If the initial velocity is 75 feet per second, it will take approximately 5.125 seconds for the ball to hit the ground.
The given formula h= -16t²+vt+s represents the height (h) of an object thrown vertically in the air at time (t), with initial velocity (v) and initial height (s). In this case, we are given that the initial height of the softball is 4 feet and the initial velocity is 75 feet per second.
We want to find out how long it will take for the ball to hit the ground, which means we want to find the time (t) when the height (h) is 0.
Substituting the given values into the formula, we get:
0 = -16t² + 75t + 4
This is a quadratic equation in standard form, which we can solve using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
Where a=-16, b=75, and c=4. Substituting these values into the formula, we get:
t = (-75 ± √(75² - 4(-16)(4))) / 2(-16)
t = (-75 ± √(5625 + 256)) / (-32)
t = (-75 ± √(5881)) / (-32)
We can simplify the expression under the square root as follows:
√(5881) = √(49121) = 711 = 77
So we have:
t = (-75 ± 77) / (-32)
Simplifying further, we get two possible solutions:
t = 0.5 seconds or t = 5.125 seconds
Since the softball player hits the ball when it is 4 feet above the ground, we can disregard the solution t=0.5 seconds (which corresponds to when the ball is at its maximum height) and conclude that it will take approximately 5.125 seconds for the ball to hit the ground.
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Select the statement that best describes √ 1 5
The measure of dispersion that measures how much the data differ from the mean is called the.
The measure of dispersion that measures how much the data differ from the mean is called the standard deviation.
What is standard deviation?Standard deviation is a statistical measure of dispersion as opposed to the measure of central tendency like mean, median and mode.
The standard deviation is a measure of how spread out data values are around the mean.
It is defined as the square root of the variance and represented with the Greek letter σ.
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If you spend $50 (including shipping) at an online store, you recieve a $10 gift card. You want to purchase CDs that cost $12 each. If shipping cost $5, write and solve an inequality to find the number of Cds you must to receive the giftcard.
Four CDs must be bought to receive a gift card from an online store.
How to determine the least number of CDs to be bought to receive a gift card
The total costs are equal to the sum of the shipping cost and the total related to the number of acquired CDs (n). The number of gift cards (m) is equal to the total costs divided by minimum spent money, that is, $ 50. We need to solve the following inequation to find the minimum quantity of CDs:
(12 · n + 5)/50 > 1
12 · n + 5 > 50
12 · n > 45
n > 45/12
n > 3.75
Four CDs must be bought to receive a gift card from an online store.
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The function f(x) = 300(0.5)x/100 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after Round to the nearest whole number.
The amount of the radioactive material in the vault after 140 years is 210 pounds
How to determine the amountWe have that the function is given as a model;
f(x) = 300(0.5)x/100
Where
x = number of years of the vault = 140 yearsf(x) is the amount in poundsLet's substitute the value of 'x' in the model
f(x) = 300(0.5)x/100
[tex]f(x) = \frac{300(0.5) * 140}{100}[/tex]
[tex]f(x) =\frac{21000}{100}[/tex]
f(140) = 210 pounds
This mean that the function of 149 years would give an amount of 210 pounds rounded up to the nearest whole number.
Thus, the amount of the radioactive material in the vault after 140 years is 210 pounds
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Find the angle between the vectors.
U=< -4,-3>
V = < -1,5>
Step-by-step explanation:
The formula for the angle between vectors
[tex] \alpha = \cos {}^{ - 1} ( \frac{uv}{ |u| |v| } ) [/tex]
To multiply vectors, multiply the first component and multiply the second component and add them.
(-4*-1) + (-3*5)= 4-15=-11.
To find magnitude of vectors, use the Pythagorean theorem
[tex]u = \sqrt{ { - 4}^{2} + { - 3}^{2} } = 5[/tex]
[tex]v = \sqrt{ - 1 {}^{2} + 5 {}^{2} } = \sqrt{26} [/tex]
so
[tex] |u| |v| = 5 \sqrt{26} [/tex]
Know we have,
[tex] \alpha = \cos {}^{ - 1} ( \frac{7}{5 \sqrt{26} } ) [/tex]
[tex] \alpha = 105.94[/tex]
in degrees,
[tex] \alpha = 1.849[/tex]
in radians
Answer:
115.6° (1 d.p.)
Step-by-step explanation:
To find the angle between two vectors:
Create a triangle with the vectors as two sides and the included angle θ between them.Find the magnitude of each vector (the length of each side of the triangle).Use the cosine rule to find the angle θ.**Please see attached for the triangle diagram**
Given vectors:
[tex]\textbf{u}=-4\textbf{i}-3\textbf{j}[/tex]
[tex]\textbf{v}=-\textbf{i}+5\textbf{j}[/tex]
Use Pythagoras Theorem to find the magnitude of each vector:
[tex]\implies |\textbf{u}|=\sqrt{(-4)^2+(-3)^2}=5[/tex]
[tex]\implies |\textbf{v}|=\sqrt{(-1)^2+5^2}=\sqrt{26}[/tex]
[tex]\overrightarrow{\text{UV}}=\textbf{v}-\textbf{u}=(-\textbf{i}+5\textbf{j})-(-4\textbf{i}-3\textbf{j})=3\textbf{i}+8\textbf{j}[/tex]
[tex]|\overrightarrow{\text{UV}}|=\sqrt{3^2+8^2}=\sqrt{73}[/tex]
Cosine Rule (for finding angles)
[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where:
C = anglea and b = sides adjacent the anglec = side opposite the angleFind angle θ using the cosine rule:
[tex]\implies \cos(\theta)=\dfrac{|\textbf{u}|^2+|\textbf{v}|^2-|\overrightarrow{\text{UV}}|^2}{2|\textbf{u}||\textbf{v}|}[/tex]
[tex]\implies \cos(\theta)=\dfrac{5^2+\left(\sqrt{26}\right)^2-\left(\sqrt{73}\right)^2}{2(5)\left(\sqrt{26}\right)}[/tex]
[tex]\implies \cos(\theta)=\dfrac{-22}{10\sqrt{26}}[/tex]
[tex]\implies \theta=\cos^{-1}\left(\dfrac{-22}{10\sqrt{26}}\right)[/tex]
[tex]\implies \theta=115.5599652...^{\circ}[/tex]
Therefore, the angle between the vectors is 115.6° (1 d.p.).
Has a base of 3, is reflected over the y-axis, has a horizontal shift right by 5 and an asymptote of y=-3
The equation of the exponential function is [tex]y = 3^{-x -5} - 3[/tex]
How to determine the equation?An exponential equation is represented as:
y = b^x
Where b represents the base.
The base is 3.
So, we have:
[tex]y = 3^x[/tex]
When reflected over the y-axis, we have:
[tex]y = 3^{-x[/tex]
When shifted right by 5 units, we have:
[tex]y = 3^{-x -5[/tex]
Lastly, the function has an asymptote of y=-3
So, we have:
[tex]y = 3^{-x -5} - 3[/tex]
Hence, the equation of the exponential function is [tex]y = 3^{-x -5} - 3[/tex]
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The system of equations is graphed on the coordinate plane.
y=x−1
y=−2x−4
Enter the coordinates of the solution to the system of equations in the boxes.
Answer:
(-1,-2)
Step-by-step explanation:
Hello!
The solution to the system is at the intersection between the two graphed lines.
Remember that a coordinate is written in (x,y) format, so we take the x-value of the points and the y-value of the point.
The coordinate is (-1, -2).
Question about a rational expression
The equation is -9=6/v
In the explanation, it tells me to multiply v on both sides. My question is why do you multiply v on both sides and not 6?
When I did the problem I multiplied 6 on both sides and got -54=v, but apparently the answer is -2/3 so I’m confused as to why you multiply v on both sides and not 6.
Show the calculation to find the μ and σ of a binomial variable whose probability of success if 0.3 with a total number of attempts of 20.
Using the binomial distribution, we have that:
The mean is of [tex]\mu = 6[/tex].The standard deviation is of [tex]\sigma = 2.05[/tex].What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
[tex]\mu = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
For this problem, the parameters are:
n = 20, p = 0.3.
Hence:
[tex]\mu = np = 20 \times 0.3 = 6[/tex][tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20 \times 0.3 \times 0.7} = 2.05[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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Melissa is driving at a constant speed. She catches up to a minivan half a mile ahead of her that is
moving at 50 miles per hour in 50 seconds. How many miles per hour is the speed of the sports
car?
The speed of the sports car is 53.6 miles per hour
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Distance covered by Melissa = 0.5 miles + Distance covered by minivan
Let speed of Melissa be x miles per second
x. 50 = 0.5 + 50x50/3600
x .50 = 0.5 + 25/36
x = 1/100 + 1/72
x = 0.001 + 0.013
x = 0.014 miles per second
x = 3600 x 0.014 = 53.6 miles per hour
Thus the speed of the sports car is 53.6 miles per hour
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Solve the following systems of inequalities and select the correct graph: 2x − y > 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.
The solution to the system of inequalities is given as Graph II.
A group of two or more inequalities in one or more variables is referred to as a system of inequalities.
When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are utilized.
What is the calculation leading to the above solution?The system of inequality,
2x - y < 4
x + y < -1
First we draw the graph of both line. So make table of each line
For line 2x - y < 4
x : -1 0 1
y : -6 -4 -2
Test point (0,0)
0 - 0 < 4
0 < 4
True (Shade towards origin)
For line x + y < -1
x : -1 0 1
y : 0 -1 -2
Test point (0,0)
0 + 0 < -1
0 < -1
False (Shade away from origin)
Plot the points graph.
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Full Question:
The graphs associated with the question are attached.
The lengths of the sides of a pentagons are 2'', 6'', 10'' , 14'', and 24''. calculate the lengths of the sides of a similar pentagon if the shortest side is 5'' .
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"How to get the lengths of the sides of a similar pentagon?
All the measures must be multiplied by the same scale factor to get a similar pentagon.
If in the original pentagon the shortest side measures 2", and in the similar pentagon the shortest side measures 5", then we have:
5" = k*2"
5"/2" = k = 2.5
Then the scale factor is 2.5
To get the other sides of the pentagon, we just need to multiply the other sides of the original pentagon by 2.5
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"If you want to learn more about similar figures:
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Express the following function, F(x), as a composition of two functions, f and g:
Answer:
There are many different answers to this question but here is one that I thought of.
g(x)=x^2
f(x)=x/(x+4)
f(g(x))=F(x): plug in x^2 into each of the x in f(x) and and answer should equal F(x)
Step-by-step explanation:
since the function F(x) had 2 x^2 in it, I thought that g(x) could easily be x^2 that way u can subsitute the x in f(x) later to x^2 and get the right answer.
The rectangular part of the field shown below is 160 yd long and the diameter of each semicircle 12 yd. How much will it cost to fertilize the field at 0.25 per square yard? Use π = 3.14 and round to the nearest cent.
It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.
Given that the field is 160 yards long and the diameter is 12 yards and charge of 1 square yard of fertilizing is $0.25.
We are required to find the total cost of fertilizing the field.
The total cost of fertilizing the field will be the product of the cost of 1 square yards and the area of the field.
When we will observe the field carefully then we will say that the diameter of the semi circle is equal to the breadth of the rectangle. There are two semicircles so we have to just find the area of 1 circle and the area of 1 rectangle.
Area of the field=Area of rectangle+Area of circle
=length* breadth+π[tex]r^{2}[/tex]
=160*12+3.14*[tex]6^{2}[/tex]
=1920+3.14*36
=1920+113.04
=2033.04 [tex]yards^{2}[/tex]
Cost of fertilzing the field=2033.04*0.25
=$508.26
Hence It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.
Question is incomplete as the figure which is attached should be included.
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if x+y=7/10 and x-y=5/14 then x^2-y^2=?
Add both
2x=1x=1/2=0.5Put in first one
y=0.7-0.5y=0.2Find
x²+y²(0.5)²+(0.2)²0.25+0.040.29At a cost of R55 per box how much would it cost to tile the training room
The total cost needed to tile the training room with an area of 100 m² is R110.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let assume that the area of the trainig room is 100 m² and one box can complete 50 m², hence:
number of box needed = 100 m² / 50 m² = 2
Total cost = R55 per box * 2 box = R110
The total cost needed to tile the training room with an area of 100 m² is R110.
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he graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units
We conclude that the graph of f(x) is the graph of g(x) translated 3 units upwards.
How do relate the graphs of f(x) and g(x)?Here we have the functions:
[tex]f(x) = log(x) + 3\\\\g(x) = log(x)[/tex]
And we want to find a relation between them.
Remember that a vertical translation of N units (the sign of N defines the direction of the translation) is written as:
[tex]f(x) = g(x) + N[/tex]
In this case, we can see that N = 3, it is positive, so the translation is upwards. (This means that the whole graph of the function f(x) is translated upwards 3 units in the coordinate axis)
Then we conclude that the relation between the graphs of the given functions is that the graph of f(x) is the graph of g(x) translated 3 units upwards.
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Which table shows a linear function?
The first table with the following values of x and y, shows a linear function.
x = -4, y = 8
x = -1, y = 2
x = 1, y = 2
x = 2, y = 4
x = 3, y = 6
Definition of a Linear Function:
A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
For the above chosen option, the value of y corresponding to a value of x is twice that of its x value. This linear function can be represented as follows,
y = | 2x | .......... (1)
In this linear function, mod represents, that y is always maintained positive. Besides, the value of y is always twice that of the x. Hence, the linear function can also be written as, y ± 2x = 0.
Since, equation (1) is of the form, y = mx + c, it produces a straight line. Here, m = 2 and c = 0. Thus, it is a linear function.
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$274 for 40 hours of work as a unit rate
Answer:
6.85 units per hourStep-by-step explanation:
$274 for 40 hours of work as a unit rate
in practice you look for the hourly wage, you find it by dividing the wages divided by the working hours
274 : 40 = 6.85 units per hour
what are the restricted values for??
Considering the domain of the function, it is restricted for:
B. [tex]x \neq -3, x \neq -2, x \neq 0[/tex].
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function.
A fraction cannot have a denominator of zero, hence:
[tex]4x^2 - 12x \neq 0[/tex].[tex]-x^2 + 5x - 6 \neq 0[/tex].We solve these two inequalities to find the restrictions, hence:
[tex]4x^2 - 12x \neq 0[/tex]
[tex]4x(x - 3) \neq 0[/tex]
[tex]4x \neq 0 \rightarrow x \neq 0[/tex]
[tex]x - 3 \neq 0 \rightarrow x \neq 3[/tex].
[tex]-x^2 + 5x - 6 \neq 0[/tex].
[tex]x^2 - 5x + 6 \neq 0[/tex]
[tex](x - 3)(x - 2) \neq 0[/tex]
[tex]x - 2 \neq 0 \rightarrow x \neq 2[/tex].
[tex]x - 3 \neq 0 \rightarrow x \neq 3[/tex].
Hence the correct option is:
B. [tex]x \neq -3, x \neq -2, x \neq 0[/tex].
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Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''. Which of the following statements is true for ΔABC and ΔA''B''C''?
Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''.
Hence:
Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.
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What is the probability of flipping a coin once and getting heads if you have gotten 5 tails in a row before that?
a. 1/32
b. 1/5
c. 1/4
d. 1/2
Answer:
Answer is..... D
Step-by-step explanation:
every single flipping may two results, head or tail.So last one has equal chance.
Marco has joined a bowling league, and is trying to raise his average to 130. On his last four games he scored 128, 127, 123, and 122. How much will he need to score on the next game to raise his mean to 130?
The score Macro needs in his next game to have a mean of 130 is 150.
What should be the next score?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
130 = (128 + 127 + 123 + 122 + x) / 5
Where x represents the fifth score
130 = (500 + x) / 5
130 x 5 = 500 + x
650 = 500 + x
650 - 500 = x
x = 150
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will give brainliest !!!!
Finding the inverse function of [tex]f(x) = 5\sqrt{x + 3} - 2[/tex], it is best described by graph B.
How to find the inverse of a function?Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.
In this problem, the function is:
[tex]f(x) = 5\sqrt{x + 3} - 2[/tex]
[tex]y = 5\sqrt{x + 3} - 2[/tex]
Exchanging x and y:
[tex]x = 5\sqrt{y + 3} - 2[/tex]
Working through the function to isolate y:
[tex]5\sqrt{y + 3} = x + 2[/tex]
[tex]\sqrt{y + 3} = \frac{x + 2}{5}[/tex]
[tex](\sqrt{y + 3})^2 = \left(\frac{x + 2}{5}\right)^2[/tex]
[tex]y + 3 = \frac{(x + 2)^2}{25}[/tex]
[tex]y = \frac{(x + 2)^2}{25} - 3[/tex]
[tex]f^{-1}(x) = \frac{(x + 2)^2}{25} - 3[/tex]
Which is best represented by graph B.
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Hurry please help!!!!
Determine which statement is true about the zeros of the function graphed below.
An upward parabola f on a coordinate plane vertex at (1, 4) and intercepts the y-axis at 5 units.
A.
Function f has exactly two complex solutions.
B.
Function f has exactly one real solution and no complex solutions.
C.
Function f has exactly two real solutions.
D.
Function f has one real solution and one complex solution.
Answer:
A. Function f has exactly two complex solutions.
Step-by-step explanation:
The function will have real solutions where the graph crosses the x-axis. It will always have a total number of solutions equal to its degree. The ones that are not real are complex.
ApplicationThe graph has its vertex above the x-axis and extends upward from there. It never crosses the x-axis, so there are no real solutions. That means both solutions are complex.
Rational expressions are often used in combining rates of work.
Rational expressions are often used in combining rates of work. Therefore, it's true.
What is rational expression?It should be noted that a rational expression is simply defined by a rational fraction.
They're are used in combining rates of work. Fir example, if Mr John performs 1/2 of his work and does 1/3 on another day. This can be expressed as:
= 1/2 + 1/3
= 5/6
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What is the length of BC?
Answer:
75/4
Step-by-step explanation:
Assuming BA and ED are parallel, we know thay the two triangles are similar.
So,
[tex]\frac{25-x}{x}=\frac{36}{12} \\ \\ \frac{25-x}{x}=3 \\ \\ 25-x=3x \\ \\ 4x=25 \\ \\ x=\frac{25}{4} \\ \\ BD=25-\frac{25}{4}=\frac{75}{4}[/tex]
Q.3. Set up the equations and solve them to find the unknown numbers in the cases given below:
1) If you add 6 to five times a number, it gives 46.
2) Two-third of a number minus 5 gives 11.
3) If you take onethird of a number and add 4 to it, gives 45.
4) When person X subtracts 12 from thrice of a number, it gives 18.
5) When Jenny subtracts twice the number of pens, she has from 40, she gets 16.
6) Virat guesses a number. If he adds 18 to that number and then divides the sum by 6, he gets answer 7.
7) Ami guesses anumber. If she subtracts 8 from two third of a number, she gets 6
I want Answer quickly
The following expressions set up as an equation to solve for the unknown numbers in the cases given below:
Algebraic equationlet
The unknown number = x5x + 6 = 46
5x = 46 - 6
5x = 40
x = 40/5
x = 8
2/3x - 5 = 11
2/3x = 11 + 5
2/3x = 16
x = 16 ÷ 2/3
x = 16 × 3/2
x = 48/2
x = 24
1/3x + 4 = 45
1/3x = 45 - 4
1/3x = 41
x = 41 ÷ 1/3
x = 41 × 3/1
x = 123
3x - 12 = 18
3x = 18 + 12
3x = 30
x = 30/3
x = 10
40 - 2x = 16
-2x = 16 - 40
-2x = -24
x = -24/-2
x = 12
(x + 18) / 6 = 7
(x + 18) = 7 × 6
x + 18 = 42
x = 42 - 18
x = 24
2/3x - 8 = 6
2/3x = 6 + 8
2/3x = 14
x = 14 ÷ 2/3
x = 14 × 3/2
= 42/2
x = 21
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You are training to compete in a 10-kilometer race, and you know the circular running trail at your park is one mile long. How many times will you need to run this trail in order to run 10 kilometers?
So to run 10km, you need to run 6.25 times the trail. (Or 7 if you only accept whole numbers as answers, we need to round up).
How many times will you need to run this trail in order to run 10 kilometers?If you run the trail x times, then you will run:
y = x*1mi
Now remember that:
1 mi = 1.6 km
Replacing that, we get the linear equation:
y = x*1.6km
Now we want to find the value of x such that:
x*1.6km = 10km
Dividing both sides by 1.6km
x = 10km/1.6km = 6.25
So to run 10km, you need to run 6.25 times the trail. (Or 7 if you only accept whole numbers as answers, we need to round up).
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Solve for x.
A) 6
B) 4
C) 5
D) 7
Answer:
c
Step-by-step explanation:
Aight, let's hop to it:
So we got
[tex] \frac{5x}{45} = \frac{20}{36} = = > \\ \frac{x}{9} = \frac{5}{9} = = > \\ x = 5[/tex]
and boom