The equation that could be used to determine the time, t, it takes to run 10,000 meters as a function of the average speed, s, of the runner where t is in minutes and s in miles per minute is t = 6.2/s miles/minute
What is an average speed?Average speed is defined as the rate of change in distance of a body. Mathematically;
Speed = Distance/TimeGiven the distance of the runner in miles to be;
d = 6.2milesTime taken = tAverage speed = sTo express t in terms of the average speed s and distance of 6.2miles, we will substitute the values into the formula;
s = D/tSubstituting D = 6.2miles into the formula;
s = 6.2/tCross multiply
St = 6.2Divide both sides by 's'
st/s = 6.2/s
t = 6.2/s
Hence, the equation that could be used to determine the time, t, it takes to run 10,000 meters as a function of the average speed, s, of the runner where t is in minutes and s in miles per minute is t = 6.2/s miles/minute
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HELP HURRY!!!! Simplify. 15÷(2+3) Enter your answer in the box.
Answer:
It's equal =3
Seven less than the product of 8 and a number is equal to 5.
Answer:
8n - 7 = 5
Step-by-step explanation:
number - n
product of 8 and a number - 8n
Seven less than the product of 8 and a number - 8n - 7.
Seven less than the product of 8 and a number is equal to 5.
8n - 7 = 5
Answer:
8n-7=5
you can do this
i cand do explaination
Prove the following using a direct proof:
The sum of the squares of 4 consecutive integers is an even integer.
It is proven that "the sum of the squares of four consecutive integers is an even integer" is the solution part.
To prove that the sum of the squares of four consecutive integers is an even integer, we need to show that it can be expressed as twice another integer.
Let's assume the four consecutive integers are n, n+1, n+2, and n+3.
The sum of their squares can be expressed as:
[tex]n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2[/tex]
Expanding the squares, we have:
[tex]n^2 + (n^2 + 2n + 1) + (n^2 + 4n + 4) + (n^2 + 6n + 9)[/tex]
Combining like terms, we simplify this expression to:
[tex]4n^2 + 12n + 14[/tex]
Now, let's consider this expression [tex]4n^2 + 12n + 14[/tex].
We can factor out 2 from each term, resulting in:
[tex]2(2n^2 + 6n + 7)[/tex]
Since [tex]2n^2 + 6n + 7[/tex] is an integer, let's denote it as k, where k is an integer.
Therefore, the expression becomes:
2k.
We have successfully expressed the sum of the squares of four consecutive integers as twice another integer (2k), which proves that it is an even integer.
Hence, the sum of the squares of four consecutive integers is an even integer.
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If cde is a straight angle, de bisects gdh, m gde = (8x-1), m edh = (6x+15), and m cdf= 43, find each measure.
Answer:
GDE = 63
EDH = 63
GDH = 126
FDG = 74
FDH = 200
FDE = 137
Step-by-step explanation:
It is stated that DE bisects <GDH. Since bisecting means halving into equal parts, <GDE = <EDH
from the question,
<GDE = (8x-1)
<EDH = (6x+15)
Since <GDE = <EDH,
(8x-1) = (6x+15), if we collect like terms
8x - 6x = 15 + 1
2x = 16
x = 8°
Again, from the diagram, we see that
<GDH = <GDE + <EDH, thus
<GDH = (8x-1) + (6x+15)
<GDH = 8x -1 + 6x + 15
<GDH = 14x + 14, substitute for x
<GDH = 14*7 + 14
<GDH = 112 + 14
<GDH = 126°
<FDG = 180 - <CDF - <GDE
<FDG = 180 - 43 - 63
<FDG = 74°
<FDH = <FDG + <GDE + <EDH
<FDH = <FDG + <GDH
<FDH = 74 + 126
<FDH = 200°
<FDE = <FDG + <GDE
<FDE = 74 + 63
<FDE = 137°
The measure of angle m∠GDE is 71.4° and the measure of angle m∠EDH is 65.6° on straight angle ∠CDE.
The straight angle ∠CDE, DE bisects GDH, m∠GDE=(8x-1)°, m∠EDH=(6x+15)° and m∠CDF=43°.
Here, m∠GDE+m∠EDH+m∠CDF = 180°
So, (8x-1)°+(6x+15)°+43°=180°
14x+57°=180°
14x=180°-57°
14x=123
x=123/14
x=8.8°
m∠GDE=8x-1
= 71.4°
m∠EDH= 65.6°
Hence, the measure of angle m∠GDE is 71.4° and the measure of angle m∠EDH is 65.6° on straight angle ∠CDE.
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please help// geometry question pt.3
Answer:
Last one - CD with a line over it with arrowheads.
Step-by-step explanation:
Last one - CD with a line over it with arrowheads.
5x + 7 is a algebraic expression. it is a mathematical phrase that includes at least one variable and one operation. what is the variable
Answer:
x is the variable
Step-by-step explanation:
The variable is the letter in the expression
x is the variable
5 is the coefficient of the variable
7 is the constant
The tallest man in medical history was Robert Wadlow. He was 12 4/5times as tall as he appears in a Book of Reords photograph. He is 7 1/2 inches tall in the photograph. How tall was Robert Wadlow?
six times a number x squared
Answer:
6x^2
Step-by-step explanation:
Because we are multiplying 6 and a number x squared, we know that x will have an exponent of 2. Then, multiplying that by 6 and using conventional algebraic techniques, we can combine the two terms together.
6 * x^2
6x^2
Answer:
[tex]\displaystyle \rm \longmapsto 6 \times x {}^{2} [/tex]
[tex]\displaystyle \rm \longmapsto {6x}^{2} [/tex]
If m∠NLO = 41° and m∠NLM = 88°, what is m∠OLM? 47° 44° 129° 23°
Answer:
∠ OLM = 47°
Step-by-step explanation:
Given:
∠ NLO = 41°
∠ NLM = 88°
Find:
∠ OLM
Computation:
⇒ ∠ NLM = ∠ NLO + ∠ OLM
⇒ 88° = 41° + ∠ OLM
⇒ ∠ OLM = 88° - 41°
⇒ ∠ OLM = 47°
Answer:
47
Step-by-step explanation:
Round to the nearest eurocent per kilo
Answer:
2 eurocent per kilo
Step-by-step explanation:
Since we are already given the conversion units, we only simply need to divide/multiply and cancel out units.
Dollars and dollars cancel out.
We are left with eurocent.
Pounds and pounds cancel out.
We are left with kilograms.
We do want eurocent over kilograms.
0.89(0.93) = 0.8277/0.4536 = 1.82474
Since we want to round it to the nearest cent, we round up because 8 ≥ 5:
1.82474 ≈ 2
Type the correct answer in the box. The motion of a clock pendulum is modeled by this graph. The function describing this graph is a transformation of the parent cosine function, y = cos x . Find the range, period, and maximum of the transformed function, D(t).
Answer:
The range of the function is -10, 10.
The period of the function is 1.2 seconds.
The maximum of the function is 10 centimeters.
Step-by-step explanation:
The range of a cosine function is the set of output values. In this situation, the range is the distance the pendulum covers, which is represented on the D(t) axis. The graph shows that the range of the function D(t) is [-10, 10].
The period is the length of a cycle. The graph shows that the cycle repeats every 1.2 seconds.
The maximum is the y-value of the highest point on the graph. The graph shows the maximum of the function is 10 centimeters.
Find slope of the line (-3, -2) ((5, 4)
Answer:
4+2/5+3=3/4 slope
Step-by-step explanation:
sssllllooooppppeeee
Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180°
x°=
(x+5)°=
5X°=
Answer:
[tex] \boxed{ \bold{ \sf{x = 25°}}}[/tex]
[tex] \boxed{ \bold{ \sf{(x + 5) = 30°}}}[/tex]
[tex] \boxed{ \bold{ \sf{5x = 125°}}}[/tex]
Step-by-step explanation:
We know that sum of angle of triangle adds up to 180°
Finding the value of x
[tex] \sf{5x + x + x + 5 = 180°}[/tex]
Collect like terms
⇒[tex] \sf{7x + 5 = 180}[/tex]
Move 5 to right hand side and change its sign
⇒[tex] \sf{7x = 180 - 5}[/tex]
Subtract 5 from 180
⇒[tex] \sf{7x = 175}[/tex]
Divide both sides of the equation by 7
⇒[tex] \sf{ \frac{7x}{7} = \frac{175}{7} }[/tex]
Calculate
⇒[tex] \sf{x = 25°}[/tex]
Finding the value of ( x + 5 )°
[tex] \sf{x + 5}[/tex]
plug the value of x
⇒[tex] \sf{25 + 5}[/tex]
Add the numbers
⇒[tex] \sf{30°}[/tex]
Finding the value of 5x
[tex] \sf{5 \times 25}[/tex]
Multiply the numbers
⇒[tex] \sf{125°}[/tex]
Hope I helped!
Best regards!!
Answer:
x° = 25°
(x + 5)° = 30°
5x° = 125°
Step-by-step explanation:
total angle inside the triangle = 180 = x + (x+5) + 5x
180 = x + x + 5 + 5x
group like terms
7x + 5 = 180
subtract 5 each sides
7x = 175
x = 175/7
x = 25°
solve for : (x + 5)°
(x + 5)° = 25 + 5
(x + 5)° = 30°
solve for 5x°
5x° = 5 * 25
5x° = 125
check
180 = x + (x+5) + 5x
180 = 25 + (25+5) + (5*25)
180 = 25 + 30 + 125
180 = 180
How do I find the exact angle for b?
Answer:
107° 30'
Step-by-step explanation:
As in part (a), the hour hand moves 30° per hour, so at 1:25, it has moved ...
(1 25/60)(30°) = 42.5°
from the vertical at noon.
Similarly, the minute hand moves 6° per minute, so at 1:25, it has moved ...
(25)(6°) = 150° from the vertical at 1 o'clock.
The exact angle difference is ...
150° -42.5° = 107.5° = 107° 30'
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→1 3x x − 1 − 3 ln(x)
Answer:
3/2Step-by-step explanation:
Given the limit of a function expressed as [tex]\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})[/tex], we are to evaluate it. To evaluate it, we will simply substitute x = 1 into the function since the variable x tends to 1.
[tex]\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= (\dfrac{3(1)}{1-1} - \dfrac{3}{ln1})\\\\= \dfrac{3}{0} - \dfrac{3}{0}\\\\= \infty - \infty (ind)[/tex]
Since we got an indeterminate function, we will find the LCM of the function and solve again.
[tex]= \lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= \lim_{x \to 1} \dfrac{3xlnx-3(x-1)}{(x-1)lnx}\\\\\\= \dfrac{3(1)ln(1)-3(1-1)}{(1-1)ln1}\\\\= \frac{3(0)-3(0)}{0(0)} \\\\= \frac{0}{0} (ind)[/tex]
Applying L'hospital rule;
[tex]\frac{x}{y} = \lim_{x \to 1} \dfrac{d/dx(3xlnx-3(x-1))}{d/dx((x-1)lnx)}\\\\= \lim_{x \to 1} \dfrac{3x(\frac{1}{x})+ 3lnx-3)}{(x-1)\frac{1}{x} +lnx}\\\\= \lim_{x \to 1} \dfrac{3 + 3lnx-3}{(x-1)\frac{1}{x} +lnx}\\\\= \frac{3ln1}{(1-1)\frac{1}{1} +ln1}\\\\= \frac{0}{0} (ind)[/tex]
Applying L'hospital rule again;
[tex]= \lim_{x \to 1} \dfrac{\frac{d}{dx} (3lnx)}{\frac{d}{dx} ((x-1)\frac{1}{x} +lnx)}\\\\= \lim_{x \to 1} \dfrac{\frac{3}{x} }{(x-1)\frac{-1}{x^2} + \frac{1}{x} +\frac{1}{x} }\\\\= \dfrac{\frac{3}{1} }{(1-1)\frac{-1}{1^2} + \frac{1}{1} +\frac{1}{1} }\\\\= \frac{3}{0(-1)+2}\\ \\= \frac{3}{2-0}\\ \\= 3/2[/tex]
Hence the limit of the function is 3/2.
In a behavioral field study, my colleagues and I found that teams of three
students exercised more than everyone else in the study.
True
False
Answer:
False
Step-by-step explanation:
The given statement is false because behavioral field study deals with the cognitive processes during field study or task.
In the given statement only the physical strength of the students is measured while behavioral field study measures or explores human behavior and how or what techniques are students using to perform the field task.
Hence, the correct option is "False".
set up a skeletal profit and loss statement in boss dollars and percentage if your year-end profit is 7800, the profit percentage is 3.9%, and the yearly cost of your goods sold is 120000
ne s o
Step-by-step explanation:
Find the value of x. Round your answer to the nearest tenth.
x
10
Blank 1:
Answer:
12.2
Step-by-step explanation:
By Pythagoras theorem:
[tex] {x}^{2} = {10}^{2} + {7}^{2} \\ {x}^{2} = 100 + 49 \\ {x}^{2} = 149 \\ x = \sqrt{149} \\ x = 12.2065556 \\ x \approx \: 12.2[/tex]
If 5 tickets cost $3.75 how much does 1 ticket cost
Answer:
0.75
Step-by-step explanation:
Answer:
$1.33 per ticket cost
Step-by-step explanation:
5 / $3.75 = $1.33 per 1 ticket cost
A ladder is leaning against the side of a 10 m house. If the base of the ladder is 3 m away
from the house, how long is the ladder? Please draw a diagram.
Answer: It depends on how you round but about 10.44 m.
Step-by-step explanation:
3 to the power of negative 2 is equivalent to what 1/9 1/6 -6 -9
Answer:
1/9
Step-by-step explanation:
You have 3 to the power of -2.You must take that and turn it into 1/3 to the power of 2, so now the exponent is no longer negative and therefore can be solved.After solving the exponent, you are left with 1/9 as your answer.WILL MARK BRAINLIEST TO FIRST CORRECT ANSWER!!!
Math the the sentence with an appropriate variable expression. The number of miles a plane can travel on 50 gallons of fuel.
a. x + 50
b. 50x
c. 50 ÷ x
d. 50 - x
Answer:
C.
Step-by-step explanation:
You will need to divide the miles in order to understand how much fuel
solve for x
pleaseee answer and explain <333
Hello! :)
Answer:
[tex]\huge\boxed{x = (\frac{b}{a})(P+c)}[/tex]
[tex]\frac{a}{b}x - c = P[/tex]
Solve for x:
Begin isolating the variable by adding "c" to both sides:
[tex]\frac{a}{b}x - c + c= P + c[/tex]
[tex]\frac{a}{b}x = P+ c[/tex]
Divide both sides by a/b, or multiply by the reciprocal (b/a)
[tex](\frac{b}{a}) \frac{a}{b}x = (\frac{b}{a})(P + c)[/tex]
Therefore:
[tex]x = (\frac{b}{a})(P + c)[/tex]
In 25 years, a bond that paid 4.75% simple interest earned $4,750 interest. What was the principal of the bond in dollars?
Answer:
$ 4000Step-by-step explanation:
Given,
Rate ( R ) = 4.75 %
Time ( T ) = 25 years
Simple Interest ( I ) = $ 4,750
Principal ( P ) = ?
Finding the principal
We know that,
[tex] \boxed{ \sf{principal = \frac{interest \: \times 100}{ \: time \: \times \: rate} }}[/tex]
plug the values
⇒[tex] \sf{ \frac{4750 \times 100}{4.75 \times 25} }[/tex]
Calculate
⇒[tex] \sf{\frac{475000}{118.75} }[/tex]
⇒$ [tex] \sf{4000}[/tex]
Hope I helped!
Best regards!!
Answer:
2000
Step-by-step explanation:
Mr. Hobbs has 10 blue markers, 6 black markers, and 8 red markers
on his desk. What fraction of black markers can be found on Mr.
Hobbs' desk? thats the question if you could answer that that'd be great.
Answer: 1/4
Step-by-step explanation:
If there are 6 black markers and they are a total combination of 24 difference colored markers.
The the fraction will be 6/24 which reduces to 1/4
-5, 4, -26, -48, 12 least to greatest
Answer:
hey!
Your answer is ...
-48 , -26 , -5 , 4 , `12
Step-by-step explanation:
HOPE THIS HELPED!
:)
In the equation A = bh,
СС
what does each of the
variables stand for?
Answer:
A= Area
B= Base of the figure
H= Height of the figure
B and H are multiplied together to find the area
Step-by-step explanation:
Find the equation of the line parallel to y= -5x-3 that passes through the point ( -5, -4). If possible, write the equation in slope-intercept form.
Answer:
y = -5x - 29
Step-by-step explanation:
y-intercept form is y = mx +b,
m is slope, for parallel line slope is the same, so m= -5
y = -5x + b
To find b, we need to use the point (-5, - 4).
- 4 = -5*(-5) + b
- 4 = 25 + b
b = - 29
y = -5x - 29
please help me. Brainiest to the first answer person
Answer:
0.3 or 30%
Step-by-step explanation:
Blue = 1/10
Red = 2 white
**************
White + red = 1 - 1/10
White +2white= 9/10
White = 3/10
Red = 6/10
So probability of white ball is 3/10 or 30%
Graph the equation.
y= 1/8(x-6)(x+2)
Answer:
see below
Step-by-step explanation:
See the attachment.
The graph will have x-intercepts where the factors are zero, at x=6 and x=-2. The y-intercept will be the value when x=0: (1/8)(-6)(2) = -1.5.
The axis of symmetry is halfway between the zeros, so is x = (6-2)/2 = 2.
The minimum value of the function is at x=2, so is ...
y = (1/8)(2 -6)(2 +2) = 1/8(-16) = -2
Other y-values can be found by substituting other x-values in the equation and evaluating it. Rather than go to that trouble, I prefer to use a graphing calculator.