Answer:
20cm
Step-by-step explanation:
You divide by 12
In the following exercises, multiply the binomials. Use any method.
241. (x + 8)(x + 3)
Answer:
Hence the expression [tex]$(x+8)(x+3)=x^{2}+11 x+24$[/tex].
Step-by-step explanation:
- The given expression is (x+8)(x+3).
- We have to multiply the given expression.
- Multiply the (x+8) by 3 , multiply the (x+8) by x then add like terms.
[tex]$$\begin{array}{r}x+8 \\\underline {\times \quad x+3} \\3 x+24 \\\underline {x^{2}+8 x+24} \\x^{2}+11 x+24\end{array}$$[/tex]
Try It #2
A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was36,800. Assume this trend continues.
a. Predict the population in 2014
Answer:
The population in year 2014 is 41100.
Step-by-step explanation:
In the question, it is given that the city's population is growing linearly. In 2008 , population was 28200 and in 2012 , it is 36800 .
It is required to predict the population in 2014 .
To do so, use the population given in two years as two points on a line and find the equation of population and year. Then, find the population in year 2014 .
Step 1 of 2
The population in 2008 was 28200 and in 2012 it was, 36800 .
The equation relating population and year is,
[tex]$$\begin{aligned}&y-28200=\left(\frac{36800-28200}{2012-2008}\right)(x-2008) \\&y-28200=\left(\frac{8600}{4}\right)(x-2008) \\&y-28200=2150(x-2008)\end{aligned}$$[/tex]
Step 2 of 2
The population in year 2014 can be determined by substituting 2014 for x,
[tex]$$\begin{aligned}&y-28200=2150(2014-2008) \\&y-28200=2150(6) \\&y-28200=12900 \\&y=41100\end{aligned}$$[/tex]
Right triangle ABC is on a coordinate plane. Segment AB is on the line y=2 and is 6 units long. Point C is on the line x=-3. What is the y value of point C is the area of ABC is 9 units squared
The y-coordinate of point C may have a value of 5 or -1.
What is a right-angle triangle?If any of its inner angles is 90 degrees, the triangle is said to be right-angled. Another term for this triangle is the right triangle or 90-degree triangle.
The given data in the problem is;
A coordinate plane contains the right triangle ABC.
AB = 6 units
Surface area, A= 9 square units
The AB symbol is located on the x-axis parallel line y=2.AB will thus be perpendicular to the x-axis.
As a result, AB will be parallel to the side that contains point C. (BC or AC). As a result, the triangle's area should be justified by the length of the side or leg containing point C, which is the point's y-coordinate.
The other triangle leg's length should be,
BC = AC = 9/3
BC = AC = 3
Therefore, the point C's y-coordinate can be,
2±3 = 5,-1
Hence, the y-coordinate of point C may have a value of 5 or -1.
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On a coordinate plane, triangle T V W has points (negative 4, 8), (0, 4), and (4, 4).
What are the coordinates of the endpoints of the segment T'V'?
T'(-3, 6) and V'(0, 3)
T'(-3, 6) and V'(0, 1)
T'(-1, 2) and V'(0, 3)
T'(-1, 2) and V'(0, 1)
The coordinates of the endpoints of line segments T'V' are; T'(-1, 2) and V'(0, 1).
What are the coordinates of the endpoints of the segment T'V'?It follows from the task content that the transformation involved in the formation of the image from the pre-image is dilation by a scale factor of 1/4.
It follows therefore that, given the coordinates of T and V from the task content are; (-4, 8) and (0,4), it follows that the coordinates of the endpoints as required are; T'(-1, 2) and V'(0, 1).
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Can someone help me out with these questions ?
Answer:
See attached image
Step-by-step explanation:
What is the value of the Pearson coefficient of skewness for a distribution with a mean of 17, a median of 12, and a standard deviation of 6
The distribution value's skewness Pearson coefficient is 2.5.
Given that the median is 12 and the standard deviation is 6, the mean value is 17.
The difference between the mean and median is multiplied by three to determine Pearson's coefficient of skewness. By dividing the outcome by the standard deviation, A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.
To determine Pearson's coefficient of skewness, use the following formula:
Skewness=(3(Mean-Median))÷standard deviation
Replace the values there with,
Skewness=(3(17-12))÷6
Skewness=(3×5)÷6
Skewness=5÷2
Skewness=2.5
Therefore, for a distribution with a mean of 17, a median of 12, and a standard deviation of 6, the value of the Pearson coefficient of skewness is 2.5.
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Simplify the following expression as a
monomial:
-60b8
————
-2065
Answer:
3b^3
Step-by-step explanation:
I assume the 6 in the denominator should be b.
-60 / -20 = 3
b^8/b^5 = b^(8 - 5) = b^3
Answer: 3b^3
Please help! Having a lot of trouble with this! Thank you so much if you do!
Answer:
option B is correct.
Explanation:
[tex]\sf Equation : y-4\ =-\frac{2}{3}\left(x+3\right)[/tex]
[tex]\sf \rightarrow y\ =-\frac{2}{3}x-2 + 4[/tex]
[tex]\sf \rightarrow y\ =-\frac{2}{3}x + 2[/tex]
comparing it with slope intercept form "y = mx + b'' where m is slope and b is y-intercept.
Here slope: -2/3 and y-intercept: 2
This means the slope is decreasing and has crosses the y axis at (0, 2)
Ten six graders will each eat 1/4 of a pizza. How many whole pizza pies need to be
ordered for the ten students? Show your work
Answer:
3 whole pizzas
Step-by-step explanation:
[tex]10 \times \frac{1}{4} = \frac{10}{4} = \frac{5}{2} = 2 \frac{1}{2} [/tex]
So 3 whole pizzas will need to be ordered.
Answer:
2 and a half pies
Step-by-step explanation:
ten sixth graders eat 1/4 each, therefore 4 kids eat 1 whole pie. similarly, 8 kids eat two whole pies, since two kids are remaining they eat 2/4 of a pie.
which can also be put in as 1/2. this means they eat half a pie. and that is how altogether it is 2 and a half pies.
hope this helps!
Triangle XYZ is a right triangle with ZQ¯¯¯¯¯⊥XY¯¯¯¯¯¯ .
Drag and drop a correct answer into each box to complete the proof of the Pythagorean theorem.
(See images for details.)
The correct answer is. Proportional.
2. ce
3. Segment Addition Postulate.
By the angle-angle similarity postulate, △YXZ∼△YZQ, and △YXZ∼△ZXQ.
The corresponding sides of two similar triangles are proportional.
What is the proportional side of a similar triangle?Since similar triangles have proportional sides, therefore
[tex]\frac{a}{c}=\frac{f}{a}[/tex] and [tex]\frac{b}{c}=\frac{b}{e}[/tex]
Solving the equation for a² and b² gives
[tex]a^2=cf[/tex] and [tex]b^2=ce[/tex]
The value of a² is cf and the value b² is ce.
Adding these together gives
[tex]a^2+b^2=cf+ce[/tex]
Factoring out the common segment gives
[tex]a^2+b^2=c(f+e)[/tex]
From the given figure it is clear that
[tex]c=f+e[/tex]
(Segment Addition Postulate)
Using the Segment Addition Postulate, we get
[tex]a^2+b^2=c(c)[/tex]
On simplification, we get
[tex]a^2+b^2=c^2[/tex]
Therefore the required answers are 1. Proportional, 2. ce, 3. Segment Addition Postulate.
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Answer:
1. Angle-Angle similarity Postulate 2.Proportional 3. C
Step-by-step explanation:
By the Angle-Angle similarity Postulate, △YXZ~ △YZQ and △YXZ~ △ZXQ. Since similar Triangles have Proportional sides, a/c= f/a and b/c= e/b. Solving the equation for a² and b² gives a² = cf and b² =ce. Adding these together gives a²+b²=cf+ce. Factoring out the common segment gives a²+b²=c(f+e). Using the segment addition postulate gives a²+b²=c(c)
, which simplifies to a²+b²=c² (Look at image for proof)
.
Gasoline is pouring into a vertical cylindrical tank of radius 55 feet. When the depth of the gasoline is 66 feet, the depth is increasing at 0.30.3 ft/sec. How fast is the volume of gasoline changing at that instant
The volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
Since the tank is cylindrical in shape, its volume can be written as:
V = πr²d,
where V is its volume, r is the radius, and d is the depth.
The radius is constant, given r = 5ft.
Thus the volume can be shown as:
V = π(5)²d,
or, V = 25πd.
Differentiating this with respect to time, we get:
δV/δt = 25πδd/δt ... (i),
where δV/δt, represents the rate of change of volume with respect to time, and δd/δt represents the rate of change of depth with respect to time.
Now, we are given that when the depth increases at 0.3 ft./sec when the depth of the gasoline is 6 feet.
Thus, we can take δd/δt = 0.3 ft./sec, in (i) to get:
δV/δt = 25πδd/δt = 25π(0.3) ft.³/sec = 23.56 ft.³/sec.
Thus, the volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
The question written correctly is:
"Gasoline is pouring into a vertical cylindrical tank of radius 5 feet. When the depth of the gasoline is 6 feet, the depth is increasing at 0.3 ft./sec. How fast is the volume of gasoline changing at that instant?"
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Which statement is true about function f, which is shown in the graph? The graph shows a cubic function. The curve is drawn using the points (minus 1, 8), (minus 1, minus 3.5), (0, 0), (1, 3.5), and (1, minus 8) which intercepts (1, 0), and (minus 1, 0) A. Function f is odd. B. Function f is even. C. Function f is neither even nor odd. D. Function f is both even and odd.
We conclude that f(x) is odd, so the correct option is A.
Which statement is true?
f(x) is an odd function if:
f(-x) = -f(x).
f(x) is an even function if:
f(x) = f(-x).
In this case, we know that the function f(x) has the points:
{ (-2, 8), (-1, -3.5), (0, 0), (1, 3.5), (2, -8)}
As you can see:
f(-2) = 8
f(2) = -8
Then:
f(-2) = -f(2)
Also:
f(-1) = -3.5
f(1) = 3.5
Then:
f(-1) = -f(1).
So we conclude that this is an odd function, and the correct option is A.
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Transportation problem is an example of a category of problems that can be modeled as __________ problems. a. Nonlinear. b. Simple. c. Network flow. d. Complex.
The transportation problem is an example of a category of problems that can be modeled as c. Network flow problems.
A transportation problem is a special kind of alignment that aims to calculate the cost of transporting a particular product from a set of sources or origins (factories, manufacturing facilities, etc.) to a set of destinations (warehouses, businesses, etc.). It's a planning issue. Minimize.
The transport problem is one of the models of linear programming problems. Its main purpose is to handle situations where goods are shipped from multiple sources to different destinations and to minimize overall shipping costs.
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If
sin
x
=
2
9
, x in quadrant I, then find (without finding x) :
sin
(
2
x
)
=
cos
(
2
x
)
=
Incorrect
tan
(
2
x
)
=
Answer:
Step-by-step explanation:
Quick algebra 1 question for 25 points!
Only answer if you know the answer, Tysm! :)
The equation regarding the algebraic information that represents the total earnings is y = 22x + 125.
How to calculate the value?From the information that's given, it can be seen that the expression is:
y = 22x + 125
She earned $555 after working for 15 hours. Therefore, the equation to represent the total earnings will be:
y = 22x + 125.
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Refer to Table 24-1. If Year 1 is the base year, then the inflation rate in Year 2 was
a. 2.10 percent.
b. 1.40 percent.
c. –3.90 percent.
d. –1.40 percent.
Answer:
c
Step-by-step explanation:
If Year 1 is the base year, then the inflation rate in Year 2 was 2.10 percent. The correct option is a.
What is inflation rate?Inflation rate is the rate at which the general level of prices for goods and services in an economy is increasing over a certain period of time, typically one year.
To calculate the inflation rate, we need to compare the price level in Year 2 to the price level in Year 1.
Using the data from Table 24-1, we can see that the price index in Year 2 is 102.1 and the price index in Year 1 is 100.0.
The inflation rate can be calculated using the following formula:
Inflation rate = (Price index in Year 2 - Price index in Year 1) / Price index in Year 1 * 100%
Plugging in the values, we get:
Inflation rate = (102.1 - 100.0) / 100.0 * 100%
Inflation rate = 2.1%
Therefore, the correct answer is (a) 2.10 percent.
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which least number can be subtracted from 82789 to make it divisible by 11
Answer: 3
Step-by-step explanation:
test the numbers
Answer:
3
Step-by-step explanation:
first you divide the given number with 11 the remainder you get substract in order to get 0
The time it takes a person to wash the dishes is uniformly distributed between 6 minutes and 14 minutes. What is the probability that a randomly selected event of washing dishes will take a person between 8 and 13 minutes? Round your answer accurate to two decimal places.
The probability that a randomly selected event of washing dishes will take a person between 8 and 13 minutes is 66.66%.
It is given that the time it takes a person to wash the dishes is uniformly distributed between 6 minutes and 14 minutes.
That means that the number of possible minutes it will take will be 6, 7, 8 ,9, 10, 11, 12, 13, 14 That's a total of 9 separate minutes or intervals.
If it takes between 8 and 13 minutes, that is only 8 ,9, 10, 11, 12, 13 that's only 6 separate minutes or intervals.
The probability of it taking between 8 and 13 minutes is therefore [tex]\frac{6}{9} = \frac{2}{3}[/tex]
Or 0.6666666667 x 100 is 66.66%.
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which of the following is a fifth root of the given complex number?
Answer: D
This result is true by De Moivre's theorem.
Can someone help please
Triangle not drawn to scale
Given: mA = 40°, m▲ B = 88°, and b = 23. Then a = to the nearest hundredth.
Answer: 14.79
Step-by-step explanation:
[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]
HELP HELP HELP
Quick algebra 1 question
What is the slope of this graph?
Hello and Good Morning/Afternoon:
To find the slope of something:
⇒ let's consider what the formula of the slope needs
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
⇒ needs any two points on the line (x₁,y₁) and (x₂,y₂)
Let's get the required information:
(x₁,y₁) ==> (0,0)(x₂,y₂) ==> (5,2)Let's solve:
[tex]Slope = \frac{2-0}{5-0} =\frac{2}{5}[/tex]
Answer: 2/5
Hope that helps!
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Find the surface area of the right cone. round your answer to the nearest hundredth. a right cone is drawn. the length of radius of the base is 8 inches and the slant height is 16 inches.
The surface area of the right cone is 602.88 inch².
What is cone ?The surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex). The path, to be definite, is directed by some closed plane curve (the directrix), along which the line always glides.Given,
length of radius of the base is = 8 inches
the slant height is =16 inches.
Now using formula ,
the surface area of right circular cone is a right circular cone = πr(r + l)
So, r = 8 inches l = 16 inches
put values in the formula ,
surface area of right circular cone = 3.14 × 8 ( 8 + 16 )
= 3.14 × 8 × 24
= 602.88 inch²
Therefore, the surface area of the right cone is 602.88 inch².
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Find the value of x. in this triangle lol
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The graph above shows a line of best fit for data collected on the output of factories in relation to the number of production hours. what is the equation of the line of best fit?
The equation of the line of best fit is y = 50x/3
How to determine the equation?The missing graph is added as an attachment
From the graph, we have the following points
(x, y) = (0,0) and (3,50)
The equation is then calculated as:
y = (y2 - y1)/(x2 - x1) * (x - x1) + y1
This gives
y = (50 -0)/(3- 0) * (x - 0) + 0
Evaluate
y = 50x/3
Hence, the equation of the line of best fit is y = 50x/3
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Rachel is now 11 years old. Five years ago, Lily was twice as old as Rachel. How old is Lily now?
Lily present age now 17 years old.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Here, Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.
Thus, unit price of something is price of 1 thing.
Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.
We have been given that Rachel is now 11 years old. Five years ago, Lily was twice as old as Rachel.
We want to find the present age of lily.
Since five years ago rachel was 6, we know that Lily was twice as old as Rachel makes lily 12 years old.
For five years ago so 12 + 5 = 17.
Therefore, Lily is now 17 years old.
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According to the table, which ordered pair is a local maximum of the function, f(x)?
(0, 64)
(3, –35)
(5, 189)
(2, 0)
The local maximum of the function f(x) is (0,64)
Given,
From the table we can notice that when ₋2<x<0, f(x) is increasing
And in case of when 0<x<3, f(x) is decreasing progressively.
we know that a local maximum is present on the graph of the function y=f(x) at the location where the graph shifts from increasing to decreasing. The tangent has zero slope at this location. And at the point when the graph shifts from declining to increasing, a local minimum is present.
Therefore, a local maximum also known as relative maximum, is a maximum that exists in a certain area and is not necessarily(but could be) a global maximum.
Hence f(0) is a local maximum of the ordered pair (0,64)
Hence we get the local maximum pair as (0,64)
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Answer:
it is 0,64
which is C for me but looks like A for you
34. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
34. Passes through (-1, 4) and (5, 2)
Answer:
The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as [tex]$y=\frac{1}{3} x-\frac{13}{3}$[/tex].
Step-by-step explanation:
A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).
It is asked to find the linear equation which satisfies the given condition.
Step 1 of 3
Determine the slope of the line.
The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 2&4 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$5 \&-1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$[/tex]
Step 2 of 3
Write the linear equation in point-slope form.
A linear equation in point slope form is given as,
[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
Substitute [tex]$-\frac{1}{3}$[/tex] for m,-1 for [tex]$x_{1}$[/tex], and 4 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,
[tex]y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$[/tex]
Step 3 of 3
Simplify the equation further.
Add 4 on each side of the equation [tex]$y-4=\frac{1}{3} x-\frac{1}{3}$[/tex], and simplify as follows,
[tex]y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$[/tex]
This is the required linear equation.
The product of two consecutive positive even integers is 8. Find the value of the greater integer.
Answer:
4
Step-by-step explanation:
n and (n + 2)
Therefore,
n × (n + 2) = 8
n^2 + 2n = 8
n^2 +2n - 8 = 0
n^2 + 4n - 2n -8 = 0
n (n + 4) -2 ( n + 4)
(n - 2 ) ( n + 4)
Therefore,
n = -4 or + 2
But since n can't be negative, n = 2
substituting
(n+2) = 2+2 = 4
Therefore, the value of the greater integer is 4
One pitcher of smoothies uses 3 cups of berries. How many pitchers of smoothies can you make with 10 cups of berries?
Click to select the two representations of the solution.
A person invested $690 in an account growing at a rate allowing the money to double
every 7 years. How much money would be in the account after 3 years, to the nearest
dollar?