Answer:D
Step-by-step explanation:
they are going up in a steady pace so they are proportional, hope this helped!
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The circumference of a circular field is 285.74 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
yards
x
?
Answer:
The diameter is 91.
Step-by-step explanation:
The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91
Answer:
91 yards
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
c=π * d
We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.
285.74= 3.14 *d
We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14
285.74/3.14= 3.14*d/3.14
285.74/3.14=d
Divide
91=d
d= 91 yards
The diameter of the field is 91 yards.
If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 6t + 4. Round your answer to the nearest hundredth.
Answer:
0.723 seconds
Step-by-step explanation:
Let h = 0
0 = -16t² + 6t + 4
Let’s solve by completing the square.
Subtract 4 from both sides.
-4 = -16t² + 6t
Since the coefficient of -16t² is -16, divide both sides by -16.
1/4 = t² - 3/8t
The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.
Then we need to add (b/2)² = 9/256 to both sides to complete the square.
Add 9/256 to both sides.
73/256 = t² - 3/8t + 9/256
Factor right side.
73/255 = (t-3/16)²
Take the square root on both sides.
±√(73/255) = t-3/16
Add 3/16 to both sides.
3/16 ± √(73/255) = t
The answer has to be positive, not negative.
0.72254626884 = t
0.723 ≈ t
Answer:
Rounding to the nearest hundredth, it is 0.72
If g(x) = 3x2 - 4x + 1, what is the value of g(-2)?
Answer:
21
Step-by-step explanation:
substitution
Answer:
21
Step-by-step explanation:
Plug in x as -2.
3(-2)² - 4(-2) + 1
3(4) - - 8 + 1
12 + 8 + 1
= 21
There are only r red counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is Find the number of red counters and the number of green counters that were in the bag originally. ( 5 marks)
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
There are only r red counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7 The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13
Find the number of red counters and the number of green counters that were in the bag originally.
Answer:
Total number of green counters = 9
Total number of red counters = 12
Step-by-step explanation:
Recall that probability is given by
P = number of desired events/total number of events
The probability that the counter is green is 3/7
P(green) = 3/7 = 3x/7x
Where 3x is the number of green counters
7x is the total number of counters
So then red counters are
red counters = 7x - 3x = 4x
4x is the number of red counters
P(green) = 3/7 = 3x/3x + 4x
The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. The probability that the counter is green is 6/13
So after addition of 3 green and 2 red new counters,
P(green) = 6/13 = (3x + 3)/(3x + 4x + 3 + 2)
Now solve for x
6/13 = (3x + 3)/(3x + 4x + 3 + 2)
6/13 = (3x + 3)/(7x + 5)
6(7x + 5) = 13(3x + 3)
42x + 30 = 39x + 39
42x - 39x = 39 - 30
3x = 9
x = 9/3
x = 3
So total number of green counters are
green counters = 3x = 3*3 = 9
So total number of red counters are
red counters = 4x = 4*3 = 12
Use the first four terms of the binomial theorem to approximate 2.2^7
Answer:
248.96 which is approximately 249
Step-by-step explanation:
2.2^7
The coefficients are;
1,7,21,35,35,21,7,1
So the terms we want to use are 1,7,21 and 35
We can write 2.2 as 2+ 0.2
So the approximations are;
1(2)^7(0.2)^0 + 7(2)^6(0.2) + 21(2)^5(0.2)^2 + 35(2)^4(0.2)^3
= 128 + 89.6 + 26.88 + 4.48 = 248.96
What is the slope of the line that passes through the points (-3,2) and (6, -9)?
Answer:
-11/9 is the slope
Step-by-step explanation:
Use the formula and u will find this is the answer, hope this helped!
Y2 - Y1 / X2 - X1
(-9 - 2) / (6 - (-3))
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Answer:
-11/9
Step-by-step explanation:
In order to find the slope from 2 points, use the following formula: [tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]
Plug in each of the numbers into their corresponding areas. Basically, we are subtracting the y values together and dividing it with the difference of the x values:
[tex]\frac{-9-2}{6-(-3)}[/tex]
The negatives cancel out and become postive, so the denominator will then read to be 6+3:
[tex]\frac{-9-2}{6+3}[/tex]
[tex]-\frac{11}{9}[/tex]
4. If 30 locusts eat 420 grams of grass in a week. How many days will it
take 21 locusts to consume 420 grams of grass if they eat at the same
rate
Answer:
The amount one locust eats in a week is 420/30 = 14 grams so it eats 14/7 = 2 grams per day, therefore 21 locusts can eat 21 * 14 = 42 grams per day. 420 / 42 = 10 so the answer is 10 days or 1 week and 3 days.
Write the given expression in terms of x and y only. tan(sin^-1(x)+cos^-1(y))
Answer:
[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]
Step-by-step explanation:
tan(sin⁻¹x + cos⁻¹y)
Use angle sum formula:
[tan(sin⁻¹x) + tan(cos⁻¹y)] / [1 − tan(sin⁻¹x) tan(cos⁻¹y)]
To evaluate these expressions, I suggest drawing right triangles.
For example, let's draw a triangle where x is the side opposite of angle θ, and the hypotenuse is 1. Therefore:
sin θ = x/1
θ = sin⁻¹x
Using Pythagorean theorem, the adjacent side is √(1−x²). Therefore:
tan θ = x / √(1−x²)
tan(sin⁻¹x) = x / √(1−x²)
Draw a new triangle. This time we'll make y the adjacent side to angle θ.
cos θ = y/1
θ = cos⁻¹y
Using Pythagorean theorem, the opposite side is √(1−y²). Therefore:
tan θ = √(1−y²) / y
tan(cos⁻¹y) = √(1−y²) / y
Substituting:
[x / √(1−x²) + √(1−y²) / y] / [1 − x / √(1−x²) × √(1−y²) / y]
Multiply top and bottom by √(1−x²).
[x + √(1−x²) √(1−y²) / y] / [√(1−x²) − x × √(1−y²) / y]
Multiply top and bottom by y.
[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]
A delivery company estimates that it will take 4 minutes for their drone to fly 7 km how long will it take the drone to fly 21 km
Answer: 12 minutes
Step-by-step explanation:
7 km ........ 4 minutes
21 km ...... ?
21/7 x 4= 12 minutes
Answer: 12 minutes.
Step-by-step explanation:
It is easy to put the numbers into a ratio form to work it out. So-
4 minutes for 7 km = 4 : 7
Then ? minutes for 21 km = ? : 21
You first divide the given value by the original value of that it is proportioned to (the number on the same side of the original ratio as 21). In this case divide 21 by 7 = 3. You now have to times the answer you got by the other original value which will be 4 x 3 = 12.
Therefore your answer is 12 minutes.
Question 11 PLEASE HELP find the slope of the line that passes through the points (6,2) and (8,8)
Answer:
Slope would equal 3.
slope= (y2-y1)/(x2-x1)
Plug in you get (8-2)/8-6)
Simplify (6)/(2)=3
Step-by-step explanation:
Which pair of quantities is LEAST likely to be directly proportional?
1. Hours worked and money earned
2. Distance and time when speed is constant
3. Area and side length of a square
4. Total cost and the number of hats purchased
Answer:
A
Step-by-step explanation:
Hours worked, probably because of commission or bonuses (the other ones seem to be proportional)
Let T be the set of things found in a toy store, and V be the set of things that cost more than $50. The set T∪V is the set of things that found in a toy store or cost more than $50 . The set T∩V is the set of things that found in a toy store and cost more than $50 . The set T′ is the set of things that_____ A cost under $50 B not found in a toy store C not found in a toy store and cost more than $50
Answer:
B. not found in a toy store
Step-by-step explanation:
Given:
T = the set of things found in a toy store.
V = the set of things that cost more than $50.
T∪V = the set of things that found in a toy store or cost more than $50.
T∩V = the set of things that found in a toy store and cost more than $50.
The set T′ is the complement of the set T and it consists of the set of things that are not found in a toy store.
The correct option is B
Dale is following this recipe to make shortbread fingers. Dale uses 75 g of butter. How many shortbread fingers does he make? Recipe: Makes 20 fingers 125 g butter 55 g sugar 180 g flour
Answer:
For 75 g butter ≈ 27 fingers
Step-by-step explanation:
Using unitary method
For 20 fingers = 55 g butter
For 1 g butter = 20/55 fingers
=> For 1 g butter = 4/11 fingers (Simplified form)
Multiplying both sides by 75
=> for 75 g butter = [tex]\frac{4}{11} * 75 {fingers}[/tex]
=> For 75 g butter ≈ 27 fingers ( approximately )
Solve for x 7 x − 4 = 6 Give your answer as an improper fraction in its simplest form.
Answer:
10\7
Step-by-step explanation:
7x-4=6
7x=6+4
7x=10
7x\7=10\7
x=10\7
Answer:-13/3
Step-by-step explanation:
How can we write 0.7 in words?
Step-by-step explanation:
You could simply say the numbers in 0.7 one at a time like this:
=> zero point seven
OR
You can also see 0.7 as a fraction (7/10) and should therefore be said and written as follows:
=> seven tenths
Hope this helps.. Good Luck
0.7 means the same thing as 7 tenths.
Below, I have made a place value chart.
You will see that 0.7 means 0 units and 7 tenths.
Here’s a graph of a linear function. Write the equation that describes that function.
Express it in slope-intercept form.
Answer:
y=3/4 x+2
Step-by-step explanation:
y=mx+b
take two points from graph
(0,2) and (4,5)
find b when x=0 then y=b=2
find m : y2-y1/x2-x1=5-2/4-0
m=3/4
y=3/4 x +2
△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. Triangle A Y X is shown. Line segment B C is drawn from side A Y to A X to form triangle A B C. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?
Explanation:
Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.
Statements Reasons
1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX 3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY • AC/AX = AB 6. division property of equality
7. AC/AX = AB/AY 7. division property of equality
8. Corresponding sides are proportional 8. Definition of proportional
9. △ABC ~ △AYX 9. SAS similarity theorem
_____
The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.
Answer:
I think its A. ∠A ≅ ∠A; reflexive property
Step-by-step explanation:
True or false
The diagonal of a square are congruent
Answer:
True
Step-by-step explanation:
As we know that all four sides and angles of a square are equal to each other plus the diagonal is right angled to each other as they intersect at 90 degree i.e perpendicular
It contains the identical length i.e congruent
Hence the given statement is true i.e diagonal of a square are congruent to each other
for the function F(x)=1/x,which of these could be a value of F(x) when x is close to zero
Answer:
C. -10,000
Step-by-step explanation:
As x approaches zero, f(x) approaches infinity or negative infinity.
Answer: C. -10,000
Answer:
-10,000
Step-by-step explanation:
Solve for x 8x−6=15 Give your answer as an improper fraction in its simplest form
Answer:
[tex]\boxed{x = \frac{21}{8} }[/tex]
Step-by-step explanation:
=> 8x-6 = 15
Adding 6 to both sides
=> 8x = 15+6
=> 8x = 21
Dividing both sides by 8
=> x = 21/8 (In its simplest form)
please help me! Bethany incorrectly simplified the following expression: (4 x 10^11) (3 x 10^-14) + 0.000005 Which of Bethany’s steps show an error based solely on her previous step? Choose all that apply: A. Step one: (4 x 10^11) (3 x 10^-14) + (5 x 10^-5) B. Step two: (12 x 10^-3) + (5 x 10^-5) C. Step three: (120 x 10^-4) + (5 x 10^-5) D. Step four: (120 x 10^-4) + (50 x 10^-4) E. Step five: 170 x 10^-8 F. Step six: 1.7 x 10^-6
Answer:
Below.
Step-by-step explanation:
Step 1: it is 5 x 10^-6 not 5 x 10^-5.
Step 5 : the result of the addition is 170 x 10^-4 not 170 x 10^-8.
Answer: yes that is correct explanation:
D. Is no solution please help
Answer:
B
Step-by-step explanation:
I can't really see the problem, however I believe B is the only one that shows an infinite number of solutions.
Answer:
B
Step-by-step explanation:
It is too blurry BTW but B is correct
the function g(x)=-5x-6
Answer:
D. the slope of f(x) is greater than the slope of g(x)
Step-by-step explanation:
slope of f(x) =rise/run
=y2 -y1 / x2 -x1
slope of f(x)= -1-2/1-0= -3
g(x)= -5x-6
slope of g(x)= -5
-3>-5
D. the slope og f(x) is greater than the slope of g(x)
Find the area of the composite figure in square mm. Round your
answer to the nearest square milimeter. (Enter only a number as
your answer.)
Answer:
521
Step-by-step explanation:
Composite figure.
Draw a straight down from C to line segment AB. This forms a triangle.
Now, the area of this figure=
Area of semicircle+area of rectangle+ area of triangle.
Rectangle area formula = l times w
Length - 20
Width =14
14 times 20 = 280
Area of rectangle = 280
Semicircle area = area of circle/2
Area of circle = π[tex]r^2[/tex]
Diameter =20= 2r
r=10
π[tex]r^2[/tex]= π 10^2 =100π
100 times 3.14 =314
314/2 = 157
Area of semicircle = 157
Area of triangle= bh/2
Triangle's base= 32-20=12
Triangles height = 14
14 times 12 = 168
168/2 = 84
Area of triangle: 84
Area of semicircle+area of rectangle+ area of triangle.
157+280+84 =521
Four whole numbers are rounded to the nearest 10 The sum of the four rounded numbers is 90 What is the maximum possible sum of the original four numbers
Answer:
110
Step-by-step explanation:
example:
rounded 20+20+20+30 = 90
original 25+25+25+35 = 110
Daniel moves no more Then 30 of his sheep and goats into another field. More than seven of his animals are sheep. Let s respond the number of sheep and g represent the number of goats. Identify to inequalities that represent this situation.
Answer:
The two inequalities are :
option B and option C.
Step-by-step explanation:
Explanation:
Daniel moves no more than 30 of his sheep and goats into another field. This means the summation of sheep and goats will be at maximum 30.
that is why it is s+g<30
And more than 7 of his animals are sheep means sheep are greater than 7. that is why =s>7
The right inequalities which corresponds to Daniel's animals are s+g<=30 and s>7 which are on option A and C.
What is an inequality?
It is a type of an equation in which we have to use greater than, less than, greater than or equal to , less than or equal to signs.
How to form an inequality?
There are total 30 animals of Daniel and s represents the number of sheeps and g responds the number of goats so the first inequality will be
s+g<=30
There are more than 7 sheeps so the second inequality will be
s>7
Hence the right inequalities are s+g<=30, s>7.
Learn more about inequality at https://brainly.com/question/24372553
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Rewrite 4 − 5 using the additive inverse and display the new expression on a number line. (5 points) 4 + 5 An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 4 − (−5) An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 5 − 4 An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 and ends at 5. Another arrow begins at 5 and ends at 1. 4 + (−5) An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Answer: 4 + (−5)
An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Step-by-step explanation: The arrow from 0 running to 4 is the graph of how the point on the line is a positive 4: Four added to 0
The "additive inverse" means start there and go in the opposite direction. The arrow is 5 units long, so they ended up at -1 . Adding -5 is the same as subtracting 5
4 + (-5) = -1 is the additive inverse of 4-5= -1
The descriptions of the number lines are well done, but difficult to sort out.
Answer:
4 + (−5)
Step-by-step explanation:
it is got it correct
Esrudiantes ganaron un concurso ,lo cual el premio fue visita a fabrica de reciclaje , A mitad de la charla se retiraron 10 mujeres y se observo que el numero de varones era el doble que el de mujeres ,casi al final de la charla se retiraron 45 varones y takbiek se obeservo que el numero de mujeres era el doble que los varones ¿que cantidad de mujeres y varones estuvieron en la charla?¿cual fue el total de asistentes?
Answer:
The total number of students who attended the talk is 100.
Step-by-step explanation:
We are given that halfway through the talk, 10 women withdrew and it was observed that the number of men was twice that of women.
Then, almost at the end of the talk, 45 men withdrew and it was observed that the number of women was twice that of men.
Let the number of women who attended the talk be 'w' and the number of men who attended the talk be 'm'.
Now, according to the question;
The first condition states that the 10 women withdrew and it was observed that the number of men was twice that of women, i.e;[tex]m = 2 \times (w-10)[/tex]
[tex]m = 2w-20[/tex] ----------------- [Equation 1]
The second condition states that at the end of the talk, 45 men withdrew and it was observed that the number of women was twice that of men, i.e;[tex](w-10) = 2(m-45)[/tex]
[tex]w-10= 2m-90[/tex]
[tex]w= 2m-80[/tex]
[tex]w= 2(2w-20)-80[/tex] {using equation 1}
[tex]w= 4w-40-80[/tex]
[tex]4w-w= 120[/tex]
[tex]3w= 120[/tex]
[tex]w=\frac{120}{3}[/tex] = 40
Now, putting the value of w in equation 1 we get;
[tex]m = 2w-20[/tex]
[tex]m = 2(40) -20[/tex]
= 80 - 20 = 60
So, the number of men who attended the talk is 60 and the number of women is 40.
Hence, the total number of students who attended the talk is (60 + 40) = 100.
which statement about magnitude is true? Magnitude is never a negative value. The magnitude of –1.9 is |–1.9| which is 1.9. The absolute value of a number is greater than its magnitude. The numbers –4 and 4 have the same magnitude. The magnitude of Negative two-thirds is less than the magnitude of Two-thirds. Which statements are true? Check all that apply.
Answer:
See the step-by-step
Step-by-step explanation:
This answer is based on the idea that magnitude is absolute value.
Absolute value is a number's distance from zero.
1. Magnitude is never negative. (True)
2. The magnitude of -1.9 is |–1.9| which is 1.9. (True)
3. The absolute value of a number is greater than its magnitude. (False, they are the same (?, maybe)
4. The numbers –4 and 4 have the same magnitude. (True)
5. The magnitude of Negative two-thirds is less than the magnitude of Two-thirds. (False)
Answer:
Which statements are true? Check all that apply.
Magnitude is never a negative value.
The magnitude of –1.9 is |–1.9| which is 1.9
The numbers –4 and 4 have the same magnitude.
Step-by-step explanation:
Proofs are used to show that a mathematical statement is true. The most common form of mathematical statements are if-then statements. Give an example of a true mathematical statement and a false mathematical statement in if-then form. For the false statement, include a counterexample showing that the statement isn't true.
Answer:
See explanation
Step-by-step explanation:
True Mathematical Statement
[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{xy}=ab[/tex]
False Mathematical Statement
[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{x+y}=a+b[/tex]
To show using a counterexample that the statement isn't true.
[tex]\text{Let x}=16\\\text{Let y}=9\\\sqrt{16}=4\\\sqrt{9}=3\\\sqrt{16+9}=\sqrt{25}=5\\a+b=3+4=7\\5\neq 7[/tex]
Therefore, the mathematical statement is false.