The four consecutive integers are 20, 21, 22, and 23 whose sum is 86.
What do you mean by integer no?using sequential means.
Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.
86 is obtained by adding together the four consecutive integers x, (x+1), (x+2), and (x+3)
x + (x+1), (x+2), and (x+3) = 86
the smallest one, x, is now solved for: 4x + 6 = 86
The numbers are 20, 21, 22, and 23, because 4x = 80 x = 20.
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Answer:
20, 21, 22 & 23
Step-by-step explanation:
Forming the equation,
→ x + (x + 1) + (x + 2) + (x + 3) = 86
→ 4x + 6 = 86
Now the the value of x will be,
→ 4x + 6 = 86
→ 4x = 86 - 6
→ x = 80/4
→ [ x = 20 ]
Then the required numbers will be,
→ x = 20
→ x + 1 = 20 + 1 = 21
→ x + 2 = 20 + 2 = 22
→ x + 3 = 20 + 3 = 23
Hence, numbers are 20, 21, 22, 23.
{3x}^{2} + 4x + 1 = 0 using factorisation method
Step-by-step explanation:
Hope it helps you ..
MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER
a and b agree to try to meet between 12 and 1pm for lunch. assuming that the arrival times and of a and b are uniform between 12 and 1pm, independently. if whoever comes first waits 15 minutes and then leaves, what is the probability that they actually meet for lunch?
PLEASE HELP FASR ILL GIVE BRAINLIEST IF CORRECT!!!!
Victor sells candles. The graph shows the number of candles sold and the
income from the sales. It represents a linear function.
Which statement best describes Victor's income from selling these candles?
A. He sells 4 candles per dollar.
B. He sells 7.5 candles per dollar.
C. He gets $4 per candle.
D. He gets $7.50 per candle.
Answer:
D
Step-by-step explanation:
22.5÷3 is 7.5 and 52.5÷3 is 7.5 as well
Money is y axis (x,y) and candles is x axis (x,y)
which of the following equation have roots 4 and -4
x² -16=0
1) Since we have two roots and any quadratic equation can be rewritten as once we have the roots:
[tex]a(x-x_1)(x-x_2)=0[/tex]So let's find one equation whose roots are 4 and -4, with coefficient a=1
(x-4)(x+4)=0
x² -16=0
2) So the equation x² -16= 0 has roots x_1=4 and x_2= -4 S={-4,4}
Element X decays radioactively with a half life of 5 minutes. If there are 860 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 230 grams? y = a(.5) k
The amount of time it would take Element X to decay to a mass of 230 grams is 9.5 minutes.
How to determine the amount of time to decay?Mathematically, the mass of a radioactive element that is remaining after time (t-hours) is given by this exponential function:
A(t) = A₀·e^{t/τ}
Where:
A(t) represents the mass remaining or current mass measured in grams.A₀ represents the initial mass measured in grams.τ is the time constant measured in minutes.t represents the half-life or time to decay measured in minutes.Next, we would determine the time constant by using this mathematical expression:
Time constant, τ = t/ln2
Time constant, τ = 5/0.6932
Time constant, τ = 7.2130 minutes.
Now, we can determine the amount of time to decay by making half-life (t) the subject of formula as follows:
A(t) = A₀·e^{t/τ}
Half-life, t = -τ·ln(A(t)/A₀)
Substituting the parameters into the formula, we have;
Half-life, t = -7.2130·ln(230/860)
Half-life, t = -7.2130 × ln(0.2674)
Half-life, t = -7.2130 × -1.3190
Half-life, t = 9.51 ≈ 9.5 minutes.
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Complete the steps to find the value of x
Answer:
2x=128⁰ x=64⁰
Step-by-step explanation:
since they are corresponding angles, the other side (2x) will also be 128⁰. This means that x=64⁰
and 2x=128⁰
look at photo and solve quick pls
Answer:what photo
Step-by-step explanation:
where
Which graph shows the line y-4-2(x+1)?
I need help with what's on the screen, thank you.
a) We know that in the northern Hemisphere we have 4 seasons: Summer where is more sun, Spring, and autumn that the sun is like 50/50 and winter that is the season with less sun. So we can made a graph with this so:
b) In this case if we have a simple interest is going to be a streight light that is going to increase. So the graph will be:
c) An item that increase it's price by 50% is going to be increasing each time more, so this case will be an exponential so the graph will be:
d) The high of a triangle and the base of the triangle are going to to have a constant rate. so the graph will be a horizontal line so:
Help please:)! Really STUCK on this question!
Answer:
Step-by-step explanation:
it 10
[tex]\sqrt{x} x^2+2x-3[/tex]
The result of the expression given is 3x - 3
Simplification of Linear EquationTo solve this problem, we have to simplify the equation, and write the expression.
Given that
[tex]\sqrt{x^2}+ 2x -3[/tex]
In the square root, we can eliminate the square and square root using the square root rule.
Lets apply that in this expression
[tex]\sqrt{x^2} + 2x - 3\\x + 2x - 3[/tex]
Lets solve the expression
[tex]x + 2x - 3\\3x - 3[/tex]
The value of the expression given is 3x - 3
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What is the y value of the y-intercept of the line that contains the points (-8,-5)
and (10, 67)?
We will see that the linear equation that passes through the two given points is:
y = 4x + 28
So the y-intercept is y = 28.
How to find the y-intercept of the line?First, we need to find the linear equation that passes through the two given points. Remember that for a line that passes through two points (x₁, y₁) and (x₂, y₂), the slope is:
m = (y₂ - y₁)/(x₂ - x₁)
Here our line passes through (-8,-5) and (10, 67), then the slope is:
m = (67 + 5)/(10 + 8) = 4
So we can write:
y = 4*x + b
To find the value of b we can use the point (-8,-5), replacing these values we get:
-5 = 4*-8 + b
-4 + 4*8 = b
28 = b
So the y-intercept is 28.
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Find the slope between these two points:
(12, -18), (-15, -18)
Answer:
The slope is 0.
Step-by-step explanation:
Using the slope formula which is m= y2 - y1 / x2 - x1, plug in the x values and y values of the two points. (12,-18) is x1 and y1. (-15,-18) is x2 and y2.
When plugging it in we get -18 - (-18)/ -15 - 12. You cannot subtract a negative so it turns from subtraction to addition. So, -18 + 18 / -15 - 12 which equals 0/-27. 0 divided by any number is 0. So the slope is 0, m=0.
Hope this helps :)
What is the result when 2a - 5 is subtracted from 3a + 3?
Answer:-1a+2
Step-by-step explanation:
add like terms
Hey there!
(2a - 5) - (3a + 5)
= 2a - 5 - 3a + 5
COMBINE the LIKE TERMS
= (2a - 3a) + (-5 + 3)
= 2a - 3a + (-5) + 3
= -1a - 2
Therefore, your answer should be:
-1a - 2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
HELP ASAP!!! (100 POINTS!!!) GIVING BRAINIEST
PLEASE HELP SOLVE ALL OF THEM!!!
Use the idea of partial quotients to solve each of the
division problems below. You can use the powers of 10 or grouping,
whichever makes the problem go faster.
1. 1,085/7
2. 7,104/32
3. 2,244/51
4. 1,584/12
5. 1,467/9
6. 2,830/28
7. 9,090/45
8. 7,000/62
9.1,150/15
HELP ASAP!!!
PLEASE HELP SOLVE ALL OF THEM!!!
Answer:
I gotchu
Step-by-step explanation:
1= 155
2= 222
3= 44
4= 132
5= 163
Let the roots of the polynomial x^2 + 7x - 2 be a and b Evaluate a^2 + b^2.
First gets brainliest, ty!
Answer:
53
Step-by-step explanation:
You want the value of a^2 +b^2, given that 'a' and 'b' are roots of the polynomial x^2 +7x -2.
FactorsIf the roots are 'a' and 'b', then the factored form is ...
(x -a)(x -b) = x^2 -(a+b)x +ab
Comparing this to the given polynomial, we see that ...
-(a+b) = 7
ab = -2
Desired expressionThe expression a^2 +b^2 can be written as the sum ...
a^2 +b^2 = a^2 +2ab +b^2 -2ab = (a+b)^2 -2ab
Using the values of (a+b) and ab from above, we see that ...
a^2 +b^2 = (-7)^2 -2(-2) = 49 +4 = 53
The given expression has a value of 53.
According to the distributive property, a(5 + b) =
Answer:
From the bit that you have given , we can say = 5a + ab = to the rest of the equation
Convert 72 weeks into hours.
8x^{3}+26x^{2}+19x+38x
3
+26x
2
+19x+3 is divided by 4x+34x+3.
Applying synthetic division, the quotient between 8x³ + 26x² + 19x + 3 by 4x + 3 is:
2x² + 5x + 1.
Synthetic division algorithmIn the synthetic division algorithm, the coefficients of a polynomial are each divided by a value.This divisor is the zero of the divided polynomial, which goes into the far left box.In this context of this problem, the coefficients of the polynomial 8x³ + 26x² + 19x + 3 are given as follows:
8, 26, 19 and 3.
The divisor is found as follows:
4x + 3 = 0
4x = -3
x = -3/4
x = -0.75.
The resulting coefficients of the quotient are given as follows:
8, 20, 4 and remainder of 0.
Hence the quotient is:
8x² + 20x + 4.
Which can be simplified as:
2x² + 5x + 1.
The first coefficient of the polynomial, of 8, was moved down, the multiplied by -0.75 and added to 26, resulting in 20. Then the same procedure was done with 20(multiplied with -0.75 and added with the next coefficient of 19), until the last coefficient of 3.
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consider the experiment of a worker assembling a product. a. define a random variable that represents the time in minutes required to assemble the product. b. what values may the random variable assume? c. is the random variable discrete or continuous?
(a) Let "X" be the random variable that represents the time in minutes required to assemble the product.
(b) The random variable may assume the values in the interval (0, ∞).
(c) The random variable "X" is continuous in nature.
A random variable is a mathematical representation of a number or object that is affected by random occurrences. It is a mapping or function between probable outcomes in a sample space and a measured space, which is frequently real numbers.A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable might be discrete (with fixed values) or continuous (any value in a continuous range).To learn more about variables, visit :
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The first equation should be multiplied by 7 and the second equation by -6.
Answer:
Step-by-step explanation:
The equation of the line that is perpendicular to the line 5x + 6y = 18 and passes through the point (10,7)
Answer:
y = ( 6 / 5 )x - 5;
Step-by-step explanation:
Perpendicular Line Theoryy = - ( 1 / m )x + c;
AlgebraConvert dual intercept to standard form.
5x + 6y = 18;
Subtract 5x from both sides.
6y = - 5x + 18;
Divide both sides by 6.
y = ( - 5x + 18 ) / 6;
y = ( - 5x / 6 ) + ( 18 / 6 );
y = ( - 5 / 6 )x + 3;
Get the perpendicular line.
y = ( 6 / 5 )x + c;
Substitute the point.
7 = ( 6 / 5 )( 10 ) + c;
7 = 12 + c;
Subtract 12 from both sides.
- 5 = c;
c = - 5;
y = ( 6 / 5 )x - 5;
consider a normal distribution with mean 20 and standard deviation 9. what is the probability a value selected at random from this distribution is greater than 20? (round your answer to two decimal places.)
The probability that a value selected at random from this distribution is greater than 20 is 0.5.
What is a probability with normal distribution?
The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean. The probabilities for values that are farther from the mean taper off equally in both directions.
Here,
Let us assume that X follows a normal distribution.
If X follows a normal distribution, then
z = (X−μ) /σ, follows a standard normal distribution.
The probability of a value selected at random from this distribution is greater than 20:
P (X > 20) = 1 − P (X ≤ 20)
P ((X − μ) / σ > 20) = 1−P((X − μ) / σ ≤ 20)
P (z > (20 − 20) /5) = 1 − P (z ≤ (20−20 / 5))
P (z > 0) = 1 − P (z ≤ 0)
The value of probability is obtained from the standard normal table as:
P (z > 0) = 1 − P (z ≤ 0)
= 1 - 0.5
= 0.5
Hence, the probability that a value selected at random from this distribution is greater than 20 is 0.5.
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i need the domain range and inc. dec. intervals
Using a graphing calculator, the features of the function are given as follows:
Domain: (-∞,∞).Range: (-∞,∞).Relative maximums: (2.816, 1.089).Relative minimums: (1.184, -1.089).End behavior: As x -> -∞, f(x) -> ∞, and as x -> ∞, f(x) -> -∞.Increasing intervals: (1.184, 2.816).Decreasing intervals: (-∞, 1.184) U (2.816, ∞).Domain and rangeIn a graph, the domain and the range of the function are given as follows:
Domain: values of x (input values).Range: values of y (output values).This function is defined for all real values and also assumes all real values, hence both the domain and the range are (-∞,∞).
Increasing and decresingFrom the graph, the function is classified as decreasing or increasing as follows:
Decreasing: moving right and down.Increasing: moving right and up.Hence the intervals are given as follows:
Increasing: (1.184, 2.816).Decreasing: (-∞, 1.184) U (2.816, ∞).Relative maximum and relative minimumThe relative minimum is when the function changes from decreasing to increasing, hence it is at this following point:
(1.184, -1.089).
The relative maximum is when the function changes from increasing to decreasing, hence it is at this following point:
(2.816, 1.089).
End behaviorThe end behavior of the function is given by the limits of the function when x go to infinity, hence:
To the left, the function goes to infinity, hence as x -> -∞, f(x) -> ∞.To the right, the function goes to negative infinity, hence as x -> ∞, f(x) -> -∞.More can be learned about functions at https://brainly.com/question/28949511
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Lana and raul are participating in a walk-a-thon at the local community college track to raise money. lana can walk around the track in 4 minutes. raul can walk around the track in 6 minutes. lana and raul started walking at the same time. question: how many minutes will it be until they complete a lap at the same time?
The minutes will it be until they complete a lap at the same time is 2.4 minutes
How to calculate the time?From the information, Lana can walk around the track in 4 minutes and Raul can walk around the track in 6 minutes.
Lana will cover a distance of 1/4 while Raul will be represented as 1/6.
This will be illustrated as:
1/4 + 1/6 = 1
3/12 + 2/12 = 1
5x/12 = 1
Cross multiply
5x = 12
x = 12/5
x = 2.4 minutes
Note that x = number of minutes
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If 6 is an element in the domain of
f(x)=8–2x, what is its corresponding element
in the range
The corresponding element in the range when 6 is an element in the domain is f(6) = -4.
What are a function's domain and range?A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.Given function f(x) = 8–2x.
6 is an element in the domain of this function.
To find the corresponding element in the range of the function,
Substitute x = 6 in the given function f(x).
So,
f(6) = 8 - 2(6)
f(6) = 8 -12
f(6) = -4
Hence, the corresponding element in the range when 6 is an element in the domain is -4.
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assuming that the population size is 1,000 people, the prevalence of smoking in epiland is 60% and the percentage of people drinking water with a high concentration of heavy metals is 30%, calculate the total number of cases of cancer x that could be prevented if each one of the exposures were eliminated. what would be your suggestion to the public health agencies if they asked you which one of the exposures would have a greater impact on reducing the prevalence of the disease if it was eliminated?
1. The total number of cases of cancer x that could be prevented if each one of the exposures were eliminated is 900.
2. The suggestion to the public health agencies if they requested the one exposure that would have a greater impact on reducing the prevalence of cancer x if eliminated is smoking.
What is the prevalence rate?The prevalence rate refers to the proportion of the population who have a particular disease or attribute or can be exposed to risks at a specified time or over a specified period.
The assumed population size in Epiland = 1,000
Prevalence of smoking in Epiland = 60%
The number of Epiland smokers = 600 persons (1,000 x 60%)
Percentage of people drinking water with a high concentration of heavy metals = 30%
The number of people drinking the water = 300 (1,000 x 30%)
The total number of people exposed to cancer x = 900 (600 + 300).
Thus, 90% of the population in Epiland is exposed to cancer x based on the prevalence rate of smoking and the high concentration of heavy metals in their drinking water.
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Jacinda works at Super Shoes and earns
a commission for her sales. A customer
purchases $259.50 in shoes, and
Jacinda receives $31.14 in commission.
What percent commission does Jacinda
earn?
Jacinda get 12% of commission
How to find percentage :
The cost of shoe that customer purchased is $259.50
The amount that Jacinda get commission is $31.14
To calculate the percentage of commission divide 31.14 by 259.50 and multiply by 100.
That is percentage of commission = 31.14/259.50 * 100
= 12%
Jacinda get 12% of commission.
What is percentage ?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%. To find 50 apples as a percentage of 1250 apples, one first computes the ratio 50/1250 = 0.04, and then multiplies by 100 to obtain 4%.To learn more about percentage refer :
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Which set of ordered pairs is a
function?
A. (-2,4), (0, 4), (2, 4), (2,6)}
B. {(-10, 4), (-8, 3), (-8, 2), (-4,1))
C. {(1, 5), (1, 6), (2,7), (3, 8))
D. Of(-1, 1), (0, 0), (1, 1), (2, 2))
A set of ordered pairs that contain only unique ordered pairs with unique x coordinates exists directed to as a function.
The set of ordered pairs is a function exists {(1, 5), (1, 6), (2,7), (3, 8)}.
What is meant by function?A set of ordered pairs that contain only unique ordered pairs with unique x coordinates exists directed to as a function. A function is defined by an equation that generates a set of ordered pairs. Each x value in a relation must have a unique value for the y value for it to be a function. if there are multiple y-values associated with an x-value.
Because no two ordered pairs have the same first coordinates with the same second coordinates, the initial set of ordered pairs is a function.
A relationship and a function vary in that a relationship can have multiple outputs for a single input, whereas a function only needs one input to produce one outcome. This is the fundamental criterion used to distinguish between relation and function. These model concepts are created through the usage of relations.
Therefore, the correct answer is option C. {(1, 5), (1, 6), (2,7), (3, 8)}.
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Help me please (please dont guess)
Answer: No the input 3 has two out puts
Step-by-step explanation:
Use ur eyes
