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.
A certain bacterium has an exponential growth rate of 25% per day. If we start with 0.5 gram and provide unlimited resources, how many bacteria can we grow in 2 weeks? Round to the nearest tenth of a gram. HINT: How many days are in a week?
Answer:
FV= 11.369 gr
Step-by-step explanation:
Giving the following information:
Growth rate (g)= 25% per day
Number of periods (n)= 14 days
Present Value (PV)= 0.5 gr
To calculate the Future Value(FV) in grams, we need to use the following formula:
FV= PV*(1+i)^n
FV= 0.5*(1.25^14)
FV= 11.369 gr
Compare each set of rational numbers.
-1
2
✓ -1.5
1
o
2
-2
-1
-1 is a negative real and rational integer.
2 is a positive real number
[tex] \sqrt{ - 1.5} [/tex]
is an imaginary or nonreal number.
1 is rational
0 is rational
2 rational counting number
-2 is a negative integer
and do is -1
(450) + (28.75x) = 967.50
solve for x
Answer:
18
Step-by-step explanation:
Hello,
In order to solve for x, we need to isolate the variable on one side of the equation.
To do this, we subtract 450 from both sides of the equation, and this will give you:
28.75x = 517.5
As mentioned, we need to isolate x, so we divide both sides by 28.75. This will give the following.
x = 18
Hope this helps!
If p(x)= 2^x, what is the value of p(3) - p(2)?
Answer:
4
Step-by-step explanation:
p(3) = 2³ = 8
p(2) = 2² = 4
8-4 = 4
are these proportional?
3/2 and 18/8
Answer:
For two fractions to be proportional, they must be equivalent. 32=1.5 and 188=2.25 , so these fractions are not proportional.
Step-by-step explanation:
A tangent-tangent angle intercepts two arcs that measure 124 degrees and 236 degrees what is the measure of the tangent-tangent angle
Answer:
It can be calculated by finding the difference between the two angles. Half of this difference will be the angle that is required.
Therefore
236 - 124 = 112
Tanget-tanget angle = 112 / 2 = 56 degrees
Please help!!! I'll mark you as brainliest!!!!
What is 0.504854369 as a percentage rounded to the nearest tenth
Is 41.77 a integer?
Answer:
nope, an integer must be a whole number, no fractions / decimals
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
An integer is a whole number or a number that is not a fraction or decimal. So, since 41.77 is a decimal it cannot be an integer. Examples of integers are 41 or -2.
Luis's car used 4/5
of a gallon to travel 29 miles. At what rate does the car use gas, in miles per gallon?
Answer:
36.25 miles per gallon
Step-by-step explanation:
4/5 = .8
29/.8 = x/1
cross-multiply:
.8x = 29
x = 36.25
la suma de los tres terminos de una sustraccion es 720. calcula el minuendo
Answer:
i dont know
Step-by-step explanation:
It costs $1.16 to buy four-fifths a pound of apples. How much would it cost to
buy 8 pounds?
Answer:
11.60
Step-by-step explanation:
If the cost of 4/5th a pound of apples is $1.16, and we need to find the cost of that of 8 pounds, then you start by finding how many 4/5ths of a pound are in 8 pounds. 8 dividided by 0.8 (the decimal form of 4/5) is 10. Taking that 10, you would multiply the original cost of $1.16, which would bring you to the total of $11.60.
During the summer Tyler delivers packages a Miranda Cares for animal on a farm to show there earnings Tyler makes a graph and Miranda makes a table, which statement is true?
Answer:
divide the earnings number by the time, and then subtract the quotient by the slope of tylers graph.
Joe earns a monthly salary of 250 plus a commission on his total sales. Last month his total sales were $7,289 and he earned a total of $1,275. What is his commission rate?
Answer: Joe earns a monthly salary of 250 plus a commission on his total sales. Last month his total sales were $7,289 and he earned a total of $1,275. What is his commission rate?
Step-by-step explanation:
250 + $7,289 + $1,275 = 8814
Find the area of the figure
Answer:
A=153.94
Step-by-step explanation:
EASY POINTS!! INCLUDE A DISC!!
pls no bots i don't want any links :(
Step-by-step explanation:
[tex]180 - 35 - 65 = \\ = 145 - 65 = \\ = 80[/tex]
Answer:
i BELIVE it will be 50 I’m super sorry if I’m wrong lovly.
Step-by-step explanation:
A spherical globe has a diameter of 10 inches. What is the approximate volume of the globe?
Answer:
523.33 in^3
Step-by-step explanation:
A sphere is a 3-dimensional version of a circle. An example of a sphere is a ball
Volume of a sphere = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]
Where
π = 3.14
r = radius
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
diameter = 2r
Radius = 10 in / 2 = 5 inches
[tex]\frac{4}{3}[/tex] × 3.14 ×[tex]5^{3}[/tex] = 523.33 [tex]in^{3}[/tex]
Find the area of the shaded sector.
Jamal uses the line of best fit y = 700x + 38,000 to predict his annual salary, y, after x years.
What is the y-intercept of the line of best fit and what is the meaning of the y-intercept?
The y-intercept is n intercept is a point on the y-axis, through which the slope of the line passes and the y-intercept of the given equation is 38,000.
What is a y-intercept?In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
The given equation is y=700x+38,000 to predict his annual salary, y, after x years.
In the given equation, y-intercept is 38,000.
Therefore, the y-intercept is n intercept is a point on the y-axis, through which the slope of the line passes and the y-intercept of the given equation is 38,000.
To learn more about the y-intercept visit:
brainly.com/question/14180189.
#SPJ2
Help Please! Find The Area Of A Circle With D=8.2
Answer:
52.81
Step-by-step explanat
Select all the true sentences!!!
Answer:
only the 1st is true
Step-by-step explanation:
the rest are wronf
On Saturday, a local hamburger shop sold a combined total of 261 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answer:
134 hamburgers
Step-by-step explanation:
Let H = # of hamburgers
# of cheeseburgers = 2H
H + 2H = 402
3H = 402
H = 402/3
H = 134
PLS hurry!! I'LL MARK BRAINLIEST!
Answer:
A. 5+x-12=2x-7
-7+x+2x-7
x=2x
x-2x=0
-x=0-> x=0
B.
when X=-0.5
5+(-0.5)-12=2 (-0.5)-7
-7.5=-8 (answer does not work)
when X=0
5+0-12=2(0)-7
-7=-7 (answer works)
when x=1
5+1-12=2(1)-7
18=-5 (answer does not work)
Step-by-step explanation:
Answer:
[tex]x=0[/tex]
Step-by-step explanation:
A) From this case you would need to narrow down the whole equation...
Like this: [tex]5+x-12=2x-7[/tex] → [tex]x-7=2x-7[/tex] → [tex]x=0[/tex]
B) To prove that one of these numbers solve the equation, we would have to check it ourselves.
Like this: [tex]5+(-0.5)-12=2(-0.5)-7[/tex] → [tex]-7.5=-8[/tex] (SO THIS WON'T WORK)
[tex]5+0-12=2*0-7[/tex] → [tex]0=0[/tex] (THIS WORKS!)
[tex]5+1-12=2(1)-7[/tex] → [tex]-6=-5[/tex] (NOR DOES THIS WORK)
Therefore: [tex]x=0[/tex] will work to solve the equation correctly
Can someone please help me answer this question asap thank you
Factor this expression completely and then placed the factors in the proper location on the grid. Note: please factors alphabetically in the grid!
ab + 4 + a + 4b
PLEASE ANSWER, WILL MARK BRAINLYEST!
Answer:
(a + 4)(b + 1)
Step-by-step explanation:
ab + 4 + a + 4b
Rearrange the expression to find the GCF.
ab + a + 4b + 4
Now find the GCF.
a (b + 1) + 4 (b + 1)
Divide the whole thing by b+1
(a + 4)(b + 1)
Select all the expressions that have a value 10
help i need the answer
Answer:
NO
Step-by-step explanation:
If the diameter of the circle is doubled the area will be increased 4 times
the radius of a circle is 18.4 inches. the circle's circumference is about ___ inches.
use 3.14 for pi
Answer:
115.552 or 116 inches.
Step-by-step explanation:
Use the circumference of a circle formula which is C= 2piR. Where C is circumference and R is radius. So you get C=2(3.14×18.4) which gives you 115.552.
d) Vegetable ghee is stored in a rectangular vessel of internal dimensions
60 cm x 10 cm x 45 cm. It is transferred into the identical cubical vessels. If the
internal length of each cubical vessel is 10 cm. how many vessels are required to
empty the rectangular vessel?
27 vessels
Step-by-step explanation:
get the volume of the rectangular vessel 60cm ×10cm ×45cm giving you 27000cm3.Find volume of one of the cube 10cm×10cm×10cm giving 1000cm3.
if 1 cube =1000cm3
? = 27000cm3
27000cm3× 1cube
1000cm3
di
vide then get your answer as 27 vessels
A person visits the store and picks up five kg vegetables for did he buy?
£6.25. Which vegetable
Tomato - £1.50 per kg Carrot - £1.75 per kg Cabbage - £2 per kg Beetroot - £1.25 per kg
Evaluate the expression: 2y-9 when y = 3
Answer:
-3
Step-by-step explanation:
2·3-9
6-9 = -3