Answer:
The quadratic formula: (-b+-sqrtb^2-4ac)/2a
Plugging in the values of a=1, b=9, and c=10, the roots of the equation are: -7.7 and -1.3.
So, the first option is correct.
Let me know if this helps!
Given the functions below, find f(x) + g(x)
f(x) = 3x - 1
g(x) = x2 + 4
Answer:
x^2+3x+3
Step-by-step explanation:
f(x) = 3x - 1
g(x) = x^2 + 4
f(x) + g(x) = 3x-1+ x^2 +4
Combine like terms
= x^2+3x+3
HELP ASAP
The graph of f(x)= |x| is chosen below. Write the equation for the stretched graph, g(x).
Answer:
y = |3x|
Step-by-step explanation:
PT= 3x+4 and TQ=5x-8
Answer:
So if PT=TQ and TQ=7x-9
PT=5x+3=TQ=7x-9
5x+3=7x-9
minus 5x both sides
3=2x-9
add 9 both sides
12=2x
divide 2
6=x
PT=5x+3
PT=5(6)+3
PT=30+3
PT=33
PT=QT=33
x=6
Hoped I helped you.sin^6x + cos^6x = 1/4
Answer:
[tex]\displaystyle x = \frac{\pi}{4} + k\, \pi[/tex] for integer [tex]k[/tex] (including negative numbers.)
Step-by-step explanation:
Pythagorean Identity: [tex]\sin^{2}(x) + \cos^{2}(x) = 1[/tex]. Equivalently, [tex]\cos^{2}(x) = 1 - \sin^{2}(x)[/tex].
Rewrite the original equation and apply this substitution to eliminate [tex]\cos(x)[/tex]:
[tex]\displaystyle \sin^{6}(x) + \cos^{6}(x) = \frac{1}{4}[/tex].
[tex]\displaystyle (\sin^{2}(x))^{3} + (\cos^{2}(x))^{3} = \frac{1}{4}[/tex].
[tex]\displaystyle (\sin^{2}(x))^{3} + (1 - \sin^{2}(x))^{3} = \frac{1}{4}[/tex].
Let [tex]y = \sin(x)[/tex] ([tex]-1 \le y \le 1[/tex].) The original equation is equivalent to the following equation about [tex]y[/tex]:
[tex]\displaystyle y^{6} + (1 - y^{2})^{3} = \frac{1}{4}[/tex].
Expand the cubic binomial in the equation:
[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, (y^{2})^{2} - (y^{2})^{3} = \frac{1}{4}[/tex].
[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, y^{4} - y^{6} = \frac{1}{4}[/tex].
Simplify to obtain:
[tex]\displaystyle 1 - 3\, y^{2} + 3\, y^{4} = \frac{1}{4}[/tex].
Rearrange and simplify:
[tex]12\, y^{4} - 12\, y^{2} + 3 = 0[/tex].
[tex]3\, (2\, y^{2} - 1)^{2} = 0[/tex].
[tex]2\, y^{2} - 1 = 0[/tex].
[tex]\displaystyle y^{2} - \frac{1}{2} = 0[/tex].
Solve for [tex]y[/tex]:
Either [tex]\displaystyle y = \frac{1}{\sqrt{2}}[/tex] or [tex]\displaystyle y = -\frac{1}{\sqrt{2}}[/tex].
If [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{\pi}{4} + 2\, k\,\pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].
On the other hand, if [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{3\, \pi}{4} + 2\, k\,\pi = \frac{\pi}{4} + (2\, k + 1) \, \pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].
Combine both situations to obtain:
[tex]\displaystyle x = \frac{\pi}{4} + 2\, k\, \pi[/tex] for all [tex]k \in \mathbb{Z}[/tex].
please help me with that
Answer:
[tex]\frac{16}{81}[/tex]
Step-by-step explanation:
[tex](\frac{27}{8} )^{-\frac{4}{3} }[/tex]
[tex]=((\frac{3}{2} )^3)^{-4/3}[/tex]
[tex]=(\frac{3}{2} )^{-4}[/tex]
[tex]=(\frac{2}{3} )^{4}[/tex]
[tex]=\frac{16}{81}[/tex]
Answer:
16/81
Step-by-step explanation:
a negative exponent means 1/...
the number in the numerator means "to the power of".
the number in the denominator means take the root of that power.
so, we have to take the third root of the expression, or this then to the power of 4, and finally build 1/... if the whole result.
and the sequence is not making a difference.
the third root of of 27/8 = 3/2
this to the power of 4 = 81/16
this 1/... = 16/81
Find a (Round to the nearest tenth). PLS HURRY!!
Answer:
a = 56.3°
Step-by-step explanation:
tan(a) = 9/6 = 1.5
atan(1.5) = 56.31°
Answer:
[tex]\boxed {\boxed {\sf 56.3 \textdegree}}[/tex]
Step-by-step explanation:
We are asked to find the measure of angle a.
This triangle is a right triangle because of the small triangle in the corner representing a 90 degree or right angle. Therefore, we can use trigonometric functions. The three main functions are:
sinθ=opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacentThe side measuring 6 is adjacent or next to angle a. The side measuring 9 is opposite angle a. Therefore, we will use the tangent function.
[tex]tan \theta= \frac{ opposite}{adjacent}[/tex]
[tex]tan \ a = \frac{ 9}{6}[/tex]
Since we are solving for an angle measure, we use the inverse trigonometric function.
[tex]tan ^{-1} * tan \ a = tan ^{-1} * \frac{9}6}[/tex]
[tex]a= tan ^{-1} * \frac{9}6}[/tex]
[tex]a= 56.30993247[/tex]
Round to the nearest tenth. The 0 in the hundredth place tells us to leave the 3 in the tenth place.
[tex]a \approx 56.3[/tex]
The measure of angle a is approximately 56.3 degrees.
what is the solution to the equation below? sqrt x-7 = 5
A. 144
B. 12
C. 2
D. 4
Answer:
I think the answer is B.12
If this not correct, Sorry.
find H.C.F OF 4x²y and xy²
Answer:
xy
Step-by-step explanation:
The HCF is known as the highest common factor. To find the HCF of two values, we have to take the greatest number that fits into all of their factors.
To start, we can list each value's factors.
For 4x²y, this can also be written as 4*x²*y = 4*x*x*y. In multiplication, we can take the factors of each value that is multiplied. Therefore, we can start with the factors of 4 and then go to the factors of x² and so on. Our factor list is thus 1,2,4,x,x²,y
Similarly, for xy² = x*y*y, our factors are x, y, and y²
The common factors for each of these are x and y. Assuming all values are positive and greater than 1, the x*y will be greater than either x or y. Therefore, the highest common factor would be x*y = xy
Determine which equations have the same solution set as 2/3 -x +1/6 = 6x by recognizing properties, rather than solving. Check all that apply.
Answer:
The answer is "0.1190".
Step-by-step explanation:
Given:
[tex]\to \frac{2}{3} -x +\frac{1}{6} = 6x\\\\\to \frac{2}{3} +\frac{1}{6} = 6x+x\\\\\to \frac{4+1}{6} = 7x\\\\\to \frac{5}{6} = 7x\\\\\to x=\frac{5}{6\times 7} \\\\\to x=\frac{5}{42}\\ \\\to x= 0.1190[/tex]
Answer:
A.) 4 - 6x + 1 = 36x
B.) 5/6 - x = 6x
F.) 5 = 42x
Step-by-step explanation:
edge.
Simplify the following without a calculator: (5)(6+4)
Answer:
your answer is 50 I hope it's helps you t
Answer:
50
Step-by-step explanation:
(5)(6+4)
5(6)+5(4)
30+20
50
THANK YOU
Hassan drove 78 miles in 1ị hours. If he drove at a constant rate, how far did he
travel in one hour? Enter your answer as a whole number, proper fraction, or mixed
number in simplest form.
Answer:
1 1/3 hours
Step-by-step explanation:
I took the same test
please helpp!!!!!!!!
Step-by-step explanation:
the answer is in picture
Someone please helppp
Answer:
k = 5/6
Step-by-step explanation:
First, we can make this have the form of a quadratic function, or ax²+bx+c=0. To do this, we can first subtract 10x from both sides to get
(2k+1)x²-8x=-6
Next, we can add 6 to both sides, resulting in
(2k+1)x²-8x+6 = 0
For a quadratic function of form ax²+bx+c=0, we can see that a=2k+1, b=-8, and c=6. We can then apply the quadratic equation, or
x= (-b ± √(b²-4ac))/(2a) to get our roots to be
x= (8 ± √(64-4(6)(2k+1)))/(2*(2k+1))
= (8 ± √(64-(48k+24)))/(4k+2)
= (8 ± √(40-48k))/(4k+2)
For the roots to be equal, we must have the two roots equal to each other. We can write this as
(8 + √(40-48k))/(4k+2) = (8 - √(40-48k))/(4k+2)
multiply both sides by (4k+2) to remove the denominator
8+√(40-48k) = 8 - √(40-48k)
subtract 8 from both sides to isolate the square roots
√(40-48k) = - √(40-48k)
The only number that is equal to its negative self (and is real) is 0. Therefore, √(40-48k) = - √(40-48k) = 0, so we have
√(40-48k) = 0
square both sides to remove the square root
40-48k = 0
add 48k to both sides to isolate the k and its coefficient
40 = 48k
divide both sides by 48 to isolate k
k = 40/48 = 5/6
A company determines that its weekly online sales, Upper S (t ), in hundreds of dollars, t weeks after online sales began can be estimated by the equation below. Find the average weekly sales for the first 3 weeks after online sales began. Upper S (t )equals2 e Superscript t
Answer:
$1272.36 ( average weekly sales for first 3 weeks )
Step-by-step explanation:
weekly online sales = S(t)
Determine average weekly sales for first 3 weeks
S(t) = 2e^t
total sales = ∫ S(t) dt
∴ Average weekly sales for first 3 weeks ( note : S(t) = 2e^t )
= [tex]\int\limits^3_0 {2e^t \, dt / ( 3 - 0 )[/tex]
= 2 [ e^t ] ³₀ / 3 = 2 ( e^3 - e^0 ) / 3 = 2 ( 6.3618 ) = 12.7236 hundreds
= $1272.36 ( average weekly sales for first 3 weeks )
Classify the polynomial 5x3 + 4x - 2 by degree.
Answer:
3
Step-by-step explanation:
3 would be the degree of the polynomial since it has the highest degree.
The equation y=2(x-1)^2-5y=2(x−1)
2
−5y, equals, 2, left parenthesis, x, minus, 1, right parenthesis, squared, minus, 5 is graphed in the xyxyx, y-plane. Which of the following statements about the graph is true?
Answer:
(b) It is symmetrical about [tex]x = 1[/tex]
Step-by-step explanation:
Given
[tex]y = 2(x - 1)^2 - 5[/tex]
See attachment for options
Required
True statement about the graph
First, we check the line of symmetric
[tex]y = 2(x - 1)^2 - 5[/tex]
Expand
[tex]y = 2(x^2 - 2x + 1) - 5[/tex]
Open bracket
[tex]y = 2x^2 - 4x + 2 - 5[/tex]
[tex]y = 2x^2 - 4x -3[/tex]
A quadratic equation [tex]y = ax^2 + bx + c[/tex] has the following line of symmetry
[tex]x = -\frac{b}{2a}[/tex]
By comparison, the equation becomes:
[tex]x = -\frac{-4}{2*2}[/tex]
[tex]x = \frac{4}{4}[/tex]
[tex]x = 1[/tex]
Hence, the line of symmetry is at: [tex]x = 1[/tex]
(b) is true.
Answer: It is symmetrical about x=1
Step-by-step explanation:
If the curved surface area of a cylinder with height 15cm is 1320cm², find total surface area
Answer:
2552cm^2
Step-by-step explanation:
C.S.A=1320cm^2 ;r=?
h=15cm.
[C.S.A. = 2πrh]
(r=1320×7/660=14cm)
Now,
TSA of cylinder = 2πr (h + r) sq
TSA=2×22/7(15+14)=2552cm^2
Find the coordinates of a point that divides the directed line segment PQ in the ratio
5:3.
A) (4,5)
B) (-6, 6)
C) (2, 2)
D) (4,1)
Answer:
C
Step-by-step explanation:
Let the coordinates be (m, n) then by using the section formula we have
m=(5*8+3*(-8))/(5+3)=2
n=(5*(-1)+3*(7))/(5+3)=2
The point is (2,2)
( 2 + 3 ) ^-1 x ( 2 ^-1 + 2^-1 )
Answer:
Step-by-step explanation:
[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boxed{ \boxed{\boldsymbol{Rule : a^{-1}=\frac{1}{a} }}} \\\\\\\\ (2+3)^{-1} \times (2^{-1}+2^{-1}) = \\\\1)\ (2+3)^{-1}=5^{-1}=\frac{1}{5} \\\\2)\ 2^{-1}+2^{-1}=\frac{1}{2} +\frac{1}{2} } =1 \\\\3)\ \frac{1}{5} \cdot 1=\boxed{\frac{1}{5} }[/tex]
Graph the relation shown in the table. Is the relation a function? Why or why not?
Answer:
what can i help u with
Step-by-step explanation:
No; the relation passes the vertical-line test. Yes; only one range value exists for each domain value
Yes; two domain values exist for range
yes; only one range value exists for each domain.
Find the Value of y. 70 60 65 40
Answer:
125
Step-by-step explanation:
360-70-60-65-40
= 125
Answered by GAUTHMATH
Express 12 000 iin standard form?
Answer:
the answer will be
1.2x10⁴
hope it helps
Answer:
We have been provided the number, 3430000. Therefore, the standard form is, 3430000=3.43×106, here, we have moved 6 places to the left. Hence, the standard form of 3430000 is 3.43×106. Note: It is important to note that the standard form of representing numbers is also called scientific form or standard index form.
Please help explanation if possible
Answer:
17.6
Step-by-step explanation:
Answer:
80 pennies ; 160 nickels
Step-by-step explanation:
Given the 2 equations
0.01p + 0.05n = 8.80 → (1)
n = 2p → (2)
Substitute n = 2p into (1)
0.01p + 0.05(2p) = 8.80
0.01p + 0.1p = 8.80
0.11p = 8.80 ( divide both sides by 0.11 )
p = 80
Substitute p = 80 into (2)
n = 2 × 80 = 160
There are 80 pennies ; 160 nickels
Let be the density function for the shelf life of a brand of banana which lasts up to weeks. Time, , is measured in weeks and . Incorrect answer icon Your answer is incorrect. Find the mean shelf life of a banana using . Round your answer to one decimal place. Mean
The question is incomplete. The complete question is :
Let [tex]p(t) = -0.0375t^2 + 0.225t[/tex] be the density function for the shelf life of a brand of banana which lasts up to 4 weeks. Time, t, is measured in weeks and [tex]$0 \leq t \leq 4$[/tex]. Incorrect answer icon Your answer is incorrect. Find the mean shelf life of a banana using . Round your answer to one decimal place.
Answer:
2.4
Step-by-step explanation:
Given :
[tex]p(t) = -0.0375t^2 + 0.225t[/tex]
Mean :
[tex]$=\int_0^4 tp (t) \ dt$[/tex]
[tex]$=\int_0^4 t (0.0375 t^2 + 0.225t) \ dt$[/tex]
[tex]$=-0.0375 \int_0^4 t^3 \ dt + 0.225 \int_0^4 t^2 \ dt$[/tex]
[tex]$=-0.0375 \left[ \frac{t^4}{4} \right]^4_0 + 0.225 \left[ \frac{t^3}{3} \right]^4_0$[/tex]
[tex]$=-0.0375 (64) + 0.225 \left( \frac{64}{3} \right)$[/tex]
[tex]$=-2.5 + 4.8$[/tex]
= 2.4
Therefore, the mean is 2.4
Simplify: 0.9(2b-1)-0.5b+1
Answer:
Step-by-step explanation:
0.9*2b = 1.8b
0.9*-1 = -0.9
So far we have 1.8b-0.9. It can't be simplified further.
Then, we add the 2nd part, -0.5b+1.
We have:
1.8b-0.9-0.5b+1. Next we combine like terms.
1.8b-0.5b = 1.3b.
-0.9+1 = 0.1
Then we put it together.
1.3b+0.1 is our answer.
Hope this helped! Have a nice day :D
Hi there!
»»————- ★ ————-««
I believe your answer is:
1.3b + 0.1
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Simplifying...}}\\\\0.9(2b-1)-0.5b+1\\--------------\\\rightarrow 1.8b - 0.9 - 0.5b + 1\\\\\rightarrow 1.8b - 0.5b - 0.9 + 1\\\\\rightarrow \boxed{1.3b +0.1}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Can someone help me on this
Answer:
The choose (C)
F(x)=x/ (x+1)(x-2)
The average of four different positive integers is 9. What is the greatest value for one of the integers?
Answer:
30Step-by-step explanation:
Sum of those 4 integers is:
4*9 = 36If the smallest ones are 1, 2 and 3, then the greatest possible integer is:
36 - (1 + 2 + 3) = 30Find the following ratios. PLEASE HELP QUICK!!
Answer:
sin(A) = 5/13 ≈ 0.38
cos(B) = 5/13 ≈ 0.38
tan(A) = 5/12 ≈ 0.42
Step-by-step explanation:
If you need more explanations just say it :)
Answer:
I hope your dreams come true! Beileve in your self! and do ur best <3
Find the approximate side length of a square game board with an area of 145 in 2 Plz help!
Answer:
Side length ≈ 12.04
Step-by-step explanation:
145 = x²
144 is the closest square, with the root 12
The square root of 145 is approximately 12.04
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
The approximate side length is 12.0 in
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
145 = s^2
Taking the square root of each side
sqrt(145) = sqrt(s^2)
12.04159458 = s
The approximate side length is 12.0 in
In the following diagram, ABCD is a parallelogram. Is AC the bisector of angle BAD? Show calculations and explain
Answer:
yes
Step-by-step explanation:
in parallelogram ,<A=<C
<C=<D
then <D=115=<C=115
X+115+30=180....TRIANGLE THEROME
X=35
so that,<A=65
<C=65