Answer:
1
Step-by-step explanation:
=sin 55 cos 35 + cos 55 sin 35 =sin (55+35)=sin 90=1
given the function R(x)= x+5/x-5 find the value of x that make the function greater then or equal to zero. write the solution in interval notation
Answer:
Step-by-step explanation:
Hello,
First of all, let s take x real number different from 5, as we cannot divide by 0
[tex]\dfrac{x+5}{x-5}\geq 0 \\ \\<=> (x+5\geq 0 \ and \ x-5> 0) \ or \ (x+5\leq 0 \ and \ x-5< 0) \\ \\<=> (x\geq -5 \ and \ x> 5) \ or \ (x\leq -5 \ and \ x< 5)\\ \\<=> x> 5 \ or \ x\leq -5[/tex]
So the solution is
[tex]\Large \boxed{\sf \bf ]-\infty;-5]\cup]5;+\infty[}[/tex]
Thanks
Answer:
(−∞,−5]∪(5,∞)
Please solve with explanation (10 points)
Answer:
Question (a)
[tex]x^2-a^2-bx-ab=0[/tex]
Write in standard form [tex]ax^2+bx+c=0[/tex]:
[tex]\implies x^2-bx-(a^2+ab)=0[/tex]
Therefore,
[tex]a=1[/tex][tex]b=-b[/tex][tex]c=-(a^2+ab)[/tex]Using quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies x=\dfrac{b\pm\sqrt{(-b)^2+4(1)(a^2+ab)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{b\pm\sqrt{b^2+4a^2+4ab} }{2}[/tex]
[tex]\implies x=\dfrac{b\pm\sqrt{(b+2a)^2} }{2}[/tex]
[tex]\implies x=\dfrac{b \pm (b+2a)} {2}[/tex]
[tex]\implies x=\dfrac{2b+2a} {2}=b+a[/tex]
[tex]\implies x=\dfrac{-2a} {2}=-a[/tex]
Question (b)
[tex]6x^2-15ax=2bx-5ab[/tex]
Write in standard form [tex]ax^2+bx+c=0[/tex]:
[tex]\implies 6x^2-15ax-2bx+5ab=0[/tex]
[tex]\implies 6x^2-(15a+2b)x+5ab=0[/tex]
Therefore,
[tex]a=6[/tex][tex]b=-(15a+2b)[/tex][tex]c=5ab[/tex]Using quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies x=\dfrac{(15a+2b)\pm\sqrt{(-15a-2b)^2-4(6)(5ab)} }{2(6)}[/tex]
[tex]\implies x=\dfrac{(15a+2b)\pm\sqrt{225a^2+60ab+4b^2-120ab} }{12}[/tex]
[tex]\implies x=\dfrac{(15a+2b)\pm\sqrt{225a^2-60ab+4b^2} }{12}[/tex]
[tex]\implies x=\dfrac{(15a+2b)\pm\sqrt{(15a-2b)^2} }{12}[/tex]
[tex]\implies x=\dfrac{(15a+2b) \pm (15a-2b) }{12}[/tex]
[tex]\implies x=\dfrac{30a }{12}=\dfrac52a[/tex]
[tex]\implies x=\dfrac{4b}{12}=\dfrac13b[/tex]
Question (c)
[tex]\dfrac{x^2}{x-1}=\dfrac{a^2}{2a-4}[/tex]
Cross multiply:
[tex]x^2(2a-4)=a^2(x-1)[/tex]
Write in standard form [tex]ax^2+bx+c=0[/tex]:
[tex](2a-4)x^2-a^2x+a^2=0[/tex]
Therefore,
[tex]a=(2a-4)[/tex][tex]b=-a^2[/tex][tex]c=a^2[/tex]Using quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies x=\dfrac{a^2\pm\sqrt{(-a^2)^2-4(2a-4)(a^2)} }{2(2a-4)}[/tex]
[tex]\implies x=\dfrac{a^2\pm\sqrt{a^4-8a^3+16a^2} }{4a-8}[/tex]
[tex]\implies x=\dfrac{a^2\pm\sqrt{a^2(a-4)^2} }{4a-8}[/tex]
[tex]\implies x=\dfrac{a^2\pm a(a-4)}{4a-8}[/tex]
[tex]\implies x=\dfrac{a^2\pm (a^2-4a)}{4a-8}[/tex]
[tex]\implies x=\dfrac{2a^2-4a}{4a-8}=\dfrac{2a(a-2)}{4(a-2)}=\dfrac12a \ \ \ (a\neq 2)[/tex]
[tex]\implies x=\dfrac{4a}{4a-8}=\dfrac{a}{a-2} \ \ \ \ (a\neq 2)[/tex]
Please help! Will award BRAINLIEST if you complete it correctly!
Jen was making cake pops for the bake sale. After 3 hours, she had completed half of the work. She called Maryna for help and together they finished everything in half an hour. How long would it take Maryna to finish the job alone if she replaced Jen after Jen baked for 3 hours?
Answer:
3 hours
Step-by-step explanation:
as jen took 3 hours maryana will take equal amount of time as jen
Well, we already know that it took Jen, 3 hours, by herself to complete half the work. Then, together they both completed it in half an hour. Now, you must summarize your given data.
3 hours = Half of the work for Jen
30 Minutes = Jen and Maryna Together To Finish
If the two girls were working at the same pace, it would take them an hour and a half. However, it only took them 30 minutes to complete that. Now, we realize that Maryna works 3x faster than Jen does.
The question is asking, how long would it take her to FINISH the job.
So that means, we must divide 3 by Jen's time.
3 / 3 = 1
So, that means that it would only take Maryna 1 hour to complete the rest of the job.
The Baltic Sea is almost completely surrounded by countries in Europe. The average depth of the Baltic Sea is 52 meters below the surface. The deepest point in the Baltic Sea is 407 meters lower than this.
What is the deepest point in the Baltic Sea relative to the surface?
Answer:
-459
Step-by-step explanation:
-52 - 407 = -552 + (-407) = -459
Which number is divisible by both 3 and 9?
OA) 21,369
OB) 27.621
OC) 27,629
OD) 36,663
Answer: A) 21,369
Step-by-step explanation: since 21,369 can be divided by 3 and = a whole number then it's divisible and also it's divided without a remainder / it's compatible so, 21,369/3= 7,123 which makes (A) your correct answer
Solve the equation. Check your solution using substitution.
{45.28 = 19.83 + z}
Group of answer choices
z=25.45
z=65.11
z=897.9
z=2.28
Answer:
z=25.45
because {45.28=19.83+25.45}
{45.28=45.28}
How many lateral faces does a triangular pyramid have?
one
two
three
four
Answer:
three
Step-by-step explanation:
The lateral faces are any faces besides the base.
In summary, we will count how many sides there are in a triangular pyramid, and subtract one for the base.
-> A triangular pyramid has four sides / faces
-> A triangular pyramid has three lateral faces
Answer: 3
Step-by-step explanation: i did the quiz
Help help math math math math
Answer:
(-2, -2)
Step-by-step explanation:
Firstly you can substitute the y= -6x -14 Directly into the other equation having one equation that looks like this 8x+3(-6x-14)= -22 then solve for X and substitute in the y equation you also get the y value
Answer:
(-2, -2)
Step-by-step explanation:
please help
every package of a certain caculator also includes 4 batteries. select all equations that represent the relationship between the number of packages and the number of batteries
a.) p = 4b
b.) b = 4p
c.) p=1/4b
d.)b= 1/4p
Answer:
c
Step-by-step explanation:
Find g'(x) given that g(x) = x^3 cos(πx)
Answer:
[tex]3x^2 cos (\pi x)-\pi x ^3sin(\pi x)[/tex]
Step-by-step explanation:
Product rule, noticing that the second function is composed.[tex]g'(x) = (3x^2)\cdot cos(\pi x) + (x^3) \cdot [-\pi sin(\pi x)] = 3x^2 cos (\pi x)-\pi x ^3sin(\pi x)[/tex]
Hello!
We can use the product rule to differentiate this function.
Let g(x) = f(x) · h(x).
Recall the following:
[tex]\frac{dy}{dx} f(x) * h(x) = f'(x)h(x) + h'(x)f(x)[/tex]
In this instance, let:
[tex]f(x) = x^3\\\\h(x) = cos(\pi x)[/tex]
Differentiate each.
f(x):
Use the product rule:
[tex]\frac{dy}{dx}x^n = nx^{n-1}\\\\f'(x) = 3x^{3-1} = 3x^2[/tex]
h(x):
Use the chain rule.
[tex]h'(x) = \pi (1) * -sin(\pi x) = -\pi sin(\pi x)[/tex]
Now, we can use the above product rule.
[tex]g'(x) = 3x^2 * cos(\pi x) + (-\pi sin(\pi x) * x^3)\\\\\boxed{g'(x) = 3x^2cos(\pi x) - \pi x^3 sin(\pi x)}[/tex]
The radii of two similar cones are 27:125. What is the ratio of their areas?
Answer:
729 : 15,625
Step-by-step explanation:
the ratio of their areas is 27² : 125² = 729 : 15,625
please help me asap
Answer:
The second option: Waxing crescent - first quarter; Waning gibbous - third quarter
Determine the value of x circles
A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?
Answer: t<40
8p+<184
Step-by-step explanation:
The inequalities representing the given condition will be [tex]t\leq40[/tex] and [tex]8p+t\leq184[/tex].
Given information:
A baker makes apple tarts and apple pies each day.
The baker receives a shipment of 184 apples every day.
A tart requires 1 apple and a pie requires 8 apples.
Let t be the number of tarts made each day and p be the number of pies made each day.
The baker makes no more than 40 tarts per day. So, the condition can be written as,
[tex]t\leq40[/tex]
And the condition for each day apple delivery can be written as,
[tex]8p+t\leq184[/tex]
Therefore, the inequalities representing the given condition will be [tex]t\leq40[/tex] and [tex]8p+t\leq184[/tex].
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$641.29 is what percent of $986,60?
I need this ASAP
Answer:
65%
Step-by-step explanation:
You start by dividing 641.29 by 986.60 (641.29/986.60). This gets you .65, which as a percentage is 65%
What is the equation in slope intercept form of a line that is perpendicular to y = 1/4x - 1 and passing through the point (4, 1)?
1. y = 4x + 17
2. y = 4x - 1
3. y = 4x + 17
4. y = 1/4x + 17
23 divided by 8 I need help
Answer:
2.875
Step-by-step explanation:
Answer:
2.875
Step-by-step explanation:
its not a whole number its a fraction or decimal but i gave u the decimal
g - 32 = 52
a) obtain a formula for g
b) Solve for g
Answer:
a) obtain a formula for g
=> g - 32 = 52
=> g = 52 + 32
b) Solve for g
=> 52 + 32
=> g = 84
Answer:
a) obtain a formula for g
Calculate the sum of first n natural numbers as sumtotal= n*(n+1)/2.
Create a variable sum to store the sum of array elements.
Traverse the array from start to end.
Update the value of sum as sum = sum + array[i]
Print the missing number as SumTotal – sum.
b) Solve for g
g = 84
Hope it helps!!!Brainliest pls!!!
What is the first step in solving In(x - 1) = In6 - Inx for x?
Answer:
x=3
Step-by-step explanation:
In(x-1) = In(6) - In(x)
In(x-1) + In(x) = In(6)
In((x-1)x) = In(6)
In(x^2-x) = In(6)
x^2-x=6
x^2-x-6=0
x^2+2x-3x-6=0
x(x+2)-3(x+2)=0
(x-3)(x+2)=0
x=3 because x=-2 need to be cancel out
Trevor folded a corner of a rectangular piece of paper to form a pentagon, as shown below. What is the area of the shaded pentagon? A. 84.5 square inches B. 75.5 square inches c. 39.5 square inches D. 35 square inches.
PLEASE HELP I WILL GIVE BRAINLIEST.
Answer:
B. 75.5 square inches
Step-by-step explanation:
Area (pentagon) = Area (rectangle) - Area (triangle)
= length x width - 1/2 x breadth x height
= 10 x 8 - 1/2 x 3 x 3
= 80 - 4.5
= 75.5 square inches
Solution :-
B. 75.5 square inches
Answer:
B) 75.5 in²
Step-by-step explanation:
Area of rectangle = width × length
⇒ area of rectangle = 8 × 10 = 80 in²
Area of triangle = 1/2 × base × height
⇒ area of triangle = 1/2 × 3 × 3 = 4.5 in²
Area of pentagon = area of rectangle - area of triangle
= 80 - 4.5
= 75.5 in²
Here is a prism. Its face is made from 6 identical squares
with side length 2 cm.
12 cm
2 cm
Diagram not drawn to scale
Work out the volume of the prism.
State the unit of your answer.
The volume of the prism that its faces is made from 6 identical squares is 48 cm³.
Volume of a square prismA square prism is a 3-dimensional cuboid where the base and top are equal squares.
v = a²hwhere
a = side length
h = height
Therefore,
a = 2 cm
h = 12 cm
Therefore,
v = a²h
v = 2² × 12
v = 4 × 12
v = 48 cm³
learn more on prism here: https://brainly.com/question/3533018
Answer:
288cm (cubed)
Step-by-step explanation:
4*2=8*12=96
6*2=12*12=144
2*2=4*12=48
144+96+48=288
Find the value of xx, yy, and zz in the parallelogram below.
Answer:
Step-by-step explanation:
Opposite sides of a parallelogram are congruent, so:
[tex]8x+3=19 \longrightarrow x=2[/tex]
[tex]27=-y-5 \longrightarrow y=-32[/tex]
Blue priced $25.00. How much would they cost if they were 60% off?
Answer:
10
Step-by-step explanation:
25 times .60 then take that answer and subtract it from 25 or half of 25 which it 12.5 then take off another 10%
Lotto Texas offers multi-million dollar jackpots with drawings every Wednesday and Saturday. Lach $1 ticket allows the player to pick 6
numbers from 54. To win the jackpot, all 6 numbers must match (in any order)
How many different lottery tickets could be sold?
How many ways are there to win the jackpot? I
How many ways are there to match 5 of 6 numbers?
How many ways are there to match 3 of 6 numbers?
How many ways are there to match 4 of 6 numbers?
The computation of the probability from the jackpots drawings of Lotto Texas shows that the number of different lottery tickets that could be sold is 25827165.
How to calculate the probability?The number of different lottery tickets that could be sold will be:
= 54C6
= 54! / (54-6)!6!
= 54! / 48!6!
= 25827165
The number of ways that are there to match 5 of 6 numbers will be:
= 6C5 × (54 - 6)C1
= 6 × 48
= 288
The number of ways that are there to match 3 of 6 numbers will be:
= 6C3 × (54 - 6)C3
= 20 × 17296
= 345920
The number of ways that are there to match 4 of 6 numbers will be:
= 6C4 × (54 - 6)C2
= 15 × 1128
= 16920
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What are the coordinates of your new IMAGE A’B’C’?
A’=____
B’=____
C’=____
Answer:
Sensor Calibration
Convert between coordinate systems of every sensor, image, vehicle and global coordinate axis system. So data from a sensor can be mapped globally.
Calibration of a camera helps to convert a pixel in an image to
Computer Vision
Step-by-step explanation:
Solve the following compound inequality: 4x + 8 15
Answer:
4x - 8 = 15
4x = 15 + 8
4x = 23 (divide both sides by 4 to get x)
4x/4 = 23/4
x = 5.75
Step-by-step explanation:
x = 5.75!!!!!
One year, the population of a city was 354,000. Several years later it was 414,180. Find the percent increase.
well, from 354000 to 414180, their difference is 414180 - 354000 = 60180.
if we take 354000 to be the 100%, what is 60180 off of it in percentage?
[tex]\begin{array}{ccll}amount&\%\\\cline{1-2}354000&100\\60180&x\end{array}\implies \cfrac{354000}{60180}=\cfrac{100}{x}\implies \cfrac{100}{17}=\cfrac{100}{x}\\\\\\100x=1700\implies x=\cfrac{1700}{100}\implies x=17[/tex]
The percent increase in the population is 17%.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the population of the city increased from 354000 to 414180.
The amount of increase is:
414180 - 354000
= 60180
The percent increase is given by:
(60180/354000) × 100%
= 17%
Hence, the percent increase in the population is 17%.
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PLEASE HELP PLEASE PLEASEEEE TY
Answer: 120
Step-by-step explanation: To find the volume of these two combined, we must use V = s*s*s. 4 * 10 * 2 = 80, and 2 * 5 * 4 = 40, and since we are combining this together for an added volume (since it is a tower), it is 120 inches cubed.
From a group of six people, two individuals are to be selected at random. How many selections are possible?
Answer:
15
Step-by-step explanation:
Find the value of x?
Answer:
x=25
All triangles must equal 180
95+35=130