Answers
Given the expression
[tex]\frac{a^4b^{-5}}{c^{-3}d^6}[/tex]To simplify the expression above, we convert all negative indices to positive indices
Applying the rule of indices
[tex]a^{-x}=\frac{1}{a^x}[/tex]Applying the rule to the given expression gives
[tex]\begin{gathered} \text{Where b}^{-5}=\frac{1}{b^5}\text{ and} \\ c^{-3}=\frac{1}{c^3} \end{gathered}[/tex]Substitute the above deduction into the given expression
[tex]\begin{gathered} \frac{a^4b^{-5}}{c^{-3}d^6}=a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6} \\ \text{Where }\frac{1}{\frac{1}{c^3}}=c^3 \\ =a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6}=a^4\times\frac{1}{b^5}\times c^3\times\frac{1}{d^6} \\ =\frac{a^4c^3}{b^5d^6} \\ \frac{a^4b^{-5}}{c^{-3}d^6}=\frac{a^4c^3}{b^5d^6} \end{gathered}[/tex]Hence, the simplified form is
[tex]\frac{a^4c^3}{b^5d^6}[/tex]Related Questions
In AFGH, f = 83 inches, g=11 inches and ZH=60°. Find the length of h, to the nearest inch
Answers
Answer:
78 in
Explanation:
We can calculate the length of h using the cosine law because we have two sides and the measure of the angle between them. So, the cosine law says that h is equal to:
[tex]h^2=f^2+g^2-2fg\cos (H)[/tex]Where h, f, and g are the sides of the triangle and H is the angle between f and g. Then, replacing f by 83 in, g by 11 in, and H by 60°, we get:
[tex]\begin{gathered} h^2=83^2+11^2-2(83)(11)\cos 60 \\ h^2=6889+121-913 \\ h^2=6097 \\ h=\sqrt[]{6097} \\ h=78.08 \end{gathered}[/tex]Therefore, the answer is 78 in.
Write the equation of the line in slope-intercept form.M = 1/8, y-intercept (0,4)
Answers
Answer:
[tex]y=\frac{1}{8}x+4[/tex]Explanation:
The information we have about the line is:
slope
[tex]m=\frac{1}{8}[/tex]Y- intercept is (0,4) here, the y-coordinate 4 is the point where the line crosses the y-axis and is the y-intercept usually represented by the letter b:
[tex]b=4[/tex]Now, the general equation for a line in the slope-intercept form is:
[tex]y=mx+b[/tex]We substitute the known values:
[tex]y=\frac{1}{8}x+4[/tex]This is the equation for the line in slope -intercept form.
Lola jumps rope for 15 minutes on Monday. She jumps rope 10 more minutes each day. How many minutes does she jump rope on Thursday?
Answers
She jumped 25 minutes on Tuesday as the problem says, "Lola jumps rope for 15 minutes on Monday. She jumps rope 10 more minutes each day."
What is addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The total amount or sum of the two whole numbers is obtained by adding them. Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more numbers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum. 5 + 11 + 3 equals 19, as an illustration of addition.
Here,
She jumped 15 minutes on Monday
On Tuesday, she will jump 10 more minutes,
=15+10
=25 minutes
As stated in the problem, she jumped 25 minutes on Tuesday "On Monday, Lola jumps rope for 15 minutes. She adds 10 more minutes of daily rope jumping."
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reduce to lowest term.4x-24/x^2-36
Answers
Explanation
[tex]\frac{4x+24}{x^2-36}[/tex]Step 1
factorize
[tex]\begin{gathered} a)\text{ 4x+24} \\ if\text{ we rewrite 24 as a product of its factors} \\ 4x+24=4x+(6\cdot4) \\ 4x+(6\cdot4)\rightarrow4\text{ is a common factor, so }\rightarrow4(x+6) \end{gathered}[/tex]and the denominator
we have
[tex]b)x^2-36[/tex]remember:When an expression can be viewed as the difference of two perfect squares, it can be factorized this way
[tex]\begin{gathered} a^2-b^2=(a+b)(a-b) \\ \end{gathered}[/tex]so, apply this .
[tex]\begin{gathered} x^{^{}2}-36=x^2-6^2=(x+6)(x-6) \\ so,\text{ } \\ x^{^{}2}-36=(x+6)(x-6) \end{gathered}[/tex]hence, the expression would be:
[tex]\frac{4x+24}{x^2-36}=\frac{4(x+6)}{(x+6)(x-6)}[/tex]Step 2
finally, eliminate the (x+6) ,so
[tex]\begin{gathered} \frac{4(x+6)}{(x+6)(x-6)}=\frac{4}{(x-6)} \\ \frac{4}{(x-6)} \end{gathered}[/tex]therefore, the lowest term is
[tex]\frac{4}{(x-6)}[/tex]I hope this helps you
What is the value of x?
Enter your answer in the box.
Answers
Answer:
x = 12
Step-by-step explanation:
Creating an equation.
The angles shown form a straight line making them supplementary.
Supplementary angles add up to 180 degrees.
Hence, the sum of the two angles = 180
So we can say that (10x - 20) + (6x + 8) = 180
Solving for x
(10x - 20) + (6x + 8) = 180
==> remove parenthesis
10x - 20 + 6x + 8 = 180
==> combine like terms
16x - 12 = 180
==> add 12 to both sides
16x = 192
==> divide both sides by 16
x = 12
A girl has scored 72, 76, 74, and 75 on her algebra tests.a. Use an inequality to find the score she must make on the final test to pass the course with an average of 78 or higher, given that the final exam counts three testsb. Explain the meaning of the answer to part (a)
Answers
Part A.
We know that the final exam counts 3 test. Let x be the score of this final exam, then we can write,
[tex]\frac{72+76+74+75+3\times x}{7}\ge78[/tex]the denominator is 7 because there are 7 scores: 72,76,74,75 and 3 times x (which is the final test). This average must be greater or equal to 78 in order to pass the course.
Then, by adding the numerator terms we get,
[tex]\frac{297+3\times x}{7}\ge78[/tex]and by moving 7 to the right hand side, we have
[tex]\begin{gathered} 297+3x\ge78\times7 \\ or\text{ equivalently} \\ 297+3x\ge546 \end{gathered}[/tex]by moving 297 to the right hand side, we obtain
[tex]\begin{gathered} 3x\ge546-297 \\ 3x\ge249 \end{gathered}[/tex]then, the score of the final exam must be
[tex]\begin{gathered} x\ge\frac{249}{3} \\ x\ge83 \end{gathered}[/tex]that is, at least greater or equal to 83.
Part B.
The last result means that our girls must obtain at least 83 points in the final test in order to pass Algebra.
What is the measure of the "Central Angle" for the 20% section?
Answers
The sum of all central angle is 360.
Determine 20% of 360 to obtain central angle for 20% section.
[tex]\begin{gathered} \frac{20}{100}\times360^{\circ}=36^{\circ}\cdot2 \\ =72^{\circ} \end{gathered}[/tex]So answer is 72 degrees.
Please help me name this figure, find the lateral surface area, and the total surface area. You can ignore the work I've done as it is incorrect.
Answers
Answer:
• (,a)Triangular Prism
,• (b)Lateral Surface Area= 36 cm²
,• (c)Total Surface Area= 48 cm²
Explanation:
(a)The figure has a triangle as its uniform cross-section. Thus, it is a triangular prism.
(b)Lateral Surface Area
The lateral surface area is the area of the sides of the prism, i.e. excluding the uniform top and base.
The sides of the triangular prism consist of the three rectangles.
[tex]\begin{gathered} \text{Lateral Surface Area}=\text{Area of Rect. 1+Area of Rect. 2+Area of Rect. 3} \\ =(3\times4)+(3\times3)+(3\times5) \\ =12+9+15 \\ =36\;cm^2 \end{gathered}[/tex]The lateral surface area is 36 cm squared.
(c)Total Surface Area
To find the total surface area, add the area of the top and base to the lateral surface area.
The top and base are the two right-triangles with a base of 3 cm and a height of 4cm.
[tex]\begin{gathered} \text{ Total Surface Area=Lateral Surface Area+2\lparen Area of Triangles\rparen} \\ =36+2(\frac{1}{2}\times3\times4) \\ =36+12 \\ =48\;cm^2 \end{gathered}[/tex]The total surface area is 48 cm squared.
Every surface of the block shown will be painted, except for one of the bases. How many square units will be painted? 3.2 cm 3.2 cm 3.2 cm
Answers
As given that the every surface of the block shown will be painted, except for one of the bases.
And a block have 6 surface but one is not painted so there are 5 surface that are painted so:
The area of the painted surface is:
[tex]A=5a^2[/tex]Where a is 3.2 cm
[tex]\begin{gathered} A=5(3.2)^2 \\ A=5\times10.24 \\ A=51.2cm^2 \end{gathered}[/tex]The area of painted surface is 51.2 square cm
Question 13Triesremaining: 3Check for UnderstandingPoints out of2.00Write the equation of the line with a slope of 10 that goes through the point(8,-2) in Slope-Intercept and Point-Slope Form.P FlagquestionSlope-Intercept Form:Point-Slope Form:CheckPrevious page
Answers
Explanation
Step 1
Let
passes throught (8,-2)
slope=20
then
a)slope -intercept form
[tex]y-y_1=m(x-x_1)[/tex]where
[tex]\begin{gathered} (x_1,y_1)\text{ is a point of the line} \\ m\text{ is the slope of the line} \end{gathered}[/tex]replace
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=10(x-8) \\ y+2=10x-80 \\ \text{subtract 2 in both sides} \\ y+2-2=10x-80-2 \\ y=10x-82\rightarrow slope\text{ intercep form} \end{gathered}[/tex]Step 2
Now, Point-Slope Form, use the same equation, but don't isolate y
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=10(x-8) \\ y+2=10x-8\rightarrow Point-SlopeForm \end{gathered}[/tex]
In circle C with mZBCD = 66 and BC = 15 units find area of sector BCD. Round to the nearest hundredth. с B D
Answers
ANSWER:
The area of sector BCD is 129.53 square units
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the area of the circle completely. That area would be for 360 °, therefore by means of a proportion we can calculate the area for the BDC sector.
The area of circle is:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ \text{replacing} \\ A=3.14\cdot15^2 \\ A=706.5 \end{gathered}[/tex]Now, we calculate the area of the BDC sector by means of the following portion
[tex]\frac{706.5}{360}=\frac{x}{66}[/tex]Solving for x:
[tex]\begin{gathered} x=66\cdot\frac{706.5}{360} \\ x=129.525\cong129.53 \end{gathered}[/tex]5.-4h + 3 + 7h 9h - 21
Answers
-4h + 3 + 7h ≥ 9h - 21
combining similar terms,
(-4h + 7h) + 3 ≥ 9h - 21
3h + 3 ≥ 9h - 21
3h is adding on the left, then it will subtract on the right.
21 is subtracting on the right, then it will add on the left.
3 + 21 ≥ 9h - 3h
24 ≥ 6h
6 is multiplying on the right, then it will divide on the left.
24/6 ≥ h
4 ≥ h
We can check the answer replacing with a value wich is a solution and another value wich is not. For example, with h = 3, we get:
-4*3 + 3 + 7*3 ≥ 9*3 - 21
-12 + 3 + 21 ≥ 27 - 21
12 ≥ 6
This result confirm that h = 3 is a solution.
Substituting with h = 5, we get:
-4*h + 3 + 7h ≥ 9h - 21
Use the graph below to find the slope of the line. Explain your steps with sentences.
Answers
Given:
The graph of a linear equation
Required:
The slope of the line
The slope of the line can be found using the formula:
[tex]\begin{gathered} \text{slope = }\frac{y_2-y_1}{x_2-x_1} \\ \text{where } \\ (x_1,y_1)\text{ and } \\ (x_2,y_2)\text{ are two points on the line} \end{gathered}[/tex]On the line, we can identify the points : (-5,0) and (-6 4)
Using the slope formula:
[tex]\begin{gathered} \text{slope = }\frac{4-0}{-6-(-5)} \\ =\text{ }\frac{4}{-1} \\ =\text{ -4} \end{gathered}[/tex]Answer:
slope = -4
determine the numbers of solutions that exist to the equation below 8 (j - 4) = 2(4j - 16)
Answers
Step 1: Write out the equation
[tex]8(j-4)=2(4j-16)[/tex]Step 2: Divide both sides by 2
[tex]\begin{gathered} \frac{8(j-4)}{2}=\frac{2(4j-16)}{2} \\ \text{Therefore} \\ 4(j-4)=4j-16 \end{gathered}[/tex]Step 3: Expand the left side of the equation to get
[tex]\begin{gathered} 4j-16=4j-16 \\ \text{Thus} \\ 4j-4j=-16+16 \\ 0=0 \end{gathered}[/tex]0 = 0 is always true no matter the value of j.
Hence, the number of solutions is infinite
QuestionFind the equation of the line with slope m=1/4 that contains the point (4,5)
Answers
The standard form equation for a line is
[tex]y=mx+b[/tex]in which m represents the slope and b the y-intercept.
start putting the value of the slope into the equation
[tex]y=\frac{1}{4}x+b[/tex]although it is a fraction we repace it as if it was a whole number
then using (4,5) as (x,y) we can find b, the y-intercept
[tex]5=\frac{1}{4}(4)+b[/tex]simplify both sides of the equation
[tex]5=1+b[/tex]subtract 1 one on both sides in order to find b
[tex]\begin{gathered} 5-1=1+b-1 \\ 4=b \\ b=4 \end{gathered}[/tex]The equation of the line is
[tex]y=\frac{1}{4}x+4[/tex]Zappo’s has marked down rain boots 25% during its spring sale. What is the sale price of a pair of boots with a regular price of $149.99?
Answers
Substract the 25% of the price to the regular price:
1. Find the 25% of the price: Multiply by 0.25 the price:
[tex]149,99\cdot0.25\approx37.50[/tex]2. Substract the result in step 1 (amount marked down) from the regular price:
[tex]149,99-37,50=112.49[/tex]Then, the sale price of the pair of boots is $112.49Solve x² + 6x + 7 = 0.x = -1 and x = -5 3+ √2-3+√2-3 ± √22
Answers
ANSWER
[tex]x=-3\pm\sqrt{2}[/tex]EXPLANATION
We want to solve for x in the equation:
[tex]x^2+6x+7=0[/tex]To do this, apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where a = 1, b = 6, c = 7
Therefore, substituting the values of a, b, and c into the formula and solve:
[tex]\begin{gathered} x=\frac{-6\pm\sqrt{6^2-4(1)(7)}}{2(1)}=\frac{-6\pm\sqrt{36-28}}{2} \\ \\ x=\frac{-6\pm\sqrt{8}}{2}=\frac{-6\pm2\sqrt{2}}{2} \\ \\ x=-3\pm\sqrt{2} \end{gathered}[/tex]That is the solution for x.
1.At 8:30am, Student Life had served 37 meals at their pancake breakfast. By 10:15am, thetotal served had reached 77. Find the serving rate, in number of meals per minute. Keep youranswer as a reduced fraction.
Answers
We have to estimate a serving rate, with units of "number of meals per minute".
To solve this we have to calculate how many meals have been served in a certain time frame, and estimate a mean service rate.
The time interval we are taking is from 8:30 am to 10:15 am. That is 30 minutes to 9 am, plus 60 minutes to 10 am, plus 15 minutes to 10:15 am.
This is a total of 30+60+15=105 minutes.
The total served at 10:15 am is 77 meals. If we substract the meals that have been already served by 8:30 am, we get that in our time interval 77-37=40 meals have been served.
So we can calculate the serving rate as:
[tex]s=\frac{\text{ \#meals}}{\text{time}}=\frac{40\text{ meals}}{105\text{ min}}=\frac{8}{21}\text{ meals/min}[/tex]The serving rate, expressed as a reduced fraction (we divide both numerator and denominator by 5), is 8/21 meals per minute.
graph f(x) = 2sin x
Answers
Explanation
We are given the function:
[tex]f(x)=2\sin x[/tex]We are required to graph the function above.
- Using a graphing calculator, we have:
Water Pressure ApplicationIn certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot,60at a depth of d feet below the surface, is given by the equation P = 13+11-If a scientific team uses special equipment to measures the pressure under water andfinds it to be 427 pounds per square foot, at what depth is the team making theirmeasurements?If the pressure is 427 pounds per square feet, the team is measuring atfeet below the surface.> Next Question0
Answers
Given that the model of taking the measurement is
[tex]P=13+\frac{6d}{11}[/tex]Explanation
To get the depth at which the team is taking their measurement if the pressure is 427 pounds per square foot, we will insert the value of the pressure into the model.
[tex]\begin{gathered} 427=13+\frac{6d}{11} \\ 427-13=\frac{6d}{11} \\ 414=\frac{6d}{11} \\ swap\text{ sides} \\ \frac{6d}{11}=414 \\ cross\text{ multiply } \\ 6d=414\times11 \\ 6d=4554 \\ d=\frac{4554}{6} \\ d=759feet \end{gathered}[/tex]Answer: 759 feet
scientific notation5.1x10⁶ x 2.3x10⁶
Answers
The given expression is
5.1 x 10^6 x 2.3 x 10^6
We would apply the law of exponents which is expressed as
a^b x a^c = a^(b + c)
By applying this, we have
5.1 x 2.3 x 10^6 x 10^6
= 11.73 x 10^(6 + 6)
= 11.73 x 10^12
Part #1: Find the solution of the inequality.[tex]n - 6 \ \textgreater \ 10[/tex]Part #2: describe the solution
Answers
so the solution is all the numbers that are greater than 16
1. if m∠6 =50° , then find m∠112. m∠2= 70°, then find m∠63. if m∠ 1=130°, then find m∠5
Answers
Answer:
1. m∠11=130°
2. m∠6= 70°
3. m∠5=130°
Explanation:
Part 1
Angles 6 and 11 are the same-side interior angles. We know that same side interior angles add up to 180 degrees, therefore:
m∠6+m∠11=180°
50°+m∠11=180°
m∠11=180°-50°
m∠11=130°
Part 2
Lines a and b are parallel lines. Therefore, angles 2 and 6 form a Z-Shape.
They are Alternate angles.
m∠2 = m∠6
Since m∠2= 70°
m∠6= 70°
Part 3
Angles 1 and 3 are Corresponding angles, this means that they are equal.
• m∠1=m∠3
Likewise, angles 3 and 5 form an X-shape, they are vertical angles and also equal.
• m∠5=m∠3
Combining the two, we have that:
m∠1=m∠3=m∠5
If m∠1=130°, then:
m∠5=130°
Examine the following graph of the system of inequalities y≤x2−4x−3 and y<−2x+4. A is the area below the line and the parabola. B is the area below the line but above the parabola. C is the area above the line and the parabola. D is the area below the parabola but above the line.© 2018 StrongMind. Created using GeoGebra. Which section of the graph represents the solution set to the system of inequalities?
Answers
The solution set to a system of inequalities represents the area that contains points that satisfy both inequalities.
The best way to answer the question is to choose one point from each area and check if they satisfy both.
Let's start by selecting a point in area A. Let's use (-6, 0).
[tex]\begin{gathered} 0\leq(-6)^2-4(-6)-3 \\ 0\leq36+24-3 \\ 0\leq57\text{ TRUE} \\ \\ 0<-2(-6)+4 \\ 0<12+4 \\ 0<16\text{ TRUE} \end{gathered}[/tex]Because out test point (-6, 0) satisfies both inequalities, then the entire area that contains it is the solution. We no longer have to test other points.
The answer is A.
The solution set is also the intersection of the graphs of the two inequalities. So you may refer to the shaded regions and you'll see that area A is shaded red and blue at the same time.
Part AWhat is the mass in grams of 17.96 mL of acetone?Express your answer to four significant figures and include the appropriate units.mass = Value and UnitsPart BWhat is the volume in milliliters of 7.40 g of acetone?Express your answer to three significant figures and include the appropriate units.V = Value and Units
Answers
Part A:
Ans: Mass=14.11 g.
Given:
The volume of acetone, V=17.96 mL.
We know, the density of acetone, D=0.7857 g/mL.
The mass in grams of acetone is,
[tex]\begin{gathered} M=VD \\ =17.96\text{ mL}\times0.7857\text{ g/mL} \\ =14.11\text{ g} \end{gathered}[/tex]Therefore, mass of acetone in grasm rounded upto four significant figures is 14.11 g.
Mass=14.11 g.
Part B:
Ans: V=9.42 mL
Given
The mass of acetone, M=7.4 g.
We know, the density of acetone, D=0.7857 g/mL.
The volume in mL of acetone is,
[tex]\begin{gathered} V=\frac{M}{D} \\ =\frac{7.40\text{ g}}{0.7857\text{ g/mL}} \\ =9.42\text{ mL} \end{gathered}[/tex]Therefore, voulme of acetone in mL rounded upto three significant figures is 9.42 mL.
Volume, V=9.42 mL
For what value of k are the graphs of 8y = 12x + 6 and 4y = k(3x + 10)
parallel? perpendicular?
Answers
The value of k when the graphs are parallel = 2 and when the graphs are perpendicular = 36/32 or 1.125
What is the slope-intercept form?
the slope-intercept for of a line is, y=mx+c, where m is the slope.
we are given the two equations 8y = 12x + 6 and 4y = k(3x + 10)
PARALLEL CONDITION
if they are parallel, their slopes will be equal,
hence,
y=mx+c
where m is the slope
converting both the equations in the slope-intercept form
8y = 12x + 6
= y= 12x/8 + 3/4
and for equation
4y = k(3x + 10)
4y = k3x+ 10k
y = k 3x/4 + 10k/4
comparing the slopes
12/8 = k3/4
12 * 4 = 3k * 8
48 = 24k
k= 48/24
k = 2
therefore when both the lines are parallel, the value of k is 2.
PERPENDICULAR CONDITION
if the two lines are perpendicular the product of their slope will be 1
so,
12/8 * 3k/4 = 1
36k/32 =1
36k = 32
k = 32/36
or
k = 1.125
therefore when they both are perpendicular, the value of k is 1.125 or 36/32.
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Using the translation that maps (3,-4) to its image (1,0), what is the image of any point (x,y)?A. (x+2,y+4)B. (x−2,y−4)C. (x+2,y−4)D. (x−2,y+4)
Answers
Explanation
Given (3,-4), its image (1,0) can be produced below;
[tex]\left(3,-4\right)\Rightarrow\left(x−2,y+4\right)\Rightarrow\left(1,0\right)[/tex]Answer: Option D
If a1 = 8 and an = 3an-1 then find the value of a4.
Answers
a_4= 216
1) Given that we have the first term and the Recursive Formula, let's find the fourth term of that Sequence
2) Let's find the second, the third to find the fourth since a Recursive formula depends on the prior term.
[tex]\begin{gathered} a_1=8 \\ a_n=3a_{n-1} \\ a_2=3(8)\text{ =24} \\ a_3=3(24)=72 \\ a_4=3(72)\text{ =216} \end{gathered}[/tex]3) Hence, the sequence is 8, 24, 72, 216 and the fourth term is 216
What is the radius of a circle whose circumference is 36pi?
Answers
The circumference of a circle of radius r is given by:
[tex]C=2\pi r[/tex]For this question we simply need to take C=36π and solve for r:
[tex]36\pi=2\pi r[/tex]If we divide both sides by 2π we get:
[tex]\begin{gathered} 36\pi=2\pi r \\ \frac{36\pi}{2\pi}=\frac{2\pi r}{2\pi}=\frac{2\pi}{2\pi}\cdot r \\ 18=r \end{gathered}[/tex]Then the answer is option A, 18.
4x-6x + 15 - x -4 how do I simply this
Answers
4x-6x + 15 - x -4 how do I simply this
4x-6x + 15 - x -4
_____________________
Rearrange
4x-6x - x -4 +15
(4-6-1)x +11
-3x+11
________________________________
you add all the x and you add all the numbers