Answer:
b = 4+15
b =19
Step-by-step explanation:
5x^2 + bx + 12 = 0
the sum of its roots = –b/a
m + n = - b/a
-4/5 + n = -b/5
-4 + 5n = -b
5n= -b + 4 -------------1
product of its roots = c/a
m*n = c/a
-4/5 * n = 12/5
-4 n = 12
n = -3 is the other root -------------2
Plug-in equation 2 in 1
5(-3) = -b + 4
-15 = -b + 4
b = 4+15
b =19
One of the solutions to the equation 5x^2+bx+12=0 is -4/5.the other solution is 2.4 + (-4/5) = 2.
The other solution to the equation 5x^2+bx+12=0 can be found by using the fact that the solutions of a quadratic equation of the form ax^2+bx+c=0 are given by the formula: x = (-b ± √(b^2-4ac)) / 2a.
In this case, a=5, b=b and c=12. We know that the product of the roots is equal to c/a and sum of roots is equal to -b/a. so the product of the roots is 12/5 = 2.4and the sum of the roots is -b/5 .
since we know that one of the solutions is -4/5, we can find the other solution by using the above formulas: -4/5 = 2.4 - other solution so the other solution is 2.4 + (-4/5) = 2.
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Graph h(x)=7sinx . Use 3.14 for π . Use the sine tool to graph the function. Graph the function by plotting two points. The first point must be on the midline and closest to the origin. The second point must be a maximum or minimum value on the graph closest to the first point.
The graph of the function h(x) = 7sin(x) is given by the image presented at the end of the answer.
How to define the sine function?The sine function is given as follows:
y = Asin(Bx) + C.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.From this problem, the amplitude is given as follows:
A = 7.
Hence:
The midline is at y = 0.The minimum value is of -7, as there is no vertical shift.The maximum value is of 7, as there is no vertical shift.As there is no phase shift, the minimum and maximum values have the x-coordinate given as follows:
Minimum: x = -π/2.Maximum: x = π/2.As the function has no phase shift, the period is given as follows:
2π.
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how to multiply fraction with one fraction having the lcm and two other fractions being a factor of it
Multiplying fractions can be a tricky task, but with the right steps, it can be easily accomplished.
To multiply two fractions together, first find the least common multiple (LCM) of the two fractions.
Once you have the LCM, divide it by each of the two fractions and multiply the resulting numbers together. This will give you the final answer to your multiplied fractions.
Let's look at an example. Suppose you wanted to multiply 3/4 and 5/8 together. First, you would need to find the LCM of 3/4 and 5/8. The LCM in this case would be 24.
Now divide 24 by 3/4 and 5/8 to get 32/24 and 30/24 respectively. Multiplying 32/24 and 30/24 together would give you 960/576 as the answer.
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mark can overhaul an engine in 20 hours and phil can do the same job by himself in 30 hours. if they both work togehter for a time and then mark finishes the job by himself in 5 hours, how long did they work together
Mark completed the job by himself in time 5 hours, so they must have worked together for 25 hours.
They worked together for 25 hours.
Mark can do the job in time 20 hours and Phil can do the job in 30 hours.
If they both work together, it will take them less than 20 hours, but more than 30 hours.
We know that Mark finishes the job by himself in 5 hours.
Therefore, they must have worked together for 25 hours.
Mark and Phil worked together for 25 hours.
Mark and Phil worked together to overhaul an engine. It took them less than 20 hours and more than 30 hours. Mark completed the job by himself in 5 hours, so they must have worked together for 25 hours.
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judith surveyed some students at her school about their favorite primary color. yellow 2 red 5 blue 3 what is the experimental probability that the next student judith talks to will pick red? write your answer as a fraction or whole number. p(red)
The experimental probability that the next student Judith talks to will pick red is 1/2.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.
Given that,
Yellow = 2
Red = 5
Blue = 3
Finding the experimental probability
Total number of trials = 2+5+3 = 10
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Probability = red/ Total number of trials = 5/10 = 1/2
Thus, the experimental probability that the next student Judith talks to will pick red is 1/2.
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Answer:
1/2
Step-by-step explanation:
Help with only even problems please no odd problems
a 2x2x2 cube is made of 8 small cubes of which 4 are blue and 4 are white. the surface of the cube is formed from 6 2x2 squares. the small cubes are arranged in such a a way that the surface has as many fully white faces (faces white no black color anywhere) as possible. how many fully white faces does the 2x2x2 cube have?
The 2x2x2 cube has 6 fully white faces.
A cube is a solid shape with six square faces. Each square face has the same side length and thus all the faces have the same size. A cube has 12 edges and 8 vertices. Each vertex refers to a corner where three edges of a cube meet.
from given conditions, a 2x2x2 cube is made of 8 small cubes of which 4 are blue and 4 are white. the surface of the cube is formed from 6 2x2 squares.
and have to arranged in such a a way that the surface has as many fully white faces (faces white no black color anywhere) as possible.
So, A 2x2x2 cube has a total of 6 faces, and since the goal is to have as many fully white faces as possible, there must be at least 1 fully white face on each of the 6 sides. hence, the 2x2x2 cube has 6 fully white faces.
Therefore, the 2x2x2 cube has 6 fully white faces.
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margaret started a stamp collection. she collected 8 stamps the first day. each subsequent day she collected 8 more stamps than she had collected the previous day. if she collected stamps for 5 consecutive days, what was the average number of stamps collected per day?
The average number of stamps collected per day was 24.
1st day: 8 stamps
2nd day: 8 + 8 = 16 stamps
3rd day: 16 + 16 = 32 stamps
4th day: 32 + 32 = 64 stamps
5th day: 64 + 64 = 128 stamps
Total number of stamps collected
= 8 + 16 + 32 + 64 + 128
= 248 stamps
Average number of stamps collected per day
= 248 / 5
= 24 stamps
Margaret started a stamp collection and collected 8 stamps on the first day. On the second day she collected 8 more stamps, for a total of 16. On the third day she collected 16 more stamps, for a total of 32. On the fourth day she collected 32 more stamps, for a total of 64. On the fifth day she collected 64 more stamps, for a total of 128. In total, she collected 248 stamps over the five days. The average number of stamps collected per day was 24.
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Help me I need help ….
Answer: A (yes) B (yes) C (yes)
Step-by-step explanation:
One half times by 28 is 14
seven times 8 is 56
15 plus 14 is 29
David has a Collection of nine gray fingerboards 4 white fingerboards and 3 yellow fingerboards. He chooses one at random locate the probability of the following events on the number line.
Answer:
B
Step-by-step explanation:
There are a total of 16 fingerboards. 4 of these are white. The probability that he will select a white fingerboard is 1/4. B represent 1/4.
The the probability of finding a white finger board is 0.25.
What is probability?Probability is the measure of how likely are the chance for any event to happen.
Given is that David has a Collection of nine gray fingerboards 4 white fingerboards and 3 yellow fingerboards.
We can write the probability of finding a white finger board as -
P{white} = 4/16
P{white} = 1/4
P{white} = 0.25
Therefore, the the probability of finding a white finger board is 0.25.
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Which list shows the numbers in order from least to greatest?
323, 3.7, 3.65
Answer: 3.65, 3.7, 323
Step-by-step explanation:
The numbers from least to greatest are as follows:
3.65, 3.7, 323
Hope this helps
describe and correct the error a student made in determining the relationship between the domain and range of f(x)
On solving the provided question, we can say that the relationship between the domain and range of f(x) = [tex]y = 9x + 1 = 10 + (x-1)(9)[/tex]
what is domain?Domain of a function is the set of possible values that it can accept. X-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. Set the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.
[tex]f(x) = y = 9x + 1 = 10 + (x-1)(9)\\f(1) = 9+1 = 10\\f(2) = 9(2)+1 = 19\\f(3) = 9(3)+1 = 28\\f(4) = 9(4)+1 = 37[/tex]
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Express y in terms of x. 0.5y - 2 = 0.25x
Answer:
y = 0.5x + 4
Step-by-step explanation:
1. Move terms to one side of the equation
0.5y - 2= 0.25x +0
+2 +2
__________________
0.5y = 0.25x + 2
2. Divide the coefficient of y (0.5) to both sides of the equation
[tex]\frac{0.5y}{0.5} = \frac{0.25x}{0.5} + \frac{2}{0.5}[/tex]
3. Solve and simifpy
[tex]y = 0.5x +4[/tex]
Which of the following is the solution set of the inequality x/4 < (5x-2)/3 - (7x-3)/ 5 ?
A. (4, 00)
B. (- [infinity], 4)
C. (4, infty)'
D. (- [infinity], 4)
The solution set of the inequality " x/4 < (5x-2)/3 - (7x-3)/ 5 is C: (4, infinity).
x/4 < (5x-2)/3 - (7x-3)/ 5
taking the LCM of the right-hand side of the given inequality which is 15.
Now multiply 15 by both sides of the inequality
15 . x/4 < [ 15 . (5x-2)/3 ] - [ 15. (7x-3)/ 5 ]
15. x/4 < [ 5 . (5x -2) ] - [ 3 . (7x -3) ]
15. x /4 < ( 25x - 10 ) - ( 21x - 9 )
15. x/4 < 25x - 10 - 21x + 9
15. x/4 < 4x - 1
Now multiply boh sides with 4
4 (15 . x/4) < 4. (4x - 1)
15 . x < 16x - 4
15x < 16x - 4
4 < - 15x + 16x
4 < x
x > 4
Hence, all real numbers x that are greater than 4 are the solution of the given inequality.
Therefore, the solution set of the given inequality is (4, infinity).
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find the component form of the unit vector obtained by rotating the vector counterclockwise about the origin.
The component form of the unit vector obtained by rotating the vector counterclockwise about the origin is v = ⟨ |v|cos(θ), |v|sin(θ) ⟩.
the term vector in math is defined as a quantity which has both magnitude and direction and it defines the movement of the object from one point to another.
Here we have given the unit vector and we need to find the component form from it.
As we all know that the vector is a quantity that has magnitude and direction.
Here we also know that it can be written in component form where the components are the horizontal and vertical coordinates of the endpoint of the vector measured from the origin.
And the vector with magnitude of |v| and direction of θ which has an angle measured from the horizontal axis in the counter clockwise direction then it has the following components form that can be written as
=> v = ⟨ |v|cos(θ), |v|sin(θ) ⟩.
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Which of the following types of functions have inverse functions?A.May-to-oneB.One-to-manyC.One-to-oneD.Many-to-many​
Therefore , the solution of the given problem of function comes out to be the one -to-one function is an inverse function.
What does the term function refer to?Math is the science of numbers, their variations, math and nearby tissues, shapes, and their actual and potential places. The relation between a group of inputs, each of which has a related output, is referred to as a "function." A function is an association between inputs and outputs where each input results in a single, unique output. Each function is assigned a scope, or realm, and a city or municipality. Functions are typically denoted by the letter f. (x). Input does contain an x. Procedures fall into four main categories: on functions, each processes, a few more features, within operations, as well as on functions.
Here,
Given : May -to-one function
One -to-many function
One-to-one function and
Many-to-many.
Thus, To find which is a inverse function .
So , by observing the following properties of function the one -to-one function is an inverse function.
Therefore , the solution of the given problem of function comes out to be the one -to-one function is an inverse function.
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Anna has $274.00 in her account on sunday. over the next week, she makes the following changes to her balance via deposits and purchases: day debit ($) credit ($) monday 194.62 35.45 tuesday --- 11.20 wednesday 145.86 24.75 thursday 53.35 33.80 friday 31.60 45.77 saturday 12.90 61.63 on which day or days does anna get charged an overdraft fee? i. wednesday ii. thursday iii. fridaya. i onlyb. i and iic. ii and iiid. iii only
Thursday and Friday show a negative balance, then the answer is option c: II and II.
Overdrafts are charged when your balance is negative because it means the bank made a loan (an unexpected one) to you.
An overdraft occurs when a bank account holder withdraws more money than they have in their account. Banks typically allow account holders to spend more money than they have in their accounts, but they charge a fee or interest for doing so.
Overdraft protection is a service offered by many banks that automatically covers a certain amount of overdrafts, usually up to a certain limit, by transferring funds from a savings account or a line of credit. Banks will also charge a fee for this service.
Initial balance: $274
Day Debit ($) Credit ($) Balance($)
Monday 194.62 35.45 274.00 - 194.62 + 35.45 = 114.83
Tuesday --- 11.20 114.83 - 0 + 11.2 = 126.03
Wednesday 145.86 24.75 126.03 - 145.86 + 24.75 = 4.92
Thursday 53.35 33.80 4.92 - 53.35 + 33.8 = - 14.63
Friday 31.60 45.77 -14.63 - 31.60 + 45.77 = -0.46
Saturday 12.90 61.63 -0.46 - 12.90 + 61.63 =48.27
Thursday and Friday show a negative balance, then the answer is option c: II and II.
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Help me please thank you
Answer: 20 + x = y.
Step-by-step explanation:
When you deposit, you are adding onto something. Because there is no real value for x, the expression would be 20 + x = y. Also, it would be = y because it says clearly the total amount would be equal to y. and also since why has no value in this context, it would still be y.
isabelle has a recipe for granola that is currently written to make 15 cups. she wants to increase the yield to 50 cups to prepare for family vacation. isabelle needs to determine the percentage that she will multiply her original quantities by to determine her new measurements. what this percentage is known as?
So Isabelle will have to multiply all the quantities in her recipe by a factor of 3.33 (or 333%) to increase the yield to 50 cups.
The percentage that Isabelle needs to multiply her original quantities by to increase the yield from 15 cups to 50 cups is known as the "scaling factor".
To find the scaling factor, you can divide the desired yield by the original yield and multiply by 100 to express it as a percentage:
Scaling factor = (50 cups / 15 cups) x 100% = 3.33 x 100% = 333%
So Isabelle will have to multiply all the quantities in her recipe by a factor of 3.33 (or 333%) to increase the yield to 50 cups.
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Find area of the rectangle
Answer:
[tex]6 {x}^{2} + 10x[/tex]
Using the sample formulas, find the mean, variance, and standard deviation for the grouped data displayed in the following table. x f 0 to less than 4 19 4 to less than 8 21 8 to less than 12 15 12 to less than 16 11 16 to less than 20 8 20 to less than 24 6 Carry out all calculations exactly, round to 2 decimal places the final answers only. Mean
Therefore, the answer to the above median problem is a) z-score = 1.50, b) age 34 has SD=1.5, and C. option B is correct.
Define median.The median value is the number that exactly lies in the middle of a dataset that has been arranged. The gap between the minimum and maximum 50% of the data is a maximum likelihood measure or average. Depending on whether you have an odd or possibly even amount of data points, different formulas are used to calculate the median and mode.
Here,
The average age is 36, it is stated.
2.5 standard deviations
a) The z-score is (34 - 28.3)/3.8 = 1.50.
b) Analysis
A 34-year-old is 1.50 standard deviations well above average in age.
c) The right answer is B.
Consequently, the provided issue of median's solution yields
Option B is right since age 34 has an SD of 1.5 and a C, and z-score is 1.50.
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David is ordering tea from an online store. black tea costs $0.80 per ounce and green tea costs $1.20 per ounce. he plans to spend a total of $12 on the town types of tea combined. write an equation that represents the different situation and write what the variables represent
Answer: A good equation would be 1.20/12 and then 0.80/12.
Step-by-step explanation: after getting the answers from both equations you can determine how much to spend on each tea to evenly spend your money on both
750=1000*(1-(1/(1.01^139)))+(R/(1.01^140)
The value of R for the given expression will be 0.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 750=1000 x (1-(1/(1.01¹³⁹)))+(R/(1.01¹⁴⁰). The expression for the R will be solved as below,
750=1000 x (1-(1/(1.01¹³⁹)))+(R/(1.01¹⁴⁰)
1000(1 - 1 / 4 + R / 4 ) = 750
1000(4 -1 + R ) / 4 = 750
1000 ( 3 + R ) = 3000
3 + R = 3
R = 3 - 3
R - 0
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What is the base if the portion is $4,570 and the rate is 55%?
Answer:
8309.09
Step-by-step explanation:
Base = Total
So we know that 4570 is 55% of the total
55% = 55/100 = 0.55
It is the same as:
4570 = 0.55 * total
Total = 4570/0.55 = about 8309.09
Hope this helps :)
Let me know if this is correct or not
Have a great day!
The diagram shows a prism.
1m
2m
front
1m
2m
2m
side
front elevation
Draw the front elevation and the side elevation.
of the prism on the grids.
Use a scale of 2 squares to 1 m.
side elevation
Therefore , the solution of the given problem of triangle comes out to be height = 2 meters = 4 squares.
Explain the triangle.Triangles are polygons due to their 3 sides and three vertices. It is an essential geometric form. Triangle ABC is a triangle whose corners are at coordinates A, B, and C. The discovery of a single plane and triangle in geometric shapes occurs when four elements are not collinear. Due to its upper right corner and three corners, triangles are classified as polygons. The corners of a triangle are the three spots at which it intersects. You may get 180 degrees by multiplying the triple triangle angles.
Here,
Drawn using the Required Elevation's Construction Method
The scale is presented as 2 squares per meter.
The front elevation plane has a total of 16 squares, which is the quantity of cubes in the plane.
Front elevation: There are 4 squares in the front elevation's width.
Closest to the observer, there are 4 + 1 squares within the front portion.
The slant surface has 3 by 4 squares as the number of squares.
The front aspect of the supplied diagram is depicted in the drawing that is attached.
A side elevation;
Following the same format as before, we have the side elevation as follows;
The side elevation's lower side is 2 meters wide, or 4 squares.
The side elevation is 2 meters high, or 4 squares.
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A drawing of a monster has an eye to head ratio of 5:1 and a head to tailratioof 2:6 if a monster has 20 eyes
The monster has 4 heads and 12 tails.
What is the ratio of the number?
A ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six .
We know that the ratio of the number of eyes to the number of heads is 5:1. If a monster has 20 eyes, we can set up the equation:
20 eyes = x heads
Where x is the number of heads.
We also know that the ratio of the number of heads to the number of tails is 2:6. We can set up the equation:
x heads = 2y tails
Where y is the number of tails.
We know the number of eyes is 20, therefore x = 20/5 = 4 heads
We also know the number of heads is 4, therefore y = 4*6/2 = 12 tails
Hence, the monster has 4 heads and 12 tails.
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an urn contains 6 white balls and 15 red balls. a sample of four balls is selected at random from the urn. what is the probability that the sample contains two white balls and two red ones?
The probability that the sample contains two white balls and two red ones is 0.264. There are multiple draws without replacement.
How to calculate probability?Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceAn urn contains 6 white balls and 15 red balls. A sample of four balls is selected at random from the urn. Find the probability that the sample contains two white balls and two red ones!
It means that there will be multiple draws without replacement.
The total balls are 6 + 15 = 21 balls.
The probability of drawing two white balls and two red ones is
= P(1st is white ∩ 2nd is white ∩ 3rd is red ∩ 4th is red)
= P(1st is white)*P(2nd is white)*P(3rd is red)*P(4th is red)
= (6/21)*(5/20)*(15/19)*(14/18)
= 0.044
There are 6 possible orders (WWRR, WRWR, WRRW, RWWR, RWRW, RRWW). So, the probability in any order would be
= 0.044 × 6
= 0.264
Hence, the probability of drawing two white balls and two red ones in any order is 0.264.
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Triangle GHI is similar to triangle JKL. Find the measure of side KL. Round your
answer to the nearest tenth if necessary.
The length of the side KL for the given similar triangles rounded to the nearest tenth is 10.6 units.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects.
What is the property of similar triangles?When two triangles are comparable, their respective sides and angles are equally spaced out and congruent. This is the property of similar triangles.
Given that the triangle GHI is similar to triangle JKL.
According to the property of similar triangles:
[tex]\frac{GH}{HI} = \frac{JK}{KL} \\\\\frac{45}{34} = \frac{14}{y} \\\\y= \frac{(14)(34)}{45} \\\\y= 10.577[/tex]
Rounding the value to the nearest tenth 10.57 is 10.6.
Hence, the value of side KL is 10.6 units.
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What is the largest 3-digit number that is divisible by both 9 and 7?
The largest 3 digit number that is divisible by 9 and 7 is 945.
What are factors of a number?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.
If a number is divisible by 7 and 9 it shows that 7 and 9 are factors of the number. Since the number is a three digit number, the product of 7and 9 which is 63 will also be a factor.
the highest three digit multiple of 63 is 945.
This means that 945 can be divided by 7 and 9. i.e 945/7 = 135 and 945/9 = 105
Therefore the largest three digit number that can be divisible by both 9 and 7 is 945
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x/4 - 3/8y = 3
5/3x - y/2 = 12
Any method is fine :)
Answer:
(6, - 4 )
Step-by-step explanation:
[tex]\frac{x}{4}[/tex] - [tex]\frac{3}{8}[/tex] y = 3
multiply through by 8 ( the LCM of 4 and 8 ) to clear the fractions
2x - 3y = 24 → (1)
[tex]\frac{5}{3}[/tex] x - [tex]\frac{y}{2}[/tex] = 12
multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions
10x - 3y = 72 → (2)
multiplying (1) by - 1 and adding to (2) will eliminate y
- 2x + 3y = - 24 → (3)
add (2) and (3) term by term to eliminate y
8x + 0 = 48
8x = 48 ( divide both sides by 8 )
x = 6
substitute x = 6 into either of the 2 equations and solve for y
substituting into (1)
2(6) - 3y = 24
12 - 3y = 24 ( subtract 12 from both sides )
- 3y = 12 ( divide both sides by - 3 )
y = - 4
solution is (6, - 4 )
21. huixian's mother buys some shares of
company a on day 0. on day 7, the share price
of company a is $4.60. if she sells all her shares
of company a and buys 2000 shares of
company b on day 7, she would receive $7400.
on day 12, the share price of company a is
less than that on day 7. if she sells all her shares
of company a and buys 5000 shares of
$4.80 and the share price of company b is $0.50
company b on day 12, she would have to pay $5800.
find
(1) the number of shares of company a huixian's
mother has,
(ii) the share price of company b on day 12.
A. Huixian's mother has 1608 shares of company A. The share price of company B on day 12 is $1.16.
B. To calculate the number of shares of company A that Huixian's mother has, we can use the equation: Shares x Price = $7400. Since we know that the share price of company A on day 7 is $4.60, we can calculate the number of shares of company A by dividing $7400 by $4.60, which is 1608 shares.
To calculate the share price of company B on day 12, we can use the equation: Shares x Price = $5800. Since we know that the number of shares of company B on day 12 is 5000, we can calculate the share price of company B by dividing $5800 by 5000, which is $1.16.
Therefore, the number of shares of company A that Huixian's mother has is 2000 and the share price of company B on day 12 is $0.50.
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