Can a triangle be drawn with the following angle measures? Why or why not?
50°, 70°, 70°
no, the 3 angles of a triangle need to equal 180 degrees
70 +70 +50 = 190 degrees so it cant be a triangle.
Bryan is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 15 km/h. After seven hours, the velocity of the cyclist is 12 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 12 hours? (5 points)
Part A.
What we can do to solve this problem is to assume that the acceleration of Bryan is constant so that the velocity function is linear. The standard form of a linear function is in the form:
y = m x + b
or in this case:
v = m t + b
where v is velocity and t is time, b is the y –intercept of the equation
The slope m can be calculated by:
m = (v2 – v1) / (t2 – t1)
m = (12 – 15) / (7 – 4)
m = -1
Since slope is negative therefore this means the cyclist are constantly decelerating. The equation then becomes:
v = - t + b
Now finding for b by plugging in any data pair:
15 = - (4) + b
b = 19
So the complete equation is:
v = - t + 19
This means that the initial velocity of the cyclists at t = 0 is 19 km / h.
Part B. What we can do to graph the equation is to calculate for the values of v from t = 0 to 12, then plot all these values in the Cartesian plane then connect the dots.
Which is not a true statement
0.3711 >0.3801
NEED URGENT HELP!
Match the graph with the correct equation.
y – 5= –(x + 3)
y – 3 = –(x + 5)
y – 3 = (x + 5)
y + 3 = –(x + 5)
Answer: The correct option is (B) [tex]y-3=-(x+5).[/tex]
Step-by-step explanation: We are given to match the graph shown with the correct equation.
From the graph, we note that
(-5, 3) and (0, -2) are two points that lie on the line graph.
So, the slope of the given graph is
[tex]m=\dfrac{-2-3}{0-(-5)}\\\\\\\Rightarrow m=\dfrac{-5}{5}\\\\\Rightarrow m=-1.[/tex]
Since the point (-5, 3) lies on the line, so its equation in point-slope form will be
[tex]y-3=m(x-(-5))\\\\\Rightarrow y-3=-(x+5).[/tex]
Thus, option (B) is CORRECT.
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.
A) The bases are congruent.
B) The solids are similar.
C) The ratio of the volumes of the first solid to the second solid is 8:1.
D)The volume of the first solid is twice as much as the volume of the second solid.
E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more
surface area than the second solid.
The correct answers about these solids are that:
The bases are congruent.The volume of the first solid is twice as much as the volume of the second solid. If the dimensions of the second solid are x by x by h, the first solid has 4xh more surface area than the second solid.What is a congruent baseThis is used to tell that the base of the triangles are the same and they have the same shape.
The volume of the first triangle is
[tex]2X^2h\\\\X^2h[/tex]is the volume of the second triangle.
The ratio is 2: 1
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Answer:
a, d, e
Step-by-step explanation:
Jackie's total number of coins is 204.. She has twice as many quarters as nickels and three times as many dimes as nickels.. How many of each coin does she have ??
Thank you so much :)
A telephone pole casts a shadow that is 37 m long. Find the height of the telephone pole if a statue that is 33 cm tall casts a shadow 83 cm long.
Two spheres of the same density have a ratio of 9 to 16 in surface area. If the small sphere weighs 15 kg, what does the large sphere weigh?
Two equations are shown: Equation A y = 4 over x + 3 Equation B y = −2x − 4 Which statement best compares the graphs of the two equations? Both are nonlinear. Both are linear. Equation A is nonlinear and Equation B is linear. Equation A is linear and Equation B is nonlinear.
SHOW WORK!!
Answer:
The answer is C. Equation A is nonlinear and Equation B is linear.
Hope This Helps!
X to the power of three equals 343
NEED HELP FAST!!
5.
(05.03 MC)
Freddy reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks:
Which equation best models the relationship between x and y? (1 point)
y = –5x + 40
y = –40x + 280
y = –40x + 200
y = –5x + 200
two consecutive even integers have a sum of 346. Find the smailler of these two numbers
Answer:
Smallest number = 172
Step-by-step explanation:
Two consecutive even integers have a sum of 346.
Let x be the smallest number.
We have other number = x + 2
We also have
x + x + 2 = 346
2x + 2 = 346
2 x = 344
x = 172
Smallest number = 172, Other number = 172 + 2 = 174
Smallest number = 172
A tree casts a shadow that is 18 feet in length. If the angle of elevation is 28 degrees, which of the following best represents the height of the tree?
to find the height
multiply the length of shadow by the tangent of the angle
18 * tan(28) =9.5708
the tree is around 9.6 feet tall
The angle of elevation is the angle at which the object is viewed from below. The height of the tree is 8,45feet
Angle of elevationThe angle of elevation is the angle at which the object is viewed from below.
If tree casts a shadow that is 18 feet in length at the angle of 28 degrees, the height is calculated as:
sin theta = opposite/hypotenuse
sin 28 = H/18
H = 18sin28
H = 8.45 feet
Hence the height of the tree is 8,45feet
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gross income £12000 tax free allowance £6475 what is taxable amount @20%, tax payable,net income and weekly net amount how to work out?
32.1in.×28.2in.×1ft.=
since 2 of the 3 are in inches convert the 3rd one to inches
1 foot = 12 inches
now multiply 32.1 x 28.2 x 12 = 10,862.64 cubic inches
1.If 70% is £14, what is the full cost
2.4 bags of cement do 18msquared, how many msquared can be done with 7 bags
3.5x+1=3
4.find the nthe term of this sequence 7,12,17,22,27
4.if t(n)=6n+2 what is the 3rd term
4.35 / 5 show the work
A sailfish can swim up to 68 miles per hour. At this rate, how far can a sailfish swim in 1 fourth hour?
1/4 of an hour
68 miles per hour
multiply 68 by 1/4 = 68/1 *1/4 = 68/4
divide 68 by 4
68/4 =17
it can swim 17 miles
Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum.
The simplest form expression for the addition of the fractions given using the lowest common multiple of of the denominator is 2/3.
Given the fractions :
1/4 + 5/12The lowest common multiple of the denominator ;
Lowest common multiple of 4 and 12 = 12
1/4 + 5/12 = (3 + 5) / 12
1/4 + 5/12 = 8/12
Expressing in simplest form :
8/12 = 2/3
Therefore, the simplest form expression of the addition is 2/3
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Suppose you have $16,000 to invest in three stocks, A, B, and C. Stock A is a low-risk stock that has expected returns of 4%. Stock B is a medium-risk stock that has expected returns of 5%. Stock C is a high-risk stock that has expected returns of 6%. You want to invest at least $1,000 in each stock. To balance the risks, you decide to invest no more than $7,000 in stock C and to limit the amount invested in C to less than 4 times the amount invested in stock A. You also decide to invest less than twice as much in stock B as in stock A. How much should you invest in each stock to maximize your expected profit?
Answer:
Stock A: 1
Stock B: 1 and 2
Stock C: 1,7,4
What is the value of x in the equation −x = 6 − 4x + 18?
24
8
−8
−24
Ankur estimated the quotient of 15 1/3 divided by (-4 2/3) to be 3. Which best describes his error?
Answer:
the anwser is b hope it helped
How does a digit in the ten thousands place compare to a digit in the thousands place
-1 = n+5 what does n equal to
if structural steel installed in 2.75 floors of a building 2 3/8 day , how long will it take to install steel in 11 floors
17.16 is 62.4%of what
divide
17.16/0.624 = 27.5
NEED HELP!
Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs.
At the end of 3 month both have equal number of CDs i.e. 33
Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write a system to find the number of months after which they will have the same number of CDs.
Equation, is values of two expression that are equal.
Let x represent the number of months and y the number of CDs.
now
For Tom
Y = 30 + X
for Nita
Y = 18 + 5X
now solving both equation
30 + X = 18 + 5X
4X = 12
X = 3
for X = 3 y = 33
Thus At the end of 3 month both have equal number of CDs i.e. 33
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Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot below shows the temperatures from the previous year during the time that Dominick will take his vacation: box plot labeled Orlando with min at 64.5, Q1 at 65.5, median at 67.5, Q3 at 71.5, max at 72.5. Box plot labeled Tampa Bay with min at 60, Q1 at 63.5, median at 66.25, Q3 at 72.5, max at 74 Which city should Dominick visit, and why?
Answer:
He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average.
Step-by-step explanation:
graph the opposite of the number shown on each number line
68.32 divided by 2.8
Answer:
24.4
Step-by-step explanation:
We are asked to divide 68.32 by 2.8.
First of all, we will write our given problem as a division problem.
[tex]\frac{68.32}{2.8}[/tex]
We can see that our numerator has two digits after decimal and denominator has one digit after decimal, so we will multiply numerator and denominator by 100 as:
[tex]\frac{68.32\times 100}{2.8\times 100}[/tex]
[tex]\frac{6832}{280}=24.4[/tex]
Therefore, the quotient of our given problem is 24.4.
24.4
Further explanationWe will determine the quotient of 68.32 against 2.8.
Notes:
The division process is the arithmetic operation of the distribution of equal parts of a number. The division is the opposite of the multiplication process.24.4 __
2.8 ) 6 8 . 3 2
- 6 7 . 2 [tex]\downarrow[/tex]
1 . 1 2
- 1 . 1 2
0
Please see the attached picture.
The terminology of the division operation associated with the above scheme is as follows:
[tex]\boxed{ \ 68.32 \rightarrow the \ dividend \ }[/tex][tex]\boxed{ \ 2.8 \rightarrow the \ divisor \ }[/tex][tex]\boxed{ \ 24.4 \rightarrow the \ quotient \ }[/tex] [tex]\boxed{ \ 0 \rightarrow the \ remainder \ }[/tex]Therefore, 68.32 divided by 2.8 is divisible because the remainder is zero.
Thus, the quotient of 68.32 divided by 2.8 is 24.4.
- - - - - - - - - -
Alternative Strategy
[tex]\boxed{ \ 68.32 = 56 + 12.32 \ }[/tex]
[tex]\boxed{ \ 68.32 \div 2.8 = (56 \div 2.8) + (12.32 \div 2.8) \ }[/tex]
[tex]\boxed{ \ 68.32 \div 2.8 = 20 + 4.4 \ }[/tex]
[tex]\boxed{\boxed{ \ 68.32 : 2.8 = 24.4 \ }}[/tex]
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