Answers
The angle on a line is 180°
The sum of the three given angles is 180°:
[tex](6x-10)+(x-5)+(x-5)=180[/tex]Use this equation to find the value of x:
[tex]\begin{gathered} 6x-10+x-5+x-5=180 \\ 8x-20=180 \\ 8x=180+20 \\ 8x=200 \\ x=\frac{200}{8} \\ \\ x=25 \end{gathered}[/tex]Then, the value of x is 25Related Questions
Find a quadratic function with the given vertex ans passing through the given point vertex forn E Vertex (4,5): passes through (1, 2)
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The quadratic function forms a parabola. The vertex form of the equation is expressed as
y = a(x - h)^2 + k
Where
h and k are the x and y coordinates of the parabola's vertex. Given that the vertex is (4, 5),
h = 4, k = 5
Substituting these values into the above equation, it becomes
y = a(x - 4)^2 + 5
Given that the parabola passes through the point, (1, 2), we would substitute x = 1 and y = 2 into y = a(x - 4)^2 + 5. It becomes
2 = a(1 - 4)^2 + 5
2 = a * 9 + 5
2 = 9a + 5
9a = 2 -5
9a = - 3
a = - 3/9 = - 1/3
Substituting a = - 1/3 into y = a(x - 4)^2 + 5, the equation would be
[tex]y\text{ = -}\frac{1}{3}(x-4)^2\text{ + 5}[/tex]A line is drawn over this rectangle . Is the line a line of symmetry?
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Answer:
The line is not a line of symmetry because the two parts are not an exact match when you fold the rectangle over the line.
Explanation:
A line of symmetry is a line that divides the figure into two equal parts, so when you fold the figure over the line, the two parts will match exactly. So, taking into account the figure, the line drawn is not a line of symmetry.
The answer is
The line is not a line of symmetry because the two parts are not an exact match when you fold the rectangle over the line.
what is the area of a sector bounded by a 114 arc
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Step1: Write out the given parameter
Θ=114°,r= 6ft
Step2; Write out the formula
The area of a sector is given as
[tex]\frac{\theta}{360}\times\pi r^2[/tex]Step3: substitute the parameters into the formula
[tex]\frac{114}{360}\times\pi\times6^2[/tex][tex]\begin{gathered} \frac{114}{10}\pi \\ \frac{57}{5}\pi \end{gathered}[/tex]Hence the area of the sector is (57/5)π interms o
Example(-9, -2) (1,3)Find the slopeWrite in point slopeWrite in slope intercept formComplete the same three steps for 50extra points using the points(-6,7)(-3,6)
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The slope, m, of a line passing therough the points (x₁, y₁ ) and (x₂, y₂) can be calculated using the formula
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]For the points (-9, -2) and (1, 3):
x₁ = -9, y₁ = -2, x₂ = 1, y₂ = 3
Substituting these points into the slope formula given above
[tex]\begin{gathered} m\text{ = }\frac{3-(-2)}{1-(-9)} \\ m\text{ = }\frac{5}{10} \\ m\text{ = }\frac{1}{2} \end{gathered}[/tex]The slope, m = 1/2
The point-slope form of the equation of a line passing through the points (x₁, y₁ ) and (x₂, y₂) can be calculated using the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - (-2) = }\frac{1}{2}(x\text{ - (-9))} \\ y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \end{gathered}[/tex]The slope-intercept form of the equation will be of the form y = mx + c
Reduce the point-slope form written above to the intercept-slope form
[tex]\begin{gathered} y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \\ y\text{ + 2 = }\frac{x}{2}+\text{ }\frac{9}{2} \\ y\text{ = }\frac{x}{2}+\frac{9}{2}-2 \\ y\text{ = }\frac{1}{2}x\text{ +}\frac{5}{2} \end{gathered}[/tex]The amount of money Jeremy makes varies directly with the number of hours he works. Ifhe earns $195 for 3 days of work, how much will he earn if he works 12 days?
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Given:
a.) Jeremy earns $195 for 3 days of work.
To be able to determine how much will he earn if he works 12 days, we will be using ratios and proportions.
Let,
x = his earnings if he works for 12 days.
[tex]\text{ 195 : 3 = x : 12}[/tex][tex]\text{ 195 : 3 = x : 12 }\rightarrow\text{ }\frac{\text{ 195}}{3}\text{ = }\frac{\text{ x}}{12}[/tex][tex]\frac{\text{ 195}}{3}\text{ = }\frac{\text{ x}}{12}[/tex][tex]\text{ (195)(12) = (x)(3)}[/tex][tex]\text{ 2,340 = 3x}[/tex][tex]\text{ }\frac{\text{2,340}}{3}\text{ = }\frac{\text{3x }}{3}[/tex][tex]\text{ 780 = x}[/tex]Therefore, he'll earn $780 for working 12 days.
What is the intersection of the sets C = {5, 7, 10, 13, 19) and D = {3, 9, 14, 15}?O null setO (5, 7, 9, 10, 13, 14, 15, 19}O {5, 9, 14)O {3, 19)
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We are given the following two sets C and D
C = {5, 7, 10, 13, 19}
Find the real part and the imaginary part of the following complex number. - 14 - 14/13
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To find the measure of
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You have the following expression:
(2z - 3) + (5z - 6) = 180
in order to solvet the previous expression for z, proceed as follow:
(2z - 3) + (5z - 6) = 180 cancel out parenthesis
2z - 3 + 5z - 6 = 180 simplify like terms left side
7z - 9 = 180 add 9 both sides
7z = 180 + 9
7z = 189 divide by 7 both sides
z = 189/7
z = 27
Hence, the value of z is 27
Next, replace the values of z into the expression for the measureof angle M:
Hence, the measure of angle M is 129°
hello I am having difficulty on this problem please help thank you
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we have a system of inequalities
Inequality A
[tex]-4x+3y<6[/tex]Isolate the variable y
[tex]\begin{gathered} 3y\lt6+4x \\ y<\frac{4}{3}x+\frac{6}{3} \\ y\lt\frac{4}{3}x+2 \end{gathered}[/tex]The solution to the first inequality is the shaded area below the dashed line y=(4/3)x+2
Inequality B
[tex]4x+7y\leq-7[/tex]Isolate the variable y
[tex]\begin{gathered} 7y\leqslant-7-4x \\ y\leqslant\frac{-7}{7}-\frac{4x}{7} \\ \\ y\leqslant-\frac{4}{7}x-1 \end{gathered}[/tex]The solution to the second inequality is the shaded area below the solid line y=-(4/7)x-1
therefore
The solution to the system of inequalities is the shaded area below the dashed line y=(4/3)x+2 and below the solid line y=-(4/7)x-1
Using a graphing tool
see the attached figure below
Remember that
If an ordered pair is a solution to the system of inequalities
then
the ordered pair must lie in the shaded region of the solution
so
the point (-2,-2) is a solution to the system of inequalities
see the figure below
Fill in the blank. The set {x|XS - 4.3) written in interval notation is
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The given expression is :
[tex]\mleft\lbrace x\mright|x\leq-4.3\}[/tex]In the given expression x is less than equal to - 4.3
so, it's domain will lie from - infinity to - 4.3
Thus :
[tex]\text{ Interval Notation: (-}\infty,-4.2\rbrack[/tex]Answer :
[tex]\text{ Interval Notation: (-}\infty,-4.2\rbrack[/tex]Cara has 42.5 pounds of coffee. If she splits the coffee into 2.5 pound bags, how many bags will she need?A)17B)19C)21D)23
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[tex] {x}^{2} - [/tex]which could be the missing term in the expression if a factor of the expression is x-2ya) 2xyb) -2yc) [tex] {4y}^{2} [/tex]d)4y
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This is a difference of two squares.
If one factor is
[tex]x+2y[/tex]An the other is
[tex]x-2y[/tex]We have that the expression is:
[tex](x+2y)\cdot(x-2y)=x^2-4y^2[/tex]So the missing term is 4y², option c
a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
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a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
the equation is equal to
Multiply the number of tanks by 24
so
24c
the answer is 24cPart 2
1/13 is the reciprocal of 13
because
(13)(1/13)=1
a number multiplied by its reciprocal is equal to 1
6. Sheila simplified an expression using the following steps. Which property justifies Step 3?
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The distributive property of multiplication is represented by the following expression:
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]Notice that Sheila uses distributive property to simplify the expression:
[tex]\begin{gathered} 5x+4(3+2x) \\ =5x+4\cdot3+4\cdot2x \\ =5x+12+8x \\ =13x+12 \end{gathered}[/tex]could i have a fast answer please? if not it’s ok
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Given:
Strip diagrams are given.
Option D represents the 175% .
Option D is the correct answer.
The graph of y = –2/x lies in ____.A. Quadrant I and IIIB. Quadrant I and IIC. Quadrant II and IVD. Quadrant III and IV
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In order to find the quadrants of y = -2/x, let's choose a positive and a negative value of x, then we calculate the corresponding values of y and check the quadrants:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{2}{-2}=1 \\ \\ x=2\colon \\ y=-\frac{2}{2}=-1 \end{gathered}[/tex]The point (-2, 1) is in quadrant II (negative x and positive y) and the point (2, -1) is in quadrant IV (positive x and negative y).
Therefore the correct option is C.
what is 10•(-1/2)= ??
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For this problem, we are given a product between an integer and a fraction.
The expression is shown below:
[tex]10\cdot(\frac{-1}{2})[/tex]To solve this problem, we need to multiply the two numerators and denominators, then simplify the fraction:
[tex]\frac{-10}{2}=-5[/tex]The result is -5.
A segment has endpoints A and C. What are two names for the segment? Choose the correct answer below O AC and CA OAC and CA O AC and CA O AC and CA
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Given that endpoints of a segment: A and C
The two names for the sgment will be:
AC and CA
ANSWER:
AC and CA
Please help. I’m not sure how to do this. the options are a)1.3b)0.3c) 2.2d)0.4
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Step 1
Given;
Step 2
[tex]\begin{gathered} constant=\text{ height}\times width \\ let\text{ us use height=0.2} \\ width=2 \end{gathered}[/tex][tex]constant=0.2\times2=0.4[/tex]Answer;
[tex]0.4[/tex].............................
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step 1
Find out the expected value
In this game, the total possible outcomes are 12
The probability of a win is P=1/12
The probability of loss is P=11/12
so
EV=(1/12)*(30-20)-(11/12)*30
EV=(1/12)*(10)-(11/12)*30
EV=(10/12)-(330/12)
EV=-320/12
EV=-26.67p ----> is negative because is a loss for the players
If 60 people play the game
26.67*60=1,600
therefore
The school expect to raise for charity 1,600p
Divide by 100
1,600p/100=$16Convert: 3 days = minutes
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ANSWER
4320 minutes
EXPLANATION
To convert from days to minutes, first, we have to convert from days to hours. It is known that 1 day has 24 hours, so 3 days have,
[tex]3\text{ }days\cdot\frac{24\text{ }hours}{1\text{ }day}=72\text{ }hours[/tex]Then, we convert from hours to minutes. If 1 hour has 60 minutes,
[tex]72\text{ }hours\cdot\frac{60\text{ }minutes}{1\text{ }hour}=4320\text{ }minutes[/tex]Hence, there are 4320 minutes in 3 days.
The following data are the distances from the workplace (in miles) for the 5 employees of a small business.
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1. Given that the population data is : 15,5,8,2,5
• number of sample in data , ,n = 5
,• Mean = sum of sample in the data / number of sample
= (15+5+8+2+5)/5
= 35/5
Therefore mean = 7
2. Calculate varience as in the box below:
[tex]\begin{gathered} _{}\text{Varience = }\frac{1}{n}\mleft\lbrace(x_i-\vec{x}\mright)^2 \\ \text{ = }\frac{1}{5}\mleft\lbrace(7-15)^2+(7-5)^2+(7-8)^2+(7-2)^2+(7-5)^2\mright\rbrace \\ \text{ = }\frac{1}{5}\mleft\lbrace(-8^2\mright)+(-2)^2+(-1^2)+(5^2)+(2^2)\} \\ \text{ =}\frac{1}{5}\mleft\lbrace64\text{ + 4+ 1 +25+4}\mright\rbrace \\ \text{ = }\frac{1}{5}(98) \\ \text{ = }\frac{98}{5} \\ \therefore S\tan dard\text{ deviation = }\sqrt[]{varience\text{ }} \\ \text{ = }\sqrt[]{\frac{98}{5}}\text{ } \\ \text{ =4.427} \end{gathered}[/tex]• This means that Standard deviation = 4.43
- Gross pay: $38,550; married,
2 dependents; state income tax rate:
3 percent.
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Answer:
Step-by-step explanation:
This is 0% of your total income of $0. 0% would also be your average tax rate. Your income puts you in the 0% tax bracket. At higher incomes, exemptions, many deductions and many credits are phased out. This increases your tax bill and your marginal tax rate. With these phase outs, adding $1,000 to your income would result in a 0% marginal tax rate.
Hello, I need help with this precalculus homework question, please? I just need help with section D for the graph. HW Q3
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The answer would be option B
An easy way to see this is to look for the Y-intercept (when X=0)
So:
(13x + 13) / (8x +16) = 13/16 = 0.81
So, which graph has a Y intercept of approximately 0.81? The B
A group of friends wants to go to the amusement park. They have no more than $225to spend on parking and admission. Parking is $5, and tickets cost $20 per person,including tax. Write and solve an inequality which can be used to determine p, thenumber of people who can go to the amusement park.3Inequality:рSubmit AnswerPrivacy Policy Terms of Service
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Answer:
Inequality: 5 + 20p ≤ 225
p ≤ 11
Explanation:
The total cost can be calculated as the sum of the parking and ticket costs. So, we can calculate the total cost as:
5 + 20p
Because 20p represents the total ticket cost for p people.
Then, this total cost should be less than or equal to 225. It means that the inequality that represents the situation is:
5 + 20p ≤ 225
Finally, we can solve the inequality by subtracting 5 from both sides as:
5 + 20p - 5 ≤ 225 - 5
20p ≤ 220
Then, divide both sides by 20, to get:
20p/20 ≤ 220/20
p ≤ 11
So, the number of people who can go to the amusement park is less than or equal to 11.
Therefore, the answers are:
Inequality: 5 + 20p ≤ 225
p ≤ 11
What is the quotient in simpilest form? 3/4÷5/16
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the given expression is
[tex]\frac{\frac{3}{4}}{\frac{5}{16}}[/tex][tex]\frac{3\times16}{5\times4}=\frac{12}{5}=2.4[/tex]so the quotient will be 2.4
solve the following: a. 1/14 - 3 1/8 b. -7/2x^2y^2. + 5/2xy^2 + 3/x^2yc. -2 1/3 + 1 1/9
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First we analyze the denominators
2x^2y^2 is the greatest common factor for all three fractions, now we just divide each denominator with that factor and then multiply the answer by numerators
Then, the new fraction will be:
e)
5/6 year = how many months
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We will solve as follows:
We multiply the value we want to know (5/6) times the number of months that are in a year(12 months) and divide it by the number of years 12 months represent:
[tex]m=\frac{(\frac{5}{6})\cdot(12)}{1}\Rightarrow m=10[/tex]So, 5/6 of a year are 10 months.
Alex is 12 years older than George, Carl is three times older than Alex, The sum of their ages is 68. Find the ratio of George's age to Carl's age to Alex's age.
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Firstly, let x represent Alex's age, y represent George's age and z represent Carl's age.
from the question;
Alex is 12 years older than George, So;
[tex]x=y+12\ldots\ldots\ldots\ldots.1[/tex]Carl is three times older than Alex, So;
[tex]z=3x\ldots\ldots\ldots..2[/tex]The sum of their ages is 68, So;
[tex]x+y+z=68\ldots\ldots\ldots\ldots\ldots3[/tex]Now we have three equations and three unknowns, so it is solvable.
Let us substitute equation 2 into equation 3; that is replace z with 3x in equation 3.
[tex]\begin{gathered} x+y+3x=68 \\ 4x+y=68\ldots\ldots\ldots\ldots\ldots\ldots4 \end{gathered}[/tex]Next, let us substitute equation 1 into equation 4. that is replace x with y+12 in equation 4.
[tex]\begin{gathered} 4(y+12)+y=68 \\ 4y+48+y=68 \\ 5y+48=68\ldots\ldots\ldots.5 \end{gathered}[/tex]we can now solve for the value of y from equation 5.
[tex]\begin{gathered} 5y+48=68\ldots\ldots\ldots.5 \\ \text{subtract 48 from both sides.} \\ 5y+48-48=68-48 \\ 5y=20 \\ y=\frac{20}{5} \\ y=4 \end{gathered}[/tex]let us now replace y with 4 in equation 1 to get the value of x. since y = 4;
[tex]\begin{gathered} x=y+12\ldots\ldots\ldots\ldots.1 \\ x=4+12 \\ x=16 \end{gathered}[/tex]then, since x =16 let us replace x with 16 in equation 2 to get z.
[tex]\begin{gathered} z=3x\ldots\ldots\ldots..2 \\ z=3(16) \\ z=\text{ 48} \end{gathered}[/tex]so we have;
[tex]\begin{gathered} \text{Alex's age = x = 4 years} \\ George^{\prime}sage_{}=y=16\text{ years} \\ Carl^{\prime}sage=z=48\text{ years} \\ \end{gathered}[/tex]We now need to find the ratio of George, Carl and Alex's age.
[tex]\begin{gathered} 16\colon48\colon4 \\ \text{dividing through by 4 we have;} \\ 4\colon12\colon1 \end{gathered}[/tex]So the ratio of their ages are;
[tex]4\colon12\colon1[/tex]Round to the nearest hundredth.1.9541
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In order to round to the neares hundreth 1.9541, consider that hundreths are the second number after the decimal point, moreover, take into account that the value of such a number depends of the value of the next number (that is, third number after decimal point).
If next number is lower than 5, then, the second number remains the same, if next number is 5 or greater, second number is increased 1 unit.
In this case, the next number is 4, then, second number or hundreths remain the same.
Hence, you have:
[tex]1.9541\approx1.95[/tex]