The degree of the provided polynomial is 18, and the leading term is √7.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have given an expression:
[tex]= \rm \sqrt{7}x ^{18} + 12.1x^{ 15} + \pi 4 x^ 6 + 1 9[/tex]
As we can see in the expression the greatest degree is 18.
So the degree of the polynomial is 18
And the coefficient of the variable which has a height degree is the leading term.
The leading term = √7
Thus, the degree of the provided polynomial is 18, and the leading term is √7.
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A boat travels upstream for 42 miles in 3 hours and returns in 2 hours traveling downstream in a river. What is the rate of the boat in still water and the rate of the current?
The rate of the boat in still water is : miles per hour
The rate of the current is: miles per hour:
Answer:
17.5 mph
Step-by-step explanation:
Let the speed of the boat in still water be B mph
Let the rate of the current be R mph
When going upstream the effective speed is B-R mph. In terms of values given effective upstream speed = 42/3 = 14 mph
So,
B-R = 14 ... (1)
Similarly downstream speed is B + R (faster downstream)
B + R = 42/2 = 21 .... (2)
(1) + (2) ==> 2B = 35
B = 35/2 = 17.5 mph
The function f(x) = 2·5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function? 2 5 10 32
The multiplicative rate of change of the function f(x) = 2 × 5ˣ is 5.
What is Exponential Function?An exponential function is a type of function in math that involves exponents. A basic exponential function is of the form f(x) = bˣ, where b > 0 and b ≠ 1.
The function is given as:
f(x) = 2 X 5ˣ
The above function is an exponential function.
An exponential function is represented as:
f(x) = abˣ
Where b represents the multiplicative rate
By comparison;
b = 5
Thus, the multiplicative rate of change of the function is 5.
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Answer:
B!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Help me with this question please and thank you!!! :):)
Answer:
A intersection B = ( elements which are common in both)
= ( 2,4,7,19)
A union B = ( all the elements which are either in A or in B).
= ( 2, 4, 7 , 13, 14, 19, 20 , 3, 5, 6, 10,11, 12 , 15,17 , 18 , 19 )
Determine the growth defined by the equation y=1.4(3.72)^x.
Answer:
the type of growth defined by the equation is Exponential growth.
Step-by-step explanation:
Exponential growth :-Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself
expression for exponential growth -
f(x) = k(1+t)^x
f(x) = exponential growth
k = initial amount
t = rate of growth
x = no of time interval
therefor,
the equation shown in the question represents exponential growth with increasing time.
hence, Exponential growth is the correct answer.
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a model airplane has two engines. it can fly if one engine fails but is in serious trouble if both engines fail. The engines function independently of one another. On any given flight, the probability of a failure is 0.10 for each engine. Design a simulation to estimate the probability that the airplane will be in serious trouble the next time it goes up.
Using the binomial distribution, it is found that there is a 0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
p = 0.1, n = 2.
The plane is in serious trouble if both engines fail, that is, the probability is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.1)^{2}.(0.9)^{0} = 0.0001[/tex]
0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.
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The high temperature on Friday was 8 degrees above zero. The low temperature was 3 degrees below zero. Which expression gives the average of the low and high temperatures?
Negative (3 + 8) divided by 2
(negative 3 + 8) divided by 2
(negative 3 + 8) divided by (negative 2)
Left-bracket negative 3 + (negative 8) right-bracket divided by (2) Right-bracket
Using the mean concept, the expression that gives the average of the low and high temperatures is:
(-3 + 8)/2.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem, the two observations are -3 and 8, hence their average is given by:
(-3 + 8)/2.
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five percent of a batch of fuel was found faullty if 27 fuses were faulty how many were inspected the price of internet service is decreased by 7% to 52.00 what is the original price
There are 540 fuses in total and the original price of the internet is $55.91
How to work with percentages?
a) We know that 5% of the fuses are faulty, and there are 27 faulty fusses, then we can write:
5% = 27
100% = x
We want to find x, to do that, we can write:
x = 27*(100%/5%) = 27*20 = 540
There are 540 fuses in total.
b) Now we know that the original price is P, and when we decrease it by 7%, then new price is $52.00
Then we can write:
$52.00 = P*(1 - 7%/100%)
$52.00 = P*(0.93)
$52.00/0.93 = P = $55.91
The original price is $55.91
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evaluate-4x + 2y - z if x = - 2, y = 3, and z = -4
Answer:
-4(-2)+2(3)-(-4)
8+6+4
16 is the answers
Step-by-step explanation:
please mark me as brainlest
Rewrite exponential expressions
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answer:
Step-by-step explanation:
20
Find the standard deviation of
the given data rounded to the
nearest hundredth.
12, 53, 141, 219, 500
Σ (x-mean)2
n
0 =
σ= [?]
The standard deviation of the data to the nearest hundredth is 173.01.
What is standard deviation?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation: 185
Determine the difference between each value and the mean and then square the result:
Determine the mean of the sum of the squared differences and then find the square root of the mean:
Following these steps, the standard deviation is 173.01
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Rob is a high school student taking both algebra and geometry. Last night he had 27 homework problems combined from the two classes, and he took a total of 90 minutes Which value of k would cause the system of linear equations 35 x + 14 y = 119 and 5 x + 2 y = k to have an infinite number of solutions?
3
7
17
21
A system of the equation to be Dependent Consistent System the system must have multiple solutions. The correct option is C.
What is a System of equation?Inconsistent System
A system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.
For the system of equations to have infinite number of solutions, the lines of the equations must coincide, therefore, the line must overlap on each other.
For the lines to overlap the equations must be in a ratio. Therefore, the ratio of the left sides of the equations must be equal to the right side,
[tex]\dfrac{35x+14y}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac{7(5x+2y)}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac71 = \dfrac{119}{k}\\\\k = 17[/tex]
Hence, the value of k must be 17, therefore, the correct option is C.
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Complete the following statement of congruence:
A. TRS
B. RTS
C. STR
D. RST
Answer:
B. △RTS
Step-by-step explanation:
△MON ≅ △RTS
What is the area of triangle ABD?
a 4.5 cm 2
b 3.5 cm 2
c 7 cm 2
d 6 cm 2
Answer: [tex]4.5 \text{ cm}^{2}[/tex]
Step-by-step explanation:
[tex]A=\frac{1}{2} bh\\\\A=\frac{1}{2}(3)(3)\\\\\boxed{A=4.5 \text{ cm}^{2}}[/tex]
The area of the triangle will be equal to 4.5 square centimeters.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space covered by the triangle in the two-dimension is called an area of the triangle.
The area of the triangle ABD will be calculated as:-
Area = [tex]\dfrac{1}{2}[/tex] x Base x height
Area = [tex]\dfrac{1}{2}[/tex] x 3 x 3
Area = 4.5 cm.
Therefore the area of the triangle will be equal to 4.5 square centimeters.
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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
36 meters
48 meters
80 meters
89 meters
The width of the cooling tower at the base of the structure will be A. 36 meters.
How to calculate the width?From the information given, the towers walls are modeled by x²/324 - (y² - 90)²/1600.
Therefore, the width of the cooling tower at the base of the structure will be:
= 2 × ✓324
= 2 × 18
= 36
In conclusion, the width is 36 meters.
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Answer:
It is actually D
Step-by-step explanation:
pls see the attachment
24 of the 720 numbers have the numbers 1, 2 and 3 in that order
How to determine the number of arrangements?The digits are given as:
1, 2, 3, 4, 5, and 6
For 1, 2 and 3 to come in that order, then the three numbers must be treated as a digit
So, we have:
(123), 4, 5, and 6
Now, there are 4 digits.
The number of arrangements is then calculated as:
Arrangements = 4!
Expand
Arrangements = 4 * 3 * 2 * 1
Evaluate
Arrangements = 24
Hence, 24 of the 720 numbers have the numbers 1, 2 and 3 in that order
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Eugene and Shanice each improved their yards by planting sod and geraniums. They bought their supplies from the
same store. Eugene spent $36 on 9 ft² of sod (s) and 2 geraniums (g). Shanice spent $63 on 9 ft² of sod and 5
geraniums. What is the solution to the system of equations? What is the cost of one ft² of sod and the cost of one
geranium?
The cost of one ft² of sod is $2 and the cost of one geranium is $9.
What are the linear equations that represent the question?9s + 2g = 36 equation 1
9s + 5g = 63 equation 2
What is the cost of one feet of sod and geranium?
Subtract equation 1 from equation 2:
3g = 27
g = 27 / 3
g = $9
Substitute for g in equation 1
9s + (2 x 9) = 36
9s + 18 = 36
9s = 36 - 18
9s = 18
s = 18 / 9
s = $2
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Determine the value(s) for which the rational expression −5u+12−2u+2 is undefined. If there's more than one value, list them separated by a comma, e.g. u=2,3.
The value(s) for which the rational expression −5u+12−2u+2 is undefined is u = 1.
What is radial expression?The expression or an equation which can be undefined at some point is a celled the radial expression.
f(u) = -5u +12 / -2u +2
For the function to be undefined, denominator must be equal to zero.
-2u +2 =0
-2u =-2
u = 1
Thus, the value for which the given expression is undefined is 1.
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look at the picture
Answer:
The x-intercept is 2.
Step-by-step explanation:
[tex]2 \sqrt[3]{x - 10} + 4 = 0[/tex]
[tex]2 \sqrt[3]{x - 10} = - 4[/tex]
[tex] \sqrt[3]{x - 10 } = - 2[/tex]
[tex]x - 10 = - 8[/tex]
[tex]x = 2[/tex]
What is the slope of the line shown below (3,-2) (2,4)?
A. -2
B. -1/2
C. 1/2
D. 2
Answer:
D. 2
Step-by-step explanation:
rise / run = slope
rise = 2
run = 1
2/1 = 2
slope = 2
Answer:
2 (Answer D)
Step-by-step explanation:
The green line has a positive slope, so we can immediately reject Answers A and B.
A line with a slope of +2 rises steeply as we move from left to right, whereas a line with slope +1/2 rises much less steeply. Also, it's quite clear, visually, that the slope of the given line is greater than 1. Thus, the slope of the given line is +2 (Answer D).
Use the Distributive Property to find $(n-6)(n-4)$ .
Answer:
n^2 -10n + 24
Step-by-step explanation:
Given expression:
(n-6)(n-4)
Solution:
Apply distributive property,then simplifying using PEMDAS,we obtain
n^2 - 4n - 6n + 24n^2 -10n +24Hence,n^2 -10n -24 is the answer.
For the function f(x)=|x−7|−4, evaluate f(x+1).
Answer:
[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]
Step-by-step explanation:
To evaluate [tex]\displaystyle{f(x+1)}[/tex], substitute [tex]\displaystyle{x}[/tex] to [tex]\displaystyle{x+1}[/tex] so we should have:
[tex]\displaystyle{f(x+1) = |x+1-7|-4}[/tex]
Evaluate the expression and finally, we have:
[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]
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Choose the function that includes the given points.
(0,−2),(5,13),(−2,−8),(4,10)
The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.
What is the function about?Note that all function of (0,−2),(5,13),(−2,−8),(4,10) can be seen as all the brackets are placed in the form (X, Y), Y=P(x)
In the case above, how we arrived at the answer, you have to fill up the X's in the brackets using the X's in the Options.
Then since P(x) is the number one see in place of Y in the brackets, then that the top Right option is correct as it has −2.
Therefore, The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.
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which number is the
same distance away from -12 as 2?
Answer:
-26
Step-by-step explanation:
2 is 14 away from -12. The other number that is 14 away from -12 is -26.
-12 + x = 2
x = 14
-12 - 14 = -26
find value o x 235 degree arc
The length of the arc given in the question is; 4.1r
How to find the length of an arc?We are given;
Angle at which arc is subtended; θ = 235°
Formula for arc length subtended at an angle θ is;
Arc Length = (θ/360) * 2πr
where r is radius of circle.
Thus;
Arc Length = (235/360) * 2πr
Arc Length = 4.1r
The complete question is;
Find the value of the length of an arc that subtends an angle of 235 degrees to the circle's center.
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For the inverse variation equation p = 8/v , what is the value of V when p = 1/2?
Substituting in p = 1/2,
[tex]\frac{1}{2}=\frac{8}{v}\\ \\ v=\boxed{16}[/tex]
What is the surface area of prism below?
Answer:
Aprism = 483.246 yd2
Step-by-step explanation:
The surface area is the sum of the 2 circles areas and the rectangle area.
Ac1 = PI*r2
Ac1 = (3.14)*(11.4/2)2
Ac1 = 102.0186 yd2
Ac1 = Ac2 then
Ac2 = 102.0186 yd2
Now the perimeter of the circle is one the sides of the rectangle:
Pc = 2PI*r
Pc = 2*3.14*(11.4/2)
Pc = 35.796 yd
Now the area of the rectangle is:
Ar = 7.8yd*35.796yd
Ar = 279.2088 yd2
Then, the surface area of prism is:
Aprism = Ac1 + Ac2 + ArAprism = 102.0186yd2 + 102.0186yd2 + 279.2088yd2Aprism = 483.246 yd2A retailer purchases postcards for $0.50 and sells them for $0.70. What is the markup?
0.70 -0.50 = 0.20 cent mark up
0.20/0.50 = 0.40 = 40% markup
What is the semiannual interest payments of a 30 year bond with a face value of $50 million and a stated annual interest rate of 4 percent?
Based on the stated annual interest rate and the face value of the bond, the semiannual payments will be $1,000,000.
How can the semiannual interest payment be found?The formula to find the semiannual payment is:
= (Face value x Stated annual interest rate) / 2 semi-annual periods per year
Solving gives:
= (50,000,000 x 4%) / 2
= 2,000,000 / 2
= $1,000,000
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y = 4/5 + square root x + 0.2 - 5x
Answer:
5
Step-by-step explanation:
Triangle X Y Z is shown. The length of X Z is 12, the length of Y Z is 11, and the length of Y X is 6.
A scalene triangle has the lengths 6, 11, and 12. Keyla uses the law of cosines to find the measure of the largest angle. Complete her work and find the measure of angle Y to the nearest degree.
1. 122 = 112 + 62 − 2(11)(6)cos(Y)
2. 144 = 121 + 36 − (132)cos(Y)
3. 144 = 157 − (132)cos(Y)
4. −13 = −(132)cos(Y)
According to law of cosines if the lengths of triangle are 12,11,6 then the angle will be 114=157-132cos(Y)
Given the length of XZ is 12, length of YZ is 11 and the length of YX=6.
According to law of cosines the angle of a triangle when the length of sides are given can be written as:
[tex]c^{2} =a^{2} +b^{2} -2abcosd[/tex]
where c is the side opposite to the angle which we have to find and a and b are the rest sides.
We have to put the values of sides in the above law:
[tex]12^{2} =6^{2} +11^{2} -2*6*11cosY[/tex]
144=36+121-132 cos Y.
Hence the angle can be written as 144=36+121-132 cos Y.
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