The shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The equation of the line is:
y = 2x + 4
Or
2x - y + 4 = 0
The point is (0, 0)
As we know, the formula for the shortest distance between the line and a point:
D = |ax + bx + c|/√(a²+b²)
Plug x = 0 and y = 0
a = 2, b = -1, and c = 4
D = |2(0) + -1(0) + 4|/√(2²+(-1)²)
D = 4/√5
D = 1,78 ≈ 1.8 units
Thus, the shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.
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Under his cell phone plan, Nathaniel pays a flat cost of $41 per month and $4 per gigabyte. He wants to keep his bill at $45.80 per month. Write and solve an equation which can be used to determine 2, the number of gigabytes of data Nathaniel can use while staying within his budget.
Answer:
equation: 41+4x=45.80
answer: x=1.20
Step-by-step explanation:
The equation is $45.80 = $41 + ($4 × x) which can be used to determine the number of gigabytes of data Nathaniel can use while staying within his budget. And Nathaniel can use up to 1.2 gigabytes of data while staying within his budget of $45.80 per month.
Let's denote the number of gigabytes of data Nathaniel can use as x.
Then the equation representing his cell phone bill can be set up as:
Total cost = Flat cost + (Cost per gigabyte × Number of gigabytes)
$45.80 = $41 + ($4 × x)
Now, we can solve for x:
$4 × x = $45.80 - $41
$4 × x = $4.80
x = $4.80 / $4
x = 1.2
So, Nathaniel can use up to 1.2 gigabytes of data while staying within his budget of $45.80 per month.
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PLEASE HELP ME I BEG IMMA FAILLLLLLLLLLLLLLLL
On a sunny day, a 4-foot red kangaroo casts a shadow that is 5 feet long. The shadow of a nearby eucalyptus tree is 20 feet long. Write and solve a proportion to find the height of the tree.
Answer:
25 feet long
Step-by-step explanation:
this is because the ratio is 4:5
so if one side is 20 then the other side must be in proportion to 4:5
multiply both sides by 5 and u get 20:25
hope that helps
A number written in expanded form is 700,000 + 5,000 + 200 + 80 + 7. What is this number written in word form?
1 seven hundred five thousand, two hundred eighty-seven
2 seventy-five thousand, two hundred eighty-seven
3 seven hundred eighty-two thousand, five hundred seventy
4 seven hundred eighty-two thousand, five hundred seven
A basketball player only scores two-point and three point goals during a game. The basketball player score a total of 25 points with a total of 11 goals during the game
Answer:
3 three pointers and 8 two pointers
Step-by-step explanation:
hope this helps
If you were to graph the function f(x)=−15x+4 on the semester test, you should first graph the y-intercept, then use the slope to graph a second point, and connect the points with a line.
Write the y-intercept of the function f(x)=−15x+4 in the first box. Just write the number, no y= or f(x) =.
Write the slope of the function f(x)=−15x+4 in the second box. Just write the number, no m= or slope=.
Answer:
4
-15
Step-by-step explanation:
(7*10 to the power of 5)*(3*10 to the power of 2)
Step-by-step explanation:
do you mean
7×10⁵ × 3×10²
as you can see, these are all multiplications. and we can do in a first step the multiplications that combine the factors with the same exponent base or simple constants :
7×3 × 10⁵×10² = 21 × 10⁷
in what format do you need the result ?
21 × 10⁷
2.1 × 10⁸ (standard format)
210,000,000
A piece of metal with a length of 2.83 cm was measured using four different devices. Which of the following measurements is the most accurate? O 2.812 cm O 2.837 cm O 2.805 cm 0 2.829 cm
Answer:
2.829
Step-by-step explanation:
ita the closest to 2.83
The most accurate measure is 2.829 cm.
What is rounding off a number?To change a number into an approximation having fewer significant digits.
Given that, A piece of metal with a length of 2.83 cm was measured using four different devices.
a) 2.812 =
Rounding off to the 10th place = 2.81 cm
b) 2.837 =
Rounding off to the 10th place = 2.84 cm
c) 2.805 =
Rounding off to the 10th place = 2.8 cm
d) 2.829 =
Rounding off to the 10th place = 2.83 cm
Hence, the correct answer is 2.829 cm
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Meriel works in a lab and needs to measure 7.5 grams of a substance with a percent error of less than
5%. What is the smallest and largest amount they can measure to stay under this percent error?
Answer:
Step-by-step explanation:
A common way of measuring the mass of objects is to use balance scales. A balance scale works by placing the object you want to weigh on one side and adding gram masses to the other side until the scales are level. Masses for weighing usually come as 1 g, 5 g, 10 g, 20 g or more!
Verify whether:
p(x)= 3x+1 has x=-1/3 as a factor
Hey there!
p(x) = 3x + 1
y = 3x + 1
y = 3(-1/3) + 1
y = -1 + 1
y = 0
Therefore, your answer SHOULD be: y = 0
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Here's the Question ~
[tex] {2 - 1}^{2} [/tex]
Answer:
The answer is 1
Step-by-step explanation:
1² = 1×1
= 1
2 - 1² = 2 - 1
= 1
if you discovered a leaking faucet in your home , do you think it would be important to get it fixed why or why not ??
Answer:
b
Step-by-step explanation:
It is important to get a leaking faucet fixed as soon as possible to save water, money, and prevent potential problems in the future.
It is important to get a leaking faucet fixed because of the following reasons;
1. Water waste: A leaking faucet wastes a significant amount of water over time, which can contribute to higher utility bills and water shortages in drought-prone areas.
2. Cost-saving: Fixing a leaking faucet can save you money in the long run by reducing your water bill.
3. Preventing bigger issues: Ignoring a leaking faucet can lead to more serious plumbing problems down the line, which can be more expensive to fix.
4. Environmental impact: Wasting water unnecessarily has a negative impact on the environment and can contribute to water scarcity.
Overall, it is important to address a leaking faucet promptly to save water, money, and prevent potential problems in the future.
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8x - 60 less than or equal to 2 (5 - 3x)
Answer:
x less than or equal to 5
i think thats what u wanted
BRAINLIEST
Please answer these
12.
Answer: 30.25π
11π = circumference
diameter * π = circumference
diameter = 11
radius = 5.5
Area = 5.5 * 5.5 * π
Area = 30.25π
13.
Answer: 52π
Area = radius * radius * pi
Area = 676π
Radius = 26
Diameter = 2 * radius
Diameter = 52
Circumference = 52π
14.
Answer: 38π
Area = radius * radius * pi
Area = 1134.11
Radius ≈ 19
Diameter = 38
Circumference = 38π
15.
Answer: 72.25π
Circumference = diameter * π
53.41 = diameter * π
Diameter ≈ 17
Radius = 8.5
Area = radius * radius * π
Area = 72.25π
Answer:
Step-by-step explanation:
Andrea runs a fruit store. She started Sunday with 20 cherries in stock. During
the day, she sold 17 cherries and got a shipment of fresh cherries. The
shipment contained 4 times as many cherries as she started the day with.
How many cherries does Andrea have in stock at the end of the day?
Answer:
Andrea has 83 cherries in stock at the end of the day.
Step-by-step explanation:
starts with 20 cherries
sold 17 cherries
3 cherries remain
get 4 times as many she starts with 20×4= 80
80 + the 3 that remained
What is the slope of a line perpendicular to the line y = 8x -5?
Answer:
-1/8
Step-by-step explanation:
the slope would be the opposite reciprocal of 8, which would be -1/8
Answer:
Y=-1/8x-5
Step-by-step explanation:
Perpendicular lines are negative reciprocals to each other
Algebra 2
What is the sum If x≠0?
Answer:
14x^4sqrt10
Step-by-step explanation:
Out of the two possible answers showing in the picture it seemed as is it was the only valid answer
write the equation of the line in fully simplified slope-intercept form
Answer:
y = 3x - 7
Step-by-step explanation:
Slope - Intercept Form : [tex]y = mx+b[/tex]
[tex]m[/tex] = slope
[tex]b[/tex] = y - intercept
Slope = [tex]\frac{rise}{run}[/tex]
= [tex]\frac3{1}[/tex]
= [tex]3[/tex]
So far: [tex]y = 3x + b[/tex]
Plug in a point from the graph, ex. (3,2)
[tex]2 = 3(3) + b\\\\2 = 9 + b\\\\b = -7[/tex]
Equation : [tex]y = 3x - 7[/tex]
-Chetan K
SOLVE THIS ASAP PLEASE
(5 + 4 - 2) x (-2) = ?
A. 22
b. -22
c.14
d. -14
A car travels 270 kilometers in 6 hours. How far will it
travel in 9 hours at the same speed?
Pls pa help po
Answer:
405
Step-by-step explanation:
divide 270 by 6 the multiply what you got with 9
:)
A rectangular prism with a square base is cut from the center of a triangular prism. Each side of the square base measures 1. 7 units. A rectangular prism with a square base is cut out of the center of a triangular prism. The triangular prism has base lengths of 5 and 4 units and a height of 5. 7 units. The rectangular prism has sides lengths of 1. 7 and 4 units. What is the volume of the shaded solid? Round to the nearest tenth of a cubic unit. 11. 6 units3 45. 4 units3 57. 0 units3 68. 6 units3.
The volume of the shaded solid round to the nearest tenth of a cubic unit is 45.4units³
The given diagram is made up of a rectangular prism and a triangular prism.
The volume of the shaded region = Volume of triangular prism - Volume of a rectangular prism.
Volume of triangular prism Vt = BH/3
Base area B = 0.5(5.7)(5)
Base area B = 14.25units²
Height = 4 units
Vt = 14.25 * 4
Vt = 57units³
Volume of the rectangular prism = l²h
Volume of the rectangular prism Vr = 1.7 * 1.7 * 4
Vr = 11.56units³
Volume of the shaded solid = Vt - Vr
Volume of the shaded solid = 57units³ - 11.56units³
Volume of the shaded solid = 45.4units³
Hence the volume of the shaded solid round to the nearest tenth of a cubic unit is 45.4units³.
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Answer:
B
Step-by-step explanation:
Can someone plss help me with this!!!
Construct a 60° angle
X^2-18x complete the square
[tex]x^2 -18x \\\\=x^2 - 2 \cdot 9x +9^2 -9^2\\\\=(x-9)^2-81[/tex]
Can i get some help :
Answer: so, option 1 and 3 are true
1. True: The left side 6 is equal to the right side 6 , which means that the given statement is always true.
2. False: The left side 39 does not equal to the right side 9 , which means that the given statement is false.
3. True: The left side 16 is equal to the right side 16 , which means that the given statement is always true.
4. False: The left side 21 does not equal to the right side 19 , which means that the given statement is false.
Step-by-step explanation:
pls answer quickly
This Histogram shows the heights in inches of members of a middle school volleyball team.
How many members are between 50 and 70 inches tall?
A. 12
B. 10
C. 6
D. 4
Answer:
B. 10
Step-by-step explanation:
Look at the chart.
Find how many members are 50-60 inches tall. (6)
Find how many members are 61-70 inches tall. (4)
Add each member count up. (10)
Look at picture this is so hard pls help
Answer:
The answer is B
Step-by-step explanation:
need help on these 2 questions
Answer: y = -1 and x = 3
Step-by-step explanation:
x=-2y+6
3x-4y = 28
There are two ways to solve this: 1) solve directly with the equations, and 2) graph the line and look for the intersection.
---
Use the definition of x from the first equation and substitute it in the second:
3x-4y = 28
3(-2y+6)-4y = 28
-6y + 18 -4y = 28
-10y = 10
y = - 1
---
Graph the two lines and find the value of y at the point they intersect. See the attachment.
y = -1 at x= 8
=======================
For the second question:
y=3x-10
4x+5y=7
---
4x+5y=7
4x+5(3x-10)=7
4x+15x-50=7
19x = 57
x = 3
----
What is the value of x
Answer:
x = 5
Step-by-step explanation:
Δ EAB and Δ EDC are similar by the AA postulate , so the ratio of corresponding sides are in proportion , that is
[tex]\frac{AB}{DC}[/tex] = [tex]\frac{EA}{ED}[/tex] , substitute values
[tex]\frac{10}{4}[/tex] = [tex]\frac{2x+10}{x+3}[/tex] ( cross- multiply )
10(x + 3) = 4(2x + 10 ) ← distribute parenthesis on both sides
10x + 30 = 8x + 40 ( subtract 8x from both sides )
2x + 30 = 40 ( subtract 30 from both sides )
2x = 10 ( divide both sides by 2 )
x = 5
what is the cosine rule
Answer:
The sum of the squares of the lengths of the other sides minus twice the product of the other two sides multiplied by the cosine of angle contained between them equals the square of the length of any side of a given triangle.
Step-by-step explanation:
hope it helps
The Bill of Rights was ___.
A) all of these
B) demanded by those considering ratification of the Constitution
C) none of these
D)the first ten amendments to the Constitution
E) added by the first Congress after the ratification of the Constitution
Answer: The answer is D, the first ten amendments to the constitution.