Answer:
x = 5/4 + √65/4 or x = 5/4 - √65/4
Step-by-step explanation:
I'm assuming you mean 2x^2-5x-5=0?
x = ( -b ± √b^2 - 4ac ) / 2a
x = ( -(-5) ± √(-5)^2 - 4(2)(-5) ) / 2(2)
x = ( 5 ± √(25 + 40) ) / 4
x = ( 5 ± √65 ) / 4
x = 5/4 ± √65/4
Therefore, x = 5/4 + √65/4 or x = 5/4 - √65/4
The line 3x-8y=k cuts the x-axis and y- axis at the point A and B respectively. If the area of ∆AOB =12sq.units, find the value of k.
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.
Can someone please do this? I need it bad
Answer:
this pdf is not downloading .
no idea what to do now .
can you give question on comments
The length of the base edge of a pyramid with a regular hexagon base is represented as x. The height of the pyramid is 3 times longer than the base edge. The height of the pyramid can be represented as The of an equilateral triangle with length x is (x ^ 2 * sqrt(3))/4 * u * n * i * t * s ^ 2 times the The area of the hexagon base is area of the equilateral triangle . The volume of the pyramid is x ^ 3 * sqrt(3) * u * n * i * t * s ^ 3
1.) 3x
2.) area
3.) six
4.) 3/2
:)
Answer:
The height of the pyramid can be represented as
3x
The
area
of an equilateral triangle with length
The area of the hexagon base is
six
The volume of the pyramid is
3/2
Step-by-step explanation:
hii can you help me please
Step-by-step explanation:
a. false
b.true
c.false
d. false
Answer:
a. False
b. True
c. True
d. False
Step-by-step explanation:
AThe formula for the area of a trapezoid treats the distance between the parallel sides as the height. Doing this lists the height as 4m.
BYou can separate a trapezoid into a rectangle with a width of 3 and a height of 4, as well as a right triangle with a width of 2 and a height of 4.
CThis expression is the written out portion of separating the trapezoid into a triangle and rectangle.
(3 * 4) represents the rectangle and (1/2 * 2 * 4) represents the triangle.
DThe area as found by the accurate expression in part C is 16.
How do i do this? With steps pleaseeeeeeeeeee thank youuu
Answer:
110°
Step-by-step explanation:
Since angle B is 30° and the ratio of a to b is 2:1, multiply 30 by 2 to get the measure of angle a = 60°.
Since angles a is 60° And the ratio of a to c is 3:1, divide 60 by 3 to get the measure of angle c = 20°.
add them up:
60 + 30 + 20 = 110°
HELPPP WHAT IS THE ANSWER DONT SENT A FILE PLZ EXPLAIN STEP BY STEP PLZ I DINT HAVE A LOT OF TIME
Answer:
2nd option
Step-by-step explanation:
Consider the coordinates of T(- 3, 3 ) → T' (3, - 1 )
- 3 → 3 is 6 units right in the positive x-direction
3 → - 1 is 4 units down in the negative y- direction
Then translation rule is
(x, y ) → (x + 6, y - 4 )
picture too 1st question:
Answer:
6 gallons and 2 pints
Thank for posting the pic, it makes sense now!
Pleaseee helppp asap
Answer:
58 percent is one of them
Step-by-step explanation:
105 freshman divided by 180 students total
solve for x
[tex]\frac{11}{x+5}[/tex] =3
Christina is making a necklace using beads. She has 20 red, 14 blue, 10 purple, 28 green, and 8 yellow beads. She randomly chooses a bead to start the necklace. What is the probability of Christina choosing a pink bead?
Answer:
0.
Step-by-step explanation:
There is a total of 20 red + 14 blue + 10 purple + 28 green + 8 yellow beads which equal 80 total beads. However, she does not have any pink beads, so the probability of picking one is 0 pink beads / 80 total beads = 0.
what is 238 rouned to the nearst houndred
Answer:
200
Step-by-step explanation:
In how many ways can 3 red balls , 4 blue balls and
5 white balls be selected from 5 red balls, 5 blue
balls and 7 white balls ?
Answer:
1050 ways
Step-by-step explanation:
Total Number of red balls = 5
Total Number of blue balls = 5
Total Number of white balls = 7
Number of red balls selected = 3
Number of blue balls selected = 4
Number of red balls selected = 5
Using the multiplication and combination relation :
nCr * nCr * nCr
Red balls = 5C3
Blue balls = 5C4
White balls = 7C5
Using calculator:
5C3 * 5C4 * 7C5 = 10 * 5 * 21
(10 * 5 * 21) = 1050 ways
Need help take your time and thank yoh
Answer:
(x - 3)(x - 12)
Step-by-step explanation:
Assuming you require to factor the expression
x² - 15x + 36
Consider the factors of the constant term (+ 36) which sum to give the coefficient of the x- term (- 15)
The factors are - 3 and - 12, since
- 3 × - 12 = + 36 and - 3 - 12 = - 15 , then
x² - 15x + 36 = (x - 3)(x - 12) ← in factored form
dividing radicals
Simplify
[tex]\mathbb{ANSWER:}[/tex]
[tex]\sf \frac{-3-\sqrt{2} }{3\sqrt{17} }[/tex]
[tex]\sf = \frac{-3-\sqrt{2} }{3\sqrt{17} } \cdot \frac{\sqrt{17} }{\sqrt{17} }[/tex]
[tex]\sf = \boxed{\sf \frac{-3\sqrt{17} - \sqrt{34} }{51} }[/tex]
Xavier is a new student, explain to him what a variable is. Use complete sentences.
Answer:a symbol, usually a letter, used to represent a number.
Step-by-step explanation:
a math process (like adding, subtracting, multiplying, or dividing)
can someone please help me solve this, ASAP!
1/5(15+10k)
PLSSSSSSSSSS
Answer:
10k+15/5
Step-by-step explanation:
What is the mean of the following data set: 100, 121, 105, 113, 108
Answer:
Mean = 109.4
Step-by-step explanation:
Mean = (Sum of all values)/(Number of values)
Mean = (100 + 121 + 105 + 113 + 108)/(5)
Mean = (547)/5
Mean = 109.4
Answer:
109
Step-by-step explanation:
Mean is just finding the average of the data set.
100+121+105+113+108=547, first add up all the numbers
547/5=109.4, then divide that sum by the amount of numbers in the set
What is the area of a
circle that has a radius of 4
inches? (Use 3.14 for pi.)
HELP ASAP
Answer:A≈50.27in²
Step-by-step explanation:
Rectangle ABCD with vertices A(-8,6), B(-2,8), C(-1,5), and D(-7,3) is reflected over the y-axis. What are the new points?
CAN SOMEONE PLEASE HELP ME WITH THIS I WILL BRAINLIEST WHO EVER TELLS ME THE ANSWERS TO THIS
Solve for X
PLEASE HELP DUE IN 10 MINS
Answer:
x = 8
Step-by-step explanation:
The measures of the angles in a triangle add up to equal 180°
That being said we can create an equation to solve for x
( note that this is a right triangle indicated by the square. A right triangle has a right angle which has a measure of 90° )
180 = 90 + 5x + 5 + 5x + 5
now we solve for x using basic algebra
step 1 combine like terms
90 + 5 + 5 = 100
5x + 5x = 10
now we have 180 = 100 + 10x
step 2 subtract 100 from each side
180 - 100 = 80
100 - 100 cancels out
now we have 10x = 80
step 3 divide each side by 10
10x / 10 = x
80 / 10 = 8
we're left with x = 8
Help if you can!! I really need some good grades or I will fail on this and that wont help anything.
Answer: 6 1/8
Step-by-step explanation:
Each x on the line represents one piece of string that long. For example, since there is one x at 1/8, she cut one piece of string 1/8 ft long. So you take all the values and add them up:
1/8+2/4+2/4+2/4+2/4+5/8+3/4+3/4+7/8
then find a common denominator (so make everything over 8)
1/8+4/8+4/8+4/8+4/8+5/8+6/8+6/8+7/8 = 41/8
when you divide this, you will get 5 1/8
since theoriginal problem says she still has 1 foot leftover, you add one to get the total value when she started.
So, Emma had 6 1/8 ft string originally
Simplify. 8*2 + 2
Please
Answer:
Step-by-step explanation:
8 exponent 2 + 2 = 64 + 2 = 66
Answer:
8^2+2
=8*8+2 [8^2=8*8]
=64+2
=66
Step-by-step explanation:
The square of a number is equal to the number my multiplied by itself 2 times i.e. n*n=n^2. Using BODMAS (Brackets of Division, Muliplication, Addition and Subtraction), we should multiply 8 first, then add 2 to it.
48 boxes are loaded onto a truck. The still need to load 96% of the boxes onto the truck. What is the total number of boxes being loaded
Answer:
the total number of boxes being loaded is 1,200 trucks
Step-by-step explanation:
Given that
There are 48 boxes that should be loaded onto a truck
And, still it is required to lead 96% of the boxes onto the truck
We need to find out the total number of boxes that should be loaded
So
Since 48 boxes represent the 4% of the boxes that are loaded
So,
The total number of boxes would be
= 48 × 100 ÷ 0.04
= 1,200 trucks
Hence, the total number of boxes being loaded is 1,200 trucks
Line d is parallel to line c in the figure below.
Parallel lines d and c are intersected by lines q and p to form 2 triangles. At lines d and p, the angle is 2, at d and q, the angle is 1, and at q and p the angle is 3. At lines c and q, the angle is 4, at p and c, the angle is 5, and the third angle is 6.
Which statements about the figure are true? Select three options.
Vertical angles prove that Angle 2 is congruent to angle 5.
In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.
Vertical angles prove that Angle 3 is congruent to angle 6.
The triangles are similar because alternate interior angles are congruent.
In the two similar triangles, Angle 2 and Angle 4 are corresponding angles.
The triangles are similar because corresponding sides are congruent.
Answer: In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.
Vertical angles prove that Angle 3 is congruent to angle 6.
The triangles are similar because alternate interior angles are congruent.
Step-by-step explanation:
Helppppppppp mmmmmmmeeeeeeeeeee
Answer:
56.25 π cm^2
Step-by-step explanation:
The circumference of a circle is given by C = 2 π r
15 π = 2 π r
Divide each side by π
15 = 2r
Divide by 2
15/2 = 2r/2
7.5 = r
We want to find tha area
A = π r^2
A = π (7.5)^2
A = π 56.25
A = 56.25 π
Find the volume of the given prism. Round to the nearest tenth if necessary.
1 m
34
8.5 m
17 m
Question 2 (4 points)
Given:
The base of the prism is a right triangle with legs 1 m and 2 m.
The height of the prism is 17 m.
To find:
The volume of the given prism.
Solution:
The area of a triangle is:
[tex]Area=\dfrac{1}{2}\times base\times height[/tex]
So, the area of base of the prism is:
[tex]Area=\dfrac{1}{2}\times 1\times 2[/tex]
[tex]Area=1[/tex]
Now, the volume of the prism is:
[tex]V=Bh[/tex]
Where, B is the base area and h is the height of the prism.
Substituting [tex]B=1,h=17[/tex], we get
[tex]V=(1)(17)[/tex]
[tex]V=17[/tex]
The volume of the prism is 17 cubic m. Therefore, the correct option is (d).
Select the approximate solution to the equation
Answer:
Step-by-step explanation:
hello : x = -0.75
A wheelbarrow has one wheel and a wagon has 4 wheels. Each day, a company has 160 wheels which makes 70 garden vehicles. How many of each vehicle can the company make?
Answer:
x = number of wheelbarrow = 40
y = number of wagon = 30
Step-by-step explanation:
Let
x = number of wheelbarrow
y = number of wagon
x + y = 70 (1)
x + 4y = 160 (2)
subtract (1) from (2) to eliminate variable x
4y - y = 160 - 70
3y = 90
y = 90/3
y =30
Substitute y = 30 into (1)
x + y = 70 (1)
x + 30 = 70
x = 70 - 30
x = 40
x = number of wheelbarrow = 40
y = number of wagon = 30