Answer:
{3 - √2; 3 + √2}Step-by-step explanation:
GivenQuadratic function y = x² - 6x + 7Solving by completing the square x² - 6x + 7 = 0 Givenx² - 2*3x + 3² - 3² + 7 = 0 Add, subtract 3²(x - 3)² - 9 + 7 = 0 Simplify(x - 3)² - 2 = 0 Difference of squares(x - 3 + √2)(x - 3 - √2) = 0 Factorizex - 3 + √2 = 0 and x - 3 - √2 = 0 Solve each rootx = 3 - √2 and x = 3 + √2 AnswerAnswer:
[tex]x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]y = x^2 - 6x+7[/tex]
To complete the square, begin by adding and subtracting the square of half the coefficient of the term in x:
[tex]\implies y = x^2 - 6x+\left(\dfrac{-6}{2}\right)^2-\left(\dfrac{-6}{2}\right)^2+7[/tex]
[tex]\implies y = x^2 - 6x+\left(-3\right)^2-\left(-3\right)^2+7[/tex]
[tex]\implies y = x^2 - 6x+9-9+7[/tex]
Factor the perfect square trinomial:
[tex]\implies y=(x-3)^2-9+7[/tex]
[tex]\implies y=(x-3)^2-2[/tex]
To solve the quadratic, set it to zero and solve for x:
[tex]\implies (x-3)^2-2=0[/tex]
[tex]\implies (x-3)^2-2+2=0+2[/tex]
[tex]\implies (x-3)^2=2[/tex]
[tex]\implies \sqrt{(x-3)^2}=\sqrt{2}[/tex]
[tex]\implies x-3= \pm\sqrt{2}[/tex]
[tex]\implies x-3+3= 3\pm\sqrt{2}[/tex]
[tex]\implies x= 3\pm\sqrt{2}[/tex]
Therefore, the solution to the given quadratic equation is:
[tex]x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}[/tex]
Name three points collinear points on plane P.
Answer:
ABC
Step-by-step explanation:
Think of a plane as a piece of paper that went on forever in all directions. Which points would be on the paper? Three examples would be points A, B and C.
Find all values of m for which the equation has two real solutions.
3x² + 7x - (m + 1) = 0
Answer:
m > - 5 1/12----------------------
Given is the quadratic equation.
A quadratic equation has two real solutions if the discriminant is positive.
Set inequality and solve for m:D = b² - 4ac, where a = 3, b = 7, c = - (m + 1)D = 7² + 4*3*(m + 1) 7² + 4*3*(m + 1) > 049 + 12m + 12 > 012m + 61 > 012m > - 61m > - 61/12 m > - 5 1/12(a) The school sells pens for $1.50 and notebooks for $2.50. The equation 1.50x+2.50y=601.50x+2.50y=60 describes the number of pens, x, and notebooks, y, that you can but for $60. Part A: Find the x- and y-intercepts. Tell what they represent. x-int: What does the x-intercept represent in the context of the problem? (b) BoldItalicUnderlineAlign Align Left Align Center Align Right Align Justify Increase IndentIncrease IndentSpecial Characters $$ 0 Words (c) y-int: What does the y-intercept represent in the context of the problem?
The x-intercept of the equation, 1.50 x + 2.50y = 60, is x = 40
The y-intercept of the equation, 1.50 x + 2.50y = 60, is y = 24
Determining the x-intercept and y-intercept of an equationFrom the question, we are to determine the x-intercept and y-intercept of the given equation.
The given equation is
1.50 x + 2.50y = 60
The x-intercept is the point where y = 0
and
The y-intercept is the point where x = 0
Determining the x-intercept
1.50x + 2.50y = 60
Put y = 0
1.50x + 2.50(0) = 60
1.50x + 0 = 60
1.50x = 60
x = 60/1.50
x = 40
The x-intercept is x = 40
Determining the y-intercept
1.50x + 2.50y = 60
Put x = 0
1.50(0) + 2.50y = 60
0 + 2.50y = 60
2.50y = 60
y = 60/2.50
y = 24
Hence, the y-intercept is y = 24
The x-intercept represent the number of pens that could be bought for $60 when one is not buying any notebooks.
The y-intercept represent the number of notebooks that could be bought for $60 when one is not buying any pens
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13 tenths + 8tenths + 32 hundredths
In the decimal for, the value of 13 tenths + 8 tenths + 32 hundredths is 2.42
Decimal
Decimal means a number that has a decimal point followed by digits that show the fractional part.
Given,
Here we have the expression 13 tenths + 8 tenths + 32 hundredths
Now, we need to find the value of this expression.
We know that, Tenths means we have one digit after the decimal point and the hundredths have two digits after the decimal point.
So, in the given expression 13 tenths is written as 1.3
And the 8 tenths is written as 0.8
And finally, the 32 hundredths is written as 0.32
Now, we have to add these numbers, then we get,
=> 1.3 + 0.8 + 0.32
=> 2.42
Therefore, the value of 13 tenths + 8 tenths + 32 hundredths is 2.42
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explain what a,h, and k do to transform the parent absolute function y=|x| to the function y= a|x|…
The a ,h and k values affect the parent absolute function ,by altering the the size , causing horizontal and vertical movements respectively.
How do the a , h and k values affect the function?a )a values
a values affect the size of the graphed parent absolute function and they have a scalar factor.When a is greater than 1 , we have a vertical stretch (Taller appearance )and a horizontal compression (Thinner appearance).When a is between 0 and 1 , we have a vertical compression( Shorter appearance) and a horizontal stretch ( wider appearance).b ) h values
h values cause left or right movement of the graph, which is known as the horizontal shift or translation.When h is negative, the graph moves right.When h is positive , the graph moves left.c ) k values
k values cause up and down movement ,which is known as the vertical shift or translation.When k is negative, the graph moves down.When k is positive , the graph moves up.To learn more about parent absolute function, refer:
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Logan's family drinks a total of 12 gallons of milk every 6 weeks.
a. How many gallons of milk does the family drink per week?
Answer: 2 gallons
Step-by-step explanation:
If they drink 12 gallons of milk every 6 weeks, to find how many gallons they drink per week, you need to divide the number of gallons by the time.
So,
12/6 = 2 gallons
Thus, they drink 2 gallons per week.
{Question 19} Please help! Need by tonight! Thanks
Answer: 3, -1/3x - 1
Step-by-step explanation:
Answer:
y= -1/3x-1
Step-by-step explanation:
Find the slope of the line by plugging two points into the slope formula
[tex]\frac{y_{2}-y_{1} }{x_2-x_1}[/tex]
[tex]\frac{-1-0}{0-(-3)}[/tex]
m= -1/3
Find the y-intercept by seeing where the graph intersects the y-axis
b = -1
y=mx+b
y= -1/3x-1
A plant is already 11.25 meters tall, and it will grow 15 centimeters every month. The plant's height, H (in meters), after x months is given by the following.
The plant's height after x months is 11.25 + 15x.
How to calculate the plants height?From the information illustrated, the plant is already 11.25 meters tall, and it will grow 15 centimeters every month.
In this case, let the plant's height be H (in meters)
Let the number of months be x.
The plant height will be:
= 11.25 + (15 × x)
= 11.25 + 15x
This is the height.
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Complete question
A plant is already 11.25 meters tall, and it will grow 15 centimeters every month. When is the plant's height, H (in meters), after x months?
What is the prime factorization of 144?
OA) 4 x 36
OB) 22x6
OC) 24x3²
OD) 12x12
The Prime factorization of 144 is ([tex]2^4[/tex]) x (3²).´
What is a factor?
A factor is a number/expression that divides another number/expression, leaves zero remainder . In other words, if multiplying two numbers/expressions gives us a product, then the numbers/expressions we are multiplying are factors of the product because they are divisible by the product.
Factors of 144:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Prime factorization:
144 = 2 x 2 x 2 x 2 x 3 x 3, which can also be written as
144 = ([tex]2^4[/tex]) x (3²).´
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find the value of b/a if a+1/b-1=5/1 and a-1/b+1=1/1
Answer:
1/2
Step-by-step explanation:
You want the value of b/a when (a+1)/(b-1)=5/1 and (a-1)/(b+1)=1/1.
SolutionThe latter equation tells you ...
a -1 = b +1
b = a -2
Then the first equation tells you ...
a +1 = 5(b -1)
a +1 = 5(a -2 -1) substitute for b
a +1 = 5a -15 . . . . eliminate parentheses
16 = 4a . . . . . . . . add 15 -a
4 = a . . . . . . . . . divide by 4
b = a -2 = 4 -2 = 2 . . . . find the value of b
b/a = 2/4 . . . . . . . . . . find the desired ratio
b/a = 1/2
10. Sean promotes certain brands on his social media page for compensation. His monthly profit can be modeled using
the quadratic function p(x) = -0.00425x² +7z-1000, where p(x) is the amount of profit earned over
number of days. The graph of the function is shown. Use the graph to find the zeros of the function and interpret
them in context.
Answer:
The zeros are (158.017, 0) and (1489.042, 0)
The profit earned in 158.017 days and 1489.042 days is equal to 0. This means that Sean only earns money (makes a profit) when the amount of days he promotes a brand is greater than 158.017 but less than 1489.042 days.
Write the given expression as an algebraic expression in x. tan(2 sin^-1(x))
The trigonometric ratio tan(2 sin⁻¹(x)) is expressed as 2sec(x)
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
In the question given, we have;
tan(2 sin⁻¹(x))
tan = sin / cos
sin/cos(2 * 1/sin x)
The expression becomes 2/cosx or 2cos⁻¹(x)
But cos⁻¹ = sec
tan(2 sin⁻¹(x)) = 2sec(x)
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Given 1000 with 100<0, and 100<0 for all x in the interval with 1-1 and 1-03, the left, right, traperoidal, and midpoint rule approximations were used to estimate
08421 and 0.8895, and the same number of subintervals were used in each case. Match the rule to its estimate
Match
left endpoint
right endpoint
midpoint
trapezoidal
actual area
Definition
A) 0.7915
08410
0.8895
DJ08421
0.5405
The estimates were 0.7915, 0.8405, 08410
Answer:
Step-by-step explanation;
a teacher gives out 12 boxes of crayons for students to use for an art project. each student is given 1/4 of a box of crayons. how many students are given crayons
Answer:
The answer is 48
Step-by-step explanation:
First you have to get the number or crayons ehich is 12 then you can multiply it by the denominator in 1/4 so 12x4=48
SAFSADFASDSADSA HELPPPPPPP
Answer:
y = - [tex]\frac{10}{3}[/tex] x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{10}[/tex] x - 8 ← is in slope- intercept form
with slope m = [tex]\frac{3}{10}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{10} }[/tex] = - [tex]\frac{10}{3}[/tex] , then
y = - [tex]\frac{10}{3}[/tex] x + c ← is the partial equation of line h
to find c substitute (3, - 9 ) into the partial equation
- 9 = - 10 + c ⇒ c = - 9 + 10 = 1
y = - [tex]\frac{10}{3}[/tex] x + 1 ← equation of line h
see picture for question
The percentage error is 0.67%
What is Linear approximation ?
A linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.
The formula is
L(x) = f(a) + f'(a) (x - a)
Given,
y = sin(2x)
Δx = 0.1 at x = 0
y'(x) = dy/dx = 2 cos 2x
As, x = 0
y'(0) = 2 cos 0
we know, cos 0 = 1
y'(0) = 2
Δy = y'(x) * Δx
= y'(0) * Δx
= 2 * 0.1
Δy = 0.2 (Approx value)
Exact value of Δy = sin(2 * 0.1) - sin 0
= sin(0.2) - 0
= 0.19867
% error = [ (Exact value - Approx value) / Exact value ] * 100
= [ (0.2 - 0.19867) / 0.19867 ] * 100
= 0.66945 or 0.67%
Hence, the percentage error is 0.67%
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State what additional information is required in order to know that the triangles are congruentfor the reason given.
44 POINTS !
The additional information is required in order to know that the triangle are congruent is, GW ≅ WX.
What is congruent triangles?
If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.
We have to show that the the triangles ΔVWX and ΔEWG are congruent by using the AAS (angle, angle, side) criteria.
From the given reasons,
∠V ≅ ∠E
∠VWX ≅ ∠EWG
From this the AA criteria is satisfied.
We want sides of the triangle are congruent.
From the figure, GW ≅ WX
Therefore, by AAS the two triangles ΔVWX and ΔEWG are congruent.
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An isosceles triangle with congruent sides of length
49.3 inches has a perimeter of 121.7 inches Find the
length of the base.
The length of the base is 22.1
An isosceles triangle with congruent sides of length 49.3 inches has a perimeter of 121.7 inches
An triangle is said to be isosceles if two sides of the trainagle have same length.
The two sides of this triangle is congurent that is they have same length = 49.3
perimeter of a triangle is the summation of all three sides.
Perimeter = length + base + length
121.7 = 49.3 + base + 49.3
base = 121.7 - 99.6
base = 22.1
Therefore, the length of the base is 22.1
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Juan and Malia make money by walking neighborhood pets. During a conversation about their work, they realize that they are both walking the same total number of pets, even though Juan walks pets in groups of 9 and Malia walks pets in groups of 3. What is the smallest total number of pets each could be walking?
The smallest total number of pets each could be walking is 2.
Given:
Juan and Malia make money by walking neighborhood pets. During a conversation about their work, they realize that they are both walking the same total number of pets, even though Juan walks pets in groups of 9 and Malia walks pets in groups of 3.
from the given statements:
Juan pets groups = 9
Malia pets groups = 3
so they both can same total number of pets is maximum 3.
so minimum number for each is 1.
Total = 1+1
= 2
Therefore The smallest total number of pets each could be walking is 2.
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What is consumidores terciarios?
Hello..!
¿What is consumidores terciarios?
They are the ones that feed on carnivores and their parasites.
An example:
When we see a dead bird, a week goes by and then there are only the bones, since as it says they feed on dead birds, that is, they eat everything without leaving anything, whether they are birds, cows or people.
Organisms that eat secondary consumers are called tertiary consumers and are carnivores that eat carnivores, such as eagles or large fish.
Producers, or autotrophs, make their own organic molecules. Consumers, or heterotrophs, obtain organic molecules by eating other organisms.
A food chain is a linear sequence of organisms through which nutrients and energy pass from one organism to another through consumption.
-1.5x+3(-0.3x-1) simplify the linear expression
Answer: -2.4x-3
Step-by-step explanation:
Wha is the y intercept of the line given by the equation below y=4x - 6
Use the graph below to answer the following question: graph of parabola going through 0, 4, 2, negative 4, and 4, 4 What is the average rate of change from x = 0 to x = 4? Group of answer choices 0 1 4 8
The rate of change of the parabola on the interval [0, 4] is 0.
How to get the average rate of change?For any function f(x), we define the rate of change on an interval [a, b] as:
R = (f(b) - f(a))/(b - a)
Here we want to get the rate of change on the interval [0, 4], and we know that the graph has the points:
(0, 4), (2, -4), (4, 4)
Then:
f(0) = 4
f(4) = 4
Replacing that in the rate of change formula we get:
R = ( f(4) - f(0))/(4 - 0)
R = (4 - 4)/4 = 0
The rate of change on that interval is 0.
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Find the y intercept
Because there is a slope of 0, the graph is a horizontal line.
Plug into the slope-intercept form: y=mx+b
Where
m = slope & b = y-intercept
m=0
y=-1
So,
y=(0)x+(-1)
therefore your final answer is:
y=-1
in a class of 50 student 35 are girls what is the probability that a student selected at random is a boy
Which of the following is equal to 6.6÷2
Answer:B
Step-by-step explanation:
A is equal to 6.3'.
none of the others are equal to 3.3 exactly.
If 7 is lessened by 2 of a number, the result is the same as 3 subtracting of the number from 10. Write an equation to represent this situation. Use 'x' as the variable.
An equation to represent this situation x is 37/12. The components of a whole or group of items are represented by fractions.
What is fraction?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. In a complex fraction, a fraction can be found in either the numerator or the denominator. A suitable fraction has a numerator that is less than its denominator.Any number of equal parts is represented by a fraction, which also represents a portion of a whole.Here 7 is lessoned by 2 of a number.
Consider x be the number.
we get 2x - 7
the result is same as 3 subtracting of the number from 10.
therefore, we get 10 ( 3 - x )
from this two equations we get,
⇒ 2x - 7 = 10 ( 3 - x )
⇒ 2x - 7 = 30 - 10x
Simplifying we get,
⇒ -37 = - 12x
⇒ x = 37/12
Therefore, An equation to represent this situation x is 37/12.
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3. A grocer has 60kg of potatoes. In one day, he sells 50% of the
potatoes. What mass of potatoes does he sell?
Answer: 30kg
Step-by-step explanation:
100% = 60kg
50% = 100% /2
60kg(100%)/2 = 30kg(50%)
Answer:
Step-by-step explanation:
Proportion:
60 kg - 100%
X kg - 50%
X = 60·50% / 100% = 30 kg
Find the final balance earned in an account with $845 invested at 4% annual simple
interest for 18 months.
The final balance is $895.7.
What is simple interest?
Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Interest = principal ×rate× time
Given, principal = $845
rate = 4%
time = 18 months = 3/2 years.
After substituting the values, we get
Interest = 845(4)(3/2)/100
= 50.7
Final balance = initial balance + interest
Therefore,
Final balance = 845 + 50.7
= $895.7
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What is 4x6x26x376x466 equal to
