The equation of parabola is [tex]y=1/4x^{2}+x/2-4\\\\[/tex].
What is parabola?A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape. A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.
Given:
The equation of parabola in vertex form is
[tex]y=a(x-h)^{2} +k[/tex]
Being vertex here
h=-2
k=-5
According to given question we have
∴
Equation of parabola in vertex form is
[tex]y=a(x+2)^{2} -5[/tex]
. The parabola passes through point (4,4) So the point (4,4) will satisfy the equation .
[tex]4=a(4+2)^{2} -5\\\\4=a*36-5\\\\9=a*36\\\\a=9/36\\\\a=1/4[/tex]
Hence the equation of parabola is
[tex]y=1/4(x+2)^{2} -5\\\\y=1/4(x^{2} +4+2x)-5\\\\y=1/4x^{2} +1+x/2-5\\\\y=1/4x^{2}+x/2-4\\\\[/tex]
Therefore, the equation of parabola is [tex]y=1/4x^{2}+x/2-4\\\\[/tex].
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the equation of parabola is missing
Tanya is 28 years older than Marcus. In 6 years, Tanya will be three times as old as Marcus. How old is Tanya now?
Answer: 36 years old
Step-by-step explanation:
T=Tanya. M=Marcus
T=M+28
T+6=3(M+6)
T+6-6=3(M+6)-6
T=3(M+6)-6
M+28=3(M+6)-6
M+34=3M+18
34=2M+18
2M=16
M=8
T=M+28
T=8+28
T=36 years old
The current age of Tanya is equivalent to 45 years old.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Tanya is 28 years older than Marcus. In 6 years, Tanya will be three times as old as Marcus
Assume the initial age of Tanya is {x} years and that of Marcus is {y} years old. So, we can write -
x = y + 28 ....... Eq[1]
x + 6 = 3y ........ Eq[2]
Using Eq[1] in Eq[2], we get -
y + 28 + 6 = 3y
y + 34 = 3y
2y = 34
y = 17
Than, we can write [x] as -
x = 17 + 28
x = 45
Therefore, the current age of Tanya is equivalent to 45 years old.
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Solve equation.
6 t-18=30
To solve the equation, add 18 to both sides, then divide by 6. The solution is t = 8.
A linear equation is an equation of which the highest degree of its variables is 1.
Steps to solve linear equations:
Simplify the expressions. If there are parentheses, remove them by multiplying the corresponding terms.Combine the same terms.Isolate the variable on one side by using subtraction of addition.Use division or multiplication to find the value of the variable.Recall that if we subtract or add the same number to both sides of an equation, it does not change the equality.
The given problem:
Solve 6t-18 = 30
The variable is t. Isolate the variable by adding 18 to both sides:
6t -18 +18 = 30 +18
6t = 48
Divide both sides by 6
6t : 6 = 48 : 6
t = 8 (solved)
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Complete the statement to describe the expression ab + cdab+cda, b, plus, c, d.
The expression consists of
terms, and each term contains
factors
The expression contains FOUR terms, each with TWO factors.
What are expressions?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one mathematical operation. This math operation can be addition, subtraction, multiplication, or division. An expression has the following structure: The expression is (Number/variable, Math Operator, Number/variable).Expression information: In algebra, the word term defined the single numbers(10), variables(y), and the product of the two (10y).
In the following expression: ab+cd+ef+ghThere are four terms:
abcdefghA factor is a component of a product.
For the given equation, we will have four terms, each with two factors.Therefore, the expression contains FOUR terms, each with TWO factors.
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The correct question is given below:
Complete the statement to describe the expression ab+cd+ef+ghab+cd+ef+gha, b, plus, c, d, plus, e, f, plus, g, h. The expression consists of ----- terms, and each term contains ----- factors. Please fill in the blanks!
Perform the following operation
and express the answer in
scientific notation.
4.3x1027.0×10²
[?]×10]
Answer:
[tex]4.4161 \times 10 ^{2} [/tex]
[tex]4.3 \times 1027 \times 10 { \\ \\ }^{2} [/tex]
[tex]4416.1 \times 10^{2} [/tex]
[tex]4.4161 \times 10 ^{2} [/tex]
if 1/3 of a gallon of paint covers 1/8 of a wall, how much paint is needed to cover the entire wall?
Answer:
8/3 or 2 2/3 gallons
Step-by-step explanation:
1/3 of gallon covers 1/8 of a wall, therefore, the amount of pain is needed to cover the entire wall is 1/3 x 8 = 8/3 or 2 2/3 gallons
A student was asked to evaluate an expression the students work is shown describe any errors and find the correct value of the expression explain your reasoning
30 is the correct value of the expression in linear equation .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.The error starts from here- 36-10 + 4
If we are doing addition or subtraction start from left
=36−10+4
=26+4
= 30
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this is very important... its for alegbra.. please help
Answer in decimal form = -0.2
Answer as a fraction = -1/5
=========================================================
Explanation:
The term "rate of change" is the same as "slope" for linear equations.
Use the slope formula to get the steps shown below.
[tex](x_1, y_1) = (-3, 3.6) \text{ and } (x_2, y_2) = (5, 2)\\\\m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{2-3.6}{5-(-3)}\\\\m = \frac{2-3.6}{5+3}\\\\m = \frac{-1.6}{8}\\\\m = \frac{-16}{80}\\\\m = -\frac{1}{5}\\\\m = -0.2\\\\[/tex]
The decimal value is exact without any rounding done to it.
A slope of -1/5 means we go down 1 unit and to the right 5 units.
slope = rise/run = -1/5
rise = -1 = go down 1
run = 5 = go to the right 5
What is the value of this expression?
40÷[24−4×(2+3)]
Answer:
10
Step-by-step explanation:
hope it helps
Answer:
10
Step-by-step explanation:
ya its right
Question is below
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The expression, evaluated to the simplest form is -4
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
(9² + 19)/(10² - 5³)
Simplifying the expression
(9² + 19)/(10² - 5³)
9² = 81
10² = 100
5³ = 125
Thus,
The expression becomes
(81 + 19)/(100 - 125)
= 100/-25
= -4
Hence, the expression, evaluated to the simplest form is -4
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The vertex of ∠A B C is located at the origin. Point A is located at (5,0) and Point C is located at (0,2). How can ∠A B C be classified?
A. acute
C. right
B. obtuse
D. scalene
As the angle is greater than 0° and less than 90°, then the angle ABC is acute. (Answer: A)
How to determine the features of an angle set on Cartesian plane
Herein we find the locations of the three vertices of the figure, of which we must determine the lengths of the two sides of the angle and determine the value of the angle by trigonometry:
BA = 5, BC = 2
θ = tan⁻¹ (BA / BC)
θ = tan⁻¹ (5 / 2)
θ ≈ 68.199°
As the angle is greater than 0° and less than 90°, then the angle ABC is acute. (Answer: A)
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HELP ASAP I DON'T UNDERSTAND
Answer:
-2
Step-by-step explanation:
I did the math, trust me. Just input -2 into the x's and solve.
Answer:
D. x = -6
( 3x-6² - 30x-6 - 72 = 0 )
Step-by-step explanation:
So first you work out:
3x² = ( 3 x -6²) = -108
Then work out 30x = ( 30 x -6 ) = -180
-108 - -180 => 72
Then just do 72 - 72 =
Which would be 0! ☆*:.｡.o(≧▽≦)o.｡.:*☆
hope this helped! xx
What value of x cannot be evaluated in the function r(x)?
I need help bc I got this one wrong twice lol.
The answer is H, B and C; And Z, K and R
Step-by-step explanation:
H, B and C; And Z, K and R form a straight line
Suppose 115.2 million households have at least one TV; if 82% have basic cable TV, how many households have basic
cable TV?
If 115.2 million million households have at least one TV and 82% have basic cable TV, then the number of households have basic cable TV is
94464000.
Given,
The total number of household have at least one TV = 115.2 millions
The percentage of household have basic cable TV = 82%
Then, the number of household have basic cable TV
=115200000×[tex]\frac{82}{100}[/tex]
=94464000
Hence, if 115.2 million million households have at least one TV and 82% have basic cable TV, then the number of households have basic cable TV is 94464000.
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Quadrilateral a has side lengths 2,3,5 and 6. quadrilateral b has single length 4,5,8 and 10 could one of the quadrilateral be a scale copy of the other
Quadrilateral b, is not a scaled copy of Quadrilateral a.
The side length of Quadrilateral a=2,3,5, and 6.
The side length of Quadrilateral b=4,5,8 and 10
Now comparing the Ratio of the Corresponding Sides of two quadrilaterals a and b
2/4 ≠ 5/8
3/5 ≠ 6/10
Since the ratio of corresponding opposite sides is not equal. The two Quadrilateral are Not Similar.
So, We can say that Quadrilateral b, is not a scaled copy of Quadrilateral a.
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Vijay's family is leaving for galactic gardens resort once his parents get home from work on friday. their house is 544 miles from the resort. they plan to stop and spend the night at a hotel after 3 hours of driving, then complete the rest of the trip on the second day. if their average speed is 64 miles per hour, how long will they drive on the second day?
The next day they will drive for about 5.5 hours
In given question, Vijay's house is 544 miles from the resort.
after 3 hours of driving, they stop and spend the night at a hotel and then complete the rest of the trip on the second day.
Let in 3 hours of driving, they completed the 'x' miles of distance from their home.
So, they complete the rest of the trip of 544 - x miles on the second day.
Let t be the time in hours they drive on the second day.
Their average speed is 64 miles per hour.
⇒ 64 = [x + (544 - x) ] / [3 + t]
⇒ 64 = 544 / 3 + t
⇒ 64(3 + t) = 544
⇒ 192 + 64t = 544
⇒ 64t = 352
⇒ t = 5.5 hours
Therefore, The next day they will drive for about 5.5 hours
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Solve the following inequality X-5 > 25
1. -20
Answer: x>10
Step-by-step explanation:
X-5 > 25-20
x-5+5>5+5
x>5+5
x>10
x+1= 10
Please step by step
Pre algebra
Answer: x=9
Step-by-step explanation:
x+1= 10
x-1+1=10-1
x=10-1
x=9
a car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet. (a) find the number of revolutions per minute the wheels are rotating.
The revolution per minutes of the wheels rotation is 912 rev/ min
How to determine the number of revolutionsGiven the parameters;
Velocity = 65 miles per hourDiameter = 2 feetConvert the velocity
[tex]v = 65mph = 65 mil/h - (1609m/mil0/(3600s/h)[/tex]
v = 29. 1 m/s
Let's find the circumference
Circumference = 2 π r
radius = diameter/ 2 = 0. 6096 meters/ 2 = 0. 30 meters
Circumference= 2 × 3. 142 × 0. 30 = 1. 915
Number of revolutions = 29. 1/ 1. 915 = 15.2 rev/ sec
Let's convert to rev/ min
= 15. 2 × 60
= 912 rev/ min
Thus, the revolution per minutes of the wheels rotation is 912 rev/ min
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is sally has 3 apples and max has 3 apples, how much is all together
Answer:
6
Step-by-step explanation:
You count with your fingers. 1,2,3,4,5,6! Congrats you got your answer.
which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays? fraction 30 over 6
Expression of the rate per minute at which air freshener dispenses sprays is equal to fraction 4 over 30.
As given,
The graph represents
x-axis: Time in minutes
y-axis: Number of sprays
Ordered pairs ( 30,4) ,(60, 8) ,( 90,12), and ( 120, 16)
Consider any two points ( 90,12) ,(120 , 16)
Expression of the rate per minute=( y₂ -y₁)/(x₂ -x₁)
=( 16 - 12)/(120 -90)
= 4/30
Therefore, expression of the rate per minute at which air freshener dispenses sprays is equal to fraction 4 over 30.
The complete question is :
The graph shows the number of sprays an automatic air freshener dispenses, y, in x minutes: A graph is shown. On the x-axis, the values are from 0 till 150 in increments of 30 for each grid line, and on the y-axis, the values are from 0 to 20 in increments of 4 for each grid line. The title of the graph on the x-axis is Time in minutes, and the title on the y-axis is Number of Sprays. A line is shown connecting ordered pairs 30, 4 and 60, 8 and 90, 12 and 120,16. The title for the graph is Dispense Rate. Which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays?
fraction 4 over 30
fraction 30 over 4
fraction 30 over 16
fraction 16 over 30
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PLEASE HELP URGENTLY
Answer:
A) (4,1)
B) (2,-1)
The length and width of a rectangle are consecutive odd integers. The perimeter of the rectangle is 80 centimeters. Find the length and width of the rectangle.
The length and width of the rectangle are 21cm and 19cm.
How to calculate the value?Let the dimensions be represented by x and x+2.
The perimeter of a rectangle is:
= 2(length + width)
= 2(x + x+2) = 80
2x + 2x + 4 = 80
4x + 4 = 80
4x = 80 - 4
4x = 76
Divide
x = 76/4
x = 19
Therefore, the second number will be:
= 19 + 2 = 21
The numbers are 19 and 21.
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Which is equivalent to 3^√8*?
Answer:
C (8 to the x/3 power)
a host served two pies, one apple and one cherry. dinner guests ate twenty-five percent of the apple pie and sixty percent of the cherry pie. in all, what fraction of the total pies remained? a 23/20 b 3/4 c 23/40 d 3/5
The fraction of the total pies remained is option (A) 23/20 is the correct answer.
In this question,
A host served two pies, one apple and one cherry.
Dinner guests ate twenty-five percent of the apple pie and sixty percent of the cherry pie.
Apple pie = 25%
∴ Remaining = 100% - 25%
⇒ 75%
⇒ Fraction of apple pie remained is 3/4
Cherry pie = 60%
∴ Remaining = 100% - 60%
⇒ 40%
⇒ Fraction of cherry pie remained is 2/5
Thus fraction of the total pies remained is
⇒ 3/4 + 2/5
⇒ (15+8) / 20
⇒ 23/20
Hence we can conclude that the fraction of the total pies remained is option (A) 23/20 is the correct answer.
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If you have a right triangle with 36 square units. what is the scaled value if you go 2-1 , 3-1?
Answer:
324, 900, 9
Step-by-step explanation:
When a shape has its size increased by a scale factor, the size of its lengths are multiplied by this scale factor, yet its area is actually multiplied by the scale factor squared. This is due to two lengths being multiplied to contribute to the area, not just one. If it was a volume, you would multiply by the scale factor cubed!
Onto the answer, just follow the advice above:
36 * 3^2 = 36 * 9 = 324 square inches,
36 * 5^2 = 36 * 25 = 900 square inches,
36 * 0.5^2 = 36 * 0.25 = 9 square inches.
Hope this helps :)
if you have a table of values like those above and you can find the value for f(n), how would you go about finding the value of f(n-1)? How do f(n) and f(n-1) compare to each other?
Answer:
spam question
Step-by-step explanation:
Answer:
If you have a table of values like those above and you can find the value for f(n) . you go about finding the value of f (n-1)
Step-by-step explanation:
Find the measures of two complementary angles if the measure of the larger angle is 2 less than 3 times the measure of the smaller angle. The measure of the smaller angle is
°,
and the measure of the larger angle is
°
The measure of the smaller angle is 23⁰ and the measure of the larger angle is 67⁰.
What are complementary angles?
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
So we can say that two angles are complementary if they sum up to 90 degrees.
From the given statement;
let the larger angle = ylet the smaller angle = xy = 3x - 2 -------(1)
y + x = 90 --------(2) (since they are complementary)
substitute for y in equation (2)
3x - 2 + x = 90
4x = 92
x = 92/4
x = 23 ⁰
y = 3(23) - 2
y = 67⁰
Thus, the measure of the smaller angle is 23⁰ and the measure of the larger angle is 67⁰.
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Which sum or difference is modeled by the algebra tiles
Answer:
The answer is C
Step-by-step explanation:
First there are 2x first then there are other x's then two 1 equals 2
f(x)=−x
2
+8x+14
\text{Find }f(-8)
Find f(−8)
The value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124
How to evaluate the function?The equation of the function is given as
f(x) = -x^2 +8x + 4
The expression f(-8) means that x = -8
So, we have:
f(-8) = -(-8)^2 + 8(-8) + 4
Evaluate the exponent and the product
f(-8) = -64 - 64 + 4
Evaluate the sum and the difference
f(-8) = -124
Hence, the value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124
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