Answer: a. The sum of two numbers is always greater than zero.
Step-by-step explanation:
A counterexample to this conjecture would be when the two numbers are both negative. For example, the sum of -5 and -3 is -8, which is less than zero.
b. The sum of a positive number and a negative number is always positive.
A counterexample to this conjecture would be when the negative number is greater than the positive number. For example, the sum of 5 and -6 is -1, which is less than zero.
c. If a figure has four sides, then it is a rectangle.
A counterexample to this conjecture would be a square. A square has four sides, but it is not a rectangle because all of its angles are 90 degrees while a rectangle has four right angles.
It's good to keep in mind that a conjecture is a statement that is made based on observations and that it hasn't been proven yet, therefore a counterexample can be used to show that the conjecture is false.
Answer:
a) -5 + 1 = -4
b) 2 + (-10) = -8
c) A scalene trapezium.
Step-by-step explanation:
A counterexample is proof that a conjecture is false.
Part aGiven conjecture:
The sum of two numbers is always greater than zero.If one of the numbers is negative, and its absolute value is equal to or greater than the value of the positive number, the result will always be equal to or less than zero.
Counterexample:
-5 + 1 = -4As -4 is less than zero, this proves that the conjecture is false.
Part bGiven conjecture:
The sum of a positive number and a negative number is always positive.If the absolute value of the negative number is greater than the value of the positive number, the result will always be negative.
Counterexample:
2 + (-10) = -8As -8 is negative, this proves that the conjecture is false.
Part cGiven conjecture:
If a figure has four sides, then it is a rectangle.Counterexample:
A scalene trapezium.The interior angles of a rectangle are congruent (90°).
A scalene trapezium has four sides, but as its interior angles are all different, it is not a rectangle. This proves that the conjecture is false.
Please help me with this question.
The matrix products are given as follows:
a. AB = [58 -6 24]
[18 63 45]
[-22, -39, -33]
b. BA = [32 -26]
[10 56]
The addition A + B is not possible to obtain, the matrices have different dimensions.
How to multiply the matrices?The dimensions of each matrix are given as follows:
A = 3 x 2.B = 2 x 3.Hence the dimensions of each product are given as follows:
AB = 3 x 3.BA = 2 x 2.To multiply matrices, the rows of the first are multiplied by the columns of the second, hence matrix AB is obtained as follows:
Row 1, column 1: -7(-6) + 4(4) = 58.Row 1, column 2: -7(-2) + 4(-5) = -6.Row 1, column 3: -7(-4) + 4(-1) = 24.Row 2, column 1: -9(-6) - 9(4) = 18.Row 2, column 2: -9(-2) - 9(-5) = 63.Row 2, column 3: -9(-4) - 9(-1) = 45.Row 3, column 1: 7(-6) + 5(4) = -22.Row 3, column 2: 7(-2) + 5(-5) = -39.Row 3, column 3: 7(-4) + 5(-1) = -33.Hence the matrix AB is given as follows:
AB = [58 -6 24]
[18 63 45]
[-22, -39, -33]
Matrix BA is obtained as follows:
Row 1, Column 1: -6(-7) - 2(-9) - 4(7) = 32.Row 1, Column 2: -6(4) - 2(-9) - 4(5) = -26.Row 1, Column 1: 4(-7) - 5(-9) - 1(7) = 10.Row 1, Column 2: 4(4) - 5(-9) - 1(5) = 56.Hence the matrix BA is given as follows:
BA = [32 -26]
[10 56]
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Select all of the expressions equivalent to (0.5p + 7) + (0.3p-6).
A.1 +0.8p
B.-6.5p+7.3
C.7.5p - 5.7
D.0.8p + 1
E.7.3 -6.5p
Help me with this question please!
Answer:
Line B slope = 9
Step-by-step explanation:
When dealing with perpendicular lines, we can let the slope we know represent m1, while the slope we don't know represents m2.
Thus, to find m2, we use the formula:
[tex]m_{2}=\frac{-1}{m_{1} }[/tex]
If we plug in -1/9 for m1, we have:
[tex]m_{2}=-\frac{1}{(-1/9)} \\m_{2}=9[/tex]
g(0)=-4x^2-3x+2
g(2)=-4^2-3x+2
The simplified value for the function at g(0) and g(2) are 2 and -20 respectively.
What is simplification?To simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
Given a function g(x) = -4x² - 3x + 2
to find the values of g(0)
and g(2)
for g(0)
substitute x = 0 in the equation,
g(x) = -4x² - 3x + 2
g(0) = -4(0)² - 3(0) + 2
g(0) = 2
for g(2), substitute x = 2 in the equation,
g(x) = -4x² - 3x + 2
g(2) = -4(2)² -3(2) + 2
g(2) = -4(4) - 6 + 2
g(2) = -16 - 6 +2
g(2) = -20
Hence the values for g(0) is 2 and for g(2) is -20.
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Factorise the following
a. x square - 16
b. 8m square - 50n square.
Answer:
(i) (x+4)(x-4)
Step-by-step explanation:
(ii)64m² - 800mn +2500n²
-2x+13<-3 please answer it in a inequality notation and number line
Answer:
x<4
Step-by-step explanation:
_2*+13<_3 take-13 crossing the less sign acting same as equal then with number line, at point 13 go 3 steps to the left to get -16 then divide it by-2 to get x<4
Write the quotient 25/4+3i in the form a + bi.
Answer:
hope this would help you!
PLEASE HELP AGAIN!!!!!!!!!!
The constant of proportionality from the graph is 5.
What is constant of proportionality?Firstly, there is proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called constant of proportionality.
The proportional relationship between x and y can be written symbolically as
[tex]x \propto y[/tex]
That middle sign is called sign of proportionality.
To find the constant of proportionality:
We can see that for every 1 unit we move to the right on the x- axis (positive), the line moves up 5 units.
Divide the change on y by that change on x:
5/1=5
For the next point;
10/2=5
Therefore, the proportionality constant will be 5
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Topic - n-th term
If x + 1 and -x + 17 are the second and sixth terms of a sequence with a common difference
of 5, find the value of x.
Answer: -2
Step-by-step explanation:
So, the arithmetic sequence formula for the nth term is as follows.
Tₙ = a + (n-1)d
So,
2nd term or (x + 1) = a + d
x + 1 = a + 5 (d = 5). - 1
6th term or (-x + 17) = a + 5d
- x + 17 = a + 25. - 2
Subtract 2 from 1, we get,
2x - 16 = -20
2x = -4
x = -2
You can check it if you want,
Second term = - 1
Sixth term will be - 1 + 5 + 5 + 5 + 5 = 19
There you go.
please help meeee :)
Answer:
9 students
Step-by-step explanation:
34 -25
Convert the following [ Use exchange rate 1CAD 0.82 USD]
1.45 CAD = ? USD
45.50 USD = ? CAD
2.50 CAD = ? USD
1,500 CAD = ? USD
Answer: For converting Canadian Dollars to US Dollars divide 1 by 0.82 to give you an answer of around 1.2195(repeating). Then multiply that number by each of the Canadian Dollar amounts. US Dollars to Canadian Dollars is much simpler, as you just multiply the amount by 0.82 to find the answer.
$1.45 CAD x 1.2195 = $1.77 USD
$45.5 USD x 0.82 = $38.31 CAD
$2.50 CAD x 1.2195 = $3.05 USD
$1,500 CAD x 1.2195 = $1,829.27 USD
Hope this helped, and have a great day!
Help pls simplify the following expression (attached to image )
Answer:
[tex]\frac{1}{343}[/tex]
Step-by-step explanation:
[tex]7^{-3}[/tex] = [tex]\frac{1}{7^{3} }[/tex] = [tex]\frac{1}{7x7x7}[/tex] = [tex]\frac{1}{343}[/tex]
Help pleaseeee I can’t figure this out
Answer: B. Exponential decay
Step-by-step explanation:
An exponential function is a function of the form f(x) = ab^x where a and b are constants, x is the independent variable, and b is a positive number not equal to 1. In this case, f(x) = -3(4^x). The base of the exponential function is 4, and it is a common base of exponential decay, because the base is less than 1, and the exponent is positive, this means that the output of the function will decrease as the input increases. Therefore, the function represented by f(x) = -3(4^x) is an exponential decay function.
Answer:
Exponential Decay
Step-by-step explanation:
In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)x wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed
Substitute the given value into the function and evaluate.
f(x)= -3⋅4^x/8
How would you solve question 12b?
The line y = 3 is shown in the diagram of the graph of y = (x + 1)² for -4 ≤ x ≤ 2.
By using the graph, the solutions of (x + 1)² = 3 to 1 decimal place include the following:
x = -2.7 or x = 0.7.
What is a graph?In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.
Next, we would use an online graphing calculator to plot the above quadratic equation with points of intersection at (-2.732, 3) and (0.732, 3) as shown in the graph attached below.
By critically observing graph of the given quadratic equation, we can logically deduce that the solutions of (x + 1)² = 3 on the x-coordinate are x is equal to -2.7 or x is equal to 0.7.
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Calculate each year-end balance using the simple
interest rates listed.
Principal
$100.00
$550.00
$1,200.00
$5,000.00
Annual interest
rate
5%
2%
7%
11%
End of year
balance
The year-end balance interest rate for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00.
What is the interest rate?Interest is the cost of borrowing money or the amount of money that is earned on an investment. It is the amount of money paid by a borrower to a lender or earned by an investment, in exchange for the use of the lender's or investor's money.
Here,
To calculate the year-end balance for each principal using the given annual interest rates, we can use the formula:
End of year balance = Principal + (Principal x Interest rate x Number of years)
For a principal of $100.00, the annual interest rate is 5%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $100.00 + ($100.00 x 0.05 x 1) = $100.00 + $5.00 = $105.00
For a principal of $550.00, the annual interest rate is 2%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $550.00 + ($550.00 x 0.02 x 1) = $550.00 + $11.00 = $561.00
For a principal of $1,200.00, the annual interest rate is 7%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $1,200.00 + ($1,200.00 x 0.07 x 1) = $1,200.00 + $84.00 = $1,284.00
For a principal of $5,000.00, the annual interest rate is 11%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $5,000.00 + ($5,000.00 x 0.11 x 1) = $5,000.00 + $550.00 = $5,550.00
Hence, the year-end balance for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00, and for a principal of $5,000.00 is $5,550.00
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ON = MN, find MN.
A.4
B.5
C. 4// 2
D.4 // 30
The value of x for the given figure is 4√2.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
ΔMNO is a right triangle.
Applying the Pythagorean theorem.
MO² = ON² + MN²
8² = x² + x²
64 = 2x²
2x² = 64
x² = 32
x = √32
x = √(16 x 2)
x = √(4² x 2)
x = 4√2
Thus,
The value of x is 4√2.
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Select the correct answer from each drop-down menu.
Identify the type of chart described and complete the sentence.
A
chart shows open and close prices and highs and lows, but over a long time period it can also show pricing
.
A particular sort of bar chart known as an OHLC chart displays the open, high, low, and final prices with each period.
What does "open-high-low-close chart" mean?It is obvious from the information provided that the chart being discussed is the Continuously compounded chart.It should be mentioned that an expansive chart (OHLC) is just a term used to describe a sort of chart that is used to depict price changes in a financial instrument over a specific time period.
Here,
The chart's vertical line depicts the price range as a function of time. Since it displays the entire price range for the time period, it is helpful in gauging volatility.
The four main data points throughout a period are displayed on OHLC charts, which are helpful since many traders believe the closing price to be the most significant of the four.
In addition to displaying the opening and closing values of the market for the same time period, open-high-low-close charts also display the high and low price that a stock achieved during that time.
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Which expression represents the total area of the rectangle. (look at picture)
 Using the Distributive Property as a good first step to solving the equation, you could simplify to get which of these choices?
7(5x + 2) = -4(6 - 5x)
0
à
Ib
0
O
0
d
e
35x + 14 = -24 - 20x
35x + 14 = -24 + 20x
5x + 14 = 6 + 20x
35x + 2 = -24 - 5x
35x + 2 = 24 - 20x
2. Kasie lives in Seattle. She can see her house from the observation deck of the Seattle Space Needle. The
observation deck is 520 feet above the ground and the angle of depression from the deck to her house
is 70. What is the direct distance from the base of the Space Needle to Kasie's house? Round your
answer to the nearest foot.
Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.
What is angle of depression?The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.
Given,
Height of the observation deck AB = 520 feet
Angle of depression = 70°
Distance of the Space needle base to house BC = ?
By the figure,
tan70° = AB/BC
BC = tan70°(AB)
BC = 2.7475(520)
BC = 1428.7 feet
Distance of the Space needle base to house to nearest foot = 1429 feet
Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.
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Kimi Skuban deposits $2,000 at the beginning of each year into an Individual Retirement Account at
Boise Bank. The account pays 7% compounded annually. How much will be in the account in 25 years?
Total amount in the account after 25 years is, $5,500.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
We have to given that;
Kimi Skuban deposits $2,000 at the beginning of each year.
The account pays 7% compounded annually.
Now, We know that;
⇒ Interest = PRT / 100
Where, P is principal amount, R is interest rate and T is time in years.
Substitute all the values, we get;
⇒ Interest = PRT / 100
⇒ Interest = 2000 × 7 × 25/ 100
⇒ Interest = $3,500
Hence, Total amount in the account after 25 years is,
⇒ $2,000 + $3,500
⇒ $5,500
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A diagram of a roundabout that is being designed to improve driver safety on a busy road is shown. The radius of the circular field planned for landscaping is 27.5 feet. What is the approximate distance around the outside of the circular field? PLEAS HELP WANT!
A. 345.4 feet
B. 172.7 feet
C. 86.35 feet
D. 2,323.1 feet
The approximate distance around the outside of the circular field is B. 172.7 feet.
Length of the circumference of a circle.A circumference is the part of a circle which is referred to as the boundary. The length of the circumference of a circle is given as;
length of a circumference = 2πr
where r is the radius of the circle.
To determine the distance around the outside of the circular field, we have;
length of the distance around the outside of the circular field = 2πr
given that;
r = 27.5 feet
length of the distance around the outside of the circular field = 2πr
= 2*(22/ 7)*27.5
= 172.7
The length of the distance around the outside of the circular field is 172.7 feet.
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Amanda is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her
13
character unlocking the treasure chest is
Find the odds in favor of her character unlocking the treasure chest.
The odds in favor of Amanda unlocking the treasure chest is 1/5.
We have to find the odds in favor of Amanda's character unlocking the treasure chest. Odds in favor is the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
[tex]P (A) = \frac{no.of favorable outcomes}{no. of unfavorable oucomes}[/tex]
P(A), is used to denote the probability of the event A.
Before finding out the odds in favor, we need to find the probability of her unlocking the treasure chest {P(T)}
Total no. of outcomes = 6 (as a dice has 6 sides)
Number of outcomes desired = 1 (that unlocks the treasure chest)
Therefore, the probability of unlocking the treasure chest
P(T) = Number of outcomes desired/ Total no. of outcomes = 1/6
P(T) is our favorable outcome.
Any other outcome would be unfavorable,
Therefore, the number of unfavorable outcomes would be
= Total no. of outcomes - number of the desired outcomes = 6-1 = 5
Thus, applying the formula for P(A)
P(A) = no. of favorable outcomes/ no. of unfavorable outcomes
= 1 / 5 (Ans)
Thus, the odds in favor of Amanda unlocking the treasure chest is 1/5.
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Suppose I deposit $500 into my bank account that earns 3% interest per year. Is the total amount in my bank account per year a linear relationship? Hint: use a table of values and look at the rate of change. Also, keep in mind that once you earn interest, the next year you will earn interest not only on your original investment but on the new amount.
Answer:
The total amount in your bank account per year is not a linear relationship, it's compound interest.
Step-by-step explanation:
The total amount in your bank account per year is not a linear relationship because it is not a straight line. Linear relationships are defined by an equation in the form of y = mx + b, where m is the slope of the line, x is the independent variable and y is the dependent variable, and b is the y-intercept.
In this case, the total amount in your bank account per year is not a straight line, it is a curve. The total amount in your bank account will increase as a function of time, but the rate of increase is not constant as it is with linear relationships.
The amount of money in your account will increase over time as the interest is compounded. The interest is calculated on the principal + accumulated interest, so the growth rate of the account is not constant, it increases as the balance grows.
For example, the first year you will earn $5000.03 = $15 in interest, and the second year you will earn $5150.03 = $15.45 in interest, the next year the interest will be $530.45*0.03 = $15.91 and so on.
a car is travelling at 18.1m/s with a constant acceleration of 3.7m/s^2. the car is attempting to pass a truck which is moving at a constant velocity of 29.7m/s. how far in meters must the car travel until it matches the trucks velocity
Answer:
Step-by-step explanation:
?
The car must travel a distance of 130.7 meters. This can be determined by using the equation for distance travelled with a constant acceleration:
Distance = Initial Velocity x Time + (1/2) x Acceleration x Time^2
In this case, the initial velocity is 18.1m/s, the acceleration is 3.7m/s^2, and the final velocity is 29.7m/s. We can set the final velocity equal to the initial velocity and solve for time:
29.7m/s = 18.1m/s + 3.7m/s^2 x Time
Time = 5.4 seconds
We can then plug this value for time into the equation for distance:
Distance = 18.1m/s x 5.4s + (1/2) x 3.7m/s^2 x 5.4s^2
Distance = 130.7 meters
During a spring clearance sale, Sears advertise 1/4 off the list of Model II microwave ovens and an additional 1/5 off the sale price for ovens that are scratched or dented. If the list price of a Model II is $240, what is the sale price? What is the price of a scratched one?
Answer:
$180.00 sales price
$144.00 for a scratched one
Step-by-step explanation:
240 x .75 = 180
1/4 is 25% (100% - 25% = 75% which is .75 as a decimal)
180 x .80 = 144
1/5 is 20% (100% -20% = 80% which is .8 as a decimal)
Math expression work
The given expression is equivalent to the expression -x² + x + 30.
What is the expression?The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Given expression,
= (5 + x)(6 - x)
Simplifying the expression using distributive property,
= 5 [6 - x] + x [6 - x]
= 30 - 5x + 6x - x²
= -x² + x + 30
Thus, the given expression is equivalent to the expression -x² + x + 30.
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A whale-watching tour boat, moving west at a constant speed 45 miles per hour, has finished viewing a whale and is returning to shore. One whale that is right next to the boat swims away in the opposite direction, moving at a constant speed of 25 miles per hour. They swim apart for 35 minutes and then change direction. The boat turns south and again the whale turns in the opposite direction of the boat. They continue moving apart for another 25 minutes. How far apart are the boat and the whale? (Round your answer to the nearest mile).
The boat and the whale are about 218.5 miles apart.
Solving for the distance between the boat and the whale:Using the Pythagorean theorem to calculate the distance between the boat and the whale.
Let's call the distance between the boat and the whale "d" and the time they moved apart "t".
1st movement:
d = 45t
2nd movement:
d = (45t + 25(t+35))²
To calculate the final distance, we need to square d from the second movement and add the result from the first movement.
d² = (45t)² + (25(t+35))²
We know that the boat and the whale were moving apart for 35 minutes and 25 minutes, so we can substitute t = 35 and t = 25 in the equation.
d² = (4535)² + (2560)²
Taking the square root of the result and get the final distance between the boat and the whale.
d = ([tex]\sqrt{4535 ^{2} +2560^{2} }[/tex])
d ≈ 218.5 miles
Hence, the boat and the whale are about 218.5 miles apart.
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If f(x)= |a³-31 |. then f(-1) is equivalent to
The value of f(-1) is either a³ - 31 or the absolute value of a³ - 31, depending on the value of a³ - 31.
We substitute -1 for x in the function: f(-1) = |a³ - 31| To find the value of f(-1), we need to find the value of a³ - 31. If a³ - 31 is positive, then |a³ - 31| will be equal to a³ - 31. If a³ - 31 is negative, then |a³ - 31| will be equal to the absolute value of a³ - 31 (which is the positive value of a³ - 31).So, the value of f(-1) is either a³ - 31 or the absolute value of a³ - 31, depending on the value of a³ - 31.It is not possible to find the exact value of f(-1) without knowing the value of a.
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Geneva treated her parents to dinner at their favorite restaurant. The bill was $73.25. She wants to leave 24% of the total bill as a tip. How much should the tip be, in dollars?
Answer:
To calculate the tip, we first need to find 24% of the total bill. To do this, we can multiply the bill amount by 24% (expressed as a decimal).
Tip = 0.24 * 73.25
= 17.58
Therefore, the tip should be $17.58 in dollars.
