The quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
We are given a quadratic function:
h (x) = x^2 + 3x − 18
We need to rewrite the function by completing the square.
We can see the coefficient of x is 3.
So, we will add and subtract the square of half that.
So, find the square of half of 3, we will get;
(3 / 2)^2 = 9 / 4 = 2.25
add and subtract the square of half of 3 from the given function, we will get;
h(x) = x^2 +3x + -18 2.25 -2.25
arrange the expression, we will get;
h(x) = (x^2 +3x +2.25) -18 -2.25
write the expression in parentheses as a square, and simplify the constant, we will get;
h(x) = (x + 1.5)^2 - 20.25
So, the square function is written as h(x) = (x + 1.5)^2 - 20.25.
Thus, the quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
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Given: x-5> -10.
Choose the solution set.
The solution set. for the given inequality : x-5> -10. is (-5, ∞]
An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.
We need to find the solution set for x-5> -10.
x - 5 > - 10
x > -10 + 5
x > -5
The solution set = (-5, ∞]
Therefore, the solution set. for the given inequality : x-5> -10. is (-5, ∞]
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The vaule of 5-a is 20 greather than the vaule of 6a-1
The value of a when the value of 5-a is 20 greater than the vaule of 6a-1 is -2.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Since the value of 5-a is 20 greater than the vaule of 6a-1. This will be:
5 - a > 6a - 1 + 20
Collect like terms
-a - 6a > - 1 + 20 - 5
-7a > 14
Divide
a > 14 / -7
a > -2
Therefore, a is greater than -2.
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The median monthly rent in 2005 was $694 and $810 in 2010. What was the percent increase in the median monthly rent prices from 2005 to 2010? Round to the nearest tenth of a percent.
The percent increase in the median monthly rent prices from 2005 to 2010, using proportions, was of:
16.7%.
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of a problem.
One application of proportions is to obtain the percent increase in the context of a problem, as it is calculated as the division of the increase by the total amount and multiplied by 100%.
The parameters to obtain the percent increase in the context of this problem are given as follows:
Initial amount: $694.Increase: 810 - 694 = $116.Hence the percent increase in the median monthly rent prices from 2005 to 2010 is calculated as follows:
P = 116/694 x 100% = 16.7%.
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When the inequality. y> x + 1 is graphed, the shade is below the line and the line is dashed.
False
True
فے
The inequality y > x+1 graphed is false.
Given,
In the question:
When the inequality y > x +1 is graphed,
The shade is below the line and the line is dashed.
Check the above information is true or false.
Now, According to the question:
The inequality is given as:
y > x +1
The graph is:
∴The shade is below the line and the line is dashed
The answer is false.
Hence, The inequality y > x+1 graphed is false.
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6 eggs in 7 months Remember to write your answer with the unit rate per something. Round to the hundredths place if necessary. PLS HELP
The unit rate which correctly corresponds to.the given rate; 6 eggs in 7 months is; 0.86 eggs per month.
What is a unit rate?A unit rate as the name implies is one in which case a given quantity is expressed in terms of one unit of the other quantity.
Such units are expressed as; a per b.
On this note, since the given rate is; 6 eggs in 7 months.
It follows that the rate can be expressed as;
6 eggs / 7 months
= 6/7 eggs per month.
= 0.85714 eggs per month.
And ultimately, when rounded to the nearest hundredth; we have; 0.86 eggs per month.
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Sandra can knit 36 rows on a scarf in 18 minutes. How many rows can she knit in 25 minutes?
This calls for applying rates:
18 minutes = 36 rows
1 minute = 36/18 = 2 rows
25 minutes = 2 x 25 = 50 rows
The answer is 50 rows in 25 minutes. I hope this helps!
Based on the graph, how many distinct real number
solutions does the equation x³ + 6x² + 12x +8=0
have?
O no real number solutions
O one real number solution
O two real number solutions
O three real number solutions
Because the graph only intercepts the x-axis only once, the equation has only one solution. The correct option is the second one.
How many solutions the equation has?Here we want to see, based on a graph, how many solutions does the cubic equation:
x³ + 6x² + 12x +8 = 0
The graph of the function:
g(x) = x³ + 6x² + 12x +8
Can be seen below, the number of real solutions that the equation:
x³ + 6x² + 12x +8 = 0
has, will depend on how many times the graph intercepts the x-axis.
We can see that there is only one intercept, so there is one real solution.
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(9t²-t-6)(9t² +9t - 1)
Help!
Answer:
we can't give an answer if there's not explanation of which "t" is
Someone please help…
Answer:
(x-5),(y+2)
Step-by-step explanation:
Griffin wants to go hiking, but the weather is not cooperating. Right now, there is 2 inches of snow on the ground and snow is falling at a rate of 0.25 in/hr. (a) Write the linear equation that represents the represents the total amount of snow, y, after x amount of hours. (b) How much snow will be on the ground after 4 hours? You must use your equation above to solve, and you must show all of your work. (c) If Griffin does not want to be hiking when there is 6 inches of snow on the ground, how long does he have to complete his hike? Do you think he will finish his hike in time? You must use your equation above to solve, and you must show all of your work.
a) The linear function is:
y = 2 + 0.25x.
b) The amount of snow on the ground after 4 hours will be of 3 inches.
c) The time that he has to complete the hike is of 16 hours, which is enough to finish the hike, as they don't take this long.
What is a linear function?The slope-intercept representation of a linear function is presented by the rule as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the unit rate of change of the output y by the input x.b is the y-intercept of the function, which is the numeric value of the output y when the input x assumes a value of zero.In this problem, the values of these coefficients are given as follows:
b = 2, which is the initial amount of snow on the ground.m = 0.25, which is the hourly rate of snow.Hence the equation is:
y = 2 + 0.25x.
After four hours, the amount of snow on the ground will be of:
y = 2 + 0.25(4) = 2 + 1 = 3 inches.
The time until the amount reaches 6 inches is of:
2 + 0.25x = 6
0.25x = 4
x/4 = 4
x = 16 hours.
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Y is inversely proportional to the square of x. If Y = 5 when x = 3, then Y=1 4/5
, when x is.
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely to }x^2}{y=\cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} y=5\\ x=3 \end{cases} \\\\\\ 5=\cfrac{k}{(3)^2}\implies 5=\cfrac{k}{9}\implies 45=k\hspace{5em}\boxed{y=\cfrac{45}{x^2}} \\\\\\ when~y=1\frac{4}{5}\textit{ what is "x"?}\implies 1\frac{4}{5}=\cfrac{45}{x^2}\implies \cfrac{9}{5}=\cfrac{45}{x^2} \implies 9x^2=(5)(45) \\\\\\ x^2=\cfrac{(5)(45)}{9}\implies x^2=25\implies x=\sqrt{25}\implies {\Large \begin{array}{llll} x=5 \end{array}}[/tex]
Pleas help congruent, triangles, and classifying and solving for sides/angels
8. The value of x is 9.
9. The value of x is 6.
What are congruent triangles?Two triangles are congruent if all the corresponding sides and corresponding angle are equal.
8.
In the given triangle ∠A=(3x-4)°, ∠B=(13x+2)° and ∠C=(5x-7)°
The sum of all three angles of a triangle is 180°,
Implies that,
∠A+∠B+∠C=180°
3x-4+13x+2+5x-7=180
21x-9=180
21x=189
x=9
9.
In the given triangle, ∠A=(7x+1)°, ∠B=(19x-18)° and ∠C=(10x-9)°
The sum of all three angles of a triangle is 180°,
Implies that,
∠A+∠B+∠C=180°
7x+1+19x-18+10x-9=180
36x-26=180
36x=216
x=6
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Can anyone solve this
Answer:
Step-by-step explanation:
y= 53/3 prob wrong but idek
raise u to the 10th power, then double the result
u raised to the 10th power, then the result doubled gives 2u¹⁰
How to write an algebraic expression?An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, multiplication, exponent, etc.
Given: raise u to the 10th power, then double the result
Step 1: Raising u to the 10th power implies: u¹⁰
Step 2: Doubling the result means multiplying what you obtained in step 1 by 2, that is, 2 × u¹⁰ = 2u¹⁰
Therefore, raising u to the 10th power and then doubling the result gives 2u¹⁰
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The penguins at the zoo eat 2 5/8 pounds of fish each day. The zookeeper bought 5 1/4 pounds of fish. How many days will the fish last?
what would the correct number line be for this compound inequality? 3x - 5 > or -2x _< -10
The correct number line that shows the solution to the compound inequality is given by:
Number Line A.
What is a compound inequality?A compound inequality is an inequality that is composed by multiple conditions.
Then these conditions are related with one of two operations, listed as follows:
and operation: the values need to respect all the conditions of the compound inequality.or operation: the values need to respect at least one of the conditions of the compound inequality.In this problem, the compound inequality is given as follows:
3x - 5 > 1 or -2x ≤ -10.
The solutions to the first condition are given as follows:
3x > 6
x > 2.
The solutions to the second condition are given as follows:
2x ≥ 10
x ≥ 5.
The interval of values that is the union of these solutions is given by:
x > 2.
Hence number line A is the solution to the inequality.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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Solve for b.
b - 14 = -10
Answer:
b=4
Step-by-step explanation:
b-14 =-10
b-14+14=-10+14
b=4
(x³ + 2x² - 8x+6) ÷ (x² +9)
Answer:
this should help
Step-by-step explanation:
it is step by step on screenshots I have above
alpha beta square +alpha square beta quadratic equation
β=-α is the solution for alpha beta square +alpha square beta quadratic equation
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
alpha beta square +alpha square beta quadratic equation
αβ²+βα²
αβ(β+α)
αβ=0
and
β+α=0
β=-α
Hence β=-α is the solution for alpha beta square +alpha square beta quadratic equation
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The annual fundraising goal of a is $100,000. So far $46,088 has been raised. How much more money is needed to reach the goal? What???
If annual fundraising goal of a is $100,000 and so far $46,088 has been raised, then they have to raise $53912 to reach the goal
The goal of the annual fund raising = $100000
The raised amount = $46088
The amount of money needed to reach the goal = The goal of the annual fund raising - The raised amount
Here we have to use the subtraction
Substitute the values in the equation
The amount of money needed to reach the goal = 100000 - 46088
= $53912
Hence, if annual fundraising goal of a is $100,000 and so far $46,088 has been raised, then they have to raise $53912 to reach the goal
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In Aurora’s candy box, of the candies are strawberry flavored and are chocolate flavored.
What is the fraction of strawberry and chocolate flavored candies that Aurora has in her box?
The fraction of strawberry and chocolate flavored candies that Aurora has in her box is 5/4
How to calculate the fraction?From the information illustrated, 30 of the candies are strawberry flavored and 24 are chocolate flavored.
Therefore, to get the fraction, we have to divide them. This will be illustrated as:
= Number of strawberry candies / Number of chocolate candies
= 30 / 24
= 5/4
The fraction is 5/4.
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Complete question
In Aurora’s candy box, 30 of the candies are strawberry flavored and 24 are chocolate flavored. What is the fraction of strawberry and chocolate flavored candies that Aurora has in her box?
Please help!
You are playing a game where you must spin a spinner that is numbered 1–8 on equal parts. What is the probability that you would get an odd number twice in a row?
25%
50%
12.5%
6.25%
The probability that your would get an odd number twice when the rolling is 1-8 is 12.5%
Probability is the chance of occurrence of an even (E) Over a period of time. That is, it is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
How to get the probability of the spinning?
From the analysis, the spinning is done twice from numbers 1-8
this means that in ever row, each number appears double.
The sample size is 8x8=64
1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8
2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8
3,1 3,2 3,3 3,4 3,5 3,6 3,7 3,8
4,1 4,2 4,3 4,4 4,5 4,6 4,7 4,8
5,1 5,2 5,3 5,4 5,5 5,6 5,7 5,8
6,1 6,2 6,3 6,4 6,5 6,6 6,7 6,8
7,1 7,2 7,3 7,4 7,5 7,6 7,7 , 7,8
8,1 8,2 8,3 ,,8,4 ,,, 8,5 ,,8,6 8,7,,, 8,8
The required outcome is 8
These outcomes are
1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8=8 outcomes
Probability of and event is
P=[tex]\frac{number of required outcome}{number of possible outcome}[/tex]
P(E)=[tex]\frac{8}{64}[/tex]
P(E)=[tex]\frac{1}{8}[/tex]
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Answer: 25%
Step-by-step explanation:
You have 4/8 chances of getting an odd number on the spinner, which equals 1/2, or 50%. Now if you are going to get another odd number, you have an additional 1/2 (half your chances) or 50% of a chance of getting it after you get the first odd number. This means you must mutliply these chances. 1/2x1/2 which is 1/4 = 25%
A square has a side length of 4x+1
What is the perimeter of the square and area of the square?
I’ll give points + brainalist
Answer:
16x+4
Step-by-step explanation:
Perimeter= side+side+side+side or 4(side)
Plug in side length
Perimeter= 4(4x+1)
Perimeter=16x+4
It can't be further simplified
4a² + 4ab-3b² = (2a+3b)(_)
Complete the factoring
Answer:
(2a + 3b)(2a - b)
Step-by-step explanation:
4a² + 4ab - 3b²
consider the factors of the product of the coefficient of a² and b² which sum to give the coefficient of the ab- term.
product = 4 × - 3 = - 12 and sum = 4
the factors are + 6 and - 2
use these factors to split the ab- term
= 4a² + 6ab - 2ab - 3b² ( factor the first/second and third/fourth terms )
= 2a(2a + 3b) - b(2a + 3b) ← factor out (2a + 3b) from each term
= (2a + 3b)(2a - b)
Need answers for these questions.
The future value of $8904.56 compounded semi annually is $13,468.95 The interest earned is approximately $4,564.39
The future value of $8904.56 compounded continuously is $66,185.90.
The interest earned is approximately $57,281.34.
What are the future values and the interests?When an investment is compounded semi annually, it means that both the amount that was invested and the interest that has already been earned increases in value twice in a year.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = semi annual interest rate = annual interest rate / number of compounding = 6% / 2 = 3%m = number of compoundingN = number of yearsFV = 8904.56 x 1.03^(7 x 2) = $13,468.95
Interest = future value - amount invested
$13,468.95 - $8904.56 = $4,564.39
When an amount is compounded continusoly, it increases in value infinitely over the investment time horizon.
The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rateFV = 8904.56 x e^0.06 x 7 = $66,185.90
Interest = future value - amount invested
$66,185.90 - 8904.56 = $57,281.34
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Solve.
1) Jake bought a bicycle that cost $65.00 when it was new...
If he eventually sold it for 20% of the original cost, how
much was it sold for?
Answer:
Jake sold the bicycle for $13.00
Step-by-step explanation:
All you have to do is know the equation would be 20% of $65.00.
That equals 65x0.20.
If you solve it, the answer is $13.00
Jake sold the bicycle for $13.00
Hope this helps!
Answer:
its 13 dollars
Step-by-step explanation:
when you have to find a precent of something you multiply the number by the percentage and divide the answer by 100
The exponential model A=302.5e^0.0211 describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003.
The population of the country in 2003 is 302.5 million
How to determine the population of the country in 2003.From the question, we have the following parameters that can be used in our computation:
Exponential model, A = 302.5e^0.0211t
Where i is the number of years after 2003
In the year 2003, the value of t is 0
i.e. 0 years after 2003
So, we have
A = 302.5e^(0.0211 * 0)
Evaluate the products
A = 302.5 * 1
So, we have the following result
A = 302.5
Hence, the population is 302.5 million
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y= -x+8
y= 2x+5
solve the following systems..
Answer:
x = 1
y = 7
Step-by-step explanation:
y = -x + 8
-y= -2x - 5 (Switch the signs of y = 2x + 5)
0= - 3x + 3 (Subtract both equations)
3x = 3 (Add 3x on both sides)
x = 1 (Divide by 3 on both sides)
y = -1 + 8 (Plug x as 1 in the equation y = -x + 8)
y = 7 (Simplify)
Leading to the answer
x = 1
y = 7
solve for x in the simplest form
Answer:
x= 12/5
Step-by-step explanation:
Distribute the fraction and solve for x.
bala had 240 cards and tom had 780 cards. after tom gave some cards to bala, bala had twice as many cards as tom. how many cards did tom give to bala?
The answer is tom will give 440 cards to Bala, using arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
The total number of cards is 780+240 = 1020.
If in the end Bala will have twice as many cards as Tom then I would divide the 1020 by 3 which equals 340.
So Bala will have 2*340 = 680 cards
Tom will have 340 cards.
Now Bala will need (680-240) = 440 more cards.
Hence Tom will give 440 cards to Bala.
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