Answer:
D) x + √x - 6.
Step-by-step explanation:
(√x-2)(√x + 3)
= √x*√x + 3*√x - 2*√x - 2*3
= x + √x - 6.
What is 28 percent as a fraction?
Answer:
28 as a fraction would be written as 56/2.
Step-by-step explanation:
The fraction can be written as 7/25.
Explanation:
Given Input Value = 28%
Place the Percentage Value at the top over 100. = 28/100
The given fraction is 28/100.
On reducing the fraction, we get the exact form 28/100. = 7/25
The exact form of the fraction is 7 /25.
An aircraft is timetabled to travel from A to B. Due to bad weather it flies from A to C then from C to B, where AC and CB make angles of 27° and 66° respectively with AB. If |AC| = 220 km, calculate |AB|.
Answer:
|AB| = 240 km
Step-by-step explanation:
Finding ∠C :
⇒ 27° + 66° + ∠C = 180°
⇒ ∠C = 180° - 93°
⇒ ∠C = 87°
Applying the Law of Sines :
⇒ sin 66° / 220 = sin 87° / AB
⇒ 0.913545458 / 220 = 0.998629535 / AB
⇒ AB = 220/0.913545458 x 0.998629535
⇒ AB = 240.819981 x 0.998629535
⇒ AB = 240.489946
⇒ |AB| = 240 km (nearest whole kilometer)
Answer:
|AB| = 240 km (nearest km)
Step-by-step explanation:
Draw a sketch with the given information (attached).
Calculate the missing angle (shown in red on the attached diagram).
Given:
∠CAB = 27°∠CBA = 66°The interior angles of a triangle sum to 180°
⇒ ∠ACB + ∠CAB + ∠CBA = 180°
⇒ ∠ACB + 27° + 66° = 180°
⇒ ∠ACB = 180° - 27° - 66°
⇒ ∠ACB = 87°
Use Sine Rule for sides to calculate |AB|:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \sf \dfrac{|AB|}{\sin ACB}=\dfrac{|AC|}{\sin CBA}[/tex]
[tex]\implies \sf \dfrac{|AB|}{\sin (87^{\circ})}=\dfrac{220}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=\dfrac{220\:\sin (87^{\circ})}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=240.4899459...[/tex]
[tex]\implies \sf |AB|=240\:km\:(nearest\:km)[/tex]
Sarah makes a red hair bow using 21 4/5 inches of ribbon. She makes a purple hair bow using 18 1/4 inches of ribbon.
How much more ribbon is used to make the red hair bow than the purple hair bow?
Answer:
91/20 or 4 11/20
Step-by-step explanation:
First, convert the 2 amounts into improper fractions
Red: 21 4/5 = 114/5
Purple: 18 1/4 = 73/4
Then, using cross multiplication, you can give them the same denominator
Red: 114/5 = 456/20
Purple: 73/4 = 365/20
Then just subtract the numerators and keep the denominator
456/20 - 365/20 = 91/20
So your answer is
91/20 or 4 11/20
Determine the exact value of sin 30° tan 45° + tan 30° sin 60⁰
Answer:
1.
Step-by-step explanation:
1) if sin30=0.5; tan45=1; tan30=1/√3; sin60=√3/2, then
2) 0.5+0.5=1.
the table represent a function? Why or why not?
A. Yes, because every x-value corresponds to exactly one y-value.
B. No, because the y-values are positive.
C. Yes, because there are different y-values.
D. No, because one x-value corresponds to two different y-values.
Answer:
D is the answer I'm pretty sure
Step-by-step explanation:
6 has to y values
The points A(4, 3) and B(4, –5) are plotted on the coordinate plane. Rectangle ABCD has a perimeter of 30 units. If points C and D were plotted on the grid shown, what would their coordinates be if point C is below point D? Alt_text C: ( , ) D: ( , )
The possible coordinates of C and D are: C = (11,3) and D = (11,-5) or C = (-3,3) and D = (-3,-5)
How to determine the coordinates of C and D?The given parameters are:
A = (4,3)
B = (4,-5)
Perimeter, P = 30 units
Since points A and B are on the same x-coordinate, then the distance between them is:
AB = 3 - - 5
AB = 8
The perimeter of the rectangle is calculated using:
P = 2 *(AB + CD)
This gives
2 * (8 + CD) = 30
Divide by 2
8 + CD = 15
Subtract 8 from both sides
CD = 7
This means that points C and D are 7 units from points A and B, respectively.
If A = (4,3) and B = (4,-5), then the possible coordinates of C and D are:
C = (11,3) and D = (11,-5) or C = (-3,3) and D = (-3,-5)
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If P is directly proportional to Q. And Q = 30 when P = 40. Find Q when P = 70
Answer:
Q = 52.5
Step-by-step explanation:
given P is directly proportional to Q then the equation relating them is
P = kQ ← k is the constant of proportion
to find k use the condition Q = 30 when P = 40 , then
40 = 30k ( divide both sides by 30 )
[tex]\frac{40}{30}[/tex] = [tex]\frac{4}{3}[/tex] = k
P = [tex]\frac{4}{3}[/tex] Q ← equation of proportion
when P = 70 , then
70 = [tex]\frac{4}{3}[/tex] Q ( multiply both sides by 3 to clear the fraction )
210 = 4Q ( divide both sides by 4 )
52.5 = Q
Hello everyone!!
This is easy;
[tex] \frac{5x}{2} + \frac{9}{5} = 25[/tex]
[tex] \frac{5x}{2} + \frac{9}{5} = 25 \\ \frac{25x + 18}{10} = 25 \\ 25x + 18 = 250 \\ \frac{250 - 18}{25} = x \\ x = \frac{232}{25} [/tex]
hope it helps
Please refer to the attachment
What is the probability that a patient shows improvement
if it is known that the patient was given the drug?
Answer:
.3375
Explanation:
Total people who were given drug: 800
Total people who showed improvement: 270
Probability:
[tex]\boxed{ \sf \dfrac{favorable \ outcomes }{total \ possible \ outcomes}}[/tex]
insert values
[tex]\rightarrow \sf \dfrac{270}{800}[/tex]
simplify
[tex]\rightarrow \sf \dfrac{27}{80}[/tex]
in decimals
[tex]\rightarrow \sf 0.3375[/tex]
Answer:
d) .3375Step-by-step explanation:
let E be the event : “the patient shows improvement”
D be the event : “the patient was given the drug”
here we are in a conditional probability situation:
Let E/D be the event “a patient shows improvement ,if it is known that the patient was given the drug”
[tex]p\left( E|D\right) =\frac{p\left( E\cap D\right) }{p\left( D\right) }[/tex]
[tex]=\frac{270}{800}[/tex]
[tex]=0.3375[/tex]
does anyone know the answer?
Answer: Choice A
40.61 square meters
==========================================================
Explanation:
The area of a full circle is
A = pi*r^2
meaning half of it (aka semicircle) will have this area
A = 0.5*pi*r^2
The diameter of the semicircle is 5.4 meters, which divides in half to get the radius of r = 2.7
The semicircle has an area of...
A = 0.5*pi*r^2
A = 0.5*3.14*(2.7)^2
A = 11.4453
which is approximate since pi = 3.14 is approximate.
Now compute the area of the triangle
area = base*height/2 = 5.4*10.8/2 = 29.16
Then add those sub-areas to get the grand total area.
semicircleArea + triangleArea = 11.4453+29.16 = 40.6053
That rounds to 40.61 which shows why choice A is the answer.
8th grade distributive property equations and solutions
The value of x will be given as for the given expression X = -1
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
2x + 12 = 10
2x = 10 - 12
2x = -2
x = -1
first you distribute 2 to x and 6 which equals 2x+12=10 then you subtract 12 from 10 which equals 2x=-2 then divide -2 by 2x to see what x equals so x=-1
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Find the area of the following figure.
300 cm2
312 cm2
252 cm2
400 cm2
Answer:
312cm2
Step-by-step explanation:
16*12=192
10*6/2=30
30*4=120
192+120=312
Solve the system of equations 3x - 2y = 8 x-2y = 4
Answer: (2, -1), or x = 2 and y = -1
By graphing:
We can solve by graphing. See attached.
-> The solution is the point of intersection. The lines intersect at (2, -1) which means x is equal to 2 and y is equal to -1.
By substituting:
We can solve this by substituting. It means we will substitute one equation into the other, then solve for the variables.
3x - 2y = 8
x - 2y = 4 -> x = 2y + 4
-
3x - 2y = 8
3(2y + 4) - 2y = 8
6y + 12 - 2y = 8
4y = -4
y = -1
-
x - 2y = 4
x - 2(-1) = 4
x + 2 = 4
x = 2
the graph of y = (x) is shown below
Answer:
Step-by-step explanation:
Solution
The question is a bit obscure. The best choice I think, would be A. F(x) could equal something like y = x - 3. When y = 0, x = 3 or put the other way, when x = 3 y= 0.
Mya bought x shirts for $14.50 each and used a $20 coupon. Which equation represents theh total amount, a, she spent?
HELP PLEASE For the following right triangle, find the side length x.
Answer:
37
Step-by-step explanation:
use Pytago ( you can search it online )
hhelp plssssssssssssssssssssssssssss
Answer:
This is false
Step-by-step explanation:
The function y = log(x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?
please help
Answer: [tex]y=\log(x-1)-2[/tex]
What is the median of the set of data?
{131, 154, 204, 244, 244, 276, 263, 289, 288, 274, 207}
Enter your answer in the box.
Proving Parallelogram
Answer:
Soln.
Given that we have proven:AB =CD and BC=DA
we will be said that the A and C is the angle of 90° and we will add the letters to get the results so let's started the A+90°+ 90°+ B+C+ D=90°
A+180°+B+C+D
180°+90°
=270°
a bottle contains 2 1/2 cups of apple juice a serving of apple juice is 1/2 cup how many servings does the bottle contain
By applying aritmethics and concept of capacity we conclude that the bottle containing 2 1/2 cups of apple juice contains 5 servings containing 1/2 cups each.
How to determine the quantity of servings from a bottle
In this question we are dealing with capacities, capacities are an application of volumes. A bottle contains a capacity equivalent to a given quantity of cups. The number of cups is found by dividing the capacity of a bottle by the capacity of a serving:
[tex]x = \frac{\frac{5}{2}\,cups}{\frac{1}{2}\,cups }[/tex]
x = 5
By applying aritmethics and concept of capacity we conclude that the bottle containing 2 1/2 cups of apple juice contains 5 servings containing 1/2 cups each.
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exam tomorrow need help
Answer:
See below ~
Step-by-step explanation:
The perimeter of a figure refers to the sum of the side lengths of its edges.
Figure (a) : Triangle
⇒ P = 2a + 1 + 3a + a - 4
⇒ P = 6a - 3
⇒ P = 3 (2a - 1)
Figure (b) : Hexagon
⇒ P = 3m - 1 + 3n + n + m + 3m + 1 + 4n + m + n + 2
⇒ P = 3m + m + 3m + m + 3n + n + 4n + n + 1 - 1 + 2
⇒ P = 8m + 9n + 2
Figure (c) : Trapezoid
⇒ P = 2a + 3 + 3a - b + 2a + 2b - 4 + b + 4
⇒ P = 2a + 3a + 2a + 2b + b - b + 4 - 4 + 3
⇒ P = 7a + 2b + 3
A. 23.7
B. 11.2
C. 9.5
D. 57.3
E. 30.0
F. 6.0
Answer:
c.9.5
Step-by-step explanation:
im awesome so so very
john saves N$250 the first month and every two month later increases it by N$75.how much will john save in the 12th month?
Answer:
750
Step-by-step explanation
Question: How many miles can we paddle in 1 hour at the Los Angeles river?
The river is going at 25 mph
and you are paddling at a consistent rate
Answer:
125 mph
Step-by-step explanation:
The river is going 25 mph every 20 minutes
[tex]20[/tex] [tex]minutes=25[/tex][tex]40[/tex] [tex]minutes=50[/tex][tex]60[/tex] [tex]minutes=75[/tex] [tex]80[/tex] [tex]minutes =100[/tex][tex]1[/tex] [tex]hour = 125[/tex]Therefore we can paddle 125 miles at consistent rate.
Scientists are tracking the population of a specific species of bird. They have determined that the function P(x) = 575 (1.025)x models the number of birds, P(x), after x years. Which of the following is true about the brid?
Marci needs to rent a storage. She needs to determine the volume of the storage unit. If the storage unit is 8 feet high, what is the volume of the storage unit
What is the simplest form of
X^4 y^7/ 3sqrt x^10 y^4
Answer is D
Answer: The answer is Undefined (a/0)
I put a screenshot of how i got that answer
Answer: She's right, it is d
Step-by-step explanation:
4.1 A bag contains 6 red, 4 green, 2 yellow and 3 blue balls. In each case, give the ratio (in simplest form) of the asked number of balls in the bag.( 4 ) 4.1.1 The number of red balls to the number of green balls.
The number of red balls to the number of green balls is 3 : 2
How to determine the ratio?The distribution of the balls is given as:
6 red, 4 green, 2 yellow and 3 blue balls
The number of red balls to the number of green balls is represented as:
Ratio = Red : Green
So, we have:
Ratio = 6 : 4
Simplify
Ratio = 3 : 2
Hence, the number of red balls to the number of green balls is 3 : 2
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Madison is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with three equal-sized sections labeled Walk, Run, Stop and spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange?
Answer:
12.
Step-by-step explanation:
There are 3 * 4 = 12 possible outcomes
for example
Walk / Red
Walk/Green
Walk/Blue
Walk/Orange
- and there are 4 similar outcomes for Run and Stop.