Answer: x = 6.32 or -0.32
Step-by-step explanation:
2x² - 6x + 10 = 0
No we divide the expression by 2 to make the coefficient of x² equals 1
We now have
x² - 3x + 5 = 0
Now we remove 5 to the other side of the equation
x² - 3x = -5
we add to both side square of half the coefficient of x which is 3
x² - 3x + ( ⁻³/₂)² = -5 + (⁻³/₂)²
(x - ³/₂)² = -5 + ⁹/₄
Resolve into fraction
(x - ³/₂)² = ⁻¹¹/4
Take the roots of the equation
x - ³/₂ = √¹¹/₄
x - ³/₂ = √11/₂
x = ³/₂ ± 3.32/₂
= 3+ 3.32 or 3 - 3.32
= 6.32 or - 0.32
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
find the values of x and y that make k ll j and m ll n
Answer:
x = 80
y = 130
Step-by-step explanation:
The 2 angles are supplementary. so, x-30 + x+50 = 180.
We solve and get 2x = 180-20
x = 80
y = x+50, because of parallel rules.
y = 130
Answer:
x = 80
y = 130
Step-by-step explanation:edge 2020
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.
A random sample of 61 Foreign Language movies made in the last 10 years has a mean length of 135.7 minutes with a standard deviation of 13.7 minutes. Construct a 95% confidence interval.
Answer:
95% confidensce interval of the mean (two-tail) = [132.2, 139.2]
Step-by-step explanation:
Given:
N = size of sample = 61
m = sample mean = 135.7
s = sample standard deviation 13.7
Need 95% confidence interval
Solution.
alpha (95% confidence interval) = 0.05
(1-alpha/2) = 0.975 [two sided]
Equation for confidence interval of the mean
= m +/- t(1-alpha/2,N-1) * s / sqrt(N)
= 135.7 +/- 2.0003 * 13.7 / sqrt(60)
= [132.16, 139.24]
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]
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:
You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) a) State the null and the alternative hypotheses. b) Compute the standard error of the mean. c) Determine the test statistic. d) Test to determine whether or not the mean of the population is significantly less than 21.
Answer:
a
The null hypothesis is
[tex]H_o : \mu = 21[/tex]
The Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
b
[tex]\sigma_{\= x} = 0.8944[/tex]
c
[tex]t = -2.236[/tex]
d
Yes the mean population is significantly less than 21.
Step-by-step explanation:
From the question we are given
a set of data
20 18 17 22 18
The confidence level is 90%
The sample size is n = 5
Generally the mean of the sample is mathematically evaluated as
[tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]
[tex]\= x = 19[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]
[tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]
[tex]\sigma = 2[/tex]
Now the confidence level is given as 90 % hence the level of significance can be evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10[/tex]%
[tex]\alpha =0.10[/tex]
Now the null hypothesis is
[tex]H_o : \mu = 21[/tex]
the Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
The standard error of mean is mathematically evaluated as
[tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]
[tex]\sigma_{\= x} = 0.8944[/tex]
The test statistic is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]
[tex]t = -2.236[/tex]
The critical value of the level of significance is obtained from the critical value table for z values as
[tex]z_{0.10} = 1.28[/tex]
Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected
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)
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
Find the total area of the prism.
Answer:
A=1,728
Step-by-step explanation:
To find the area of a prism, you must find the area of one side, then multiply it by so it would be Width*Hight*Depth, W*H*D.
The width is 12, the hight is 12, and the depth is 12 so you can write
A=12*12*12
Multiply 12 by 12
A=144*12
Multiply 12 by 144 to get your final total area
A=1,728
Hope this helps, feel free to ask follow-up questions if confused.
Have a good day! :)
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:
what is 3141 times X. x=5783978
Answer:
18167474898
Step-by-step explanation:
I used a calculator.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
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.
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
a warehouse had 3 shelves long enough to hold 8 boxes and high enough to hold 4 boxes. all the shelves are full how many boxes are on the shelves all together?
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I think. I just multiplies the 3 numbers. Hope this helps (:
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I just multiplies the 3 numbers.
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!
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
24=3(n-5) solve for n
Answer:
n = 13
Step-by-step explanation:
24 = 3 (n-5)
3n - 15 = 24
3n = 24 +15
3n = 39
n = 39/3
n = 13
Answer:
[tex]\boxed{\sf n=13}[/tex]
Step-by-step explanation:
[tex]\sf 24=3(n-5)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]\sf 24=3n-15[/tex]
[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]
[tex]\sf 24+15=3n-15+15[/tex]
[tex]\sf 39=3n[/tex]
[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]
[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]
[tex]\sf 13=n[/tex]
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
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
Line segment TS is tangent to circle O at point N.
Circle O is shown. Line segment Q N goes from one side of the circle to the other side. Tangent T S intersects the circle at point N. Point P is on the circle between points Q and N. Point R is on the circle between points Q and N. Angle Q N T is 74 degrees.
If the measure of Angle Q N T is 74°, what is the measure of Arc Q P N?
37°
74°
148°
212°\
Answer:
148°
Step-by-step explanation:
The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.
arc QN = 2(74°) = 148°
_____
Comment on the question and answer
Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.
__
We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.
Answer:
148
Step-by-step explanation:
Edge 2020
Hi any help is appreciated. Just wanna graduate:))
Answer: C
Step-by-step explanation:
h · k(x) = 2(3x - 5)(-2x + 1)
= (6x - 10)(-2x + 1)
= -12x² + 6x + 20x - 10
= -12x² + 26x - 10
Answer:
C
Step-by-step explanation:
h(x) × k(x)
= 2(3x - 5)(- 2x + 1) ← expand factors using FOIL
= 2(- 6x² + 3x + 10x - 5)
= 2(- 6x² + 13x - 5) ← distribute parenthesis by 2
= - 12x² + 26x - 10 → C
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;
please help me out with these questions. Its trigonometry.
Find the value of the lettered angles
In case the pic's not clear;
[tex] \cos \alpha = \sin(50 + \alpha ) [/tex]
Answer: i) θ = 30°, 60°, 210°, & 240°
ii) θ = 20° & 200°
Step-by-step explanation:
i) sin (2θ) = cos 30°
[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]
To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above. θ = 30°, 60°, 210°, 240°
If you need ALL of the solutions (more than one rotation), add 180n to the solutions. θ = 30° + 180n & 60° + 180n
*********************************************************************************************
ii) cos α = sin (50 + α)
Use the Identity: cos α = sin (90 - α)
Use Transitive Property to get: sin (50° + α) = sin (90° - α)
50° + α = 90° - α
50° + 2α = 90°
2α = 40°
α = 20°
To find all solutions for one rotation, add 360/2 = 180 to the solution above.
α = 20°, 200°
If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n
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
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.
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
(25 points) PLEASE HELP, I gotta get this done or my mom will beat the hell out of me
Solve
x + y = 2
4y = -4x + 8
by elimination (not Gaussian!)
Thanks!
(also, please show work!)
Answer:
x=1
y=1
Step-by-step explanation:
Please look at the image below for solutions⬇️
Answer:
Step-by-step explanation:
Add the equations in order to solve for the first variable . Plug this value into the equations in order to solve for the remaining variables.
Point form
(x, 2-x)
Transformations of exponential functions
Answer:
Since the transformation is made by shifting the function right, it is a horizontal transformation.
What is the image of (-8, 10) when reflected in the y-axis?
Answer:
if you're just reflecting the point over the y-axis it just becomes (8,10)
Answer: (8, 10)
Explanation and Example:
I have a trick that I use. I'm not sure if it will make sense to you but I'll explain it. When the question asks you to reflect over the x-axis, then keep the x in (x,y) the same and just flip the sign for the y. If the question asks you to reflect over the y-axis, then keep y the same and flip the sign for x.
Reflect over x-axis:
(-2, 6) -----> (-2, -6)
Reflect over y-axis:
(-4, -8) -----> (4, -8)