The sum of the interior angles of a triangle must add 180°.
C : 20 + 80 + 100 = 200 NO
D : 35+35+105 = 175 NO
A : 10+ 10+160 = 180 Yes
B : 15 +75 + 90 = 180 Yes
E :60+60+60 = 180 Yes
The length of the smaller rectangle is 12 inches and the width is x inches. The length of the larger rectangle is 20 inches and the width is 15 inches. What is the area of the smaller rectangle?
The area of the smaller rectangle is 108 inches².
What is the Area of a Rectangle?The area of a rectangle is calculated to determine the area occupied by the rectangle within its boundary. A rectangle's area (A) is the product of its length 'a' and width or breadth 'b'. As a result, the Area of the Rectangle = (a × b) square units.
Given the dimensions of the smaller rectangle:
Length = 12 inches
Width = x inches
Given the dimensions of the larger rectangle:
Length = 20 inches
Width = 15 inches
To find the value of x we use proportion,
[tex]\frac{12}{x} = \frac{20}{15}[/tex]
Cross-multiplying, we get
12 × 15 = 20x
x = 180/20 = 9
Hence, the width of the smaller rectangle is 9 inches.
Area of the smaller rectangle = length × width
= 12 × 9
= 108 inches²
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PLEASE HELP WILL MARK BRANLIEST!!!
What is the equation of a line that is parallel to y = x + 2 and passes through the point (5,7)?
Enter your answer with no spaces.
Answer:
See below
Step-by-step explanation:
Slope of given line is 1 y = (1) x + 2
parallel line has same slope
so it will start to look like this y = (1) x + b
sub in the point 5,7 to find b = 2
final answer y=x+2
however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation
Explanation:
For the given equation
[tex]50^x=17[/tex]For Erika to resolve the question
Step 1: We will take the logarithm of both sides
[tex]\log (50^x)=\log (17)[/tex]Step 2: Simplify the expression
Thus
[tex]x\log 50=\log 17[/tex]Step 3: Solve for x
[tex]x=\frac{\log 17}{\log 50}[/tex][tex]x=0.724[/tex]
The admission fee to an amusement park is $18. It costs an additional "c" dollars to rent a locker to hold your belongings. The total cost for 9 people to
enter the amusement park and each rent a locker is $252. How much does it cost for one person to rent a
Where ya got 12 from ?
Answer:
12 is the number that comes after 11 and before 13. 12 represents the number between 11 and 13. 12 is a composite number.
Step-by-step explanation:
12 is the number that comes after 11 and before 13.
12 represents the number between 11 and 13. 12 is a composite number.
A print shop borrows $4200 from a credit union for 178 days. The credit union charges simple interest at an annual rate of 6.5% for this loan. Assume each day is 1/365 of a year.
round your final answers to the nearest cent.
A) Find the interest that will be owed after 178 days.
B) Assuming the print shop doesn't make any payments, find the amount owed after 178 days.
Using percentages, the answer to both the subparts are:
(A) Interest that will be owed after 178 days: $4,336.5(B) Interest after 178 days if sop doesn't repay: $4,473What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.So, since the interest is annual 6.5%:
(A) Interest that will be owed after 178 days:
Interest/2 ⇒ 6.5/2 ⇒ 3.25%Now, 3.25% of 4200:
4200/100 × 3.25 = 136.5$4,336.5(B) Interest after 178 days if sop doesn't repay:
Interest ⇒ 6.5%Now, 6.5% of 4200:
4200/100 × 6.5 = 273$4,473Therefore, using percentages, the answer to both the subparts are:
(A) Interest that will be owed after 178 days: $4,336.5(B) Interest after 178 days if sop doesn't repay: $4,473Know more about percentages here:
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Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.
Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.
__________________________________
30 miles / 2 hours = 15 miles/hour
_________________________________________
Answer
15 miles/hour
What are the dimensions, a, b, and c, of the net? 13 cm a = v cm b= cm cm 12 cm 15 cm 6 5 cm a с
Looking at the diagram of the triangular prism and its net, we can see that
a = width of the base = 5 cm
b = the slant height = 13 cm
c = length of the base = 15 cm
what is the value of f(x)=2(0.75)^x when x=3
Answer: f(3) = 0.84375
Step-by-step explanation:
f(3) is asking for the value of the function when x = 3, not multiplying f by 3. (f(x) is basically the output, y)
So we just plug in 3 for x and simplify (use PEMDAS)
f(3) = 2(0.75)^3
f(3) = 2(0.421875)
f(3) = 0.84375
Answer:
[tex]\frac{27}{32}[/tex]
Step-by-step explanation:
It may be a bit easier to represent 0.75 as a fraction, since we can use the following property of exponents: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex]
We can represent 0.75 as: [tex]\frac{3}{4}[/tex]
And substituting this into the function we get: [tex]f(x)=2(\frac{3}{4})^x[/tex]
calculating the value when x=3, we get: [tex]f(3)=2(\frac{3}{4})^3[/tex]
using the property previously stated we get: [tex]f(3)=2(\frac{3^3}{4^3})[/tex]
Raising each value to the exponent we get: [tex]f(3)=2(\frac{27}{64})[/tex]
When we multiply by two, we can simplify by splitting up 64, into two factors: 2 and 32, to get: [tex]\frac{2*27}{32*2}[/tex]
From here it's easy to see that we can cancel out the values 2, to get: [tex]\frac{27}{32}[/tex]
Which is our answer!
(x ^ 2 + 11x + 18) / (x + 3) =
Answer:
x+8 - 6/x+3
Step-by-step explanation:
Question #36 Multiple-Choice Reduce -2 + b2 by 7 + b2. C5 0 2b2-7 C9
Answer:
[tex]-2+b^2-7-b^2=-9[/tex]Step-by-step explanation:
Reduce the following expressions:
[tex]-2+b^2-(7+b^2)[/tex]Operate like terms:
[tex]-2+b^2-7-b^2=-9[/tex]7. Select all the equations that have the same solution as 3x - 6 = 18.
a. 3x = 12
b. 3x = 24
f.
c. 3(x - 2) = 18
d. 6x 12 = 36
e. 3x 12 = 36
18 = 5 - 3x
The equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.
How simplification method work?
In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.
According to the question, the given equation can be simplified by using simplification method and it is written below:
The given equation is: 3x - 6 = 18
3x = 18 + 6 = 24 ⇒ 3x = 24
Similarly, 3x - 6 = 18
3(x - 2) = 18
Hence, the equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.
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The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars)
t
years after 1995.
420
t
+
5750
Use this expression to predict what the total average credit card debt was or will be in the year 2006.
Answer: In the year 2006, the total average credit card debt for a U.S. household will be (or was)
dollars.
In the year 2006, the total average credit card debt for a U.S. household was 10370 dollars.
How to solve Exponential functions?
We are given the expression that gives an approximate value of the total average credit card debt in a U.S. household (in dollars), t years after 1995 as;
420t + 5750
where t represents number of years after the year 1995. Thus, for the year 2006, the value of t is;
t = 2006 - 1995
t = 11 years
Thus;
f(11) = 420(11) + 5750
f(11) = 10370 dollars
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ANSWER ONLY A-Ca. what is the students speed from the 3rd to 5th minute?b. at what times during the bike ride did the student come to a stop?c. During what time intervals did the students speed increase?
SOLUTION:
Case: Distance time graph
Method:
a) the students speed from the 3rd to 5th minute
[tex]\begin{gathered} Speed,s \\ s=\frac{4-2.25}{5-3} \\ s=\frac{1.75}{2} \\ s=0.875miles\text{ }per\text{ }minute \end{gathered}[/tex]b) the times during the bike ride did the student come to a stop
d and h
8 minutes and 23 minutes
c) the students speed increase during.
b to c. 1 and 3 minutes
e to f. 11 and 15 minutes
f to g. 15 and 17 minutes
You have one box that is 2 and 5 11 feet tall and a second box that is 2.45 feet tall. Write the decimal expansion for 2 and 5 11. If you stack the boxes, about how tall will the stack be
You have one box that is 2 and 5/11
feet tall and a second box that is 2.45 feet tall. Write the decimal expansion for
2 and 5/11. If you stack the boxes, about how tall will the stack be
we have that
[tex]2\frac{5}{11}=2+\frac{5}{11}=\frac{22+5}{11}=\frac{27}{11}=2.454545\ldots[/tex]If you stack the boxes,
we have
2.45+2.45=4.90 ft
Are the triangles congruent using AAS?
True
False
Jordan wants to use the Starz princess hall, the Dynamic DJ's as his music And Roscoe's for his equipment. If Jordan has a total of $800 and wants the music to play for 4 hours, how many people can Jordan party?
The number of people that can attend Jordan's party is 50 people.
How many people can attend Jordan's party?The equation that represents the total amount that would be spent at the party would be a linear equation. A linear equation increases at a constant rate.
The form of the linear equation would be:
Total amount = rental fee + (charge per hour of the Dynamic DJ x number of hours he plays) + (cost per person of Roscoe's rentals x number of people)
$800 = $400 + ($50 x 4) + ($4 x p)
$800 = $400 + $200 + $4p
$800 = $600 + $4p
$800 - $600 = $4p
$200 = $4p
p = $200 / $4
p = 50 people
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Divide 6.1 x 10^20 by 3.2 x 10^5. Express your answer in scientific notation.
PLEASE HELP!!!!
The division of the two numbers in scientific notation is equal to 1.91*10^15
Division of NumbersTo solve this problem, we have to divide the two numbers in scientific notation and to do this, we can simply apply division law of indices here;
We can first divide 6.1 by 3.2.
This will give us 1.90625 which is approximately 1.91.
Then applying the law of indices and subtract the power from one another. This becomes 20 - 5 = 15
The final value will be 1.91 * 10^15
The division of 6.1*10^20 by 3.2*10^5 is equal 1.91 *10^15
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Use the drawing tool(s) to form the correct answer on the provided graph.The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.g(x) = -1/2f(x + 2)
Given:
The graph of the function f is given and the function g is as:
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]Required:
To graph the function g.
Explanation:
The graph of the function f(x+2), shift the graph f(x) left 2 units by subtracting 2 from the x-coordinates of the points on the graph of f.
The graph of the function
[tex]\frac{1}{2}f(x+2)[/tex]here
[tex]a=\frac{1}{2}[/tex]So the graph of g has undergone a vertical shrinking by a factor of
[tex]\frac{1}{2}[/tex]The graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]reflect the graph of
[tex]\frac{1}{2}f(x+2)[/tex]across the x-axis by multiplying the y coordinate of the points on the graph of
[tex]\frac{1}{2}f(x+2)[/tex]by -1.
Thus the graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]is as:
Final Answer:
The graph of the function g is attached in the explanation part.
differentiate y = (x²-7x)^5 (3x^5-5x)
The given expression is
y = (x²-7x)^5 (3x^5-5x)
To differentiate, we would apply the product rule which is expressed as
(fg)' = f'g + fg'
Let f = (x²-7x)^5 and g = (3x^5-5x)
f' = 5(2x - 7)(x²-7x)^4
g' = 15x^4 - 5
By applying the product rule, it becomes
y' = 5(2x - 7)(3x^5-5x)(x²-7x)^4 + (15x^4 - 5)(x²-7x)^5
can you help please this is really important
The value of x is 10 and the length of SU is 50.
Here SU is the line and T is the mid-point of the line
So from this we have
SU = ST + TU
ST = TU
SU = 2ST = 2TU
ST = 3x - 5 and TU = 2x + 5
As ST = TU
3x - 5 = 2x + 5
x = 10
SU = 2ST
= 2( 3x - 5)
= 2( 3 × 10 - 5)
= 2( 30 - 5)
= 2× 25
= 50
Therefore the value of x is 10 and the length of SU is 50.
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In AUVW, UW is extended through point W to point X, mZUVW = (3x + 16)°, mZWUV = (2x + 8), and mZVWX= (8x - 18). Find mZWUV.
Let's draw the figure to better understand the problem.
(b) Use the function to predict the average price per square foot in 2032 .
Answer:
1187.49
Step-by-step explanation:
[tex]P(40)=0.023(40)^3-0.289(40)^2+3.068(40)+55.170=1187.49[/tex]
BE is the diameter of circle A. What's the measure of ∠BCE?Question 12 options:1) 90°2) 88°3) 180°4) 93°
Since BCE is an inscribed angle, it measures half the measure of the inscribed arc.
Angle BCE inscribes the arc BE of 180°, we have:
[tex]\begin{gathered} \text{BCE}=\frac{BE}{2} \\ BCE=\frac{180}{2} \\ \text{BCE}=90\degree \end{gathered}[/tex]Therefore the correct option is 1)
What does it mean by non collinear points and another name for angle ABD?
a) Point = could be any point A to D = for example A
b) Line : AD
Could be any line named by the endpoints.
c) Segment: Fragment of a line
AB
d) Ray: part of a line that has a fixed star but no end:
BE
e) Angle : Could be any angle, the middle letter is where the angle rests.
f) 3 collinear points: A,B,C
3 points that are in the same line
g)Opposite rays: same end point but opposite directions
BE and BC
h) Plane: infinite set of points forming a connected flat surface.
ABDC
i) 3 non collinear points: AEC
Three points that aren't on the same line
j) another name for m
Identify the segments that are skew to line EF. There are four answers.
The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.
The four lines that are skew to line EF are AB, GB, CH, and DC.
What are skew lines?The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.
We have,
A line EF on the given square figure.
We have the following lines on the given figure.
DG, CB, HA, FA, FG, GB, AB, EH, ED, DC,CH,
We see that,
FG, FA, EH, and ED are perpendicular and intersecting to line EF.
DG, CB, and HA are parallel to line EF.
So the remaining lines will be skew to line EF
i.e AB, GB, CH, and DC
Thus,
The four lines that are skew to line EF are AB, GB, CH, and DC.
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A parking garage charges a flat fee of $3 to enter the garage and then an additional hourly
charge to park. The cost to park in the garage can be modeled by the equation: P = 3+c.h
where c is the hourly rate to park and h is the number of hours parked in the garage.
a) Write an equation to find the number of hours a person parked if we know P and c.
b) If c=$2.25, find P if the person parks for 6 hours.
c) If P=$25.50, find how many hours the person parked if the cost per hour is $2.25.
If the cost to park in garage can be modeled by the equation P = 3+ch
Part A
The equation to find the number of hours a person parked h = (P-3) / c
Part B
If c = $2.25 and number of hours h =6 hours, then the cost to park in garage is $16.5
Part C
If P = $25.50, the person parked 10 hours if the cost per hour is $2.25
The flat fee of parking = $3
The cost to park in garage can be modeled by the equation
P = 3+ch
Where c is the hourly rate to park
h is the number of hours parked in the garage
Part A
The equation to find the number of hours a person parked is
P = 3+ch
c × h = P-3
h = (P-3) / c
Part B
c = $2.25
h = 6 hours
P = 3 + 2.25×6
= 3 + 13.5
= $16.5
Part C
P = $25.50
c = 2.25
h = (P-3)/c
= (25.50-3)/2.25
= 10 hours
Hence, if the cost to park in garage can be modeled by the equation P = 3+ch
Part A
The equation to find the number of hours a person parked h = (P-3) / c
Part B
If c = $2.25 and number of hours h =6 hours, then the cost to park in garage is $16.5
Part C
If P = $25.50, the person parked 10 hours if the cost per hour is $2.25
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Identify the domain and range of the function. y=x−−√−1
The domain of the function is [1, ∞) and the range of the function is [0,∞).
Domain and range:
The domain and range of a function are refers the set of all the inputs and outputs a function can give respectively.
Basically, domain takes all the possible input values from the set of real numbers whereas the range takes all the output values of the function.
Given,
Here we have the function
y = √x - 1
Now, here we need to find the domain and range of the function.
The given function is rewritten as,
√x - 1 > 0
Square both sides then we get,
x - 1 > 0
Add 1 on both sides then we get,
x > 1
Therefore, the domain is [1, ∞).
Similarly, let us consider, y ≥ 0
Therefore, the range is [0,∞).
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Let f(x) = 9x - 8. Find (f o f)(1).
Let f(x) = 9x - 8. Find (f o f)(1).
we know that
(f o f)(1).=f(f(1))
step 1
find f(1)
f(1)=9(1)-8
f(1)=1
substitute
f(f(1))=f(1)=1
therefore
the answer is 1
Figures 1 and 2 are shown in the coordinate grid. Which is a true statement?
As per given by the question,
There are given two figure on coordinate grid, figures 1 and 2.
Now,
From concept of similar figure:
Similar figure means, that have the same shape and exactly the same in every way, on the other hand;
The similar figure means they are same shape but not the same size, then these figure is also called similar figure.
Now,
From concept of the congruent figure:
The congruent means, that two figure exactly the same that means, we can say that they are congruent, when both figure have same shape and same size.
So,
According to both concept, similar and congruent;
The given figure 1 and 2 is simililar, because of same shape. But due to different size, both figure have not congruent.
So, the given figures 1 and 2 is similar, but not congruent.
Hence, the option first is correct.