Which point is a solution to the system of inequalities?
StartLayout Enlarged left-brace first row y greater-than-or-equal-to one-half x squared + 4 second row y less-than StartRoot x + 2 EndRoot + 6 EndLayout
(–2, 6)
(1, 9)
(2, 8)
(0, 4)
Answers
D) (0,4)
Correct on Edge 2021
The correct option is 4. (0,4)
Given inequalities are [tex]y\geq \frac{1}{2} x^{2} +4[/tex] and [tex]y< \sqrt{x+2}+6[/tex] .
Taking first inequality,
[tex]y\geq \frac{1}{2} x^{2} +4[/tex]
Or, [tex]y=\frac{1}{2} x^{2} +4[/tex]
now checking which option satisfy the above equation.
Taking option 1.(–2, 6)
on putting x= - 2 and y=6, we get
[tex]6= \frac{1}{2} (-2)^2+4[/tex]
[tex]6=6[/tex]
Hence option 1 (–2, 6) satisfy the equation.
Similarly checking for option 2 and 3 we find that these options totally not follow inequality, so option 3 and option 2 must not be the solution of given inequality.
Now option 4 (0, 4).
Putting x=0 and y = 4, we get
[tex]4=0+4\\4=4[/tex]
Hence option 4 also satisfy the first inequality.
Now we have two option to choose our final answer option 1 and option 4.
since option 4 lies in the shaded region so option 4 will be correct option.
Hence the correct option is 4. (0,4)
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Related Questions
Solve the rational equation:
1 1 1
x-2x+3 5
O A. X=-6.09, x= 5.09
B. There is no solution.
O C. x=-3.09, x= 2.09
D. X=-3, x= 2
Answers
………………. ……………
The solutions for the equation 23 - x² - 2x = 0 are:
x = 4
x = -6
Option A is the correct answer.
We have,
To solve the rational equation:
1/(x - 1) - 1/(x + 3) - 1/5 = 0
We need to find the common denominator and combine the fractions on the left-hand side.
The common denominator is (x - 1)(x + 3)(5).
Multiplying each term by the common denominator:
[(x + 3)(5) - (x - 1)(5) - (x - 1)(x + 3)] / [(x - 1)(x + 3)(5)] = 0
Simplifying:
[5(x + 3) - 5(x - 1) - (x - 1)(x + 3)] / [(x - 1)(x + 3)(5)] = 0
[5x + 15 - 5x + 5 - (x² + 3x - x - 3)] / [(x - 1)(x + 3)(5)] = 0
[5x + 15 - 5x + 5 - x² - 3x + x + 3 ] / [(x - 1)(x + 3)(5)] = 0
Simplifying further:
[23 - x² - 2x ] / [(x - 1)(x + 3)(5)] = 0
Now, we set the numerator equal to zero since a fraction is zero if and only if its numerator is zero:
23 - x² - 2x = 0
To solve the quadratic equation 23 - x² - 2x = 0, we can rearrange it to the standard form:
x² + 2x - 23 = 0
Now, we can solve it using factoring, completing the square, or the quadratic formula. Let's solve it using the quadratic formula:
The quadratic formula states that for an equation in the form
ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a)
For our equation x² + 2x - 23 = 0, the coefficients are a = 1, b = 2, and
c = -23.
Substituting these values into the quadratic formula:
x = (-2 ± √(2² - 4(1)(-23))) / (2(1))
Simplifying:
x = (-2 ± √(4 + 92)) / 2
x = (-2 ± √96) / 2
x = (-2 ± 4√6) / 2
Simplifying further:
x = -1 ± 2√6
Therefore,
The solutions for the equation 23 - x² - 2x = 0 are:
x = -1 + 2√6 = 3.89 = 4
x = -1 - 2√6 = -5.89 = -6
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Joey opened a bank account 5 years ago with $100.
Today he has $1,000 in the account.
What is the percentage of increase?
_____%
Answers
2. A movie theater charges $15 for adults and children and $10 for seniors. A
total of $1,270 was collected for movie ticket sales one night for a selected
movie. The total number of tickets sold for that movie was 93. How many
adult and senior tickets were sold?
b. Write the equations:
Answers
Answer:
A. Adult=68, seniors=25B. 10a + 10s=1270. a + s=93
Step-by-step explanation:
15a + 10s =1270 equation 1
a + s =93 equation 2
a=93-s. Isolate a for equation 2
15(93-s) + 10s =1270 substitute value of a in equation 2 (93-s) with value of a in equation 1
1395-15s+10s=1270
-5s=-125
S=25
solve for a
a + s =93
a + 25=93
a=68
‘check answer
15a + 10s=1270
15(68) + 10(25)=1270
1020+ 250=1270
A company has 200 employees. There are 150 female employees. There are 40 employees who are under the age of 30. The probability
of randomly selecting an employee who is female or is under the age of 30 is 85%.
What is the probability of randomly selecting an employee who is female and under the age of 30?
O A 10%
O B. 20%
O c. 85%
OD. 95%
Answers
Answer:
c. 85 % is the probability
What is the correct answer I will mark brainlist
Answers
Answer:
3rd
Step-by-step explanation:
MARK AS BRAINLEST!!
1. Which point is a solution to this system of equations? 3х - у = 7 and 2x + 3y = 1
Answers
9514 1404 393
Answer:
(x, y) = (2, -1)
Step-by-step explanation:
A graphing calculator can find a solution quickly. (see attached)
__
The first equation can give an expression for y:
y = 3x -7
We can substitute this into the second equation:
2x +3(3x -7) = 1
11x -21 = 1 . . . . . . simplify
11x = 22 . . . . . . . add 21
x = 2 . . . . . . . divide by 2
y = 3(2) -7 = -1 . . . . using our equation for y
The solution is (x, y) = (2, -1).
Evaluate f(3m-4) given
Answers
3fm-4f
Answer= 3fm-4f
The expected value of a fair 6-sided die is 3.5.
Which of the following statements are true?
Choose all answers that apply:
А
3.5 is one of the possible outcomes of rolling a fair 6-sided die.
A fair 6-sided die is more likely to land on the number 4 than the number 6.
If you rolled a fair 6-sided die a large number of times, you should expect the average of the
numbers rolled to be about 3.5.
Answers
Answer: if you roll a fair 6 sided for a large number of times the average would be 3.5
Step-by-step explanation:
Khan
Find the distance between the points (-15, 3) and (-9, 8).
Answers
Answer:
61 units
Step-by-step explanation:
A transformation is applied to the graph of f (x) = 2x2 + 3x - 4 to create a new graph for g(x) = 2x2 + 3x + 7.
Which statement describes the transformation?
OA. The graph will shift up 7 units.
OB. The graph will shift up ll units.
O C. The graph will shift down 7 units.
OD. The graph will shift down 11 units.
Answers
Answer:
b
Step-by-step explanation:
Find the value of x, if angle X measures 102°.
х
to
w7x+4yº(5x - 4yº
w
Z
Answers
Answer:
A. 13
Step-by-step explanation:
The non-vertex angles of a kite are always congruent. Therefore,
m<X = m<Z = 102°
Sum of all angels of a kite = 360°
Thus:
m<X + m<Y + m<Z + m<W = 360°
Substitute
102 + (5x - 4) + 102 + (7x + 4) = 360
102 + 5x - 4 + 102 + 7x + 4 = 360
Add like terms
204 + 12x = 360
12x = 360 - 204
12x = 156
x = 156/12
x = 13
ILL GIVE BRAINLIEST
YOUR FRIEND JUST OPENED THEIR FIRST CREDIT CARD WHAT ADVICE WOULD YOU GIVE THEM BEFORE THEY START MAKING PURCHASES?
Answers
Answer:
I would tell them to buy a ps5 for me
Step-by-step explanation:
For a credit card be careful with what you buy, save it for the important stuff. Also make sure to constantly check your credit score and to check your purchases to make sure that only what you purchased is on there.
Which BEST describes the system of equations graphed on a coordinate plane?
A) Consistent
B) Inconsistent
C) Consistent and Dependent
D) Consistent and Independent
Answers
Answer:
D) Consistent and Independent
Answer:
D.consistent and independent
. Find the volume of a sphere with a radius of 23 feet. Round your answer to 2 decimal places. [Use pi = 3.14] *
Answers
Answer:
50.965.01
Step-by-step explanation:
Mark borrowed $5,500 at 11.5 percent for five years.
How much did Mark pay in interest?
$1,150
$1,520
$1,757
$2,300
Answers
Answer:
$ 1 , 150
Step-by-step explanation:
Find the values of x and y in the special right triangle below.
Answers
Answer:
x=6 y=12
Step-by-step explanation:
30-60-90 triangle
shorter leg is x
longer leg is [tex]x\sqrt{3}[/tex]
hypotenuse is 2x
since the longer leg is [tex]6\sqrt{3}[/tex] than makes x=6
and y=2(6)=12
Lauren is making string bracelets with black and silver beads added in for decoration.
Black beads come in packages of 24, and silver beads come in packages of 36.
Each bracelet will have the same number of each color bead.
Lauren has one package of each bead color, and she will use all of the beads.
What is the greatest number of bracelets Lauren can make?
Answers
The greatest number of bracelets Lauren can make using the black beads and the silver beads is 12.
What is the greatest number of bracelets that can be made?In order to determine the greatest number of bracelets that can be made, the highest common factor of both numbers have to be determined.
Highest common factor is the highest factor that is common to two or more numbers
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24Factors of 36 = 1, 2, 3, 4, 6, 12, 18, 36 Highest common factor = 12To learn more about highest common factor, please check: https://brainly.com/question/26073850
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Henry is fishing from a small boat. His fishing hook is in the water 8 meters directly below his boat. A fish is swimming at the same depth as the hook, however it is 15 meters away from the hook. What is the shortest distance between Henry and the fish?
Answers
Answer: 17
Step-by-step explanation:
what is 15t—7=28 + 8t
Answers
7t=35
t=35/7
So t=5
If the radius of a cylinder is 3 centimeters, then the area of one of the circular bases is 18.84 square centimeters. True False
Answers
Answer:
false
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
To calculate the area of a circle you need to multiply the radius by itself, then multiply that number by [tex]\pi[/tex].
In this case, our radius is 3, so we multiply 3 × 3 × [tex]\pi[/tex] (which can be estimated as 3.14)
3×3 is 9
9×3.14 is 28.26
28.26≠18.84
So, the correct answer is false. Hope this helps ^.^
Find the mean. Round to the nearest tenth. 19, 13, 14, 18, 9, 2, 14.
Mean:
Answers
Answer:
12.7
Step-by-step explanation:
19 + 13 + 14 + 18 + 9 + 2 + 14 = 89
89 / 7 = 12.7142857143
12.7
Instructions: Find the missing side lengths. Leave your answers
radicals in simplest form.
Please help, no links
Answers
Answer:
Im pretty sure the first one is [tex]4\sqrt{3}[/tex]
and the second is 4
Express in words 18.01
Answers
Answer:
Eighteen point zero one
Step-by-step explanation:
Eighteen point zero one
3. Triangle JKL is the preimage. Write two algebraic
representations, one for the dilation to triangle I'K'L' and
one for the dilation to triangle J"K"L".
K
K
-241
J"
TL
HOMM Harcourt
Answers
What are some basic steps that you can take to protect yourself from identity theft or fraud?
Answers
1. Use sharpie to cover up private information before throwing it away (because people can look through your trash for your info). For example: credit card information, your address, etc.
2. Secure your mail box. Get a lock to make sure that people won't steal your credit card information.
3. Never ever leave your receipts behind.
4. Don't lose your credit card!! People can steal it can spend your money!
5. Just don't give random people or friends your credit card information...
Well, I hope this helped! Be careful and stay safe!
Select the correct answer. Consider functions fandg f(3) = 5.2.1, for 3 + 2 and = + -6 4:2 – 16: + 16 96) = 4+ 48, for : * -12 Which expression is equal to 10) (+? OA . OB. 1 Ос. OD. 5+2 6
Answers
Answer:
A
Step-by-step explanation:
Agree or Disagree? plz help no link plz
Answers
Answer:
Agree
Step-by-step explanation:
What is the missing length?
8 mi
Area of shaded region = 33.2 mi?
W =
miles
Answers
Hey does anyone please can help me with this
Answers
Answer:
Step-by-step explanation:
Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components, 35% contain one defective component, and 15% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions?
a. Neither tested component is defective.
b. One of the two tested components is defective
Answers
Answer:
a) P (0 defective component) = 0.5
P( 1 defective component ) = 0.35
P( 2 defective component ) = 0.15
b) P( 0 ) = 0
p ( 1 ) = 1
p ( 2 ) = 0.33
Step-by-step explanation:
p( no defective ) = 0.5
p( 1 is defective ) = 0.35
p( 2 is defective ) = 0.15
Given that 2 components are selected at random
a) Given that neither component is defective
Probability of 0 defective component = 0.5
P( 1 defective component ) = 0.35
P( 2 defective component ) = 0.15
b) Given that one of the two tested component is defective
P( 0 defective ) = 0
P( 1 defective ) = P ( [tex]\frac{x=1}{x\geq 1}[/tex] ) = p( x = 1 ) / 1 - P ( x = 0 )
= ( 0.5 )^1 ( 0.5 )^0 / 1 - ( 0.5)^0 (0.5)^1
= 0.5 * 1 / 1 - 0.5 = 0.5 / 0.5 = 1
p ( 2 defective ) = p( x = 3 ) / 1 - P ( x = 0 )
= ( 0.5 )^2 ( 0.5 )^0 / 1 - ( 0.5)^0 (0.5)^2
= 0.25 / 0.75 = 0.33