Answers
Answer:
x = 22, y = 12.
Step-by-step explanation:
5x + 4 = 114 (opposite angles).
5x + 4 + 3x - 24 + 2y = 180 (adjacent angles are supplementary)
From first equation:
5x = 110
x = 22.
Substituting for x in the second equation:
114 + 3(22) - 24 + 2y = 180
2y = 180 - 114 - 66 + 24
2y = 24
y = 12.
Related Questions
Danielle sells beauty supplies and earns a base salary of $320.00 per week plus a 8% comission on sales. During one particular week, she sells $2879 worth of beauty supplies. How much does she make for that week? Round to the nearest cent.
Answers
Answer$550.32
Step-by-step explanation: 7day = $320
commission = 8% of 2879
=230.32
total earnings = 320 + 230.32
= 550.32
La edad de maria es igul al quintuple de la edad de daniel
Answers
Answer:
m = 5d
Step-by-step explanation:
m = 5d
Evaluate each.
a.
-4+|51|-4
b. -3•-8
C.
32 ÷ -2
Answers
b) -3•-8 = 24
c) 32/ -2 = -16
Write each logarithmic expression as a single logarithm. log₃ y + 4 log₃ t
Answers
The given lograthimic expression log₃ y + 4 log₃ t can be written as log₃(yt^4).
According to the given question.
We have an logarithmic expression
log₃ y + 4 log₃ t
As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.
Also according to the product and power rule we know that
log(mn) = logm + logn
Thereofore, the given lograthimic expression log₃ y + 4 log₃ t can be written as
log₃ y + 4 log₃ t
= log₃ y + log₃ t ^4
= log₃(yt^4)
Hence, the given lograthimic expression log₃ y + 4 log₃ t can be written as log₃(yt^4).
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Under his cell phone plan, Logan pays a flat cost of $58 per month and $3 per gigabyte. He wants to keep his bill under $70 per month. Use the drop-down menu below to write an inequality representing gg, the number of gigabytes he can use while staying within his budget.
PLEASE HELPPPP 3
Answers
The inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is x < 4
How to write and solve an equation which can be used to determine the number of gigabytes?The given parameters are
Flat cost = $58
Rate = $3 per gigabyte
Budget = Under $70
The equation is represented as:
Total cost = Flat cost + Rate * Number of gigabyte
So, we have
y = 58 + 3x
The budget is under 70
So, we have
58 + 3x < 70
Subtract 58 from both sides
So, we have
3x < 12
Divide both sides by 3
So, we have
x < 4
Hence. the inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is x < 4
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Bob is making a model of an ant for a play. Find the scale factor of the model if the ant is 1/2 inch long and the model is 1 foot long.
Answers
The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.
What exactly is a scale factor?The Scale Factor is employed to scale shapes in different dimensions. Geometry teaches us about numerous geometrical shapes in two and three dimensions. The scale factor is a metric considering similar figures that appear the same but have distinct scales or measures.
How do you calculate the scale factor?The basic formula for computing this same scale factor is, Scale factor = Dimension of the new shape x Dimension of the original shape If indeed the original figure is scaled up, then the formula is expressed as Scale factor = Larger figure dimensions /Smaller figure dimensions.
According to the given data:The size of the ant = 1/2 inch.
the model size is = 1 foot.
= 1 foot = 12 inch
The scale factor of the model = Larger figure dimensions ÷ Smaller figure dimensions.
= 12/.5
= 24 inch or 2 foot
The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.
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13. Compount Interest An initial deposit of $8500 is compounded continuously at an annual
percentage rate of 3.5%.
xmp+81
Find the number of years required for the investment to double. Round to the nearest whole
number. What is the amount after 10 years?
Use the formula: A = Pert
Answers
Answer:
It will take approximately 20 years for the investment to double. The amount after 10 years will be $17,033.
Step-by-step explanation:
Give me Brainliest if that helped! :)
(question in the in image above the other side if angle Q is 113
Find x
Answers
Answer:
x = 85
Step-by-step explanation:
the exterior angles of a polygon sum to 360°
note the exterior angle at P = 180° - 90° = 90°
sum the 4 exterior angles and equate to 360
x + 72 + 113 + 90 = 360
x + 275 = 360 ( subtract 275 from both sides )
x = 85
Write an equation in point-slope form of the line having the given slope that contains the given point.
m=-3/4, (8,-1)
Answers
The equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]
Given,
m = [tex]\frac{-3}{4}[/tex]
The point = (8,-1)
The point-slope form of the line
[tex](y-y_{1} )=m(x-x_{1})[/tex]
Substitute the values in the equation
[tex](y-(-1))=-\frac{3}{4}(x-8)\\ y+1=-\frac{3}{4}(x-8)[/tex]
Hence, the equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]
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Elemer travels 66 miles per hour for 10 hours .find the distance traveled in miles
Answers
Answer: 660 miles
Step-by-step explanation:
66 miles * 10 hours/1 hour =
66*10/1=
66*10=660 miles
You deposit $400 into a savings account that earns interest annually. the function g(x) = 400(1.05)x can be used to find the amount of money in the savings account, g(x), after x years. what is the range of the function in the context of the problem? â„ [0, 400] [0, [infinity]) [400, [infinity])
Answers
The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.Principal - $400
rate of interest is compounded annually
g(x) = 400( 1.03)ˣ equation 1.
Formula used
A = P( 1 + r )ⁿ
here n = x
Solution:
Putting the value of n, and principal in the formula
A = P( 1 + r )ⁿ ................... equation 2
now comparing both equation 1 and equation 2,
400( 1.05)ˣ = 400( 1 + r )ˣ
( 1.05)ˣ = ( 1 + r )ˣ
1.05 = 1 + r
r = 1.05 - 1
r = 0.05
r % = 0.05 × 100
r % = 5 %
thus, the constant percent rate of change = 5 %
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HELP Finding the initial amount and rate of change given a table for a linear function
Answers
The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
How to find the initial amount and rate of change given a table for a linear function?The table of linear function represents the given parameter
On the table, we have the following points
(x, y) = (6, 467) and (10, 647)
The rate of change is calculated as
Rate = (y2 - y1)/(x2 - x1)
So, we have
Rate = (647 - 467)/(10 - 2)
Evaluate
Rate = 22.5
This means that the rate of change is $22.5
The initial amount is calculated as
y = m(x - x1) + y1
Where
m = 22.5
So, we have
y = 22.5(x - x1) + y1
Using one of the points, we have
y = 22.5(x - 6) + 467
Set x = 0
So, we have
y = 22.5(0 - 6) + 467
Evaluate
y = 332
Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
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Fine the volume and surface area of the figure below
Answers
Answer:
1470 in³, 716 in²
Step-by-step explanation:
The figure is a cylinder, and it's volume can be found using the following formula:
Volume of cylinder
= area of circle base ×height
= πr²h
Identify the value of r and h:
From the diagram, the radius (r) is 6 in. while the height (h) is 13 in.
Using the formula,
volume of cylinder
= π(6²)(13)
= 468π
= 1470 in³ (3 s.f.)
The surface area of a cylinder is the total area of all its faces, i.e. the sum of the area of its two circular bases and its curved surface area.
Formula
Surface area of cylinder
= 2πr² +2πrh
Surface area of cylinder
= 2(π)(6²) +2(π)(6)(13)
= 72π +156π
= 228π
= 716 in² (3 s.f.)
Additional:
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order from smallest to greatest
urgent !
Answers
At the Olympic games, many events have several rounds of competition. One of these
events is the men's 100-meter backstroke.
The upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of
the 2012 Olympics. The lower dot plot shows the times of the same 8 swimmers, but in the
semifinal round.
Final round
Semifinal round
distribution.
56
56.5
The center of the semifinal round distribution is
distribution.
57
Time (seconds)
The variability in the semifinal round distribution is
V
57.5
v
58
the center of the final round
the variability in the final round.
Answers
The 100–meter backstroke swimming times of the 8 swimmers during the semifinal and the finals of the Olympic games gives;
First part;
The center of the semifinal round is approximately 57.3625
The variability in the semifinal round is 0.0998
Second part;
The center of the final round is approximately 57.0125
The variability in the final round is 0.3336
How can the center and variability of the data in the dot plot be found?The times of the swimmers in the semifinal round are;
56.7, 57.2, 57.3, 57.3, 57.4, 57.5, 57.7, 57.8
The central value is given by the mean of the data, is found as follows;
(56.7+57.2+57.3+57.3+57.4+57.5+57.7+57.8)/8 = 57.3625
The variability is given by the standard deviation which is found by the formula;
[tex] \sigma = \sqrt{ \frac{ x_{i} - \mu}{n} } [/tex]
Where;
[tex]x _{i} = the \: ith \: value[/tex]
[tex] \mu = the \: mean[/tex]
The standard deviation found using the given values above and an online tool is presented as follows;
[tex] \sigma = \sqrt{ \frac{ x_{i} - 57.3625}{8} \approx 0.316 } [/tex]
The variance ≈ √(0.316) ≈ 0.0998Second part;
In the final, we have the following values from the dot plot;
56, 56.6, 56.6, 57, 57.1, 57.2, 57.7, 57.9
From the above values, using an online calculator, the center, which is taken as the mean is 57.0125
The variance for the final, [tex] \sigma^2 [/tex] ≈ 0.3336
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At a convention, 192 speakers gave one or more presentations of varying lengths. The histogram
summarizes the total presentation time, in hours, of each speaker.
Number of speakers
90
80
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7
Total presentation time (hours)
What interval contains the 25th percentile for this data?
Answers
The 25th percentile of the data is represented by the 0 to 1 hour range.
48 speakers, or around 25% of the total of 192 speakers, are present.
According to the graph, 60 presenters gave presentations that lasted between 0 and 1 hours.
This means that 48 is between0 and1.
A score that compares a certain score to the scores of the other group members is known as a percentile. It shows the percentage of scores that a particular score outperformed.
A person's performance is gauged by using the percentile calculation to compare it to others. A student's test score is compared to that of other applicants using the percentile approach.
Therefore, the 0 to 1 hour period contains the data's 25th percentile.
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A string is vibrating at 220 MHz and the wavelength of the waves on the string is 2.20m. Find the speed of these waves as they travel up and down the string
Answers
The wavelength of the waves on a string that is vibrating at 220 MHz is 2.20 m. These waves move at a 4840 rpm rate as they move up and down the string.
What is a wave length?A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm). According to the available data, the wavelength is more frequently expressed in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (VL), ultraviolet (UV), and gamma radiation ().
V=∧F
V=220×22
V=4840m/s
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Lindsey is building a skateboard ramp. She wants the ramp to be 1 foot tall at the end and she wants it to make a 15^{\circ} angle with the ground. What length of board should she buy for the ramp itself? Round to the nearest foot.
Answers
The term "length" is used to describe an object's size or the separation between two points. Lindsey must buy 4 feet of the board for the ramp itself.
What is meant by length?The term "length" refers to the measurement or size of something from end to end. In other terms, it is the greater of the upper two or third dimension of a geometric shape or object.
Distance exists estimated in length. The length contain the dimension of distance in the International System of Quantities. The majority of measurement systems select a base unit for length from which all other units exists derived. The meter serves as the foundational unit of length in the International System of Units.
A rectangle, for instance, has length and width as its dimensions.
1/x = 15°
x = 1/sin 15°
simplifying the above equation, we get
x = 3.9ft
x ≈ 4 ft
Therefore, the value of x ≈ 4 ft.
Lindsey must buy 4 feet of the board for the ramp itself.
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find the center and foci of the ellipse:
4x^2+9y^2+8x-36y+4=0
Answers
The center of the given ellipse is given as (-1, 2)
Center of the Ellipse
To find the center of the ellipse, we need to rearrange the equation into the standard equation of ellipse.
[tex]4x^2 + 9y^2 + 8x - 36y + 4 = 0\\\frac{(x+1)^2}{2} + \frac{(y-2)}{4} = 1[/tex]
The center of the ellipse is given as
[tex]center = (-1, 2)[/tex]
FociThe foci of the ellipse are the reference points in an ellipse and it helps to derive the equation of the ellipse. There are two foci for the ellipse i.e F1 and F2
[tex]F_1= (-1 + \sqrt{5}, 2)\\ F_2 = (-1, -\sqrt{5}, 2)[/tex]
The center of the given ellipse is (-1,2) while the foci are stated above.
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Given f(x) = 2 cos x, find the exact value of f (pi/6) in simplest form with a rational
denominator.
Answers
Using trigonometric functions, the value of 2 cos x is equals to √3.
What are trigonometric functions?One of the six mathematical functions used to express the side ratios of right triangles, the trigonometric function includes the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). The graphic shows these six trigonometric functions in respect to a right triangle.
Cos (π/6) = √3/2
So. f(x) = 2 cos x
⇒ f(x) = 2 cos(π/6)
⇒ f(x) = 2 × √3/2
f(x) = √3
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which set of mixed numbers has a difference less than 1
1 1/2-1 1/9
3 3/4-2 1/7
2 4/5-1 1/3
2 7/9- 1 1/3
Answers
Only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.
We have a set of mixed numbers.
We have to identify which set of mixed numbers has a difference less than 1.
What are Mixed Numbers ?A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers. Any mixed fraction can be converted into normal fraction using the formula -
[tex]X\frac{Y}{Z} =\frac{Z\times X+Y}{Z}[/tex]
According to the question -
Let us solve them one by one (for difference to be less than 1, the denominator should be less than numerator) -
A = [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] B = [tex]$3\frac{3}{4} - 2\frac{1}{7} = \frac{45}{28}[/tex]C = [tex]$2\frac{4}{5} - 1\frac{1}{3} = \frac{22}{15}[/tex]D = [tex]$2\frac{7}{9} - 1\frac{1}{3} = \frac{13}{9}[/tex]Hence, only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.
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Noah is buying a pair of jeans and using a coupon for 10% off.
The total price is $56.70, which includes $2.70 in sales tax.
Noah's purchase can be modeled by the equation:
`x-0.1x+2.70=56.70`
What does the solution to the equation mean in this situation?
Answers
Answer: The answer to this equation is 53.91
How many ways can five of the nine us supreme court justices agree? (With solution)
(This is Combinations and Permutations)
Answers
The number of ways can five of the nine us supreme court justices agree is 3024 ways.
How to compute the value?The number of ways that five of the nine us supreme court justices agree will be calculated thus:
= 9! / 5!
= (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2) / (5 × 4 × 3 × 2)
= 3024
There'll be 3024 ways.
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betty worked at the golf course during the summer after 8th grade. after working for 2 weeks she added her earnings to the gifts she got for graduation and found she had $750. after four more weeks of work she had a total of 870$.
Plss help immidiatly
What does the y intercept represent in this situation?
Write the equation in slope intercept form
Answers
The y-intercept is the amount she got as gifts during her graduation.
The equation in slope intercept form is $630 + $60b
What does the y-intercept represent?The slope intercept form is used to write equations for equations for linear equations with two variables. The graph for a slope intercept form is a straight line.
The form for slope intercept form is: y = mx + b
Where:
y = y coordinatem = slopex = x coordinateb = y interceptThe y-intercept is the constant. It represents the point where the slope touches the y-axis.
The first step is to determine how much are earnings are and how much the gift is.
The equations that would be used to determine this are:
a +2b = 750 equation 1
a + 4b = 870 equation 2
Where:
a = gift
b = amount earned weekly while working on the golf course
Subtract equation 2 from equation 1: 2b = 120
Divide both sides of the equation by 4: b = $60
Substitute for b in equation 1
a + 2(60) = 750
a + 120 = 750
a = 750 - 120
a = 630
The y-intercept is $630.
The equation in slope intercept form is: $630 + $60w
Where w is the number of weeks that Betty works.
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Determine the truth value of the following statement for the set of conditions. Explain your reasoning.
If you are over 18 years old, then you vote in all elections.
You are 21 years old and do not vote.
Answers
The given statement is not correct because anyone above 18 years can vote.
It is given that if you are over 18 years old, then you vote in all elections.
We have to determine the truth value , if you are 21 years old and do not vote.
What is the truth value ?
Truth value is the attribute which states that whether the statement is true or false.
As per the question ;
If you are over 18 years old , then you vote in all elections, and if you are 21 years old and do not vote.
The criteria to vote in the elections is to be over 18 years.
Here ;
21 years age is greater than 18 years criteria , that's why it is not possible that you can't vote if you are 21 years old.
The statement is not correct.
Thus , the given statement is not correct because anyone above 18 years can vote.
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Julio walks 3 1/2 miles in 1 1/4 hours. Find unit rate
Answers
Answer:
3 1/2 ÷ 1 1/4
7/2 ÷ 5/4
7/2 · 4/5
28/10
2.8
Step-by-step explanation:
The residents of a city voted on whether to raise property taxes. The ratio of yes votes 4 to 5 no votes was to . If there were 5364 total votes, how many no votes were there?
Answers
Step by step
You have 5364 votes total
You have 4 to 5 yes to no votes
So you have 5/9 no votes
5/9 = 5364
26820 / 9 = 2980 no votes
If you did the same with yes votes
4/9 = 5364
21456 / 9 = 2384 yes votes
Add 2980 and 2384 = 5364 total votes
Problem solved
What is 45% of 315. I need work shown in explanation area
Answers
45% of 315 = 141.75
When you are using a % number convert it into a decimal ( 45% would be 0.45 or 55% would be 0.55 ). After you convert it into a decimal you can multiply it by the number ( Here it would be 315 )
0.45 x 315 = 141.75
Answer:
141.75
Step-by-step explanation:
To do this question, first, we can write 45% as 45/100.
Now, we have to multiply.
45/100x315
=141.75
Hope that helped!
:D
√ 81 )^2 I can't figure this out. Sorry to bother anyone!
Answers
Answer: 81
Step-by-step explanation: The square root and the squared function cancel each other out
14x futher simplfied
Answers
Answer:
14x cannot be simplified any further.
Answer:
No, 14x can not be further simplified.
Step-by-step explanation:
I hope this helps.
