Answer:
To verify the Cauchy-Bunyakovsky-Schwarz Inequality, (p,q) must be less than (or equal to) ||p|| • ||q||
(1,1,1) is not equal to (-10,5)
Step-by-step explanation:
a°b° + a^1b^1 + a^2b^2 < 5x (-2x^2 + 1)
Any algebra raised to the power of zero is equal to 1.
a°b° = 1 × 1 = 1
1 + ab + a^2b^2 < -10x^3 + 5x
The vectors:
(1,1,1) < (-10,5)
This verifies the Cauchy-Schwarz Inequality
Triangle Inequality states that for any triangle, the sum of the lengths of two sides must be greater than or equal to the length of the third side.
which formula would be used to find the measure of angle 1
Answer:
Option (4)
Step-by-step explanation:
By the Angle of intersecting secants,
"If two lines intersect outside a circle, then the measure of the angle between these lines or secants will be one half of the difference between the intercepted arcs."
From the picture attached,
Angle between the secants = ∠1
Measure of intercepted arcs are a° and b°.
By this theorem,
m∠1 = [tex]\frac{1}{2}(a-b)[/tex]
Option (4) will be the answer.
PLEASE HELP ASAP!! Write a polynomial f(x) that satisfies the following conditions. Polynomial of lowest degree with zeros of -4 (multiplicity of 1), 2 (multiplicity of 3), and with f(0)=64
Answer:
See below.
Step-by-step explanation:
So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.
Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.
Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.
Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:
In other words, we will have:
[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.
Let's determine n first. We know that f(0)=64, thus:
[tex]f(0)=64=4(-2)^3\cdot n[/tex]
[tex]64=-32n, n=-2[/tex]
Now, let's expand:
Expand:
[tex]f(x)=(x+4)(x^2-4x+4)(x-2)(-2)[/tex]
[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]
[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]
[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]
This is the simplest it can get.
The parabola y= x2 - 4 opens:
O up
O down
O right
O left
Answer:
it opens up
goes up 4 but doesn't move left or right
An anchor lowered at a constant rate into the ocean takes 5 seconds to move -17.5 meters. What is the rate of the anchor in meters per second?
Answer:
-3.5 meters per second
Step-by-step explanation:
Take the distance and divide by the time
-17.5 meters/ 5 seconds
-3.5 meters per second
Answer:
-3.5 m/s
Step-by-step explanation:
Rate of the anchor = [tex]\frac{distance}{time}[/tex]
[tex]\frac{-17.5}{5}[/tex]
-3.5 meters per second.
Samantha has 5 granola bars. She wants to give 1/3 of a granola bar to each friend. Which expression can she use to find the number of friends to whom she can give granola bars?
Answer:
5/(1/3)
Step-by-step explanation:
She has 5 granola bars and gives 1/3 of one to each of her friends. To find how many friends she can give it to, divide 5 by 1/3. You would get a total of 15 friends that you can give granola bars to. The question is asking for an expression so the expression would be 5/(1/3) or 5*3
Answer:
1/3 x = 5
x=15
Step-by-step explanation:
You’re multiplying 1/3 times the number of friends (x), and then multiplying both sides by the reciprocal to solve for x
PLZ IM ON THE CLOCK!!!!! A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store can stock no more than 80 balls total during a single month. What is the maximum profit the store can make from selling footballs and baseballs in a typical month? $457.50 $460.00 $462.50 $572.50
Answer:
460
Step-by-step explanation:
Answer:
460
Step-by-step explanation:
Transformations of exponential functions
Answer:
Since the transformation is made by shifting the function right, it is a horizontal transformation.
explain square roots
Answer:A square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16. The symbol is √ which always means the positive square root. Example: √36 = 6 (because 6 x 6 = 36)
Which of the following is an exterior angle of triangle BHE? Yes or no
Answer:
Im not 100% sure, but I think it is:
No
No
No
Yes
what is 3141 times X. x=5783978
Answer:
18167474898
Step-by-step explanation:
I used a calculator.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
The population of fruit flies in a laboratory grows geometrically and is checked everyday at noon. If the population began with 80 fruit flies and reached 125 in two days, what is the population after 4 days?
Answer:
[tex]\boxed{195}[/tex]
Step-by-step explanation:
The fruit flies grows geometrically.
[tex]125=80k^2[/tex]
Find the value of k.
[tex]\sqrt{\frac{125}{80} } =k[/tex]
[tex]1.25=k[/tex]
[tex]P=80(1.25)^t[/tex]
[tex]t[/tex] is number of days.
[tex]P=80(1.25)^4[/tex]
[tex]P=195[/tex]
A fisherman uses a spring scale to weigh a tilapia fish. He records the fish weight as a kilograms and notices that the spring stretches b centimeters. Which expression represents the spring constant (1 =9.8 )? A). 980ab B). 9.8ab C). 9.8ab D). 980ab
Answer:
k = [tex]\frac{980a}{b}[/tex]
Step-by-step explanation:
Fisherman noticed a stretch in the spring = 'b' centimetres
Weight of the fish = a kilograms
If force applied on a spring scale makes a stretch in the spring then Hook's law for the force applied is,
F = kΔx
Where k = spring constant
Δx = stretch in the spring
F = weight applied
F = mg
Here 'm' = mass of the fish
g = gravitational constant
F = a(9.8)
= 9.8a
Δx = b centimetres = 0.01b meters
Therefore, 9.8a = k(0.01b)
k = [tex]\frac{9.8a}{0.01b}[/tex]
k = [tex]\frac{980a}{b}[/tex]
Therefore, spring constant of the spring will be determined by the expression, k = [tex]\frac{980a}{b}[/tex]
BRAINLIEST ANSWER GIVEN Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions. The length of a rectangle is 2 feet longer than the width. The perimeter is 20 feet. Find the dimensions of the rectangle. Length= ?; width=?
Answer:
length = 6 feetwidth = 4 feetStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where l is the length
w is the width
The length of the rectangle is 2 feet longer than the width is written as
l = 2 + w
Perimeter = 20feet
So we have
20 = 2( 2 + w ) + 2w
20 = 4 + 2w + 2w
4w = 16
Divide both sides by 4
w = 4
Substitute w = 4 into l = 2 + w
That's
l = 2 + 4
l = 6
length = 6 feetwidth = 4 feetHope this helps you
Answer:
w = 4 and L = 10
Step-by-step explanation:
perimeter of a rectangle = 2(l+w)
p = 20
L = 2 + w
w = ?
20 = 2(2 + w + w)
20 = 2(2 + 2w)
20/2 = 2 + 2w
10 = 2 + 2w
10 - 2 = 2w
8 = 2w
w = 8/2 = 4
L = w + 2
L = 4 +2 = 6
w = 4 and L = 10
What is 4sqrt7^3 in exponential form?
Answer:
[tex]\boxed{7^{\frac{3}{2} } \times 4}[/tex]
Step-by-step explanation:
[tex]4 (\sqrt{7} )^3[/tex]
Square root can be written as a power.
[tex]4(7^{\frac{1}{2} })^3[/tex]
Multiply the exponents.
[tex]4(7^{\frac{3}{2} })[/tex]
Answer:
A (7^3/4)
Step-by-step explanation:
ed 2020
The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 (4x – 8y = 12) → x – 2y = 3 2x = 18
Answer:
x+2y=12-------(1)
x-2y=3---------(2)
Adding equations 1 and 2
we get
2x=18
x=9
Equation 1
9+2y=15
2y=15-9
2y=6
y=3
The solution of the given system is x=9, y=3
Step-by-step explanation
what is that is the derivative of
x^2-x+3 at the point
x=5
What value of x where
x²-x+3
a minimum?
Answer:
see explanation
Step-by-step explanation:
differentiate using the power rule.
[tex]\frac{d}{dx}[/tex]( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] , thus
[tex]\frac{d}{dx}[/tex](x² - x + 3 ) = 2x - 1
x = 5 → 2(5) - 1 = 10 - 1 = 9
To find the value of x for minimum , equate [tex]\frac{d}{dx}[/tex] to zero
2x - 1 = 0 , then
2x = 1 and
x = [tex]\frac{1}{2}[/tex]
what is the measure of SR?
Answer:
RS = 8
Step-by-step explanation:
Given:
Secant QU = internal secant segment PU + external secant segment PQ = 7 + 9 = 16
Secant QS = internal secant segment RS + external secant segment RQ = (3x - 5) + 8
To find the measure of RS, we need to find the value of x.
Thus, recall the "Two Secant Theorem"
According to the theorem,
(RS + RQ)*RQ = (PU + PQ)*PQ
Thus,
[tex] (3x - 5 + 8)*8 = (7 + 9)*9 [/tex]
[tex] (3x + 3)*8 = (16)*9 [/tex]
[tex] 24x + 24 = 144 [/tex]
Subtract 24 from both sides
[tex] 24x + 24 - 24 = 144 - 24 [/tex]
[tex] 24x = 120 [/tex]
Divide both sides by 24
[tex] \frac{24x}{24} = \frac{120}{24} [/tex]
[tex] x = 5 [/tex]
Plug in the value of x into (3x - 5) to find the measure of RS
RS = 3(5) - 5 = 15 - 7
RS = 8
Trigonometry Dilemma
Answer:
17.1
Step-by-step explanation:
The missing side is x
tan 25° = [tex]\frac{opposite }{adjacent }[/tex] tan 25° = [tex]\frac{8}{x}[/tex]switch tan 25° and x
x = [tex]\frac{8}{tan 25}[/tex] x= 17.15≈17.1What is the slope of the line x = 4?
Answer:
slope is undefined
Step-by-step explanation:
x = 4 is the equation of a vertical line parallel to the y- axis.
The slope of a vertical line is undefined
Answer:
Undefined
Step-by-step explanation:
If the line is strait up like x = 4 that means it is undefined.
Olivia, a golfer, claims that her drive distance is more than 174 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 10% significance level, to persuade them. She hits 15 drives. The mean distance of the sample drives is 188 meters. Olivia knows from experience that the standard deviation for her drive distance is 14 meters. H0: μ=174; Ha: μ>174 α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
Answer:
3.87
Step-by-step explanation:
The computation is shown below:
Data provided in the question
mean distance = [tex]\bar x[/tex] = 188 meters
Standard deviaton = [tex]\sigma = 14[/tex]
Hits drivers = 15
The distance = 174 meters
H_0: μ≤174;
H_a: μ>174
Based on the above information, the test statistic z-score is
[tex]z = \frac{\bar x - \mu }{\sigma / \sqrt{n} } \\\\ = \frac{188 - 174}{\ 14 / \sqrt{15} }[/tex]
= 3.87
Hence, the test statistic is 3.87
Note:
We take the μ≤174 instead of μ=174;
what other numbers can you square that result in 9 ?
Step-by-step explanation:
I'm not sure what your answers are, but you can only square 3 and -3 to get 9.
Answer:
3, -3
Step-by-step explanation:
3*3 = 9
-3 * -3 = 9
These are the only two numbers that square to 9
Need help solving hi
Answer:
See below.
Step-by-step explanation:
[tex]2 \ln(x+2)=6[/tex]
[tex]\ln (x+2)=3[/tex]
[tex]e^{\ln(x+2)}=e^3[/tex]
[tex]x+2=e^3[/tex]
[tex]x=e^3-2[/tex]
[tex]x\approx 18. 09[/tex]
Item 25
The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function.
0
1
2
3
4
5
6
7
8
9
10
Item 25
The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function.
0
1
2
3
4
5
6
7
8
9
10
Answer:
5
Step-by-step explanation:
Find the sum of 1342, -295, -456,89.
Answer:
680
Step-by-step explanation:
add 1342+89 to get 1431
then add -295+-456 to get -751
then subtract 751 from 1431 to get 680
Step-by-step explanation:
Hope this is correct and helpful
HAVE A GOOD DAY!
One number is 2 more than another. The difference between their squares is 52. What are the numbers?
Answer:
The aprox, numbers:
4.1633 and 8.3266
Step-by-step explanation:
a = 2b
a² - b² = 52
then:
(2b)² - b² = 52
4b² - b² = 52
3b² = 52
b² = 52/3
b² = 17.333
√b² = √17.333
b = 4.1633 aprox.
a = 2b
a = 2*4.1633
a = 8.3266
Check:
8.3266² - 4.1633² = 52
69.333 - 17.333 = 52
WHY CAN'T ANYONE HELP ME? Twice last month, Judy Carter rented a car in Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 440 miles, and the rental cost her $286. On her second business trip she drove 190 miles in 3 days, and paid $165.50 for the rental. Find the daily fee and the mileage charge.
Answer:
The daily rate is $33 and the per mile rate is $0.35
Step-by-step explanation:
4x + 440y = 286
3x + 190y = 165.5
We can solve this systems of equations by multiplying the second statement by [tex]-\frac{4}{3}[/tex] to try and eliminate the x variable.
4x + 440y = 286
-4x - [tex]\frac{760}{3}[/tex]y = -220[tex]\frac{2}{3}[/tex]
[tex]\frac{560}{3}[/tex] y= [tex]\frac{196}{3}[/tex]
560y = 196
y = 0.35
So, the rate per mile is 0.35. Now, with this info, let's find the daily rate by plugging it into the equation.
[tex]4x + 440\cdot0.35 = 286\\4x + 154 = 286\\4x = 132\\x = 33[/tex]
So, the daily rate is $33 and the mile rate is $0.35.
Hope this helped!
Answer:
the daily fee =33 dollars
and the mileage charge.=0.35
let d: be daily fee and m for mileage
cost of rental =(d*number of days)+ (m*number of mileage)
her first trip: 4d+440m=286
her second trip: 3d+190m=165.5
solve by addition and elimination
4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286
3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)
12d+1320m=858
12d+760m=662
subtract two equation to eliminate d
12d+1320m-12d-760m=858-662
560m=196
m=7/20=0.35 for on mileage
d: 4d+440m=286
4d=286-440(0.35)
d=(286-154)/4 33 dollars
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps
Answer:
123 domestic stamps
89 foreign stamps
Step-by-step explanation:
Answer:
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
Which equation represents the total number of stamps Malik collected?
✔ x + y = 212
Which equation represents the difference in the number of foreign and domestic stamps Malik collected?
✔ x – y = 34
Which system of linear equations represents the situation?
✔ x – y = 34 and x + y = 212
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
This system of equations models the given information for both stamp types.
x – y = 34
x + y = 212
Solve the system of equations.
How many foreign stamps does Malik have?
✔ 89 foreign stamps
How many domestic stamps does Malik have?
✔ 123 domestic stamps
Step-by-step explanation:
its right on 2021 edge! :) hope this helps
Of the cartons produced by a company, % have a puncture, % have a smashed corner, and % have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing%. (Type an integer or a decimal. Do not round.)
Full Question
Of the cartons produced by a company, 10% have a puncture, 6% have a smashed corner, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing ____%. (Type an integer or a decimal. Do not round.)
Answer:
[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]
Step-by-step explanation:
Given
[tex]Puncture\ Corner = 10\%[/tex]
[tex]Smashed\ Corner = 6\%[/tex]
[tex]Punctured\ and\ Smashed\ Corner = 0.4\%[/tex]
Required
[tex]P(Punctured\ or\ Smashed\ Corner)[/tex]
For non-mutually exclusive event described above, P(Punctured or Smashed Corner) can be calculated as thus;
[tex]P(Punctured\ or\ Smashed\ Corner) = P(Punctured\ Corner) + P(Smashed\ Corner) - P(Punctured\ and\ Smashed\ Corner)[/tex]
Substitute:
10% for P(Puncture Corner),
6% for P(Smashed Corner) and
0.4% for P(Punctured and Smashed Corner)
[tex]P(Punctured\ or\ Smashed\ Corner) = 10\% + 6\% - 0.4\%[/tex]
[tex]P(Punctured\ or\ Smashed\ Corner) = 15.6\%[/tex]
Convert % to fraction
[tex]P(Punctured\ or\ Smashed\ Corner) = \frac{15.6}{100}[/tex]
Convert to decimal
[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]
Using Venn probabilities, it is found that:
The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.In this problem, the events are:
Event A: Puncture.Event B: Smashed corner.The "or" probability is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
10% have a puncture, hence [tex]P(A) = 0.1[/tex]6% have a smashed corner, hence [tex]P(B) = 0.06[/tex].0.4% have both a puncture and a smashed corner, hence [tex]P(A \cup B) = 0.004[/tex].Then:
[tex]P(A \cup B) = 0.1 + 0.06 - 0.004 = 0.156[/tex]
The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.
To learn more about Venn probabilities, you can check https://brainly.com/question/25698611
what is the value of this expression when a = 2 and b = -3 ? a^3 - b^3 / 5
Answer:
13 2/5
Step-by-step explanation:
a = 2 and b = -3
so the question asks whats.... a^3 - b^3/5
First we plug in the values of a and b
(2)^3 - (-3)^3 /5
Now we solve the ones in paranthesis first
(2)^3 = 8 because 2×2×2 and
-(-3)^3 forget about the - outside the parenthesis so
(-3)^3 = (-27) because (-3)×(-3)×(-3)
now we put it back together
8 -(-27)/5
the two minus become plus so
8 + 27/5
Now we solve it like fractions
8 and 27/5
simplify
13 and 2/5
Hope that helps!
solve for x in the diagram below
Answer:
45
Step-by-step explanation:
Both angles (2x+45) and x together form a straight angle which measures 180 degrees.
Together should make you think of adding the angle measurements.
So we have that (2x+45)+x should be 180 degrees.
The equation we want to solve is:
(2x+45)+x=180
2x+45+x=180
(2x+x)+45=180
3x+45=180
3x=180-45
3x=135
x=135/3
x=45
Let's confirm that x is 45.
(2x+45) with x=45:
(2*45+45)
(3*45)
135
So (2x+45)+x at x=45 gives us:
135+45
180
Answer has been confirmed.
Answer:
[tex]\boxed{x = 45}[/tex]
Step-by-step explanation:
=> [tex]x+2x+45 = 180[/tex] (Angles on a straight line add up to 180 degrees)
=> [tex]3x+45 = 180[/tex]
Subtracting 45 to both sides
=> 3x = 180-45
=> 3x = 135
Dividing both sides by 3
=> x = 45