If a warren of bunnies is growing at 14% per month then the approximate doubling time is 5 months.
A warren of bunnies is growing at 14% per month
r = 14% = 0.14
Let the initial population of bunnies be N
Then the final population of bunnies = 2N
N(1 + r)ˣ = 2N
here x is time in months
(1 + 0.14)ˣ = ln 2
x ln 0.14 = ln 2
x = 5.29 months
b) doubling time = 5months
number of cycle = 24/5
population = 400(2)²⁴/⁵
= 11143
c) exact doubling time is 5.29 months
Therefore, if a warren of bunnies is growing at 14% per month then the approximate doubling time is 5 months.
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the perimeter of a square box is 12x + 32 drag number to complete an equivalent expression that shows the premier has four times the side length of the box
The perimeter of the box is given as
12x + 32
To write an equivalent expression that shows the premier has four times the side length of the box , we would factorise the expression. It becomes
4(12x/4 + 32/4)
= 4(3x + 8
Find the perimeter of quadrilateral ABCD with vertices A(0,4), B(4,1), C(1, -3), and D(-3,0).25 units100 units5 units20 units
The perimeter is the sum of the length of each side of the quadrilateral. We would find the length of each side by applying the formula for finding the distance between two points which is expressed as
[tex]\text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Thus, we have
[tex]\begin{gathered} ForAB,x1=0,y1=4,x2=4,\text{ y2 = 1} \\ \text{Distance = }\sqrt[]{(4-0)^2+(1-4)^2\text{ }}\text{ = }\sqrt[]{16\text{ + 9}} \\ AB\text{ = 5} \\ \text{For BC, x1 = 4, y1 = 1, x2 = 1, y2 = - 3} \\ \text{Distance = }\sqrt[]{(1-4)^2+(-3-1)^2}\text{ = }\sqrt[]{9\text{ + 16}} \\ BC\text{ = 5} \\ \text{For CD, x1 = 1, y1 = - 3, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-1)^2+(0--3)^2}\text{ = }\sqrt[]{16\text{ + 9}} \\ CD\text{ = 5} \\ \text{For AD, x1 = 0, y1 = 4, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-0)^2+(0-4)^2\text{ }}\text{ = }\sqrt[]{9\text{ + 16}} \\ AD\text{ = 5} \end{gathered}[/tex]Perimeter = AB + BC + CD + AD = 5 + 5 + 5 + 5
Perimeter = 20 units
Enter your answer, rounded to the nearest tenth, in the box.
ANSWER:
-11.4
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f\mleft(x\mright)=\frac{100}{-10+e^{-0.1x}}[/tex]We calculate the result when x = -2, just like this:
[tex]\begin{gathered} f(-2)=\frac{100}{-10+e^{-0.1\cdot-2}} \\ f(-2)=\frac{100}{-10+e^{0.2}} \\ f(-2)=\frac{100}{-10+1.22} \\ f(-2)=\frac{100}{-8.78} \\ f(-2)=-11.4 \end{gathered}[/tex]When x = -2, the value of the function is equal to -11.4
the triangles are similar. find the similarity ratio of the first to the second
To get the similarity ratio between both triangles, write down a ratio between two similiar sides. Let's take the base, for example
[tex]4\colon6[/tex]Simplifying,
[tex]2\colon3[/tex]Thereby, the similarity ratio between both triangles is:
[tex]2\colon3[/tex]Ans: Option B
use the diagram at the right name the following three points ray
From the geometric diagram below
(1) Three diagram
[tex]\text{ Points JQE is a 3 points}[/tex](2) A ray
[tex]RP\text{ is a ray}[/tex](3) Two intersecting lines but not perpendicular
[tex]\text{ line RF and line NI are the two intersecting lines but not perpendicular}[/tex]The local weather report states that there is 3/5 a chance of rain today, but it is more likely to rain tommorrow than today. What is a possible probability of rain for tommorrow? A.0.4 B. 0.5 I C. 0.6 D. 0.7
D. 0.7
Explanations:Probability is the chance (likelihood) that an event will take place
The probabilty that it will rain today = 3/5 = 0.6
There is more likelihood that it will rain tomorrow that today.
This means that the probabilty that it will rain tomorro is greater than the probability that it will rain today.
Therefore, the probability of rain tomorrow is more than 0.6
Only option D (0.7) is greater than 0.6, and it is the only correct choice
Select all sets of triangles that can be provencongruent using Side-Angle-Side(SAS).
SOLUTION
We want to select all triangles from the image that can be proven by the side angle side theorem which states that
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
Now looking at the triangles
We can see that triangles in number 1, 2, 3 follows this theorem.
4 does not because the equal angles are not present
5, the triangles are congruent, but do not follow the SAS theorem
6 follows as we can see the equal sides and angle
7 shows two equal angles only, but we need one equal angles and two equal sides.
Hence the answer is 1, 2, 3 and 6 only
translate and simplify subtract 18 from -11 .enter only the simplified results
Problem
translate and simplify subtract 18 from -11 .enter only the simplified results
Solution
For this case we can do the following:
-11- 18= -29
Final answer: -29
what is the difference in a probability that the student will spin a factor of 83 times in a row in the probability that a student will spin a number greater than 63 times in a row
The number 8 has factors 1, 2, 4 and 8.
The only numbers in the spin greater than 6 are 7 and 8,
The probability that the student will spin a factor of 8 three times in a row is given by: (4/8)*(4/8)*(4/8) = (1/2)*(1/2)*(1/2) = 1/8
The probability that the student will spin a number greater than 6 three times in a row is given by (2/8)*(2/8)*(2/8) = (1/4)*(1/4)*(1/4) = 1/64
Then, the difference between these two probabilities is given by 1/8 - 1/64 = 7/64
Which is the best estimate for 2 2/3 × 3 1/4
The best estimate of the real number expression; 2 ⅔ × 3 ¼ as given in the task content is; 8 ⅔.
What is the best estimate of the real number expression given?It follows from the task content that the best estimate of the real number expression given is to be determined.
On this note, the mixed numbers must be converted to fractions for ease of computation as follows;
Therefore; 2 ⅔ = 8 / 3.
And, 3 ¼ = 13 / 4.
Therefore, the required evaluation of the expression is;
2 ⅔ × 3 ¼ = 8 / 3 × 13 / 4
= 104/12
= 26 / 3
Hence, the best estimate for the given expression is; 26 / 3 Or 8 ⅔.
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What is the residual of a performance with a revenue of $700 and 70 seats occupied?
b) Use the graph to estimate the
value of x when y = 1
Answer:
Hey bro you're welcome.
Step-by-step explanation:
Question 7b: Let g(x) be a polynomial function. Name all horizontal andvertical intercepts of the graphsg(x) = (x - 1)2 (x + 2)Horizontal intercepts: 1, -2; vertical intercepts: 2Horizontal intercepts: 2, vertical intercepts: 1,-2Horizontal intercepts: -1, 2, vertical intercepts: 4Horizontal intercepts: 4, vertical intercepts: -1,2
The given function is expressed as
g(x) = (x - 1)^2(x + 1)
It can be written as
y = (x - 1)^2(x + 1)
The horizontal intercept is also known as the x intercept. The x intercept is the value of x when y = 0
If we substitute y = 0 into the function, it becomes
0 = (x - 1)^2(x + 2)
This means that
(x - 1)^2 = 0 and x + 2 = 0
For (x - 1)^2 = 0, if we take the square root of both sides, it becomes
x - 1 = 0
x = 1
For x + 2 = 0,
x = - 2
Thus, the horizontal intercepts are 1 and - 2
The vertical intercept is also known as the y intercept. The y intercept is the value of y when x = 0
If we substitute x = 0 into the function, it becomes
y = (0 - 1)^2(0 + 2)
y = (- 1)^2(2)
y = 1 * 2 = 2
Thus, the vertical intercept is 2
Thus, the correct option is
Horizontal intercepts: 1, -2; vertical intercepts: 2
Need help with number five. The question is solve each system
5)
The given equations are
- 4x - 2y + 3z = 7
- 3x + 5y - 3z = 13
- 5x + y - z = 11
From equation 3, we have
y = 11 + 5x + z
We would substitute y = 11 + 5x + z into equations 1 and 2. For equation 1, we have
- 4x - 2(11 + 5x + z) + 3z = 7
- 4x - 22 - 10x - 2z + 3z = 7
- 4x - 10x - 2z + 3z = 7 + 22
- 14x + z = 29
For equation 2, we have
- 3x + 5(11 + 5x + z) - 3z = 13
- 3x + 55 + 25x + 5z - 3z = 13
- 3x + 25x + 5z - 3z = 13 - 55
22x + 2z = - 42
Dividing both sides of the equation by 2, we have
11x + z = - 21
z = - 21 - 11x
Substituting z = - 21 - 11x into - 14x + z = 29, we have
- 14x - 21 - 11x = 29
- 14x - 11x = 29 + 21
- 25x = 50
x = 50/- 25
x = - 2
z = - 21 - 11(- 2) = - 21 + 22
z = 1
Substituting x = - 2 and z = 1 into y = 11 + 5x + z, we have
y = 11 + 5(-2) + 1
y = 11 - 10 + 1
y = 2
The solutions are
x = - 2, y = 2, z = 1
3. What is the domain of the relation described by the set of ordered pairs {(-2, 8), (-1, 1), (0, 0), (3, 5), (4, -2)}?{-2, -1, 0, 4,5){-2, 0, 1, 5, 8}{-2, -1,0,3,4}{-2, -1, 0, 1,5}
The domain is related to x axis coordinates. So, you have to take the x coordinate of each point
-2,-1,0,3,4
hi help I've been trying to solve this for an hour and this is due in 10 minutes I just really need the correct answer please help
We have the following:
We can confirm the intercepts with the y-axis, since it is when x = 0, in the case of the first equation it is 2 and in the second equation it is 1
Therefore, we limit ourselves to the answers C and D, now we can calculate the slope as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The point are (0, 2) and (-6, -1)
[tex]m=\frac{-1-2}{-6-0}=\frac{-3}{-6}=\frac{1}{2}[/tex]The slope is 1/2, therefore, the equations are
[tex]\begin{gathered} y=\frac{1}{2}x+2 \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]The answer is the option C
How much money will he raise based on the two donations?
The neighbor will donate $0.25 for every 40ft run.
The aunt will donate $18 for every mile run.
To determine how much he will raise if he runs 5miles, you have to calculate the amount per donor and then add them:
Neighbor
1 mile is equal to 5280 feet
To determine how many feet correspond to 5 miles, multiply the distance by 5280
[tex]5\cdot5280=26400ft[/tex]Next, calculate how much we will make:
40ft → $0.25
26400ft → $x
[tex]\begin{gathered} \frac{0.25}{40}=\frac{x}{26400} \\ 26400\cdot\frac{0.25}{40}=26400\cdot\frac{x}{26400} \\ 165=x \end{gathered}[/tex]For running 5miles, Dustin will raise $165 from the neighbor.
Aunt
The aunt will donate $18 per mile run, to determine how much she will donate, multiply $18 by 5
[tex]18\cdot5=90[/tex]For running 5 miles, Dustin will raise $90 from the neighbor.
Next, add both amounts:
[tex]165+90=255[/tex]Dustin will raise $255 for running 5 miles.
write an equation of a line passing through the point (-6,-3) and perpendicular to JK with J (-2, -7) and K (6,5)
EXPLANATION
Given the point: (-6,-3) and the vector JK with J=(-2,-7) K=(6,5)
First we need to the slope of the vector applying the slope formula:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing the ordered pairs J=(-2,-7) and K=(6,5) give us the slope:
[tex]\text{Slope}=\frac{(5-(-7))}{(6-(-2))}=\frac{12}{8}=\frac{3}{2}[/tex]Now, we have the slope and we can use this to find the line that contains the point (-6, -3) applying the generic form:
y= -2x/3 + b where -2/3 is the negative and reciprocal slope perpendicular to the vector JK.
Finally, replacing the point (-6,-3) give us the y-intercept, b,
-3 = -2(-6)/3 + b
Multiplying terms:
-3 = 12/3 + b ---> -3 = 4 + b
Subtracting 4 to both sides:
-3 - 4 = b
Switching sides:
b= -7
The linear equation is y = (-2/3)x - 7 OPTION B
State weather the triangles are similar. If so write a similarity statement and that postulate or theorem you used. The diagram is not drawn to scale.
Given:
To prove the similarity.
Two triangles similarity condition:
If two triangles are similar then the corresponding sides are proportional.
[tex]\Delta\text{OKJ Similar to }\Delta ONM[/tex][tex]\begin{gathered} \frac{OK}{ON}=\frac{OJ}{OM}=\frac{KJ}{NM} \\ \frac{3}{3+1}=\frac{30}{30+10} \\ \frac{3}{4}=\frac{30}{40} \\ \frac{3}{4}=\frac{3}{4} \end{gathered}[/tex]From the given values the corresponding sides are proves as propotional.
[tex]\Delta\text{OKJ Similar to }\Delta ONM[/tex]1v=9. Which equation represents the equation of theparabola with focus (-3,3) and directrix y = 7?A),= (x+3)2 – 5B) y = 5(? – 3)2 +5C) y=-( + 3)2 +5D) y=-2 (2-3)2 +5
SOLUTION
From the focus (-3, 3) and the directrix y = 7 given, note that the vertex is usually between the focus and the directrix.
So, the vertex will have the same x-coordinate as the focus, which is -3, and the y-coordinate of the vertex becomes
[tex]\begin{gathered} \frac{3+7}{2} \\ that\text{ is 3 from the y-coordinate of the focus and 7 from the directrix} \\ y=7 \\ \frac{3+7}{2}=\frac{10}{2}=5 \end{gathered}[/tex]Hence coordinate of the vertex is (-3, 5)
Now, equation of a parabola is given as
[tex]\begin{gathered} (x-h)^2=4p(y-k) \\ where\text{ \lparen h, k\rparen is the coordinate of the vertex and p is the focal length} \\ y=k-p,\text{ so we have } \\ 7=5-p \\ p=5-7=-2 \end{gathered}[/tex]So putting in the values of h, k and p into the equation, we have
[tex]\begin{gathered} (x-h)^{2}=4p(y-k) \\ (x-(-3)^2=4(-2)(y-5) \\ (x+3)^2=-8(y-5) \\ -\frac{1}{8}(x+3)^2=y-5\text{ that is dividing through by -8} \\ making\text{ y the subject, we have } \\ y=-\frac{1}{8}(x+3)^2+5 \end{gathered}[/tex]Hence the answer is
[tex]y=-\frac{1}{8}(x+3)^{2}+5[/tex]Find the equation of this line.(2,2) and (0,-4)
To find the equation;
x₁ = 2 y₁ = 2 x₂ = 0 y₂=-4
we will use the formula;
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x_{}-x_1)[/tex]substituting the values into the above;
[tex]y-2=\frac{-4-2}{0-2}(x-2)[/tex]Then, we will go ahead and evaluate;
[tex]y-2\text{ = }\frac{-6}{-2}(x-2)[/tex][tex]y-2\text{ =3(x-2)}[/tex]y - 2 = 3x - 6
add 2 to both-side of the equation
y = 3x -6+ 2
y = 3x -4
b.InOut133171066co38Rule:
Suppose that the rule is of the form
[tex]y=mx+b[/tex]Where m is the slope and b is the intercept
The slope can be found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You can take any two consecutive x and y values from the given table.
[tex]\frac{17-3}{3-1}=\frac{14}{2}=7[/tex]Similarly,
[tex]\frac{66-17}{10-3}=\frac{49}{7}=7[/tex]As you can see, you will end up with the same slope.
Now let us find the intercept b.
Take any x, y coordinates from the table
[tex](x,y)=(1,3)[/tex]Now substitute them in the slope-intercept equation.
[tex]\begin{gathered} y=7x+b \\ 3=7(1)+b \\ 3=7+b \\ b=-7+3 \\ b=-4 \end{gathered}[/tex]So the rule is
[tex]y=7x-4[/tex]Verification:
Let us verify whether we got the correct rule or not
Substitute the input x coordinates into the rule and check the outputs y coordinates.
[tex]\begin{gathered} y=7(1)-4=7-4=3 \\ y=7(3)-4=21-4=17 \\ y=7(10)-4=70-4=66 \\ y=7(6)-4=42-4=38 \end{gathered}[/tex]As you can see, we have got the same results therefore, the rule is correct.
Consider parallelogram VWXY below using information given in the figure to find x, m angle zvw and m angle zwv
ANSWERS
• x = 5
,• m∠ZVW = 46°
,• m∠ZWV = 41°
EXPLANATION
The diagonals of a parallelogram bisect each other, so
[tex]11=5x+1[/tex]To find x subtract 1 from both sides of the equation,
[tex]\begin{gathered} 11-1=5x+1-1 \\ 10=5x \end{gathered}[/tex]And divide both sides by 5,
[tex]\begin{gathered} \frac{10}{5}=\frac{5x}{5} \\ 2=x \end{gathered}[/tex]Hence x = 5
By the SAS property, triangle VZW and XZY are congruent:
Therefore, corresponding angles are also congruent. Angle ZXY is the one formed by the blue half-diagonal and the third side of the triangle, therefore its corresponding angle for the other triangle is the one formed also by the blue half-diagonal and the third side of the triangle, which is angle ZVW,
[tex]\angle ZVW\cong\angle\text{ZXY}[/tex][tex]m\angle ZVW=46[/tex]It is a similar situation for angle ZWV. This angle is formed by the light blue half-diagonal and the third side of triangle VZW, so its corresponding angle in triangle XZY is the one also formed by the light blue half-diagonal and the third side of the triangle, which is angle ZYX,
[tex]\angle\text{ZWV}\cong\angle\text{ZYX}[/tex][tex]m\angle ZWV=41[/tex]A survey of 85 persons was conducted at TCC, and it was found that 54 persons carried a cell phone, 19 persons carried a tablet computer, and 16 carried both a cell phone and a tablet.How many people carried a cell phone or a tablet?How many people carried neither a cell phone nor a tablet?How many people carried a cell phone only?How many people carried a tablet but not a cell phone?
Answer:
The universal set is given below as
[tex]\xi=85[/tex]The number of people with cell phone is
[tex]n(C)=54[/tex]The number of persons with tablet is
[tex]n(T)=19[/tex]The number of people who carry both cellphone and tablet
[tex]n(C\cap T)=16[/tex]Step 1:
To figure our the number of students that carry cellphone or tablets will be
[tex]\begin{gathered} =38+16+3 \\ =57\text{ }people \end{gathered}[/tex]Hence,
The number of people that carried cell phone or tablet
[tex]\Rightarrow57people[/tex]Step 2:
How many people carried neither a cell phone nor a tablet?
[tex]\begin{gathered} =85-(38+16+3) \\ =85-57 \\ =28 \end{gathered}[/tex]Hence,
The number of people that carried neither cell phone nor a tablet is
[tex]\Rightarrow28people[/tex]Step 3:
How many people carried a cell phone only?
Hence,
The number of people who carried cell-phone only is
[tex]\Rightarrow38people[/tex]Step 4:
How many people carried a tablet but not a cell phone?
Hence,
The number of people that carried a tablet but not a cell phone is
[tex]\Rightarrow3people[/tex]The ages (in years) of the 6 employees at a particular computer store are the following.31, 41, 35, 22, 38, 31Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.(If necessary, consult a list of formulas.)
The standard deviation of the population = 6.08
Explanations:The given ages of the employers are:
31, 41, 35, 22, 38, 31
Find the mean of the dataset:
[tex]\begin{gathered} \mu\text{ = }\frac{\sum ^{}_{}x_i}{N} \\ \mu\text{ = }\frac{31+41+35+22+38+31}{6} \\ \mu\text{ = }\frac{198}{6} \\ \mu\text{ = }33 \end{gathered}[/tex]Find the summation of the square of each deviation from the mean
[tex]\begin{gathered} \sum ^6_{i\mathop=0}(x_i-\mu)^2=(31-33)^2+(41-33)^2+(35-33)^2+(22-33)^2+(38-33)^2+(31-33)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=(-2)^2+(8)^2+(2)^2+(-11)^2+(5)^2+(-2)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=4+64+4+121+25+4 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=222 \end{gathered}[/tex]The standard deviation is given by the formula:
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum ^{}_{}(x_i-\mu)^2}{N}} \\ \sigma\text{ = }\sqrt[]{\frac{222}{6}} \\ \sigma\text{ = }\sqrt[]{37} \\ \sigma\text{ = }6.08 \end{gathered}[/tex]The standard deviation of the population = 6.08 (rounded to 2 decimal places)
its asking for the approximate depth of the river. but I don't know how to determine that
From figure, trngles VWX and VYZ are similar.
So, the ratio of corresponding sides of triangles will be equal. Hence,
[tex]\begin{gathered} \frac{VW}{VY}=\frac{WX}{YZ} \\ \frac{3}{62}=\frac{5}{d} \\ d=\frac{5\times62}{3} \\ =103.3\text{ m} \end{gathered}[/tex]Therefore, the approximate depth of the river is d=103.3 m.
which function will have the greatest value of x equals 80
In order to solve this, we can replace 80 for x into each one of the three given functions, then we identify what value of y is the greatest, like this:
For the first function:
y = 4x
y = 4×80
y = 320
For the second function:
y = x² - 15x + 88
y = 80² - 15×80 + 88
y= 6400 - 1200 + 88
y = 5288
For the third function:
[tex]\begin{gathered} y=1.1135^{80} \\ y=5435.23 \end{gathered}[/tex]As you can see, at x = 80 the function that has the greatest value is the third one.
Find the area of each rectangle using the given information.(A=W x H)Question 9:6 and a height of 36 inches.
The rule of the area of a rectangle is
[tex]A=W\times H[/tex]W is the width
H is the height
Since the ratio between width and height is 9: 6 and the height is 36 inches, then we will use the ratio method
[tex]\begin{gathered} W\rightarrow H \\ 9\rightarrow6 \\ W\rightarrow36 \end{gathered}[/tex]By using the cross multiplication
[tex]\begin{gathered} W\times6=9\times36 \\ 6W=324 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6W}{6}=\frac{324}{6} \\ W=54 \end{gathered}[/tex]Then the width of the rectangle is 54 inches
Substitute W by 54 and H by 36 in the rule of the area to find it
[tex]\begin{gathered} A=54\times36 \\ A=1944inches^2 \end{gathered}[/tex]The area of the rectangle is 1944 square inches
The scores at the end of a game are shown.List the scores in order from greatest to least.Scores:Vince:-0.5, Allison: 3/8, Mariah:-7/20
To arrange the numbers from greatest to least, let us begin by changing all the numbers to decimals.
Vince's Score: -0.5
Allison's Score: 0.375
By long division, we can convert the fraction to a decimal:
Mariah's Score: -0.35
By long division, we have:
Given that we have calculated the scores in decimal, we can clearly see the bigger and smaller numbers.
The order from biggest to smallest is:
Allison: 3/8, Mariah: -7/20, Vince: -0.5
how would I solve the system of equations using elimination?8x - 5y = 114x - 3y =5
Using elimination. In elimination process the two system of equations are multiplied by a apropiate factor , in order to eliminate one of the variables
then
multiplicate first equation by 4
and multiplicate second equation by 8
once obtained both results, then substract them
So then
4• (8x-5y) = 4•11= 44
8• (4x-3y) = 8•5= 40
32x -20y= 44
32x - 24y= 40
4y= 4 then y=1
now replace y=1 in any of both equations
8x -5= 11. Then x= (11+5)/8= 2
x=2