The coordinates of the foot of the perpendicular drawn from the point (6, 3) to the line by segment joining (4,1) and (8,3). is (6.4, 2.2)
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
The equation of the line passing through (4,1) and (8,3) is:
y - 1 = [(3 - 1)/(8 - 4)](x - 4)
y = 0.5x - 1
The line perpendicular to y = 0.5x - 1 has a slope of -2. It passes the point (6, 3), hence:
y - 3 = -2(x - 6)
y = -2x + 15
The line y = 0.5x - 1 and y = -2x + 15 intersect at point (6.4, 2.2)
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Point B is on line segment AC. Given BC=9 and AB=11, determine the length AC.
Answer:
[tex]AC=20[/tex]
Step-by-step explanation:
The line segment AC is the entire length of the line. Within this segment, point B is found.
Point B, in a way, splits the segment into two, creating the segments AB and BC.
To find the length of AC, add the lengths of the lines AB and BC together:
[tex]AB=11\\BC=9\\AB+BC=AC\\11+9=AC\\20=AC[/tex]
The length of AC is 20.
:Done
Answer:
20 units.
Step-by-step explanation:
Segment AC is broken into two parts by point B. That means that the length of segment AB plus the length of segment BC equals the length of segment AC.
If BC = 9, and AB = 11, AC = 9 + 11 = 20 units.
Hope this helps!
Please help me! I am trying to complete this question!
Answer:
131.25 in ^2
Step-by-step explanation:
Find the area of the rectangle on the left
A = l*w
A = 11.75 * 6 = 70.5 in ^2
Now find the area of the rectangle on the right
The length is 9 and the height is 11.75 - 5 = 6.75
A = 9 * 6.75
A = 60.75 in ^2
Add the areas together
70.5+60.75 = 131.25 in ^2
Answer:131.25
Step-by-step explanation:
11 3/4 x 6 = 70.5 (area of first rectangle)
11 3/4 - 5 = 6.75 (to find the height of the other figure)
6.75 x 9 = 60.75 (area of 2 figure)
60.75 + 70.5 = 131.25
ANSWER QUICKLY PLZZZZZZ
ANSWER QUESTION B
Answer:
16
Step-by-step explanation:
We know that: 5 + ? = 10.5
we now need to solve for ? , by using the inverse method
10.5 x 2 = 21
21 - 5 = 16
Now to double check the answer, we substitute the ? with the answer
so, 5 + 16 = 21
21/2 = 10.5 so it is clearly correct
I HOPE THIS HELPED :)
Please give me the correct answer
Answer:
Height = 15Step-by-step explanation:
[tex]Volume = 392.5\\r = 5\\h =?\\\\V= \frac{1}{3} \pi r^2 h\\\\392.5 = \frac{1}{3} \times 3.14 \times 5^2 \times h\\\\392.5 = \frac{78.5h}{3} \\\\392.5 = 26.16h\\\\\frac{392.5}{26.16} =\frac{26.16h}{26.16} \\\\h = 15.00[/tex]
Answer:
h=15 in
Step-by-step explanation:
V=πr²(h/3)
h=3v/πr²
h=[3(392.5)]/[3.14(5)²]
h= 15 in
Tom finished reading 3/7 of a book in the first week, and he read 3/4 of the remainder in the second week. what fraction is left?
Answer:
1/7 is left
Step-by-step explanation:
What is left to read after the first week
1 - 3/7
7/7 - 3/7
4/7
He read 3/4 of this the second week
4/7 * 3/4
3/7 was read
4/7 - 3/7 is what is left
1/7 is left
Answer:
The correct answer is
Step-by-step explanation:
1/7 of the book is left to read.
Hope this helps....
Have a nice day!!!!
Vertical plane R intersects horizontal plane P. Points A, D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right half of plane P. Point H is above and to the right of the planes. Point J is below and to the left of the planes. Which statements are true based on the diagram? Check all that apply.
Answer:
1,2,4,5
Step-by-step explanation:
Answer:
line DB, H, and D
Step-by-step explanation:
PLEASEEEEEEE HELP with this question
Answer:
second table
Step-by-step explanation:
Out of the 8 options on the spinner, 2 of them are 0's, 1 of them is a 1, 2 of them are 2's and 3 of them are 3's so the probability of spinning a 0, 1, 2 or 3 is 2/8, 1/8, 2/8 or 3/8 which becomes 0.25, 0.125, 0.25 or 0.375 respectively. Therefore, the answer is the second table.
Q4) Using Euclid's algorithm, find the HCF of 240 and 228
[tex] \LARGE{ \underline{ \boxed{ \purple{ \rm{Solution : )}}}}}[/tex]
Euclid's division lemma : Let a and b are two positive integers. There exist unique integers q and r such that
a = bq + r, 0 [tex]\leqslant[/tex] r < b
Or We can write it as,
Dividend = Divisor × Quotient + Remainder
Work out:
Given integers are 240 and 228. Clearly 240 > 228. Applying Euclid's division lemma to 240 and 228,
⇛ 240 = 228 × 1 + 12
Since, the remainder 12 ≠ 0. So, we apply the division dilemma to the division 228 and remainder 12,
⇛ 228 = 12 × 19 + 0
The remainder at this stage is 0. So, the divider at this stage or the remainder at the previous age i.e 12
[tex] \large{ \therefore{ \boxed{ \sf{HCF \: of \: 240 \: \& \: 228 = 12}}}}[/tex]
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how 45 degree angles does it take to make a full turn?
PLSSSSSSSSSSSSSSS HELP
Answer:
8 turns
Step-by-step explanation:
If we want to take a full turn, we'd turn around 360° since we'd be in the same position.
If we turn in intervals of 45°, we need to find how many times 45 goes into 360. To do this, we can divide.
[tex]360\div45=8[/tex]
Hope this helped!
Answer:
It will take 8 45 degree angles to make a full turn
Step-by-step explanation:
360 degrees is a full turn
360/45 =8
It will take 8 45 degree angles to make a full turn
Using the conversion 1 mile equals 1.6093 km to convert 4.9 kilometers to miles, round o the nearest tenth of a mile
Answer:
3.0 miles
Step-by-step explanation:
Using the conversion 1 mile equals 1.6093 km to convert 4.9 kilometers to miles, round to the nearest tenth of a mile.
1 mile = 1.6093 km
Convert 4.9km to mile
We can use cross multiplication :
Let the number of miles = m
1 mile = 1.6093 km
'm' miles = 4.9 km
Cross multiply :
m × 1.6093 = 4.9 × 1
m = 4.9 / 1.6093
m = 3.0448020 miles
Rounding 3.0448020 to the nearest tenth :
3.0 miles
Which data set has the greatest spread for the middle 50% of its data?
OA
{18, 13, 22, 17, 21, 24}
B.
{17, 19, 22, 26, 17, 14}
OC. {13, 17, 12, 21, 18, 20)
OD.
{18, 21, 16, 22, 24, 15)
Answer:
b
Step-by-step explanation:
the answer is b because b have the greatest spread for the middle 50%
I hope this was helpful
Please help me i don’t know if I’m right
Answer:
your choice is correct
Step-by-step explanation:
The magnitude of the difference between the target amount and the actual amount will be no greater than the allowed error.
|x -34| ≤ 0.25
If ABCD is a parallelogram find the value of unknow size
Step-by-step explanation:
Hey, there!!
As it is a parallelogram, remember basic properties of parallelogram,
Their opposite sides are parallel and equal to eachother. Their opposite angles are equal.They have properties of parallel lines too.Now, lets solve your question.
b = (7×10)°
Therefore, b= 70°.
now, (3x+10°)+b=180° { co- interior angle of a triangle sum is 180°}.
or, 3x= 180°-80°
or, x= 100°/3
Therefore, x= 33° { rounding off we get 33}.
w+ b =180°
w+70°=180° { coointerior angles are equal}.
Therefore, w =110°
Hope it helps....
Each day the chill canteen meal can be 1 of three things. The probability that it is pizza is 0.3. The probability that it is curry is 0.42. What is the probability that it is pasta
Its [tex]1-0.3-0.42=0.28[/tex].
Hope this helps.
1 - 0.3 - 0.42= 0.28
hope you understand.
A point is randomly chosen on a map of North America. Describe the probability of the point being in each location: North America: New York City: Europe:
Answer:
We know that the map is of North America:
The probabilities are:
1) North America:
As the map is a map of North America, you can point at any part of the map and you will be pointing at North America, so the probability is p = 1
or 100% in percentage form.
2) New York City.
Here we can think this as:
The map of North America is an extension of area, and New Yorck City has a given area.
As larger is the area of the city, more probable to being randomly choosen, so to find the exact probability we need to find the quotient between the area of New York City and the total area of North America:
New York City = 730km^2
North America = 24,709,000 km^2
So the probability of randomly pointing at New York City is:
P = ( 730km^2)/(24,709,000 km^2) = 3x10^-5 or 0.003%
3) Europe:
As this is a map of Noth America, you can not randomly point at Europe in it (Europe is other continent).
So the probaility is 0 or 0%.
Answer:
North America: certain
New York City: unlikely
Europe: impossible
Step-by-step explanation:
simply
Simplify 18-2[x + (x - 5)].
O8-4x
28 - 4x
28 - 2x
Answer:
28-4x
Step-by-step explanation:
Step 1: Open most inner bracket and simplify
=18-2(x+x-5)
=18-2(2x-5)
Step 2: Expand brackets by multiplying 2 in and simplify
=18-2(2x)-2(-5)
=18-4x+10
=28-4x
Therefore the answer is 28-4x
Can y’all please help me I need this done before 4:00 if y’all help me I’ll give y’all sum
Answer/Step-by-step explanation:
1. The linear equation, [tex] y = mx + b [/tex] represents that of a straight line, where,
(x, y) is the coordinate pair of any point on the line,
m = slope, and
b = the y-intercept
2. Area of rectangle and parallelogram can be found using [tex] A = bh [/tex]
3. r stands for radius in the equation for circumference of a circle. It is half of the diameter of a circle.
4. Total surface area of a prism can be calculated using, [tex] Ph + 2B [/tex], where,
P = perimeter of the base of the prism
h = height of prism
B = base area of the prism
5. Formula for the Pythagorean theorem is given as [tex] a^2 + b^2 = c^2 [/tex], where,
a, b, and c are sides of a right triangle, however, c is the hypotenuse or the longest side.
6. Types of interest we solve for are simple and compound interest
7. h, in the area of a triangle (½*b*h) stands for height of the triangle.
8. The two formula for solving for circumference of a circle are C = 2πr or C = πd (note: radius is half of the diameter of a circle)
9. Formula for finding slope = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Where, [tex] (x_1, y_1), (x_2, y_2) [/tex] could be any two coordinate pairs on the line.
10. Surface area of a cylinder is given as 2πrh, where,
r = radius
h = height of cylinder
11. d represents diameter of circle in C = πd
12. The word, "linear", means a straight line, or along a straight line.
Simplify square roots
Simplify.
Remove all perfect squares from inside the square root.
12
Answer:
[tex]2\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{12}[/tex]
[tex]\sqrt{(4)(3)}[/tex]
square root of 4 is 2
[tex]2\sqrt{3}[/tex]
the 3 stays inside
Look at this graph:
10
9
8
7
6
5
4
3
2
X
0
1
2
3
4
5
6
8
9
10
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Submit
e to search
o
La
Answer:
3/5
Step-by-step explanation:
The rise is 3 while the run is 5, so the slope = rise over run = 3/5.
Answer:
5/6
Step-by-step explanation:
slope = change in y over change in x
Theresa swims in a pool that is 75 meters long. Everyday Theresa swims ten lengths of the pool. After 5 days, how many kilometers has Theresa swan?
Answer:
She swam 2 kilometers
Step-by-step explanation:
Consider 6x2 + 6x + 1. Which term immediately tells you that this expression is NOT a perfect square trinomial? Justify your answer.
Answer:
Step-by-step explanation:
The 6x^2 because 6 is not a perfect square.
Answer:
6x^2
Step-by-step explanation:
6 isn't a perfect square
31. Solve for w:
[tex] \frac{3w + 6}{28} = \frac{3}{4} [/tex]
HELP! answer if you can
Answer:
w = 5
Step-by-step explanation:
Hey there!
Cross multiply,
84 = 12w + 24
-24 to both sides
60 = 12w
Divide both sides by 12
w = 5
Hope this helps :)
Write the phrase as an expression. Then evaluate the expression when x = 5.
the sum of a number x and 4, all divided by 3
Expression:
When r= 5, the value of the expression is
Answer:
Step-by-step explanation:
expression = (x + 4) / 3
x = 5
(5 + 4) / 3
= 9/3
= 3
Hope this helps
plz mark as brainliest!!!!!!
G(x)= -\dfrac{x^2}{4} + 7g(x)=− 4 x 2 +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, squared, divided by, 4, end fraction, plus, 7 What is the average rate of change of ggg over the interval [-2,4][−2,4]open bracket, minus, 2, comma, 4, close bracket?
Answer:
-1/2Step-by-step explanation:
Given the function [tex]G(x)= -\dfrac{x^2}{4} + 7[/tex], the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;
Rate of change of the function is expressed as g(b)-g(a)/b-a
where a - -2 and b = 4
[tex]G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\[/tex]
[tex]G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6[/tex]
average rate of change of g(x) over the interval [-2,4] will be;
[tex]g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2[/tex]
The reciprocal of 1 is *
Answer:
[tex]\boxed{1}[/tex]
Step-by-step explanation:
When finding the reciprocal of a value, it flips the denominator with the numerator and vice versa.
The number 1 can be represented as the fraction 1/1 and 1 divided by 1 is still equivalent to 1.
Therefore, the reciprocal of 1 will always be 1.
I NEED HELP PLEASE I GIVE 5 STARS !
Answer:
C. 2[tex]\sqrt{29}[/tex]
Step-by-step explanation:
Square root of 116 is 10.7703296
Square root of 29 is 5.38516481, but as it is multiplied by 2, it becomes 10.7703296
Solve the equation for x.
[tex] \frac{1}{8} x + 8 = 12[/tex]
Answer: x=32
Step-by-step explanation:
[tex]\frac{1}{8}x+8=12[/tex]
subtract 8 on both sides
[tex]\frac{1}{8}x+8-8=12-8[/tex]
[tex]\frac{1}{8}x=4[/tex]
multiply 8 on both sides
[tex]8\cdot \frac{1}{8}x=4\cdot \:8[/tex]
[tex]4\cdot8=32[/tex]
[tex]x=32[/tex]
Write a division sentence that describe how many dispensers can be filled if the cafeteria uses 1/6 of coffee to fill a large coffee dispenser if the cafeteria has 2/3 pounds of coffee to use
Answer:
2/3 ÷ 1/6
I hope this helps.
chose the equivelent expresion 5⁶ a.(5⁴)² b.(5⁻²)⁻³ c.(5¹)⁵
Answer:
[tex]\Large \boxed{(5^{-2})^{-3}}[/tex]
Step-by-step explanation:
Applying the law of exponents : [tex](a^b)^c=a^{bc}[/tex]
[tex](5^4)^2 = 5^{4 \times 2} = 5^{8}[/tex]
[tex](5^{-2})^{-3}=5^{-2 \times -3}=5^6[/tex]
[tex](5^1)^5 =5^{1 \times 5}=5^5[/tex]
Answer:
[tex]\huge\boxed{Option \ B}[/tex]
Step-by-step explanation:
[tex]5^6[/tex] is equivalent to
=> [tex](5^4)^2 = 5^{4*2} = 5^ 8[/tex]
=> [tex](5^{-2})^{-3} = 5^{-2*-3} = 5^6[/tex] ← Correct
=> [tex](5^1)^5 = 5^{1*5} = 5^5[/tex]
The angle \theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant \text{I}Istart text, I, end text, and \sin(\theta_1)=\dfrac{1}{2}sin(θ 1 )= 2 1 sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction . What is the value of \cos(\theta_1)cos(θ 1 )cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Answer:
√3/2Step-by-step explanation:
Given an angle θ₁ located on in the first quadrant and sinθ₁ = 1/2, we are required to calculate the value of cosθ₁.
Firstly, we need to find the value of the angle θ₁ from the expression sinθ₁ = 1/2.
Given sinθ₁ = 1/2
Take the arcsin of both sides
arcsin(sinθ₁) = arcsin(1/2)
The arcsin will cancel out the sin at the left hand side to have only θ₁. Hence;
θ₁ = arcsin(1/2)
Using the calculator, θ₁ = 30°
Since we are to find the value of cosθ₁
cosθ₁ = cos30°
cos30° = √3/2
Hence the value of cosθ₁ is √3/2
Answer:
60/61
Step-by-step explanation:
60/61
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