The domain of the parabola is all real numbers, and the range is f(x) ≤ -31/8.
The domain of a parabola is all real numbers unless there are restrictions on the variable. In this case, there are no such restrictions, so the domain is (-∞, ∞). To find the range, we can complete the square to rewrite the function in vertex form: f(x) = -2(x - 4)² + 1.5.
Since the squared term is negative, the parabola opens downward, and the vertex is at (4, 1.5). The maximum value of the function occurs at the vertex, so the range is f(x) ≤ 1.5. However, since the coefficient of the squared term is negative, we need to multiply the range by -2 to get the correct inequality. Thus, the range is f(x) ≤ -31/8.
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What is the area of the shaded portion of the figure? Express your answer in terms of pi.
с
A
F
OA. 56 T
OB. 22 T
728
Oc.
45
π
112°
OD. 56 T
ㅠ
E
B
AE = 4 cm
AB= 6 cm
The given radii of 4 and 6 and the sector angle of 112°, gives;
[tex] C.\: \frac{56 \cdot \pi}{9} [/tex]
How can the measure of the shaded portion be found?The possible figure that relates to the question can be described as follows;
Two concentric circles having radii of AE = 4, and AB = 6, respectively.
Sector of the circles formed by lines AC and AB, with angle of sector = 112°
The shaded portion is described by arcs FE and CB
Therefore;
Area of the sectors are found as follows;
[tex]AFE = \frac{112 ^\circ}{360 ^\circ} \times \pi \times {4}^{2} = \frac{224 \cdot \pi}{45} [/tex]
[tex]ACB = \frac{112 ^\circ}{360 ^\circ} \times \pi \times {6}^{2} = \frac{56 \cdot \pi}{5} [/tex]
Area of the shaded portion, A is therefore;
[tex] A= \frac{56 \cdot \pi}{5} - \frac{224 \cdot \pi}{45} =\frac{56 \cdot \pi}{9} [/tex]
[tex] Shaded \: area, \: A= \frac{56 \cdot \pi}{9} [/tex]
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Find the missing segment in the image below.
The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the form
g(x) = (x – h)3 + k.
What are the values of h and k?
h = 4
k = –2
h = –4
k = –2
h = 4
k = 2
h = –4
k = 2
Using translation concepts, the correct values are given as follows:
h = 4.k = -2.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, we have that:
The function was shifted 4 units right, hence x -> x - 4, that is, h = 4.The function was shifted 2 units down, hence y -> y - 2, that is, k = -2.More can be learned about translation concepts at https://brainly.com/question/4521517
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Find the term that must be added to the equation x2−6x=7 to make it into a perfect square.
answer:
+16
steps:
number without the x should be 9
number without the x should be 9c to be 9 needs +16
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divide the number next to the x by 2
-6 divided by 2 is -3
find the square
-3 squared is 9
number without the x should be 9
x²-6x=7
make the equation = 0
x²-6x-7=0
a is the number next x²
b is the number next to x
c is the number without the x
c has to be 9
c is -7
c to be 9 needs +16
x²-6x+9 =0
x²-6x+(-3)² =0
(x-3)²
Answer:
9
Step-by-step explanation:
Completing the square is a method used to solve the quadratic equation.
Divide the co efficient of 'x' by 2.Coefficient of x is '6'. 6 ÷ 2 = 3
Square the quotient of (x ÷ 2) and add to the both side of the equation.3² = 9
x² - 6x + 9 = 7 + 9
Answer: To make into a perfect square, 9 must be added.
Which expression is equivalent to 144 3/2
Answer:
144=12², so 144^3/2=(12²)^(3/2)=12³=1728.
this answer is not from the internet
go check yourselves
mark me brainliest
In a group of 75 student 20 like football only 30 like circket ony and 18 didn't like any of wo game
(i) 57students liked at least one game.
(ii) 7 students who liked both the games.
(iii) 27 students liked football.
(iv) 37 students liked cricket.
(v) Below we represented the result in a Venn diagram.
What is Venn diagram?
John Venn popularized the Venn diagram in the 1880s, which is a type of diagram that displays the logical relationship between sets. The illustrations are used in probability, logic, statistics, linguistics, and computer science to demonstrate basic set relationships and to teach rudimentary set theory.
Part (i)- We have to get number of people who like at least one game, there are total 75 students and only 18 did not like any of two games, so students who like at least one game are-
75-18 = 57
Part (ii)- There are 57 students who like at least one game, from the question statement we know that 20 students like football only and 30 liked cricket only, so student who like both games are-
57-20-30 = 7
Part (iii)- There are 7 students who liked both games and 20 who liked football only, so student who liked football are-
20+7 = 27
Part (iv)- There are 7 students who liked both games and 30 who liked cricket only, so student who liked cricket are-
30+7=37
Part (v)- Venn Diagram will look like-
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Complete Question- In a group of 75 students, 20 liked football only, 30 liked cricket only and 18 did not like any of two games? (i) How many of them liked at least one game? (ii) Find the number of students who liked both the games. (iii) How many of them liked football? (iv) How many of them liked cricket? (v) Represent the result in a Venn diagram.
To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? first equation: second equation:
Answer:
See below.
Step-by-step explanation:
Here is an example:-
Solve by elimination:
2x - 3y = 0
3x + 2y = 13
To eliminate the y terms Multiply the first equation by 2 and the second by 3. This gives:
4x - 6y = 0
9x + 6y = 39 Adding the 2 equations:
13x + 0 = 39
13x = 39
x = 39/13 = 3
Finally we find y by plugging x = 3 into the first equation:
2(3) - 3y = 0
3y = 2(3) = 6
y = 2.
A summer camp has 32 campers. 22 of them swim, 20 play softball, and 5 do not play softball or swim. which values correctly complete the table? a) a = 15, b = 10, c = 7, d = 5, e = 12 b) a = 15, b = 7, c = 5, d = 10, e = 12 c) a = 14, b = 7, c = 5, d = 12, e = 10 d) a = 14, b = 12, c = 7, d = 5, e = 10
The values which completes the table regarding summer camp is option b which is a=15,b=7, c=5, d=10, e=12.
Given that there are 32 campers, 22 of them can swim, 20 play softball and 5 do not play softball or swim.
We have to find the values of a,b,c,d,e so that we can complete the table.
Table is a combination of rows and columns. In our case the third row and third column shows the total.
from the table we can write that 22+d=32-----------1
so d=32-22
=10
d=10
c+5=d-----------2
c=10-5=5
c=5
a+c=20------------------3
a+5=20
a=20-5
a=15
a+b=22--------------3
15+b=22
b=7
20+e=32----------4
e=32-22
e=10.
Hence the values which completes the table is a=15,b=7, c=5, d=10, e=12.
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Question is incomplete as it should include figure showing table of values.
Cruz and erica were both getting ready for soccer. cruz ran 1 lap around the school. erica ran 3 laps around the playground. erica said, i ran more laps, so i ran farther. cruz said, 4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. my laps are much longer, so i ran farther. 1. who is right?
Both ran equal and both covered equal distance.
As cruz ran 1 lap out of 4 to cover one mile.
and erica ran 3 lap out of 12 to cover one mile:
3/12 = 1/4
So Cruz = Erica = 1/4.
Hence Both ran equal.
Fraction:
Fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
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What is the domain of the function graphed below?
X<7
x≤7
-2
all real numbers
Answer:
x < 7
Step-by-step explanation:
The domain encompasses all the "x" values (or inputs) of a function.
The arrow on the left line symbolizes that the function continues into the negative region for infinity. As such, this eliminates option C.
Closed dots are points whose "x" values are included in the function. Open-dots are on points whose "x" values are not included in the function. Although the open-dot on the left line at x = -1 generally means it is not included in the function, the closed dot on the right line overrides this. Therefore, x = -1 is in the domain. The value x = 7 is not within the domain of the function due to the open-dot. This eliminates option B and option D.
With this said, the domain of the function is x < 7.
can someone please help mee (will give brainliest 20 points!!!)
[a] x = 175 - 7.5p
For a, we are isolating the x variable to one side of the equation.
0.4x + 3p = 70
0.4x = - 3p + 70
x = - 7.5p + 175
[b] x = 115
For b, we are solving for x when p = 8.
x = - 7.5p + 175
x = - 7.5(8) + 175
x = 115
A car dealer acquires a used car for $7,000, with terms fob shipping point. compute total inventory costs assigned to the used car if additional costs include
$290 for transportation-in.
$190 for shipping insurance.
$1,000 for car import duties.
$200 for advertising.
$1,400 for sales staff salaries.
$190 for trimming shrubs.
Shipping points are independent organizational entities within which processing and monitoring of the deliveries, as well as goods issue, is carried out. A delivery is processed by one shipping point only.
"FOB shipping point" or "FOB origin" means the buyer is at risk once the seller ships the product. The purchaser pays the shipping cost from the factory and is responsible if the goods are damaged while in transit. "FOB destination" means the seller retains the risk of loss until the goods reach the buyer.
Please check the attached file for a complete answer.
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Annel sells a phone which costs $180 and earns $9 commission. If he sells $640 worth of phones the following days, how much will he earn in commission?
The percentage of the cost of the phones Annel earns in commission is 5%. If he sells $640 worth, the amount he earns as percentage will be $32.
How can the amount Annel earns be found?The amount in commission Annel earns when he sells the phone worth $180 = $9
The percentage of the amount sold, Annel earns as commission is therefore;
[tex] \frac{9}{180} \times 100 = 5\%[/tex]
The amount earned as commission if he sells $640 worth of phones is found as follows;
Amount earned = 5% × 640 = 32
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how much more did lan deposit each week than Jeremy?
Describe a relationship that can be modeled by the function shown in the table, and explain how the function models the relationship.
x ------ f(x)
1 ------ 4
4 ------ 8
9 ------ 12
16 ------ 16
25 ------ 20
B: Identify and interpret the key features of the function in the context of the situation you described in part A
The relationship that can be modeled by the function shown in the table is y = 4·√x
How to illustrate the information?f(x) is defined as a product of 4 into √x
4 × √1 = 4
4 × √4 = 8
4 × √9 = 12
4 × √16 = 16
4 × √25= 20
Therefore, the relationship is defined as y is 4 times the square root of x that is, y = f(x) = 4√x
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PLEASE HELP
Graph the triangle with the given vertices. Find the length and the slope of each side of the triangle. Then find the coordinates of the midpoint of each side. Is the triangle a right triangle? isosceles? Explain (Assume all variables are positive and m ≠ n)
D (0,n), E(m,n), F(m,0)
The given triangle is a right triangle
The length and slopeThe coordinates are given as:
D (0,n), E(m,n), F(m,0)
The length is calculated using:
[tex]l=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2[/tex]
So, we have:
[tex]DE=\sqrt{(0-m)^2 + (n-n)^2} = m[/tex]
[tex]DF=\sqrt{(0-m)^2 + (n-0)^2} = \sqrt{m^2 + n^2[/tex]
[tex]EF=\sqrt{(m-m)^2 + (n-0)^2} = n[/tex]
The slope is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]DE = \frac{n -n}{0- m} = 0[/tex]
[tex]DF = \frac{n -0}{0- m} = -\frac nm[/tex]
[tex]EF = \frac{n -0}{m- m} = \mathbf{unde fined}[/tex]
The coordinates of the midpointsThis is calculated using
[tex]m = 0.5 * (x_1 + x_2, y_1 + y_2)[/tex]
So, we have:
[tex]DE = 0.5 * (0 + m, n+ n)=(0.5m, n)[/tex]
[tex]DF = 0.5 * (0 + m, n+ 0)=(0.5m, 0.5n)[/tex]
[tex]EF = 0.5 * (m + m, n+ 0)=(m, 0.5n)[/tex]
The type of triangleIn (a), we have:
Lengths
[tex]DE= m[/tex]
[tex]DF = \sqrt{m^2 + n^2[/tex]
[tex]EF= n[/tex]
Slope
[tex]DE = 0[/tex]
[tex]DF = -\frac nm[/tex]
[tex]EF = \mathbf{unde fined}[/tex]
The sides are not equal.
However, the 0 and the undefined slope implies that the triangle is a right triangle because the sides are perpendicular
It should be noted that the triangle cannot be graphed because the coordinates are not numeric
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Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0
The general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41
How to determine the general form of the equation for the given circle centered at O(0, 0)?The given parameters are
Center = (0, 0)
Point = (4, 5)
Rewrite the given parameters are
(a, b)= (0, 0)
(x, y) = (4, 5)
The general form of the equation for the given circle is represented as:
(x - a)^2 + (y - b)^2 = r^2
Substitute the known values in the above equation to calculate the radius r
(4 - 0)^2 + (5 - 0)^2 = r^2
Evaluate the difference
4^2 + 5^2 = r^2
Evaluate the exponent
16 + 25 = r^2
Evaluate the sum
41= r^2
Rewrite as
r^2 = 41
Substitute r^2 = 41 in (x - a)^2 + (y - b)^2 = r^2
(x - a)^2 + (y - b)^2 = 41
Substitute (a, b)= (0, 0) in (x - a)^2 + (y - b)^2 = 41
(x - 0)^2 + (y - 0)^2 = 41
Evaluate the difference
x^2 + y^2 = 41
Hence, the general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41
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What is the x-intercept of p(x) = -x + 8?
Answer:
x-intercept = 8
Step-by-step explanation:
Hello!
An x-intercept is when the y-value is 0, or when the graph intersects the x-axis.
We can replace p(x) with 0 and solve for x.
Solve for x[tex]p(x) = -x + 8[/tex][tex]0 = -x + 8[/tex][tex]-8 = -x[/tex][tex]8 = x[/tex]The x-intercept is 8.
What is the slope of the line through (-3, 3) and (-1, -1)?
(-3, 3)
-3 -2 -1
(-1,-1)
4
3
2
You
1
-1
2.
y
1 2
3
4
X
Answer:
The slope is -2
Step-by-step explanation:
To find the slope, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= (-1 -3)/(-1 - -3)
= ( -1-3)/(-1+3)
= -4/2
= -2
The slope is -2
Use the given information to find the unknown value. Y varies inversely with the cube of x. When x=5, then y=1. Find y when x=1
Answer:
125
Step-by-step explanation:
y = 1k/x^3 I am trying to find the constant k. I will use the information that I have been given to find k
1 = k/5^3
1 = k/125 Multiply both sides by 125
125 = k
Now, we will find y when x = 1
y = 125/1^3
y = 125
The value of y is 125 when x is 1.
Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.
y = 1k/x^3 I am trying to find the constant k. I will use the information that I have been given to find k
1 = k/5^3
1 = k/125
Multiply both sides by 125
125 = k
Now, we will find y when x = 1
y = 125/1^3
y = 125
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14 m
10 m
what is the volume of the following cylinder?
The volume of the cylinder is approximately, 1,539.4 cubic meters.
What is the Volume of a Cylinder?Volume of a cylinder = πr²h
Given the following:
Diameter of cylinder = 14 m
Radius (r) = 14/2 = 7 m
Height of cylinder = 10 m
Volume of cylinder = πr²h = π(7²)(10)
Volume of cylinder ≈ 1,539.4 cubic meters.
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2. The lengths in centimeters of four line segments
are shown below.
3.12, 3.24, 31, √10
Write the lengths in order from least to greatest.
Answer:
I'm pretty sure it is √10, 3.12, 3.24, 31
Step-by-step explanation:
I don't know if you messed up but I got a question similar that is the length 31 in your quesion is actually 3 1/4 in my question. but i did the math and 31 is still the greatest number.
Find the volume of the solid to the nearest whole cubic unit. use a calculator, if needed. yellow solid v = ______
The volume of the cuboid is 132 cubic inches.
Given length of cuboid 7 1/3 inches, breadth being 6 2/3 inches , height being 2 7/10 inches.
Volume is amount of liquid a container can hold in its capacity. Cuboid is a 3 dimensional figure having length , breadth and height.Volume of cuboid is the product of length, breadth and height of cuboid.
We have to calculate volume of cuboid.
We have to make a simple fraction showing length , breadth and height.
Length=(3*7+1)/3=22/3
Breadth=(3*6+2)/3=20/3
Height=(10*2+7)/10=27/10
Volume=22/3*20/3*27/10
=11880/90
=132 cubic inches.
Hence the volume of cuboid having length of 22/3 inches, breadth of 20/3 inches and height of 27/10 is 132 cubic inches.
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Question is incomplete as it should include figure.
Need to type in SSS, SAS, ASA, AAS, or HL
The triangles are congruent by SAS congruence theorem
How to determine the congruence theorem?From the figure, we have the following congruent sides
Sides AB and DBSides A F and D FAlso, both triangles share a common vertex at B
This means that:
<B = <B
Two sides and one angle are congruent in the triangles
Hence, the triangles are congruent by SAS congruence theorem
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Drag each number to the correct location on the table. classify the real numbers as rational or irrational numbers.
The rational numbers are -5/250, [tex]\sqrt{400}[/tex] ,and irrational numbers are 5.012121212......., [tex]\sqrt[3]{30}[/tex] , 0.01562138411........,[tex]\sqrt{1000}[/tex]
Given six numbers:5.012121212..,[tex]\sqrt{1000}[/tex],[tex]\sqrt[3]{30}[/tex], -5/250, 0.01562138411.....,[tex]\sqrt{400}[/tex].
We have to identify which numbers are rational and which are irrational numbers.
Rational numbers are those numbers which can be written in p/q form where q cannot be equal to zero because if q is zeo then the value of p/q will be infinity.
Irrational numbers are those numbers which cannot be written in p/q form.
First number :5.0121212121....
In the above numbers 12 is repeating next to the decimals. So it is a irrational numbers.
Second number:[tex]\sqrt{1000}[/tex]
If we solve the above number we will find it 31.6227766017 . It is cannot be expressed in p/q form, so it is irrational number.
Third number:[tex]\sqrt[3]{30}[/tex]
The abov number is irrational number as we cannot express it in p/q form.
Fourth number:-5/250
The value of above number is -0.02.It can be in the form of -2/100. so it is rational number.
Fifth number:0.01562138411........
Because the digits are repeating after decimals so it is irrational number.
Sixth number:[tex]\sqrt{400}[/tex]
The value of above number is 20, so it is rational number.
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Question is incomplete as it should include figure.
Which function is negative for the interval [-1, 1]?
ty
3
2
-3-2-11
-3
ty
O
Intro
123
x
3
2
1
-3-2-1₁
-3
O
x
23
2,
-3-2-1
2 of 11
O
x
123
321
-3-2-11
-2
MAR
-3
ty
x
23
Done
O
Answer:
Graph number 2
Step-by-step explanation:
See attached image.
Find the original price if the price was:
$520 after a 30% increase
(Please Help with explanation that makes sense...will mark brainliest)
Given that price was $520 after a 30% increase, the original price was $400.
What is the the original price?Given that;
Percentage increase = 30%Price after the increase = $520Original price = x
To determine the original price, we say;
x × ( 100% + 30% ) = $520
x × ( 130% ) = $520
x × (130/100) = $520
130x / 100 = $520
130x = $52000
x = $52000 / 130
x = $400
Given that price was $520 after a 30% increase, the original price was $400.
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SELECT ALL THAT APPLY. The probability of rolling an even number with a six-sided, equally weighted die is ______.
The probability of rolling an even number with six sided equally weighted die is 0.5.
Given a six sided equally weighted die.
We are required to find the probability of rolling an even number.
Probability is the calculation of likeliness of happening an event among all the events possible. It lies between 0 and 1. It can be calculated through simple values and with the formula of combination also. The formula of calculating probability is as under:
Probability= number of items/ total number of items.
Total sides in die=6
Total numbers=1,2,3,4,5,6, therefore 6.
Even numbers=2,4,6. Therefore 3.
Probability = even numbers/total numbers.
=3/6
=1/2
=0.5
Hence the probabilty of receiving an even number from a six sided equally weighted die is 0.5.
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A single die is rolled twice. Find the probability of getting a 1 the first time and a 5 the second time. Express the probability as a simplified fraction.
The probability of first rolling a 1, then a 5, will be [tex]\frac{1}{36}[/tex].
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur.To find the probability of getting a 1 the first time and a 5 the second time:
Probability of getting 1 in 1st time = [tex]\frac{1}{6}[/tex]
Probability of getting 5 in 2nd time = [tex]\frac{1}{6}[/tex]
The probability of first rolling a 1, then a 5, will be = [tex]\frac{1}{6}[/tex] × [tex]\frac{1}{6}[/tex]
[tex]= \frac{1}{36}[/tex]
Therefore, the probability of first rolling a 1, then a 5, will be [tex]\frac{1}{36}[/tex].
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Which represents the inverse of the function f(x) = 4x?
the one you selected is correct