consider the function w(x) = 2x^3 + 15x^2 -36x - 6 on interval -6 ≤ x ≤ 2
On the given interval this function has absolute:
Minimum at the point -
Maximum at the point -
Answers
The minimum absolute value of the function is at x = 1 and the maximum absolute value is at x = -6.
What is absolute value?Absolute value describes the distance from zero that a number is on the number line, without considering direction.
Given a function, f(x) = 2x³+15x²-36-6
f'(x) = 6x²+30-36
Let f'(x) = 0
6x²+30-36 = 0
On solving, we get,
x = 1 or -6
Putting x = 1,-6, 2 for maximum and minimum values
f(1) = -25
f(-6) = 318
f(2) = -2
Hence, the minimum absolute value of the function is at x = 1 and the maximum absolute value is at x = -6.
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Related Questions
Please help me solve question 6 on this algebra assignment
Answers
At the zero of the function, f(x) = 0. Substituting f(x) = 0, we get:
[tex]0=\frac{3}{5}x-\frac{4}{3}[/tex]Adding 4/3 at both sides of the equation:
[tex]\begin{gathered} 0+\frac{4}{3}=\frac{3}{5}x-\frac{4}{3}+\frac{4}{3} \\ \frac{4}{3}=\frac{3}{5}x \end{gathered}[/tex]Multiplying by 5/3 at both sides of the equation:
[tex]\begin{gathered} \frac{5}{3}\cdot\frac{4}{3}=\frac{5}{3}\cdot\frac{3}{5}x \\ \frac{5\cdot4}{3\cdot3}=x \\ \frac{20}{9}=x \end{gathered}[/tex]Therefore the coordinates of the zero of the function are:
[tex](x,f(x))=(\frac{20}{9},0)[/tex]
Please help on average rate of change!
Answers
The average rate of change on the interval [-1, 2] is 1/3.
How to get the average rate of change?For any function f(x), we define the average rate of change on an interval [a, b] as:
r = ( f(b) - f(a))/(b - a)
In this case, the function is graphed, and the interval is [-1, 2]
On the graph we can see that:
f(-1) = -3
and
f(2) = -2
Replacing these we will get:
r = ( f(2) - f(-1))/(2 - (-1))
r = (-2 + 3)/(3) = 1/3
The average rate of change is 1/3.
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A) What does the point (1,8) represent in the context of the situation? B) Is the amount of money proportional to the number of hours worked? C) Write an equation that represents this situation? D) What will be Amber’s Wages after 6 hours worked?
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Answer:
A) Amber's wages for 1 hour is $8.
B) Yes
C) y = 8x
D)
Explanation:
A) Looking at the graph, we can deduce that the point (1, 8) shows how much Amber makes in one hour. So in 1 hour, Amber makes $8.
B)To determine whether the amount of money is proportional to the number of hours worked, we have to look at the graph and see if it starts from the origin (0, 0), if it does then we can conclude that they are proportional.
Since the graph starts from the origin (0, 0), then the amount of money is proportional to the number of hours worked.
C) The slope-intercept equation of a line is given as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
So let's go ahead and determine the slope of the line at points (1, 8) and (2, 16) using the below formula;
[tex]m=\frac{y_2-y_1_{}_{}_{}}{x_2-x_1_{}}=\frac{16-8}{2-1}=\frac{8}{1}=8[/tex]Since the line starts from the origin, therefore the y-intercept, b, is zero.
Since m = 8 and b = 0, the equation can then be written as;
[tex]\begin{gathered} y=8x+0 \\ y=8x \end{gathered}[/tex]D
For each problem below find the missing factor by computing the inverse operation
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Given:
There are given that the fraction:
[tex]4\frac{1}{2}-\text{ \lbrack \rbrack}=2\frac{7}{8}[/tex]Explanation:
Suppose missing information is x
Then,
Ater that we need to find the value of x
So,
[tex]4\frac{1}{2}-x=2\frac{7}{8}[/tex]Then,
[tex]\begin{gathered} 4\frac{1}{2}-x=2\frac{7}{8} \\ \frac{9}{2}-x=\frac{23}{8} \\ \frac{9}{2}-x-\frac{9}{2}=\frac{23}{8}-\frac{9}{2} \\ -x=\frac{23}{8}-\frac{9}{2} \end{gathered}[/tex]Now,
[tex]\begin{gathered} -x=\frac{23}{8}-\frac{9}{2} \\ -x=\frac{23-36}{8} \\ -x=\frac{-13}{8} \\ x=\frac{13}{8} \\ x=1\frac{5}{8} \end{gathered}[/tex]Final answer:
Hence, the missing factor is shown below:
[tex]x=1\frac{5}{8}[/tex]If Karen has 6 cups of oatmeal and she divides it into 1/3 cup servings, how many servings of oatmeal will she have?
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Problem
If Karen has 6 cups of oatmeal and she divides it into 3/4 cup servings, how many servings of oatmeal will she have?
Solution
For this case the operation that we need to do is:
[tex]\frac{6\text{cups}}{\frac{3}{4}\frac{\text{cups}}{\text{serving}}}=\frac{6\cdot4}{3}==\frac{24}{3}=8\text{servings}[/tex]And for this case the final answer would be 8 servings
I need help with number 7 the first question on the top of the page please
Answers
SK= 13x-5
KY= 2x+9
SY=36-x
By looking at the line segment we can state:
SY = SK+KY
Replacing with the values, and solving for x:
36-x=13x-5+2x+9
Sum and subtract alike terms
36+5-9=13x+2x+x
32= 16x
Divide both sides by 16:
32/16=16x/16
2=x
Replace the value of x in each expression:
SK= 13x-5=13(2)-5=26-5=21
KY= 2x+9=2(2)+9=4+9=13
SY=36-x =36-(2)=34
So, the answers are:
x=2
SK=21
KY=13
SY=34
Choose the correct answer. 1. Shari made a net of a box to find how much wrapping paper she will need to . wrap the box 8 in. 5 in.
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The total area needed to be covered is 158 square inch.
It is calculated by adding all the area
[tex]2\ast(8\ast5)+\text{ 2}\ast(5\ast3)+2\ast(8\ast3)=158in^2\text{ }[/tex](calc) which graph shows a function and its inverse ?
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Answer: We have to pick a graph that represents a function and its inverse function, or:
[tex]\begin{gathered} f(x)\rightarrow\text{ and }\rightarrow f^{-1}(x) \\ \end{gathered}[/tex]The inverse function switches the x and y variables, therefore the axes with it, the final result is two functions that are symmetrical about y = x line.
Example:
[tex]\begin{gathered} f(x)=\sqrt{x}\rightarrow\text{ Function} \\ \\ f^{-1}(x)=x^2\rightarrow\text{ Inverse Function} \end{gathered}[/tex]Graph:
Therefore the graph out of the options which has these properties is:
[tex]\text{ Graph\lparen C\rparen}[/tex]The answer, therefore, is Graph(C).
In your Grandpa Will's recipe for a marinade, each serving uses 3.5 tablespoons of ketchup and 7 tablespoons of vinegar. If 31.5 tablespoons of ketchup will be used for a larger batch of marinade, how much vinegar is needed? tablespoons of vinegar are needed. Submit answer
Answers
The rate of ketchup to vinegar should be preserved. Let V be the volume of vinegar that will be used for the larger batch of marinade. Since the recipe uses 7 tablespoons of vinegar for each 3.5 tablespoons of ketchup, then:
[tex]\frac{V}{31.5}=\frac{7}{3.5}[/tex]Then, the volume of vinegar for the larger batch of marinade can be calculated as:
[tex]\begin{gathered} V=\frac{7}{3.5}\times31.5 \\ =63 \end{gathered}[/tex]Therefore, 63 tablespoons of vinegar are needed.
A couple took a small airplane for a flight to the wine country for a romantic dinner and then returned home. The plane flew a total of 5 hours and each way the trip was 233 miles. If the plane was flying at 170 miles per hour, what was the speed of the wind that affected the plane?
Answers
Answer:
114.26 miles per hour
Explanation:
Let us call
v = wind speed
Then
speed with the wind = 170 + v
speed against the wind = 170 -v
Therefore,
The time taken on the outward journey ( with the wind):
[tex]\frac{233}{170+v}[/tex]
Time take on the return journey
[tex]\frac{233}{170-v}[/tex]These two times must add up to 5 hours, the total time of the journey.
[tex]\frac{233}{170+v}+\frac{233}{170-v}=5[/tex]Solving the above equation for v will give us the wind speed.
The first step is to find the common denominator of the two rational expressions. We do this by multiplying the left rational expression by (180-v)/(180-v) and the right expression by (180 + v)/(180 + v).
[tex]\frac{170-v}{170-v}*\frac{233}{170+v}+\frac{233}{170-v}*\frac{170+v}{170+v}=5[/tex][tex]\frac{233(170-v)+233(170+v)}{(170-v)(170+v)}=5[/tex]Dividing both sides by 233 gives
[tex]\frac{(170-v)+(170+v)}{(170-v)(170+v)}=\frac{5}{233}[/tex]The numerator on the left-hand side of the equation simplifies to give
[tex]\frac{2\times170}{(170-v)(170+v)}=\frac{5}{233}[/tex][tex]\Rightarrow\frac{340}{(170-v)(170+v)}=\frac{5}{233}[/tex]Expanding the denominator gives
[tex]\operatorname{\Rightarrow}\frac{340}{170^2-v^2}=\frac{5}{233}[/tex][tex]\frac{340}{28900-v^2}=\frac{5}{233}[/tex]Cross multipication gives
[tex]5(28900-v^2)=340\times233[/tex]Dividing both sides by -5 gives
[tex]v^2-28900=-\frac{340\times233}{5}[/tex][tex]v^2-28900=-15844[/tex]Adding 28900 to both sides gives
[tex]v^2=13056[/tex]Finally, taking the sqaure root of both sides gives
[tex]\boxed{v=114.26.}[/tex]Hence, the speed of the wind, rounded to two decimal places, was 114.26 miles per hour.
simple interest interest: $50principal:$350rate: 6.5time:x
Answers
Given:
Interest (SI) = 50
Principal (P) = 350
rate (R) = 6.5. (Here, rate is 6.5 %)
To find time,
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=P\times R\times T \\ 50=350\times\frac{6.5}{100}\times x \\ x=\frac{50}{22.75} \\ x=2.197 \\ x\approx2\text{ years ( approximated) } \end{gathered}[/tex]Answer: x = 2 years.
ActiveApplying the Triangle Inequality Theoremin triangle ABC, AB measures 25 cm and AC measures 35 cm.The inequalitycentimeters.
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Using the Triangle inequality:
[tex]zso:[tex]undefined[/tex]if frita goes to the mall, then alice will go to the mall
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Given
The statements,
If Frita goes to the mall, then Alice will go to the mall.
If Wally goes to the mall, then Frita will go to the mall.
To find: The conclusion using the law of Syllogism.
Explanation:
It is given that,
If Frita goes to the mall, then Alice will go to the mall.
If Wally goes to the mall, then Frita will go to the mall.
That implies,
If Wally goes to the mall, then Frita will go to the mall.
If Frita goes to the mall, then Alice will go to the mall.
Here, consider the statement Wally goes to the mall as p, the statement Frita will go to the mall as q, and the statement Alice will go to the mall as r.
Therefore,
[tex]Conclusion:\text{ }If\text{ }Wally\text{ }goes\text{ }to\text{ }the\text{ }mall,\text{ }then\text{ }Alice\text{ }will\text{ }go\text{ }to\text{ }the\text{ }mall.[/tex]Hence, the answer is option C).
Which of the following graphs could be a representation of a geometric sequence?Check all that apply.A.B.C.D.
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SOLUTION:
We want to find the graph corresponding to a geometric sequence.
The equation of a geometric sequence is;
[tex]a_n=a_1(r)^{n-1}[/tex]This is clearly an exponential function with a starting value a.
The correct graphs are OPTION B and OPTION D
Need help with homework
Answers
Domain interval are the interval for the x - values on the linear graph
Therefore the domain intervals from the attached graph is
[tex]-3\leq x\leq4[/tex]The constant of variation for a function is 2. Which of the following graphs best represents this situation
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The required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
Given that,
To determine the graphs which show the constant of variation for a function is 2.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
in the graphs only graph, A and B show the given condition of the constant of variation for a function is 2. Because in both graphs shows that y = 2x and 2y = x.
Thus, the required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
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FEΗIdentify the similar triangles.ΔH FEΝΔΔΗFE Δ
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According to the given figure, the common parts between triangles are angle G, side GH and angles H and E being equal to 90°.
So, the similar triangles are FHG and HEG because that's the position where the corresponding equivalent parts match.
Additionally, triangle HFE would be similar to triangles FGH and HGE.if your able to answer all of them i will be giving you 5 stars
Answers
The function given is:
[tex]f(x)=-16x^2+60x+16[/tex]PART AThe factorization steps are shown below:
[tex]\begin{gathered} f(x)=-16x^2+60x+16 \\ f(x)=4(-4x^2+15x+4) \\ f(x)=4(-4x^2+16x-x+4) \\ f(x)=4(-4x(x-4)-1(x-4)) \\ f(x)=4(-4x-1)(x-4) \end{gathered}[/tex]PART BTo find the x intercepts, we set f(x) equal to 0 and solve for x:
[tex]\begin{gathered} f(x)=4(-4x-1)(x-4) \\ f(x)=0 \\ 4(-4x-1)(x-4)=0 \\ -4x-1=0--------(1) \\ OR \\ x-4=0---------(2) \end{gathered}[/tex]Solving (1), we have:
[tex]\begin{gathered} -4x-1=0 \\ 4x=-1 \\ x=-\frac{1}{4} \\ x=-0.25 \end{gathered}[/tex]and, solving (2), we have:
[tex]\begin{gathered} x-4=0 \\ x=4 \end{gathered}[/tex]The x-intercepts are
[tex]\begin{gathered} x=-0.25 \\ x=4 \end{gathered}[/tex]PART CThe standard equation of a quadratic is
[tex]f(x)=ax^2+bx+c[/tex]The parabola opens upward when a is positive and opens downward when a is negative
1. When parabola opens upward, the end behavior can be described as:
[tex]\begin{gathered} x\rightarrow\infty \\ y\rightarrow\infty \\ \text{and} \\ x\rightarrow-\infty \\ y\rightarrow\infty \end{gathered}[/tex]2. When parabola opens downward, the end behavior can be described as:
[tex]\begin{gathered} x\rightarrow\infty \\ y\rightarrow-\infty \\ \text{and} \\ x\rightarrow-\infty \\ y\rightarrow-\infty \end{gathered}[/tex]Our equation has an "a" value that is negative! So, the parabola opens downward and the end behvaior can be described as:
As x goes to infinity (gets infinitely large), y goes to negative infinity (gets infinitely small) and as x goes to negative infinity (gets infinitely small), y goes to negative infinity (get infinitely small).
PART D
In Part B, we found the x-intercepts. Those are the x-axis cutting points. We can draw those first.
Then,
Using the end behavior information that we found in Part C, we can draw the parabola. The rough sketch is shown:
The exact graph is shown below, for reference:
Suppose that y varies directly as the square root of x, and that y = 25 when x = 289. What is y when x= 134? Round your answer to two decimal places if necessary.
Answers
Answer
When x = 134, y = 17.02
Explanation
We are told that y varies directly as the square root of x.
y ∝ √x
Introducing the constant of proportionality, k
y = k√x
We are then told that
when y = 25, x = 289, with this, we can solve for k
y = k√x
25 = k × √289
25 = k × 17
25 = 17k
17k = 25
Divide both sides by 17
(17k/17) = (25/17)
k = (25/17)
We are then to solve for y when x = 134
y = k√x
y = (25/17) × √134
y = (25/17) × 11.58
y = 17.02
Hope this Helps!!!
f(x)=4•2^2x,g(x)=2^4x+2, and h(x)=4^2x+1
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Let's use the following property:
[tex]x^y\cdot x^z=x^{y+z}[/tex][tex]\begin{gathered} f(x)=4\cdot2^{2x} \\ g(x)=2^{4x+2}=2^{4x}\cdot2^2=4\cdot2^{4x} \\ h(x)=4^{2x+1}=4^{2x}\cdot2^{1^{}}=2\cdot4^{2x} \\ \text{Therefore:} \\ \text{None of them are equivalent} \end{gathered}[/tex]List the sides of FGH in order from least to greatest if m
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We have a triangle FGH
The three angles of the triangle FGH are given as
[tex]\begin{gathered} m\angle F=4x+7 \\ m\angle G=5x-31 \\ m\angle H=7x-52 \end{gathered}[/tex]Recall that the sum of all three angles of a triangle must be equal to 180°
[tex]\begin{gathered} m\angle F+m\angle G+m\angle H=180\degree \\ 4x+7+5x-31+7x-52=180 \\ 16x-76=180 \\ 16x=180+76 \\ 16x=256 \\ x=\frac{256}{16} \\ x=16 \end{gathered}[/tex]Now, we can calculate the exact measure of the angles
[tex]\begin{gathered} m\angle F=4x+7=4(16)+7=64+7=71\degree \\ m\angle G=5x-31=5(16)-31=80-31=49\degree \\ m\angle H=7x-52=7(16)-52=112-52=60\degree \end{gathered}[/tex]Let us draw the triangle FGH
Recall that the side opposite the least angle is the least side and vice versa.
The means that the side opposite the angle G is the least side (FH)
Then the side opposite the angle H is the greater side (FG)
Finally, the side opposite the angle F is the greatest side (GH)
Therefore, the sides of the triangle FGH in order from least to greatest is
FH, FG, GH
PLS HELP FAST I WILL GIVE 25 POINTS simplify 10^6/10^-3. answers:A. 1/10^3. B. 1/10^18. C. 10^3. D. 10^9
Answers
D
Let's simplify that expression
1) Remember of the Exponents Rule, we have to subtract them
2) Note that for the exponents 6 -(-3) = 6+3 = 9 So it's D
There are 14 girls and 12 boys in a class. What is the ratio of gris to students in simplest form
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Number of girls = 14
Number of boys = 12
Number of students = 14 + 12 =26
Ratio of girls to students = 14/26 = 7 : 13
4^2 * 4^3 simplified
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]4^2\ast4^3[/tex]STEP 2: Simplify the expression using the law of indices
[tex]\begin{gathered} \mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c} \\ 4^2\cdot \:4^3=4^{2+3} \\ =4^{\left\{2+3\right\}} \\ =4^5=1024 \end{gathered}[/tex]Hence, the evaluation gives:
[tex]1024[/tex]the five number summary for a set of data is given in the picture.what is the interquartile range of the set of data?
Answers
ANSWER
[tex]IQR=13[/tex]EXPLANATION
The interquartile range can be found by finding the difference between the first quartile, Q1, and the third quartile, Q3.
That is:
[tex]IQR=Q3-Q1[/tex]Therefore, the interquartile range is:
[tex]\begin{gathered} IQR=81-68 \\ IQR=13 \end{gathered}[/tex]write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the graph of the given equations(0,0); y = -6x+3y =
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To find the equation of the line we need a point and the slope. We have the point but we need to find the slope, to do this we need to remember that two lines are perpendicular if and only if their slopes fullfils:
[tex]m_1m_2=-1[/tex]Now, the slope of the line given is -6, this comes from the fact that the line is written in the form y=mx+b, hence comparing both equation we conclude that.
Pluggin this value into the condition above we have:
[tex]\begin{gathered} -6m_1=-1 \\ m_1=\frac{-1}{-6} \\ m_1=\frac{1}{6} \end{gathered}[/tex]Therefore the slope of the line we are looking for is 1/6. The equation of a line is given as:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values of the slope and the point we have:
[tex]\begin{gathered} y-0=\frac{1}{6}(x-0) \\ y=\frac{1}{6}x \end{gathered}[/tex]Therefore the equation we are looking for is:
[tex]y=\frac{1}{6}x[/tex]if the endpoints of KB are K(-4, 5) and B(2, -5), what is the length of KB?
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The length of the line can be found by distance formula as,
[tex]\begin{gathered} KB=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ KB=\sqrt[]{(2-(-4)_{})^2+(-5-5)^2} \\ KB=\sqrt[]{(2+4)^2+(-10)^2} \\ KB=\sqrt[]{6^2+100} \\ KB=\sqrt[]{36+100} \\ KB=\sqrt[]{136} \\ KB=11.66 \end{gathered}[/tex]RATIOS, PROPORTIONS, AND PERCENTSFinding the principal, rate, or time for a simple interest loan...Ann took out a loan for $17,000 and was charged simple interest at an annual rate of 6.8%.The total interest she paid on the loan was $867.How long was the loan for, in months?Do not round any intermediate computations. If necessary, refer to the list of financial formulas.monthsI need help with this mathProblem
Answers
The time formula for simple interest is:
[tex]t=\frac{I}{Ci}[/tex]Where I is the interest, C is the capital and i is the rate
In this case, we have:
I= 867
i=6.8%
C=17000
Replace and solve:
[tex]t=\frac{867}{17000*0.068}[/tex][tex]t=0.75\text{ years}[/tex]The time is 0.75 years because the rate is in years.
Convert years to months:
[tex]0.75years*\frac{12months}{1years}=9\text{ months}[/tex][tex]2x ^{2} - 6x + 10 = 0[/tex]solve by completing the square
Answers
We know that we can use the quadratic equation
Using this we have
[tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot2\cdot10}}{2\cdot2}=\frac{6\pm\sqrt[]{36-80}}{4} \\ =\frac{6\pm\sqrt[]{-44}}{4}=\frac{6\pm\sqrt[]{4\cdot-11}}{4}=\frac{6\pm2\cdot\sqrt[]{-11}}{4} \\ =2\cdot(\frac{3\pm\sqrt[]{-11}}{4})=\frac{3\pm\sqrt[]{-11}}{2}=\frac{3\pm\sqrt[]{11}i}{2} \\ =\frac{3}{2}\pm\frac{\sqrt[]{11}}{2}i \end{gathered}[/tex]So the answer is B)
(x + y)² – 3zz when X = -2, y = -4, and z = 5.
Answers
-39
Explanation
[tex]\begin{gathered} \mleft(x+y\mright)^2-3zz \\ \end{gathered}[/tex]Step 1
let
x=-2
y=-4
z=5
Step 2
Now, replace those values in the expression
[tex]\begin{gathered} (x+y)^2-3zz \\ (-2+(-4))^2-3\cdot5\cdot5 \\ (-2-4)^2-75 \\ (-6)^2-75 \\ 36-75 \\ -39 \end{gathered}[/tex]I hope this helps you