Answers
Answer:
16
Step-by-step explanation:
If triangle GFE is similar to triangle RST, using the similarity theorem
RS/RT = GF/EF
Using pythagoras theorem;
RT² = 10² - 6²
RT² =100 - 36
RT² = 64
RT = √64
RT = 8
Recall that RS/RT = GF/EF
10/8 = 20/EF
Cross multiply
10EF = 8 * 20
10EF = 160
EF = 160/10
EF = 16
Hence the missing length is 16
Related Questions
Melissa, Dan, and Henry have $87 in their wallets. Dan has 3 times what Henry has. Melissa has $8 less than Henry. How much does each have?
Answers
Answer:
Henry has $19, Dan has $57, and Melissa has $11
Step-by-step explanation:
Let x represent how much money Henry has
Since Dan has 3 times what Henry has, his amount is 3x
Since Melissa has $8 less than Henry, her amount is x - 8
Create an equation that sets these 3 values equal to 87, then solve for x
(x) + (3x) + (x - 8) = 87
5x - 8 = 87
5x = 95
x = 19
So, Henry has $19
Find how much Dan has by multiplying 19 by 3
19(3)
= 57
Find how much Melissa has by subtracting 8 from 19
19 - 8
= 11
So, Henry has $19, Dan has $57, and Melissa has $11
Answer:
Dan has $261 and Melissa has $79
You roll a special 103 sided die. What is the probability of you rolling a 79? Round your answer to the thousandths place.
Answers
Answer:
0.010
Step-by-step explanation:
there is one 79 in the dice, and since there are 103 numbers in total, you use
1/103
= 0.00970873786
round to thousandths
= 0.010
Use the distance that these 9 students skimmer cars traveled in inches to calculate the MIDDLE 50%
468, 376, 540, 198, 230, 531, 281, 426, 346
a. 458 - 353.3
b. 255.5 - 499.5
c. 281 - 468
d. 230 - 531
Answers
9514 1404 393
Answer:
b. 255.5 to 499.5
Step-by-step explanation:
The middle 50% is the range between the first and third quartiles. In this group of 9 numbers, the first quartile is the average of numbers 2 and 3 when the numbers are listed from smallest to largest.
first quartile = (230 +281)/2 = 255.5 . . . . . . matches answer choice B
The third quartile is the average of numbers 7 and 8:
third quartile = (468 +531)/2 = 499.5 . . . . . also matches answer choice B
The middle 50% is 255.5 to 499.5.
_____
When I put the numbers in order, I get ...
198 230 ^ 281 246 376 426 468 ^ 531 540
^ indicates that the quartile here is the average of the adjacent numbers
bold indicates the median (2nd quartile)
An auditorium contains 224 occupied seats and was 7/11 filled. How many empty seats were there?
Answers
Answer:
128 seats
Step-by-step explanation:
7/11 = 224 seats
11/11 = ?
(11/11 × 224) ÷ 7/11
224 ÷ 7/11 =
224 × 11/7 = 352 seats(total number of seats)
352 - 224 = 128 seats
I need help with this question can someone help plz
Answers
Answer:
The height is 13.3 in
Step-by-step explanation:
Pythagorean Theorem
23.5²+b²=27²
552.25+b²=729
b²=729-552.25
b²=176.75
b=√176.75
13.2947
Directions: Read the following questions. Write the letter of the
correct answer.
1. Which of these lines pass a common point?
A. intersecting lines
C. line segment
B. parallel lines
D. perpendicular lines
2. Which of these lines meet at a point and produce square
corner or right angle?
A. connecting lines
C. intersecting lines
B. parallel lines
D. perpendicular lines
3. Which of these lines never meet or intersect in any point?
A. connecting lines
C. intersecting lines
B. parallel lines
D. perpendicular lines
4. Which of the following has the same distance apart at all
times?
A. intersecting lines
C. line segment
B. parallel lines
D. perpendicular lines
5. Which of the following is not shown in the figure at the
right?
A. a line intersects parallel lines
B. there are intersecting lines
C. there are perpendicular lines
D. two lines are parallel
Answers
Answer:
1. A
2.D
3.B (parallel lines)
4.B
5. i don't have a picture of the figure so i'm not sure
2D
3B
4B
5there isn’t picture there
Help please I need to complete this before 12
Answers
Answer:
Look at the answers bolded below
Step-by-step explanation:
To get the reference angle, just subtract 115° from 180°
180 - 115 = 65
So the reference angle is 65°
I'm not sure how many coterminal angles you need, but to get them you could just add or subtract 360°.
For example, a positive coterminal angle could be:
115 + 360 = 475°
a negative coterminal angle could be:
115 - 360 = -245°
Hope this helped :)
Find x to the nearest tenth. Click on the pic i really need help
Answers
Answer:
140 degrees i think
Step-by-step explanation:
How many eggs does a rooster lay a day???
Answers
Answer:
a rooster can't lay eggs
Step-by-step explanation:
a rooster is a male-
Answer:
0, A rooster is a male, it does not lay eggs. Hens lay eggs
Step-by-step explanation:
For f(x) = 5x – 3 and g(x) = 2x2 - 5, find the following functions.
a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (gof)(2)
Answers
Answer:
See answer below
Step-by-step explanation:
Given the functions f(x) = 5x – 3 and g(x) = 2x2 - 5, find the following functions.
a)(fog)(x) = f(g(x))
f(g(x)) = f(2x^2-5)
f(g(x)) = 5(2x^2-5) - 3
f(g(x)) = 10x²-25-3
f(g(x)) = 10x² - 28
b) g(f(x)) = g(5x-3)
g(f(x)) = 2(5x-3)²-5
g(f(x)) = 2(25x²-30x+9)-5
g(f(x)) = 50x²-60x+18-5
g(f(x)) = 50x²-60x+13
c)(fog)(2) = f(g(2))
f(g(x)) = f(2x^2-5)
f(g(2)) = 10(2)² - 28
f(g(2)) = 10(4)-28
f(g(2)) = 12
d) g(f(x)) = g(5x-3)
g(f(x)) = 2(5x-3)²-5
g(f(x)) = 50x²-60x+13
g(f(2)) = 50(2)²-60(2)+13
g(f(2)) = 200-120+12
g(f(2)) =80+12
g(f(2)) = 92
find the missing length
Answers
Answer: 14
Step-by-step explanation:
VW corresponds to BA. VW is twice the length of BA, so VU must be twice the length of BC
Marvin earns $9.75 per hour at his summer job. He wants to buy a video game system that costs $224.25
Enter an equation to model the relationship between the number of hours worked h and the amount earned e
The equation is:
Answers
Answer:
slope- (261)
Step-by-step explanation:
Writing ratios as a percentage
In the past year Heather watched 16 movies that she thought were very good. She watched 50 movies over the whole year. Of the movies she watched, what percentage did she rate as very good?
Answers
She rated 32% percent of the movies very good
A triangular prism was sliced parallel to its base. What is the shape of the cross section shown in the figure?
© a triangle that has the same dimensions as either base of the prism
O a triangle that does not necessarily have the same dimensions as either base of the prism
• a parallelogram that is not a rectangle
a rectangle
Answers
If you work 7 miles from your home and work 5 days a week, how many miles do you travel for work each week?
Answers
7 miles for 5 days is 35 miles if we were to multiply.
help me please, im also timed!!
Answers
Answer:
Point A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
4 to the right, 1 up is point A
Suppose the graph of f(x)=x^2 is translated 3 units eight and 1 unit down. If the resulting graph represents g(x), what is the value of g(2.7)?
Answers
Answer:
The value of g(2.7) is 31.49.
Step-by-step explanation:
Translations of a function:
Suppose that we have a function f(x).
The translation of f(x) a units to the left is given by g(x) = f(x+a).
The translation of f(x) a units to the right is given by g(x) = f(x-a).
The translation of f(x) a units up is given by g(x) = f(x) + a.
The translation of f(x) a units down is given by g(x) = f(x) - a.
Suppose the graph of f(x)=x^2 is translated 3 units right and 1 unit down.
Three units right:
[tex]g(x) = f(x+3) = (x+3)^2[/tex]
One unit down:
[tex]g(x) = f(x+3) - 1 = (x+3)^2 - 1[/tex]
What is the value of g(2.7)?
This is g when [tex]x = 2.7[/tex]. So
[tex]g(2.7) = (2.7+3)^2 - 1 = (5.7)^2 - 1 = 31.49[/tex]
The value of g(2.7) is 31.49.
Reduce the following differential equation to first-order and solve it.
Answers
Given that y₁(x) = x is a solution to the given second-order ODE, assume a second solution of the form
y₂(x) = y₁(x) v(x) = x v(x)
Take the first two derivatives and substitute this solution into the ODE:
y₂ = x v
y₂' = x v' + v
y₂'' = (x v'' + v' ) + v' = x v'' + 2 v'
→ (1 - x ²) y₂'' - 2 x y₂' + 2 y₂ = 0
→ (1 - x ²) (x v'' + 2 v' ) - 2 x (x v' + v) + 2 x v = 0
→ (x - x ³) v'' + (2 - 4 x ²) v' = 0
Next, reduce the order by substituting w(x) = v'(x) and w'(x) = v''(x) :
→ (x - x ³) w' + (2 - 4 x ²) w = 0
and now you have a linear equation in w. Solve for w(x) however you like; I'll just separate variables.
Write w'(x) = dw/dx, then separate variables as
(x - x ³) dw/dx + (2 - 4 x ²) w = 0
(x - x ³) dw/dx = (4x ² - 2) w
dw/w = (4x ² - 2) / (x - x ³) dx
Integrate both sides:
∫ dw/w = (4x ² - 2) / (x - x ³) dx
ln|w| = ∫ (4x ² - 2) / (x - x ³) dx
For the remaining integral, expand the integrand into partial fractions.
x - x ³ = x (1 - x ²) = x (1 - x) (1 + x)
→ (4x ² - 2) / (x - x ³) = a /x + b / (1 - x) + c / (1 + x)
→ 4x ² - 2 = a (1 - x ²) + b x (1 + x) + c x (1 - x)
→ 4x ² - 2 = (-a + b - c) x ² + (b + c) x + a
→ -a + b - c = 4, b + c = 0, a = -2
→ a = -2, b = 1, c = -1
→ (4x ² - 2) / (x - x ³) = -2/x + 1 / (1 - x) - 1 / (1 + x)
Then
ln|w| = ∫ (-2/x + 1 / (1 - x) - 1 / (1 + x)) dx
ln|w| = -2 ln|x| - ln|1 - x| - ln|1 + x| + C
ln|w| = -ln|x ² (1 - x ²)| + C
exp(ln|w|) = exp(-ln|x ² (1 - x ²)| + C )
w = C / (x ² (1 - x ²))
v' = C / (x ² (1 - x ²))
Solve for v(x) by integrating both sides, expanding the right side into partial fractions again:
x ² (1 - x ²) = x ² (1 - x) (1 + x)
→ 1 / (x ² (1 - x ²)) = a / x + b / x ² + c / (1 - x) + d / (1 + x)
→ 1 = a x (1 - x ²) + b (1 - x ²) + c x ² (1 + x) + d x ² (1 - x)
→ 1 = (-a + c - d) x ³ + (-b + c + d) x ² + a x + b
→ -a + c - d = 0, -b + c + d = 0, a = 0, b = 1
→ a = 0, b = 1, c = 1/2, d = 1/2
→ 1 / (x ² (1 - x ²)) = 1/x ² + 1/2 (1 / (1 - x) + 1 / (1 + x))
dv/dx = C (1/x ² + 1/2 (1 / (1 - x) + 1 / (1 + x)))
dv = C (1/x ² + 1/2 (1 / (1 - x) + 1 / (1 + x))) dx
Integrate both sides:
∫ dv = ∫ C (1 / x ² + 1/2 (1 / (1 - x) + 1 / (1 + x))) dx
v = C₁ (-1/x - 1/2 ln|1 - x| + 1/2 ln|1 + x|) + C₂
v = C₁ (1/2 ln|(1 + x) / (1 - x)| - 1/x) + C₂
Solve for y₂(x) by multiplying both sides by x :
y₂ = C₁ (1/2 x ln|(1 + x) / (1 - x)| - 1) + C₂ x
Now, y₁(x) = x, so we can omit the last term from the second solution, giving us
y₂(x) = C (1/2 x ln|(1 + x) / (1 - x)| - 1)
Snow fell at a rate of
of an inch/hour. How much
snow fell in a period of 6
hours?
Answers
Answer:
Step-by-step explanation:
that implies a simple multiplication:
snow = (3/4)(6) = 4.5 inch
and note the units elimination in the operation as well:
= [inch/hour][hour] = inch
My fault if im wrong :(
Pls help me on this question
Answers
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
If probablikty is 5/12 then, not picking is 7/12
Lucy wants to buy a new laptop for school. She has a $25 off coupon, but the store is also having a sale for 15%. Unfortunately she can not get both discounts and must pick one. If the laptop costs $200, which one should she use?
Answers
Answer:
15% discount
Step-by-step explanation:
200 x .15 is 30 which means that you save 5 dollars more when using that discount rather than just 25.
Yolanda brought a CD to listen to on the bus the CD is 78 minutes long The bus ride was 2 1/2 hours long How many minutes longer was the bus ride than thr CD?
Answers
Answer:
2.5 times 60 equals 150. 150-78 equals 72. So the answer is 72.
Step-by-step explanation:
Hope this helps.
Solve this for me (geometry)
Answers
Given:
A figure of a circle. [tex]KJ=6,KL=x-2,ML=4[/tex].
To find:
The length of KJ.
Solution:
From the given figure it is clear that the number 6 is marked between K and J it means the number 6 represents the distance between the points K and j.
Therefore, the length of KJ is 6 units.
Note: In the given question we need to find KL instead of KJ because KJ is already given.
According to the tangent secant theorem:
[tex]a^2=bc[/tex]
Where,
a is the length of the tangent.b is the length of the external segment of the secant.c is the measure of the secant.Using the tangent secant theorem, we get
[tex]ML^2=KL\times JL[/tex]
[tex](4)^2=(x-2)\times (6+x-2)[/tex]
[tex]16=(x-2)\times (4+x)[/tex]
[tex]16=4x+x^2-8-2x[/tex]
On further simplification, we get
[tex]16=x^2+2x-8[/tex]
[tex]0=x^2+2x-8-16[/tex]
[tex]0=x^2+2x-24[/tex]
Splitting the middle term, we get
[tex]x^2+6x-4x-24=0[/tex]
[tex]x(x+6)-4(x+6)=0[/tex]
[tex](x+6)(x-4)=0[/tex]
[tex]x=-6,4[/tex]
For [tex]x=-6[/tex],
[tex]KJ=-6-2[/tex]
[tex]KJ=-8[/tex], which is not possible because side cannot be negative.
For [tex]x=4[/tex],
[tex]KJ=4-2[/tex]
[tex]KJ=2[/tex]
Therefore, the measure of KL is 2 units.
original price $50 mark up 10% selling price?
Answers
Answer:
$55
Step-by-step explanation:
$50 + 0.10($50) = 1.1 * 50 = $55
Harvey is placing a microwave oven on his kitchen counter. What information does Harvey need?
A. the volume of the microwave oven and the volume of the kitchen counter
B. the area required for the microwave oven and the area of the kitchen counter
C. the perimeter of the microwave oven and the perimeter of the kitchen counter
Answers
Answer:
b the area
Step-by-step explanation:
you will need to see if you have enough area for the microwave to fit
hey my silly little bakas );) help me out here okay ????
Answers
Answer:
The answer is A
Step-by-step explanation:
Yep im so smart. You defininetly need this answer a month later ;)
Solve the following polynomial function. y=x^4−21x^2−100
Answers
Answer:
y= x⁴ -21x²-100
combine x's I think
x⁴= 1x? cuz if it's 1x⁴ that's 1x*1x*1x*1x = 1x
1x * -21x²
-21x * -21x = 441x
+1x = 442x
y= 442x -100
I'm not sure if I did that right
What is the value of this expression?
5+6×(5−2)+9
77
62
42
32
Answers
Answer:
32
Step-by-step explanation:
5 + 6 * (5 - 2) + 9
5 + 6 * 3 + 9
5 + 18 + 9
23 + 9
32
Solve for x. round to the nearest tenth
Answers
Answer:
41.81
Step-by-step explanation:
∠B = arcsin(b·sin(A)a)
= 0.72973 rad = 41.81° = 41°48'37"
∠C = 180° - A - B = 0.84107 rad = 48.19° = 48°11'23"
c = a·sin(C)sin(A)=4.47214 = 2√5
Select all equations that have at least one integer solution.
Answers
Answer:
b and d
Step-by-step explanation:
The equations have at least one integer solution are equation B: √(3x) = 75 and equation D:√x = x - 12.
What is the solution to the given equations?The value of x is known as the solution.
A. √(4x) = 5
On squaring, we have
4x = 25
x = 6.25
The value is not an integer.
B. √(3x) = 75
On squaring, we have
3x = 5625
x = 1875
The value is an integer.
C. 8√x = √16
On squaring, we have
64x = 16
x = 0.25
The value is not an integer.
D. √x = x - 12
On squaring, we have
(x - 12)² = x
x² - 24x + 144 = x
x² - 25x + 144 = 0
(x - 16)(x - 9) = 0
x = 9, 16
The value is an integer.
E. √(10 - x) = x - 2
On squaring, we have
(x - 2)² = 10 - x
x² - 4x + 4 = 10 - x
x² - 3x - 6 = 0
(x - 4.37)(x + 1.37) = 0
x = -1.37, 4.37
The value is not an integer.
More about the solution of the equation link is given below.
https://brainly.com/question/545403