)-4\cdot0)\cdot j+(4\cdot2-0\cdot(-6))\cdot k \\ c=-14i-42j+8k \\ c=(-14,-42,8) \end{gathered}\)Answer:
i) c = 49i - 14k = (49,0,-14)
ii) c = - 14i - 42j + 8k = (-14, -42, 8)
[Note: you can express it either way, you have to pick one option to input the answer]
Your basketball team scored 4 fewer than twice as many points, x
, as the other team.
a. Write an expression for the number of points your team scored.
expression:
b. The other team scored 24 points. How many points did your team score?
Your team scored
points.
a. The expression for the number of points scored by your team is 2x - 4.
b. Your team scored 24 points.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
a. As per the given situation,
The expression for the number of points your team scored can be written as 2x - 4.
b. If the other team scored 24 points, we can substitute that value into the expression we found in part (a) and solve for x:
2x - 4 = 24
2x = 28
x = 14
Therefore, your team scored 2x - 4 = 2(14) - 4 = 24 points.
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Sebastian is going to choose design elements that include color, pattern, font, and image for the design of a sweatshirt for his dance team. There are 10 colors, 14 patterns, 12 fonts, and 9 images for him to choose from. (He will choose only one of each.)
How many different sweatshirt designs are possible?
Answer:
Sebastian is going to choose design elements that include color, pattern, font, and image for the design of a sweatshirt for his dance team. There are 10 colors, 14 patterns, 12 fonts, and 9 images for him to choose from. (He will choose only one of each.)
How many different sweatshirt designs are possible?
Step-by-step explanation:
the answer is 4320
There are
\(10 \times 14 \times 12 \times 9\)
different ways to design his sweatshirt.
Filomena applies the commutative property to the product. (7/15)⋅(−11)⋅(30) Which expression illustrates the commutative property applied to the product? A (7/15)⋅(30)⋅(−11) B (7/15)⋅[(−11)⋅(30)] C (7/15)⋅(−11)⋅(30) D[(7/15)⋅(−11)]⋅(30)
a x b = b x a
a x b x c = a x c x b = b x c x a
Note: " . " in the question also means "x" (multiplication)Applying commutative property to the question:(7/15)⋅(−11)⋅(30)
(7/15) ⋅ (−11) ⋅ (30) = (7/15) . (30) . (11)
The values interchanged are: 11 and 30. The result of the multiplication remains unchanged.
Option A is the correct answer.
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Paula received her bank statement at the end of the month. The details of her transactions are shown below.
Bill Payment
Check Deposit
Interest Payment
Online Purchase
Which is the transaction with the smallest magnitude?
OA. -$67.45
OB. -$50.87
OC. $35.09
OD. $59.56
-$50.87
$59.56
$35.09
-$67.45
The transaction done by Paula with the smallest magnitude is option A: -$ 67.45.
What is a transaction?
An executed contract between a buyer and a seller to trade goods, services, or financial assets in exchange for money is known as a transaction. The phrase is also frequently used in business accounting. This straightforward definition might be challenging in corporate bookkeeping.
The bank statement of Paula shows the following transactions -
She spent -$ 50.87 on Bill Payment.
She spent $ 59.56 on Check Deposit.
She spent $ 35.09 on Interest Payment.
She spent -$ 67.45 on Online Purchase.
It can be seen that Paula's transaction with largest magnitude or largest sum of money is on Check Deposit which is $ 59.56.
The second highest transaction of Paula is on Interest Payment which is $ 35.09.
The third highest transaction of Paula is on Bill Payment which is -$ 50.87.
The least amount of transaction done by Paula is on Online Purchase which is -$ 67.45.
Therefore, the transaction of -$ 67.45 is the lowest.
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state , giving reasons, which of the following if meaningless:
a. (-12, 0 ]
b. ( 1, -13 ]
Both of the intervals given are meaningful intervals in mathematics, but they are different types of intervals.Therefore, the interval (1, -13] is meaningless because it does not contain any real numbers.
What is intervals?An interval is a number or range of values between two endpoints.
The endpoints can be included or excluded from the interval, and the interval can be open, closed, or half-open depending on whether the endpoints are included or excluded.
The interval (-12, 0] is a closed interval, which includes the endpoint 0, and all real numbers between -12 and 0.
The square bracket indicates that the endpoint 0 is included in the interval.
The interval (1, -13] is an empty interval, which includes no real numbers, since there is no number that is greater than 1 and less than or equal to -13. This interval is meaningless because it does not contain any numbers.
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Explain why there is no solution to the simultaneous equations x + y = 5 and x + y = 7
The same quantity, x+y, cannot be equal to 2 different values, in this case 5 and 7.
you sailed 0.032 units to the left and found treasure at 0.248 units find where the ship started
242. ___________ statistics summarize numbers and _____________ statistics determine whether the results are significant.
Descriptive statistics summarize numbers, and inferential statistics determine whether the results are significant.
Descriptive statistics are used to summarize and describe a set of data. They include measures such as the mean, median, and standard deviation, which provide information about the central tendency and spread of the data.
Inferential statistics, on the other hand, are used to draw conclusions about a population based on a sample of data. They include tests such as the t-test and ANOVA, which are used to determine whether the results of a study are statistically significant, or whether they could have occurred by chance.
So, Descriptive statistics summarize numbers, and inferential statistics determine whether the results are significant.
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A police officer invested $5,000 in a treasury bond paying 4.75% interest compounded quarterly. After 25 years, the value of the bond will be $16,280.08. If the police officer's investment was compounded continuously instead of four times per year, what would be the difference in the account balances after 25 years?
Answer:
114.29
Step-by-step explanation:
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answer: x < 3
Explanation: Once you reach step 3, you divide -2 on both sides. -2x cancels out, and -6 divided by -2 is 3
To which subsets of 3/4 belong.
The given number 3/4 which subsets belong to a rational number. The answer is option (A) rational numbers.
As per the question,
The given number is 3/4.
As we know that a rational number is one that can be written as a ratio of two integers, where the denominator is greater than zero.
The result is rational because 3/4, can be expressed as a ratio of two integers can be 3/4 of two integers, a numerator 3, and a denominator 4 (which is a non-zero).
So, the given number 3/4 which subsets belong to a rational number.
Therefore, the correct answer is option (A) rational numbers.
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The complete question is as follows:
To which subset of real numbers does the number 3/4 belong?
A. rational numbers
B. irrational numbers
C. whole numbers, integers, rational numbers
D. whole numbers, natural numbers, integers
If you draw a card from a standard deck of 52 playing cards, what is the probability that it is a heart or a diamond?
Answer:
1/2
Step-by-step explanation:
In a deck of cards, there are 13 hearts and 13 diamonds
13+13 = 26 hearts or diamonds
P( hearts or diamonds) = numbers of hearts or diamonds / total
=26/52
= 1/2
Rotation 90° clockwise about the origin
N
O
G
An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.
What is a rotation?In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;
(x, y) → (y, -x)
Point N = (-4, -1) → Point N' (-1, 4)
Point O = (-4, -3) → Point O' (-3, 4)
Point G = (0, -1) → Point G' (-1, 0)
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|-3|>2 true or false
Answer:
True
Step-by-step explanation:
l-3l>2
3>2= True
Write 0.000000624 in scientific notation
Answer:
6.24 x \(10^{-7}\)
Step-by-step explanation:
0.000000624 in scientific notation is 6.24 x \(10^{-7}\)
Answer:
Step-by-step explanation:
The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.
Use the distributive property
Please help me to solve this question
Answer:
5
Step-by-step explanation:
what is the difference of twice a number and 3 is 11
Answer:
2x - 3 = 11
x = -21
Step-by-step explanation:
Select the coordinates of two points on the line y = 8.
At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds
Which algebraic expression represents this phrase?
the product of 50 and the number of employees
• A. 50
n
• B. 50 • n
• C. 50 + n
• D. 50 - n
Answer: B
Step-by-step explanation:
'Product' means to multiply, in this case, we are multiplying 50 and n.
A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 5% margin of error at a 99% confidence level, what size of sample is needed
Answer:
A sample size of 664 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).
The margin of error is:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
99% confidence level
So \(\alpha = 0.01\), z is the value of Z that has a pvalue of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).
If the candidate only wants a 5% margin of error at a 99% confidence level, what size of sample is needed
A sample size of n is needed.
n is found when M = 0.05.
We have no estimate, so we use \(\pi = 0.05\). Then
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.05 = 2.575\sqrt{\frac{0.5*0.5}{n}}\)
\(0.05\sqrt{n} = 2.575*0.5\)
\(\sqrt{n} = \frac{2.575*0.5}{0.05}\)
\((\sqrt{n})^{2} = (\frac{2.575*0.5}{0.05})^{2}\)
\(n = 663.1\)
Rounding up
A sample size of 664 is needed.
If cosθ=-1/3 and θ is in quadrant III, find the exact values of sinθ,tanθ,secθ,cscθ,and cotθ. You can use the identities or x, y, r.
The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
Given: cosθ = -1/3 and θ is in quadrant III.
This means that sinθ = ± √(1 - (cosθ)2).
We know that cosθ is negative, so sinθ will be negative.
Therefore, sinθ = -√(1 - (-1/3)2 )
sinθ = - √(1 - 1/9)
sinθ = -√8/9
tanθ = sinθ/cosθ
tanθ = (-√8/9)/-1/3
tanθ = √8/3
secθ = 1/cosθ
secθ = 1/-1/3
secθ = -3
cscθ = 1/sinθ
cscθ = 1/-√8/9
cscθ = -√9/8
cotθ = cosθ/sinθ
cotθ = -1/3/-√8/9
cotθ = √9/8
Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
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Duval went to bat 80 times
Answer:
Duval got a hit 30% of the time during the season. The total number of hits was 24. 24/80 is 0.30. Multiply by 100 to obtain the percentage. 0.30*100 = 30%.
Step-by-step explanation:
Which of the following is the equation of a line with a slope of -5/9
Answer:
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Step-by-step explanation:
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● Blondies are squares with 3 inch sides. ● Brownies are squares with 6 inch sides. ● The tray that displays the blondies and brownies has an area of 648 square inches and is completely full. If she has 4 rows of blondies and 4 rows of brownies, what fraction of the area of the tray, in square inches, is blondies? Show your work.
The fraction of the area of the tray occupied by the blondies is 1/9.
To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.
Let's calculate the area of each individual blondie:
The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.
Now, let's calculate the area occupied by the blondies in each row:
Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.
So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.
Next, let's determine the area occupied by the brownies:
The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.
Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.
Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.
Now, let's calculate the total area of the tray:
Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:
Total area of the tray - Area occupied by the brownies = Area occupied by the blondies
648 square inches - 576 square inches = 72 square inches.
So, the fraction of the area of the tray occupied by the blondies is:
Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:
72 square inches / 648 square inches = 1/9.
Therefore, the blondies' percentage of the tray's surface area is 1/9.
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Examine the following typical corporate bond listing:
In the name column, NYTel is the abbreviated name of the company (New York Telephone) issuing the bond. What was the closing price of the bond? What was the dollar amount? (See attachments)
a. 101 3/4; $101,750
b. 7 1/4; $7250
c. 101 3/4; $1017.50
d. 107 1/4; $1072.50
Answer:
C. 101 3/4; $1017.50
Step-by-step explanation:
Correct on E2020!
8% of the employees at a shop work part-time.
If there are 4 part-time employees at the shop, how many employees are there in total?
There are 50 employees in total
How to determine the total employee?The given parameter is:
Part-time = 8% of total employee
Rewrite as:
Part-time = 8% * total employee
There are 4 part-time employees.
So, we have:
8% * total employee = 4
Divide both sides by 8%
total employee = 50
Hence, there are 50 employees in total
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