Actual miles is [tex]\frac{2492}{13}[/tex]
According to the question,
Given that,
Map is 5.6 ft
scale of Map is 2.6 ft which is equal to 89 miles
Actual miles = [tex]\frac{5.6 * 89}{2.6}[/tex]
= [tex]\frac{498.4}{2.6}[/tex]
multiply both the numerator and denominator with the same integer
= [tex]\frac{4984}{26}[/tex]
= [tex]\frac{2492}{13}[/tex]
Actual miles is [tex]191\frac{9}{13}[/tex] ≈ 1.916923 ×[tex]10^{2}[/tex]
Definition of miles per hour unit: ≡ 1 mi / 3600 s = 1609.344 m / 3600 s. In American public life, this is the most commonly used speed unit. Cars speeds are measured in mpg. Interpretation: The speed at which the body moves 1 mile (or 1609.344 metres) in 1 hour.
Definition of feet per second unit: ≡ 1 ft / 1 s = 30.48 cm / 1 s. Abbreviation is fps. In America, perhaps this is the second most commonly used speed unit in public life (after miles per hour). Definition: The speed at which the body moves 1 foot (or 30.48 centimetres) in 1 second.
Convert Miles to Feet
Multiply your speed in miles per hour by 5,280. This is the number of feet in a mile. The result is your speed in feet per hour. For example, 60 miles per hour times 5,280 feet per mile is 316,800 feet per hour.
Convert to Feet per Minute
Divide your speed in feet per hour by 60. This is the number of minutes in an hour. Therefore, the result is your speed in feet per minute. For example, 316,800 feet per hour divided by 60 minutes per hour is 5,280 feet per minute.
Convert to Feet per Second
Divide your speed in feet per minute by 60. This is the number of seconds in a minute. Therefore, the result is your speed in feet per second. For example, 5,280 feet per minute divided by 60 seconds in a minute equals 88 feet per second.
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Duo makes 65 percent of his dumplings with vegetarian fillings.
What fraction of Duo's dumplings have vegetarian fillings?
The fraction 13/20 of Duo's dumplings have vegetarian fillings.
What is fraction?
A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
Duo makes 65 percent of his dumplings with vegetarian fillings.
According to given question we have
A percentage is a number or ratio expressed as a fraction of 100.
65 percent
=65 %
=65/100
Simplify fraction into simpler fraction,
⇒13/20
Therefore, the fraction 13/20 of Duo's dumplings have vegetarian fillings.
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The vertices of a quadrilateral are A(−5, 3), B(2, 2), C(4,−3), and D(−2,−2). Find the slope of each side.
The sole of AB = 1/7, BC = -5/2, CD= -1/6, DA= -5/3
Here we have to find the slope of the side of the quadrilateral
The formula of the slope between A(x1, y1), B (x2, y2)
slope = (y2 - y1)/( x2- x1)
Slope of AB , where A = (-5, 3), B = (2,2)
AB = (2-3)/ ( 3- (-5))
= 1/ 8
Slope of BC, where B= (2,2 ), C = (4, -3)
BC = (-3 -2)/ (4-2)
= -5/2
Slope of CD, where C= (4,-3), D=(-2,-2)
CD = (-2-(-3))/ (-2-4)
= 1/ (-6)
=-1/6
Slope of DA , where D=(-2,-2), A=(-5,3)
DA= (3-(-2))/(-5-(-2))
= (3+2)/(-5+2)
= 5/-3
=-5/3
Therefore the slope of AB, BC, CD, DA = 1/7, -5/2, -1/6, -5/3 respectively.
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i need help with this
Answer:of not
Step-by-step explanation: ops
Forty two billion, three hundred and seven million, one hundred and Two thousand, three hundred and fourteen in number. Please help me
Answer:
42,307,0102,014 is the number form
I need this answered please
Answer: 1. x-8
2. x/8
3. x squared
4. 4x
When they say "a number" that just means "x".
Christopher is the oldest of three siblings whose ages are consecutive odd integers. If the sum of their ages is 6363, find Christopher's age.
Christopher's age given the sum of the ages of the three siblings is 23.
What is Christopher's age?An odd number is a number that is not perfectly divisible by 2. An odd number can be a positive number or a negative number. An example of an odd number is 3 and 7.
Consecutive odd integers are odd integers that follow each other on the number line. Consecutive odd integers increase by a value of (x + 2). Examples of consecutive odd integers are 11, 13, 15.
Let x represent the youngest sibling's age
Second sibling's age : x + 2
Christopher's age : x + 4
x + x + 2 + x + 4 = 63
3x + 6 = 63
3x = 63 - 6
3x = 57
x = 57 / 3
x = 19
Christopher's age : x + 4 : 19 + 4 = 23
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Given the expression -7x -1/6y +2z - xy+28 answer the questions below
A. how many terms are there? How did u find them
B. how many different variables are there list all of them.
C. what is the coefficient of the 4th term.
Answer:
A. 5 || how? uh counting; -7x -1/6y +2z -xy +28
B. 3 (2;x | 2;y | 1;z)
C. 28
Hope this helps!
--Blu
What is the value of x+26
The value of x can not be told as there is no answer to the question "x+26".
Hence, can not be solved and it is left as 'x+26'
i need help on this 4−d<4+d
For all the values of 'd' the expression 4-d will be less than 4+d.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given that 4−d < 4+d. The inequality expression will be solved as:-
4−d < 4+d
4 - 1 < 4 + 1
3 < 5
4 - 2 < 4 + 2
2 < 6
It is concluded that for all the values of d in the given expression the portion 4 - d will be less than 4 + d.
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2x² + 5x-11
+3x² -11x +2
please solve thankyou!!
Answer:
5x^2 - 6x -9
Step-by-step explanation:
A recipe requires 3/4 cups if milk.Paula is making 1/2 of the recipe .How many cups of Milk will Paula use?
The answer to this question is:
No. of cups of milk will Paula use = 3/8
Given that recipe requires 3/4 cups of milk.
Paula is making half (1/2) of the recipe.
And we are asked to find that No. of cups of milk will Paula use.
To solve this question, we have to multiply the quantity of milk required by the quantity she is going to make.
The quantity of milk required * the quantity she is going to make
= 3/4 * 1/2
= 3/8
Therefore, No. of cups of milk will Paula use = 3/8
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an oil tank is being filled at a constant rate of .2 feet per minute. After 15 minutes the tank is 6 feet deep. Write an equation that can be used to determine the amount of oil in the tank at any time.
The equation that represent amount of oil in the tank at x minutes is
6- 0.2t
What is an equation?A mathematical statement that shows that two mathematical expressions are equal.
Given:
rate of filling the tank = 0.2 feet/ minute
After 15 minutes,
height = 6 feet
let the time take be x minutes
So, the equation that represent amount of oil in the tank at x minutes.
=6- 0.2t
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Work out ( 3 × 10 − 3 ) − ( 6 × 10 − 5 ) Give your answer in standard form.
Answer:
-28
Step-by-step explanation:
Simplify those in parenthesis first.
( 30 - 3) - (60 - 5)
27 - 55
= -28
Find the inverse of each function.
y=log (x-6)
The inverse of the function y = log(x ₋ 6) is y = 10ˣ + 6.
Given the function is :y = log₁₀ (x ₋ 6)
we are asked to find the inverse of the function.
steps to find inverse function are:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.
Here, find y and solve for x = ay + b.
Then we get :
y = (x - b/a).
Finally, we can substitute y = f⁻¹(x) with f⁻¹(x) = (x - b)/a.
now interchange the positions of x and y in the function.x = log₁₀(y ₋ 6)
the next step is to isolate the dependent variables.
y = 10ˣ + 6
hence we get the inverse of the function y = log₁₀ (x ₋ 6) as y = 10ˣ + 6.
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Solve each equation.
ln (x+2)- ln 4=3
After solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].
What exactly is an equation?An equation is a mathematical statement made up of two expressions joined by an equal sign.An example of an equation is 3x - 5 = 16.After solving this equation, we obtain the value of the variable x as x = 7.So,
Given equation: ln(x+2)-ln4=3Then,
ln(x+2)-ln4 = 3log(e)(x+2)-In4 = 3log(e)(x+2)-4In = 3[tex]x=e^{4 \ln +3}-2[/tex]Therefore, after solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].
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Solve each equation for θ with 0 ≤ θ <2 π.
cotθ=-10
Answer:
0 with 0 2 pi cot0=-10 am not sure what It is
Find the midpoint of the segment with the following endpoints.
(9, 6) and (5, 2)
The midpoint of the segment is (7, 4).
According to the section formula-
If a point (x , y) divides a line in the ratio of m : n, where the two endpoints of the line are (x1, y1) and (x2, y2), then-
x = (nx1 + mx2)/ (m + n)
and y = (ny1 + my2)/ (m + n)
Here, we are given two points- (9, 6) and (5, 2)
Therefore,
x1 = 9, y1 = 6
x2 = 5, y2 = 2
Since, midpoint divides a line segment into two equal halves, m : n = 1 : 1
Now, substituting the values in the section formula we get-
x = (9 + 5)/2
x = 14/2
x = 7
and y = (6 + 2)/2
y = 8/2
y = 4
Thus, the midpoint of the segment is (7, 4).
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Alice, Billy, and Anna are spending the weekend baking cookies for
winter holiday gifts. For each batch of cookies, they’ll need 21
/2 cups of
flour and 11
/4 cups of butter. Each person contributed supplies from
their mothers’ kitchens and met at Anna’s house.
The fraction that Alice, Billy, and Anna should bring when they are spending the weekend baking cookies for winter holiday is 11/12 cups.
How to calculate the value?It should be noted that based on the information, for each batch of cookies, they’ll need 2 1/2 cups of flour and 1 1/4 cups of butter.
In this case, it should be noted that there are 3 people.
The fraction will be:
= (2 1/2 + 1 1/4) / 3
= 3 3/4 ÷ 3
= 11/12
Therefore, the fraction will be 11/12 cups for each person.
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Alice, Billy, and Anna are spending the weekend baking cookies for.winter holiday gifts. For each batch of cookies, they’ll need 2 1/2 cups of flour and 1 1/4 cups of butter. Each person contributed supplies from their mothers’ kitchens and met at Anna’s house. What fraction should each person bring?
Steve is going to prom with a group of friends. steve's group of friends decide to rent a limo. a local company is willing to rent a limo for $130 an hour. the limo can hold up to six people. steve and his five friends decide to split the cost of the limo evenly. if they rent the limo for four hours, how much will steve and his friends expect to pay? (round up to the nearest dollar amount)
$ 86.67 , Steve and his five friends has to pay $86.67 each to rent limo for four hours.
According to the question,
rent of limo for five hours = $130
now by multiplication ,
rent of limo for four hours = $130 * 4
= $520
now we know that there are six people including Steve hence we divide this $520 by 6 to get the share of each individual,
by division ,
hence the amount for each = $520 / 6
= 86.666666
amount round up to the nearest dollar is $86.67
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Translate each of the following verbal descriptions into an algebraic rule.The total cost of the order, t, is 11 dollars multiplied by the number of pizzas ordered, p.
The algebraic expression which correctly represents the verbal description; The total cost of the order, t, is 11 dollars multiplied by the number of pizzas ordered, p is; t = 11p.
Which algebraic expression correctly represents the verbal description as in the task content?It follows from the task content that the expression which correctly represents the verbal description be determined.
On this note, since total cost is; t and the number of pizzas ordered is; p.
The required expression is therefore;
t = 11 × p
t = 11p.
Ultimately, the verbal representation of the algebraic expression where total cost of the order, t, is 11 dollars and number of pizzas ordered, is p is given by t = 11p.
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I would really appreciate some help. I am confused with this problem..it says Solve for
Find all solutions to 8x³-10x² - 21x + 18 = 0 if x= 2 is one solution.
According to the given cubic equation 8x³-10x² - 21x + 18 = 0 the other value of x will be 4.
How does one solve a three-degree equation?Traditionally, a cubic problem can be solved by converting it to a quadratic equation and then solving it using factoring or the quadratic formula. A cubic equation, like a quadratic equation, has three roots.
What is the simplest method for solving a cubic equation?The typical strategy for solving a cubic problem is to convert it to a quadratic equation and then solve the quadratic using the standard methods, either factoring or using the formula. All of them are cubic equations. A cubic equation, like a quadratic equation, may have two or three real roots.
According to the given data:8x³-10x² - 21x + 18 = 0
x= 2
substituting the value in the equation we get:
8x³-10x² - 21x + 18 = 0
8(2)³-10(2)² - 21(2) + 18 = 0
68 - 40 - 42 + 18 = 0
4 = 0
According to the given equation 8x³-10x² - 21x + 18 = 0 the other value of x will be 4.
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Please help with problem 8
Answer:
The correct answer is A.
Find the average rate of change for the following functions over the interval.
Given the function and interval, the average rate of change of the function over the given interval is 1.
What is the average rate of change of the function over the given interval?The average rate of change of a function is calculated by dividing the change in y-values over the change in x-values of the two point.
r = ( f(1) - f(0) / ( (1) - (0) )
Given the data in the question;
f(x) = 2x² - x - 2
Intervals: [0, 1]
Plug the given values into the average rate of change formula and simplify.
r = ( f(1) - f(0) / ( (1) - (0) )
r = ( (2(1)² - (1) - 2) - ( 2(0)² - (0) - 2 )) / ( (1) - (0) )
r = ( (2 - 1 - 2) - ( 0 - 0 - 2 )) / 1 -0
r = ( (-1) - (-2 )) / 1r = ( -1 - (-2 ) / 1
r = ( -1 + 2 ) / 1
r = 1/1
r = 1
Therefore, the average rate of change of the function over the given interval is 1.
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The average rate of change of the function f(x) = 2x² - x - 2 over the intervals of 0 to 1 is 1.
What is the average rate of change of the function over the given interval?The average rate of change of a function is calculated by dividing the change in y-values over the change in x-values of the two point.
AVR = ( f(1) - f(0) / ( (1) - (0) )
Given the data in the question;
f(x) = 2x² - x - 2Intervals: [0, 1]Plug the given values into the average rate of change formula and simplify.
r = ( f(1) - f(0) / ( (1) - (0) )
r = ( (2(1)² - (1) - 2) - ( 2(0)² - (0) - 2 )) / ( (1) - (0) )
r = ( (2 - 1 - 2) - ( 0 - 0 - 2 )) / 1 -0
r = ( (-1) - (-2 )) / 1
r = ( -1 - (-2 ) / 1
r = ( -1 + 2 ) / 1
r = 1/1
r = 1
The average rate of change of the function f(x) = 2x² - x - 2 over the intervals of 0 to 1 is 1.
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9)
Find the length of
the hypotenuse of
the right triangle.
6 ft
6 ft
The hypotenuse of the right triangle is found to be 6√2 ft.
What is defined as the Pythagorean theorem?A right triangle contains a single 90 angle within it, which is known as a right angle.The hypotenuse is really the side straight from the right angle in a right triangle. It is the only side of a triangle that does not form a right angle.The Pythagorean Theorem describes the relationship between the sides of a right triangle, where c represents the hypotenuse and a and b represent the sides that form the right angle.The formula is as follows:
H² = B² + P²
where, H is the hypotenuse.
B is the base
P is the perpendicular.
In the given question, hypotenuse is to be calculated.
Lets, base B = 6 ft and
Perpendicular P = 6 ft.
Thus, put the values in the formula;
H² = 6² + 6²
H² = 2×6²
Taking square root on both sides.
H = 6√2
Thus, the value of the hypotenuse if the right angled triangle is found as 6√2 ft.
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What is the slope of a line perpendicular to the line whose equation is 3x+y=8. Fully simplify your answer.
(-3 1/3 n +1/6) + (1 3/6n - 3/12 )
- 2/6n-1/12
-29/6 n + 1/12
-11/6n - 1/12
- 11/6n+5/12
(-3 1/4d +3/5) -2 7/8 d +7 /10
Answer:
[tex]\frac{4080n+1585d-188}{240}[/tex]
Step-by-step explanation:
I simplified it to the best possible state
Simplify each radical expression. Use absolute value symbols when needed. 4√16 x¹²
The simplified value of radical expression 4√16 x¹² is 2x^3.
By considering the given expression
4√16 x¹²
=(16x^12)^1/4
=(2^4)^1/4( x^12)^1/4
=2x^3.
An expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.
The 'V'-shaped portion of the radical symbol will have a superscript number when it is used to represent any root other than a square root. For instance, the expression 3(8) denotes the cube root of 8.
The radical symbol, which resembles a check mark, the index, a small number written outside the radical symbol, and the radicand, a quantity written beneath the horizontal bar of the radical symbol, are the three main components of the radical expression ab.
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Scarlett made a scaled copy of the following quadrilateral. She used a scale factor greater than 1.
A
B
C
D
What could be the length of the side that corresponds with AD on the scaled copy of the
quadrilateral?
Answer:
Step-by-step explanation:
First of all AD is 9 units long. Anything less than or equal to 9 is not an answer because the scale factor is greater than 1. That means that anything over 9 will work.
So the answer must be 12 or 15 from those answers given.
Factor each expression.
x²+x-6
After solving, the factors of equation x²+x-6 are:
(x-2) and (x+3)What is an equation, clearly?A mathematical statement made up of two characterizations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We get the value for the variable x as x = 7 after solving this equation.So,
Given the equation: x²+x-6
Then,
x²+x-6x²+x( - )-6x²+x(3-2)-6x²+3x-2x-6x(x+3)-2(x+3)Factors are: (x+3) and (x-2)
Therefore, after solving, the factors of equation x²+x-6 are:
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