Given:
The equation is:
[tex]3x-8y=k[/tex]
It cuts the x-axis and y- axis at the point A and B respectively.
The area of ∆AOB =12 sq.units.
To find:
The value of k.
Solution:
We have,
[tex]3x-8y=k[/tex]
Substituting [tex]x=0[/tex] to find the y-intercept.
[tex]3(0)-8y=k[/tex]
[tex]0-8y=k[/tex]
[tex]y=\dfrac{k}{-8}[/tex]
[tex]y=-\dfrac{k}{8}[/tex]
Substituting [tex]y=0[/tex] to find the x-intercept.
[tex]3x-8(0)=k[/tex]
[tex]3x-0=k[/tex]
[tex]x=\dfrac{k}{3}[/tex]
Area of a triangle is:
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
The height of the ∆AOB is [tex]OB=\dfrac{k}{8}[/tex] because distance cannot be negative and the base of the ∆AOB is [tex]OA=\dfrac{k}{3}[/tex]. So, the area of the ∆AOB is:
[tex]A=\dfrac{1}{2}\times \dfrac{k}{8}\times \dfrac{k}{3}[/tex]
[tex]A=\dfrac{k^2}{48}[/tex]
It is given that, the area of ∆AOB = 12 sq.units.
[tex]\dfrac{k^2}{48}=12[/tex]
[tex]k^2=576[/tex]
[tex]k=\pm \sqrt{576}[/tex]
[tex]k=\pm 24[/tex]
Therefore, the value of k is either 24 or -24.
In the US, 77% of all teens have a TV in their bedrooms, while 59% of all teens in Spain have them. A simple
random sample of 500 teens from the US and 300 from Spain are selected and all are asked whether they have a
TV in their bedrooms. Let 9, -be the difference in the sample proportions of teens with a TV in their bedrooms,
where
is the sample proportion of US teens with a TV in their bedrooms and is the sample proportion of
Spanish teens with a TV in their bedrooms.
What is the shape of the sampling distribution of the difference in the two sample proportions?
approximately uniform
approximately Normal
skewed to the right
skewed to the left
Answer:
the answer is approximately normal
Step-by-step explanation:
Which line is parallel to the line y=x+7?
1) x+y=-2
2)x=1
3) x-y=5
4)y=1
Answer:
3
Step-by-step explanation:
to find the parallel of this line we need to find function with same slope
1) x+y=-2 ⇒ y=-x-2
2)x=1
3) x-y=5 ⇒ y=x-5
4)y=1
so third
HIII I need help with this I just took a screenshot its for 7th grade.
hii please help asap ill give brainliest thanks
Answer:
The decimal number system in use today was first recorded in Indian mathematics.
Step-by-step explanation:
In the classical period of Indian mathematics (400 AD to 1200 AD), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, and Varāhamihira. The decimal number system in use today was first recorded in Indian mathematics.
Answer:
Decimal point system.
Step-by-step explanation:
Quadrilateral ABCD has vertices AC-3.6), B(6,0), C(9. -9), and D(0, -3). Prove that ABCD is a) a parallelogram
9514 1404 393
Explanation:
The quadrilateral will be a parallelogram if the diagonals bisect each other. That will be the case if the sums of their end-point coordinates are the same.
A + C = (-3, 6) +(9, -9) = (6, -3)
B + D = (6, 0) +(0, -3) = (6, -3)
Both diagonals have their midpoint at (3, -1.5), so the diagonals are mutual bisectors. The figure ABCD must be a parallelogram.
___
The midpoint of AC is (A+C)/2 = (6, -3)/2 = (3, -1.5).
Flora drew the following graph to answer the question. What was her mistake when she drew her graph?
Answer:
She drew the graph too steep, if she is going down at a constant rate of 300 ft per hour, at 1 hour she would be at 2,700 ft. it would take her about 10 hours to get down the mountain.
Polynomials are written with the exponents of the terms in_____order.
Answer:
descending order, meaning standard form.
Step-by-step explanation:
Ex: x^2-5x+2
or
Ex: 2x^3 -5x^2 -2x +3
tell me if it doesn't make sense
-3.5 x 0.2 =??? ;w;
A. -0.7
B. 0.7
C. -3.3
D. -0.7
Answer:
A and D
Step-by-step explanation:
It can't be B because of the negative...
It would have to be less than 3.3 since 0.2 is less than and the 3.3 is negative
A and D are the same?
-3.3 * 0.2 = -0.7
Answer these questions
Answer:
well well well
Step-by-step explanation:
dont cheat on live classwork pls
Based on the statment, below which statement could be used to prove <1=<2?
vertical angles are congruent
supplementary angles are congruent
complementary angles are congruent
two angles that form a linear pair are congruent
Answer:
Vertical angles are congruent
Select the correct answer.
What is the corresponding point on the unit circle for the given radian measure?
0 = 7pi/6
Answer:
Answer is B: (-sqrt(3/2 , -1/2)
Step-by-step explanation:
First convert radians to degrees
theta = (7pi/6)*(180/pi)
=210 degrees
Cos(210 degrees)= -sqrt3/2
Thats the x coordinate
sin(210 degrees)= -1/2
thats the y coordinate
Answer:
The corresponding point on the unit circle for the radian measure is [tex](\frac{\sqrt{3} }{2},\frac{1}{2})[/tex]
Step-by-step explanation:
What is unit circle?
A unit circle is typically drawn around the origin (0,0) of a X,Y axes with a radius of 1.
What is radian measure?
One radian is the measure of a central angle that intercepts an arc s equal in length to the radius r of the circle.
The radian measure is,
α=[tex]\frac{7\pi }{8}[/tex]
Changing to degree measure,
[tex]\frac{7\pi }{6} *\frac{180}{\pi } \\=210^{o}[/tex]
The measure on the unit circle is,
(cos [tex]\alpha[/tex] , sin [tex]\alpha[/tex])=(cos 210 , sin 210)
=[tex](\frac{\sqrt{3} }{2},\frac{1}{2})[/tex]
Option A.
To know more about unit circle, radian measure here
https://brainly.com/question/10675916
#SPJ2
if a=-4h^2-h+5 and b=8h-3h+12 find a-b
Answer:
4h^2-6h-7
Step-by-step explanation:
[tex](4h^{2} -h+5) - (8h-3h+12)\\4h^{2} -h+5 - 8h+3h-12\\4h^{2}-9h+3h-7\\4h^{2}-6h-7\\[/tex]
find the volume of a sphere that has a radius of 4cm.
Answer:
V≈268.08
Step-by-step explanation:
V=4
3πr3=4
3·π·43≈268.08257
The height in feet,h , of a model rocket t seconds after launch is given by the equation h(t) = 3+70t-16t^2.
Answer:
speed of the rocket is 6feet
Step-by-step explanation:
Complete question
The height in feet, h, of a model rocket t seconds after launch is given by the equation h(t) = 3+70t - 16t^2. The average rate of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?
Note that the average rate is also known as the speed
Average rate = h(3)-h(1)/3 - 1
h(3) = 3+70(3) - 16(3)^2
h(3) = 3 + 210 - 144
h(3) = 69
h(1) = 3+70(1) - 16(11)^2
h(1) = 3 + 70 - 16
h(1) = 73 -16
h(1) = 57
Average rate = 69-57/3-1
Average rate = 12/2
Average rate = 6ft/s
This shows that the speed of the rocket is 6feet
Answer:
If you're looking for the answer for edge, its;
B. The rocket is at a greater height when t = 3 than when t = 1.
Step-by-step explanation:
edg- answers ;p
In which sampling method is the sample selected from the population according to a specific item or time interval?
A) convenience sample
B) simple random sample
C) stratified random sample
D) systematic random sample
hey in need of help please help me
Write the equation of the circle graphed below
Answer:
(x-4)² + (y-3)² =29
Step-by-step explanation:
The equation of a circle is
(x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius.
In this circle, the center is at (4, 3)
(x-4)² + (y-3)² = r²
and we have point (-1 ; 1)
r²=(-1-4)² + (1-3)² = 25+4=29
(x-4)² + (y-3)² =29
Answer:
(x - 4)² + (y - 3)² = 29
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (4, 3 )
The radius r is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (4, 3)
r = [tex]\sqrt{(4+1)^2+(3-1)^2}[/tex]
= [tex]\sqrt{5^2+2^2}[/tex]
= [tex]\sqrt{25+4 }[/tex] = [tex]\sqrt{29}[/tex]
Then
(x - 4)² + (y - 3)² = ([tex]\sqrt{29}[/tex] )² , that is
(x - 4)² + (y - 3)² = 29 ← equation of circle
Plz put the work clearly plzz I really need these
Answer:
m∠C = 26°
m∠D = 108°
m∠E = 46°
Step-by-step explanation:
Set up the equation adding the expressions together to equal 180 (sum of all angles in a triangle)
(2x) + (x+3) + (5x-7) = 180
Remove the parentheses
2x + x+ 3 + 5x - 7 = 180
Add like terms
8x - 3 -7 = 8x -4 = 180
8x - 4 = 180
Add 4 on each side to cancel it out on the right
8x - 4 = 180
+4 = +4
8x = 184
Divide each side by 8 to get the variable by itself
8/8 =1 184/8 = 23
x = 23
Substitute x in eac expression
2x = 2(23) = 46°
x + 3 = 23 + 3 = 26°
5x - 7 = 5(23) - 7 = 115 -7 = 108
Chek it by adding all the degrees to make sure it equals 180
46 + 26 + 108 = 72 + 108 = 180
WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!
WHAT IS THE AMPLITUDE OF THIS FUNCTION
your answer should be three.
~iwa-chan
A cylinder with a base diameter of x units has a volume
of zor cubic units.
Which statements about the cylinder are true? Select
two options
The radius of the cylinder is 2x units.
The area of the cylinder's base is Ax2 square units.
The area of the cylinder's base is žm1x2 square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Answer:
its B and E
Step-by-step explanation:
I already did the review
im quite behind and i dont know how to do this.. thank you
Answer:
455 ( I think )
Step-by-step explanation:
Lets start with the red shape.
The triangle on top is 5x3, and the equation for a triangle is base•height•1/2
So each triangle equals 7.5, as 15/2=7.5. Remember there are 2 triangles so the total of both triangles is 15.
The front side of the red shape is 6x5, which equals 30.
Same with the back.
The side though, is 3x6, which equals 18.
So 15 (both triangles)+60 (the front and back of the shape)+18 (the side)= 93
The red shape is 93 inches cubed.
The green shape is a rectangular prism.
The sides, are both 3x7, which equals 21. Remember there are 2 sides so together they equal 42.
The next part is 3x16= 48. There are 2 of these so it equals 96.
The top and bottom is 7x16=112, which is 224.
42 (sides) + 96 (front and back) + 224 (top and bottom)= 362
The green shape is 362 inches cubed.
362+93=455 inches cubed as a total
(I think)
what is the slope of the line?
Answer:
The slope of the line would be -2/3
Megan spent $9.85 on ingredients and made one pan of cereal bars. the pan has lengh of 24 inches and width of 16 inches
Answer:
Step-by-step explanation:
Please answer this correctly.
Answer:
EF=FC =22 ( diagonals bisect each other )
then EC=2 EF =2 x 22 =44
6 x 3/16 in simplist form
Answer:
9/8 or 1.125
Step-by-step explanation:
multiply 6/1 * 3/16 = 18/16
divide both by 2
9/8
is this quadrilateral a parallelogram?If yes, state the definition or theorem that justifies your answer.
Answer:
SOLUTION: Yes; one pair of opposite sides are parallel and congruent. From the figure, one pair of opposite sides has the same measure and are parallel. By the definition of congruence, these segments are congruent. By Theorem 6.12 this quadrilateral is a parallelogram.
Answer:
Below.
Step-by-step explanation:
The definition of a parallelogram is a 4 sided figure with 2 pairs of oppsoite parallel sides.
One of the properties of a parallelogram is that opposite sides are congruent.
In this figure the opposite sides are both parallel and congruent, so it must be a parallelogram.
Determine the volume of the rectangular prism.
Answer:
50 ft³Step-by-step explanation:
We know the formula for a rectangular prism is length × width × height
We also know all the sides so we can rewrite the formula replacing variables.
The length is 8, the width is 2[tex]\frac{1}{2}[/tex] and the height is 2[tex]\frac{1}{2}[/tex]
8 × 2[tex]\frac{1}{2}[/tex] × 2[tex]\frac{1}{2}[/tex]
Multiply which ever way is easy for you. I am just multiplying from left to right.
8 × 2[tex]\frac{1}{2}[/tex] = 20
20 × 2[tex]\frac{1}{2}[/tex] = 50
Now we get 50. Before we put our answer as 50, there are two more steps.
First we need to add the measurement unit which is feet or ft
We also need to add ³ since it is volume
50 ft³ is our final answer
PLZ HELP!!! I'm begging you! Problem: If each letter of the alphabet is worth two more numbers than the number before it (1=1, 2=3), what is the entire alphabet worth?
Answer:
676
Step-by-step explanation:
I think this is an arithmetic series, so
Sn = 26/2[2(1) + (26 - 1)2]
Sn = 13[2 + 50]
Sn = 13[52]
Sn = 676
Answer:
676
Step-by-step explanation:
A = 1
B = 3
C = 5
D = 7
...
Z = 51
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25
(+) + 51 + 49 + 47 + 45 + 43 + 41 + 39 + 37 + 35 + 33 + 31 + 29 + 27
---------------------------------------------------------------------------------------------------
52 + 52 + 52 + 52 + 52 + 52 + 52 + 52 + 52 + 52 + 52 + 52 + 52
13 * 52 = 676
Answer: 676
celia ate 5/8 of a pizza what decimal is equivalent to the fraction of pizza celia ate
Answer:
0.625
Step-by-step explanation:
5÷8=0.625
This is equal to the number of pizzas Celia ate.
plz mark me as brainliest.
Answer:
0.625
Step-by-step explanation:
Fraction of pizza she ate = 5/8
5/8 x 125 = 625/100= 0.625
I hope im right!
There are 45 students in a class. If 60% of them are girls, find the number of girls and boys
please help me i am requesting I will mark u as brain list
Step-by-step explanation:
here's your solution
==> Total number of students in class = 45
==> percentage of girls in class = 60%
==> number of girls in class = (60/100)*45
==> number of girls = 27
==> number of boys = 45 - 27
==> number of boys = 18
hope it helps