a triangular course for a canoe race is marked with buoys. the first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg is 2/5 mi. how long is the race?
(the numbers are fractions)
Answers
Answer:
1 1/5 mi
Step-by-step explanation:
We need to add the three legs together
3/10 + 1/2 + 2/5
The common denominator is 10
3/10 =3/10
1/2 *5/5 = 5/10
2/5 *2/2 =4/10
3/10 + 5/10+4/10 = 12/10
10/10 = 10/10+2/10 = 1+2/10 = 1 1/5 mi
Answer:
Length of race = 1.2 miles
Step-by-step explanation:
Length of race is given by the perimeter of triangle.
Refer the given figure.
The first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg is 2/5 mi.
[tex]\texttt{Perimeter =}\frac{3}{10}+\frac{1}{2}+\frac{2}{5}=\frac{3}{10}+\frac{5}{10}+\frac{4}{10}=\frac{3+5+4}{10}\\\\\texttt{Perimeter =}\frac{12}{10}=1.2 miles[/tex]
Length of race = 1.2 miles
Related Questions
The two triangles below are similar. What is the similarity ratio of ∆ABC to ∆DEF?
A) 3:1
B) 1:3
C) 2:1
D) 1:2
Answers
Answer:
Option C is correct
Step-by-step explanation:
The two triangles are similar if there sides are proportional to each other
So, In Triangle ABC and Triangle DEF
AB/DE=BC/EF=AC/FD
according to definition of similar triangles.
We are given AC = 8
and FD = 4
So, AC/FD = 8/4 = 2/1
or 2:1
So, Option C is correct
Answer: Option C
2:1
Step-by-step explanation:
Two triangles are similar if the ratio of their sides is proportional.
In this case we have the triangle ∆ABC and ∆DEF so for the sides of the triangles they are proportional it must be fulfilled that:
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]
In this case we know that:
[tex]AC=8[/tex]
[tex]DF=4[/tex]
Therefore
[tex]\frac{AC}{DF} = \frac{8}{4}\\\\\frac{AC}{DF} = \frac{2}{1}[/tex]
The similarity ratio of ∆ABC to ∆DEF is 2:1
what is the equation for the line of reflection?
x=3
y=3
y=x
x=6
Answers
Answer:
y=x
Step-by-step explanation:
If you draw the line y=x on the shown graph a and a' are the same distance away from the line. This is the same for all the other points and its prime.
Hello I don’t get this, I don’t want the answer I just need someone to teach it to me because it wasn’t in the lesson
Answers
Answer:
[tex]3 \le x \le 7[/tex].
Step-by-step explanation:
Hopefully this will help. Let me know in the comments if it doesn't.
The domain is all the x's where the function exists. The function you have starts at x=3 and ends at x=7. There are no breaks in your line between those numbers for x. So your domain is all x's between 3 and 7 ( inclusive).
So that means all values of x that is greater than or equal to 3 and values of x less than or equal to 7.
[tex]3 \le x \le 7[/tex].
A woman bought a dress at a discount of 16 2/3%. If the woman paid $32.50, what was the original price of the dress?
Answers
Answer:
$39
Step-by-step explanation:
Let original price be x, so we need to subtract 16 2/3 % from that to get 32.50
So we can write:
[tex]100x-16\frac{2}{3}x=3250\\83\frac{1}{3}x=3250\\x=39[/tex]
So basically, the original price was $39.
Which logarithmic equation has the same solution as x-4=2^3
Answers
Answer:
[tex]log_{3}(x-4)= 3log_{3}(2)[/tex]
Step-by-step explanation:
The given equation is:
[tex]x-4=2^{3}[/tex]
We have to find the logarithmic equation with same solution as the given equation.
If we take the log of both sides, we can get a logarithmic equation. Since the log operation is applied to both sides the solution of the equation will stay the same.
Taking the logarithm to the base 3 of both sides, we get:
[tex]log_{3}(x-4)= log_{3}(2)^{3}\\\\ log_{3}(x-4)= 3log_{3}(2)[/tex]
Answer: The CORRECT answer is C: log2(x-4)=3
A city determines that a planned community must have at least 4 acres of developed and open space, and the difference
between the number of developed acres, y, and the number of open acres, x, can be no more than 1. Which graph
represents the system of inequalities for this scenario?
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x -----> the number of open acres
y ----> the number of developed acres
we know that
[tex]x+y \geq 4[/tex] -----> inequality A
[tex]x\leq 1[/tex] ----> inequality B
Remember that
if the number of open acres, x, can be no more than 1. then the number of open acres, x must be less than or equal to 1
Solve the system of equations by graphing
The solution is the shaded area (Note The number of acres cannot be a negative number)
The graph in the attached figure
Answer: It's B
Step-by-step explanation: I just did it on edge 2020
Deshawn has five CDs that he is going to give away. He lets his best friend choose three of five CDs. How many different groups of three CDs are possible?
Answers
Answer:
10 different groups of three CDs are possible
Step-by-step explanation:
Total CDs are five and 3 has to be chosen where order doesn't matter.
In these kind of scenarios, combinations are used for calculating different ways in which the CDs can be given.
So,
Number of ways in which groups of CDs are possible = ⁵C₃
[tex]= \frac{n!}{r!(n-r)!} \\= \frac{5!}{3!(5-3)!}\\=\frac{5!}{3!2!}\\=\frac{5*4*3!}{3!2!}\\=\frac{5*4}{2}\\=\frac{20}{2}\\=10[/tex]
Therefore, 10 different groups of three CDs are possible ..
Which of the following is a soultion to the quadratic equation below x^2 - 3x - 54 =0
Answers
Answer:
9 or -6
Step-by-step explanation:
To solve, I would suggest factoring.
You need to find two numbers which can be multiplied for 54 and also combined in some way to get 3. In this case, 9 and 6 are perfect.
[tex]x^2-3x-54=0\\(x-9)(x+6)=0[/tex]
Next, you can set both of your terms equal to zero to find your possible solutions.
[tex]x-9=0\\x=9\\[/tex]
or
[tex]x+6=0\\x=-6[/tex]
Determine the solution for x²-3x-28≥0
Answers
Answer:
(- ∞, - 4 ] ∪ [7, + ∞ )
Step-by-step explanation:
Determine the zeros by equating to zero, that is
x² - 3x - 28 = 0 ← in standard form
(x - 7)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 4 = 0 ⇒ x = - 4
The zeros divide the domain into 3 intervals
(- ∞ , - 4 ], [ - 4, 7 ], [ 7, + ∞)
Choose a test point in each interval and compare value with required solution
x = - 5 : (- 5)² - 3(- 5) - 28 = 25 + 15 - 28 = 12 > 0
x = 0 : 0 - 0 - 28 = - 28 < 0
x = 10 : 10² - 3(10) - 28 = 100 - 30 - 28 = 42 > 0
Solutions are the first and third interval, that is
x ∈ (- ∞, - 4 ] ∪ [ - 7, + ∞)
Answer:
it's C on edge
Step-by-step explanation:
got it right:)
perform the indicated operation 3/4 ÷ 1/3
Answers
Answer:
9/4 or 2 1/4.
Step-by-step explanation:
3/4 / 1/3
=3/4 * 3/1
= 9/4
Answer:
3/4 ÷ 1/3 equals
(3/4 x 3/1) = 9/4
Step-by-step explanation:
At the mall, buying a pair of shoes and buying a book are independent events.
The probability that a shopper buys shoes is 0.15. The probability that a
shopper buys a book is 0.10.
What is the probability that a shopper buys shoes and a book?
Answers
Answer:
0.015
Step-by-step explanation:
The probability two independent events take place is the product of their individual probabilities.
p(shoes & book) = p(shoes) * p(book) = 0.15 * 0.10 = 0.015
Answer:
0.015 ~apex
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The solution set of n2 − 14n = -45 is [ ]
Answers
Answer:
n=5 n=9
Step-by-step explanation:
n^2 − 14n = -45
Add 45 to each side
n^2 − 14n +45 = -45+45
n^2 -14n +45 = 0
Factor the equation
What 2 number multiply to 45 and add to -14
-5*-9 = 45
-5+-9 = -14
(n-5) (n-9) =0
Using the zero product property
n=5 n=9
Help asap
The scale of a town map is 1 inch to 3 miles. On the map, a lake and the downtown are 4 inches apart. What is the actual distance between the lake and the downtown?
3/4 mile
1/3 mile
7 miles
12 miles
Answers
Answer:
Step-by-step explanation:
The answer is 12 miles, if every inch is 3 miles on the map then 3x4=12.
Answer:
12 miles
Step-by-step explanation:
In order to solve the problem you only have to use the scale of the map, we know that the ratio is 1 inch to 3 miles, so if one inch in the map represent 3 miles on real scale, now we just do a rule of three like this:
[tex]\frac{1 inch}{4 miles}=\frac{3 inches}{x}[/tex]
So now that we have our function we can clear the x to solve the problem:
[tex]x=\frac{3x4}{1}[/tex]
[tex]x=\frac{12}{1}[/tex]
[tex]x=12 miles.[/tex]
By doing this we now know that there are 12 miles from downtown to the lake.
A pedestal for a statue is in the shape of a hexagon, formed by a square and two congruent triangles, with the dimensions shown below. What is the area of the top of the pedestal?
Answers
You are told the middle part is a square, so all 4 sides are equal.
The height is shown as 4 feet, so the width of the square is also 4 feet.
This means the height of the 2 triangles is 7 - 4 = 3 feet, so each triangle is 1.5 feet high ( 3 feet / 2 = 1.5).
The area of the square is 4 x 4 = 16 square feet.
The area of 1 triangle is 1/2 x base x height = 1/2 x 4 x 1.5 = 3 square feet.
The total area = 16 + 3 + 3 = 22 square feet.
HELP PLEASE REALLY NEED IT
Answers
Answer:
x=65
Step-by-step explanation:
The angle with the measurement of 125 degrees is supplementary to the one adjacent to it (sharing the same vertex and on same line).
What that means is that the measurement of the angle adjacent to that angle of 125 degrees is 180-125=55.
So now we know the sum of the interior angles of a triangle add up to be 180 degrees.
That is we have to solve the following equation for x:
x+55+60=180
Add 55 and 60:
x+115=180
Subtract 115 on both side:
x=180-115
Simplify:
x= 65
Point C is the center of the circle. Angle ACB measures 56 . What is the measure of arc AB?
Answers
Answer:
=56°
Step-by-step explanation:
The degree measure of an angle is the measure of the central angle that intercepts the arc at the circumference.
The central angle is bound by two radii.
In the provided question, the central angle ACB=56° and intercepts the circle at A and B, with the vertex at C the center of the circle.
Answer:56
Step-by-step explanation:
Value of x, -5x-15>10+20x
Answers
Answer:
x<-1
Step-by-step explanation:
-5x-15>10+20x
Add 5x to each side
-5x+5x-15>10+20x+5x
-15> 10+25x
Subtract 10 from each side
-15-10 > 25x
-25 >25x
Divide each side by 25
-25/25 >25x/25
-1>x
x<-1
(01.03 MC)
Which of the following is a step in simplifying the expression
(Xy^4/x^-5y^5)^3
Answers
[tex]\displaystyle\tt\left(\frac{xy^4}{x^{-5}y^5}\right)^{-3} =\frac{x^{-3}y^{4\cdot(-3)}}{x^{-5\cdot(-3)}y^{5\cdot(-3)}}=\boxed{\tt\frac{x^{-3}y^{-12}}{x^{15}y^{-15}}}[/tex]
Kira swam 17 4/7 laps in the pool on Monday. On Wednesday, she increased
her workout to 23 5/14 laps. Estimate the total number of laps Kira swam on
Monday and Wednesday
14
A.41 laps
B.40 laps
C.31 laps
D.42 laps
Answers
Answer:
A) 41 laps
Step-by-step explanation:
Round 17 4/7 to the nearest whole number:
18
Round 23 5/14 to the nearest whole number:
23
18 + 23 = 41
Final answer:
By rounding the fractional laps to the nearest whole numbers (18 for Monday and 23 for Wednesday), and adding them together, we estimate that Kira swam a total of 41 laps. Option A is the closest answer.
Explanation:
To estimate the total number of laps Kira swam on Monday and Wednesday, we should round the numbers to the nearest whole number and then add them together. Kira swam 17 4/7 laps on Monday, which we can round to 18 laps for estimation purposes. On Wednesday, she swam 23 5/14 laps, which rounds to 23 laps. Adding the estimated numbers together, we get:
Monday: 18 (estimated from 17 4/7)
Wednesday: 23 (estimated from 23 5/14)
Therefore, the estimated total number of laps is 18 + 23 = 41 laps.
The closest answer to our estimation is Option A: 41 laps.
After working 10 years as a bus driver, Izabel Antocicco was in an accident and became permanently disabled. She was 63 years old at the time and was planning to retire on her 65th birthday. Her final salary was $55,700 per year. Her rate of benefits was 4.5%. What is her monthly disability benefit?
A. $2,506.50
B. $3,458.90
C. $3,508.11
D. $6,458.22
Answers
Answer:
A. $2,506.50
Step-by-step explanation:
which values of x and y would make the following expression represent a real number? (4+5i)(x+yi)
Answers
Answer:
So x=4 and y=-5 would work.
Step-by-step explanation:
When you multiply complex conjugates, you get a real result.
Example:
[tex](a+bi)(a-bi)=a^2-b^2i^2=a^2+b^2[/tex]
I replace [tex]i^2[/tex] with -1 since [tex]i^2=-1[/tex].
[tex]a^2+b^2[/tex] is a real number (there is no imaginary part, no i).
So what is the conjugate of 4+5i?
4-5i
So x=4 and y=-5 would work.
A multiple of the complex conjugate would work as well.
[tex](a+bi)(ca-cbi)[/tex]
[tex]c(a+bi)(a-bi)[/tex]
[tex]c(a^2-b^2i^2)[/tex]
[tex]c(a^2+b^2)[/tex]
This is still a real number; there is no imaginary part,no i.
Is (4y-8)cm divided by 2 equals to 4y-8cm over 2 and then a cm or is it (2y-4)cm?
Answers
Answer:
(2y-4)cm
Step-by-step explanation:
In the given question we have (4y-8) divided by 2
which can be written mathematically as [tex]\frac{\left ( 4y-8 \right )cm}{2}[/tex]
Now (4y-8) is a quatity with unit cm. and the whole expression is in parentheses. Moreover, two quatity can only be added or subtracted only when their units are same. Therefore 4y and 8 must have same unit that is cm.
Therefore, [tex]\frac{\left ( 4y-8 \right )cm}{2}=(2y-4)cm[/tex] and not anything else
Evaluate 2^-4 TOOOOOOOOOOONGAAAAAAAAAAAAAA
Answers
Answer:
1/16
Step-by-step explanation:
2 ^ -4
The negative puts the number in the denominator
1 / 2^4
1/16
What is the solution to the following equation? 4(3x − 6) + 15 = 27 2 3 4 5
Answers
Answer:
Hi there!
The answer to this question is 3
Step-by-step explanation:
You first distribute the four into the parenthesis to get: 12x-24+15+ 27
Next you add -24 to 15 to get: -9 your equation should now look like 12x-9=27
Then you add 9 on both side to get 12x=36
Last you divide twelve on both sides to x=3
Answer:
3
Step-by-step explanation:
Francisco’s bank offers car financing for 3,4 or 5 years.if Francisco chooses 3-year financing ,how many monthly payment will he have?
Answers
Answer:
How much money the payment is in one year, then divided by 12.
Step-by-step explanation:
To do this, lets say that Francisco's bank earns 120036$ a year.
120036/12=1003$ a month
How much payment in one year, then divided by 12.
Answer:
36 months
Step-by-step explanation:
simple math
Hiring the bus will cost $25 a day for the driver, $2 per mile traveled, and $3 for gas per mile traveled. The field trip will total 8 miles round trip.
Mrs. Garcia needs to calculate the cost of the bus. Which expression could she write that uses the distributive property?
Answers
Answer:
65
Step-by-step explanation:
25+2x8+3x8
Answer:
25 + 8(2 + 3)
Step-by-step explanation:
The equation below has one solution.
9x-10 = 3x+2
What is the solution to the equation?
1) -2
2)-1
3) 1
4) 2
Answers
Answer:
x = 2
Step-by-step explanation:
Given
9x - 10 = 3x + 2 ( subtract 3x from both sides )
6x - 10 = 2 ( add 10 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Answer:
x=2
Step-by-step explanation:
Given
9x - 10 = 3x + 2 ( subtract 3x from both sides )
6x - 10 = 2 ( add 10 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Which expression is equivalent to 2a+1/10a-5 / 10a/4a^2-1
Answers
Answer:
[tex]\large\boxed{\dfrac{(2a+1)^2}{50a}}[/tex]
Step-by-step explanation:
[tex]10a-5=5(2a-1)\\\\4a^2-1=2^2a^2-1^2=(2a)^2-1^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2a-1)(2a+1)\\\\\dfrac{2a+1}{10a-5}\div\dfrac{10a}{4a^2-1}=\dfrac{2a+1}{5(2a-1)}\div\dfrac{10a}{(2a-1)(2a+1)}\\\\=\dfrac{2a+1}{5(2a-1)}\cdot\dfrac{(2a-1)(2a+1)}{10a}\qquad\text{cancel}\ (2a-1)\\\\=\dfrac{2a+1}{5}\cdot\dfrac{2a+1}{10a}=\dfrac{(2a+1)^2}{50a}[/tex]
Answer: The answer is D
Step-by-step explanation: got it right 2023 edge
Which shows the correct solution of the equation, when 1/2a+2/3b=50, when b=50 ?
Answers
Answer:
[tex] a = \frac{100}{3}[/tex]
Step-by-step explanation:
We have the following equation:
[tex]\frac{1}{2} a + \frac{2}{3} b = 50[/tex]
If [tex]b=50[/tex], then:
[tex]\frac{1}{2} a + \frac{2}{3}[/tex]×50 [tex] = 50[/tex]
Solving for 'a':
[tex]\frac{1}{2} a = \frac{50}{3}[/tex]
[tex]\frac{1}{2} a = \frac{50}{3}[/tex]
[tex] a = 2\frac{50}{3}[/tex]
[tex] a = \frac{100}{3}[/tex]
Answer a=60 (3rd option)
Step-by-step explanation:
What is the constitutional basis for the expressed powers of the federal
government?
Answers
Answer:
Article I, Section 8.
Step-by-step explanation:
The expressed powers of the federal government are given in Article I, Section 8 of the Constitution. This includes the many specific powers which the framers intended for the federal government to have, such as to declare war, regulate commerce, establish post offices, and establish rules of naturalization.
Answer:
They are directly listed in the Constitution.