State which pairs of lines are:(a) Parallel to each other.(b) Perpendicular to each other.
Answers
So first of all we should write the three equations in slope-intercept form. This will make the problem easier to solve. Remember that the slope-interception form of an equation of a line looks like this:
[tex]y=mx+b[/tex]Where m is known as the slope and b the y-intercept. The next step is to rewrite the second and third equation since the first equation is already in slope-intercept form. Its slope is 4 and its y-intercept is -1.
So let's rewrite equation (ii). We can begin with substracting 4 from both sides of the equation:
[tex]\begin{gathered} 8y+4=-2x \\ 8y+4-4=-2x-4 \\ 8y=-2x-4 \end{gathered}[/tex]Then we can divide both sides by 8:
[tex]\begin{gathered} \frac{8y}{8}=\frac{-2x-4}{8} \\ y=-\frac{2}{8}x-\frac{4}{8} \\ y=-\frac{1}{4}x-\frac{1}{2} \end{gathered}[/tex]So its slope is -1/4 and its y-intercept is -1/2.
For equation (iii) we can add 8x at both sides:
[tex]\begin{gathered} 2y-8x=-2 \\ 2y-8x+8x=-2+8x \\ 2y=8x-2 \end{gathered}[/tex]Then we can divide both sides by 2:
[tex]\begin{gathered} \frac{2y}{2}=\frac{8x-2}{2} \\ y=\frac{8}{2}x-\frac{2}{2} \\ y=4x-1 \end{gathered}[/tex]Then its slope is 4 and its y-intercept is -1. As you can see this equation is equal to equation (i).
In summary, the three equations in slope-intercept form are:
[tex]\begin{gathered} (i)\text{ }y=4x-1 \\ (ii)\text{ }y=-\frac{1}{4}x-\frac{1}{2} \\ (iii)\text{ }y=4x-1 \end{gathered}[/tex]It's important to write them in this form because when trying to figure out if two lines are parallel or perpendicular we have to look at their slopes:
- Two lines are parallel to each other if they have the same slope (independently of their y-intercept).
- Two lines are perpendicular to each other when the slope of one of them is the inverse of the other multiplied by -1. What does this mean? If a line has a slope m then a perpendicular line will have a slope:
[tex]-\frac{1}{m}[/tex]Now that we know how to find if two lines are parallel or perpendicular we can find the answers to question 4.
So for part (a) we must find the pairs of parallel lines. As I stated before we have to look for those lines with the same slope. As you can see, only lines (i) and (iii) have the same slope (4) so the answer to part (a) is: Lines (i) and (iii) are parallel to each other.
For part (b) we have to look for perpendicular lines. (i) and (iii) are parallel so they can't be perpendicular. Their slopes are equal to 4 so any line perpendicular to them must have a slope equal to:
[tex]-\frac{1}{m}=-\frac{1}{4}[/tex]Which is the slope of line (ii). Then the answer to part (b) is that lines (i) and (ii) are perpendicular to each other as well as lines (ii) and (iii).
Related Questions
If TW =6, WV =2, and UV =25, find XV to the nearest hundredth.
Answers
TW = 6
WV = 2
UV = 25
XV = ?
XV/UV = WV/TV
XV/25 = 2 /(6 + 2)
XV = 2(25)/7
XV = 50/7
XV = 7.1428
Rounded to the nearest hundredth
XV = 7.14
match the system of equations with the solution set.hint: solve algebraically using substitution method.A. no solutionB. infinite solutionsC. (-8/3, 5)D. (2, 1)
Answers
We will solve all the systems by substitution method .
System 1.
By substituting the second equation into the first one, we get
[tex]x-3(\frac{1}{3}x-2)=6[/tex]which gives
[tex]\begin{gathered} x-x+6=6 \\ 6=6 \end{gathered}[/tex]this means that the given equations are the same. Then, the answer is B: infinite solutions.
System 2.
By substituting the first equation into the second one, we have
[tex]6x+3(-2x+3)=-5[/tex]which gives
[tex]\begin{gathered} 6x-6x+9=-5 \\ 9=-5 \end{gathered}[/tex]but this result is an absurd. This means that the equations represent parallel lines. Then, the answer is option A: no solution.
System 3.
By substituting the first equation into the second one, we obtain
[tex]-\frac{3}{2}x+1=-\frac{3}{4}x+3[/tex]by moving -3/4x to the left hand side and +1 to the right hand side, we get
[tex]-\frac{3}{2}x+\frac{3}{4}x=3-1[/tex]By combining similar terms, we have
[tex]-\frac{3}{4}x=2[/tex]this leads to
[tex]x=-\frac{4\times2}{3}[/tex]then, x is given by
[tex]x=-\frac{8}{3}[/tex]Now, we can substitute this result into the first equation and get
[tex]y=-\frac{3}{2}(-\frac{8}{3})+1[/tex]which leads to
[tex]\begin{gathered} y=4+1 \\ y=5 \end{gathered}[/tex]then, the answer is option C: (-8/3, 5)
System 4.
By substituting the second equation into the first one, we get
[tex]-5x+(2x-3)=-9[/tex]By combing similar terms, we have
[tex]\begin{gathered} -3x-3=-9 \\ -3x=-9+3 \\ -3x=-6 \\ x=\frac{-6}{-3} \\ x=2 \end{gathered}[/tex]By substituting this result into the second equation, we have
[tex]\begin{gathered} y=2(2)-3 \\ y=4-3 \\ y=1 \end{gathered}[/tex]then, the answer is option D
3 166.40 266.24 3. Consider the following functions which all have an or decay? By what percent? Rewrite as (1+r) or (1-r) f(t) = 30(1.04) p(x) = 30(0.65)Solve f(t)
Answers
ANSWER
Function f(t) represents a growth by 4%
EXPLANATION
If the function represents a decay it is written as:
[tex]f(t)=a(1-r)^t[/tex]and if it represents a growth it's:
[tex]f(t)=a(1+r)^t[/tex]We can see if it's a growth or decay by looking at the number we have between parenthesis: if it's greater than 1, then it's a growth and if it's less than 1 then it's a decay.
For function f(t) we have
[tex]1+r=1.04[/tex]Therefore, r = 0.04 which, expressed as a percent is 4%
solving systems by graphing and tables : equations and inequalities
Answers
Given,
The system of inequalitites are,
[tex]\begin{gathered} 2x+3y>0 \\ x-y\leq5 \end{gathered}[/tex]The graph of the inequalities is,
The are three possible solution for the inequality.
For (0, 0),
[tex]\begin{gathered} 2x+3y>0 \\ 2(0)+3(0)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 0-0\leq5 \\ 0\leq5 \end{gathered}[/tex]For (3, -2),
[tex]\begin{gathered} 2x+3y>0 \\ 2(3)+3(-2)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 3-(-2)\leq5 \\ 5=5 \end{gathered}[/tex]For (5, 0),
[tex]\begin{gathered} 2x+3y>0 \\ 2(5)+3(0)>0 \\ 5>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 5-(0)\leq5 \\ 5=5 \end{gathered}[/tex]Hence, the solution of the inequalities is (5, 0).
The function is defined by h(x) = x - 2 . Find h(n + 1) .
Answers
SOLUTION:
Case: Functions
Method:
The function
[tex]\begin{gathered} h(x)=x-2 \\ Hence \\ h(n+1)=(n+1)-2 \\ h(n+1)=n+1-2 \\ h(n+1)=n-1 \end{gathered}[/tex]Final answer:
[tex]h(n+1)=n-1[/tex]A psychology test has personality questions numbered 1, 2, 3, intelligence questions numbered 1, 2, 3, 4, and attitudequestions numbered 1,2. If a single question is picked at random, what is the probability that the question is an intelligence question OR has an odd number?
Answers
Answer:
7/9.
Step-by-step explanation?
Total number of questions: 3 + 4 + 2 = 9.
Number of Intelligence questions: 4
Number of questions that have an odd number: 5
The probability of a question is Intelligence questions = 4/9
The probability a question has an odd number = 5/9
The probability a question is Intelligence questions and has an odd number = 2/9
The probability a question is Intelligence question OR has an odd number is:
4/9 + 5/9 - 2/9 = 7/9.
Which representation does not show y as a function of x?1.II.€9> 10III.x 1 3 5 7y -6 -18 -30 -42IV. {(-2,3), (-1,4), (0,4), (3, 2)}a) I and IIb) I, II, and IIIc) I and IVd) All of the above are functions
Answers
We can say that I is not a function because inputs can only have one output.
II it's not a function since if you draw an horizontal line through the function intersect in two points, then it's not a function.
The answer is A.
why does a cubic graph have both an x intercept and a y intercept
Answers
Answer:
All cubic function has domain (-∞,∞) and range (-∞,∞)
Step-by-step explanation:
Some airlines charge a fee for each checked luggage item that weighs more than 21,000 grams. How many kilograms is this?
Answers
The value of 21,000 grams to kilograms is 21 kilograms
How to convert kilograms to grams ?1000 grams = 1kg
The first step is to convert 21,000 grams to kilograms
It can be calculated as follows;
= 21000/1000
= 21
Hence the value of 21,000 grams in kilograms is 21 kilograms
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3/5 ÷ 1/3 = ?????????
Answers
Change the division sign to multiplication and then invert 1/3
That is;
[tex]\frac{3}{5}\times3[/tex][tex]=\frac{9}{5}\text{ =1}\frac{4}{5}[/tex]“Use the properties to rewrite this expression with the fewest terms possible:3+7(x - y) + 2x - 5y”
Answers
Expanding 7(x - y) in the above expression gives
[tex]-5y^{}+2x+7x-7y+3[/tex]adding the like terms (2x+ 7x) and (-5y-7y) gives
[tex](-5y-7y)+(2x+7x)+3[/tex][tex]\rightarrow\textcolor{#FF7968}{-12y+8x+3.}[/tex]The last expression is the simplest form we can convert our expression into.
Can you please help me because I don’t understand this and I would like to really understand it
Answers
Answer:
Explanation:
Given the expression:
[tex]\sqrt{12(x-1)}\div\sqrt{2(x-1)^{2}}[/tex]By the division law of surds:
[tex]\sqrt[]{x}\div\sqrt[]{y}=\sqrt[]{\frac{x}{y}}[/tex]Therefore:
[tex]\sqrt[]{12(x-1)}\div\sqrt[]{2(x-1)^2}=\sqrt[]{\frac{12(x-1)}{2(x-1)^2}}[/tex]The result obtained can be rewritten in the form below:
[tex]=\sqrt[]{\frac{2\times6(x-1)}{2(x-1)(x-1)^{}}}[/tex]Canceling out the common factors, we have:
[tex]=\sqrt[]{\frac{6}{(x-1)^{}}}[/tex]An equivalent expression is Opt
Determine the minimum and maximum value for f(x) = -5x²-3x+7 over interval [-1, 3].
Answers
The maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. A number that can be entered for the variable to produce a true number statement is the solution to an equation. 3(2)+5=11, which states that 6+5=11, is accurate. The answer is 2, then. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the minimum and maximum values when x are -1 and 3:
(1) When x = -1:
f(x) = -5x²-3x+7f(x) = -5(-1)²-3(-1) +7f(x) = -5(1) + 3 +7f(x) = -5 + 10f(x) = 5(2) When x = 3:
f(x) = -5x²-3x+7f(x) = -5(3)² -3(3)+7f(x) = -5(9) -9 +7f(x) = -45 -9 +7f(x) = - 54 + 7f(x) = - 47Therefore, the maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.
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Calculate Sse for the arithmetic sequence {a,}5sequence {1,3 ={}+}=Ο Α. 1463OB. 91220 C. 8,6716D. 9,26767
Answers
Answer:
[tex]\frac{8,671}{6}[/tex]Explanation:
Here, we want to get the sum of the 58 terms in series
Mathematically, we have the formula to use as:
[tex]S_n\text{ = }\frac{n}{2}(a\text{ + L)}[/tex]where a is the first term and L is the last term
The first term is when n is 1
We have this calculated as:
[tex]\text{ a}_{}\text{ = }\frac{5}{6}+\frac{1}{3}\text{ = }\frac{5+2\text{ }}{6}\text{ = }\frac{7}{6}[/tex]The last term is the 58th term which is:
[tex]\text{ a}_{58}\text{ = }\frac{290}{6}\text{ + }\frac{1}{3}\text{ = }\frac{292}{6}[/tex]We finally substitute these values into the initial equation
Thus, we have it that:
[tex]S_{58}\text{ = }\frac{58}{2}(\frac{292}{6}+\frac{7}{6})\text{ = 29(}\frac{299}{6})\text{ = }\frac{8671}{6}[/tex]
Find the area of the circle. Use 3.14 or 227for π . thxQuestion 2
Answers
Step 1
State the area of a circle using the diameter
[tex]\frac{\pi d^2}{4}[/tex]Where d=diameter=28in
[tex]\pi=\frac{22}{7}[/tex]Step 2
Find the area
[tex]A=\frac{22}{7}\times\frac{28^2}{4}=616in^2[/tex]Answer;
[tex]Area\text{ = }616in^2\text{ when }\pi\text{ =}\frac{22}{7}[/tex]The profit of a cell-phone manufacturer is found by the function y= -2x2 + 108x + 75 , where x is the cost of the cell phone. At what price should the manufacturer sell the phone tomaximize its profits? What will the maximum profit be?
Answers
Hello!
First, let's rewrite the function:
[tex]y=-2x^2+108x+75[/tex]Now, let's find each coefficient of it:
• a = -2
,• b = 108
,• c = 75
As we have a < 0, the concavity of the parabola will face downwards.
So, it will have a maximum point.
To find this maximum point, we must obtain the coordinates of the vertex, using the formulas below:
[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ Y_V=-\frac{\Delta}{4\cdot a} \end{gathered}[/tex]First, let's calculate the coordinate X by replacing the values of the coefficients:[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ X_V=-\frac{108}{2\cdot(-2)}=-\frac{108}{-4}=\frac{108}{4}=\frac{54}{2}=27 \end{gathered}[/tex]So, the coordinate x = 27.
Now, let's find the y coordinate:[tex]\begin{gathered} Y_V=-\frac{\Delta}{4\cdot a} \\ \\ Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \\ \\ Y_V=-\frac{108^2-4\cdot(-2)\cdot75}{4\cdot(-2)} \\ \\ Y_V=-\frac{11664+600}{-8}=\frac{12264}{8}=1533 \end{gathered}[/tex]The coordinate y = 1533.
Answer:
The maximum profit will be 1533 (value of y) when x = 27.
can I please getsome help with this question here, I can't really figure out how to find side PQ
Answers
SOLUTION
The following diagram will help us solve the problem
(a) From the diagram, the height of the parallelogram is given as TR, and it is 40 mm
Now we can use the area which is given to us as 3,600 square-mm to find the base of the parallelogram, which is PQ
So,
[tex]\begin{gathered} \text{Area }of\text{ a parallelogram = base}\times height \\ So\text{ } \\ 3600=PQ\times TR \\ 3600=PQ\times40 \\ 3600=40PQ \\ \text{dividing by 40, we have } \\ \frac{3600}{40}=\frac{40PQ}{40} \\ PQ=90 \end{gathered}[/tex]Hence PQ is 90 mm
(b) Now, note that the side
[tex]PS=QR[/tex]So, we will find QR
Also, since we have PQ, we can find TQ, that is
[tex]\begin{gathered} PQ=PT+TQ \\ 90=60+TQ \\ TQ=90-60 \\ TQ=30mm \end{gathered}[/tex]Note that triangle QRT is a right-angle triangle, and QR is the hypotenuse or the longest side
From pythagoras
[tex]\text{hypotenuse}^2=opposite^2+adjacent^2[/tex]So,
[tex]\begin{gathered} QR^2=TR^2+TQ^2 \\ QR^2=40^2+30^2 \\ QR^2=1600+900 \\ QR^2=2,500 \\ QR=\sqrt[]{2,500} \\ QR=50mm \end{gathered}[/tex]Now, since
[tex]\begin{gathered} PS=QR \\ \text{then } \\ PS=50mm \end{gathered}[/tex]Hence PS is 50 mm
An airplane is taking off at angle of 9 degrees and traveling at a speed of 200 feet per second in relation to the ground. If the clouds begin at an altitude of 4,000 feet, how many seconds will it take for the airplane to be in the clouds?
Answers
ANSWER
[tex]\begin{equation*} 127.85\text{ }seconds \end{equation*}[/tex]EXPLANATION
First, let us make a sketch of the problem:
To find the time it will take the airplane to be in the clouds, we first have to find the distance flown by the airplane in attaining that height, x.
To do this, apply trigonometric ratios SOHCAHTOA for right triangles:
[tex]\sin9=\frac{4000}{x}[/tex]Solve for x:
[tex]\begin{gathered} x=\frac{4000}{\sin9} \\ x=25,569.81\text{ }ft \end{gathered}[/tex]Now, that we have the distance, we can solve for the time by applying the relationship between speed and distance:
[tex]\begin{gathered} speed=\frac{distance}{time} \\ \Rightarrow time=\frac{distance}{speed} \end{gathered}[/tex]Substitute the given values into the formula above and solve for time:
[tex]\begin{gathered} time=\frac{25569.81}{200} \\ time=127.85\text{ }seconds \end{gathered}[/tex]That is the number of seconds that it will take.
If a and b are the measure of two first quadrant angles, find the exact value of the functioncsc a =5/3 and tan 5/12 find the cod (a+b)
Answers
Input data
[tex]\begin{gathered} \cos a=\frac{5}{3} \\ \tan b=\frac{5}{12} \end{gathered}[/tex]
Now for cos(a+b)
[tex]\begin{gathered} a=\csc ^{-1}(\frac{5}{3})^{} \\ a=36.87 \end{gathered}[/tex][tex]\begin{gathered} b=\tan ^{-1}(\frac{5}{12}) \\ b=22.62 \end{gathered}[/tex][tex]\begin{gathered} \cos (a+b) \\ \cos (36.87+22.62) \\ \cos 59.5 \\ \frac{33}{65}=0.507 \end{gathered}[/tex]What is the average rate of change from g(1) to g(3)?Type the numerical value for your answer as a whole number, decimal or fractionMake sure answers are completely simplified
Answers
The average rate of change from g(1) to g(3)
[tex]\frac{g(x)_3-g(x)_1}{X_3-X_1}_{}[/tex]where
[tex]g(x)_3=-20,g(x)_1=-8,x_3=3,x_1=\text{ 1}[/tex][tex]\begin{gathered} =\frac{-20\text{ --8}}{3-1}\text{ = }\frac{-20\text{ +8}}{2} \\ =\frac{-12}{2} \\ -6 \end{gathered}[/tex]Hence the average rate of change is -6
Raphael has an odd-shaped field shown in Figure 13-2. He wants to put a four-strand barbed wire fence around it for his cattle.A. What is the perimeter of the field?b. How many 80-rod rolls of barbed wire does he need topurchase?c. How many acres will be fenced?
Answers
Answer: Total perimeter = 9, 962.01 feet
The figure is a composite structure
It contains a rectangle and triangle
The perimeter of a rectangle is given as
Perimeter = 2( length + width)
length of the rectangle = 1500ft
Width of the rectangle = 1390 ft
Perimeter = 2( 1500 + 1390)
Perimeter = 2(2890)
Perimeter = 5780 ft
To calculate the perimeter of a triangle
[tex]\begin{gathered} \text{Perimeter = a + b + }\sqrt[]{a^2+b^2} \\ a\text{ = 1050ft and b = 1390 ft} \\ \text{Perimeter = 1050 + 1390 + }\sqrt[]{1050^2+1390^2} \\ \text{Perimeter = 2440 + }\sqrt[]{1,102,\text{ 500 + 1, 932, 100}} \\ \text{Perimeter = 2400 + }\sqrt[]{3,034,600} \\ \text{Perimeter = 2440 + 1,742,01} \\ \text{Perimeter = }4182.01\text{ f}eet \end{gathered}[/tex]The total perimeter of the field = Perimeter of the rectangle + perimeter of the right triangle
Total perimeter = 5780 + 4182.01
Total perimeter = 9, 962.01 feet
Given the conversion factor which cube has the larger surface area?
Answers
Given the surface area of a cube as
[tex]\begin{gathered} SA=6l^2 \\ \text{where l is the length} \end{gathered}[/tex]Given Cubes A and B
[tex]\begin{gathered} \text{Cube A} \\ l=19.5ft \end{gathered}[/tex][tex]\begin{gathered} \text{Cube B } \\ l=6m\text{ } \\ \text{ in ft}\Rightarrow\text{ 1m =3.28ft} \\ l=6\times3.28ft=19.68ft \end{gathered}[/tex]Find the surface area of the cubes and compare them to know which one is larger
[tex]\begin{gathered} \text{Cube A} \\ SA=6\times19.5^2=6\times380.25=2281.5ft^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Cube B} \\ SA=6\times19.68^2=6\times387.3024=2323.8144ft^2 \end{gathered}[/tex]Hence, from the surface area gotten above, Cube B has a larger surface area than Cube A
Help me with my schoolwork what is the slope of line /
Answers
The two points given on the line are
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(-2,9) \\ (x_2,y_2)\Rightarrow(6,1) \end{gathered}[/tex]The slope of line that passes through (x1,y1) and (x2,y2) is gotten using the formula below
[tex]\begin{gathered} m=\frac{\text{change in y}}{\text{change in x}} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1-9}{6-(-2)} \\ m=-\frac{8}{6+2} \\ m=-\frac{8}{8} \\ m=-1 \end{gathered}[/tex]Therefore,
The slope of the line = -1
What is the measure of EDH?EHFO 10°O 40°50°90
Answers
To find the measure of angle EDH we must solve for x first. Formulating an equation to find x, we have:
5x + 4x= 90 (Given that the sum of the angles EDH and HDG is equal to 90°)
9x = 90 (Adding like terms)
x= 90/9 (Dividing on both sides of the equation by 9)
x= 10
Replacing in the expression for angle EDH, we have:
m∠EDH = 5*(x) = 5*(10) = 50° (Multiplying)
The answer is m∠EDH =50°.
Find the sum of the arithmetic series given a1 =2, an =35 an n = 12
Answers
Given:
[tex]a_1=2,a_n=35,n=12[/tex]Required:
Find the sum of the arithmetic series.
Explanation:
The sum of the arithmetic series when the first and the last term is given by the formula.
[tex]S_n=\frac{n}{2}(a_1+a_n)[/tex]Substitute the given values in the formula.
[tex]\begin{gathered} S_n=\frac{12}{2}(2+35) \\ =6(37) \\ =222 \end{gathered}[/tex]Final Answer:
Option D is the correct answer.
Question 13 of 18Graph the solution to the following inequality on the number line.x² - 4x ≥ 12
Answers
Step 1
Given; Graph the solution to the following inequality on the number line.
x² - 4x ≥ 12
Step 2
[tex]\begin{gathered} x^2-4x\ge \:12 \\ Rewrite\text{ in standard form} \\ x^2-4x-12\ge \:0 \\ Factor\text{ the inequality} \\ \left(x+2\right)\left(x-6\right)\ge \:0 \end{gathered}[/tex][tex]\begin{gathered} Identify\text{ the intervals} \\ x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6 \end{gathered}[/tex]Thus, the number line will look like
Answer; The solution to the inequality graphed on a number line is seen below
[tex]x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6[/tex]w=3? What is the value of the expression below when w = 5w+ 2
Answers
Answer:
The value of the expression at w=3 is;
[tex]17[/tex]Explanation:
Given the expression;
[tex]5w+2[/tex]Then when w=3, the value of the expression is;
[tex]\begin{gathered} 5w+2 \\ =5(3)+2 \\ =15+2 \\ =17 \end{gathered}[/tex]The value is gotten by replacing/substituting w with 3 in the expression;
Therefore, the value of the expression at w=3 is;
[tex]17[/tex]hannah paid 15.79 for a dress that was originally marked 24.99 what js the percent of discount
Answers
The percentage of discount is 37%
Here, we want to calculate the percentage of discount
The first thing we need to do here is to calculate the discount amount
Mathematically, we have this as;
[tex]24.99-15.79\text{ = 9.2}[/tex]Now, we find the percentage of 24.99 is this discount
We have this as;
[tex]\frac{9.2}{24.99}\text{ }\times100\text{ \% = 36.8\%}[/tex]The percentage of discount is approximately 37%
A half-marathon has 53 runners. A first-, second-, and third-place trophy will be awarded. Howmany different ways can the trophies be awarded?
Answers
Let's use the combination formula:
[tex]\begin{gathered} C(n,k)=nCk=\frac{n!}{k!(n-k)!} \\ n=53 \\ k=3 \\ C(53,3)=53C3=\frac{53!}{3!(50)!}=23426 \end{gathered}[/tex]i need help, plotting the ordered pair (0, 0.5) and I need to state in which quadrant or on which axis the point lies.
Answers
The ordered pair:
[tex](x,y)=(0,0.5)[/tex]it is located at:
Since the point lies on the y-axis it doesn't not lie in any quadrant