Since the given expression can be factored in the form (2t+1) and (t+2) so 2t² + 5t + 2 cannot be a prime number.
A whole number greater than 1 that has no factor other than 1 and the number itself is called a prime number.
Some examples of prime numbers are 3,11,19 ... all these numbers can only be divided by 1 or the number itself so they are called prime.
In the given expression 2t² + 5t + 2 , it is said that t is positive whole number. So if t is a positive whole number then the expression can be written as another positive whole number.
Now the expression 2t² + 5t + 2 can be factored into two smaller factors.
2t² + 5t + 2
= 2t² + 4t + t + 2
= 2t (t + 2 )+1 (t+2)
= (t+2) (2t+1)
If t is a positive whole number then t+2 is a whole number and 2t+1 is another positive whole number.
Hence these two numbers are factors of 2t² + 5t + 2 . But a prime number does not have any factors.
So 2t² + 5t + 2 is not a prime number.
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In Δ J L P, m ∠J M P=3 x-6 J K=3 y-2 , and L K=5 y-8 .
Find L K if PK is a median.
In Δ JLP, m ∠ JMP = 3x - 6, JK = 3y - 2, and LK = 5y - 8 then the value of LK = 7.
What is a median?The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution. It is sometimes referred to as "the middle" value in a data set.
The middle number is discovered by sorting all data points and selecting the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).
Since [tex]$\overline{P K}$[/tex] is a median, JK = KL.
3y - 2 = 5y - 8
simplifying the above equation, we get
3y - 5y - 2 = 5y - 5y - 8
-2y - 2 = -8
Adding 2 on both sides of the equation
-2y - 2 + 2 = -8 + 2
-2y = -6
y = 3
Substitute the value of y in LK, then we get
LK = 5y - 8
= 5(3) - 8
= 15 - 8
LK = 7
Therefore, the value of LK = 7.
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For each of the following statistics, determine
whether the value of the statistic is greater for Data
Set 1, equal for both data sets, or greater for Data
Set 2.
Answer:
greater for the data set 1.
Describe a pair of independent events and a pair of dependent events. Explain your reasoning.
Independent events are the ones whose occurrence is unrelated to any other event.
Dependent events include those that are dependent on previous events.
What is described as independent events?If the probability of an event A occurring is not impacted by the occurring of some other event B, then A & B are referred to as independent events.
Consider the example of a die roll. If A is the event 'the number appearing is odd' and B is the event 'the number showing up is a multiple of 3,'
P(A) = 3/6 = 1/2
P(B) = 2/6 = 1/3
A and B are also the events 'the number showing up is odd & a multiple of 3', implying that;
P(A ∩ B) = 1/6
P(A│B) = P(A ∩ B)/ P(B) = 1/2
Then P(A) = P(AB) = 1/2, implying that the happening of event B has had no effect on the probability of occurring of event A.
What is described as dependent events?Dependent events include those that are dependent on previous events. The outcomes of previous events have an impact on these events. Dependent events are two or maybe more events that are dependent on one another.
When two events, A and B, are interdependent, the probability of their occurrence is:
P(A and B) = P(A) · P(B|A)
Assume we desire to have a queen.
The chances of obtaining a queen on the first draw are 4 from out 52 cards. If we receive a queen in the first draw, we have a 3 out of 51 chance of obtaining a queen in the second draw.
As a result, these are referred to as dependent events because the probability of a second event is determined by the results of the first draw.
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Q is in the interior of
Answer:
...
Step-by-step explanation:
For every x ∈ R and each δ > 0 the interval (x−δ, x δ) carries both rational and irrational numbers. This implies that x can't be an interior factor of Q, and that x is a boundary point of Q. Therefore the indoors of Q is empty and the boundary of Q is R. Thus Q = b(Q) ∪ Q = R ∪ Q = R.
determine whether the following graph represent a function.
1. one to one function
2. function but not one to one
3. not a function
8x=10x+22
pls show work ty
Answer:
-11
Step-by-step explanation:
step 1
Move the variable to the left-hand side and change its sign
8x-10x=22
step 2
collect like terms
-2x=22
step 3
Divide both sides of the equation by -2
x=-11
Using a calculator, what is the solution of 1080=15³ˣ⁻⁴ ? Round the answer to the nearest hundredth.
The solution of the given equation 1080 = 15³ˣ⁻⁴ is (x = 2.19), round to the nearest hundredth.
What is defined as the logarithmic functions?A logarithmic term represents a number in logarithmic form. A log term is another name for it.
A quantity can also be the sum of two or even more quantities. As a result, a term can consist of the product of two or more quantities, one of which must be in logarithmic form. For such cases, this same terms are known as log terms.
A quantity can also be defined as the quotient of two quantities. But, if a term includes a quotient of quantities, or at least one of the quantities can also be expressed in log form, this same terms are known as log terms.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, consider the given equation given in the question;
1080=15³ˣ⁻⁴
Take log on the both sides;
㏒1080 = ㏒15³ˣ⁻⁴
Using the power rule on the second side of the equation;
㏒1080 = (3x - 4)㏒15
Taking log on one side and other variables on other side.
3x - 4 = ㏒1080/㏒15
Use calculator to find the values of both log.
3x - 4 = 2.57
3x = 6.57
x = 2.19
Therefore, the solution of the given function 1080=15³ˣ⁻⁴ is (x = 2.19), rounded up to nearest hundredth.
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Please answer///////////
Answer: the circle is not a function
the square is a function
Step-by-step explanation:
In the equation |x| = b, if b < 0, then how many solutions are there for x?
O One
Ο TWO
O Zero
O Can't be determined without more information
HELP ASAP!!! WILL MARK BRAINLIEST!!!
What are the coordinates of G after it is rotated 90 degrees clockwise?
Answer:
See below
Step-by-step explanation:
Rotating CLOCK wise would result in -4,3 becoming 3,4 in the first quadrant
Jeff, Gene, and Mike need to eat an entire cake before it goes bad. The cake is cut into 8 pieces.
- Jeff could eat 6 pieces of cake in 2 hours
- Gene can eat 2 pieces of cake in 30 minutes
- Mike can eat 4 pieces of cake in 48 minutes
The pieces can be divided into smaller pieces as necessary - the rates are based on the size of pieces that result when dividing the cake into 8 equal pieces.
Answer these questions below:
1) How many pieces of cake can jeff eat in 1 hour? _________________
2) How many pieces of cake can Gene eat in 1 hour? _____________________
3) How many pieces of cake can Mike eat in 60 minutes? ____________________
4) Will it take Mike, Gene, and Jeff more than 1 hour to each eat the cake, or less that an hour to eat the cake? Explain how you know.
The pieces of cake that Jeff will eat in 1 hour is 3
The pieces of cake that Gene will eat in 1 hour is 4
The pieces of cake that Mike will eat in 1 hour is 5
It will take Mike, Gene, and Jeff more than 1 hour to each eat the cake
How many pieces of cake would they eat in 1 hour?In order to determine the pieces of cake that Jeff can eat in 1 hour, divide 6 by 2.
6/2 = 3 pieces of cake
In order to determine the pieces of cake that Gene can eat in 1 hour, multiply 2 pieces of cake by 2.
2 x 2 = 4 pieces of cake
In order to determine the pieces of cake that Gene can eat in 1 hour, multiply 4 pieces of cake by 60 minutes and divide the result by 48 minutes.
(4 x 60) / 48 = 5 pieces of cake
It will take Mike, Gene, and Jeff more than 1 hour to each eat the cake, because they all eat less than 8 slices of cake in one hour.
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simplify this with all the steps
Answer:
[tex]\frac{x}{x+2}[/tex]
Step-by-step explanation:
[tex]\frac{x^2+5x}{x^2+7x+10}[/tex] ← factorise numerator and denominator
= [tex]\frac{x(x+5)}{(x+5)(x+2)}[/tex] ← cancel (x + 5) on numerator / denominator
= [tex]\frac{x}{x+2}[/tex]
Write a function rule to model the cost per month of a long-distance cell phone calling plan. Then evaluate the function for the given number of minutes.
Monthly service fee: 4.52 Rate: .12 pet minute Minutes used: 250
$34.52 is the function for the given number of minutes.
What is a formula for linear equations?
Y = mx + b, where x and y are the variables, m is the slope of the line, and b is the y-intercept, is a straightforward way to write the linear equation formula. Slopes provide information about a line's direction and steepness.The function is
long- distance cell phone calling fee = Monthly service fee + Rate*Minutes used
long- distance cell phone calling fee = $4.52 + $0.12*250 = $34.52
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gina wilson unit 3 homework 1
If an analysis of variance is used for the following data, what would be the effect of changing the value of ss1 to 50? sample data m1 = 10 m2 = 20 ss1 = 90 ss2 = 70
The decreases SSwithin and increase the size of the F-ratio be the effect of changing the value of ss1 to 50 option (D) is correct.
What are the population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
It is given that:
Sample Data
M1 = 10 M2 = 15
SS1 = 90 SS2 = 70
As we know,
The F ratio:
F = S²(x)/S²(y)
From the data given we can say:
Reduce SSwithin and boost the F-magnitude. ratio's
Thus, the decrease SSwithin and increase the size of the F-ratio be the effect of changing the value of ss1 to 50 option (D) is correct.
The question is incomplete.
The complete question is attached in the picture.
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A women went shopping and spent 2/3 of all the money she had. Then she lost 3/5 of what she had left after shopping. how much money did she have in the begining if she has $10.00 left
Answer:
Total Money = $ 75.00
Step-by-step explanation:
Let X be the Total Money
Amount Spent for Shopping = 2/3 of X = 2X/3
Money Lost = 3/5 of (X -2X/3) = 3/5 of (3X-2X)/3 = 3X/15 = X/5
Balance in hand = $ 10.00
is X - 2X/3 - X/5 = $ 10.00
LCM of 3 and 5 = 15
ie (15X - 10X - 3X)/15 = $ 10.00
(15X - 10X - 3X) = 150.00
2X = $ 150.00
X = $ 150.00/2
X = $ 75.00
given x + y = -2 solve for y
Answer:
what is the value of x? Ans. varies
Step-by-step explanation:
Find the measures of the sides of Δ X Y Z and classify
triangle by its sides.
X(-5,9), Y(2,1), Z(-8,3)
The measures of the sides of ΔXYZ are XY = 10.6, YZ = 11.2, XZ = 6.7 and the triangle XYZ must be an acute triangle
In this questions we have been given the the coordinates of the triangle XYZ.
X(-5, 9), Y(2, 1), Z(-8, 3)
We need to find the measures of the sides of ΔXYZ .
We find the the measures of the sides using distance formula.
XY = √[(1 - 9)² + (2 + 5)²]
XY = √[-8² + 7²]
XY = √(64 + 49)
XY = √(113)
XY = 10.6
Now side YZ
YZ = √[(3 - 1)² + (-8 - 2)²]
YZ = √[(2)² + (-10)²]
YZ = √4 + 100
YZ = √104
YZ = 11.2
And the length of side XZ would be,
XZ = √[(3 - 9)² + (-8 + 5)²]
XZ = √(-6² + -3²)
XZ = √(36 + 9)
XZ = √45
XZ = 6.7
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
the sum of the squares of the two smaller sides is,
= 6.7² + 10.6²
= 44.89 + 115.54
= 160.43
= 12.67²
And 11.2² = 125.44
Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.
Therefore, the measures of the sides of ΔXYZ are XY = 10.6, YZ = 11.2, XZ = 6.7 and the triangle XYZ must be an acute triangle
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(c) 10y+12-7y-8-3y…..
Answer:
4
Step-by-step explanation:
Hello!
Simplify the expression by combining like terms.
Simplify10y + 12 - 7y - 8 - 3y10y - 7y - 3y + 12 - 8 Collect like terms3y - 3y + 4 Combine like terms4 SimplifyThe simplified expression is 4.
The simplified form of the given expression is 4.
To solve the expression 10y + 12 - 7y - 8 - 3y,
We need to combine like terms and simplify.
Simplify the expression by combining the like terms (the terms that have the same variable and the same exponent).
We have 10y, -7y, and -3y,
Which can be combined to give us a total of 0y.
This means that the variable y has been eliminated from the expression.
Combine the constant terms (the terms that don't have a variable or that have a variable raised to the power of 0).
We have 12 and -8, which can be combined to give us 4.
So, the simplified expression is 4.
We can express this mathematically as follows:
10y + 12 - 7y - 8 - 3y = (10y - 7y - 3y) + (12 - 8)
= 0y + 4 = .
In other words, the expression simplifies to the constant term 4.
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Refer to ®R .
If SU = 16.2 centimeters, what is RT ?
The diameter of a circle is defined as being twice the length of its radius.
If SU = 16.2 centimeters then the value of RT = 8.1 cm.
What is the difference between the radius and diameter of a circle?The diameter of a circle is defined as being twice the length of its radius. The radius of a circle is measured from the center to one of the circle's endpoints, whereas the diameter is measured from one end of the circle to another end of the circle, passing through the center.
In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.
The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.
Here, SU is the diameter and RT is the radius.
Radius of the circle = 1/2 d
Where d = 16.2 then
substitute the value of d in the above equation, and we get
Radius of the circle = 1/2 (16.2)
Radius of the circle = 8.1
Therefore, the value of RT = 8.1 cm.
The complete question is:
If SU = 16.2 centimeters, what is RT?
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What is an equation of each line?
The equation of line is ax + by + c = 0.
A line's equation has the conventional form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.
With the aid of the line's slope and a point on the line, the equation of a line may be created. For a better understanding of how a line's equation is created, let's learn more about the line's slope and the necessary point on the line. The slope of a line is the angle that the line makes with the positive x-axis and can be stated as a numerical integer, fraction, or as the tangent of that angle. The term "point" refers to a coordinate system point with the x and y coordinates.
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Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha bought is 3/5 of the number of red balloons. The number of green balloons is also 2/3 of the number of yellow balloons.
The number of green and yellow balls is 24 and 36 respectively.
Given that,
Masha bought red, green, and yellow balloons for a party.
red balloons = 40 .
The number of green balloons Masha purchased = 3/5 of the red balloons.
The number of green balloons is again = 2/3 of yellow balloons.
Fraction is described as the number of compositions that comprise the Whole.
Here,
according to the question
Number of red ballons = 40
The number of green balloons Masha bought is 3/5 of the number of red balloons = 40 * 3/5
= 8* 3
= 24
The number of green balloons is also 2/3 of the number of yellow balloons.
= 3/2 * 24
= 36
Thus, the number of green and yellow balls is 24 and 36 respectively.
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An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $2,600 1.7%
Municipal Bond $3,700 3.2%
Preferred Stock $575 12.9%
Common Stock A $1,225 −5.6%
Using technology, calculate the weighted average ROR of the investments. Round to the nearest tenth of a percent.
2.1%
3.1%
5.9%
7.5%
Based on the investment portfolio given, the weighted average ROR of the investments would be 2.1%
What is the weighted average?First, find the total portfolio value:
= 2,600 + 3,700 + 575 + 1,225
= $8,100
The weighted average Rate of Return (ROR) on the investments is:
= (2,600 / 8,100 x 1.7%) + (3,700 / 8,100 x 3.2%) + (575 / 8,100 x 12.9%) + (1,225 / 8,100 x -5.6%)
= 2.076
= 2.1%
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Answer:
2.1%
Step-by-step explanation:
I got it right.
Solve for R
60 = -12r
Add -4 3/8 + 8 6/7 enter your answer
Answer:
Step-by-step explanation:
first you need to make the 3/8 and 6/7 into 21/56 and 48/56 then you take the -4 and 8 then add then together you get 4 then you still have the 21/56 and 48/56 which you need to add so 48 + 21 = 69/56 or 1 and 13/56 you then add the 1 to the 4 which gives you 5 then add the 13/56 to it which gives you your answer of 5 and 13/56
Brooklyn has 3 shelves in her bedroom that have 40 books on each shelf in another room,she has 4 shelves that each contain 20 books if she buys 17 books at a resale shop, how many books does brooklyn have now
Answer:120 plus 80 plus 17 equals 217
Step-by-step explanation:
Answer:
Step-by-step explanation:
217
Which expression equals 5x/x² - 9 - 4 x / x² + 5x + 6?
(A) 7 x/(x-3)(x+3)(x+2) (B) x²-2 x / (x-3)(x+3)(x+2)
(C) x²+22x / x-3)(x+3)(x+2)
(D) 9x² - 2 x / (x-3)(x+3)(x+2)
The expression that is equal to [tex]\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex] is [tex]\frac{x^{2}+22x }{(x+2)(x+3)(x-3)}[/tex].
In the given question
[tex]=\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex].....(i)
First solving the denominator of both the terms ,
=x²-9
=x²-(3)²
=(x+3)(x-3) ...using identity a²-b²=(a+b)(a-b) .....(ii)
=x²+5x+6
=x²+3x+2x+6 ...by splitting the middle term
=x(x+3)+2(x+3)
=(x+2)(x+3) ....(iii)
Substituting the value of (ii) and (iii) in (i)
we get,
[tex]=\frac{5x}{(x+3)(x-3)} -\frac{4x}{(x+2)(x+3) }[/tex]
taking LCM as (x+2)(x+3)(x-3) we get ,
[tex]=\frac{5x(x+2)-4x(x-3)}{(x+2)(x+3)(x-3)} \\ \\ =\frac{5x^{2} +10x-4x^{2} +12x}{(x+2)(x+3)(x-3)}[/tex]
Simplifying the like terms in the numerator we get
[tex]=\frac{x^{2} +22x}{(x+2)(x+3)(x-3)}[/tex]
Therefore , the expression that equals [tex]\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex] is [tex]\frac{x^{2} +22x}{(x+2)(x+3)(x-3)}[/tex].
The correct option is (c).
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PLEASE HELP
The Central Islip community has 9,649 homes in it. Smart Boards cost the school district $5,200 each. The HS needs 175, the Reed School needs 150 and the Mulligan school needs 50 new boards. Network Outsource the schools tech company has 12 workers for the HS, 8 for the Reed School and 4 for Mulligan. They all work 8 hours a day. They work 5 days a week, Monday thru Friday. They earn $58 per hour. It will take 45 weeks to finish the job. Find: a) Total Product Cost b) Total Labor Cost c) Total Cost d) Cost per Home e) Cost per Week
Using proportions, the costs are given as follows:
a) Total Labor Cost: $2,505,600.
b) Total Product Cost: $1,950,000.
c) Total Cost = $4,455,600.
d) Cost per home = $461.77.
e) Cost per week = $99,013.33.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For item a, the labor cost is found using the earnings of the workers, as follows:
45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)
Hence:
Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.
For item b, the product cost is the cost of the boards, hence:
(175 + 150 + 50 boards) x 5,200
Total Product Cost = 375 x 5,200 = $1,950,000.
For item c, the total cost is the sum of the product cost and the labor cost, hence:
Total Cost = 2,505,600 + 1,950,000 = $4,455,600.
For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:
Cost per home = 4455600/9649 = $461.77.
For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:
Cost per week = 4455600/45 = $99,013.33.
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c. Find the exact lengths of the altitudes of triangles B and C.
The length of the altitude of triangle B is
The length of the altitude of triangle C is
The right triangle B and c altitude length are same that is 6.
Given that,
In the given picture there are 2 right triangles.
They are B and C.
2 sides of the triangle B is 3 and [tex]3\sqrt{3}[/tex].
2 sides of the triangle C is 6 and [tex]6\sqrt{2}[/tex].
The angle for both the right triangle B and C is 90°.
We have to find the length of the altitude of right triangles B and C.
By using the Pythagorean theorem we can find the length of the altitude of the right triangle B and C.
The simplest way is to use the Pythagorean theorem if you are aware of two additional right triangle sides:
[tex]a^{2} +b^{2} =c^{2}[/tex]
Where the sides of the right triangle are a, b, and c.
First, We will find for the right triangle B.
Here, a=[tex]3\sqrt{3}[/tex] and b=3
Now, substitute in the formulae
[tex](3\sqrt{3})^{2} +3^{2}=c^{2}[/tex]
[tex]27+9=c^{2}[/tex]
[tex]36=c^{2} \\[/tex]
[tex]c^{2} =36\\[/tex]
Taking square root on both sides
[tex]\sqrt{c^{2} } =\sqrt{36}[/tex]
[tex]c=6[/tex]
Therefore, the length of the altitude of right triangle B is 6.
Now, We will find for the right triangle C.
Here, b=6 and c=[tex]6\sqrt{2}[/tex]
Now, substitute in the formulae
[tex]a^{2} +6^{2}=(6\sqrt{2}) ^{2}[/tex]
[tex]a^{2} +36=72[/tex]
[tex]a^{2}=72-36 \\[/tex]
[tex]a^{2} =36\\[/tex]
Taking square root on both sides
[tex]\sqrt{a^{2} } =\sqrt{36}[/tex]
[tex]a=6[/tex]
Therefore, the length of the altitude of right triangle B is 6.
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The formula for simple interest is I=Prt
a. Solve the formula for t, when r is the simple interest per year.
t=_
b. Use the new formula to find the value of t in the table.
The value of t in the table is _ years
a. The formula solved for t when r is the simple interest per year is t = I/Pr
b. Using the new formula, the value of t in the table is 3 years
Simple InterestFrom the question, we are to solve the given formula for t
The given formula is
I = Prt
To solve for t, we will divide both sides of the equation by Pr
I/Pr = Prt/Pr
I/Pr = t
∴ t = I/Pr
b.
I = $75
P = $500
r = 5% = 0.05
t = 75/(500×0.05)
t = 75/25
t = 3 years
Hence, the value of t in the table is 3 years
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