Answers
Answer:
Step-by-step explanation:
The first one I would factor the difference of cubes on top and then cancel a common factor this would end up giving you sin^2(A/2)+sin(A/2)cos(A/2)+cos^2(A/2)
(the 1st+3rd term here actually equals 1)
now you have
1+sin(A/2)cos(A/2)
1+1/2*2sin(A/2)cos(A/2) (this step was just to help show how I'm going to use the next identity)
1+1/2sin(A) (double angle identity for sine)
hint for the next one: I would multiply top and bottom by bottom's conjugate first
Related Questions
Steven earns extra money babysitting. He charges $25.00 for 4 hours and $37.50 for 6 hours. Write an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represents the amount he charges. The equation is y=
Answers
An easy way to solve this problem is divide $23.25 by 3 or $54.25 by 7. Either way, you get $7.75. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:
$7.75x = y
I hope this helped! :)))
Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet?
Answers
Answer:
40 Miles Per Hour is 211,200 Feet per Hour, 3520 Feet Per Minute, and 58.67 Feet Per Second.
Which of the following translates the sentence the difference of three times a number and 20 is 13"?
x x - x - 20 = 13
3x - 20 = 13
3x + 20 = 13
Answers
Answer:
3x - 20 = 13
Step-by-step explanation:
it says difference so it cant be the last one and three times a number is 3 x so it cant be the first one leaving the middle.
please mark brainliest
Use the quadratic formula to solve the equation. 2x^2-6x+1=0 Enter your answers, in simplified radical form, in the boxes.
x=__or x=
please send me image and explain work
Answers
Answer:
(3 (pm) sqrt(7))/2
Step-by-step explanation:
First step: Identify a,b, and c
a=2
b=-6
c=1
Second step: Find b^2-4ac (this is called the discriminant-I will call this D)
(-6)^2-4(2)(1)=36-8=28
Third step: Find the square root of the discriminant aka sqrt(D)
sqrt(28)
Let's see if we can simplify sqrt(28)
Here is there a factor of 28 that is a perfect square? How about 4? Yep!
sqrt(28)=sqrt(4)sqrt(7)=2sqrt(7).
Fourth Step: What is -b? If b=-6 then -b=6.
Fifth step: What is 2a? 2(2)=4
So the formula is
x=(-b (pm) sqrt(D))/(2a)
or
x=(step4 (pm) step 3)/(step 5)
x=(6 (pm) 2sqrt(7))/4
Simplify
x=(3 (pm) sqrt(7))/2
*pm means plus or minus
*sqrt( ) means square root of the number that follows in the ( )
Answer:
Just took it!
Step-by-step explanation:
If
[tex] log_{5}(3) = a[/tex]
and
[tex] log_{5}(4)= b[/tex]
then
[tex] log_{15}(2) [/tex]
is?
a)2b/a+1
b)a+b/ab
c)2b-a/2b
d)b/2a+2
e)2a+2/b
Answers
[tex]\bf \log_5(3)=a\qquad \qquad \log_5(4)=b\ \\\\\\ \log_5(4)=b\implies \log_5(2^2)=b\implies 2\log_5(2)=b\implies \log_5(2)=\cfrac{b}{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{15}(2)\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_5(2)}{\log_5(15)}}\implies \cfrac{~~\frac{b}{2}~~}{\log_5(3\cdot 5)}\implies \cfrac{~~\frac{b}{2}~~}{\log_5(3)+\log_5(5)} \\\\\\ \cfrac{~~\frac{b}{2}~~}{a+1}\implies \cfrac{b}{2}\cdot \cfrac{1}{a+1}\implies \cfrac{b}{2a+2}[/tex]
HELPP!!!! I need the answer please
Answers
Answer:
x = 4
Step-by-step explanation:
Using the 90-60-30 theorem, the hypotenuse is equal to 2a, so a = 4 sqrt(2). The shortest leg is therefore 4 sqrt(2). Using this, to find x, plug it into the smaller triangle. The hypotenuse of the smaller triangle is therefore 4 sqrt(2). Using the 45-45-90 theorem, 4 sqrt(2) = x sqrt(2), so x = 4. This is because there are two sqrt(2)'s', so taking that out of the equation leaves x = 4.
Hope this helps!
Write the following ration as a reduced fraction. Simplify your answer when possible: 14 to 84
Answers
Answer:
Hi there!
Since you asked for a simplified fraction, the answer to this question is: 1/6
Step-by-step explanation:
Look at the fraction 14/84, there is a definite similar factor between 14 and 84, 2. So all you do is divide the two numbers by two to reduce the fraction into 7/42
then you divide both 7 and 42 by 7 to get 1/6
Answer:
1/6
Step-by-step explanation:
14 to 84
First lets make it a fraction
14/84
Divide the top and bottom by 14
1/6
What is a Probabibility
Answers
Answer:
Probability
Step-by-step explanation:
Probability is the likelihood or chance of an event occurring. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .
what are the solutions to the equation 0 equals x squared minus x minus 6 check all that apply
Answers
Answer:
I don't understand the question can you add more information or maybe show the page where you got this question?
Step-by-step explanation:
Answer:
the answer is zero
Step-by-step explanation:
3. Mr. Terence had 18 boxes containing 36 donuts each. He sold 162 donuts and
repacked the rest into 81 boxes. How many donuts did he put into cach box?
Answers
6 donuts. He repacked 6 donuts into each box .
Mr. Terence had 18 boxes containing 36 donuts each, that means:
Total donuts = n° boxes*n° donuts
Total donuts = 18*36 = 648
He had in total 648 donuts.
He sold 162 donuts and repacked the rest into 81 boxes. Then:
Rest donuts = Total donuts - sold donuts
Rest donuts = 648 - 162 = 486
The rest donuts are 486 donuts.
He repacked the rest into 81 boxes, then:
n° donuts (each box) = Rest donuts/n° boxes
n° donuts (each box) = 486/81 = 6
The number of donuts that he put in each box is 6 donuts.
wich number can each term of the equation be multiplied by to eliminate the fractions before solving 6-3/4x+1/3=1/2x+5
Answers
Answer:
12x
Step-by-step explanation:
We require the lowest common multiple of 4x, 3 and 2x
the lowest common multiple of 4, 3 and 2 is 12
the lowest common multiple of x and x is x
Combining the two gives lowest common multiple of 12x
Multiplying through by 12x gives
72x - 9 + 4x = 6 + 60x ← no fractions
The range of the function f(x) = x + 5 is {7, 9). What is the function's domain?
Answers
Answer:
(2,4)
Step-by-step explanation:
The range is the y values
y = x+5
Let y=7
7 =x+5
Subtract 5
7-5 x+5-5
2=x
Let y= 9
Subtract 5
9-5 x+5-5
4=x
The domain is (2,4)
What is the solution to log 25x = 3?
Answers
Answer: x=40
Step-by-step explanation:
The solution to log (25x) = 3 is 40. This is calculated by using log rules.
What are the rules of a logarithmic function?A function that has log terms is said to be a logarithmic function.
Some of the rules for solving log functions are as follows:
The basic form of a logarithmic function is [tex]log_b(m)=n[/tex] ⇒ [tex]m=b^n[/tex].Product rule: [tex]log_b(x)+log_b(y)=log_b(xy)[/tex]Quotient rule: [tex]log_b(x)-log_b(y)=log_b(\frac{x}{y})[/tex]Power rule: [tex]log_b(x)^n=nlog_b(x)[/tex]Identity rule: [tex]log_b(b)=1[/tex] where [tex](b^1=b)[/tex]Finding the solution for the given function:Given that,
log (25x) =3
Using basic form [tex]log_b(m)=n[/tex] ⇒ [tex]m=b^n[/tex]
Here base b=10, m=25x and n=3
Then,
log (25x) =3
⇒ [tex]25x = 10^3[/tex]
⇒ 25x = 1000
⇒ x = 1000/25
∴ x = 40.
Hence the solution of the given function is 40.
Learn more about logarithmic functions here:
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What is the slope of the line x = 4?
Answers
Answer: Undefined
Step-by-step explanation: Since there is no change in x, and it is a horizontal line, that means that the denominator is zero. Dividing anything with the denominator being 0 will always be undefined (Not to be confused with the numerator, which is just dividing by 0, thus giving you 0.) That means that our answer will be undefined.
Connie has $660,000 she wants to save. If the FDIC insurance limit per
depositor, per bank, is $250,000, which of these ways of distributing her
money between three banks will guarantee that all of her money is insured?
O
A. $220,000 in bank A, $160,000 in bank B, $280,000 in bank C
O
B. $180,000 in bank A, $220,000 in bank B, $260,000 in bank C
O
c. $220,000 in bank A, $300,000 in bank B, $140,000 in bank C
O
D. $180,000 in bank A, $240,000 in bank B, $240,000 in bank C
SUBMIT
Answers
Answer:
The answer would be D) $180,000 in bank A, $240,000 in bank B, $240,000 in bank C.
Step-by-step explanation:
You can immediately eliminate A, B and C because the question clearly states that the limit per bank is $250,000.
Answer:
D. $180,000 in bank A, $240,000 in bank B, $240,000 in bank C
Step-by-step explanation:
She needs to deposit less than $250,000 in each bank in order to be able to have that sum of money insured, in this case she could deposit it this way:
$250,000
$250,000
$160,000
But that could be too risky and too on the verge of not being accepted, you she just takes $10,000 out of every $250,000 deposits to make them $240,00, and add it to the $160,000 deposit, so she is left with three deposits of:
$240,000
$240,000
$180,000
And with this she makes sure all of her deposits are insured by staying below the $250,000 limit.
Factor the binomial using its GCF: 10x-15x^4
Answers
Answer:
5x(2 - 3x³)
Step-by-step explanation:
10x-15x^4
The GCF( Greatest Common Factor) of 10x-15x^4 is 5x
Solve:
10x/5x = 2
-15^4/5x = -3x³
Final answer is
5x(2 - 3x³)
Check
5x(2 - 3x³)
distribute
5x(2) + 5x(-3x³)
10x - 15x^4
Answer:
5x(2 - 3x^3)
Step-by-step explanation:
The GCF is 5x 10x/5x=2 15x^4/5x=3x^3
A. What is the area of the base? Use complete sentences to explain your reasoning.
B. What is the volume of the prism? Use complete sentences to explain your reasoning.
Answers
Answer:
For the first answer (A)
The area of the base is the area of the 8 by 4 rectangle, minus the missing 2 by 2 square in the top-right. This is 8*4-2*2=32-4=28 square centimeters.
For the second answer (B)
The volume of the prism is the base area multiplied by the height, or 28*10=280 cubic centimeters.
Answer:
Area = 28 cm² and Volume = 280 cm³
Step-by-step explanation:
A. Area of the base of the prism = Area of rectangle with dimensions 4 × 8 cm. minus area of a rectangle with dimensions 2×2 cm.
Area = 4 × 8 - 2 × 2
= 32 - 4 = 28 cm²
B. Volume of the given prism = Volume of full prism with dimensions 10 × 4 × 8 cm. minus volume of small prism (missing) having dimensions 2×2×10 cm.
Volume = 10 × 4 × 8 - 2 × 2 × 10
= 320 - 40
= 280 cm³
Area = 28 cm² and Volume = 280 cm³
Use a transformation to solve the equation. w/4 = 8 can you also leave a detailed explanation on how this equation = 32
Answers
Answer:
w=32
Step-by-step explanation:
w/4 = 8
4/1 * w/4 = 8*4
w=32
if m
17
27
90
63
** picture is attached below!!
Answers
Answer:
Last option: 63
Step-by-step explanation:
You need to observe and analize the triangle XWZ provided in the image attached.
You can observe that the lenght of the side XW of the triangle XWZ is congruent to the lenght of the side ZW. This means that the lenght of the side XW and the lenght of the side ZW are equal.
Therefore, if the measure of the angle ∠X is 63, then the measure of the angle ∠YZW is 63:
[tex]m\angle YZW=m\angle X[/tex]
[tex]m\angle YZW=63[/tex]
This matches with the last option.
What is f(g(13))? A mapping diagram is shown
Answers
Answer:
Step-by-step explanation:
It's 32, just follow the row when g=13.
Answer: We want to know f( g (13) ), here g(13) is just a number, so you are evaluating f in a number, first we need to know the value of g(13). Looking in the diagram you can see that g(13) = 16.
So f(g(13)) = f(16)
Also, looking in the diagram you can see that f(16) = 32
So, f ( g (32) ) = 32
Candlelight Books kept a record of how its sales increased based on
discounts it offered. The scatterplot shows the results. Based on the line of
best fit, which of the following statements is true? ANSWER PLEASE LIKE RIGHT NOW
Answers
Answer:
D
Step-by-step explanation:
We need to understand the meaning of slope. The slope means the rate of change of y with every unit change of x.
In our case, it will be rate of change of sales increase (%) with respect to unit change of discount(%).
The formula for slope is the change in y divided by change in x.
From the 2 points given, we can say that slope is:
[tex]\frac{62-32}{20-10}=\frac{30}{10}=\frac{3}{1}[/tex]
This means "as discount increases 1%, sales increase by 3%". Option D is right.
Answer:
D
Step-by-step explanation:
Please help me find this shaded reigon fast
Answers
Answer:
=293.7m²
Step-by-step explanation:
Area of the shaded region = area of the circle-area of the minor segment.
The area of the minor segment is calculated as follows.
Area= Area of sector - area of the triangle bound by the radii.
=∅/360πr²-1/2r²sin∅, where r is the radius of the circle and ∅ the obtuse angle bound by the radii.
=130/360×π×11.1²-1/2×11.1²sin130
=93.43m²
Area of the whole circle =πr²
=π×11.1²
=387.08m²
Area of the shaded region
=387.08m²-93.43m²
=293.65m²
≅293.7m² to the nearest tenth.
Find the equation of the line graph below in slope intercept form. please show your work. (will make brainiest.)
Answers
Answer:
y=2/3x+3
Step-by-step explanation:
the slope is 2 over 3 because you ride 2 up and 3 to the right to get to the next dot and the y intercept is 3 because that's where the line intercepts the y axis.
Rachel has a box in the shape of a prism with a square base. The capacity of the box is 150 cubic inches. The height of the box (y) is times the base length of the box (x). Find the approximate height and the length of the box.
A. x = 4 and y = 6
B. x = 5 and y = 7.5
C. x = 4.2 and y = 6.3
D. x = 4.6 and y = 6.9
Answers
Answer:
Step-by-step explanation:
What do we know about that prism?
It's a rectangular prism with a square base.
Height: y (from question)
base length: x (from question)
base width: x (from question, since it's a square base).
Total volume: 150 cu inches
The question lacks a relationship between x and y the "is __ times", but we can see from the answer choices that they all show a constant relationship:
y = 1.5 x
The volume of a prism is obtained by multiplying the lengths of its 3 dimensions: V = length * width * height. In our case, we then have
150 = x * x * y
then we replace y by its x-expressed equivalent:
150 = x * x * (1.5x) = 1.5x³
then we isolate x³ by dividing each side by 1.5
x³ = 100, we do the cubic root on each side
x = 4.64
So, answer is D. x = 4.6 and y = 6.9
If you you 4.64 * 4.64 * 6.96 = you get 149.8, which is very close to 150.
Which graph represents the function g(x) = |x + 4| + 2?
Answers
Answer:
Step-by-step explanation:
Graph y = |x|. This graph is v-shaped, opening up, with vertex at (0, 0). Now translate this graph 4 units to the left and 2 units up. The result is the graph of g(x) = |x + 4| + 2.
Next time, please share the possible answer choices. Thanks.
The function g(x) is derived from the function f(x) by translating f(x) graph 4 units to the left and 2 units up
The equation of the function is given as:
[tex]g(x) = |x + 4| + 2[/tex]
The above is an absolute value function, and the equation of the parent function is:
[tex]f(x) = |x|[/tex]
This means that the function g(x) is derived from the function f(x) by translating f(x) graph 4 units to the left and 2 units up
Read more about function transformation at:
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What is the simplified form of x+6/2x+5 + x+5/x+3
Answers
Answer:
Step-by-step explanation:
6/2 evaluates to 3
Multiply x and 3
Multiply x and 1
The x just gets copied along.
The answer is x
x
6/2*x evaluates to 3x
x+6/2*x evaluates to 4x
x+6/2*x+5 evaluates to 4x+5
4x + x = 5x
The answer is 5x+5
x+6/2*x+5+x evaluates to 5x+5
To divide 1 by x
The x just gets copied along in the denominator.
The answer is
5/x evaluates to
The answer is
x+6/2*x+5+x+5/x evaluates to
5 + 3 = 8
The answer is
B
x+6/2*x+5+x+5/x+3 evaluates to
The final answer is
B
use only positive exponents (4vy^-9) * (2x^-6 x^6 y^6) * (3v^4)
Answers
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (4vy^{-9})\cdot (2x^{-6}x^6y^6)\cdot (3v^4)\implies 4vy^{-9}2x^{-6}x^6 y^6 3v^4 \\\\\\ 4\cdot 3\cdot 2vv^4y^{-9}y^6x^{-6}x^6 \implies 24v^{1+4}y^{-9+6}x^{-6+6}\implies 24v^5y^{-3}x^0 \\\\\\ 24v^5\cdot \cfrac{1}{y^3}\cdot 1\implies \cfrac{24v^5}{y^3}[/tex]
the function f(x)= sqrt x is translated left 5 units and up 3 units to create the function g(x). what is the domain of g(x)?
Answers
Answer:
the domain is from -5 to infinity
Step-by-step explanation:
f(x+5)+3=√x+5 +3
x+5>0
x>-5
the domain is from -5 to infinity
Answer:
A. {x | x > –5}
the greater than sign should be greater than or equal to
Two asteroids are 1000 km apart and are heading straight for each other. One asteroid is travelling at 59 km per second and the other at 41 km per second. How long does it take for them to collide?
Answers
Answer:
10 seconds.
Step-by-step explanation:
The velocity at which they are approaching each other = 59 + 41 = 1000 km per second.
Velocity = distance / time
So time = distance / velocity
= 1000 / 100
= 10 seconds.
10 seconds long does it take for them to collide.
Velocity
Velocity exists as the measurement of the amount of distance an object covers in a given amount of time. Here's a term equation that describes the connection between distance, velocity, and time: Velocity equals distance traveled divided by the time it brings to get there.
The velocity at which they exist approaching each other = 59 + 41
= 1000 km per second.
Velocity = distance / time
So, time = distance / velocity
= 1000 / 100
= 10 seconds.
Therefore, 10 seconds long does it take for them to collide.
To learn more about Velocity
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h. A. h(13) = 18 B. h(-3) = -1 C. h(2) = 16 D. h(8) = 21
Answers
Answer:
C. h(2) = 16
True statement
Step-by-step explanation:
The function has
Domain
-3 ≤ x ≤ 11
Range
1 ≤ h(x) ≤ 25
h(8) = 19
h(-2) = 2
Lets analyze each statement
A. h(13) = 18
False, x = 13 is not part of the domain
B. h(-3) = -1
False, -1 is not part of the range
C. h(2) = 16
True statement
D. h(8) = 21
False, the problem tells us that h(8) = 19