Answer:
The equation of the perpendicular line (PR) to line PQ is; y = -0.5x - 1.5
Step-by-step explanation:
The line is perpendicular to line adjoined by points P(-3,0) and Q(0,6)
The slope of line PQ is;
Slope = change in y ÷ change in x = [tex]\frac{6 - 0}{0 -- 3}[/tex] = 2
The product of slopes of two perpendicular lines = -1
Hence the slope of line PR = -1 ÷ slope of line PQ = -1/2
Taking another point (x,y) and point P(-3,0) the equation of line PR is;
Slope = [tex]\frac{y - 0}{x - -3} = -\frac{1}{2}[/tex]
Cross-multiplying gives;
2y = -x - 3 , y = -x/2 - 3/2 , y = -0.5x - 1.5
A boy on top of a building observe that the angle of depression of a goat in horizontal ground is 47.if the goat is 23m away from the foot of the building,how high is the building,correct to the nearest meter? (ignore the height of the boy)
Answer:
Step-by-step explanation:
tan 47° = opposite side /adjacent side
=>1.072 = AB/BC
=>1.072 × BC = AB(height of the building)
=>1.072 × 23 = h ( As assumed height of building is h )
h = 24.656
= 25 metres ( nearest metre )
if we put a marble in 10 ml of water how can we find its volume
please answer
i will mark brainliest
Answer: See below
Step-by-step explanation:
This relates to the usage of water displacement.
Have the 10 ml of water ready in a measuring flask (or any container that has a scale)Put the marble into the waterObserve how much did the water riseSubtract the current water level by the original 10 mlThe final answer would be the volume.------------------------------------------------------------------------
EXTRA (Only for advanced purposes, if you do not understand, it is totally fine)
Refer to the attachment below to finish the question.
Assuming the water levels are integer,
The original water level is 13.33 mlAfter the rock is put in, the water level is raised to 30 mlThen, we do the fourth step which is subtraction
30 - 13.33 = 16.66 mlHope this helps!! :)
Please let me know if you have any quesitons
Given a line segment that contains the points A,B, & C in order, if AB = x - 2, and BC = 2x + 6, and AC = 19, find x.
Find the solution of this system of equations
4x - 5y = -12
-X + 5y = 18
4x - 5y = -12
-x + 5y = 18
Add the equations together:
4x + -x = 3x
-5y + 5y = 0
-12 + 18 = 6
So now you have:
3x = 6
Divide both sides by 3:
X = 2
Now you have the value of x, replace x with 2 in one of the equations and solve for y:
4(2) -5y = -12
8 -5y = -12
Subtract 8 from both sides:
-5y = -20
Divide both sides by -5:
Y = 4
The solution is x = 2 and y = 4 which is written as (2,4)
First one gram equals 1000 grams, so a 39 kilogram equals 39000 grams. Then, 1000 pillows times 300 equals a 39 kilogram sofa. Is my answer correct?
Answer:
No
Step-by-step explanation:
Kilogram is the unit of weight. Kilogram is the measure of how much matter or the mass an object has in it. Kilogram is the bigger unit of measurement while gram and milligram are the smaller units to measure the weight of any object.
We know,
1 kilogram = 1000 gram x 1
So, 1000 gram is equal to 1 kilogram
That means, 39,000 gram is equal to 39 kilogram.
In the question it is asked whether 1000 pillows times 300 is equal to 39 kilogram sofa or not.
The answer is not correct, because we do not know the weight of the 1000 pillows.
And also, 1000 x 300 will give you 300,000 and not 39 kilogram or 39,000 grams.
what is the solution to this equation?
3x+x-13+4-6x=12
A. x= -21/2
B. x= 21/2
C. x= 3/2
D. x= -3/2
Answer:
A.
Step-by-step explanation:
3x + x - 13 + 4 - 6x = 12
we try to combine the elements with the same power of x (including the ones without any x) :
3x + x - 6x
-13 + 4
so, we get
-2x - 9 = 12
-2x = 21
x = -21/2
Answer:
A
Step-by-step explanation:
group the like terms
3x+x-6x-13+4=12
-2x=12+9
divide both sides by -2
-2x/-2=21/-2
x= -21/2
hope it helps
There is a bag with 50 popsicles inside. 5 are red, 15 are orange, 12 are blue, 8 are
yellow and 10 are purple. If you were to
grab one popsicle from the bag, what is
the probability that it is red or not orange?
P(red or not orange)
Simplify this expression.
Can anyone help pls
Answer:
Step-by-step explanation:
Which of the graphs represent y=-x^2
Answer:
Step-by-step explanation:
Can't see all the graphs, but the graph of [tex]y=-x^2[/tex] is an upside down parabola with the vertex at the origin.
Two factory plants are making TV panels. Yesterday, Plant A produced 8000 panels. Four percent of the panels from Plant A and 1% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 2%?
Answer:
The answer is "16,000"
Step-by-step explanation:
In this question the amounts of panels created by B the x.
[tex]\therefore[/tex]
Calculating the amounts of defective panels from B:
[tex]\to \frac{1}{100} \times x = 0.01x[/tex]
Calculating the amounts of defective panels from A:
[tex]\to \frac{4}{100} \times 8000 = 320[/tex]
Calculating the total defective panels are :
[tex]\to 320+ 0.01x[/tex]
Calculating the total panels manufactured:
[tex]\to 8000 + x[/tex]
when the overall percentage of the defective panels is [tex]2\%[/tex]
[tex]\to \frac{(320 + 0.01x)}{(8000 + x)} = 0.02\\\\\to (320 + 0.01x) = 0.02 (8000 + x)\\\\\to 320 + 0.01x = 160 + 0.02x\\\\\to 320 -160 = -0.01x + 0.02x\\\to 160 = 0.01x\\\\\to x=\frac{160}{0.01}\\\\\to x=16,000\\\\[/tex]
Mr. Atkinson manages playgrounds for the 8 elementary schools in the Franklin School District. This year, he wants to put new sandboxes at each of the schools. He estimates that he will need 3 tons of sand for this project. How many 50-pound bags of sand should he order for each school?
Answer: 5 bags of sand
Step-by-step explanation:
Given
There are 8 elementary schools
3 Tons of sand is needed
It is contained in a 50- Pound bag
1 ton is equivalent to 2000 Pound
No of 50- Pound bag required is
[tex]\Rightarrow n=\dfrac{2000}{50}\\\\\Rightarrow n=40[/tex]
These 40 bags will be required in 8 schools. So, each school requires
[tex]\Rightarrow \dfrac{40}{8}=5\ \text{bag}[/tex]
Answer:
The number of bags required for each school is 16.53
Step-by-step explanation:
Number of schools = 8
Total sand required = 3 tons
mass of each bag = 50 pounds
Sand required for each school = 3 ton/ 8 = 3000 / 8 kg = 375 kg
1 pound = 0.454 kg
1 kg = 2.205 pounds
So, 375 kg = 826.7 pounds
So, the number of bags required for each school = 826.7/50 = 16.53 bags
suppose the team wins ten of it's following remaining 18 games. What is it's winning percentage?
the graph of a linear function is given below
Answer:
A
Step-by-step explanation:
The zero of the function is where the y-value is zero.
then it's -5
differentiate with product rule
Answer:
[tex]{ \boxed{ \bf{ \frac{dy}{dx} = v \frac{du}{dx} + u \frac{dv}{dx} }}}[/tex]
u = ( x + 1 )
v = ( 2x + 5 )²
[tex]{ \tt{ \frac{dy}{dx} = {(2x + 5) {}^{4} .(1) + (x + 1).(2)(2x + 5) {}^{3} } }} \\ = { \tt{ {(2x + 5)}^{3} ((2x + 5) +(2x + 2) }} \\ = { \tt{ \frac{dy}{dx} = {(2x + 5)}^{3}(4x + 7) }}[/tex]
what is the square root of 25
the answer would be 5 because 5*5 or 5 squared (5^2) is equal to 25, hope this helps!
Solve the system of equations using the substitution method.
y = 5x
7x + 2y = -17
(x, y) = ( , )
PLSSS HELP
Answer:
1. = 5 10 15 20 25
2. 2 4 6 8 10 12 14
X, y =10
Subtract the second equation from the first.
Answer:
2y = 8
Step-by-step explanation:
4x+3y = 17
- ( 4x+y = 9)
----------------------
Distribute the minus sign
4x+3y = 17
- 4x -y =- 9
----------------------
0x +2y = 8
Answer:
2y = 8
Step-by-step explanation:
4x+3y=17
-4x-y=9
_______
0+2y=8
2y=8
Find the surface area of the solid given the net
Help Now!!!!
The Base Of A triangle prism
Answer:
Volume=Area × height
=35×7
volume = {245} m³
OAmalOHopeO
Answer:
Since the area of the triangle(base) is known we now multiply it to the height so we can get the volume.
7 x 35 = 245 m3 is your answer
You can picture it too:
(sorry my drawing is bad with the marker)
can someone answer this
Answer:sadwer
Step-by-step explanation:
Help pls!
Suppose ten distinct, positive integers have a median of 10. ("Distinct integers" means that no two integers are the same.)
What is the smallest the average of those ten integers could be?
Explain your answer in complete sentences.
Answer:
8.4
Step-by-step explanation:
Since we want to minimize the average, the integers should be made as small as possible. So, we have 4 integers:
1, 2, 3, 4
However, the median must be 10. The next two integers must have an average of 10 - and since the integers are distinct, we should use:
9, 11
From there, we use the smallest integers (that are still above 11) possible:
12, 13, 14, 15
The average of these 10 integers is 84/10, or 8.4.
The median is still 10, because (9+11)/2 is 10.
Answer:
8 (or 8.4)
Step-by-step explanation:
First, the problem states the words: Distinct and positive.
That means that the smallest number we can use is 0.
We can make 10 blanks for 10 numbers for us to fill in.
_ _ _ _ _ _ _ _ _ _
Since 10 is an even number, and the median is not one single number, it will be the middle of the two numbers.
In this case, our two numbers are the 5th and 6th blank.
Any two numbers can be used, as long as they are the same actual value from 10.
Let us first put in the numbers we can, which are the numbers before the two middle blanks.
0,1,2,3, _ _ _ _ _ _
To find the median between two numbers, we can do:
(a+b) divided by 2 = median
We can use the smallest following number, 4. Then the 6th number will have to be 16 for 10 to be in the middle.
Also try the largest possible number for the 5th blank, 9. Then the 6th number will be 11.
4+16 and 9+11 both equal 20, and 20 divided by 2 is 10. So both of these work.
Now let's place the other numbers in for these two equations.
0,1,2,3,4,16,17,18,19,20
0,1,2,3,9,11,12,13,14,15
If we add the numbers of each together, we get:
0,1,2,3,4,16,17,18,19,20=100
0,1,2,3,9,11,12,13,14,15= 80
If we now divide each sum by 10 (to find the average) we get:
10
8
Since both of these were the most we could go, one with the 5th number as small as possible and one with the 5th number as large as possible.
Since the smaller answer we got was 8, the answer must be 8.
(I believe 0 is a positive integer because it doesn't carry a negative sign. If 0 is not a positive integer, the answer is 8.4. Use the same process
A 90 ° angle is divided into 2 angles. Find the size of the angles. 5x+10 and 6x-41 Not drawn to scale
Answer:
65 and 25
Step-by-step explanation:
90=(5x+10)+(6x-41)
121=11x
11=x
Going back to the angles:
5(11)+10
=55+10
=65 this is the first angle
6(11)-41
=66-41
25 this is the second angle
Next year, air fares will rise by 3%.
Calculate the new price of a R 1 400 ticket.
9514 1404 393
Answer:
₹1442
Step-by-step explanation:
The new price will be 1+3% = 1.03 times the old price.
₹1400 × 1.03 = ₹1442
Find questions attached.
Show workings.
Answer:
Solution given:
7.<OYM=15°base angle of isosceles triangle
<OYL=50°base angle of isosceles triangle.
<OYL=<OYM+<MYL
50°=15°+<MYL
<MYL=50°-15°
<MYL=35°
again;
<MOL=35*2=70°central angle is double of a inscribed angle.
18.
Solution given:
<PQR+<PSR=180°sum of opposite angle of a cyclic quadrilateral is supplementary
<PQS+42°+78°=180°
<PQS=180°-120°=60°
<PQS=60°
<SPR=42°inscribed angle on a same arc is equal
:.<QPS=18°+42°=60°
<QSR=18°inscribed angle on a same arc is equal
again.
<PSR=78°
<QSR+<PSQ=78°
18°+<PSQ=78°
<PSQ=78°-18°
<PSQ=60°
In ∆ PQS
<PSQ=60°
<QPS=60°
<PQS=60°
In triangle ∆PQS all the angles are equal.
so it is a equilateral triangle.I need help with this I don't understand
Answer:
Sin ? = 4/7
? = arcSin (4/7)
? = 35° (rounded to the nearest degree)
So the answer is 35°
Answered by GAUTHMATH
Ibrahim likes to run a loop around the park near his house that is ⅞ mile long. There is a water fountain ½ way around the loop. Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?
Answer:
7/16 mile
Step-by-step explanation:
Distance of the loop = 7/8 mile
Distance of Water fountain = 1/2 of the Distance of the loop
= 1/2 of 7/8
Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?
= 1/2 of 7/8
= 1/2 * 7/8
= (1 * 7) / (2 * 8)
= 7/16
Ibrahim ran 7/16 mile to drink water at the water fountain around the loop
In a recent storm, an 18-foot utility pole broke and fell leaving a 5-foot tall portion upright. How far is the top of the pole from the base of the pole?
Answer: [tex]12\ ft[/tex]
Step-by-step explanation:
Given
Total height of utility pole is 18 ft
After breakage, only 5 foot tall portion is standing
The fallen part is [tex]18-5=13\ ft[/tex] in length
From the figure, apply the Pythagoras theorem
[tex]\Rightarrow 13^2=x^2+5^2\\\Rightarrow x^2=169-25\\\Rightarrow x=\sqrt{169-25}\\\Rightarrow x=\sqrt{144}\\\Rightarrow x=12\ ft[/tex]
Thus, the fallen part is [tex]12\ ft[/tex] away from the base of the pole.
please help with math properties I need 5 and 8 :)
Answer:
Step-by-step explanation:
Statements Reasons
1. m∠A = 6x - 10 1. Given
2. m∠B = 2x 2. Given
3. m∠C = 8x - 2 3. Given
4. m∠A + m∠B + m∠C = 180° 4. Triangle sum theorem
5. (6x - 10) + (2x) + (8x - 2) = 180° 5. Substitution
6. 16x - 12 = 180 6. Algebra
7. 6x = 192 7. Addition property of equality
8. x = 12 8. Division property of equality
The probability that Sara wins a raffle is given by the expression n/n+3
Write down an expression, in the form of a combined single fraction, for the probability that Sara does not win.
Answer:
3/(n + 3)
Step-by-step explanation:
The given probability that Sara wins a raffle draw, P = n/(n + 3)
Given that the sum of all probabilities is 1, we get
The probability that Sara does not win, Q = 1 - P
Therefore;
Q = 1 - n/(n + 3) = (n + 3) - n/((n + 3) = 3/(n + 3)
The probability that Sara does not win, Q = 3/(n + 3)
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!!
Answer:
For 25) it's option C. -1/2
For 26) it's option D. 7π/6, 11π/6
Step-by-step explanation:
If you are finding sin−1 of a positive value, the answer will be between 0 and π/2. Using the unit circle, the angle with a sine of 1/2 in the first quadrant is π/6.
Answer:
-1/2
7π/6, 11π/6
Step-by-step explanation:
First problem:
31π/6 = 31/6 π = 5 1/6 π
A full circle is 2π radians. π radians = 180°
Start at 0 radians (positive x axis), and go 5 half circles counterclockwise.
You end up at π radians, or 180°, or the negative x axis.
Now go π/6 radians more counterclockwise.
You end up at 7π/6 or 210°.
Read the y-coordinate of the point on the unit circle.
Answer: -1/2
Second problem:
Look in the figure of the first problem.
The sine corresponds to the y-coordinate.
Look at the points on the circle, below the x-axis, that have a y-coordinate of -1/2.
They correspond to 7π/6 and 11π/6