To write the given quadratic equation, y = (x + 1)^2 - 4, in factored form, we can start by expanding the equation using the square of a binomial:
y = (x + 1)(x + 1) - 4
y = (x^2 + 2x + 1) - 4
y = x^2 + 2x + 1 - 4
y = x^2 + 2x - 3
Now, to find the zeros of the equation, we set y = 0 and solve for x:
x^2 + 2x - 3 = 0 To factor this quadratic equation, we need to find two numbers whose product is -3 and whose sum is 2. The numbers that satisfy this condition are 3 and -1:
(x + 3)(x - 1) = 0
Now, setting each factor equal to zero, we can find the values of x:
x + 3 = 0 => x = -3
x - 1 = 0 => x = 1
Therefore, the factored form of the equation y = (x + 1)^2 - 4 is (x + 3)(x - 1) = 0, and the zeros of the equation are x = -3 and x = 1.
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Problem #2
Andy is supplying his class members with colored paper tomorrow. He has 4 times
as many orange papers as blue papers. There are a total of 37 students in his
class. How many blue papers and orange papers did Andy bring to class?
27
Answer:
what is 478/6 +7*25+78+123-568
he following items are available for use in a pan balance to measure the
weight of a large rock. Which items will yield the greatest level of accuracy,
mat is, approximate the true weight of the rock with the least error? You may
nly use items of the kind selected, and may not mix items.
OA. Bricks
OB. Potatoes
O C. Pennies
OD. Sand
Note: Your teacher will review your response to ensure you receive proper credit for your answer.
18. Does the relation in the table represent direct variation, inverse variation, or neither? If it is
direct or inverse variation, write an equation to represent the relation. Explain your answer.
x
5
2
10
1
y
Its not direct variation or inverse
15
|2|3
20
1
2
an equation to represent the relation is,
⇒ y = 10/x
We know that,
Proportion is extensively explained. Proportion is mostly discussed using ratios and fractions. A fraction is written as a/b, while a ratio is represented as a:b, and a proportion states that two ratios are equal. In this case, a and b can be any two integers. The ratio and proportion are important foundations for understanding numerous ideas in mathematics and science.
Since, The relation represents an inverse variation because as the values of x is increasing the values of y is decreasing.
Hence, We can formulate;
y = k/x
Plug y = 5, x = 2;
5 = k/2
Solve for k;
k = 5 x 2
k = 10
Thus, The required equation is y = 10/x
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The complete question is :
does the relation in the table represent direct variation, inverse variation, or neither? if it is direct or inverse variation, write an equation to represent the situation. Explain your answer
x 5, 10, 15, 20
Y 2, 1, 2/3, 1/2
Can someone help me solve question number 14? I've tried to solve it and got 3426 while the answers in the book say it's 2,6. Can someone pls explain why it's wrong?
Answer:
x = 2, 6
Step-by-step explanation:
differentiate f(x) using the power rule
f'(a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and f'( constant) = 0
given
f(x) = x³ - 12x² + 6x - 8
f'(x) = 3x² - 24x + 6
equate f'(x) to - 30
3x² - 24x + 6 = - 30 ( add 30 to both sides )
3x² - 24x + 36 = 0 ( divide through by 3 )
x² - 8x + 12 = 0 ← in standard form
(x - 2)(x - 6) = 0 ← in factored form
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 6 = 0 ⇒ x = 6
solution is x = 2, 6
the difference between the roots of the equation 3x^2-5x+q=0 is 1/3. find q
Answer:
q = 2
Step-by-step explanation:
You want to find q such that the difference between the two roots of 3x²-5x+q is 1/3.
Sum of rootsIn quadratic ax²+bx+c, the sum of the roots is (-b/a). For roots p and s, this tells us ...
p + s = -(-5)/3 = 5/3
The problem statement tells us the difference is ...
p - s = 1/3
Adding these two equations gives ...
2p = (5+1)/3 = 2
p = 1 . . . . . . . . . . . . . divide by 2
s = p -1/3 = 2/3 . . . . find the smaller root
Product of rootsThe product of the two roots is (c/a) = (q/3):
ps = (1)(2/3) = q/3
q = 2 . . . . . multiply by 3
The value of q is 2.
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Multiply –8m(–6m – 7).
–14m2 – 15m.
48m2 + 56m.
–14m – 15.
48m + 56
Answer:
48m^2 + 56m
Step-by-step explanation:
-8m(-6m - 7)
Use the distributive property. (-8m*-6m & -8m*-7)
-8m*-6m = 48m^2
-8m*-7 = 56m
48m^2 + 56m
let g(x)=xe^-x+be^-x where b is a positive constant
The possible value of positive constant b for an absolute maximum value of function g(x), [tex]g(x) = xe^{-x} + be^{-x} [/tex] at x = [tex] \frac{2}{3} [/tex] is equals to the [tex] \frac{1}{3} [/tex].
An absolute maximum point is a point where the function acquires its largest possible value. To drive the max or min absolute value, we have to substitute the derivative value of function equals to zero. We have a function, [tex]g(x) = xe^{-x} + be^{-x} [/tex], where b is positive constant. We have to determine the possible value of b for absolute maximum of g at x= 2/3.
Differentiating the function g(x) with respect to x
=> [tex]g'(x) = - x e^{-x} + e^{-x} - be^{-x} [/tex]
[tex]= (1 - x - b )e^{-x}[/tex]
[tex]= \frac{1 - x - b }{e^{x}}[/tex]
For obtaining absolute maximum value put, g'(x) = 0
=> [tex]\frac{1 - x - b }{e^{x}} = 0[/tex]
Substitute x = 2/3, in above expression,
[tex] \frac{1 - \frac{2}{3} - b }{e^{\frac{2}{3}}} = 0[/tex]
=> [tex]1 - \frac{2}{3} - b = 0[/tex]
=> [tex] b = \frac{1}{3}[/tex]
Hence, the required value of b is [tex] \frac{1}{3} [/tex].
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Complete question:
Let g(x)=xe^(-x)+be^(-1), where b is a positive constant. For what positive value of b does g have an absolute maximum at x=2/3 .Justify your answer.
please helppp question 13
The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes
U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.
Solution:
When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, y reflection )'s across the x-axis is (x, -y).
the point (x , y)→ (x , -y).
In the question given 4 coordinates,
U(1 , -3)
V(4 , -3)
T(1 , -4)
W(5 , -4)
the reflection across x-axis
U(1 , -3) →U' (1, 3)
V(4 , -3) → V'(4 , 3)
T(1 , -4) → T'(1 , 4)
W(5 , -4) → W'(5 , 4)
so after the reflection across the x axis the coordinates of the vertices becomes ,
U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)
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complete question:
Find the coordinates of the vertices of each figure after the given transformation
3) reflection across the x-axis
Enter Question Text
A U'(1,3),V'(4,3), W'(5,4),T'(1,4)
B U'(3,1),V'(3,4,), W'(4,5),T'(4,1)
D U'(-1,3),V'(-4,3), W'(-5,4),T'(-1,4)
(3)(4-3);W(Sp-4)T(4)
U
T
X
frankie bought a new computer. he made an initial payment of to the store, and he will pay each month until the computer is paid off. which equation represents the relationship between , the number of monthly payments frankie has made, and , the total amount that frankie has paid the store?
We need to use some basic algebraic equations. Let's assume that the initial payment made by Frankie was x, and the total amount he has to pay for the computer is y. Also, let's assume that Frankie will make n monthly payments.
Now, we know that Frankie has already paid x, and he has to pay y-x more. Since he will pay this amount in n monthly installments, we can represent the monthly installment as (y-x)/n.
So, the equation that represents the relationship between n and y can be written as:
y = x + n*(y-x)/n
Simplifying this equation, we get:
y = x + y-x
y = y
This means that the equation is true for any value of n and y, as long as x is a valid initial payment amount. Therefore, the equation that represents the relationship between n and y is:
y = x + n*(y-x)/n
The equation we derived above is a simple but important concept in mathematics and finance. It shows us that we can calculate the total amount we need to pay for something by multiplying the monthly installment by the number of payments and adding the initial payment to it. This concept is used in many financial transactions, such as car loans, mortgages, and credit card payments.
Moreover, this equation also helps us to plan our finances and manage our budget effectively. We can use it to calculate how much we need to save every month to reach our financial goals, or to compare different payment options and choose the one that suits us best.
In conclusion, the equation that represents the relationship between the number of monthly payments and the total amount paid is an essential tool for anyone who wants to make wise financial decisions. By understanding this equation, we can save money, avoid debt, and achieve our financial goals more easily.
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a recent study found that 30% of all opioid prescriptions are missing a documented medical justification for use. a hospital administrator wonders if a smaller proportion of patients at her hospital are missing a medical justification for their opioid prescriptions. suppose the hospital administrator conducts a review of a random sample of 25 opioid-prescribed patient files at her hospital and 5 of those files are missing a documented medical justification for the opioid prescription. a statistician carries out a significance test of the null hypothesis versus the alternative hypothesis. what is the value of the standardized test statistic for this significance test (rounded to the nearest tenth)?
The value of the standardized test statistic for this significance test is -1.3
For the standardized test statistic for this significance test, we need to compare the sample proportion to the hypothesized population proportion.
The null hypothesis (H₀)
H₀: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is equal to 30%.
The alternative hypothesis (H₁)
H₁: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is different from 30%.
The sample size is 25 and 5 of those files are missing a medical,
The sample proportion (p) can be calculated as
(p) hat = (Number of files missing justification) / (Total number of files)
(p) hat = 5 / 25
(p) hat = 0.2
The standard error is given by
SE = √[((p) hat × (1 - (p) hat)) / n]
SE = √[(0.2 × (1 - 0.2)) / 25] = √(0.16 / 25) = 0.08
For the standardized test statistic, we use the formula:
z = ((p) hat - p₀) / SE
where p₀ is the hypothesized population proportion.
p₀ = 30% = 0.3
z = (0.2 - 0.3) / 0.08 = -0.1 / 0.08 = -1.25 = -1.3
The value of the standardized test statistic for this significance test is approximately -1.3
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The function models the cost in dollars, c(x) = 72(1.04)X, of 1 ounce of a certain chemical used in
a laboratory. & represents the number of years since 2010.
Part a: By What percer tage does the cost of the chemical increase per year?
An ounce of the chemical cost in 2018 is $98.54.
Given:
The function c(x) = 72 ⋅ (1.04)ˣ models the cost in dollars, c, of 1 ounce of a certain chemical used in a laboratory.
Exponential function, involves exponents. an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.
In mathematics, an exponential function is a function of form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
x represents the number of years since 2010.
An ounce of the chemical cost in 2018 is,
= 72 × (1.04)⁸
= $98.54
Therefore, the cost is $98.54.
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A spirit banner for a pep rally has the shape of a triangle. The base of the banner
is 8 feet and the height is 6 feet. Find the area of the banner.
The area of the banner is 24 square feet.
We have,
Since the spirit spanner is in the form of a triangle.
We can use the area of a triangle to calculate the area of the banner.
The area of a triangle is given by the formula:
Area = (1/2) x base x height
Substituting the given values.
Area = (1/2) x 8 feet x 6 feet
Area = 24 square feet
Therefore,
The area of the banner is 24 square feet.
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Transform the equation x-3y=15 to express it in slope-intercept form
Answer:
y = (1/3)x - 5
Step-by-step explanation:
x - 3y = 15
x - 15 = 3y
3y = x -15
y = (1/3)x - 5
Hello !
Answer:
[tex]\boxed{y=\frac{1}{3}x-5}[/tex]
Step-by-step explanation:
An equation in slope-intercept form is [tex]y=mx+b[/tex].
Let's isolate y in our equation :
[tex]x-3y=15\\-3y=-x+15\\3y=x-15\\y=\frac{1}{3}x-5[/tex]
Our equation is in the form [tex]y=mx+b[/tex] with [tex]m=\frac{1}{3}[/tex] and [tex]b=-5[/tex].
Have a nice day
Which property does the following equation illustrate?
3 + (5+6) = (5+6) + 3
A) Distributive Property
B) Associative property of addition
C) inverse property of addition
D) commutative property of addition
Answer:
The Correct answer is C
communicative property
Please answer quickly I need it asap ill give brainiest!!!
The correct matching of the items of math in the columns is:
a number that has more factors than just 1 and itself - composite numbersmallest number that all the given denominators divide into evenly - least common denominatordata grouped using non-numerical criteria - categorical datafractions with the same numerical value; fractions that are equal to each other - equivalent fractionsa line segment that goes through the center of the circle to connect two points on the circle - diametera plane figure that is one side of a solid figure - facethe measurement of the space inside a plane figure - areaa shape or object that has been transformed - imagehaving the same exact size and shape - congruentWhat are some terms in math ?A composite number is a number that possesses additional factors besides 1 and its own value. The smallest number that can be divided evenly by all the denominators given is known as the least common denominator.
Non-numeric criteria are used to group data in categorical data. Fractions that have identical numerical values are referred to as equivalent fractions. When a line segment passes through the center of a circle and joins two points on its circumference, it is known as the circle's diameter.
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Find tan 0, where 0 is the angle shown.
Give an exact value, not a decimal approximation.
Answer:
4/3
Step-by-step explanation:
Tan(x)=Opposite/adjacent
We need to find the opposite side.
We can use the Pythagorean theorem to help us:
5^2=3^2+x^2
25=9+x^2
16=x^2
x=4
4 is the measure of the opposite side
The adjacent side has measure of 3
Tan(theta)= 4/3
*theta is the weird 0 with a bar thingy at the angle, its some letter in the greek alphabet that denotes an unknown angle in geometry
kyra coverted some australian dollars to pounds she received £67.50
kyra coverted some australian dollars to pounds she received £67.50
Kyra will receive $125 USD when she converts £67.50 to USD.
Given that, Kyra wants to convert some Australian dollars to pounds she received £67.50.
Exchange rate =
Exchange rates are typically quoted as currency pairs, where one currency is the base currency and the other is the counter currency.
To convert £67.50 into USD using the exchange rate of $1 = £0.54, you can multiply the amount in pounds by the exchange rate.
Here's the calculation:
£67.50 x $1/£0.54 = $125
Therefore, Kyra will receive $125 USD when she converts £67.50 to USD.
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Which research method involves collecting data repeatedly on the same person as he or she ages?
a. correlational
b. longitudinal
c. cross-sectional
d. cross-sequential
The research method that involves collecting data repeatedly on the same person as he or she ages is longitudinal.
Longitudinal research involves studying the same group of individuals over an extended period of time, typically years or even decades. This type of research allows researchers to collect data on changes in behavior, attitudes, or health outcomes over time, and can provide valuable information on the effects of age, development, or life events on these outcomes. Longitudinal research can be especially useful in studying developmental processes, as it allows researchers to track changes in individuals as they grow and develop.
However, longitudinal studies can also be expensive and time-consuming, as researchers must track and collect data from the same group of individuals over many years, and there is a risk of attrition or drop-out over time.
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find y. the number on the leg is 9.
The length of y of the triangle is y = 9√2 units
Given data ,
Let the Triangle be ΔABC , such that
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
On simplifying , we get
From the trigonometric relations , we get
sin θ = opposite / hypotenuse
sin 45° = 9 / y
Multiply by y on both sides , we get
y = 9 / sin 45°
On simplifying , we get
y = 9√2 units
Hence , the length is y = 9√2 units
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please help me, I don't understand this...
Answer:
Down below
Step-by-step explanation:
2)(-6,3)
where h=-6&k=3
(x-h)²+(y-k)²=R²
(x-(-3)²+(y-6)²=11²
(x+3)²+(y²-6²)=11²
3)(x-3)²+(y+4)²=25
(x-h)²+(y-k)²=R²
h=3
k=-4
(
C(3,-4)
4)(x+1)²+(y-6)²=361
(x-h)²+(y-k)²=R²
R²=361
√R²=√361
R=19
If the height of a rectangular prism is cut in half, which of the following statements would be true?
The volume would be divided by 1/2
1/2 would be added to the volume.
The volume would be multiplied by 1/2
1/2 would be subtracted from the volume.
the actual car is 8 feet long and 4 feet wide. grace wants her model to be 12 inches in length. which proportion could be used to find the width of her model?
The proportion that could be used to find the width of Grace's model car is 1/2 = Model width / 12 inches.
To find the width of Grace's model car, a proportion can be set up using the lengths of the actual car and the desired model:
Proportion: Actual width / Actual length = Model width / Model length
Given values:
Actual length = 8 feet
Actual width = 4 feet
Model length = 12 inches
Converting the units:
12 inches = 1 foot (since 1 foot = 12 inches)
Substituting the values into the proportion:
4 feet / 8 feet = Model width / 12 inches
Simplifying the proportion:
1/2 = Model width / 12 inches
To find the model width, cross-multiply and solve for the unknown:
Model width = (1/2) * 12 inches = 6 inches
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John plans to hike a distance of 21 miles. If he
only travels 1 3/4 miles per hour, how long will it
take him to finish his journey?
Answer:
12 hours
Step-by-step explanation:
1 3/4=1.75
21÷1.75=12
HALP FAST FOR BRAINIEST TO FIRST PERSON
Hello !
Minimum = 6 (the smallest value)
First quartile = 8 (25% of 7 = 1,75 => 2nd value)
Median = 15 (the value in the middle)
Third quartil = 23 (75% of 7 = 5,25 => 6th value)
Maximum = 31 (the greatest value)
It's C
Answer:
C. The 3.rd Answer :)
100 points pls hurry and mark brainly
Each pail of plaster covers 95 square feet of ceiling. How many pails of
plaster would you need to buy to cover the ceiling of a room with walls 15
feet long?
Answer:
2.02
Explanation:
Each pail of plaster covers 97 Square feet of ceiling
The ceiling of the room is 14 ft long
= 14×14
= 196
Therefore the pail of plaster that will be needed to cover the rooms can be calculated as follows
= 196/97
= 2.02
Recruitment Costs
Interview Costs
Job Posting fee
1st year fee
Real Estate Fee
Shipping fee
Family travel cost
A. $43,600
C. $47,600
$2,000 per person
$1,000
10%
6% of sales price
$4,000
$400 per person
A company hires
an employee with a family
of 5 for a salary of $130,000
over 2 other candidates. If
the employee sold her
house for $360,000, what is
the total recruiting
expense?
B. $46,000
D. $45,600
The total recruiting expense is $91,200 which includes Recruitment Cost, Interview Costs, Job Posting fee, Family travel cost and more
The total recruiting expense would be:
Recruitment Costs: $43,600
Interview Costs: $2,000 x 3
= $6,000
Job Posting fee: $1,000
1st year fee: 10% x $130,000
= $13,000
Real Estate Fee: 6% x $360,000
= $21,600
Shipping fee: $4,000
Family travel cost: $400 x 5
= $2,000
Total = $43,600 + $6,000 + $1,000 + $13,000 + $21,600 + $4,000 + $2,000
= $91,200
Hence, the total recruiting expense is $91,200
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help help helpppppppppppppppppppppppp
Answer:
B, D, F
Step-by-step explanation:
You want the diagrams that show lines through the center of enlargement, where the smaller triangle is enlarged to form the larger triangle.
EnlargementEach point in an enlarged figure is moved toward or away from the center of enlargement along a line through that center. That is, corresponding vertices of a triangle and its enlargement will lie on a line through the enlargement center.
The diagrams of interest are those that show lines through corresponding vertices of the triangles.
Diagrams B, D, F show lines through the center of enlargement.
__
Additional comment
The center of enlargement is marked in the attachment by a blue dot. Enlargement is by a factor of 3.
Points are moved away if the scale factor is greater than 1; toward the center of enlargement for a scale factor less than 1.
<95141404393>
Help me please??????
The mean absolute deviation of the given data set, 94, 86, 95, 99, 88, 90, is 4
The values differ from the mean by an average of 4.
Calculating the mean absolute deviationFrom the question, we are to calculate the mean absolute deviation of the given data
The given data
94, 86, 95, 99, 88, 90
To calculate the mean absolute deviation of the given data,
First, we will calculate the mean
Mean = (94 + 86 + 95 + 99 + 88 + 90) / 6
Mean = 552 / 6
Mean = 92
Now,
We will determine the absolute value of the difference between each data and the mean
|94 - 92| = 2
|86 - 92| = 6
|95 - 92| = 3
|99 - 92| = 7
|88 - 92| = 4
|90 - 92| = 2
Now,
We will determine the mean of these absolute differences
Mean absolute deviation = (2 + 6 + 3 + 7 + 4 + 2) / 6
Mean absolute deviation = 4
Hence,
The mean absolute deviation is 4
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Graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7).
The steps to graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7) are given below.
To graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7), we need to apply the following steps:
Plot the original figure on a coordinate plane.
Draw a point at the center of dilation (2, −7).
Draw lines connecting the vertices of the original figure to the center of dilation.
Extend each line from the center of dilation by a factor of 3.
Plot the new vertices where the extended lines intersect.
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Find the value of x in the figure.
