Answer:
C: (-8, 2)
Step-by-step explanation:
Given parabola:
[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]
For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.
Therefore, the x-value of the vertex of the given parabola is:
[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]
To find the y-value of the vertex, input x = -8 into the given equation:
[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]
Therefore, the vertex (h, k) of the parabola is (-8, 4).
The focus of the parabola is (h, k+p) where:
(h, k) is the vertex[tex]p=\dfrac{1}{4a}[/tex]Therefore:
[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]
Solve this problem
Step by step
The value of x in the shape we have here is given as 18.7 cm
How to solve for the value of xIn this question we are to find the value of x using the values that we already have in the shape.
The base of the diagram has its length as 40 cm.
The shape is made up of two right angled triangles.
since the top of the shape is 26 m, the triangles would be gotten by
40 - 26 = 14
14 / 2 = 7cm
each rectangular base is therefore 7 cm
we have to solve for the value of x using the Pythagorean theorem
hence we would have:
7² + x² = 20²
49 + x² = 400
x² = 400 - 49
x² = 351
x = 18.7 cm
Read more on trapeziums here:https://brainly.com/question/1410008
#SPJ1
Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides 5 times as fast as Bella walks. The distance between their houses is 2 miles, which is 10,560 feet, and Bella covers $2\frac{1}{2}$ feet with each step. How many steps will Bella take by the time she meets Ella
Since Bella takes 4,224 steps, and Ella takes 844.8 steps, they meet at 4,224 steps.
To determine this:
We can start by using the information given to find out how long it takes Bella and Ella to meet.
Since Ella rides 5 times faster than Bella walks, we can use the following equation to find out how long it takes each of them to cover the 2-mile distance:
Time (Ella) = Time (Bella) / 5
We can also use the distance formula to find out how long it takes Bella to cover the 2-mile distance:
Distance = Speed x Time
We know that Bella's speed is [tex]$2\frac{1}{2}$[/tex] feet per step, and the distance between their houses is 10,560 feet. So:
10,560 feet = [tex]$2\frac{1}{2}$[/tex] feet/step x Time (Bella)
Solving for Time (Bella), we get:
Time (Bella) = 10,560 feet / [tex]$2\frac{1}{2}$[/tex] feet/step = 4,224 steps
Now we can use this information to find out how long it takes Ella to meet Bella:
Time (Ella) = Time (Bella) / 5 = 4,224 steps / 5 = 844.8 steps
And since Bella takes 4,224 steps, and Ella takes 844.8 steps, they meet at 4,224 steps.
To learn more about the Distance, visit:
brainly.com/question/15172156
#SPJ4
PLEASE HELP!! WILL MARK BRAINLIEST IF RIGHT
Answer:
10 feet, option D
Step-by-step explanation:
Got it right on my test.
Which equation shows a way to find 3075/15. A 30/15+75=2+5 B 30/15x75=2x5 C 3000/15+75=200+5 D 3000/15x75=200x5. I need the answer quick please its for a test!!!!!!! HURRY!
Answer:
C. 3,000÷15+75÷15=200+5
Step-by-step explanation:
I got this because 3075 ÷ 15 = 205. That whole equation is equal to 200+5. 200+5=205.
Hope it's correct cause I have the same question on a quiz !
Answer:30/15+75=2+5 B 30/15x75=2x5
Step-by-step explanation: Because i am a teacher so i know the answer
The ratio of the four sides of a trapezoid is 2:1:1:1.$ The area of the trapezoid is 27*sqrt3. Find the length of the median of the trapezoid.
The length of the median = 6[tex]\sqrt{3}[/tex]
If we call the longer base "a" and the shorter base "b", then we know that:
a:b = 2:1
Since the ratio of the four sides is 1:1:1:1, we know that the height, median and the longer base are all equal.
We can use that information to determine the area of the trapezoid. The formula for the area of a trapezoid is:
Area = (a + b) * h / 2
We know that the area is 27[tex]\sqrt{3}[/tex] and the height and median are equal, so we can set up the equation:
(a + b) * h / 2 = 27[tex]\sqrt{3}[/tex]
We also know that a:b = 2:1, so we can substitute that in:
(2b + b) * b / 2 = 27[tex]\sqrt{3}[/tex]
Simplifying, we get:
3b^2 = 54 * [tex]\sqrt{3}[/tex]
So the length of the median (h) is b
= [tex]\sqrt{(54 * \sqrt{3} / 3) }[/tex]
= 6[tex]\sqrt{3}[/tex]
To know more about trapezoid refer to:
brainly.com/question/30033073
#SPJ4
Two ferries travel across a lake 50 miles wide. One ferry goes 5 miles per hour slower than the other. If the slower ferry leaves 1 hour before the faster and arrives at the opposite shore at the same time as the other ferry, what is the speed of the slower ferry
The first ferry's speed is 18.5 mph and the second ferry, which is slower, travels at 13.5 mph.
How to find the calculation?Let x represent the first ferry's speed.
The second, slower ferry's speed is then x-5 (since 5 miles per hour slower)
First ferry time equals distance/speed equals
50/x
Time spent on the second ferry:
50 / x - 5
The difference in times is 1 hour because the second ferry departs an hour earlier.
50 / x - 5 - 50/x = 1
50x - 50(x - 5) = x (x - 5 )
250 = x² - 5x
x² - 5x - 250 = 0
(x - 10 )(x + 5) = 0
x = 18.5 - 13.5
Speed can never be detrimental.
Therefore, the first ferry's speed is 18.5 mph.
and the second ferry, which is slower, travels at 13.5 mph.
To Learn more About ferry's speed Refer To:
https://brainly.com/question/28757057
#SPJ4
Answer the given question and show workings.
Question :
Given that θ = 3/5 , Cos alpha = 3/5 , where θ and alpha are acute. Find Sin ( θ+alpha).
Note : I'm writing alpha in words cuz I don't know how to type in the symbol.
Answer:
alpha=cos^-1(0.6)
alpha=53°
sin(37+53)
=1
Answer:
1Step-by-step explanation:
Givensin θ = 3/5cos α = 3/5Both angles are acuteSolutionSince both sin θ and cos α have same value of 3/5 and both angles are in the I quadrant, the angles θ and α are complementary.
It means:
θ + α = 90°sin (θ + α) = sin 90° = 1If A=(7,9) and B=(3,12) what is the length of AB
The distance between two points A and B is 5 units.
City Fitness, a popular gym, currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by a factor of
1
4
each year.
Write an exponential equation in the form y=a(b)x that can model the number of members, y, in x years.
The growth in x years for the gym will be represented as [tex]y = 840(1.25)^x[/tex].
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
City Fitness, a popular gym currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by a factor of 1/4.
The expression can be written as,
[tex]y = 840(1.25)^x[/tex].
To know more about an expression follow
https://brainly.com/question/11737323
#SPJ1
Tamara and Jason work at a widget factory. Tamara arrived at work before Jason and began making widgets. Tamara had already made 20 widgets when Jason began his work. Tamara was producing widgets at a rate of 8 widgets per hour. Jason was able to produce widgets at a rate of 12 widgets per hour. At some point, Tamara and Jason will have produced the same number of widgets.
Part A:
Write a system of equations to represent the situation. Let x = hours and y = widgets.
Part B:
How much time does it take for Tamara and Jason to produce the same number of widgets?
Part C:
How many widgets will Tamara and Jason have produced?
Answer:
To solve this problem we can construct an linear algebraic expression for each person, principally denoted as:
where
y :is our dependent variable (which is a function of )
x :is our independent variable
a :is the slope
c :is the y-intercept constant value (if any present)
Part A: Write a system of equations to represent the situation. Let x = hours and y = widgets.
Tamara
Has already made 20 widgets and produces at a rate of 8 widgets per hour thus here c=20 and a=8 , so Tamara's equation reads: yT=8x+20
Jason
Has not produced any widgets yet and produces at a rate of 12 widgets per hour thus here c=0 and a=12 , so Jason's equation reads:yj=12x
So the system of equations will be
yT=8x+20
yj=12x
Part B: How much time does it take for Tamara and Jason to produce the same number of widgets?
Since we want to find the amount of time (i.e. the value of x ) it takes for both of them to produce the same number of widgets we can just equate the two equations ans solve for x as follow:
yT=yj
8x+20=12x
8x-12x=-20
-4x=-20
x=5
So it takes them 5 hours to produce the same amount of widgets
Part C: How many widgets will Tamara and Jason have produced?
Now we can simply plug in the value of x=5 in any of the two equations (i.e. either for Tamara or Jason) to find the number of widgets produced.
yT=8(5)+20=40+20=60
So in a time-space of 5 hours Each will have produced 60 widgets and in total will be 60+60 = 120 widgets.
Step-by-step explanation:
mrk me brainliest i worked really hard on this plzzzzzzzzzzzzzzz
hey! please help i’ll give brainliest
Answer:
False.
Step-by-step explanation:
It says Jacob walked to the store to get milk. The use of the word walked means it was past tense. He had already walked to the store.
The data below represents the number of strikes each Sam's Inc. employee got on the company bowling outing.
36
1, 3, 6, 8, 10, 12, 13, 13, 16, 18, 19
Answer:
Mean: 10.8
Median: 12
Mode: 13
Step-by-step explanation:
I hope this is what you were looking for! If you have and questions ask in the comments :D
The expression $12y^2-65y+42$ can be written as $(Ay-14)(By-3),$ where $A$ and $B$ are integers. What is $AB + A$?
Answer:
[tex]AB + A = 16[/tex]
Step-by-step explanation:
Given
[tex]12y^2 - 65y + 42 = (Ay -14)(By - 3)[/tex]
Required
Find [tex]AB + A[/tex]
[tex]12y^2 - 65y + 42 = (Ay -14)(By - 3)[/tex]
Expand
[tex]12y^2 -56y -9y + 42 = (Ay - 14)(By -3)[/tex]
Factorize
[tex]4y(3y -14) -3(3y - 14) = (Ay - 14)(By -3)[/tex]
Factor out 3y- 14
[tex](3y - 14)(4y -3) = (Ay - 14)(By -3)[/tex]
By comparison:
[tex]Ay - 14 = 3y - 14[/tex]
and
[tex]By - 3 = 4y - 3[/tex]
So, we have:
[tex]Ay - 14 = 3y - 14[/tex]
Add 14 to both sides
[tex]Ay = 3y[/tex]
Divide both sides by y
[tex]A = 3[/tex]
[tex]By - 3 = 4y - 3[/tex]
Add 3 to both sides
[tex]By = 4y[/tex]
Divide both sides by y
[tex]B = 4[/tex]
So, the expression [tex]AB + A[/tex] is:
[tex]AB + A = 3 * 4 + 4[/tex]
[tex]AB + A = 12 + 4[/tex]
[tex]AB + A = 16[/tex]
A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is red, what is the probability that the other side is red? Express your answer as a common fraction.
The probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].
What is conditional probability?The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood conditional, occurrence to determine the conditional probability.
Suppose you choose a red/black card:
The probability of choosing a red and black card is [tex]\frac{1}{6}[/tex].
Now, since this card has one side as red the probability of seeing a red side in this card is [tex]\frac{1}{2}[/tex].
Suppose you choose a red/red card:
The probability of choosing red and red card is 2/6.
Now, since the card has two red sides the probability of seeing red side in this card is [tex]\frac{2}{2}[/tex] .
Considering we see a single side of the card we have the following probability:
[tex]\frac{2}{6} * \frac{2}{2} = \frac{1}{3}[/tex]
The total probability of seeing a red side is [tex]\frac{1}{12} + \frac{1}{3} = \frac{5}{12}[/tex].
The probability that you pick red-red card and see a red side is [tex]\frac{1}{3}[/tex].
So, the conditional probability of both red sides is given as:
[tex]\frac{\frac{1}{3} }{\frac{5}{12} } = \frac{4}{5}[/tex]
Hence, the probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].
Learn more about conditional probability here:
https://brainly.com/question/30144287
#SPJ4
Find the area of the composite figure. Correct answer gets marked brainliest!!!!!
Answer:
170.52 in
Step-by-step explanation:
please give a step by step explanation please
The radius of a sphere whose surface area is 324*pi cm² is:
R = 9 cm.
What is the radius of the sphere in the image?We know that the surface of a sphere of radius R is given by:
S = 4*pi*R^2
Where pi = 3.14
Here we know that a sphere has a surface of 324*pi cm², then we can write the equation:
S = 324*pi cm² = 4*pi*R^2
We can divide both sides by pi, so we get:
324 cm^2 = 4*R^2
Now we can solve that equation for R, we will get:
R^2= (324 cm^2)/4 = 81cm^2
R = √(81 cm^2)
R = 9cm
The radius of the sphere is 9cm.
Learn more about spheres by reading:
https://brainly.com/question/10171109
#SPJ1
Molly needs 4.65 feet of fencing to
complete the fence she is building.
She has a piece of fencing that is 4 5/8 ft
long. Does she have enough fencing?
Explain.
Answer:
No
Step-by-step explanation:
4 5/8 = 4.625 because 458=4+(5÷8)=4+0.625=4.625
4.65>4.625 so she has less
The temperature in Paris, France is -7°C and the temperature in Malé, Maldives is -3°C
(a) write down how many degrees colder it is in Paris than Malé
(b) Rome is 23 degrees warmer than Paris
Write down the temperature in Rome.
Answer:
a) 3
b) 16 Celsius
Answer:
A. -4°C
B. 16°C
Step-by-step explanation:
A. (-7°C)-(-3°C)= -4°C
Therefore Paris is -4°C colder than Malé.
B. 23+(-7°C)=16°C
Therefore the temperature in Rome is 16°C
Hope it helps you
PLS RATE AS BRAINLIEST ANSWER
Part 1: Use the Pythagorean Theorem to find the length of the missing side in each triangle below
Part 2: Use the Pythagorean Theorem to determine whether the triangles below are right triangles. (c is the longest side)
will give brainliest
Answer:
down there with the work :)
Step-by-step explanation:
formula: a^2+b^2=c^2
Page 1:
1)
6^2+8^2=c^2
36+64=c^2
100=c^2
take the square root of both sides
c=10
2)
8^2+b^2=12^2
64+b^2=144
80=b^2
b=[tex]4\sqrt{5}[/tex]
3)
14^2+b^2=48^2
196+b^2=2304
b^2=2108
b=[tex]2\sqrt{527}[/tex]
Page 2:
1)
5^2+11^2=13^2
25+121=169
no this is not true so this is not a right triangle
2)
10^2+24^2=26^2
100+576=676
this is true so this IS a right triangle
hope this helps!
EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-
(if you put links or don't answer accordingly im reporting your account)
Answer:
i think it's a quadrilateral it's a rhombus.
Step-by-step explanation:
hope this helps
Find the measure of angle 5,6,7 Someone please help
Answer:
ly/3gVQKw3
Step-by-step explanation:
you can look on ly/3gVQKw3 Don't PRESS ON THAT LINK
Solved previously.How many three-digit positive integers $x$ satisfy $3874x 481\equiv 1205 \pmod{23}$
The solution indicates 40 positive three-digit integers of this kind are available.
What are Positive integers?The numbers used for counting as well as organizing are known as natural numbers in mathematics. Cardinal numbers and ordinal numbers are two different types of numbers that are used for counting and ordering, respectively.
Which of these integers are negative?Left of zero on the number line, a negative number is an integer. It is not zero, though.
According to the given information:Any solution x will mod 23 will also have x+23n as a solution, for some integer n.
Since;
900/23 = 39 3/23,
we know:
There are 39 or 40 three-digit integers of this form.
As it happens,
100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n,
hence 40 solutions to the equation.
The equation reduces, mod 23, to
10x = 11
Its solutions are x = 23n +8.
This shows There are 40 three-digit positive integers of this form.
To know more about positive integers visit:
https://brainly.com/question/24929554
#SPJ1
what is the distance of the cookie?
A., 10 inches.
Hope this helps!
What is the equation of a line with a slope of 3 and y-intercept equal to 5?
The equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Given that the slope is 3 and the y-intercept is 5, the equation of the line is y = 3x + 5.
The equation of a line is a mathematical expression of the form y = mx + b, where m is the slope and b is the y-intercept. This equation can be used to describe the relationship between the x-coordinate and y-coordinate of points on a line. In this specific equation, the slope is 3 and the y-intercept is 5, which means that the line passes through the point (0, 5) and has a slope of 3. Substituting 3 for m and 5 for b in the equation, we get y = 3x + 5, which is the equation of the line with a slope of 3 and a y-intercept of 5. We can use this equation to determine the y-coordinate of any given point on the line, provided we know the x-coordinate of the point. It is important to note that this equation is only applicable to straight lines, and not curves.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
2) Place the following numbers in order from least to greatest:
9 22
1,3' 7.3.15
Answer:
hairy ball sack
Step-by-step explanation:
Dose anyone know the answer??
In any function y = f(x) , set of all possible values of x define the domain of f(x), in the graph The curve in terms of x-axis(in 1st & 3rd quadrant) goes from -4 to -2(doesnt include -2).
So domain = [-4, -2)
Similarly, in 2nd and 4th quadrant, for x-axis
It goes from 2 to 5 (doesnt include 2 & 5)
So domain = (2, 5)
Hence,
Domain of the f(x) is [-4, -2) U (2, 5).
Range tells the possible values of y, for this function it goes from -5 to +3(doesnt include 3).
Range is [-5, 3)
A triangle ha two ide of length 7 and 17. What i the mallet poible whole-number length for the third ide?
According to triangle inequality theorem a triangle with two sides 7 units and 17 units, has a third side which measures 10 units.
What is Triangle Inequality Theorem?
According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The two sides of a triangle are -
a=7, b=x and c=17, where a, b and c are the sides of the triangle.
As, 17 is a bigger number so let it be the biggest side.
Now, according to triangle inequality theorem -
a + b = c
7 + x = 17
x = 17 -7
x = 10
Therefore, the third side of the triangle measures 10 units.
To learn more about triangle inequality theorem from the given link
https://brainly.com/question/309896
#SPJ4
What is the probability that andre olivia and zack all win gift cards that are at least $25
The probability that Andre, Olivia, and zack all win gift cards that are at least $25 is 1/4. Hence option C is the correct option.
What is an event?
An event is a collection of experiment results (a subset of the sample space) to which a probability is ascribed in probability theory.
The wheel consists of 8 equal sections. Each section contains the price of a gift card. 4 sections contain a $5 gift card, 2 sections contain a $5 gift card, one section contains a $25 gift card, one section contains a $50 gift card.
To win at least $5, they have to get either $25 or $50.
Thus the number of outcomes of favorable event is 2.
Total number of outcomes is 8.
The probability to win at least $25 is 2/8
Divide denominator and numerator by 2:
2/8 = 1/4
To learn more about probability, click on the below link:
https://brainly.com/question/743479
#SPJ4
On Tuesday Leah bought four hats. On Wednesday half of all the hats that she had were destroyed. On Thursday there were only 13 left. How many did she have on Monday? W: 22 hats N: 20 hats M: 10 hats O: 5 hrs
The number of hats that Leah had on Monday, given that half the hats were destroyed and four hats were bought, was, A. 22 hats.
How to find the number of hats ?If half the hats that Leah owns were destroyed on Wednesday such that only 13 hats were left, then it means that the total hats before the destruction, was :
= 13 hats x 2
= 26 hats
Seeing as Leah bought four hats on Tuesday, this means that the hats she had on Monday were :
= Total hats - Hats purchased on Tuesday
= 26 - 4
= 22 hats
Find out more on hats at https://brainly.com/question/28748609
#SPJ1
Compare your response to the sample response above. Did your explanation include that distance is a function of time? include that the constant rate of change, or slope, is 64? include the equation y = 64x + 22? say to substitute 4 in for x to get 278 miles?
Yes the explanation satisfy the questions stated.
How to compare the value?From the question, distance is said to be a function of time and the constant rate of change is 64.
y = 64x + 22
The above is in the form of a Linear equation:
y = mx + c
Where y = dependent variable (distance)
x = unrelated variable (time)
m = slope = time/distance
22 for c = constant.
m = constant rate of change = 64
If x (time) = 4
y (distance) = 278 miles
y = 64(4) + 22
y = 256 + 22
y = 256 + 22
y = 278 miles
Therefore the value of y is 278 miles.
The complete question is : Distance is a function of time. The constant rate of change is 64. Write
the equation Y=64x + 22. Substitute 4 in for x to get 278 miles,
Compare your response to the sample response above. Did your explanation
include that distance is a function of time?
include that the constant rate of change, or slope, is 64?
include the equation y = 64x + 22?
say to substitute 4 in for x to get 278 miles?
To learn more about linear equation refer to :
https://brainly.com/question/2030026
#SPJ4