Answer:
vertex = (2, - 10 )
Step-by-step explanation:
given a quadratic function in standard form
ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
x² - 4x - 6 ← is in standard form
with a = 1 and b = - 4 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{-4}{2}[/tex] = 2
substitute x = 2 into the function for corresponding y- coordinate
2² - 4(2) - 6
= 4 - 8 - 6
= - 10
vertex = (2, - 10 )
the missing variable y varies directly with x. If y=75 when x=25, find x when y=25
The answer is value of x when y=25 are 8.33.
The missing variable y varies directly with x, which means that y = kx, where k is a constant.
We can use this equation to find the value of k and then use it to find the value of x when y=25.
First, let's find the value of k:
y = kx
75 = k*25
k = 75/25
k = 3
Now that we know the value of k, we can use it to find the value of x when y=25:
y = kx
25 = 3x
x = 25/3
x = 8.33
Therefore, the value of x when y=25 is 8.33.
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What are the other three angle measures if ∠1 has a measure of 45°?
The measures of the other three angles are: ∠2 = ∠3 = 67.5° and ∠4 = 0°.
Define an angle?An angle is a geometric figure formed by two rays that share the same endpoint called vertex. It is measured in degrees, radians or gradians and is usually denoted by the vertex letter in its center, with the endpoints labeled by two other letters or points.
Since the sum of the measures of the angles in a triangle is 180 degrees, we can use this information to find the measures of the other three angles.
If ∠1 has a measure of 45°, then we know that the sum of the measures of ∠2 and ∠3 is 135° (180° - 45°).
If the triangle is isosceles, then ∠2 and ∠3 have the same measure. Therefore, we can divide 135° by 2 to get:
∠2 = ∠3 = 67.5°
Finally, we can use the fact that the angles of a triangle add up to 180° to find the measure of ∠4:
∠4 = 180° - 45° - 67.5° - 67.5° = 0°
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what is the simplest form of the radical expression sqrt2+sqrt3/sqrt2-sqrt3
please show work
Answer:
-5 - 2sqrt6
Step-by-step explanation:
To simplify (sqrt2+sqrt3)/(sqrt2-sqrt3), we can rationalize the denominator, which involves multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of sqrt2-sqrt3 is sqrt2+sqrt3, so we can multiply both the numerator and denominator by sqrt2+sqrt3:
(sqrt2+sqrt3)/(sqrt2-sqrt3) * (sqrt2+sqrt3)/(sqrt2+sqrt3) = ((sqrt2+sqrt3)(sqrt2+sqrt3))/((sqrt2-sqrt3)(sqrt2+sqrt3))
Expanding the numerator and simplifying, we get:
(sqrt2+sqrt3)^2 / (sqrt2^2 - sqrt3^2)
= (2 + 2sqrt2sqrt3 + 3) / (2 - 3)
= (5 + 2sqrt6) / (-1)
= -5 - 2sqrt6
Therefore, (sqrt2+sqrt3)/(sqrt2-sqrt3) simplifies to -5 - 2sqrt6.
The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).
We have,
To simplify the expression (√2 + √3) / (√2 - √3), we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
The conjugate of (√2 - √3) is (√2 + √3).
Multiplying the numerator and denominator by (√2 + √3), we get:
[(√2 + √3) x (√2 + √3)] / [(√2 - √3) x (√2 + √3)]
Expanding both the numerator and denominator:
[(√2 + √3)(√2 + √3)] / [√2 x √2 - √2 x √3 + √3 x √2 - √3 x √3]
Simplifying:
[2 + 2√2√3 + 3] / [2 - 3]
Combining like terms:
[5 + 2√6] / [-1]
Since the denominator is -1, we can multiply both the numerator and denominator by -1 to simplify further:
[5 + 2√6] / 1
Finally, we have:
(5 + 2√6)
Therefore,
The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).
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Please help!!!!!! Math is hard and I don't know how to find scale factor using fractions.
50 points: You are given rectangle ABCD with point E as the intersection of the diagonals. If the measure of angle AEB=13x and the measure of angle ECD=3x-5, find x.
Answer:
Since the diagonals of a rectangle bisect each other, we know that angle AEB is congruent to angle CED. Therefore, we can set the expressions for these angles equal to each other and solve for x:
13x = 3x - 5
Subtracting 3x from both sides gives:
10x = -5
Dividing both sides by 10 gives:
x = -0.5
Therefore, the value of x that satisfies the equation is x = -0.5. Note that this means that angle measures are negative, which doesn't make sense in this context. It's possible that there is an error in the problem statement or that some additional information is needed to determine a valid value of x.
Answer: bob
Step-by-step explanation:
Evaluate each of the following, using special products of algebraic expressions: 52^(2)=52
The answer is 49
To evaluate the given expression, we will use the special product formula for the square of a binomial:
(a+b)^(2)=a^(2)+2ab+b^(2)
In this case, we have:
52^(2)=(5+2)^(2)=5^(2)+2(5)(2)+2^(2)=25+20+4=49
Therefore, the answer is:
52^(2)=49
So, using the special products of algebraic expressions, we can evaluate the given expression to be 49.
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Find A - B Enter the element in row 3 column 2. A=[[-1,0,2],[4,1,-1],[2,0,1]],B=[[2,1,0],[-1,0,2],[4,-3,-1]]
A - B is 5.
To find A - B, subtract each corresponding element in B from the corresponding element in A.
For the element in row 3, column 2, it is 2 - (-3) = 5.
Therefore,
the element in row 3, column 2 of A - B is 5.
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jimmy has 28 candy bars from Halloween. he eats 7, and his mom takes 9, how much does jimmy have left?
Answer:
jimmy has 12 candy bars left
Step-by-step explanation:
28-7-9=12
Answer:
Jimmy has 12 candy bars.
Step-by-step explanation:
Subtract 28 from 7.
=21
21-9=12.
Jimmy has 12 candy bars left if he eats 7 and his mom takes 9.
Riya is applying mulch to her garden. She applies it at a rate of
250
,
000
cm
3
250,000 cm
3
250, comma, 000, start text, space, c, m, end text, cubed of mulch for every
m
2
Riya applying mulch in m³/ m² at the rate of 0.25 m³
To calculate the rate of mulch application in m³/m², we need to convert the given rate of 250,000 cm³/m² into m³/m². We can do this by using the conversion factor: 1 m³ = 1,000,000 cm³.
So, 250,000 cm³/m² can be converted to m³/m² as follows:
250,000 cm³/m² × (1 m³/1,000,000 cm³) = 0.25 m³/m²
This means that for every square meter of garden space, Riya is applying 0.25 m³ of mulch.
It's important to note that rate refers to the amount of mulch applied per unit of garden space. In this case, the unit is m². By expressing the rate in m³/m², we're specifying the volume of mulch applied per unit of area.
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Complete Question:
Riya is applying mulch to her garden. She applies it at a rate of 250,000 cm³ of mulch for every m² of garden space. At what rate is Riya applying mulch in m³/ m²?
Find the tangent of ZS.
T
68
60
Simplify your answer and write it
S
U
The tangent of <S is 8/15
What is Trigonometry?Trigonometry is a discipline of mathematics dealing with specific angle functions and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).
Given:
ST = 68
UT = 60
so, SU = √ST² - UT²
= √68² - 60²
= √4624 - 3600
= √1024
= 32
So, Tangent of <S = P/ B
tan S = SU / UT
tan S = 32 / 60
tan S = 8/15
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hey you can you help and if your don’t know then don’t answer pls thx
The cοrrect statement is the segment GC is transversal tο segments KG and QC.
What is a transversal line?A line that crοsses twο οr mοre lines in the same plane at different lοcatiοns is said tο be transversal. Accοrding tο the fundamental prοpοrtiοnality theοrem (alsο knοwn as Thales' theοrem), if three οr mοre parallel lines crοss acrοss twο transversals, they prοpοrtiοnally cut οff the transversals.
We have given the statements are:
A). KG QC.
B) KG and QC intersect at a right angle.
C) KQ || GC.
D) GC is transversal tο KG and QC.
Therefοre, here in the figure, segment GC intersects segments KG and QC in the same plane at different lοcatiοns.
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Dalton flies a plane against a headwind for 4661 miles. The return trip with the wind took 20 hours less time. If the wind speed is 10 mph, how fast does Dalton fly the plane when there is no wind?
Dalton flies the plane at a speed of 251 mph when there is no wind.
To solve this proble,m we can use the formula for distance, which is distance = speed × time. We can also use the fact that the speed of the plane with the wind is the sum of the speed of the plane without the wind and the wind speed, and the speed of the plane against the wind is the difference between the speed of the plane without the wind and the wind speed.
Let x be the speed of the plane without the wind, and t be the time it takes for the return trip with the wind. Then we can write the following equations:
4661 = (x - 10) × (t + 20) (1) for the trip against the wind
4661 = (x + 10) × t (2) for the return trip with the wind
Multiplying equation (2) by (t + 20) and subtracting equation (1) from it, we get:
4661t + 93220 = 4661t + 20x^2 + 200x - 200x - 200
20x^2 = 93220
x^2 = 4661
x = 251
Therefore, Dalton flies the plane at a speed of 251 mph when there is no wind.
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Determine whether the following trinomial is a perfect square trinomial. 16a^(2)-40ab+25b^(2)
Yes, the given trinomial is a perfect square trinomial.
To determine whether a trinomial is a perfect square trinomial, we can use the formula:
(a-b)^(2) = a^(2) - 2ab + b^(2)
In this case, we can compare the given trinomial with the formula and see if it matches.
16a^(2)-40ab+25b^(2) = (4a)^(2) - 2(4a)(5b) + (5b)^(2)
This matches the formula, so we can conclude that the given trinomial is a perfect square trinomial.
Another way to determine whether a trinomial is a perfect square trinomial is to factor it and see if it can be written as a binomial squared.
In this case, we can factor the given trinomial as follows:
16a^(2)-40ab+25b^(2) = (4a-5b)(4a-5b) = (4a-5b)^(2)
Since the trinomial can be written as a binomial squared, we can conclude that it is a perfect square trinomial.
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The Book Barn is having a sale. All hardback
books are 20% off, and all paperbacks are
10% off. Suppose you buy four paperbacks
that originally cost $9 each and two
hardbacks that originally cost $20. What
percent of the total have you saved? Round to
the nearest percent.
We have saved approximately 15% of the total cost.
What is the process to calculate the percentage saved in a sale?
When items are on sale, they are usually offered at a discounted price. The percentage saved is a measure of the amount that a buyer has saved on the original price of the item. The process to calculate the percentage saved in a sale involves determining the original price, the discounted price, and then using a formula to find the percentage saved.
The formula for the percentage saved is:
Percentage saved = (Amount saved / Original price) x 100%
Calculation of the total amount saved and the percentage saved :
For the paperbacks, the original price is $9 each and we bought four of them, so the total original price is:
$9/book × 4 books = $36
With a 10% discount, the discounted price of each paperback is:
$9/book × 0.10 = $0.90 discount
$9/book - $0.90 discount = $8.10 discounted price
So, the total discounted price for the four paperbacks is:
$8.10/book × 4 books = $32.40
Therefore, we saved:
$36 - $32.40 = $3.60
For the hardbacks, the original price is $20 each and we bought two of them, so the total original price is:
$20/book × 2 books = $40
With a 20% discount, the discounted price of each hardback is:
$20/book × 0.20 = $4 discount
$20/book - $4 discount = $16 discounted price
So, the total discounted price for the two hardbacks is:
$16/book × 2 books = $32
Therefore, we saved:
$40 - $32 = $8
The total original price of all the books is:
$36 + $40 = $76
The total discounted price of all the books is:
$32.40 + $32 = $64.40
Therefore, we saved:
$76 - $64.40 = $11.60
Plugging in the values , we get:
percentage saved = ($11.60 / $76) × 100%
percentage saved ≈ 15%
Therefore, we have saved approximately 15% of the total cost.
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what is 92199+20923+29290+83292+2819+99279+38471+378141
92199+20923+29290+83292+2819+99279+38471+378141
= 744414
Determine the solution to each linear system by using the substitution method
2x+3y=34
y=5x
(2, 10)
(2, -6)
(-3, 5)
(4, 3)
put y = 5x in equation 1 :
2x + 3 (5x) = 34
2x + 15x = 34
17x = 34
x = 2
Now put x = 2 in any of the two equation to get
y :
y = 5x
y = 5 × 2
y = 10
THE 14 BUSINESSES IN A SHOPPING CENTER ELETRICITY BILL. THIS MONT THEY USED 2,996 KILOWATT HOURS OF ELECRICITY HOW MANY KILOWATT HOURS MUST EACH BUSINESSES PAY FOR
Therefore , the solution of the given problem of fraction comes out to be 214 kilowatt hours of electricity for the month.
A fraction is what?Any combination of equal portions or fractions can be combined to represent a whole. In standard English, the quantity of a certain size is defined as a fraction. 8, 3/4. Wholes also include fractions. The ratio of numerator to ratio is a mathematical symbol for integers. All of these number fractions are simple fractions. There is a fraction inside of the fraction but rather remainder in a difficult fraction. because the values, numerators, and numerators of real fractions vary
Here,
We must divide the total amount of electricity used by the number of businesses in order to calculate how many kilowatt hours each business is responsible for paying for:
=> 14, 14 businesses x 2,996 kilowatt hours = 214 kilowatt hours per company
As a result, each company is required to pay for roughly 214 kilowatt hours of energy per month.
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Meg surveyed some students at her school about their favorite professional sports. Of the students surveyed, 2 said football was their favorite sport, while 8 of the students had other favorite sports. What is the experimental probability that the next student Meg talks to will pick football?
So, the experimental probability that the next student Meg talks will pick football is 0.2 or 20%.
What is Probability?Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. It is used to quantify the uncertainty or risk associated with a particular event or situation.
Given by the question.
The experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials or observations. In this case, the event is selecting football as the favorite sport, and the trials are the number of students Meg talks to.
Based on the information given in the problem, Meg surveyed a total of 10 students (2 who selected football and 8 who selected other sports). Therefore, the probability of the next student she talks to selecting football as their favorite sport is:
P (selecting football) = number of students who selected football / total number of students surveyed
P (selecting football) = 2 / 10
P (selecting football) = 0.2
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What number must be added to both sides of the equation x2 + 12x = 13 so
that the method of completing the square can be used to solve the roots?
A. 64
B. 49
C. 36
D. 25
The number that must be added to both sides of the equation x2 + 12x = 13 so that the method of completing the square can be used to solve the roots is 36. The correct answer is C. 36.
To complete the square, we need to add the square of half the coefficient of the x term to both sides of the equation. In this case, the coefficient of the x term is 12, so half of it is 6. The square of 6 is 36, so we need to add 36 to both sides of the equation. Hence the correct option is C) 36.
The equation then becomes:
x2 + 12x + 36 = 13 + 36
Simplifying the right side of the equation gives us:
x2 + 12x + 36 = 49
Now we can factor the left side of the equation into a perfect square:
(x + 6)2 = 49
From here, we can use the square root property to solve for x:
x + 6 = ±√49
Solving for x gives us:
x = -6 ± 7
So the roots of the equation are x = 1 and x = -13.
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The temperature in Madadeni one morning was -5°C at 08:00 and increased by 2°C every hour until 12:00. What will the temperature be at 11:30
Answer:
Step-by-step explanation:
20c is the answer
Answer:
ans is 14
Step-by-step explanation:
i do not think is this by i know is 14
What is 98% of 349
so can you tell me what it is tell me once ya found out
Answer:
342.02
Step-by-step explanation:
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
1. Would
you prefer to work for a large corporation or small business whose
owners you know? Give at least two reasons for your
choice.
Large corporations often offer better benefits and opportunities for career advancement.
Large corporations often have more resources available for employee training and development.
I would prefer to work for a large corporation for two reasons. First, large corporations often offer better benefits and opportunities for career advancement. Second, large corporations often have more resources available for employee training and development. While working for a small business whose owners I know may provide a more personal and intimate work environment, I believe that the benefits of working for a large corporation outweigh the potential drawbacks.
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Jake uses the formula d=rt
d
=
r
t
to find d, the distance when he rides his bike for t hours at a rate, r, of 15 miles per hour. What is the value of d when t=3
t
=
3
?
The value of d when t=3 is 45 miles. This means that Jake has covered a distance of 45 miles in 3 hours riding his bike at a rate of 15 miles per hour.
How to calculate distance?Distance is a measure of the length between two points. To calculate distance, we need to know the coordinates of the two points. We can use the Pythagorean theorem to calculate the distance.
The formula d=rt is used to calculate the distance traveled when a rate, r, and time, t, are given. In this case, Jake is riding his bike at a rate of 15 miles per hour for 3 hours. To calculate the distance, d, traveled, we can substitute the given values into the formula.
d = 15 * 3
d = 45
Therefore, the value of d when t=3 is 45 miles. This means that Jake has traveled 45 miles in 3 hours riding his bike at a rate of 15 miles per hour. This formula can also be used to calculate the time, t, when the rate, r, and distance, d, are known. To find the time, t, simply divide the distance, d, by the rate, r.
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a x=6 angle measure is 36
b x=9 angle measure is 36
c x=6 angle measure is 54
d x=9 angle measure is 54
Answer:
A
Step-by-step explanation:
6x° and 54° form the angle of 90° , that is
6x + 54 = 90 ( subtract 54 from both sides )
6x = 36 ( divide both sides by 6 )
x = 6
then
6x = 6 × 6 = 36°
A savings account balance is compounded annually. If the interest rate is 2% per year and the current balance is $1,932. 00, what will the balance be 7 years from now?
As per the concept of compound interest, the balance after 7 years will be $2,200.24.
In your case, you have a savings account balance that is compounded annually. The interest rate is 2% per year, which means that at the end of each year, the balance will increase by 2% of the previous year's balance. So, if your current balance is $1,932.00, the balance after one year will be:
Balance after one year = $1,932.00 + 2% of $1,932.00
= $1,932.00 + $38.64
= $1,970.64
After two years, the balance will be:
Balance after two years = $1,970.64 + 2% of $1,970.64
= $1,970.64 + $39.41
= $2,010.05
The formula for compound interest is:
A = P(1 + r/n)ⁿˣ
where:
A = the final amount
P = the principal amount (initial balance)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
ˣ = the number of years
In your case, the interest is compounded annually, so n = 1. The annual interest rate is 2%, which is equivalent to 0.02 as a decimal. The initial balance is $1,932.00, and you want to know the balance after 7 years, so t = 7. Using these values in the formula, we get:
A = $1,932.00(1 + 0.02/1)¹ˣ⁷
= $1,932.00(1.02)⁷
= $2,200.24
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Determine whether the complex number is a solution of the equation. 5-i;x^(2)-10x+26=0
That the complex number 5-i is indeed a solution of the equation [tex]x^2-10x+26=0[/tex].
To determine whether the complex number 5-i is a solution of the equation [tex]x^2-10x+26=0[/tex], we can substitute the value of x with the complex number and see if the equation holds true.
Substituting [tex]x = 5-i[/tex] into the equation:
[tex](5-i)^2 - 10(5-i) + 26 = 0[/tex]
Expanding the squared term:
[tex]25 - 10i + i^2 - 50 + 10i + 26 = 0[/tex]
Simplifying the equation:
[tex]25 - 50 + 26 + i^2 = 0[/tex]
Since[tex]i^2 = -1[/tex], we can substitute that value into the equation:
[tex]25 - 50 + 26 - 1 = 0[/tex]
Simplifying further:
[tex]0 = 0[/tex]
Since the equation holds true, we can conclude that the complex number 5-i is indeed a solution of the equation [tex]x^2-10x+26=0[/tex].
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rewrite as an equation . A number divided by 6 equals 3
The statement, a number divided by 6 equals 3, is written as an equation is x/6 = 3
What are algebraic expressions?Algebraic expressions are simply defined as expressions that are made up of terms, coefficients, variables, constants and factors.
These expressions are also identified with arithmetic operations, such as;
AdditionMultiplicationDivisionBracketParenthesesSubtractionFrom the information given, we have that;
A number divided by 6 equals 3
Now, let's say the number be x
This is represented as an equation thus;
x/6 = 3
Hence, the equation is x/6 = 3
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"Find the x-values (if any) at which f is not
continuous. Which of the discontinuities are removable? (Use
k as an arbitrary integer.)
f(x) = [[x − 2]]
Please explain how to solve I'm stuck."
Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.
The function f(x) = [[x − 2]] is discontinuous at any value of x that is two units away from an integer. That means it is discontinuous at x = k - 2 and x = k + 2, where k is any arbitrary integer.
The discontinuities at x = k - 2 and x = k + 2 are both removable. That is because the discontinuities occur when the left- and right-hand limits of the function are not equal, and the limits can be made equal by redefining the value of the function at the point of discontinuity.
To solve the problem, set the left- and right-hand limits equal to each other and solve for x.
Left-hand limit: lim x→k-2 f(x) = lim x→k-2 [[x − 2]] = [[k - 2 - 2]] = [[k - 4]]
Right-hand limit: lim x→k+2 f(x) = lim x→k+2 [[x − 2]] = [[k + 2 - 2]] = [[k]]
Equating the two limits, we have [[k - 4]] = [[k]]. Solving for x, we get x = k - 2 and x = k + 2.
Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.
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Consider the following polynomial. 6x^(2)-12xy+18xy^(2) Find the GCF of 6x^(2),-12xy, and 18xy^(2). Factor the polynomial by factoring out the GCF.
The expression when factored by the GCF is 6x(x - 2y + 3y^2)
How to factor the expression by the GCFFrom the question, we have the following parameters that can be used in our computation:
6x^2 - 12xy + 18xy^2
The greatest common factor (GCF) of 6x^2, -12xy, and 18xy^2 is 6x, which is the largest number that divides each term evenly.
To factor the polynomial by factoring out the GCF, we can divide each term by 6x to get:
6x^2/6x = x
-12xy/6x = -2y
18xy^2/6x = 3y^2
So the polynomial can be factored as:
6x^2 - 12xy + 18xy^2 = 6x(x - 2y + 3y^2)
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Point R is the midponit of XY. If XR = 5x+2 cm and XY= 14x+1 cm , what is the ength of RY in cm ?
Using midpoints, The length of RY is (9x - 1)/2 cm.
What is the midpoint?
A midpoint is a point that is exactly halfway between two other points. In geometry, the midpoint of a line segment is the point on that line segment that is equidistant from both endpoints.
For example, in a line segment AB, the midpoint M is the point on AB that is equidistant from A and B. In other words, the distance from A to M is the same as the distance from M to B. The midpoint M is located at the exact center of line segment AB, and it divides the segment into two equal parts.
The midpoint can also be thought of as the average of the x-coordinates and y-coordinates of the endpoints. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint has coordinates:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Since R is the midpoint of XY, we know that RX = RY.
We are given that XR = 5x+2 cm and XY = 14x+1 cm.
Thus, RX + RY = XY
Substituting RX = RY, we get:
RY + RY = 14x + 1 - (5x + 2)
Simplifying the right side, we get:
RY + RY = 9x - 1
2RY = 9x - 1
RY = (9x - 1)/2
Therefore, the length of RY in cm is (9x - 1)/2.
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