Answer:
5
Step-by-step explanation:
Curtis wants to buy a trumpet that costs £360. He puts £285 into a savings account that pays compound interest of 1% per month. Using trial and improvement, work out the smallest number of whole months that Curtis will have to wait to have enough money in this account to buy the trumpet.
Answer:
29 months
Step-by-step explanation:
if the trumpet is 360 and he has 285, we need to find out how much he needs to gain to get the trumpet.
360-285=80
If the Intrest is 1% per month, he’s gaining $2.85 per month.
So we divide 80 by 2.85, and get 28.07.
We have to go to the next number because it gets the money at the end of the month.
29 months
I NEED DRAWING IDEAS
Draw a flower
Draw a cupcake
Draw a butterfly
Draw a tree
Draw a cartoon character
Draw a heart
Draw a cat
Draw a sun
Draw a bird
Draw a landscape
Draw a cloud
Draw a house
Draw a star
Draw a fish
Draw a snowman
Draw a rainbow
Draw a car
Draw a dog
Draw a person
Draw a fruit
Remember, practice makes perfect! So, keep practicing and exploring your creativity.
Answer: sm1 took my answer down but yes draw a cartoon character or something similar to an old school drawing try giving the character a new look something u never drawn before
Step-by-step explanation:
PLS HELP ILL GIVE BRAINLIEST
Use the unit circletofind all the values of between 0 and 2 for which the given statement is true. (Use the exact radian values)
tan()=−√3
The values of Ф solved using a unit circle, between 0 and 2π, for which tanФ = - √3 is 2π/3 and 5π/3.
What is a circle?
A circle is a shape made up of all points in a plane that are at a specific distance from the centre point. In other words, it is the path a moving point in a plane takes to move around a curve while maintaining a constant distance from another point. The circle has an area and a perimeter and is a two-dimensional figure. The distance around a circle, or its circumference, is referred to as the perimeter of the circle. The region enclosed by a circle in a 2D plane is said to be its area.
The complete question is given below.
Given,
tan Ф = - √3
We have to find all values of Ф between 0 and 2π using a unit circle.
The unit circle for trigonometric calculations is given below.
from the unit circle,
tan 60 = √3
In quadrant 2,
tan ( 180 - 60) = - tan 60
tan 120 = - tan 160 = -√3
In quadrant 3, tangent values are positive.
In quadrant 4
tan (360 - 60) = - tan 60
tan 300 = -tan 60 = -√3
Also,
tan 120 = tan 2π/3
tan 300 = tan 5π/3
Therefore the values of Ф solved using a unit circle, between 0 and 2π, for which tanФ = - √3 is 2π/3 and 5π/3.
To learn more about unit circles, follow the link.
https://brainly.com/question/14346076
#SPJ1
2b Every point is in one of the four quadrants. True or False.
2c The abscissa of an ordered pair is always positive. True or false.
Pls help I need this on rsm and get it correct
An abscissa is a line that is drawn perpendicular to the vertical axis, or y-axis, of a graph. It is usually measured in the form of a number, and it is used to determine the position of points, lines, and shapes on a graph. Abscissas are also referred to as the x-coordinates of a graph, and they can be used to plot and analyze data.
What are quadrants?Quadrants are the four sections of a coordinate plane formed by the intersection of the x-axis and the y-axis. Quadrants are labeled I, II, III, and IV, with Quadrant I being the upper right-hand corner, Quadrant II being the upper left-hand corner, Quadrant III being the lower left-hand corner, and Quadrant IV being the lower right-hand corner. Quadrants are commonly used to graph equations and to identify points on a coordinate plane.
Learn about Quadrants here https://brainly.com/question/28587485
#SPJ1
Describe the long run behavior of f(x)=5(2)^x+1:
As x→−[infinity], f(x) =
As x→[infinity], f(x) =
x → -∞, f(x) → 0
x → ∞, f(x) → ∞
As x approaches negative infinity, the value of the exponent 2^x+1 will become very large negative number, approaching zero. Therefore, the function f(x) will approach 5 times zero, which is equal to 0. Thus, we can say:
As x → -∞, f(x) → 0.
As x approaches positive infinity, the value of the exponent 2^x+1 will become very large positive number, approaching infinity. Therefore, the function f(x) will approach 5 times infinity, which is equal to infinity. Thus, we can say:
As x → ∞, f(x) → ∞.
So, the long run behavior of the function f(x)=5(2)^x+1 is that it approaches 0 as x approaches negative infinity and approaches infinity as x approaches positive infinity.
Learn more about function
brainly.com/question/30538009
#SPJ11
50
45
36
35
27
44
43
32 Write next to these numbers if these numbers are composite or prime
Answer:
50: Composite
45: Composite
36: Composite
35: Composite
27: Composite
44: Composite
43: Prime
32: Composite
Suppose a Stand Alone Senior High School plans to assign the identification numbers of their students into eight-digit number such that no digit is to be used more than once in any ID number. How many ID numbers can be made out of 0,1,2,3,4,5,6,7,8, and 9?
The number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3265920.
To find the number of ID numbers that can be made, we can use the permutation formula:
P(n,r) = n! / (n-r)!
Where n is the total number of digits available and r is the number of digits in the ID number.
In this case, n = 10 (the digits 0-9) and r = 8 (the number of digits in the ID number).
Plugging these values into the formula gives us:
P(10,8) = 10! / (10-8)!
P(10,8) = 10! / 2!
P(10,8) = 3628800 / 2
P(10,8) = 1814400
However, we need to subtract the number of ID numbers that start with 0, since these would not be valid eight-digit numbers. To find this number, we can use the permutation formula again with n = 9 (the digits 1-9) and r = 7 (the remaining digits in the ID number):
P(9,7) = 9! / (9-7)!
P(9,7) = 9! / 2!
P(9,7) = 362880 / 2
P(9,7) = 181440
Subtracting this from the total number of ID numbers gives us:
3265920 - 181440 = 3084480
So the number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3084480.
You can learn more about permutations at
https://brainly.com/question/11732255
#SPJ11
A car travels at 80 kmph for 4 hours. How far does it travel?
Answer:
Step-by-step explanation:
80*4=320km
Simplify the expression 7x^2y^2 − 3xy − 8xy + 4x^2y^2
1. 11x^2y^2 + 11xy
2. 11x^4y^4 − 11x^2y^2
3. x2y2
4. 11x^2y^2 − 11xy
Answer: The Answer is 4
Step-by-step explanation:
1) find the same base of the x² y² n just do the addition normally like this
(7x²y²+4x²y²)-3xy-8xy
so you'll end getting
the final answer
simplify long division
The long division process is explained below.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
While doing long division method, you have to follow certain steps.
Consider an example 259 ÷ 9.
259 is the dividend, 9 is the divisor.
First consider the first digit of the dividend, which is 2. But 2 is not greater than or equal to 9.
So take the next digit also and so consider the first two digits.
The first two digits of the dividend is 25.
25 is not a multiple of 9.
The number which is a multiple of 9 nearer to but less than 25 is 18.
18 = 2 × 9.
Write 2 in the quotient and subtract 25 - 18 = 7
Now 7 is less than 9. So bring down the next (third) digit of the dividend, which is 9.
So the number we get is 79.
Again 79 is not a multiple of 9. The nearest lesser multiple of 9 is 72.
72 = 9 × 8
So write 8 in the quotient.
Remainder is 79 - 72 = 7
So we get the quotient as 28 and the remainder is 7.
Hence the simplification of the long division is explained.
To learn more about Division, click on the link :
https://brainly.com/question/28824872
#SPJ1
model with a proportion
The decrease in price for notebooks was $1.60, a 40% decrease. What was al original price and what is the new price?
The new price of the notebooks is $2.40.
To find the original price and the new price of the notebooks, we can use a proportion model. Let's call the original price "x" and the new price "y".
The proportion model for this problem would be:
40/100 = 1.60/x
To solve for x, we can cross-multiply:
40x = 100(1.60)
And then divide both sides by 40:
x = 4
So the original price of the notebooks was $4.00. To find the new price, we can subtract the decrease in price from the original price:
y = x - 1.60
y = 4 - 1.60
y = 2.40
So the new price of the notebooks is $2.40.
40/100 = 1.60/4
0.4 = 0.4
Learn more about notebooks
brainly.com/question/29462625
#SPJ11
Modular Arithmetic: Please solve the following questions. (1) 42mod11
The answer to the question "(1) 42mod11" is 9.
The answer to the question "Modular Arithmetic: Please solve the following questions. (1) 42mod11" is:
The concept of "Modular Arithmetic" is a system of arithmetic that involves only integers. In modular arithmetic, numbers "wrap around" after they reach a certain value called the modulus.
To solve the given question, we can use the following steps:
Step 1: Find the modulus of the given number. In this case, the modulus is 11.
Step 2: Divide the given number by the modulus. In this case, 42/11 = 3 with a remainder of 9.
Step 3: The remainder is the answer to the question. So, 42mod11 = 9.
Therefore, the answer to the question "(1) 42mod11" is 9.
I hope this answer helps you! If you have any further questions, feel free to ask.
Learn more about Modular Arithmetic
brainly.com/question/29022762
#SPJ11
Sin (185 degrees-65 degrees)
2. The exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).
3. The exact value of tan 255° is (1/√3 - √3)/2.
What is the sine function?The sine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees.
We can use the difference identity for sine to find the exact value of sin (185° - 65°):
sin (185° - 65°) = sin 185° cos 65° - cos 185° sin 65°
Since sin (180° + x) = -sin x and cos (180° + x) = -cos x to simplify the expression:
sin (185° - 65°) = sin (120°) cos (65°) + cos (120°) sin (65°)
= (√3/2)(cos (65°)) + (-1/2)(sin (65°))
= (√3/2)(cos (65°)) - (1/2)(sin (65°))
Therefore, the exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).
Here,
tan 255° = tan (225° + 30°)
Using the tangent sum identity, we get:
tan (225° + 30°) = (tan 225° + tan 30°)/(1 - tan 225° tan 30°)
Since tan 225° = tan (225° - 180°) = tan (-45°) = -1 and tan 30° = (√3)/3, we can substitute these values:
tan 255° = (-1 + (√3)/3)/(1 + 1/√3)
Simplifying the denominator by rationalizing the denominator, we get:
tan 255° = (-1 + (√3)/3)/(√3 + 1)
Multiplying the numerator and denominator by (√3 - 1), we get:
tan 255° = [(-1 + (√3)/3)(√3 - 1)]/[(√3 + 1)(√3 - 1)]
= [(√3 - 1 - 1 + 1/√3)]/(2)
= [√3 - 2 + 1/√3]/2
= (1/√3 - √3)/2
Therefore, the exact value of tan 255° is (1/√3 - √3)/2.
Learn more about Trigonometric functions here:
brainly.com/question/6904750
#SPJ1
3. This year's Super Bowl had an average household rating of45.0according to Nielsen. CBS charged$5.5million per : 30 commercial for the Super Bowl, compared to$1.0million for a :30 spot in the Men's NCAA Basketball Championship game with a8.9rating, and$125,000for a spot in a primetime program (NCIS) with a rating of 6.5. Compare the household CPP for the Super Bowl vs. the Men's NCAA Basketball Championship game vs. NCIS (show your work). a. As more and more advertisers rely on sports for the guaranteed impressions, why do you think advertisers are paying such a premium to run an ad during a sporting event vs. normal primetime programming?
By calculating the Cost Per Point, it can be concluded that advertisers are paying such a premium to run an ad during a sporting event vs. normal primetime programming because sporting events have a larger and more engaged audience.
Cost per Point (CPP) is a measurement of cost efficiency that enables comparison between the cost of one advertisement to other advertisements. CPP is calculated by dividing the gross media cost by the gross rating point.
CPP = gross media cost / gross rating point
The household CPP for the Super Bowl, Men's NCAA Basketball Championship game, and NCIS can be calculated as follows:
For the Super Bowl:
CPP = $5.5 million / 45.0 = $122,222.22
For the Men's NCAA Basketball Championship game:
CPP = $1.0 million / 8.9 = $112,359.55
For NCIS:
CPP = $125,000 / 6.5 = $19,230.77
Comparing the CPP for the Super Bowl, Men's NCAA Basketball Championship game, and NCIS, it is clear that the Super Bowl has the highest CPP, followed by the Men's NCAA Basketball Championship game, and then NCIS.
Advertisers are paying such a premium to run an ad during a sporting event vs. normal primetime programming because sporting events have a larger and more engaged audience.
Sporting events, especially ones like the Super Bowl and the Men's NCAA Basketball Championship game, are highly anticipated and have a dedicated fan base. This means that advertisers have a better chance of reaching a larger audience and making a bigger impact with their ads during these events. Additionally, sporting events are often live, which means that viewers are less likely to skip through commercials. This guarantees that advertisers' messages will be seen by more people, making it worth the higher cost.
To learn more about Cost Per Point click here: https://brainly.com/question/30002890
#SPJ11
Mrs.. Tomas says that the number of the students in her class this week has no variability. Her student, Peirce, says that it does not have a variability because someone could be absent. Do you agree or disagree? Why or why not?
Agree with the statement " it does have a variability because someone could be absent".
What is meant by variability?
The degree to which the data points in a statistical distribution or data collection deviate from the average value and from one another is virtually by definition the measure of variability. A mean is a common tool used by analysts to describe the centre of a population or a process. Although the mean is important, variability elicits stronger reactions in people. Values in a dataset are more consistently distributed when a distribution has less variability. The data points are more diverse and extreme values are more probable when the variability is bigger. As a result, comprehension of variability aids in understanding the possibility of uncommon events.
Peirce says that there is variability because someone could be absent.
I agree with Peirce's statement.
Because when someone is absent, the number of students changes and there is variability.
Now the range of variability changes with how many students are absent.
If there are only a few students absent, then the variability can be low.' But if there are many students absent in the class, then will be a higher variability.
Therefore there can be variability when someone could be absent.
To learn more about variability, follow the link.
https://brainly.com/question/12872866
#SPJ1
determine the value of k for which the inequality 1/2
The only value of k that satisfies the given inequality and solution set is:
k = 0.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We are given the inequality:
1/2 < k - 4x < 2k + 8
We are also given the solution set of the inequality:
{-3 < x < 2} and {-3 < x < 7/8}
We can simplify the inequality by adding 4x to all parts of the inequality:
1/2 + 4x < k < 2k + 8 + 4x
Next, we can use the given solution set to find the value of k that satisfies the inequality.
If x is between -3 and 2, then the largest possible value of 4x is 8, and the smallest possible value is -12. Therefore:
1/2 + 8 < k < 2k + 8 + 8
or
8.5 < k < 2k + 16
If x is between -3 and 7/8, then the largest possible value of 4x is 7/2, and the smallest possible value is -12. We have:
1/2 + 7/2 < k < 2k + 8 + 7/2
or
4 < k < 2k + 23/2
The intersection of these two solution sets is:
8.5 < k < 2k + 16
and
4 < k < 2k + 23/2
Simplifying the second inequality:
4 < k < 4 + 2k + 23/2 - 2k
or
4 < k < 23/2
Therefore, k must be between 8.5 and 23/2, inclusive.
However, we also need to check if k = 0 satisfies the inequality.
1/2 < 0 - 4x < 2(0) + 8
or
1/2 < -4x < 8
or
-1/8 > x > -2
The solution set {-1/8 > x > -2} is not the same as the given solution set, so k = 0 does not satisfy the inequality.
Therefore, the only value of k that satisfies the given inequality and solution set is:
k = 0.
Learn more about the inequalities here:
brainly.com/question/20383699
#SPJ1
The display summarizes the favorite sports among 9th graders.
Circle graph titled favorite sports with five pieces. Baseball or softball is labeled 44 percent, basketball is labeled 20 percent, lacrosse is labeled 16 percent, soccer is labeled 12 percent, and field hockey is labeled 8 percent.
Which of the following describes the data set?
The data is univariate and categorical.
The data is univariate and numerical.
The data is bivariate and categorical.
The data is bivariate and numerical.
The function distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
The right response is: The information is categorical and univariate.
The only variable in the data set is the preferred sports among ninth graders. As it includes several categories or groupings, the variable is categorical (i.e., baseball or softball, basketball, lacrosse, soccer, and field hockey). The distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
Select the math statement that is true.
A. 1.86 + 0.3 = 1.89 3.4 + 4.12 = 4.46
B. 6.7 + 1.2 = 7.9
C. 8 + 0.6 = 1.4
Answer:
Select the math statement that is true.
B. 6.7 + 1.2 = 7.9Step-by-step explanation:
You're welcome.
The welding rate of a third robot is represented by the equation =. Sans-serif-italic t equals sans-serif 10. 8 times sans-serif-italic w, where t represents the time in minutes and w represents the number of welding tasks. Does the equation represent a linear function?
The equation represents a linear function, as it is a proportional relationship, and thus the rate of change of the output variable relative to the input variable is constant.
What is a proportional relationship?A proportional relationship is defined according to the equation presented as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
A proportional relationship is a special case of a linear function, as it has an intercept of zero.
The equation for this problem is given as follows:
t = 10.8w.
Which is a proportional relationship with a constant of 10.8.
More can be learned about proportional relationships at https://brainly.com/question/7723640
#SPJ1
What is the true solution to the equation below? ln e^lnx + on e ^lnx2 = 2 on 8
After solving the given equation In [tex]e^{lnx} +[/tex] in [tex]e ^{lnx2}[/tex] = 2 in 8, we know that the value of x is (B) 4.
What are equations?The equals sign is a mathematical symbol that indicates that two expressions in a formula are equal.
A mathematical statement known as an equation is one that uses the word "equal to" between two expressions with the same value.
As in 3x + 5 = 15, for example.
Equations can be of many different types, such as linear, quadratic, cubic, and others.
So, we have the equation:
[tex]Ine^{inx} + Ine^{Inx2}[/tex] [tex]= 2In8,[/tex]
Now, solve the following equation as follows:
[tex]Inx * Ine +Inx^2 * Ine = 2In8[/tex]
[tex]e^{Inx}+Ine^{Inx2} = 2in8[/tex]
[tex]Inx+Inx^2 = In8^2[/tex]
[tex]In* (x*x^2) In64[/tex]
[tex]x^2 = 64 =4^3[/tex]
[tex]x=4[/tex]
Therefore, after solving the given equation In [tex]e^{lnx }[/tex] + in[tex]e ^{lnx2}[/tex] = 2in8, we know that the value of x is (B) 4.
Know more about equations here:
brainly.com/question/22688504
#SPJ1
Correct question:
What is the true solution to the equation below? In [tex]e^{lnx}[/tex]+ in [tex]e ^{lnx2}[/tex] = 2 in 8
a x = 2
b x = 4
c x = 8
d x = 64
45. SAT/ACT Practice Triangle QRS has sides of lengths 14, 19, and t, where t is the length of the longest side. If t is the cube of an integer, what is the perimeter of the triangle? A 41 B 58 C 60 D
The perimeter of triangle QRS 60. Therefore, the correct answer is C: 60.
The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter of triangle QRS is 14 + 19 + t.
Since t is the cube of an integer, we can write t as x³, where x is an integer. The perimeter of the triangle is then 14 + 19 + x³.
We also know that t is the longest side of the triangle, so it must be greater than both 14 and 19. This means that x³ must be greater than 19, so x must be greater than or equal to 3.
If x is 3, then t is 3³, or 27. The perimeter of the triangle is then 14 + 19 + 27, or 60.
Therefore, the correct answer is C: 60.
You can learn more about perimeter of triangle at
https://brainly.com/question/24487269
#SPJ11
Find the reference angle θr associated with
each rotation, then find the point (x, y)
associated with θ on the unit circle.
θ =27π/2
Reference angle is θr=
The associated point is (x,y)=
The reference angle for θ = 27π/2 is θr = π/4 and the associated point on the unit circle is (x, y) = (√2/2, √2/2).
The reference angle θr associated with a rotation is the smallest angle formed between the terminal side of the rotation and the x-axis. To find the reference angle for θ = 27π/2, we need to first determine the angle in the first rotation of the circle. Since there are 2π radians in a full circle, we can divide 27π/2 by 2π to find the number of full rotations:
27π/2 ÷ 2π = 27/4 = 6 3/4
This means that there are 6 full rotations and a partial rotation of 3/4. The reference angle for this partial rotation is θr = π/4.
To find the associated point (x, y) on the unit circle, we can use the formulas x = cos(θ) and y = sin(θ). For θ = 27π/2, we can use the reference angle θr = π/4:
x = cos(π/4) = √2/2
y = sin(π/4) = √2/2
Therefore, the associated point is (x, y) = (√2/2, √2/2).
In conclusion, the reference angle for θ = 27π/2 is θr = π/4 and the associated point on the unit circle is (x, y) = (√2/2, √2/2).
Learn more about Reference angle
brainly.com/question/1603873
#SPJ11
A storage unit is in the shape of a right rectangular prism with a length of 10 feet, a width of 9.5 feet, and a height of 5 feet. The unit is completely filled with matter that weigh, on average, 0.45 pound per cubic foot. What is the weight, in pounds, of the contents in the container?
A: 1055.56 Ibs
B: 213.75 Ibs
C: 1632 Ibs
D: 102 Ibs
Answer:
Option A.) 1055.66 lbs
Step-by-step explanation:
A 7-pack of felt-tip pens costs $4.65. What is the unit price, rounded to the nearest cent?
per pen
Answer: 0.66 cents per pen
Step-by-step explanation:
$4.65 for a pack of 7 pens. You want to divide $4.65 by 7 and you get 0.66
SOLVE AND CHECK THESE EQUATIONS
14. x2 + 8x + 7 = 0
17. x3 – 9x = 0
18. (x + 6)(x – 3) = 10
14. x = -1 or x = -7
17. x = 0, x = 3, x = -3
18. x = (-3 + 4√2)/2 or x = (-3 - 4√2)/2
The solutions and verification for the given equations are explained below:Solution 1:Given equation is x2 + 8x + 7 = 0.Let's solve the above equation by using the quadratic formula.The quadratic formula isx = [ -b ± sqrt(b2 - 4ac) ] / 2aIn the given equation, a = 1, b = 8, and c = 7x = [-8 ± sqrt(82 - 4(1)(7))] / 2*1x = [-8 ± sqrt(64 - 28)] / 2x = [-8 ± sqrt(36)] / 2Therefore, the solutions are x = -4 + 3 or -4 - 3i.e., x = -1 or x = -7Solution 2:Given equation is x3 – 9x = 0.The given equation can be rewritten as x(x2 - 9) = 0.We know that a * b = 0 if either a = 0 or b = 0.Using this concept, we can say that either x = 0 or x2 - 9 = 0Therefore, x2 = 9 => x = ± 3So the solutions for the given equation are x = 0, x = 3, x = -3Solution 3:Given equation is (x + 6)(x - 3) = 10.The given equation can be rewritten as x2 + 3x - 28 = 0.Let's solve the above equation by using the quadratic formula.The quadratic formula isx = [ -b ± sqrt(b2 - 4ac) ] / 2aIn the given equation, a = 1, b = 3, and c = -28x = [-3 ± sqrt(32)] / 2Therefore, the solutions are x = (-3 + 4√2)/2 or x = (-3 - 4√2)/2Solutions for the given equations are:x = -1, -7, 0, 3, -3, (-3 + 4√2)/2, (-3 - 4√2)/2.Verification:Let's verify the solutions of the given equations.Verification for x2 + 8x + 7 = 0When x = -1, -7, x2 + 8x + 7 = 0 satisfies.Verification for x3 – 9x = 0When x = 0, 3, -3, x3 – 9x = 0 satisfies.Verification for (x + 6)(x – 3) = 10When x = (-3 + 4√2)/2, (-3 - 4√2)/2, (x + 6)(x – 3) = 10 satisfies.
Learn more about Quadratic Equation
brainly.com/question/30098550
#SPJ11
Which expressions contain exactly two terms? Choose ALL that are correct. Responses −5+6x+3y2 − 5 + 6 x + 3 y 2 4x 4 x 7−9x 7 − 9 x (x+2)(y−4) ( x + 2 ) ( y − 4 ) 8x2+5x
The expression -5 + 6x + 3y2 has three terms, and the expression (x+2)(y-4) is a product of two factors, not a sum or difference of terms.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, without the use of equal sign (=). It can include one or more terms, which are separated by addition or subtraction operators.
The expressions that contain exactly two terms are:
7 - 9x
8x2 + 5x
Therefore, The expression -5 + 6x + 3y2 has three terms, and the expression (x+2)(y-4) is a product of two factors, not a sum or difference of terms.
To learn more about Algebraic expression from given link.
brainly.com/question/28884894
#SPJ1
A= (5,-5) B=(9,9)
The point on the line segment connecting A and B that
is 3/4 of the way from A to B is: (? ,? )
The point on the line segment that is 3/4 of the way from A to B is (8,5.5).
To find the point on the line segment that is 3/4 of the way from A to B, we can use the formula for finding a point on a line segment:
P = (1-t)A + tB
Where P is the point we are trying to find, A and B are the endpoints of the line segment, and t is the fraction of the distance from A to B that we want to find. In this case, t = 3/4.
Plugging in the values for A, B, and t, we get:
P = (1-3/4)(5,-5) + (3/4)(9,9)
Simplifying, we get:
P = (1/4)(5,-5) + (3/4)(9,9)
P = (1.25,-1.25) + (6.75,6.75)
P = (8,5.5)
So the point on the line segment that is 3/4 of the way from A to B is (8,5.5).
For more such questions on Line segment.
https://brainly.com/question/17248193#
#SPJ11
You need a home loan of $65,000 after your down payment. How much will your monthly house payment be in the bank charges 6.25% APR for a loan of 15 years?( simplify your answer completely. Round your answer to the nearest cent)
Your monthly house payment given that the bank charges 6.25% APR for a loan of 15 years will be $51.95.
To find the monthly house payment for a loan of $65,000 with a 6.25% APR for 15 years, we can use the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
Where:
M = monthly payment
P = principal amount
i = monthly interest rate
n = number of monthly payments
First, we need to find the monthly interest rate and the number of monthly payments:
i = 6.25% / 12 = 0.00625
n = 15 years(12 months/year) = 180 months
Now we can plug these values into the formula:
M = 65,000 [ 0.00625(1 + 0.00625)^180 ] / [ (1 + 0.00625)^180 - 1]
M = 65,000 [ 0.00625(1.00625)^180 ] / [ (1.00625)^180 - 1]
M = 65,000 [ 0.024636 ] / [ 0.171184 ]
M = 65,000 [ 0.143875 ]
M = 9,351.88
So, the monthly house payment will be $9,351.88 / 180 = $51.95.
Therefore, the monthly house payment for a loan of $65,000 with a 6.25% APR for 15 years will be $51.95.
Learn more about APR here: https://brainly.com/question/3861581.
#SPJ11
Assume binomial distribution where n = 3 and p = 0.6. Determine
the mean and standard deviation of the distribution.
The mean and the standard deviation of the binomial variable are given as follows:
Mean of 1.8.Standard deviation of 0.8485.What is the binomial distribution formula?The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.
The mass probability formula(PMF) is given by the equation presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters, along with their meaning, are listed as follows:
n is the fixed number of independent trials.p is the constant probability of a success on a single independent trial of the experiment.The parameter values for n and p in this problem are given as follows:
n = 3, p = 0.6.
The mean of the binomial distribution is given by the following equation:
E(X) = np.
Hence:
E(X) = 3 x 0.6
E(X) = 1.8.
The standard deviation of the binomial distribution is given by the following equation:
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)}[/tex]
Hence:
[tex]\sqrt{V(X)} = \sqrt{3 \times 0.6 \times 0.4}[/tex]
[tex]\sqrt{V(X)} = 0.8485[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24756209
#SPJ1
Show two steps and determine
[tex] \frac{ {2}^{3} } { {2}^{3} } = {2}^{3 - 3} [/tex]
Answer:
1
Step-by-step explanation:
2 power 3 in numerator mean it is 8.
Divide th 2 power 3 in denominator it means 8.
Now upo dividing 8 and 8 it gives 1.
Same it can be understood by any number with exponent 0 is equal to 1.