Given:
The expression is:
[tex]\dfrac{g^2+7g+12}{g^2-2g-24}[/tex]
To find:
The domain restrictions of the given expression.
Solution:
We have,
[tex]\dfrac{g^2+7g+12}{g^2-2g-24}[/tex]
To find the domain restrictions, we need to find the input values such that the denominator is equal to 0.
[tex]g^2-2g-24=0[/tex]
Splitting the middle term, we get
[tex]g^2-6g+4g-24=0[/tex]
[tex]g(g-6)+4(g-6)=0[/tex]
[tex](g-6)(g+4)=0[/tex]
Using zero product property, we get
[tex](g-6)=0[/tex] and [tex](g+4)=0[/tex]
[tex]g=6[/tex] and [tex]g=-4[/tex]
Therefore, the domain restrictions of the expression are -4 and 6. It means domain is set of all real numbers except -4 and 6.
Help what’s the answer!!!
Answer:
maybe the answer is
A.12-12HOPE IT HELPEDpls help!! due in 20 min. if u respond just to earn points im reporting <3.
6. The distance between Dallas and Austin on a map is 1.5 centimeters. The map
uses a scale in
which 2.5 centimeters represents 300 miles. What is the actual distance
between these two
cities in miles?
Answer:
182 miles
driving distance is 196
Which of the following is a true statement based on the graph shown?
A)P > Q
B)R ≥ Q
C)R > S
D)R < Q
Answer:
B
Step-by-step explanation:
The numbers on the right are major than the numbers on the left
I need help again... please and thank you very much you are helping
Answer:
$3.15
Step-by-step explanation:
Method 1:
4 oranges = 1.40
9 oranges = x
1.40 / 4 = 0.35
This is 0.35 per orange
0.35 x 9 = 3.15
$3.15
Method 2:
1.40/4 = x/9
12.6 = 4x (cross multiply 9 and 1.4 and cross multiply 4 and x)
x = 12.6 / 4
x = 3.15
$3.15
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Find the measure of x in each figure.
Answer:
x=130 degree
Step-by-step explanation:
because 50+x=180
=x=130
Find the solution set of this inequality. Enter your answer in interval notation using grouping symbols. -2x+5<3
Step-by-step explanation:
-2x+5<3
-2x>3-5
-2x>-2
Divide both sides by -2
x>1
Answer:
-2x+5<3
-2x<-2
x<1
Two runners are participating on a 720-metre circular track. They run in opposite directions, each at a constant speed. The first runner needs four minutes to complete the full loop and the second runner needs five minutes. How many metres does the second runner travel between two consecutive meetings of the two runners?
Happy Pride Month!
Answer:
320m
Step-by-step explanation:
let the two runners be A and B
with Va and Vb as their velocities
velocity=distance/time
Va=720/4*60
=3m/s
Vb=720/5*60
=2.4m/s
Let the 2 runners start from a common position X and meet at Y
so the 2 consecutive meetings happen at X and Y
so we have to find time of meeting at Y as we know that of X (which is t=0)
720=Va*t+Vb*t
t(5.4)=720
t=133.33 or t=720/5.4
therefore distance travelled by B =Vb*t
=2.4*720/5.4
=319.99m
=320m
Given a circle in the complex plane with a diameter that has endpoints at:
-12 − i and 18 + 15i
Find the center of the circle.
Answer:
the second part to the question is 17
Step-by-step explanation:
edge 2021 :)
have a lovely day!
There's a piece of a pyramid is a rectangle with a width of 4.6 cm and the length of the 9 cm. What is the height in centimeters of the pyramid if it's volume is 82.8 cm^3
Answer:
6cm
Step-by-step explanation:
Given data
Width= 4.6cm
Length= 9cm
Volume= 82.8cm^3
The expression for the volume is given as
V= lwh/3
82.8= 9*4.6*h/3
cross multiply
82.8*3= 9*4.6*h
248.4= 41.4h
h= 248.4/41.4
h= 6cm
How many times would the cricket mostly likely chirp per minute if the temperature outside were 76^{\circ} ∘ F?
Answer:
834 chirps
Step-by-step explanation:
Given the data:
Chirps in 1 min Temperature (°F)
781 74
1039 85.9
1156 87.2
1218 87.8
1131 91.4
888 75.5
Using technology, the regression model obtained will be in the form :
y = bx + c
b = slope ; c = intercept
y = temperature ; x = chirps per minute
The regression model is :
ŷ= 43.28 + 0.0390x
If outside temperature, y = 76 ; x will be ;
76 = 43.28 + 0.0390x
76 - 43.28 = 0.0390x
32.72 = 0.0390x
x = 32.72 / 0.0390
x = 838.97435
x = 834 chirps per minute
a man in a boat rowing from light house whose height is 200 meter.he takes 2minutes to change the angle of elevation top of light house from 60⁰ and 45⁰ find speed of boat
Answer:
The speed of the boat is approximately 0.704 m/s
Step-by-step explanation:
The time it takes the man in the boat to change the angle of elevation from 60° to 45°, t = 2 minutes = 120 seconds
The height of the light house = 200 m
Given that the angle of elevation is reducing, the direction of the man is away from the lighthouse
The initial distance of the man in the boat from the lighthouse = 200 m/(tan(60°)) = (200/√3) m
The final distance of the man in the boat from the lighthouse = 200 m/(tan(45°)) = 200 m
The distance traveled in 2 minutes, d = 200 m - (200/√3) m ≈ 84.53 m
The speed of the boat, v = d/t
∴ v = 84.53 m/(2 min × 60 s/min) ≈ 0.704 m/s
The speed of the boat, v ≈ 0.704 m/s.
There are 16 girls and 18 boys in a class. The teacher chooses a student's name at random to answer a question.
What is the probability that the teacher chooses a girl to answer the question?
ОА. и
O B. 1 /
8
17
OD
Answer:
8/17
Step-by-step explanation:
total students = 34
no of girls = 16
no of boys = 18
probability to choose a girl to answer the question = no of girls/total students
=16/34
=8/17
Which algebraic expression would NOT be equivalent if the number and the variable were reversed? A. N+8 B. M−5 C. K×8 D. 4+x
Answer:
B) M-5
Step-by-step explanation:
the commutative property does not apply to subtraction or division, only addition and multiplication
The profit from a business is described by the function P(x) = -x^2 + 10x - 4, where x is the number of items made, in thousands, and P(x) is the
profit in dollars. How many items will maximize the profit?
A 5,000
B. 10,000
C. 20,000
D. 50,000
Therefore, 5000 items can maximize the profit
The correct answer is an option (a)
What is Profit ?The money that you make when you sell something for more than it cost you.
For given example,
profit is described by the equation :
[tex]P (x) = -x^2 + 10x -4[/tex]
We need to maximize the profit P(x)
[tex]\Rightarrow \frac{d}{dx}P(x)=0\\\\\Rightarrow \frac{d}{dx}( -x^2 + 10x -4 ) =0\\\\\Rightarrow -2x+10=0\\\\\Rightarrow -2x=-10\\\\\Rightarrow x=5[/tex]
since , x is the number of items made in thousand
Therefore, 5000 items can maximize the profit
The correct answer is an option (a)
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Which number could not be a value of x?
Answer:
21
Step-by-step explanation:
The values for the third side of a triangle must be greater than the difference of the two other sides and less than the sum of the two other sides
12 -8 < x < 12+8
4 < x < 20
The third side cannot be 21
Answer:
21
Step-by-step explanation:
The sum of two sides of a triangle must be greater than the third side
How does the graph of y = 3^xcompare to the graph of y = 3^-x?
A. The graphs are the same.
B.The graphs are reflected across the x-axis.
C. The graphs are reflected across the y-axis.
Answer:
C
Step-by-step explanation:
The graphs are reflected across the y-axis.
I’m so lost guys lol send help
Answer:
(x−10)(x^2+10x+100)
Explanation:
I talked to my partner, you can call them "G00gle"
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
Firstly , You'll have to know the formula of a³ - b³ i.e a³ - b³ = ( a - b ) ( a² + ab + b² )What's the cube root of 1000 ? - It's 10 ! How ? [tex] \sqrt[3]{1000} = \sqrt[3]{ \underline{10} \times \underline{ 1 0} \times \underline{ 10} } = \boxed{10}[/tex][tex] \large{ \tt{❁ \: LET'S\: START}} : [/tex]
[tex] \large{ \bf{ ❀ \: \ {x}^{3 } - 1000}}[/tex]
- Write the number into the exponential form with the exponent 3 :
[tex] \large{ \bf{↦ {x}^{3} - {10}^{3} }}[/tex]
- Here , Suppose ' x ' as ' a ' & ' 10 ' as ' b '. Use the formula of a³ - b³ :
[tex]↦{ \large{ \bf{(x - 10)( {x}^{2} + x \times 10 + {10}^{2} }}})[/tex]
[tex]↦ \boxed{\large{ \bf{(x - 10)( {x}^{2} + 10x + 100) }}}[/tex]
Hence , Second option is the correct choice ! ☪ Educate Yourself. Make Yourself Smart. Grades And Knowledge Do Matter. Work On Your Subjects. Fill your brain. Move Ahead And Keep On Moving Ahead! ♪ツ Hope I helped! ۵
☼ Have a wonderful day / evening ! ☃
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3. Timmy is 3 feet 4 inches tall. There are 2 54 centimeters in 1 inch. What is Timmy's height in
centimeters?
a 30.48 cm
b. 101.6 cm
C 9.54 cm
d. 42.54 cm
WILL GIVE BRAINLIEST: What is the local minimum value of the function g(x)=x^4-5x^2+4? (Round answer to the nearest hundredth)
Answer:
Step-by-step explanation:
you can find where the first derivative is 0 to find the critical points
g'(x) = ( x^4 -5x^2 +4)' = 4x³-10x
g'(x) =0, make y =0 to find find where g'(x) is 0
4x³-10x =0 , factor 2x
2x(2x²-5)= 0 , each factor must be 0
2x= 0, so x= 0
2x²-5 =0, so x = ±√5/2
we now have 3 critical points -√5/2, 0, and √5/2
make intervals (-∞, -√5/2), (-√5/2, 0) , (0, √5/2) and (√5/2, +∞)
pick a point to test on each interval: -2, -1, 1 and 2 for example, and
calculate g'(x) = 4x³-10x at those points
for x= -2 we have 4(-2)³-10(-2) = -12 , negative number, decrease
for x= -1 we have 4(-1)³-10(-1) =6, positive number, increase
for x= 1 we have 4(1)³-10(1) = -6, negative number, decrease
for x= 2 we have 4(2)³-10(2) = 12, positive number, increase
we went from a decrease to an increase on intervals (-∞, -√5/2), (-√5/2, 0) so x= - √5/2 ≈ -1.58 is a minimum
we went from a decrease to an increase on intervals (0, √5/2), (√5/2, +∞) so
x= √5/2 ≈ 1.58 is a minimum as well
Find the sale price of an $70 item after a 50% discount.
Answer:
$35
Step-by-step explanation:
[tex]\frac{50}{30}*70=35[/tex]
Which statement correctly describes the translations used to graph the following exponential function?
h (2) = 32-2 +4
translate 2 units left and 4chgits up
translate 2 units left and 4 units down
translate 2 units right and 4 units up
translate 2 units right and 4 units down
1
2
3
Answer:
1.is the answer:)............
How many 3-coin combinations exist if we can choose from nickels, dimes, quarters, and half-dollars?
4!
4
12
20
There are 4 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars
The number of coin combinationThe coins to select from are nickels, dimes, quarters, and half-dollars.
So, we have:
Coins (n) = 4
The number of coin to select is:
Coin (r) = 3
The coin combination is then calculated using:
Combination = ⁴C₃
Apply the combination formula
Combination = 4
Hence, there are 4 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars
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SOMEONE HELP ME PLEASE!
Step-by-step explanation:
please see the attachment
The ratio of boys who play soccer, hockey and
rugby at a high school is 6:4:5 respectively.
If there are 72 boys playing hockey, how many
boys are there altogether at this high school?
Answer:
270
Step-by-step explanation:
72 ÷ 4 = 18
6 + 5 = 11
18 × 11 = 198
198 + 72 = 270
=) Asif deposits $650 into a bank paying a simple interest. He leaves the money there
for 5 years. At the end of the 5 years, the amount in the bank is $763.75.
Calculate the percentage rate of interest the bank paid per year.
Answer:
interest he got per year is 22.75
Step-by-step explanation:
deposited money = 650
after 5 years = 763.75
interest he got = 763.75 - 650
= 113.75
interest he got each year = 113.75 / 5
= 22.75
In Texas, the distance from Austin to Brownwood is 141 miles. It is 171 miles from Brownwood to Corsicana and 157 miles from Corsicana to Austin.
Determine the angle between the routes from Brownwood. Show your work
Answer: acute angles
Step-by-step explanation:
The angle between the routes from Brownwood is Acute angle.
What is Acute angle?Acute angle is an" angle that measures less than 90 degree".
According to the question,
Distance from Austin to Brownwood is 141 miles and distance from Brownwood to Corsicana to Austin 171miles and distance from Corsicana to Austin is 157 miles.
In order to find an angle between routes from Brownwood is Acute angle.
Hence, the angle between the routes from Brownwood is Acute angle.
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Which set of three angles could represent the interior angles of a triangle?
19 degrees, 70 degrees, 91 degrees
47 degrees, 12 degrees, 31 degrees
50 degrees, 20 degrees, 20 degrees
25 degrees, 25 degrees, 100 degrees
Answer:
19 degrees, 70 degrees, 91 degrees
Step-by-step explanation:
to make an interior angle of a triangle you need to make a 180-degree triangle and 19+70+91 make 180 degrees
Answer:
19, 70, 91
Step-by-step explanation:
19 + 70 + 91 = 180. Everything else doesn't add up to 180.
which inequality is represented by the graph
A. 7/10x-2y > or equal 5
B. 10/7x -2y< or equal 5
C. 7x+10y > or equal 5
D. 2x-7y> or equal 3
Answer:
i would be a be i solve 15 minutes
B
this is the question
Answer:
Step-by-step explanation:
The sum of the measures of the interior angles of a
convex quadrilateral is
a. 180°
b. 270°
c. 540°
d. 360°
Answer:
d. 360°
Hope this help!