Using the vertex of a quadratic equation, it is found that P is at a maximum for l = -0.5 thousand foot-candles.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the function for P is given by:
[tex]P(l) = \frac{110l}{l^2 + l + 4}[/tex]
The function will be at a maximum when the denominator is at a minimum. The denominator is a quadratic function with coefficients a = 1, b = 1, c = 4, hence:
[tex]l_v = -\frac{b}{2a} = -\frac{1}{2} = -0.5[/tex]
P is at a maximum for l = -0.5 thousand foot-candles.
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A square pyramid has a volume of 1024 cm3. If one edge of the square base is 16 cm, find the height.
Answer:
Step-by-step explanation:
v = 1/3* L * w * h
1024 = 1/3 * 16 * 16 * height
1024 = 85.3333333 * height
divide both sides by 85.3 to isolate height = 12 cm
check your work
1024 = 1/3 * 16 * 16 * 12
1024 = 1024
yes they equal so its correct
Solve for x. Leave your answer in simplest radical form.
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER
Answer:
x = 7
Step-by-step explanation:
I used the formula c^2 = a^2 + b^2
if you need further explanation,let me know
What do we do to both sides of this equation to solve?
x+3=5
Question 1 options:
Subtract 3 from both sides
Add 3 to both sides
Multiply both sides by 3
Divide both sides by 3
Answer:
Subtract 3 from both sides.
Step-by-step explanation:
x + 3 = 5
x = 5 - 3
x = 2
I know I`m late sorry, still wanted to answer
. _ .
Answer:
First option
Step-by-step explanation:
Given the following question:
[tex]x+3=5[/tex]
To find the answer we need to subtract three on both sides, since we are given a positive three ( + 3) instead of a negative three (- 3) If the equation was " x - 3 = 5 " we would then add three on both sides but in this case we have a positive three.
[tex]x+3=5[/tex]
[tex]3-3=0[/tex]
[tex]5-3=2[/tex]
[tex]x=2[/tex]
Which means your answer is the first option or "subtract 3 from both sides."
Hope this helps.
An airplane flies with a constant speed
of 680 miles per hour. How long will it
take to travel a distance of 2720 miles?
4 hours
T= d/s
= 2720/680
= 4
Hope this helps!
Carl Lewis one United States of America greatest athletes in Track and field,Ran a hundred meters in 10.1 seconds,
at this speed what is his rate in
kilometers per
hour?
Answer:
35.64 km / hour
Step-by-step explanation:
100m = 10.1s
100/10.1 m per second
3600 seconds in a hour
100/10.1 X 3600 = 35643.56436
= 35.64356436 km per hour
PLEASE HELP! PLEASE HELP! I NEED TO GET THIS RIGHT! PLEASE ANSWER FULLY!
Answer:
what do you need help with
The lateral area of a cone is 9.81 in. The radius is 1.4 in. Find the slant height.
Answer:
As Per Provided Information
Lateral area of cone is 9.81 in Radius of cone is 1.4 inWe have been asked to determine the slant height of the cone .
Formula used to calculate the lateral area of a cone is
[tex] \boxed{\bf \: \purple{ Lateral \: Area _{(Cone)} \: = \pi\:rl}}[/tex]
here
l denote slant height
r denote radius
Substituting the value we obtain
[tex] \longrightarrow\tt \: 9.81 = 3.14 \times 1.4 \times l \\ \\ \\ \longrightarrow\tt \:9.81 = 4.396 \times l \\ \\ \\ \longrightarrow\tt \: \cfrac{9.81}{4.396} = l \\ \\ \\ \longrightarrow\tt \: \: l \: = \cfrac{9.81}{4.396} \\ \\ \\ \longrightarrow\tt \: \: l \: = \cancel\cfrac{9.81}{4.396} \\ \\ \\ \longrightarrow\tt \: \: l \: = 2.23 \:inch \: \: (approx)[/tex]
Therefore,
Slant height of the cone is 2.23 in .Which property of addition is shown below?
If x = a + bi and y = –a – bi, x + y = 0.
commutative property
identity property
associative property
inverse property
Answer: D
Step-by-step explanation:
please help. 50 points on the line
Answer:some where from 65-75 feet
Step-by-step explanation:
yoooo somebody help me please!!
Answer:
the answer is 202 square inch
Step-by-step explanation:
Ref. to the diagram I have attached.
First, we can find the area of the square.
Here the side of the square is given 4 inches.
1. So Area of the square= side * side= 4*4= 16 square inches.
Now let's find the area of the smaller rectangle. Now here,
As one side of the square is the same as the breadth of the rectangle, the breadth of the rectangle will be 4 inches, and the length is given 9 inches.
2. So, Area of the smaller rectangle= length* breadth= 9*4= 36 square inches.
Now, lastly, we will find the area of the bigger rectangle:
Here, the length will be 15 inches and the breadth will be 10 inches (as the opposite sides in a rectangle are equal and the values are already given).
3. ∴ Area of bigger rectangle= l*b= 15*10= 150 square inches.
So now,
To find the total area of the figure, we need to add all the areas:
36+ 16+ 150= 202 square in.
ANSWER IS 202 sq. in.
I know it's a bit long and boring to read, but hope it helps!!
for a area and perimeter math question what is 2/3x2/3????????
Answer:
4/9
Step-by-step explanation:
2/3 × 2/3 is 4/9
2×2 is 4 and 3×3 is 9
Sophia, a yoga instructor at Yoga for You, selected random samples of 210 students from a nearby high school and 210 students from a nearby college to compare levels of physical fitness. The mean and standard deviation of the fitness levels of the high school students were 82 and 14 respectively. The mean and standard deviation of the fitness levels of the college students were 86 and 17 respectively. She conducted a two-sided t-test with a resulting t-value of 2. 63. Lf a = 0. 05, what is an appropriate conclusion from this study?
Because the sample means only differ by four, the population means are not significantly different.
Because the second group has a larger standard deviation, their mean fitness score is significantly higher.
Because the second group has a larger standard deviation, the mean fitness score of the first group is significantly higher
Because the p-value is greater than a 0. 05, the mean fitness scores for the two groups of students are not significantly different.
Because the p-value is less than a 0. 05, the mean fitness scores for the two groups of students are significantly different
Because the p-value is less than 0.05, the mean fitness scores for the two groups of students are significantly different
========================================================
Explanation:
Use a T calculator to find that P(T > 2.63) = 0.00459 approximately when we have 209 degrees of freedom.
Double this to get 2*0.00459 = 0.00918 and this is the approximate p-value
Since the p-value is less than alpha = 0.05, this means we reject the null and conclude that the two population means are significantly different.
Abraham is three times as old as Sylvia.
In eight years' time, Abraham will be
twice as old as Sylvia. How old is
Abraham?
Answer:
24 years old
Step-by-step explanation:
let x = age of abraham, y = age of sylvia
x = 3y
x + 8 = 2y+16 => (2(y+8))
3y + 8 = 2y + 16
y = 8
x = 3(8)
x = 24
Question 3:
Solve for e.
m=-2e+c/3
Answer:
5
Step-by-step explanation:
IMAGE IS DOWN BELOW!!
SOMEONE PLEASE HELP ME!!
ILL GIVE YOU BRAINLIST ANSWER AND POINTS!!
Answer:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
a and b are legs, c is the hypotenuse
[tex]9^{2}[/tex] + [tex]11^{2}[/tex] = [tex]c^{2}[/tex]
81 + 121 = [tex]c^{2}[/tex]
202 = [tex]c^{2}[/tex] ( square root each side [tex]\sqrt{202}[/tex]
14.2126704036 = c
c = 14.2
2
1) You have a 24 foot round swimming pool
that is four feet deep. What is the surface
area of the sides and bottom of the pool?
Round to the nearest tenth of a foot.
Answer:
The surface area is 301.4ft
Step-by-step explanation:
To find the surface area of a circular pool, you multiply the diameter and depth and then multiply by 3.14.
24*4 = 96
96*3.14 = 301.44
If the poh of vinegar is 9.45, what is its [oh− ]? round to the nearest hundredth. × 10n m n =
The [OH] of vinegar to the nearest hundredth is 2.82 * 10^-5
How to calculate the [OH] of a substance:The sum of the pH and pOH of a substance is 14. Mathematically
[OH−] = Antilog (pOH)
Given the following parameters
[OH−] = Antilog (9.45)
Substitute
[OH−] = 2.82 * 10^-5
Hence the [OH] of vinegar to the nearest hundredth is 2.82 * 10^-5
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Answer:
The person above me is incorrect
1st blank is 3.55
2nd blank is -10
Step-by-step explanation:
Look at the image (bottom left corner)
what make this equation true? 4s+3=63
★ 1st solve the given equation to find value of "s".
[tex]\sf{⇝4s+3=63} \\ \\ \sf{⇝arranging \: terms} \\ \\ \sf{⇝4s=63-3} \\ \\ \sf{⇝4s=60} \\ \\ \sf{⇝s=\cancel\frac{60}{4}} \\ \\ \sf{⇝s=15} \\ \\ [/tex]
★ substituting s= 15 to check whether the equation is true or not?
4(15)+3=6360+3=6363=63 LHS=RHS★ hence,the above equation is true !
[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]
Jonathan is making his favorite pasta dish. His mom ate 2/7 of the pasta, and his brother ate 1/6 of the pasta. How much did they eat in all?
Answer:
23/42
Step-by-step explanation:
2/7 = 12/42
1/6 = 7/42
12/42 + 7/42 = 19/42
42/42 - 19/42 = 23/42
WRITE INEQUALITY AND SOLVE• Lamar weighs 250 pounds. If he loses 10 pounds
and then 2 pounds per week after that, how many
weeks will it take him to weigh less than 175 pounds?
Answer:
40 weeks
Step-by-step explanation:
2 x 40 = 80
240-80=160
so for him to get under 175 it could be 40
i am so sorry if this is inccorect.
can y’all help me answer question 4 pleas e
Answer:
b = a + 13
Step-by-step explanation:
bc 1 + 13 = 14
Hope this helps !
find four rational number between -1/7 and 2/7...
Rational numbers are numbers which can be expressed as a fraction or in decimals. Integers, Whole numbers, Natural numbers are rational.
======================================================
Rational numbers between -1/7 and 2/7 : -
-0.1-0.0500.050.10.150.20.25Make a number line and find the numbers between the two given numbers.
the 7th grade has 207 students. there are 23 more girls than boys in the grade. how many boys are in the 7th grade
Answer:
92 boys
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
Answer:
42 boys
Step-by-step explanation:
Represent the number of boys with 'b' and that of girls with 'b + 23.'
Then b + (b + 23) = 207.
Simplifying, we get 2b = 84, so that b is 42. There are 42 boys and
(42 + 23) girls, or 65 girls.
Sam filled 4 large bottles and 6 small bottles with 6.8 litres of orange juice . Each large bottle could hold 0.5 litres more than each small bottle. How much orange juice can a small bottle hold?
Answer:
0.48 litres
Step-by-step explanation:
let the large bottles be x and small bottles be y
4x + 6y = 6.8
x = 0.5 + y
so substituting x in equation 1:
4(0.5 + y) + 6y = 6.8
2 + 4y + 6y = 6.8
10y = 4.8
y = 0.48
hello, people, can you help me please if you get it right I will give you the CROWN
Answer:
[tex]\sf 343\dfrac{3}{4} \ mi[/tex]
1 inch = 125 miles
[tex]\rightarrow \sf 2\dfrac{3}{4} \ * \ 125[/tex]
[tex]\rightarrow \sf \dfrac{11}{4} \ * \ 125[/tex]
[tex]\rightarrow \sf \dfrac{1375}{4}[/tex]
[tex]\rightarrow \sf 343\dfrac{3}{4} \ mi[/tex]
Answer:
Option A
Step-by-step explanation:
Given:
1 inch = 125 milesTo avoid confusion, let's convert 2 3/4 into decimals. To convert a fraction into decimals, multiply and divide the fraction by 100.
⇒ (2 3/4 x 100)/100 = (11/4 x 100)/100 = (1100/4)/100 = 275/100 = 2.75
Now, multiply 2.75 to both sides of the equation "1 inch = 125 miles", as we need to find the actual distance of 2.75 inches
⇒ 1 inch = 125 miles
⇒ 1 × 2.75 = 125 × 2.75
⇒ 2.75 inches = 343.75 miles
The options given are in fraction form. So, we need to reconvert 343.75 into fraction form. Once again, multiply and divide the decimal by 100.
⇒ (343.75 × 100)/100 = (34375)/100
We can clearly tell that this is a mixed fraction because 34375 is greater than 100. To convert this fraction into mixed fraction, let's write the expanded form of this fraction.
⇒ (34375)/100 = 34000/100 + 300/100 + 75/100
⇒ (343 x 100)/100 + 75/100
⇒ 343 + 75/100 = 343 + 3/4
⇒ 343 3/4 miles (Option A)
What is the additive inverse of the polynomial –9xy2 + 6x2y – 5x3?
Answer:
The answer 9xy^2-6x^2y+5x^3
Step-by-step explanation
You are working for the company Trinity Mathematical Concepts are
asked for create the following logo for the company. If each vertices of the triangle are the centers of the circles, what is the area of the shaded region?
Your answer will be in terms of "x", where "x" is the radius of the circles.
Answer:
[tex](2\pi -3\sqrt{3})x^2/4[/tex]Step-by-step explanation:
The sides of the triangle in the middle are equal to x so tis is equilateral triangle.
Its interior angle is 60°.
Each shaded part is the area of 60° segment of circle with the radius x.
The area of each segment is the difference between 60° sector and the area of triangle.
[tex]A_{segment}=A_{sector}-A_{triangle}[/tex]Area of sector
[tex]A_{sector} = (60/360)*\pi r^2=(1/6)\pi x^2[/tex]Area of triangle
[tex]A_{triangle}=(\sqrt{3}/4)a^2= (\sqrt{3}/4)x^2[/tex]The shaded area is
[tex]A = 3((1/6)\pi x^2 - (\sqrt{3} /4)x^2)=((1/2)\pi -3\sqrt{3} /4)x^2=(2\pi -3\sqrt{3})x^2/4[/tex]in a town of 120 people,it is know that 40 are teachers,25 are students and 9 are doctors amd the rest are office workers.what is the possibility that he or she is an office workers?
23/60
hope it helps...!!!!
Order the steps to solve the equation
log(x^2-15)= log(2x) form 1 to 5
x^2-2x-15=0
Potential solutions are -3 and 5
x^2-15=2x
x-5=0 or x+3=0
(x-5)(x+3)=0
Answer:
Step-by-step explanation:
When the base of a logarithm is not specified, it is assumed that the base is 10. Therefore we have:
[tex]log_1_0(x^2-15)=log_1_0(2x)[/tex]
Intuitively you can see that if the two arguments inside of the logarithm equal each other, then both sides will be equal to each other. Therefore, you can say the following requirement:
[tex]x^2-15=2x[/tex]
Subtract 2x on both sides to get:
[tex]x^2-2x-15=0[/tex]
Use the quadratic formula to solve for 'x' to get:
[tex]x=(-b+\sqrt{b^2-4ac} )/2a[/tex]
[tex]x=(-b-\sqrt{b^2-4ac} )/2a[/tex]
Beginning with the first solution:
[tex]x=(-(-2)+\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]
[tex]x=2+\sqrt{4+60} )/2[/tex]
[tex]x=(2+\sqrt{64}) /2[/tex]
[tex]x=(2+8)/2[/tex]
[tex]x=5[/tex]
Second solution:
[tex]x=(-(-2)-\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]
[tex]x=(2-\sqrt{4+60} )/2[/tex]
[tex]x=(2-8)/2[/tex]
[tex]x=-6/2[/tex]
[tex]x=-3[/tex]
Since the 'x' value inside of the logarith is squared, the -3 is a valid solution. Ordinarily, the log function cannot take on negative values.
Which of the following functions best models the data represented by the scatterplot shown below
y=25x+20
y=160x−100
y=8x2+10
y=2x+12
Answer:
I am pretty sure the answer is going to be y=25x+20 :)
Have an amazing day!!
Please rate and mark brainliest!!
The correct function for the given data representation will be,
y = 8x² + 10
What is Function?
A relation between a set of inputs having one output each is called a function.
Data representation is given by the scatterplot in the graph.
Now,
Take a function y = 8x² + 10
Then, Check each point on the x - axis for the value of y - axis.
So. Substitute x = 1 in the function we get;
y = 8 × 1 + 10
y = 8 + 10
y = 18
So, Point is (1, 18)
For, x = 3
y = 8 × 3² + 10
y = 72 +10
y = 82
So, Point is (3, 82)
For, x = 5
y = 8 × 5² + 20
y = 200 + 20
y = 220
So, Point is (5, 220)
Thus, All points are satisfy the given scatterplot graph.
So, The correct function for the given data representation will be,
y = 8x² + 10
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