Answer:
19
Step-by-step explanation:
9+10=19.
Answer:
19.
Step-by-step explanation:
9 plus 10 = 19.
I know someone else already answered this simple question first but, if you want to help me out and give me brainliest that'd be nice, that's the only reason I'm answering it.
Doe has 2 3/8 pounds of hamburger meat. He is making 1/4 pound hamburgers .Does doe have enough meat to make 10 hamburgers
Please help!!!! It’s urgent
Which of the following rational functions is graphed below?
-10
10-
-10
1
A. F(x) = 1/x(x+3)
B. F(x)= x/x+3
C. F(x)= 3/x
D. F(x)= 1/x(x-3)
Answer:
the answer is D. F(x) = 1/x(x-3)
Step-by-step explanation:
What is the area of the polygon below?
Answer:
C. 26 ft²
Step-by-step explanation:
You can view the shape as a rectangle of 4.25x4 with two triangles attached to it. Those triangles each have a width of (8.75-4.25)/2 = 2.25 ft.
Together they form a rectangle of 2.25x4, so the balcony area can be calculated as the area of a rectangle of (4.25+2.25)x4 = 6.5x4 = 26.
Answer:
C
Step-by-step explanation:
the figure is a trapezoid
the area (A) of a trapezoid is calculated as
A = \(\frac{1}{2}\) h (b₁ + b₂ )
where h is the perpendicular height between bases b₁ and b₂
here h = 4 , b₁ = 8.75 , b₂ = 4.25 , then
A = \(\frac{1}{2}\) × 4 × (8.75 + 4.25) = 2 × 13 = 26 ft²
A company produced in the first quarter 6,905 pieces in the second quarter the same company produced 795 pieces more than in the first quarter under these conditions how many pieces did the company produce in the first semester?
Answer: 14,605 pieces.
Step-by-step explanation:
In the second quarter, the company produced 795 pieces more than in the first quarter.
So, the total pieces produced in the second quarter can be calculated as:
6905 + 795 = 7700
The total pieces produced in the first semester (two quarters) can be calculated as:
6905 + 7700 = 14,605
Therefore, the company produced 14,605 pieces in the first semester.
The number of pieces the company produced in the first semester was 14,605 pieces.
How many?The question asks to calculate how many pieces a company produced in the first semester, considering the production of two quarters.
In the first quarter, the company produced 6,905 pieces, as indicated in the question.
Already in the second quarter, the company produced 795 more pieces than in the first quarter, which means that the production in the second quarter was:
6,905 + 795 = 7,700 pieces.
To know the company's total production in the first semester, just add the productions of the two quarters:
6,905 + 7,700 = 14,605 pieces
The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Maggie is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer.
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years.
r (number of years) 1 2 3 4
g(r) (amount in dollars) 8,972 8,074.80 7,267.32 6,540.59
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer.
The amount of money in account A is decreasing by 8% per year.
The account that recorded a greater percentage change in amount of money over the previous year is account B.
How to calculate the percentage?From the information, the amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Therefore, this shows a decrease and the percentage will be:
= 1 - 0.92
= 0.08
= 8%
The account that recorded a greater percentage change will be:
Account B = (8,972 - 8,074.80) / 8,972 × 100
= 10%
Therefore, B has a higher percentage.
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5. There are two kinds of products (called DA and GA) produced in your company every day. Alsothere are two kinds of materials (denoted by A and B) in need One DA costs one unit of A, one unit of B: one GA costs one unit of A, two units of B. You get $3000 when you sell one DA and $5000 for one GA. The supply of the two materials every day is 12,22. a)What is the maximal profit $ b) How many DA and GA should be produced every day to obtain this maximal profit? Number of DA = Number of GA
Answer:
a) $56000b) DA = 2, GA = 10Step-by-step explanation:
Given
DA = A + B ⇒ $3000GA = A + 2B ⇒ $5000Number of A = 12Number of B = 22We can see from the equations that
GA - DA = B ⇒ $2000 andA = $1000 and B = $2000 in terms of profitSo greater use of unit B brings greater profit. We don't want any unit is left over, so get this equation.
A + B = 12A + 2B = 22Is the equation set to indicate use of the units A and B
Solving we get
A = 2 and B = 10It this case all the units are used and profit is maximum
2*$3000 + 10*$5000 = $56000Number of DA = 2Number of GA = 10Obtaining a simple random sample is either not practical or inappropriate for these hypothetical research studies. Determine which alternative random sampling technique(s) would be appropriate to use for each study. In each case, choose techniques that are efficient and can be used on their own to acquire an unbiased population estimate. More than one technique may be appropriate for a study. Brianna wants to take a random sample of students at public four-year colleges in the United States to determine the mean number of social media posts students make per montlh It would be ???binlbr3???too expensive and time consuming for Brianna to obtain a list of all college students in the ???bin1br3???United States. She does not think the number of social media posts students make varies systematically ???binlbr3???among colleges Josh wants to obtain a random sample of students at his college to determine the proportion of students who have experienced clinical depression. He does not believe a simple random sample ???bi3br12???to be appropriate because he suspects that the proportion of students who have experienced clinical depression ???bin3br12???varies by gender Emily wants to obtain a random sample of students attending four-year colleges in the Boston metropolitan region to determine the average amount of time students spend at the library each semester. She cannot take a simple random sample because it would take too long for her to obtain ???bin2brl???a complete list of all students attending the 50 four-year colleges in the area. Also she suspects ???bin2br1???that the amount of time spent at the library will vary by major Answer Bank stratified sampling multistage sampling cluster sampling
1. Cluster sampling / Multistage sampling
2. Stratified sampling
3. Multistage sampling
Stratified sampling
Stratified sampling is a method of random sampling that divides the population into subgroups or strata and draws a random sample from each. Each subgroup or stratum is made up of items that share characteristics. This sampling technique is commonly used in human research and political polls.1. Cluster sampling / Multistage sampling
Explanation:Brianna can use cluster sampling and multistage sampling in this case because the number of social media posts students make per month is constant. As a result, the resulting cluster will be heterogeneous, and this method is less expensive and time consuming.
2. Stratified sampling
Explanation: Josh can use stratified sampling in this case. Because clinical depression differs by gender, he can create strata based on the gender of the students.
3. Multistage sampling
Explanation: Emily must use a multistage sampling technique to collect the students attending four-year colleges in the Boston metropolitan region to determine the average amount of time students spend at the library each semester in this case.
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Provide the reasons for the following proof.
The figure shows triangle W X Y with a segment X Z drawn from vertex X to point Z on side W Y.
Given: Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y
Prove: triangle W X Z is congruent to triangle Y X Z
Statements Reasons
1.Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y 1. Given.
2. angle W X Z is congruent to angle Y X Z 2. Definition of an angle bisector.
3. Segment X Z is congruent to segment X Z. 3. _____________
4. triangle W X Z is congruent to triangle Y X Z 4. _____________
A. Reflexive Property of congruent to; SSS
B. Symmetric Property of congruent to; SSS
C. Reflexive Property of congruent to; SAS
D. Symmetric Property of congruent to; SAS
SOMEONE HELP! PLEASE!
The two column proof showing that ΔWXZ ≅ ΔYXZ is as shown below
From the given triangle, we see that;
Given: WX ≅ XY, XZ bisects WXY
Prove: ΔWXZ ≅ ΔYXZ
The two column proof for the above is as follows;
Statement 1; WX ≅ XY, XZ bisects 2
Reason 1; Given
Statement 2: ∠WXZ ≅ YXZ
Reason 2; Angle bisector
Statement 3; XZ ≅ XZ
Reason 3: Reflexive property of congruence
Statement 4: ΔWXZ ≅ ΔYXZ
Reason 4: SAS Congruence Postulate
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NEED HELP ASAP GIVING BRAINLIEST!!!!!!!!!!!!!!!!!!
Answer:
option D
Step-by-step explanation:
\(sin^2 ( \frac{3\pi}{2}) + cos^2(\frac{3\pi}{2}) = 1\\\\( -1)^2 + 0^2 = 1\)
Explanation:
\(sin x = cos( \frac{\pi}{2} - x)\\\\sin(\frac{3\pi}{2}) = cos ( \frac{\pi}{2} - \frac{3\pi}{2})\\\)
\(=cos(\frac{\pi - 3\pi}{2})\\\\ =cos(\frac{2\pi}{2})\\\\=cos \ \pi\\\\= - 1\)
Therefore ,
\(sin^2( \frac{3\pi}{2}) = ( - 1)^2\)
Owen receives $10 and puts it into his saving account. He adds $0.50 to the account each day for a number of day, d, after that. He writes the expression 10+ 0.5(d-1) to find the amount of money in his account after d days. Which statement about his expression is true?
The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.
What does the expression 10+0.5(d−1) represent in Owen's savings account?The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.
By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.
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Note: If p(a) = 0 then (x - a) is a factor of p(x)
given that f(-1), f(-2) are zeros of f(x) find the missing values of these coefficients p, q
f(x) = x³ + px² - qx - 4
After finding the values of the coefficients factor and find the solutions of x1, x2 and x3.
Answer:
Since f(-1) = 0 and f(-2) = 0, we can set up two equations:
(-1)³ + p(-1)² - q(-1) - 4 = 0
(-2)³ + p(-2)² - q(-2) - 4 = 0
Simplifying each equation, we get:
-1 + p - q - 4 = 0
-8 + 4p - 2q - 4 = 0
Simplifying further, we get:
p - q = 5
2p - q = 6
Solving for p and q, we can add the two equations together to eliminate q:
p - q + 2p - q = 5 + 6
3p - 2q = 11
Then, we can substitute the value of q from the first equation into this equation to solve for p:
3p - 2(q + 5) = 11
3p - 2q - 10 = 11
3p - 2q = 21
3p - 2(5 + p) = 21
p - 10 = 7
p = 17
Substituting this value of p into either equation for q, we get:
q = p - 5 = 12
Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:
-1 | 1 17 -12 -4
|__ -1 -16 28
1 1 12
This gives us the factorization:
f(x) = (x + 1)(x² + x + 12)
To find the solutions, we can use the quadratic formula on the quadratic factor:
x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)
x = (-1 ± sqrt(1 - 48)) / 2
x = (-1 ± sqrt(-47)) / 2
x1 = (-1 + i(sqrt(47))) / 2
x2 = (-1 - i(sqrt(47))) / 2
Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.
Step-by-step explanation:
give me thanks for more! your welcome bud!
What is the range of the following numbers: 12,8,17,12,15,18,30
Answer: 22
Step-by-step explanation: The range is the difference between the greatest number in the data set and the least numbe rin the data set.
In this case, thats 30 - 8 or 22.
Answer:
22
Step-by-step explanation:
30 - 8 = 22
highest number - lowest number
1.44 /0.6 in long division
Answer:
The answer is 2.4
Step-by-step explanation:
because I division 1.44/0.6 its gave me 2.4
A company produces and sells solar panels for $520. The company's daily profit, P(x), can be modeled by the function P(x) = −6x2 + 156x + 1,000, where x is the number of $5 price increases for each solar panel. Use the graph to answer the questions. Graph of function p of x equals negative 6 x squared plus 156 x plus 1,000. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 1000), increases to the vertex at about (13, 2014), and decreases through about (31, 0). Part A: Identify the approximate value of the y-intercept. Explain what the y-intercept means in terms of the problem scenario. (3 points) Part B: Identify the approximate value of the x-intercept. Explain what the x-intercept means in terms of the problem scenario. (3 points) Part C: Identify the approximate value of the maximum of the function. Explain what the maximum of the function means in terms of the problem scenario. (4 points)
The maximum daily profit the company can earn is $2,350.
It is a set of points in a coordinate plane that represents the values of the function for different inputs.
The function P(x) = −6x² + 156x + 1,000 models the daily profit of the company, where x is the number of $5 price increases for each solar panel. The graph of the function has a vertex at approximately (15, 2350), which represents the maximum point on the graph.
Therefore, the maximum daily profit the company can earn is $2,350.
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Select the correct answer. Joel and Kevin are each putting money in a savings account to buy a new bicycle. The amount, in dollars, in Joel's savings account, x weeks after the start of the year, is modeled by function j. The amount of money in Kevin's account, at the same time, is modeled by function k. j(x) = 25 + 3x k(x) = 15 + 2x Which function correctly represents how much more money, in dollars, is in Joel's account than in Kevin's account x weeks after the start of the year? O A. (j − k)(x) = 40 + 5x (j − k)(x) = 40 + x (j-k)(x) = 10 + 5x (j-k)(x) = 10 + x O B. C. O D. Reset dtry Next
The correct answer is (j - k)(x) = 10 + x.
To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).
(j - k)(x) = (25 + 3x) - (15 + 2x)
= 25 - 15 + 3x - 2x
= 10 + x
This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.
Therefore, the correct function is (j - k)(x) = 10 + x.
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According to a survey conducted by the Association for Dressings and Sauces, 80% of American adults eat
salad once a week. A nutritionist suspects that this percentage is not accurate. She conducts a survey of
445 American adults and finds that 374 of them eat salad once a week. Use a 0.005 significance level to
test the claim that the proportion of American adults who eat salad once a week is equal to 80%.
Claim: Select an answer which corresponds to [Select an answer
Opposite: Select an answer which corresponds to [Select an answer
The test is: Select an answers
The test statistic is: z-
(to 2 decimals)
The Critical Value is: z-
Based on this we: [Select an answer
Conclusion: There Select an answer appear to be enough evidence to support the claim that the
proportion of American adults who eat salad once a week is equal to 80%.
Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.
How to solveTo test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.
Claim: p = 0.80
Opposite: p ≠ 0.80
The test is a two-tailed z-test.
Sample proportion (p) = 374/445 = 0.8404
Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)
z = 2.53 (rounded to 2 decimals)
Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.
Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.
Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.
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Find the average speed. A= d\t
9) 120 miles in 3 hours
Prove or disprove that the point lies on the circle centered at the origin
Answer:
Step-by-step explanation:
Compute.-3.53 + 46.78 =- 52.6 + (-84.7) =
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Compute -3.53 + 46.78
\(\begin{gathered} -3.53+46.78 \\ We\text{ write the one with the positive first and subtract the one with the negative},\text{ we have;} \\ 46.78-3.53=43.25 \end{gathered}\)STEP 2: Compute - 52.6 + (-84.7)
\(\begin{gathered} -52.6+(-84.7) \\ \text{We open the bracket by finding the product of the two signs} \\ +\times-=- \\ -52.6+(-84.7)\Rightarrow-52.6-84.7 \\ -52.6-84.7=-(52.6+84.7)---By\text{ factorization} \\ -(52.6+84.7)=-(137.3) \\ =-137.3 \end{gathered}\)Hence, the computations of the two questions are written below:
\(\begin{gathered} -3.53+46.78=43.25 \\ -52.=+(-84.7)=-137.3 \end{gathered}\)please answer a little quiet
IT is urgent
.Factorize: 4(x-y)^2 -9
.Evaluate : 1001×99
Answer:
1. (2x - 2y)² - 9
2. 99099
Step-by-step explanation:
We know the a+b formula :
(a-b)² = a² - 2ab + b²
1. 4(x-y)^2 -9
4(x² - 2xy + y²) - 9
4x² - 8xy + 4y² - 9
(2x - 2y)² - 9
2. 1001 × 99
= 99099
1001
× 99 ----------
9009
9009× ----------- 99099
Can someone help me? Please I’m not great at math. Everything is in the pictures.
Answer:
Hi There
Your answers are:
4) 12/3
-10) YES!
0/10) 0 (zero)
2 & 3/4 ) 11/4
10 & 1/2 ) 21/2
.3) 3/10
-.16) -4/ 25
3.17) 3 & 17 /100
.3 repeating ) YES
.16 repeating) 1/ 6
-1.2 repeating ) YES!
If a decimal does not terminate or repeat is is not a rational number
Step-by-step explanation:
For 4)
4/1 = 12/x
Ask yourself, how do i get from 4 to 12?
Multiply by 3! HOWEVER, whats done to the numerator MUST be done to the denominator!
4/1 * 3/3 = 12/3
For -10 )
-10/1 = -20/2
Simplify -20/2!
Divide -20 by 2 = -10
-10/1 = -10/1 YES!
For 0/10 )
When you have ZERO tenths, what does that equal? Zero!
For 2 & 3/4ths )
To change to an improper fraction, multiply the 2 by the denominator and add that to the numerator. Put that over the original denominator
(2*4 +3) / 4
8+3 / 4 = 11/4
For 10 & 1/2 )
Repeat what you did for 2& 3/4ths!
(10*2+1)/2
20+1/2
21/2
Bound
Figure 2.
Jenny would like to buy a new air conditioner for his home. As seen in Figure 2 above he has
3 types of brands that he can consider. The cash price for Daewoo is RM1,899, Daikin at a
price of RM1,699 and last choice is Mitsubishi at a price of RM1.999. He plans to make 18
monthly instalments, if he pays RM300 as a down payment for the air conditioner that he would
like to buy, find the interest charge for each brand if the interest rate is 4% based on originall
balance if he chooses to buy from Daikin, find the monthly instalment price and instalment
price that he needs to pay.
if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
How to determine the monthly instalment price and instalment price that Daikin needs to pay.Calculating the loan amount for each brand by subtracting the down payment from the cash price:
Loan amount for Daewoo = RM1,899 - RM300 = RM1,599
Loan amount for Daikin = RM1,699 - RM300 = RM1,399
Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699
Calculating the interest charge for each brand:
Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96
Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96
Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96
To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:
Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22
Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89
Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72
Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
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what is the sum 3/x+9+5/x-9
Answer:
\(\frac{8}{x}\)
Step-by-step explanation:
what is the sum 3/x+9+5/x-9
\(\frac{3}{x} + 9 + \frac{5}{x} - 9 =\) (add \(\frac{3}{x}\) and \(\frac{5}{x}\))
\(\frac{8}{x} + 9 - 9 =\) (solve 9 - 9 = 0)
\(\frac{8}{x}\) ( your answer)
The Heflin household is laying down mulch around their garden. The following image depicts the shape and dimension of their garden and the area they want to place the mulch:
A triangular garden inside a rectangular mulch area. The garden has a base of 6 feet and a height of 5 feet, and the mulch area has a height of 9 feet and a base of 12 feet.
If the mulch costs $0.59 per square foot, determine the total cost.
Answer:
$54.87
Step-by-step explanation:
The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.
The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.
The total area to be covered with mulch is 108 - 15 = 93 square feet.
The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.
Therefore, the total cost of the mulch will be $54.87.
vention 1 of 10
These box plots show daily low temperatures for a sample of days in two
different towns
TWINA
M
41
41
Town 1
1620
MI
D
10
152025 M3540
Degrees (0)
Which statement is the most appropriate comparison of the centers?
O A. The median temperature for both towns is 20"
B. The mean for town A, 30", is greater than the mean for town 8,25"
C. The median temperature for both towns is 30'
D. The median for town A, 30', is greater than the median for town B,
25
PREVIOUS
9 M
I really need this pls A certain brand of coffee costs $6.99 for 24.2 ounces. What is the unit rate? Enter your answer, rounded to the nearest cent, in the box.
Answer: $0.29 per oz, or 29 cents per oz.
Step-by-step explanation:
To find a unit rate, divide the numerator AND denominator by the denominator. The rate is $6.99/24.2 ounces. We will divide $6.99 by 24.2, and 24.2 ounces by 24.2. The answer will be $0.288843/1 ounce. If we round, it will be $0.29/1 ounce.
Two fire-lookout stations are 13 miles apart, with station B directly east of station A.
Both stations spot a fire. The bearing of the fire from station A is N35°E and the
bearing of the fire from station B is N49°W. How far is the fire from station B?
Choose the correct formula given below.
The distance between the fire and station B is 10.7miles
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The angle at A = 90- 35
= 55°
The angle at B = 90-49
= 41°
Angle at the fire = 180-(41+55)
= 180-96 = 84°
Using sine rule
sin84/13 = sin55/x
xsin84 = 13sin55
0.995x = 10.65
x = 10.65/0.995
x = 10.7 miles
Therefore the distance between the fire and station B is 10.7 miles.
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Dana bought 3 tuna
sandwiches and 3 fruit punch drinks. How much
money did Dana spend? How do you know?
Aidan bought 5 tuna sandwiches. How much
If the cost of 1 tuna sandwich be, x and 1 fruit punch drink be, y
The amount spent by Dana be, 3(x + y)
The amount spent by Aiden be, 5x
Given, Dana bought 3 tuna sandwiches and 3 fruit punch drinks.
Let the cost of 1 tuna sandwich be, x
the cost of 1 fruit punch drink be, y
So, the amount dana spent be,
3x + 3y = 3(x + y)
Now, Aiden bought 5 tuna sandwiches,
So, he spent 5x amount.
Hence, the amount spent by Dana be, 3(x + y)
the amount spent by Aiden be, 5x
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How do you do this question?
Answer:
a) -7/9
b) 16 / (n² + 15n + 56)
c) 1
Step-by-step explanation:
When n = 1, there is only one term in the series, so a₁ = s₁.
a₁ = (1 − 8) / (1 + 8)
a₁ = -7/9
The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.
sₙ = sₙ₋₁ + aₙ
(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ
(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ
aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)
If you wish, you can simplify by finding the common denominator.
aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]
aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)
aₙ = 16 / (n² + 15n + 56)
The infinite sum is:
∑₁°° aₙ = lim(n→∞) sₙ
∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)
∑₁°° aₙ = 1
Write a quadratic function with zeroes – 1 and 6. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Answer:
If the zeroes of a quadratic function are -1 and 6, then its factored form is:
(x + 1)(x - 6) = 0
Expanding the left side:
x^2 - 5x - 6 = 0
So the quadratic function in standard form is:
f(x) = x^2 - 5x - 6
Answer:
f(x) = x^2 - 5x - 6
Step-by-step explanation:
To create a quadratic function with zeroes -1 and 6, we can start by using the zero product property to write out the factors of the equation:
(x + 1)(x - 6) = 0
Expanding the factors, we get:
x^2 - 5x - 6 = 0
This quadratic equation is in standard form with a leading coefficient of 1. Therefore, the quadratic function with zeroes -1 and 6 is:
f(x) = x^2 - 5x - 6
This function can also be graphed on the coordinate plane as a parabola with a vertex at (2.5, -10.25) and its axis of symmetry at x = 2.5. The graph would intersect the x-axis at -1 and 6, confirming that these are the zeroes of the function.