Answer:
Assuming the gas tank was filled to the maximum of 13 gallons, the car motorcycle achieves 39 miles per gallon.
Step-by-step explanation:
507/13 = 39
The function y=x²-4x+8 approximates the height, y, of a bird, and its horizontal distance, x, as it flies from one
fence post to another. All distances are in feet. Complete the square to find and interpret the extreme value
(vertex).
Select two answers: one extreme value and one interpretation.
Height (feet)
Distance (feet)
A. When the bird is 4 feet away from the first fence post, it reaches its minimum height of 8 feet.
B. Minimum at (4,8)
C. When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet.
D. Minimum at (2,4)
When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet , Minimum at (2,4)
Therefore Option C and D is the correct answer.
What is a Quadratic Function?The equation for a quadratic function is given by
y = a(x-h)² +k²
where (h,k) is the extreme value(vertex).
Here the equation given is
y = x²-4x +8
y = x²-4x+4+4
y = (x-2)² +4
Here the value of a = 1 , h = 2 and k = 4
The extreme value is at (2,4)
Therefore When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet , Minimum at (2,4)
Therefore Option C and D is the correct answer.
To know more about Quadratic Function
https://brainly.com/question/5975436
#SPJ1
4. What is the slope of the line that passes through the points (2, 7) and (6, 21)? Answer may be in decimal
point. Someone please please help I would really appreciate it
Answer:
About 3.5
Step-by-step explanation:
To get slope, you essentially need to find the rise (the y values) over run (the x values). You'll most likely see the formula for slope written like this:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Thankfully, you have the values you need to solve the problem!
x1 = 2
x2 = 6
y1 = 7
y2 = 21
So plugging these numbers in, we get:
[tex] \frac{(21) - (7)}{(6) - (2)} \\ \\ \frac{14}{4} \\ \\ 3.5 [/tex]
[EDIT: I misread 6 as 5. Answer has been updated!]
Which is a valid prediction about the continuous
function f(x)?
Of(x) ≥ 0 over the interval [5, ∞).
Of(x) ≤0 over the interval [-1, %).
Of(x) > 0 over the interval (-∞, 1).
Of(x) < 0 over the interval (-∞. –1).
33333333333333333333333333333333333
hey! Solving linear equations with integers! i don’t think it should be that hard since it’s practice, I just need some help with a bit more problems! :’)
1) -3 ( 3 - x ) = 2x + 5
2) -6 - 9p = + 3p
3) -5 (-4 - a ) = 3a + 8
4) s - 6 = -5s
that should be it! Ty
Solution 1 :-
>> -3 (3 - x) = 2x + 5
>> -3 × (3 - x) = 2x + 5
>> -9 + 3x = 2x + 5
>> 3x - 2x = 9 + 5
>> x = 14
Solution 2 :-
>> -6 - 9p = 3p
>> -9p - 3p = 6
>> -12p = 6
>> p = -1/2
Solution 3 :-
>> -5 (-4 - a) = 3a + 8
>> -5 × (-4 - a) = 3a + 8
>> 20 + 5a = 3a + 8
>> 5a - 3a = 8 - 20
>> 2a = -12
>> a = -12 / 2
>> a = -6
Solution 4 :-
>> s - 6 = -5s
>> s + 5s = 6
>> 6s = 6
>> s = 6 / 6
>> s = 1
Answer:
1) x = 14
2) p = - [tex]\frac{1}{2}[/tex] (- 1/2)
3) a = -6
4) s = 1
work shown in image :)
hope this helps!!
PLease help due today! I will give brainliest!!
Select the correct answer.
Simplify the expression.
[tex][tex]\sqrt[5]{224x^{11}yx^{8} }[/tex][/tex]
Suppose f(x) = x² and g(x)= (1/5x)^2
Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted units left.
B. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 5.
OC. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 5.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 5.
Answer:
B. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.
Nancy was baking a cake for her mom’s birthday. She spent 1/3 of her time measuring the ingredients and 1/4 of her time mixing. Next, she put the cake in the oven to bake. If Nancy spent 35 minutes altogether on measuring ingredients and mixing them, how much total time did it take her to complete all the steps involved in baking the cake?
How to write a two column proof for number 12?
1) [tex]\overline{EJ} \parallel \overline{KF}, \overline{JG} \parallel \overline{KH}, \overline{EF} \cong \overline{GH}[/tex] (given)
2) [tex]\overline{FG} \cong \overline{FG}[/tex] (reflexive property)
3) [tex]\overline{EG} \cong \overline{FH}[/tex] (segment addition postulate)
4) [tex]\angle JEF \cong \angle KFG, \angle JGE \cong \angle KHF[/tex] (if two parallel lines are cut by a transversal, the corresponding angles are congruent)
5) [tex]\triangle EJG \cong \triangle F\text{ }KH[/tex] (SAS)
The sides of a square bedroom measure 3.5 yards. if carpet costs $16 per square yard, how much will it cost to cover the floor?if one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
Answer:
£196 and 400cm
Step-by-step explanation:
3.5^2 = 12.25 will give the whole floor
12.25 × 16 = 196
20^2= 400cm is the front cover of the book
can someone please help me(20 points and I will give brainliest!!!)
Answer:
a)(0,k)
b)(0,-k)
Step-by-step explanation:
Finding the vertex: Using calculusGiven:
[tex] \begin{cases} y = a {x}^{2} + k \\ y = a {x}^{2} - k \end{cases}[/tex]
Taking the derivative of y's yields
[tex] \begin{cases} y '= \dfrac{d}{dx} a {x}^{2} + k \\ \\ y '= \dfrac{d}{dx} a {x}^{2} - k \end{cases} \\ \implies\begin{cases} y '= 2a x\\ \\ y '=2ax\end{cases} [/tex]
Now set y' to 0 and solve for x:
[tex] \implies\begin{cases} 2a x = 0\\ \\ 2ax = 0\end{cases} \\ \implies\begin{cases} x= 0\\ \\ x= 0\end{cases} [/tex]
plug in the value of x into the original equation thus
[tex] \begin{cases} y = a ({0}^{2}) + k \\ y = a ({0}^{2} )- k \end{cases}\\ \implies \begin{cases} y = k \\ y= - k \end{cases} [/tex]
Hence,
a. vertex (0,k)b. vertex (0,-k)The graphs of f(x) and g(x) are shown below: graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 7, negative 2. If f(x) = (x + 7)2, which of the following is g(x) based on the translation? (5 points) a g(x) = (x + 9)2 b g(x) = (x + 5)2 c g(x) = (x + 7)2 + 2 d g(x) = (x + 7)2 − 2
The equation of the function is g(x)=(x+7)² -2 , Option D is the correct answer.
What is a Function ?A function is a mathematical statement that defines relation between two variables.
The f(x) = (x+7)²
The equation for g(x) is ?
graph of function f of x open upward and has its vertex at (-7,0).
Graph of function g of x opens upward and has its vertex at (-7,2).
g(x) is formed by the translation of the function f(x) such that it's vertex is (-7,-2)
Therefore the equation of the function is
g(x)=(x+7)² -2
Therefore , the translation is a shift of the function f(x) 2 units down
Option D is the correct answer.
To know more about Function
https://brainly.com/question/12431044
#SPJ1
The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square bas-
is x units.
Which expression represents the volume of the prism, in cubic units?
x³ +9
x³ + 3x²
x³ + 3x + 3
x³ + 6x² + 9x
Answer:
College dropout is the greatest album of all-time
11. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n=12, x = 5, p = 0,25
A) 0.082
B) 0.091
C) 0.027
D) 0.103
Answer
D
Step-by-step explanation:
The probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.
The correct answer is A) 0.082.
The probability of x successes given the probability p of success on a single trial, with n trials, can be calculated using the binomial probability formula:
[tex]P(x) = (n_C_x) * p^x * (1-p)^{(n-x)[/tex]
In this case, n = 12, x = 5, and p = 0.25. Let's substitute these values into the formula:
[tex]P(5) = (12C5) * (0.25)^5 * (1-0.25)^{(12-5)[/tex]
Using the combination formula ([tex]n_C_r[/tex]) to calculate ([tex]{12}_C_5[/tex]):
[tex]P(5) = (12!)/(5!(12-5)!) * (0.25)^5 * (0.75)^7[/tex]
Simplifying the combination:
[tex]P(5) = (12!)/(5!7!) * (0.25)^5 * (0.75)^7[/tex]
Calculating the factorial terms:
[tex]P(5) = (12111098)/(54321) * (0.25)^5 * (0.75)^7[/tex]
[tex]P(5) = 792 * 0.0009765625 * 0.1334838867[/tex]
P(5) ≈ 0.082
Therefore, the probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.
The correct answer is A) 0.082.
Learn more about binomial probability here:
https://brainly.com/question/12474772
#SPJ2
What type of relationship is expressed below?
5x = 2x 9
O equation
O function
O inequality
Answer:
The answer will be equation
A group of friends wants to go to the amusement park. They have no more than $280 to spend on parking and admission. Parking is $19.50, and tickets cost $33.75 per person, including tax. Which inequality can be used to determine semanticsp, the maximum number of people who can go to the amusement park?
The number of people who can go to the amusement park is 8.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given: the group of friends had $280.
For parking= $19.50
Remaining will be,
=$(280-19.50)
= $ 260.5
Cost of ticket per person = $33.75
Thus, number of tickets they can buy
=260.5 / 33.75
=7.718 = 8 peoples
Hence, number of people who can go to the amusement park is 8.
Learn more about this concept here:
https://brainly.in/question/51469249
#SPJ1
Solve for x. Round to the nearest tenth, if necessary
[tex]\tan 61^{\circ}=\frac{59}{x}\\\\x=\frac{59}{\tan 61^{\circ}} \approx \boxed{32.7}[/tex]
Maggie and Tanya went to a fruit store. Maggie bought 10 oranges and 5 apples for $4. Tanya bought 9 oranges and 3 apples for $3. What is the cost of an orange and an apple?
Answer:
orange: 0.2$, apple: 0.4$
Step-by-step explanation:
we mark the price of an orange x and the price of an apple y. then we write down Maggie's and Tanya's purchases as a set of equations:
10 oranges and 5 apples for 4$ means:
[tex]10x + 5y = 4[/tex]
9 oranges and 3 apples for 3$ means:
[tex]9x + 3y = 3[/tex]
we use the second equation to isolate y:
[tex]3y = 3 - 9x \\ y = 1 - 3x[/tex]
and plug it in the first equation:
[tex]10x + 5(1 - 3x) = 4 \\ 10x + 5 - 15x = 4 \\ 1 = 5x \\ x = 0.2[/tex]
and then we find y:
[tex]y = 1 - 3 \times 0.2 \\ y = 0.4[/tex]
help me please grade 5 math fast as possible please
Answer:
21/4
Step-by-step explanation:
Answer:
[tex]\frac{42}{8}[/tex]
Step-by-step explanation:
• First multiply the numerators:
6 x 7 = 42
• Then multiply the denominators:
(6 doesn't have a denominator, which is the same as having a denominator of 1)
1 x 8 = 8
∴ The answer is [tex]\frac{42}{8}[/tex] .
Determine the equation of the line with slope -2 that passes through the point M(-1, -3).
Answer:
Given:
Let, the slope of the line passing through the point ( m) = -2
The line passing through the point M(-1,-3)= (x1 , y1)
The equation of the line passing through the point M(-1,-3) is
y-y1 = m (x-x1)
or, y-(-3) = -2 (x-(-1))
or, y+3 = -2 (x+1)
or, y+3 = -2x-2
or, 2x+y = -2-3
Hence, 2x+y =-5 is the required equation.
(a) is the correct answer .
HELP PLEASE IM BEGGING PLEASEEE I NEED IT NOWWW
cylindrical-shaped aquarium is to be filled with water for the newly bought salt water fishes. How much salt water is needed if the aquarium has a 2 ft radius of its base and a height of 3 ft?
Volume = πr²h
V = (3.14) (2)² (3)
V = (3.14) (4) (3)
V = 37.68 ft³
37.68 ft³ of salt water is needed to fill the cylindrical aquarium.
Mr. Lee is buying a spherical water tank for his tomato plantation. How much water could be stored if the water tank has a radius of 2 meters?
Volume = (4/3) πr³
V = (4/3) (3.14) (2)³
V = (4/3) (3.14) (8)
V = (4/3) (25.12)
V = 33.493 m³
Mr. Lee can store 33.493 m³ of water in the spherical tank.
https://brainly.ph/question/15441850
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$500 and $550.
Need the answer as a % !!!
Answer:
2.15%
Step-by-step explanation:
If you were to get the z-score for both 500 and 550 and then get the probability of both those z-scores. After getting the probability you would subtract both probability and get your answer.
Z-score:
550-400/2=3
500-400/2=2
Probability:
3 (from the Z-table) is .9987
2 (from the Z-table) is .9772
.9987-.9772= .0215
.0215 as a percentage is 2.15%
Mean: 400
Standard deviation: 50
Check to see if 500 and 550 fall within the standard deviations:
400+2(50) =500
400+3(50) =550
These values lie between the 2nd and 3rd deviations, so
the value is 0.0235
Percentage: 2.35%
Hope it helps!
The length of a rectangle is 7 inches and the width is 42 inches. What is the ratio,
using whole numbers, of the length to the width?
Answer:
6 : 1
Step-by-step explanation:
The length is the longer side compared to the width.
Hence, the length is 42 inches and width is 7 inches.
Taking the ratio :
Length : Width42 : 77 x 6 : 76 : 1Answer:
1 : 6
Step-by-step explanation:
42 /7 = 6
We will have to simply the ratios in order to get the answer.
Given: AM||RZ , angle R is congruent to angle Z
Prove: angle RAM is congruent to angle ZMA
They are congruent because the word congruent means the same shape and size and if you look at the picture angle RAM and angle ZMA have the same shape and the same size.
PLS HELP
What is the relationship between \blueD{\angle a}∠astart color #11accd, angle, a, end color #11accd and \greenD{\angle b}∠bstart color #1fab54, angle, b, end color #1fab54?
Two angles whose sum is 180° are called supplementary angles. The correct option is C.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
In the given Image, ∠a and ∠b are supplementary angles to each other. Therefore, the correct option is C.
Learn more about Supplementary Angles:
https://brainly.com/question/2882938
#SPJ1
For a biology experiment, students labeled the plants in a greenhouse in order to track their heights over the next few weeks. The greenhouse contained ROSES labeled 1, 2, 3, 4, 5, 6, LILIES labeled 1, 2, 3, 4, 5, and VIOLETS labeled 1, 2, 3, 4. If a single flower is picked at random, what is the probability that the flower is NOT A ROSE?
Using it's concept, it is found that there is a 0.6 = 60% probability that the flower is NOT A ROSE.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 6 + 5 + 4 = 15 flowers, out of which 5 + 4 = 9 are not roses, hence the probability is given by:
p = 9/15 = 0.6 = 60%.
0.6 = 60% probability that the flower is NOT A ROSE.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
A car travels a distance of 210 m in a time of 6 seconds. Calculate the time in seconds for the car to travel a distance of 1928 m.
Answer:
It will take 55.08 seconds.
Step-by-step explanation:
6 seconds = 210m
1 second = (210÷6)
= 35m
1928m ÷ 35m
=55.08 seconds
Answer = it will take 55.08 seconds to travel 1928m
The angle of depression from the hot-air
balloon to the car is 34°.
How high is the hot-air balloon flying?
Give your answer to 2 s.f.
6400 feet
Not drawn accurately
Answer:
Ans : 3578.83 feet from the ground
Step-by-step explanation:
You can use sine theory so
sine 32 = height/6400
6400 x sine 32 = height
Easy
15 points for this need help badly
Answer:
check image below
Step-by-step explanation:
A roll of paper towels is wound around a hollow cardboard tube. the
cardboard tube in the middle of the roll has an outside radius of 2.4 cm. the
thickness of the paper is 0.3 mm. the sequence of distances of the loops of
paper away from the center of the roll (in centimeters) is the following:
21, 22, az, a4 a5, ... = 2.40, 2.43, 2.46, 2.49, 2.52, ..
what is the radius of the 85th loop of paper, starting from the center of the
tube?
a. 4.95 cm
b. 4.86 cm
c. 4.92 cm
d. 4.89 cm
The correct Option is Option C: The radius of the cardboard tube of 85th loop of paper is 4.92cm
The arithmetic sequence is the sequence where every term is increased or decreased by a fixed number from the previous number.
Here the outer radius of the tube is 2.4 cm
the thickness of the paper is 0.3mm= 0.03cm
i.e. in every loop the increase in the radius of the loop is 0.03cm
then the radius in every sequence will be 2.40, 2.43, 2.46, 2.49, 2.52, .....
so here it is clear that it is an arithmetic sequence with a common difference of 0.03.
nth term of the sequence, aₙ = a₁ + (n - 1)d where a₁ is the first term, n is the index of the loop, and d is a common difference.
here a₁ =2.40
d=0.03
n=85
the radius of tube of the 85th loop will be= r= 2.40+(85-1)0.03= 2.40+ 2.52= 4.92
Therefore The radius of the cardboard tube of the 85th loop of paper is 4.92cm
Learn more about the arithmetic sequence
here: https://brainly.com/question/6561461
#SPJ10
Question 8 of 10
What are the zeros of f(x) = x² − 8x + 16?
A. x= -4 and x = 4
B. x=-2 and x = 8
C. x = 4 only
D. x = -4 only
Answer:
c ×=4, only
Step-by-step explanation:
4*-8×+16=0
16-32=-16
-16=-16
Answer:
D. x=4 only
Step-by-step explanation:
You can solve using the quadratic equation which is [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]
where in this case a=1, b=-8, and c=16. But there is any easier way to solve the equation. You can solve by completing the square which consists of moving the constant to the right side and then adding [tex](\frac{b}{2})^2[/tex]. To both sides that way you can rewrite the left side as a perfect square binomial. This is because [tex](x+b)^2[/tex] will expand to [tex]x^2 + 2xb + b^2[/tex]. So when you add [tex](\frac{b}{2})^2[/tex] to both equations. You're able to rewrite the left side as [tex](x+(\frac{b}{2}))^2[/tex]. Because once you expand it out, it becomes [tex]x^2 + 2(\frac{b}{2})x + (\frac{b}{2})^2[/tex]. Which simplifies to [tex]x^2 + bx + (\frac{b}{2})^2[/tex] which is the original equation. In this case there is no need to move the constant, which in this case is 16, to the other side. Since if you calculate the value of (-8/2)^2 it's equal to 16! So this can already be written as a perfect square binomial.
So the equation becomes
[tex]0 = (x+\frac{b}{2})^2[/tex]
Plug values in
[tex]0 = (x+(-\frac{8}{2}))^2[/tex]
Simplify
[tex]0 = (x-4)^2[/tex]
Take the square root of both sides
[tex]0 = x-4[/tex]
Add 4 to both sides
[tex]4 = x[/tex]
