Answers
Answer:
3:5
Step-by-step explanation:
The areas of two similar octagons are 9m² and 25m²
The scale factor of their areas is [tex]\frac{25}{9}[/tex] or 9:25
The scale factor of their side lengths is [tex]\sqrt{25/9}[/tex] or 3:5
ANSWER
3:5
EXPLANATION
The given similar octagons have areas 9 m² and 25m² .
Let the scale factor of their side lengths be in the ratio:
m:n
[tex] {( \frac{m}{n}) }^{2} = \frac{9}{25} [/tex]
We take square root of both sides to get;
[tex] \frac{m}{n} = \sqrt{ \frac{9}{25} } [/tex]
We simplify the square root to get
[tex] \frac{m}{n} = \frac{3}{5} [/tex]
Therefore the scale factor of their side lengths is 3:5
Related Questions
PLS HELP WITH ALL QUESTIONS WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
THANK YOU IN ADVANCE.
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
The opposite sides of a rectangle are congruent, hence
x + 1 = 5 ( subtract 1 from both sides )
x = 4
Or
x - 1 = 3 ( add 1 to both sides )
x = 4
(b)
The sum of the 3 angles in a triangle = 180°, hence
3y + 2y + y = 180
6y = 180 ( divide both sides by 6 )
y = 30
Answer:
PART A "4"
PART B "30"
Step-by-step explanation:
PART A
If you refer to my picture below, then you will know that the sides are equal.
The x-1 side is equal to 3 and the x+1 sign is equal to 5. So it best makes sense that 4 is equal to x. That's because x-1 is 3 and x+1 is 5.
PART B
This is tricky. As you know all sides of a triangle add up to 180 degrees. I would divide by 3, but that would be incorrect. Whenever you see these y's, you have to divide by that amount. The y's are there for a reason, so that some sides are bigger than the other. Divide 180 by 6(number of y's). That is 30. This gives you the solution to one y so if it asks you for 2y or 3y, then you would multiply. But it's not. 30 is the answer
NEED HELP WITH A MATH QUESTION
Answers
You have a rectangle that is 8 ft by 10 ft
Area = 8 * 10 = 80 square feet.
Then there is a triangle 8 ft high with a base of 4 feet.
Area = /2 x 8 x 4 = 16 square feet.
Add together for total area:
80 + 16 = 96 square feet.
A simple method of calculating Area is multiplying the Length times the Width. It is much harder to calculate the entire thing all at once, so it is easier to rather keep the shapes separate.
10 x 8 = 80. This is the area of your first shape, the Rectangle.
You can do the same with the triangle, although triangles are only half a square. You also only multiply the flat sides, not the slanted side, the side with 8.9.
8 x 4 = 32. Because the shape is a triangle wedge, half a square, you divide your answer, 32, by 2, to get half of 32, which is 16.
Then add the two areas, 16 and 80, which is 96.
(The little box in the bottom right corner of the square is just an angle, it represents that it is a right angle, ignore it if you didn't know what it was.)
The vertices of a hyperbola are located at (−4, 1) and (4, 1). The foci of the same hyperbola are located at (−5, 1) and (5, 1). What is the equation of the hyperbola?
Answers
The equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
How to determine the equation of the hyperbola?The vertices of the hyperbola are given as:
Vertices = (±4, 1)
The foci of the hyperbola are given as:
Foci = (±5, 1)
The coordinates of the vertices is represented as::
Vertices = (±a, n)
By comparing (±a, n) and (±4, 1), we have:
a = 4
n = 1
The coordinates of the foci is represented as::
Foci = (±c, n)
By comparing (±c, n) and (±5, n), we have:
c = 5
n = 1
Calculate b using:
b = √(c² - a²)
So, we have:
b = √(5² - 4²)
Evaluate
b = 3
The equation of a hyperbola is:
[tex]\frac{x^2}{a^2} - \frac{(y - n)^2}{b^2} = 1[/tex]
So, we have:
[tex]\frac{x^2}{4^2} - \frac{(y - 1)^2}{3^2} = 1[/tex]
Evaluate the exponent
[tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
Read more about hyperbola at:
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On a coordinate grid Ming's house is located 2 blocks to the right and 5 blocks up from (0,0). Joe house is located 3 blocks to the right and 2 blocks down from Ming's house. What ordered pair describes the location of joe house?
Answers
Answer:
(5, 3)
Step-by-step explanation:
Conventionally, the ordered pairs are (right, up). Then ...
Ming's = (0, 0) + (2, 5) = (2, 5)
Joe's = Ming's + (3, -2) = (2, 5) + (3, -2) = (2+3, 5-2)
Joe's = (5, 3)
Answer:
( 5,3 )
Step-by-step explanation:
i am doing this test too
If log_3(x)=4.5 and log_3(y)=3, what is log_3(x^2/y)?
a. 3
b. 6.75
c. 6
d. 1.5
Answers
There all log base 3, the base won't matter as long as they're all the same.
log(x^2/y)=2log(x)-log(y)=2(4.5)-3=6
Answer: c. 6
what undefined term does a circle use
Answers
Answer:
The definition of a circle uses the undefined term Arc
Step-by-step explanation:
There are three terms generally considered to be undefined in geometry: point, line and plane. A circle is the set of all points in a plane the same distance from a given point called the center. The only of our options that is used in this definition is plane.
Find the product.
(4c + 7)^2
Answers
Answer:
16c^2+56c+49
Step-by-step explanation:
(4c+7)^2 means (4c+7)(4c+7)
Use foil to multiply: 4c(4c)+4c(7)+7(4c)+7(7)
Simplifying : 16c^2+28c+28c+49
16c^2+56c+49
[tex](4c + 7)^2=16c^2+56c+49[/tex]
Kim took out a $55,000 loan for college she is borrowing money from 2 banks bank a charges an interest rate of 8% and b charges an interest rate of 11% after one year Kim owes 5000 in interest how much money did she borrow from bank a.
Answers
Answer:
$35,000
Step-by-step explanation:
Let x represent the amount borrowed from Bank A. Then (55000-x) is the amount borrowed from Bank B. Kim's total 1-year interest is ...
0.08x + 0.11(55000 -x) = 5000
-0.03x + 6050 = 5000 . . . . . simplify
-0.03x = -1050 . . . . . . . . . . . . subtract 6050
x = 35,000 . . . . . . . . . . . . . . . divide by -0.03
Kim borrowed $35,000 from Bank A.
The area of a parking lot is 1710 square meters. A car requires 5 square meters and a bus requires 32 square meters of space. There can be at most 180 vehicles parked at one time. If the cost to park a car is $2.00 and a bus is $6.00, how many buses should be in the lot to maximize income? Please help :(
Answers
Answer:
To maximize the income should be 30 buses and 150 cars
Step-by-step explanation:
Let
x-----> the number of cars
y ----> the number of bus
we know that
[tex]5x+32y\leq1,710[/tex] ------> inequality A
[tex]x+y\leq 180[/tex] ----> inequality B
The function of the cost to maximize is equal to
[tex]C=2x+6y[/tex]
Solve the system of inequalities by graphing
The solution is the shaded area
see the attached figure
The vertices of the solution are
(0,0),(0,53),(150,30),(180,0)
Verify
(0,53) ---> [tex]C=2(0)+6(53)=\$318[/tex]
(150,30) ---> [tex]C=2(150)+6(30)=\$480[/tex]
therefore
To maximize the income should be 30 buses and 150 cars
Answer:
Givens
The area of the parking lot is 1710 square meters.A car requires 5 square meters.A bus requires 32 square meters.There can be a maximum of 180 vehicles.The cost for a car is $2.00.The cost for a bus is $6.00.To solve this problem we need to create a table to order all this information and express it as a system of inequations.
Car Bus Total Capcity
Sq. Meters 5c 32b 1710
N° vehicles c b 180
Therefore, the inequalities are
[tex]5c+32b\leq 1710\\c+b\leq 180[/tex]
The expresion which represents the income is
[tex]I=2c+6b[/tex], because a car is $2.00 and a bus is $6.00.
Now, we first need to find the critical points of the solution of the inequality system, which is attached. Observe that the only points that can be a solution is (150,30), because there can't be just car or just buses.
Then, we replace this point in the income expression
[tex]I=2c+6b\\I=2(150)+6(30)=300+180=480[/tex]
Therefore, in order to maximize incomes, we need to park 150 cars and 30 buses, to make $480 income.
Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm? 1. acute, because 62 + 102 < 122 2.acute, because 6 + 10 > 12 3.obtuse, because 62 + 102 < 122 4.obtuse, because 6 + 10 > 12
Answers
Answer:
The best represents a triangle is obtuse, because 6 + 10 > 12 ⇒ answer 4
Step-by-step explanation:
* Lets talk about some facts in the triangle
- The triangle is formed when the sum of the lengths of the shortest
two side is greater then the length of the longest side
∵ The lengths of the sides are 6 cm , 10 cm , 12 cm
∵ 6 + 10 > 12
∴ 6 , 10 , 12 are the sides of a triangle
- Two know the type of the triangle use these rules
# The three sides of the triangle have lengths a , b , c where a and b
are the shortest sides means a , b < c, then
- If a² + b² > c² , the triangle is acute triangle (its 3 angles are acute)
- If a² + b² = c² , the triangle is right triangle (the angle opposite to c is a
right angle and the other 2 angles are acute angles)
- If a² + b² < c² , the triangle is obtuse triangle (the angle opposite to c is an
obtuse angle and the other 2 angles are acute angles)
∵ (6)² + (10)² = 36 + 100 = 136
∵ (12)² = 144
∵ 136 < 144
∴ (6)² + (10)² < (12)²
∴ The triangle is obtuse
* The best represents a triangle is obtuse, because 6 + 10 > 12
Point c is the center of the circle what is the measure of
A.
B.
C.
D.
Look at the circle down below
Answers
Answer:
93°
Step-by-step explanation:
Angle ACB is a central angle. The theorem regarding central angles and the arcs they intercept is that the angle and the arc are congruent. That means that arc AB is also 93°
Given the following linear functions determine the relationship
Answers
Answer:
Perpendicular
Step-by-step explanation:
Linear equations will describe parallel lines when the lines have the same slope. These equations are written in slope-intercept form, so we can easily determine that the slopes are ...
f(x): slope is 5/6
g(x): slope is -6/5
These are not the same, so the lines are not parallel.
__
The lines will be perpendicular when the product of their slopes is -1. Here, that product is ...
(5/6)(-6/5) = -30/30 = -1
These equations describe lines that are perpendicular.
Need help with a math question
Answers
Answer:
b = 17
Step-by-step explanation:
The angle bisector of the apex angle of an isosceles triangle is also a median and altitude. PS=RS=17
b = 17
What is the exponential form of log5 9 = x?
x^9 = 5
5^x = 9
x^5 = 9
9^x = 5
Answers
Answer:
B
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Hence
[tex]log_{5}[/tex] 9 = x ⇒ 9 = [tex]5^{x}[/tex] → B
Answer:
its d 5 < x ≤ 9 .
15. What is the value of (1/2)3?
A. 1/6
B. 1/8
C. 1/2
D. 11/2
Answers
Answer:
(1/2)^3
= (1/2) (1/2) (1/2)
= 1/4 (1/2)
= (1)(1)/(4)(2)
= 1/8
Step-by-step explanation:
Please mark brainliest!
Express 256^-3/4 as a fraction. Write the fraction in the form a/b, where a and b are positive integers with no common factor greater than 1 .
Answers
Answer:
1/64
Step-by-step explanation:
[tex]256^{-\frac{3}{4}}=2^{8(-\frac{3}{4})}=2^{-6}=\dfrac{1}{2^6}=\dfrac{1}{64}[/tex]
256^-3/4 can be converted into a positive fraction by interpreting the negative exponent as a reciprocal and the fractional exponent as a root. It simplifies to 1/(4th root of 256^3), which equals 1/64.
Explanation:To express the numeral 256^-3/4 in the form of a fraction, we first need to understand how negative and fractional exponents work. The number is in the form of a^(-m/n) which is equivalent to the nth root of a^-m or 1/(nth root of a^m). The negative sign in the exponent implies a reciprocal of the number and the fractional exponent denotes a root of the number.
Now applying this understanding to our number which is 256^-3/4. Here, the base a is 256 and the fractions -m/n is -3/4. Therefore, it is equivalent to the 4th root of 256^-3, which can also be written as 1/(4th root of 256^3).
The 4th root of 256 is 4. So, the expression now becomes 1/(4^3), which after simplifying gives us the result 1/64.
So, the expression 256^-3/4 written as a positive fraction is 1/64.
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In which figure is line DE parallel to line BC?
A)figure 1
B)figure 2
C)figure 3
D)figure 4
Answers
Answer:
figure four
Step-by-step explanation:
this is because 5.5/15 = 6.6/18 which means they are proportional making the two lines parallel.
please help
Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample.
If you live in Ohio, then you live in the United States
Answers
If you live in the United States, then you live in Ohio.
False.
Answer with explanation:
The converse of conditional statement "if p then q" is given by "if q then p".
The given conditional statement : If you live in Ohio, then you live in the United States.
Then , the converse of the given conditional statement will be :-
If you live in United states , then you live in Ohio.
, which is not true since there are so many states in United states other than Ohio.
Counter-example: If some one lives in Indiana, then he is also lives in United states.
Becky is using the expression 2z + 3 to represent the number of chairs in her classroom. There are twice as many chairs as tables, and there are three extra chairs in the back. What does z represent?
The number of chairs.
The number of tables.
The number of chairs at tables.
The number of chairs and tables
Answers
Answer:
The number of tables
Step-by-step explanation:
Let
z ----> the number of tables
y-----> the number of chairs
we know that
[tex]y=2z+3[/tex]
therefore
z represent the number of tables
Answer:
the number of tables :]
Step-by-step explanation:
Which of the following numbers is closest to the mean of this distribution?
A. 5
B. 3
C. 6
D. 7
E. 4
Answers
Answer:
The answer is E
Step-by-step explanation:
add all the numbers together then count how many numbers there are in tottally then divide
all the numbers added together is 64
there is a total of 16 numbers
64/16=4
Answer:
B)mean of data is closest to number 3.
Step-by-step explanation:
Given : Histogram .
To find : Which of the following numbers is closest to the mean of this distribution.
Solution : We have given that histogram
We have data 1 , 2, 3, 4, 3, 2, 1.
Total number of data = 7
We need to find mean of the data
Mean = [tex]\frac{1+2+3+4+3+2+1}{7}[/tex].
Mean = [tex]\frac{16}{7}[/tex].
Mean = 2.2
Therefore, mean of data is closest to number 3.
Please help, refer to picture
Answers
Answer:
99°
Step-by-step explanation:
∠7 and ∠8 are a linear pair, so are supplementary. Numbers are assumed to be degrees.
∠7 + ∠8 = 180
2x+15 + 3x = 180 . . . . . substitute given values
5x = 165 . . . . . . . . . . . . subtract 15, collect terms
x = 33 . . . . . . . . . . . . . . . divide by the coefficient of x
∠8 = 3x = 3·33 = 99 . . . . . degrees
Alex takes a full-time position that pays a salary of $58,000 per year. What is her pre-tax monthly income? Do not include a "$" in your answer.
please explain
Answers
Answer:
4833.33
Step-by-step explanation:
The salary of $58,000 is Alex's pre-tax income. It is presumed to be divided evenly between the 12 months of the year, so his monthly income is ...
$58,000/12 = $4833.33
A bag contains 7 pieces of paper numbered 1 to 7. P(2)=. Is this an experimental or theoretical probability and why?
CAN YOU GUYS PLEASE HELP ME I NEED TO TURN THIS IN IN 30 MINUETS!!!!!
Answers
Answer:
theoretical probability
Step-by-step explanation:
This is theoretical probability. The 7 pieces of paper each bear one number from {1, 2, ... , 6, 7}. There is only one piece of paper marked 7. So the probability of drawing a 2 is 1/7.
Keshawn is asked to compare and contrast the domain and range for the two functions. f(x) = 5x g(x) = 5x Which statements could he include in his explanation? Check all that apply. The domain of both functions is all real numbers. The domain of f(x) is x > 5. The domain of g(x) is x > 5. The range of both functions is y > 5. The range of f(x) is y > 0. The range of g(x) is y > 0.
Answers
Answer:
"The domain of both functions is all real numbers."
Step-by-step explanation:
Given
[tex]f(x) = 5x\\and\\g(x) = 5x[/tex]
We can see that the function will have some value for any value of x and is not undefined on any value of x. So the domain of f(x) is all real numbers.
Similarly, g(x) is also not undefined on any value of x so it also has domain of all real numbers.
The range of f(x) and g(x) will be all real numbers as the functions do not produce infinity on any of the input.
Only the statement that
"The domain of both functions is all real numbers."
is true for the given functions ..
The polygons are similar. Find the value of X and Y. (PLEASE HELP⚠️⚠️)
Answers
Answer:x=13
Step-by-step explanation:
Answer:
x = 13
Step-by-step explanation:
Since the polygons are similar, their side lengths will be proportionate.
So, The ratio (x - 3)/2.5 will be proportionate to 16/4 (4).
That said, we can get that (x - 3)/2.5 = 4
Multiply: x - 3 = 10
Add: x = 13
Evelyn has a bag containing red (R), blue (B), and green (G) marbles as shown below. If each marble is replaced after it is drawn, what is the probability of randomly drawing three consecutive red (R) marbles
Answers
Answer:
the probability of drawing three consecutive red marbles is based on how many red marbles you have and many marble there is in total.
Answer:
27/512
Step-by-step explanation:
P(3 consecutive red)=P(red)×P(red)*P(red)=3/8*3/8*3/8=27/512.
The reason P(red)=3/8 for each picking of marble us because you are putting the marble back in and there are 3 red while you have 8 marbles in all.
Alice and Will are measuring a liquid solution using graduated cylinders. Alice uses 6.5liters of the liquid solution, and Will uses 4,750milliliters of the liquid solution. What is the ratio of Alice's measurements to Will's measurements? Simplify your answer.
Answers
The simplified ratio of Alice's measurements to Will's measurements is 26:19 when both measurements are converted to milliliters.
Explanation:The ratio of Alice's measurements to Will's measurements can be found by converting both measurements to the same units and then simplifying the resulting fraction. Alice's measurement is in liters and Will's measurement is in milliliters. We know that 1 liter equals 1,000 milliliters, so Alice's measurement converted to milliliters is 6.5 liters * 1,000 = 6,500 milliliters.
Therefore, the ratio of Alice's measurement to Will's measurement in milliliters is 6,500:4750. To simplify this ratio, you can find the greatest common divisor (GCD) of the two numbers and divide both numbers by the GCD. In this case, the GCD of 6,500 and 4,750 is 250. Thus, the simplified ratio is 26:19.
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The ratio of Alice's measurements to Will's measurements is approximately [tex]\[ \frac{4750 \text{ milliliters}}{1000} = 4.75 \text{ liters} \][/tex]
To compare Alice's measurement to Will's, we need to express them using the same unit. Let's convert Will's measurement from milliliters to liters:
1 liter = 1000 milliliters
So, Will's measurement of 4750 milliliters is equivalent to:
[tex]\[ \frac{4750 \text{ milliliters}}{1000} = 4.75 \text{ liters} \][/tex]
Now, we can compare Alice's and Will's measurements:
Alice's measurement: 6.5 liters
Will's measurement: 4.75 liters
The ratio of Alice's measurements to Will's measurements is:
[tex]\[ \frac{\text{Alice's measurement}}{\text{Will's measurement}} = \frac{6.5}{4.75} \][/tex]
To simplify the ratio, we can multiply both the numerator and the denominator by 4 to get rid of the decimal in the denominator:
[tex]\[ \frac{6.5 \times 4}{4.75 \times 4} = \frac{26}{19} \][/tex]
So, the ratio of Alice's measurements to Will's measurements is [tex]\( \frac{26}{19} \)[/tex].
Simplify the expression.
the quantity x to the two fifths power end quantity to the power of 10
Answers
Answer:
x^4
Step-by-step explanation:
(x^(2/5))^10 is what I understand the words to mean
x^(2/5*10)
x^(20/5)
x^4
Answer:
The simplified form of given expression is [tex]x^4[/tex].
Step-by-step explanation:
The given expression is
[tex](x^\frac{2}{5})^{10}[/tex]
According to the power of power property of exponent, if x, a and b are any real number, then
[tex](x^a)^b=x^{ab}[/tex]
Using power of power property of exponent, the given expression can be written as
[tex](x^\frac{2}{5})^{10}=x^{\frac{2}{5}\times 10}[/tex]
[tex](x^\frac{2}{5})^{10}=x^{\frac{20}{5}}[/tex]
[tex](x^\frac{2}{5})^{10}=x^{4}[/tex]
Therefore the simplified form of given expression is [tex]x^4[/tex].
A sofa costs $50 less than three times the cost of a chair. If the sofa and chair together cost $650, how much more does the sofa cost than the chair?
A) $175
B) $225
C) $300
D) $475
Answers
1. Let S represent the cost of the sofa and C represent the cost of the chair.
If the sofa costs $50 less than three times the cost of the chair, then effectively we can write this as:
S = 3C - 50
If the sofa and chair together cost $650, we can write this as:
S + C = 650
2. Now, we can find out how much the sofa and chair cost by solving the two equations we obtained above for C, and substituting S = 3C - 50 into S + C = 650. Thus, we get:
S + C = 650
if S = 3C - 50, then:
3C - 50 + C = 650
4C - 50 = 650 (Add C and 3C)
4C = 700 (Add 50 to both sides)
C = 175 (Divide both sides by 4)
Thus, the cost of the chair is $175. Now, to find the cost of the sofa we need to simply substitute C = 175 into our first equation, S = 3C - 50:
S = 3(175) - 50
S = 525 - 50
S = 475
Thus, the sofa costs $475.
3. Now that we know that the sofa costs $475 and the chair costs $175, all we need to do is to subtract the cost of the chair from the cost of the sofa to find the difference in price:
475 - 175 = 300
Therefor, the sofa costs $300 more than the chair (answer C).
Need help with math question
Answers
Answer:
D
Step-by-step explanation:
This is a vertical opening parabola, since the focus is above the vertex on the axis of symmetry x = 2
The standard form of a vertically opening parabola is
(x - h)² = 4a(y - k)
where (h,k) are the coordinates of the vertex and a is the distance from the vertex to the focus.
here (h, k) = (2, - 1) and a = 4, hence
(x - 2)² = 16(x + 1) → D
Answer:
D
Step-by-step explanation: