The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y ≤ x^2 – 3
y > –x^2 + 2
The shaded region is the solution of the given functions f(x) = x² – 3 and g(x) = –x² + 2.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The functions f(x) = x² – 3 and g(x) = –x² + 2 are shown on the graph.
Now for the point (0, 0). Then we have
0 ≤ 0² – 3
0 ≤ – 3
which is false
Then the region is opposite to the origin.
Similarly, we have
0 > 0² + 2
0 > 2
which is false
Then the region is opposite to the origin.
Thus, the shaded region is the solution of the given functions f(x) = x² – 3 and g(x) = –x² + 2.
The graph is shown below.
More about the function link is given below.
https://brainly.com/question/5245372
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Two bags, A and B, each contain only green marbles and red marbles.
There are 6 green marbles and 4 red marbles in bag A.
There are 8 green marbles and 2 red marbles in bag B.
One marble is going to be taken at random from bag A and placed in bag B.
A marble is then going to be taken at random from bag B.
Work out the probability that this marble will be a green marble.
Using it's concept, it is found that there is a 0.7818 = 78.18% probability that this marble will be a green marble.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
There are two ways to end up with a green marble selected.
Green in bag A(6/10 probability) and in bag B(9/11 probability).Red in bag A(4/10 probability) and green in bag B(8/11 probability).Hence, the probability that this marble will be a green marble is given by:
[tex]p = \frac{6}{10} \times \frac{9}{11} + \frac{4}{10} \times \frac{8}{11} = \frac{54 + 32}{110} = 0.7818 = 78.18\%[/tex]
More can be learned about probabilities at https://brainly.com/question/14398287
Work out 4 5 ÷ 7 15 Give your answer as a mixed number in its simplest form.
Answer:
1/9
Step-by-step explanation:
look up mixed numbers calculator soup , it helps you <3
Answer:
1 37/50
Step-by-step explanation:
4/5÷7/15 =
1.74 =
1 74/100 =
1 37/50
Arrange from greatest to least the regions whose populations have 9 as the power
Answer:
i dont know
Step-by-step explanation:
What is the first step in constructing an inscribed circle inside triangles XYZ?
What remainder is represented by the synthetic division below?
A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0.
–5
0
1
2
Answer:
the asnwer is 0
Step-by-step explanation:
Hope it help :D
Answer:
B
Step-by-step explanation:
The answer is 0 on edge
· Write the equation of the circle in standard form. Then, find its
radius and center.
x2 + y2 + 14x – 12y + 4 = 0
Answer:
Center: (-7,6)
Radius: 4
Step-by-step explanation:
Hope this helps :)
Which expression represents these words?
6 less than the quotient of 36 and 4
(36−4)+6
(36−4)−6
364+6
364−6
Answer:
[tex]\frac{36}{4} -6[/tex]
Step-by-step explanation:
the quotient of 36 and 4 is:
[tex]\frac{36}{4}[/tex]
Mathematically we write 6 less than 36/4 like this :
[tex]\frac{36}{4} -6[/tex]
PLEASE HELP FAST!!! I’ll give brainliest
Use the formula A = bh to find the
area of a rectangular-shaped garden
with a base of 8 feet and a height of
7 feet
Answer:
Hope it helps.....................
Ebony had a sum of money.
She kept ½ for herself. She decided to give the rest away to family and charity.
¾ of the money she gave away went to family.
a) What fraction of the total amount did Ebony give to charity?
a)If the amount was £200, how much money did she give to family?
Answer: She gave a fraction of 1/4 to charity, and she gave $150 to family
Step-by-step explanation: Ebony had a totaly of $200 dollars to start with to give away that means if she gave 3/4 of $200 to family that would mean she gave $150 dollars to her family
Now the other part of the question is how much of the total amount did Ebony give to charity now if I understand that part correctly then it wants you to give the fraction of the total which would be she gave 1/4 out of the $200 she had for family and charity which means she gave 1/4 of $200 which is $50 to charity
Hope this Helps!
What is the volume of the pyramid? 2.5 cm3 5 cm3 6 cm3 7.5 cm3
Answer:
the anwer is 5 cm3
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
What is the initial value of a=75t + 125?
i need t know the answer and what that's called
the answer is around 1.73, so its a little over the 1.5 mark. also, im not sure if this is what you meant, but the phrase is radical 3, or the square root of 3 :)
its the blue line!!!!
When calculating a loan’s effective rate, if the interest compounds every two months, what value of n do you plug into your equation? a. 2 b. 0.167 c. 6 d. 60
The value of n you plug into your equation will be 6. Then the correct option is C.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
When calculating a loan’s effective rate.
If the interest compounds every two months.
Then the value of n you plug into your equation will be
If the interest is compounded every two months, the interest will be applied six times every year.
Because there are 12 months in a year, the value of n that you will plug into your equation is 6, and it will be compounded every two months.
More about the compound interest link is given below.
https://brainly.com/question/25857212
The sixth term is 22. the common difference is 6 what is the 15th term?
Answer:
The general formulaa for an arithmetic sequence is:
a(n) = a + d(n - 1)
Step-by-step explanation:
Answer is a(n) = a + d(n - 1)
find the surface area. help i’m confused
How many miles can be driven using 5.5 gallons of gas?
Answer:
it depends on the car mpg but based on the average (24.9 mpg) you can drive about 136.95 miles
Step-by-step explanation:
24.9 x 5.5
Given that x + y= 180, p + 9 = 180, and p = x. Show that y= q. 1) Which step would be used to prove the argument? es A) x + p = 180 B) x + y = p +9 (9y+ = 180 D) 2x + 2y = 180
Answer:x + y = 180
p + q = 180
p = x
Show that y = q
x = 180 - y
p = 180 - q
p = x
180 - q = 180 - y
-q = 180 - y - 180
-q = -y
-q/-1 = -y/-1
q = y OR y = q
x + y = p + q CHOICE B.
180 - y + y = 180 - q + q
Step-by-step explanation: your welcome
If a bicyclist travels at 15 km/, how long will it take her to travel 50 km?
A. 6 h
B. 3.33 h
C. 450 h
D. D 0.3 h
Answer:B
Step-by-step explanation: Distance covered = speed × time
Time = Distance /speed = 50/3
What is the value of this expression?
{5×(13−8)}+12÷6
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's evaluate ~
[tex]\qquad \tt \dashrightarrow \: \{5 \times (13 - 8) \} + 12 \div 6[/tex]
[tex]\qquad \tt \dashrightarrow \: \{5 \times (5) \} + 12 \div 6[/tex]
[tex]\qquad \tt \dashrightarrow \: \{5 \times 5\} + 2[/tex]
[tex]\qquad \tt \dashrightarrow \:25 + 2[/tex]
[tex]\qquad \tt \dashrightarrow \:27[/tex]
{5×(13−8)}+12÷6
to find:the value of the expression.
solution:we'll have to follow the BODMAS rule to solve this.
{5×(13−8)}+12÷6
= {5 × (5)} + 12 ÷ 6
= 25 + 2
= 27
What polygon is shown?
Answer:
Pentagon
Step-by-step explanation:
10 \frac { x ^ { 2 } } { y ^ { 2 } } - 1 - 3 \frac { y ^ { 2 } } { x ^ { 2 } }
Answer:
[tex]\frac{(2x^{2} + y^{2}) (5x^{2} - 3^{2} }{x^{2} y^{2} }[/tex]
Step-by-step explanation:
Find the solution below.
Answer: (5x2 + 3y2) • (2x2 + y2) ———————————————————————— x2y2
Step-by-step explanation:
STEP 1: y2
Simplify ——
x2
Equation at the end of step 1: (x2) y2
((10•————)-1)-(3•——)
(y2) x2
STEP 2 : x2
Simplify ——
y2
Equation at the end of step 2: x2 3y2
((10 • ——) - 1) - ———
y2 x2
STEP 3:Rewriting the whole as an Equivalent Fraction 3.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using y2 as the denominator : 1 1 • y2
1 = — = ——————
1 y2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominatorAdding fractions that have a common denominator : 3.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: 10x2 - (y2) 10x2 - y2
——————————— = —————————
y2 y2
Equation at the end of step 3: (10x2 - y2) 3y2
——————————— - ———
y2 x2
STEP 4:Trying to factor as a Difference of Squares: 4.1 Factoring: 10x2-y2 Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)Proof : (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2 = A2 - B2Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated from the expression.Check : 10 is not a square !! Ruling : Binomial can not be factored as thedifference of two perfect squaresCalculating the Least Common Multiple : 4.2 Find the Least Common Multiple The left denominator is : y2 The right denominator is : x2 Number of times each Algebraic Factor appears in the factorization of: Algebraic Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} x 022 y 202 Least Common Multiple: x2y2 Calculating Multipliers : 4.3 Calculate multipliers for the two fractions Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_Deno Left_M = L.C.M / L_Deno = x2 Right_M = L.C.M / R_Deno = y2Making Equivalent Fractions : 4.4 Rewrite the two fractions into equivalent fractionsTwo fractions are called equivalent if they have the same numeric value.
Place the following numbers on the number line. -2.42,-0.8, 0.33, 1.23
Answer:
On a number line, -2.42 would be first on the left, then -0.8, 0.33, and 1.23
Step-by-step explanation:
anyone know this??!!!
Step-by-step explanation:
[tex] - \frac{1}{5} + \frac{1}{4} \times \frac{1}{20} [/tex]
choice 3
Rewrite the polynomial in the form ax^2+bx+c and then identify the values of a, b, and c
WILL GIVE BRAINLIEST!!!
Solve 2(3y + 7 + 5) = 180. Solve ALL steps.
[tex]2(3y + 7 + 5) = 180\\\\ \implies 3y+12=\dfrac{180}2 \\ \\ \implies 3y+12 = 90\\\\\implies 3y = 90-12\\\\\implies 3y = 78\\\\\implies y= \dfrac{78}3 \\\\\implies y=26[/tex]
Answer:
y = 26
Step-by-step explanation:
2(3y + 7 + 5) = 180
6y + 14 + 10 = 180
6y + 24 = 180
-24 -24
6y = 156
÷6 ÷6
y = 26
I hope this helps!
Someone please help ASAP!!! I need both of these done before 12:00!!! Giving brainliest to best answer!!! you can do it!!
Answer:
8. 6/12
9. 8/ 42
..........
Hope it helps.
Do comment if you have any query.
The length is 2 units,the width is 5 units,and the height is 7 units
Which is a TRUE statement about slope?
A. The slope of a line is never 0.
B. When a line increases as you read it from left to right, the slope of the line is negative.
C. When the slope of a line is negative, the y-values decrease as the 3-values increase.
D. The slope of a line is always positive.
Answer:
C)
Step-by-step explanation: