Answers
As you can see in the given figure, there are two different shapes.
One is a rectangle and the other is a triangle.
Recall that the area of a rectangle is given by
[tex]A_R=L\cdot W[/tex]Where L is the length and W is the width.
As you can see from the figure,
W = 4
L = 5
So the area of the rectangle is
[tex]A_R=L\cdot W=5\cdot4=20[/tex]Recall that the area of a triangle is given by
[tex]A_T=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base of the triangle and h is the height of the triangle.
As you can see from the figure,
b = 4
h = 2
So the area of the triangle is
[tex]A_T=\frac{1}{2}\cdot b\cdot h=\frac{1}{2}\cdot4\cdot2=\frac{1}{2}\cdot8=\frac{8}{2}=4[/tex]Now the total area of the shaded region is the sum of the area of the rectangle and the area of the triangle.
[tex]A=A_R+A_T=20+4=24[/tex]Therefore, the area of the shaded region is 24
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Related Questions
Jessica made 619 cups of punch. Herpunch had two different types of juice init. If the punch had 4 cups of one type ofjuice, how many cups of the other type ofjuice did it have?
Answers
Given:
Total cups of punch made = 619
The punch contains tw different types of juice
Write this absolute value function as a piecewise function. y= 2|x|-3
Answers
A function can be written as piecewise function if it changes its behaviour ( increasing or decreasing ) about a point.
[tex]\begin{gathered} Thefunctionf\mleft(x\mright)=y=|x|changesitsbehaviourat|x|=0ie,x=0. \\ y=|x|=x,ifx<0=-x,ifx>0 \\ |x|=a\Rightarrow x=\pm a \end{gathered}[/tex]Here Here,
The given function is : y = 2|x| - 3
Here,
The function will change its behaviour when
| x | = 0
=> x = 0
Now,
If x < 0 , then ;
=> y = 2[–(x)] – 3
=> y = –2x – 3
=> y = – 2x – 3
If x ≥ 0 , then ;
=> y = 2(x) – 3
=> y = 2x – 3
=> y = 2x -3
Hence ,
y = – 2x – 3 , if x < 0
y = 2x - 3 , if x ≥ 0
[tex]f(x)=\begin{cases}-2x-3\text{ , if x < }0 \\ \\ 2x-3\text{ , if x }\ge0\end{cases}[/tex]One half of a number increased by a second number equals 5. One half of the first number decreased by the second number equals 1. Find the two numbers.
Answers
let the first no. is 'a'
second no. is 'b'
so from the statement, One half of a number increased by a second number equals 5.
[tex]\frac{a}{2}+b=5[/tex]and One half of the first number decreased by the second number equals 1.
[tex]\frac{a}{2}-b=1[/tex]add both the equations,
[tex]\begin{gathered} \frac{a}{2}+\frac{a}{2}+b-b=5+1 \\ a=6 \end{gathered}[/tex]put a= 6 in first equation
[tex]\begin{gathered} \frac{6}{2}+b=5 \\ 3+b=5 \\ b=5-3 \\ b=2 \end{gathered}[/tex]so the answer is,
a = 6 & b = 2
Write a function g(x), the translation of... that has a horizontal asymptote at y=2 and..
Answers
we have that
Vertical asymptote at x=3
so
The denominator could be (x-3)
Horizontal asymptote at y=2
so
Degree on Top is Equal to the Bottom
The numerator could be equal to 2x and the leading coefficient of the denominator is 1
therefore
[tex]g(x)=\frac{2x}{(x-3)}[/tex]1. Graph the system of equations.2. What are all the values for x for which f(x)=g(x)?
Answers
Solution:
Given the system of equations:
[tex]\begin{gathered} f(x)=-x^2+6x-4 \\ g(x)=|x-3|-1 \end{gathered}[/tex]1) The graphs of the system of equations are as shown below:
2) Values of x for which
[tex]f(x)=g(x)[/tex]From the graph of the system of equations, the points at which the graph functions cut or intersect each other, give the solution of the system of equations.
Thus, in the graph of the system of equations, the functions intersect each other at the point (1,1) and (5,1) as shown below:
Thus, the values of x for which f(x) = g(x) are
[tex]\begin{gathered} x=1,\text{ } \\ x=5 \end{gathered}[/tex]Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey, 43% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability of the following.
Answers
The probability of matching x successes on n further trials in an experiment with two possible outcomes. There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.
Given that,
The probability of matching x successes on n further trials in an experiment with two possible outcomes is known as the binomial probability (commonly called a binomial experiment).
The following formula gives it:
[tex]P=C_{n,x}p^{n}.(1-p)^{n-x}[/tex]
Where is the number of distinct combinations of x items drawn from a set of n elements, as determined by the formula below.
[tex]C_{n,x}=\frac{n!}{x!(n-x)!}[/tex]
And p is the probability that anything will happen.
Being aware that employers are monitoring phone calls is a victory in this issue.
43% of adults fear that their employers are listening to their phone calls,
p=43%=0.43
We must locate Four persons were questioned, and none expressed concern about phone call monitoring by companies.
We count four adults, n=4.
Is there a probability of success of 0? If so, then x = 0.
[tex]P=C_{n,x}p^{n}.(1-p)^{n-x}[/tex]
[tex]P=C_{4,0}(0.43)^{0}.(0.57)^{4}[/tex]
P=0.0488
Therefore, There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.
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2+2+13-2/35? please help
Answers
Answer: 16.94285714
Step-by-step explanation: 2/35 is 0.05714285714. 13+2+2 = 17.
17- 0.05714285714 is 16.94285714.
Answer the questions below.
Answers
Answer:21
Step-by-step explanation:
Find x and the measure of angle 1
Answers
The measure of angle 1 is 42° . Angles Central angles can be expressed as Central angle = (Arc length 360o)/(2r) degrees or Central angle = Arc length/r radians, where r is the radius of the circle.
What is meant by angle?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex exists as the familiar point of contact. Angle is derived from the Latin word angelus, which means "corner." An angle is formed when two line segments are joined at a single point, or when two line segments meet at a common endpoint. This common point is known as the angle's vertex, and the two line segments are known as the angle's sides or arms. Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation are the names of basic angles. An angle is a geometrical shape formed by connecting the ends of two rays.∴ The measure of angle 1 is 42°
180 - 48 - 90 = 42
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(1 2/7-3/14)/8/15trying to remember how to do this
Answers
We will write it as a fraction in ordet to solve, that is:
[tex]\frac{(1\frac{2}{7}-\frac{3}{14})}{(\frac{8}{15})}[/tex]We then operate as follows:
[tex]\frac{((\frac{7}{7}+\frac{2}{7})-\frac{3}{14})}{(\frac{8}{15})}\Rightarrow\frac{(\frac{9}{7}-\frac{3}{14})}{(\frac{8}{15})}\Rightarrow\frac{(\frac{15}{14})}{(\frac{8}{15})}\Rightarrow\frac{15\cdot15}{14\cdot8}\Rightarrow\frac{225}{112}[/tex]We have this, since 1 integer will be equal as a numerator divided by a denominator with equal values. Examples 1 = 2/2, 1 = 45/45, ...
Find Point F so that angle ABC is = to angle DEF
Answers
Answer
(5, 2)
Step-by-step explanation
Point D in triangle DEF is the equivalent to point A in ABC. Similarly, E is the equivalent to B. In consequence, F is the equivalent to C.
We can obtain points D and E by translating points A and B 6 units to the right and 4 units up.
Translation 6 units to the right and 4 units up transforms the point (x, y) into (x+6, y+4). Applying this rule to point C:
C(-1, -2) → (-1+6, -2+4) → F(5, 2)
Solve using proportions.
Andrew is on a low-carbohydrate diet. If his diet book tells him that an 8-oz serving of pineapple contains 19.2 g of carbohydrate,
how many grams of carbohydrate does a 5-oz serving contain?
Answers
Using proportions we know that a 5-oz serving contains 12g of carbohydrates.
What are proportions?A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls, and 0.25 are males (by dividing 1 by 4).
So, the carbohydrates in a 5-oz serving:
Now, calculate as follows:
8:19.2g = 5:xg8/19.2 = 5/xg8xg = 19.2(5)8xg = 96xg = 96/8x = 12gTherefore, using proportions we know that a 5-oz serving contains 12g of carbohydrates.
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qwdqdqwdwqdqdwqdqwwqdd
Answers
Answer:
qwdqdqwdwqdqdwqdqwwqdd
haha lol
Step-by-step explanation:
I need help with these please you don't need to write the explanation you could write the answers
Answers
is it 3, right?
3.- B, angle 1 and angle 8
2.- It's incomplete, Number two it's incomplete I think I need a picture of this problem.
2 .- 4, letter J
Done, bye
Been struggling on this for days, some help would be appreciated.
Answers
Answer:
-b plus or minus square root of b square - 4ac
divided by 2a
where by a is the first term
b is the second term
c is the third term
Step-by-step explanation:
a = 1
b = -5
c = 4
x = 4 & 1
explanation
What is anequation of the line that passes through the points (-4, -1) and(6, -1)?
Answers
We are given the following two points
[tex](-4,-1)\text{and }(6,-1)[/tex]We are asked to find the equation of the line that passes through these points.
Recall that the equation of the line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The slope of the line is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex][tex]\text{where}(x_1,y_1)=(-4,-1)\text{and}(x_2,y_2)=(6,-1)[/tex]Let us substitute the given values into the slope formula
[tex]m=\frac{-1-(-1)}{6-(-4)}=\frac{-1+1}{6+4}=\frac{0}{10}=0[/tex]So, the slope of the equation is 0
The equation of the line becomes
[tex]y=0x+b[/tex]Now let us find the y-intercept (b)
Choose any one point from the given two points
Let choose (-4, -1) and substitute it into the above equation
[tex]\begin{gathered} y=0x+b \\ -1=0(-4)+b \\ -1=0+b \\ b=-1 \end{gathered}[/tex]Therefore, the equation of the line in slope-intercept form is
[tex]y=-1[/tex]Note that this equation has 0 slope that is why mx part becomes 0
What is the probability that a randomly selected Shopper is a man given that he shops at Home Depot? Round the answer to the nearest hundredth of a percent.
Answers
Out of all the 500 people, how many are Men, shopping at Home Depot?
See the cell crossing "Men" row and "Home Depot" column.
it is 37
Hence, probability of shopper being a men who shops at Home Depot is:
37/500
In decimal:
0.074
In percentage:
7.40%Graph 1(90°,0)(FGHJ).Which graph below shows the preimage FGHJ and the image F'G'H''?
Answers
Given the figure FGHJ with coordinates
F(0, 5), G(-5, 1), H(5, -7) and J(6, 4)
When we rotate a figure of 90 degrees clockwise, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.
Therefore, for clockwise rotation, the coordinates of the image of FGHJ becomes
[tex]\begin{gathered} \text{ F(0, 5)}\to\text{ F'(5, 0)} \\ \text{ G(-5,}1)\to\text{ G'(1, 5)} \\ \text{ H(5, -7)}\to\text{ H'(-7, -5)} \\ \text{ J(6, 4)}\to\text{ J'(4, -6)} \end{gathered}[/tex]Note that, the blue graph represents the pre-image FGHJ and the green graph represents the image F'G'H'J'
When we rotate a figure of 90 degrees anti-clockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.
Therefore, the anti-clockwise rotation the coordinates of the image of FGHJ becomes
[tex]\begin{gathered} \text{ F(0, 5)}\to\text{ F'(-5, 0)} \\ \text{ G(-5,}1)\to\text{ G'(-1, -5)} \\ \text{ H(5, -7)}\to\text{ H'(7, 5)} \\ \text{ J(6, 4)}\to\text{ J'(-4, 6)} \end{gathered}[/tex]Note that, the blue graph represents the pre-image FGHJ and the green graph represents the image F'G'H'J'
Identify the transformation from ABC to A'B'C' .(x+4, y+8)(x-4, 4-8)(x+8, y+4)(x-8, y-4)
Answers
When you locate the coordinates of A it is (-4, 1)
Locate the coordinates of A', it is : (4, 5)
This implies, 8 was added to the x coordinate and 4 was added to the y-coordinate
Hence, the transformation is;
(x + 8, y+4)
31. Find the circumference.
a. 18.84 in
b. 36 in
c. 9 in
Answers
On a unit circle, the terminal point of theta is (1/2,square root 3/2). what is theta
Answers
Given the terminal point of Θ:
[tex](\frac{1}{2},\frac{\sqrt[]{3}}{2})[/tex]Let's find the value of Θ.
In polar coordinates, we have the points as
[tex]P=(R,\theta)[/tex]Where:
R is the radius and Θ is the angle.
We know in rectangular coordinates, we have:
x = R * cosΘ
Y = R * sinΘ
Thus, to find the value of Θ, we have:
[tex]\sin \theta=\frac{\sqrt[]{3}}{2}[/tex]Solve for Θ.
[tex]\begin{gathered} \\ \text{sin}\theta=\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Take the inverse cosine of both sides:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{\sqrt[]{3}}{2}) \\ \\ \theta=\frac{\pi}{3} \end{gathered}[/tex]ANSWER:
[tex]C.\text{ }\frac{\pi}{3}radians[/tex]Alyssa's algebra test score was 8 points lower than Jennifer's. The total of their two tests was 180. What did each girl receive?
Answers
Based on the equation, each girl received the following Algebra test scores:
Alyssa's = 86 pointsJennifer's = 94 points.What is an equation?An equation is a mathematical expression that claims that two values are equivalent.
Equations use the equation symbol (=) to illustrate the equality of two or more expressions.
Algebraically, let Alyssa's algebra test score = x
Let Jennifer's test score = x + 8
The total of their two tests = 180
x + x + 8 = 180
2x + 8 = 180
2x = 180 - 8
2x = 172
x = 86 (172/2)
Alyssa's test score = 8 points lower
Shareable points = 172 (180 - 8)
Each received 86 points from the shareable points
Alyssa's test score = 86 points
Jennifer's test score = 94 points
Check:
86 + 94 = 180
94 = 8 points greater than 86
Thus, using an equation, we can conclude that Alyssa scored 86 points on the Alegra test, which is 8 points less than Jennifer's 94 points.
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.......................
Answers
we have that
Part c)
the probability is equal to
P=0.14+0.27+0.58
P=0.99because is the sum of
x=1, x=2 and x=3
Part D
the probability is
P=0.01+0.14+0.27
P=0.42because is less than or equal 2
Rodney opens a savings account with $75 and also deposits $40 each month. Morgan opens an account with $50 and also deposits $40 each month. Will they have the same amount in their account at any point? If so, after how many months? Explain.
FAST RESPONSE ALSO EQUATION AND STEPS
Answers
Answer:
Yes, after 3 and a half months, they will both have 215$ in their account.
Step-by-step explanation:
if x is the number of months
Rodney's equation: y=40x+75
Morgan: y = 50x + 40
Equate them together:
50x+40 = 40x+75
10x=35
x=3.5
:]
Yes, after 3 and a half months, they will both have 215$ in their account.
Shay's net pay is $575.50 biweekly. If her gross annual income is$17,500, how much is deducted from each paycheck?a. $153.67b. $2,537c. $97.58d. $3,688
Answers
a. $157.67
Explanation:
>> net income (total amount without the taxes etc...)
. biweekly = $575.50
. per month = $575.50 * 2 = $1,151 (~since it happens 2 times per month)
. per year = $1,151 * 12 = $13,812
>> gross income (total amount with the taxes etc...)
. per year = $17,500
>> amount deducted (~going to taxes etc...)
. per year = $17,500 - $13,812 = $3,688
. per month = $3,688 / 12 =~ $307.33
. per paycheck = $307.33 / 2 =~ $153.67
mary has scored 78 , 60 , 82 , 94 , and 88 on her previous fice tests . What score does she need on her next test so that her average ( mean ) is 80 ?
Answers
Mary has scored 78, 60, 82, 94, and 88 on her previous fice tests.
What score does she need on her next test so that her average (mean) is 80?
Let x be the next test score
Recall that the mean is given by
[tex]mean=\frac{\text{sum of test scores}}{total\text{ numbers of tests}}[/tex]We have the following information,
mean = 80
sum of test scores = 78 + 60 + 82 + 94 + 88 + x = 402 + x
total number of tests = 6
So, let us substitute these values into the above formula
[tex]\begin{gathered} mean=\frac{\text{sum of test scores}}{total\text{ numbers of tests}} \\ 80=\frac{402+x}{6} \\ 6\times80=402+x \\ 480=402+x \\ 480-402=x \\ 78=x \\ x=78 \end{gathered}[/tex]Therefore, Mary need to score 78 on her next test so that her mean is 80
8.4m^9n^5 divided by 2.1m^3n^5
Answers
Answer: [tex]4m^{6}[/tex]
Step-by-step explanation:
[tex]\frac{8.4m^{9} n^{5} }{2.1m^{3}n^{5}}[/tex]
Dividing exponents is the same as subtracting the exponents, so
[tex]\frac{m^{9}}{m^{3}} =m^{9-3}=m^{6}[/tex]
[tex]\frac{n^{5}}{n^{5}} =n^{5-5}=n^{0}=1[/tex]
So now our equation looks like
[tex]\frac{8.4m^{6}}{2.1}[/tex]
Now we can divide the numbers
8.4/2.1 = 4
So your final answer is [tex]4m^{6}[/tex]
2y-4=3y-5 How Many solutions have?
Answers
Solve the above equation by combining like terms and isolating the variable and it should give you y = 1
Answer:
one solution
Step-by-step explanation:
solve it.
2y-4=3y-5
-y=-1
y=1
how much accumulated interest should the investor expect at the end of 10 years?
Answers
Answer:
The correct option is D
The accumulated interest after 10 years is $2,125.00
Explanation:
We have the following parameters:
Principal (P) = $2,500
Rate (R) = 8.5%
Time (T) = 10 years
To calculate the interest after 10 years, we use the formula:
[tex]A=\frac{PRT}{100}[/tex][tex]\begin{gathered} A=\frac{2500\times8.5\times10}{100} \\ \\ =2125 \end{gathered}[/tex]The interest is $2,125
1) The table represents the relationship between a length measured in meters and th same length measured in kilometers. a. Complete the table. meters kilometers 1,000 1 3,500 500 b. Write an equation for converting the number of meters to kilometers. 75 1 X
Answers
Explanation:
1)
1 kilometer is equal to 1000 meters:
1 km = 1000 m
So,
1m = 1/1,000 km
To complete the table, we can use the rule of three:
a) 1,000 m?
1m - 1/1,000 km
1,000m - x
x = 1/1000 * 1,000 = 1 km
As we can see, we only have to divide the measure in meters by 1000.
b) 3,500 m = 3,500/1,000 = 3.5 km
c) 500 m = 500/1,000 = 0.5 km
d) 75 m = 75/1,000 = 3/40 km = 0.075 km
e) 1 m = 1/1000 = 0.001 km
f) x = x/1,000 = 0.001x km
2)
The relation is:
Y = 0.001x
Where x is the measure in km and x in meter.