68/80 as a fraction,percent,and decimal
Answers
Divide by 4 to get 17/20
(68/4)/(80/20)
Percent: 85%
Using 17/20 -Multiply each side by 5 to get ____/100
17*5/20*5 = 85/100 or 85%
Decimal: 0.85
Using 85/100, divide it out to get 0.85.
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Answers
D=
when you want to find the distance between points (x1,y1) and (x2,y2)
we nee
distace from
b to c
c to d
d to b
b to c is (-3,3) to (3,5)
D=
c to d is (3,5) to (-1,0)
D=
d to b is (-1,0) to (-3,3)
D=
add
b to c+c to d+d to b=2√10+√41+√13
perimiter=2√10+√41+√13 units
Answers
Answer:
x = - 1
Step-by-step explanation:
= 2x + 1 ( multiply both sides by 5 to clear the fraction )
4x - 1 = 5(2x + 1) ← distribute parenthesis
4x - 1 = 10x + 5 ( subtract 10x from both sides )
- 6x - 1 = 5 ( add 1 to both sides )
- 6x = 6 ( divide both sides by - 6 )
x = - 1
4x-1=10x+5
2) take 4x to right side n 5 to left
-5-1=10x-4x
-6=6x
x=-1
Answers
Answer:
Austin has been the goalie in 6 games.
Step-by-step explanation:
The diagram that models the ratio in the story is a fraction diagram.
Let's represent Austin playing forward as F and Austin being the goalie as G.
According to the story, Austin has played forward in 4 games for every 3 games he has been the goalie. This can be represented as the fraction 4/3.
Now, we know that Austin has played forward in 8 games.
To find out how many games he has been the goalie, we can set up a proportion using the ratio from the story:
4/3 = 8/x
To solve for x, we can cross-multiply:
4x = 3 * 8
4x = 24
Dividing both sides of the equation by 4, we get:
x = 6
Therefore, Austin has been the goalie in 6 games
Answers
Answer: a=4, b=16, c=12
Step-by-step explanation:
Use the intercept form: a(x - p)(x - q) where p & q are the intercepts.
Given: p = -3, q = -1, and y-intercept (c) = 12
a[x - (-3)][x - (-1)]
= a(x + 3)(x + 1)
= a(x² + 4x + 3)
= ax² + 4ax + 3a
y-intercept = 12
3a = 12
a = 4
Substitute a = 4
4x² + 4(4)x + 3(4)
= 4x² + 16x + 12
Answers
and the
saucer = S
then
(S + 3) + S = 12
2s + 3 = 12
2s = 9
s = 4.50
So by itself the saucer costs $4.50. To find the cost of the cup look to the beginning of the problem where we learned that
Cup = S + 3
cup = 4.50 + 3
cup = 7.50
So the saucer is $4.50 and the cup is $7.50...
4.50 + 7.50 = $12.00
It checks!
Answers
Answer:
1) The equation of the line is y = x + 4
2) The equation of the line is y = -12x + 8
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
- m is the slope of the line, m = Δy/Δx (chang of y/change of x)
- b is the y-intercept (value y at x = 0)
Let us solve the two questions
1)
∵ points (-2, 5) and (2, 3) lie on the same line
→ Find the slope m
∵ Δ x = 2 - (-2) = 2 + 2 = 4
∵ Δ y = 3 - 5 = -2
∴ m =
∴ The slope of the line is
→ Substitute the value of m in the form of the equation above
∴ y = x + b
→ To find b substitute the x and y in the equation by the coordinates
of a point on the line
∵ Point (-2, 5) lies on the line
∴ x = -2 and y = 5
∵ 5 = (-2) + b
∴ 5 = 1 + b
- Subtract 1 from both sides
∴ 5 - 1 = 1 - 1 + b
∴ 4 = b
→ Sustitute it in the equation
∴ y = x + 4
The equation of the line is y = x + 4
2)
∵ The slope of the line is -12
∴ m = -12
∵ The line passes through point (0, 8)
∵ b is the value of y at x = 0
∴ b = 8
→ Substitute the values of m and b in the form of the equation above
∴ y = -12x + 8
The equation of the line is y = -12x + 8
Final answer:
The equations of the lines are y=-0.5x+4 and y=-12x+8 respectively. For the first line, the slope is computed using provided points and the y-intercept is calculated using one of the points and the slope. For the second line, we use provided slope and point to write the equation.
Explanation:
Firstly, let's deal with the first part of the question. To write the equation of the line, we first need to calculate the slope. The slope (m) is calculated as (y2-y1)/(x2-x1). Using the points (-2,5) and (2,3) we find m=(3-5)/(2-(-2))= -2/4 = -0.5. The y-intercept (b) is the y value when x = 0. To find b, let's use the point (-2,5) and the slope in the equation y=mx+b. We get 5=(-0.5)*-2+b, hence b= 5-1= 4. So line equation is y=-0.5x+4.
For the second part of the question, we know that the slope (-12) and it passes through the point (0,8). So the y-intercept is 8 when x=0. Therefore, the equation of this line is y=-12x+8.
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