Answers
Given
[tex]x^2-3x+1=0[/tex]Find
Exact solution by quadratic formula
Explanation
Quadratic formula is given by
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]here a = 1 , b = -3 and c = 1
substitute the values in quadratic formula ,
[tex]\begin{gathered} x=\frac{-(-3)\pm\sqrt{(-3)^2-4\times1\times1}}{2\times1} \\ \\ x=\frac{3\pm\sqrt{9-4}}{2} \\ \\ x=\frac{3\pm\sqrt{5}}{2} \end{gathered}[/tex]Final Answer
Therefore , the correct option is 4.
Related Questions
A triangle has a 30 degree angle and two sides that are each 6em in length. Select ALL the statements below that are TRUE1. The triangle might be an equilateral triangle (having all the same sides and angles) 2. One of the angles in triangle must be 120 3. The length of the third side must be 11cm or smaller4. One of the angles in the triangle might be 50
Answers
The value of x can be determined as,
[tex]\begin{gathered} x+30+30=180 \\ x=120 \end{gathered}[/tex]In triangle ABC,
[tex]\begin{gathered} BCThus, option (2) is the correct solution.A skydiver jumps out of a plane form a certain height. The graph below shows their height h in meters after t seconds. What is the skydiver’s initial height?
Answers
The x-intercept and the slope Set y=0 giving 0=10x+3000 x=300010=300 seconds, or precisely 5 minutes.
How to you interpret the x-intercept and the slope?Y is described as being "above ground" in height. He will get into problems if he descends below ground!
In regard to time x, the right hand side (RHS) has negative 10x, which decreases 3000. Consequently, the starting height must be 3000 feet. Moreover, it is the y-intercept.
The number of feet that the parachutist will descend in x seconds must be the -10x. It is also the graph's gradient or slope.
The graph's intersection with the x-axis indicates that y=0 and y is the height above the earth.
The point when the item is about to strike the ground is therefore the x-intercept.
The rate of descent, or slope, remains constant as time (x) passes.
The rate of fall is actually a extremely rounded value In metric form, I believe the speed to be 9.81 meters per second per second, to two decimal places.
It is approximately 32.2 feet per second per second in imperial form.
to determine how long it will take to reach the ground.
Set y=0 giving 0=10x+3000 x=300010=300 seconds, or precisely 5 minutes.
The complete question is : A skydiver parachutes to the ground. The height y (in feet) of the skydiver after x seconds is y=−10x+3000, how do you graph and Interpret the x-intercept and the slope?
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Answer 5 mins
becasue i solved in. my phone and my teacher said its right
determine if the statement is true or false if it is false explain why must be changing the statements and make it true if it's true explain why you believe to be true the common difference for a geometric sequence given 5:1 -1 negative 3 negative 5 negative 7 is 2
Answers
The common difference can be determined by subtracting the first term with the second term, second term with the third term, and so forth.
In this case we have:
[tex]1-(-1)=1+1=2[/tex][tex]-1-(-3)=-1+3=2[/tex][tex]-3-(-5)=-3+5=2[/tex]In this way we can determine that the common difference of the sequence is 2, so the statement is true.
i need help on this question
Answers
a) Based on the naming of the triangle, the line segment WR is congruent with the line segment PL.
[tex]\bar{WR}\cong\bar{PL}[/tex]b) Based on the naming of the triangle, the third point for triangle BGT is T. The third point for the other triangle, DSN, is N. Hence, the angle for T is congruent with angle N.
[tex]\angle T\cong\angle N[/tex]c) The name of the triangle RHK is rearranged as KRH. This means that name of the triangle WVO can also be rearranged as OWV and is congruent with the triangle KRH.
[tex]\Delta KRH\cong\Delta OWV[/tex]The following system is graphed below: x - y = 2 -X = -y - 1 14 Which of the following best describes the system?
Answers
Since the graphs are parallel to each other, there is no solution to the system. If a system has no solution, it is said to be an inconsistent system. So, the given system is inconsistent.
Identify the quadrant in which the point (−3,2) is located.Question 19 options:Quadrant IQuadrant IIQuadrant IIIQuadrant IV
Answers
The given point is (-3,2). It is required to identify the quadrant in which the point is located.
Notice that the x-coordinate of the point is negative, while the y-coordinate is positive.
This implies that the point is located in the second quadrant.
Plot the point on the coordinate plane:
The answer is quadrant II.
Module 17 - Distribution of Sample Proportions (6 of 6 discussion 3)20 20 unread replies. 20 20 replies.Learn by DoingSome features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.ContextRecall the use of data from the National Health Survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U.S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16.PromptSuppose that we randomly select 100 U.S. adults who are smokers and find that 25% of this sample started smoking before the age of 16. In this random sample, the sample proportion (25%) differs from the estimated population proportion (30%) by 5%. In other words, there is a 5% error in the sample proportion; this sample under-estimates the population proportion by 5%.Is this much error surprising? To answer this question, find the probability that a sample proportion will over- or under-estimate the parameter by more than 5%.Show your work by checking normality conditions, calculating a z-score, explaining how the area under the normal curve is used to answer the question, and stating a conclusion in the context of this problem. Module 17 - Distribution of Sample Proportions (6 of 6 discussion 3)20 20 unread replies. 20 20 replies.Learn by DoingSome features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.ContextRecall the use of data from the National Health Survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U.S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16.PromptSuppose that we randomly select 100 U.S. adults who are smokers and find that 25% of this sample started smoking before the age of 16. In this random sample, the sample proportion (25%) differs from the estimated population proportion (30%) by 5%. In other words, there is a 5% error in the sample proportion; this sample under-estimates the population proportion by 5%.Is this much error surprising? To answer this question, find the probability that a sample proportion will over- or under-estimate the parameter by more than 5%.Show your work by checking normality conditions, calculating a z-score, explaining how the area under the normal curve is used to answer the question, and stating a conclusion in the context of this problem. m the National Health Survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U.S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16.PromptSuppose that we randomly select 100 U.S. adults who are smokers and find that 25% of this sample started smoking before the age of 16. In this random sample, the sample proportion (25%) differs from the estimated population proportion (30%) by 5%. In other words, there is a 5% error in the sample proportion; this sample under-estimates the population proportion by 5%.Is this much error surprising? To answer this question, find the probability that a sample proportion will over- or under-estimate the parameter by more than 5%.Show your work by checking normality conditions, calculating a z-score, explaining how the area under the normal curve is used to answer the question, and stating a conclusion in the context of this problem. Content by the Open Learning Initiative (Links to an external site.) and licensed under CC BY (Links to an external site.).Search entries or author
Answers
Given:
Sample size = 100
p = 30% = 0.30
p' = 25% = 0.25
Let's find the probability that a sample proportion will over- or under-estimate the parameter by more than 5%.
Here, the error is:
Errror = |p' - p| = |0.25 - 0.30| = |-0.05| = 0.05
This error is not surprising.
Now, apply the formula:
[tex]\begin{gathered} \sigma p^{\prime}=\sqrt{\frac{p(1-p)}{n}} \\ \\ \sigma p^{\prime}=\sqrt{\frac{0.3(1-0.3)}{100}} \\ \\ \sigma p^{\prime}=\sqrt{\frac{0.3(0.7)}{100}}=\sqrt{\frac{0.21}{100}}=\sqrt{0.0021}=0.0458 \end{gathered}[/tex]Now, to find the probability that a sample proportion will be over or underestimate more than 5% will be:
[tex]\begin{gathered} p(p^{\prime}<0.3-0.05)+p(p^{\prime}>0.3+0.05) \\ \\ p(p^{\prime}<0.25)+p(p^{\prime}>0.35) \\ \\ z=\frac{p^{\prime}-\mu p^{\prime}}{\sigma p} \\ \\ Where:\mu p^{\prime}=0.3 \\ \end{gathered}[/tex]Hence, we have:
[tex]\begin{gathered} p(z<\frac{0.25-0.3}{0.0458})+p(z>\frac{0.35-0.3}{0.0458}) \\ \\ p(z<\frac{-0.05}{0.0458})+p(z>\frac{0.05}{0.0458}) \\ \\ p(z<-1.09)+p(z>1.09) \end{gathered}[/tex]Using the standard normal distribution table, we have:
NORMSDIST(-1.09) =0.1379
NORMSDIST(1.09) = 0.8621
Hence, we have:
p(z<-1.09) = 0.1379
p(z>1.09) = 1 - 0.8621 = 0.1379
p(z<-1.09) + p(z>1.09) = 0.1379 + 0.1379 = 0.2758
Therefore, the probability is 0.2758.
ANSWER:
0.2758
The product of two consecutive positive odd numbers is 323. Find the smaller of the two numbers. The small number is _
Answers
To answer this question, we need to know that we can represent, algebraically, two consecutive positive odd numbers as follows:
[tex]2n+1,2n+3[/tex]Then, if we have that the product of both consecutive positive odd numbers is 323, then:
[tex](2n+1)(2n+3)=323[/tex]Now, we will need to expand the formula as follows:
[tex](2n+1)(2n+3)=2n\cdot2n+2n\cdot3+(1)(2n)+1\cdot3[/tex]We applied the FOIL method to expand the expression. Then, we have:
[tex]4n^2+6n+2n+3=4n^2+8n+3[/tex]Now, we have:
[tex]4n^2+8n+3=323[/tex][tex]4n^2+8n+3-323=0\Rightarrow4n^2+8n-320=0_{}[/tex]We have here a polynomial (a quadratic equation) that we can solve using the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a},ax^2+bx+c=0[/tex]Then, we have that:
• a = 4
,• b = 8
,• c = -320
Then
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\Rightarrow x=\frac{-8\pm\sqrt[]{8^2-4(4)(-320)}}{2\cdot4}[/tex][tex]\Rightarrow x=\frac{-8\pm\sqrt[]{64^{}-4(4)(-320)}}{2\cdot4}\Rightarrow x=\frac{-8\pm\sqrt[]{64+5120}}{8}[/tex][tex]x=\frac{-8\pm\sqrt[]{5184}}{8}\Rightarrow x=\frac{-8\pm72}{8}[/tex]Then, the solutions are:
[tex]x=\frac{-8+72}{8}\Rightarrow x=\frac{64}{8}\Rightarrow x=8[/tex][tex]x=\frac{-8-72}{8}\Rightarrow x=-\frac{80}{8}\Rightarrow x=-10[/tex]Therefore, we have two solutions for n, n = 8 or n = -10.
If we substitute the value of n = 8 in the original equations, we have:
[tex](2n+1)(2n+3)=323\Rightarrow(2\cdot8+1)(2\cdot8+3)=323[/tex][tex](16+1)(16+3)=323\Rightarrow17\cdot19=323[/tex]If we use the negative value for the solution, we obtain:
[tex](2(-10)+1)(2(-10)+3)=323\Rightarrow(-20+1)(-20+3)=323[/tex][tex]-19\cdot-17=323[/tex]Since these two numbers are negative, we have that the appropriate solution is n = 8.
Therefore, we have that the smaller of the two numbers is 17:
[tex]17\cdot19=323[/tex]The numbers 17 and 19 are consecutive positive odd numbers.
In summary, we have that the smaller number is 17.
The are of a square is 49m2. What is its side length?
Answers
We know that the area of a square is 49 square meters.
The area of a square is defined by
[tex]A=l^2[/tex]Where l is the length of each side.
Replacing the given are, we have
[tex]\begin{gathered} 49=l^2 \\ l=\sqrt[]{49} \\ l=7 \end{gathered}[/tex]Therefore, the side length is 7 meters long.Solve a system of two linear inequalities graphically. Graph the solution set of the second linear inequality. Type of boundary line? Two points on the boundary line? Region you wish to be shaded?
Answers
ANSWER
EXPLANATION
The second inequality is y > -5x + 10. To graph this inequality we have to draw a dashed line y = -5x + 10 and since the inequality represents the values of y greater than the line, the shaded area is the one above the line.
Two points on the line are the y-intercept (0, 10) and the x-intercept (2, 0).
consider the discrete random variable x given in the table below calculate the mean variance and standard deviation of eggs also calculate the expected value of x around solution to three decimal places if necessary
Answers
The mean and the expected value are computed as follows:
[tex]\mu=\sum ^{}_{}x_i\cdot P(x_i)[/tex]Substituting with data:
[tex]\begin{gathered} \mu=1\cdot0.07+6\cdot0.07+11\cdot0.08+15\cdot0.09+18\cdot0.69 \\ \mu=0.07+0.42+0.88+1.35+12.42 \\ \mu=15.14 \\ E(x)=15.14 \end{gathered}[/tex]The variance is calculated as follows:
[tex]\sigma^2=(x_i-\mu)^2\cdot P(x_i_{})[/tex]Substituting with data:
[tex]\begin{gathered} \sigma^2=(1-15.14)^2\cdot0.07+(6-15.14)^2\cdot0.07+(11-15.14)^2\cdot0.08+(15-15.14)^2\cdot0.09+(18-15.14)^2\cdot0.69 \\ \sigma^2=(-14.14)^2\cdot0.07+(-9.14)^2\cdot0.07+(-4.14)^2\cdot0.08+(-0.14)^2\cdot0.09+2.86^2\cdot0.69 \\ \sigma^2=199.9396\cdot0.07+83.5396\cdot0.07+17.1396\cdot0.08+0.0196\cdot0.09+8.1796\cdot0.69 \\ \sigma^2=26.860 \end{gathered}[/tex]And the standard deviation is the square root of the variance, that is:
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{26.8604} \\ \sigma=5.183 \end{gathered}[/tex]On Thursday Tyler‘s math teacher helped him write the expression T equals -2 parentheses 3+ age parentheses to represent the temperature change for that day indicate all the expressions below the equivalent to T equals negative age parentheses 3+ H parentheses
Answers
t = - 2 (3 + h )
Step 1: Expand the parenthesis so that -2 multiplies all the terms in the bracket
t = -2 x 3 - 2 x h
t = - 6 - 2h
Comparing the answer to the options provided
Option C is the best option
What is the value of m?
Answers
In this case, we have two similar triangles (the angles are congruents).
So, the next relations holds:
[tex]\frac{m}{18}=\frac{4}{6}[/tex]So, we only need to solve for m:
[tex]m=\frac{18\cdot4}{6}=12[/tex]Dominick weighs 30 pounds more than his sister. Together they weigh 330 pounds. How much does Dominick weigh?
Answers
Domik weights 30 pounds more than his sister
Together they weigh 330 pounds
Let "x" represent the weight of Dominik's sister, then his weight can be expressed as "x+30"
And their total weight can be calculated as:
[tex]x+(x+30)=330[/tex]From this expression you can calculate the value of x:
[tex]\begin{gathered} 2x+30=330 \\ 2x+30-30=330-30 \\ 2x=300 \\ \frac{2x}{2}=\frac{300}{2} \\ x=150 \end{gathered}[/tex]x=150 pounds
x+30=150+30=180 pounds
Dominik weights 180pounds and his sister 150 pounds
Give the following numberin Base 10.1215 = [ ? ]10
Answers
To convert a number in base five to base ten, we shall use the expanded notation with the place value of each of the base five numbers.
The procedure is shown below;
[tex]\begin{gathered} 121_5 \\ \text{Assign place values starting from the right to the left} \\ \text{That is 0, 1 and 2.} \\ We\text{ now have}; \\ (1\times5^2)+(2\times5^1)+(1\times5^0) \end{gathered}[/tex]We can now simplify this as follows;
[tex]\begin{gathered} (1\times25)+(2\times5)+(1\times1) \\ =25+10+1 \\ =36 \end{gathered}[/tex]ANSWER:
[tex]121_5=36_{10}[/tex]I think you have to create a tree diagram PLS HELP
Answers
Given a coin and spinner
We need to flip the coin once and spin the spinner once
so, the tree diagram will be as following :
So, the all possible outcomes will be :
H1 , H2 , H3 , H4 , H5 , T1 , T2 , T3 , T4 , T5
(-25) + (42) + (-62) + (20) =
Answers
Answer
The answer = -25
Explanation
As long as we note that
(+) × (-) = (-)
(-) × (+) = (-)
We can easily solve this,
(-25) + (42) + (-62) + (20)
= -25 + 42 - 62 + 20
= 17 - 62 + 20
= -45 + 20
= -25
Hope this Helps!!!
From the diagram below, if side AB is 48 cm., side DE would be ______.
Answers
The triangle ABC is similar to the triangle DCE.
Hence, we need to find a proportion to find side DE:
If side AB = 48, it will represent the double value of the side DE.
Hence, DE = 48/2 = 24
The correct answer is option b.
Could you please help me with questions 36 & 37?
Answers
We have to determine if the functions are linear or not.
We can do this by rearranging the equations in this form:
[tex]y=mx+b[/tex]where m and b are constants.
NOTE: There are many ways to prove that a function is linear, but this is the easiest for this question.
36.
[tex]\begin{gathered} x+\frac{1}{y}=7 \\ \frac{1}{y}=-x+7 \end{gathered}[/tex]As this function can not be written in the form y=mx+b, then it is not linear.
37.
[tex]\begin{gathered} \frac{x}{2}=10+\frac{2y}{3} \\ \frac{x}{2}-10=\frac{2y}{3} \\ \frac{2y}{3}=\frac{1}{2}x-10 \\ y=\frac{3}{2}(\frac{1}{2}x-10) \\ y=\frac{3}{4}x-15 \end{gathered}[/tex]This function is now in the form y=mx+b, where m=3/4 and b=-15. Then, this function is a linear function.
Answer:
36. Non-linear.
37. Linear.
The points (2,-2) and (-4, 13) lie on the graph of a linear equation. What isthe linear equation? *
Answers
Answer:
[tex]y=-\frac{5}{2}x+3[/tex]Explanation:
Given the two points on the graph to be (2, -2) and (-4, 13), we can use the point-slope form of the equation of a line below to write the required linear equation;
[tex]y-y_1=m(x-x_1)[/tex]where m = slope of the line
x1 and y1 = coordinates of one of the points
Let's go ahead and determine the slope of the line;
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{13-(-2)}{-4-2}=\frac{13+2}{-6}=-\frac{15}{6}=-\frac{5}{2}[/tex]Let's go ahead and substitute the value of the slope into our point-slope equation using x1 = 2 and y1 = -2;
[tex]\begin{gathered} y-(-2)=-\frac{5}{2}(x-2) \\ y+2=-\frac{5}{2}x+5 \\ y=-\frac{5}{2}x+5-2 \\ y=-\frac{5}{2}x+3 \end{gathered}[/tex]What is the equation in slope-intercept form of a line that has a slope of −1/2
and passes through the point (−2, 7)?
Answers
The equation in slope-intercept form of a line that has a slope of −1/2
and passes through the point (−2, 7) is y = (-1/2)x + 6.
Given:
slope-intercept form of a line that has a slope of −1/2 and passes through the point (−2, 7).
slope m = -1/2
substitute m and (-2,7) in standard form y = mx + c
7 = -1/2*-2 + c
7 = 2/2 + c
7 = 1 +c
c = 7 - 1
c = 6
substitute c and m value
y = mx+c
y = (-1/2)x + 6
Therefore The equation in slope-intercept form of a line that has a slope of −1/2 and passes through the point (−2, 7) is y = (-1/2)x + 6.
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According to the model, how many marriage licenses were issued in 2006? Round your answer to the nearest hundred.
Answers
ANSWER:
C. 124,900
STEP-BY-STEP EXPLANATION:
We have that the following function is the one that models the situation:
[tex]y=3.4905\left(x\right)^2-17674\left(x\right)+21533000[/tex]We evaluate when x = 2006, like this
[tex]\begin{gathered} y=3.4905\left(2006\right)^2-17674\left(2006\right)+21533000 \\ \\ y=4024036\cdot\:3.4905-35454044+21533000 \\ \\ y=14045897.658-13921044 \\ \\ y=124853.658\cong124900 \end{gathered}[/tex]Therefore, the correct answer is C. 124,900
Suppose that the functions and s are defined for all real numbers x as follows r(x) = 4x; s(x) = 3x ^ 2 Write the expressions for (s + r)(x) and (sr)(x) and evaluate (s - r)(2) .
Answers
Solution
Given
[tex]\begin{gathered} r(x)=4x \\ \\ s(x)=3x^2 \end{gathered}[/tex]Then
[tex]\begin{gathered} (s+r)(x)=s(x)+r(x)=4x+3x^2 \\ \\ \Rightarrow(s+r)(x)=4x+3x^2 \end{gathered}[/tex][tex](s\cdot r)(x)=s(r(x))=s(4x)=3(4x)^2=3\times16x^2=48x^2[/tex][tex](s-r)(2)=s(2)-r(2)=3(2)^2-4(2)=12-8=4[/tex]EXERCISE Carlos is jogging at a constant speed. He starts a timer when he is 12 feet from his starting position. After 3 seconds, Carlos is 21 feet from his starting position. Write a linear equation to represent the distance d of Carlos from his starting position t seconds after starting the timer.
Answers
The linear equation that represent the distance d of Carlos from his starting position is d=3t+12 where d denotes the distance and t denotes the time.
What is the meaning of speed?
The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined.
Given that when Carlos is 12 feet from his starting position, starts a timer.
He is 21 feet from his starting position after 3 s.
He covers (21 - 12) = 9 feet in 3 second.
The speed of an object is the distance that covers in unit time.
The Carlos's speed is 9/3 = 3 feet/s.
After t seconds, he covers (3×t) = 3t feet.
The distance of his from his starting position after t seconds is (3t + 12) feet.
The linear equation is d = 3t + 12.
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Hi I’m I don’t understand a variable of what this is saying.
Answers
given expression to simplify,
[tex]q^{-3}r^0s^{-1}\cdot\: q^3r^{-9}s^0[/tex][tex]\begin{gathered} q^{-3}r^0s^{-1}\cdot\: q^3r^{-9}s^0 \\ q^{-3}\cdot q^3=1 \\ \: =r^0s^{-1}r^{-9}s^0 \\ =1\cdot\frac{1}{r^9}s^{-1}s^0 \\ =1\cdot\frac{1}{r^9}\cdot\frac{1}{s} \\ =\frac{1}{r^9}\cdot\frac{1}{s} \\ =\frac{1}{r^9s} \\ =r^{-9}s^{-1} \end{gathered}[/tex]find bounds on the real zeros of the polynomial functionf(x)= 17x^4 + 17x^3 - x^2 - 68x - 68
Answers
In order to identify bounds on the real zeros of this polynomial, first we need to find tendencies about the signal of f(x)
We know that the two term with highest degree is being multiplied by a positive coefficient. Therefore, we can initially conclude the f(x) tends to positive infinite as x grows either positive or negative.
We can check that, for x = -2, the first term is 272, and the remaining thermis togheter are given by:
[tex]17\cdot(-2)^3-(-2)^2-68\cdot(-2)-68=-72[/tex]Then for x < -2, and for also for x > 2, we can state for sure that f(x) remains always positive.
Then, any possible roots must lies in the intervel (-2,2)
e can also chegck that, for x = 1, f(x) = -103, and, for x = -1, f(x) = -1.
Therefore, f(x) must have a root between
asymptoteg(x) = -3*2^x+5
Answers
Question 13 of 19 Use the elimination method to solve the system of equations. Choose the correct ordered pair x+y=9 x-y=7 O A. (8,1) B. (12,-3) C. (16, -7) D. (7.0) SUBMIT
Answers
The solution for the system of equations is x = 8, y = 1
Explanation:Given the pair of equations:
x + y = 9 .....................................................(1)
x - y = 7 ......................................................(2)
To solve by elimintation, add (1) and (2) to eliminate y
2x = 16
x = 16/2 = 8 ............................................(3)
Subtract (2) from (1) to eliminate x
2y = 2
y = 2/2 = 1 ................................................(4)
(3) and (4) form the solution of the equation.
x = 8, y = 1
A stick is 10 1/5 inches in length. A carpenter will cut it into shorter pieces, each 1 2/15 inches in length. How many pieces will the stick be cut into?
Answers
Answer:
9 pieces
Explanation:
From the question, we're told that the length of the stick is 10 1/5 inches, let's convert the mixed fraction into an improper fraction;
[tex]10\frac{1}{5}=\frac{51}{5}[/tex]Also, we're told that the stick was cut into shorter pieces of length 1 2/15 inches each. Converting 1 2/15 into an improper fraction, we'll have;
[tex]1\frac{2}{15}=\frac{17}{15}[/tex]To determine the number of pieces that the stick will be cut into, we'll need to divide 51/5 by 17/15;
[tex]\frac{\frac{51}{5}}{\frac{17}{15}}=\frac{51}{5}\ast\frac{15}{17}=\frac{15}{1}\ast\frac{3}{17}=\frac{153}{17}=9[/tex]What Is 3×10³=3×10×10×10=
Answers
3 x 10 ^3 = 3 x 10 x 10 x10 = 3 x 100 = 300
100 x 3 = 300 = 3 x 10 x 10 x 10
300