The speed of the faster cyclist is 30 mph.
Two cyclists, distance = 90 miles.
let the speed of one cyclist is = x and
let the speed of the other cyclist = 2x
time after which both the cyclists will meet = 3 hours.
Since they are travelling towards each other the effective speed = 2x ₊ x
= 3x
we know that time = distance/speed
3 = 90/3x
3x = 30
x = 10 mph speed of one cyclist.
speed of the other cyclist will be 3x = 3 × 10 = 30 mph
The speed of the fastest cyclist is 30 mph.
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use the point and the slope to graph each line. Write the equation of each line. The line contains point (2,-2) and is perpendicular to a line with slope "-1"
Answer:
y = x - 4
Step-by-Step Explanation:
Perpendicular lines have slopes that are negative reciprocals—multiplying their slopes result in -1.Given the slope of a line m = -1, then it means that the slope of the other line must be 1 (because multiplying the slope of line 1 (m1 = -1), and the slope of the other line (m2 = 1) results in: -1 × 1 = -1).Therefore, given the slope of line 2 (m2 = 1), and the point (2, -2), we could plug these values into the slope-intercept form and solve for the y-intercept (b):y = mx + b-2 = 1(2) + b-2 = 2 + bSubtract 2 from both sides to solve for b:-2 - 2 = 2 - 2 + b-4 = bTherefore, the y-intercept (b) = -4.Hence, the equation of the perpendicular line is: y = x - 4
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Given the function ()=−4‾‾‾‾‾‾√,
g
(
m
)
=
m
−
4
,
evaluate
The required solution is 1(one) as per the given functions.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the sphere of the function and the set Y is called the codomain of the function. Functions were firstly the idealization of how a varying volume depends on another volume, an expression, rule, or law that defines a relationship between one variable( the independent variable) and another variable( the dependent variable). Functions were firstly the idealization of how a varying volume depends on another volume. For illustration, the position of the earth is a function of time.Every function has a(one) domain and codomain or range. A function is generally(ax) denoted by f(x) where x(ax) is the input
Given :
The function(one)
g(m)= m-4(four).
By put m is equal to 5(five) we get,
g(5)=5-4(four)
=1(one)
Hence, the required solution is 1(one) as per the given functions.
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How long would it take for a ball dropped from the top of a 121-foot building to hit the ground? Round your answer to two decimal places.
I don't need to know the actual answer, I'm just not sure what to plug in where into this formula: h=-½gt^2 +v0t+h0
The time that it will take the ball to hit the ground in 4 seconds.
How to solve equation of motion?To solve this problem you need the function;
h(t) = -16t² + v₀t + h₀
where;
t = time
v₀ is the initial velocity, which in our case is 0
h₀ is initial height, which in our case is 121 ft
h(t) = 0 since we want to know when the ball will hit the ground.
Thus;
0 = -16t² + 121
And we can solve for t;
If we rearrange the terms we see that this is a difference of 2 squares
0 = 121 - 16t²
0 = (11 - 4t)(11 + 4t)
Setting each factor = 0 gives;
11 - 4t = 0 11 + 4t = 0
t = 11/4 or t = -11/44
The second solution is discarded as time cannot be negative.
Thus, the ball will hit the ground in 4 seconds.
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(a) Use the iteration formula +1=10-2x, to find the values of X₁, X2 and xs
Start with Xo = 2
The value for the given question is x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.
Given iteration formula as xₙ ₊ ₁ = ∛ 10 - 2xₙ
Given x₀ = 2
We have to find the values of x₁, x₂, and x₃ as
For finding the value of x₁ we need to substitute n = 0 as
xₙ ₊ ₁ = ∛ 10 - 2xₙ
x₀ ₊ ₁ = ∛ 10 - 2x₀
x₁ = ∛ 10 - 2(2) (∵ x₀ = 2)
x₁ = ∛ 10 - 4
x₁ = ∛ 6
x₁ = 1.8
For finding the value of x₂ we need to substitute n = 1 as
xₙ ₊ ₁ = ∛ 10 - 2xₙ
x₁ ₊ ₁ = ∛ 10 - 2x₁
x₂ = ∛ 10 - 2(1.8) (∵ x₁ = 1.8)
x₂ = ∛ 10 - 3.6
x₂ = ∛ 6.4
x₂ = 1.85
For finding the value of x₃ we need to substitute n = 2 as
x₂ ₊ ₁ = ∛ 10 - 2xₙ
x₂ ₊ ₁ = ∛ 10 - 2x₂
x₃ = ∛ 10 - 2(1.85) (∵ x₀ = 1.85)
x₃ = ∛ 10 - 3.7
x₃ = ∛ 6.3
x₃ = 1.846
Therefore, the value of x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.
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reflection across y = -1
Please I need help ASP I will mark you brainless please
Answer:
See picture below.
Step-by-step explanation:
Evaluate h(r) given that h(t) = 6 - 18t. h(r) =
This problem is related to the formation of a function. We need to know how an function is formed. Here it is given that there is a function which is affected by the value of t. Which means the value of t in the function decides the value of that function.
Similarly we have to write the function as the variable r so that the value of function is related to the value of r.
h(r)=6-18r ; where 6 is the constant and 18r is the variable in the function.
Hence, the required function is h(r)=6-18r.
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If you only have a 1/3 measuring cup and a recipe calls for 12 2/3 cups of flour, how many 1/3 cups would you need to use? 1/3 * t th cups
====================================================
Explanation:
Imagine drawing a circle and splitting it into 3 equal slices. Repeat this process to get 12 identical such circles. We have 12*3 = 36 slices so far.
Then add a 13th circle that has 2 of the 3 slices shaded, to represent 2/3. So we add 2 extra slices to the 36 original to get 36+2 = 38 total slices.
Each slice represents 1/3 of a cup. So each full circle represents 1 full cup.
-------------
Another approach:
Let's convert the mixed number 12 & 2/3 into an improper fraction
We use the formula
a & b/c = (a*c+b)/c
So,
12 & 2/3 = (12*3+2)/3 = (36+2)/3 = 38/3
Then rewrite the 38/3 as 38*(1/3) to show we have 38 copies of the 1/3 cup.
Answer: 38 cups
Step-by-step explanation:
We will divide 12 2/3 cups by our measurement, 1/3 cup, to find how many 1/3 cups will be needed.
(12 + 2/3) / (1/3) = 38 cups
Suppose that the x-intercepts of the graph of y = f(x) are -5 and 3. . a) What are the x-intercepts of the graph of y = 7f(x)?
Answer:
[tex](-5)[/tex] and [tex]3[/tex].
Step-by-step explanation:
The [tex]x[/tex]-intercepts of a graph refer to points where the graph intersects the [tex]x\![/tex]-axis. These are [tex]x\!\![/tex] values for which [tex]f(x) = 0[/tex].
For example, since [tex]x = (-5)[/tex] is one of the [tex]x[/tex]-intercepts of [tex]y = f(x)[/tex], it must be true that [tex]f(-5) = 0[/tex]. Likewise, since [tex]3[/tex] is one of the [tex]x[/tex]-intercepts of [tex]y = f(x)\![/tex], [tex]f(3) = 0[/tex].
Since [tex]f(-5) = 0[/tex], the expression [tex]7\, f(-5)[/tex] would also evaluate to [tex]0[/tex] (that is, [tex]7\, f(-5) = (7)\, (0) = 0[/tex].) Thus, [tex]x = (-5)[/tex] would be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex].
Likewise, since [tex]f(3) = 0[/tex], [tex]7\, f(3) = (7)\, (0) = 0[/tex], such that [tex]x = 3[/tex] would also be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex].
No other points could be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex] without being an [tex]x\![/tex]-intercept of [tex]y = f(x)[/tex]. For example, assume that [tex]x = x_{0}[/tex] is an [tex]x[/tex]-intercept of [tex]y = 7\, f(x)[/tex] but not [tex]y = f(x)[/tex]. [tex]7\, f(x_{0}) = 0[/tex], such that [tex]f(x_{0}) = (1/7)\, (7\, f(x_{0})) = (1/7)\, (0) = 0[/tex]- contradiction.
Therefore, the [tex]x[/tex]-intercepts of the new graph would be [tex]x = (-5)[/tex] and [tex]x = 3[/tex].
Solve the following system of equations using either Gaussian elimination or a
matrix. Write your answer as a point and explain how you would check your work:
2x-y + 4z = 33
x + 2y-3z = -26
-5x - 3y + 5z = 23
Using Gaussian elimination, the solution to the given system of equations is given as follows:
x = 5, y = -11, z = 3.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are x, y and z, and the system is given as follows:
2x - y + 4z = 33.x + 2y - 3z = -26.-5x - 3y + 5z = 23.There are multiple ways in which a system can be solved, and for this one, Gaussian elimination will be used.
The first step is writing the augmented matrix of the system, as follows:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]
Then, the first column, which is equivalent to be coefficient of y, has to be of zero on the second and on the third row, hence:
R2 -> 2R2 - R1.R3 -> 5R1 + 2R3.The updated matrix will be given by:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]
Then, the second column, equivalent to the coefficient of y, on the third row has to be zero, hence:
R3 -> 11R2 + 5R3.
Then the matrix is:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]
From each row of the system, from bottom up, we find the variables, as follows:
40z = 120
z = 120/40
z = 3.
5y - 10z = -85
5y - 30 = -85
5y = -55
y = -11.
2x - y + 4z = 33
2x + 11 + 12 = 33
2x = 10
x = 5.
Hence the solution for the system is:
x = 5, y = -11, z = 3.
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The ratio of saving to spending is 9:4 how does she spend and how mush does she save
She will spend £250 and save £400.
Ratio is an expression that indicates how many times one quantity is more than the other.
Here, we are given that Miss penny inherits £650.
Her saving to spending ratio is 9 : 4
Thus, the proportion of money she saves is 9/ (4+9) = 9/13
therefore, the amount of money saved will be-
9/13 of 650
= 9/13 * 650
= 9 * 50
= 450
Thus, Miss Penny saves £400.
The remaining amount left with her = 650 - 400 = 250.
Thus, she spends the remaining £250.
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Your question was incomplete. Check for full content below-
Miss penny inherits £650. She decides to save some of the money and spend the rest. The ratio of saving to spending money is 9:4. How much does she save and how much does she spend?
Ivan has $1098 worth of $12 and $14 stock shares. The number of $14 shares is seven more than
twice the number of $12 shares. How many of each does he have?
Number of 12$ Shares?
Number of 14$ Shares?
Answer:
Number of 12$ Shares? 25
Number of 14$ Shares? 57
Step-by-step explanation:
Let x = number of $12 shares.
Let y = number of $14 shares.
"Ivan has $1098 worth of $12 and $14 stock shares."
12x + 14y = 1098
The number of $14 shares is seven more than twice the number of $12 shares.
y = 2x + 7
We have a system of equations.
12x + 14y = 1098
y = 2x + 7
We can use the substitution method since the second equation is already solved for y. Substitute 2x + 7 for y in the first equation.
12x + 14(2x + 7) = 1098
12x + 28x + 98 = 1098
40x = 1000
x = 25
There are 25 $12 shares.
y = 2x + 7 = 2(25) + 7 = 57
There are 57 $14 shares.
Check:
25 × $12 + 57 × $1`4 = $300 + $798 = $1098
The total value is correct, so the answer is correct.
Melissa is simplifying an expression using the order of operations. She adds 3 and 4, squares the result, and subtracts 9. Which expression is Melissa simplifying? (3+4-9)², 3+4²-9, 3²+4²-9, (3+4)² - 9
we get that Melissa is trying to solve the expression ( 3 + 4) ² - 9.
We are given that:
Melissa is simplifying an expression using the order of operations which can be addition, subtraction, multiplication or division.
She adds 3 and 4, squares the result, and subtracts 9.
We will first add 3 and 4:
3 + 4
Now we will square them:
( 3 + 4) ²
Now, we will subtract 9 from it:
( 3 + 4) ² - 9
So, the expression becomes:
( 3 + 4) ² - 9
Therefore, we get that Melissa is trying to solve the expression ( 3 + 4) ² - 9.
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HELP PLS, I NEED AN ANSWER ASAP, 25 POINTS AVALIABLE
The gradient of the line y = x/3 - 4 is; 1/3
What is the gradient of the given line?
Slope is defined as the gradient of a graph at any point
We are given the equation of the line as;
y = x/3 - 4
Now, the formula for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, from the given equation, we can tell that the gradient which is the slope is 1/3.
Thus, we conclude that the gradient of the line y = x/3 - 4 is; 1/3
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Shirley and Pam, working together, can mow the lawn in 6
6
hours. Working alone, Pam takes three times as long as Shirley. How long does it take Shirley to mow the lawn alone?
The time it would take Shirley to mow the lawn alone is 3 hours
How to determine the value
From the information given;
Let Shirley's working hours be x
Let Pam's working hours be y
We have that;
Shirley and Pam work 6 hours together, this is expressed as;
x + y = 6
Given that Pam work 3 hours alone, we have;
y = 3
Substitute the value of y as 3 in the equation
x + 3 = 6
x = 6 - 3
x = 3
Thus, the time it would take Shirley to mow the lawn alone is 3 hours
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The table shows the side lengths and perimeters of four squares.
Side Length (x)
Perimeter (y)
4.5
18
8.5
34
10.25
41
13.75
55
Which equation represents the relationship between the side length, x, and the perimeter, y?
y = one-fourth x
y = 4x
y = x + 13.5
y = x – 13.5
Answer:
12 ×13.5 y 13.5
Step-by-step explanation:
es igual a 400
Answer:
y=4x
Step-by-step explanation:
Can someone please help me Write the ordered pair for each
letter on the graph
The ordered pair for each letter on the graph would be A at (2, 4), B at (-1, 2), C at (-3, -2), D at (2, 0), E at (0, 4), and F at (5, -5).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
As per the given graph,
The coordinates of point A would be (2, 4)
The coordinates of point B would be (-1, 2)
The coordinates of point C would be (-3, -2)
The coordinates of point D would be (2, 0)
The coordinates of point E would be (0, 4)
The coordinates of point F would be (5, -5)
Therefore, the ordered pair for each letter on the graph would be A at (2, 4), B at (-1, 2), C at (-3, -2), D at (2, 0), E at (0, 4), and F at (5, -5).
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Can someone ppl me lease help me with this question and not text me ab random stuff… :/
Answer:
{2,3,5,6,8}
Step-by-step explanation:
U={1,2,3,4,5,6,7,8}
A{3,4,5,6}
B{1,4,8}
C{2,3,4,5,6}
We are to find
{A' n B} U {A' n C'}
={3,5,6,8}. U. {2}
= {2,3,5,6,8}
f(x)=x+2
g(x) = 3x² - 5
Find (f ·g)(x).
Step-by-step explanation:
f(x) = x + 2
g(x) = 3x² - 5
= (f.g)(x)
= (x + 2).(3x² - 5)
= 3x³ - 5x + 6x² - 10
= 3x³ + 6x² - 5x - 10
Solve: x0.09=0.81. Round to the hundredths place. Do not include "x=" in your answer.
The value of x in the equation x0.09 = 0.81 is 9
How to determine the value of x?The equation is given as
x0.09 = 0.81
Rewrite the above expression properly
So, we have:
x * 0.09 = 0.81
Divide both sides by 0.09
So, we have:
x = 0.81/0.09
Evaluate
x = 9
Hence, the value of x in the equation x0.09 = 0.81 is 9
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(-1,4) and (8,2)
The distance between the two points rounding to the nearest tenth is
9.2 units.
Given that the two points are (-1,4) and (8,2).
We are required to find the distance between two given points.
Distance is basically a numerical or occasionally qualitative measurement of how far apart objects or points are.
The points are (-1,4) and (8,2).
The formula to calculate the distance between two points (x,y),(,a,b) is as under:
Distance=[tex]\sqrt{(a-x)^{2} +(b-y)^{2} }[/tex]
Distance=[tex]\sqrt{(8+1)^{2} +(2-4)^{2} }[/tex]
=[tex]\sqrt{(9)^{2} +(-2)^{2} }[/tex]
=[tex]\sqrt{81+4}[/tex]
=[tex]\sqrt{85}[/tex]
=9.2195
After rounding off to nearest tenth we will get 9.2.
Hence the distance between the two points rounding to the nearest tenth is 9.2 units.
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Which fraction is less than 1 chose all of the correct answer, and explain why you chose and write it down and explain your answer. 7/6 5/6 3/4 2/3 6/4 5/3 explain why you got that answer.
Answer:
[tex](3/4)[/tex] and [tex](2/3)[/tex].
Step-by-step explanation:
For a fraction of the form [tex](p / q)[/tex], the number in front of the division ([tex]p[/tex]) is the numerator. The number after the division ([tex]q[/tex]) is the denominator.
[tex]\begin{aligned} \frac{p}{q} \quad \genfrac{}{}{0}{}{(\text{numerator})}{(\text{denominator})}\end{aligned}[/tex].
A positive fraction [tex](p/q)[/tex] ([tex]p,\, q > 0[/tex]) is less than [tex]1[/tex] as long as the numerator [tex]p[/tex] is smaller than the denominator [tex]q[/tex] (that is, [tex]p < q[/tex].) The reason is that as long as [tex]p,\, q > 0[/tex]:
[tex]\begin{aligned} & \frac{p}{q} < 1 \\ \iff & (q)\, \left(\frac{p}{q}\right) < (q)\, (1) && (\text{given that $q > 0$}) \\ \iff & p < q\end{aligned}[/tex].
For example, in the fraction [tex](2/3)[/tex], [tex]2[/tex] is the numerator while [tex]3[/tex] is the denominator. Both the numerator and the denominator are positive, while the numerator [tex]2\![/tex] is smaller than the denominator [tex]3\![/tex]. Therefore, [tex](2/3)[/tex] would be less than [tex]1[/tex].
What does 1/4+2/3 equal
Answer:
[tex]\frac{11}{12}[/tex]
Step-by-step explanation:
[tex]Rule: \frac{x}{y} \pm \frac{a}{b} = \frac{x \pm y}{z}\\\frac{1}{4}+\frac{2}{3} = \frac{3}{12}+\frac{8}{12} (LCM)\\=\frac{3+8}{12}\\=\frac{11}{12}\\[/tex]
O-13
13
O-5
O 5
Simplify 9-(-4)=
Answer:
B. 13
Step-by-step explanation:
[tex]Rule:a-\left(-b\right)=a+b\\=9-\left(-4\right)=9+4\\=9+4\\=13[/tex]
The larger room is twice as wide as the smaller room which is 29 3/4’. How wide is the
larger room?
Answer: 59.5
Step-by-step explanation: 29 3/4 times 2
I think
0.007349 to three significant figures
Answer:
Step-by-step explanation:
From the question above, there are two zeros after the decimal point, so it will be ignored because it is not a significant figure.
0.007349 to 3 significant figure=0.00735
Two children weigh 160 pounds together the oldest weighs 120 pounds more how much do they each weigh 
write 336 mi in 11.2 h as a rate in simplest form
Answer:
30 mL/h
Step-by-step explanation:
You want the rate 336 ml in 11.2 h as a rate in simplest form.
Unit rateThe rate can be expressed in simplest form in a number of ways. We usually want rates involving time to be expressed with time units in the denominator:
(336 mL) / (11.2 h) = 30 mL/h
__
Additional comment
Medicine is often prescribed on a "per day" basis. In 24 hours, this rate would be ...
(30 mL/h)×(24 h/day) = 720 mL/day
The machine setup to dispense this medicine might use time units of minutes:
(30 mL/h) / (60 min/h) = (1/2) mL/min
What is 22 divided 2.630 and what’s the remainder
Answer:
22 divided by 2.630= 8 remainder 0.96
Answer: 22/2.630 is 8, remainder is 0.365 or 73/200
Using the slope formula, find the slope of the line through the given points.
(9,4) and (6,7)
Answer:
The slope of the line is -1.
We can find this by using the slope formula, where [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]. Substitute in our points; [tex]\frac{7-4}{6-9} =\frac{3}{-3}[/tex]. Remember that a negative in either the numerator or the denominator of a fraction makes the entire fraction negative, so [tex]\frac{3}{-3}=-\frac{3}{3}[/tex] Remember that an identical numerator and denominator is equal to 1. Same rule applies here, except it's negative, so the slope of the line is -1. You can see this in action if you were to use a graphing tool. I recommend checking out desmos graphing calculator.
Solve x/4>_-1 and -4x-4<_-3 and write the solution in interval notation. If there is no solution, type the no solution symbol.
The solution interval for x is x ∈ (-1/4 , ∞)
An inequality shows the relationship of a non-equal comparison between two numbers or mathematical expressions.
Here, we are given two inequalities
x/4 > -1 and -4x - 4 < -3
Let us take the first equation
x/4 > -1
⇒ x > 4(-1)
x > -4
Now, the second equation
-4x - 4 < -3
-4x < -3 + 4
-4x < 1
Now since we are dividing both sides by a negative number, that is 4, the sign of the inequality will be reversed,
x > 1/-4
x > -1/4
Thus, we get x > -4 and x > -1/4
This means that all values of x greater than -1/4 will satisfy.
Thus, x ∈ (-1/4 , ∞)
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