Answer:
The ansewer is D. I just took the test. Happy Holidays!
Step-by-step explanation:
If two lines are perpendicular describe the relationship between their slopes
Claire made 1⁄2 pound of trail mix. If she puts 1⁄4 pound of trail mix into each bag, how many bags are filled?
please help me find the perimeter of this triangle please
How many n's are there in an atom of p-33?
Jenny has been saving quarters in a piggy bank since she was born. She currently has 192 quarters in her piggy bank. She wants to save $75 to buy a new Ipod, so she decides to add 2 quarters every day. She sets up and solves the equation shown. What does her solution mean?
y = 192(.25) + .25x
75 = 192(.25) + .25x
27 = .25x
x = 108
Question 1 options:
She needs to save an additional $108.
She needs to save 216 more quarters.
She needs to save for 108 more days.
She needs to save an additional 108 quarters.
When functions are defined by more than one equation, they are called?
When functions are defined by more than one equation, they are called Piecewise defined functions.
What is Piecewise- defined function?
A Piecewise defined function is one which is defined not by a single equation, but by two or more.
Hence,
When functions are defined by more than one equation, they are called Piecewise defined functions.
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Subtract (enter answer is standard form)
(-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)
Which graph represents the inequality? (has picture)
2x-3y≤6
Multiply
8y^4(2y^4-3y^3+5y)
Solve for x
0=7x^2+x+5
Harold and Helen both spend 3 hours reading a novel. Helen reads 30 more pages than Harold. Helen reads at least 40 pages in 1 hour, but no more than 70 pages in 1 hour.
Which statement correctly describes the range of pages Harold reads?
Harold reads more than 90 pages, but less than 180 pages.
Harold reads at least 90 pages, but no more than 180 pages.
Harold reads more than 150 pages, but less than 240 pages.
Harold reads at least 150 pages, but no more than 240 pages.
PB&P sells peanut butter and pickle sandwiches. The Standard special sells for $2 and the Deluxe special sells for $4.50. When all related business expenses are included, the Standard special costs $0.50 to prepare and the Deluxe special costs $1.25 to prepare.
Last Monday, PB&P sold at least $200 worth of Standard and Deluxe peanut butter and pickle sandwich specials and its expenses were no more than $100. At least 30 Standard special were sold.
Let x be the number of Standard Specials sold last Monday and y be the number of Deluxe specials sold last Monday.
Which ordered pairs representing a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation?
Select each correct answer.
(30,68)(30,68)
(80,40.5)(80,40.5)
(60,70)(60,70)
(40,60)(40,60)
(50.5,40)
Effie is selling candles to raise money for new soccer league equipment. A small candle sells for $8 and a large candle sells for $12. The number of large candles Effie sells must be greater than or equal to 2 times the number of small candles she sells. She has at most 48 candles to sell.
The number of small candles sold is represented by x and the number of large candles sold is represented by y.
What is the maximum revenue she can make?
$448
$512
$576
$588
What is the product of 4−5i and 2+3i?
Enter your answer, in standard form, in the box.
Answer:
Part 1) [tex]-3x^4+3x^3+8x^2-2x-5[/tex]
Part 2) The graph in the attached figure
Part 3) [tex]16y^8-24y^7+40y^5[/tex]
Part 4) [tex]x1=\frac{-1+\sqrt{139}i} {14}[/tex] and [tex]x2=\frac{-1-\sqrt{139}i} {14}[/tex]
Part 5) Harold reads more than [tex]90[/tex] pages, but less than [tex]180[/tex] page
Part 6) [tex](30,68)[/tex], [tex](40,60)[/tex]
Part 7) [tex]\$576[/tex]
Part 8) [tex]23 + 2i[/tex]
Step-by-step explanation:
The complete answers in the attached figure because is too long
Part 1) Subtract (enter answer is standard form)
we have
[tex](-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)[/tex]
Eliminate parenthesis
[tex]-2x^4-2x^3+8x^2+2-x^4+5x^3-2x-7[/tex]
Combine like terms
[tex](-2x^4-x^4)+(-2x^3+5x^3)+8x^2-2x+(2-7)[/tex]
[tex]-3x^4+3x^3+8x^2-2x-5[/tex] ------> standard form
Part 2) Which graph represents the inequality?
we have
[tex]2x-3y\leq 6[/tex]
Rewrite the inequality ------> [tex]3y\geq2x-6[/tex]
the solution is the shaded area above the solid line
the equation of the line is equal to [tex]3y=2x-6[/tex]
the slope of the line is positive
the y-intercept of the line is the point [tex](0,-2)[/tex] ---> value of y when the value of x is equal to zero
the x-intercept of the line is the point [tex](3,0)[/tex] ---> value of x when the value of y is equal to zero
The solution in the attached figure
Part 3) Multiply
we have
[tex]8y^4(2y^4-3y^3+5y)\\=( 8y^4*2y^4)-(8y^4*3y^3)+(8y^4*5y)\\=16y^8-24y^7+40y^5[/tex]
Part 4) Solve for x
we have
[tex]0=7x^2+x+5[/tex]
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]7x^2+x+5=0[/tex]
so
[tex]a=7\\b=1\\c=5[/tex]
substitute in the formula
[tex]x=\frac{-1(+/-)\sqrt{1^{2}-4(7)(5)}} {2(7)}[/tex]
[tex]x=\frac{-1(+/-)\sqrt{-139}} {14}[/tex]
remember that
[tex]i=\sqrt{-1}[/tex]
so
[tex]x=\frac{-1(+/-)\sqrt{139}i} {14}[/tex]
[tex]x1=\frac{-1+\sqrt{139}i} {14}[/tex]
[tex]x2=\frac{-1-\sqrt{139}i} {14}[/tex]
Part 5) Harold and Helen both spend [tex]3[/tex] hours reading a novel. Helen reads [tex]30[/tex] more pages than Harold. Helen reads at least [tex]40[/tex] pages in [tex]1[/tex] hour, but no more than [tex]70[/tex]pages in [tex]1[/tex] hour.
Which statement correctly describes the range of pages Harold reads?
Let
x------> the number of pages that Harold read
y------> the number of pages that Helen read
we know that
[tex]y=30+x[/tex] -----> equation A
[tex]y\geq 40\ pages[/tex] ------> in one hour
so
in three hours -------> [tex]y\geq 120\ pages[/tex] ------> inequality B
[tex]y\leq 70\ pages[/tex] ------> in one hour
so
in three hours ------->[tex]y\leq 210\ pages[/tex] ------> inequality C
Substitute equation A in the inequality B
[tex]x+30\geq 120\ pages[/tex] ------> [tex]x\geq 90\ pages[/tex]
Substitute equation A in the inequality C
[tex]x+30\leq 210\ pages[/tex] ------> [tex]x\leq 180\ pages[/tex]
therefore
Harold reads more than [tex]90[/tex] pages, but less than [tex]180[/tex] page
Part 6) Let
x------> the number of Standard Specials sold last Monday
y------> the number of Deluxe specials sold last Monday
we know that
[tex]2x+4y\geq 200[/tex] -----> inequality A
[tex]0.50x+1.25y\leq100[/tex] -----> inequality B
[tex]x\geq30[/tex] -----> inequality C
Remember that
If a ordered pair representing a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation
then
the ordered pair must satisfy all restrictions
Verify
A) [tex](30,68)[/tex]
Substitute the value of x and y in each inequality
Inequality A
[tex]2(30)+4(68)\geq 200[/tex]
[tex]332\geq 200[/tex] ------> is true
Inequality B
[tex]0.50(30)+1.25(68)\leq100[/tex]
[tex]100\leq100[/tex] -----> is true
Inequality C
[tex]30\geq30[/tex] -----> is true
The ordered pair [tex](30,68)[/tex] represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation
B) [tex](80,40.5)[/tex]
The value of [tex]y=40.5[/tex] not make sense in the context of the situation, because is not a whole number
C) [tex](60,70)[/tex]
Substitute the value of x and y in each inequality
Inequality A
[tex]2(60)+4(70)\geq 200[/tex]
[tex]400 \geq 200[/tex] ------> is true
Inequality B
[tex]0.50(60)+1.25(70)\leq100[/tex]
[tex]117.5\leq100[/tex] -----> is not true
therefore
the ordered pair [tex](60,70)[/tex] is not a solution
D) [tex](40,60)[/tex]
Substitute the value of x and y in each inequality
Inequality A
[tex]2(40)+4(60)\geq 200[/tex]
[tex]320\geq 200[/tex] ------> is true
Inequality B
[tex]0.50(40)+1.25(60)\leq100[/tex]
[tex]95\leq100[/tex] -----> is true
Inequality C
[tex]40\geq30[/tex] -----> is true
The ordered pair[tex](40,60)[/tex] represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation
E) [tex](50.5,40)[/tex]
The value of [tex]x=50.5[/tex] not make sense in the context of the situation, because is not a whole number
If |x| = 6 then x = -6 or
4 pieces of wood each 11 and a half inches long are required to build a cabinet. If all four pieces are cut from one board and 1 inch is allowed for waste in cutting each piece, how long should the board be?
25. What is (2.5 X 102)(6.3 X 105) in scientific notation? Show all your work below
a. 1.575 X 107
b. 1.575 X 106
c. 1.575 X 1010
d. 1.575 X 108
Evaluate the function for x = m/4
f(x) = 8x^2 - 4x
A. 2m^2 - m
B. m^2 - m
C. m^2/2 - 4m
D. m^2/2 - m
Final answer:
To evaluate the function for x = m/4, substitute m/4 for x in the function[tex]f(x) = 8x^2 - 4x[/tex]and simplify to get the result [tex]m^2/2 - m.[/tex]
Explanation:
To evaluate the function [tex]f(x) = 8x^2 - 4x[/tex] for x = m/4, we substitute m/4 for x in the function and simplify.
Substitute x with m/4:
[tex]f(m/4) = 8(m/4)^2 - 4(m/4)[/tex]
Simplify the equation:
[tex]f(m/4) = 8(m^2/16) - m[/tex]
[tex]f(m/4) = (8/16)m^2 - m[/tex]
[tex]f(m/4) = m^2/2 - m[/tex]
Therefore, the correct answer is D. [tex]m^2/2 - m.[/tex]
Sue receives a base salary of $90 weekly plus a 12% commission on all sales. sue had $3,000 in sales this week. how much did she make total?
Her gross pay was the amount of $450 for last week.
What is the commission?The commission is determined by the product of the commission rate and the total sales.
Commission = Commission rate x Total sales
As per the question, we have data :
Commission rate = 12 %
Total sales = $3,000
The base salary = $90
We know that,
Commission = Commission rate x Total sales
= 12% x $3,000
= 0.12 x $3,000
= $360
The total pay is then the base salary increased by the commission:
Total pay = base salary + Commission
Total pay = $90+ $360
Total pay = $450
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How do I solve a liner equation in the form a(x-b)=cx? I have no idea plz help
Tony will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $60 and costs an additional $0.30 per mile driven. The second plan has no initial fee but costs $0.80 per mile driven. How many miles would Tony need to drive for the two plans to cost the same?
Harry buys a sofa set that costs $2000.00. He pays for it by installments at an interest rate of 5% per year. What is the total amount he has to pay at the end of the one year?
Harry is required to pay an additional $100 as interest for one year on the $2000 sofa, bringing the total payment to $2100 at the end of the year.
Harry buys a sofa set at a cost of $2000 with an installment plan that includes an interest rate of 5% per annum. To calculate the total amount Harry needs to pay at the end of one year, you need to calculate the interest and then add it to the principal amount.
The interest for one year is calculated as follows:
Interest = Principal imes Rate imes Time.
Interest = $2000 imes 5% imes 1 year.
Interest = $2000 imes 0.05 imes 1.
Interest = $100.
Now, we add the interest to the principal amount to find the total amount Harry has to pay by the end of the year:
Total Amount = Principal + Interest.
Total Amount = $2000 + $100.
Total Amount = $2100.
Therefore, Harry will have to pay a total of $2100 at the end of one year.
Which expression represents the phrase, "one third the sum of 12 and a number"?
Let
x--------> the number
we know that
1) the phrase, "the sum of 12 and a number"
represent the expression --------> [tex](12+x)[/tex]
and
2) the complete phrase, "one third the sum of 12 and a number"
represent the expression --------> [tex]\frac{1}{3}(12+x)[/tex]
therefore
the answer is
[tex]\frac{1}{3}(12+x)[/tex]
If the composite functions f(g(x)) and g(f(x)) equal x then the function g is the __________ function of ff.
Three sides of a fence and an existing wall form a rectangular enclosure. the total length of fence used for three sides is 240 ft. write the area function in terms of one variable, then find the domain of that function
Need help finishing problem 27.
Write the polynomial in standard form. identify the degree and leading coefficient of the polynomial. then classify the polynomial by the number of terms
The Standard Form: -w¹² + 4w¹¹,
Degree: 12 degree
Leading Coefficient: -1
What is polynomial?Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given equation
4w¹¹ - w¹²
Standard form of polynomial,
List the exponents in decreasing order of importance.
-w¹² + 4w¹¹
Degree of polynomial,
The degree, or the exponent in the first term, if it is in standard form, is the biggest exponent.
degree is 12.
Leading coefficient,
the first term's standard form coefficient Before the w in the first phrase, there is and understood 1.
for equation coefficient is -1,
Hence degree = 12, and leading coefficient is -1.
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The complete Question is
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial.
Then classify the polynomial by the number of terms.
4w11 - w12
standard form
degree
leading coefficient.
Amy leaves a rest stop at 2 PM traveling west, at 45 miles per hour. Sarah leaves 2 hours later, also traveling west, but at 55 miles per hour. At what time will Sarah catch up with Amy?
55(t-2) =45t
55t-110 = 45t
-110 = -10t
t = 11 hours
2 pm plus 11 hours = 1 am
Answer: mathematics, central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data? ... If the range and IQR are small, the values are clustering around some central value.
Step-by-step explanation:
The sum of two numbers is 180. One number is 5 times the other.
x +5x =18
6x =180
x = 180/6 = 30
1 number is 30
2nd number is 5*30 = 150
Solve 2x - 5 = 2x + 4x - 12 plz :)
-3x+2y=-10, -2x+y=-6 solve by substitution
The elevation of Death Valley-282 feet. The Mississippi River in Illinois has an elevation of 279 feet. Which is closer to sea level?
The Mississippi River is closer to sea level.
What is the length?It is the measure of distance between the two points called length.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The elevation of Death Valley is 282 feet.
The Mississippi River in Illinois has an elevation of 279 feet.
If the length of the elevation of Death Valley 282 is greater than the length of the Mississippi River 279.
The Mississippi River is closer to sea level.
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Find the value of x in the triangle
I've never even seen a box and whiskers plot before!! Should be pretty straight forward though. Thanks!
Twice a number is added to the number and the answer is 90. find the number
a 12-ft-by-15-ft swimming pool has a 3-ft-wide no-slip surface around it. what is the outer perimeter of the no-slip surface?
Answer:
A
Step-by-step explanation:
78 ft
The graphs below have the same shape. The equation of the blue graph is f(x) = 2x. Which of these is the equation of the red graph, g(x)?
The functions f(x)=x² and g(s)=s² are essentially the same function with different variable notations. The f(x)=2x graph is linear, and the red graph g(x) with the same shape would also be linear, involving a transformation that retains the proportional relationship between x and y.
Explanation:Based on the provided information, the equation of f(x) is given as f(x) = x². If the blue graph represents this function, and we are looking for the red graph equation g(x), which has the same shape, we need to understand the transformation involved.
Regarding the equations provided in the examples, functions f and g are both defined as taking an input, squaring it, and outputting the result. Although they use different variable names (x for f and s for g), they are effectively the same function. When you have a transformation such as f(x-2), the graph of the function shifts to the right without changing its shape. Similarly, if the red graph were g(x) = 2x, the transformation applied would be to double the output, stretching the graph vertically relative to f(x).
Since the blue graph equation is given as f(x) = 2x and the red graph has the same shape, it means the red graph, g(x), also has a linear relation with a proportional transformation applied. Common linear transformations include multiplying by a scalar to scale the graph or adding/subtracting a number to shift the graph along the x-axis or y-axis.