The quadratic equation with roots 4 and -2 and leading coefficient 4 is;
⇒ 4x² - 8x - 32
What is Quadratic equation?
A quadratic equation is an algebraic equation of the second degree of x.
Given that;
Roots of a quadratic equation = 4 and -2
Leading coefficient = 4
Now, The quadratic equation whose roots 4 and -2 with leading coefficient is calculated as;
⇒ 4 ( x - 4) (x + 2)
Solve as;
= 4 (x - 4) (x + 2)
= 4 (x² + 2x - 4x - 8)
= 4 (x² - 2x - 8)
= 4x² - 8x - 32
Thus, The quadratic equation with roots 4 and -2 and leading coefficient 4 is;
⇒ 4x² - 8x - 32
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Factor completely
4v6+18v5-10v4
Answer:
[tex]2v^4 (v+5)(2v-1)[/tex]
Step-by-step explanation:
[tex]4v^6+18v^5-10v^4 \\ \\ =2v^4 (2v^2 + 9v-5) \\ \\ =2v^4 (v+5)(2v-1)[/tex]
Simplify fully the following
2√5 × 5√5
2√3 x 3√8
Question
Simplify the expression:
(4/9)^3
Answer:
Step-by-step explanation:
(4^3/(9^3)
= 64/729 or0.09
please solve this question
We have a random variable, the time it takes to wash the dishes, that is uniformly distributed between 7 minutes and 16 minutes.
We have to calculate the probability that this random variable will have a value between 11 and 15 minutes.
We can calculate this probability as:
[tex]P(11Answer: the probability is 0.44.how to solve this one
how do i solve this
We are basically asked to perform the product of expressions that contain complex numbers a s roots of polynomials. So it is essential to identify the complex root in order to facilitate our products that otherwise could be really time consuming.
First product:
(x + 3 + 5i) (x + 3 - 5i) we are going to write as: ((x +3) +5i) ((x+3) - 5i). So this is going to be interpreted as a difference of squares (a + b) ( a - b) = a^2 - b^2:
((x +3) +5i) ((x+3) - 5i) = (x+3)^2 - (5i)^2 = (x+3)^2 - (-25) = (x+3)^2 + 25
We are using the fact that (i)^2 = -1 to convert - 25 (i)^2 = + 25
Now we solve the square of the binomial (x+3) , that is:
(x+ 3)^2 = x^2 + 6x + 9
Now this combined with + 25 gives: x^2 + 6x + 34 This is one of the options in blue background shown at the tops (the fourth one starting from the left)
Second product:
(x - 4i) (x + 4i) which is an easirer product than the one above because we can solve it just using difference of squares: (a - b) (a + b) = a^2 - b^2:
(x - 4i) (x + 4i) = x^2 - (4i)^2 = x^2 - 16 (i)^2 = x^2 +16
This is the second expression in blue background from left to right.
Third product:
(x - 6 + i) (x - 6 - i) for which we apply the same technique as in the first product we solve above:
(x - 6 + i) (x - 6 - i) = ((x - 6) + i) ((x - 6) - i) = (x-6)^2 - (i)^2 = (x-6)^2 - (-1) = (x-6)^2 + 1 = x^2 - 12 x + 36 + 1 = x^2 - 12 x + 37 which is the very first expression in blue background in the image you uploaded.
Olease move the bue background boxes so as to match the indicated products.
Question 4
Two diagonally opposite vertices of a square on a coordinate grid are located at (-5,7). (1,1). What is the
perimeter of the square? (7.G.6)
1p
Check the picture below.
find the slope of the line that passes through (-82, -26) and (-81, 4)
PROBLEM
Slope of a line passes through (-82,-26) and (-81,4)
Method
Step 1
Write out slope formula
[tex]\text{Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex]Step 2
write out all parameters
x1 = -82, y1 = -26
x2 = -81 , y2 = 4
Step 3
Input all parameter
[tex]\begin{gathered} \text{Slope = }\frac{4\text{ - (-26)}}{-81\text{ - }(-82)} \\ \text{Slope = }\frac{4\text{ + 26}}{-81+82} \\ \text{Slope = }\frac{30}{1} \\ \\ \text{Slope = 30} \end{gathered}[/tex]Find the width w
184 = 2w + 64 + 2w
Answer:
the aswer is 30 glad i could help
Step-by-step explanation:
Answer:
w = 30
Step-by-step explanation:
184 = 2w + 64 + 2w
(2w + 2w)
184 = 4w + 64
(184 - 64)
120 = 4w
(÷4)
w = 30
Hi I need help on my homework only number 1
) Let us assume that the interest was compounded annually. The formula for calculating compound interest is expressed as
A = P(1 + r/n)^nt
where
A is the amount after t years
P is the principal or initial amount invested
r is the interest rate
n is the number of compounding periods in a year
t is the number of years
From the information given,
P = 130
r = 4% = 4/100 = 0.04
n = 1 because it was compounded once in a year
t = 10
By substituting the values into the formula, we have
A = 130(1 + 0.04/1)^1 * 10
A = 130(1.04)^10
A = 192.43
Rounding to the nearest whole number, the amount after 10 years is $192
Need help, please.Quick answer is okay
xplanation:
Step 1. e are given the following zeros of a polynomial function.
- 1 with a multiplicity of two, which means that is a zero two times:
[tex]\begin{gathered} x_1=1 \\ x_2=1 \end{gathered}[/tex]and the other two zeros are:
[tex]\begin{gathered} x_3=2+\sqrt{2} \\ x_4=2-\sqrt{2} \end{gathered}[/tex]And we need to find the equation that has these four zeros.
tep 2. 2R
[tex]f(x)=(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]tep 3. S
[tex]f(x)=(x-1)(x-1)(x-(2+\sqrt{2}))(x-(2-\sqrt{2}))[/tex]tep 4. S
[tex]f(x)=(x-1)(x-1)(x-2-\sqrt{2})(x-2+\sqrt{2})[/tex]tep 5. T
[tex]f(x)=(x^2-2x+1)(x-2-\sqrt{2})(x-2+\sqrt{2})[/tex]Then, let's multiply the second and third parentheses:
[tex]f(x)=(x^2-2x+1)(x^2-2x+x\sqrt{2}-2x+4-2\sqrt{2}-x\sqrt{2}+2\sqrt{2}-2)[/tex]Multiple terms cancel and the result is:
[tex]f(x)=(x^2-2x+1)(x^2-4x+2)[/tex]tep 6. TT
[tex]f(x)=x^4-4x^3+2x^2-2x^3+8x^2-4x+x^2-4x+2[/tex]Combining like terms:
[tex]f(x)=x^4-6x^3+11x^2-8x+2[/tex]This is shown in option D.
Answer:
D
[tex]f(x)=x^4-6x^3+11x^2-8x+2[/tex]what is the answer to -6 2/5 + 7/3
A population that consists of 500 observations has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. Assume this is an infinite population. What is the standard error of the sample mean?
The standard error of the sample nean for a population that consists of 500 observations is 1.5
How to calculate the sample mean?From the information, the population that consists of 500 observations has a mean of 40 and a standard deviation of 15.
It should be noted that the sample mean is calculated as:
= Standard deviation / ✓number
= 15 / ✓100
= 15 / 10
= 1.5
Therefore, the standard error is 1.5.
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PLS HELP!! 20 POINTS ASAP
18 5/12+ 8 10/17 + 23 7/12 + 28 7/17
Answer:
79
Step-by-step explanation:
same thing as 79/1
use this equation to write an equation that has many /infinite solutions, no solution one solution y =3x + 4
the initial expression is:
[tex]y=3x+4[/tex]So this equation has already one solution
Now if we want to have infinit solution we an rest 3x so:
[tex]\begin{gathered} y=3x-3x+4 \\ y=4 \end{gathered}[/tex]So x can have any value, so there are infinit solutions
And to have no solutions we can add 5 -y at the left an
what is the standard error of mean if o=64 and n=64?
The standard error of mean if o=64 and n=64 will be 8 given the parameters standard deviaion of = 64 and n = 64.
How can the standard error mean be obtained?The formula N provides the standard error mean. We must be aware that the standard error means in the given question is denoted by the letter M.
Applying the formula now, we get the following:
σM = 64/√64
64 divided by its square root gives us the number 8.
The standard error means is thus equal to 64 divided by 8, or 8.
We may then conclude that the standard error means will be 8 given the standard error means of = 64 and n = 64.
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What are the order pairs for y=2/5x?(14,35)(30,1250,2010,440,2425, 5/2
Ok
y = 2/5x
ok
a) y = 2/5(14)
y = 28/5
y = 5.6 the first one is not an order pair
b) y = 2(30)/5
y = 60/5
y = 12 the second one is an order pair
c) y = 2/5(50)
y = 100/5
y = 20 the third one is an order pair
d) y = 2/5(10)
y = 20/5
y = 4 the four one is an order pair
e) y = 2/5(40)
y = 80/5
y = 16 the fifth one is not an order pair
f) y = 2/5(25)
y = 50/5
y = 10 the sixth one is not an order pair.
The solutions are (30, 12), (50, 20) and (10, 4)
Help me please
15+ points
The equation is y=5x+16.
How to form the required equation?The formula y=mx+b is expressed in slope-intercept form. We are aware of the slope (m) as well as a point (-2,6). We now require the y-intercept (b).We need to enter the information we are aware of in order to solve the y-intercept (b).Y = 6, M = 5, and X = -2 are known values. The equation must be like this: 6=5(-2)+bContinuing, 5(-2) is just 5 times -2, or -10. The new formula is 6=-10+b.Since we must repeat this process for both sides, we must add 10 to the right side to cancel it out and 10 to the left to obtain b. 6+10=-10+10+bB must therefore be 16 because of this.The last step is to construct the equation, where all that is required is to correct the values of m and b in the slope-intercept equation y=mx+b. We know that m is 5 and b is 16.y - 6 = 5(x - (-2)) y=5x+16Therefore, y=5x+16 is the solution.To learn more about equations, refer
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Isaiah is going to invest in an account paying an interest rate of 4.9% compounded
monthly. How much would Isaiah need to invest, to the nearest ten dollars, for the
value of the account to reach $1,150 in 14 years?
3
Answer:
579.93
Step-by-step explanation:
trust me bro
Answer: 580
Step-by-step explanation:
write the expression as a power and evaluate it. 16*32
The expression as power [tex]16^{3/2}[/tex] is 64.
What are exponents and power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
Given:
[tex]16^{3/2}[/tex]
using law of exponent
[tex]x^{(a * b)} = (x^a)^b[/tex]
Now, splitting 16 as 4 square
[tex]16^{3/2}[/tex]
=(4²[tex])^{3/2}[/tex]
=4³
=4 x 4 x 4
=64
Hence, expression as power [tex]16^{3/2}[/tex] is 64.
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Answer: 16^2.25
This is the correct answer thanks
1. The total number of pancakes that can be made for a pancake breakfast fundraiser is directly related to the
amount of batter that is available. If 28 cups of batter make 112 pancakes, then which of the following is
closest to the number of pancakes that can be made with 45.4 cups of batter?
If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.
What is unitary method?The unitary approach is a technique for problem-solving that involves first calculating the value of a single unit, then multiplying that value to figure out the required value.
Given Data
28 cups of batter to make 112 pancakes
To make 1 unit
28 cups of batter = 112 pancakes
1 cup of batter = 4 pancakes
If we have 45.4 cups of batter, we can make,
1 cup of batter = 4 pancakes
45.4 cup of batter = 45.4(4)
45.4 cup of batter = 181 pancakes ( approximately )
If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.
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Will the number of bananas get smaller or larger as you move down the table. How do you know
With the help of the given tabular data, we can conclude that the number of bananas will become smaller as one moves down the table.
What is tabular data?Data given in the form of rows and columns are known as tabular data.Tabular data is very useful in statistics.Here,
Bill can only place 5 fruits in a bowl.According to the table,
If there are zero apples, there are 5 bananasIf there is 1 apple, there are 4 bananasIf there are 2 apples, there are 3 bananasIf there are 3 apples, there are 2 bananasIf there are 4 apples, there is 1 bananaIf there are 5 apples, there are 0 bananasThe number of bananas will become smaller as one moves down the table.
Therefore, with the help of the given tabular data, we can conclude that the number of bananas will become smaller as one moves down the table.
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Complete question:
Bill has 5 apples and 5 bananas. He can only put 5 pieces of fruit in a bowl. Will the number of bananas get smaller or larger as you move down the table? How do you know?
The table has been attached
56 a) -1 < x < 6
d) 7,1
b) x > 0,4
2
e) x ≤
7
c) 3,9 < x
f) x ≥ 5
Answer:
a) -1< x < 6
Step-by-step explanation:
you no. how true answer
please help thank you
Let f be the function given by f(x)=∣∣x2−2∣∣(x+0.4)(x2−2)(x+0.4). On which of the following open intervals is f continuous?
Using the continuity concept, it is found that the function is continuous on the following interval:
C. (0, 1).
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In the context of this problem, the numeric values are especially relevant, as the function not continuous at the zeros of the denominator.
The denominator of the function is given as follows:
(x² - 2)(x + 0.4).
Hence the discontinuity points are:
x² - 2 = 0 -> x = -1.41 and x = 1.41.x + 0.4 = 0 -> x = -0.4.Hence the only interval in which the function is continuous over the entire interval is given by option C.
What is the missing information?The function and the possible options are given by the image at the end of the answer.
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Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a diameter of 5.2 centimeters. The volume of the sphere is about cm?.
Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a diameter of 5.2 centimeters. The volume of the sphere is about cm?.
we know that
the volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]In this problem we have
r=5.2/2=2.6 cm -----> the radius is half the diameter
pi=3.14
substitute the given values
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot2.6^3 \\ V=73.6\text{ cm\textasciicircum{}3} \end{gathered}[/tex]answer is 73.6 cubic centimetersA dinner theater charges $20 per person. Your table can hold a maximum of five people. Does the situation represent a function?
If so, find the domain and range. If not, leave this blank.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Domain: Response area
Range: Response area
The situation represents a function, while the domain and the range are 0 <= x <= 5 and 0 <= y <= 100, respectively
How to determine if the situation is a function?From the question, we have
Charges = $20 per person
Let the number of people be x and the total charges be y
So, we have
y = 20x
The above equation is a linear function
The domain and the rangeFrom the question, we have
Total number of people per seat = 5
So, the domain is 0 <= x <= 5
Substitute 5 for x in y = 20x
y = 20 x 5
Evaluate
y = 100
So, the range is 0 <= y <= 100
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Tom worked 28 hours last month and earned $9 per hour. He spent $17 of his earnings since then. How much money does he have left?
Answer:
He would have $235
Step-by-step explanation:
If Tom worked 28 hours and earned $9 per hour he would have 252 dollars. Then if he spent $17 dollars he would have $235
Answer:
235
Explanation:
If Tom worked 28 hours last month, and his hourly rate is $9.
Start by multiplying 9 times 28. 9 × 28 = 252
Faster way I do the math is in my head, what is 9*3=27, Add a zero 9×30=270. 30-2=28;2×9=18, Subtract 270-18=252...
Tom spent $17 of his earnings, $252-$17=$235
In Savannah's World Religions class Quizzes are worth 15% of the final grade, Exams are worth 55%, Projects are worth 25%, and Attendance is worth 5%.
At mid-semester Savannah scored 118 out of 150 points on quizzes, 73, 89, and 97 on the first three exams,each worth 100 points. She got extra credit on her project with a score of 28 out of 25 possible points, and she had perfect attendance to class. Compute Savannah's grade percentage in the class so far.
Savannah's grade percentage in the class so far is 92.28%.
What is the grade percentage?
Percentage is a measure of frequency that is used in mathematics. The sign that represents percentage is %. In order to convert a number to percentage, multiply the fraction of that amount by 100 or by the given percentage.
Savannah's grade percentage can be determined by adding her percentage score in each component that makes up the total grade.
Percentage score in quizzes = (score obtained / maximum score) x percentage allocated to quizzes
(118 / 150) x 15% = 11.80%
Percentage score in the three exams = (average of the three scores / maximum score) / percentage allocated to exams
Average of the three scores = (73+ 89 + 97) / 3 = 86.33
(86.33 / 100) x 55% = 47.48%
Percentage score in the project = (score in the project / maximum points) x percentage allocated to project
(28 / 25) x 25% = 28%
Percentage score in attendance = 5%
Total grade percentage so far: 5% + 28% + 47.48% + 11.80% = 92.28%
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Hey I really need help on this question
We have
[tex]9x+5y-10[/tex]We will substitute the values given
x=6 y=1
[tex]9(6)+5(1)-10[/tex]we solve the operations in order to obtain the result
[tex]54+5-10=49[/tex]the answer is 49