The distance required for a speed 59 mph is 243.67 feet
Step-by-step explanation:
The direct variation is a relation ship between two quantities, the
ratio between them is constant
If y varies directly with x, then y = k xx is the constant of variationTo find k substitute y and x by their initial values∵ The distance it takes stop a car varies directly at the square
of the speed of the car
∴ d = k v², where d is the distance in feet and v is the speed in mph
∵ it takes 112 feet for a car traveling at 40 mph to stop
∴ d = 112 feet , v = 40 mph ⇒ initial values
- Substitute these values in the rule above to find k
∵ 112 = k (40)²
∴ 112 = 1600 k
- Divide both sides by 1600
∴ k = 0.07
∴ d = 0.07 v² ⇒ equation of variation
∵ The speed v = 59 mph
- To find the distance required for this speed substitute v in
the equation of variation by 59
∵ d = 0.07 (59)²
∴ d = 243.67 feet
The distance required for a speed 59 mph is 243.67 feet
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Applying the direct variation formula between the speed and stopping distance of a car, we deduce that a car traveling at 59mph would require approximately 245 feet to stop.
Explanation:In this problem, we use the relation that the distance it takes to stop a car varies directly with the square of the speed- this is an example of a direct variation. Given the initial condition we can establish an equation to relate the speed and the stopping distance: D = kV² where D represents the stopping distance, V is the speed, and k is a constant of variation.
First, we utilize the given information (D=112 feet and V=40 mph) to determine the constant k: 112 = k(40²), yielding k = 112/(40²) = 0.07. This factor remains constant for the car irrespective of its speed.
With the constant k determined, we then substitute V=59 and the constant k into our original equation to calculate the distance required to stop at this speed: D = 0.07*(59²), resulting in D approximately equal to 245 feet. Therefore, a car traveling at 59 mph would require approximately 245 feet to stop.
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Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 0.83 hours. Who runs faster?
Answer:
Maura runs faster
Step-by-step explanation:
To avoid decimals ,multiply all by 100
Maura 500 mi/125h = 4 mi/h
Ava 300 mi /83 h =3.61445.....mi/h
Answer:
still from 2019
wsp my dude
Step-by-step explanation:
Graph a line with a slope of 2/5 that contains the point (-2,4)
A graph of the line with slope 2/5 and passing through the point (-2, 4) is shown on the coordinate plane in the image below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
x and y represent the data points.m represent the slope.At data point (-2, 4) and a slope of 2/5, an equation for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = m(x - x_1)[/tex]
y - 4 = 2/5(x - (-2))
y - 4 = 2/5(x + 2)
y = 2/5(x) + 4/5 + 4
y = 2/5(x) + 24/5
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Solve the system by graphing. Write the solution as an ordered pair.
y = –3x + 3
y = 12x – 4
The solution on the graph is the coordinate of the point where both lines intersect
Given the equation of two lines expessed as;
y = -3x + 3 and y = 12 x - 4
Since both expressions ara y values, equating both will give;
-3x + 3 = 12x - 4
-3x - 12x = -4 - 3
-15x = -7
x = 7/15
Substitute x = 7/15 into any of the equatons;
y = -3x + 3
y = -3(7/15) + 3
y = -7/5 + 3
y = 8/5
Hence the solution as an ordered pair is (7/15, 8/15)
The solution on the graph is the coordinate of the point where both lines intersect as shown in the graph below;
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The height of a skydiver jumping out of an airplane is given by h=16t +3200
Answer:
The answer is yes :)
Step-by-step explanation:
20 pts! A line passes through (3, 7) and (6, 9). Which equation best represents the line?
y = 3 over 2 x + 5
y = 2 over 3 x + 5
y = 3x + 2
y = 2 over 3 x + 2
Answer:
y = 2 over 3 x + 5
Step-by-step explanation:
m= y2-y1/x2-x1
m= (9-7)/(6-3)
m=2/3
y=mx+b
y= 2/3x+b
(3,7)
7=2/3(3)+b
7=6/3+b
7=2+b
5=b
b=5
y=2/3x+5
[tex]3x - 7 = 3x + 1[/tex]
solve for x
Answer:
No Solution.
Step-by-step explanation:
3x-7=3x+1
3x-3x-7=1
0-7=1
-7=1
no solution
Solve linear equations :
Solve step by step for each one
7. 10n - 11 = 3 + 4n + 6n
8. -8(k + 4) = -96
9. -6(2k + 5) + 7k = -6 + 7k
Answer: 7.) Wrong Question
8.) 8
(9.) - 2
Step-by-step explanation:
7.) 10n - 11 = 3 + 4n + 6n
Collect like terms
10n - 4n - 6n = 3 + 11
10n - 10n = 14
It's not possible to have zero n = 14
8.) -8(k + 4) = - 96
Exland the bracket
-8k - 32 = - 96
Collect like terms
-8k = - 96 + 32
-8k = - 64
Divide through by -8
-8k/-8 = - 64/-8
k = 8
9.) -6(2k + 5) + 7k = -6 + 7k
Open the bracket
-12k - 30 +7k = -6 + 7k
Collect like terms
-12k + 7k - 7k = - 6 + 30
-12k = 24
Divide both sides by -12
-12k/-12 = 24/-12
k = -2
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 350 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 cents per square
centimeter. The top will be made of glued paper, costing 0.08 cents per square centimeter. Find the dimensions for
the package that will minimize production cost.
Helpful information:
To minimize the cost of the package:
Radius:
Height:
Minimum
To minimize production cost, we need to find the dimensions of the package that will satisfy the volume equation and minimize the cost equation. Taking the partial derivatives of the cost equation with respect to the variables 'r' and 'h', and setting them equal to zero, we can find the critical points. Solving these equations, we find that the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
Explanation:To find the dimensions of the package that will minimize production cost, we need to consider the cost of the sides and bottom made of styrofoam and the cost of the top made of glued paper. Let's denote the radius of the base of the cylinder as 'r' and the height of the cylinder as 'h'.
The volume of a cylinder is given by the formula V = πr²h. We know that the volume of the package needs to be 350 cubic centimeters, so we can write the equation as πr²h = 350.
The cost of the sides and bottom of the container is given by the formula C1 = 0.03 * (2πrh + πr²), and the cost of the top is given by the formula C2 = 0.08 * πr².
To minimize the cost, we need to find the values of 'r' and 'h' that satisfy the volume equation and minimize the cost equation.
Since this is a calculus problem, we will differentiate the cost equation with respect to 'r' and 'h', and set the derivatives equal to zero to find the critical points.
Taking the partial derivatives of C1 and C2 with respect to 'r' and 'h', we get:
∂C1/∂r = 0.03 * (2πh + 2πr) = 0∂C1/∂h = 0.03 * (2πr) = 0∂C2/∂r = 0.08 * (2πr) = 0∂C2/∂h = 0Solving these equations, we find that h = 7 cm and r = 2.5 cm. Therefore, the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
find the value for x.
Answer: x = -13
=========================
Work Shown:
19 = 38/2
19 & 1/2 = 19 + 1/2
19 & 1/2 = 38/2 + 1/2
19 & 1/2 = (38+1)/2
19 & 1/2 = 39/2
-------
In the original equation, replace the "19 & 1/2" with "39/2" to get
(5/2)x + (1/2)x = 39/2 + (9/2)x
Each term involves a fraction with a denominator of 2. If we multiply both sides by the common denominator, then the fractions will cancel out
For example: 2*(5/2)x = (10/2)x = 5x
So after multiplying both sides by 2, you should have this new equation
5x + 1x = 39 + 9x
--------
Let's solve that latest equation for x
5x + 1x = 39 + 9x
6x = 39 + 9x
6x-9x = 39 + 9x-9x ... subtract 9x from both sides
-3x = 39
-3x/(-3) = 39/(-3) .... divide both sides by -3
x = -13
is y=5-2x and 4x+2y=10 a single solution
Answer:
X= 0
Step-by-step explanation:
What should the following rate be divided by to convert it to a unit rate?
6 inches
12 hours
Answer:
so if all of the awnsers are whole numbers it is going to be 12/12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Unit rate is a rate that has 1 as denominator.
Given the rate: 6 inches / 12 hours, we have to divide numerator and denominator by 12 to transform the denominator in 1, as follows:
[tex]\frac{6}{12} = \frac{6/12}{12/12} =[/tex] 0.5 inches/hour
five numbers that have 3, 7, and 13 as prime factors
Step-by-step explanation:
(3)(7)(13) = 273
(3)(3)(7)(13) = 819
(3)(7)(7)(13) = 1911
(3)(7)(13)(13) = 3549
(3)(3)(3)(7)(13) = 2457
(3)(7)(7)(7)(13) = 13377
(3)(7)(13)(13)(13) = 46137
....
Need help with this math problem
Answer:
[tex]x=16[/tex]
Lenght of the equal sides: [tex]71\ units[/tex]
Step-by-step explanation:
You can observe in the picture that the triangle have two angles that have equal measure; therefore, it is an Isosceles triangle.
By definition, Isosceles triangles have two equal angles and two equal sides.
Based on this, you can write the following equation:
[tex]9x-73=3x+23[/tex]
Solving for "x", you get this value:
[tex]9x-3x=23+73\\\\6x=96\\\\x=\frac{96}{6}\\\\x=16[/tex]
Finally, you can subsitute the value of "x" into any expression to find the lenght of the equal sides:
[tex]3(16)+23=71\ units[/tex]
How can I factor 24 + 32x
Answer:
8(3+4x)
Step-by-step explanation:
it it can be pulled out of both 24 and 32.
Marie will earn $15 per hour at a new job. During training, she will earn $10 per hour. What percent of Marie's regular rate will she earn during training?
Answer:
66.67%
Step-by-step explanation:
Marie's earnings at a new job : $15 per hour
Her earnings during training : $10 per hour
percentage of Marie's regular rate earned by her during training
= [tex]\frac{Her\ earnings\ during\ training}{Her earning\ at\ a\ new\ job}[/tex]×100
= [tex]\frac{10}{15}[/tex]×100
= [tex]\frac{200}{3}[/tex]
= 66.67%
∴percentage of Marie's regular rate earned by her during training = 66.67%
Final answer:
To find what percentage of Marie's regular rate she will earn during training, divide her training rate by her regular rate and multiply by 100%.
Explanation:
Marie will earn $10 per hour during training. Her regular rate is $15 per hour. To calculate what percentage of her regular rate she will earn during training, we use the formula: percentage = (training rate / regular rate) * 100%. Plugging in the values, we get (10 / 15) * 100% = 66.67%. Therefore, Marie will earn 66.67% of her regular rate during training.
Find the exact volume of a cone 6yd height 5yd base
Answer:
The exact volume of a cone is 10 yd³.
Step-by-step explanation:
Given:
Height of cone (h) is 6 yd and base (b) is 5 yd.
Now, to get the volume we need to find the radius.
So, to find radius we put the formula of base:
Let the radius be [tex]r[/tex]
Base=[tex]\pi r^2[/tex]
[tex]b=\pi\times r^{2}[/tex]
[tex]5=\pi\times r^{2}[/tex]
Dividing both sides by π and using square root on both the sides:
[tex]5\div \pi=(\pi \times r^{2}) \div \pi[/tex]
[tex]\frac{5}{\pi}=r^{2}[/tex]
[tex]\frac{5}{\pi}=r^{2}[/tex]
[tex]r^{2}=\frac{5}{\pi}-----1[/tex]
Now, putting the formula for getting the volume (v) of cone:
Volume = [tex]\pi r^2\frac{h}{3}[/tex]
[tex]v=\pi\times r^{2}\times \frac{6}{3}[/tex]
[tex]v=\pi\times r^{2}\times 2[/tex]
Substituting the value of [tex]r^2[/tex] from equation (1), we get:
[tex]v=\pi\times \frac{5}{\pi}\times 2[/tex]
[tex]v=10[/tex] yd³
Volume of cone is 10 yd³
Therefore, the exact volume of a cone is 10 yd³.
The cost of having one pizza delivered is $14. Each additional pizza cost $9 more. Write the explicit and recursive formula to represent the situation.
Answer:
14 +(9×x) = y x being the number of pizzas that are not the first one and y is the amount it all cost
Answer:
See explanation below:
Step-by-step explanation:
Here we want to express the number of pizza delivered. Lets try to understand the case.
If we buy one pizza (p1) the cost is 14 because of the delivery plus 9 for the cost of the pizza. So:
p1 = 14 + 9 = 23
If we buy 2 pizzas (p2) we have to pay 14 for the delivery and 9 for each pizza:
p2 = 14 + 9 + 9 = 14 + 2*9 = 32
If 3 pizzas are bought (p3) the reasoning is the same, 14 for the delivery and 9 for each pizza:
p3 = 14 + 9 + 9 + 9 = 14 + 3*9 = 41
Here we can see a pattern: for any amount of pizzas n the cost will be 14 plus n-times 9, the price of a pizza. It is:
pn = 14 + 9*n
But we can separate the last equation in such a way:
pn = 14 + 9*(n-1) + 9 , as 9*(n-1) + 9 = 9*n
But if our general formula it true, the first to terms on the right are the vost of buying n-1 pizzas, so:
pn = pn-1 + 9
We can keep on separating terms as we did to arrive to this form, this is, separating the 9n in 9*(n-2) + 9*2, 9*(n-3) + 9*3, ..., 9*(n-m) + 9*m for any m < n . Here I will keep pn = pn-1 + 9 as the Recursive Formula, but you could use other formulation with, e.g., pn-2, pn-3, etc, using the above recursion.
Now, the explicit formula is such that gives as the value of any amount, finding all the terms of the sequence with those not depending on previous terms (contrary to the recursive). This formula was showed above and is: pn = 14 + 9*n. This is, given any number of pizzas we can find the cost without knowing the cost of previous values.
So, we have:
Recursive: pn = pn-1 + 9
Explicit: pn = 14 + 9*n
Solve for y. Then find the values of y that correspond
to the given values of x for the linear function.
7. y + 8x = -2 for x = 0, 1,2-2,
8. 12x + 3y = 15 for x = -1, 0, 1
y - 3x = 9 for x = -2,0, 2
10. 0.4y + 2x = 1.2 for x = -3,0,
7.
y + 8x = -2
f(x) = y = -8x - 2
f(0)=-2, f(1)=-10, f(2)=-18, f(-2)=14
8.
12x + 3y = 15
3y = -12x + 15
f(x) = y = -4x + 5
f(-1)=9, f(0)=5, f(1)=1
9.
y - 3x = 9
f(x) = y = 3x + 9
f(-2)=3, f(0)=9, f(2)=15
10.
0.4y + 2x = 1.2
4y + 20x = 12
4y = -20x + 12
f(x) = y = -5x + 3
f(-3) = 18, f(0)=3
Grant has 2/3
of ice cream in a bowl. He then removes two 1/6
cups of ice cream to share with his little br
amount of ice cream left in Grant's bowl?
Answer: 2/6 or 1/3
Step-by-step explanation:
2/3 = 4/6. 1 /6 Two times is 2/6 so by subtracting you should get 2/6 or 1/3
no one helped me with the last question but i got it can someone help me with this
y = 2x
Step-by-step explanation:
The linear functions are given by:
y = mx+b
To find the slope, we have to find the change in x and y
The change in x is:
[tex]-14-(42) =-14+42 =28\\14+14= 28[/tex]
The change in y is:
[tex]-28-(-84) = -28+84 = 56\\28-(-28) = 28+28 = 56[/tex]
The slope is:
[tex]Slope = \frac{change\ in\ y}{Change\ in\ x}\\=\frac{56}{28}\\= 2[/tex]
Putting slope in equation of linear function
[tex]y =2x+b[/tex]
To find the value of b, we will put any pair of input and output in the slope-intercept form
So, putting (14,28)
[tex]28 = 2(14) + b\\28 = 28+b\\b = 28-28\\b = 0[/tex]
Hence,
the linear equation for function is:
y = 2x
Keywords: Linear function, slope intercept form
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There are 70 students attending summer camp, 21 girls and 49 boys. What is
the ratio of girls to boys at summer camp?
O A. 7:3
O B. 3:7
O 6. 2:1
SUBMIT
h/2 + 3 = 3(h/4 - 1)
Answer:
h=24
Step-by-step explanation:
h/2+3=3(h/4-1)
h/2+3=3h/4-3
h/2-3h/4=-3-3
2h/4-3h/4=-6
-h/4=-6
-h=-6*4
-h=-24
h=24
Find the Slope and Y-Intercer
1) y = x+3
slope =
y-intercept =
What’s the slope
Answer:
slope is 1 and y-intercept is 3
Step-by-step explanation:
equation is in the format y=mx+c
c = y-intercept
m = slope
if there is no number in front of x it is assumed that 1 is in front of x
Answer:
The slope is 1 and the y-intercept is 3
Step-by-step explanation:
y = x+3 has the form y = mx + b. If we compare these two equations, it becomes readily apparent that m = 1 and b = 3.
The slope is 1 and the y-intercept is 3 (or (0, 3) )
how do you write six times the quantity two x plus three y with numbers??
Answer:
12x + 18y
Step-by-step explanation:
Lets first write the quantity "two x plus three y", this means, that we have x and y as unknowns. x is 2 times, so we have 2x; and y is 3 times, so he have 3y:
2x + 3y
Additionally we have that this quantity is six times, what means that it is multiplied by a number 6:
6(2x +3y)
If you like, we can apply the distributive property that means that given any three numbers a, b, c we have that a(b+c)=ab + ac. In our case a is 6, b is 2x and c is 3y. Thus, operating:
6(2x +3y) = 6*2x + 6*3y = 12x + 18y
So, "six times the quantity two x plus three y" is 12x + 18y
The sum of 3 consecutive odd numbers is 183
Answer:
Step-by-step explanation:The sum of three consecutive odd numbers is 183. Find the numbers. 57; 59; 67 59; 61; 63 60; 61; 62 65; 67; 69.
A scientist measured the wavelength of an X-ray as 0.0000000065 meters. Write the number in scientific notation.
Answer:
[tex]6.5 \times 10^{-9}[/tex]
Step-by-step explanation:
The scientific notation of a number is to express the number in the form [tex]x\times 10^{y}[/tex] where x is the base of ten.
So, if we want to express the number 0.0000000065, then we can write it as
[tex]\frac{6.5}{1000000000} = 6.5 \times 10^{-9}[/tex].
So, we can write 0.0000000065 as [tex]65\times 10^{-10}[/tex] or [tex]0.65 \times 10^{-8}[/tex] but those are not the scientific notation.
Therefore, [tex]6.5 \times 10^{-9}[/tex] is the scientific notation of 0.0000000065. (Answer)
Bills annual salary is 2/3 of Jen's annual salary.if bills salary is$64,000, what is Jen's salary?
Answer:
$96,000
Step-by-step explanation:
To find Jen's annual salary, divide Bill's annual salary of $64,000 by 2/3, resulting in Jen's salary being $96,000.
Explanation:To calculate Jen's annual salary based on the information that Bill's annual salary is 2/3 of Jen's, first express Bill's salary as a fraction of Jen's:
Let J represent Jen's annual salary.According to the problem, we have that Bill's salary equals 2/3 of Jen's, so (2/3)*J = $64,000.To find Jen's salary J, divide Bill's salary by 2/3, so J = $64,000 / (2/3).After calculation, J = $64,000 * (3/2), which simplifies to J = $96,000.Therefore, Jen's annual salary is $96,000.
What is the quotient of the complex numbers below?
(5-5i) = (3-i)
Answer:
A. 2- i
Step-by-step explanation:
Answer:
2 + i
Step-by-step explanation:
Find the area of a circle with a circumference of 18.84 units
welp
Answer:
A=28.25 is the rounded form of the answer.
A = 28.245673384359 in^2
Answer:
Area: 28.25
Step-by-step explanation:
Area = Circumference^2
4 (pi)
18.84^2 = 354.9456
4(pi) = 12.5663706144
354.9456 ÷ 12.5663706144 = 28.2456733843
Rounded to the nearest hundreth, the 5 in the thousandths place converts the 4 in the hundreths place into 5.
A local hamburger shop sold a combined total of 500 hamburgers and cheeseburgers on Tuesday. There were 50 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Tuesday?
Answer: 275
Step-by-step explanation:
Let the total number of hamburger be x and the total number of cheeseburgers be y. That is
x + y = 500 ................... equation 1
Since there were 50 fewer cheeseburgers sold than hamburgers, this means that the number of hamburgers sold is more than cheeseburgers by 50 , that is
x - y = 50 ............. equation 2
solving the resulting linear equation by substitution method;
From equation 2 , make x the subject of the formula , that is
x = 50 + y ................ equation 3
substitute equation 3 into equation 1 , we have
50 + y + y = 500
50 + 2y = 500
2y = 500 - 50
2y = 450
y = 450/2
y = 225
substitute y = 225 into equation 3 to find the value of x. we have
x = 50 + y
x = 50 + 225
x = 275
Therefore 275 hamburgers were sold