The graph represents a person's heart rate in beats per minute during 30 minutes of exercise.
Which statement best describes the relationship between heart rate and time doing exercise?
Answers
Looking at the graph closely we can see that the heart rate increases from 0 to 6 min then became steady from 6 to 25 min then finally decreases from 25 to 30 min. Therefore the correct answer is:
“The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.”
In real life cardiac exercises, we can interpret that the period from 0 to 6 min is the period where the person is still warming up thus leading to an increase in heart rate. At 6 min, the person is fully warmed up hence reaching a stable heart rate. Then at 25 min, the person starts cooling down which means that the exercise is ending soon.
Related Questions
what is the correct name for the angle shown
Answers
Answer: The correct name is (B) ∠S.
Step-by-step explanation: We are given to find the correct name for the angle shown in the figure.
We can see in the figure that the rays RS and ST are intersecting at the point S. Therefore, RS and ST are making an angle at the point 'S'.
So, the name of the angle will be ∠S or ∠RST or ∠TSR.
First option is ∠R. This is not correct.
Second option is ∠S. This is the correct option.
Third option is ∠RTS. This is also not correct.
Fourth option is ∠SRT. This is not correct.
Thus, the correct option is (B) ∠S.
Pythagoras is planting a rose garden in the center of his rectangular yard, which is 20 feet long and 8 feet wide. He wants to dig up an area in the shape of an equilateral triangle with sides 5 feet each. After he digs up the rose-bed section, approximately how much grass will be left? Round to the nearest foot.
Answers
Area=[area of rectangle]-[area of the triangle]
area of rectangle will be:
A1=length*width
=20*8
=160 square feet
The area of the triangle will be:
A2=1/2absin theta
since the triangle is equilateral, all the angles are equal and the size of each angle is 60°. Thus the area will be:
A2=1/2*5*5sin 60
=18.3
thus the remaining area of the grass will be:
Area=160-18.3
=149.7 square feet
Answer:
The approximate remaining grass area is 144 square feet.
Explanation:
To find the area of the rectangular yard, we use the formula:
Area of rectangle [tex]= \text{length} \times \text{width} \)[/tex]
Given that the length is 20 feet and the width is 8 feet, we have:
Area of Rectangle [tex]= 20 \times 8 = 160 \text{ square feet} \)[/tex]
Next, we find the area of the equilateral triangle. Since we know the length of each side (5 feet) and an equilateral triangle can be divided into two congruent 30-60-90 triangles, we can use the formula for the area of an equilateral triangle:
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (\text{side length})^2 \)[/tex]
Plugging in the value of the side length (5 feet), we get:
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (5)^2 \)[/tex]
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times 25 \)[/tex]
Area of equilateral triangle [tex]= \frac{25\sqrt{3}}{4} \text{ square feet} \)[/tex]
Now, to find the remaining grass area after Pythagoras digs up the rose-bed section, we subtract the area of the equilateral triangle from the total area of the rectangle:
Remaining grass area [tex]= \text{Area of rectangle} - \text{Area of equilateral triangle} \)[/tex]
Remaining grass area [tex]= \ 160 - \frac{25\sqrt{3}}{4} \)[/tex]
Using a calculator, we find:
Remaining grass area [tex]\approx 144.3 \text{ square feet} \)[/tex]
Rounded to the nearest foot, the approximate remaining grass area is 144 square feet.
Find the directrix of the parabola y = (1/8)(x – 5)2 - 3.
Answers
Answer:
y= -5
Step-by-step explanation:
rewrite as standard form [tex]4.2(y-(3-))=(x-2)^{2}[/tex]
(h.k) = (2, -3), P=2
y= -3 -P
y= -3 -2
y= -5
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Which of the following expressions is not equal to p^2?
A.
p^-3 * p^5 * p^-2 * p^2
B.
p^-9 * p^0 * p^2 * p^5
C.
p^-3 * p^-1 * p * p^5
D.
p^-5 * p^9 * p^-2 * p^0
Answers
so since they're all being multiplied, just add the exponents and see which one doesn't add to 2
A. -3+5-2+2=2+0=2, yep
B. -9+0+2+5=-9+7=-2, nope
C. -3-1+1+5=-4+6=2, yep
D. -5+9-2+0=4-2=2, yep
answer is B
Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].
Here,
We have to find the expression is not equal to p^2.
What is Property of addition in power of number?
This property states that when multiplying two powers with the same base, we add the exponents.
Now,
Let an expression [tex]x^{a} x^{b}[/tex]
Then it can be written as, [tex]x^{a} x^{b} = x^{a+b}[/tex]
So, Option B is given as,
[tex]p^{-9} *p^{0} * p^{2} *p^{5} = p^{-9+0+2+5} = p^{-2}[/tex]
Which is not equal to [tex]p^{2}[/tex].
Similarly, we check all options.
We get only option B is not equal to [tex]p^{2}[/tex].
Hence,
Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].
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Given the function g(x) = 4(3)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
A) Find the average rate of change of each section. (4 points)
Answers
g(2)=4*9=36
g(1)=4*3=12
36-12/2-1=24
g(4)=4*81=324
g(3)=4*27=108
324-108/4-3=216
If f(x)=5x-7 and g(x)√x-2 which statement is true?
-5 is in the domain or
-5 is not in the domain
Answers
-5 is in the domain of the function f(x)=5x-7, but not in the domain of the function g(x)√x-2. The domain of a function is the set of all acceptable input values.
Explanation:The question is asking whether -5 is in the domain of the given functions, f(x)=5x−7 and g(x)√x−2. The domain of a function is the set of all permissible inputs or arguments, i.e. x-values that can be inserted into the function.
In the case of f(x)=5x-7, the domain is all real numbers, as we can substitute any real number into 'x' and obtain a valid result. Hence, -5, indeed, is in the domain of the function f(x). However, for the function g(x)√x-2, the domain is all non-negative real numbers since we can't take the square root of a negative number in the real number system, hence -5 is not in the domain of g(x).
Thus, the statement '-5 is not in the domain' would be true if we are referring to g(x). However, if we are referring to f(x), the statement would be false because -5 is in the domain.
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Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius round to the nearest hundredth
Answers
volume for cylinder = pi x r^2 x h
radius = half the diameter = 8/2 =4
height = 3 times the radius = 3*4 =12
using 3.14 for pi
volume = 3.14 x 4^2 x 12 = 602.88 cubic inches
How many ways are there to arrange the first five letters of the alphabet?
Answers
In combination, the number of ways of arranging 'r' items out of 'n' items is determined using n!/r!(n-r)!. In this case, you want to arrange all 5 letters. So, r=n=5. Therefore, 5!/5!(505)! = 5!/0!=5!/1. It is simply equal to 5! or 120 ways.
Answer:
120 ways
Explanation:
Since there are no repeating letters, and there are 5 total letters, there are 5!= 120 ways to arrange them. In other words, there are 5 slots to place the first letter in, then 4 slots for the second letter, 3 for the third, 2 for the fourth, and then the last letter goes in the 1 slot that is left.
I hope this is correct and if it is I hope it helps. I hope you have a great day and remember it doesn't matter what other people say or think about you, you are still and always will be strong, smart, and an amazing person. Have a wonderful day.
I am happy to help with anything.
At what angle do the angle bisectors of two same side interior angles intersect in construction with two parallel lines and a transversal?
Answers
The sum of same-side interior angles is equal to 180 degrees.
A transversal line is a line that intersects other lines.
Parallel lines are lines that run alongside each other that never intersect.
An angle bisector is a line that divides an angle into two equal parts.
Given that the sum of same side interior angles is equal to 180 degrees, then the sum of the angle formed by the angle bisector is equal to 90 degrees.
Thus the angle bisectors intersect at an angle 90 degrees.
Therefore, the angle bisectors of two same side interior angles in construction with two parallel lines and a transversal intersect at angle 90 degrees.
What is the area the shaded triangle?
Answers
Answer:
96
Step-by-step explanation:
The area of the shaded triangle will be 96 mm² so option (B) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given two inscribed triangles.
The bigger one is the right-angle triangle.
The area of the right-angle triangle will be as,
A = 1/2 x 8 x (6 + 24)
A = 4 x 30= 120 mm².
The area of the smaller right-angle triangle,
a = 1/2 x 8 x 6 = 24 mm²
The area of the shaded triangle = 120 - 24 = 96 mm².
Hence "The area of the shaded triangle will be 96 mm²".
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Evaluate the expression:
the difference of 26 and 22
Select one:
a. 48
b. 91
c. 4
d. 13/11
Answers
To do this, all you have to do is subtract 22 from 26. 26-22=4.
Answer: C.) 4
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Prove that for any x in the reals 5 divides x if and only if 5 divides x squared
Answers
if the statement is true then the contrapositive is also true:-
If, for any real x, 5 does not divide x^2 then 5 does not divide x.
Any number that 5 will divide into must end in 0 or 5 so the above is evidently true.
So the original statement is also true.
A student reader is making $5.90 per hour and gets a $0.52 raise. what is the percent increase? (round to the nearest tenth of a percent.)
Answers
There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.
Answers
To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we need to find the largest perfect square that is less than or equal to $n + 23$. The largest such $n$ is $41$.
Explanation:To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we can start by considering the numerator. The expression $(n + 1)^2$ is a perfect square, so it will always be divisible by $n + 23$ if $n + 23$ is also a perfect square. Therefore, we need to find the largest perfect square that is less than or equal to $n + 23$.
Let's consider some examples. If $n + 23 = 25$, then $n = 2$. If $n + 23 = 36$, then $n = 13$. If $n + 23 = 49$, then $n = 26$. If $n + 23 = 64$, then $n = 41$. Therefore, the largest value of $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer is $41$.
There are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.
To find the largest positive integer $n$ such that $\frac{(n + 1)^2}{n + 23}$ is an integer, we need to consider the factors of the numerator and denominator.
Let's expand the numerator, $(n + 1)^2$, using the binomial expansion formula:
$(n + 1)^2 = n^2 + 2n + 1$
Now, we divide this expression by $n + 23$ and express the result as an integer:
$\frac{n^2 + 2n + 1}{n + 23}$
We can use polynomial long division to divide $n^2 + 2n + 1$ by $n + 23$:
- (n - 21)
__________
n + 23 | n^2 + 2n + 1
- (n^2 + 23n)
_____________
-21n + 1
- (-21n - 483)
_____________
484
We obtain a remainder of 484. In order for the fraction to be an integer, the remainder must be 0. However, in this case, the remainder is not 0, which means that $\frac{(n + 1)^2}{n + 23}$ is not an integer for any positive integer $n$.
Therefore, there are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.
Complete question :-
There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.
If ABCDE is translated 3 units to the right and 4 units down, what will happen to the polygon?
Answers
B] It will move but won't change shape or size.
When polygon ABCDE is translated 3 units to the right and 4 units down, its shape and size remain unchanged, but its position on the coordinate plane changes, maintaining the same orientation and angles.
Explanation:If a polygon ABCDE is translated 3 units to the right and 4 units down, the shape and size of the polygon will remain the same, but its position will change. Each vertex (point) of the polygon will move 3 units to the right on the x-axis and 4 units down on the y-axis. This type of transformation is known as a translation, which is a slide of the entire figure in a specific direction. As a result, the translated polygon will maintain the same orientation and angles; it will simply be in a different location on the coordinate plane.
Classify the variable as discrete or continuous. weights of backpacks of first graders on a school bus
Answers
Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5).
Answers
notice, the center is clearly at the origin, and notice how long the "a" component is, also, bear in mind that, is opening towards the y-axis, that means the fraction with the "y" variable is the positive one.
Also notice, the "c" distance from the center to either foci, is just 5 units.
[tex]\bf \textit{hyperbolas, vertical traverse axis }\\\\ \cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1 \qquad \begin{cases} center\ ({{ h}},{{ k}})\\ vertices\ ({{ h}}, {{ k}}\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{{{ a }}^2+{{ b }}^2} \end{cases}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \begin{cases} h=0\\ k=0\\ a=4\\ c=5 \end{cases}\implies \cfrac{(y-{{ 0}})^2}{{{ 4}}^2}-\cfrac{(x-{{ 0}})^2}{{{ b}}^2}=1\implies \cfrac{y^2}{16}-\cfrac{x^2}{b^2}=1 \\\\\\ c=\sqrt{a^2+b^2}\implies c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \\\\\\ \sqrt{5^2-4^2}=b\implies \boxed{3=b} \\\\\\ \cfrac{y^2}{16}-\cfrac{x^2}{3^2}=1\implies \boxed{\cfrac{y^2}{16}-\cfrac{x^2}{9}=1}[/tex]
80 POINTS!
Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (give the polynomial with the GCF of 2 AND give two more forms and explain how you got it.
Answers
You can rewrite this as 2y * 2y or 4 * y * y
Katie earned $54.30 in interest from two accounts. One account Paid 4.1% apr and the other paid 3.2% apr. if she had a total of $1500 in the two accounts, How much was in each account?
Answers
Solve for x
0.032x+61.5-0.041x=54.3
0.032x-0.041x=54.3-61.5
-0.009x=-7.2
X=7.2/0.009
X=800 invested at 3.2%
1500-800=700 invested at 4.1%
Please help me I'm so confused and it's due at 7:30
Answers
Rewrite in simplest radical form 1/x^3/6.
Can anyone solve this.
Answers
find the slope of the line through points (1,8) and (2,7). write the answer in simplest form.
Answers
So, the slope is -1.
Y2-Y1/X2-X1
so the answer is -1
If $10,000 is invested in an account at the rate of 6.25% compounded monthly, then the amount after 15 years is approximately
Answers
A=p (1+r/k)^kt
A future value?
P present value 10000
R interest rate 0.0625
K compounded monthly 12
T time 15 years
A=10,000×(1+0.0625÷12)^(12×15)
A=25,473.84
The amount after 15 years is approximately $26,971.67.
Explanation:To calculate the amount after 15 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amountP = the principal amount (initial investment)r = annual interest rate (in decimal form)n = number of times interest is compounded per yeart = number of yearsIn this case, P = $10,000, r = 0.0625 (6.25% as a decimal), n = 12 (monthly compounding), and t = 15. Substituting these values into the formula:
A = $10,000(1 + 0.0625/12)^(12*15) = $26,971.67 (approximately).
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How do i graph the line y=2/3x+ 490 using the slope intercept method?
Answers
slope = rise/run. With the point 490 on the y-axis, move 3 units to the left and two units upward, and mark another point there. Draw a straight line through it, and make sure the line is rising (left to right) because the slope is positive.
Hope this helped!
Graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.
What is slope?
"Slope of the line is defined as the ratio of difference in the increment in y coordinates to the difference in increment in x-coordinates."
Formula used
standard equation of line
y = mx + c
m = slope of the line
c = y- intercept
According to the question,
Given equation of line,
[tex]y = \frac{2}{3} x+490[/tex]
Compare it with standard equation of line y = mx + c we get,
Slope [tex]m = \frac{2}{3}[/tex]
y-intercept = 490
Calculate x-intercept by putting y=0
x-intercept = -735
Now plot it on the graph as shown and join the points with slope [tex]m = \frac{2}{3}[/tex]
Hence, graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.
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Evaluate the following expression using the values given: Find 3x − y − 3z if x = −2, y = 1, and z = −2. −13 −1 1 13
Answers
The correct answer is -1
What is the value for B, after the equation A=3/7(B-25) is rearranged?
Answers
Hope this helps!
Answer:
[tex]B=\frac{7A}{3}+25[/tex]
Step-by-step explanation:
We have been given an equation [tex]A=\frac{3}{7}(B-25)[/tex]. We are asked to find the value of B for our given equation.
Upon multiplying both sides of our equation by [tex]\frac{7}{3}[/tex], we will get:
[tex]\frac{7}{3}*A=\frac{7}{3}*\frac{3}{7}(B-25)[/tex]
[tex]\frac{7}{3}*A=B-25[/tex]
[tex]\frac{7A}{3}+25=B-25+25[/tex]
[tex]\frac{7A}{3}+25=B[/tex]
[tex]B=\frac{7A}{3}+25[/tex]
Therefore, the value of B is [tex]\frac{7A}{3}+25[/tex].
What is the sum of the measures of the exterior angles of any convex polygon
Answers
Answer:
360 degrees is sum of the measures of the exterior angles of any convex polygon.
Step-by-step explanation:
Convex Polygon:
A convex polygon is a polygon with all its interior angle less than 180 degrees.Thus, all the vertices of the polygon will be away from the interior of the polygon.If all the angles are not less than 180 degrees then it becomes concave polygon.Example: Triangle is a convex polygon with three sides.Exterior angle sum Property:
If we extend the side of the polygon, then the angle formed by the extended side and polygon side is an exterior angle.The sum of all the exterior angles if a convex polygon is 360 degrees.If this convex polygon is a regular polygon, then the sum is 360 degrees and each exterior angle is equal to [tex]\frac{360}{n}[/tex], where n is the number of sides in regular polygon.The sum of the measures of the exterior angles of any convex
polygon is 360°.
What is a Convex polygon?This is the polygon that is the boundary of a convex set and has
all the interior angles to be less than 180°.
The interior angles is 180(n-2) degrees and each exterior angle
is supplementary to its interior angle thereby resulting in the
sum of the exterior angles to be 360°.
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Which graph represents the function of f(x) = 9x 2 -36/3x+6 Please help
Answers
(9x^2 - 36)
f(x) = ---------------------
3x + 6
You can simplify that function to a linear function for all x for which 3x + 6 ≠ 0
=> x ≠ - 2.
So, for x ≠ - 2, you can do:
(9x^2 - 36)
f(x) = --------------------- =
3x + 6
9(x^2 - 4)
f(x) = ---------------------
3(x + 2)
3(x + 2)(x - 2)
f(x) = --------------------- = 3(x - 2) = 3x - 6
(x + 2)
So, the graph is a right line that intercepts the y-axis at - 6 and the x-axis at x = 2, excluding x = -2 as the function is not defined for x = -2. That is the second graph of the second picture.
The given function is a quadratic equation, not a linear one, and so it would be represented by a parabolic curve on a graph, not a straight line.
Explanation:The function you're asking about, f(x) = 9x² - 36/3x + 6, is a quadratic equation. Quadratic equations are represented by parabolas on the graph not a straight line. Parabolas usually have a shape like a U (or an upside down U, depending on the equation).
The equation you've given should result in a parabolic graph. The straight line equations and graphs you’re referring to, like y = 9+3x, would not represent your function. The line graph with a y-intercept of 9 and a slope of 3 is not a representation of your function.
Also, it's important to note that the equation you provided, f(x) = 9x² - 36/3x + 6, can be simplified to f(x) = 9x² - 12x + 6.
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solve the equation 14.50-p=53 please help
Answers
14.50 - p = 53
To solve for this, we need to isolate p and see what else may need to be done afterwards.
First, isolate p by subtracting 14.50 from both sides (what you do to one side of the equation you must do to the other).
14.50 - 14.50 = 0
53 - 14.50 = 38.50
-p = 38.50
We need to solve for p, so divide both sides by -1 to get rid of the negative sign.
-p / -1 = p
38.50 / -1 = -38.50
P = -38.50
I hope this helps!
Mike forgot to replace the cap on a bottle of room freshener. The room freshener began to evaporate at the rate of 15% per day. If the original amount of room freshener in the bottle was 40 grams, which of the following graphs best represents the amount of room freshener f(x) that would remain in the bottle after x days?
graph of function f of x equals 30 multiplied by 0.88 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
graph of function f of x equals 50 multiplied by 0.82 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis
Answers
The decay equation is f(x) = 40(0.75)ˣ
Where f(x) is the mass of air freshener left after x days of use
The graph of this function is given below
The correct description of the graph is statement 2:
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
The person under is wrong but there chart is right. 100%-15%=85%
85%=.85
F(x)= 40(.85)^x
Write that in desmos graphing and you will get the chart.
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