I need help with his practice problems from my ACT prep guidePlease show your work in steps
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Answer:
[tex]-\sqrt[]{6}+1[/tex]Explanation:
Given the below expression;
[tex]\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\sec (-\pi)[/tex]Recall that;
[tex]\begin{gathered} \sec x=\frac{1}{\cos x} \\ \sin x=\cos (\frac{\pi}{2}-x) \end{gathered}[/tex]So we can rewrite the expression as;
[tex]\begin{gathered} \frac{\tan(-\frac{2\pi}{3})}{\cos(\pi-\frac{7\pi}{4})}-\frac{1}{\cos(-\pi)} \\ \frac{\tan(-\frac{2\pi}{3})}{\cos(-\frac{5\pi}{4})}-\frac{1}{\cos(-\pi)} \end{gathered}[/tex]Also, recall that;
[tex]\begin{gathered} \cos (-x)=\cos x \\ \tan (-x)=-\tan x \end{gathered}[/tex]So we'll have;
[tex]\frac{-\tan (\frac{2\pi}{3})}{\cos (\frac{5\pi}{4})}-\frac{1}{\cos (\pi)}[/tex]From the Unit circle, we have that;
[tex]\begin{gathered} \cos \pi=-1 \\ \cos (\frac{5\pi}{4})=\frac{-\sqrt[]{2}}{2} \\ \tan (\frac{2\pi}{3})=-\sqrt[]{3} \end{gathered}[/tex]Substituting the above values into the expression and simplifying, we'll have;
[tex]\begin{gathered} \frac{-(-\sqrt[]{3})}{\frac{-\sqrt[]{2}}{2}}-\frac{1}{-1}=\frac{\sqrt[]{3}}{\frac{-\sqrt[]{2}}{2}}+1=-\frac{2\sqrt[]{3}\sqrt[]{2}}{\sqrt[]{2}\cdot\sqrt[]{2}}+1 \\ =-\sqrt[]{6}+1 \end{gathered}[/tex]Related Questions
What is an
equation of the line that passes through the points (5, 7) and (-5, -1)?
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Answer:
y - 7 = 0.8(x - 5) ory = 0.8x + 3Step-by-step explanation:
Given2 points (5, 7) and (- 5, - 1)To findEquation of the line passing through the given pointsSolutionFind the slope of the line using slope equation:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\dfrac{-1-7}{-5-5}=\dfrac{-8}{-10}=0.8[/tex]Use one of the points and the point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex][tex]y-7=0.8(x-5)[/tex]This can be converted to slope-intercept form:
[tex]y = mx + b[/tex][tex]y -7=0.8(x-5)[/tex][tex]y -7=0.8x-0.8*5[/tex][tex]y -7=0.8x-4[/tex][tex]y =0.8x-4+7[/tex][tex]y=0.8x+3[/tex]The cost of a pair of skis to a store owner was $700, and she sold the pair of skis for $1020.Step 3 of 3: What was her percent of profit based on selling price? Follow the problem-solving process and round your answer to thenearest hundredth if necessary.
Answers
Answer:
Explanation:
• The ,cost price ,of the pair of skis = $700
,• The ,selling price ,of the pair of skis = $1020
To calculate the percentage of profit, use the formula below:
[tex]\text{Percent of Profit=}\frac{Selling\text{ Price-Cost Price}}{\text{Selling Price}}\times\frac{100}{1}[/tex]Substitute the given values:
[tex]\text{Percent of Profit=}\frac{1020\text{-7}00}{\text{7}00}\times\frac{100}{1}\text{=}\frac{320}{\text{7}00}\times\frac{100}{1}=45.71\%[/tex]The percentage profit is % (correct to the nearest hundredth).
Operations in Scientific NotationWrite two numbers in scientificnotationFind their sum, difference, product& quotient
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Solution:
Let the two numbers be
[tex]20\text{ and 10}[/tex]In scientific notation, the numbers are
[tex]\begin{gathered} 20=2\times10^1 \\ 10=1\times10^1 \end{gathered}[/tex]The sum of the numbers will be
[tex]=(2\times10^1)+(1\times10^1)=10^1(2+1)=10^1(3)=3\times10^1[/tex]Hence, the sum is
[tex]3\times10^1[/tex]The difference between the two numbers will be
[tex]=(2\times10^1)-(1\times10^1)=10^1(2-1)=10^1(1)=1\times10^1[/tex]Hence, the difference is
[tex]1\times10^1[/tex]The product of the numbers will be
[tex]=(2\times10^1)\cdot(1\times10^1)=(2\times1)(10^{1+1})=2(10^2)=2\times10^2[/tex]Hence, the product is
[tex]2\times10^2[/tex]The quotient of the numbers will be
[tex]=\frac{2\times10^1}{1\times10^1}=\frac{2}{1}\times(10^{1-1})=2(10^0)=2\times10^0[/tex]Hence, the quotient is
[tex]2\times10^0[/tex]Yasmin went to the store and bought 3 and 1/2 pounds of ground beef for 11:20 how much do the ground beef cost per pound
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Yasmin bought 3 1/2 pounds of ground beef, we can express the amount that she bought as a fraction like this:
[tex]3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{6+1}{2}=\frac{7}{2}[/tex]Since she bought it for $11.2, if we divide the cost by the amount that she purchased, we get the cost per pound, like this:
[tex]\frac{11.2}{\frac{7}{2}}[/tex]To divide by a fraction, we just have to invert its numerator and denominator:
[tex]\frac{11.2}{\frac{7}{2}}=11.2\times\frac{2}{7}=\frac{22.4}{7}=3.2[/tex]Then, the cost per pound equals $3.2
help meeeeeeeeee pleaseee !!!!!
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If the average daily sales price of the toy is $6.50, then 2750 toys will have been sold overall.
Variables and functionsIn the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and codomain are respectively referred to as the sets X and Y as a whole.
While the dependent values are the codomain, the independent values are known as the domain.
Given that y = 6000 - 500x is the function that depicts the price-sales relationship for the quantity of toys
The total number of toys sold if the toy sells for $6.50 per day is: y = 6000 - 500 (6.50) y = 6000 - 3250 y = 2750 toys
The total quantity of toys sold is provided above.
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hi i need help here please help me i am in need of the helps
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The area of the octagon shaped stop sign = areas of the 4 rectangles + 4 triangles + square = 478 in.².
How to Find the Area of a Triangle and the Area of a Rectangle?Area of rectangle = (length)(width).Area of triangle = 1/2(base)(height).Area of square = (side length)².If the octagon can be decomposed into 4 identical triangles, 4 identical rectangles, and a square, the following are the dimensions of each of the shapes given:
Height of the triangle = (24 - 10)/2 = 7 in.
Base of the triangle = 7 in.
Side length of the square = 10 in.
Length of rectangle = 10 in.
Width of rectangle = 7 in.
The area of the octagon shaped stop sign = 4(1/2 × base × height) + 4(length × width) + (side length)²
Substitute the values into the equation
The area of the octagon shaped stop sign = 4(1/2 × 7 × 7) + 4(10 × 7) + (10)²
The area of the octagon shaped stop sign = 478 in.².
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A rectangular field is nine times as long as it is wide. If the perimeter of the field is 1100 feet, whatare the dimensions of the field?The width of the field isfeet.The length of the field isfeet.
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Given:
The perimeter of the rectangular field is 1100 feet.
According to the question,
l=9w
To find the dimensions:
Substitute l=9w in the perimeter formula,
[tex]\begin{gathered} 2(l+w)=1100 \\ 2(9w+w)=1100 \\ 20w=1100 \\ w=55\text{ f}eet \end{gathered}[/tex]Since the width of the rectangle is 55 feet.
The length of a rectangle is,
[tex]55\times9=495\text{ f}eet[/tex]Hence,
The width of the rectangle is 55 feet.
The length of a rectangle is 495 feet.
Stacia has 28 red and blue marbles. The ratio of red to blue marbles is 1: 6.
How many blue marbles does Stacia have?
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Answer:You have 24
Step-by-step explanation:
How do we determine the strength of a correlation?
OA. The more closely two variables follow the general trend, the stronger the correlation (which may be positive or negative).
GB. Negative correlation is stronger than no correlation. Positive correlation is stronger than negative correlation.
OC. The more closely two variables follow the general trend, the weaker the correlation (which may be positive or negative).
OD. No correlation is stronger than negative correlation. Positive correlation is stronger than no correlation
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We can determine the strength of a correlation by A. The more closely two variables follow the general trend, the stronger the correlation (which may be positive or negative).
What is correlation?Correlation is a statistical term that reflects how closely two or more variables are related to one another. Correlation is measured on a scale of -1 to +1, with 0 indicating a negative correlation and > 0 indicating a positive correlation. A value of 0 implies that there is no association.
A positive correlation is a two-variable association in which both variables move in lockstep. A positive correlation exists when one variable declines while the other increases, or when one variable increases while the other falls. The number one represents a perfect positive association.
If there is an increase or decrease in one variable results in increase or decrease in the other then there is correlation. If the value of correlation is close to either extremities (+1 or +1) then there is strong correlation.
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Meghan measures the heights and arm spans of the girls on her basketball team. She plots the data and makes a scatterplot comparing heights and arm spans, in inches. Meghan finds that the trend line that best fits her results has the equation y=x+2 . if a girl on her team is 64 inches tall, What should Meggan expect her span to be?
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EXPLANATION
Let's see the facts:
The equation is given by the following expression y= x + 2
---> 64 inches tall
As we can see in the graph of arm span versus height, and with the given data the arm span should be:
arm span = y = 64 + 2 = 66 inches
So, the answer is 66 inches. [OPTION C]
I need help with this practice problem The subject is trigonometry
Answers
SOLUTION
The range of the function is given as:
[tex](-\infty,-9\rbrack\cup\lbrack5,\infty[/tex]The asymptote of the function is at points
[tex]x=0,x=2\pi[/tex]The function is shown in the graph below
Therefore, the equation of the session is
[tex]f(x)=7\csc (\frac{x}{2})-2[/tex]X+87°2x⁰ i have to solve for x it’s a 180 angle HELP ME!!!!!!!!!
Answers
Collect Like terms
X+2x°=180°-87°
3x=93°
Divide both sides by 3 to eliminate the coefficient of “x”
3x/3=93°/3
X=31°
3 A free diver can dive at a rate of -0.75 meters per second. About how long would it take to reach a depth of -145 meters?
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Answer:193.33s or 3.2 mins
Step-by-step explanation:
Here the diver dives at -0.75 constant velocity. So we can use the formula s = vt
from there we can find out the time when s = -145 m and v = -0.75m/s
Lauren was going to by her mom her favorite perfume for Christmas at a price of $31.95. She waited until it got too close to Christmas and the price went up to $41.49. What was the percent of increase in the price?
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The percent of increase in the cost of the perfume is 29.86%
What is percentage and how can it be calculated?
A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "%" is used to denote it. No dimension exists for percentages. Thus, it is referred to as a dimensionless number.
Mathematically,
Percent of increase = [(Final value - Initial value)/(Initial value)]×100
Given, the final value of the perfume at purchase = $41.49
Also, the initial value of the perfume as assessed = $31.95
Therefore using the formula established in the literature above,
Percentage increase = [(41.49 - 31.95)/31.95]×100 = 29.86%
Thus, the percent of increase in the cost of the perfume is 29.86%
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what would the annual rate of interest have to be? round to two decimal places.
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To find:
The rate of interest.
Solution:
It is known that the rate of interest is given by:
[tex]r=n[(\frac{A}{P})^{\frac{1}{nt}}-1][/tex]Here. P = 60000, A = 61200, t = 2.5 and n = 12.
[tex]\begin{gathered} r=12[(\frac{61200}{60000})^{\frac{1}{12(2.5)}}-1] \\ r=0.00792366 \end{gathered}[/tex]Change into the percentage by multiplying by 100:
[tex]\begin{gathered} r=0.00792366 \\ r=0.79\% \end{gathered}[/tex]Thus, the answer is 0.79% per year.
Which of the following numbers is divisible by 6?
A. 342 543
B. 322 222
C. 415 642
D. 123 456
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A. 342 543 is odd
B. 322 222 is even but the digits add to 13 which is not a multiple of 3
C. 415 642 is even but the digits add to 22 which is not a multiple of 3
D. 123 456 is even and the digits add to 21 so it is a multiple of 6
123 456 / 6 = 20 576 with no remainder
If you bought a stock last year for a price of $90 and it is gone down 13% since then how much is the stock worth now to the nearest cent
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The stock worth is $78.3
Given,
Bought a stock last year for a price of $90
And, price gone down is 13%
To find how much is the stock worth?
No, According to the question
Firstly, find the 13% of 90 i.e.,
= 13/100 x90
= $11.7
Stock worth is
= 90 - 11.7
= 78.3
Hence, The stock worth is $78.3
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How do I graph a line with a equation in slope intercept form?An example is y=-3x+3, how do I graph this?
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we have
y=-3x+3
to graph a line we need at least two points
so
Find out the intercepts
y-intercept (value of y when the value of x is zero)
For x=0
y=-3(0)+3
y=3
y-intercept is (0,3)
x-intercept (value of x when the value of y is zero)
For y=0
0=-3x+3
3x=3
x=1
x-intercept is (1,0)
therefore
Plot the points (0,3) and (1,0)
and join them to graph the line
see the attached figure to better understand the problem
help meeeeeeeeee pleaseee !!!!!
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The composition of the two functions evaluated in x = 2 is:
(f o g)(2) = 33
How to find the composition?Here we have the next two functions:
f(x) = x² - 3x + 5
g(x) = -2x
And we want to find the composition:
(f o g)(2) = f( g(2))
So we need to evaluate f(x) in g(2).
First, we need to evaluate g(x) in x = 2.
g(2) = -2*2 = -4
Then we have:
(f o g)(2) = f( g(2)) = f(-4)
f(-4) = (-4)² - 3*(-4) + 5 = 16 + 12 + 5 = 28 + 5 = 33
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Is (x + 3) a factor of 7x4 + 25x³ + 13x² - 2x - 23?
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According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0. Finding the polynomials' n roots and factoring them are two of their principal applications.
What is the remainder and factor theorem's formula?When p(x) is divided by xc, the result is p if p(x) is a polynomial of degree 1 or higher and c is a real number (c). For some polynomial q, p(x)=(xc)q(x) if xc is a factor of polynomial p. The factor theorem in algebra connects a polynomial's components and zeros. The polynomial remainder theorem has a specific instance in this situation. According to the factor theorem, f(x) has a factor if and only if f=0.The remainder will be 0 if the polynomial (x h) is a factor. In contrast, (x h) is a factor if the remainder is zero.The factor theorem is mostly used to factor polynomials and determine their n roots. Factoring is helpful in real life for comparing costs, splitting any amount into equal parts, exchanging money, and comprehending time.To learn more about Factor theorem refer to:
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2. what is equivalent ratio of 9:63. How will you find equivalent ratiosA. add counting number to both ends of given ratioB. divide a counting number to the numerator off the first termC. multiply a counting number to the denominator onlyD. multiply divide a counting number both terms of the given ratio4. what is equivalent ratio of 3:8 5. what kind of rats you have different numbers but represent the same relationshipA. Fraction B. rate C. terms D. equivalent ratios
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Given:
The ratio is 9:6.
The equivalent ratio is,
[tex]9\colon6=\frac{9}{6}=\frac{3\cdot3}{3\cdot2}=\frac{3}{2}[/tex]Answer: the ratio equivalent to 9:6 is 3:2.
y varies inversely as x. y = 18 when x = 7. Find y when x = 3.y=(Simplify your answer.)
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May I please get help with this math. I have tried several times but still could not get the right answer
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Given:
m∠3 = 63°
Let's find the m∠5 and m∠8.
• m∠5:
Angle 5 and angle 3 are alternate interior angles.
Alternate interior angles are angles formed on the opposite sides of the transversal.
To find the measure of angle 5, apply the Alternate Interior Angles theorem which states that when two parallel lines are cut by a transversal, the alternate interior angles are congruent.
The measure of angle 5 will also be 63 degrees.
Thus, we have:
m∠3 = m∠5 = 63°
m∠5 = 63°
• m∠8:
Angle 8 and angle 5 are linear pair of angles.
Angles that form a linear pair are supplementary.
Supplementary angles are angles that sum up to 180 degrees.
Thus, we have:
m∠8 + m∠5 = 180
m∠8 + 63 = 180
Subtract 63 from both sides:
m∠8 + 63 - 63 = 180 - 63
m∠8 = 117°
Therefore, the measure of angle 8 is 117 degrees.
ANSWER:
• m,∠,5 = 63°
,• m∠8 = 117°
Find the slope of the line that goes through the given points.
(-3,-2) and (– 15,13)
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(13 - -2)/(-15 - -3) = (13 + 2)/(-15 + 3) = 15/-12 = -5/4 (after simplifying by dividing by 3).
So your answer is -5/4
Answer:
Answer:
Slope m= [tex]-\frac{5}{4}[/tex]
As a decimal:
m = -1.25
Step-by-step explanation:
[tex]m=\frac{Rise}{Run} =\frac{y}{x} \\m=\frac{y2-y1}{x2-x1} \\m=\frac{13--2}{-15--3} \\m=\frac{15}{-12} \\m=-\frac{5}{4}[/tex]
Which of the following numbers are not natural numbers?Select one:a. 1,000,000b. 5,032c. 1/4d. 25
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Natural numbers are those who you use to count elements, they are by definition positive integers.
C. is not an integer, so it is not a natural number
b. 5032, a. 1000000 and d.25 are positive integers. These are natural numbers.
Which of the following equations shows the correct way to apply the Associative Property of Addition? (1 point)0 6x (2 + 3) = 6 x 2) + 3O 9+8 = 8+9O 6+2 = 4+4O 3+ (4+5) = (3+4) +5
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This property indicates that when there are or more digits in these operations, the result does not depends on the way the terms are grouped. Therefore:
[tex]\begin{gathered} 3+(4+5)=(3+4)+5 \\ 3+9=7+5 \\ 12=12 \end{gathered}[/tex]therefore, the answer is the last option 3+ (4+5) = (3+4) +5
compute the value of the discriminant and give the number of real solutions of the quadratic equation. -2x²+3x+5=0
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Given a quadratic equation in standard form
[tex]y=ax^2+bx+c[/tex]The discriminant D
[tex]D=b^2-4ac[/tex]tells the types of roots the equation has.
In this case, we have
[tex]\begin{gathered} -2x^2+3x+5=0 \\ a=-2 \\ b=3 \\ c=5 \end{gathered}[/tex]Then, the discriminant of this quadratic equation will be
[tex]\begin{gathered} D=b^2-4ac \\ D=(3)^2-4(-2)(5) \\ D=9+40 \\ \mathbf{D=49} \end{gathered}[/tex]Finally, the value of discriminat is 49 and as he discriminant is greater than zero then this quadratic equation has 2 different real solutions.
match the system of equations with the solution set.hint: solve algebraically using substitution method.A. no solutionB. infinite solutionsC. (-8/3, 5)D. (2, 1)
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We will solve all the systems by substitution method .
System 1.
By substituting the second equation into the first one, we get
[tex]x-3(\frac{1}{3}x-2)=6[/tex]which gives
[tex]\begin{gathered} x-x+6=6 \\ 6=6 \end{gathered}[/tex]this means that the given equations are the same. Then, the answer is B: infinite solutions.
System 2.
By substituting the first equation into the second one, we have
[tex]6x+3(-2x+3)=-5[/tex]which gives
[tex]\begin{gathered} 6x-6x+9=-5 \\ 9=-5 \end{gathered}[/tex]but this result is an absurd. This means that the equations represent parallel lines. Then, the answer is option A: no solution.
System 3.
By substituting the first equation into the second one, we obtain
[tex]-\frac{3}{2}x+1=-\frac{3}{4}x+3[/tex]by moving -3/4x to the left hand side and +1 to the right hand side, we get
[tex]-\frac{3}{2}x+\frac{3}{4}x=3-1[/tex]By combining similar terms, we have
[tex]-\frac{3}{4}x=2[/tex]this leads to
[tex]x=-\frac{4\times2}{3}[/tex]then, x is given by
[tex]x=-\frac{8}{3}[/tex]Now, we can substitute this result into the first equation and get
[tex]y=-\frac{3}{2}(-\frac{8}{3})+1[/tex]which leads to
[tex]\begin{gathered} y=4+1 \\ y=5 \end{gathered}[/tex]then, the answer is option C: (-8/3, 5)
System 4.
By substituting the second equation into the first one, we get
[tex]-5x+(2x-3)=-9[/tex]By combing similar terms, we have
[tex]\begin{gathered} -3x-3=-9 \\ -3x=-9+3 \\ -3x=-6 \\ x=\frac{-6}{-3} \\ x=2 \end{gathered}[/tex]By substituting this result into the second equation, we have
[tex]\begin{gathered} y=2(2)-3 \\ y=4-3 \\ y=1 \end{gathered}[/tex]then, the answer is option D
Hello, i was in the middle of a tutor explaining and that appt glitched and lost the tutor
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The expression is -16 when m = 6
Explanation:Given:
[tex]m^2-9m+2[/tex]When m = 6, we have:
[tex]\begin{gathered} 6^2-9(6)+2 \\ =36-54+2 \\ =-16 \end{gathered}[/tex]DATE IN OUT IN OUT HOURS TEMPORARY EMPLOYEE TIME CARD NAME: Eugene Mueller 8/8 7:00 4:10 8/9 6:50 11:00 DEPT Sales 8/10 8/11 12:00 4:35 Note: No overtime rate. 10:55 3:25 EMPLOYEE SIGNATURE RATE per hour: $8.50 TOTAL HOURS:
