Answers
x = 1, y = 3
Explanation:The given system of equations is:
y = 4x - 1.......................(i)
y - 2x = 1..................(ii)
Substitute equation (i) into equation (ii)
4x - 1 - 2x = 1
4x - 2x = 1 + 1
2x = 2
x = 2/2
x = 1
Substitute x = 1 into equation (i)
y = 4x - 1
y = 4(1) - 1
y = 4 - 1
y = 3
The solution to the system of equations is x = 1, y = 3
Related Questions
Find the measure of chord EF. Enter your numerical answer.
Answers
Notice that each chord (CD and EF) defines a segment in the circle whose arc length has the same value. Thus, the length of both chords has to be the same; then,
[tex]\begin{gathered} CD=EF \\ \Rightarrow9x-1=41-5x \\ \Rightarrow14x=42 \\ \Rightarrow x=3 \end{gathered}[/tex]Finding the length of EF,
[tex]\begin{gathered} x=3 \\ \Rightarrow EF=41-5*3=26 \end{gathered}[/tex]Therefore, the answer is 26
If you make $13.00/hour at your job and you work on average 35 hours a week, how much do you bring home if you get $80 taken out in taxes????
Answers
If you make $13/ hour and you work 35 hours, you make:
[tex]13\cdot35\text{ = \$455}[/tex]Then, you substract the $80 in taxes:
[tex]455-80\text{ = \$375}[/tex]So in total, you should bring home $375
choose the x-intercept and the y-intercept for each equationx+4y=24a (0,4)b (0,6)c (6,0)d (24,0)e (24,6)
Answers
Given:
The equation is x + 4y = 24
Required:
Find the x - intercept and y - intercept?
Explanation:
We know that
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]Where, a is x - intercept
and b is y - intercept
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.
Now,
[tex]\begin{gathered} x+4y=24 \\ \frac{x}{24}+\frac{y}{6}=1 \end{gathered}[/tex]From this we can say that x - intercept (24, 0) and y - intercept (0, 6).
Answer:
Hence, (24, 0) and (0, 6) are intercept of given equation.
The number of protozoa in a biology laboratory experiment is given by the polynomial functionp(t) = 0.02t^4 + 0.3t^3 + 7t^2, where p is the number of protozoa after t hours.Step 2 of 2: How many protozoa are present after 2 days? Round your answer to the nearest wholenumber.
Answers
In order to calculate the number of protozoa after 2 days (that is, 48 hours), let's use t = 48 in the function p(t) and calculate its value:
[tex]\begin{gathered} p(t)+0.02t^4+0.3t^3+7t^2 \\ p(48)=0.02\cdot48^4+0.3\cdot48^3+7\cdot48^2 \\ p(48)=0.02\cdot5308416+0.3\cdot110592+7\cdot2304 \\ p(48)=106168.32+33177.6+16128 \\ p(48)=155473.92 \end{gathered}[/tex]Rounding to the nearest whole number, the number of protozoa is 155474.
Find the lowest multiple of each group.show the factors you used.1. 5,20,28
Answers
Given the following question:
1, 5, 20, 28
1 = 1
5 = 5
20 = 2 × 2 × 5
28 = 2 × 2 × 7
2 × 2 × 5 × 7
2 × 2 = 4
4 × 5 = 20
20 × 7 = 140
LmM = 140
13. If a trapezoid has base lengths of 18and 40, what is the length of themedian?I●
Answers
The median of a trapezoid is a straight line that goes from the midpoint of one of the sides to the midpoint of the opposite side and is parallel to both bases.
Its length is the average of the lengths of both bases:
[tex]median=\frac{(upper.base+lower.base)}{2}[/tex]One of the bases of the trapezoid has a length of 18 units and the other base has a length of 40 units. Average both bases to determine the length of the median:
[tex]\begin{gathered} median=\frac{18+40}{2} \\ median=\frac{58}{2} \\ median=29 \end{gathered}[/tex]The length of the median is 29 units.
5 markers cost $6.55.Which equation would help determine the cost of 4 markers?
Answers
5 markers -------> $6.55
4 markers -------> x
[tex]undefined[/tex]What is the range of the function?2.-54-3-22-1-2 -3 -4
Answers
We need to find the range of a function given in graph form. The graph is shown below:
So we need to recall what Range is: the set of y-values that are in fact connected to x-values in our function.
So looking at the image given we realize that the curve that represents such connection does not go further up in the y-axis than the value y = 4.
On the other hand, since the image has branches going down, it seems that all the values for y are represented in that portion of the lower part of the graph.
We can then say that the set of y-values of the Range is defined as:
(in set-builder notation form) ;
[tex]\text{Range}=\left\lbrace y\right|y\leq4\}[/tex]which reads as:
Range = the set of all the y-values that are less than or equal to 4.
> Next question Get a similar question You can retry this a 8.1 ft 9.7 10.6 Name the Shape: • triangle trapezoid kite parallelogram
Answers
The given figure is has three sides and three vertices : Triangle
In the given triangle, height = 9.7 ft, base = 8.1 ft,
Area of triangle = 1/2 x Base x Height
Area of traingle = 1/2 x 8.1 x 9.7
Area of traingle = 39.28 ft²
Area of the given figure = 39.28 ft²
√10=Rational or Irrational
Answers
Square roots are rational only when has perfect square factors.
√10 = √(2*5) = √2 * √5
2 and 5 are not perfect squares, then √2 and √5 are irrational. In consequence, √10 is also irrational.
QuestioA team of physicians is studying a weight-loss pill. They recruited volunteers for a study. The volunteers were in the agegroup of 30 to 35 and were more than 40 pounds overweight. The physicians gave the new weight-loss pill pack to onegroup. The other group received a pill pack that resembled the new weight-loss pill pack but was a placebo. In thedescription of the above situation, determine the experimental group
Answers
The experimental group will be the group who received the new weight-loss pill. This group will be used to identify or estimate the effect of the variable or the ingredient which will cause weight loss.
The other group who received the resemblanced of the new weight-loss pill but placebo will only be used for the comparison effect from the experimental group.
So the answer will be :
1st Option, The group that received the new weight-loss pill pack is the experimental group.
graph the equation shown below by transforming the given graph of the parent function. y = 2x²
Answers
We have that the parent function is multiplied by 2, therefore, the graph for y = 2x^2 will compress in comparison with the graph of y=x^2
Both graphs would looke like this:
where the black graph represents the functon y = 2x^2 and the red graph represents the function y = x^2
percentage of the people surveyed said Lombardi?
How many radians are in a full rotation around a circle, or 360°?
Answers
Given:-
A full rotation.
To find the correct radians.
So as we know full rotation means 360 degree.
Also we know,
[tex]\pi=180[/tex]So for getting 360 degree. we get,
[tex]2\times180=360[/tex]So the required solution is,
[tex]2\pi[/tex]Which of the following is an arithmetic sequence? A. 1, 0, 1, 0, 1, 0, ...B. 800, 200, 50, ...C. 10, 7, 4, 1, -2, ...D. 1, 3, 9, 27,...
Answers
Given:
The sequences in options.
Required:
Which of the sequence is an arithmetic sequence.
Explanation:
The arithmetic sequence has a common ration, that is equal for every pair of number
[tex]d=a_2-a_1,d=a_3-a_2[/tex]Now, in option c
[tex]\begin{gathered} d=7-10=-3 \\ d=4-7=-3 \\ d=1-4=-3 \end{gathered}[/tex]So, common ratio is -3 and hence sequence is arithmetic sequence.
Answer:
So, option c is correct.
Sophie put $3330 in a savings account at a simple interest rate of 7.4% per year.
Adam put $2795 in a savings account at a simple interest rate of 8.1% per year.
Who will have earned more interest after 5 years? How much more?
Answers
Sophie earned more simple interest of $100.
Simple interest is a short and easy technique for calculating the interest price on a mortgage. simple interest is decided with the aid of multiplying each day's interest charge via the most important by the variety of days that elapse among bills.
To calculate Simple interest, multiply the main quantity by using the interest charge and the time. The method written out is Simple interest = principle x interest price x Time." This equation is the most effective way of calculating interest.
Calculation:-
For Sophie
SI = PRT/100
= ($3330 × 7.4 × 5 ) /100
= $1232
For Adam
SI = PRT/100
= ($2795 × 8.1 × 5 ) /100
= $1132
Therefore, Sophie earned more interest of $1232 - $1132 = $100
simple interest is based on the most important amount of a loan or the primary deposit in a financial savings account. simple interest doesn't compound, and because of this a creditor will most effectively pay interest on the foremost amount, and a borrower might in no way have to pay extra interest at the previously amassed interest.
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if f(x) = 13 when f(x)=5x -√8, find x.
Answers
Given that we have the function f(x) = 5x-√8, it is equal to 13 at some value of x. This relation can be written in equation as
[tex]5x-\sqrt[]{8}=13[/tex]Move √8 to the other side of the equation so that only the term with x will be left on the left-hand side. We have
[tex]5x=13+\sqrt[]{8}[/tex]Divide both sides by 5, we get
[tex]\begin{gathered} \frac{5x}{5}=\frac{13+\sqrt[]{8}}{5} \\ x=\frac{13+\sqrt[]{8}}{5} \end{gathered}[/tex]The square root of 8 can be further simplified as
[tex]\sqrt[]{8}=\sqrt[]{4\cdot2}=2\sqrt[]{2}[/tex]Hence, the value of x can also be rewritten as
[tex]x=\frac{13+2\sqrt[]{2}}{5}[/tex]Thus, the value of x to satisfy f(x) = 13 when f(x)=5x -√8 is
[tex]x=\frac{13+\sqrt[]{8}}{5}=\frac{13+2\sqrt[]{2}}{5}=\frac{13}{5}+\frac{2\sqrt[]{2}}{5}[/tex]what's false 16 / 10 equal 25 / 40
Answers
10/16 = 25/40
Divide each
0.625 = 0.625
Second option:
15/60= 35/140
0.25 = 0.25
Third option
24/36=50/75
0.6666= 0.6666
Fourth option
14/35=35/70
0.4=0.5
FALSE
Jack needs to order some new supplies for the restaurant where he works. The restaurant needs at least 711 glasses. There are currently 206 glasses. If each set on sale contains 10 glasses, write and solve an inequality which can be used to determine ss, the number of sets of glasses Jack could buy for the restaurant to have enough glasses.
Answers
505 / 10 = 50.5 (round up to 51)
ss > 51 (use the ‘greater than or equal to’ sign instead of just the ‘greater than’ sign)
Jack needs to buy at least 51 sets of glasses to ensure that the restaurant has enough glasses.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Let s be the number of sets of glasses that Jack needs to buy.
According to the problem, the restaurant needs at least 711 glasses, and currently has 206. So Jack needs to buy:
711 - 206 = 505 glasses
Since each set contains 10 glasses, the total number of glasses Jack can buy is:
10s
To have enough glasses, the total number of glasses Jack buys must be greater than or equal to 505. So we can write the inequality:
10s ≥ 505
To solve for s, we can divide both sides by 10:
s ≥ 50.5
Since s must be a whole number (you can't buy half a set of glasses), we round up to the nearest integer:
s ≥ 51
Therefore, s ≥ 51.
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Solve x2-12x + 11 = 0 by completing the square.
Answers
Given: A quadratic equation-
[tex]x^2-12x+11=0[/tex]Required: To solve the equation by completing the square method.
Explanation: The general form of a quadratic equation is-
[tex]ax^2+bx+c=0[/tex]The given equation can be solved by the method of completing the square by adding and subtracting the term-
[tex](\frac{b}{2})^2[/tex]Hence, the given equation can be written as-
[tex]x^2-12x+36-36+11=0[/tex]Now solving further as-
[tex]\begin{gathered} x^2-2\times6\times x+6^2-25=0 \\ (x-6)^2=25 \\ (x-6)=\sqrt{25} \\ (x-6)=\pm5 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} x-6=5\text{ or } \\ x-6=-5 \end{gathered}[/tex]This gives-
[tex]\begin{gathered} x=11\text{ or} \\ x=1 \end{gathered}[/tex]Final Answer: The solution to the equation is x=11 or x=1.
three points a b and c exist in space such that b is between a and C it is known that AB = 7 , BC= 4 and AC = 9 . Ar epoints a b and c Collinear? give a written explanation supported by mathematical evidence for your answer.
Answers
Points are collinear if they are in the same line.
So:
AB+BC = AC
Replacing with the values given:
7+4 = 9
11 =9 False
A,b, and c aren't collinear.
Find the value of x and the value of y.A. x = 15, y = 10sqrt3B. r = 20, y = 10sqrt3C. r = 20sqrt3, y = 5sqrt3D. x=15, y = 5sqrt3
Answers
To find the values of x and y it is necessary to use trigonometric ratios.
To find x it is necessary to use sine. Sine is the ratio between the opposite side to a given angle and the hypotenuse. In this case, the given angle is 60°, the opposite side is x and the hypotenuse is 10 sqrt 3. Use this information to find x:
[tex]\begin{gathered} \sin 60=\frac{x}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\sin 60=x \\ x=15 \end{gathered}[/tex]To find y it is necessary to use cosine. It is the ratio between the adjacent side to a given angle and the hypotenuse. The given angle is 60°, the adjacent side is y and the hypotenuse is 10 sqrt 3. Follow the same procedure as with sine:
[tex]\begin{gathered} \cos 60=\frac{y}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\cos 60=y \\ y=5\sqrt[]{3} \end{gathered}[/tex]The correct answer is D. x=15, y=5sqrt3.
A. 12in ^2B. 30 in ^2C. 24 in ^2 D. 27 in 2pls help with guided practice
Answers
The given figure is a parallelogram. The formula for determining the area of a parallelogram is expressed as
Area = base * height
From the diagram,
base = 9 inches
height = 3 inches
Area = 9 * 3 = 27 in^2
The correct option is D
Perform the indicated operation 4.8L +12.6L
Answers
To perform a operation with the same variable (L), add or subtract the coefficients before the variable and keep the variable.
4.8 L + 12.6 L
(4.8 + 12.6) L
17.4L
Answer: 17.4 L.
The following sequence has a degree of 3:3, -4, -23, -60, -121, -212, -339, ....TrueFalse
Answers
-4 -23 -60 -121 -212 -339
27 37 61 91 127
False, this sequence does not have a degree of 3
Solve Brain Teaser
Write an expression that has a value of 40 using two operations and each of the numbers 1, 2, 3, 4, and 5 exactly once.
More Rules for Your Expression
You can use parentheses or other grouping symbols.
You can make one of your numbers an exponent.
You can use either operation as many times as you like, but you can use each number only one time in the expression.
Bonus Challenge
This brain teaser has more than one solution. Can you find one more?
Answers
The required expression is given as 2×4×5, this gives the value 40.
Given that,
To write an expression that has a value of 40 using two operations and each of the numbers 1, 2, 3, 4, and 5 exactly once.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
From the multiple iterations, we have to choose appropriate numbers,
first the greatest multiplied value can be calculated by two number is given as,
4 × 5 = 20,
Now we have to determine only one operation.
So when we multiply 20 by 2 we get 40,
So.
40 = 2×4×5
Thus, the required expression is given as 2×4×5, this gives the value 40.
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Simplify the following union and/or intersection.Answer(-∞, 3] n [3, 13)
Answers
Given:
[tex](-\infty,3]\cap[3,13)[/tex]Required:
Simplify the intersection.
Explanation:
The given intersection is
[tex](-\infty,3]\cap[3,13)[/tex]The first interval includes the values greater than
[tex]-\infty[/tex]to equal 3 and the second interval includes the values from 3 to less than 13.
The intersection in both intervals is only the value 3.
Final Answer:
The intersection value is 3.
Probability of dependent events2/5EspanolA department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 5 live in the town of Gaston,2 live in Pike, and 2 live in Wells. Two winners will be selected at random. What is the probability that both winners live in Gaston? Write your answer as afraction in simplest form.0DOХ5?
Answers
Given there are 9 customers who have entered the drawing, 5 live in the town of Gaston, 2 live in Pike, and 2 live in wells. Two winners will be selected at random.
We have to find the probability that both winners live in Gaston.
The probability that the first winner selected is from Gaston is:
[tex]P(A)=\frac{5}{9}[/tex]The probability that the second winner selected is from Gaston is:
[tex]P(B|A)=\frac{4}{8}=\frac{1}{2}[/tex]The probability that both winners live in Gaston is:
[tex]\begin{gathered} P(A\cap B)=P(A)\cdot P(B|A) \\ =\frac{5}{9}\cdot\frac{1}{2} \\ =\frac{5}{18} \end{gathered}[/tex]Thus, the answer is 5/18.
Help Dalton explain his work. Complete the paragraph.One way to show that FGHI is a rectangle is to show that all 4 of its angles are rightangles. So, I found the slope of each side. The slope of FG and IH wasTheslope of FI and GH wasThen I knew that ZF, LG, ZH, and ZI were all rightangles becauselines have
Answers
ANSWERS
...The slope of FG and IH was 4/5. The slope of FI and GH was -5/4. Then I knew that ∠F, ∠G, ∠H, and ∠I were all right angles because perpendicular lines have opposite reciprocal slopes.
EXPLANATION
The slope of a line is given by,
[tex]m=\frac{\Delta y}{\Delta x}[/tex]For lines FG and IH, the slope is,
[tex]m_{FG}=m_{IH}=\frac{8}{10}=\frac{4}{5}[/tex]Similarly, the slope of lines FI and GH is,
[tex]m_{FI}=m_{GH}=\frac{5}{-4}=-\frac{5}{4}[/tex]Note that the slopes are opposite reciprocals, which makes each pair of lines perpendicular lines.
A rock is thrown upward from the top of a 80-foot high cliff overlooking the ocean at a speed of 64 feetper second The rock's height above ocean can be modeled by the equationH (t) = -16t^2 +64t + 80.a. When does the rock reach the maximum height?The rock reaches its maximum height after ________second(s).b. What is the maximum height of the rock?The maximum height obtained by the rock is_______feet above sea level.c. When does the rock hit the ocean?The rock hits the ocean after_____seconds.
Answers
Given:
The speed is 64 feet per second.
The height of the high cliff is 80 feet.
The function is
[tex]H(t)=-16t^2+64t+80[/tex]a)
We need to find the maximum value of t in the given function to find a time when the rock reaches its maximum height.
Differentiate the given equation, we get
[tex]H^{\prime}(t)=-16(2t)^{}+64[/tex][tex]H^{\prime}(t)=-32t^{}+64[/tex]Set H'(t)=0 and solve for t.
[tex]0=-32t^{}+64[/tex]Adding 32t on both sides, we get
[tex]0+32t^{}=-32t+64+32t[/tex][tex]32t^{}=64[/tex]Dividing both sides by 32, we get
[tex]\frac{32t}{32}^{}=\frac{64}{32}[/tex][tex]t=2[/tex]Hence the rock reaches its maximum height after 2 seconds.
b)
Substitute t=2 in the given equation to find the maximum height of the rock.
[tex]H(2)=-16(2)^2+64(2)+80[/tex][tex]H(2)=144[/tex]Hence the maximum height obtained by the rock is 144 feet above sea level.
c)
Substitute H(t)=0 in the given function to find the time when the rock hit the ocean.
[tex]0=-16t^2+64t+80[/tex]Dividing both sides by (-16), we get
[tex]0=-\frac{16t^2}{-16}+\frac{64t}{-16}+\frac{80}{-16}[/tex][tex]0=t^2-4t-5[/tex][tex]t^2-4t-5=0[/tex][tex]t^2+t-5t-5=0[/tex][tex]t(t+1)-5(t+1)=0[/tex][tex](t+1)(t-5)=0[/tex][tex](t+1)=0,(t-5)=0[/tex][tex]t=-1,t=5[/tex]Omitting the negative value, we get t= 5 seconds.
Hence the rock hits the ocean after 5 seconds.
what is the perimeter? and what unit should i use?
Answers
The given information is:
- 7-gon: it has 7 sides.
- a=15 ft
- s=14 ft
The perimeter, is the sum of the side lengths, as it has 7 sides, then its perimeter is:
[tex]\begin{gathered} P=7s \\ P=7*14ft \\ P=98ft \end{gathered}[/tex]Now, the area is given by the formula:
[tex]\begin{gathered} A=\frac{7}{2}(s*a) \\ \\ A=\frac{7}{2}(14ft*15ft) \\ \\ A=\frac{7}{2}(210ft^2) \\ \\ A=\frac{1470ft^2}{2} \\ \\ A=735ft^2 \end{gathered}[/tex]The area is 735 square feet