Answer:
x^2 -8x -5 = -3
x^2 -8x -2 = 0
We complete the square by:
1) Moving the "non X" term to the right:
x^2 -8x = 2
2) Dividing the equation by the coefficient of X²
The coefficient of x is 1 so we don't do anything
3) Now here's the "completing the square" stage in which we:
• take the coefficient of X
that is -8
• divide it by 2
-8 ÷ 2 = -4
• square that number
-4*-4 = 16
• then add it to both sides of the equation.
x^2 -8x +16 = 2 +16
That becomes
(x -4)^2 = 18
we take the square root of both sides:
(x -4) = sqr root (18)
x1 = sqr root (18) +4
AND
(x+4) = sqr root (18) -4
x1 = sqr root (18) +4 = 4.2426406871 + 4 = 8.2426406871
x2 = sqr root (18) -4 = = 4.2426406871 - 4 = .2426406871
Step-by-step explanation:
A box of coins contains nickels, dimes and quarters. The value of the coins is $4.00. If there were 3 times as many nickels, half as many dimes, and 6 more quarters, the value of the coins would be $5.50. How many quarters are in the box?
There are 4 quarters in the box of coins.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
A box of coins contains nickels, dimes and quarters.
The value of the coins is $4.00.
And, There were 3 times as many nickels, half as many dimes, and 6 more quarters, the value of the coins would be $5.50.
Now,
Let number of nickels in a box = n
Number of dimes = d
Number of quarters = q
Here, The value of the coins is $4.00.
Hence, We get;
⇒ 5n + 10d + 25q = 400 cents .... (i)
And, There were 3 times as many nickels, half as many dimes, and 6 more quarters, the value of the coins would be $5.50.
Hence, we get;
⇒ 3(5n) + 5d + 25(q+6) = 550 cents
⇒ 15n + 5d + 25q + 150 = 500
⇒ 15n + 5d + 25q = 350 .. (ii)
After solving equation (i) and (ii), we get;
Number of nickels in a box = n = 12
Number of dimes = d = 24
Number of quarters = q = 4
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Hi! I have trouble with these type of questions, what is 3.478 divided by 37?
Answer:
0.094
Step-by-step explanation:
3.478 ÷ 37 = 0.094I hope this helps!
"Samuel spent $16 for 4 erasers and 2 pencils. Alva spent $10.50 for 3 erasers and 1 pencil. How much do 5 erasers and 3 pencils cost?"
4
A line has slope 3. Through which two points could this line pass?
a. (24, 19), (8, 10)
b. (10,8), (16, 0)
C. (28, 10), (22, 2)
d. (4, 20), (0, 17)
1. On a given day, Tyler runs twice as fast as his brother Ian on the local track. In one race, Ian gets a 330 meter head start, and they start running at the same time. After 21 seconds, Tyler catches up to Ian. Let x represent Ian’s rate (in meters/second). Write and solve an equation to find the rate that Ian runs. (Remember that distance = rate x time.) If you get a decimal answer, round to the nearest tenth.
Write the equation (2pts):
Solve the equation to find Ian’s rate (x) (2 pts):
Answer:
imma say 184 rpm
Step-by-step explanation:
-9=2x+9y what is the answer
Answer:
9y= -9-2x
y=-(2/9)x-1
Step-by-step explanation:
I'm not sure what to do about this problem, so please help me out.
Answer:
21
Step-by-step explanation:
Let the three consecutive integers be;
x , x + 1 and x + 2:
The sum of squares of the two smaller numbers:
The two smaller numbers are x and x+ 1
Sum of their squares:
x² + (x+1)²;
x² + x² + 2x + 1 = 2x² + 2x + 1
It is 45 more than the square of the larger number:
Larger number = x + 2
(x+2)² = x² + 4x + 4
45 more;
x² + 4x + 4 + 45 = x² + 4x + 49
Both are equal:
2x² + 2x + 1 = x² + 4x + 49
2x² - x² + 2x - 4x + 1 - 49 = 0
x² - 2x - 48 = 0
x² - 6x + 8x - 48 = 0
x(x - 6) + 8(x - 6) = 0
(x + 8)(x-6) = 0
x + 8 = 0 or x - 6 = 0
x = -8 or x = 6
We choose x = 6 because it makes the solution true as a positive integer
Sum of the three numbers:
x + x + 1 + x + 2 = 6 + 6 + 1 + 6 + 2 = 21
g(x) = x + 2h (x) = x^2 – 4Find: g(x) • h(x)
See attachment for math work and answer.
Which best describes independent events?
The results of all events have different individual probabilities.
The results of any previous events affects the probability of future events.
The results of all events have the same individual probability.
The results of all previous events do not affect the probability of future events.
The statement (D) The results of all previous events do not affect the probability of future events best describes independent events option (D) is correct.
What is independent events?An independent event is one that is unaffected by other events. The occurrence of one event has no bearing on the other.
We have a statement:
Which best describes independent events?
As we know from the definition of independent events, the events that is unaffected by other events.
Also, the probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Thus, the statement (D) The results of all previous events do not affect the probability of future events best describes independent events option (D) is correct.
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Please answer all ASAP (no explanation needed), extra points and will mark brainliest (don’t comment “idk” it’s not helpful :(, u will be reported)
1. After buying some bottle caps for $81.74, Peter has $6.74 left. How much money did Peter have to begin with?
2. Henry has $97.95 and Marilyn has $74.71. How much more does Henry have than Marilyn?
3. Helen has $84.51 and Joseph has $17.93. How much money do they have together?
4. Emily has $27.09 and David has $6.17. How much more does Emily have than David?
5. Cynthia has $74.45 and Amy has $38.44. How much more does Cynthia have than Amy?
6. After buying some Skittles for $71.18, Irene has $17.36 left. How much money did Irene have to begin with?
7. Steven has $98.25 and Joe has $4.97. How much money do they have together?
8. Ralph starts with $74.53 and spends $4.97 on candies. How much money does Ralph have left?
9. Christopher has $26.34 and Beverly has $4.15. How much money do they have together?
10. Eugene gives $2.89 to Sarah. If Eugene started with $56.03, how much money does he have left?
11. Keith has $56.49 and Theresa has $3.43. How much money do they have together?
12. Peter gives $20.85 to Nancy. If Peter started with $84.26, how much money does he have left?
13. Bruce has $67.72 and Charles has $29.62. How much more does Bruce have than Charles?
14. Sandra gives $9.13 to Stephen. If Sandra started with $11.66, how much money does she have left?
15. After buying some marbles for $93.52, Donald has $6.35 left. How much money did Donald have to begin with?
Krista invested money in the stock of a foreign company. Lately, the government of the country where the company is based introduced new tax laws and fiscal policies. What type of risk does Krista face as an investor? A. Credit risk B. Inflationary risk C. Legislative risk D. Liquidity risk
Answer:
C
Step-by-step explanation:
legislative risk is when the government could significantly alter the business prospects of one or more companies.
To plot the point (5, -3) you would move up 5, then left 3.
1. False
2. True
Answer:
False
Step-by-step explanation:
Positive in the X-axis is always to the right and negative is left and in the Y-axis positive is up and negative is down
what odd number is less than 12
Answer:
theirs many 1, 3, 5, 7, or 9.
Step-by-step explanation:
Answer:
1, 3, 5, 7, 9, 11
Step-by-step explanation:
I Hope That This Helps! :)
Find three consecutive even integers suche
that one half of their sum is between 15
and 21.
9514 1404 393
Answer:
10, 12, 14 and maybe {8, 10, 12} and {12, 14, 16}, depending on the meaning of the question
Step-by-step explanation:
If x is the middle one, then their sum is 3x. You want ...
15 < 3x/2 < 21 . . . . assuming "between 15 and 21" does not include 15 or 21
30 < 3x < 42
10 < x < 14
The only even integer in that range is 12, so the three integers are ...
10, 12, 14 . . . . . half their sum is 18
__
We have used <, rather than ≤ in the above solution. This assumes that "between" does not include the values at the end of the range. If those values are included, then two additional solutions are possible: {8, 10, 12} and {12, 14, 16}. For the first set, the half-sum is 15; for the second set, the half-sum is 21.
Solve the inequality:
||x−4|+3|≤5
Answer:
inequality form:
x<17
interval notation:
(-∞,17]
Step-by-step explanation:
Answer:
thanks
Step-by-step explanation:
The function f(x) = 4x + 5 has domain 0sxs 50. What is its range?
The range of the function is
9514 1404 393
Answer:
range: 5 ≤ f(x) ≤ 205
Step-by-step explanation:
You can put the extreme values of x in this linear function to see its range:
f(0) = 4·0 +5 = 5
f(50) = 4·50 +5 = 205
The range is 5 ≤ f(x) ≤ 205.
Can you show me the answers step by step please?
Answer:
3490
Step-by-step explanation:
What are all of the factors pairs of 25
Answer:
Step-by-step explanation:
1, 5, 25 are the factor pairs and the multiples are 50.
Factor pairs of 25 :
1 , 5, 25
Given ,
Factors of 25 .
Now,
Factor is a number that divides the given number completely and remainder will be zero .
So,
25 = 5*5
25 = 5²
And,
1 and the number itself is an universal factor of any number .
Thus the factors of 25 are:
1, 5 , 25 .
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What numbers are missing from these patterns?
plz helpp fast (10 points)
Parker the dog is 2 feet 6 inches long. There are 2.54 centimeters in 1 inch. How many centimeters is Parker the dog?
Answer:
Parker the dog is 76.2 centimeters long.
Step-by-step explanation:
Parker the dog is 2 feet 6 inches long. There are 2.54 centimeters in 1 inch. How many centimeters is Parker the dog? 2 feet = 12 inches. 2(12) + 6 = 30
30(2.54) = 76.2.
Please let me know if you have anymore questions.
Good Luck! :)
1 foot = 12 inches
1 inch = 2.54 centimeters
1 foot = 30.48 centimeters
2 x 30.48 = 60.96
6 x 2.54 = 15.24
60.96+15.24=76.20
Parker the Dog is 76.20 centimeters tall.
You have $427 in your bank account and need to pay some bills.The electric bill is $62. The cable bill is $78 and the phone bill is $54. How much will you have in your account after you pay these bills?
Answer:
233
Steps:
427-62=365
365-78=287
287-54=233
here is the correct answer
Use the figure to decide the type of angle pair that describes <6 and <4.
Answer:
i think it is corresponding angle
science pls answer I give brainliest
Answer:
b
Step-by-step explanation:
because air is cooler in the mountains so it'll be cold not humid
a scaled drawing of a rectangular parking lot is 6 inches long and 5 inches wide. the actual parking lot is 72 feet long what is the area of the actual parking lot in square feet
$1000 is invested in an account at interest rate r=0.045, compounded continuously. Find the time required for the amount to double
Answer:
The formula you'll need is:
Years = ln (total / principal) / rate
ln means natural log
Years = ln (2,000 / 1,000) / .045
Years = ln (2) / .045
Years = 0.69314718056 / .045
Years = 15.4033
Step-by-step explanation:
A researcher wishes to estimate, with % confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within % of the population proportion.
Answer:
The minimum sample size required is 1068.
Step-by-step explanation:
The complete question is:
A researcher wishes to estimate, with 95% confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within 3% of the population proportion.
No preliminary estimate is available. Find the minimum sample size needed.
Solution:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
[tex]MOE=0.03\\\text{Confidence level}=95\%[/tex]
Assume that the sample proportion is 50%.
The critical value of z is, 1.96.
Compute the minimum sample size required as follows:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\cdot \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\times\sqrt{0.50(1-0.50)}}{0.03}]^{2}\\\\=1067.1111\\\\\approx 1068[/tex]
Thus, the minimum sample size required is 1068.
what is the composition f•g if f(x)=4-2x and g(x)=3x^2
Answer: 4-6x^2
Step-by-step explanation:
f•g = f(g(x))
f(g(x)) = 4-2(3x^2) = 4-6x^2
Solve the following equation.
150 - x - 2x = 120 +2x
Answer:
X = 6
Step-by-step explanation:
150 - 3x = 120 + 2x
150 = 120 + 5x
30 = 5x
6 = x
x = 6
The solution to the equation is x = 6.
To solve this equation 150 - x - 2x = 120 +2x , we need to isolate the variable x.
To simplify the equation ;
Distribute the negative sign to the terms inside the parentheses:
150 - x - 2x = 120 + 2x
150 - 3x = 120 + 2x
Combine like terms on both sides of the equation:
-3x - 2x = 120 - 150
-5x = -30
Divide both sides of the equation by -5 to solve for x:
-5x / -5 = -30 / -5
x = 6
Therefore, the solution to the equation is x = 6.
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A line with a positive slope is parallel to one of the lines shown. What is its slope? Use the graph shown below.
Answer:
2/5
Step-by-step explanation:
first select the line that is positive which is the purple one
slope = change in y / change in x
two clear points are (0,2) and (5,4)
so you do y2-y1 / x2-x1
=(4-2)/(5-0)
=2/5
so the slope is 2/5
What is 59 rounded to the nearest half?
Answer:
30
Step-by-step explanation:
59 divided by 1/2 or 2 is 29.5 which round up to 30
The round-off to the number 59 is 59.5 to the nearest half.
When a number is rounded off, it is approximated to a specific level of precision or place value. You may simplify or make a number easier to work with while still retaining a fair degree of precision by rounding it off.
To round a number to the nearest half, find the nearest half-number (0.5, 1.0, 1.5, etc.). The decimal place immediately to the right of the half is taken into account since we are trying to get the closest half in this situation.
The digit after the decimal point in the number 59 is 9. We round up since 9 is larger than 5, not 5. Consequently, the outcome is 59.5 after rounding 59 to the closest half.
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