The quadratic function in the standard form containing the point (-7, 5) and vertex (1, 9) is y = (-1/16)(x - 1)² + 9.
How is a quadratic function formed with a vertex and a point?The vertex form of a quadratic function with vertex (h, k) is written as
y = a(x - h)² + k, where (x, y) denotes a point on the parabola. Real integers a, h, and k are also included.
Given:
Point (x, y) = (-7, 5)
Vertex (h,k) = (1, 9)
The general equation of quadratic function in vertex form is:
y = a(x - h)² + k
To solve for a, substitute the given point (x,y) = (-7,5) into the equation.
5 = a(-7 - 1)² + 9
a(-8)² = -4
a = -4 /64
a = -1/16
Therefore, the required quadratic function is,
y = (-1/16)(x - 1)² + 9
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What is the inverse function of d(x)=2x-4?
d-¹(x) = 1/2x+2
d-¹(x) =4x+2
d-¹(x) =4x-2
d-¹(x) =1/2x-2
Inverse function of expression is [tex]\frac{1}{2}[/tex]x + 2.
What is an inverse function?An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f1.
In the broadest sense, inverse functions are functions that "reverse" one another. The inverse, f 1 f-1 f1f, start superscript, minus, 1, end superscript, must take b to a, for instance, if f takes a to b.
Given Data
d(x) = 2x -4
Inverse function-
d⁻¹(x)
y = 2x-4
2x = y-4
x = [tex]\frac{y +4}{2}[/tex]
y = [tex]\frac{x+4}{2}[/tex]
y = [tex]\frac{1}{2}[/tex]x + 2
Inverse function of expression is [tex]\frac{1}{2}[/tex]x + 2.
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What is $609,786 rounded to the nearest 1,000 dollars?
Answer:
$610.000
Step-by-step explanation:
The thousands digit is and the hundreds is 7 so we round up the 9.
Answer is $610.000
(-4.8) (-0.6) please explain the answer
Answer : These are points on a coordinate plane
Which numbers are greater than 59 1/3
592/10
59 4/12
59 2/3
179/3
The numbers that are greater than 59 1/3 are; C: 59 2/3 and D: 179/3
How to interpret Inequalities?We want to find the numbers that are greater than 59 ¹/₃.
Now, the given fraction is written in mixed fraction. Looking at the fraction side, we can see that 1/3 can be written as 0.333. Thus;
59 ¹/₃ = 59.333
When we talk about the inequality greater than, we are simply referring to sayin that a figure is more than another figure which could be given or not given.
Looking at the given options, let us rewrite each of the mixed or improper fractions in decimal form to get;
59 ²/₁₀ converted to decimal form gives 59.2
59 ⁴/₁₂ = 59 ¹/₃ converted to decimal form gives 59.333
59 ²/₃ converted to decimal form gives 59.667
179/3 = 59 ²/₃ converted to decimal form gives 59.667
Comparing the options to the given number in the question, we can conclude that 59 2/3 and 179/3 are greater than 59 1/3
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Which of the following best defines an output? (4 points)
Question 1 options:
1)
An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.
2)
An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
3)
An output is a special type of relation for which there is a rule that pairs each input with exactly one output.
4)
An output is a set of ordered pairs in which no y-value repeats.
Answer:
i go with the first one cause
Step-by-step explanation:
its the only true one
Solve for x, ty/ wlc!
[tex]\sf 3+6x=2x+27[/tex]
3 + 6x = 2x + 27
Move the 2x on the left side with changed sign and the 3 on the right side with changed sign aswell.
6x - 2x = 27 - 3
4x = 24
Now devide 24 by 4.
x = 24 : 6 = 4
Answer:
[tex]\bf x=6[/tex]Step-by-step explanation:
[tex]\bf 3 + 6x = 2x + 27[/tex]
Subtract 3 from both sides:-
[tex]\bf 3+6x-3=2x+27-3[/tex]
Simplify:-
[tex]\bf 6x=2x+24[/tex]
Subtract 2x from both sides:-
[tex]\bf 6x-2x=2x+24-2x[/tex]
Simplify:-
[tex]\bf 4x=24[/tex]
Divide both sides by 4:-
[tex]\bf \cfrac{4x}{4}=\cfrac{24}{4}[/tex]
Simplify:-
[tex]\bf x=6[/tex]
_____________________
10. How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will
reach a point on the house 36 feet from the ground? Draw a picture!
The distance from the base of the ladder to the house is 15 ft.
How to find the side of a right triangle?The length of the ladder is 39 ft.
The ladder is placed to reach a point on the house 36 feet from the ground.
This situation forms a right angle triangle.
The distance from the base of the ladder to the house is as follows:
The distance from the base of the ladder to the house is the other leg of the right angle triangle.
The ladder length is the hypotenuse of the right triangle.
Hence, using Pythagoras theorem,
39² - 36² = b²
b² = 1521 - 1296
b² = 225
b = √225
b = 15 ft
Therefore, the distance is 15 ft.
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Jessie estimates the weight of her cat to be 8 pounds. The actual weight of the cat was 10 pounds. Find the percent error.
The product of two positive integers x and
y is 36 and their sum is 20. What is x and y?
Answer:
2 and 18
Step-by-step explanation:
2*18 = 36, and 2+18 = 20
Answer:
2 and 18.
Step-by-step explanation:
18 * 2 = 36
18 + 2 = 20
how many horseshoes are needed to fit 5 horses
Answer:
20 horseshoes
Step-by-step explanation:
How many horseshoes are needed to fit 5 horses?
5 horses with 4 hooves each:
5 × 4 = 20 horseshoes
It took a plane 2 hours to fly from Dallas to New York with the headwind and 1.5 hours to return with the tailwind. If the speed of the wind was 30 mph, how far apart are the two cities?
Please help
The distance between in two cities is 360 miles.
Given,
It took a plane 2 hours to fly from Dallas to New York
The headwind and 1.5 hours to return with the tailwind.
and, the speed of the wind was 30 mph.
To find the how far apart are the two cities?
Now, According to the question:
Let speed of be x
Speed of wind be c
Also note D = RT, where
D is distance and R is rate and T is time
For First Leg:
we can write:
(x - c) × 2 = D
2x - 2c = D
For Second Leg:
we can write:
(x+ c) × 1.5 = D
1.5x + 1.5c = D
We can equate and write:
2x - 2c = 1.5x + 1.5c
0.5x = 3.5c
We know Speed of Wind, c, is 30, so we have:
0.5x = 3.5(30)
0.5x = 105
x = 105/0.5 = 210 [speed of airplane]
We know distance is
D = 2x - 2c
D = 2(210) - 2(30)
D = 420 - 60
D = 360 miles
Hence, The distance between in two cities is 360 miles.
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-2+(-6) is units from -2, in the
direction.
-2+(-6) is -3 unit(s) from -2. in the negative direction.
Answer:
-8
Step-by-step explanation:
6 + 2 = 8,just make 8 negative
How many of kg of mixed nuts that contain 40% peanuts must bill add to 18 kg of mixed nuts that contain 62% peanuts to make a mixture with 52% peanuts
To find, let the no. of kg of mixed nuts that contains 40% peanuts be called [tex]x[/tex].
We know,
Total peanuts already in the mixture = 18 x [tex]\frac{62}{100}[/tex] = 11.16 kg
The new mixture contains 52% peanuts, then, [tex]\frac{x_{peanuts} }{x_{total} }[/tex] = 0.52.
Furthermore, 40% must be added.
[tex]x_{peanuts}[/tex] = [tex]0.4x[/tex] + [tex]11.16[/tex]
This gives us the following equation,
[tex]\frac{0.4x + 11.16}{18 + x } = 0.52[/tex]
Total mass =[tex]x + 18[/tex]
⇒ [tex]0.52 x +[/tex] 0.52 x 18 = [tex]0.4x + 11.16[/tex]
⇒ 0.12[tex]x[/tex] = (0.62 - 0.52 ) x 18
⇒ [tex]x[/tex] = 15 kg
Hence, 15 kg must be added.
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Please help and thanks!!! :))
A clothing store is tracking how much money adults are spending on clothes each month from their only store. Which description represents a population?
adults who buy any clothes
adults who buy their children’s clothes
adults who are not married
adults who are in college
A clothing store is tracking, adults who are spending on clothes each month from their only store then the adults who buy any clothes consider as population of the store.
Adults who buy any clothes represents a population, who are spending money on clothes each month from their only store.As others adults who buy their children’s clothes does not include them selves, while buying clothes.Adults who are not married will buy clothes buy them selves.So, we cannot consider as population of the store.
Adults who are in college will not buy adults clothes, a teenagers.So, they are not consider as population of the store.
Therefore,
Adults who buy any clothes consider as population of the store.
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R.3 Write a ratio: word problems SBQ
There are 38 empty parking spots and 12 full parking spots in the parking garage. What is
the ratio of the number of empty parking spots to the number of full parking spots?
Answer:
[tex]19:6[/tex]
Step-by-step explanation:
What is a ratio in math?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
So as per the question we have :-
38 empty parking spots
12 full parking spots
the ratio of the number of empty parking spots to the number of full parking spots can be expressed as :
[tex]= 38:12[/tex]
And by simplifying it to the shortest value possible we get it as
[tex]19:6[/tex]
Hope this helped you out and if so please help me out by marking me as the brainliest answer,
a fellow student,
Cheers
Clare wants to make an open-top box by cutting out corners of a 30 inch by 25 inch piece of poster board and then folding up the sides. The volume `V\left(x\right)` in cubic inches of the open-top box is a function of the side length `x` in inches of the square cutouts.
c) Use the Distributive Property or an Area Diagram to find the product and rewrite your polynomial.
Your original V(x)=4x^{3}-110x^{2}+750x
Your new polynomial:
V(x)=
Clare plans to fold up the sides of a poster board that is 30 inches by 25 inches of box. The volume V(x)=4x³-110x²+750x.
Given that,
Clare plans to fold up the sides of a poster board that is 30 inches by 25 inches and trim the corners to create an open-top box. The open-top box's volume, "V(x)," in cubic inches, depends on the square cuts' side length, "x," in inches.
Length =30 inch
Width=25 inch
The box's size changes when x is taken out of the container.
Length=30-2x
Width=25-2x
Height=x
Because x is eliminated from both ends, we subtract 2x.
The volume is then determined as follows:
V(x)=length×width×height
V(x)=(30-2x)×(25-2x)×x
V(x)=(30-2x)×(25x-2x²)
V(x)=750x-110x²+4x³
V(x)=4x³-110x²+750x
Therefore, the volume V(x)=4x³-110x²+750x.
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Kurt bowled 4 strikes in his 10 frames. Write his occurrence of strikes as a
fraction, then as a percent.
Answer:
4/10 and 40%
Step-by-step explanation:
He had 4 Strikes out of a total 10 Tries. 4 of his 10 tries were strikes.
So its 4/10.
Find x if:
B is between A and C
AB=x+5
BC= 2(x-3); and
AB BC
Answer:
If B is between A and C, then AB = BC.
x + 5 = 2(x - 3)
x + 5 = 2x - 6
x = 11
what is the written standard form for 4x-8=9y-5
Answer: y = 4/9 x - 1/3
Step-by-step explanation:
standard form means y = mx + c
so,
4x-8=9y-5
4x-8+5=9y
(4x-3)/9=y
y = (4/9)x - (1/3)
What is the distance between the following points?
Choose 1 answer.
7
9
√65
√80
The distance between points (-6 , 4 ) and (-5 , -4 ) marked in the graph
is [tex]\sqrt{65}[/tex]
solution:From the given graph the two points are:
A = ( -6 , 4 ) , B = (-5 , -4 )
we have the distance from A to B ,
to find distance the formula is,
Distance = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
= [tex]\sqrt{(-5 - (-6))^{2} + (-4 -4)^{2} }[/tex]
= [tex]\sqrt{1^{2} + (- 8)^{2} }[/tex]
= [tex]\sqrt{1 + 64}[/tex]
= [tex]\sqrt{65}[/tex]
so the distance between points (- 6 , 4 ) and ( -5 , -4 ) is [tex]\sqrt{65}[/tex]
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If it is an equilateral triangle, then all sides of a triangle are congruent. converse: __________________________ inverse: ____________________________ contrapositive: _______________________
All sides of an equilateral triangle are congruent [equal]
Triangles are categorized into three
The sides and angles of a scalene triangle are not equalIsosceles triangle; two sides are equal and the opposing angles of the equal sides are also equalEquilateral triangle is a triangle whose three sides are equal in length. the angles are also equal, [tex]60^{0}[/tex] .it is the only regular polygon with three sidesRead more here
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Determine the intercepts of the line.
Answer:
y=(0,-45)
x=(-10,0)
Step-by-step explanation:
The circumference of a circle of diameter 3,5 cm is 11 cm. What is the circumference of a circle of diameter 42 cm?
Answer ... cm
The circumference of a circle with diameter of 42 cm is 131.88 cm
How to find the circumference of a circle?The circumference of a circle of diameter 3.5 cm is 11 cm.
The circumference of a circle of diameter 42 cm can be found as follows:
Therefore,
circumference of a circle = 2πr
where
r = radius of the circleHence,
diameter = 42 cm
radius = 42 / 2
radius = 21 cm
circumference of a circle = 2 × 3.14 × 21
circumference of a circle = 42 × 3.14
circumference of a circle = 131.88 cm
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Farmer Bob is going out to feed the cattle. He feeds seven pounds of cowchow to each cow. He uses at least 84 pounds of cowchow every time he feeds. Write an inequality and solve to find how many cows farmer Bob has
Each cow receives seven pounds of cow chow from Bob. Every time he feeds, farmer Bob uses at least 84 pounds of cow chow, which means that each time he feeds, 12 cows in total.
What is the concept of Unitary Method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Cow chow fed to each cow by the farmer =7 pounds
Total cow chow used by the farmer to feed the cows every time = 84 pounds
Total cow chow used = no. of cows *cow chow fed to each cow
No. of cows = Total cow chow / cow chow fed to each cow
= 84/7
=12
No. of cows = 12
Therefore, 84 pounds of cow chow is used to feed 12 cows each time.
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Whats the answer to 1 1/2 X 3 2/3
Answer:
5 1/2 or 5.5
Step-by-step explanation:
First, we can convert these values to improper fractions, where the numerator is larger than the denominator.
Then, we'd get:
3/2 x 11/3
Now, we can multiply the numerators and denominators, and we would get the answer of 33/6
When we convert 33/6 to a mixed number, we get 5 3/6, which can then be further simplified to 5 1/2 OR 5.5 (whichever you prefer)
Answer:
5 1/2
Step-by-step explanation:
1 1/2×3 2/3
[tex](2 \times 1 + 1) \times (3 \times 3 + 2) \\ [/tex]
3/2×11/3
33/6
=5 1/2
20. A work crew is building a new biking path that will be 28 miles long. Each day,
the crew builds 0.5 mile of the path. Write an expression for the length of the bike
path left to build at any point during the construction. Explain what your variable
represents.
PLEASE HELP
The most appropriate choice for linear equation will be given by-
[tex]l = 28 - 0.5d[/tex] is the required expression for the length of the bike
path left to build at any point during the construction.
[tex]l[/tex] is the length of the bike path left to build at any point during the construction
[tex]d[/tex] is the number of days
What is Linear equation?
A one degree equation is called a linear equation.
Here,
Let the length of the bike path left to build at any point during the construction be [tex]l[/tex] and the number of days be [tex]d[/tex]
In one day, the crew build 0.5 miles of the path
In d days, the crew can build [tex]0.5 \times d[/tex] miles of the path
Length of path left to construct after [tex]d[/tex] days = [tex]28-0.5d[/tex]
By the problem,
[tex]l = 28 - 0.5d[/tex]
This is the required expression for the length of the bike
path left to build at any point during the construction.
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. If a number is decreased by 4 and divided by 6, the result is
8.What would be the result if 2 is subtracted from the number
and then it is divided by 5 ?
Answer:
10
Step-by-step explanation:
The number is 52. If you subtract 2 you get 50, then after dividing by 5 you get 10.
Pease help me this is dew tonight!
Answer:
-2v+2u+5
Step-by-step explanation:
Distribute the negative sign outside of the parentheses to the values within the parentheses (2v, -2u, and -5). This will give you -2v+2u+5. Let me know if you want a more detailed explanation, hope this helps
hi, i need help with this:)
Answer:
3
Step-by-step explanation:
Vol = length x width x height
Vol = 3 x 3 x3
Vol = 27