Hello,
x⁴ + 12x³ - 64x² = 0
x²(x² + 12x - 64) = 0
x² = 0 or x² + 12x - 64 = 0
x = 0
∆ = b² - 4ac = 12² - 4 × 1 × (-64) = 400
x1 = (-b -√∆)/2a = (-12 - 20)/2 = -32/2 = -16
x2 = (-b + √∆)/2a = (-12 + 20)/2 = 8/2 = 4
S = {-16 ; 0 ; 4 }
→ factorizacion de x⁴ + 12x³ - 64x² : x(x - 4)(x + 16)
A diagonal of a cube measures StartRoot 294 EndRoot cm. The diagonal of a face measures 14 cm. What is the length of an edge of the cube? Round to the nearest tenth of a centimeter.
The side of the edge of the cube is 9. 9cm
How to determine the length
Given that the diagonal of a cube measures the square root of 294cm and the diagonal of a face measures 14cm
To find the edge of the face, we know that the face of the cube is a square
Formula for diagonal of a square = [tex]\sqrt{2a}[/tex]
Where is the side of the square
We then have,
[tex]\sqrt{2a} = 14[/tex]
Make 'a' the subject
a = [tex]\frac{14}{\sqrt{2} }[/tex]
Simplify the surd
a = [tex]\frac{14}{\sqrt{2} }[/tex] × [tex]\frac{14}{\sqrt{2} }[/tex]
a = [tex]\frac{14\sqrt{2} }{2}[/tex]
a = [tex]7\sqrt{2}[/tex]
a = 9. 9cm
Therefore, the side of the edge of the cube is 9. 9cm
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Answer: Its 9.8 cm
Step-by-step explanation: I said so
In music theory, a musical chord is named according to its roots, or its first root. by knowing the root of a chord, a musician can find the rest of the notes in a chord. how are the roots of chords similar to roots of polynomial functions?
The roots of a polynomial function tells us about the position of the equation on a graph and the roots also tells us about the complex and imaginary roots. So, Roots of chords are similar to the roots of polynomial functions.
A real root of a polynomial function is the point where the graph crosses the x-axis (also known as a zero or solution). For example, the root of y=x^2 is at x=0.
Roots can also be complex in the form a + bi (where a and b are real numbers and i is the square root of -1) and not cross the x-axis. Imaginary roots of a quadratic function can be found using the quadratic formula.
A root can tell you multiply things about a graph. For example, if a root is (3,0), then the graph crosses the x-axis at x=3. The complex conjugate root theorem states that if there is one complex root a + bi, then a - bi is also a complex root of the polynomial. So if you are given a quadratic function (must have 2 roots), and one of them is given as complex, then you know the other is also complex and therefore the graph does not cross the x-axis.
So, The roots of a polynomial function tells us about the position of the equation on a graph and the roots also tells us about the complex and imaginary roots. So, Roots of chords are similar to the roots of polynomial functions.
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Which relationship has a zero slope?
X
-3
-1
1
3
O
y
2222
2
X
-3
-1
1
3
O
y
3
1
-1
-3
+
Answer:
The table that has the y-value as 2 for each input
Step-by-step explanation:
The table that has the y-value as 2 for each input. This is because as x increases by 1, the y-value is increasing by 0, so the slope is 0/1 or 0. The vertical line doesn't have a zero slope, since it's undefined, because if you take any two points the "run" is 0, thus you would be dividing by 0, the slope cannot be defined.
Solve the system of equations 6x+3y=9 and -9x−2y=9 by combining the equations.
Answer:
x = -3
y = 9
Step-by-step explanation:
6x + 3y = 9 ⇒ ( 1 )
Divide the whole equation by 3.
2x + y = 3 ⇒ ( 2 )
-9x - 2y = 9 ⇒ ( 3 )
Let us take equation (2) and make y the subject of the equation.
2x + y = 3
y = 3 - 2x ⇒ ( 4 )
Now let us take equation (3) and find the value of x.
For that, we can replace y with ( 3 - 2x ).
Let us solve it now.
-9x - 2y = 9
-9x - 2 ( 3 - 2x ) = 9
-9x -6 + 4x = 9
-5x - 6 = 9
-5x = 9 + 6
-5x = 15
Divide both sides by (-5).
x = -3
And now let us take equation (4) to find the value of y.
For that, we can replace x with -3.
Let us solve it now.
y = 3 - 2x
y = 3 - 2 × -3
y = 3 + 6
y = 9
Help please!!!
Determine the domain and range of each function.
31.
32.
Compare the graphs f(x)=(x-10)^2+8 with the graph of f(x)=x^2
Yea
Answer:
b. The graph of g(x) is a translation 10 units right and 8 units up from the graph of f(x).
Step-by-step explanation:
See attached image.
a + c = 405
12a + 5c = $3,590
Answer:
a=223.57
c=181.43
Step-by-step explanation:
a=405-c
substitute for a in the equation :
12a+5c=3590
12(405-c)+5c=3590
4860-12c+5c=3590
-7c=3590-4860
-7c=-1270
c=1270/7=181.43
a=405-1270/7
a=1565/7=223.57
linear pair theorem
ZADCZBDC
given
2m BDC=180°
definition of supplementary
mzADC-mzBDC
definition of
congruence
m *ADC +
m BDC=180°
ADC is complementary
to BDC
substitution property of
equality
m BDC=180°
ADC is supplementary
to BDC
⠀⠀
m BDC=90°
division property of
equality
What the given proof is trying to show us is that; ∠3 = 126°
How to prove supplementary angles?From the attached line, we see that angle 1 and angle 3 form a straight line. Now, since we know that angles on a straight line sum up to 180°, then it means that they are supplementary.
We are given;
1) ∠1 and ∠2 are supplementary
2) ∠1 = 36°
Thus from definition of complementary angles, we can say that;
36° + ∠2 = 90°
Subtraction property of equality when applied gives;
∠2 = 54°
We are told that ∠2 and ∠3 are linear pairs and as such;
∠2 + ∠3 = 180° from linear pairs theorem.
By substitution property of equality we have;
54° + ∠3 = 180°
Solving gives ∠3 = 126°
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The graph below shows the solution set of a certain inequality. State one solution represented by the graph.
Answer:
(1,3)
Step-by-step explanation:
since they are open circles they will not have brackets instead they will have parentheses.
one answer for this number line (graph) is (1,3)
In this figure, AB || CD & m<6 =75 degrees
What is m<3?
Answer:
∠ 3 = 105°
Step-by-step explanation:
∠ 3 and ∠ 6 are same- side interior angles and sum to 180° , that is
∠ 3 + ∠ 6 = 180°
∠ 3 + 75° = 180° ( subtract 75° from both sides )
∠ 3 = 105°
What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 i?
Answer:
C
Step-by-step explanation:
on edge
If the dimensions of the prism below were doubled, by what factor would the of the prism increase?
Answer:
probably c
Step-by-step explanation:
State the type of model that best fits the data shown and write the regression
equation. Round any decimals to 3 places.
The regression equation is y = 3.231x + 10.138
How to determine the regression equation?The regression model that fits the data is a linear model.
This is so because as x increases by 1, the y value increases by an almost constant rate
To determine the regression equation, we make use of a graphing calculator
From the graphing calculator, we have the following summary:
Sum of X = 15Sum of Y = 109.3Mean X = 2.5Mean Y = 18.2167Sum of squares (SSX) = 17.5Sum of products (SP) = 56.55The regression equation is then calculated as;
y = bx + a
Where
b = SP/SSX = 56.55/17.5 = 3.23143
a = MY - bMX = 18.22 - (3.23*2.5) = 10.1381
So, we have:
y = 3.23143x + 10.1381
Approximate
y = 3.231x + 10.138
Hence, the regression equation is y = 3.231x + 10.138
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Lori wants to design a computer simulation to study how many spins it takes to land on each color once there are 4 colors on the wheel using the digits 0 through 9 she will assign a digit to each section of the wheel which option describes how the digits can be assigned
Answer:
The number of ways in which the digits can be assigned in the color wheel can be determined by the permutation of 8 taken 4 since it is in circular formation and whichever comes first is not important.
number of ways = 9P4 = 3024 ways
Laboratory test show that the lives of light bulbs are normally distributed with a mean of 750 hours in a standard deviation of 75 hours find the probability that a randomly selected light bulb will last between 825 hours and 900
The probability that a randomly selected light bulb will last between 825 hours and 900 is 0.477.
How to illustrate the probability?From the information given, a standard deviation below the mean will be:
= 750 - 75 = 675
Two standard deviations below the mean will be:
= 750 - 75(2)
= 600
In this case, we ant to know the probability that make up the areas. This is illustrated in the graph.
In conclusion, the correct option is 0.477.
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For the following exercises, find the average rate of change of the functions from x = 1 to x =2.
24. f(x) = 4x − 3
Answer:
For the function [tex]$f(x)=4 x-3$[/tex] the average rate change from x is equal 1 to x is equal 2 is 4 .
Step-by-step explanation:
A function is given f(x)=4x-3.
It is required to find the average rate change of the function from x is 1 to x is 2 . simplify.
Step 1 of 2
A function f(x)=4 x-3 is given.
Determine the function [tex]$f\left(x_{1}\right)$[/tex] by putting the value of x=1 in the given function.
[tex]$$\begin{aligned}&f(1)=4(1)-3 \\&f(1)=1\end{aligned}$$$$f(1)=1$$[/tex]
Determine the function [tex]$f\left(x_{1}\right)$[/tex] by putting the value of x is 2 in the given function.
[tex]$$\begin{aligned}&f(2)=4(2)-3 \\&f(2)=5\end{aligned}$$[/tex]
Step 2 of 2
According to the formula of average rate change of the equation [tex]$\frac{\Delta y}{\Delta x}=\frac{f\left(x_{2}\right)-f\left(x_{2}\right)}{x_{2}-x_{1}}$[/tex]
Substitute the value of [tex]$f\left(x_{1}\right)$[/tex] with, [tex]$f\left(x_{1}\right)$[/tex] with [tex]$3, x_{2}$[/tex] with 2 and [tex]$x_{1}$[/tex] with 1 .
[tex]$$\begin{aligned}&\frac{\Delta y}{\Delta x}=\frac{5-1}{1} \\&\frac{\Delta y}{\Delta x}=4\end{aligned}$$[/tex]
5 Quick algebra 1 questions for 50 points!
Only answer if you know all 5, Tysm! :)
The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
How to determine the equations?When a linear equation is represented as:
Ax + By = C
The slope (m) is:
m = -A/B
When the linear equation is represented as:
y = mx + c
The slope is m
A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m
Using the above highlights, the equations of the lines are:
6. y = -2x + 5; (2, 7)
The slope is:
m = -2
The perpendicular slope is:
n = 1/2
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/2(x - 2) + 7
Evaluate
y = 1/2x - 1 + 7
This gives
y = 1/2x + 6
7. y = -5; (11, 15)
The slope is:
m = 0
The perpendicular slope is:
n = 1/0 = undefined
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 15
8. Graph ; (-12, 10)
The slope is:
m = (y2 - y1)/(x2 - x1)
Using the points on the graph, we have:
m = (2 - 3)/(3 - 4)
m = 1
The perpendicular slope is:
n = -1
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = -1(x + 12) + 10
y = -x - 12 + 10
Evaluate
y = -x - 2
9. y = -1/6x + 1; (-2, -9)
The slope is:
m = -1/6
The perpendicular slope is:
n = 6
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 6(x + 2) - 9
Evaluate
y = 6x + 12 - 9
This gives
y = 6x + 3
10. 6x + 2y = 14; (12, 0)
The slope is:
m = -6/2
m = -3
The perpendicular slope is:
n = 1/3
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/3(x - 12) + 0
Evaluate
y = 1/3x - 4
Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
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two numbers add up to 30, and one of them is greater than the other by 8. what are these numbers?
Answer:
11 and 19
Step-by-step explanation:
X + (X+8) = 30
Open bracket
X plus X + 8 = 30
2x + 8= 30
Collect like terms
2x = 30 - 8
2x = 22
X=11
And x + 8 = 11 + 8= 19
Verify csc^2t-cos t sect= cot^2 t
Rewriting the left hand side,
csc²t - cost sec t
= (1/sin²t)-(cost)(1/cost)
= 1/sin²t - 1
= 1/sin²t - sin²t/sin²t
= (1-sin²t)/sin²t
= cos²t/sin²t
= cot²t
20 POINTS!!! PLEASE HELP
Find the logarithm base 10 of each number:
10
Please show work. Thanks!!
The logarithm of 10 to base 10 is 1
How to determine the logarithm?The given parameters are:
Base = 10Number = 10So, the logarithm expression can be represented as:
[tex]\log_{10}10[/tex]
The law of logarithm states that:
[tex]\log_{x}x = 1[/tex]
The above means that;
When the base and the number are the same, the logarithm is 1
So, we have:
[tex]\log_{10}10 = 1[/tex]
Hence, the logarithmic value is 1
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In the following exercises, multiply the binomials. Use any method.
257. (4z − y)(z − 6)
Answer:
Hence the expression [tex]$$(4z-y)(z-6)=4z^2-yz-24z+6y$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (4 z-y)(z-6).We have to multiply the given expression.Multiply the (4 z-y) by -6, multiply the (4 z-y) by z then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 4z & - & y \\ \times & {} & {} & {} & z & - & 6 \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}{} & {} & {} & - & 24z & + & 6y \\ 4{{z}^2} & - & yz & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}4{{z}^2} & - & yz & - & 24z & + & 6y \\ \end{matrix}$$[/tex]
The sum of ages Kate and Gift is 38 years now.What was the sum of their ages five years ago
Answer:
28
Step-by-step explanation:
Simple solution:
Each one was 5 years younger 5 years ago, so subtract 5 from 38 for each one.
38 - 5 - 5 = 28
The sum of their ages was 28.
Algebra solution:
Kate is x years old now.
Gift is y years old now.
The sum of their ages now is x + y.
The sum of their ages is 38, so x + y = 38.
5 years ago:
Kate was x - 5 years old.
Gift was y - 5 years old.
The sum of their ages 5 years ago was x - 5 + y - 5 = x + y - 10.
Substitute 38 for x + y.
The sum of their ages was 38 - 10 = 28
WILL GIVE BRAINLIEST! PLEASE HELP FAST!!
A) The function ƒ(x) has a steeper slope than g(x).
B) The functions ƒ(x) and g(x) have the same slope.
C) The function g(x) has a steeper slope than ƒ(x).
D) There isn't enough information to determine which function has a steeper slope.
[tex]m = \frac{ - 5 - 4}{3 - 0} = \frac{ - 9}{3} = - 3[/tex]
[tex]g(x) = - 3x + 4[/tex]
C)[tex]g(x) \: ha s \: a \: steeper \: slope[/tex]
6.7 Section 6.7 Integer Exponents and Scientific Notation
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
742. The thickness of a dime is about 0.053 inches.
Answer:
742 is 7.42x10^2
0.053 inches is 5.3x10-2 inches
Step-by-step explanation:
The goal is to convert he number into a format that has one digit to the left of the decimal point. When moving the decimal point more to the left, each step reduces the number by a factor of 10/
742
74.2 is the original number reduced by 10. To keep the number valid, we need to multiply by 10, which can be written as 74.2 x 10.
7.42 is reduced by another factor of 10: 7.42 x10x10 This is the same as 7.42x10^2
742 is 7.42x10^2
0.053
0.53 is the original number multiplied by 10. To keep the number valid, we need to divide by 10, which can be written as 0.53x10^-1
5.3 is the original number divided by another factor of 10. This can be written as 5.3x10^-2
0.053 inches is 5.3x10-2 inches
The graph represents the heights of two climbers on a climbing wall over a 12-minute time period.
A graph titled The Climbing Wall where the horizontal axis shows time (minutes), numbered 1 to 12, and the vertical axis shows height (feet) numbered 2 to 24. The line labeled Brynn's climb begins at 0 feet in 0 minutes, to 15 feet from 5 to 7 minutes, to 0 feet in 10 minutes. The line labeled Abby's climb begins at 4 feet in 0 minutes, to 14 feet from 4 to 6 minutes, to 22 feet in 8 minutes, to 0 feet in 12 minutes.
Which statement is true about the climbers’ heights?
Brynn was resting at a constant climbing height when Abby’s climbing height was decreasing.
Abby’s climbing height was decreasing when Brynn’s climbing height was increasing.
The heights of both climbers increased, then decreased, with no rest at a constant height.
Both climbers rested on the wall at a constant height for 2 minutes.
Both climbers rested on the wall at a constant height for 2 minutes.
How to determine the true statement?The illustrative graph that represents the climbers' movement is added as an attachment
From the attached graph, we have the following observation
The line of Abby's movement is horizontal from x = 4 to x = 6The line of Brynn's movement is horizontal from x = 5 to x = 7The difference between the endpoints of both horizontal line is
Difference = 6- 4 = 2
Difference = 7 - 5 = 2
This means that both Brynn and Abby stopped for 2 minutes
Hence, the true statement about is that (d) Both climbers rested on the wall at a constant height for 2 minutes.
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Work out 2 1 2 − 1 2 7 Give your answer as a mixed number where appropriate.
Answer:
185 when we subtract 212-127 it gives 185 thanks for the seeing image
If 16g if a radioactive substance are present initially and 5yr later only 8g remain how much substance will be present after 5yr
4.59 g will be the amount of substance that will be present after 5 year.
Given: 16g of radioactive substance
8g left after 8 year
Concept: In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to drop to half its original value. In a first-order reaction, the half-life of the reactant is ln(2)/λ, where λ (also referred to as k) is the reaction rate constant.
The half-life is given as 5 years, so the amount remaining after 9 years will be found by using the steps done below:
Remaining amount of radioactive substance = initial × (1/2)^(t/(half-life))
Remaining substance = (16 g)×(1/2)^(9/5) ≈ 4.59 g
After 9 years i.e., after 8 years have passed
About 4.59 g of the substance remains.
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Please help me with Algebra 2 problems.
Answer:
[tex]5)\ \ \left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]
[tex]6)\ \ \frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }=1[/tex]
Step-by-step explanation:
[tex]\left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4[/tex]
[tex]=x^{\frac{8}{10}}y^{\frac{4}{10}} +3x^{\frac{4}{5}}y^{\frac{4}{10} }[/tex]
[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}} +3x^{\frac{4}{5}}y^{\frac{2}{5} }[/tex]
[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}}\times(1+3)[/tex]
[tex]=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]
……………………………………
[tex]\frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }[/tex]
[tex]=\frac{(2+7) \times\sqrt{9^{5}} }{\sqrt{9^{2}} \times \sqrt{9^{5}} }[/tex]
[tex]=\frac{9 \times\sqrt{9^{5}} }{9 \times \sqrt{9^{5}} }[/tex]
[tex]=1[/tex]
Assume that all conditions are met. The mean of the differences was 1. 33 and the standard deviation of those differences was 2. 90. What is the test statistic for this procedure?.
The test statistic for this procedure is using two sample T-test is 0.458.
Definition of Two Sample T-test
A variation of the Student's t-test used to determine if two sample means are substantially different is known as the two sample T-test (also known as Welch's t-test, Welch's adjusted T, or unequal variances t-test). The test's degrees of freedom have been changed, which generally boosts the test's power for samples with unequal variance.
T-Test Statistic for The Procedure
It is given that mean of the differences = 1.33
And, the standard deviation of the differences, standard error = 2.90
The test static formula is given as,
t = (estimate - hypothized value) / standard error
Here, t is the t- test statistic, and estimate is the mean of the differences.
Since it is given that all conditions are met, the hypothized value can be taken as 0
Substituting substituting estimate = 1.33 and standard error = 2.90 in the t-test statistic formula, we get,
t = (1.33-0)/2.90
or t = 0.458
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there are 4 people at a party. each person brings one gift for each other person . what is the total number of gifts at the party
Answer:
4 gifts
Step-by-step explanation:
4÷4=0
so you get each other a gift so there none to spare
Answer:
12 gifts
Step-by-step explanation:
If there are 4 people, and each person brings a gift for each of the other three people, that means that there are 12 gifts at the party. Let's say there are four people: A, B, C, and D. Person A would have to bring 3 gifts to give B, C, and D. Similarly, B would bring a gift each for A, C, D. C would bring a gift for A, B, D. Lastly, D would bring a gift for A, B, and C. Each person brings three gifts to give to the other three people at the party, and 3*4 people is 12. I hope that makes sense.