Answer:
[tex]\large \boxed{\sf \ \ a = 2, \ b = -2, \ c = -3 \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]2x^2 - 8x + 5=2(x^2-4x)+5\\\\\text{*** We notice that *** }\\\\\text{*** } x^2-4x=(x-2)^2-2^2=(x-2)^2-4\\\\\text{*** So we can write ***}\\\\2x^2 - 8x + 5=2(x^2-4x)+5=2\left( (x-2)^2-4\right)+5\\\\=2\left(x-2\right)^2-8+5=\boxed{2\left(x-2\right)^2-3}[/tex]
So a = 2, b = -2, c = -3
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Show that: (sec theta - cosec theta) (1 + tan theta + cot theta) = sec theta tan theta - cosec theta cot theta)
Answer:
see derivation below
Step-by-step explanation:
Show that:
( sec(t) - cosec(t) ) ( 1 + tan(t) + cot(t) ) =
sec(t) tan(t) - cosec(t) cot(t)
Some trigonometric definitions used:
tan(t) = sin(t)/cos(t)
cot(t) = cos(t)/sin(t)
sec(t) = 1/cos(t)
csc(t) = 1/sin(t)
some trigonometric identities used:
sin^2(t) + cos^2(t) = 1 ......................(1)
rewrite left-hand side in terms of sine and cosine
(1/cos(t) - 1/sin(t) ) ( 1 + sin(t)/cos(t) + cos(t)/sin(t) )
Simplify using common denominator sin(t)cos(t)
= ( (sin(t) - cos(t))/(sin(t)*cos(t)) ) * ( ( sin(t)cos(t) + sin^2(t) + cos^2(t)) / ( sin(t)cos(t) ) )
= ( sin(t) -cos(t) ) * (1 + sin(t)cos(t) ) / ( sin^2(t) cos^2(t) ) ...... using (1)
Expand by multiplication
= ( sin(t) -cos(t) + sin^2(t)cos(t) - sin(t)cos^2(t) ) / ( sin^2(t) cos^2(t) )
Rearrange by factoring out sin(t) and cos(t) in numerator
= ( sin(t) (1-cos^2(t) - cos(t)(1-sin^2(t) ) / ( sin^2(t) cos^2(t) )
= ( sin^3(t) - cos^3(t) ) /( sin^2(t) cos^2(t) ) .........................using (1)
Cancel common factors
= sin(t)/(cos^2(t)) - cos(t)/(sin^2(t))
Rewrite using trigonometric definitions
= sec(t)tan(t) - csc(t)cot(t) as in Right-Hand Side
which binomial is the additive inverse of 5 + 2C
Answer:
-5-2c
Step-by-step explanation:
The additive inverse of a term must be the opposite of it.
●-(5+2c)
●-5-2c
Answer:
Step-by-step explanation:
The additive inverse is just the opposite of the binomial in terms of the signs. The additive inverse of 5 + 2C is -(5 + 2C) which is, without parenthesis, -5 - 2C.
In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all directions. Assuming that the area polluted is a circle and that its radius is increasing at a rate of 3ft/sec, determine how fast the area is increasing when the radius of the circle is 30 feet. Hint: consider that the radius r is a function, and we know the rate of change of r with respect to time.
Answer:
180π ft/secStep-by-step explanation:
Since the area pollute sis assumed to be a circle, we will be using the formula for calculating the area of a circle to solve the problem.
Area of a circle A = πr²
r is the radius of the circle
The rate at which the area is increasing is expressed as dA/dt. According to chain rule, dA/dt = dA/dr*dr/dt where;
dr/dt is the rate at which the area is increasing.
If dA/dr = 2πr (by mere differentiation)
dA/dt = 2πr * dr/dt
Given dr/dt = 3ft/sec and r = 30feet
dA/dt = 2π(30) * 3
dA/dt = 180π ft/sec
Hence, the area is increasing at the rate of 180π ft/sec
Find the interquartile range for a data set having the five-number summary: 7.8, 17.1, 23.6, 31.1, 36.9
Answer:
Interquartile Range: 21.549999999999997 = 21.55
Step-by-step explanation:
a
simplified form of -3 + 2(x - 1)?
8. Which expression
a. -X + 1
b. 2x-5
c. 2x - 4
d. -X-1
Answer:
2x -5
Step-by-step explanation:
-3 + 2(x - 1)
Distribute
-3 +2x -2
Combine like terms
2x -5
Answer:
5x -2
Step-by-step explanation:
which ones have no solution? a. -14x+23=14x-23 b. 14x+23=14x-23 c. -23x-14=14x-23 d. 14x-23=14x-23
Answer:
B and D
Step-by-step explanation:
B: 14x and 14x cancel out, so there would be no x left.
D: 14 x and 14x cancel out, as well as -23 and -23, therefore leading to no solution.
Hope this is helpful! :)
Answer:
The answer is B
Step-by-step explanation:
I got this answer on Khan Academy.
Hope this helps! :)
15 points are placed on a circle. How many triangles is it possible to form, such that their vertices will be the given points?
Answer: 445 triangles can be form with 15 dots of a circle (I hope good luck)
Step-by-step explanation:
Answer:
455
Step-by-step explanation:
There are 15 points on a circle.
We need three points to form a triangle
Therefore the number of triangles = 15 choose 3 = 15!/(3!x12!) = (15x14x13)/(3x2x1) = 5x7x13 = 455
Hence the number of triangles formed is 455
Joe and Danny have just won 350 arcade tickets. If each arcade game can be played with 12 tickets, how many will they have left over at the end of the day, if they play the maximum number of games?
Answer:
2 tickets left
Step-by-step explanation:
12✖️29=348
350-348=2
Answer:
If they play the maximum number of games, there will be two tickets left over.
Step-by-step explanation:
For this problem, I used long division.
350 divided by 12 comes out to be 29.
29 is the maximum number of games they could play.
29 times 12 is 348.
350 (the total number of tickets) minus 348 (number of tickets used) comes out to be two.
Hope this helps! Brainliest would really help me out :)
Someone can u help please! Thx
======================================================
Explanation:
The radius of the circle is r, which doubles to 2r to get the diameter. The diameter of the circle is also the diagonal of the square. Consequently, this means we have two right triangles in which they have the same hypotenuse of 2r.
Let x be the side length of the square. Use the pythagorean theorem to isolate x
a^2 + b^2 = c^2
x^2 + x^2 = (2r)^2
2x^2 = 4r^2
x^2 = 2r^2 ... divide both sides by 2
x = sqrt(2r^2) ... apply the square root to both sides; keep in mind that x > 0
x = sqrt(r^2*2)
x = sqrt(r^2)*sqrt(2)
x = r*sqrt(2)
The side length of the square is r*sqrt(2)
Therefore, the area of the square is
Area = (side)*(side)
Area = ( r*sqrt(2) )*( r*sqrt(2) )
Area = r*r * sqrt(2)*sqrt(2)
Area = r^2 * sqrt(2*2)
Area = r^2 * sqrt(4)
Area = r^2 * 2
Area = 2r^2
Find the vertex of the graph
Answer:
(-3, -11)
i needed to put more characters so here
Write a rule for the nth term of the arithmetic sequence. d =1/2 , a6 =18.
Answer:
[tex]a_{n}[/tex] = [tex]\frac{1}{2}[/tex] n + 15
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₆ = 18 and d = [tex]\frac{1}{2}[/tex] , then
a₁ + 5d = 18 , that is
a₁ + [tex]\frac{5}{2}[/tex] = 18 ( subtract [tex]\frac{5}{2}[/tex] from both sides )
a₁ = [tex]\frac{31}{2}[/tex]
Thus
[tex]a_{n}[/tex] = [tex]\frac{31}{2}[/tex] + [tex]\frac{1}{2}[/tex] (n - 1) = [tex]\frac{15}{2}[/tex] + [tex]\frac{1}{2}[/tex] n - [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] n + 15
the expression for the number of diagonals that we can make from one vertex of a n sided polygon is
Answer:
[tex]\frac{n(n-3)}{2}[/tex]
Step-by-step explanation:
Polygon Diagonals are a pattern that follows a specific rule which can be used through a specific formula. Remember that Math focuses on patterns to create equations that help to study them, and this case is not an exception.
The equation for polygon diagonals is
[tex]\frac{n(n-3)}{2}[/tex]
Where [tex]n[/tex] refers to the number of sides of the polygon.
You see, a diagonal is defined as the union between two non-consecutive vertices. For a convex n-sided polygon, there are going to be n vertices, and we can draw [tex]n-3[/tex] from each vertex, then we multiply this by [tex]n[/tex], because that's the total number of sides.
In the end, we divide by 2, because with the method described, we will have double number of diagonals.
This problem is kinda hard for me can you please help
Answer:
A
Step-by-step explanation:
If the post of the fence is 10 feet long. And we know that 3(1/3) of the fence is underground. We just need subtract 3(1/3) from 10.
10-3=7
7-(1/3)=6(2/3)
Use a calculator to find the measure of
Answer:
mRT = 4√13 ≈ 14.42
mST = 10√2 ≈ 14.14
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
Since we have right triangles, in order to find the missing side, we use Pythagorean Theorem:
mTR:
12² + 8² = c²
144 + 64 = c²
c² = 208
c = √208 = 4√13
mST:
15² = 5² + b²
225 - 25 = b²
b² = 200
b = √200 = 10√2
To get your decimals, simply evaluate the square roots:
4√13 = 14.4222
10√2 = 14.1421
Answer:
6. 56.3 degrees.
7. 70.5 degrees.
Step-by-step explanation:
6. We are given the opposite and adjacent side lengths, so we can use tangent to solve this (TOA = Tangent; Opposite over Adjacent).
tan(R) = 12 / 8
tan(R) = 3 / 2
R = cotan(3/2)
R = 56.309932474020213
So, the measure of angle R is about 56.3 degrees.
7. We are given the adjacent and the hypotenuse, so we can use cosine to solve this (CAH = Cosine; Adjacent over Hypotenuse).
cos(R) = 5 / 15
cos(R) = 1/3
R = sec(1/3)
R = 70.528779365509
So, the measure of angle R is about 70.5 degrees.
Hope this helps!
a fraction is such that the numerator is 2 less than the denominator if you add 3 to the numerator and 5 to the denominator the resulting fraction is 3/5 find the fraction
Answer:
The required fraction is 3/5
Answer: 3/5
Step-by-Step Explanation:
Let x represent the denominator of the fraction, then we have [tex]\dfrac{x-2}{x}[/tex]
Now add 3 to the numerator and 5 to the denominator and set it equal to 3/5:
[tex]\dfrac{(x-2)+3}{(x)+5}=\dfrac{3}{5}\\\\\\\text{Simplify:}\\\dfrac{x+1}{x+5}=\dfrac{3}{5}\\\\\\\text{Cross Multiply and solve for x:}\\5(x+1)=3(x+5)\\5x+5=3x+15\\2x=10\\x=5[/tex]
Substitute x = 5 into the original fraction:
[tex]\dfrac{(5)-2}{(5)}\quad =\large\boxed{\dfrac{3}{5}}[/tex]
The factor tree for 3,025 is shown. A factor tree starts with 3,025 at the top. 3,025 branches down to 5 on the left and 605 to the right. 605 branches down to 5 on the left and 121 on the right. 121 branches down to 11 on the left and 11 on the right. What is the simplest form of StartRoot 3,025 EndRoot?
Answer:
(5^2)(11^2)
Step-by-step explanation:
Taking all the factors in the left hand side of the factor tree, we have
5,5,11,11
5 twice
5^2=25
11 twice
11^2=121
The factor of 3,025=(5^2)(11^2)
Alternatively
3025÷5=605
605÷5=121
121÷11=11
11÷11=1
We have prime number 5 as divider twice and prime number 11 as a divider twice
Therefore,
5^2*11^2=3,025
Check
(5^2)(11^2)
=(25)(121)
=3,025
Answer:
c
Step-by-step explanation:
A cube has a side length of 5 cm. Determine the surface area of the largest pyramid that will fit inside the cube. Round if necessary.
Answer:
The surface area of the pyramid is 80.9 cm²
Step-by-step explanation:
The side length, s of the cube is given as 5 cm
Therefore, the largest pyramid that can fit into the cube will have a base side length, s = The side length of the cube = 5 cm
The height, h of the largest pyramid = The height of the cube = 5 cm.
The surface area of a pyramid = Area of base, A + 1/2 × Perimeter of base, P × Slant height, S
The slant height of the pyramid = √(h² + (s/2)²) = √(5² + (5/2)²) = (5/2)×√5
The perimeter of the base = 4×5 = 20 cm
The area of the base = 5×5 = 25 cm²
The surface area of a pyramid = 25 + 1/2×20×(5/2)×√5 = 80.9 cm².
The surface area of a pyramid = 80.9 cm².
very simple challenge hard question
Answer:
-58.41509433
Step-by-step explanation:
0.4+8(5-0.8*5/8)-5/(2.5)=34.4
[0.4+8(5-4/8)-(2)]=
[0.4+8(40-4)/8)-2=34.4 ( nominator)
15-(8.9-2.6/(2/3))*34*2/5 =-53
15-(8.9-3.9)*68/5
15-5*68/5=
15-68=-53 ( denominator)
(34.4/-53) *90
-58.41509433
At the end of any year a car is worth 5%
less than what it was worth at the beginning
of the year. If a car was worth $9 500 in
December 2016, then its value in January
2016 was
Answer:
Step-by-step explanation:
Multiply $9500 by .05 (5%) to get 475. That is 5% of $9500. Now subtract 475 from 9500 to get 9025. That is your answer!
The value of car in month of January is, [tex]\$ 9975[/tex]
Percentage :It is given that, At the end of any year a car is worth 5% less than what it was worth at the beginning of the year.
Since, car was worth $9 500 in December 2016.
Then, the value of car in month of January is, 105 % of value of car in moth of December.
So that, value of car in month of January is,
[tex]=9500*\frac{105}{100}\\ \\=9500*1.05=9975[/tex]
The value of car in month of January is, [tex]\$ 9975[/tex]
Learn more about percentage here:
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the baseball team equipment manager received a shipment of new baseballs. out of 200 balls 12.5% had defects. How many baseballs were without defects?
Answer:
175 balls
Step-by-step explanation:
If 12.5 percent of the balls had defects, then [tex]100-12.5=87.5[/tex]% of balls didn't have defects.
We can find 87.5 percent of 200 by converting 87.5 to a decimal.
87.5% as a decimal is 0.875.
Now we multiply this decimal by 200.
[tex]200\cdot0.875 = 175[/tex]
So, 175 balls didn't have defects.
Hope this helped!
PLEASE HELP!!!!!
A sphere has a circumference of its great circle equal to 20 Pi what is the volume of that sphere?
Answer:
Step-by-step explanation:
The formula for the volume of a sphere is
[tex]V=\frac{4}{3}\pi r^3[/tex] In order to use this formula we have to have a value for the radius and right now we don't. But we can find it indirectly by using the circumference formula. The circumference formula is
[tex]C=2\pi r[/tex] If the circumference is 20π, then we will fill that in for "C" and solve for r:
20π = 2πr and if you divide both sides by 2π, you'll get that r = 10. Now we have a radius.
Using that in the volume formula:
[tex]V=\frac{4}{3}\pi (10)^3[/tex] and then simplifying a bit:
[tex]V=\frac{4}{3}\pi (1000)[/tex] and
[tex]V=\frac{4000\pi}{3}[/tex] which divides to give you
[tex]V=1333.33\pi[/tex], third choice down.
Explain why a drop in temperature would lead to adding a negative integer.
Step-by-step explanation:
a drop in temperature means the temperature will decrease.
That decrease is represented with a negative integer which should be added to the previous temperature.
PLS SOLVE THIS QUESTION. The first one to get it right get's a brainliest.
Answer:
-3
Step-by-step explanation:
You have get a graphing calculator and press y=.
Then you would type in the equation.
Then click second, graph after you type the equation.
Then scan through the t graph for the value that causes the equation to be 0
Select the correct answer. An inverse variation includes the point (2,12). Which point would also belong in this inverse variation? A. (3,-8) B. (-8,-3) C. (1,6) D. (-6,1)
Answer:
d
Step-by-step explanation:
A baby bird jumps from a tree branch and flutters to the ground. The function "f" models the bird's height (in meters) above the ground as a function of time (in seconds) after jumping. What is bird's height above the ground when it jumped.
The answer to this question will depend on the function f itself. Basically you will find the height in meters above the ground of the bird when it jumped when the time t=0s. This is substsitute every t in the function for a value of zero and that way you will get the bird's height at the time it jumped. If you were given a graph for this function, you can find the y-intercept of the graph and that will be the answer as well. The question could be written like this:
A baby bird jumps from a tree branch and flutters to the ground. The function "[tex]f(t)-4.9t^{2}+25[/tex]" models the bird's height (in meters) above the ground as a function of time (in seconds) after jumping. What is bird's height above the ground when it jumped.
Answer:
25m
Step-by-step explanation:
Once your function is given, you can substitute t=0 since 0s is the time measured at the moment the bird jumped. So our function will be:
[tex]f(0)=-4.9(0)^2+25[/tex]
[tex]f(0)=25m[/tex]
So the height of the bird above the ground when it jumped is 25m in this particular function.
Answer:
It is (0,12) on the graph , if you are doing it on Khan Academy.
Step-by-step explanation:
Just try it . se what happens. :))
Tyler and Katie started a lemonade stand to raise money. They donated 2/10 of their profits to their school library, 1/10 to the animal shelter, and 2/5 to the food bank. They saved the rest to buy materials for their next project. What fraction of their profits did Tyler and Katie donate to others?
Answer:
They donated 7/10 of their profits. This cannot be simplified any further.
mark me BRAINLIEST
Tysmm!!
Answer:
Step-by-step explanation:
2/10 and 1/10 are easily addable fractions so all you have to do is add the numerator to get, 3/10. After that you need to convert 2/5 into tenths so that you can continue to add it correctly. If you multiply the numerator and the denominator of 2/5 to convert it, you will get 4/10 to add.
Answer: 7/10
ali needs to solve the equation x^2 + 6x + 22 = 0 by completing the square. which pair of steps is the most efficient way to begin?
a. x^2 + 6x + 9 = -22 + 9
b. x^2 + 6x + 36 = -22 + 36
c. x^2 + 6x + 3 = -22 + 3
d. x^2 + 6x + 81 = -22 + 81
Answer:
a. x² + 6x + 9 = -22 + 9
Step-by-step explanation:
they moved the 22 to the right by subtracting it. this leaves a binomial on the left side, which if what you want to solve it.
then they completed the square by dividing b (6) by 2 = 3. then squaring 3 to get 9.
if you added 9 to the left, then you have to add 9 to the right, therefore resulting in -22 + 9.
Answer:
In TTM/Imagine Math it is top left or a.
Step-by-step explanation:
I'm marking people brainliest. ------ One of the solutions to this inequality is _____ (-1,-2) (-1, 2) (0.5,2) (-2, -1)
Answer:
(-1, -2)
Step-by-step explanation:
Look up each point in the choices on the graph. If it is on the line or in the shaded area it is a solution.
Answer: (-1, -2)
Answer:
First & Last
Step-by-step explanation:
See what is in the red portion(Shaded or line), that is what can work to the inequality.
(-1, -2) -- In the red(works)
(-1, 2) -- Out of the red(Nope)
(0, 5.2) -- Out of the red(Nope)
(-2, -1) -- In the red(works)
To make a chocolate sponge cake for 8 people you need:
300g flour
100g cocoa
400g sugar
350g butter
1 egg
a) How much of each ingredient do you need to make a cake for 10 people?
b) if you only had 60g of cocoa,how much of each ingredient would you now need?
Answer:
this is som A sorry if you can't read it
Ten points! Solve for x: 1 < x + 3 < 4
4 > x > 7
4 < x < 7
−2 > x > 1
−2 < x < 1
Brainly, please don't remove the 4 in the equation, and the first and last answers like last time
brainly you did it again
actually, it's very easy all u have to do is minus 3 from every number (not x) and you'll easly get -2 < x < 1
If u see this pls give me brainliest
The solution of the provided inequality equation is −2 < x < 1. Option D is the correct option, which says x is greater than number -2 but less than 1.
What is the inequality equation?Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs.
The inequality equation, which has to be solved for x is,
[tex]1 < x + 3 < 4[/tex]
In this equation, subtract 3 in each side of the equation,
[tex]1 -3 < x + 3-3 < 4-3[/tex]
Solve it further,
[tex]1 -3 < x + 3-3 < 4-3\\-2 < x < 1[/tex]
Thus, the solution of the provided inequality equation is −2 < x < 1. Option D is the correct option, which says x is greater than number -2 but less than 1.
Learn more about the inequality equation here:
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