Answer:
[tex]\frac{5}{1}[/tex]
Step-by-step explanation:
45 : 9
= [tex]\frac{45}{9}[/tex] ← divide numerator and denominator by 9 )
= [tex]\frac{5}{1}[/tex] ← in simplest form
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 expression is equivalent to -3[4*-0.50]?
–12x – 1.50
–12x + 1.50
–12x – 2.50
–12x – 3.50
In given expressions no one is equivalent to the expression -3 [4 × -0.50]
Given,
The expression : -3 [4 × -0.50]
We have to find the expression equivalent to the above expression from the given options.
Solve the expression:
-3 [4 × -0.50] = -3 × -2 = 6
Now we can solve the expressions given in the options:
1) -12 × -1.50 = 18
Not equal to the given expression
2) -12 × 1.50 = -18
Not equal to the given expression
3) -12 × -2.50 = 30
Not equal to the given expression
4) -12 × -3.50 = 42
Not equal to the given expression
So, we can conclude that, there is no equivalent expression in the options for the expression -3 [4 × -0.50]
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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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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]
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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What value correctly fills in the blank so that the expressions are equivalent?
32 + 72 = blank x (4 + 9)
4
8
12
13
Answer: The answer is 8 because you add 32 + 72 and get 104 x and then 4 +9 = 13 then you divide 104 divided by 13 = 8
Answer:
8, because you add 32 and 72, which will get 104x and then 4+9 which is 13 then you divide 104 divided by 13 = 8
Step-by-step explanation:
hope this helps!
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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Create an equation equivalent to x - y = 3 by multiplying each term on both sides by any number you choose.
Step-by-step explanation:
you can plus for obtain a multiply
5×-2y=3
HELP PLS WILL GIVE BRAINLIST
Answer:
AB + BC + AC a. segment addition postulate
2x+6x+8 = 32 b. substitution property of equality
8x + 8 = 32 c. Combine like terms
8x = 24 d. subtraction property of equality
x = 3 e. division property of equality
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.
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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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
If principal=p,rate of interest=R and time=T,then write the formula to find the compound amount
It is given that P = principal, R = rate of interest and T = time
Formula to find compound interest is:
A = P(1 + R/100)^T
where A = amount received after n years
P = principal amount invested
R = rate of interest
T = time for which the amount is invested
The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.
It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
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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
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
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:
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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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 inequality and graph on number line
3|14-m|>18
Answer:
Hey Rey
Step-by-step explanation:
[tex] \mathsf{\red{m∈( - ∞, \: 8)U(20,∞)}}[/tex]
Answer:
Hey Rey ...
Step-by-step explanation:
[tex]\mathsf{\blue{m∈( - ∞, \: 8)U(20,∞)}}[/tex]
A figure is multiplied by a scale factor of 1/3. Did the figure get smaller or larger? How do you know?
I will give Brainiest answer
Answer:
Smaller
Step-by-step explanation:
If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.
PLS HURRY DUE A HOUR AGO
1. Show an example of two numbers that are additive inverses.
Step-by-step explanation:
Greetings !
Definition:-In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite, sign change, and negation.
For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0. Similarly, the additive inverse of a − b is −(a − b) which can be simplified to b − a. The additive inverse of 2x − 3 is 3 − 2x, because 2x − 3 + 3 − 2x = 0.
Hope it helps!!!
what is the least common denominator of 3/4 and 1/10
Answer: 20
Step-by-step explanation:
3/4= 15/20
1/10=2/20
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:
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 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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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
Write an equation for the number of miles y it travels in x hours how many miles will it travel in 3
The equation for the given statement is y=3x.
The given equation is the number of miles y it travels in x hours.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
We need to find the number of miles travelled in 3 hours.
Now, using the formula Distance = Time × Speed
y = 3x
Therefore, the equation for the given statement is y=3x.
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Which graph represents y-³√x?
Answer:
There wasn't an image put to choose which graph it would be.
Step-by-step explanation:
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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