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
Related Questions
A person places $531 in an investment account earning an annual rate of 6.1%,compounded continuously. Using the formula V = Pe", where V is the value of theaccount in t years, P is the principal initially invested, e is the base of a naturallogarithm, and ris the rate of interest, determine the amount of money, to thenearest cent, in the account after 16years.
Answers
This is the solution, Qxk:
Step 1: Let's review the information provided to us to answer the problem correctly:
Principal = $ 531
Interest rate = 6.1% (0.061) compounded continously
Term = 16 years
Step 2: Let's find the future value of this investment, as follows:
V = Pe^t*r
V
I need to know what a cordanate plain is
Answers
A coordinated plane is
Please help will mark Brainly
Answers
Using the properties of a linear function we get the value of y as 2 when x is 0.
A linear function is of the form: y = mx + c , where m is the slope
Now the function satisfies (-4,3) and (4,5)
So we substitute these values in the function.
At (-4,3) we get 3 = -4m + c
At (4,5) we get 5 = 4m + c
Adding the two equation we get:
2c = 8
or, c = 4
Now at c = 4 , and at (4,5) we get
5 = 4m + 2
or, m = 3/4
So the linear function is of the form :
y = 3/4 x + 2
or, 4y = 3x + 8
Now at x = 0 ,
4y = 8
or, y = 2
A function which graph (in Cartesian coordinates) is a non-vertical straight in the plane is known as a linear function as from real numbers to the real numbers in calculus and related mathematical fields. When the input variable is modified, the output often changes in a manner that is proportionate to the input variable's change.
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Try to evaluate 1001/2 without using a calculator. Enter DNE if the number is not real.
Answers
Rational exponent rule
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]Applying this rule to the case given:
[tex]100^{\frac{1}{2}}=\sqrt[]{100^1}=\sqrt[]{100^{}}=10[/tex]MATH HELP WILL MARK BRAINLEST
Answers
The objective function ( S for score ) in the given linear programming problem is S = 3x + 5y , the correct option is (a) .
In the question ,
it is given that ,
number of points that a multiple choice question gives = 3 points
number of points that a short answer gives gives = 5 points ,
let the number of multiple choice questions be = x
let the number of short answer questions be = y ,
the final score is denoted by S ,
So , the function , to represent the above situation is ,
S = 3x + 5y
Therefore , The objective function ( S for score ) in the given linear programming problem is S = 3x + 5y , the correct option is (a) .
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Find the equation of the linear function represented by the table below in slope-intercept form.xy1-52-73-94-11
Answers
Answer:
[tex]y=-2x-3[/tex]Explanation:
Given the table:
x | 1 2 3 4
y | -5 -7 -9 -11
Find the slope using the two point formula.
Take the points (1, -5) and (2, -7).
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-7-(-5)}{2-1} \\ =\frac{-7+5}{1} \\ =-2 \end{gathered}[/tex]Substitute the value of the slope into the slope-intercept form y = mx+c.
[tex]y=-2x+c[/tex]Plug the point (1, -5) into y = -2x+c to find c.
[tex]\begin{gathered} -5=-2+c \\ c=-5-(-2) \\ =-3 \end{gathered}[/tex]Thus, y = -2x - 3, which is the required equation of the given linear function.
Which point on the number line below best represents V30?
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We should try different squared numbers that are bigger and smaller than 30 as:
[tex]\begin{gathered} \sqrt{16}=4 \\ \sqrt{25}=5 \\ \sqrt{36}=6 \end{gathered}[/tex]Since 30 is between 25 and 36, the square root of 30 is going to be between 5 and 6. So the point that best represents the square root of 30 is M.
Answer: Point M
I need a very fast answer to this question please I’m in a hurry
Answers
To find f(3 + h) we need to substitute x = 3 + h, into the function, as follows:
[tex]\begin{gathered} f(x)=\frac{1}{(3+h)+2} \\ \text{ Combining similar terms:} \\ f(x)=\frac{1}{h+(3+2)} \\ f(x)=\frac{1}{h+5} \end{gathered}[/tex]
how do I solve this linear equations by substitution x=5 x + y = 4
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Substitute 5 for x in the equation x+y=4 to obtain the value of y.
[tex]\begin{gathered} 5+y=4 \\ y=4-5 \\ =-1 \end{gathered}[/tex]So solution of the equations is (5,-1).
An online store started its business with 15 sales per week. If their sales increased 18% each week, use an exponential model to find the week in which they exceeded 1000 sales per week. Remember, A= P(1+r)^t26 weeks31 weeks38 weeks15 weeks
Answers
Given,
The initial sale is 15.
The rate of increase of sale per week is 18 %.
The final sale is 1000.
The week at which the sales exceeds 1000 is:
[tex]\begin{gathered} 1000=15\times(1+\frac{18}{100})^t \\ \frac{1000}{15}=(\frac{118}{100})^t \\ \frac{200}{3}=(1.18)^t \\ log\text{ \lparen}\frac{200}{3})=t\text{ log\lparen1.18\rparen} \\ t=25.37 \end{gathered}[/tex]The sales of the business reach to 1000 in 25th week.
Hence, the sales of the business exceed to 1000 in 26th week.
For questions 5-6, g(x) is a transformation of f(x) = x2. What is the function g(x) that is represented by the graph? QUESTION 5
Answers
The transformation in question 5 shows a shift to the left by 3 units.
A shift to the left by b units has the rule:
[tex]f(x)\to f(x+b)[/tex]Therefore, the shift to the left by 3 units will yield the function:
[tex]x^2\to(x+3)^2[/tex]Hence, the function g(x) will be:
[tex]g(x)=(x+3)^2[/tex]Express the following expression in the form of a + bi : (16 + 6i) ((12 - 10i) - (2 - 5i))
Answers
Given:
There is an expression given as below
[tex]\left(16+6i\right)(\left(12-10i\right)-(2-5i))[/tex]Required:
We need to simplify the given expression and express in form of a+ib
Explanation:
[tex]\begin{gathered} (16+6i)((12-10i)-(2-5i)) \\ =(16+6i)(12-10i-2+5i) \\ =(16+6i)(10-5i) \\ =160-80i+60i+30 \\ =190-20i \end{gathered}[/tex]Final answer:
a + ib = 190 - 20i
The English Channel is the waterway between England and France. It is about 21 kilometers across, and many people have successfully swam across it. In the United States, many pools at gyms are 25 yards long, and 1 lap equals the pool length.Assuming a person swims in a straight line, how can you calculate the number of complete laps a person must swim in a 25-yard pool to equal swimming across the English Channel?A) First, convert the distance across the channel to approximately 13 miles. Next, convert the distance in miles to 22,880 feet. Then, convert the pool length to 75 feet. Finally, multiply the distance by 1 lap 75 ft. to get about 305 laps.B) First, convert the distance across the channel to approximately 34 miles. Next, convert the distance in miles to 179,520 feet. Then, convert the distance in feet to 59,840 yards. Finally, multiply the distance by 1 lap 25 yd. to get about 2,394 laps.C) First, convert the distance across the channel to approximately 34 miles. Next, convert the distance in miles to 59,840 feet. Then, convert the pool length to 75 feet. Finally, multiply the distance by 1 lap 75 ft. to get about 798 lapsD) First, convert the distance across the channel to approximately 13 miles. Next, convert the distance in miles to 68,640 feet. Then, convert the distance in feet to 22,880 yards. Finally, multiply the distance by 1 lap 25 yd. to get about 915 laps.
Answers
The first step to find the correct answer indeed is to convert the distance across the channel from kilometers to miles.
Because 1 km is equal to approximately 0.62 miles, 21 kilometers will be just 21 times the 0.62 miles. From this, we are able to calculate the following:
[tex]\begin{gathered} 25\operatorname{km}=25\times0.62mi \\ 25\operatorname{km}\text{ }\cong13mi \end{gathered}[/tex]From this, we are able to say that the correct answer is not B or C.
Now, because 1 mi is equal to 5,280 ft, we can say that 13 mi is equal to 13 times 5,280 ft. From this, we calculate:
[tex]\begin{gathered} 13mi=13\times5,280ft \\ 13mi=68,640ft \end{gathered}[/tex]From this, we are able to say that the correct answer is not A also. To convert it to yards, we need to remember that 1 foot is equal to (1/3) yards, which means that 68,640 ft is equal to 68,640 times (1/3) yards. Calculating, we get the following:
[tex]\begin{gathered} 68,640ft=68,640\times\frac{1}{3}yd \\ 68,640ft=22,880yd \end{gathered}[/tex]Because the lap in the pool is 25 yd, we need to DIVIDE, not to multiply, the distance of the channel in yards we found by the distance of the pool, which is 25 yd.
From this, we get the following answer:
[tex]N_{of\text{ laps}}=\frac{22,880yd}{25\frac{yd}{lap}}=915.2\text{ laps}[/tex]From this, we know that the number of laps a person who wants to swim the same distance of the channel mentioned is equal to approximately 915 laps
And the final answer is D.
How much sales tax will Justin pay on a computer priced at $1,723.42 if the sales tax rateis 9.25 percent?
Answers
Given : the price of the computer = $1,723.42
The sales tax = 9.25% = 9.25/100 = 0.0925
The sales tax = 9.25% of $1,723.42 = 0.0925 * $1,723.42 = $159.42 (to the nearest cent)
So,
The sales tax = $159.42
complete the Pattern 444 4440 44,400 there are three empty lines I need to finish the pattern
Answers
Given:
d. 444 4,440 44,400
e. 9.5 950 9500
The pattern for d as you can see all numbers have 444 but they keep adding extra 0's to each number.
So the next number should have another extra 0 after 44400.
The pattern for all parts a to e seem to be multiplying each number by 10 or dividing by 10 that is why for d. 444 has no 0's but then if you multiply by 10 you get 4440.
If you do 4440*10 you get 44400.
Answer:
The same pattern applies to e.
For the first blank divide 9.5 by 10 so then 9.5 ÷ 10 = 0.95
For the 2nd blank. Multiply by 10 to 95,000 so you get 950,000. Notice how 950,000 has an extra 0.
3rd blank should be 9500000
-3х – 10у = -20 -5x — бу = 20
Answers
You can solve a system of equations by graphing
The solution of a system of linear equations is the intersection point both graphs
using a graphing tool
the solution is the point (-10,5)
so
x=-10
y=5
the solution is the intersection point both lines
I will solve the system by substitution
we have
-3х – 10у = -20 --------> equation A
-5x — бу = 20 --------> equation B
isolate the variable y in the equation A
10y=-3x+20
y=-0.3x+2 --------> equation C
substitute equation C in equation B
-5x-6(-0.3x+2)=20
solve for x
-5x+1.8x-12=20
-3.2x=20+12
-3.2x=32
x=-10
substitute the value of x in the equation C
y=-0.3x+2
y=-0.3(-10)+2
y=3+2
y=5
the solution is x=-10 and y=5
3. Mindi forgot to pay her water bill of $79.45, and it is now 28days late. Below is the water department's late fee charges.1-10 Days Late$1.50 per day11-20 Days Late10-Day Late Fee+$2.00 per additional day21-30 Days Late10-Day Late Fee+20-Day Late Fee+$2.50 per additional dayHow much will Mindi owe if she pays her water bill today?
Answers
The amount she was supopose to pay = $79.45
It's now 28 days late . The charges will be $2.50 per additional day. Therefore,
[tex]total\text{ additional fe}e=2.50\times28=\text{ \$70}[/tex]The amount she will pay if she pays today will be
[tex]70+79.45=\text{ \$}149.45[/tex]Help me please just plot the points on the graph
Answers
As per given by the question,
There are given that the equation,
[tex]y=4x-2[/tex]Now,
For plot the point on the grpah;
Put the value of x is 0 in the given equation and find the value of y,
So,
[tex]\begin{gathered} y=4x-2 \\ y=4(0)-2 \\ y=-2 \end{gathered}[/tex]And,
Put the value of y is 0 in the given equation to find the value of x,
So;
[tex]\begin{gathered} y=4x-2 \\ 0=4x-2 \\ 4x=2 \\ x=\frac{2}{4} \\ x=0.5 \end{gathered}[/tex]The point on the graph is,
[tex](0,\text{ -2) and (0.5, 0)}[/tex]Hence, the grpah of the given equation is;
7) A spherical balloon is inflated so that its radius increases at a rate of 2 cm/sec. How fastis the volume of the balloon increasing when the radius is 3 cm?4(Use V =for the volume of a sphere)3A) 7270 cm/sec B) 791 cm/sec C) 70 cm/sec D) 8210 cm/sec
Answers
The formula for the volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]Since we are asked the rate of change of the volume with repect to time, we take the derivative on both sides, taking into account the chain rule:
[tex]\frac{dV}{dt}=\frac{d(\frac{4}{3}\pi r^3)}{dt}[/tex]taking out the constants:
[tex]\frac{dV}{dt}=\frac{4}{3}\pi\frac{d(r^3)}{dx}[/tex]Now we derivate, using the chain rule, that is:
[tex]\frac{df(g(x))}{dx}=f^{\prime}(x)g^{\prime}(x)[/tex]Applying the rule:
[tex]\frac{dV}{dt}=\frac{4}{3}\pi(3r^2)\frac{dr}{dt}[/tex]Simplifying:
[tex]\frac{dV}{dt}=4\pi(r^2)\frac{dr}{dt}[/tex]We have the following known values:
[tex]\begin{gathered} \frac{dr}{dt}=\frac{2\operatorname{cm}}{s} \\ r=3\operatorname{cm} \end{gathered}[/tex]Replacing we get:
[tex]\frac{dV}{dt}=4\pi(3)^2(2)[/tex]Solving we get:
[tex]undefined[/tex]i really need help can you help me?
Answers
1. Madison's work is correct. Her there is no mistake
2. Kaleb's work is not correct. His mistake was when he divided by 4
A parabola can be drawn given a focus of (-5, 9) and a directrix of y = 5. Write the equation of the parabola in any form. 12 10 8 6 4 cu 2 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 -2 directrix 1 -6 -8 F(-5,9) -10 -12
Answers
The distance from the directrix to the focus is 4, so p=2. So the vertex of the parabola is (-5,7). Having this we get that
[tex]\begin{gathered} 4p(y-k)=(x-h)^2 \\ 8(y-7)=(x+5)^2 \end{gathered}[/tex]
Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 4.)Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.Relativefrequency Temperature 109 112 110 94 102 106 104 94 108 105 103 107 105 101 93103 99Relative Frequency 93 to 9697 to100101 to 104105 to 108109 to 112
Answers
Above you have the given 17 data ordered from least to greatest.
To find the relative frequency:
1. Frequency: Identify the number of data that goes in each temperature range:
93 to 96: 3 data (93,94,94)
97 to 100: 1 data (99)
101 to 104: 5 data (101, 102, 103, 103, 104)
105 to 108: 5 data (105, 105, 106, 107, 108)
109 to 112: 3 data (109, 110, 112)
2. Relative frequency: Find the ratio of the number of data you get in step 1 (Frecuency) to the total number of data (17):
93 to 96:
[tex]\frac{3}{17}\approx0.18[/tex]97 to 100:
[tex]\frac{1}{17}\approx0.06[/tex]101 to 104:
[tex]\frac{5}{17}\approx0.29[/tex]105 to 108
[tex]\frac{5}{17}\approx0.29[/tex]109 to 112
[tex]\frac{3}{17}\approx0.18[/tex]Then, the relative frequencies are:
93 to 96: 0.18
97 to 100: 0.06
101 to 104: 0.29
105 to 108: 0.29
109 to 112: 0.18
Answer: the other person is correct
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.(4,5) and (9, 2)
Answers
Answer: (6.5, 3.5)
Explanation:
The midpoint between two points can be found by taking the mean of the x coordinates, and the mean of the y coordinates.
The points we have are:
(4, 5) where we will call
[tex]x_1=4,y_1=5[/tex]and also the point
(9, 2) where we will call
[tex]x_2=9,y_2=2[/tex]Now, the midpoint will be at
[tex](x_m,y_m)[/tex]Where xm is the mean of the x coordinates, and ym is the mean of the y coordinates:
[tex]x_m=\frac{x_1+x_2}{2}[/tex]subtituting the values:
[tex]x_m=\frac{4+9}{2}=\frac{13}{2}=6.5[/tex]we have xm, now we need ym:
[tex]y_m=\frac{y_1+y_2}{2}[/tex]Substituting the values
[tex]y_m=\frac{5+2}{2}=\frac{7}{2}=3.5[/tex]Thus, the midpoint is at:
[tex](x_m,y_m)=(6.5,3.5)[/tex]Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 18 people took the trip. She was able to purchase coach tickets for $170 and first class tickets for $1010. She used her total budget for airfare for the trip, which was $10620. How many first class tickets did she buy? How many coach tickets did she buy:
Answers
Explanation
Let the number of people with coach tickets be x and the number of people with first class tickets be y. Since the trip goers contained a total of 18 people we will have;
[tex]x+y=18[/tex]A coach ticket cost $170 dollars and the first class tickets cost $1010. Also, Sarah spent a total of $10620 to buy the tickets. This would give us;
[tex]170x+1010y=10620[/tex]We will now solve the equation simultaneously.
[tex]\begin{gathered} \begin{bmatrix}x+y=18\\ 170x+1010y=10620\end{bmatrix} \\ isolate\text{ for x in equation 1}\Rightarrow x=18-y \\ \mathrm{Substitute\:}x=18-y\text{ in equation 2} \\ 170\left(18-y\right)+1010y=10620 \\ 3060+840y=10620 \\ 840y=10620-3060 \\ 840y=7560 \\ y=\frac{7560}{840} \\ y=9 \\ \end{gathered}[/tex]We will substiuite y =9 in x=18-y. Therefore;
[tex]\begin{gathered} x=18-9=9 \\ x=9 \end{gathered}[/tex]Answer: From the above, Sarah bought 9 coach tickets and 9 first-class tickets.
What is the equation of the boundary of this inequality?
Answers
We have the following:
[tex]y<-3x-5[/tex]The slope of the line -3 and the y-intercept is -5
So the equation of the boundary line is:
[tex]\begin{gathered} y=-3x-5 \\ \end{gathered}[/tex]a) graph the following transformation b) draw asymptotec) set domain and range
Answers
Given the function :
[tex]f(x)=\log _5x+2[/tex]The graph of the function will be as shown in the following picture
The function will have a vertical asymptote which is the line : x = 0
As shown in the figure :
Domain = ( 0 , ∞ )
Range = ( -∞ , ∞ ) or all real numbers
Tell whether each set of measures for a triangle determines more than one triangle or notriangle.10. 5 cm , 10 cm, 2 cm11. 60°, 60°, 60°12. 7 cm, 7 cm, 15 cm
Answers
A triangle is valid if sum of its two sides is greather than the third side. If three sides are a, b and c, then three conditions should be met.
10. 5cm, 10cm, 2cm
[tex]\begin{gathered} 5+10>2 \\ 15>2\text{ -> False} \end{gathered}[/tex]This cannot be a triangle.
11. Since it has all its angles equals, that means it is a equilateral triangle.
12. 7cm, 7cm, and 15cm
[tex]\begin{gathered} 7+7>15 \\ 14>15\text{ -> False} \end{gathered}[/tex]It cannot be a triangle.
1Select the correct answer.Which equation represents a line that is parallel to the x-axis, is perpendicular to the y-axis, and has a slope of 0?A.y=4/5x+5/4B.y=5/4xC.y=4/5D.x=5/4
Answers
The slope os the value that accompanies the dependent term.
Therefore, A and B, they are wrong.
If it is parallel to the x-axis and perpendicular to the y-axis, it must have the following form:
[tex]y=c[/tex]Therefore, the answer correct is C. y = 4/5
Subtract and simplify: (6 + 10i) – (11 + 7i)
Answers
Given:
an expression is given as (6 + 10i) - (11 + 7i)
Find:
we have to subtract and simplify the expression.
Explanation:
(6 + 10i) - (11 + 7i) = 6 + 10i - 11 -7i = (6 - 11) + ( 10i - 7i) = -5 + 3i
Therefore, (6 + 10i) - (11 + 7i) = -5 + 3i
fing the probability of .14 .73 .03 is
Answers
The probabilities are:
*0.14 -> 14%.
*0.73 -> 73%.
*0.03 -> 3%.