The sum of two numbers is 9 and their difference is 7. Find the two numbers.8 and 14 and 56 and 39 and 0
Answers
Step 1
Given; The sum of two numbers is 9 and their difference is 7. Find the two numbers.
Step 2
Let the two numbers be x and y
\(\begin{gathered} x+y=9--(1) \\ x-y=7---(2) \end{gathered}\)Step 3
Solve using the elimination method
\(\begin{gathered} x+y=9 \\ - \\ x-y=7 \\ ------- \\ 0+2y=2 \\ 2y=2 \\ y=\frac{2}{2}=1 \end{gathered}\)\(\begin{gathered} From\text{ equation 1, x+y=9} \\ x+1=9 \\ x=9-1 \\ x=8 \end{gathered}\)Answer;
\(\begin{gathered} x=8,y=1 \\ So\text{ the two numbers are 8 and 1} \end{gathered}\)Related Questions
If cp-Rs 200 , sp-Rs 300, find profit amount
Answers
Answer:
Rs 100
Step-by-step explanation:
cp=rs 200
sp=rs 300
profit (p)=sp - cp
=rs 200-rs 300
=rs 100
If the statement if I'm hungry, then I am not happy is assumed to be true is it's inverse of I am not hungry then I must be happy also always true
Answers
Answer:
yes!
Step-by-step explanation:
"i am not happy when hungry" is the inverse of "i am not hungry, i am happy."
Answer:
No
Step-by-step explanation:
Admission to a baseball game is $4.00 for general admission and $5.50 for reserved seats. The receipts were $5973.50 for 1358 paid admissions. How many of each
ticket were sold? (Round to nearest Integer if necessary.)
Answers
Answer:
997 admission tickets were sold and 361 reserved seats were sold.
Step-by-step explanation:
There is a couple of ways to calculate this.
Multiply the cost of an admission ticket by the total paid admissions:
\(4 \times 1358 = 5432\)
Subtract this from the total cost:
\(5973.5 - 5432 = 541.5\)
Divide the above value by the difference between the cost of the two tickets:
\(5.5 - 4 = 1.5\)
\(541.5 \div 1.5 = 361\)
Now we know the number of general admission tickets, we can subtract the cost of this from the total cost:
\(361 \times 5.5 = 1985.5\\5973.50 - 1985.5 = 3988\)
Divide this by the cost of general admission:
\(3988 \div 4 = 997\\\)
So there were 997 admission tickets sold and 361 reserved seats sold.
Hope this helps!
Help please? Which are the following key feature are the same for both functions.
Answers
The following conclusions can be made regarding the given graph -
the slope of the line is -3.the {y} - intercept of the line is at the point (0, 2.4).the unit rate for the given line is negative.What is proportional relationship?A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.
Given is the graph of a straight line as shown in the image.
Only one single graph of a straight line is given. We cannot compare it, so we will analyze its meaning itself.
We can write the slope of the line -{m} = (0 - 2.4)/(0.8 - 0)
{m} = -2.4/0.8
{m} = - 3
The {y} - intercept of the line is at the point (0, 2.4).The unit rate for the given line is negative.Therefore, the following conclusions can be made regarding the given graph -
the slope of the line is -3.the {y} - intercept of the line is at the point (0, 2.4).the unit rate for the given line is negative.To solve more questions on unit rate, visit the link-
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we want to factor the following expression: (x - 3)^2 - 64y^4 which pattern can we use to factor the expression? u and v are either constant integers or single variable expression.
Answers
The factored expression of (x - 3)^2 - 64y^4 is given as follows:
(x - 3)^2 - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
What is the subtraction of perfect squares?The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares as follows:
a² - b² = (a - b)(a + b).
In this problem, the expression is presented as follows:
(x - 3)^2 - 64y^4
This expression is a subtraction of perfect squares, as the terms are given as follows:
Term a: square root of (x - 3)² = x - 3.Term b: square root of 64y^4 = 8y².Then the expressions are given as follows:
a - b = x - 3 - 8y².a + b = x - 3 + 8y².Then the factored expression is presented as follows:
a² - b² = (a - b)(a + b).
(x - 3)² - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
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HELP PLEASE...........
Answers
Answer:
1. 9
2. 12
3. 26
Step-by-step explanation:
Answer:
1. 9
2. 12
3. 26
Step-by-step explanation:
An easy way to solve problems like this is to convert the percentage into a decimal, then multiply that decimal by the whole. For example, if I had the question "What is 10% of 100?", I would first convert the 10% to a decimal. 10% is the same as 10/100, which in decimal form is 0.1. I would then multiply 0.1 by 100 to find out how much 10% of 100 is. I get 10, so my answer is 10. Hope this helps!
The table of values represents a quadratic function f(x).
x f(x)
−7 14
−6 7
−5 2
−4 −1
−3 −2
−2 −1
−1 2
0 7
1 14
What is the equation of f(x)?
f(x) = (x − 4)2 − 1
f(x) = (x − 3)2 − 2
f(x) = (x + 3)2 − 2
f(x) = (x + 4)2 − 1
Answers
The vertex-form of the quadratic function f(x) is given as follows:
f(x) = (x + 3)² - 2.
How to define the quadratic function given it's vertex?The quadratic function of vertex(h,k) is given by the rule presented as follows:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The vertex is the turning point of the function, where it changes from decreasing to increasing, or vice versa, hence it's coordinates are given as follows:
(-3, -2).
Then the equation is:
f(x) = a(x + 3)² - 2.
When x = 0, h(x) = 7, hence the leading coefficient a is obtained as follows:
7 = a(3)² - 2
9a = 9
a = 1.
Hence the equation is:
f(x) = (x + 3)² - 2.
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ITS ALMOST DUEE I’ll brainlist
Answers
Answer:
10/3
Step-by-step explanation:
One of the legs of right triangle measures 16 cm and the other leg measures 2 cm.
round to the nearest tenth.
Find the measure of the hypotenuse. If necessary, round
Answers
Answer:
16.1 cm (nearest tenth)
Step-by-step explanation:
Pythagoras’ Theorem
\(a^2+b^2=c^2\)
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = 16 cmb = 2 cmSubstitute the given values into the formula and solve for c:
\(\implies 16^2+2^2=c^2\)
\(\implies 256+4=c^2\)
\(\implies c^2=260\)
\(\implies c=\sqrt{260}\)
\(\implies c=2\sqrt{65}\)
\(\implies c=16.1 \sf \: cm\:(nearest\:tenth)\)
16.1 is rounded to the nearest tenth
An object’s speed and direction is its ________.
Answers
Hope this helps :)
-Rae
the diffrence of 54 and 32 mutlipted by the diffrence of 8 and 5
Answers
Answer:
66
Step-by-step explanation:
the difference of 54 and 32 is 54 - 32 = 22
the difference of 8 and 5 is 8 - 5 = 3
then
22 × 3 = 66
The perimeter of the rectangle below is 76 units. Find the value of y.
Answers
The solution is : the value of y is 7.
Here, we have,
The perimeter of a rectangle is found by
P = 2 (l+w)
P = 2( 3y+3+2y)
Combine like terms
P = 2(5y+3)
We know the perimeter is 76
76 = 2(5y+3)
Divide each side by 2
76/2 = 2/2(5y+3)
38 = 5y+3
Subtract 3 from each side
38-3 = 5y+3-3
35 = 5y
Divide each side by 5
35/5 = 5y/5
7 =y
We want the length of AD = BC = 2y
AD = 2y=2*y = 14
Hence, The solution is : the value of y is 7.
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In calculus, it can be shown that
e^x=infintesigmak=0 x^k/k!
We can approximate the value of for any x using the following sum e^x=infintesigmak=0 x^k/k!
a) Approximate e^2.2 n=3
Answers
Answer: \(7.39466666\)
Step-by-step explanation:
Setting \(x=2.2\) and \(n=3\),
\(e^{2.2} \approx \sum^{3}_{k=0} \frac{2.2^{k}}{k!}=\frac{2.2^0}{0!}+\frac{2.2^1}{1!}+\frac{2.2^2}{2!}+\frac{2.2^3}{3!} \approx 7.39466666\)
Answer:
7.39466667 (8 d.p.)
Step-by-step explanation:
We can approximate the value of eˣ for any x using the following sum formula:
\(\boxed{e^{x} \approx \displaystyle \sum^n_{k=0}\dfrac{x^k}{k!}}\)
To approximate \(e^{2.2}\) with n = 3, substitute x = 2.2 and n = 3 into the given sum formula:
\(e^{2.2} \approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\)
To calculate the sum, substitute k with each value from 0 to 3 and add the results together:
\(\begin{aligned}e^{2.2} &\approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\\\\&= \dfrac{2.2^0}{0!}+\dfrac{2.2^1}{1!}+\dfrac{2.2^2}{2!}+\dfrac{2.2^3}{3!}\\\\&= \dfrac{1}{1}+\dfrac{2.2}{1}+\dfrac{4.84}{2}+\dfrac{10.648}{6}\\\\&= 1+2.2+2.42+1.774666666...\\\\&=7.39466667\; \sf (8\;d.p.)\end{aligned}\)
Therefore, the approximate value of \(e^{2.2}\) is:
\(\large \textsf{$e^{2.2}$}=\boxed{7.39466667}\; \sf (8\;d.p.)}\)
Note: To obtain a more accurate approximate value, increase the value of n.
PLEASE HELP DUE SOON! PLEASE SHOW WORK SO I KNOW HOW TO IT FOR NEXT TIME! IM STUCK ON THIS AND ITS DUE TODAY!!!!! YOU WILL GETT 100 POINTS REAL ANSWERS ONLY! MANY THANKS! QUESTIONS DOWN BELOW!!!!!
Answers
Answer:
a) zero triangles.
b) one triangle.
Step-by-step explanation:
In triangle ABC:
A, B and C are the interior angles.a, b and c are the sides opposite the corresponding interior angles.Part (a)Given:
∠A = 51°a = 10 cmb = 28 cmLaw of Sines
\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:
\(\implies \sf \dfrac{\sin 51^{\circ}}{10}=\dfrac{\sin B}{28}\)
\(\implies \sf \sin B=\dfrac{28\sin 51^{\circ}}{10}\)
\(\implies \sf \sin B=2.176008...\)
As -1 ≤ sin B ≤ 1, there is no solution for angle B.
Therefore, zero triangles are possible.
----------------------------------------------------------------------------------
Part (b)Given:
∠C = 30°a = 24 cmc = 12 cmLaw of Sines
\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle A:
\(\implies \sf \dfrac{\sin A}{24}=\dfrac{\sin 30^{\circ}}{12}\)
\(\implies \sf \sin A=\dfrac{24\sin 30^{\circ}}{12}\)
\(\implies \sf \sin A=1\)
\(\implies \sf A=\sin^{-1}(1)\)
\(\implies \sf A=90^{\circ}\)
Therefore, one triangle is possible (see attachment).
What is the equation of the line that passes through the point (-6,8) and has a slope of -5/3? Please show step by step solution,
Answers
Answer:
The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
We have the point (-6,8) and a slope of -5/3.
Step 1: Use the point-slope formula to find the equation of the line in point-slope form.
y - y1 = m(x - x1)
where x1 and y1 are the coordinates of the given point.
y - 8 = (-5/3)(x - (-6))
Simplify this equation:
y - 8 = (-5/3)(x + 6)
Step 2: Convert the equation to slope-intercept form.
Distribute (-5/3) to get:
y - 8 = (-5/3)x - 10
Add 8 to both sides:
y = (-5/3)x - 2
This is the equation of the line in slope-intercept form. Therefore, the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.
Find the length of the line below.
A. 2 in.
B. 2 3/16 in.
C. 2 5/16 in.
D. 3 in.
Answers
Answer:
A)
Step-by-step explanation:
Starting point is at o and ending point at 2.
So, 2 in
unit 5 homework 3 all things algebra anwser key
Answers
Plot −5/4 and its opposite on the number line.
Select the points on the line to plot.
-3 | | | -2 | | | -1 | | | 0 | | | 1 | | | 2 | | | 3
Answers
I need help with this question please with details
Answers
The dimensions of the rectangular box are given as follows:
All the dimensions.
A. 6 inches long, 3 inches wide, 3 inches tallB. 9 inches long, 2 inches wide, 3 inches tallC. 18 inches long, 3 inches wide, 1 inch tallD. 27 inches long, 2 inches wide, 1 inches tallHow to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The box's volume is obtained as follows:
54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)
Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.
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Real numbers a and b satisfy
a + ab = 250
a - ab = -240
Enter all possible values of a, separated by commas.
Answers
The only possible value of "a" that satisfies the given equations is a = 5.
The possible values of "a" that satisfy the given equations, let's solve the system of equations:
a + ab = 250 ---(1)
a - ab = -240 ---(2)
We can solve this system by using the method of substitution. Rearranging equation (2), we get:
a = ab - 240 ---(3)
Substituting equation (3) into equation (1), we have:
(ab - 240) + ab = 250
2ab - 240 = 250
2ab = 250 + 240
2ab = 490
ab = 490/2
ab = 245
Now we have the value of "ab."
We can substitute this back into equation (3) to solve for "a":
a = (245) - 240
a = 5
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suppose that a population parameter is .7 and many samples were taken. if the size of each sample is 30 what is the standard error
Answers
The standard error is 0.0912.
The standard error (SE) is a measure of the precision of the sample mean estimate compared to the true population mean. To calculate the SE, we use the formula SE = standard deviation / square root of sample size.
In this scenario, the population parameter is 0.7, and the sample size is 30. If we assume that the sample mean is an unbiased estimator of the population mean, then the SE can be calculated using the above formula. However, we do not know the standard deviation of the population, so we use the sample standard deviation as an estimate.
Assuming the sample is large enough to assume normality, the formula becomes SE = \(\sqrt{(0.7*0.3)/30}\) = 0.0912. Therefore, the standard error for a sample size of 30 is 0.0912. This means that if we were to take multiple samples of size 30 from the same population, the standard deviation of the means of those samples would be around 0.0912 away from the population parameter of 0.7 on average.
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I need help on this I will give brainlist help it will mean a lot this is my last math problem help me!
Answers
Answer:answer is b
Step-by-step explanation: Just makes since
1. Find the value of x in the figure.
(1 point)
40°
O 40°
O 50°
O 140°
O 180°
Answers
Answer:
the value of x = 40
I hope it's helps you
Answer:
\(x = 40 \\ \\ \)
it's vertical angel they are equal each other ( = )
The figure is cut into 15 equal pieces. Shade 2/5 of the figure
Answers
Answer: Shade 6 pieces
Step-by-step explanation:
Because 2/5 of 15 is 6
In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothing and carry‑on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not normally distributed, especially when the population includes both men and women, but they are not very non‑Normal. A commuter plane carries 22 passengers. What is the approximate probability P that the total weight of the passengers exceeds 4500 pounds? Use the four‑step process to guide your work. Give your answer as a percentage precise to two decimal places. P=___?
Answers
The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Total of 22 is more than 4500 is equivalent to average of 22 is more than \($\frac{4500}{22}\)=204.545
\($$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$\)
= 1 - 0.8997
= 0.1003
= 10.03%
Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.
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Maddys house consist of two stories and an attic. The first floor is 8 5/6feet tall. The second floor is 8 1/2 feet tall. The entire house is 24 1/3 feet tall how tall is the Attic
Answers
The entire house is 24 1/3 feet tall and attic is 7 feet tall.
What is subtraction?Mathematical operations like subtraction exist. It is employed to delete words or objects from the phrase.
Given:
Maddy's house has two stories and an attic.
The first floor is 8 5/6 feet tall.
The second floor is 8 1/2 feet tall.
The entire house is 24 1/3 feet tall.
So, the height of the attic,
= height of the entire house - ( height of the first floor + height of the second floor)
= 24 1/3 - (8 5/6 + 8 1/2)
In order to simplify the equation,
converting mixed fraction to improper fraction,
we get,
= 73/3 - 53/6 - 17/2
= 42/6
= 7 feet.
Therefore, the height of the attic is 7 feet.
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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.
Answers
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 0.07 is a tenth of?
Answers
The decimal 0.7 is a tenth of 0.07.
0.07 is a tenth of
0.07 \(\times\)10= 0.7
What is a Decimal?
When the whole of something is divided into smaller parts, we get decimals.There are two parts to decimal: the whole number and a fractional part.The whole part of decimals has the same place as that of the complete number.After the decimal point, when we move toward the right, we get the fractional part of the decimal.A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of expressing numbers that uses digits or symbols to represent them.To learn more about decimal, visit: https://brainly.com/question/28222265
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Michaela plans on installing heated tile in her kitchen. A diagram of the kitchen floor plan is shown below.
Calculate the area of the floor, to the nearest 10th, to determine how many square metres of tile Michaela will need to buy.
*Hint: Divide the shape into 2! You will need to use trig!
Answers
Check the picture below.
so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".
\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)
A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Find the probability of getting exactly one tail.
Answers
The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
What is probability?Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
In the given question,
There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH)
We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:
P(HHT) = (1/2) * (1/2) * (1/2) = 1/8
P(HTH) = (1/2) * (1/2) * (1/2) = 1/8
P(THH) = (1/2) * (1/2) * (1/2) = 1/8
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8
Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
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