A = votes to Abe
G = votes to George
we know that all votes together were 539, so A + G = 539, we also know that George got 23 more than Abe, so "G = A + 23"
[tex]\stackrel{Abe's}{A}~~ + ~~\stackrel{George's}{(A+23)}~~ = ~~\stackrel{total}{539}\implies 2A+23=539\implies 2A=516 \\\\\\ A=\cfrac{516}{2}\implies \boxed{\stackrel{Abe}{A=258}}\hspace{12em}\boxed{\underset{George}{\stackrel{258~~ + ~~23}{281}}}[/tex]
The perimeter of a rectangular parking lot is 370 m.
If the width of the parking lot is 86 m, what is its length?
Answer:
the length is 99m
Step-by-step explanation:
you have to add 86 to 86 to get 172, subtract 172 from 370 then you have 198 then divide to have 99m the length.
Given the sequence:
5, 12, 19, 26, 33 ...
1. Determine the function that represents this sequence?
2. What is the 30th term of this sequence?
Answer:
Step-by-step explanation:
solve the value equation -6 | 2x+7|=-90
The value of equation is 4,-11
What is algebraic expression ?When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement. Let's say James and Natalie were tinkering with matchsticks when they had the idea to arrange the sticks into number patterns. James used four matchsticks to make the numeral 4 in the air. Adding three additional matchsticks allowed Natalie to create a pattern with two 4s. They understood that they may continue to add three matchsticks each round to make a total of four. They deduced from this that, generally speaking, 4+ 3(n-1) sticks are required to create a pattern with n numbers of 4s. The algebraic statement 4+ 3(n-1) is referred to here.
Given that : the equation -6 | 2x+7|=-90
-6 | 2x+7|=-90
|2x +7|=[tex]\frac{-90}{-6}[/tex]
|2x +7|=15
2x + 7 =±15
2x + 7 = 15 ... (i)
2x = 8
x =4
2x + 7 = -15....(ii)
2x = -22
x =-11
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y = 3x + 2 is reflected in the line y=-1. What is the equation of the image?
The equation of the image is y = 3x - 4
In this question, we have been given a line y = 3x + 2 is reflected in the line y = -1.
We need to find the equation of the image.
The reflected line must be parallel to the line y = 3x + 2
So, the slope of the image must be equal to the slope of the line y = 3x + 2
The y-intercept of the line y = 3x + 2 is (0, 2)
The distance between point (0, 2) and the line y = -1 is 3 units.
So, the y-intercept of the reflected line must be (0, -4)
With slope m = 3 and y-intercept (0, -4) the equation of the line would be,
y = 3x - 4
Therefore, the equation of the image is y = 3x - 4
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I need help with this question
Answer:
a) 69 b) -11
Step-by-step explanation:
-8 + 77 or 77 - 8 = 69
-21 + 10 = 11
Omar has been training for the Candlewood Footrace. The first week he trained, he ran 7 days and took the same two routes each day: 3 miles around the track before work and a longer route through his neighborhood after work. By the end of the week, Omar had run a total of 63 miles.
Which equation can you use to find how many miles, x, Omar ran each day after work?
The equation that can be use to find the how many miles, x, Omar ran each day after work is x = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days after work
The total number of days he run = 7 days
Total distance he ran in one week = 63 miles
The distance he run before the work = 3 miles
The total distance he run before the work in one week= 7×3
= 21 miles
The total distance he run after the work = 63 - 21
= 42 miles
The equation that can use to find how many mile x, Omar ran each day after work = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7
Substitute the values in the equation
= 42/7
= 6 miles
Hence, The equation that can be use to find the how many miles, x, Omar ran each day after work is x = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days after work
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Please help me with this question!
The two swimming pools will have same amount of water using this equation, where x represents the time in minutes
3300 - 24x = 3696 - 35x
How to find the equation when the two pools will have same amount of waterinformation given in the question is as follows
the first pool had 3300 liters of water and drains at a rate of 24 liters per minute
the second pool had 3696 liters of water and drains at a rate of 35 liters per minute.
The given information implies that
every minute in x minutes 24x liters of water is drained from the first tank.
3300 - 24x
Similarly, in the second tank in x minutes 35x liters of water in drained from the second tank
3696 - 35x
The tanks will have equal volume of water when the two equations are equal
3300 - 24x = 3696 - 35x
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Help please whoever awnsers correctly I will put as brainliest!!
Based on the fact that the triangles are similar, the length of x is 7.2 cm and the length of y is 7.4 cm
How to find the lengths?If the triangles are similar then it means that the difference between their dimensions can be found by a scale factor.
The scale factor is:
= Dimension of larger similar side / Dimension of smaller similar side
= 11.6 / 5.8
= 2
With a scale factor of 2, then x is:
= 3.6 x 2
= 7.2 cm
The value of y would be:
= 14.8 / 2
= 7.4 cm
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Adriana mows lawns. She charges an initial fee and a constant fee for each hour of work.
Answer: It's $12 an hour.
Step-by-step explanation:
help me with the pirates
For Roberts the equation is:
[tex]5y-x=-25[/tex]to we can write it as slope intercept so:
[tex]\begin{gathered} 5y=x-25 \\ y=\frac{1}{5}x-5 \end{gathered}[/tex]Now we replace x = 5 so
[tex]\begin{gathered} y=\frac{5}{5}-5 \\ y=1-5 \\ y=-4 \end{gathered}[/tex]So the two points are ( 0 , -5) and ( 5 , -4)
Fo Hookthe equation is:
[tex]2x-5y=0[/tex]In slope intercept is:
[tex]\begin{gathered} 5y=2x \\ y=\frac{2}{5}x \end{gathered}[/tex]so we replace x = 5 so:
[tex]y=2[/tex]So the two points are: ( 0 , 0) and ( 5 , 2 )
For Elizabeth the equation is:
[tex]y-6=\frac{1}{2}(x-2)[/tex]and slope intercept:
[tex]\begin{gathered} y=\frac{1}{2}x-1+6 \\ y=\frac{1}{2}x+5 \end{gathered}[/tex]now we replace x = 2 so:
[tex]\begin{gathered} y=1+5 \\ y=6 \end{gathered}[/tex]So the coordinates are ( 0 , 5) and ( 2, 6 )
And for Silver the equation is:
[tex]4x-y+6=9[/tex]In slope intercept is:
[tex]\begin{gathered} y=4x+6-9 \\ y=4x-3 \end{gathered}[/tex]now we replace x = 1 so:
[tex]\begin{gathered} y=4-3 \\ y=1 \end{gathered}[/tex]So the coordinates are: ( 0, -3) and ( 1, 1 )
So now you can made the graph of the lines and find the message.
(-8,5); y= -4x+2 find the parallel equation
Answer: y=-4x-27
Step-by-step explanation:
[tex]y=mx+b[/tex]
Lines are parallel if their slopes are equal
[tex]y=-4x+2[/tex]
⇒ m=-4
⇒ y=-4x+b
A line passes through (-8.5)
⇒ x=-8 y=5
[tex]5=-4(-8)+b\\5=32+b\\5-32=32+b-32\\-27=b[/tex]
So, y=-4x-27
in exercises 17–30, (a) find the function’s domain, (b) find the function’s range, (c) describe the function’s level curves, (d) find the boundary of the function’s domain, (e) determine if the domain is an open region, a closed region, or neither, and (f) decide if the domain is bounded or unbounded.
The domain of f { (x,y) ∈ R² x² + y² < (3/5)² } is bounded.
What does the math term domain mean?
Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.Given f(x,y) = [tex]\frac{1}{\sqrt{9 - 25x^{2} - 25y^{2} } }[/tex]
a) the domain of f is the value of ( x, y) for which 9 - 25x² -25y² >0
9 - 25x² -25y² ⇒ 9/25 > x² + y² ⇒ x² + y² < (3/5)²
∴ domain of f = [ (x,y) ∈ R² : x² + y² < (3/5)²}
B) Let z = f = [tex]\frac{1}{\sqrt{9 -25x^{2} - 25y^{2} } }[/tex]
its range is { z ∈ R² : 3z > 1}
c) let f = k ⇒ k = [tex]\frac{1}{\sqrt{9 - 25x^{2} - 25y^{2} } }[/tex]
k² ( 9 - 25x² - 25y²) = 1 = 9 - 25x² - 25y² = 1/k²
⇒ 25x² + 25y² = 9 - 1/k² ⇒ x² + y² = 1/25( 9 - 1/k²)
The level curves are circles for different k values .
d) The boundary of the function's domain
= { (x,y) ∈ R² x² + y² = (3/5)²}
e) Since x² + y² < (3/5)² is the circular open disk , the domain of f is an open set
f) The domain of f { (x,y) ∈ R² x² + y² < (3/5)² } is bounded.
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In 6 Minutes, Rita can type 24 words. What is her rate in words per minute?
Answer:
4 words per minute
Step-by-step explanation:
In 6 minutes Rite typed 24 words, 24 divided by 6 is 4
23. A shipment of goods weighs 5 tons.
Which of the following expressions could
be used to express the weight in metric
tons?
Answer:
write a semi formal letter to your father's friend
in a survey of group people showed that 60 liked tea, 45 liked coffee, 30 liked milk,25 liked coffee as well as tea,20 liked tea as well as milk,15 liked coffee as well as milk and 10 liked all the three. How many people were asked this question?
Answer:
85 people were surveyed
Step-by-step explanation:
Let n(X0 represent the number of people who belong in set X
We have 3 sets here
T = set of all people who like tea
C = set of all people who like coffee
M = set of all people who like milk
From the info given
n(T) = 60
n(C) = 45
n(M) = 30
The intersection of the sets are
n(C ∩ T) = 25
n(T ∩ M) = 20
n(C ∩ M) = 15
n(C ∩ T ∩ M) = 10
The number of people who were asked this question is given by
n(T U C U M)
= n(T) + n(C) + n(M) - n(C ∩ T) - n(T ∩ M) - n(C ∩ M) + n(C ∩ T ∩ M)
= 60 + 45 + 30 - 25 - 20 - 15 + 10
= 85
Venn Diagram is attached
5
Please put all the numbers above your phone on the number line
1.
(a) 2π - 9
= 2 x 3.142 - 9 = 6.284 - 9
= -2.716
This will be closest to the letter C on the number line.
(b) [tex]\sqrt{3}[/tex]
= 1.732
This will be closest to the letter T on the number line.
(c) [tex]\sqrt[3]{9}[/tex] - 8
= 3-8
= -5
This will be closest to the letter S on the number line.
What are Real numbers?In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line. Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolize complex numbers. Real numbers include things like 23, -12, 6.99, 5/2, and so on.Most physical constants, like the universal gravitational constant, and physical variables, including position, mass, speed, and electric charge, are represented using real numbers in the physical sciences.Although the Zermelo-Fraenkel axiomatization of set theory is the method most frequently used to formalize the real numbers, other mathematicians also explore the real numbers using other logical mathematical foundations. Electronic calculators and computers, with a few notable exceptions, do not work with real numbers. Instead, they frequently use floating-point numbers, which are finite-precision approximations that resemble scientific notation.To learn more about Real numbers, refer to:
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Which letter is inside the square and pentagon? *
O A
O B
O C
A and C because it asks which word is in the square and pentagon, it is the a and the c
Passes through (9, 0) and (0, -3).
do you mind explaining with the answer so that i’ll understand it and be able to continue without being confused? thank you! :)
Answer: y = (1/3)x - 3
Step-by-step explanation:
It passes through -3 at 0, so we know the y = mx + b form will include -3
Next, we want to find the slope:
Change in y = 0 - -3 = 3
Change in x = 9 - 0 = 9
Change in y / Change in x = slope
3/9 = 1/3
How many 14-pound hamburgers can you make from 312 pounds of ground beef?
You can make ? hamburgers.
Answer:
You can make 22 burgers.
Step-by-step explanation:
If you have 312 pounds of ground beef and burgers are 14 pounds, divide 312 by 14 ( 312 / 14). This gives you an answer of 22.28 You will have leftovers because 14 does not go into 312 perfectly. You can also check the answer by doing multiplication ( 22 * 14) which gives you 308. You cannot have another burger because 308 + 14 = 322 which is over the amount of beef you have.
on jan 22 0217 the cost to mail a letter in the us was raised from 47 to 49 centrs. find the relative change in the cost
The relative change is 2%.
What is relative change?In contrast to the reference value, the absolute change's size is expressed as a fraction called the relative change: relative change = absolute change reference value = new value reference value reference value. The absolute change is expressed as a percentage of the value of the indicator in the prior period, or "relative change" expresses the absolute change as such. When measuring indicators in percentage terms, such as the unemployment rate, absolute and relative change principles also apply. To determine the absolute change, subtract the starting value from the ending value. Simply deduct 1,000 from 1,100 to arrive at 100 in the example. The student population increased by 100 pupils throughout the course of the year because this is the absolute change.
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PLEASE HELP Conditional Statement: If the object has a remote, then it is a television.
Part A: Write the converse to the conditional statement.
Part B: Write a biconditional statement from the conditional statement.
Part C: Validate the biconditional statement from Part B. Use details to support your answer.
Answer:
Step-by-step explanation:
Latisha has $40 in her checking account. She makes a withdrawal of $20 and then writes a check for $40. Then she deposits $30.
If Latisha has $40 in her checking account and she makes a withdrawal of $20 and then writes a check for $40, then she deposits $30, then the amount she has in her checking account is $10
The amount she has in her checking account = $40
The amount she withdraw from her account = $20
The amount she writes a check = $40
The deposited amount = $30
To find the final checking account balance we have to use the arithmetic operations
The final balance amount = The amount she has in her checking account -The amount she withdraw from her account - The amount she writes a check + The deposited amount
= 40-20-40+30
= $10
Hence, by using arithmetic operations, if Latisha has $40 in her checking account and she makes a withdrawal of $20 and then writes a check for $40, then she deposits $30, then the amount she has in her checking account is $10
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a number of sweets were shared among eight children and each child receives 30. if 12 children share the same number of sweets how many will each receive
1.8 as decimal in it simplest form
Answer:
1.8 = 9
5
= 14
5
as a fraction
Solve the following inequality. 3x - 4 > 11
A. (∞ ,5)
B. (15, ∞)
C. (5, ∞)
D. [5, ∞)
Please look at photo for further clarification, the length of a conduit is needed for sections and be shown in the picture. you may round the final answer to the nearest hundred if needed as well as all the intermediate values rounded to the nearest hundred if needed.
Using trigonometric functions :
From the problem, we have a hypotenuse of 22.25 cm and an angle of 31°28'
To find A, we will use the sine function :
[tex]\begin{gathered} \sin 31^{\circ}28^{\prime}=\frac{A}{22.25} \\ A=22.25\sin 31^{\circ}28^{\prime} \\ A=11.615 \end{gathered}[/tex]To find B, we will use the cosine function :
[tex]\begin{gathered} \cos 31^{\circ}28^{\prime}=\frac{B}{22.25} \\ B=22.25\cos 31^{\circ}28^{\prime} \\ B=18.978 \end{gathered}[/tex]The total length is the sum of A and B :
A + B = 11.615 + 18.978 = 30.59
The answer is 30.59 cm
On Monday, the high temperature in Frostbite, Alaska, was -5 F. On Tuesday, it rose 14 F. On Wednesday, it dropped 20 F. What was the temperature on Wednesday?
Answer:
-11 F
Step-by-step explanation:
So we need to just add or decrease the temperature.
-5 + 14
9 - 20
-11
Answer:
-5 + 14 = 9
9 - 20 = -11
the answer is -11°f
Raise 7 to the 2nd power, then add the result to b
(7)^2 +
2nd power means squaring a number and since you need to do that first, it goes in brackets.
answer: 49 + b, or just 7^2 + b
explanation: 7^2 = 7x7, so it is equal to 49. then add b to 49
Suppose that $25,200 is invested in a certificate of deposit for 2 years at 11.1 % annual interest to be compounded semi-
annually. How much interest will this investment earn?
Suppose that $25,200 is invested in a certificate of deposit for 2 years at 11.1 % annual interest to be compounded semi-annually, compound interest will this investment earn is $5,904.8892.
What is compound interest?Compound interest, also known as interest on the principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on principal amount plus any accumulated interest. In the finance and economics, compound interest is common.
In contrast to the simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time. The interest per period multiplied by number of periods in a year yields the simple annual interest rate. The nominal interest rate is the another term for the basic annual interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).
It is known that the compound interest is given as
Compound Interest = [total amount of the principal and interest in future]-[total amount of the principal in present]
=[tex]P(1+i)^{2} - P\\P(1+i)^{2} - 1\\[/tex]
where, p= principal, i= nominal annual interest, n= the number of the compounding period
Given
P = $25,200
i= 11.1% = 0.111
n= 2
compound interest is
C = 25,200 [[tex](1+0.111)^{2}[/tex]-1]
= $5,904.8892
The investment will earn the interest of $5,904.8892.
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I just need the answer to this question
THE VOLUME OF A RECTANGULAR PRISM ID GIVEN BY
[tex]v = l \times b \times h \\ = ( \frac{7}{2} in) \times ( \frac{5}{2} in) \times ( \frac{3}{2} in) \\ \\ v = \frac{35}{2} {in}^{2} \times \frac{3}{2} in \\ v = \frac{105}{2} {in}^{3} \\ v = 52\times \frac{3}{2} {in}^{3} [/tex]
THE FIRST OPTION IS THE ANSWER!!