Answer:
-4, -1, 4
95
Step-by-step explanation:
when n is 1
n² - 5 = 1² - 5
1 - 5 = -4
when n is 2
n² - 5 = 2² - 5
4 - 5 = -1
when n is 3
n² -5 = 3² - 5
9 - 5 = 4
10th term, when n is 10
n² - 5 = 10² - 5
100 - 5 = 95
Please help asap! I will mark brainliest for correct answer!!
a softball player hits a pitched ball when it is 4 feet above the ground. the initial velocity is 75 feet per second. Use the formula: h=-16t^2+vt+s. How long will it take for the ball to hit the ground?
Answer: Do the math, the positive solution
t = 5.0495 seconds (If it's wrong sorry, I havent done a problem like this one in awhile!)
Step-by-step explanation:
PLEASE HELP QUESTION IN PIC
Answer:
(5, -4)
Step-by-step explanation:
Answer:
(5,-4)
Step-by-step explanation:
((0+10/2),(-2-6/2))
(10/2, -8/2)
(5,-4)
A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of the container costs $5/m2 to construct whereas the top and sides cost $3/ m2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost
The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
The given parameters are:
Volume = 480m^3Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
[tex]V = xyz[/tex]
Substitute 480 for V
[tex]xyz =480[/tex]
And the objective cost function would be:
[tex]C =8xy + 6xz + 6yz[/tex]
Differentiate the cost function using Lagrange multipliers
[tex]8x + 6z = \lambda xz[/tex]
[tex]8y + 6z = \lambda yz[/tex]
[tex]6x + 6y = \lambda xy[/tex]
Divide equation (1) by (2)
[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]
[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]
Factor out 2
[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]
Cross multiply
[tex]4xy + 3yz = 4xy + 3xz[/tex]
Evaluate the like terms
[tex]3yz = 3xz[/tex]
Divide both sides by 3z
[tex]y = x[/tex]
Divide the first equation by the third
[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]
[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]
Factor out 2
[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]
Cross multiply
[tex]4xy+3xz = 3xz + 3yz[/tex]
Cancel out the common terms
[tex]4xy = 3yz[/tex]
Divide both sides by y
[tex]4x = 3z[/tex]
Make z the subject
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
Recall that:
[tex]xyz =480[/tex]
Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
[tex]x \times x \times \frac 43x = 480[/tex]
So, we have:
[tex]\frac 43x^3 = 480[/tex]
Multiply both sides by 3/4
[tex]x^3 = 360[/tex]
Take the cube roots of both sides
[tex]x = \sqrt[3]{360}[/tex]
Recall that:
[tex]y = x[/tex]
So, we have:
[tex]y = \sqrt[3]{360}[/tex]
Also, we have:
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Read more about Lagrange multipliers at:
https://brainly.com/question/4609414
If no denominator equals zero, which expression is equivalent to ? A. B. C. D.
The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] and it can be determined by using LCM and fraction.
Given that,Expression;[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]
If no denominator equals zero,
We have to determine,Which expression is equivalent to the given expression?
According to the question,Expression;
[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]
If no denominator equals zero,
To determine the equivalent relation of the given equation following all the steps given below.
Step1; First take the LCM,[tex]\rm= \dfrac{15}{x-6}+\dfrac{7}{x+6}\\\\=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}[/tex]
Step2; Multiply the terms and simplify the equation,[tex]\rm=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}\\\\= \dfrac{15x+90 + 7x-42}{x(x+6) -6 (x+6)}\\\\= \dfrac{22x+48}{x^2+6x -6 x-36}\\\\= \dfrac{22x+48}{x^2-36}\\\\[/tex]
Hence, The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] .
For more details about Expression refer to the link given below.
https://brainly.com/question/14610993
Write the following equations.
Answer:
Step-by-step explanation:
4. 2x + 1 = 17
5. x-13 = 94
6. x/2 = 7
7. 5x = 35
8. x + 43 = 84
9. x-18 = 36
10. x = 8y
11. x = y - 5
12. x + (x+1) + (x+2) = 18
13. x = y + 4
14. 2x + 8 = 24
(a) The area of a rectangular garden is 5658 m?.
If the width of the garden is 69 m, what is its length?
(b) The perimeter of a rectangular window is 262 cm.
If the length of the window is 73 cm, what is its width?
A) Length is 82 m
B) Width is 58 cm
Hope this is helpful!
One research study of illegal drug use among 12- to 17-year-olds reported a decrease in use (from 11.4% in 1997) to 9.8% now. Suppose a survey in a large high school reveals that, in a random sample of 1046 students, report using illegal drugs. Use a 0.05 significance level to test the principal's claim that illegal drug use in her school is below the current national average.
Using the z-distribution, it is found that since the test statistic is more than the critical value for the left-tailed test, it is found that there is not enough evidence to conclude that illegal drug use in her school is below the current national average.
At the null hypothesis, it is tested if drug use in her school is not below the national average, that is:
[tex]H_0: p \geq 0.098[/tex]
At the alternative hypothesis, it is tested if it is below, that is:
[tex]H_1: p < 0.098[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.93 out of 1046 reported using illegal drugs, hence the parameters are:
[tex]n = 1046, \overline{p} = \frac{93}{1046} = 0.0889, p = 0.098[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.0889 - 0.098}{\sqrt{\frac{0.098(0.902)}{1046}}}[/tex]
[tex]z = -0.99[/tex]
The critical value for a left-tailed test, as we are testing if the proportion is less than a value, is [tex]z^{\ast} = -1.645[/tex]
Since the test statistic is more than the critical value for the left-tailed test, it is found that there is not enough evidence to conclude that illegal drug use in her school is below the current national average.
To learn more about the use of the z-distribution to test an hypothesis, you can take a look at https://brainly.com/question/25584945
PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS
Answer:
y = 3x
Step-by-step explanation:
Let's select two points from the given graph.
(1,3) (3,9)
Now, let's use slope formula to find the slope.
m = y2-y1/x2-x1
= 9-3/3-1
= 6/2
= 3
Let's substitute/plug this value into the slope-intercept form.
y = 3x + b
We can see that the y-intercept is 0, from the graph.
b = 0
Therefore,
y = 3x
A group of three friends receives a dinner bill for $87.50. The sales tax rate is 5%. They want to leave a 15% tip on the total bill after tax.
Answer:
The total would come out to be $105.66
Step-by-step explanation:
Answer:
87.50%5=17.50=5%
Step-by-step explanation:
87.50%5=17.50
17.50x3=52.5
52.50
IS IT VALID OR NOT (explaining would be helpful) you want to determine how many students consider math to be their favorite school subject. you randomly survey 75 students. thirty-three students consider math to be their favorite subject while forty-two does not. so, you conclude that 40% of students at your school consider math to be their favorite subject.
Answer:
I would say not valid
Step-by-step explanation:
well, it would actually be 44% since 33/75= 0.44 to represent the number of ppl hat consider math their favorite subject
3,408 divided by 41
Explanation in traditional method
52 POINTS PLS HELP
Answer:
83.1219512195
Step-by-step explanation:
Hope this helps!
look at the graph. which equation represents the graph?
What is the number of solutions to the system of
equations?
Infinitely Many
Solutions
No Solution
One Solution
Two Solutions
Answer:
infinitely many solutions
Step-by-step explanation:
The lines over lap
Can someone help me please?
Answer: a=(3,-4)
B=(3,-1)
C=(5,-2)
Step-by-step explanation:
What is the equation of the line that passes through the point (-5, 6) and has
a
slope of o?
Answer:
y = 6
Step-by-step explanation:
A line with a slope of zero is a horizontal line parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (- 5, 6 ) with y- coordinate 6 , then
y = 6 ← equation of line
At Jared's school, he earns reward
points.
He has earned 350 points.
He wants to have at least 100 points left
at the end of year for prizes.
He wants to use 20 points each week
for Free-Sit Friday.
How many weeks can Jared have Free-
Sit Friday and still have at least 100
points at the end of the year?
Write the Inequality.
Answer:
ok so first take a way 100 from 350
250 then divide by 20
12
Hope This Helps!!!
Someone please help meh
Answer:
1100
Step-by-step explanation:
Answer:
A = 55.15
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos A = adj side / hypotenuse
cos A = 4/7
Taking the inverse cos of each side
cos ^-1 ( cos A) = cos ^-1( 4/7)
A =55.15009542
To the nearest hundredth
A = 55.15
2x+5(x+1) = -8;
Can someone help me solve this problem step by step please?
Answer:
-13/7
Step-by-step explanation:
2x+5(x+1)=-8
2x+5x+5=-8
7x+5=-8
7x=-8-5
7x=-13
7x/7=-13/7
x=-13/7
Answer:
x = -13/7
Step-by-step explanation:
2x+5(x+1) = -8
2x+5x+5 = -8
7x+5 = -8
7x = -8-5
7x = -13
x = -13/7
The minute hand of a clock has a length of 12 cm, and the hour hand has a length of 8 cm
a) How far does the tip of the minute hand travel in one hour?
b) How far does the tip of the hour hand travel in 12 hours?
c) How far does the tip of each hand travel in one week?
Answer:
I have no any ideas
Step-by-step explanation:
sorry
What is 35 + 34 ? I cant use calcu pls help me
Answer:
the answer is 69
Step-by-step explanation:
for your answer you need to understand fast that when you add 34 and 35 what will be the answer you need to think that your answer will be cirrect or not and its very easy question
Kyle was playing archery and shot 20 arrows. 30% of them hit the bullseye. how many of the arrows hit the bullseye?
send help pleaseeeeeeeeeeeeee
MY ANSWER WITH SOLVING STEPS
#CARRYONLEARNING
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What is the approximate value of t?
Answer:
8.48
Step-by-step explanation:
36 + 36 = 72
t^2 = 72
t = 6[tex]\sqrt{2}[/tex] = 8.48
Answer: 6
Step-by-step explanation:
What is the volume of this container?
Answer:
64 in 2 is it the answers im not shure
how many possible number of facemask and face shield can an online seller could sell to get an amount of the least php2 000 based on the data above
During crawfish season, Xavier sells crawfish for $62. 50 per sack and charges a $20. 00 delivery fee. Write an equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer.
The equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer is y = 20 + 62.50x
Given:
cost per sack of crayfish = $62. 50
Delivery fee = $20. 00
y = Total cost
x = sacks of crawfish
The equation:
Total cost = Delivery fee + cost per sack of crayfish(sacks of crawfish)
y = 20 + 62.50x
Therefore, the equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer is y = 20 + 62.50x
Learn more about equation:
https://brainly.com/question/4916384
3) A straight line passes through points (0,7) and (2, -1).
What is its equation?
Answer:
y=-x+A
Step-by-step explanation:
Answer:
y=-4x+7
Step-by-step explanation:
1) find the slope first between the two points
m= y2-y1/x2-x1
m= -1-7/2-0
m=-8/2
m=-4
2) use the linear equation y=mx+c
using the slope we find earlier and the coordinate
to substitute into the equation which is,
y=mx+c
7=-4(0)+c
c=7
3) the answer
y=-4x+7
i will make you brainliest
Answer:
Answers given in the photo
Can you help me with number 45 please ?
Answer:
h = 84
f = 132
g= 28
Step-by-step explanation:
h = 180 - 48 - 48 = 84
f = 180 - 48 = 132
g = 180 -132 - 20 = 28
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answer: A. they will have too much butter
Step-by-step explanation: to much