The statement that If a figure has four congruent angles, then it is a square is a false conditional statement which is the correct option (A).
What is the conditional statement?A conditional statement is defined as the two fundamental components that make up a conditional statement are Hypothesis (if) and Conclusion (then).
Let us consider the example to understand the parts of a conditional statement.
Conditional Statement: If today is Friday, then yesterday was Thursday.
Hypothesis: "If today is Friday."
In the given problem,
Conditional Statement: If a figure has four congruent angles, then it is a square
Hypothesis: "If a figure has four congruent angles"
One example of a counterexample is a rectangle, which although not a square, has four congruent angles.
Hence, the statement that If a figure has four congruent angles, then it is a square is a false conditional statement which is the correct option (A).
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Mick has a bag with 2 mint sticks, 11 jelly treats, and 7 fruit tart chews. If he eats one piece every 10 minutes, what is the probability his first two pieces will be a jelly treat and a mint stick?
Give your answer in a percent.
To find the probability, calculate the probabilities of selecting a jelly treat and a mint stick. Then multiply these probabilities together to find the overall probability.
Explanation:To find the probability that Mick's first two pieces will be a jelly treat and a mint stick, we need to calculate the probability of selecting a jelly treat and a mint stick from the bag.
First, we need to find the total number of pieces in the bag: 2 mint sticks + 11 jelly treats + 7 fruit tart chews = 20 pieces.
The probability of selecting a jelly treat as the first piece is: 11 jelly treats / 20 total pieces = 0.55 or 55%.
After Mick has eaten one piece, there are now 19 pieces left in the bag.
The probability of selecting a mint stick as the second piece is: 2 mint sticks / 19 remaining pieces = 0.105 or 10.5%.
Therefore, the probability that Mick's first two pieces will be a jelly treat and a mint stick is 55% * 10.5% = 0.055 or 5.5%.
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
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.
Find the value of x in the triangle
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]
Twice a number is added to the number and the answer is 90. find the number
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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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.
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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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
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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Is the following definition of perpendicular reversible? If yes, write it as a true biconditional. Two lines that intersect at right angles are perpendicular.
A. The statement is not reversible.
B. Yes; if two lines intersect at right angles, then they are perpendicular.
C. Yes; if two lines are perpendicular, then they intersect at right angles.
D. Yes; two lines intersect at right angles if (and only if) they are perpendicular.
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.
How many n's are there in an atom of p-33?
Sarah has a job at a salon and she earns $50 per day plus tips. Her average tip is 15% of the total amount her customers spend on services. Sarah's daily income is represented by the variable y and the amount her customers spend is represented by the variable x. Which equation represents Sarah's daily income?
If two lines are perpendicular describe the relationship between their slopes
You are making balloon arrangements for a birthday party. there are 16 white balloons and 24 red balloons. each arrangement must be identical. what is the greatest number of arrangements you can make using every balloon?
This is basically a GCF problem. To find the
GCF, we list the factors of each number.
24 = 1×24, 2×12,
4×6, 8×3 ...
16 = 1×16, 2×8,
4×4, ...
The greatest common factor is 8 because it is the greatest
factor we can find.
So 8 arrangements
If the composite functions f(g(x)) and g(f(x)) equal x then the function g is the __________ function of ff.
Solve 2x - 5 = 2x + 4x - 12 plz :)
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]
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
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?
If |x| = 6 then x = -6 or
How do I solve a liner equation in the form a(x-b)=cx? I have no idea plz help
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
please help me find the perimeter of this triangle please
Joe earns $10 per hour babysitting and $5 per hour dog walking. He also earns tips for each job. Last week Joe spent 6 more hours walking dogs than babysitting. He received $5 in tips for babysitting and $10 in tips for dog-walking. Joe earns the same total amount for each job. Write an equation to represent the situation. Use the variable H to represent the number of hours Joe spent babysitting.
Answer:
54
Step-by-step explanation:
Math Quiz Question! Measuring segments and Angles
In the diagram, m < ACB = 65
m < BCD =
Use the data from the following chart to answer the question below.
it was 1.0 that was water this is what i have g/cm3
According to the chart, one milliliter of water would have a density of _____.
100 g/cm 3
10 g/cm 3
1 g/cm 3
cannot be determined
Answer:
1 g/cm 3
Step-by-step explanation:
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