Answers
Answer:
1) [tex](4x)(x+2)-x(3x+5)[/tex]
2A) [tex]w^2+3w[/tex]
2B) [tex]28\text{ in}^2[/tex]
Step-by-step explanation:
1)
First, let's write the expressions for the area of the entire shaded region and the white area.
The formula for the area of a rectangle is given by:
[tex]A=lw[/tex]
For the entire shaded rectangle, the length is (4x) and the width is (x+2). So, the area is:
[tex](4x)(x+2)[/tex]
For the white rectangle, the length is (3x+5) and the width is (x). So, the area is:
[tex]x(3x+5)[/tex]
The shaded area is the entire shaded rectangle minus the area of the white rectangle. Therefore, our expression would be:
[tex](4x)(x+2)-x(3x+5)[/tex]
2)
Part A)
So, we are given that the length of the rectangle is 3 inches greater than the width.
The area of a rectangle is given by:
[tex]A=lw[/tex]
So, let w be width and let l be the length.
Since the length is 3 inches greater than the width, this means that the l is (w+3).
Thus, substitute. Our expression will therefore be:
[tex]lw\\w(w+3)[/tex]
Since we want a polynomial, let's expand:
[tex]=w^2+3w[/tex]
Part B)
To find the area when the width is 4, substitute 4 for w:
[tex]w^2+3w\\=(4)^2+3(4)[/tex]
Square and multiply:
[tex]=16+12[/tex]
Add:
[tex]=28\text{ in}^2[/tex]
So the area is 28 square inches.
Related Questions
Need help fast...
Match the input values on the left with the output values on the right. y = x/2 + 1 1)3 X 2)Y 2 3)2 4 4)4.5 7 5)5.5 9
Answers
Answer:
(X,Y)
(2,2)
(4,3)
(7,4.5)
(9,5.5)
Step-by-step explanation:
To match the input values with the output, substitute each value on the right into the equation.
1) x
[tex]\displaystyle\begin{aligned} y & = \frac{(x)}{2}+1 \\ \\ & = \frac{x}{2} + 1\end{aligned}[/tex]
The equation remains the same. Hence, x maps onto y.
2) 2
[tex]\displaystyle \begin{aligned} y &= \frac{(2)}{2}+1 \\ \\ & = 2\end{aligned}[/tex]
Therefore, map 2 with 2.
3) 4
[tex]\displaystyle \begin{aligned} y& = \frac{(4)}{2}+1 \\ \\ & = 3\end{aligned}[/tex]
Therefore, match 4 with 3.
4) 7
[tex]\displaystyle \begin{aligned} y& = \frac{(7)}{2}+1 \\ \\ & = 3.5 + 1 \\ \\ & = 4.5\end{aligned}[/tex]
Therefore, match 7 with 4.5.
5) 9
[tex]\displaystyle \begin{aligned} y& = \frac{(9)}{2}+1 \\ \\ & = 4.5 + 1 \\ \\ & = 5.5\end{aligned}[/tex]
And finally, match 9 with 5.5.
Answer:
thanks for the points
Step-by-step explanation:
Which of the following is true statement?
Answers
The awncer is: B
just do it by 2
Find (a) PQ to the nearest tenth and (b) the coordinates of the midpoint of PQ. P(-6,6), Q(4,-1)
Answers
Answer:
a) PQ = 12.2
b) M (-1, 2.5)
Step-by-step explanation:
a) PQ
use pythagorean PQ = [tex]\sqrt{(6+4)^2 +(6+1)^2}[/tex]
PQ = [tex]\sqrt{149}[/tex] = 12.2
b) Midpoint
Mx = (-6 + 4)/2 = -1
My = (6 + -1)/2 = 2.5
Answer:
[tex]\Huge \boxed{\mathrm{a) \ 12.21}} \\\\\\\\ \huge \boxed{\mathrm{b) \ -1, \ \frac{5}{2}}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
(a)We can use Pythagorean theorem to solve for the length of PQ.
[tex]PQ=\sqrt{10^2 +7^2 }[/tex]
[tex]PQ=\sqrt{149} \approx 12.2066[/tex]
The length of PQ is approximately 12.21.
(b)We can find the midpoint with the midpoint formula:
[tex]\displaystyle \frac{x_1 + x_2 }{2}, \ \frac{y_1+y_2}{2}[/tex]
[tex]\displaystyle \frac{-6+4 }{2}, \ \frac{6+-1}{2}[/tex]
[tex]\displaystyle \frac{-2 }{2}, \ \frac{5}{2}[/tex]
[tex]\displaystyle -1, \ \frac{5}{2}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Find the product: -5(-3)(-3)
Answers
Answer:
-45
Step-by-step explanation:
Answer:
((−5)(−3))(−3)
=−45
hope this was helpful!
Plot the following points to create a rectangle.
Find the missing vertex.(5.3): (-5,3): (-5.-1) *
Answers
Answer:
(5, -1)
Step-by-step explanation:
The three coordinates of a triangle are given as:
(5,3), (-5,3), (-5,-1).
To find:
The missing vertex = ?
Solution:
Let us label the vertices:
A (5,3),
B(-5,3),
C(-5,-1).
Let the missing vertex be ([tex]x, y[/tex]).
Let us recall the properties of a rectangle.
The opposite sides of the rectangle are equal and parallel to each other.
Let us consider the side AB, we can see that only x coordinate is changed from A to B.
Let us consider the side BC, we can see that only y coordinate is changed from B to C.
A and B are adjacent vertices.
Similarly the opposite vertices will be C and D.
Same pattern will be followed in CD as that of AB.
x coordinate will be changed by same difference as that of AB.
Change in x coordinate from D to C = [tex]-5-x[/tex]
Change in x coordinate from A to B = [tex]-5-5 =-10[/tex]
Equating them:
[tex]-5-x=-10\\\Rightarrow x = 5[/tex]
Same pattern is followed in BC and AD.
Their change in y coordinate will be same.
[tex]-1-3=y-3\\\Rightarrow y =-1[/tex]
Missing vertex is (5, -1).
Please refer to the attached image for the rectangle.
Class: Constructing graphs Student Activity Sheet 2; Exploring "Representing data" Date Page 2 of 7 3. What do you notice about the vertical axis used in Graph A? How does this affect the way the data are displayed? FA Graph A 24 The 520 16 Benton population in 1000s 12 2002 2004 2008 2008 2010 Year.
Answers
Answer:
Explained below.
Step-by-step explanation:
The vertical axis of Graph A represents the year for which the population of Benton is recorded.
Also the axis represents every other year, i.e. 2002, 2004, 2006 and so on.
This implies that the data is recorded for every other year.
Consider the data provided:
Benton population in 1000s Year
10 2002
11 2004
12 2006
13 2008
14 2010
For every 2 years the population of Benton is increasing by 1000.
That is for every year the population of Benton is increasing by 500.
If we make the vertical axis using the years:
2001, 2002, 2003, 2004, 2005, 2006 and so on, the graph will remain same with more points to plot.
So, on altering the vertical axis the graph does not changes much.
1 .What is the median of the set of values?What is the median of the set of values? 6, 8, 10, 4, 8, 2,
2 .What is the mode of the data set below?
5, 4, 0, 1, 1, 0, 2, 2, 3, 1, 0, 4, 1, 1, 5, 2, 4
3.On spring break, Mirna went to Florida. She collected 6 seashells. The following set of data shows the weight of each seashell in ounces. 16, 17, 13, 12, 18, 20 What is the mode of this set of data? The data set shows the ages of students going to the museum. Choose the values that are equal to 12.
Answers
Answer:
1. 7
2. 1
3. no mode
Step-by-step explanation:
1. Ordering the data from least to greatest, we get:
[tex]2, 4, 6, 8, 8, 10[/tex]Since there is an even number of items, we compute the median by taking the mean of the two middlemost numbers, 6 and 8:
[tex]6+8=14[/tex][tex]14\div2=7[/tex]So the median is 7.
2. Put in order:
[tex]0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5[/tex]Count:
0 (3 times)1 (5 times)2 (3 times)3 (1 time)4 (3 times)5 (2 times)Find the number that occurs most frequently which is 1 (5 times)
3. Put in order:
[tex]12, 13, 16, 17, 18, 20[/tex]If the values in a given set all occur the same number of times, the data set has no mode because no number is any more common than any other.
In the adjoining figure, find the value of x for which
The lines l and m are parallel.
Answers
hope it helps I tried my best
The advertisement above shows the terms of a certificate of deposit (CD) at a local bank.
Suppose Robert invests $1,200 in the CD for a period of 3 years. How much interest will he earn? How much will Robert have after 3 years?
Answers
Answer:
1. The interest is $ 117.
2. The amount is $ 1,317.
Step-by-step explanation:
The following data were obtained from the question:
Principal (P) = $ 1,200
Rate (R) = 3.25%
Time (T) = 3 years
Interest (I) =..?
Amount (A) =...?
1. Determination of the interest.
Principal (P) = $ 1,200
Rate (R) = 3.25%
Time (T) = 3 years
Interest (I) =..?
I = P × R × T / 100
I = 1200 × 3.25 × 3 / 100
I = $ 117
Therefore, the interest is = $ 117
2. Determination of the amount.
This can be obtained as follow:
Interest (I) = $ 117
Principal (P) = $ 1,200
Amount (A) =?
Amount (A) = principal (P) + interest (I)
A = P + I
A = 1200 + 117
A = $ 1,317
Therefore, the amount at the end of 3 years is $ 1,317
Mr.ben has a3/4 pound of flour to use for 6 cakes . how much flour is used for each cake
Answers
Answer:
1/4 OF FLOUR IS USED FOR EACH CAKE
Step-by-step explanation:
[tex]\frac{3}{4} X 6[/tex]=4.5
[tex]\frac{4.5}{6}[/tex]=0.75
If x = 6 and y=5, find y when x = 3
Answers
Answer:
If x=6 and y=5 and we are to find y when x=3.
it will be 6=5,3=y....
5×3=6×y.
y=15/6=2.5 or 2 whole number 1/2.
This is the answer I hope it helps
For x > 3, values of the function f(x) = –(x – 3)2(x + 2) are negative. On this same interval, which statement correctly describes the values of the additive and multiplicative inverses?
Both the additive inverse and the multiplicative inverse are positive. Both the additive inverse and the multiplicative inverse are negative. The additive inverse is positive, while the multiplicative inverse is negative.
The additive inverse is negative, while the multiplicative inverse is positive.
Answers
Answer:
its c The additive inverse is positive, while the multiplicative inverse is negative.
Step-by-step explanation:
The additive inverse is positive, while the multiplicative inverse is negative.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
A relation is a function if it has only One y-value for each x-value.
The given function is f(x) = –(x – 3)²(x + 2)
Function equal to minus x minus three whole square times of x plus two.
as x>3, the values of x will be positive.
So the additive inverse is positive, while the multiplicative inverse is negative.
Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
A multiplicative inverse or reciprocal for a number x, denoted by 1/x.
Hence, the additive inverse is positive, while the multiplicative inverse is negative.
To learn more on Inequality click:
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help me please:)) ........
Answers
Answer:
True
Step-by-step explanation:
<---------->
Please help I keep getting this Wrong
Answers
Answer:
43
Step-by-step explanation:
if EF(part) = 18 and DF(the whole line) = 61
61-18 is 43. 43=DE
Please give brainliest thanks
PLZ HELP ME OUT How do I know a number is rational or irrational?
Answers
Answer: If a number is rational, it can be represented as a simple fraction, it can be written as a terminating decimal, and a repeating decimal.
If a number is irrational, it cannot be represented as a simple fraction, it cannot be written as a terminating decimal, and not as a repeating decimal. It never ends, never repeats, just like the constant pi.
Step-by-step explanation:
So if a number is rational, it can be represented as a simple fraction, it can be written as a terminating decimal, and a repeating decimal.
If a number is irrational, it cannot be represented as a simple fraction, it cannot be written as a terminating decimal, and not as a repeating decimal. It never ends, never repeats, just like the constant pi.
A random sample of 13 hotels in Boston had an average nightly room rate of $172.10 with a sample standard deviation of $23.90. The approximate standard error of the mean for this sample is ________.
Answers
Answer:
6.63Step-by-step explanation:
Standard error of the mean is expressed as shown below.
SE = S/√n where;
S is the standard deviation
n is the sample suze
Given parameters
Standard deviation = $23.90
sample size = 13
Required
Standard error of the mean for this distribution.
Substituting the given value into the formula we have;
SE = 23.90/√13
SE = 23.90/3.6056
SE = 6.6286
Hence the approximate standard error of the mean for this sample is 6.63
Simplify five subtract -1
Answers
I used a highly analytical formula to find out that the simplified formula to this complex equation is indeed:
4
Answer:
4
Step-by-step explanation: You cant simplify five, and if you do want to make 5 in to a fraction it's 5/1
5/1 simplifyed it 5
5-1=4
y=2 + x; use x= 1, and y= 2
Answers
2+1=3
So y=3
The answer is y=3
Write an equation for the nth term of the sequence 4, 12, 36, 108, .
Answers
Answer:
26,244
Step-by-step explanation:
First, find the pattern with the numbers you already have. That pattern is × 3.
Since you're already at the fourth term, just keep multiplying your product by 3 until you get to the ninth term.
108 × 3 = 324
324 × 3 = 972
972 × 3 = 2,916
2916 × 3 = 8748
8748 × 3 = 26244
Therefore, your answer is 26,244.
Question 1 (9 points)
Combine like terms.
10 - 3 - 2 + 4
After combing like terms, the simplified expression is
Blank 1:
Answers
Answer:
-19
Step-by-step explanation:
10-3-2+4
= -3 -2 +4 +10
= -10
A train cover 828 km in 9 hours what distance will it covers in 1 hour
Answers
Answer:
Step-by-step explanation:
distance covered in 9 hours = 828 km
therefore, distance covered in 1 hour = 828 / 9
= 92 km
Hope this helps
plz mark as brainliest!!!!!
Answer:
Step-by-step explanation:
Hello,
A train cover 828 km in 9 hours what distance will it covers in 1 hour
828 km => 9 hours
? km => 1 hour
= 1 x 828 / 9
= 92 km
3. Bob Baffert hos iwo thoroughbred horses in his bom that he brings out
every morning to train for the upcoming rocos. Hoppertunity is a horso
training for a 2.400 meter race and Dortmund is a horse training for an
1,800 meter race. In a given workout, Hoppertunity and Dortmund start
running at the same time. Dortmund runs twice as fast at Hoppertunity:
however, Hoppertunity starts 200 meters ahead of Dortmund. After 12.5
seconds, Dortmund catches up with Hopperlunily.
Letr represent Hoppertunity's rate, Match expressions to the boxes and
symbols to the circles to create an equation that can be used to find the
rate at which Hoppertunity runs. Not all expressions and symbols will be
used, and you may use an expression and/or symbol twice.
2r
2
12.5
15
200
400
000000000 3
Answers
Answer:
12.5r + 200 = 12.5*2r
Step-by-step explanation:
GivenRate of Hoppertunity = r
Rate of Dortmund = 2r as it is twice as fast
SolutionLet the distance Hoppertunity runs be d, then the distance Dortmund runs is d + 200 m
Since it took 12.5 seconds Dortmund to catch Hoppertunity, it can be expressed as:
d = 12.5r for Hoppertunity d + 200 =12.5*2r for DortmundBy replacing d in the second equation, we get:
12.5r + 200 = 12.5*2rSoving:
12.5r = 200r = 200/12.5r = 16 m/secHoppertunity's rate is 16 m/sec
Dortmund's rate is 32 m/sec
Find the corrdinates of the missing endpoint if e is the midpoint of DF F(2’9) e(-1,6)
Answers
Answer:
(-4,3)
Step-by-step explanation:
(x1 + 2)/2 = -1
x1 = -4
(y1 + 9)/2 = 6
y1 = 3
So, the other endpoint is (-4,3) .
The missing endpoint is D(-4,3).
What is midpoint of line segment?In geometry, the midpoint of the line segment is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Now it is given that,
Midpoint of line segment, e(x,y) = (-1,6)
one endpoint of line segment, F(x₁,y₁) = (2,9)
∴one endpoint of line segment, D(x₂,y₂)
Now since endpoint of line segment is given as,
{[(x₁+x₂ )/2] , [(y₁+y₂ )/2]}
Therefore,
x = (x₁+x₂ )/2
y = (y₁+y₂ )/2
Put the values we get,
-1 = (2+x₂)/2
-2 = (2+x₂)
⇒ x₂ = -2 -2
⇒ x₂ = -4
Again,
6 = (9+y₂ )/2
12 = 9+y₂
⇒ y₂ = 12-9
⇒ y₂ = 3
So, the endpoint is (-3,4)
Hence,The missing endpoint is D(-4,3).
To learn more about midpoint of line segment :
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Which transformations to the graph of j(x) would result in the graph of j(4x) – 27?
A) horizontal stretch by a factor of 4, and a translation 27 units right
B) horizontal stretch by a factor of 4, and a translation 27 units down
C) horizontal compression by a factor of 4, and a translation 27 units right
D)horizontal compression by a factor of , and a translation 27 units down
Answers
Answer:
Option D.
Step-by-step explanation:
It is given that, graph of j(x) transformed in the graph of j(4x) – 27.
We need to find the transformations.
Consider the new function is
[tex]f(x)=j(4x)-27[/tex] ... (1)
The translation is defined as
[tex]f(x)=j(kx+a)+b[/tex] ... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph stretched horizontally by factor of 1/k and if k>1, then the graph compressed horizontally by factor of 1/k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
k=4>1, the graph j(x) compressed horizontally by factor of 1/4.
a=0, so there is no horizontal shift.
b=-27<0, so the graph of j(x) shifts 27 units down.
So, the required transformations are horizontal compression by a factor of 1/4, and a translation 27 units down.
Therefore, the correct option is D.
Answer:
D) horizontal compression by a factor of 1/4, and a translation 27 units down
Step-by-step explanation:
got it right on edge :)
Which variable(s) in the data set are measured using a nominal scale? Environment Environment and Age Group Age Group None of the variables
Answers
Answer:
Environment
Step-by-step explanation:
Level of measurement used in statistics summarizes what statistical analysis that is possible. We have three types of level of measurement.
Nominal Scale
Ordinal Scale
Interval/ Ratio Scale
The nominal scale known as categorical or qualitative is the most basic level of measurement. Examples include numbers, colour, sex.
Ordinal are variables categorize according to hierarchy they usually have a meaningful order, but the intervals between the variables may not be equal.
In interval/ratio level of measurement, are measured and ordered. Examples are weight or size.
From the given question, it is only the environment that is measured using a nominal scale.
Age group is ordinal because it can be ordered based on hierarchy.
Help me out please thank you!
Answers
Answer:
[tex]8^{18}[/tex]
Step-by-step explanation:
[tex]8^15 / 8^-3\\=8^{15-(-3)}\\=8^{15+3}\\=8^{18}[/tex]
Refer to the table of body temperatures (degrees Fahrenheit). Is there some meaningful way in which each body temperature
recorded at 8 AM is matched with the 12 AM temperature?
1
97.0
97.6
8 AM
12 AM
Subject
3
97.6
98.0
2
98.5
97.8
4
97.7
98.4
5
98.7
98.4
Choose the correct answer below.
A. No. The 8 AM temperatures are from one individual over five days and the 12 AM temperatures are from another
individual over five days.
B. Yes. The 8 AM temperatures are all from one individual over five days and the 12 AM temperatures are from a different
individual on the same five days, so each pair is matched.
C. Yes. Each column of 8 AM and 12 AM temperatures is recorded from the same subject, so each pair is matched.
D. Yes. The 8 AM temperatures are all from one individual over five days and the 12 AM temperatures are from the same
individual on the same five days, so each pair is matched.
Answers
Answer:
C
Step-by-step explanation:
i just did that question and got it right!!
Ok remember these things im saying before you do the answer A=1 B=3 C=2 D=4 E=5 What is A-6+D-C-B=?
Answers
Answer:
the answer is 0
Answer: 1-6=5+4=9-2=7-3=4
Which best describes the association shown in the scatter plot?
A. no association
B. strong negative
C. strong positive
D. moderate positive
Answers
Do you see how the dots in the graph are close enough together so that you are able to see a line going downward? That’s how you know the association in this graph is negative.
If the y values decrease as the x values increase, you know that the line/association of points is negative.
If the y values increase as the x values increase, you know that the line/association of points is positive.
When the points are scattered all over the graph and you can’t see any kind of line or pattern, there is no association.
Hope this helped! If you have any questions about what I mentioned here, feel free to comment!
Solve the equation using the Properties of Equality.
79 + 3 = 45
Step 1 out of 4:
7a + 3 - [ ] = 45- [ ]
Answers
Answer:
7a + 3 -3 =45 - 3
7a + 0 = 42
7a = 42
7a/7 = 42/7
a = 6