Find the distance from point A(-1/4,5) to the line -x+2y=14. Round your answer to the nearest tenth.
Answers
Answer:
The distance from A(-1/4, 5) to the line -x + 2·y = 14 is approximately 1.7 units
Step-by-step explanation:
The shortest distance from a point to a line is the perpendicular from the line to the point
The equation of the given line is -x + 2·y = 14, which can be written in slope and intercept form as follows;
-x + 2·y = 14
2·y = 14 + x
y = 14/2 + x/2 = x/2 + 7
y = x/2 + 7
The slope, m₁ = 1/2 and the y-intercept = 7
Therefore, the slope, m₂, of the perpendicular line to the line -x + 2·y = 14 which was rewritten as y = x/2 + 7 is m₂ = -1/m₁ = -1/(1/2) = -2
Therefore, we have that the slope of the line from A(-1/4, 5) to the line -x + 2·y = 14, is -2
The equation of the line is therefore;
y - 5 = -2(x - (-1/4))
y - 5 = -2·x - 1/2
y = -2·x - 1/2 + 5 = -2·x + 9/2
y = -2·x + 9/2
The coordinates of the point on the line -x + 2·y = 14 (y = x/2 + 7) that coincides with the perpendicular from the point A(-1/4, 5) is therefore given as follows;
-2·x + 9/2 = x/2 + 7
9/2 - 7= x/2 + 2·x
-2.5 = 2.5·x
x = -2.5/2.5 = -1
x = -1
y = x/2 + 7 = -1/2 + 7 = 6.5
y = 6.5
The coordinates of the point on the line -x + 2·y = 14 (y = x/2 + 7) that coincides with the perpendicular from the point A(-1/4, 5) is (-1, 6.5)
The distance from A(-1/4, 5) to B(-1, 6.5), is given as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where;
(x₁, y₁) = (-1/4, 5), and (x₂, y₂) = B(-1, 6.5)
Plugging in the values, we have;
[tex]l_{AB} = \sqrt{\left (6.5-5 \right )^{2}+\left ((-1)-(-1/4) \right )^{2}} = \sqrt{\left (-0.75 \right )^{2}+\left (1.5 \right )^{2}} = \sqrt{\dfrac{45}{16} } = \dfrac{3}{4} \cdot \sqrt{5}[/tex]
[tex]l_{AB} = \dfrac{3}{4} \cdot \sqrt{5} \approx 1.677[/tex]
Therefore, the distance from A(-1/4, 5) to the line -x + 2·y = 14 ≈ 1.7 units, rounding to the nearest tenth.
Answer:
Step-by-step explanation: no work shown?
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A cake recipe for 5 people requires two eggs. How many eggs do you need for a 15 person cake
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Answer:
6 eggs
Step-by-step explanation:
15=5*3
so times the eggs by 3
2*3=6
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B: 0.5 v
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A: 10 v
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Answers
Answer:
A: 10v
B: 5v
Step-by-step explanation:
A: Smallest increment can be found by doing 100/ number of tick marks to 100/ (so 100/10)
B: Uncertainty is smallest increment /2 or 10/2
Answer:
A: 10v
B: 5v
Step-by-step explanation: Hoped this helped :3
Maria is ordering trophies for school. Company Christopher charges $3.50 for each trophy and a one-time engraving fee of $25. Company Asya charges $7.50 for each trophy and a one-time engraving fee of $17 Develop an equation where the two companies would be the same.
Answers
Answer:
An equation where the two companies would be the same is given as:
25 + 3.50x = 17 + 7.50x
Step-by-step explanation:
Let the number of trophies ordered be represented by x
Maria is ordering trophies for school. Company Christopher charges $3.50 for each trophy and a one-time engraving fee of $25.
$25 + $3.50 × x
25 + 3.50x
Company Asya charges $7.50 for each trophy and a one-time engraving fee of $17
$17 + $7.50× x
17 + 7.50x
An equation where the two companies would be the same is given as:
Company Christopher = Company Asya
25 + 3.50x = 17 + 7.50x
Simplifying further:
Collect like terms
25 - 17 = 7.50x - 3.50x
8 = 4.00x
x = 8/4
x = 4
Hence, the two companies would be the same after 4 trophies.
Factor completely 4x^2-81
Answers
Answer:
(2x - 9)(2x + 9)
Step-by-step explanation:
4x^2 - 81 = (2x - 9)(2x + 9)
Answer:
(2x+9)(2x-9)
Step-by-step explanation:
kind of simple actually
4x^2-81=(2x+9)(2x-9)
I need help fast plz
Answers
Answer:
1. m = -3, b = 4
2. m = 0, b = 7
3. m = -1.5, b = -4
4. m = 3, b = 0
5. m = 1.5, b = -7
What are the two things that do NOT prove that triangles are congruent?
Answers
Answer:
If the side which lies on one ray of the angle is longer than the other side, and the other side is greater than the minimum distance needed to create a triangle, the two triangles will not necessarily be congruent. to "swing" to either side of point G, creating two non-congruent triangles using SSA.
Step-by-step explanation:
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1-x/1+x=2x+1/-2x+5 find x
Answers
Answer:
x = [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1-x}{1+x}[/tex] = [tex]\frac{2x+1}{-2x+5}[/tex] ( cross- multiply )
(2x + 1)(1 + x) = (1 - x)(- 2x + 5) ← expand parenthesis on both sides using FOIL
2x + 2x² + 1 + x = - 2x + 5 + 2x² - 5x , simplify
2x² + 3x + 1 = 2x² - 7x + 5 ( subtract 2x² from both sides )
3x + 1 = - 7x + 5 ( add 7x to both sides )
10x + 1 = 5 ( subtract 1 from both sides )
10x = 4 ( divide both sides by 10 )
x = [tex]\frac{4}{10}[/tex] = [tex]\frac{2}{5}[/tex]
Answer:
x = 2/5
Step-by-step explanation:
[tex]\frac{1-x}{1+x}=\frac{2x+1}{-2x+5}[/tex]
Cross multiply,
(1 - x)(-2x + 5) = (2x +1)(1 + x)
Use FOIL method to multiply,
1*(-2x) + 1*5 - 2x *(-x) + 5*(-x) =2x *1 + 2x *x + 1*1 + 1*x
-2x + 5 + 2x² -5x = 2x + 2x² + 1 + x
Combine like terms,
-2x - 5x + 2x² + 5 = 2x² + 2x +x + 1
-7x + 2x² + 5 = 2x² + 3x + 1
-7x + 2x² - 2x² - 3x = 1 - 5
-7x - 3x = - 4
-10x = -4
x = -4/-10
x = 2/5
in a baseball game the ball traveled 350.7 feet in 4.2 seconds what was the average speed of the ball in feet per second?
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Answer:
0.0119760479
Step-by-step explanation:
Answer:
the answer is 83.5
Step-by-step explanation:
Johnny scored a 75% on his math test. He got 18 questions
correct. How many questions were on the test? *
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Answer:
24
Step-by-step explanation:
18/24=0.75
Hope this helps!
A computer technician charges $75 for a consultation plus $35 per hour. Write the linear equation that models this situation.
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A triangle with vertices J(3, 0), K(4, 3), and L(6, 0) is rotated clockwise 90° about the origin. What are the new coordinates for J' K' and L' ?
Answers
Answer:
The new coordinates of the triangle J'K'L' are J'(0, -3), K'(3, -4), and J'(6, 0)
Step-by-step explanation:
The given coordinates of the triangle JKL are;
J(3, 0), K(4, 3), L(6, 0)
The rotation of the point of a preimage (x, y) by 90° clockwise gives the point of the image after rotation as (y, -x)
Therefore;
The rotation of point J(3, 0) by 90° clockwise gives J'(0, -3)
The rotation of point K(4, 3) by 90° clockwise gives K'(3, -4)
The rotation of point L(6, 0) by 90° clockwise gives J'(6, 0)
The new coordinates of the triangle J'K'L' are J'(0, -3), K'(3, -4), and J'(6, 0)
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When f(c)= 10x^2 + 3x -4, evaluate f(-4)
Answers
Answer:
[tex]f(x) = 144[/tex]
Step-by-step explanation:
This problem deals with a function. All this question is asking is to plug in -4 every time an x appears.
So, let's do that:
[tex]f(-4) = 10(-4)^{2} + 3(-4) - 4[/tex]
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1. Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, y, after x days. In how many days will the water level be 26 feet?
Slope(m)=
y-intercept(b)=
equation y=
Answer=
Answers
Slope = -0.5
Y-intercept = 34
Equation: y = -0.5x + 34
Answer = It will take 16 days for the water level to be 26 feet.
The question is an illustration of a linear function.
The equation of the function is: [tex]\mathbf{y = 34- 0.5 x}[/tex]The number of days to reach 26ft is 16The given parameters are:
[tex]\mathbf{Level = 34ft}[/tex]
[tex]\mathbf{Rate = -0.5ft/day}[/tex]
The equation of the function is:
[tex]\mathbf{y = Level +Rate \times x}[/tex]
Where:
y represents the water level
x represents the number of days
So, we have:
[tex]\mathbf{y = 34- 0.5 \times x}[/tex]
[tex]\mathbf{y = 34- 0.5 x}[/tex]
A linear equation is represented as;
[tex]\mathbf{y = mx + b}[/tex]
So, by comparison:
[tex]\mathbf{Slope(m) = -0.5}[/tex]
[tex]\mathbf{y-intercept (b) = 34}[/tex]
When the water level is 26, it means y = 26.
So, we have:
[tex]\mathbf{y = 34- 0.5 x}[/tex]
[tex]\mathbf{26 = 34 - 0.5x}[/tex]
Collect like terms
[tex]\mathbf{26 - 34= - 0.5x}[/tex]
[tex]\mathbf{-8= - 0.5x}[/tex]
Divide both sides by -0.5
[tex]\mathbf{16= x}[/tex]
Rewrite as:
[tex]\mathbf{x = 16}[/tex]
Hence, the number of days to reach 26ft is 16
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Answers
Find the measure of ∠7.
Given:
∠1 is a right angle
∠3 = 37°
∠8 =62°
A. 53°
B. 65°
C. 105°
D. 127°
E. 245°
Answers
Answer:
The answer is B: 65.
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Answers
Answer:
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Step-by-step explanation:
b) Since XB = XC, triangle BXC is therefore an isosceles triangle.
Angle XBC = Angle XCB
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110⁰ + Angle BXC = 180⁰
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Answer:
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Step-by-step explanation:
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—— + 6 = -8 please help me I don’t understand do if you could explain I’d appreciate it.
7
Answers
Answer:
-14
Step-by-step explanation:
_____ + 6 = - 8
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Thus, - 14 + 6 = - 8
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Step-by-step explanation:
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Jose earned 45 points in a video game. He lost 40 points, earned 80 points, then lost 25 more points. Enter and evaluate an expression to find his final score in the video game.
im confused any help?
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Answer:
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Step-by-step explanation:
Every time he earns points we add.
Every time he loses points we subtract.
We can write an equation to resemble the problem and simplify.
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A function has a derivative f 1(x)=3-2x. An equation of a line tangent to the graph of the function at x =2 is y-7=-(x-2). What is an equation of the function f?
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Answer:
v1 positive v2 negative
Step-by-step explanation: