Answer:
4 11/20
Step-by-step explanation:
The length of road unpaved is 7 3/10 less 2 3/4 miles The LCD of the fractions is 20 (both 10 and 4 divide evenly into 20).
Thus, the problem becomes 7 6/20 - 2 15/20.
We have to borrow 1 from that 7 because 15/20 is larger than 6/20. This results in
6 26/20 - 2 15/20, or
4 11/20
The total length of the main road in Belleville is [tex]7^{(3/10)}[/tex] miles. So far, [tex]2^{3/4}[/tex] miles have been repaved, leaving [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex] miles that have not been repaved.
1. The total length of the main road is given as [tex]7^{(3/10)}[/tex] miles. In mathematical notation, [tex]7^{(3/10)}[/tex] represents the cube root of 7, which is then raised to the power of 3. So, the total length of the road is the cube root of 7, and then that result is cubed.
2. The length of the repaved portion is given as [tex]2^{3/4}[/tex] miles. In mathematical notation, [tex]2^{3/4}[/tex] represents the fourth root of 2, which is then raised to the power of 3. So, the repaved length is the fourth root of 2, and then that result is cubed.
3. To find the remaining length that has not been repaved, we simply subtract the repaved length from the total length:
Remaining length = [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex]
Calculating the values, the total length is approximately 2.262 miles (rounded to three decimal places) and the repaved length is approximately 1.682 miles (rounded to three decimal places). Now, subtracting the repaved length from the total length, we get approximately 0.580 miles (rounded to three decimal places) as the length that has not been repaved.
Therefore, the remaining length that has not been repaved is approximately 0.580 miles (rounded to three decimal places).
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21. Three vertices of DEFG are D(2,3),E(-5,2),G(6,6). Find the coordinates of F.
The calculated coordinates of the point F is (-1, 5)
How to determine the coordinates of F
From the question, we have the following parameters that can be used in our computation:
D(2,3),E(-5,2),G(6,6)
We have that
The quadrilateral DEFG is a parallelogram
This means that the opposite sides have equal slopes
i.e.
Slope of DE = Slope of FG
Using slope formula, we have
(3 - 2)/(2 + 5) = (y - 6)/(x - 6)
This gives
1/7 = (y - 6)/(x - 6)
Cross multiply
x - 6 = 7y - 42
x = 7y - 36
Set y = 5
So, we have
x = 7 * 5 - 36
x = -1
So, we have
(x, y) = (-1, 5)
Hence, the coordinates of the point F is (-1, 5)
Question
Consider the parallogram DEFG with three vertices D(2,3),E(-5,2),G(6,6). Find the coordinates of F.
Final answer:
To find the coordinates of vertex F in the parallelogram DEFG with given vertices D(2,3), E(-5,2), and G(6,6), we can use vector subtraction to deduce that the coordinates of F are (-1, 5).
Explanation:
The question requires us to find the coordinates of vertex F of the quadrilateral DEFG given that we have the coordinates of vertices D(2,3), E(-5,2), and G(6,6). Assuming that DEFG is a parallelogram (as the question implies a symmetry-based approach though it doesn't specify), we can find F using the properties of parallelograms, which dictate that opposite sides are equal and parallel. The vector from D to E is ∂D = (-5 - 2, 2 - 3) = (-7, -1), and the vector from G to F (let's call it F's coordinates (x, y)) would be equivalent, as they are opposite sides. So, G + ∂D = F. Substituting G's values, we get (6 - 7, 6 -1), which simplifies to (-1, 5). Thus, the coordinates of F are (-1, 5).
I’m so condfused! Can someone please get the answer for me?
Answer:
36
Step-by-step explanation:
If you see this kind of problem do this two steps:
1. Multiply the numerator and the multiplier.
2. Divide the result with the denominator.
[tex]\frac{3}{10}[/tex] × 120
3 × 120 = 360 (STEP 1)
360 ÷ 10 = 36 (STEP 2)
Answer:
36
Step-by-step explanation:
4. A geometric sequence is defined recursively by a(1) = 40 and a(n)= a(n-1)
(a) Write out the first four terms of this sequence.
(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.
The complete question is:
A geometric sequence is defined recursively by
[tex]a_{(1)}=40\text{ and }a_n=(-1/2)a_{(n-1)}[/tex]
(a) Write out the first four terms of this sequence.
(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.
Answer:
The 9th term is larger than 1/10.Explanation:
You are given the first term, [tex]a_(1)=40[/tex] , and the recursive formula
[tex]a_{(n)}=(-1/2)a_{(n-1}[/tex]
Thus, you can find the sequence of terms by multiplying each term by the constant ratio, (-1/2).
(a) First four terms of the sequence
[tex]a_{(1)}=40\\ \\ a_{(2)}=40\times (-1/2)=-20\\ \\ a_{(3)}=-20\times (-1/2)=10\\\\ a_{(4)}=10\times (-1/2)=-5[/tex]
Those are the first four terms.
(b) 9th term
You can write the explicit formula of the sequence as:
[tex]a_{(n)}=a_{(1)}\times r^{(n-1)}\\ \\ a_{(n)}=40(-1/2)^{(n-1)}[/tex]
Thus, for the 9th term, n = 9, and the term is:
[tex]a_{(9)}=40\times (-1/2)^{(9-1)}\\ \\ a_{(9)}=40\times(-1/2)^8\\ \\ a_{(9)}=40\times(1/256)=0.1526[/tex]
Since 1/10 = 0.1, and 0.1 < 0.1526, the 9th term is larger than 1/10.
Factor the following polynomial by grouping.
xy + 2y2 + 3x + 6y
OA) (x+y)(2y + 3)
OB) (x+2y)(y + 3)
OC) (x+3y) (y + 2)
OD) (x+y)(3y + 2)
Option B
The factored form by grouping is:
[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]
Solution:
Given that we have to factor the given polynomial by grouping
Given polynomial is:
[tex]xy+2y^2+3x+6y[/tex]
Factoring by grouping means that you will group terms with common factors before factoring.
This is done by grouping a pair of terms. Then factor each pair of two terms
In the given polynomial, group the terms that has "x" as common and group the terms that has "y" as common
[tex](xy+3x)+(2y^2+6y)[/tex]
Factor out "x" from first group and factor out "2y" from second group
[tex]x(3+y)+2y(y+3)[/tex]
Factor out y + 3
[tex]x(3+y)+2y(y+3) = (x+2y)(y+3)[/tex]
Thus the factored form by grouping is:
[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]
The function y = log (x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?
On a coordinate plane, a curve starts at (negative 1, negative 5) and curves up into quadrant 1. It approaches y = 1.
On a coordinate plane, a curve starts at (1, negative 4) and curves upwards. It approaches y = negative 1.
On a coordinate plane, a curve starts at (negative 1, negative 1) and curves up into quadrant 1. It approaches y = 5.
On a coordinate plane, a curve starts at (1, negative 3) and curves up into quadrant 1. It approaches y = 5.
See the graph below
Explanation:
We need to remember the following rules:
[tex]For \ any \ function \ f(x) \ we have: \\ \\ \\ \bullet \ g(x)=f(x-k) \ Translation \ k \ units \ to \ the \ right \\ \\ \bullet \ g(x)=f(x+k) \ Translation \ k \ units \ to \ the \ left \\ \\ \bullet \ g(x)=f(x)+c \ Translation \ c \ units \ up \\ \\ \bullet \ g(x)=f(x)-c \ Translation \ c \ units \ down \\ \\ With \ c>0 \ and \ k>0[/tex]
Here we know that The function y = log (x) is translated 1 unit right and 2 units down, so:
[tex]k=1 \\ \\ c=2 \\ \\ \\ Finally: \\ \\ g(x)=log(x-1)-2[/tex]
Below you can see the graph. The red one is the original function while the blue one is the translated one.
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Answer:
B
Step-by-step explanation:
Took test on edge
What does y+3>5 equal
Answer:
if you're solving for inequality its y>2
a=πr^2 solve for π please help
Answer:
π = a/(r²) = a÷(r²)
Answer:
pie is equal to the square root of A divided by r
Step-by-step explanation:
Set the equation first...a=pie times r squared. Then u need to get rid of everything to make pie by itself. U square both sides or all the equation. the square cancels out and on the other side, it will be the square root of a. Next, divide by r on each sides. The r cancels out. Then it's gonna be pie =the square root of a all over r. It can't be a/r square because in the original...pie is being multiplied by r which is squared so that means both variables are squared. U cant find pie if the square is stopping it so u square for the very first step
10 4/5 - 2 1/5
I am having trouble finding this answer please help
Answer:
8 3/5
Step-by-step explanation:
subtract the whole numbers first and then the fractions. you have 10 4/5-2 1/5. subtract the whole numbers and you have 8(put that off to the side). then do 4/5-1/5. 4-1=3 and the denominators stay the same so you have 3/5. you don’t need to simplify so your final answer is 8 3/5.
Answer:
43 / 5 or 8 3/5
Step-by-step explanation:
What is the absolute value and solution set of |x|=-4
PLEASE HELP 15 POINTS.
the lines a and b intersect at point D. What is the value of z? Enter your answer in the box. z = Lines a and b intersect at point D. Acute vertical angles measure five z plus eight degrees and four z plus twenty degrees.
Answer:
[tex]z=12[/tex]
Step-by-step explanation:
The lines a and b intersect at point D. Angles with measures [tex](5z+8)^{\circ}[/tex] and [tex](4z+20)^{\circ}[/tex] are vertical angles.
Vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent.
Congruent angles have equal measures.
Hence,
[tex]5z+8=4z+20\\ \\5z-4z=20-8\\ \\z=12[/tex]
Answer:
12
Step-by-step explanation:
Identify all factors of the expression 〖4x〗^2+17x-15.
The factors of given expression are: -5 and 3/4
Step-by-step explanation:
Given equation is:
[tex]4x^2+17x-15[/tex]
Making pairs for the mid-term 17x by factoring the product of co-efficient of 4x^2 and 15
[tex]4x^2+20x-3x-15[/tex]
[tex]= 4x(x+5) - 3(x+5)[/tex]
[tex]=(4x-3)(x+5)[/tex]
Now
[tex]4x-3 = 0\\4x = 3\\x = \frac{3}{4}[/tex]
[tex]x+5 = 0\\x = -5[/tex]
Hence,
The factors of given expression are: -5 and 3/4
Keywords: Quadratic equation, factors
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About 106 baby boys are born for every 100 baby girls. Write this as a simplified ratio of males to females
Answer:
53/50
Step-by-step explanation:
The ratio of males to females is 53:50.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
Number of baby boys = 106
Number of baby girls = 100
So, the ratio of males to females
= 106/100
= 53/50
Hence, the ratio of males to females is 53:50.
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Write 2339 in scientific notation
Answer:
2.339×10^3
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
2.339×10^3
6 times 4 - 12 divided by 3 - 8
Answer:
-4
Step-by-step explanation:
6 times 4 equals 24
24 minus 12 equals 12
12 divided by 3 equals 4
4 minus 8 equals -4
(btw i did this in the order from the question and not BIDMAS )
16-(-12)=
As soon as possible please
The price of a pair of headphones at Store A is 3/4
the price at Store B. The price at Store A is $72.75. Find how much you save by buying the headphones at Store A.
Answer:
Step-by-step explanation:
A = 3/4B
A = 72.75
3/4B = 72.75
B = 72.75 * 4/3
B = 291/3 = 97
you would save (97 - 72.75) = $ 24.25 when buying them at store A
By calculating the original price of the headphones at Store B and subtracting the price at Store A, we find that you would save $24.25 by purchasing the headphones at Store A.
Explanation:To find out how much you save by buying the headphones at Store A, we need to determine the original price of the headphones at Store B.
Let's denote the price at Store B as P. According to the information given, the price at Store A is 3/4 of the price at Store B. We can write the following equation:
P × (3/4) = $72.75
Solving for P, we get:
P = $72.75 ÷ (3/4)
P = $72.75 ÷ 0.75
P = $97.00
Therefore, the price of the headphones at Store B is $97.00. To find the savings, subtract the price at Store A from the price at Store B:
Savings = Price at Store B - Price at Store A
Savings = $97.00 - $72.75
Savings = $24.25
By buying the headphones at Store A, you save $24.25.
What is the length of line segment AB?
1 inch
v3 inches
4 inches
475 inches
Answer:
[tex]AB=\sqrt{3}\ in[/tex]
Step-by-step explanation:
The correct question is
The diagonal of rectangle ABCD measures 2 inches in length.
What is the length of line segment AB?
The picture of the question in the attached figure
we know that
In the right triangle ABD
[tex]cos(30^o)=\frac{AB}{BD}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(30^o)=\frac{AB}{2}[/tex]
Remember that
[tex]cos(30^o)=\frac{\sqrt{3}}{2}[/tex]
so
[tex]\frac{AB}{2}=\frac{\sqrt{3}}{2}[/tex]
[tex]AB=\sqrt{3}\ in[/tex]
Answer:
B
Step-by-step explanation:
the answer is B on edge.
classify the triangle by its angels :
A. acute
B. right
C. obtuse
D. scalene
Answer:
B. right
Step-by-step explanation:
In the bottom left corner there is a square. The square represents a 90 degree angle. A 90 degree angle is named a right angle.
Find the values of x and y that satisfy both equations below.
[tex]27 ^{x - 2} = 9^{y} \\ 32 ^{y - \frac{3}{5} } = \frac{1}{8 ^{2x} } [/tex]
Answer:
The answer to your question is (4/3, -1)
Step-by-step explanation:
Convert both equations to the same base
[tex]27^{x - 2} = 9^{y}[/tex]
27 = 3 x 3 x 3 = 3³
9 = 3 x 3 = 3²
Substitution
[tex]3^{3(x - 2)} = 3^{2y}[/tex]
Simplify
3x - 6 = 2y Equation l
[tex]32^{y - 3/5} = \frac{1}{8^{2x}}[/tex]
32 = 2 x 2 x 2 x 2 x 2 = 2⁵
8 = 2 x 2 x 2 = 2³
2[tex]^{5(y - 3/5)} = 2^{-3(2x)}[/tex]
Simplify
5y - 3 = -6x Equation ll
Equal to zero both equations
3x - 2y - 6 = 0 Equation l
6x + 5y - 3 = 0 Equation ll
Solve by elimination
Multiply equation l by 5 and equation ll by 2
15x - 10y - 30 = 0
12x + 10y - 6 = 0
27x -36 = 0
Solve for x
27x = 36
x = 36 / 27
Simplify x = 4/3
Find the y value
6(4/3) + 5y - 3 = 0
8 + 5y - 3 = 0
5y = -8 + 3
5y = -5
y = -5/5
y = -1
Solution
(4/3, -1)
Which values of x is the solution set of the inequality 7 (x+1) > -14?
The solution of given inequality is: [tex]x>-3[/tex]
Solution:
Given inequality is:
[tex]7(x+1)>-14[/tex]
We have to find the value of "x"
Let us solve the given inequality
Divide both sides of inequality by 7
[tex]\frac{7\left(x+1\right)}{7}>\frac{-14}{7}\\[/tex]
Simplify the above expression
[tex](x+1)>-2[/tex]
[tex]x+1>-2[/tex]
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides\: of\: inequality}[/tex]
[tex]x+1-1>-2-1\\\\x>-3[/tex]
Thus the value of x is [tex]x>-3[/tex]
Brian sold half of his baseball cards. The next day, he bought 10 more. Now he has a total of 50 cards. Write and solve an equation to determine how many baseball cards he had before he sold any. Let b represent the number of baseball cards he had.
Answer:
80
Step-by-step explanation:
50*2= b b/2=40 40+10=50
Answer: 20 pencils and 80 cards
Step-by-step explanation:
8. A farmer owns a total of 10 acres of land. The land is separated into 6
equally sized sections. How many
acres are in each section?
Write your answer as a mixed number in simplest form.
Answer: 8/5 or 1 ⅗ acres
Step-by-step explanation:
A Web music store offers two versions of a popular song the size of the standard version is 2.7 MB the size of a high-quality version is 4.1 MB yesterday there were 1130 downloads of the song for a total download size of 3723 MB. How many downloads of the high-quality version where there
Answer:
480
Step-by-step explanation:
Let h represent the number of high-quality downloads. Then the total download size is ...
4.1h +2.7(1130-h) = 3723
1.4h = 672 . . . . . . . . . . . . . . subtract 2.7·1130 = 3051
h = 480 . . . . . . . divide by 1.4
There were 480 downloads of the high-quality version.
If f(x) = 4x - 2, what is the y-intercept of f^-1 (x)?
1/4, 1/2, -1/2, -2
Answer:
1/2
Step-by-step explanation:
The y-intercept is [tex]\frac{1}{2}[/tex].
Given that f(x) = 4x-2.
To find the inverse function:
1) Write f(x) = y
2) Switch x and y.
3) Solve for y.
4) Write [tex]y=f^{-1}\left(x\right)[/tex].
So,
[tex]f(x) = 4x - 2\\y=4x-2\\x=4y-2\\4y=x+2\\y=\frac{\left(x+2\right)}{4}\\y=\frac{1}{4}x+\frac{2}{4}\\y=\frac{1}{4}x+\frac{1}{2}\\f^{-1}\left(x\right)=\frac{1}{4}x+\frac{1}{2}[/tex]
Comparing this with y=mx+b,
b = y-intercept = [tex]\frac{1}{2}[/tex]
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Katy bought a candy bar and shared it with her two sisters. She gave her youngest sister 1/4 of the candy bar. Her older sister received 1/3 of the candy bar. How much of the candy bar did Katy keep?
Answer:
5/12
Step-by-step explanation:
1/4×3/3=3/12
1/3×4/4=4/12
4/12+3/12=7/12
12/12-7/12=5/12
Guys please help!! I need the answer as fast as possible.
Answer:
It is NOT possible for a solution to be both x<9 and x>9
It IS possible for a solution to be both x≤9 and x≥9
Step-by-step explanation:
Because for x<9 and x>9 the GREATER than symbol means it less than 9 and cannot be 9 or it is greater than 9 but cannot be 9.
With x≤9 and x≥9 the greater than or EQUAL sign makes a big difference. Because x≥9 may be the actual solution but since it is possible to be equal to 9 so can x≤9.
(Sorry if this seemed very confusing to explain).
Find the slope given in the graph above.
Answer:
-1/3
Step-by-step explanation:
it goes down one and over three
Answer: your slope would be -[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Help, please! And also attempt to show work, thank you!
Since you know the value of n = 3, plug in 3 for n in the equation
4(n + 1)
4(3 + 1)
4(4)
= 16
find a bank account balance if the account starts with $100 has an annual rate of 4% and the money left in the account for 12 years
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The midpoint of AB??
Answer:
(0, 0)
Step-by-step explanation:
You can see immediately that the line AB passes through (0, 0) (the origin) and that points A and B are equidistant from the origin. In other words, (0, 0) is the midpoint of line AB.
Answer:
( 0 , 0 )Step-by-step explanation: