Answer: the actual correct answer is D
Step-by-step explanation: i know the test answers because i am in flvs too
In the equation C=2.5r+15 with is the constant and which is the coefficient
Answer:
constant = 15
coefficient = 2.5
Step-by-step explanation:
A constant does not change value no matter what, and a constant's derivative is always 0. In this equation, 15 does not change with any variable, therefore it is the constant.
A coefficient is the number that comes before a variable. In the equation, r is a variable, and the number 2.5 comes before it, making it the coefficient.
Solve for the variable c in this equation.
a(b – c) = d
I'm confused can someone help me?
Answer:
c = (ab -d) /a
Step-by-step explanation:
a(b – c) = d
Divide each side by a
a/a(b – c) = d /a
b-c = d/a
Subtract b from each side
b-b-c = d/a -b
-c = d/a -b
Multiply by -1
-1*-c = -1(d/a -b)
c = -d/a +b
c = b - d/a
Get a common denominator
c = b*a/a -d/a
Combine over the common denominator
c = (ab -d) /a
The Law of Large Numbers states that as the number of trials of an experiment increases, the experimental probability of an event occurring approaches the theoretical probability of the event occurring. Jake received a "magic" coin from his uncle. He flipped it 100 times, and found that it came up heads 64% of the time. He flipped it another 500 times, and it came up heads 57% of the time. He then flipped it 1000 times, and it came up heads 58% of the time. Then, he flipped it 1500 times, and it came up heads 62% of the time. Based on the Law of Large Numbers, what do you think the theoretical probability of the magic coin coming up heads is? Explain how you could test your hypothesis.
Answer: Explained.
Step-by-step explanation: We are familiar with the theory of probability and the Law of 'Large Numbers'.
According to this law, if same experiment is repeated a large number of times, then the average of the experimental results in each trial shoul be very close to the theoretical probability.
When Jake flipped the magic coin 100 times, the probability of getting hesd was 0.64.
When he flipped 500 times, the probability of getting head was 0.57.
When he flipped 1000 times, the probability of getting head was 0.58
and when he flipped 1500 times, the probability was 0.62.
Also, the theoretical probability of the magic coin coming up head is
[tex]p=\dfrac{1}{2}=0.5.[/tex]
Therefore, we see that as the number of experiments increases, the value becomes closer to the theoretical value which is 0.5.
what is the value of c when the value of the expression 2(3–5c) is 1 less than the value of the expression 4(1–c)?
The answer in fraction form is c = 1/2
The answer in decimal form is c = 0.5
=============================
Explanation:
Saying "A is 1 less than B" means A = B-1. So whatever B is, subtract 1 from it and you get the value of A.
Replace A with the expression 2(3-5c). Replace B with 4(1-c)
We go from this
A = B - 1
to this
2(3-5c) = 4(1-c) - 1
----------
Let's isolate c
2(3-5c) = 4(1-c) - 1
2(3)+2(-5c) = 4(1)+4(-c) - 1
6-10c = 4 - 4c - 1
6-10c = 3 - 4c
6-3 = -4c+10c
3 = 6c
6c = 3
c = 3/6
c = 1/2
c = 0.5
The value of c in the given expressions is 1.
The value of c when the expression 2(3–5c) is 1 less than the expression 4(1–c) is 1.
First, we set up the equation: 2(3-5c) = 4(1-c) - 1.
Solving this equation step by step will lead us to the value of c.
In this case, the solution is c = 1.
1/2 of a box of cereal is divided equally between 4 bowls.How much cereal is in each bowl
Answer:
0.125
Step-by-step explanation:
you have half of box divide that by 4
a store marks up the wholesale cost of all bikes by 30% . Andre wants to buy a bike that has a price tag of $196. What was the wholesale cost of te bike?
Answer:
$150.77
Step-by-step explanation:
The cost of the bike after a 30% markup is equal to $196. In order for this to happen we have to understand that to mark something up means 100% + 30% in this case. 100% represents the original price of the item and 30% is the markup. In decimals 100% is = 1 since 100÷100=1 and 30% is 30÷100=0.3, therefore to mark the original item "x" we have to multiply that number by 1.30 and so mathematically speaking:
[tex]x(1.3)=196\\\\x=\frac{196}{1.3}\\\\x=150.77[/tex]
The wholesale price of the bike is $150.77
What is the value y of 3x + y = 9 y = –4x + 10
Answer:
1
Step-by-step explanation:
first of all, use substitution.
3x + - 4x +10 =9
Then move all x's to one side.
10 = 9 + x
Move all normal numbers to one side
1 = x
Answer:
y=6
Step-by-step explanation:
A family goes on a long car trip. The number of miles, y, they have left to drive is given by the equation y=510−60x, where x represents the time in hours. Which of the following values could be in the domain in this problem? Check all that apply.
1.5
10
0
60
-3
Answer:
0,1.5
Step-by-step explanation:
y = 510 - 60x
We want to find the domain or the x values where x represents the time
We need to determine the possible values for x
Y cannot be greater than 510 or less than 0. 510 means they have not started the trip, and 0 means they have arrived
510 = 510 -60x
Subtract 510 from each side
510-510 = 60x
0 = 60x
The smallest value of x can be 0
0 = 510 - 60x
Subtract 510 from each side
-510 = 510-510-60x
-510=-60x
Divide by -60
-510/-60 = -60x/-60
8.5 = x
The maximum value of x is 8.5 hours
So x must be between 0 and 8.5 inclusive.
Answer:
1.5 and 0
Step-by-step explanation:
The domain is the set of all possible x-values that make the function work and generate real y-values.
y = 510 – 60x
y cannot be greater than 510, because that would mean they are not yet at their starting point.
y cannot be less than 0, because that would mean they have passed their destination
We can get an idea of the domain if we solve the function for x. We get
x=(510 – y)/60
If y = 510, x = 0.
If y = 0, x = 510/60 = 8.5.
Thus, the domain is 0 ≤ x ≤ 8.5.
The only numbers in your list that could be in the domain are 1.5 and 0.
10 and 60 are wrong, because they give negative values for y.
-3 is wrong, because it gives y > 510.
Which expression is equivalent to: (x^1/4 y^16)^1/2 ?
A. X^1/2 Y^4
B. X^1/8 Y^8
C. X^1/4 Y^8
D. X^1/4 Y^4
Answer: B. X^1/8 Y^8
Step-by-step explanation:
The equivalent expression for (x^1/4 y^16)^1/2 is x^1/8 y^8, using the power of a power rule in properties of exponents.
The expression (x^1/4 y^16)^1/2 can be simplified through the properties of exponents. To simplify, we apply the power of a power rule, which states that (a^m)^n = a^(m*n). Applying this rule:
(x^1/4 y^16)^1/2 = x^(1/4 * 1/2) * y^(16 * 1/2) = x^(1/8) * y^8
Therefore, the equivalent expression is x^1/8 y^8, which corresponds to option B.
Explain why i^18 must be equal to -1.
Answer:
i is equal to the square root of -1, and -1 to any power equals -1
Step-by-step explanation:
[tex]i^18[/tex] must be equal to 1 because [tex]i^4[/tex] is equal to 1, and 18 is a multiple of 4.
The imaginary unit i is defined as the square root of -1. Therefore, by definition, [tex]i^2[/tex] = -1.
Now let's consider higher powers of i:
[tex]- i^3 = i^2 i = -1 i = -i[/tex]
[tex]- i^4 = i^2 = -1 = 1[/tex]
Notice that when we raise i to the fourth power, we get 1. This is a key observation because it means that the powers of i repeat every four powers. This is known as the cyclical nature of the powers of i.
Given that [tex]i^4 = 1[/tex], we can express any power of i that is a multiple of 4 as 1. This is because raising i to any multiple of 4 will result in an even number of -1 factors, which will always multiply to 1.
Now, let's consider [tex]i^18[/tex]:
- Since 18 is divisible by 4 (18 = 4 * 4.5), we can express [tex]i^18 as (i^4)^4.5[/tex].
- We know that [tex]i^4 = 1[/tex], so [tex](i^4)^4.5 = 1^4.5 = 1[/tex].
Therefore, [tex]i^18[/tex] = 1, not -1 as initially stated. The power of i cycles through -1, -i, 1, and i, repeating every four powers. Since 18 is a multiple of 4, i^18 lands on 1 in this cycle.
Sara worked 45 hours one week, of which 5 hours were overtime. She earned $10.48 per hour and gets paid time and a half for overtime. How much did she earn for the week?
Answer:
$497.80
Step-by-step explanation:
First, you want to find half of 10.48. This should be 5.24.
So, add 10.48 and 5.24. This gives you 15.72.
Now, you want to multiply that by 5, since 5 hours were overtime.
This gives you 78.60.
Lastly, you want to multiply 10.48 by 40.
This gives you 419.20
Now, add 78.60 and 419.20 together, giving you your answer of $497.80
Sara got $497.80 for the week.
Factor the trinomial below x2+14x+48
Answer:
(x + 6)(x + 8)
Step-by-step explanation:
Multiply x^2 by 48.
48 * x^2 = [tex]48x^2[/tex]
Factor 48.
Find two factors which add to 14.
6 and 8.
Check
6 * 8 = 48
6 + 8 =14
Add x by 6
Add x by 8
Answer
(x + 6)(x + 8)
The factors of the given trinomial are (x+6) & (x+8)
What is trinomial ?
If an algebraic expression has three non-zero terms or monomials, then it is called trinomial.
Example : [tex]x^{2} +x+1[/tex] , where [tex]x^{2} , x, 1[/tex] are three non-zero terms or monomials.
How to solve the given trinomial ?Given trinomial is [tex]x^{2} +14x+48[/tex]
First, we have to factorise 48 & find two factors whose addition is 14.
The factors are 6 & 8, since 6×8=48 & 6+8=14
Rewrite the terms : [tex]x^{2} +6x+8x+48[/tex]
Regroup terms into two proportional parts : [tex](x^{2} +6x)+(8x+48)[/tex]
Taking common from both parts : [tex]x(x+6)+8(x+6)[/tex]
Factor the expression : [tex](x+6)(x+8)[/tex]
∴ The factors are (x+6) & (x+8).
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trish is taking care of the Han family's dogs. The Hans leave 7 cans of dog food for the 3 days they will be away. How much food will the dogs get each day ifTrish feeds them an equal amount each day?
Answer: 2 and 1/3 cans per day
Step-by-step explanation:
Attempt to divide the cans into 3 equal piles. you get 2 cans in each pile and one left over. Divide the last can into three parts.
A company employee is planning a promotion party with her friends. She orders 6 pizzas for $7 each, 2 bowls of mixed salad for $12 each, and 4 cases of assorted soft drinks for $5 each. How much is she spending on the party?
Answer:
$86 is she spending on the party.
Step-by-step explanation:
As per the statement: A company employee is planning a promotion party with her friends. She orders 6 pizzas for $7 each, 2 bowls of mixed salad for $12 each, and 4 cases of assorted soft drinks for $5 each.
⇒ 6 pizzas for $7 each
Total cost for 6 pizzas = [tex]6 \times 7 = \$42[/tex]
2 bowls of mixed salad for $12 each.
Total cost for 2 bowls = [tex]2 \times 12 = \$24[/tex]
and
4 cases of assorted soft drinks for $5 each.
Total cost for 4 cases of assorted soft drinks = [tex]4 \times 5 = \$20[/tex]
She spending on party = Total cost for 6 pizzas + Total cost for 2 bowls + Total cost for 4 cases of assorted soft drinks
Substitute the values we get;
Total cost she spending on party = [tex]\$42 + \$24 + \$20 =\$86[/tex]
Latoya is on her way home in her car. She has driven 30 miles so far, which is five-sixths of the way home. What is the total length of her drive?
Answer:
36
Step-by-step explanation:
5/6 of x = 30 miles
Multiply each side by 6 to get rid of the fraction
5x = 180
Divide each side by 5
x = 36
Determine whether the lines are parallel. Use slope to explain your answer. Use the graph shown below
(graph)
The slope is of the red line is __
The slope is of the blue line is __
The lines do/do not have the same slope so they are/are not parallel.
If the line segment shown is reflected over the x-axis, what will be the new coordinates of point B? A) (4, 3) B) (-4, 3) C) (4, -3) D) (-4, -3)
Answer:
The answer is C (4,-3)
Step-by-step explanation:
When you reflect over the x axis that means you flip the image to the opposite side over the x (horizontal) line. So if the first line is (4,3) then the reflection is (4,-3)
what is the solution of −1.2b−5.3≥1.9
Answer:
[tex] b \le -6 [/tex]
Step-by-step explanation:
[tex] -1.2b - 5.3 \ge 1.9 [/tex]
Add 5.3 to both sides of the inequality.
[tex] -1.2b - 5.3 + 5.3 \ge 1.9 + 5.3 [/tex]
[tex] -1.2b \ge 7.2 [/tex]
Divide both sides by -1.2. When you multiply or divide both sides of an inequality by a negative number, the inequality sign changes direction. In this case, the "greater than or equal to" sign changes to a "less than or equal to" sign.
[tex] \dfrac{-1.2b}{-1.2} \le \dfrac{7.2}{-1.2} [/tex]
[tex] b \le -6 [/tex]
The solution set of the given inequality is {-6, -7, -8, -9, -10,......}.
The given inequality is -1.2b-5.3≥1.9.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The solution of given inequality can be solved as follows:
Add 5.3 to both side of the inequality, we get
-1.2b-5.3+5.3≥1.9+5.3
⇒ -1.2b≥7.2
Divide -1.2 to both side of the inequality, we get
-1.2b/(-1.2) ≤ 7.2/(-1.2)
⇒ b ≤ -6
So, solution set = {-6, -7, -8, -9, -10,......}
Therefore, the solution set of the given inequality is {-6, -7, -8, -9, -10,......}.
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What is the area of the rectangle?
50 units^2
54 units^2
60 units^2
65 units^2
The area of the rectangle is 60 units²
Since from the graph, we have the vertices of the rectangle at (-1,1), (8, -2), (-3, -5) and (6, -8).
The pair (-1, 1) and (8, -2) represent the coordinates for the length of the rectangle while the pair (-1, 1) and (-3, -5) represent the coordinates for the width of the rectangle.
So, we find the length of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₂, y₂)
So, the length, L = √[(x₂ - x₁)² + (y₂ - y₁)²] where (x₁, y₁) = (-1, 1) and (x₂, y₂) = (8, -2)
So, L = √[(x₂ - x₁)² + (y₂ - y₁)²]
L = √[(8 - (-1))² + (-2 - 1)²]
L = √[(8 + 1))² + (-3)²]
L = √[(9)² + (-3)²]
L = √[81 + 9]
L = √90
L = 3√10 units
Also, we find the width of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₃, y₃)
So, the width, W = √[(x₃ - x₁)² + (y₃ - y₁)²] where (x₁, y₁) = (-1, 1) and (x₃, y₃) = (-3, -5)
So, W = √[(x₃ - x₁)² + (y₃ - y₁)²]
W = √[(-3 - (-1))² + (-5 - 1)²]
W = √[(-3 + 1))² + (-6)²]
W = √[(-2)² + (-6)²]
W = √[4 + 36]
W = √40
W = 2√10 units
Since the area of a rectangle A = LW, we have
A = 3√10 units × 2√10 units
A = 3 × 2 × √10 × √10 units²
A = 3 × 2 × 10 units²
A = 60 units²
So, the area of the rectangle is 60 units²
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The area of the rectangle is 60 units².
To find the area of a rectangle, you need to multiply its length by its width.
Since from the graph, we have the vertices of the rectangle at (-1,1), (8, -2), (-3, -5) and (6, -8).
The pair (-1, 1) and (8, -2) represent the coordinates for the length of the rectangle while the pair (-1, 1) and (-3, -5) represent the coordinates for the width of the rectangle.
So, we find the length of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₂, y₂)
So, the length, L = √[(x₂ - x₁)² + (y₂ - y₁)²] where (x₁, y₁) = (-1, 1) and (x₂, y₂) = (8, -2)
So, L = √[(x₂ - x₁)² + (y₂ - y₁)²]
L = √[(8 - (-1))² + (-2 - 1)²]
L = √[(8 + 1))² + (-3)²]
L = √[(9)² + (-3)²]
L = √[81 + 9]
L = √90
L = 3√10 units
Also, we find the width of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₃, y₃)
So, the width, W = √[(x₃ - x₁)² + (y₃ - y₁)²] where (x₁, y₁) = (-1, 1) and (x₃, y₃) = (-3, -5)
So, W = √[(x₃ - x₁)² + (y₃ - y₁)²]
W = √[(-3 - (-1))² + (-5 - 1)²]
W = √[(-3 + 1))² + (-6)²]
W = √[(-2)² + (-6)²]
W = √[4 + 36]
W = √40
W = 2√10 units
Since the area of a rectangle A = LW, we have
A = 3√10 units × 2√10 units
A = 3 × 2 × √10 × √10 units²
A = 3 × 2 × 10 units²
A = 60 units²
So the area of the rectangle is 60 units².
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Can someone please help me with these 4 math pronlems, I can't figure them out! Please, please, please, help me!
1. The direction of the vector [tex]\theta[/tex] relative to the positive x-axis satisfies
[tex]\tan\theta=\dfrac35\implies\theta\approx30^\circ[/tex]
2. A vector with magnitude [tex]\|\mathbf v\|[/tex] and direction [tex]\theta[/tex] has component form
[tex]\mathbf v=\langle\|\mathbf v\|\cos\theta,\|\mathbf v\|\sin\theta\rangle[/tex]
We have [tex]\|\mathbf v\|=5[/tex], but "angle of 60 degrees with the negative x-axis" is a bit ambiguous. I would take it to mean "60 degrees counterclockwise relative to the negative x-axis", so that the direction is [tex]\theta=240^\circ[/tex]. Then
[tex]\mathbf v=\langle5\cos240^\circ,4\sin240^\circ\rangle\approx\langle-2.5,-4.3\rangle[/tex]
But this doesn't match any of the options, so more likely it means the angle is 60 degrees clockwise relative to the negative x-axis, in which case [tex]\theta=120^\circ[/tex] and we'd get
[tex]\mathbf v=\langle5\cos120^\circ,4\sin120^\circ\rangle\approx\langle-2.5,4.3\rangle[/tex]
3. Same as question 2, but now we're using [tex]\mathbf i,\mathbf j[/tex] notation. The vector has magnitude [tex]\|\mathbf v\|=14[/tex] and its direction is [tex]\theta=-30^\circ[/tex]. So the vector is
[tex]\mathbf v=14\cos(-30^\circ)\,\mathbf i+14\sin(-30^\circ)\,\mathbf j=12.1\,\mathbf i-7\,\mathbf j[/tex]
4. The velocity of the plane relative to the air, [tex]\mathbf v_{P/A}[/tex] is 175 mph at 40 degrees above the positive x-axis. The velocity of the air relative to the ground, [tex]\mathbf v_{A/G}[/tex], is 35 mph at 60 degrees above the positive x-axis. We want to know the velocity of the plane relative to the ground, [tex]\mathbf v_{P/G}[/tex].
We use the relationship
[tex]\mathbf v_{P/G}=\mathbf v_{P/A}+\mathbf v_{A/G}[/tex]
Translating the known vectors into component form, we have
[tex]\mathbf v_{P/G}=\langle145\cos40^\circ,145\sin40^\circ\rangle+\langle35\cos60^\circ,35\sin60^\circ\rangle\approx\langle152,143\rangle[/tex]
This vector has magnitude and direction
[tex]\|\mathbf v_{P/G}\|\approx\sqrt{152^2+143^2}\approx208\,\mathrm{mph}[/tex]
[tex]\tan\theta\approx\dfrac{143}{152}\implies\theta\approx43^\circ[/tex]
(or 43 degrees NE)
Answer: #3 is v=12.1i-7j
got it right on my test
#4 is C 208 mph and 43 northeast
Step-by-step explanation:
Write the phrase "one more than the product of six and nine" as a mathematical expression.
A. 6 – 9 + 1
B. 6 + 9 + 1
C. 6 ⋅ 9 + 1
D. 6⁄9 + 1
Answer:
C. 6 ⋅ 9 + 1
Step-by-step explanation:
Start with the multiplication:
"one more than the product of six and nine"
6 ⋅ 9
Now take care of the addition by adding 1 to the product.
"one more than the product of six and nine"
6 ⋅ 9 + 1
Answer: C. 6 ⋅ 9 + 1
a calculator costs 12.99. if its on sale for 20% off and sales tax is 6.25% what is the final cost of the calculator?
I’m pretty sure you can first do 10% at a time which you can round to 13 which is 3 so 3 plus 3 then add tax
Hi There!
Step-by-step explanation:
20% = 0.2
6.25% = 0.0625
Discount: 12.99 * 0.20 = $2.598
Sale Price: 12.99 - 2.598 = $10.392
Tax: 10.392 * 0.0625 = 0.6495
Price After Tax: 10.392 - 0.6495 = 9.7425
Round: 9.7425 = 9.74
Answer:
$9.74
Hope This Helps :)
What expression is equivalent (25points)
Answer:
30b
Step-by-step explanation:
-6(-5) is 30.
Let f(x)=3x+5 and g(x) =x^2 find g(x)/f(x) and state its domain
[tex]\text{Let}\ f(x)=3x+5\ \text{and}\ g(x)=x^2\\\\\dfrac{f(x)}{g(x)}=\dfrac{3x+5}{x^2}\\\\\text{The domain:}\\\\x^2\neq0\to x\neq0\\\\Answer:\ \boxed{x\in\mathbb{R}-\{0\}}\to\boxed{x\in(-\infty,\ 0)\ \cup\ (0,\ \infty)}\\\\\text{All real numbers except 0.}[/tex]
How do you solve 64x^2=1
The picture is what I did before-which was wrong.
Answer:
x = ± 1/8
Step-by-step explanation:
64 x^2 =1
Divide each side by 64
64 x^2/64 = 1/64
x^2 = 1/64
Take the square root of each side, remembering to take the positive and negative.
sqrt(x^2) = ±sqrt(1/64)
x = ±sqrt(1)/ sqrt(64)
x = ± 1/8
Does anyone have any Idea how to solve this?
Answer:
x = 12
Step-by-step explanation:
Remark
These two angles are corresponding angles and as such, they are equal.
Equation
8x+ 36 = 5x + 72
Solution
Subtract 5x from both sides
8x - 5x + 36 = 5x - 5x + 72 Combine like terms.
3x + 36 = 72 Subtract 36 from both sides
3x + 36 - 36 = 72 - 36 Collect like terms
3x = 36 Divide by 3
3x/3 = 36/3 Divide
x = 12 Answer
[tex]1 = \frac{u}{2} - 1[/tex]
Multiply by 2:
2=u-2
4=u or u=4.
find the area of washers whose external and internal diameter are 15cm and 13cm
Answer:
≈ 44 cm²
Step-by-step explanation:
the area (A) of the washer is found using A = πr² ( r is the radius )
A = external area - internal area
external radius = [tex]\frac{15}{2}[/tex] = 7.5 cm
internal radius = [tex]\frac{13}{2}[/tex] = 6.5 cm
A = π ( 7.5² - 6.5² ) = π (56.25 - 42.25 ) = 14π ≈ 44 cm²
The area of the washer is calculated by finding the area of the external circle using its radius and then subtracting the area of the internal circle determined by its radius.
Explanation:To find the area of a washer, we need to calculate the area of the larger outer circle and subtract the area of the smaller inner circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.
Firstly, we calculate the area of the outer circle with a diameter of 15 cm. The radius r is half the diameter, so r = 15cm / 2 = 7.5 cm. The area, A₁, of the outer circle is:
A₁ = π × (7.5 cm)²
Secondly, we calculate the inner circle's area with a diameter of 13 cm. Similarly, its radius r is 13cm / 2 = 6.5 cm. The area, A₂, of the inner circle is:
A₂ = π × (6.5 cm)²
To find the washer's area, we subtract the inner area from the outer area:
Area of Washer = A₁ - A₂ = (π × (7.5 cm)²) - (π × (6.5 cm)²)
The result will be the cross-sectional area of the washer.
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The table show the total distance d, in miles, a car traveled after t hours. Time in hours (h) Distance in miles (d) 0 0 1 50 2 100 3 150 Which equation shows the relationship between d and t? d=50t d=t+150 d=150t d=t+50
Answer:
Option A is correct.
d = 50t shows the relationship between d and t
Step-by-step explanation:
Point slope form: For a point [tex](x_1, y_1)[/tex] and a slope m, the equation of the line can be written as
[tex]y-y_1=m(x-x_1)[/tex] ......[1], where m is the slope of the line.
Here, d represents the total distance ( in miles) and t represents the time (in hours).
From the given table:
Consider any two points (1, 50) and (2, 100).
Calculate slope:
Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{100-50}{2-1}=\frac{50}{1} =50[/tex]
⇒[tex]m= 50[/tex]
Now, by point slope intercept form:
Substitute m= 50 and (1, 50) in [1]
we have;
[tex]y -50 = 50(x-1)[/tex]
Using distributive property: [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]
y -50 = 50x -50
Add both sides 50 we get;
y -50+ 50= 50x -50 + 50
Simplify:
[tex]y =50x[/tex]
∵y = d represents the distance and x = t represents the time;
then, our equation become:
[tex]d = 50t[/tex]
The equation representing the relationship between the distance covered (d) and time (t) in the given situation is d = 50t. This signifies that the distance covered is equal to 50 times the time.
In the given data, we observe that the total distance (d) travelled by the car in an hour is always 50 miles. This means that every hour, the car covers a distance of 50 miles.
Therefore, the relationship between the distance covered (d) and time (t) can represent this situation is d = 50t.
This signifies that 'd', the distance covered, is equal to 50 times 't', the time in hours. For example, when t=1 hour, d = 50*1 = 50 miles. Similarly, when t=2 hours, d = 50*2 = 100 miles. This continues accordingly.
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What is 5x + 8y =16 in slope intercept form
ABOUT SLOPE INTERCEPT FORM:
y = mx + bm represents the slopeb represents the y-interceptYou have to get y by itself:
5x + 8y = 16
-5x -5x
8y = -5x + 15
8 8
y = -5/8x + 15/8
OR
I you wants to simplify 15/8, it's this:
y = -5/8x +1.875
HI!!! Really really sorry if I'm incorrect...