Identify all the real roots of 4x^4+31x^3-4x^2-89x+22=0
The real roots of a function are the rational and the irrational roots of the function
The real roots are: [tex]\mathbf{x = -2}[/tex], [tex]\mathbf{x = \frac 14}[/tex], [tex]\mathbf{x = -3 - 2\sqrt{5}}[/tex] and [tex]\mathbf{x = -3 + 2\sqrt{5}}[/tex]
The equation is given as:
[tex]\mathbf{ 4x^4+31x^3-4x^2-89x+22=0}[/tex]
Factorize
[tex]\mathbf{(x + 2) (4 x - 1) (x^2 + 6 x - 11) = 0}[/tex]
Split
[tex]\mathbf{x + 2 = 0\ or\ 4 x - 1 = 0 \ or\ x^2 + 6 x - 11 = 0}[/tex]
Solve for x
[tex]\mathbf{x = -2\ or\ x = \frac 14 \ or\ x^2 + 6 x - 11 = 0}[/tex]
Solve
[tex]\mathbf{x^2 + 6 x - 11 = 0}[/tex] using the following quadratic formula:
[tex]\mathbf{x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
So, we have:
[tex]\mathbf{x = \frac{-6 \pm \sqrt{6^2 - 4 \times 1 \times -11}}{2 \times 1}}[/tex]
[tex]\mathbf{x = \frac{-6 \pm \sqrt{80}}{2}}[/tex]
[tex]\mathbf{x = \frac{-6 \pm 4\sqrt{5}}{2}}[/tex]
[tex]\mathbf{x = -3 \pm 2\sqrt{5}}[/tex]
Hence, the real roots are:
[tex]\mathbf{x = -2}[/tex], [tex]\mathbf{x = \frac 14}[/tex], [tex]\mathbf{x = -3 - 2\sqrt{5}}[/tex] and [tex]\mathbf{x = -3 + 2\sqrt{5}}[/tex]
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Huey works 175 hours each month and earns $14.25 per hour after taxes. His monthly budget is shown. How much money is left over in his budget for unplanned expenses?
Answer:
Nothing will be left over.
Step-by-step explanation:
You need to multiply the 175 by 14.25 to get his total income each month.
Then you add all of the expenses of 1250, 200, 350, 400, 225, 300.
Huey earns 2,493.75 every month, and his expenses are 2,725.
2,493.75 - 2725 = a negative rational number
I ain't gonna do it, because he ain't got no money in his wallet.
(I don't talk like that above, I'm just pretending to be an official Texan.)
If he has negative money left over, I don't think he would spend some more tbh, so the answer would be nothing would be left over.
Hope this helps someone in the future!
At 6 1/2¢ per pound of string beans, how much does 7 pounds cost?
a skateboard that cost $53 was put on sale for 25% discount. What was the sale price of the skateboard?
67 ,73 ,77,82,86,,86,91,98 find the median
Jill sold half of her comic books and then bought sixteen more. she now has 43. how many comic books did she begin with?
Answer: 54
Step-by-step explanation: 43-16=27 times 2 =54
Given two vectors a⃗ = 4.60 i^+ 7.20 j^ and b⃗ = 5.10 i^− 2.70 j^ , find the scalar product of the two vectors a⃗ and b⃗ .
In this exercise we have to use the knowledge of vectors to find the dot product between them, in this way we can say that:
[tex]|a|*|b|=42.9[/tex]
Knowing that it was stated by the text that the vectors have the value of :
[tex]a=<4.60,7.20>\\ b=<5.10,2.70> [/tex]
The scalar product, or the inner product, or the dot-product, is by summing the products of the respective directions, will be:
[tex]|a|*|b|=4.6*5.1+7.2*2.7\\ =23.46+19.44\\ =42.9 [/tex]
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Let be the linear transformation that first reflects points through the -axis and then then reflects points through the line . find the standard matrix for
In the case above, the standard matrix A for T:
T= [0 1]
[-1 0]
What is linear transformation about?A linear transformation is known to be a kind of a function that exist from one vector point to another and it is one that often respects the linear) structure of all of vector space.
Note that in the linear transformation;
T: R² R²
T= (x, y), (-x, y)
Since:
(x,y) - (x,-y) - (y,-x)
A= [-1 0]
[0 1]
A= [-1 0] = A= [-x]
[0 1] [y]
Then [tex]T_{b}[/tex] is the reflection of (x- y); Since;
B = [0 1]
[1 0]
Then [tex]T_{B} (T_{a}(x) )[/tex] = [0 1] = A= [-x]
[0 1] [y]
= [-x]
[y]
Then: T: = [0 1] [x]
[0 1] [y]
Therefore, In the case above, the standard matrix A for T:
T= [0 1]
[-1 0]
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factor 64a^2b^36-1
1. (8ab6 + 1)(8ab6 – 1)
2. (8ab18 – 1)
3. (8ab18 + 1)(8ab18 – 1)
4. (8ab6 – 1)
Ron is taking an inventory at his store. Based on previous sales, he predicted sales of 25 folders and 230 erasers. He actually sold 30 folders and 200 erasers. What is the percent error for the erasers?
Answer: There is 15% error for the erasers
Step-by-step explanation:
Since we have given that
Number of folders he predicted = 25
Number of erasers he predicted = 230
Total number of inventories he predicted is given by
[tex]230+25=255[/tex]
Number of erasers he actually sold = 200
Number of folders he actually sold = 30
Total number of inventories he actually sold is given by
[tex]200+30=230[/tex]
Error in estimation is given by
[tex]230-200=30[/tex]
Percentage of error for the erasers only
[tex]\frac{30}{200}\times 100\\\\=\frac{30}{2}\\\\=15\%[/tex]
Hence, there is 15% error for the erasers.
Answer:
15 %
Step-by-step explanation:
2.4.5 journal: graphs of exponential functions
When filled, a particular round balloon has a diameter of 14 inches. What is the approximate volume of air needed to fill this balloon?
Answer:
the answer is 1,437
Step-by-step explanation:
The amount of a chemical solution is measured to be 2 liters. What is the percent error of the measurement?
The amount of a chemical solution is measured to be 2 liters. What is the percent error of the measurement?
25%
<5 and <6 are complementary angles m<5=13 what is the measure of <6
write a doubles fact that can help you solve 6+5=11
Mr Thomas shoveled 12 1/2 yards of sand in 2 1/2 hours . At that rate how many yards did he shovel in one hour ?
List 3 values that would make this inequality true 43 < y -30
Final answer:
To make the inequality 43 < y - 30 true, add 30 to both sides to get 73 < y. Any number greater than 73, such as 74, 80, or 90, will satisfy the inequality.
Explanation:
To find values that make the inequality 43 < y - 30 true, you simply need to add 30 to both sides of the inequality. This gives you:
73 < y
This means that any value greater than 73 will make the inequality true. Here are three examples:
y = 74 (since 74 is greater than 73)y = 80 (since 80 is greater than 73)y = 90 (since 90 is greater than 73)You can choose any three numbers greater than 73, and they will satisfy the inequality 43 < y - 30.
Brent tosses a quarter 4 times and 3 times it comes up heads. the probability of heads is:
The level of nitrogen oxides (nox) in the exhaust after 50,000 miles or fewer of driving of cars of a particular model varies normally with mean 0.03 g/mi and standard deviation 0.01 g/mi. a company has 64 cars of this model in its fleet. what is the level l such that the probability that the average nox level x for the fleet is greater than l is only 0.01? (hint: this requires a backward normal calculation. round your answer to three decimal places.)
We can use the z-score formula with the known z-score corresponding to a probability of 0.01 to calculate the exhaust NOx emission level. This gives us approximately 0.001 g/mi.
Explanation:In this scenario, we're dealing with a normal distribution problem wherein we use the formula for z-score to answer it. The z-score formula is =(−)/(/√), where x is the data point, μ is the population mean, n is the size of the data set, and σ is the standard deviation.
In this case, we want to find x, or the NOx emission level, such that the probability of finding an automobile with a level greater than x is 0.01. So, we need to find the z-score that corresponds to a probability of 0.01 and then use it in our formula to solve for x.
Using standard z-score tables or an online z-score calculator, we find that a probability of 0.01 corresponds to a z-score of approximately -2.33 (p and z have opposite signs). We then substitute this z-score, along with the given mean μ=0.03 and standard deviation σ=0.01 into the z-score formula, solving for x. The value of n is 64 (number of vehicles in the fleet).
Inserting these values into the formula gives us = + z/√ =0.03 + (-2.33)*(0.01/√64), which simplifies to =0.03 - (2.33/80) = 0.03 - 0.029125= 0.000875 g/mi. Therefore, the NOx emission level, such that the probability of finding an automobile with a level greater than it, is 0.01 for this fleet is approximately 0.001 g/mi when rounded to three decimal places.
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To find the level l such that the probability that the average NOx level x for the fleet is greater than l is only 0.01, we can use the z-score formula and the properties of the normal distribution. The z-score formula allows us to convert a probability into a corresponding value on the distribution. Rearranging the z-score formula, we can find the value of l.
Explanation:To find the level l such that the probability that the average NOx level x for the fleet is greater than l is only 0.01, we can use the z-score formula and the properties of the normal distribution. The z-score formula is z = (x - µ) / (σ / √n), where x is the average NOx level, µ is the mean, σ is the standard deviation, and n is the sample size. We want to find the value of l such that the area to the right of l under the normal curve is 0.01.
First, we need to find the z-score corresponding to a right-tail probability of 0.01. This can be done using a z-table or a calculator. In this case, the z-score is approximately 2.326. Now we can use the z-score formula to find the value of l. Rearranging the formula, we have l = µ + (z * σ / √n). Substituting the given values, l = 0.03 + (2.326 * 0.01 / √64). Calculating this, we get l ≈ 0.031.
Therefore, the level l such that the probability that the average NOx level x for the fleet is greater than l is only 0.01 is approximately 0.031 g/mi.
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Find the common ratio of the sequence
-125,-25,-5,-1.....
1/5
5
-100
100
Answer:
Step-by-step explanation:
common ratio of a Geometric series can be found by dividing the second term by first term of the series .
we are given that first term a1= -125 and second term a2 =-25
so the common ratio must be
[tex]r=\frac{a2}{a1}[/tex]
[tex]r=\frac{-25}{-125}[/tex]
[tex]r= \frac{1}{5}[/tex]
Hence the common ratio is 1/5.
solving radical equations
check for extraneous solutions
[tex] \sqrt{2x + 30} = x + 3[/tex]
Jack and Jill are 20m apart. Jack sees the top of the building at 30 degrees and Jill sees the top of the building at 40 degrees. What is the height of the building
The height of the building seen by both Jack and Jill is 37m to the nearest whole metre.
Let the distance of Jill from the base of the building be represented with x while the height of the building be y so that by observation we get two right triangles with same opposite sides to the angles formed by Jack and Jill. We can solve for x and y using tangent of the angles as follows:
tan 40 = y/x {opposite/adjacent}
y = xtan40 {cross multiplication}
tan 30 = y/(20 + x)
y = tan30(20 + x)
Thus;
xtan40 = tan30(20 + x)
xtan40 = 20tan30 + xtan30
xtan40 - xtan30 = 20tan30 {collect like terms}
x(tan40 - tan30) = 20tan30
x = 20tan30/(tan40 - tan30)
x = 44.1230m
Putting the 44.1230m for x in y = xtan40 we have;
y = 44.1230m × tan40
y = 37.0236m.
Therefore, the height of the building approximately to the nearest whole metre is 37.
what is -10-6=?. Please I need an answer and it's my grade
Please help me with the question 15 POINTS
Vicki started jogging. The first time she ran she ran 3/16 mile. The second time, she ran 3/8 Mile, and the third time, she ran 9/16 mile. If she continue this pattern, when was the first time she ran more than one mile explain
Answer:
In seventh time she ran more than one mile from first time she ran.
Step-by-step explanation:
Given Vicki started jogging. The first time she ran she ran 3/16 mile. The second time, she ran 3/8 Mile, and the third time, she ran 9/16 mile.
We have to find when was the first time she ran more than one mile.
The sequence followed is
[tex]\frac{3}{16}, \frac{6}{16}, \frac{9}{16}, \frac{12}{16}, \frac{15}{16}, \frac{18}{16}, \frac{21}{16}....[/tex]
First time she ran more than 1 mile is [tex]\frac{3}{16}+1=\frac{19}{16}[/tex]
In the seventh time she ran [tex]\frac{21}{16}[/tex] miles which is more than one mile from the first time.
Hence, in seventh time she ran more than one mile from first time she ran.
Express in exponential form. log100.001 = -3
Answer:
I believe you meant to put " log10 (0.001)= -3
10^-3=0.001
The expression log100.001 = -3 in exponential form is 10^-3 = 0.001. This demonstrates that 10 raised to the power of -3 equals 0.001, showing the inverse relationship between logarithms and exponents.
To express log100.001 = -3 in exponential form, recall that the logarithm is the exponent to which the base, in this case, 10, must be raised to produce the given number. The equation log10(0.001) = -3 tells us that the base 10 raised to the power of -3 equals 0.001.
In exponential form, this can be written as 10-3 = 0.001.The concept of converting a decimal to a negative power of 10 involves moving the decimal point to make the number into a whole number, and the negative exponent indicates how many places the decimal point needs to move to the left. In our case, 10-3 means we move the decimal three places to the left: 1 becomes 0.001.
Helps with this math problem please
51 divided by 3 is k
51 divided by 3 is k, the value of k is 17.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
51 divided by 3 is k
51/3=k
17=k
Therefore, by algebra the answer will be 17
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Two people taking the test are chosen at random. what is the probability that at least one of them scores more than 500 points?
The contour plot of is shown below. determine if the given quantity in each part is positive, negative, or zero.