The solution of the expression, [tex]x^{2} -10x+25 = 0[/tex], using completing the square method is [tex](x-5)^{2}[/tex].
According to the question,
We have the following expression:
[tex]x^{2} -10x+25 = 0[/tex]
Now, we will use completing the square method to solve this expression.
We will first try to convert the first and last term into perfect squares and rewrite the expression by splitting the middle term in multiplication of 2 and the squares .
[tex]x^{2}[/tex]-2*x*5+[tex]5^{2}[/tex] = 0
Now, we know that this expression fits in the identity:
[tex](a-b)^{2} = a^{2} +b^{2} -2ab[/tex]
In this case, we have a = x and b = 5
[tex](x-5)^{2}[/tex]
Hence, the solution of the expression, [tex]x^{2} -10x+25 = 0[/tex], using completing the square method is [tex](x-5)^{2}[/tex].
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Which of the following numbers is a composite number? A. 9 B. 2 C. 29 D. 5
Answer: A. 9
Step-by-step explanation:
Today, I want you to challenge yourself. Don't let word problems intimidate you. In this task you are not solving but rather setting up equations. I know you have the
ability to do this. Here we go!
19
A store sells two brands of headphones: high definition (HD) and basic. It buys x HD headphones at z dollars each, and y basic headphones at w dollars each.
In a-c, write an equation whose solution is the given quantity. Solve Each Equation and set them up.
a) The number of basic headphones the store can purchase if it spends a total of $10,000 on headphones and buys 110 HD headphones for $70 each.
b)
The price the store pays for HD headphones if it spends a total of $2,000 on headphones and buys 55 basic headphones for $20 each.
c) The price the store pays for HD headphones if it spends a total of $800 on headphones and buys eight basic headphones for $80 each.
d) Please give me the actual cost of the headphones and an explanation with a-c
The solution to these are in form of equation as follows.
What is equation?
In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
x= number of HD headphones y= number of basic headphones
z = price of HD headphones. w = price of basic headphones
a)
110 (70) + y*w = 10,000
7,700+ y*w = 10,000
y*w = 2,300
y = 2,300/w
b)
x*z+ 55(20) = 2000
x*z = 2000 -1100
x*z = 900
z = 900/x
c)
x*z+y*w = 800
x*z+8(80) = 800
x*z+640=800
X*z=160
Hence the values to the equation are as follows.
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maths enlargements calculations of lines in shapes help pls
The length of the line segment BD is 3 centimeters.
How to find the missing length of triangle proportional to another triangle
Herein we find two triangles proportional to each other. According to Thales's theorem, two triangles are proportional when both have congruent angles. The geometric system is represented by the following expression:
AB / AD = BC / DE = AC / AE
By direct inspection we notice that the two triangles are proportional as they have congruent angles. If we know that DE = 10 cm, BC = 8 cm and AB = 12 cm, then the side AD has the following measure:
12 cm / AD = 8 cm / 10 cm
AD = (10 cm / 8 cm) × 12 cm
AD = 15 cm
And the length of the line segment BD is:
BD = AD - AB
BD = 15 cm - 12 cm
BD = 3 cm
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Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. If she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account?
As per the given percentage, Sherry want to invest $2,000 amount in mutual fund and $13,200 amount in bonds.
Percentage:
Percentage means the number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Given,
Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.
Here we need to find if she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account.
It is given that the total amount is 15200.
So, let us consider x be the amount invested in mutual funds then 15200 - x be the amount invested in bonds.
Therefore, it can be written in the following matrix,
[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}[/tex]
Now, we have know that the total interest amount after 1 year is 548,
So, it can be written like the following expression
amount invested x percentage = final amount
Therefore,
[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}\times\begin{bmatrix}\frac{1}{100} \\\frac{4}{100}\end{bmatrix}=548[/tex]
It can be simplified as,
[tex]\begin{bmatrix}x\times(\frac{1}{100})+(15200-x)\times(\frac{4}{100}) \end{bmatrix}=[548][/tex]
=> x/100 + 60800-4x/100 = 548
=> x + 60800 - 4x = 54800
=> -3x = 54800 - 60800
=> -3x = -6000
=> x = 2000
=> 15200 - 2000 = 13200
Therefore, she invests $2,000 in mutual funds and $13, 200 in bonds.
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an urn contains 6 blue balls and 6 orange balls. in how many ways can we select 2 blue balls and 2 orange balls from the urn?
The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545
No. of Blue balls in the urn = 6
No. of Orange balls in the urn = 6
Total no. of balls in the urn = No. of blue balls + No. of orange balls
= 6 + 6
= 12 balls
No. of blue balls to be selected = 2
No. of orange balls to be selected = 2
No. of balls to be selected = 4
The total. no of ways 4 balls can be selected =[tex]^{12}C_{4}[/tex]
The No. of ways 2 blue balls can be selected = [tex]^{6}C_{2}[/tex]
The No. of ways 2 orange balls can be selected = [tex]^{6}C_{2}[/tex]
Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn
= [tex]^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}[/tex]
Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls
P = (15×15)/495
= 225 / 495
P = 0.4545
Therefore, the no. of ways to select blue and orange balls is 0.4545
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Find the inequality represented by the graph
The inequality represented by the graph is y ≥ -x + 2
How to find the inequality the graph representsA graph is a pictorial representation of data and the graph presented represents inequality data
The graph shows a linear function written in the form
y = mx +c
where slope, m calculated as
c = intercept
x = input variables
y = output variables
calculation of slope
The points used for the slope is gotten from the graph as (0. 2) (1, 1)
m = (y₂ -y₁) / (x₂ - x₁)
substituting the values
= ( 2 - 1 ) / ( 0 - 1 )
= 1 / -1
= -1
y intercept, c this is a point where the graph cuts the y axis
c = 2
The graph contains a solid line as result there will be "equal to" attached to the inequality symbol usedshading above the line means greater thanThe two points result greater than or equal to written with the symbol ≥
hence the equation is
y ≥ -x + 2
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If y varies directly as x and y=8 when x=2 find when x=6
The equation is y = 4x. And the value of the function at x = 6 will be 24.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If y varies directly to x. Then the relationship between them is written as,
y ∝ x
y = kx
When y = 8 and x = 2, then the value of the constant k is given as,
8 = k (2)
k = 8 / 2
k = 4
Then the equation is written as,
y = 4x
Then the value of the function at x = 6 will be given as,
y = 4 (6)
y = 24
The equation is y = 4x. And the value of the function at x = 6 will be 24.
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Nora leans a 24-foot ladder against a wall so that it forms an angle of 76^{\circ} ∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
23.29 ft
Step-by-step explanation:
The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.
To find how high up the wall the ladder reaches, use the sine trigonometric ratio:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
where:
θ is the angle.O is the side opposite the angle.H is the hypotenuse (the side opposite the right angle).The angle of elevation is 76°, so θ = 76°.
Let x be the height the ladder reaches up the wall, so O = x.
H is the length of the ladder, so H = 24.
Substitute the given values into the sine ratio and round the answer to the nearest hundredth:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]
[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]
[tex]24 \sin(76^{\circ})= x[/tex]
[tex]x=24 \sin(76^{\circ})[/tex]
[tex]x=23.28709743...[/tex]
[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]
Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.
Can someone help me on this question? I think it’s the 2nd choice but I’m not sure
Answer:
5√3
Step-by-step explanation:
There are two triangles shown in the image.
First one is a 45°-45°-90° right triangle with side lengths represented with a-a-a√2 respectively to the angle measures.
The second triangle is 30°-60°-90° special right triangle with side lengths represented with b-b√3-2b respectively to the angle measures.
In first triangle hypotenuse (the side length represented with a√2) is given as 10√2 so a = 10.
This is also the measure of hypotenuse for the second triangle which is represented with 2b, so b = 5 in this case.
x is the side length that sees angle measure 60° which we said is represented with b√3, we said b = 5 so the value of x = 5√3 the answer is the first option.
A social worker earns an average bi-weekly net pay of $1,465.87. Which compound inequality correctly shows the amount of money, m, the social worker can spend if the monthly budget for debt is between 5% and 10%? $73.29 ≤ m ≤ $146.59 $158.80 ≤ m ≤ $317.61 $146.59 ≤ m ≤ $293.17 $190.56 ≤ m ≤ $349.37
The amount of money the social worker can spend is $146.59 ≤ m ≤ $293.17
What is an equation?An equation shows the relationship between two or more numbers and variables.
Let m represent the amount of money the social worker can spend.
A social worker earns an average bi-weekly net pay of $1,465.87. Hence:
Monthly revenue = 2 * $1465.87 = $2931.74
For a debt of 5%:
m = 5% of $2931.74 = 0.05 * $2931.74 = $146.59
For a debt of 10%:
m = 10% of $2931.74 = 0.1 * $2931.74 = $293.17
$146.59 ≤ m ≤ $293.17
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Answer:
$158.80 ≤ m ≤ $317.61
Step-by-step explanation:
Hello,
So first step is we would use the bi-weekly net pay of $1465.87 then times it by 26 so it would look like this
1465.87 × 26 = 38112.62
Then we would divide 38112.62 by 12
38112.62 ÷ 12 = 3176.0516
Then, we would determine how much the social worker can spend if the monthly budget for debt is between 5% and 10%.
3176.0516 × 5% = 158.80
3176.0516 × 10% = 317.61
So, therefore the answer is $158.80 ≤ m ≤ $317.61.
Ameekah is working with consecutive integers. If she uses x to represent her first number, what should she use to represent her second number?
x
x + 1
x + 2
2x
She should use (b) x + 1 to represent her second number
How to determine the representation of the second number?From the question, we have the following statements that can be used in our computation:
She uses x to represent her first numberThe numbers are consecutive numbersAs a general rule
Consecutive numbers are number that have a difference of 1 i.e both numbers are next to each other
Take for instance:
2 and 3, 5 and 6, 10 and 11 are all instances of consecutive numbers
Recall that she uses x to represent her first number
This means that the next number is
Next number = First number + 1
Substitute the known values in the above equation, so, we have the following representation
Next number = x + 1
Hence, the second number is (b) x + 1
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Jane was asked to solve the equation `2-4=2(-5+1)`. she believes the solution to the equation is `x=\frac{1}{2}` . explain how jane could confirm that her solution is correct
the solution for the given equation is x= 1/2
an equation could be a formula that communicates the balance of two expressions, by interfacing them with the equals sign. Understanding an equation containing factors comprises deciding which values of the factors make the equality true. The factors for which the equation must be fathomed are moreover called unknowns, and the values of the unknowns that fulfill the balance are called solutions of the condition. There are two sorts of equations such as conditional and identities equations. An identity is genuine for all values of the factors. A conditional equation is as it were genuine for specific values of the factors
since the given expression is :
`(2-4)=2(-5+1)x²
so solving for the simple arithmetic expression on both sides :
=>-2 =2(-4)x²
=> -2 = -8x²
=>2/8=x²
=>1/4= x²
=>x= 1/2
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The length, L, of a rectangular garden is twice its width, W. The perimeter of the garden is 36 feet.
Answer:
L=12, W=6
Step-by-step explanation:
L=2W
(L+2L)=36
3L=36
2L=12
L=6
a haunted house claims that 80% of customers are scared speechless. if this is true, what is the probability that 60% or less out of a group of 50 customers will be scared speechless?
Answer: The probability of 60% or less scared speechless out of a group of 50 customers (i.e. 30 customers) is 0.0932% or 0.000932.
Step-by-step explanation: Given problem meets all criteria for application of a binomial distribution with the probability of success; p=0.8 or 80% (which makes probability of failure; q=0.2 or 20%) and the total number of trials; n=50.
Let probability of 30 or less people scared (30 is 60% of 50 people) be P(x≤30), where x≤30 encapsulates all possibilities from 0 to 30 people scared speechless.
Then, by binomial distribution,
P(x≤30) =r=030nCr*pr*q(n-r)
Now we can substitute given values and find the desired probability,
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)(50-r)
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)-r*(0.2)50
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*(0.8)r*(0.2)-r
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*4r
The first value on the right hand side of equation is a very small number while the summation factor on second is a relatively larger number.
P(x≤30) = 0.000932
Thus, there is a 0.09% chance of 30 or less people scared speechless out of a group of 50.
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Impact Sports is having a sale this week. A portable basketball hoop has an original price of $159. It is on sale for 35% off the original price. What is the sale price of the basketball hoop?
Answer: 150*40/100=60
60+150=210.
Step-by-step explanation:
How much of a radioactive kind of promethium will be left after 265 hours if the half-life is 53
hours and you start with 15,488 grams?
grams
some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 234 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions be?
The length, breadth and height will be 78 cm, 78cm, 78cm each.
let consider the length = l
breadth = b
height = h
we are provided that
l + b + h = 234cm .......(1)
Also we have to maximize the volume , provided length is equal to breadth
∴ eqn (1) becomes
2b + h = 234
h = 234 - 2b
also ,
volume(v) = lbh
v = b²(234 - 2b)
v = b²234 - 2b³
now to maximize the volume we take the first derivative of the volume wrt 'b' and place it equal to zero. ( lagrange method )
i.e. d( v)/db = 0
∴ 468b - 6b² = 0
6b² - 468b = 0
6b( b - 78 ) = 0
∴ b = 78 cm
now as length = breadth
l = b = 78 cm
also putting this value in eqn (1)
h = 234 - 2b
h = 78 cm
So , the dimensions will be equal and will be 78cm , 78cm, 78cm each .
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A polynomial can be factored by grouping if:
W/4+12.5-7z
What which term has a coefficient?
Answer:
The coefficient is 7 and the term that has it.
A nautilus shell is made up of many chambers, each chamber roughly 5% larger than the
previous one. Assuming a nautilus creates a new chamber every year, and this year's
chamber has a volume of 880 microliters, how large will the chamber created in 8 years be?
If necessary, round your answer to the nearest tenth.
microliters
Answer:
1300.2 µL
Step-by-step explanation:
You want to know the volume of a nautilus chamber in 8 years if it is 880 µL in year 0 and increases at 5% per year.
Growth factorThe growth factor is ...
growth factor = 1 + growth rate
growth factor = 1 + 0.05 = 1.05
Exponential functionSince the problem statement is about volume, we assume the growth factor applies to the chamber volume. If it applies to the linear dimension of the chamber, then the growth factor for volume will be 1.05³.
The function describing the chamber volume can be written as ...
volume = (initial volume)(growth factor)^years
In 8 years, the chamber volume will be ...
volume = (880µL)(1.05^8) ≈ 1300.2 µL
The chamber created in 8 years is expected to be 1300.2 µL.
__
Additional comment
If the 5% growth rate is the rate of growth of the linear dimensions of a chamber, then its volume will grow at the rate of 1.05³ per year. In 8 years, the volume will be about 2838.1 µL.
(The wording "5% larger" is ambiguous here.)
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a local hamburger shop sold a combined total of 483 hamburgers and cheeseburgers on Wednesday there were 67 fewer cheeseburgers sold in hamburgers how many hamburgers were sold on Wednesday
In linear equation, 275 hamburgers were sold on Wednesday .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.Let x = the number of hamburgers sold
Let x - 67 = the number of cheeseburgers sold
x + x - 67 = 483
2x = 483 + 67
2x = 550
x = 275
x = 275 hamburgers
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Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead?
Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.
Given statement;
Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.
→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.
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Paula bought p packages of 5 rolls of tape. Then, she bought 4 individual rolls of tape. Which expression shows how many total rolls of tape Paula bought? SOLVE AND I'll MARK BRAINST AHAHAHHA
Y=5p+3
Y equals the total amount of tape rolls
P is for the number of packages there are.
Hope this helped!
:)
Answer:
Y=5p+4
Y equals the total amount of tape rolls
P is for the amount of packages there are
Step-by-step explanation:
The Lopez family uses up a
1
2
-gallon jug of milk every 3 days. At what rate do they drink milk?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
gallons per day
Answer: 4
Step-by-step explanation: in average, they drink 12/3 = 4 milk jugs per day.
[tex]log_{2} (\sqrt[3]{16})[/tex]
The value of the given expression will be 4 / 3.
What is a logarithmic expression?An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given logarithmic expression is log₂(∛16). The expression will be solved as below,
[tex]E = log_2\sqrt[3]{16}\\E = log_2(2^{\frac{4}{3})\\E = \dfrac{4}{3}log_22\\E = \dfrac{4}{3}[/tex]
Therefore, the solution of the expression will be equal to 4 / 3.
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How would you solve (5x - 7) (4x + 1)?
Using distributive property, the simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.
In the given question we have to solve the given expression.
The given expression is (5x - 7)(4x + 1).
To simplify the given expression we use the distributive property.
According to property; a(b+c) = ab+bc
Now simplifying the expression;
(5x - 7)(4x + 1)=5x(4x + 1) - 7(4x + 1)
(5x - 7)(4x + 1)=(5x*4x + 5x*1) - (7*4x + 7*1)
(5x - 7)(4x + 1)=(20x^2 + 5x) - (28x + 7)
Simplifying
(5x - 7)(4x + 1)=20x^2+5x -28x - 7
(5x - 7)(4x + 1)=20x^2- 23x - 7
The simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.
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ella has 1/3 as many trading cards as kip. Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. write an expression for the total number of cards the groups has. writ an expression for the total number of cards?
If Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. The expression for the total number of cards the groups has is: 1/3 ⋅9+(3+0.5⋅18)+18.
How to determine the expression?Given data:
Number of trading cards = 1/3
Adira number of cards = 23 more than 50%
Kip number of cards = 18 cards
Now let formulate an expression and then make use of the formulated expression to find the number of cards
Hence,
Number of cards = 1/3 ⋅9+(3+0.5⋅18)+18
Number of cards = 1/3 ⋅9+(3+9)+18
Number of cards = 1/3 ⋅9+(12)+18
Number of cards =3 + 12+18
Number of cards = 33 cards
Therefore the expression is : 1/3 ⋅9+(3+0.5⋅18)+18.
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Which of these equations represent functions where is x is the input and y is the output ?
The equations represent functions where x is the input and y is the output are y = 2x and x+y = 2
The 1st equation is x =2
Since there is no component of y and the value of x is fixed. So this is not the desired option.
The 2nd equation is y = 2
Since there is no component of x, and the value of y is fixed. So this is not the desired option.
The 3rd equation is y = 2x
In this equation, x is the input and y is the output. For different values of x, we will have different values of y.
Thus, this is the desired option.
The 4th equation is x =2y
In this equation, y is the input and x is the output. For different values of y, we will have different values of x.
The 5th equation is x+y = 2
So, x + y = 2
y = 2 - x
In this equation, x is the input and y is the output. For different values of x, we will have different values of y.
Thus, this is the desired option.
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The actual marked price of the stove is $2400. This includes a sales tax of 12.5%. Calculate the selling price of the stove if no sales tax is included.
Answer: $2100
Step-by-step explanation:
Since 12.5 percent of 2400 is 300, Just subtract 300 from 2400 to get the selling price with no sales tax. And the final answer is $2100.
PLEASE HELP WHAT IS THE SLOPE OF THIS LINE
Answer: A. [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
To find the slope we must find the change in y over the change in x. Δ
Or rise over run. [tex]\frac{rise}{run}[/tex]
In the graph, we have two "good" points. (0, -6) and (4,0)
So for Δy 0 to -6 = -6
So -6 goes on top [tex]\frac{-6}{x}[/tex]
Now Δx goes from 4 to 0 so the change would be -4.
So now it becomes [tex]\frac{-6}{-4}[/tex]
Since there are two negatives it becomes a positive. [tex]\frac{6}{4}[/tex] Or simply put, [tex]\frac{3}{2}[/tex]