The equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1
The line is passing through the y intercept = (0, 1)
Here at x = 0, the values of y = 1
Then the y intercept of the line is 1
The slope of the line = 4
The slope of the line is the change in y coordinate with respect to the change in x coordinates of the function
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
x is the x coordinate
y is the y coordinate
Then the equation in the slope intercept form
y =4x + 1
Hence, the equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1
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Students are going to conduct an experiment to study the effect of a net force applied to an object on the object’s motion. In each trial of the experiment, the students will apply a net force on the object. They also need to take two other measurements. What are the other quantities they should measure in each trial of the experiment?.
For conducting experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.
As given in the question,
To conduct a experiment based on the effect of net force applied to an object the dependable quantities are as follow:
Force = mass × acceleration
As object remain same ⇒ mass is constant as object remain same.
And there is change in the acceleration.
Acceleration depends change in velocity over total time taken.
Acceleration depends on velocity and time.
Net force also depends on velocity and time.
Two measurements need to know while conducting trail experiments are velocity and time.
Therefore, to conduct experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.
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(3^4)^2 as a product question below help
The expression (3⁴)² in repeated multiplication is (3⁴) * (3⁴)
How to rewrite the expression as products?From the question. the expression is given as
(3⁴)²
The task is that we rewrite the expression as products i.e. repeated multiplication
This in other words means that:
We rewrite the (3⁴)² as repeated multiplication
To do this, we apply the exponent rule of indices
This rule states that:
a^m = a * a * a .... in m places
So, we have
(3⁴)² = (3⁴) * (3⁴)
Hence, the equivalent expression is (3⁴) * (3⁴)
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|| x²-2x|-|3x-20|| = |x²+x-20|.
Find the positive integral value of x
Answer:
x ∈ {2, 3, 4, 5, 6}
Step-by-step explanation:
You want the positive integer solutions of ||x²-2x|-|3x-20|| = |x²+x-20|.
DomainsEach of the absolute value functions has turning points where the argument is zero. Those turning points are ...
x²-2x ⇒ x(x-2) = 0 ⇒ turning points at x=0 and x=2
3x-20 ⇒ x -20/3 = 0 ⇒ turning point at x=20/3
x²+x-20 ⇒ (x+5)(x-4) = 0 ⇒ turning points at x=-5 and x=4
In numerical order, the turning points are ...
x ∈ {-5, 0, 2, 4, 20/3}
These divide the domain of the equation into 6 intervals. Since we are concerned only with positive integer solutions, we are only interested in the intervals ...
[0, 2), [2, 4), [4, 20/3), [20/3, ∞)
Domain [0, 2)In this domain, x²-2x < 0, 3x-20 < 0, and x²+x-20 < 0. This means the equation becomes ...
|-(x² -2x) +(3x -20)| = -(x² +x -20)
The difference in the absolute value bars is negative, so we get the equation ...
-(-x² +2x +3x -20) = -x² -x +20
2x² -4x = 0 . . . . . . . add x²+x+20
x = 0 . . . . . x = 2 is not in the domain
There are no positive integer solutions in this domain.
Domain [2, 4)In this domain, x²-2x > 0, 3x-20 < 0, and x²+x-20 < 0. This means the equation becomes ...
|(x² -2x) +(3x -20)| = -(x² +x -20)
The difference in the absolute value bars is negative, so we get the equation ...
-(x² -2x +3x -20) = -x² -x +20
0 = 0 . . . . . . . . . . . . add x² +x -20
2 ≤ x < 4 . . . . . . . . all x-values in the domain are solutions
The positive integer solutions are x = 2, x = 3.
Domain [4, 6 2/3)In this domain, x²-2x > 0, 3x-20 < 0, and x²+x-20 > 0. This means the equation becomes ...
|(x² -2x) +(3x -20)| = x² +x -20
The difference in the absolute value bars is positive, so we get the equation ...
(x² -2x +3x -20) = x² +x -20
0 = 0 . . . . . . . subtract x² +x -20
4 ≤ x < 6 2/3 . . . . . . . . . all values of x in the domain are solutions
The positive integer solutions are x = 4, x = 5, x = 6.
Domain [6 2/3, ∞)In this domain, x²-2x > 0, 3x-20 > 0, and x²+x-20 > 0. This means the equation becomes ...
|(x² -2x) -(3x -20)| = x² +x -20
The difference in the absolute value bars is positive, so we get the equation ...
x² -2x -3x +20 = x² +x -20
-6x +40 = 0 . . . . . . . subtract x² +x -20
x = 6 2/3 . . . . . . . add 6x, divide by 6
There are no positive integer solutions in this domain.
The positive integer values of x are {2, 3, 4, 5, 6}.
7. What is the slope of the line that passes through the pair of points (2, 5) and (8, 3)?
1/3
-1/3
3
-3
Answer:
The answer would be -1/3.
Step-by-step explanation:
If you plug the coordinates into slope formula (y 2 - y 1 )/ (x 2 - x 1) , you'd have 3-5 over 8-2, and once you solve that, you'll have -1/3 as your slope. Hope this helps ! :D
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Which equation represents the same line as the points in the table?
y= −x−7y is equal to negative x minus 7
y= −x
x= −y
y= −x+5
The equation of line passes through the points (2, 0) and (0, -1) will be;
⇒ y = 1/2 x - 1
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (2, 0) and (0, -1).
Now,
Since, The equation of line passes through the points (2, 0) and (0, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - 0) / (0 - 2)
m = - 1 / - 2
m = 1 / 2
Thus, The equation of line with slope 1 / 2 is,
⇒ y - 0 = 1 / 2 (x - 2)
⇒ y = 1/2 x - 1
⇒ y = 1/2 x - 1
Therefore, The equation of line passes through the points (2 , 0) and
(0, - 1) will be;
⇒ y = 1/2 x - 1
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Jim gets $50 every 10 minutes, He needs $114058 to buy something. How many hours will he need to get $114058?
Answer:
380.2 hours
Step-by-step explanation:
find how much he receives an hour:
$50/10min × 6 = $300/hr
find out the number of hours it takes:
$114,058 ÷ $300 = 380.19hours
≈ 380.2 hours (to 1 decimal point)
How many ounces are in 4 pounds?
*
5 points
48 ounces
36 ounces
64 ounces
16 ounces
2. Divide: 1,111 ÷ 11 = ____________ (Write out)
*
5 points
11
111
101
110
3. Subtract: 6000 - 3,444= _______ ( write out)
*
5 points
2,456
2,656
2,556
2,655
4. Would a bottle of shampoo contain about 400ml or 400 liters?
*
5 points
400 ml
400 liters
5. Multiply: 3,540 x 9 = __________ ( write out to solve)
*
5 points
31,660
31,680
31,860
31,760
6. Any number multiplied by zero is equal to _____.
*
5 points
10
0
100
5
7. Mr. Williams left his house at 7:30. he drove for 4 hours and 20 minutes. At what time did he reach his destination? (hint: create a clock line.)
*
5 points
11:30
11:50
12:30
1:00
8. 7 x 6 = _______
*
5 points
13
42
54
49
9. Find the missing minuend. 92 - ____= 58
*
5 points
38
36
34
44
10. Subtract: $ 43.99 - $18.45= ________ (remember: Whenever you add or subtract using decimals, they MUST BE LINED UP.)
*
5 points
$25.45
$25.44
$25.54
$24.54
11. Divide: 4,842 ÷ 2= _________ (write out)
*
5 points
2,241
2,421
2,412
2,402
12. Multiply: 15 x 14 = _________ ( write out)
*
5 points
220
210
190
240
13. IF it is 11:50 now, what time was it 3 hours and 20 minutes ago? (hint: create a clock line.)
*
5 points
8:30
9:30
8:50
10:30
14. Find the estimated sum of 953 and 413.
*
5 points
≈1150
≈1350
≈1250
≈1500
15.Add: 5,218 + 6,970 = ________. (write out)
*
5 points
12, 218
12,178
12,188
13,168
16. Divide: 54 ÷ 9 = ____________. Hint: think related facts.
*
5 points
7
6
8
5
17. Arianna baby-sat from 7:00pm until 12:00 am. IF she earns $ 4.50 per hour for babysitting, how much did she earn? (multi-step. solve for the time first.)
*
5 points
$18.00
$20.50
$16.50
$22.50
18. Select a rectangle that shows 5/6 shaded.
*
5 points
A
B
C
D
19. Multiply: 12 x 3 = ______
*
5 points
24
36
18
46
20. A closed figure made up of three or more line segments that do not intersect is a _______________.
*
5 points
pentagon
polygon
hexagon
heptagon
am answering from two to ten
Solve.
−5/6 = −1/4 − 7/10x
Enter your answer as a fraction in simplest form.
I don't know how brainly works :b
Answer:
[tex]\boxed{\sf x=\cfrac{5}{6}}[/tex]
Step-by-step explanation:
[tex]\sf -\cfrac{5}{6}=-\cfrac{1}{4}-\cfrac{7}{10}x[/tex]
[tex]\sf -\cfrac{1}{4}-\cfrac{7}{10} \; x=-\cfrac{5}{6}[/tex]
Add 1/4 to both sides:-
[tex]\sf -\cfrac{1}{4}-\cfrac{7}{10}x+\cfrac{1}{4}=-\cfrac{5}{6}+\cfrac{1}{4}[/tex]
Simplify:-
[tex]\sf -\cfrac{7}{10}x=-\cfrac{7}{12}[/tex]
Multiply both sides by 10:-
[tex]\sf 10\left(-\cfrac{7}{10}x\right)=10\left(-\cfrac{7}{12}\right)[/tex]
Simplify:-
[tex]\sf -7x=-\cfrac{35}{6}[/tex]
Divide both sides by -7:-
[tex]\sf \cfrac{-7x}{-7}=\cfrac{-\cfrac{35}{6}}{-7}[/tex]
Simplify:-
[tex]\sf x=\cfrac{5}{6}[/tex]
____________________
Hope this helps!
Have a great day! :)
Answer:
x = 5/6
Step-by-step explanation:
Given equation,
→ (-5/6) = (-1/4) - (7/10)x
Now the value of x will be,
→ (-5/6) = (-1/4) - (7/10)x
→ (-7/10)x = (-5/6) + (1/4)
→ (-7/10)x = (-10 + 3)/12
→ x = (-7/12) × (-10/7)
→ x = 10/12
→ [ x = 5/6 ]
Hence, the answer is 5/6.
a manufacturing machine has a 1% defect rate. if 8 items are chosen at random, what is the probability that at least one will have a defect?
a manufacturing machine has a 1% defect rate. if 8 items are chosen at random, then the probability that at least one will have a defect is 0.077255 or 7.72 %
Given data
defect rate = 1%
no of sample = 8
to find out
probability at least one will have a defect solution
we know here probability of defect is
Probability (defect) = 0.01
and n is 8
so
probability (at least one defect is) = 1 - probability (none)
we know probability (none) = 0.99^n
probability (none) = 0.99^8
put this in equation 1
probability (at least one defect is) = 1 - 0.99^8
probability (at least one defect is) is 0.077255 or 7.72 %
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15% discount on $60 plus 5% tax
op op op op op o plnlbloblbbjbb
Consider rolling two number cubes, each of which has its faces numbered from 1 to 6. The cubes will be rolled and the sum of the numbers landing face up will be recorded. Let the event E represent the event of rolling a sum of 5. How many outcomes are in the collection for event E ? Responses
The outcomes in the collection for event E is four and they are (1, 4) (2,3) (3,2) (4, 1).
Two number cubes, each of which has its faces numbered from 1 to 6 is rolled.
The cubes will be rolled and the sum of the numbers landing face up will be recorded.
The total sample space for two cubes = 6² = 36
Let the event E represent the event of rolling a sum of 5
Total possible outcomes for a sum of 6 is (1, 4) (2,3) (3,2) (4, 1)
We need to find the probability of event E, P(E)
P(E) = possible outcomes/ sample space
P(E) = 4/ 36 = 1/9
Therefore, the outcomes in the collection for event E is four and they are (1, 4) (2,3) (3,2) (4, 1).
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Write an equation of the line that passes through (1, 2) and is perpendicular to the line y = x + 4.
The equation of the line is y = -x +3
We need to calculate the line which is perpendicular to y = x +4 and passes through the point (1, 2)
The given equation is y = x +4
Comparing this equation with the general equation of the line, y = mx +c, we get the slope of the equation as 1
Now, When two lines are perpendicular to each other, the product of their slopes is -1.
So, the slope of the required equation is -1.
Now, the equation of the line which passes through the points, and has slope m, is given by
[tex]y - y_{1} = m(x -x_{1} )[/tex]
Putting the values in the general equation, we get,
y - (2) = -1(x - 1 )
y - 2 = -x +1
y = -x +3
The equation of the line is y = -x +3.
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Find the greatest common factor of 20 and 25. Factors of 201 Factors of 25: ____ Greatest common factor: ____ please help me
Answer:
factors of 20: 1, 2, 4 , 5, 10, 20
factors of 25: 1, 5, 25
gcf: 5
Step-by-step explanation: the common factors of 20 and 25 is 1 and 5. the greater one is 5, therefore the gcf is 5.
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A point (x, y) is on the unit circle. If its y-coordinate is 1/2 and the point lies in Quadrant I, what is the other coordinate?
Express your answer as a fraction, NO DECIMALS!
The other coordinate is x = [tex]\sqrt{3} /2[/tex].
Given:
A point (x, y) is on the unit circle. If its y-coordinate is 1/2 and the point lies in Quadrant I.
we know that :
In unit circle radius r = 1.
[tex]x^{2} +y^{2} = r^{2}[/tex]
[tex]x^{2} +(1/2)^2 = 1^2[/tex]
[tex]x^{2} +1^2/2^2 = 1[/tex]
[tex]x^2 + 1/4 = 1[/tex]
[tex]x^{2} = 1-1/4[/tex]
[tex]x^{2} = 4- 1 / 4[/tex]
[tex]x^{2} =3/4[/tex]
[tex]x =[/tex] ±[tex]\sqrt{3/4}[/tex]
[tex]x =[/tex] ±[tex]\sqrt{3} /2[/tex]
since x is in first quadrant it has only positive value
[tex]x =\sqrt{3} /2[/tex].
Therefore the other coordinate is x = [tex]\sqrt{3} /2[/tex].
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9-6 Worksheet: Dilations
Graph the polygon and its image after a dilation with the given scale factor
1. J(2, 4), K(4, 4), P(3, 2); r = 2
5.1-2.
ty
of
X
The coordinates of the polygon before and after dilation is below
preimage image
J (2, 4) J' (4, 8)
K (4, 4) K' (4, 4)
P (3, 2) P' (6, 4)
How to find the coordinates of the imageDilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
following similar procedure for the given problem we have
preimage image
J (2, 4) → (2 * 2, 4 * 2) → J' (4, 8)
K (4, 4) → (4 * 2, 4 * 2) → K' (8, 8)
P (3, 2) → (3 * 2, 2 * 2) → P' (6, 4)
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Solve for t. t squared=9
Answer:
3
Step-by-step explanation:
3 x 3 = 9
When 20 tons of iron ore are smelted, 12 tons of iron are obtained. How much iron is obtained when 45 t of iron ore is smelted?
Answer:
Step-by-step explanation:
It is clear that after smelting the amount of iron obtained is 12\20 = 60%.
Therefore when 45t is smelted the amount obtained = 60% x 45t
= 27t
What is the largest y-value that satisfies this system?
1/2(x-3)(x-2)=y
2(x-1/2)=y
Answer: 15
Step-by-step explanation:
screenshot
Answer:
What is the largest y-value that satisfies this system?
1/2(x-3)(x-2)=y
2(x-1/2)=y
Step-by-step explanation:
the first one has a binomial times a binomial which you have to do the generic rectangle if you did you would get
x² - 5x + 6 = y you keep parenthesis and the 1/2 and bring down to get
1/2(x² - 5x + 6) = y then distribute
1/2x² - 5/2 + 3 = y
2(x - 1/2) = y the distribute and get
2x - 1 = y
so the first one has the largest y-value
Taylor bought some dog grooming and pet supplies from an online store. For shipping, the store charges a fee of $8.95 or 5.5% of the total
purchase, whichever is greater. If Taylor's total purchase is $140, how much shipping will he pay?
The Taylor has to pay $8.95 as shipping charge for his total purchase of some dog grooming and pet supplies for $140.
What is percentage?Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of all of it in measures of 100 is what percentage calculation is.To Determine Percent
Calculate the total or entire amount.Divide the sum by the amount to also be expressed in percentage form. The lower number will often be divided by the bigger amount.The result is multiplied by 100.Here given shipping charge ,
Shipping charge = $8.95 or 5.5% of total purchase, which is greater.
Total purchase of Taylor = $140.
Here given shipping charge = 5.5 % of $140.
5.5 % of 140
= (5.5 /100)*140
= (5.5*140) / 100
= 770 / 100
= 7.7
5.5 % of total purchase = $7.7
Since $8.95 is greater that $7.7.
They take $8.95 as shipping charge.
Therefore the Taylor pay's $8.95 as shipping charge .
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Given m ||n, find the value of x.
t
(x-17)
(5x-1)
Linear pair of x for the given figure will be 33
Linear pair:
Linear pair of angles are formed when two lines intersect each other at a single point.
The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.
The sum of angles of a linear pair is always equal to 180°.
For the given figure,
m ||n
given angles are (x-17)° and (5x-1)° ,both the angles are linear pair.
using the properties of linear pair,
Sum of the angles will be equal to 180°
that is,
(x-17)° + (5x-1)° =180°
(x + 5x) + (-17 -1) = 180
6x - 18 = 180
6x = 180 + 18
6x =198
x = 198/6
x =33
Thus, the value of x will be 33
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Carl is boarding a plane. He has 222 checked bags of equal weight and a backpack that weighs 4 \text{ kg}4 kg4, start text, space, k, g, end text. The total weight of Carl's baggage is 35 \text{ kg}35 kg35, start text, space, k, g, end text.
Write an equation to determine the weight, www, of each of Carl's checked bags.
The weight of each of his checked bags will be; 15.5 kg.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that; Number of checked bags = 2
Backpack weight = 4 kg
The total weight of Carl's baggage 35kg
Let w be the weight of each checked bag.
Weight of 2 checked bags = 2w
It can be found as; Weight of 2 checked bags + Backpack weight = Total weight of Carl's baggage
Then;
2w + 4 = 35
Subtract 4 from both sides;
2w + 4 = 35
2w = 31
Divide 2 from both sides;
w = 15.5
Therefore, the weight of each of his checked bags will be; 15.5 kg.
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you are constructing a box for your cat to sleep in. the plush material for the square bottom of the box costs 7 dollars per square foot and the material for the sides costs 3 dollars per square foot. you need a box with volume 4 ft3. use x to represent the length of the square base, and use h to represent the height of the box.
The height in terms of x is 4/x², the cost function is C(x) = 7x² + 16/x, and the dimensions for minimum cost are 2/∛7 and ∛14.
a)
It is given that we need to consider the length of the square side to be x ft and the height to be h ft.
The volume of any cuboid
= Length X breadth X height
Here,
length = breadth = x ft
height is h ft.
Volume id 4 ft³
Hence,
x²h = 4
or, h = 4/x²
b)
Since this is a box for the kitten to sleep in, it cannot have any lid.
Hence it will have one square side of area x² and 4 rectangular sides each of area xh
h = 4/x²
Hence,
xh = 4/x
The square bottom costs $7 per ft and the sides cost $4 per sq. ft
Hence cost to make the box
= 7x² + 4 X 4/x
= 7x² + 16/x
Hence, C(x) = 7x² + 16/x
c)
Here,
C(x) = 7x² + 16/x
Hence, to minimize the cost we will equate its first-order derivative with 0 to get
C'(x)= 0
or, 14x - 16/x² = 0
or, 14x³ - 16 = 0
or, 14x³ = 16
or, x³ = 16/14
or, x = 2/∛7
Hence h = 4∛14/4
= ∛14
Therefore, the dimensions are 2/∛7 and ∛14
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Complete Question
You are constructing a box for your cat to sleep in. The plush material for the square bottom of the box costs 7 dollars per square foot and the material for the sides costs 4 dollars per square foot. You need a box with a volume of 4 ft³. Use x to represent the length of the square base, and use h to represent the height of the box.
(a) Determine a formula for the height h in terms of x.
(b) Determine a formula for the total cost C(x) of the materials for the box.
(c) Find the dimensions (in ft) of the box that minimize cost. (length of base and height)
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mark's brother is five years older than mark. their combined ages add up to 23. how old is mark's brother?
Based on the sum of their ages, Mark's brother is 14 years old.
Let us assume the age of Mark be x. Now forming the equation based on mentioned information.
Mark's age = x
Mark's brother's age = x + 5
x + x + 5 = 23
Performing addition on Left Hand Side of the equation
2x + 5 = 23
Shifting 5 to Right Hand Side of the equation
2x = 23 - 5
Performing subtraction on Right Hand Side of the equation
2x = 18
Shifting 2 to Right Hand Side of the equation
x = 18a1 ÷ 2
Performing division on Right Hand Side of the equation
x = 9
So, Mark's age = 9
Mark's brother's age = 9 + 5
Mark's brother's age = 14
Hence, Mark's brother's age is 14 years.
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need help with this one
The number of real solution of the system y = [tex]3x^2[/tex] and y = 3x - 2 is zero
The system of equations are
y = [tex]3x^2[/tex]
y = 3x - 2
Then the equation will be
[tex]3x^2[/tex] = 3x - 2
Move 3x - 2 to the left hand side of the equation
[tex]3x^2[/tex] - 3x + 2 = 0
Find the value of [tex]b^2[/tex] - 4ac
Here value of a = 3
The value of b = -3
The value of c = 2
Substitute the values in the expression
= [tex](-3)^2[/tex] - 4×3×2
= 9 - 24
= -15
Here the value of [tex]b^2[/tex] - 4ac is -15
Therefore there is no real valued solution
Hence, the number of real solution of the system y = [tex]3x^2[/tex] and y = 3x - 2 is zero
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Problem: A company has a small budget for printing presentation handouts for an important meeting. The function 2x + y = 20 represents the relationship between the remaining budget balance, y, in dollars if printing
Question: What is the y-intercept of this situation and what does it represent?
The y-intercept of this situation is -20 and it means, the remaining budget balance is -20 dollars if no printing presentation handouts
In this question, we have been given a function 2x+y=20 that represents the relationship between the remaining budget balance(y) dollars in dollars if printing x presentation handouts.
We write given equation in slope-intercept form,
y = -2x - 20
when x = 0,
y = -20
So, y-intercept is -20
This means, the remaining budget balance is -20 dollars if no printing presentation handouts (x = 0).
Therefore, the y-intercept of this situation is -20 and it means, the remaining budget balance is -20 dollars if no printing presentation handouts
Given question is incomplete.
The complete question is:
A company has a small budget for printing presentation handouts for an important meeting. The function 2x+y=20 represents the relationship between the remaining budget balance, y, in dollars if printing x presentation handouts. What is the y-intercept of this situation and what does it represent?
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two trains going in opposite directions leave at the same time. one train tave4ls 15 mph faster than the other. in 6 hours the trains are 630 miles apart. find the speed of each
Using the formula of speed, the speed of first trains is 45 mph and the speed of second train is 60 mph.
In the given question, we have to find the speed of each.
Two trains going in opposite directions leave at the same time.
One train tavels 15 mph faster than the other.
In 6 hours the trains are 630 miles apart.
Let the speed of the first vehicle be s mph, then according to the question, the speed of the second vehicle would be (s+15) mph.
Let the first vehicle covers the distance D(1) and the second one D(2) in the prescribed time.
So, find the distance covered by the first vehicle in 6 hours by using the formula
Distance = Speed × Time
So the distance D(1) is;
D(1) = s*6
D(1) = 6s
So the distance D(2) is;
D(2) = (s+15)*6
D(2) = 6s+90
Since, after 6 hours both the vehicles are at the distance 630 miles. So, the sum of the two distances D(1) and D(2) will be equal to 630.
D(1)+D(2) = 630
Puttimg the value of D(1) and D(2)
6s+6s+90=630
Simplifying
12s+90=630
Subtract 90 on both side we get
12s=540
Divide by 12 on both side we get
s=45 mph
So the value of speed of the faster vehicle
s+15 = 45+15
s+15 = 60 mph
Hence, the speed of first train is 45 mph and the speed of second train is 60 mph.
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X^2 + 2x - 3x -6 simplified
Answer:
[tex]x^{2}[/tex] -x -6
Step-by-step explanation:
You combine the like terms 2x and -3x which is -x
the waitress at the restaurant provided really good service so you and your friends decided to add on an 20% tip to your $32 bill. how much money will be added onto the bill for the tip?
Using the concepts of ratio and proportion, we got that $6.4 as the money will be added onto the bill for the tip to the the waitress at the restaurant who provided really good service.
We are given that we are giving the waitress 20% tip, means that apart from the actual bill we give her 20% of actual bill cost
So, 20%of $32 is given by
=(20/100)×32
=32/5
=$6.4
Hence, if the waitress at the restaurant provided really good service, so me and my friends decided to add on an 20% tip to your $32 bill, the money that will be added onto the bill for the tip is $6.4
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The numbers of pairs of shoes sold during the 10
days of the sale were:
86 84 100 97 96 88 89 60 78 99
For the numbers of pairs of shoes sold in the New
Year sale:
Find the median
The median of the given data is 88.5
The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.
Given the numbers of pairs of shoes sold during the 10 days of the sale were:
86 84 100 97 96 88 89 60 78 99
We have to determine the median for the given data
The data given must be arranged in ascending order.
60, 78, 84, 86, 88, 89, 96, 97, 99, 100
median = middle most value
∴ 88,89 are middle values
∴ Median =(88+89)/2
= 177/2
= 88.5
Therefore the median of the given data is 88.5
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Solve proportion using the multiplication property of equality 1/5 = t/3
Solving the proportion using the multiplication property of equality gives
t = 3/5 How to solve the equation using the multiplication property of equalityThe both ratio showing fractions of one-fifth on the left hand side of the equation is equal to the right hand side of the equation which have t as the numerator and 3 as the denominator
The fractions will be solves by cross multiplying as below
1/5 = t/3
5 * t = 3 * 1
5t = 3
dividing through by 5
5t / 5 = 3 / 5
t = 3/5
plugging in t back to the initial equation gives
1/5 = t/3
1/5 = 3/5 / 3
1/5 = 1/5
Therefore t = 3/5
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