The sides of triangle ABC are: AB = 6 cm,BC = 12 cm, AC = 10cm. K, M and P arethe midpoints of the sides AB, BC and AC respectivelyare the midpoints of the sides and the midpoints of the sides. Calculate the perimeter of KMP.
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Answer: By inspecting the triangle we can come up with the following relationships, using the proportionality:
[tex]\begin{gathered} \frac{12}{10}=\frac{6}{x}\rightarrow(1) \\ \frac{12}{6}=\frac{6}{y}\rightarrow(2) \\ \frac{6}{12}=\frac{3}{z}\rightarrow(3) \end{gathered}[/tex]Solving the three equations, (1) (2) and (3) gives the answer for x,y,z which are the three sides of the smaller triangle, the steps are as follows:
[tex]\begin{gathered} x=KM=5 \\ y=MP=3 \\ z=KP=6 \end{gathered}[/tex]Therefore the perimeter is as follows:
[tex]\begin{gathered} P=x+y+x=5+3+6=14 \\ P_{(KMP)}=14 \end{gathered}[/tex]Related Questions
Andre and Lin are discussing whether it is possible to define latitude and temperature in a way that makes sense to talk about temperature as a function of latitude. They are considering different options. Here are the options: a. Finding the temperature right now in cities with different latitudes b. Finding the daily high temperature at cities that have different latitudes c. Finding the average high temperature in a specific month, e.g., September, at cities that have different latitudes d. Finding the average yearly temperature at cities that have different latitudes None of these options are perfect. All have flaws. Choose one option and give the advantages and disadvantages of the option for talking about temperature as a function of latitude. Answer in the space below
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All answers are kind of similar and none of these options are perfect.
We are going to chose the opcion b, the advantage is that the daily high temperature at cities give us a statistical sample about how latitude impact the temperature and how is the clime in those days.
Disadvantages is that we dont know the lower temperature and how the latitude impact in this case.
if the radius of the circle is 5 units, find the arc length of RQ
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The radius of the circle is r = 5 units.
The formula for the arc length of RQ is,
[tex]RQ=2\pi r\times(\frac{\theta}{360})[/tex]Substitute the values in the formula to obatin the arc length RQ.
[tex]\begin{gathered} RQ=2\pi\cdot5\cdot(\frac{142}{360}) \\ =12.391 \\ \approx12.39 \end{gathered}[/tex]So arc length of RQ is 12.39 units.
Jx+Ky< assume J<0
The equivalent inequality with x isolated in the left side is
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The equivalent inequality with x isolated in the left side is x<(L-Ky)/J
What is equivalent inequality?A positive number divided by both sides of an inequality results in an equal inequality. And if the inequality symbol is reversed, division on both sides of an inequality with a negative value results in an analogous inequality.
Following step by step process-
Jx+Ky<L (Given)
Subtracting Ky on both the side
Jx<L-Ky
Now dividing by J both side
x<(L-Ky)/J
Therefore, equivalent inequality with x isolated in the left side is x<(L-Ky)/J.
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The complete question is:
"Jx+Ky<L assume J<0
The equivalent inequality with x isolated in the left side is"
the Anderson are going on a long sailing trip during the summer however one of the sails on their sailboat ripped and they have to replace it the sail is pictured below if the sailboat sails are sale for 2$ per square foot how much will the new sail cost?
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Firs we need to calculate the area of a triangle
[tex]A=\frac{b\cdot h}{2}[/tex]b= base
h=heigth
in our case
b=8ft
h=12ft
[tex]A=\frac{8\cdot12}{2}=\frac{96}{2}=48ft^2[/tex]then we will calculate the total cost
1 square foot ----- $2
48 square feet ----- x
the total cost is 48*2=96
total cost is $96
how many liters of 10% salt water do you need to add to 5 liters of 25% salt to make 15% salt?
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Answer:
You will need 10 liters of 10% salt water
Step-by-step explanation:
1.In hockey, a player gets credited with a "point" in their statistics when they get an assist or goal.The table shows the number of assists and number of points for 15 hockey players after a season.assistspoints222816184672292691322allo San818131750712173427581834Make a scatter plot of this data. Make sure to scale and label the axes
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From the information given, the number of points gotten depends on the number of assists. this means that the independent variable, x which would be on the horizontal axis is the number of assists and the dependent variable, y which would be on the vertical axis is the number of points. We would plot these values on the scatter plot. the plot is shown below
The number of points is on the vertical axis.
The number of assists is on the horizontal axis
number one name three collinear points number to name four coplanar Point number three name two sets of lines intersect number for name two points not contained in the plane
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The points lying on a single line are called colinear points. So here,
KJD are colinear points as they are lying on a same line.
Points lying on the same plane are called coplanar points. So here, IJFE are coplanar points.
The two sets of line intesects are KD and CF, IG and FH.
The two points that are not in the plane are A and B.
A 4-pound bag of potatoes costs $3.96. What is the unit price?
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Given that 4-pound bag of potatoes costs $3.96 then the unit price which is same as the cost of a pound
= $3.96/4
= $0.99
The unit price is $0.99
When 8 is subtracted from a number and that difference is doubled, the result is 10. What is the number?
A) 6
B) 5
C) 18
D) 13
Answers
Answer:
n = 13
Step-by-step explanation:
Find the number
8 is subtracted from a number
(n-8)
that difference is doubled
2(n-8)
the result is 10
2(n-8) = 10
Solve the equation by dividing each side by 2
2(n-8)/2 = 10/2
n-8 = 5
Add 8 to each side
n-8+8 = 5+8
n = 13
Tina designed an electric skateboard that has a speed of 4 miles per hour. She wants to write a function that represents the distance the skateboard will travel over a given amount of time.Which is the dependent variable in this scenario?the skateboardthe speedthe time traveledthe distance traveled
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ANSWER
The distance traveled
EXPLANATION
We want to identify the dependent variable from the scenario.
The dependent variable in a function is the variable that changes as a result of a change in the independent variable. This implies that it depends on the independent variable for its value.
From the scenario, the distance that the skateboard travels is dependent on the amount of time spent traveling.
Therefore, the dependent variable is the distance traveled.
Reece increases the amount of money he pays into his savings account by 4% each year. This year, he paid £3000 into his account. To the nearest penny, how much did Reece pay into his account a) 1 year ago? b) 10 years ago?
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The money deposited 1 year ago is $2884.61 and the money deposited 10 years ago is $2142.85.
Given that, Reece increases the amount of money he pays into his savings account by 4% each year.
What is savings account?A savings account is a bank account at a retail bank. Common features include a limited number of withdrawals, a lack of cheque and linked debit card facilities, limited transfer options and the inability to be overdrawn.
We know that, simple interest = (P×R×T)/100
a) P=$x, R=4% and T=1 year
SI=3000-x
⇒ 3000-x = (x×4×1)/100
⇒ 3000-x=0.04x
⇒ 1.04x=3000
⇒ x=3000/1.04
⇒ x=$2884.61
Money deposited 1 year ago is $2884.61.
b) P=$y, R=4% and T=10 year
SI=3000-y
⇒ 3000-y = (y×4×10)/100
⇒ 3000-y = 0.4y
⇒ 1.4y = 3000
⇒ y=3000/1.4
⇒ y=$2142.85
Therefore, the money deposited 1 year ago is $2884.61 and the money deposited 10 years ago is $2142.85.
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Ashley pounds 98 pounds one year ago .If she weight 112 pounds what is the percent increase in her weight ?
Answers
Answer:
The increase to the nearest percent is 14%
Step-by-step explanation:
[tex]\frac{112 - 98}{98}[/tex] The percent of increase is the weight change over the original amount
.14285714285 To change a decimal to a percent, move the decimal two places to the right.
Rounded to the nearest percent is
14%
The roots of unity (1) may be calculated from the equation x3-1=0. What are they?
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we find the root of x² + x + 1 has it can't be factorized
Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]for a² + bx + c = 0
comparing: x² + x + 1
where a = 1, b = 1, c = 1
[tex]\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{(1)^2^{}-4(1)(1)}}{2(1)} \\ x\text{ = }\frac{-1\pm\sqrt[]{1^{}-4}}{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{-3}}{2}\text{= }\frac{-1\pm\sqrt[]{-1(3)}}{2} \\ Since\text{ we can't find the square root of a negative number, we apply complex root} \\ \text{let i}^2\text{ = -1} \\ x\text{ = }\frac{-1\pm\sqrt[]{3i^2}}{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{3i^2}}{2}\text{ = }\frac{-1\pm i\sqrt[]{3^{}}}{2} \\ x\text{ = }\frac{-1+i\sqrt[]{3^{}}}{2}or\text{ }\frac{-1-i\sqrt[]{3^{}}}{2} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{The roots of x}^3\text{ - 1 = 0 are:} \\ 1\text{ and }\frac{-1\pm i\sqrt[]{3^{}}}{2} \\ 1\text{ and }\frac{\text{-1 }}{2}\pm\text{ }\frac{i\sqrt[]{3^{}}}{2}\text{ (option C)} \end{gathered}[/tex]Bert opened a savings account 4 years ago the account earns 13%interest compounded monthly if the current balance is 1,000.00 how much did he deposit initially
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To answer this question we need to remember the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where r is the interest rate, n is the number of times it is compounded in a given time t.
In this case we know that A=1,000, r=0.13, n=12 and t=13. Plugging this values in the formula and solving for P we have:
[tex]\begin{gathered} 1000=P(1+\frac{0.13}{12})^{12\cdot4} \\ P=\frac{1000}{(1+\frac{0.13}{12})^{12\cdot4}} \\ P=596.19 \end{gathered}[/tex]Therefore, the initial deposit was $596.19
Josh wants to use Rockaway Hall, the Groove Guru Band, and PJ's Party Supplies. Josh has a total of
650 dollars and wants to invite 25 people. His friend told him he would be able to afford the band for 4 hours. Is that true?
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1) Assume that x is the number of hours and that y is the total cost. To model, write an equation. 2) Tutoring his friend in geometry is the second way he can get money.
One of the first areas of mathematics is geometry, along with arithmetic.
What is the Bernoulli inequality?A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used. It contains a few helpful variations, including those for any integer r 0 and real number x > 1. If x 0 and r 2, the inequality is strictly true.A statement about raising a number to a natural power is made by the binomial inequality: and. It can be easily demonstrated by induction and is essentially a condensed version of the binomial theorem.A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used.To learn more about Bernoulli inequality refer to:
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what must be a factor if the polynomial function f(x) graphed ib the coordinate plane below ?
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Solution
The question gives us a graph that crosses the x-axis at 3 points: x = 1, x = 2, and x = -3. We are asked to find which of the factors on the graph is in the options given.
- Whenever a graph crosses the x-axis at a point "a", it implies that x = a is a root of the graph and as a result, (x - a) must be a factor of the graph.
- We can apply this to the question and derive the factors of the graph as follows:
[tex]\begin{gathered} \text{ When }x=-3\colon \\ x=-3 \\ \text{Add 3 to both sides} \\ x+3=0 \\ \\ \text{Thus, }(x+3)\text{ is a factor of the graph.} \\ \\ \\ \text{When }x=1\colon \\ x=1 \\ \text{Subtract 1 from both sides} \\ x-1=0 \\ \\ \text{Thus, }(x-1)\text{ is a factor of the graph} \\ \\ \\ \text{When }x=2\colon \\ x=2 \\ \text{Subtract 2 from both sides} \\ x-2=0 \\ \\ \text{Thus, (}x-2)\text{ is a factor of the graph.} \\ \\ \\ \text{Thus, we can conclude that the 3 factors of the graph are:} \\ (x+3),(x+1),\text{ and }(x-2) \end{gathered}[/tex]- Going through the options, we can see that only (x - 1) is present in the options.
- Thus, (x - 1) is the answer
Final Answer
(x - 1) is the answer (OPTION B)
2+2 is what i need help???
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We have the following problem given:
[tex]2+2=4[/tex]Then the final answer for this case would be 4
A rectangle is graphed on a coordinate plane and then reflected across the y-axis. If a vertex of the rectangle was at (x, y), which ordered pair represents the corresponding vertex of the new rectangle after the transformation? F (y, x) G (-x, -y) H (-x, y) J (x, y)
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Let's say that the vertex is the following red point:
Then, its reflection across y-axis would be the blue point:
If we observe the coordinates, we will have that:
(5, 3) is transformed into (-5, 3). This is going to happen no matter the coordinate:
12) A row of roses is planted in a repeating pattern of "red, red, yellow, yellow, pink, pink
There is a total of 56 roses planted in the row. How many red roses are there?
Answer:
********
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Answer:
22
Step-by-step explanation:
XXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXX
Each of the capital X's are red roses, and there are 56 x's in total.
what is the mean of 36,38,39,28,34
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We are to find the mean of
[tex]36,\text{ 38, 39, 28, 34}[/tex]Finding mean
[tex]\begin{gathered} M\text{ean = }\frac{36\text{ + 38 + 39 + 28 + 34 }}{5} \\ Mean\text{ = }\frac{175}{5} \\ M\text{ean = 35} \end{gathered}[/tex]Therefore,
mean = 35
Consider the following equation find the X- and y- Intercepts, if possible
Answers
Answer:
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
Explanation:
The x-intercept is the point where the graph crosses the x-axis, so to find the x-intercept, we need to replace y = 0 on the given equation and solve for x
y - 2x = 1
0 - 2x = 1
-2x = 1
-2x/(-2) = 1/(-2)
x = -1/2
Then, the x-intercept is (-1/2, 0)
The y-intercept can be calculated replacing x = 0 and solving for y, so
y - 2x = 1
y - 2(0) = 1
y - 0 = 1
y = 1
Then, the y-intercept is (0, 1)
Therefore, the answers are
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
can u pls help me with this question and this is homework
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the probability is:
[tex]\frac{15+5}{50}=\frac{20}{50}=\frac{2}{5}[/tex]so the answer is 2/5
Determine the perimeter of this shape. Use 3.14 for pi. the numbers are 12m and 15 m
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We are asked to find the perimeter of the figure. To do that we will add the perimeters of the semi-circle and the rectangle.
To determine the perimeter of the semi-circle we will use the following formula:
[tex]P_{c\text{ }}=\frac{\pi D}{2}[/tex]The diameter is 12 m. Replacing in the formula we get:
[tex]P_c=\frac{\pi(12m)}{2}[/tex]Solving the operations:
[tex]P_c=\frac{3.14(12)}{2}=6.28m[/tex]Now we will find the perimeter of the rectangle by adding the length of all of its sides:
[tex]P_R=15m+12m+15m=42m[/tex]Now, the perimeter of the figure is the sum of the perimeters we found:
[tex]\begin{gathered} P=P_c+P_R \\ \end{gathered}[/tex]Replacing:
[tex]P=6.28m+42m=48.28m[/tex]Therefore, the perimeter of the figure is 48.28m
Please assist me in understanding how to solve number 4
Answers
Solution:
Given that;
y varies directly with the square of x
[tex]y\propto x^2[/tex]This expression above becomes
[tex]\begin{gathered} y=kx^2 \\ Where\text{ k is the constant} \end{gathered}[/tex]When
[tex]y=10\text{ and x}=5[/tex]Substitute the values for x and y into the expression above to find k
[tex]\begin{gathered} y=kx^2 \\ 10=k(5)^2 \\ 10=k(25) \\ 10=25k \\ Divide\text{ both sides 25} \\ \frac{25k}{25}=\frac{10}{25} \\ k=\frac{2}{5} \end{gathered}[/tex]The expression becomes
[tex]\begin{gathered} y=kx^2 \\ y=\frac{2}{5}x^2 \end{gathered}[/tex]a) The value of y when x = 20
[tex]\begin{gathered} y=\frac{2}{5}x^2 \\ y=\frac{2}{5}(20)^2 \\ y=\frac{2}{5}(400) \\ y=160 \end{gathered}[/tex]Hence, the value of y is 160
b) The value of x when y = 40
[tex]\begin{gathered} y=\frac{2}{5}x^2 \\ 40=\frac{2}{5}x^2 \\ Crossmultiply \\ 40(5)=2x^2 \\ 200=2x^2 \\ Divide\text{ both sides by 2} \\ \frac{200}{2}=\frac{2x^2}{2} \\ 100=x^2 \\ x^2=100 \\ Square\text{ root of both sides} \\ \sqrt{x^2}=\sqrt{100} \\ x=10 \end{gathered}[/tex]Hence, the value of x is 10
The drama club is selling tickets to their play to raise money foe the show's expenses. They are selling both adult tickets and student tickets. The auditorium can hold no more than 109 people. Write an inequality that could represent the possible values for the number of student tickets sold,s, and the number of adult tickets sold,a, that would satisfy the constraint
Answers
Adult (A)
student (S)
Total people= 109
the maximum number of tickets is 109, in this case is possible 109.
than means
A + S ≤ 109
or
109 ≥ A + S
Hi I need help with question 3 :) . Directions: For each real world situation, write and solve a system of equations . Give the solution as either an ordered pair or list what each variable is worth . Then explain what the solution means in terms of the situation
Answers
3.
We know that Hobby Land sells art supplies two different ways.
We can represent the situation with a system of equations
[tex]\begin{cases}x+y=139\ldots(1) \\ 4x+7y=781\ldots(2)\end{cases}[/tex]Where x is the cost of one easel and y represents the cost of one paint set.
Now, we must solve the system of equations.
We can multiply equation (1) by -4
[tex]\begin{gathered} -4(x+y)=-4(139) \\ -4x-4y=-556\ldots(3) \end{gathered}[/tex]Then, we can add (3) + (2)
[tex]\begin{gathered} -4x-4y=-556 \\ 4x+7y=781 \\ -------------- \\ 3y=225 \end{gathered}[/tex]Now, we can solve the equation for y
[tex]\begin{gathered} 3y=225 \\ y=\frac{225}{3}=75 \end{gathered}[/tex]Finally, to find x we can replace the value of y in the equation (1)
[tex]\begin{gathered} x+75=139 \\ x=139-75=64 \end{gathered}[/tex]So, the cost of one easel is $64.
Solution as either an ordered pair:
- (64, 75).
During a heavy rainstorm a city in Florida received 12 1/4 inches of rain in 25 1/2 hours.What is the approximate rainfall rate in inches per hour?
Answers
Data:
The city received 12 (1/4) inches of rain in 25 (1/2) hours.
Procedure:
Rewriting the numbers as decimals.
[tex]12\cdot\frac{1}{4}=12.25[/tex][tex]25\cdot\frac{1}{2}=25.5[/tex]To find the approximate rainfall rate in inches per hour, we have to do as follows:
[tex]\frac{12.25}{25.5}\approx0.48\frac{in}{h}[/tex]Rounding the result, we get...
[tex]0.48\approx0.5\approx\frac{1}{2}[/tex]Answer: D. about 1/2 inch per hour
Lines from Point/Slope (Diagonal Only) Nov 23, 9:40:49 AM What is the equation of the line that passes through the point (-4, -2) and has a slope of - Answer: Submit Answer attempt 2 out of 2
Answers
The point-slope form of a line is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope
Replacing with point (-4, -2), we get:
y - (-2) = m(x - (-4))
y + 2 = m(x + 4)
If the slope is, for example, 3, the equation would be:
y + 2 = 3(x + 4)
If the slope is -2/5, the equation would be:
y + 2 = -2/5(x + 4)
The Consumer Price Index (CPI), which measures the cost of a typical package of consumer goods, was 202.9 in 2011 and 233.2 in 2016. Let x=11 correspond to the year 2011 and estimate the CPI in 2013 and 2014. Assume that the data can be modeled by a straight line and that the trend continues indefinitely. Use two data points to find such a line and then estimate the requested quantities. Let y represent the CPI. The linear equation that best models the CPI is____ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to the nearest hundredth as needed.)
Answers
The first thing we have to identify in our problem are the variables
[tex]\begin{gathered} x\to\text{time} \\ y\to\text{CPI} \end{gathered}[/tex]Now we see the points (x,y) that gives us the problem
[tex]\begin{gathered} 2011\to(11,202.9) \\ 2016\to(16,233.2) \end{gathered}[/tex]Since behavior can be modeled by a straight line, we use the general equation of the straight line
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
Taking this into account and with the 2 points that they give us, we proceed to calculate the equation of the line starting with the slope:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{233.2-202.9}{16-11} \\ m=\frac{30.3}{5} \\ m=6.06 \end{gathered}[/tex][tex]\begin{gathered} y=6.06x+b \\ 202.9=6.06(11)+b \\ b=202.9-66.66 \\ b=136.24 \end{gathered}[/tex]The equation that models the behavior of the CPI is
[tex]y=6.06x+136.24[/tex]Now we calculate the CPI values for the years 2013 and 2014
[tex]\begin{gathered} 2013\to x=13 \\ y=6.06(13)+136.24 \\ y=78.78+136.24 \\ y=215.02 \end{gathered}[/tex][tex]\begin{gathered} 2014\to x=14 \\ y=6.06(14)+136.24 \\ y=84.84+136.24 \\ y=221.08 \end{gathered}[/tex]What is the value of 32 / (-4)?- 128 8- 828
Answers
The expression given is,
[tex]\frac{32}{(-4)}[/tex]Let us now evaluate the expression
[tex]\frac{32}{(-4)}=\frac{32}{-4}=-8[/tex]Hence, the answer is -8.