need to divide 4 1/8 by 1 1/4
4 1/8 = 33/8
1 1/4 = 5/4
33/8 / 5/4 = 33/8 * 4/5 = 132/40 reduces to 33/10 = 3 3/10
100* 3 3/10 = 330 miles
Final answer:
Using the map scale of 1 1/4 inches equals 100 miles, and the measured map distance of 4 1/8 inches, the actual distance between the two cities is calculated to be 330 miles.
Explanation:
To find the actual distance between two cities on a map, we can set up a proportion based on the scale of the map. In this case, the scale is 1 1/4 inches = 100 miles. The measured distance on the map between the two cities is 4 1/8 inches.
We'll convert these measurements to an easier-to-calculate form by changing the mixed numbers to improper fractions.
First, we convert 1 1/4 inches to an improper fraction: 1 1/4 = 5/4 inches. Likewise, we convert 4 1/8 inches to an improper fraction: 4 1/8 = 33/8 inches. Now we set up the proportion using the scale.
(5/4 inches) / (100 miles) = (33/8 inches) / (x miles)
To solve for x, cross-multiply and divide:
(5/4) * x = (33/8) * 100
x = (33/8 * 100) / (5/4)
x = (33 * 100 * 4) / (8 * 5)
x = (33 * 4) / (2)
x = 66 miles
Therefore, the actual distance between the two cities is 330 miles.
Are the following figures similar?
The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?
To comply with the triangle inequality theorem, the smallest possible length of the congruent sides in an acute isosceles triangle with the longest side being 8 centimeters, would be slightly greater than 4 centimeters, rounded to the nearest tenth (4.1 centimeters).
Explanation:In the context of an acute isosceles triangle, the longest side is the base and the other two sides are congruent or have equal length. The smallest possible length of the congruent sides comes into play in respect of the triangle inequality theorem, stating that the sum of the lengths of any two sides must be greater than the length of the third side. Thus, for the smallest possible length, each of the congruent sides must hence be just slightly larger than half the length of the longest side. So for an 8 centimeter base, the smallest length for the congruent sides should be slightly more than 4 centimeters, let's call it 4.1 centimeters, when rounded to the nearest tenth.
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(Solve for v) 2v − 6 = 4
A ball is thrown from 4 feet off the ground with a vertical velocity of 30 feet per second.
Is the ball at its maximum height after 1 second? In two or more complete sentences, explain how you know whether or not the ball is at its maximum height.
What is the value of x 20 35 60 70
Answer:
Value of x is:
20
Step-by-step explanation:
Clearly, the two angles are vertically opposite
and vertically opposite angles are always equal
So, x+40=3x
Subtracting both sides by x, we get
x+40-x=3x-x
i.e. 40= 2x
Dividing both sides by 2, we get
x = 20
Hence, Value of x is:
20
(05.03)The equation shows the relationship between x and y:
y = −7x + 9
What is the slope of the equation?
−7
−2
7
9
Answer:
Option 1) -7
Step-by-step explanation:
Given : The equation shows the relationship between x and y : [tex]y=-7x+9[/tex]
To find : What is the slope of the equation?
Solution :
The general slope form of the equation is [tex]y=mx+b[/tex]
Where, m is the slope and b is the y-intercept.
Now, We compare the given equation with general form of the equation
[tex]y=-7x+9[/tex]
On comparing, m=-7 and b=9
So, The slope of the given equation is -7.
Therefore, Option 1 is correct.
Which of the following inequalities matches the graph?
graph of an inequality with a solid vertical line through the point negative 7, 0 and shading to the left of the line
Both windows are congruent. What is the combined area of the two windows?
Please help me explain your answer
convert 2 2/5 into a fraction
2 2/5 = 12/5
12/5 * 1/9 =12/45 reduces to 4/15
Suppose you are making yourself a sandwich. how many different sandwiches can you make if you have 4 choices in bread, 2 choices in meat, and 5 choices in cheese?
The amount of candy left in a Halloween bucket is given by the function A(t) = 50(0.8)t where t stands for the number of minutes the candy is available and A(t) stands for the amount of candy left at any given time. How much candy is there after five minutes?
50 pieces
40 pieces
16 pieces
200 pieces
From January through October, ACE Autos sold 150 cars. The number of cars sold in November and the number of cars sold in December were in the ratio of 3:5. If the total number of cars sold in the year was 390, find the number of cars sold in December. Solve algebraically.
390-150 = 240 cars were sold in November & December
ratio is 3:5
240/8 = 30
30*3 = 90
3*5 = 150
90 cars sold in November
150 cars sold in December
Evaluate 5a^2 + 2b^3 when a=4 and b =-4
what operation represents a ratio
what is the common difference in the arithmic sequence 30,27,24,21,18
Answer:
-3
Step-by-step explanation:
Its decresing by -3.
HELP! 5/x+3 - 3/x-2 = 5/3x+6 please show your work. :)
Where can the perpendicular bisectors of the sides of a right triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A. I only
B. II only
C. I or II only
D. I, II, or II
please show your work
A drawing shows 4 apples and 6 bananas. Which is the ratio of bananas to apples? 6:4 3:2 6 4 all of the above
What is the answer to this?
What is the square root of 26 in simplest radical form?
Final answer:
The square root of 26 in simplest radical form is just √26, as 26 has no perfect square factor. It can also be expressed as 26 raised to the power of 0.5 based on the concept of fractional powers corresponding to roots.
Explanation:
The square root of 26 in its simplest radical form cannot be simplified further as a perfect square factor because 26 is not a perfect square. However, if we apply the concept of expressing numbers as fractional powers, we can say that any number 'x' squared, written as x², is equivalent to the square root of 'x'. Thus, the square root of 26 can also be written as 26 to the power of 0.5 or 26⁰.⁵.
Expressing the concept mathematically, we can write the square root of any number 'x' as x to the power of 0.5, which is a helpful way to solve for unknown values in various equations. This idea is useful in scenarios where different roots of a number or expressions involving fractional exponents are to be calculated, and it is essential to remember that the square root is just another form of an exponent.
Use the distributive property to remove the parentheses.
-5(5v-4x-1)
Chris bought clothes for school. She bought 3 shirts for $12 each and a skirt for $15.
How much did she spend on the shirts?
Question 1 options:
Joan likes to watch the birds in her yard.one morning,she notices that there are twice as many robins as blue jays.if she counted 21 blue jays and robins in all, how many blue jays did she count. Need help badly
What is the slope and the y intercept of the line y=6x-9?
Hello there! :)
This equation is written in slope-intercept form. which means we can easily idenify the slope and the y-intercept.
First of all, slope-intercept form looks like this:
y=mx+b
The letter m represents the slope, while the letter b represents the y-intercept.
Now, let's look at the values that we have.
We are given the equation of the line:
y=6x-9
We know that m is the slope; therefore, in this equation, 6 is the slope.
-9 is the y-intercept (the letter b)
Therefore, 6 is the slope and b is the y-intercept.
I hope it helps you. Let me know if you have any queries.
~A smiley teen
[tex]MagicalNature[/tex] here to help
Which function represents g(x), a reflection of f(x) =2/5 (10)x across the x-axis? g(x) =-2/5 (10)x g(x) =-2/5(1/10)^x g(x) =2/5(1/10)^-x g(x) =2/5 (10)-x
Answer:
A. [tex]g(x)=-\frac{2}{5}(10)^x[/tex].
Step-by-step explanation:
We are given the function [tex]f(x)=\frac{2}{5}(10)^x[/tex].
Now, g(x) is obtained by reflecting the function f(x) over x-axis.
Reflection of f(x) over x-axis changes f(x) to -f(x).
So, we get,
[tex]g(x)=-f(x)[/tex]
i.e. [tex]g(x)=-\frac{2}{5}(10)^x[/tex]
Thus, the reflected function is [tex]g(x)=-\frac{2}{5}(10)^x[/tex].
So, option A is correct.
Suppose that y varies inversely with x, and y=0.2 when x=2. What is an equation for the inverse variation
My past due bill is $585.00, and I just made payment arrangements for the next 3 months to keep my account from being suspended. My normal monthly bill is $50.00 per month. How much will I need to pay each month?"
Answer:
$245
Step-by-step explanation:
Given : My past due bill is $585.00, and I just made payment arrangements for the next 3 months to keep my account from being suspended. My normal monthly bill is $50.00 per month.
To Find: How much will I need to pay each month?"
Solution:
Past due bill = $585
Now just made payment arrangements for the next 3 months to keep my account from being suspended
So, Payment each month of past bill = [tex]\frac{585}{3}=195[/tex]
My normal monthly bill is $50.00 per month.
So, I need to pay per month = $50+$195= $245
Thus ,I need to pay $245 per month .
A car is a vehicle with four wheels.
Rewrite the statement as a true conditional with a converse that is false.
Write a similar true conditional with a converse that is true
Identify the property used in the first 5 steps to solve the equation 2(x-5)-6x=-22
Answer choices:
Step 1: Associative, Commutative or Distributive Property
Step 2: Associative, Commutative or Distributive Property
Step 3: Addition or Multiplication Property of Equality
Step 4: Addition Property or Combine Like Terms
Step 5: Addition or Multiplication Property of Equality
Answer:
Distributive property
Step-by-step explanation:
What is the sum of 12 and the quantity 8 times a number k is equal to 48? It was on my math homework, it hardly makes any sence to me, please help me, whats the answer?
The question is asking for the solution to the algebraic problem 12 + 8k = 48. By isolating 'k', it is found that the value of 'k' is 4.5.
Explanation:The problem presented here belongs to the branch of algebra. It is showing a relationship between the sum, multiplication, and is presented in a typical algebraic equation format. Let's break it down:
The sum of 12 and a number (which is 8 times k) is equal to 48. This can be written in equation form as:
12 + 8k = 48
To find the value of k, we need to isolate 'k' in the equation. First, subtract 12 from both sides of the equation:
8k = 48 - 12
Then, simplify the right side:
8k = 36
Finally, divide both sides by 8 to solve for k:
k = 36 / 8
So, k = 4.5.
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