Since they're in arithmetic progression, the difference between consecutive terms is fixed.
[tex](x + 2) - (x - 1) = 3[/tex]
[tex]3x - (x + 2) = 2x - 2 = 3 \implies 2x = 5 \implies x = \dfrac52[/tex]
Then the first term is
[tex]x-1=\dfrac52 - 1 = \boxed{\dfrac32}[/tex]
and the fifth term is
[tex]3x + 3 + 3 = 3\cdot\dfrac32 + 3 + 3 = \boxed{\dfrac21}2[/tex]
Help, the Question is attached.
the box select is:
Right triangle
Not a right triangle.
The triangle with lengths 6cm, 8cm and 10cm are right triangles.
What are right triangles?A right triangle is a polygon with three sides. It is a triangle in which the sum of the square of the two sides is equal the square of the longest side. The sum of the angles in a right triangle is 180 degrees. One of the angle in a right triangle measures 90 degrees.
According of the Pythagorean Theorem, a triangle is a right triangle if the sum of the square of the two sides is equal the square of the longest side.
The Pythagorean Theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse6² + 8² = 10²
36 + 64 = 100
The triangle is a right triangle because it means the parameters set forth by the Pythagorean Theorem.
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Would Diagonal FH be considered perpendicular to side FE?
Answer:
No
Step-by-step explanation:
You want to know if baseline FH can be considered to be perpendicular to one of two congruent sides in isosceles triangle EFH.
Isosceles triangleThe base angles of an isosceles triangle are congruent. That means they can never be right angles.
Base line FH cannot be perpendicular to side FE.
__
Additional comment
Angle E can be a right angle in isosceles triangle EFH, but neither of angles F or H can be.
Diagonal FH bisect angles EFG and EHG and the angle FEH is congruent to angle FGH.
Why is the triangle congruent?
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them.Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.We need to check all the statements that are applicable for the diagram.1) EFGH is a rectangle.
The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.
2). EFGH has 4 congruent sides.The above statement is also false. EFGH has two opposite sides are congruent.
3). Diagonal FH bisect angles EFG and EHG.
The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.
4). Diagonal FH is perpendicular to side Fe.
The above case is not true in general.
5). Angle FEH is congruent to angle FGH.
Yes, the above statement is the correct one, because both the triangles are congruent to each other.
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The complete question is -
Triangle FGH is the image of isosceles triangle FEH after a reflection across line HF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent
Use the Change of Base Formula to evaluate each expression.
log₂9
The value of the expression log₂9 after using change of base theorem is 3.17.
Given that the expression be log₂9.
We are required to find the value of the expression by finding the value of log values.
Change of base formula is basically used in a situation where we have to solve the log values with different bases at one time. It says that
[tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex].
The expression is log₂9.
We know that [tex]log_{b}a[/tex]=log a/log b.
log₂9=log 9/log 2
Now,we have to use the values of log in the above expression.
=0.9542/0.3010
=3.17
Hence the value of the expression log₂9 after using change of base theorem is 3.17.
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what is the conjecture of 0, 2, 6, 12, 20, _, _,
Answer:
The next 2 numbers would be 30 and 42
Step-by-step explanation:
If the last number in the sequence was 20, and the sequence started at 0 with a constant change, we know that since this constant change is +2 every time the input increases. If 12 + 8 was 20, the next number would be 30. If 20 + 10 is 30, then the next output will be 42, because 30 + 12 = 42.
Hope this helps!
Helllllp!!!! PLEASE...
the complete table is:
zeros: x = -2, x = 0, x = 2.
Increasing: (-∞, -1.25) and (1.25, ∞)
Decreasing: (-1.25, 1.25)
End Behavior: as x →∞, y →∞
as x → -∞, y→ -∞
How to find the zeros?Let's solve for the first function.
First, we want to find the zeros of the function. The zeros are the values of x such that the function becomes zero (intercepts the horizontal axis)
So we can see that the zeros are:
x = -2, x = 0, x = 2.
Now we want to see when the function is increasing. The function is increasing when it goes (reading from left to right) the function goes upwards.
The function is increasing on the intervals:
(-∞, -1.25) and (1.25, ∞)
And the function is decreasing between these two intervals:
(-1.25, 1.25)
Now we need to look at the end behavior.
When x tends to infinity, (right side) we can see that the function goes upwards, then:
as x →∞, y →∞
In the left side the function goes downwards, so:
as x → -∞, y→ -∞
Then the complete table is:
zeros: x = -2, x = 0, x = 2.
Increasing: (-∞, -1.25) and (1.25, ∞)
Decreasing: (-1.25, 1.25)
End Behavior: as x →∞, y →∞
as x → -∞, y→ -∞
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or
On Saturday mornings, Madelyn volunteers at the hospital where her mother works. One Saturday, she answers phone calls at the information desk while the receptionist is away. Then she spends 40 minutes delivering flowers to patients' rooms. In all, Madelyn volunteers at the hospital for 90 minutes that day.
Which equation can you use to find the amount of time t that Madelyn answers phone calls?
Answer:
90-50=40 so she answers phone calls for 50 min
Step-by-step explanation:
Write one million,three hundred ninety-two thousand, three hundred and fifty-two in standard form and multiplication form
Of the 54 students in the school library one afternoon, 32 participate in school clubs, sports, or activities. at this rate, if there are 243 students in the school altogether, how many of them would you expect to participate in school clubs, sports, or activities? 144 139 99 142
Using ratio and proportion, of the 243 students in the school altogether, 144 students are expected to participate in school clubs, sports, or activities.
Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other. On the other hand, proportion is the equality of two ratios, such that a : b = c : d.
If 32 students participate in school clubs, sports, or activities out of the 54 students, then the ratio between the number of students who participate in school clubs, sports, or activities and the total number of students is:
32 : 54
Using proportion, solve for the number of students who are expected to participate in school clubs, sports, or activities out of 243 students.
32 : 54 = n = 243
where n = number of students who are expected to participate in school clubs, sports, or activities out of 243 students
32 : 54 = n = 243
32(243) = 54n
n = 144
Hence, 144 students are expected to participate in school clubs, sports, or activities out of 243 students.
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What shape has rotational symmetry of 40 degrees?
The shape that has rotational symmetry of 40 degrees is a nonagon.
What is a nonagon?It should be noted that a nonagon is a nine-sided polygon and it is also called a 9-gon. In other words, it should be noted that a nonagon is a nine sided closed two dimensional figure.
It should be noted that the degree of rotation for a nonagon is 40º. Since 360° of rotation is a full circle. We need to divide 360° by 40°
360/40=9 the shape has 9 sides
The shape is a nonagon, which has 9 sides.
Therefore, the shape that has rotational symmetry of 40 degrees is a nonagon.
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In the figure below, n || find the values of x and y.
Answer:
[tex]{ \tt{x + 83 = 180}}[/tex]
[ Property of angles on a straight line ]
[tex]{ \tt{x = 180 - 83}} \\ \\ { \boxed{ \tt{x = 97 \degree}}}[/tex]
[tex]{ \tt{(4y - 27) = x}} \\ [/tex]
[ Property of alternate angles ]
[tex]{ \tt{4y - 27 = 97}} \\ { \tt{4y = 124}} \\ { \tt{ \frac{4y}{4} = \frac{124}{4} }} \\ \\ { \boxed{ \tt{y = 31 \degree}}}[/tex]
Solve the math problem
Answer:
you don't have an image
Step-by-step explanation:
Multiply. State any restrictions on the variables.
2 x+12 / 3 x-9 . 6-2 x / 3 x+8
According to the question, the given rational expression can be simplified which is as shown below:
Rational expression = [tex]\frac{2x+12}{3x-9}.\frac{6-2x}{3x+8}[/tex]
To simplify the given rational expression, calculate the factors of numerator as well as denominator. And later divide them from each other. The expressions are also called as polynomial expressions.
Rational expression = [tex]\frac{2(x+6)}{3(x-3)}.\frac{2(3-x)}{3x+8}[/tex]
The final answer of the expression is [tex]\frac{-4(x+6)}{3(3x+8)}[/tex]
What is polynomial expression?
Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.
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Peter says the least common multiple of 4 and 6 is 24, Do you agree or disagree? Explain.
Answer:
I Disagree with Peter, the explanation is down below.
Step-by-step explanation:
I disagree because to find the least common multiple or the LCM, you need to first list the first several multiples of each number. So, because the numbers are 4 and 6, I would write:
4 - 4, 8, 12, 16, 20, 24, 28, 32
6 - 6, 12, 18, 24 30, 36, 42, 48
The next step would be to find the same multiples in the list. If there are no same multiples, then I would keep on adding multiples.
If we look at the list, the first numbers that we see that are the same are 12 and 12.
12 would be the LCM, not 24.
If the two numbers were 24 and 12, then the LCM would have been 24, but in this case, the LCM is 12. So that is why I disagree.
Hope this helped! :D
Have a wonderful day!~~
Solve each equation.
5³x=1/125
Value of x in given exponential equation is = -1
What is exponential function ?In, mathematics a exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]a^x[/tex] .
where, a is the base of function
x is the expression
Mathematically, if [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as [tex]a^x = N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.
Some important formulas of logarithms :
[tex]a^x . a^y = a^{x+y}[/tex][tex]\frac{a^x}{a^y} = a^{x-y}[/tex][tex]a^x.b^x=(ab)^x[/tex][tex](a^x)^y = a^{xy}[/tex][tex]a^{-x} = \frac{1}{a^x}[/tex]According to given statement,
[tex]5^{3x} = \frac{1}{125}[/tex]
=> [tex]5^{3x}=\frac{1}{5^3}[/tex]
=> [tex]5^{3x}=5^{-3}[/tex] (as [tex]\frac{1}{a^x} =a^{-x}[/tex])
=> 3x = -3
=> x = -1
Thus solution for this equation is x =-1.
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Find the value of x so that line m is parallel to line l.
The value of x that makes line m parallel to line l is 15.
How to find the value of x that makes the lines parallel?When parallel lines are cut across by a transversal, angle relationships are formed.
The angle relationship form includes corresponding angles, alternate angles, vertically opposite angles etc.
Therefore, for line m to be parallel to line l,
5x - 10 + 8x - 5 = 180
Hence,
5x - 10 + 8x - 5 = 180
5x + 8x - 10 - 5 = 180
13x - 15 = 180
13x = 180 + 15
13x = 195
Therefore, divide both sides by 13
13x / 13 = 195 / 13
x = 15
Therefore, the value of x that makes line m parallel to line l is 15.
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A cylinder has a diameter of 16 feet
and a height of 5 feet. What is the
volume of the cylinder??
Answer:
V = 1,005.31ft³
Step-by-step explanation:
V = [tex]\pi[/tex][tex](\frac{d}{2} )^{2}[/tex]h
V = [tex]\pi[/tex][tex](\frac{16}{2} )^{2}[/tex](5)
V = 1,005.30965ft³
Step-by-step explanation:
diameter is 16 feet
height is 5 feet
For you to find the volume you have to know the
formula for finding it
the formula is πr^2h
π=22/7,
r=radius=16/2=8
h=height=5
πr^2h
22/7 x 8^2 x 5
22/7 x 64 x 5
22/7 x 320
=1005.71 feet^3
The half-life of a radioactive substance is the time it takes for half of the material to decay. Phosphorus-32 is used to study a plant's use of fertilizer. It has a half-life of 14.3 days. Write the exponential decay function for a 50 -mg sample. Find the amount of phosphorus-32 remaining after 84 days.
The exponential decay model of phosphorus-32 is [tex]P=P_0e^{-0.0483t}[/tex] and
the amount of phosphorus-32 remaining after 84 days is 0.85 mg
If the population declines at a constant rate proportional to population size, it is called exponential decline. Volume decreases slowly, then rate of change and growth decrease rapidly over a period of time. This growth reduction is calculated using the exponential decay formula. The formula for exponential decay is [tex]P=P_0e^{rt}[/tex] ..(1) where "[tex]P_0[/tex]" is the initial amount , "t" time interval (time can be specified in years, days, (or) months , r = constant of proportionality , e = Euler constantIt is given that half-life of Phosphorus-32 is 14.3 days.
Putting P = 25 , P₀ = 50 and t = 14.3 in equation (1) , we get
[tex]25=50e^{14.3r}\\\\0.5=e^{14.3r}[/tex]
Taking log on both sides , we get
[tex]log0.5=log_{10}e^{14.3r}\\\\-0.301=14.3rlog_{10}e\\\\\frac{-0.301}{14.3}=r\times0.434 \\\\\r=\frac{-0.0210}{0.434} \\\\r=-0.0483[/tex]
The exponential decay model of phosphorus-32 is [tex]P=P_0e^{-0.0483t}[/tex]
We have to find the amount after 84 days .
Putting [tex]P_0=50mg , \ r=0.0483 , \ t=84[/tex] in equation (1) , we get
[tex]P=50\times e^{(-0.0483\times84)}\\\ P=50\times e^{-4.064}\\P=50\times 0.0171\\P=0.85mg[/tex]
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Find the stantard deviation of the fowling data
Step-by-step explanation:
the standard deviation is first of all based on the squared differences of every data point to the mean value (squared, so that the direction of the difference does not matter, each number is positive).
this number is normalized to the number of data points (divided by "N").
and from that number we calculate the positive square root.
we take the square root to bring things back from the squared dimension of the data differences to the mean value and make it better understandable in size compared to the sizes of the data points. otherwise there is benefit to the squared variance (the whole thing without the last square root).
we have 15 data points (8 + 7).
first we need the mean value, which is the sum of all data points divided by the number of data points :
(7+10+5+5+6+3+5+5+6+5+5+5+9+3+5)/15 = 84/15 =
= 5.6
the standard variance is now the sum of the squares of the difference of each data point to the mean value.
e.g. the squared difference of 7 to 5.6 is
(7-5.6)² =(-1.4)² = 1.96
(1.96+19.36+0.36+0.36+0.16+5.76+0.36+0.36+0.16+0.36+0.36+0.36+11.56+5.76+0.36) / 15
= 47.6 / 15 = 3.173333333...
and the standard deviation is
SD = sqrt(3.173333333...) = 1.781385229... ≈ 1.78
bro help I’ve stuck doing this for more than an hour
Answer:
Check the attached image above for solution
pls help me asapppppppppppppppppppp i need it quickly i will mark brainliest
The value of the maximum profit is 680
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the value of the maximum profit?The equation of the profit function is given as
P(x) = 230 + 30x - 0.5x^2
Differentiate the function
So, we have
P'(x) = 0 + 30 - x
Evaluate the like terms in the function
So, we have
P'(x) = 30 - x
Set the function to 0
So, we have
30 - x = 0
Evaluate
x = 30
Substitute x = 30 in the equation P(x) = 230 + 30x - 0.5x^2
So, we have
P(30) = 230 + 30 x 30 - 0.5 x 30^2
Evaluate
P(30) = 680
Rewrite as
Pmax = 680
Hence, the value of the maximum profit is 680
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Year
1960
1970
1980
1990
2000
2010
U.S. national debt (in U.S. dollars)
written in standard form
$286,330,760,848.37
$370,918,706,949.93
$907,701,000,000.00
$3,233,313,451,777.25
$5,674,178,209,886.86
$13,561,623,030,891.79
U.S. national debt (in U.S. dollars)
written in scientific notation
$2.863-10
$3.709 10
$9.077 10
$3.2333 10
$5.6742 10
$1.35616-10
The terms given in US national debt in standard form when converted to scientific notation form will be 2.86 * 10^11, 3.70 * 10^11, 9.07 * 10^11, 3.23 * 10^12, 5.67 * 10^12 and 1.35 * 10^13 respectively.
Scientific notation if the process of conversion of very large numbers which are otherwise inconvenient to read into decimal form raised to some power of 10. During this conversion, the numbers in standard form are written such that only one place value before decimal is left and written as coefficient and all other numbers are then counted and written in the form of base 10 raised to some exponent value. The coefficient value must be such that its value lies between 1 and 9 and less than 10. Thus, the following numbers can be written as follows in scientific form.
286330760848.37 = 2.86 * 10^11
370918706949.93 = 3.70 * 10^11
907701000000.00 = 9.07 * 10^11
3233313451777.25 = 3.23 * 10^12
5674178209886.86 = 5.67 * 10^12
13561623030891.79 = 1.35 * 10^13
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Thang decided to borrow $2000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 7%.How much interest will Thang pay?
The amount that Thang would pay in interest is $420 based on the loan of $2000 and simple interest of 7%
What is simple interest?
The simple interest on the loan is determined as the amount borrowed multiplied by the interest rate of 7% and as well multiplied by the number of years it takes for the loan to be repaid
I=PRT
I=simple interest payable by Thang=unknown
P=principal=amount borrowed=$2000
R=interest rate=7%
T=number of years before the loan is repaid=3
I=$2000*7%*3
I=$420
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the height of a house is 52 ft. a tree beside the house is 7 ft more than twice as tall. what is the height of the tree? enter your answer in the box. ft
Answer: 111 ft tall. Thats a big tree!
Step-by-step explanation: if its seven more than two times the height of the house, do 52 X 52 + 7 which equals 111 ft.
Ben spent 2/3 of his allowance on video games. What is the fraction of his allowance expressed as a decimal?
answer:
0.66666666666
step-by-step explanation:
2/3
2 divided by 3 = 0.66666666666
If < A and < B are vertical angles, and < A is 43 ° , then what is the measure of < B?
Answer: m∠B°=43°
Step-by-step explanation:
If < A and < B are vertical angles, hence, m∠A°=m∠B°=43°
WILL BE GIVING BRAINLIEST
Answer:
The two angles are congruent or estimated to be congruent because of the "≅" that is showed in the statement.
Step-by-step explanation:
Congruent/Congruence: Having the same size and shape or matching in size and shape: congruent figures.
≅ --> Means to be congruent of seen to be congruent
≈ --> About the same, or seems equal
I hope this helped <3
A ship captain is attempting to contact the deep sea diver in the maximum range for communication is 50 meters will he be able to communicate with the diver based on their current positions? Explain.
Using the distance between two points, it is found that the distance between the positions of the ship and of the diver is greater than 50 meters, hence the ship captain will not be able to communicate with the diver based on their current positions.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Looking at the graph, the positions of the ship and of the diver are given as follows:
Ship: (8,8).Diver: (48, -36).Hence, applying the formula presented at the beginning of the explanation. the distance is given by:
[tex]D = \sqrt{(48 - 8)^2+(-36-8)^2}[/tex]
D = 59.6.
The distance between the positions of the ship and of the diver is greater than 50 meters, hence the ship captain will not be able to communicate with the diver based on their current positions.
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What is the equation of the parabola with focus (1, -3) and directrix y = 2?
OA. y=-3x²+2x-2
OB. y=-4x²+8x-21
OC. Y=2/3x^2-4/3x+7/6. OD. Y=-1/10x^2+1/5x-3/5
Answer:
y = -x^2/10 + x/5 - 3/5
Step-by-step explanation:
The answer is D: just rearrange
which calculation and answer /shows how to convert 5/16 to a decimal
Answer:
I think it's C, I hope this helps!
Calculate the sample standard deviation of the data shown. Round to two decimal places. X 18 11 12 15 13 22 26 sample standard deviation =
please help me out it's due in 10 minutes
Answer: The SD is 5.589
Step-by-step explanation: