A waterfall has a height of 1400 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 16 feet per second. The height, h, of the pebble after t seconds is given by the equation h equals negative 16 t squared plus 16 t plus 1400
h=−16t2+16t+1400. How long after the pebble is thrown will it hit the ground?
Answer
The pebble hits the ground after 9.8675 s
Step-by-step explanation:
Given
waterfall height = 1400 feet
initial velocity = 16 feet per second
The height, h, of the pebble after t seconds is given by the equation.
[tex]h(t) = -16t^{2}+16t+1400[/tex]
The pebble hits the ground when [tex]h = 0[/tex]
[tex]h=-16t^{2}+16t+1400[/tex] ---------------(1)
put [tex]h=0[/tex] in equation (1)
[tex]0=-16t^{2}+16t+1400[/tex]
[tex]-16t^{2}+16t+1400=0[/tex]
Divide by -4 to simplify this equation
[tex]4t^{2}-4t-350=0[/tex]
using the Quadratic Formula where
a = 4, b = -4, and c = -350
[tex]t=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]t=\frac{-(-4)\pm\sqrt{(-4)^{2}-4(4)(-350) } }{2(4)}[/tex]
[tex]t=\frac{4\pm\sqrt{16-(-5600) } }{8}[/tex]
[tex]t=\frac{4\pm\sqrt{16+5600 } }{8}[/tex]
[tex]t=\frac{4\pm\sqrt{16+5616 } }{8}[/tex]
The discriminant [tex]b^{2}-4ac>0[/tex]
so, there are two real roots.
[tex]t=\frac{4\pm12\sqrt{39 } }{8}[/tex]
[tex]t=\frac{4}{8}\pm\frac{12\sqrt{39 }}{8}[/tex]
[tex]t=\frac{1}{2}\pm\frac{3\sqrt{39 }}{2}[/tex]
Use the positive square root to get a positive time.
[tex]t=9.8675 s[/tex]
The pebble hits the ground after 9.8675 second
What are the measures of the missing angles x°, y° of a regular triangle if one angle measure equals 60°?
Answer:
So each interior angle measurement of the regular triangle is 60 degrees.
Step-by-step explanation:
If the triangle is regular, this means all the side measurements are congruent to each other and that all the angle measurements are congruent to each other.
If the sum of the angles in a triangle is 180 degrees and you know they are each the same then you could either solve x+x+x=180 or know we are just dealings with an equiangular triangle in which all angles have measurement 60 degrees.
If need more convincing, let's actually solve:
x+x+x=180
3x=180
x=180/3
x=60
So each interior angle measurement of the regular triangle is 60 degrees.
Boxes of different sizes are stacked to create a small sculpture. The openings of the boxes are all similar rectangles. The bottom edge of the smallest rectangular opening 3 centimeters, while the bottom edge of the largest rectangular opening is 9 centimeters. The perimeter of the smallest rectangular opening is 15 centimeters What is the perimeter of the largest rectangular opening?
I’ll put you as brainliest
A) 90 cm
B)42cm
C) 45 cm
Answer:
I believe C)45cm but I know for sure its not B)42cm
Step-by-step explanation:
PLEASE HELP ME
I REALLY NEED IT
ITS DUE TODAY
PLEASE
Answer:
[tex]A=16\pi\ units^{2}[/tex]
[tex]A=50.24\ units^{2}[/tex]
Step-by-step explanation:
we know that
The shape of the figure is a quarter of circle
so
The area of the figure is equal to the area of a circle divided by 4
[tex]A=\frac{1}{4}\pi r^{2}[/tex]
we have
[tex]r=8\ units[/tex]
substitute
[tex]A=\frac{1}{4}\pi (8)^{2}[/tex]
[tex]A=16\pi\ units^{2}[/tex] ----> exact answer
assume
[tex]\pi =3.14[/tex]
[tex]A=16(3.14)=50.24\ units^{2}[/tex] ----> decimal answer
A 60 - kilogram person stands on a compression spring . The spring constant is 2500 Newtons per meter .
What is the displacement of the spring ?
A) 0.00392m
B)0.024m
C)0.1176 m
D) 0.2352m
Step-by-step explanation:
Let the mass of the person be [tex]m[/tex].
Let the spring constant be [tex]k[/tex].
Let the displacement in spring be [tex]x[/tex]
Let the acceleration due to gravity be [tex]g[/tex]
As it is given that the person just stands,the forces are balanced.
So,[tex]mg=kx[/tex]
Given,
[tex]m=60Kg\\k=2500Nm^{-1}\\g=9.8ms^{-2}[/tex]
[tex]60\times 9.8=2500\times x\\x=\frac{588}{2500}=0.2352m[/tex]
In a psychological experiment, a person is able to memorize M words in t minutes, where M= -0.001t^3 + 0.1t^2. Find the average rate of change in the number of words a person can memorize between 10 minutes and 20 minutes
What operation must be done to both sides of the equation to solve for p- -3 7/9 = 5/6?
A) add 5/6. B) subtract 3 7/9. C) subtract 5/6. D) add 3 7/9
Given equation: p - -3 7/9 = 5/6
When you subtract a negative number you automatically change it to adding a positive number.
p - -3 7/9 = 5/6 → p + 3 7/9 = 5/6
To isolate p in this equation we need to subtract 3 7/9 to both sides.
p + 3 7/9 - 3 7/9 = 5/6 - 3 7/9
p = -161/18
_______
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7/8 of a rectangle is colored red. Damien cuts this red part into a number of pieces so that each piece is 1/24 of the whole rectangle. Find the number of red pieces Damien has.
Answer: Damien has 21 red pieces
Step-by-step explanation:
First, 7/8 of the rectangle is coloured red.
Then, the 7/8 was cut into a size 1/24 of the rectangle each.
That consequently means that 24 of those pieces will form the whole shape.
Since red covers 7/8 of the rectangle, the number of red pieces invariably becomes
⅞ × 24 pieces, which is equal to 21 pieces
Therefore, Damien has cut the red part of the rectangle into 21 pieces
Final answer:
Damien has 21 red pieces after dividing the red part of the rectangle, which is 7/8, into pieces that are each 1/24 of the whole rectangle.
Explanation:
To find the number of red pieces Damien has, we first determine the fraction of the rectangle that is colored red, which is 7/8. Then, we find the size of each piece that Damien cuts, which is 1/24 of the whole rectangle.
Since each piece is 1/24, and Damien is cutting up only the red part which is 7/8 of the whole, we calculate the number of pieces by dividing the red part by the size of each piece: number of red pieces = (7/8) / (1/24).
To do this division, we multiply by the reciprocal of the divisor: (7/8) * (24/1) = 21. Therefore, Damien has 21 red pieces.
Which of the following charts showing angle measures implies that quadrilateral ABCD and quadrilateral EFGH are not congruent
Answer:
D
Step-by-step explanation:
One or more corresponding angles are not congruent.
ABC is not congruent to EFG
BCD is not congruent to FGH
CDA is not congruent to GHE
DAB is congruent to HEF
Answer: D
Step-by-step explanation:
Stephanie knows that don has a bunch of nickels and dimes in his pocket and that the total amount is $3.25
Answer:
The quantity of currency in the pockets does Stephanie has is 45 nickles and 10 dims .
Step-by-step explanation:
Given as :
The total amount of money does Stephanie have = $ 3.25
The total money is in the form of nickels and dimes
Let the number of nickels = n
And The number of dims = d
∵ we know that 20 nickles makes 1 dollar
And 10 dimes makes 1 dollar
So , in total of 3.25 dollar the number of dime and nickles be
∵ 20 nickles makes 1 dollar
∴ 45 nickles will makes [tex]\frac{1}{20}[/tex] × 45 dollar
I.e 45 nickles will makes 2.25 dollar
Now, ∵ 10 dimes will make 1 dollar
So, The total number of nickles and dimes satisfying equation
45 nickles + 10 dimes = 2.25 dollar + 1 dollar = 3.25 dollar
Hence The quantity of currency in the pockets does Stephanie has is 45 nickles and 10 dims . Answer
Answer:
4.40
Step-by-step explanation:
The amount of money Ivan has in his pocket is n.
Meg has $3.25 more than Ivan. Meg has $7.65.
Complete the equation that models the situation. Then, give the value of n.
$3.25
÷
+
$7.65
×
$10.90
$4.40
how do you find x in y=4x+6
Answer:
impossible!
Step-by-step explanation:
There is no solution! 0=0
Answer:
x = (y/4) - (3/2)
Step-by-step explanation:
y=4x+6 (subtract 6 from both sides)
y - 6 = 4x (divide both sides by 4 and rearrange)
x = (y-6) / 4
x = (y/4) - (6/4)
x = (y/4) - (3/2)
Two parallel lines are intersected by another line, as shown below.
What is the measure of ∠1?
A
61°
B
74°
C
81°
D
119°
The measure of the angle 1 for the given figure is 61 degree.
Hence the correct option is (A).
From the given figure we have two parallel lines and a transversal which intersects them.
The 119 degree angle and the angle above the angle 1 are corresponding angles, so they are equal.
And the angle above angle numbered 1 and the angle numbered 1 are straight line angles, so the sum of them is 180 degrees.
119 + angle 1 = 180
angle 1 = 180 - 119
angle 1 = 61
Hence the measure of the angle 1 for the given figure is 61 degree.
Hence the correct option is (A).
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3. (First picture answer options are the 4 graphs after it.)
Answer:
The correct graph is attached below.
Step-by-step explanation:
Given:
Initial temperature is 0°.
Decrease in temperature per hour is 12°.
Since, the initial temperature is 0°, the line must pass through the origin as temperature is plotted along the y-axis.
Also, decrease in temperature per hour is 12°. So, this represents the slope of the line. So, the slope should be -12 as there is decrease in temperature with increasing time.
So, the correct graph will be a line passing through origin and the slope of the line must be -12. Also, the temperatures will be along the negative y-axis as the values are decreasing with time.
Hence, the third graph is the correct one and is shown below.
which value of x is in the solution set of the inequality -x+8>6
Solving the inequality [tex]-x+8>6[/tex] we get [tex]x<2[/tex]
Step-by-step explanation:
We need to find the value of x from the inequality [tex]-x+8>6[/tex]
Solving:
[tex]-x+8>6[/tex]
Subtract 8 on both sides:
[tex]-x+8-8>6-8[/tex]
[tex]-x>-2[/tex]
Divide both sides by (-1). For doing this the sign of inequality is reversed i.e, > is changed into <
[tex]x<2[/tex]
So, Solving the inequality [tex]-x+8>6[/tex] we get [tex]x<2[/tex]
Keywords: Solving inequalities
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Which is the best first step and explanation for solving this system of equations?
Answer:
Subtract equation 1 from equation 2
Step-by-step explanation:
Solve the following system:
{3 x + 4 y = 12 | (equation 1)
3 x = 2 y - 8 | (equation 2)
Express the system in standard form:
{3 x + 4 y = 12 | (equation 1)
3 x - 2 y = -8 | (equation 2)
Subtract equation 1 from equation 2:
{3 x + 4 y = 12 | (equation 1)
0 x - 6 y = -20 | (equation 2)
Divide equation 2 by -2:
{3 x + 4 y = 12 | (equation 1)
0 x+3 y = 10 | (equation 2)
Divide equation 2 by 3:
{3 x + 4 y = 12 | (equation 1)
0 x+y = 10/3 | (equation 2)
Subtract 4 × (equation 2) from equation 1:
{3 x+0 y = (-4)/3 | (equation 1)
0 x+y = 10/3 | (equation 2)
Divide equation 1 by 3:
{x+0 y = (-4)/9 | (equation 1)
0 x+y = 10/3 | (equation 2)
Collect results:
Answer: {x = -4/9 , y = 10/3
Solve for x.
7x + 14 – 2x = −x + 12 – x − 19
A. x = −3
B. x = −1
C. x = 1
D. x = 3
Answer:
x=-3
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
A
A.K.A – 3.
Step-by-step explanation:
on a field trip the ratio of students who brought a water bottle to those who didnt was 7 to 4. If 60 students did not bring a water bottle, determine the total number of studens on the field trip
3 11/16 into a decimal
Answer:
3.6875
Step-by-step explanation:
Answer:
3.6875
Step-by-step explanation:
First, let's leave 3 alone since its a whole number. So now we're dividing the actual fraction. Remember that the top dog goes under, which means that the place where the numerator goes is where the dividend should be, and the denominator is where the divisor should be. Add a decimal point and then after that a few zeros to the 11. Divide like a decimal. You should get 0.6875. Now take that 3 that we left alone before and add it, so you should get 3.6875.
Is x÷9=-4 an expression or equation
solve for x,
-3x = -15
Answer:
x=5
Step-by-step explanation:
so to isolate the x you dived the -3 to both sides
so it will now be
x=5 because a negative times or divided by a negative equals a positive so to prove that x=5
-3(5)=-15
which is true
the ratio of berries to Oranges is 10:1 if there are 25 oranges how many berries would there be
Answer:
250 berries
Step-by-step explanation:
10 to 1 means 10 times as many berries as oranges
25x10=250
If there are 25 oranges then the number of berries would be 250 and this can be determined by using the arithmetic operations.
Given :
The ratio of berries to Oranges is 10:1.
The following steps can be used to determine the number of berries if there are 25 oranges:
Step 1 - Let the total number of berries be 'a' and the total number of oranges be 'b'.
Step 2 - As per the given data:
[tex]\dfrac{a}{b}=\dfrac{10}{1}[/tex]
Step 3 - If there are 25 oranges then the number of berries would be:
[tex]\dfrac{a}{25}=\dfrac{10}{1}[/tex]
[tex]a = 25\times 10[/tex]
a = 250
So, if there are 25 oranges then the number of berries would be 250.
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Please need help on this
Answer:
Culinary school because it is shorter schooling and costs less
Step-by-step explanation:
When Sierra gets home 3/4, of a sandwich is left in the refrigerator. She cuts the remaining part into three equal
parts and eats two of them. What fraction of the whole sandwich did she eat?
The fraction of the whole sandwich she ate is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The given is:
When Sierra gets home 3/4, of a sandwich is left in the refrigeratorShe cuts the remaining part into three equal partsShe eats two of themWe need to find What fraction of the whole sandwich she ate
∵ The remaining of the whole sandwich in the refrigerator is [tex]\frac{3}{4}[/tex]
∵ Sierra cuts the remaining part into 3 equal parts
- That mean divide [tex]\frac{3}{4}[/tex] by 3
∴ Each part = [tex]\frac{3}{4}[/tex] ÷ 3
- Replace ÷ by × and reciprocal 3
∴ Each part = [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{3}[/tex]
∴ Each part = [tex]\frac{1}{4}[/tex] of the whole sandwich
∵ She ate two of them
∴ She ate = 2 × [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex]
- Divide up and down by 2 to simplify it
∴ She ate = [tex]\frac{1}{2}[/tex] of the whole sandwich
The fraction of the whole sandwich she ate is [tex]\frac{1}{2}[/tex]
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Can anyone help solve this equation?
Answer:
13
Step-by-step explanation:
3 x 3 = 9
7 + 3 = 10
7 + ? = 3 + 7 + 3 + 7
7 + ? = 20
? = 13
Answer:
13Step-by-step explanation:
[tex]p\times p=9\\\\p^2=9\to p=\sqrt9\to \boxed{p=3}\\\\c+p=10\qquad\text{put the value of}\ p\\\\c+3=10\qquad\text{subtract 3 from both sides}\\\\\boxed{c=7}\\\\c+s=p+c+p+c\qquad\text{put the values of}\ p\ \text{and}\ c\\\\7+s=3+7+3+7\\\\7+s=20\qquad\text{subtract 7 from both sides}\\\\\boxed{s=13}[/tex]
To perform car maintenance, a mechanic
charges for parts and $45 an hour for
labor. The total cost that Terri spent for
2 hour of car maintenance is $125.
Assume the relationship is linear. Find
and interpret the rate of change and the
initial value
Answer:
C = 35 + 45h
In the equation above $35 is the initial value which interprets the cost for motor parts and $45/hour is the rate of charge of the mechanic per hour.
Step-by-step explanation:
Charges for parts and $45 per hour for labor that takes a mechanic for maintenance of a car.
It costs $125 as Terri spent 2 hours for car maintenance.
Since the function is linear, so we can write
125 = 45 × 2 + x {Where x is the charges for parts}
⇒ x = 35
Therefore, the equation that models the situation is given by
C = 35 + 45h ......... (1)
where C is the total cost and h is the number of hours.
Here, in equation (1) $35 is the initial value that interprets the cost for parts and $45/hour is the rate of charge of the mechanic per hour. (Answer)
What is 7 divided by 24.15
Answer:
20/69=0.2898550724637...
Step-by-step explanation:
a calculator
The result of 7 divided by 24.15 is approximately 0.29 when rounded to two decimal places.
Explanation:The student has inquired about the result of the mathematical operation, division, specifically what is 7 divided by 24.15. To solve this question, you simply divide 7 by 24.15 on a calculator or by manual long division. The answer is approximately 0.29 when rounded to two decimal places. It should be noted that the exact quotient might vary depending on the number of decimal places you consider.
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Which of the following is a true statement?
A. |-15| = -15
B. |-12| > -15
C. |-12| > |15|
D. |15| > |-15|
Answer:
A. is False
B. is True
C. is False
D. is False
Step-by-step explanation:
Its absolute value so that means all numbers are now positive only with the ones that are with the double lines
1. What elevation is Point A on Map 1? *
10 feet
30 feet
50 feet
70 feet
Will make brainliest
According to the map, each line is 10 feet.
A is 4 lines from the one marked 30 ft.
4 x 10 = 40 feet.
30 +40 = 70 feet.
The answer is 70 feet.
Students at a high school were polled regarding whether or not they would like to change the vending options at the school. Use the tree diagram to determine how many students responded “yes”.
A. 250
B. 550
C.750
D.450
A total of 750 students responded yes.
As it is given in the tree diagram that is lower there was a total of 450 students who responded yes.
Now, in upper there were a total of 400 students of which 100 students responded no which means (400-100), students responded yes i.e., a total of 300 students responded yes.
So, upper+lower responses of yes will be total responses of students as yes.
So, a total of 300+450=750 students responded yes.
Hence, 750 students responded yes.
Therefore, option C is the correct answer.
What is meaning of the respond?1 : to say something in return : make an answer respond to criticism. 2a : to react in response responded to a call for help. b : to show favorable reaction respond to surgery. 3 : to be answerable respond in damages.
What are examples of respond?Respond is defined as to answer or reply or to act in return. An example of to respond is to answer a question in class. An example of to respond is for an ambulance to rush to the scene of an accident after a phone call requesting their service. (intransitive) To say something in return; to answer; to reply.
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Which equation has NO solution? A) 10x + 5 2 = 3x + 6 B) 8 − 6x 4 = 4 + 2x C) 12x − 11 4 = 3x − 2 D) 18x − 10 2 = 9x − 5
Answer:
B) 16x+11/4 =4x+5-2
Step-by-step explanation:
the equation that has no solution is B)[tex]\( \frac{16x + 11}{4} = 4x + 5 \).[/tex]
The correct option is (B).
To find out which equation has no solution, let's solve each equation and see if any leads to a contradiction.
A)[tex]\( \frac{10x + 5}{2} = 3x + 6 \)[/tex]
Multiply both sides by 2 to eliminate the fraction:
[tex]\( 10x + 5 = 6x + 12 \)[/tex]
Subtract (6x) from both sides:
[tex]\( 4x + 5 = 12 \)[/tex]
Subtract 5 from both sides:
( 4x = 7 )
Divide both sides by 4:
[tex]\( x = \frac{7}{4} \)[/tex]
B) [tex]\( \frac{16x + 11}{4} = 4x + 5 \)[/tex]
Multiply both sides by 4:
[tex]\( 16x + 11 = 16x + 20 \)[/tex]
Subtract (16x) from both sides:
( 11 = 20 ) - Contradiction
C) [tex]\( \frac{8 - 6x}{4} = 4 + 2x \)[/tex]
Multiply both sides by 4:
[tex]\( 8 - 6x = 16 + 8x \)[/tex]
Subtract 8 from both sides:
[tex]\( -6x = 8x + 8 \)[/tex]
[tex]\( -6x = 8x + 8 \)[/tex]
[tex]\( 0 = 14x + 8 \)[/tex] - Contradiction
D)[tex]\( \frac{18x - 10}{2} = 9x - 5 \)[/tex]
Multiply both sides by 2:
[tex]\( 18x - 10 = 18x - 10 \)[/tex] - No contradiction, the equation holds true for all ( x ).
So, the equation that has no solution is B)[tex]\( \frac{16x + 11}{4} = 4x + 5 \).[/tex]
complete question given below:
Which equation has NO solution?
A) (10x+5)/2 =3x+6
B) (16x+11)/4 =4x+5
C) (8-6x)/4 =4+2x
D) (18x-10)/2 =9x-5
HELP ASAP
The dinner check was $85.00. If Tyler gave the waiter a 20% tip, how much was the tip?
The dinner check was $85.00. If Tyler gave the waiter a 20% tip, how much did Tyler spend in total?
Answer:
It is $17.
Step-by-step explanation: