Answer: \frac{2x^3-3x^2+5}{x-4}
Step-by-step explanation:
What is the average of the following equations? X + 3, 2x - 4, 3x - 6, 2x - 5, and 2x.
Please show your work. I will give you 50 points. I have 6 of these questions I need help with very badly. Thank you!!
The average of the given 5 equations is; x' = 2x - 1.6
What is the average of the equations?In mathematics, average is also called the mean and it has the formula as;
x' = ∑fx/∑f
Now, we are given the equations as;
x + 3, 2x - 4, 3x - 6, 2x - 5, and 2x.
Thus;
∑fx = x + 3 + 2x - 4 + 3x - 6 + 2x - 5 + 2x
∑fx = 10x - 8
The number of expressions given is 5 and so ∑f = 5
Thus;
x' = (10x - 8)/5
x' = 2x - 1.6
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There are three roses and eight daisies in a vase what is the ratio of all flowers in the vase to daisies???what is the ratio of roses to all flowers in the vase ???
Answer:
11:8
3:11
Step-by-step explanation:
The total is 11 (3+ 8)
helpp this us due by 12 its 11:49 rnn
The values of the segments formed by the median lines in the triangles are;
1. KG = 22
2. [tex]\overline{JE}[/tex] = 19.5
3. FL = 11
9) CI = 4
10) XK = 4
14) x = 3
What is a median of a triangle?A median line of a triangle is a line drawn from a vertex of the triangle to the the middle of the of the opposite side, thereby bisecting the opposite side into two segments of the same length.
The median lines are; [tex]\overline{JE}[/tex], [tex]\overline{KF}[/tex], and [tex]\overline{LD}[/tex]
1. The length of [tex]\overline{GF}[/tex] = 11
The properties of a median line indicates;
[tex]\overline{GF}[/tex] = (1/3)·[tex]\overline{KF}[/tex]
Therefore;
11 = (1/3)·[tex]\overline{KF}[/tex]
[tex]\overline{KF}[/tex] = 3 × 11 = 33
[tex]\overline{KG}[/tex] = (2/3)×[tex]\overline{KF}[/tex]
Therefore;
[tex]\overline{KG}[/tex] = (2/3) × 33 = 22
[tex]\overline{KG}[/tex] = 22
2. [tex]\overline{JG}[/tex] = 13
[tex]\overline{JG}[/tex] = (2/3) × The median line [tex]\overline{JE}[/tex]
Therefore;
[tex]\overline{JG}[/tex] = (2/3) × [tex]\overline{JE}[/tex]
[tex]\overline{JE}[/tex] = (3/2) × [tex]\overline{JG}[/tex]
[tex]\overline{JE}[/tex] = (3/2) × 13 = 19.5
3. JL = 22
[tex]\overline{KF}[/tex] is a median line, therefore, the point F is the midpoint JL
JF = FL
JL = JF + FL by segment addition postulate
JL = FL + FL = 2·FL (substitution property of equality)
JL = 22 = 2·FL
FL = 22 ÷ 2 = 11
9) CS = 6
Where CS is a median line of the triangle ΔABC, then;
CI = (2/3) × CS
CI = (2/3) × 6 = 4
10) UX = 8
Where UX is a median of the triangle ΔTUX, we get;
XK = (1/3) × UK
UX = (2/3) × UK
UK = (3/2) × UX = (3/2) × 8 = 12
XK = (1/3) × 12 = 4XK = 4
14) KL = 7·x + 1
LE = 2·x + 5
The properties of median line indicates that, KL = (2/3)·KE
LE = (1/3)·KE
Therefore;
KL = 2 × LE
7·x + 1 = 2 × (2·x + 5) = 4·x + 10
7·x + 1 = 4·x + 10
7·x - 4·x = 10 - 1 = 9
3·x = 9
x = 9 ÷ 3 = 3
x = 3
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Water i draining from a conical tank at the rate of 2 m3
/min. The tank i 16 meter high
and the top radiu i 4 meter. How fat i the water level falling when the water’ level
i 12 meter high?
By using the concept of rate of change, it is obtained that
Water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute
What is rate of change?
Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.
Here the concept of rate of change has been used
Let the radius of cone at any point be r m and height be h m
Volume of cone = [tex]\frac{1}{3}\pi\times r^2\times h[/tex]
Now,
By the concept of similarity,
[tex]\frac{r}{h} = \frac{4}{16}\\\\\frac{r}{h} = \frac{1}{4}\\\\r = \frac{1}{4}h[/tex]
Volume of cone (V) =
[tex]\frac{1}{3}\times \pi \times (\frac{1}{4} h)^2\timesh\\\\\frac{1}{48}\times \pi \times h^3\\[/tex]
[tex]\frac{dV}{dt} = \frac{1}{48} \times \pi \times 3h^2\times \frac{dh}{dt}\\\\\frac{dV}{dt} = \frac{1}{16} \times \pi \times h^2\times \frac{dh}{dt}\\\\[/tex]
Now,
[tex]\frac{dV}{dt} = -2,\ h = 12[/tex]
So,
[tex]-2 = \frac{1}{16}\times \pi \times (12)^2 \times \frac{dh}{dt}\\\\\frac{dh}{dt} = -\frac{2 \times 16}{\pi \times 12 \times 12}\\\\\frac{dh}{dt} =- \frac{2}{9\pi}[/tex]
So water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute
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Carley cycled 72 miles in 3 hours. His cousin Catie drove 132
miles in 2 hours. Assume both cousins were driving at constant
speeds. How much faster was the faster person traveling?
Answer:
Speed at which Carley was cycling at
= 72 miles ÷ 3 hours
= 24 miles/hour
Speed at which Catie was driving at
= 132 miles ÷ 2 hours
= 66 miles/hour
66 miles/hour - 24 miles/hour = 42 miles/hour
∴ The faster person, Catie, was travelling 42 miles/hour faster than Carley, the slower person.
Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
4. x-int: (5,0) , (12, 0)
P (7, -4)
Answer:
y = 0.4(x - 5)(x - 12)Step-by-step explanation:
Givenx- intercepts (5, 0) and (12, 0),Point P (7, - 4).SolutionThe given translates as:
p = 5, q = 12, x = 7, y = - 4Use given x - intercepts to get the equation:
y = a(x - 5)(x - 12)Use the coordinates of P to find the value of a:
- 4 = a(7 - 5)(7 - 12)- 4 = a*2*(-5)- 4 = - 10aa = -4 / - 10a = 0.4The equation of this parabola is:
y = 0.4(x - 5)(x - 12)Answer:
[tex]\textsf{Intercept form}: \quad y=\dfrac{2}{5}(x-5)(x-12)[/tex]
[tex]\textsf{Standard form}: \quad y=\dfrac{2}{5}x^2-\dfrac{34}{5}x+24[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (5, 0) and (12, 0) then:
p = 5q = 12Substitute the values of p and q into the formula:
[tex]\implies y=a(x-5)(x-12)[/tex]
To find a, substitute the given point on the curve P (7, -4) into the equation:
[tex]\implies -4=a(7-5)(7-12)[/tex]
[tex]\implies -4=a(2)(-5)[/tex]
[tex]\implies -4=-10a[/tex]
[tex]\implies a=\dfrac{-4}{-10}[/tex]
[tex]\implies a=\dfrac{2}{5}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=\dfrac{2}{5}(x-5)(x-12)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=\dfrac{2}{5}(x^2-17x+60)[/tex]
[tex]\implies y=\dfrac{2}{5}x^2-\dfrac{34}{5}x+24[/tex]
evelyn is trying to pick out an outfit for the first day of school. she can choose from 2 pairs of pants, 2 t-shirts, and 8 pair of shoes. how many different outfits can evelyn make?
There are 32 outfits that Evelyn can make.
This is basic combination.
Evelyn has 2 shirts each shirt can be worn with each of the 2 pair of pants.
So, there are 4 ways to wear them.
she also has 8 pairs of shoes and each pair can be worn with each of the 4 outfits.
total number of outfits that she can make = 8*4
=32 outfits
Evelyn can make 32 different outfits.
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Xylem and Phloem in plants transport water and nutrients throughout the plant similar to ______ humans.
O hormones
O blood vessels
O bones
O neurons
Answer:
blood vessels
Step-by-step explanation:
Blood vessels carry nutrients throughout your body
Answer:
Step-by-step explanation:
the answer is blood vessels.
Xylem and phloem constitute the vascular bundle. Xylem distribute and store water. Phloem is responsible for transporting sugars, proteins, and other organic material. Similarly blood vessels in humans perform the function of delivering blood that contains gases, nutrients, waste, cells and hormones throughout the body.
Gwen measured a kitchen and made a scale drawing. The scale she used was
11 inches : 5 feet. If a countertop in the kitchen is 22 inches long in the drawing, how long is
the actual counter?
As per the given ratio, the length of the actual counter is 120 feet.
Ratio:
Basically, the ratio refers an ordered pair of numbers a and b, written a / b where b does not equal 0. And a proportion is an equation in which two ratios are set equal to each other.
Given,
Gwen measured a kitchen and made a scale drawing. The scale she used was 11 inches : 5 feet.
Here we need to find the length of the actual counter if a countertop in the kitchen is 22 inches long in the drawing.
While looking into the given question, we have identified the following things,
Scale drawing ratio = 11 inches : 5 feet
And the length of the drawing = 22 inches.
When we convert the inches into feet,
Then we get,
=> 11 inches = 11/12 feet.
So the actual length can be calculated as,
=>22 : 11/12 : 5
=> 22 x 12/11 x 5
=> 2 x 12 x 5
=> 120
Therefore, the length of the actual counter is 120 feet.
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Given 49−−√=7, which of the following statements is true?
The correct statement regarding the sentence square root of 49 = 7 is given as follows:
C. 7 is the length of the side of a square whose area is 49.
How to obtain the area and the perimeter of a square?
Considering a square of side length s, we have that the area and the perimeter of the square are given as follows:
In the context of this problem, the expression is given as follows:
square root of 49 = 7.
For a square with area of 49 units squared, the side length is obtained as follows:
s² = 49
s = square root of 49
s = 7.
Which means that option C is the correct option.
Missing InformationThe problem is given by the image shown at the end of the answer.
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If a rectangle
has a width of 3w² and a
length of 2w5, write an expression to
represent the area of the rectangle.
The expression to represent the area of the rectangle is A = 6w⁷
Area of the rectangle:The rectangle is a four-sided polygon with an internal angle of 90° at the corner of every side. The opposite sides of the rectangle are equal.
The formula for the area of the rectangle is given below
Area = Length × width
Here we have
Width of the rectangle = 3w² and
Length of the rectangle = 2w⁵
As we know the area of the rectangle = Length × width
Area of the rectangle, A = 3w² × 2w⁵
=> A = 6w²×w⁵
=> A = 6w²⁺⁵
=> A = 6w⁷
Therefore,
The expression to represent the area of the rectangle is A = 6 w⁷
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McKenzie found a correlation coefficient on a set data to be -0.20 which term describes the correlation ?
weak positive
strong negative
strong positive
weak negative
Weak positive term describes the correlation .
What does a weak positive indicate?
Negative correlation does not necessarily indicate a weak correlation between two variables. Although both variables have a tendency to rise in response to one another, a weak positive correlation suggests that the relationship between the two is not very strong.A weak positive graph is what?
Dots are used to indicate values for various numerical variables in a scatter plot, sometimes referred to as a scatter graph or scatter chart. One can see that there is a slight increase in the value of Y as the value of X increases, demonstrating a weak positive correlation.Learn more about weak positive
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GEOMETRY PROOFS!!!!!
From given information,
6] the reason for line 2 of the proof: Given
7] the statement for line 4 of the proof: BL ≅ LK
8] the reason for line 4 of the proof: Definition of midpoint
9] the statement of line 5 of the proof: Δ BWL ≅ ΔKTL
10] the reason for line 5 of the proof: SAS postulate of triangle congruence
In this question, we have been given two triangles BWL and KTL.
We need to complete the proof.
A point L is the midpoint of line segment BK
Also, LW ≅ LT,
∠WLB ≅ ∠TLK
Consider,
Statement Reason
1) LW ≅ LT Given
2) ∠WLB ≅ ∠TLK Given
3) L is the midpoint of BK Given
4) BL ≅ LK Definition of midpoint
5) Δ BWL ≅ ΔKTL SAS postulate of triangle congruence
Therefore, from given information,
6] the reason for line 2 of the proof: Given
7] the statement for line 4 of the proof: BL ≅ LK
8] the reason for line 4 of the proof: Definition of midpoint
9] the statement of line 5 of the proof: Δ BWL ≅ ΔKTL
10] the reason for line 5 of the proof: SAS postulate of triangle congruence
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A collector of hand-woven rugs has an oval rug that is 42 years old and a circular rug that is 14 years old. How many years ago was the oval rug five times as old as the circular rug was then?
i need an equation plsss help.
Answer:
7
Step-by-step explanation:
Suppose P= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and V= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. What is
POV?
The P∩V is {2,4,6,8}.
From the question, we have
P= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
V= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
P∩V = {2,4,6,8}
Intersection of Sets:
The set that contains all the elements that are shared by two given sets is the intersection of the two sets. The intersection of sets is represented by the symbol "∩". The intersection A∩ B (also written as A intersection B) lists all the elements that are shared by any two sets A and B that are present in both sets.
For instance, if Set A = 1, 2, 3, 4, and Set B = 3, 4, 6, then A ∩B = {3,4}.
Complete question:
Suppose P = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and V = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. what is P ∩ V ?
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Laura made $342 for 18 hours of work.
At the same rate, how much would she make for 8 hours of work?
Which of the following numbers is a composite number? A. 31 B. 47 C. 43 D. 33
Point K is located at (-5,-5) on the coordinate plane. Point K is reflected over the y-axis to create point K. What ordered pair describes the location of K'?
The reflection of the point K across the y-axis is (5, -5)
How to determine the image of the reflection?From the question, the point is given as:
Point K = (-5, -5)
Rewrite this point as
K = (-5, -5)
The transformation is given as
Reflection across the y-axis
Mathematically, this transformation can be represented as
(x, y) = (-x, y)
So, we have
K' = (5, -5)
Hence, the image of the reflection is (5, -5)
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Answer:
(5, -5)
Step-by-step explanation:
The other guy is 100% right!
Gretta has a savings account with $6,500 in it that earns 9.5% simple interest per year. How much interest, to the nearest cent, will Gretta earn in 1 year? Give your answer in dollars.
Answer: $617.50
Step-by-step explanation:
9.5% of 6500 = 9.5*6500/100=9.5*65=617.5
So the interest is $617.5 or $617.50
Hope this helped. If you have any questions or clarifications please ask.
Thanks and please rate!
Answer:
Gretta will earn $617.50 interest
A = $7,117.50
Equation:
A = P(1 + rt)
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 9.5%/100 = 0.095 per year.
Solving our equation:
A = 6500(1 + (0.095 × 1)) = 7117.5
A = $7,117.50
The total amount accrued, principal plus interest, from simple interest on a principal of $6,500.00 at a rate of 9.5% per year for 1 years is $7,117.50.
If a farmer wants his irrigation system to cover an area of 2 square miles, and his
sprinkler rotates through 50 degrees, what is the diameter of his circular field to the
nearest hundredth of a mile?
The diameter of his circular field is 18miles
What is sprinkler?
A sprinkler irrigation system is a tool used to irrigate (water) lawns, gardens, golf courses, and other areas. They are also utilised for cooling and dust control in the air. Sprinkler irrigation is a technique for applying water in a way that is similar to rainfall: it is controlled. Pumps, valves, pipes, as well as sprinklers are just a few of the possible components of the network used to distribute the water. Sprinklers for irrigation can be used in residential, commercial, and agricultural settings. Both sandy soil and uneven terrain with insufficient water supply can benefit from it. The rotating nozzle-topped perpendicular pipes are linked to the main pipeline at regular intervals. Water leaks from the rotating nozzles when it is pressurised and forced through the main pipe.
The irrigation sprinkler in this instance is angled.
θ = 50 = 50 π/ 180 rad.
It mists a sphere-shaped area.
A = 2/(2 miles).
If the sprinkler's length is
miles, L. It will be watered within the circle's radius.
Hence,
L^2 = A when divided by two in radians.
⇒ L = √ (2 A / θ)
= √ [(2 x 2 x 180) /40 π]
≈ 18 miles
Hence, The diameter of his circular field is 18 miles
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what is the equation of the line perpendicular to y=2x+5
Answer:
y = 1/2x + 4Step-by-step explanation:
If the line is perpendicular to y = -2x + 5 then the new line has a slope of 1/2.
So solve for b: using y = mx + b
2 = 1/2(-4) + b
2 = -2 + b
4 = b
Put it all together
y = 1/2x + 4
In the figure, triangle LMN is similar to triangle PQR. Whats the length of PQ?
Given m and n are parallel lines. 1 is a transversal.
Which of the following angles are congruent to <5? Select ALL that apply
Answer: Angles 1, 3, 7
Step-by-step explanation:
∠7 is vertical to ∠5
∠1 is corresponding to ∠5
∠3 is opposite interior angle of ∠5, it is also vertical to ∠1
What is the quotient of (-168) + (-14) + (-3)? Pls help me
A: -36
B: -4
C: 4
D: 36
Answer: B: -4
Step-by-step explanation: -168/-14 = 12
12/-3 = -4
Reasoning Joanne cannot decide which of two washing machines to buy. The selling price of each is $720. The first is
marked down by 50%. The second is marked down by 30% with an additional 20% off. Find the sale price of each
washing machine. Use pencil and paper. Explain why Joanne should buy the first washing machine rather than the
second if the machines are the same except for the selling price.
The sale price of the second washing machine is $
(Round to the nearest dollar as needed.)
CT
Answer:
Step-by-step explanation:
First Selling price is $360, after mark down.
The second's selling price is $403, after both mark downs
Joanne should buy the first, because of the selling price after mark downs.
which of the following is a probability sample?
a. Quota sample
b. Convenience sample
c. Cluster sample
d. Judgment sample
e. Snowball sample
The correct option is option (C) .
Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .
Sampling :
Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.
Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.
There are two main types of sampling:
i) probability sampling
ii) Non-probability sampling
A) probability sampling:
It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.
The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.
Probability Samples:
1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.
2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.
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What is an equation of the line that passes through the points (-1, 3) and (-2,-1)?
Answer: y = 4x + 7
Step-by-step explanation:
It's a line, so the formula is y = mx + b.
(x₁, y₁) = (-1, 3)(x₂, y₂) = (-2, -1)Slope(m): [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}} =\frac{-1-3}{-2-(-1)} =\frac{-4}{-1} =4[/tex]
Y-intercept(b):
[tex]y=4x+b\\3=4(-1)+b\\3=-4+b\\b=3+4=7\\[/tex]
Therefore, y = mx + b = 4x + 7.
the length of the longer leg of a right triangle is 25 cm more than seven times the length of the shorter leg. the length of the hypotenuse is 26 cm more than seven times the length of the shorter leg. find the side lengths of the triangle.
The side lengths of the triangle is 17, 144, 145
Let x be the length of the short leg
The length of the longer leg of a right triangle is 25 cm more than seven times the length of the shorter leg
The length of the long leg is 25 + 7x
The length of the hypotenuse is 26 cm more than seven times the length of the shorter leg.
The length of the hypotenuse is 26 + 7x
(26 + 7x)² = (25 + 7x)² + x²
676 + 364x + 49x² = 625 + 350x + 49x² + x²
0 = x² -14x - 51
0 = (x - 17)(x + 3)
{-3, 17}
Length cannot be negative.
The length of the long leg is 25 + 7x = 25 + 7(17) = 144
The length of the hypotenuse is 26 + 7x = 26 + 7(17) = 145
Therefore, the side lengths of the triangle is 17, 144, 145
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helppppppppppp plssssssssssssssssssssssssssss
Answer:
answer is 5
Step-by-step explanation:
A _____________ t-test evaluates data from dependent samples in which the two treatments are applied to the same individual.
A Paired t-test evaluates data from dependent samples in which the two treatments are applied to the same individual.
T-test is a statistical statistics mainly use when population variance is unknown and sample size is small.
In Paired t-test , we compare means of two dependent samples . It gives hypothesis examination on difference between of mean.
It uses same items or people in both sample that's why they are also known as dependent t-test
Paired t-test also increases the statistical power of our analysis.
Formula of paired t-test :
[tex]t = \frac{m}{s/\sqrt{n} }[/tex] with (n-1) degree
where , m is mean difference
s is standard deviation
n is sample size
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