The functions f(4x-3)≥f(2-x^2) and f(5-x^2)≥f(3x-5) are quadratic functions
The values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2
How to solve the inequalities?Inequality 1: f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4)
The function increases at (-8,4).
So, we have:
4x - 3 ≥ 2 - x^2
Rewrite as:
x^2 + 4x - 2 - 3 ≥ 0
Evaluate the like terms
x^2 + 4x - 5 ≥ 0
Expand
x^2 + 5x - x - 5 ≥ 0
Factorize the expression
x(x + 5) - 1(x + 5) ≥ 0
Factor out x + 5
(x - 1)(x + 5) ≥ 0
Solve for x
x ≥ 1 or x ≥ -5
Rewrite as:
-5 ≤ x ≤ 1
Inequality 2: f(5 - x^2) ≥ f(3x - 5), Df=(-∞,4)
The function decreases at (-∞,4).
So, we have:
5 - x^2 ≥ 3x - 5
Rewrite as:
x^2 + 3x - 5 - 5 ≤ 0
Evaluate the like terms
x^2 + 3x - 10 ≤ 0
Expand
x^2 + 5x - 2x - 10 ≤ 0
Factorize the expression
x(x + 5) - 2(x + 5) ≤ 0
Factor out x + 5
(x - 2)(x + 5) ≤ 0
Solve for x
x ≤ 2 or x ≤ -5
Rewrite as:
-5 ≤ x ≤ 2
Hence, the values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2
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What is the coefficient of x in 4+[tex]3y^{2}[/tex]+x?
ASAP PLS ANSWER
Hello!
Please remember that
The coefficient is the number before a variable.Example:
4T+5H
In this example, the coefficient of T is 4, and the coefficient of H is 5.
So let's identify the coefficient of x.
It seems like x doesn't have a coefficient, but it does.
It's equal to 1.
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
Which reason best explains why m^10n^3 is NOT equal to (mn)^13?
Answer:This law of exponents can only be used when the bases are equal.
Step-by-step. explanation:
In a certain triangle, two of the sides have measures of 13 and 16. If the triangle is isosceles, then which of the following could be the measure of the third side?
A. 3
B. 29
C. 13
D. 32
PLEASEEE help! I think it's A or B
Answer:
Choice C.
An isosceles triangle always has two sides of the same length.
A=
B=
C=
? ? ? ? ? ? ? ? ? ? ? ? ? ?
Answer:
a=5 b=7 c=9
hope I helped :)
The area labeled B is 9 times the area labeled A. Express b in terms of a.
b=_____?
Hi there!
For the graph on the left, we know that the area A is equal to:
[tex]A = \int\limits^a_0 {e^x} \, dx[/tex]
Area 'B' is 9 times this area, so:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx[/tex]
We can evaluate the integral:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx \\\\B = 9 \cdot e^x \left \| a}} \atop {0}} \right. \\\\B = 9 (e^a - 1)[/tex]
We also know that:
[tex]B = \int\limits^b_0 {e^x} \, dx[/tex]
Evaluate:
[tex]B = e^x \left \| b}} \atop {0}} \right. = e^b - 1[/tex]
Set the two equations for 'B' equal:
[tex]e^b - 1 = 9(e^a - 1)\\\\e^b - 1 = 9e^a - 9 \\\\e^b = 9e^a - 8[/tex]
Take the natural log of both sides:
[tex]ln(e^b) = ln(9e^a - 8)\\\\\boxed{b = ln(9e^a - 8)}[/tex]
lesson 8 practice probelms position,speed, and directions
14. You deposit $500 in a savings account that
carns 7% interest compouncted anually.
A.) write a function that represents the balance
after t years
B.) What is the balance after 2 years?
Answer:
A) A(t) = 500e^(0.07)(t)
B) 575.137
Step-by-step explanation:
Stephanie has brought 12 bottles of juice to a party but there are more than 12 children. If she gives each child
3/4 of a bottle, how many children will she be able to serve?
Answer:
16 children
Step-by-step explanation:
divide 12 by .75 you get 16
hope that helps
carlos made a list of the scores he obtained on 10 test. 43, 72, 75, 86, 91, 91, 91, 95. The teacher will remove the lowest score from the list. which statical measure will increase if the lowest scored is removed?
Answer:
mean
Step-by-step explanation:
The mean will decrease, in an option of mean, mode, median and range:)
Trey will attend a -year college, and he is planning his budget.
Answer the following.
(a) Below is an estimate of all his expenses and sources of funding for his -year college education.
For each, select whether it is an expense or a source of funding.
Expense Funding
Scholarships:
Grants:
Housing and food:
Work-study (part-time job):
Personal expenses:
Transportation:
Tuition and fees:
Books and supplies:
(b) What is the total of his estimated expenses?
(c) What is the total of his estimated funding?
(d) Can Trey expect to have enough money for his education? How much is the difference?
The examples of funding include scholarship, grants, part time job, etc.
What is funding?Your information is incomplete as the values aren't given. Therefore, an overview will be given.
The funding are needed to cater for school fees and other necessary fees. They include scholarship, grants, and part time job.
The expenses are books, transportation, housing, books, and food.
Learn more about funding on:
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Question Help
8.6.PS-13
A circular plate has circumference 28.3 inches. What is the area of this plate? Use 3.14 for it.
The area of this plate is about square inches.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest
thousandth as needed.)
Answer:
Step-by-step explanation:
Area = 63.9 inches²
5b-4a+6, when a= 7 and b= 6
Answer:
Use Substitution Method -
5(6)-4(7)+6=30-28+6
=2+6
=8
Find f(x+2) if f(x)=(5x^2)-2x+3
Answer:
Use the given functions to set up and simplify f(x+2).
5x2+18x+19 This is the Answer if using The Function Operation.
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10x−2 This is the Answer if you want to find the Derivative
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I don't know if my answer is right if it's wrong I am sorry.
Anyways have an amazing day!
NOW I NEED HELP NOW PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Mya is redecorating her bedroom. The room is in the shape of right rectangular prism.
The dimensions of the room are: 12 feet in length by 14 feet in width by 8 feet in height.
She plans to cover the floor with tile. The cost of the tile is $4 per square foot.
She plans to cover the walls and the ceiling with paint. Each container of paint costs $16 and can cover 146 ft².
What is the total cost of the tile flooring and paint needed for this room?
Drag and drop the responses to correctly complete these sentences.
The total square feet of flooring needed is ____ and the flooring cost will be ____
The total square feet that will need to be painted is ____ and the paint cost will be ____
The total cost of the tile flooring and paint needed for this room is ____
Answer: took the test and the answers are at the bottom. cheers mate :)
Step-by-step explanation:
The mean on a statewide biology test was 76 with a standard deviation of 11. Harris county sampled the scores of some of its students and reported a mean of 80 with a margin of error of ± 2.3.
What is the range of reasonable means for Harris County's sample?
Range: ____ to ____
The margin of error would tell how many percentage differs from Harris County's sample
The range of reasonable means for Harris County's sample is 77.7 to 82.3
How to determine the range?The given parameters are:
Population mean, [tex]\mu = 76[/tex]Population standard deviation, [tex]\sigma = 11[/tex]Sample mean, [tex]\bar x = 80[/tex]Margin of error , [tex]E = 2.3[/tex]The range (R) is calculated as:
[tex]R = \bar x \pm E[/tex]
Substitute known values
[tex]R = 80 \pm 2.3[/tex]
Expand
[tex]R = (80 - 2.3,80 + 2.3)[/tex]
Evaluate the difference and sum
[tex]R = (77.7,82.3)[/tex]
Hence, the range of reasonable means for Harris County's sample is 77.7 to 82.3
Read more about margin of error at:
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the question is below
Answer:
£59.25
Step-by-step explanation:
Hello!
To solve this problem, we must:
Solve for the length of the fence (aka height)Find the area of the lawn (trapezoid)Find the number of cans neededFind the price of all the cansArea of a trapezoid, and why the formula works:
A trapezoid is a quadrilateral with one set of parallel sides known as bases. The other two sides are known as the legs.
To find the area of a trapezoid, we use the formula:
[tex]\frac{B_1 + B_2}{2}* h[/tex]
This works because if we used the formula, we would be duplicating the trapezoid to form a rectangle with a side length of B1 + B2, and a height of h. Since the trapezoid is half of that, we divide by 2.
Solve for height:
The height is unknown but can be found using the Pythagorean Theorem.
The difference between the bases is the length of the bottom leg of the right triangle, and 17 is the hypotenuse.
Difference = 20 - 12 = 8
Hypotenuse = 17
8² + fence² = 17²64 + fence² = 289225 = fence²fence = 15The height is 15
Solve for area:
Now we can solve for the area.
[tex]A = \frac{B_1 + B_2}{2} * h[/tex][tex]A = \frac{12 + 20}{2} * 15[/tex][tex]A = \frac{32}{2} * 15[/tex][tex]A = 16 * 15 = 240[/tex]The area is 240
Cans:
The area of the lawn is 240 square meters. Each can cover 100 square meters.
240 ÷ 100 = 2.4Since we can't use part of a can, we round up to three whole cans.
The price of 3 cans :
3 * 19.7559.25£59.25
The Pythagorean Theorem:
The Pythagorean theorem is a very common geometry formula used to find the length of the hypotenuse in a right triangle, given the lengths of the two other bases.
The formula is : [tex]a^2 + b^2 = c^2[/tex]
a is a legb is a legc is the hypotenuseImages attached for your reference
Quite urgent lol but should probably be quick I guess :(
Answer:
(a) [tex]y=x^2-2x-8[/tex]
(b) [tex]y= -\dfrac12x^2+4x-6[/tex]
Step-by-step explanation:
(a) From inspection of the graph, the x-intercepts (where [tex]y = 0[/tex]) are at
[tex]x = -2[/tex] and [tex]x =4[/tex].
Therefore [tex]y = a(x + 2)(x - 4)[/tex] where [tex]a[/tex] is some constant
The y-intercept is at (0, -8)
Expanding the equation:
[tex]y = a(x + 2)(x - 4)[/tex]
[tex]\implies y = a(x^2-4x+2x-8)[/tex]
[tex]\implies y= ax^2-2ax-8a[/tex]
Therefore, -8a is the y-intercept
Comparing y-intercepts: -8 = -8a ⇒ a = 1
Substituting a = 1, the final equation in standard form is:
[tex]y=x^2-2x-8[/tex]
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(b) From inspection of the graph, the x-intercepts (where [tex]y = 0[/tex]) are at
[tex]x = 2[/tex] and [tex]x =6[/tex].
Therefore [tex]y = a(x -2)(x - 6)[/tex] where [tex]a[/tex] is some constant
The y-intercept is at (0, -6)
Expanding the equation:
[tex]y = a(x -2)(x - 6)[/tex]
[tex]\implies y = a(x^2-6x-2x+12)[/tex]
[tex]\implies y= ax^2-8ax+12a[/tex]
Therefore, 12a is the y-intercept
Comparing y-intercepts:
[tex]-6 = 12a \implies a = -\dfrac12[/tex]
Substituting found value of a into the equation:
[tex]\implies y= (-\dfrac12)x^2-8(-\dfrac12)x+12(-\dfrac12)[/tex]
[tex]\implies y= -\dfrac12x^2+4x-6[/tex]
y = a(x-h)²+k where (h,k) denotes the vertex
Q.1)
vertex: (1, -9) where h=1, k = -9
coordinates: (0, -8) where x = 0, y = -8
find for a:
y = a(x-h)²+k
-8 = a(0-1)²-9
-8 = a -9
a = 1
============
equation: y = (x-1)²-9
Q.2)
vertex: (4, 2) where h=4, k = 2
coordinates: (2, 0) where x = 2, y = 0
find for a:
y = a(x-h)²+k
0 = a(2-4)²+2
-2 = 4(a)
a = -1/2
============
equation: y = -1/2(x-4)²+2
What is the characteristics of a scatterplot
Answer:
Graphs pairs of numerical data, with one variable on each axis, to look for a relationship between them
Step-by-step explanation:
The scatter diagram graphs pairs of numerical data, with one variable on each axis, to look for a relationship between them. If the variables are correlated, the points will fall along a line or curve. The better the correlation, the tighter the points will hug the line.
The table below shows a proportional relationship. True or False?
True
False
Answer:
False
Step-by-step explanation:
2/10 is not equal to 4/16.
Nine times the sum of a number and 2 is equal to 4.
Answer:
9(n+2) = 4
Step-by-step explanation:
9(n+2) = 4
to solve for 'n' first distribute the 9 to get:
9n + 18 = 4
subtract 18 from each side to get:
9n = -14
n = -14/9
Solve For X.
6x + 9 - 4x = -3
Answer:
x = -6
Step-by-step explanation:
6x + 9 - 4x = -3
2x +9 = -3
2x = -12
x = -6
the formula P=F/A,where P=pressure,F=force,andA=area,is used to caculate pressure.solve this formula for F
[tex]P= \dfrac FA \implies F = PA[/tex]
A trapezoid has sides of length 16.7 centimeters, 12.9 centimeters, 16.7 centimeters, and 18.9 centimeters. What is the perimeter? centimeters
Answer:
65.2 cm
Step-by-step explanation:
P = a + b + c + d
P = 16.7 cm + 12.9 cm + 16.7 cm + 18.9 cm
P = 65.2 cm
The perimeter of the trapezoid is 65.2 cm.
Answer:
To find the perimeter of this trapezoid, simply add all four sides (since there are only four sides to a trapezoid):-
16.7 + 12.9 + 16.7 + 18.9
= 65.2 centimetres is the perimeter.
You can picture it like this;
Please help me. I really need help. and I'm not smart
A researcher weighed watermelons grown across a certain region. The data are rounded to the nearest pound and displayed in this histogram.
What does the fourth bin represent?
Select from the drop-down menu to correctly complete the statement.
Four watermelons weigh:
at least 12 pounds but less than 16 pounds
at least 12 pounds but no more than 16 pounds
more than 12 pounds but less than 16 pounds
.
more than 12 pounds but no more than 16 pounds
.
In the given histogram, the correct option regarding the representation of the fourth bin is:
at least 12 pounds but less than 16 pounds.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed. The lower bound is inclusive, while the upper bound is exclusive.
Hence, considering the inclusiveness and exclusiveness of the bounds, the correct option regarding the fourth bin, given by [12, 16) is:
at least 12 pounds but less than 16 pounds.
More can be learned about histograms at https://brainly.com/question/25836450
Answer:
The answer is "at least 12 pounds but less than 16 pounds"
Explanation:
I took the quiz! Hope this helps! :)
A string of decorative lights has 32 bulbs for every 2 feet of wire.
What is the unit rate of bulbs per yard?
HELP !!!!!
Answer:
First convert two feet into yards, knowing that:
1 foot = 0.333... yards
So,
2 feet in yards would mean double of 0.333... because one single foot is 0.333... yards.
2(0.333...)
= 0.666..., which we can round to 0.67.
So our new ratio will be 32 bulbs per 0.67 yards.
Now we convert this ratio into a unit rate,
Order your units;
Bulbs 32 47.76
______ ______ = ______, which rounds to about 48.
Yards 0.67 1
So the unit rate is 48 bulbs per yard.
Joshua deposits $310 every month into an account earning an annual interest rate of 7.8% compounded monthly. How much would he have in the account after 6 years, to the nearest dollar? Use the following formula to determine your answer.
Can you please help
Answer:
used formula to find Area of parallelogram
area of parallelogram =b× h
Step-by-step explanation:
solution :
given ,
h = 7cm
b = 9 cm
we know ,
Area of parallelogram = b× h
=63cm²
The family soent 125$ in may for electric bills, in june the bill increased by 12% bc they used the ac more often. Write a equation to calculate their total electricity bill in june. Let y equal the total cost
Answer:
125x 12 and divide the answer
Step-by-step explanation:
Answer:
125x 12 and divide the answer
Step-by-step explanation:
There are several ways to reduce how much does it cost to run an air conditioner. The two main ones are:Buying an air conditioner with a high energy efficiency rating (EER, SEER, CEERratings are valid specifications).Reducing the number of hours per day that you use a given air conditioner.Note: It’s recommended to estimate how much electricity does an air conditioner use before buying a specific unit.On average, running an air conditioner costs between $0.06 and $0.88 per hour. Let’s calculate how much does air conditioning cost per month (running 8h per day):
Given that V=1,3,4,2 and W= 6,4,7,2 then VW is
Select one:
of
O 4
0 1,3,6,7
O 2
0 2,4
Answer:
2,4 possibly
Step-by-step explanation:
if its V (intersection) W
then its 2,4
if it has something to do with patterns then i dont know
A cell phone measures 10 cm long, 6 cm long, and 2 cm high. What is the volume of the cell phone?
Answer: 120cm
Step-by-step explanation:
Multiply length x width x height
10 x 6 x 2 is equal to 120, so the volume is 120cm or centimetres.
Answer:
10cmx6cmx2cm
6x2=12
12×10=120cm