Mary’s age ten years ago is:
m−10
So Danilo’s age is:
5 (m−10)
= 5m−50
We may answer this by calculating a proportion based on the area-to-price ratio:
1,500⁄$300,000 = 2,000⁄x
Cross multiply and solve for x:
1,500x = $600,000,000
x = $400,000
The simplest solution is as follows:
2x+5 = 8x
8x−2x = 5
6x = 5
6x⋅2 = 5⋅2
12x = 10
A line's slope-intercept form is:
y = mx+b
There are three alternatives because the line crosses through (1,2). The line will be vertical (x=1), horizontal (y=2), or have a slope (the "m" in front of the "x" variable).
To determine which equation is not satisfied, substitute x=1 into each of the four equations. The only option that does not result in y = 2 is y = x+1.
The correct answer:
1⁄4
Explanation:
To factor the quadratic equation, we must find the two 15 (constant term) components that add up to 8 (the coefficient of x):
15 = 3⋅5
8 = 3+5
As a result, 3 and 5 are the two factors that satisfy our criteria. The quadratic's completely factored form is:
(x+3)(x+5)=0
Recall that if ab=0, then either a=0, or b=0.
If (x+3)(x+5) = 0
Then either (x+3)=0, or (x+5)=0
That is, either: x=−3, or x=−5
The roots of the quadratic are: −3, and −5
At the x-intercept, the value of y is equal to zero. By setting y=0 in the equation of the line, we may solve for the x-intercept:
2y = 3x−6
2(0) = 3x−6
0 = 3x−6
3x = 6
x = 2
In 5 days, ten people can paint a building. In 5 days, each person paints a tenth of the building.
7 individuals would paint 7/10 of the building in 5 days.
Seven individuals would paint 7/10 of the building in five days.
Explanation:
The first step is to determine which variables will be used:
Let the number of pens Donna purchased =x
Let the number of pencils Donna purchased =y
By creating two equations and solving for x, we can figure out how many pens Donna bought.
0.6x+0.4y=8.2
x+y=17
y=17−x
0.6x+0.4(17−x)=8.2
0.6x+6.8−0.4x=8.2
0.2x=1.4
x = 1.4⁄0.2 = 14⁄2 = 7
The correct answer is (A). The formula for the area of a rectangle:
A=Width⋅Length
From the question, we know that L=2W and that A=50. So we can plug these values into our equation and solve for W:
50=W⋅L
50=W⋅2W
50=2W2
W2=25
W=5
We know that L=2W , so L=10
Perimeter =2L+2W
Perimeter =2⋅10+2⋅5
Perimeter =30
We can simplify the equation as follows:
3(x+1)=5(x−2)+7
3x+3=5x−10+7
3x+3=5x−3
We can add 3 to both sides to get the following:
3x+6=5x
We can subtract 3x from both sides and then divide the resulting equation by 2 to solve for x as follows:
6=2x
3=x
The correct answer is (B). The slope-intercept form of a line is:
y=mx+b
Since the line passes through (−1,2), there are three possibilities: The line will have a slope (the “m” in front of the “x” variable), it will be vertical (x=−1), or it will be horizontal (y=2).
Plug x=−1 into all four equations to see which equation is not satisfied. The only answer choice that doesn’t give us y=2 is y=x+1.
The correct answer is (C). Martina’s age ten years ago is:
m−10
So Diego’s age is:
5(m−10)
=5m−50
Here is the easiest way to solve this:
2x+5=8x
8x−2x=5
6x=5
6x⋅2=5⋅2
12x=10
The correct answer is (D). At the x-intercept, y=0. We can solve for the x-intercept by setting y=0 in the equation of the line:
2y=3x−6
2(0)=3x−6
0=3x−6
3x=6
x=2
