[tex] d \propto v^2[/tex]
$\implies d=kv^2$
substitute the given values, $5=k(10)^2\implies k=\frac1{20}$
now, $d=\frac{1}{20}\times( 70)^2=\frac{70\times70}{20}=245$
A big blunder from my side, now fixed!
Find the remainder when x^3-ax^2 +6x -a is divided by x-a
Answer:
When x^3 - ax^2 + 6x -a is divided by x-a
Remainder = 5a
[tex] \frac{ {x}^{2} + 4x + 5 }{ {x}^{2} + 3 \sqrt{x + 4} } [/tex]
Hi
is this a rational expression or not pls reply asap
Answer:
NOT a rational expression.
Step-by-step explanation:
A rational expression is a fraction of two polynomials.
Since the denominator contains a square-root radical, it is not considered a polynomial.
Therefore the given exprssion is NOT a rational expression.
On a plane trip, baggage over 40 pounds is charged at the rate per pound of 1% of the one-way fare. The charge for a bag weighing 52 pounds on a trip where the one-way fare is $98 is:
Answer:
$11.76 is the charge for bag.
Step-by-step explanation:
Given:
One way fare = $98
Weight of bag = 52 pounds
Rate per pound Charges on baggage over 40 pounds = 1% of the one-way fare
To find:
Charge for bag = ?
Solution:
Pounds more than 40 pounds = Weight of baggage - 40 pounds
[tex]\Rightarrow 52-40 = 12\ pounds[/tex]
Charges on extra baggage = 1% of one-way fare multiplied by pounds more than 40.
Here one way fare is $98.
So, charges on extra baggage will be:
[tex]1\%\ of\ 98 \times (52-40) \\\Rightarrow 1\%\ of\ 98\times (12)\\\Rightarrow \dfrac{1}{100}\ of\ (98 \times 12)\\\Rightarrow \dfrac{1}{100}\times (98 \times 12)\\\Rightarrow \bold{\$11.76}[/tex]
So, the charge for the baggage is $11.76.
How many equilateral triangles in the plane have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)}?
Answer:
12
Step-by-step explanation:
There are 4 points, so there are C(4,2) = 4C2 = 6 pairs of
points and since two equilateral triangles can be drawn having
that pair of points as vertices, there are 12 equilateral
triangles that can be drawn having two vertices in the set
{(0,0), (0,1), (1,0), (1,1)}.
The number of the equilateral triangles in the plane have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)} will be 12.
What is an equilateral triangle?An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
There are 4 points, so there are C(4,2) = 4C2 = 6 pairs of points and since two equilateral triangles can be drawn having that pair of points as vertices, there are 12 equilateral triangles that can be drawn having two vertices in the set {(0,0), (0,1), (1,0), (1,1)}.
Therefore, the number of the equilateral triangles in the plane that have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)} will be 12.
To know more about equilateral triangles follow
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Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
[tex]5\sqrt{2}[/tex]
[tex]\frac{5\sqrt{2} }{2}[/tex]
[tex]5\sqrt{3}[/tex]
[tex]\frac{5\sqrt{3}}{2}[/tex]
Answer:
[tex]$\frac{5\sqrt{2} }{2}$[/tex]
Step-by-step explanation:
[tex]x: \text{opposite side of the angle of 45\º}[/tex]
[tex]5: \text{hypotenuse of the right triangle}[/tex]
[tex]$\sin(\theta)=\frac{\text{opp}}{\text{hyp}} \Rightarrow \sin(45\º)=\frac{x}{5} $[/tex]
[tex]$\text{Once }\sin(45\º)=\frac{\sqrt{2} }{2} $[/tex]
[tex]$\frac{\sqrt{2} }{2} =\frac{x}{5} \Rightarrow 2x=5\sqrt{2} \Rightarrow x=\frac{5\sqrt{2} }{2} $[/tex]
You can just remember that 5 is the diagonal of a square of side length x.
[tex]$5=x\sqrt{2} \Rightarrow x=\frac{5}{\sqrt{2} } \Rightarrow x=\frac{5}{\sqrt{2} } \cdot \frac{\sqrt{2} }{\sqrt{2} } = \frac{5\sqrt{2} }{2} $[/tex]
I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 600 pounds more than each of her trucks, but no more than 1/3 of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?
Answer:
The load the large truck can carry is 2400 pounds
Step-by-step explanation:
Let the load the large truck can carry = X
Let the load each of the four trucks owned by the neighbor can carry = Y
The given parameters are;
The load the large truck can carry X = 600 + Y......(1)
The number trucks owned by the neighbor = 4
The load the large truck can carry X ≤ 1/3 × 4 × Y
Therefore, X ≤ 4/3 × Y
At maximum capacity, we have;
X = 4/3 × Y
Substituting the value of X into equation (1), we have;
4/3 × Y = 600 + Y
600 = 4/3 × Y - Y = 1/3·Y
Y = 3 × 300 = 1800 pounds
Y = = 1800 pounds
Therefore, the load the neighbors truck can carry = 1800 pounds
X = 600 + Y gives;
X = 600 + 1800 = 2400 pounds
∴ The load the large truck can carry = 2400 pounds
after allowing 5 percent discount on the marked price of a radio 10 percent vat is charged on it , then its price became rs 1672 .how much amount was given in the discount ans80
Answer:
The discount was rs 80.
Step-by-step explanation:
The item started at an original undiscounted price of x.
Then a 5% discount was applied. The price is now 0.95x.
Then a 10% VAT was applied. The price is now 1.1(0.95x).
The price is now rs 1672.
1.1(0.95x) = 1672
Divide both sides by 1.1 and by 0.95.
x = 1600
The original price was rs 1600.
5% of rs 1600 = 0.05 * rs 1600 = rs 80
The discount was rs 80.
A stone is thrown downward straightly its speed at speed of 20 second what and it reaches the ground at 40 metre second what will be the height of building
Answer:
[tex]\Huge \boxed{\mathrm{61.22 \ m}}[/tex]
Step-by-step explanation:
A stone is thrown downward straightly with the velocity of 20 m/s and it reaches the ground at the velocity of 40 m/s. What will be the height of building? (Question)
The initial velocity ⇒ 20 m/s
The final velocity ⇒ 40 m/s
We can apply a formula to solve for the height of the building.
[tex](V_f)2 - (V_i)^2 =2gh[/tex]
[tex]V_f = \sf final \ velocity \ (m/s)[/tex]
[tex]V_i = \sf initial \ velocity \ (m /s)[/tex]
[tex]g = \sf acceleration \ due \ to \ gravity \ (m/s^2 )[/tex]
[tex]h = \sf height \ (m)[/tex]
Plugging in the values.
Acceleration due to gravity is 9.8 m/s².
[tex](40)^2 - (20)^2 =2(9.8)h[/tex]
Solve for [tex]h[/tex].
[tex]1600 - 400 =19.6h[/tex]
[tex]1200 =19.6h[/tex]
[tex]\displaystyle h=\frac{1200}{19.6}[/tex]
[tex]h= 61.22449[/tex]
The height of the building is 61.22 meters.
Find the value of x in each case:
Answer:
x = 36
Step-by-step explanation:
To obtain the value of x, we must first obtain the value of y and z as shown in the attached photo.
i. Determination of y
2x + y = 180 (angle on a straight line)
Rearrange
y = 180 – 2x
ii. Determination of z.
z + 4x = 180 (angle on a straight line)
Rearrange
z = 180 – 4x
iii. Determination of x
x + y + z = 180 (sum of angles in a triangle)
But:
y = 180 – 2x
z = 180 – 4x
Therefore,
x + y + z = 180
x + 180 – 2x + 180 – 4x = 180
Collect like terms
x – 2x – 4x = 180 – 180 –180
– 5x = – 180
Divide both side by – 5
x = – 180 / – 5
x = 36
Therefore, the value of x is 36.
The city school district is considering increasing class size in the elementary schools. However, some members of the school board are concerned that larger classes may have a negative effect on student learning. In words, what would the null hypothesis say about the effect of class size on student learning?
Answer:
The null hypothesis would say that class size has no effect on students learning.
Step-by-step explanation:
Null hypothesis is a type of hypothesis that is used in statistics which proposes that there is no difference between a certain characteristic of a population or the data - generating process.
Now, in this question,the school district is considering increasing class size in the elementary schools but we want to check whether larger classes may have a negative effect on students learning.
Thus, the null hypothesis would reject this claim of larger classes having negative effect on students and say that class size has no effect on students learning.
By SAA conjecture, determine which triangles are congruent.
Answer:
The correct option is;
[B] ΔABF ≅ ΔEDF
Step-by-step explanation:
GIven that ∠FAE is congruent to ∠FEA
Therefore, triangle ΔFAE is an isosceles triangle (Definition of isosceles triangle)
Segment FA is equal to segment FE (Equal segments of isosceles triangle)
Angle ∠EFD is congruent to angle ∠AFB (Vertically opposite angles)
Therefore, triangle ΔABF is congruent to triangle ΔEDF (Angle Angle Side AAS rule of congruency)
The correct option is ΔABF ≅ ΔEDF.
the points (-2,1), (1,1), (0,-2), and (-3,-2) are vertices of a polygon. what type of polygon is formed by these points? A. rectangle B. square C. pentagon D. parallelogram
Answer:
[tex]\boxed{\sf D. \ Parallelogram}[/tex]
Step-by-step explanation:
When we graph the points, the polygon is a quadrilateral with opposite parallel sides. The type of polygon formed by these points is a parallelogram.
Answer:
Parallelogram
Step-by-step explanation:
We'll graph all of the points from which we'll come to know that it is a parallelogram having opposite sides equal and parallel.
See the attached file for more understanding.
Which parent function is f(x)= |3|
A. The quadratic parent function
B.The linear parent function
C. An exponential parent function
D. The absolute value parent function
Answer:
D. Absolute value parent function
we can know fro the symbol |x| in the question written f(x)= |3|
help meeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
I believe the correct answer from the choices listed above would be the first option. The graph that shows a function where f(2) = 4 would be the graph that passes through point (2,4) which is shown in the first graph. Hope this answers the question.
Hey There!!
Your best choice is 1.
Because, We have to find a function where f(2)=4. It means the value of function is 4 at x=2.
In graph 1, the value of function is 4 at x=2, therefore option 1 is correct.
In graph 2, the value of function is -4 at x=2, therefore option 2 is incorrect.
In graph 3, the value of function is not shown in the graph at x=2, therefore option 3 is incorrect.
In graph 4, the value of function is not shown in the graph at x=2, therefore option 4 is incorrect.
Thus, correct option is 1.
Hope This Helps!!
A culture started with 2000 bacteria. after 2 hours it grew to 2400 bacteria. predict how many bacteria will be present after 10 hours. round your answer to the nearest whole number. P=Ae^kt
Answer: There will be 4977 bacteria present after 10 hours.
Step-by-step explanation:
The exponential function for continuous growth in t years is given by :-
[tex]P=Ae^{kt}[/tex] (i)
, where A = initial population, k= rate of growth.
As per given, A= 2000,
After t= 2 hours, P=2400
Put these values in (i), we get
[tex]2400=2000e^{2k}\\\\\Rightarrow\ 1.2=e^{2k}[/tex]
Taking log on both sides
[tex]\ln 1.2=2k\\\\\Rightarrow\ k=\dfrac{\ln1.2}{2}=\dfrac{0.182321556794}{2}\\\\\Rightarrow\ k\approx0.09116[/tex]
put value of A=2000, k= 0.09116 and t= 10 , we get
[tex]P=2000e^{0.09116\times10}\\\\=2000e^{0.9116}\\\\=2000\times2.4883\\\\=4976.6\approx4977[/tex]
Hence, there will be 4977 bacteria present after 10 hours.
Answer:
Step-by-step explanation:
In a circle, an arc measuring 130° is what percentage of the circumference of the circle
Answer:
≈ 36.1%
Step-by-step explanation:
In any circle the following ratio is equal
[tex]\frac{arc}{circmference}[/tex] = [tex]\frac{centralangle}{360}[/tex] = [tex]\frac{130}{360}[/tex] , thus
percentage = [tex]\frac{130}{360}[/tex] × 100% ≈ 36.1%
an arc measuring 130° is approximately 36.11% of the circumference of the circle.
To find the percentage of the circumference that an arc measuring 130° represents, we need to calculate the ratio of the arc length to the circumference of the circle and then convert it to a percentage.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
Let's assume the radius of the circle is r.
The circumference of the circle is C = 2πr.
To find the length of the arc corresponding to 130°, we need to calculate the fraction of the total angle (360°) that 130° represents:
Fraction of the angle = (130° / 360°) = (13/36).
Since the fraction of the angle is equal to the fraction of the arc length to the circumference, the length of the arc can be calculated as:
Arc length = Fraction of the angle * Circumference = (13/36) * (2πr).
Now, to find the percentage of the circumference that the arc length represents, we divide the arc length by the circumference and multiply by 100:
Percentage = (Arc length / Circumference) * 100
Percentage = [(13/36) * (2πr)] / (2πr) * 100
Percentage = (13/36) * 100
Percentage = 36.11%
Therefore, an arc measuring 130° is approximately 36.11% of the circumference of the circle.
Learn more about arc length here
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please help
The midpoint (x, y) and the end point (x2, y2) are known. Find (x1, Y1) using the midpoint formula.
a. (x1,y1) = (2x + x2, 2y+y2)
b. (x1,y1) = (2x - x2, 2y - y2)
c. (x1,y1) = (x + x2, y + y2)
d. (x1,y1) = (x - x2, y - y2)
Answer:
B
Step-by-step explanation:
So this was a pretty difficult question to do algebraically so I just came up with an example.
Step-by-step explanation:
Hey,there!!!
Let's simply work with it,
We have,
One point is (x2,y2) and midpoint is(x,y).
Now, let's use midpoint formulae,
[tex](x ,\: y) = \frac{x1 + x2}{2} + \frac{y1 + y2}{2} [/tex]
Now, let's equate with their corresponding elements we get,
[tex]x = \frac{x1 + x2}{2} [/tex]
now, 2x=x1+x2
or, x1=2x-x2
and
[tex]y = \frac{y1 + y2}{2} [/tex]
now,
2y = y1+y2
or, y1 = 2y-y2
Therefore, the answer is (x1,y1)= { (2x-x2),(2y-y2) }
Hope it helps...
Given the equation y = 2x + 3 what is the slope?
x
3
2
idk
Answer:
The slope is 2Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question the equation is
y = 2x + 3
Comparing this equation with the general equation above
Slope / m = 2
Hope this helps you
4) 101
Is it rational or irrational
Answer:
rational
Step-by-step explanation:
according to google the definition of RATIONAL is
(of a number, quantity, or expression) expressible, or containing quantities that are expressible, as a ratio of whole numbers. When expressed as a decimal, a rational number has a finite or recurring expansion. Examples of rational numbers are 4 3 and 9
AND THE DEFINITION OF IRRATIONAL IS
(of a number, quantity, or expression) not expressible as a ratio of two integers, and having an infinite and nonrecurring expansion when expressed as a decimal. Examples of irrational numbers are the number π and the square root of 2.
so 101 is a whole number and whole numbers are always rational
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answer:
108º
Step-by-step explanation:
subtract outer angle from circle
360º - 252º = 108º
I hope this helps you
find DCG
360-252=108°
angle DBG=1/2(252-108)
angle DBG=72°
when would you write an x in an equation?)
Answer:
[tex]\Large \boxed{\mathrm{When \ a \ number \ is \ not \ known}}[/tex]
Step-by-step explanation:
For example, a sum of a number and 6 is 12.
The number is unknown.
Let the number be x.
x + 6 = 12We can solve for x (unknown number). Subtract 6 from both sides of the equation.
x = 6PLEASE HELP I HAVE LIKE 10 MINUTES A coin toss is used to determine which team will receive the ball at the beginning of a football game. The Cougars always choose heads in the toss. What are the odds in favor of the Cougars winning the toss in exactly two of three games? A. 3:5 B. 3:8 C. 5:3 D. 8:3 A coin toss is used to determine which team will receive the ball at the beginning of a football game. The Cougars always choose heads in the toss. What are the odds against the Cougars winning the toss in exactly one of three games? A. 3:5 B. 5:3 C. 3:8 D. 8:3 A summer camp has 20 boys and 20 girls. Each day, all camper names are put in a hat, and one name is drawn to receive a prize. What are the odds in favor of boys names being drawn on three out of three nights? A. 1:1 B. 1:7 C. 1:8 D. 7:1
Answer:
a
Step-by-step explanation:
Offering 20 points and a thanks with 5 stars for your help please
Answer:
$70000
Step-by-step explanation:
For this problem, we need to convert the fractions into common denominators so we can get his total donated portion. From here, we can set up a proportion to fin his total income.
The greatest common denominator of 5 and 7 is 35. So
1/5 = 7/35. && 1/7 = 5/35
Add those together to get 7+5 = 12/35
So he gave away 12/35 of his income.
Now we set up a proportion to find his total.
35 / 12 = x / 24000
And now we solve for x:
x = (24000 * 35) / 12
x = 70000
So Mr. Pollard made $70000.
We can verify this by saying 24000 / 70000 to get the same reduced fraction 12/35.
Cheers.
Answer:
$70000Step-by-step explanation:
[tex]church + medical \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{1}{5} + \frac{1}{7} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{12}{35} [/tex]
He gave away combined $24000 both,
So,
[tex] \frac{12}{35} =24000[/tex]
[tex] \frac{1}{35} = \frac{24000}{12} \\ \: \: \: \: \: \: \: \: = 2000[/tex]
Therefore,
[tex] \frac{35}{35} = 2000 \times 35 \\ \: \: \: \: \: \: \: \: = 70000[/tex]
hi, please help me :)
Answer:
D. Linear
The answer is negative linear, because when it incresing from 0 to 1 to 2 to 3 (year) it always deacreasing in the value($).
Solve for xxx. 12x+7 4012x+7 4012, x, plus, 7, is less than, minus, 11, start color #ed5fa6, start text, space, O, R, space, end text, end color #ed5fa6, 5, x, minus, 8, is greater than, 40 Choose 1 answer: Choose 1 answer: (Choice A) A x \dfrac{48}{5}x> 5 48 x, is greater than, start fraction, 48, divided by, 5, end fraction (Choice B) B -\dfrac32 \dfrac32x> 2 3 x, is greater than, start fraction, 3, divided by, 2, end fraction or x<\dfrac{48}{5}x< 5 48 x, is less than, start fraction, 48, divided by, 5, end fraction (Choice D) D There are no solutions
Answer:
x < -3/2 and x>48/5Step-by-step explanation:
Given the inequality function 12x+7< -11 and 5x-8>40, we are to solve for the value of x. To solve for x, the following steps must be followed.
For the inequality 12x+7< -11
Step 1: Subtract 7 from both sides of the inequality
12x+7-7< -11-7
12x < -18
Step 2: Divide both sides of the inequality by 12
12x/12 < -18/12
x < -3/2 .............. 1
For the inequality 5x-8> 40;
Step 1: Add 8 to both sides of the inequality
5x-8+8 > 40+8
5x > 48
Step 2: Divide both sides of the inequality by 5
5x/5 > 48/5
x>48/5....... 2
Combining equation 1 and 2, we will have;
x < -3/2 and x>48/5
If x>48/5 then 48/5<x
Combining 48/5<x with x < -3/2 will give 48/5<x<-3/2
Answer:
there are no soulutions
Step-by-step explanation:
Mia’s house and her aunt’s house are 15.4 inches apart on the map. If every 4 inches on the map represents 10 miles, what is the actual distance from Mia’s house to her aunt’s house, to the nearest tenth of a mile? 2.6 6.2 38.5 61.6
Answer:
38.5 miles
Step-by-step explanation:
Proportions:
4 inches ⇔ 10 miles
15.4 inches ⇔ M miles
M = 15.4*10/4
M = 38.5 miles
Answer: 38.5
Step-by-step explanation: cuz im smart
Please answer the question in the image below ASAP
Answer:
c
Step-by-step explanation:
diameter will be 36, radius 18 and the height is 6
Calliope solved the equation 4x+3=2x−8 using the steps shown below. She was asked to provide her reasoning by choosing the properties of equality that correctly justify her work. Help Calliope by matching her steps of work in the left column with the appropriate reason in the right column.
Answer:
4x + 3 = 2x -8
subtraction property of equality: 4x - 2x = -8 - 3
2x = -11
division property of equality: x = -11/2
Corinna has $80. She wants to buy a $256 plane ticket. She will save up her earnings from working at the museum where she earns $16 per hour. Which inequality shows the number of hours, n, Corinna must work so that she has a total of at least $256?
Answer:
80+16h≥256
Step-by-step explanation:
the 80 represents the $80 that Corinna already has
the 16h represents the amount of money made at the museum, with h being the number of hours worked
the inequality symbol is a greater than or equal sign because Corinna must have at least $256 to get the plane ticket, which means you either have to have the exact amount amount or more than the exact amount needed
4x3+ 13x2 + 5x- 4 is divided by x+ 1?
Answer:
The quotient to this equation is 4x² + 13x + 1
Step-by-step explanation:
When we divide exponents, we subtract the exponential numbers.
4x³ + 13x² + 5x - 4 / x + 1
Now, we divide. For this problem, we are only dividing the like terms of x because anything divided by 1 will equal to itself.
4x² + 13x + 5 - 4
Now, we combine like terms.
4x² + 13x + 1
