what is the solution set for the inequality
A. x ≤ -5
B. x ≤ 5
C. x ≤ 1
d. x ≤ -14
Answers
The solution set to the inequality, 4x + 12 ≤ -8, is determined as: A. x ≤ -5.
How to Find the Solution Set of an Inequality?The solution set is the value of x that would make an inequality statement true. To find the value of x, solve as you would solve a normal equation.
Using the key to the given model in the diagram, we can write the inequality as follows:
On the left, we would have, 4x + 12.
On the right, we would have, -8.
The inequality would be expressed as:
4x + 12 ≤ -8
Solve for x
4x + 12 - 12 ≤ -8 - 12 [subtraction property of equality]
4x ≤ -20
4x/4 ≤ -20/4
x ≤ -5
The solution set is: A. x ≤ -5.
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Related Questions
Solve the inequality: -1 <= x - 3 > 7
Answers
-1 ≤x-3>7
So:
-1≤x-3
x-3>7
Solve each
-1≤x-3
Add 3 to both sides:
-1+3≤x-3+3
2≤x
x-3>7
add 3 to both sides:
x-3+3>7+3
x>10
Solution:
2≤x or >10
Help I’ll give extra points!10. Camilla is saving to purchase a new pair of bowling shoes that will cost at least $39. She hasalready saved $19. What is the least amount of money she needs to save for the shoes?11. Suppose you earn $20 per hour working part time at a tax office. You want to earn at least$1,800 this month, before taxes. How many hours must you work?For problem 12, translate the phrase intoalgebraic inequality.12. A tour bus can seat 55 passengers. A minimum of 15 people must register for the tour to bookthe bus.
Answers
the least amount of money she needs to save is 20
the number of hours you must work is at least 90hours
Explanation:
10) The pair of shoes cost at least $39
at least $39 means: the cost is ≥ 39
≥ means greater than or equal to
Amount saved = $19
Let the least amount of money = x
x + 19 ≥ 39
x ≥ 39-19
x ≥ 20
This means the least amount of money she needs to save is 20
11) Let the number of hours worked = x
Amount earned per hour = $20
Amount to be earned this month is at least $1,800
This means amount to be earned this month ≥ 1800
[tex]\begin{gathered} 20\times x\text{ }\ge\text{ 1800} \\ 20x\text{ }\ge\text{ 1800} \\ \text{Divide through by 20} \\ x\text{ }\ge\text{ }\frac{1800}{20} \\ x\text{ }\ge\text{ 90} \end{gathered}[/tex]This means the number of hours you must work is at least 90hours
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is divisible by 6". Find P(A). Outcome Probability 1 0.394 - 2. 0.152 3 0.001 4 0.09 5 0.112 6 0.047 7 0.053 8 0.151
Answers
Problem-Solving in Probability.
Prob( A ) = Prob( Outcome divisible by 6 ):
only outcome 6 is divisible by 6, and it has a probability of 0.047
Hence,
[tex]\text{Prob(A) =Prob(outcome 6) = 0.047}[/tex]Hence, the correct answer is 0.047
Determine the vertex and the axis of symmetry based on the equation, y =-12 -8x - 36
Answers
Solution
Determine the vertex and the axis of symmetry based on the equation:
[tex]y=-x^2-8x-36[/tex]Therefore the correct answer is Option A
Make a table for the graph labeled hours studies average grade
Answers
We can easily create a table with the first column labeled "hours studied" and second column labeled "average grade".
The hours studied are:
0, 1, 2, 3, and 4
The respective average grades are:
56, 75, 85, 90, 100
The table can look like this:
Answer:
To make the table, you must correlate the average test grade with the hours spent studying.
The graph shows the idea that the more we learn, the higher will be our test grades.
The table is attached.
slope= 2; point on the line (-2,1) in slope intercept form I know y=m*x+b but all I know is 2 would be m
Answers
y=2x+5
1) Since we were told the slope is m=2, one point on the line (-2,1), and the slope-intercept form is:
[tex]y=mx+b[/tex]2) The next step is to find the value of "b", the y-intercept. So, let's pick that point, the slope, and plug them into the Slope-Intercept form:
[tex]\begin{gathered} y=mx+b,m=2,(-2,1) \\ 1=2(-2)+b \\ 1=-4+b \\ 1+4=b \\ b=5 \end{gathered}[/tex]3) Now that we know the y-intercept (b), we can write the function's rule as
[tex]y=2x+5[/tex]In an electrical circuit, the voltage across a resistor is directly proportional to the current running through the resistor. If a current of 14 amps produces 280 volts across a resistor, how many volts would a current of 5.5 amps produce across an identical resistor?
Answers
A current of 5.5 amps produce across an identical resistor will produce 110Volts across an identical resistor
What is a current?From above,
Current 1 (I₁) = 14 amps
P.d (V₁) = 280 V
By Ohm's law which states that that for a linear circuit the current flowing through it is proportional to the potential difference across it so the greater the potential difference across any two points the bigger will be the current flowing through it.
V₁ = I₁R
= 280 = 14R
= 20Ω = R
Current 2 (I₂) = 3.5 A
Resistance (R) = 20 Ω
Assuming the resistance stays the same,
Using Ohm's law,
V₂ = I₂R
= 5.5*20
= 110 Volts
110Volts would be produced across an identical resistor
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HELP ME PLS!!!!!!!
Total consumption of fruit juice in a particular country in 2006 was about 2.15 billion gallons. The population of that country in 2006 was 400 million. What was the average number of gallons of fruit juice consumed per person in the country in 2006? using the per person amount from this problem, about how many gallons would your class consume?
Answers
Answer:
5.375 gallons/personStep-by-step explanation:
Total consumption of fruit juice in 2006:
2.15 billion gallonsThe population of the country:
400 million people.Average consumption of fruit juice per person in 2006 was:
2.15 billion / 400 million = 2.15 × 10⁹ / 400 × 10⁶ = 21.5 × 10⁸ / 4 × 10⁸ = 21.5 / 4 = 5.375 gallons/personTo find how many gallons of fruit juice would your class consume multiply the average consumption by the number of your class mates.
Solve the following equations. (You may leave your answer in terms of logarithms or you can plug your answer into a calculator to get a decimal approximation.)
Answers
Given the equation:
[tex]200(1.06)^t=550[/tex]We divide each side by 200:
[tex]\begin{gathered} \frac{200}{200}(1.06)^t=\frac{550}{200} \\ 1.06^t=2.75 \end{gathered}[/tex]Now, we take the natural logarithm:
[tex]\begin{gathered} \ln (1.06^t)=\ln (2.75) \\ t\cdot\ln (1.06)=\ln (2.75) \\ \therefore t=\frac{\ln (2.75)}{\ln (1.06)} \end{gathered}[/tex]Sketch the vectors u and w with angle θ between them and sketch the resultant.|u|=45, |w|= 25, θ=30°
Answers
Step 1
Find the resultant of the vectors
[tex]undefined[/tex]Interpreting the parameters of a linear function that models a real-world situation
Answers
SOLUTION
The equation relating x and y is
[tex]\begin{gathered} y=27x+600 \\ \text{Where } \\ x=\text{Total number of minutes } \\ y=\text{Total amount of water in the pond} \end{gathered}[/tex]The equation connecting x and y is an equation of the form
[tex]\begin{gathered} y=mx+c \\ \text{Where m is the slope or chnages betwe}enx\&y\text{ } \\ \end{gathered}[/tex]Since slope is also refers to as changes between two variables,
Hence
Cmparing with the equation given,
[tex]\begin{gathered} m=27 \\ \text{Slope}=27 \end{gathered}[/tex]Therefore,
The change per minute in the total amount of water in the pond is 27 litres
The starting amount ot water is when the time is at 0 minutes .
Hence, substite x=0 into the equation given and obtain the value of y which stands for the amount of water at the begining.
[tex]\begin{gathered} y=27x+600 \\ \text{put x=0} \\ y=27(0)+600 \\ y=0+600 \\ \text{Then } \\ y=600 \end{gathered}[/tex]Therefore,
The starting amount of water is 600 litres
Answer: A) 27 litres B). 600 litres
find the percent notation 7/10
Answers
A notation is a way of communicating through symbols or signs, or it might be a brief written message. A chemist notating AuBr for gold bromide is an illustration of a notation. A quick list of things to accomplish is an illustration of a notation.
Explain about the percent notation?Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.
When expressing a fraction as a percentage, we multiply the provided fraction by 100.7/10, which is 70%.
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The volume of a square-based rectangular cardboard box needs to be at least 1000cm^3. Determine the dimensions that require the minimum amount of material to manufacture all six faces. Assume that there will be no waste material. The Machinery available cannot fabricate material smaller than 2 cm in length.
Answers
We have to find the dimensions of a box with a volume that is at least 1000 cm³.
We have to find the dimensions that require the minimum amount of material.
We can draw the box as:
The volume can be expressed as:
[tex]V=L\cdot W\cdot H\ge1000cm^3[/tex]The material will be the sum of the areas:
[tex]A=2LW+2LH+2WH[/tex]Since the box is square-based, the width and length are equal and we can write:
[tex]L=W[/tex]Then, we can re-write the area as:
[tex]\begin{gathered} A=2L^2+2LH+2LH \\ A=2L^2+4LH \end{gathered}[/tex]Now, we have the area expressed in function of L and H.
We can use the volume equation to express the height H in function of L:
[tex]\begin{gathered} V=1000 \\ L\cdot W\cdot H=1000 \\ L^2\cdot H=1000 \\ H=\frac{1000}{L^2} \end{gathered}[/tex]We replace H in the expression for the area:
[tex]\begin{gathered} A=2L^2+4LH \\ A=2L^2+4L\cdot\frac{1000}{L^2} \\ A=2L^2+\frac{4000}{L} \end{gathered}[/tex]We can now optimize the area by differentiating A and then equal the result to 0:
[tex]\begin{gathered} \frac{dA}{dL}=2\frac{d(L^2)}{dL}+4000\cdot\frac{d(L^{-1})}{dL} \\ \frac{dA}{dL}=4L+4000(-1)L^{-2} \\ \frac{dA}{dL}=4L-\frac{4000}{L^2} \end{gathered}[/tex][tex]\begin{gathered} \frac{dA}{dL}=0 \\ 4L-\frac{4000}{L^2}=0 \\ 4L=\frac{4000}{L^2} \\ L\cdot L^2=\frac{4000}{4} \\ L^3=1000 \\ L=\sqrt[3]{1000} \\ L=10 \end{gathered}[/tex]We now can calculate the other dimensions as:
[tex]W=L=10[/tex][tex]H=\frac{1000}{L^2}=\frac{1000}{10^2}=\frac{1000}{100}=10[/tex]Then, the dimensions that minimize the surface area for a fixed volume of 1000 cm³ is the length, width and height of 10 cm, which correspond to a cube (all 3 dimensions are the same).
Answer: the dimensions are length = 10 cm, width = 10 cm and height = 10 cm.
I’m the relationship shown by the data linear, if so, model with an equation . A. The relationship is linear;
Answers
The relation is data if the difference between every 2 x is equal and the difference between every 2 y is equal
Since:
-5 - (-7) = -5 + 7 = 2
-3 - (-5) = -3 + 5 = 2
-1 - (-3) = -1 + 3 = 2
Since:
9 - 5 = 4
13 - 9 = 4
17 - 13 = 4
Then
The difference between every 2 x is constant and the difference between every 2 y constant
Then the relation is linear
Since the form of the linear equation is
[tex]y-y_1=m(x-x_{1)}[/tex]m is the rate of change of y with respect to x (the slope of the line)
(x1, y1) is a point on the line
Let us find m
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ \Delta y=4 \\ \Delta x=2 \\ m=\frac{4}{2} \\ m=2 \end{gathered}[/tex]Since x1 = -7 and y1 = 5, then
[tex]\begin{gathered} y-5=2(x--7) \\ y-5=2(x+7) \end{gathered}[/tex]its composition of fractions in pre-calculus.I know how to do these types of questions, im just not sure how u would set it up if there are 2 x's in one of the equations.
Answers
Answer:
(f o g)(x) = x
Explanation:
Given f(x) and g(x) defined below:
[tex]\begin{gathered} f(x)=\frac{1-x}{x} \\ g(x)=\frac{1}{1+x} \end{gathered}[/tex]The composition (f o g)(x) is obtained below:
[tex]\begin{gathered} (f\circ g)(x)=f\lbrack g(x)\rbrack \\ f(x)=\frac{1-x}{x}\implies f\lbrack g(x)\rbrack=\frac{1-g(x)}{g(x)} \end{gathered}[/tex]Substitute g(x) into the expression and simplify:
[tex]\begin{gathered} f\lbrack g(x)\rbrack=\frac{1-g(x)}{g(x)}=\lbrack1-g(x)\rbrack\div g(x) \\ =(1-\frac{1}{1+x})\div(\frac{1}{1+x}) \\ \text{ Take the LCM in the first bracket} \\ =\frac{1(1+x)-1}{1+x}\div\frac{1}{1+x}\text{ } \\ \text{Open the bracket} \\ =\frac{1+x-1}{1+x}\div\frac{1}{1+x}\text{ } \\ =\frac{x}{1+x}\times\frac{1+x}{1}\text{ } \\ =x \end{gathered}[/tex]Therefore, the composition (f o g)(x) is x.
The vertex of the parabola below is at the point
Answers
SOLUTION
The equation of a parabola in a vertex form is given
since the parabola is on the x-axis.
[tex]\begin{gathered} x=a(y-h)^2+k \\ \text{Where } \\ \text{Vertex}=(h,k) \end{gathered}[/tex]From the diagram given, we have
[tex]\text{vertex}=(-4,-2)[/tex]Substituting into the formula above, we have
[tex]\begin{gathered} x=a(y-h)^2+k \\ h=-4,k=-2 \end{gathered}[/tex]We have
[tex]\begin{gathered} x=(y-(-2)^2-4 \\ x=(y+2)^2-4 \end{gathered}[/tex]Since the parabola is a reflection from the parent function, then
[tex]a=-2[/tex]The equation of the parabola becomes
[tex]x=-2(y+2)^2-4[/tex]Answer; x = -2(y + 2)^2-4
Consider the graph shown. Which ordered pairs are on the inverse of the function? Check all that apply.
Answers
Notice that the graph of the function is a cubic polynomial. Also, the graph is moved one unit upwards, then, the function f(x) is:
[tex]f(x)=x^3+1[/tex]now, we can see from the y and x intercepts, that if we evaluate x= 0 and x = 1, we get:
[tex]\begin{gathered} f(0)=-1 \\ f(1)=0 \end{gathered}[/tex]then, applying the inverse function on both sides (we can do this since f(x) is a polynomial function and they always have inverse function), we get the following:
[tex]\begin{gathered} f^{-1}(f(0))=f^{-1}(-1) \\ \Rightarrow0=f^{-1}(-1) \end{gathered}[/tex]we can see that the first point that is on the graph of the inverse function is (-1,0). Doing the same on the second equation, we get:
[tex]\begin{gathered} f^{-1}(f(1))=f^{-1}(0) \\ \Rightarrow f^{-1}(0)=1 \end{gathered}[/tex]thus, the points that lie on the inverse function are (-1,0) and (0,1)
What is the height of a parallelogram with an area of 50 square meters
and a base length of 5 meters?
Answers
The height of a parallelogram with an area of 50 square meters and a base length of 5 meters is 10 meters
What is a parallelogram?The word "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bounded by parallel lines." As a result, a quadrilateral that is bound by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides. Square, rectangle, and rhombus are the three primary varieties of parallelograms, and each one has distinct characteristics. If a quadrilateral's opposite sides are parallel and congruent, it will be a parallelogram. So a quadrilateral with both pairs of opposite sides being parallel and equal is known as a parallelogram.
Various forms of parallelograms can be distinguished from one another based on their unique characteristics. It can be broadly classified into three distinct types:
RectangleSquareRhombusArea = 50
Base = 5
Area of ║gm = base (height)
50 = 5(X)
x = 10
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Question 16
Given AEFHAGFH below, what is the measure of GFH?
F
21.6°
E<
(6x - 12)° H
G
1 pts
Answers
The most appropriate choice for congruency of triangles will be given by-
[tex]\angle GFH =68.4^{\circ}\\[/tex]
What is congruency of triangles?
Two triangles are said to be congruent if all the corrosponding sides and the corrosponding angles of the triangle are equal.
There are five axioms of congruency. They are -
SSS axioms, SAS axioms, ASA axiom, AAS axiom, RHS axiom.
Here,
[tex]\Delta EFH \cong \Delta GFH[/tex] [Given]
[tex]\angle E = \angle G = 21.6^{\circ}[/tex] [Corrosponding parts of congruent triangles are congruent]
[tex]\angle GFH[/tex] = 180 - (90 + 21.6) [Sum of the three angles of a triangle is 180°]
[tex]\angle GFH = 180 - 111.6\\\angle GFH =68.4^{\circ}\\[/tex]
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Write the following numbers in decreasing order: −4; 1 2/3 ; 0.5; −1 3/4 ; 0.03; −1; 1; 0; -103; 54
Answers
Decreasing order means from largest to smallest
The ordered list is:
54, 1 2/3, 1, 0.5, 0.03, 0, -1, -1 3/4, -4, -103
Using pH=-log{H3O+}, what is pH for 3.4 X 10^-4 ?
Answers
The value of the pH for pH=-log{H3O+} is found as 3.47.
What is defined as the pH?The pH of aqueous or some other liquid solutions is a quantitative measure of their acidity or basicity. The concentration of hydrogen ion, which normally ranges between around 1 and 10∧14 gram-equivalents per litre, is converted into a number between 0 and 14. The concentration of hydrogen ion in pure water, which really is neutral (nor acidic and neither alkaline), is 10∧7 gram-equivalents per litre, corresponding to a pH of 7. A solution with such a pH less than 7 is classified as acidic, while one with pH greater than 7 is classified as basic, or alkaline.For the given equation,
pH = - log [H3O+]
and , H3O+ = 3.4 X 10^-4
The, the pH will be estimated as;
pH = - log [ H3O+]
pH = - log [ 3.4 x10 ^-4]
pH = - [log 3.4 + log 10^-4]
pH = - [0.53 + (-4)]
pH = -[-3.47]
pH = 3.47
Thus, the value of the pH is found as 3.47.
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Steve has been training for a 5-mile race. Before the race, he predicts he will finish in 42minutes. He actually finishes the race in 40 minutes. What is the percent error for hisprediction?
Answers
To find the percent error
percent error = | (actual - expected)/ actual| * 100 %
The actual is 40 and the expected is 42
percent error = | ( 40 - 42) / 40 | * 100 %
= | -2/40| * 100%
= .05 * 100 %
= 5%
Find the value of x in this equation.
|2x − 3| − 11 = 0
Answers
Answer:7
Step-by-step explanation:
Answer:
x=−4
x=7
Step-by-step explanation:
1. Combine similar terms and use the equality properties to get the variable on one side of the equals sign and the numbers on the other side. Remember to respect the order of operations.
2. Add 11 to both sides of the equation.
3. Use the absolute value definition.
4. Add 3 to both sides of the equation.
5. Divide both sides by 2.
6. The answer is: x=7
x=−4
Sorry for the bad English, love from Vanuatu!
What is the vertex of the graph of the function below?y = x^2 + 10x + 24O A. (-4,-1)O B. (-5, -1)O C. (-5,0)O D. (4,0)
Answers
For any given parabola in the form
[tex]f(x)=ax^2+bx+c[/tex]The vertex is the point:
[tex]V=(-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]This way,
[tex]\begin{gathered} y=f(x)=x^2+10x+24 \\ \rightarrow a=1 \\ \rightarrow b=10 \\ \rightarrow c=24 \\ \\ \rightarrow-\frac{b}{2a}=-\frac{10}{2\cdot1}=-5 \\ \\ \rightarrow f(-5)=(-5)^2+10(-5)+24=-1 \end{gathered}[/tex]Therefore, the vertex is:
[tex]V(-5,-1)[/tex]Answer: Option B
Solve each system of equations algebraically.[tex]y = {x}^{2} + 4 \\ y = 2x + 7[/tex]
Answers
From the problem, we two equations :
[tex]\begin{gathered} y=x^2+4 \\ y=2x+7 \end{gathered}[/tex]Since both equation are defined as y in terms of x, we can equate both equations.
[tex]\begin{gathered} y=y \\ x^2+4=2x+7^{} \end{gathered}[/tex]Simplify and solve for x :
[tex]\begin{gathered} x^2+4=2x+7 \\ x^2-2x+4-7=0 \\ x^2-2x-3=0 \end{gathered}[/tex]Factor completely :
[tex]\begin{gathered} x^2-2x-3=0 \\ (x-3)(x+1)=0 \end{gathered}[/tex]Equate both factors to 0 then solve for x :
x - 3 = 0
x = 3
x + 1 = 0
x = -1
We have two values of x, x = 3 and -1
Substitute x = 3 and -1 to any of the equation, let's say equation 2 :
For x = 3
y = 2x + 7
y = 2(3) + 7
y = 6 + 7
y = 13
One solution is (3, 13)
For x = -1
y = 2x + 7
y = 2(-1) + 7
y = -2 + 7
y = 5
The other solution is (-1, 5)
The answers are (3, 13) and (-1, 5)
What is the midpoint of the x-intercepts off(x) = (x – 4)(x + 4)?(0,0)(0,4)(–4,0)(2,0)
Answers
Given:
[tex]f(x)=(x-4)(x+4)[/tex]Required:
To find midpoint of intercepts.
Explanation:
We know that when y=0,x=4,-4
therefore x- intercept of the function are (4,0) and (-4,0)
We know that the midpoint of this intercept is at equidistance from both the graph, therefore the points from which graph is equidistance is at origin (0,0)
Required answer:
Hence the midpoint of the x- intercepts of f(x) will be at (0,0) or at the origin of the graph so option 1 is correct.
Find the radius of a circle with a circumstance of 28π
Answers
We have the next formula to find the circumference of a circle
[tex]C=2\pi r[/tex]where C is the circumference and r is the radius
In our case we have
C= 28π
we substitute the value in the formula
[tex]28\pi=2\pi r[/tex]then we isolate the r
[tex]r=\frac{28\pi}{2\pi}=14[/tex]the radius is 14.
The marching band director is standing on a platformoverlooking the band practice. The pit section is located 8feet from the base of the platform. If the angle ofdepression from the band director to the pit section is 67°find the height of the platform.
Answers
Through trigonometry, we calculated that the height of the platform is 18.8 feet.
The director of the marching band is observing the band practice from a platform. 8 feet separate the base of the platform from the pit area. If the pit section's angle of depression is 67 degrees from the band director,
The angle formed by the horizontal line and the item as seen from the horizontal line is known as the angle of depression. When the angles and the separation of an object from the ground are known, it is mostly used to calculate the distance between the two objects.
We have,
So, the Angle of Depression = [tex]\alpha[/tex] = 67
Let x be the height of the platform,
Tan [tex]\alpha = \frac{x}{8}[/tex]
[tex]Tan 67 = \frac{x}{8} \\\\2.35 =\frac{x}{8} \\x = 2.35 *8 = 18.8[/tex]
Hence, The height of the platform is 18.8 feet.
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RecoverySolve for x usingcross multiplication.2x + 132x11 -=x + 22x = [?]Enter
Answers
Answer:
x = 4
Step-by-step explanation:
Cross-multiplying means multiplying the numerator of one side by the denominator of the other side.
So, let's multiply the sides:
[tex]\begin{gathered} \frac{2x+1}{3}=\frac{x+2}{2} \\ 2\cdot(2x+1)=3\cdot(x+2) \end{gathered}[/tex]Now, we can solve each side:
[tex]\begin{gathered} 4x+2=3x+6 \\ 4x-3x=6-2 \\ 1x=4 \\ x=4 \end{gathered}[/tex]So, x = 4.
f(x)=3x-4g(x)=-x^2+2x-5h(x)2x)^2+1j(x)=6x^2-8xk(x)=-x+7calculate (g+j)(x)
Answers
To calculate (g+j)(x) we need the function:
[tex]\begin{gathered} g(x)=-x^2+2x-5 \\ j(x)=6x^2-8x \end{gathered}[/tex]and we can made the addition so:
[tex]\begin{gathered} (g+j)(x)=g(x)+j(x) \\ (g+j)(x)=-x^2+2x-5+6x^2-8x \end{gathered}[/tex]and we can simplify
[tex](g+j)(x)=5x^2-6x-5[/tex]