The solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.
The equation 4x^2 - 20x + 25 = 10 can be rewritten as 4x^2 - 20x + 15 = 0. To find the solutions to this equation, we can factor it or use the quadratic formula.
Factoring:The equation factors as (2x - 5)(2x - 3) = 0. Setting each factor equal to zero, we get 2x - 5 = 0 and 2x - 3 = 0. Solving these equations, we find x = 5/2 and x = 3/2.
Quadratic Formula:Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± sqrt(b^2 - 4ac)) / 2a, we can determine the solutions.
In this case, a = 4, b = -20, and c = 15. Substituting these values into the quadratic formula, we get x = (-(-20) ± sqrt((-20)^2 - 4 * 4 * 15)) / (2 * 4), which simplifies to x = (20 ± sqrt(400 - 240)) / 8.
Simplifying further, we have x = (20 ± sqrt(160)) / 8, which becomes x = (20 ± 4sqrt(10)) / 8. Finally, simplifying again, we obtain x = 5/2 ± sqrt(10)/2, which gives us the same solutions as before: x = 5/2 and x = 3/2.
Therefore, the solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.
To find the solutions to the equation, we can either factor it or use the quadratic formula. In this case, factoring and using the quadratic formula both yield the same solutions: x = 5/2 and x = 3/2. These values of x satisfy the equation 4x^2 - 20x + 25 = 10 when substituted back into the equation.
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Find the absolute maximum and absolute minimum of the function z = f(x, y) = 3x² – 12x + 3y2 – 12y on the domain D: x2 + y2 < 4. (Use symbolic notation and fractions where needed.)
The absolute maximum and minimum of the function z = f(x, y) = 3x² - 12x + 3y² - 12y on the domain x² + y² < 4 are not provided.
To find the absolute maximum and minimum of the function z = f(x, y) = 3x² - 12x + 3y² - 12y on the domain D: x² + y² < 4, we need to locate the critical points and examine the boundaries of the domain.
First, we find the critical points by taking the partial derivatives with respect to x and y, setting them equal to zero, and solving for x and y. However, in this case, the given function is a quadratic expression without any cross-terms, so it does not have critical points.Next, we consider the boundary of the domain D: x² + y² = 4, which represents a circle of radius 2 centered at the origin. To find the extreme values on this boundary, we can use methods like Lagrange multipliers or parametrize the boundary and evaluate the function.Since the absolute maximum and minimum values are not provided, further calculations are needed to determine these values for the given function on the given domain.
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If the longest side of a triangle is 12 inches, what must be true about the lengths of the remaining sides?
Help me with this please
Answer:
x = 138
Step-by-step explanation:
Exterior angle thm:
68 + 70 = x
x = 138
i need help please explain to me the answer !
Answer:
If the triangle is similar then their ratio is also same
x = 8
6 4.8
X =8×6
4.8
x = 10 cm
hope this helps
good day mate
Determine whether the following equation is separable. If so, solve the given initial value problem. dy/dt = 2ty +1, y(0) = -3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation is separable. The solution to the initial value problem is y(t) = ___ B. The equation is not separable. 9.3.28
The equation is separable. The solution to the initial value problem is y(t) = y(0) = -3.
A. The equation is separable. The solution to the initial value problem is y(t) = ___
To determine whether the given differential equation is separable, we need to check if it can be written in the form dy/dt = g(t) * h(y), where g(t) is a function of t only and h(y) is a function of y only.
In this case, the equation is dy/dt = 2ty + 1. We can rearrange it as:
dy = (2ty + 1) dt
Now, we can see that we have both y and t terms on the right-hand side, indicating that the equation is not yet separable.
Therefore, the correct choice is B. The equation is not separable.
Unfortunately, no solution can be provided for the initial value problem y(0) = -3 since the equation is not separable.
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A tank contains 2380 L of pure water. A solution that contains 0.07 kg of sugar per liter enters a tank at the rate 7 U/min The solution is mixed and drains from the tank at the same rate. (a) How much sugar is in the tank initially? 0 (kg) (b) Find the amount of sugar in the tank after t minutes. amount = 166.6(1-e^(-t/340)) your answer should be a function of t) (kg) (c) Find the concentration of sugar in the solution in the tank after 33 minutes. concentration = 166.6 (kg/L)
The concentration of sugar in the solution in the tank after 33 minutes is approximately 0.00734 kg/L or 7.34 g/L.
(a) Initially, the tank contains pure water, so there is no sugar in the tank. Therefore, the amount of sugar in the tank initially is 0 kg.
(b) The amount of sugar in the tank after t minutes can be calculated using the formula:
amount = 166.6(1 - [tex]e^{-t/340}[/tex])
Here, t is the time in minutes. This formula is derived from the exponential decay model, where the rate of sugar leaving the tank is proportional to the amount of sugar present. The constant 166.6 represents the equilibrium amount of sugar in the tank.
As time passes, the term [tex]e^{-t/340}[/tex] approaches 1, and the amount of sugar in the tank approaches the equilibrium amount of 166.6 kg.
(c) To find the concentration of sugar in the solution in the tank after 33 minutes, we need to divide the amount of sugar by the volume of the tank. The volume of the tank is given as 2380 L.
First, let's calculate the amount of sugar in the tank after 33 minutes using the formula from part (b):
amount = 166.6(1 - [tex]e^{-33/340}[/tex])
amount ≈ 166.6(1 - 0.895)
amount ≈ 166.6(0.105)
amount ≈ 17.493 kg
Now, we can calculate the concentration:
concentration = amount / volume
concentration = 17.493 kg / 2380 L
concentration ≈ 0.00734 kg/L
Therefore, the concentration of sugar in the solution in the tank after 33 minutes is approximately 0.00734 kg/L or 7.34 g/L.
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*HURRY* Kale purchased a new car. The car had a list price of $28,730. Kale made a down payment of $2,750 and financed the rest, paying 4.9% interest compounded monthly over a payment period of four years. If Kale also had to pay 8.4% sales tax, a $750 vehicle registration fee, and an $88 documentation fee, what is his monthly payment
Answer:
$5934
Step-by-step explanation:
OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS- PLSS TELL ME WHAT TO DRAW
Answer:
The answer to this question is $14,916
Step-by-step explanation:
18,469 - 3,553 = 14916
As he already has money for the car.
A bar model is shown in the linked picture.
Tamika is making a flag design in the shape of a parallelogram. Which x- and y-values must she use in order to guarantee that the flag is in the shape of a parallelogram?
Answer:
x = 1/2
y = 3
Step-by-step explanation:
Remark
The diagonals of a parallelogram cut each other in half. That means that x lengths are equal and the y lengths are equal
Equations
3y = y + 6
10x = 6x + 2
Solution for x
10x = 6x + 2 Subtract 6x from both sides
10x - 6x = 6x - 6x + 2
4x = 2 Divide by 4
4x/4 = 2/4
x = 1/2
Solution for y
3y = y + 6
3y - y = y- y + 6
2y = 6
y = 3
Answer:
Step-by-step explanation:
How many more gift card raffle tickets will
be entered than shopping spree raffle tickets
if there are 500 total raffle tickets?
Answer:
25 tickets
Step-by-step explanation:
If the answer is wrong, I don't know what to say because the answer I got is 25
The would be 25 more gift card raffle ticket than shopping spree raffle tickets if there are 500 total raffle tickets
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The shopping spree raffle tickets is 35% while the gift card tickets is 40%. Hence for 500 tickets:
Difference = (40% - 35%) * 500 = 25 tickets
The would be 25 more gift card raffle ticket than shopping spree raffle tickets if there are 500 total raffle tickets
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can someone help plz ... mark brainliest ❤️
Answer:
Top:(4r⁹+3r³-5)
Bottom: r⁵
Step-by-step explanation:
Please help me with the
Answer: i think its 10
Step-by-step explanation:
Serenity is going to invest $850 and leave it in an account
for 5 years. Assuming the interest is compounded
annually, what interest rate, to the nearest hundredth of a
percent, would be required in order for Serenity to end up
with $1,130?
Answer:
5.86
Step-by-step explanation: its right on delta math
can somebody help me please
Answer:
B
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² = 4² + ([tex]\sqrt{5}[/tex] )² = 16 + 5 = 21 ( take the square root of both sides )
x = [tex]\sqrt{21}[/tex] → B
How many pints is 80 cups
Answer:
40
Step-by-step explanation:
2 cups = 1 pt
therefore
1/2 is the equation
...
80/2 = 40
what is the longitudinal position latitudinal position of Nepal
Step-by-step explanation:
I think that is your answer because in the Himalayas it lies between latitudes 26.
10 points!! Please give me real help!!
Answer:
32
Step-by-step explanation:
Test for equality of population means against the alternative that the means are different assuming normality, choosing ? 5% and using two samples of sizes 12 and 18, with mean 10 and 14, respectively, and equal standard deviation 3.
The p-value (0.0208) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to suggest the case.
Null hypothesis (H0): The population means are equal, μ1 = μ2.
Alternative hypothesis (Ha): The population means are different, μ1 ≠ μ2.
Select the significance level (α): In this case, α = 0.05.
Now, The test statistic for a two-sample t-test is given by:
t = (sample mean 1 - sample mean 2) / √((s1² / n1) + (s2² / n2))
where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Here X₁ = 10, X₂ = 14, s= 3, n₁ =12, n₂ = 18
So, t= (10-14) / √(3²/12) + (3²/18) et:
t= (-4)/ √(3/4 + 1/2)
t= -4 / (5/4)
t= -2.7931
Now, degrees of freedom (df):
= (9/12 + 9/18)² / (((9/12)² / 11) + ((9/18)² / 17))
= 25.164
So, the p value will be 0.0208.
As, p-value is less than α (0.0208 < 0.05), we reject the null hypothesis.
Since the p-value (0.0208) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to suggest the case.
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this is 9th grade math.funfdjvnuvuv
y = -2/5 x + 22/5 is the required equation of the line passing the coordinates
Determining the equation of a lineThe equation of a line in slope intercept form is expressed as y = mx +b
where;
m is the slope
b is the y-intercept
Given the coordinate points (-4, 6) and (6, 2), the slope of the line is expressed as:
Slope = 2-6/6+4
Slope = -4/10
Slope = -2/5
For the y-intercept
2 = -2/5(6) + b
2 + 12/5 = b
b = 22/5
Hence the equation of the line passing the coordinate is y = -2/5 x + 22/5
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In 20 seconds, a roller coaster goes up a 100-meter hill, then down 72 meters and then back up a 48-meter rise. what integer represents the vertical change from the start of the ride for the coaster after the 20 seconds
This is the answer
I hope if you get it correct or right
Good luck everyone
The total vertical change from the start of the ride for the roller coaster after the 20 seconds 76 m.
What is vertical change?The rise is the vertical difference between two points called vertical change.
Calculation for the vertical change:Step 1: Calculation for the the total rise when roller coaster goes up a 100 meter hill and the down 72 meter.Thus, the total vertical rise will be,
100 (upward) - 72 (downward) = 28(upward)
Step 2: Calculation for the total rise after the roller coaster again goes vertical to 48 meter.So, the total rise will become,
28(upward) + 48(upward) = 76(upward)
Therefore, the total vertical rise of the roller is 76 meter during the time of 20 seconds.
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HELP ASAPPPPPPPPPPPPPP
3.14 x 11 = 34.54
Pi = 3.14 so times by 11 = 34.54
Can someone help out? No BS please.
Answer:
Angle EHG
Step-by-step explanation:
If you want explanation tell me in comments
Answer:
the correct answer is angle EHB
Determine the surface area of a cereal box with these dimensions width: 3 inches length: 8 inches height: 12 inches
The results of an empirical study reveal the following: n=27, sample mean = 3,000, sample standard deviation = 900. The 90% confidence interval of the true population mean is closet to: = = 2,400 and 3,400 1,200 and 4,800 2,700 and 3,300 0 2,000 and 4,000.
The 90% confidence interval is approximately 2,400 and 3,400.
The 90% confidence interval of the true population mean can be calculated using the formula: sample mean ± (critical value * standard error). Since the sample size is small (n=27), we need to use the t-distribution and its corresponding critical value. For a 90% confidence level with 26 degrees of freedom (n-1), the critical value is approximately 1.706.
Using the given values, the standard error is calculated as the sample standard deviation divided by the square root of the sample size: 900 / sqrt(27) ≈ 171.97.
Substituting the values into the formula, the 90% confidence interval is approximately 3,000 ± (1.706 * 171.97), which yields a range of approximately 2,424.5 to 3,575.5.
Therefore, the closest option to the 90% confidence interval is 2,400 and 3,400.
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PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
pi, and square root of 2
I don't think you're ACTUALLY going to give me brainliest
For a given confidence interval and significance level, and assuming a relatively small sample size, say 25, the relationship between a T critical value and a Z critical value can be best expressed as: a T-Value > Z-Value a True O False
T-value is not always greater than Z-value. Therefore, the statement is false
False. The relationship between a T critical value and a Z critical value is not that a T value is always greater than a Z value. The choice between using a T critical value or a Z critical value depends on the specific context and assumptions of the statistical analysis.
In general, when the sample size is small (typically below 30) and the population standard deviation is unknown, a T critical value is used. The T distribution accounts for the additional uncertainty introduced by the smaller sample size, resulting in wider confidence intervals and more conservative hypothesis tests compared to the Z distribution.
On the other hand, when the sample size is large (typically above 30) or the population standard deviation is known, a Z critical value is used. The Z distribution assumes a large sample size, and it is based on the known population standard deviation or the approximation of the sample standard deviation to the population standard deviation.
Therefore, it is incorrect to state that a T-value is always greater than a Z-value. The choice between T and Z critical values depends on the specific conditions and assumptions of the statistical analysis being performed.
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Prove or disprove the following statement: if A, B, and C are
sets with finite cardinalities that satisfy A ∩ B ∩ C = ∅, then |A
∪ B ∪ C| = |A| + |B| + |C|.
The statement |A ∪ B ∪ C| = |A| + |B| + |C| is true, which means the statement is proven.
Let A, B, and C be sets with finite cardinalities that satisfy A ∩ B ∩ C = ∅.
We have to prove that |A ∪ B ∪ C| = |A| + |B| + |C|.
The addition law of sets states that the cardinality of a union of two finite sets is equal to the sum of the cardinalities of the sets minus the cardinality of their intersection.
Thus, we get: |A ∪ B ∪ C| = |A ∪ B| + |C| − |(A ∩ B) ∪ C| = (|A| + |B| − |A ∩ B|) + |C| − |(A ∩ B) ∩ C| = |A| + |B| + |C| − |A ∩ B ∩ C|.Since A ∩ B ∩ C = ∅, we get |A ∪ B ∪ C| = |A| + |B| + |C|.
Thus, the statement is proven.
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Find the particular solution determined by the given condition. ds/dt = 16t^2 + 9t - 6; s = 120 when t = 0 The particular solution that satisfies the given condition is s =
The particular solution that satisfies the given condition is s = (16/3)t³ + (9/2)t² - 6t + 120
To find the particular solution of the differential equation ds/dt = 16t² + 9t - 6 with the condition s = 120 when t = 0, we need to integrate the right-hand side of the equation with respect to t and then solve for the constant of integration using the given condition.
First, let's integrate the right-hand side of the equation:
∫(ds/dt) dt = ∫(16t² + 9t - 6) dt
Integrating term by term, we get:
s = (16/3)t³ + (9/2)t² - 6t + C
Now, we can use the given condition s = 120 when t = 0 to determine the value of the constant of integration C:
120 = (16/3)(0)³ + (9/2)(0)² - 6(0) + C
120 = C
Therefore, the particular solution that satisfies the given condition is:
s = (16/3)t³ + (9/2)t² - 6t + 120
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Please answer correctly I will mark you Brainliest!
Answer:
1047.12in³
Step-by-step explanation:
The volume of the sphere is:
V= 4/3 πr³
Where r is radius
Therefore the volume of each pinata is:
V= 4/3 x π x 5³
V= 523.6in³
The total:
V = 523.6 + 523.6 = 1047.12in³
Solve the inequality
*
2x^2+ 5x – 3 < 0.
Answer:
heres the answer I think
Step-by-step explanation:
-3 < x < 1/2