Answer:
1. 6 feet
2. 6.25 feet
3. 1 feet
4. 6 feet
Step-by-step explanation:
The equation is : [tex]$h(x)=x^2-7x+6$[/tex]
1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.
So, substituting x = 0 in the equation, we get
[tex]$h(0)=0^2-7(0)+6$[/tex]
[tex]$=0-0+6$[/tex]
[tex]$=6$[/tex]
So, the diving board is 6 feet above the surface of the water.
2. From the equation, we known that it is a parabola and the vertex is minimum.
It is the minimum height which represents the depth Kendra dives into the water.
So the [tex]$x$[/tex] coordinate of the vertex is = [tex]$\frac{-b}{2a}$[/tex]
Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,
a = 1 and b = -7
∴ x coordinate = [tex]$\frac{-(-7)}{2 \times 1} $[/tex]
[tex]$\frac{7}{2}=3.5$[/tex]
Now substituting to find f(x),
[tex]$h(3.5)=(3.5)^2-7(3.5)+6$[/tex]
= -6.25
Therefore, the diver dives 6.25 feet below the water surface.
3. The horizontal distance from the board the diver enters into the water.
This is the y-intercept and it is the value of x when h(x)=0.
∴ [tex]$0=x^2-7x+6$[/tex]
Factorizing, we get [tex]$(x-1)(x-6)=0$[/tex]
∴ [tex]$x=1 \text{ or}\ x=6$[/tex]
So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.
4. We know that the equation given has [tex]$\text{two}$[/tex] x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height [tex]$h(x)=0$[/tex]. The height is the water surface level.
The first x intercept represents the points where Kendra dives into the water.
And the second x intercept is the point where Kendra comes out of the water surface. This this is [tex]$x=6$[/tex] for [tex]$h(x)=0$[/tex].
Thus Kendra dives out of the water surface at 6 feet from the board.
How many kilograms are equivalent to 450 grams?
I need step by step explanation please
Step-by-step explanation:
0.45 kilograms. you decide the mass value by 1000.
Don’t put no links just put a answer now can someone help me
Simplify the expression (x + 3) +9
A. 3x + 9
B. x + 9
C. x + 3
D. x + 12
Answer:
x +12
Step-by-step explanation:
Answer:
x + 12
Step-by-step explanation:
[tex](x + 3) + 9[/tex]
[tex]x + 3 + 9[/tex]
[tex] = x + 12[/tex]
Which equation matches the table?
X 4 5 6 7 8
Y 8 10 12 14 16
y = x - 4
y = x ÷ 2
y = x + 4
y = 2 x
Answer:
y=2x
Step-by-step explanation
anybody know how to do this or what to do
Answer:
we know that 25% of something is = to 1/4 of something and we know 1/4 of that number is 8 so we have to do 8 plus 8 plus 8 plus 8 to get the answer or 8 times 4 which = 32
Step-by-step explanation:
The seesaw moves and the angle created by the left side of the seating board and the central support is now 80 degrees. Create and use a model, to find the distance from point Q to the ground when the angle created by the left side of the seating board and the central support is 80 degrees. Show your work or explain your answer. Round your final answer to the nearest tenth of a foot. Enter your model, your answer, and your work or explanations in the space provided.
Answer:5.7
Step-by-step explanation:
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance between the point Q and the ground is h-[L cos(80°)].
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The Base is the adjacent smaller side of the angle θ.
Let the height of the support be h and the height between the point q and the ground is x. Also, the distance between point Q and the support of the seesaw is L.
Now if we look at the ΔQAR, the measure of the ∠QRA is 80°, therefore, the sine of ∠QRA can be written as,
[tex]\rm Cos(\theta)=\dfrac{Base}{Perpendicular}\\\\Cos(\angle QRA) = \dfrac{AR}{QR}\\\\Cos(\angle QRA) = \dfrac{h-x}{L}\\\\L \times Cos(80^o)=h-x\\\\x=h-[L\ Cos(80^o)][/tex]
Hence, the distance between the point Q and the ground is h-[L cos(80°)].
Learn more about Tangent (Tanθ):
https://brainly.com/question/10623976
What is |6 3/8 - 2| + |-8 5/8 + (-1)|?
Answer:
14
Step-by-step explanation:
2. Dibuja la mesa de tu casa, denota los puntos evidentes y nombra los siguientes elementos u objetos geométricos.
a) Tres planos.
b) Dos rectas de planos distintos.
c) Dos ángulos de un plano y dos de otro.
d) Dos rayos. e) Dos semirrectas.
Answer:
a) The floor of the room, each edge and the top of the table.
b) The edge of one side and one leg of the table.
c) The angle formed between the sides of the table and the angle between the legs of the table and its edges.
d) The vertices of the top of the table.
e) These are same lines.
Step-by-step explanation:
An angle is the amplitude between the two lines. Plane is an object which consists of two dimensions and infinite points. The segment is a fragmented line. A ray is a line which a starting point and a direction.
A) Tres planos que surgen a partir de la mesa de mi casa son la superficie de la mesa, la superficie del suelo sobre el cual se apoya la mesa, y la superficie de la pared sobre la cual reposa la mesa.
B) Dos rectas de planos distintos pueden ser el borde de la mesa, por una parte, y la pared, por el otro.
C) Dos ángulos de un plano y dos de otro son el vértice de la mesa y el ángulo formado entre el borde de la misma y un vaso, por un lado, y el ángulo formado por una baldosa y la pata de la mesa y el ángulo recto formado por las líneas de una baldosa, por la otra.
D) Dos rayas pueden ser la línea a ras del suelo y la línea a ras de la mesa.
E) Dos semirrectas pueden ser ambas patas de la mesa.
Aprende más sobre geometría en https://brainly.com/question/11266123
someone help pleas ewill give brain
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
Equation - [tex]10=2x[/tex]
Solve - divide both sides by 2 - [tex]5 = x[/tex]
HELP ME PLEASEEEEEEEEEEEE
Answer:
Step-by-step explanation:
There is really only one solution which is the third choice. When you are dealing with the equation in the form of y = mx + b, the b stands for the y-intercept. So, your y-intercept equals -1. When you are finding the x-intercept you can just substitute y for 0(the definition of x-intercept is where the graph crosses the x-axis, meaning y needs to be equal to 0) and you get that x equals 1/5.
A diver begins rising toward the surface from 180 feet below sea level. A few
minutes later, the diver is 40 feet below sea level. How many feet did the diver rise in
those few minutes?
Answer:
140
Explanation: cause -180 + 40 = -140 (but absolute value is 140)
26.2 miles in 4 hours. Find the unit rate
Answer:
Step-by-step explanation:
Unit rate = 26.2 ÷ 4 = 6.55
Can y’all help me with this one?
-44+18=-26degrees
negative 26 degrees is your answer
please mark brainliest and have a nice day
Which of the following conditions is/are necessary to justify the use of t procedures in a significance test for the slope of a regression line? (4 points)
I. For each given value of x, the values of the response variable y are Normally distributed.
II. For each given value of x, the values of the response variable y are independent.
III. For each given value of x, the standard deviation of y is the same.
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
The conditions that are required to validate the use of t for the significance test would be:
D). l and ll only
Regression Line"Regression Line" is described as the line that most adequately fits the provided data in order to display the efficacy of the model.
In the given situation, the I and II exemplify the conditions which will validate the process for the significance test.
The normal distribution, and among x and y and the independent response of y over x display that it suits the data successfully.
Thus, option D is the correct answer.
Learn more about "Standard Deviation" here:
brainly.com/question/12402189
Answer: Answer is THREE only.
Step-by-step explanation: Took the test. Also for the other guy's solution, he said one and two were REQUIRED. Make sure you read the question first ya'll. He still answered it.
are all vertical lines parallel?
Answer: Yes
Step-by-step explanation: All vertical lines have the same slope and because of that they are always parallel.
Please hurry lol I’ll give brainliest
Answer:
this is true but what do we have to do?
Step-by-step explanation:
Answer: x = 35, angle 1 = 85, angle 2 = 70, angle 3 = 25
Step-by-step explanation:
Finding x: 85+2x+x-10=180
3x= 105
x= 35
x-10 = angle 3 due to a property of parallels lines so put x in to get that angle 3 is 25 degrees
angle 2x = 70 degrees
70 + 25+angle 1 = 180
angle 1 = 85
angle 2 = 180-85-25 = 70
Write an equation in point-slope form of the line that passes through the point (7, -4) and has a slope of m=-6.
Answer:
(-4-y) = -6(7 - x)
Step-by-step explanation:
Can someone help me with this. Will Mark brainliest.
Answer:
(1.5, -4)
Step-by-step explanation:
( -1, -5) and (4, -3)
[tex](\frac{-1+4}{2} ,\frac{-5-3}{2} )\\\\(\frac{3}{2} ,\frac{-8}{2} )\\\\(1.5,-4)[/tex]
surface area does anyonr know it im confused on the formula
Answer:
131.92ft²
Step-by-step explanation:
okay, so we have to find the area of both circles, and the circumference then multiply that with the height, it's confusing, so:
3² x 3.14 = 28.26 x 2 = 56.52 so that the area of the bases
3 x 2 x 3.14 = 18.85 x 4 = 75.4
75.4 + 56.52 = 131.92
So the surface area of the cylinder is 131.92ft²
How many possible sandwiches can be made from 3 types of bread, 5 types of cheese, and 6 types of filling, assuming each sandwich is made with 1 type of bread, 1 type of cheese, and 1 filling type?
Total combinations = each item x each item:
3 breads x 5 cheese x 6 filling = 90 different combinations
Which of the following equations could be the line of best fit?
A. x = 100
B. y = 100
C. y = x + 100
D. y = x - 100
The real answer is B
Find the area of the shaded sector.
Suppose that 5% of athletes at a certain university are using steroids or other
performance-enhancing drugs (PEDs). Unfortunately, the tests used to detect PEDs
aren't perfect. Suppose that 3% of athletes who are not using PEDs will test positive
and be accused of using PEDs. Meanwhile, 1% of athletes who are using PEDs will test
negative and escape detection. Calculate the probability that a randomly selected
athlete will test positive.
Answer:
There is a 8.11% of any randomly selected athlete to test positive.
Step-by-step explanation:
To make it easier, let's assume there are 100 athletes
5/100 have it
3/95 do not have it, but will test positive
1% of the 5 athletes who are using PEDs = 0.05%
This means that 4.95/100 will test positive
3/95 = 3.16%
(rounded, if you need a more precise answer, it's 3.1578947368421053)
3.16% + 4.95% = 8.11%
Which expression is equivalent to 10(−45x+3)−2x?
−8x+3
−10x+3
−10x+30
−30x+30
Answer:
-10x+30
Step-by-step explanation:
just got it right on edg 2021 :)
None of these are correct
I need help on this
Answer: 1/9
Step-by-step explanation: 9(1/3)^5-1, which is 9(1/3)^4.
Solve and you get 1/9.
i need help pleaseeee
Answer:
Step-by-step explanation:
Answer: -6,-7,-8 etc.
Step-by-step explanation: -2 times -6 = 12 bc a negative times a negative = a positive, and -2×-5=10 which is equal to 10 so if we try -6 it gives us 12 which is greater than 10.
Hope this helps!
The sum of a number and 12 is 31. What is the number? 31 n 12.
Answer:
N=19
Step-by-step explanation:
BNA Brand New Animal is the best anime
The high school soccer team can have no more
than 22 players on the roster. Write and solve an
inequality finding the number of players the
coach may choose if the coach already has 13
players.
Answer:
13 + x ≤ 22
x ≤ 9
Step-by-step explanation:
Total players = 22
Players available = 13
Players remaining = x
The inequality can be written as:
Players available + Players remaining ≤ Total players
13 + x ≤ 22
x ≤ 22 - 13
x ≤ 9
What is the slope of a line perpendicular to the line y=2/3 x + 3 ( just find the slope)
Write the equation of the line graphed at the right(please help I really need this)
the correct answer is X= -3