[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: 9w² - 13w + 10[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + (20 {w}^{2} - 15w + 10) + 2w[/tex]
[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + 20 {w}^{2} - 15w + 10+ 2w[/tex]
[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + 20 {w}^{2} - 15w +2w + 10[/tex]
[tex]\qquad \tt \rightarrow \: 29 {w}^{2} - 13w + 10[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
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.
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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Dan's Dependable Delivery Given the following information calculate Dan’s Dependable Delivery’s debt ratio for two consecutive years. Show your calculations using Excel formulas. After the calculations, write a short message to Dan explaining what the ratios mean. Is there improvement? Current year Last year Total Assets $3,750,250 $3,590,750 Total liabilities $1,500,250 $1,470,000 Debt Ratio for the current year Debt Ratio for last year Message to Dan below:
Current year's debt ratio is 2.50
Last year's debt ratio is 2.44
Compute Dan's Dependable Delivery debt ratio for two consecutive years?
The debt ratio is the total liabilities divided by the total assets
The debt ratio for the current year = 2.50
The debt ratio for last year =2.44(find attached excel file and formula sheet)
Debt ratio means the portion of the firm's total assets funded using borrowing(external funding), the lower the ratio, the better since having a higher debt means a higher interest would be paid, the higher the debt, the higher the chance of the firm defaulting on paying interest and repaying the principal borrowed.
The fact that the debt ratio has increased in the current year, means that the ratio has worsened because more debt has been taken.
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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]
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°
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
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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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
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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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.
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.
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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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.
Triangle MRN is created when an equilateral triangle is folded in half.
Triangle N R M is shown. Angle N R M is a right angle. An altitude is drawn from point R to point S on side M N to form a right angle. The length of N S is 6, the length of S M is 2, the length of R M is x, the length of N R is y, and the length of R S is z.
What is the value of y?
2 StartRoot 3 EndRoot units
4 units
4 StartRoot 3 EndRoot units
8 units
Answer:
4 units
Step-by-step explanation:
The roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x=0 and 28. The vertex is a minimum at (14,−40).
the quadratic equation is:
y = 0.2*x*(x - 28)
How to find the quadratic equation?
If we know that the roots are J and K, and the leading coefficient is a, then the quadratic equation is:
y = a*(x - K)*(x - J)
Here we know that the roots are at x = 0 and x =28, then:
y = a*(x - 0)*(x - 28).
We also know that the vertex is a minimum, so a is positive, and we know that the vertex is (14, -40), then we have:
-40 = a*(14)*(14 - 24) = -a*196
a = 40/196 = 0.20
Then the quadratic equation is:
y = 0.2*x*(x - 28)
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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:
a + c = 405
12a + 5c = $3,590
Answer:
a=223.57
c=181.43
Step-by-step explanation:
a=405-c
substitute for a in the equation :
12a+5c=3590
12(405-c)+5c=3590
4860-12c+5c=3590
-7c=3590-4860
-7c=-1270
c=1270/7=181.43
a=405-1270/7
a=1565/7=223.57
For the following exercises, find the average rate of change of the functions from x = 1 to x =2.
24. f(x) = 4x − 3
Answer:
For the function [tex]$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]
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]
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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need help finding this C measure
Answer:
<C = 45 degrees.
Step-by-step explanation:
This is a right triangle (indicated by the square representing <A). All angles in a triangle add up to 180 degrees
180 - 90 is 90. Knowing that there are only two angles left, you can divide 90 by 2, resulting in 45.
<C = 45.
How many sides has a regular polygon if it's interior angles are:144 each, 135 each
The measure of each interior angle of a regular polygon is [tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides.
Question 1
[tex]144=\frac{180(n-2)}{n}\\\\144n=180(n-2)\\\\144n=180n-360\\\\-36n=-360\\\\n=10 \text{ sides}[/tex]
Question 2
[tex]\frac{180(n-2)}{n}=135\\\\180(n-2)=135n\\\\180n-360=135n\\\\-360=-45n\\\\n=8 \text{ sides}[/tex]
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]
There were three parts to Rita's race. She ran the first part, which was 4/9
of the total distance, in 20 minutes. She ran the second part, which was 2/5
of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at a speed of 300 meter per minute.
How long was the second part of the race? What was Rita's speed in that section of the race?
Hello!
d₁ = distance covered in Part 1
d₂ = distance covered in Part 2
d₃ = distance covered in Part 3
Distance in Part 2 :
⇒ d₃ = 15 x 300 = 4500 m
⇒ d₂ = 2/5d₃
⇒ d₂ = 2/5 x 4500
⇒ d₂ = 1800 meters
Speed in Part 2 :
⇒ v₂ = 1800 m / 12 min
⇒ v₂ = 150 meters per minute
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
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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A line of a slope 1/4 and passes through the point (0.2,4/5)
Find the value of b, the y-intercept.
The y-intercept of the line is 0.75 or 3/4
How to determine the y-intercept?The given parameters are:
Slope, m = 1/4
Point (x, y) = (0.2, 4/5)
A linear equation is represented as:
y = mx + b
This gives
4/5 = 1/4 * 0.2 + b
Evaluate the product
4/5 = 0.05 + b
Subtract 0.05 from both sides
b = 0.75
Hence, the y-intercept of the line is 0.75 or 3/4
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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