Answer:
yes, but there is a better way
Step-by-step explanation:
instead of multiplying x+3 on both sides, I would instead subtract 2 on both sides. If you do this, it would be easier to write this equation in standard form and find the intervals.
In summary, to solve the inequality (x - 2)/(x + 3) ≥ 2, we can multiply both sides of the inequality by x + 3 only when x > -3 to preserve the direction of the inequality.
To solve the inequality (x - 2)/(x + 3) ≥ 2, we need to consider the impact of multiplying both sides of the inequality by x + 3.
When multiplying both sides of an inequality by a positive number, the direction of the inequality remains the same. However, if we multiply both sides by a negative number, the direction of the inequality is reversed.
In this case, the expression x + 3 is in the denominator of the left side of the inequality. If we multiply both sides of the inequality by x + 3, we need to consider two scenarios:
If x + 3 is positive: In this case, we can multiply both sides of the inequality by x + 3 without changing the direction of the inequality.
If x + 3 is negative: Multiplying both sides of the inequality by x + 3 would require flipping the direction of the inequality.
Therefore, we need to ensure that x + 3 is positive before multiplying both sides by x + 3 to preserve the direction of the inequality.
To determine when x + 3 is positive, we set the denominator equal to zero and solve for x:
x + 3 = 0
x = -3
So, if x > -3, then x + 3 is positive.
In summary, to solve the inequality (x - 2)/(x + 3) ≥ 2, we can multiply both sides of the inequality by x + 3 only when x > -3 to preserve the direction of the inequality.
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plz plz help plz plz
Answer:
1
Step-by-step explanation:
when dividing numbers with exponents with the same base, subtract the exponents.
[tex]\frac{8^{7} }{8^{7} }[/tex]
7 - 7 = 0
[tex]\frac{8^{7} }{8^{7} }[/tex] = [tex]8^{0}[/tex]
anything to the power of 0 is 1
[tex]8^{0}[/tex]= 1
Answer:
1
Step-by-step explanation:
Any number divided by itself equals 1 with the exception of 0 since 0/0 is undefined.
8^7 is not equal to zero, so without doing any calculations or using any other rules, we know that
8^7/8^7 = 1
We can use the rule of exponents for dividing powers.
Rule:
[tex] \dfrac{a^m}{a^n} = a^{m - n} [/tex]
Here we have a = 8, m = 7, and n = 7.
Applying the rule, we get
[tex] \dfrac{8^7}{a^7} = 8^{7 - 7} = 8^0 [/tex]
Another rule of exponents:
[tex] a^0 = 1 [/tex]
We the zero power rule now:
[tex] 8^0 = 1 [/tex]
Therefore,
[tex] \dfrac{8^7}{a^7} = 1 [/tex]
Answer: 1
A car travelling at a constant speed travels 90km in 50 min .How far travelling at the same constant speed will the car travel in 2 hours and 25 minutes?
Answer:
261 km
Step-by-step explanation:
given,s=constant
d1/T1=d2/T2
d1=90km,t1=50 min
d2=? ,t2=(120+25)min
=145min
therefore,d2=(90×145)/50
=261 km
Find a solution to the equation 4(x + 7) = 38
Answer:
4(x+7)=38
4x+28=38
4x=38-28
4x=10
(divide by 4)
x=2whole number 2/4
=2whole number 1/2
or x=2.5
What is the constant term in the expression 6׳y + 5× + 4
PLEASE HELP ME OUT I begging you guys p.s. if u give me the correct answer I'll give u brainillesst points
Answer:
the constant is x
Answer:
its 4
Step-by-step explanation:
Write an equation in Standard form for a line that goes through the points
(-2,-6) and (3, 4).
A 10 METER PIECE OF WIRE IS CUT IN TO TWO PIECES ONE PIECE IS 2 METERS LONGER THAN THE OTHER HOW LONG ARE THE PIECES
one piece is 2m
one is 8m
Write the fraction as a decimal.
Round to the nearest hundredth.
7/18~ [?]
Answer:
0.39
Step-by-step explanation:
7/18= 3.888888888
round up
0.39
what is the value of this example?
[tex] \frac{1}{6} | \div 12[/tex]
Answer: I will give you the answer in fraction form and in decimal form. Here is 1/6 divided by 12... Answer: 1/72
Step-by-step explanation:
Jessica has 1,386 books. She must pack them into boxes to ship to a bookstore. Each box holds 10 books. How many boxes will she need to pack all of the books?
algebraically find the x-coordinates where the line y=2x+3 intersects the circle (x-3)^2 + (y+6)= 50
** please help its due soon **
Answer:
x = {-4, -2}Step-by-step explanation:
To find the intersection we need to solve the system:
y = 2x + 3(x - 3)² + (y + 6)² = 50Solve by substitution, replace y with 2x + 3 in the second equation:
(x - 3)² + (2x + 3 + 6)² = 50x² - 6x + 9 + 4x² + 36x + 81 - 50 = 05x² + 30x + 40 = 0x² + 6x + 8 = 0x² + 6x + 9 = 1(x + 3)² = 1x + 3 = ± 1x = -4, x = -2David has 48 baseball cards. Toby has 25% more cards than David. How many cards does Toby have?
Answer:
he has 60
Step-by-step explanation:
25% of 48 is 12, he has 12 more cards then david
Find the value of x.
Answer:
6
Step-by-step explanation:
Because they are the same
An adult ticket costs twice as much as a child's ticket. You purchased 5 child tickets and 2 adult tickets and paid $36. Find the price of an adult ticket. Find the price of a child's ticket.
Answer:
adult ticket =$8 child ticket = $4
Step-by-step explanation:
2x =y
2y + 5x =36
4y + X=36
y =8 so X=4
A. f(x) =1/2 (4,000)^x
B. f(x) = 4,000(2)^x
C. f(x) = 2,000 (1/2)^x
D. f(x) = 4,000 (1/2)^x
Gregs parents tell him if he works more than 60 hours in May, they will buy him a new lawn mower. In the month of May, Greg earns $1,387-50. Are Greg's parents going to buy Greg a new lawn mower?How many hours did he work?Expain using math terms and words.
Answer:
how much money did he make an hour ?? you cant calculate hours if you dont know his rate
Step-by-step explanation:
total made / hourly rate = hours worked and then you can determine if he gets a lawn mower
If the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y-intercept of the regression line to three decimal places. y 2 21 3 69 4 261 5 1029 6 4101
Answer:
log y = 0.576x + 0.139Step-by-step explanation:
Given data:
x | 2 | 3 | 4 | 5 | 6 y | 21 | 69 | 261 | 1029 | 4101Logarithms of y-values:
log 21 = 1.322log 69 = 1.839log 261 = 2.417log 1029 = 3.012log 4101 = 3.613The ordered pairs:
(2, 1.322), (3, 1.839), (4, 2.417), (5,3.012), (6, 3.613)Using an online calculator found the equation of the regression line:
y = 0.576x + 0.139In our case it is:
log y = 0.576x + 0.139Jessica picks tomatoes in her garden. She fills several bags. This line plot shows the weight of each bag.
How many more pounds does one of the heaviest bags weigh than one of the lightest bags?
Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:
1 1/4 is the answer
Step-by-step explanation:
If f (x) = x-5 and g(x) = 4x what is the value off [g(4)]?
Step-by-step explanation:
f[g(4)]
g(x) = 4x
g(4) = 4(4)
= 16
f(x) = x-5
f[g(4)] = f(16) = 16 - 5 = 11
So, f[g(4)] = 11
Which of these is a function please answer.
Answer:
1 and 3
Step-by-step explanation:
Answer:
Options 1 and 4Step-by-step explanation:
Option 1
x-values are different and y-values are sameThis is a functionOption 2
x-values are repeated (3) with different y-valuesThis is not a functionOption 3
x-values are repeated and y-values are differentThis is not a functionOption 4
x- values are different, y-values are differentThis is a functionReflect across the y-axis. Fill in the new coordinates below:
Answer:
A(-1,2)
B(-4,4)
C(-3,1)
Step-by-step explanation:
simply reflect across the y-axis. pls give brainliest
try to zoom in the picture if you can’t see the numbers , but can someone please help me with this ?
Step-by-step explanation:
This is my answer, if you need it
Circle the volume, in cm^3, of a cylinder with radius 5 cm and height 8 cm
[1 mark]
A)40π
B)80π
C)200π
D)1600π
Answer:
C
Step-by-step explanation:
Volume of a cylinder is πr²h
V = π * 5² * 8
V = π * 25 * 8
V = π * 200
V = 200π
. Find f(3) for the following function
[tex]f(x)=3(2)^x+6[/tex]
a.f(3) = 222
b.f(3) = 9
c.f(3) = 24
d.f(3) = 30
Answer:
[tex]\boxed {\boxed {\sf D. \ f(3)= 30}}[/tex]
Step-by-step explanation:
We are given the function:
[tex]f(x)= 3(2)^x+6[/tex]
We want to find f(3), so we must substitute 3 in for x.
[tex]f(3)= 3(2)^3+6[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
Solve the exponent first.
2³= 2*2*2= 4*2= 8[tex]f(3)= 3(8)+6[/tex]
Multiply 8 and 3.
[tex]f(3)= 24+6[/tex]
Add.
[tex]f(3)=30[/tex]
For the function given, f(3) is 30.
I need help with this question
Answer:
Part A
D
Part B
76
Step-by-step explanation:
I don't know how to explain it
factorise p² + pq - p³ - q² completely
Answer:
The expression is not factorable with rational numbers.
p ^2 + p q − p ^3 − q ^2
Step-by-step explanation:
4s - 3
9r - 17
3r + 13
7s
Solve for s
Step-by-step explanation:
step 1. the diagram is very unclear and should be redone
step 2. I'll assume 9r - 17 and 3r + 13 are vertical angles and are equal
step 3. 9r - 17 = 3r + 13
step 4. 6r = 30 or r = 5
step 5. I'll assume 4s - 3 and 7s - 24 are alternate interior angles and are equal
step 6. 4s - 3 = 7s - 24
step 7. 3s = 21 or s = 7.
Last summer, Marrero was at Newgrange, a stone mound in Ireland that has a diameter of 250 feet. He found a walkway 62 feet long that leads to the center of the mound. Help Marrero find perpendicular distance x from the end of the walkway to either side of the mound.
Answer:
108 ftStep-by-step explanation:
The line connecting the center with the end of the walkway is radius and is the hypotenuse of the right triangle.
Horizontal leg is the distance x.
Vertical leg has the length:
(250)/2 - 62 = 63 ftUsing Pythagorean theorem to find the length of x:
x² = (250/2)² - 63²x² = 125² - 63²x² = 11656x = √11656x = 107.96 ≈ 108find the inverse of y=100-x^2
Answer:
The inverse is ±sqrt(100-x)
Step-by-step explanation:
To find the inverse, exchange x and y
x = 100 -y^2
Solve for y
Subtract 100 from each side
x - 100 = -y^2
Divide by -1
-x +100 = y^2
Take the square root of each side
±sqrt(100-x) = sqrt(y^2)
±sqrt(100-x) =y
The inverse is ±sqrt(100-x)
an element with mass 630 grams decays by 18.8% per minute. How much of the element is remaining after 7 minutes, to the nearest 10th of a gram?
Answer:
Step-by-step explanation:
Total Depreciation: 60.24%
Total depreciation: $9,759.50
Car Value after 6 years: $6,440.50
The element is remaining 146.6 grams after 7 minutes, to the nearest 10th of a gram.
What is exponential decay?An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.
The exponential decay function:
Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.
Given:
An element with mass 630 grams decays by 18.8% per minute.
That means, 18.8% = 0.188
Here, we will use the exponential decay function.
Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.
Here,
A₀ = 630 grams
r = 0.188
x = 7 minutes
Substituting the values to the formula,
A₇ = 630(1-0.188)⁷
A₇ = 630(0.812)⁷
A₇ = 630(0.23275134787)
A₇ = 146.633
A₇ = 146.6 grams.
Therefore, element is remaining 146.6 grams.
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Garth is building a square shaped frame for a mirror. The area of the mirror is 144 square inches. How long is each side of the frame, in inches?
Answer: 12 inches
Step-by-step explanation:
This is a square shaped mirror which means that it takes the shape of a square.
All sides on a square are equal and because the way the find the area of a square is to multiple the Length by the Width, you would be squaring the same number to find the area.
Length of each side = √area
= √144
= 12 inches