Saul is training for a mud-obstacle race. Saul takes in 2,450 calories per day. Because he runs more now,Saul has been tracking how many calories he burns. Running for 30 minutes burns 354 calories.Find the slope, y-intercept, and whether the function is increasing or decreasing. Write your response in fullsentences
Answers
Saul is training for a mud-obstacle race. Saul takes in 2,450 calories per day. Because he runs more now,
Saul has been tracking how many calories he burns. Running for 30 minutes burns 354 calories.
Find the slope, y-intercept, and whether the function is increasing or decreasing. Write your response in full sentences
Saul takes 2450 calories per day=
he burns 345 calories running 30 minutes
Step 1
Identify the variables,
the variable y will be the calories Saul burns ( it depends on the time he runs)
the variable x will be the time he runs
Step 2 identify two points.
so, with the data , we can take 2 points.
he burns 345 calories running 30 minutes P1(30,354)
he burns 0 calories when he runs 0 minutes P2(0,0)
Step 3
find the function, first, find the slope of the line
\(\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{354-0}{30-0} \\ m=11.8 \end{gathered}\)so, the slope of the line is 11.8
Step 4
the y intercept is when x =0
so,we need to find the value y, when x=0( in this point the line intercept the y -axis)
and, we define this as (0,0), so the y intercept is x=0, y=0
this is a linear function, the slope is more than 0, so, the function is increasing
Related Questions
In exercises 17-20, approximate the logarithm using the properties of logarithms, given the values logb2 = 0.3562, logb3 = 0.5646, and logb = 0.8271. Round your result to four decimal places.
I only need 19 and 20!
19. logb 16/25
20. logb \(\sqrt{3}\)
Answers
The solution of the logarithmic expressions will be:-
19) 2logb4 - 2logb5
20) (1/2)logb (3)
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two expressions are logb 16/25 and logb √3.
The expressions will be solved as:-
E = logb 16/25
E = logb 16 - logb 25
E = logb 4² - logb 5²
E = 2logb 4 - 2logb 5
The second expression will be solved as:-
E = logb √3.
E = ( 1 / 2 ) logb 3
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Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage?
Answers
Answer:
The range is found by subtracting the minimum data entry from the maximum data entry.
Step-by-step explanation:
The range is found by subtracting the minimum data entry from the maximum data entry.
It is easy to compute.
It uses only two entries from the data set.
The triangles shown below must be congruent
A. True
B. False
Answers
A 3 dimensional shape is created when the shape isrotated around the y-axisFind the volumen of shape
Answers
By rotating the shape of the graph, we get the following cylinder:
So we have a cylinder with:
• radius r = 4,
,• height h = 6.
The volume of the cylinder using π = 3.14 is given by:
\(V=\pi *r^2*h=3.14*4^2*6=301.44.\)AnswerThe solid obtained is a cylinder of volume 301.44.
Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
Answers
Answer:
To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:
A' = (-3, 3 + 3) = (-3, 6)
B' = (0, 7 + 3) = (0, 10)
C' = (-3, 0 + 3) = (-3, 3)
Therefore, the coordinates of the vertices for the image triangle A'B'C' are A'(-3, 6), B'(0, 10), and C'(-3, 3).
So the correct answer is: A′(−3, 6), B′(0, 10), C′(−3, 3).
approximate sqrt (39) to the nearest whole number
Answers
Answer:
\({ \boxed{ \sqrt{39} \approx 6 }}\)
Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.
Answers
Answer:
(a). y = 3x - 11 ; (b). y = \(-\frac{1}{3}\) x - 1
Step-by-step explanation:
Parallel lines have the same slopes
Slopes of perpendicular lines are opposite reciprocals.
(3, - 2)
The slope of given line is 3
(a). Equation of ║ line is
y + 2 = 3(x - 3)
y = 3x - 11
(b). Slope of perpendicular line is \(-\frac{1}{3}\)
y + 2 = \(-\frac{1}{3}\) (x - 3)
y = \(-\frac{1}{3}\) x - 1
The required equation of a line parallel to the line will be y = 3x - 7
The required equation of the perpendicular line is y = -1/3 - 7
Using the coordinate points to get the equation of the line (1, -4) and (2, -1)
The standard form of the equation is expressed as y = mx + b
m is the slope
b is the y-intercept
Get the slope:
m = y2-y1/x2-x1
m = -1+4/2-1
m = 3/1
m = 3
Get the y-intercept
-4 = 3(1) + b
b = -4-3
b = -7
The required equation of a line parallel to the line will be y = 3x - 7
For the equation of the line perpendicular, the slope of the line will be -1/3
The required equation of the perpendicular line is y = -1/3 - 7
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3
Solve for x. Round answer to the nearest tenth.
X
759
17
Answers
Answer:
x ≈ 4.6
Step-by-step explanation:
Reference angle = 75°
Opposite side to reference angle = 17
Adjacent side = x
Applying TOA:
Tan 75 = opp/adj
Tan 75 = 17/x
Multiply both sides by x
x*Tan 75 = 17
Divide both sides by Tan 75
x = 17/Tan 75
x ≈ 4.6
I need someone to solve b ASAP please help
Answers
b) The 99% confidence interval for the population proportion is given as follows: (0.57, 0.68).
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.
The parameters for this problem are given as follows:
\(n = 520, \pi = \frac{325}{520} = 0.625\)
Then the lower bound of the interval is given as follows:
\(0.625 - 2.575\sqrt{\frac{0.625(0.375)}{520}} = 0.57\)
The upper bound of the interval is given as follows:
\(0.625 + 2.575\sqrt{\frac{0.625(0.375)}{520}} = 0.68\)
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What is the area of a triangle whose vertices are D(3, 3), E(3, −1), and F(−2, −5)?
Answers
Answer:
10 units²
Step-by-step explanation:
The Heflin household is laying down mulch around their garden. The following image depicts the shape and dimension of their garden and the area they want to place the mulch:
A triangular garden inside a rectangular mulch area. The garden has a base of 6 feet and a height of 5 feet, and the mulch area has a height of 9 feet and a base of 12 feet.
If the mulch costs $0.59 per square foot, determine the total cost.
Answers
Answer:
$54.87
Step-by-step explanation:
The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.
The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.
The total area to be covered with mulch is 108 - 15 = 93 square feet.
The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.
Therefore, the total cost of the mulch will be $54.87.
Three quarters of a number is 27. What is two ninths of the number?
Answers
Answer:
8
Step-by-step explanation:
let x be the number , then
\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )
3x = 108 ( divide both sides by 3 )
x = 36
the number is 36, so
\(\frac{2}{9}\) × 36 = 2 × 4 = 8
The two ninths of the number is 8
We know that Three quarters of a number is \(\frac{3}{4}\) times of a number
Hence we will assume the number x ,
\(\frac{3}{4} of x = 27\)
\(x = 27 X \frac{4}{3}\)
\(x = 36\)
Now as we know the number is 36
Therefore , the two ninths of the number assumed as y
We will multiply the number 36 by 2 and then divide by 9
Hence,
\(y = 36 X \frac{2}{9}\)
\(y = 8\)
Thus, the two ninths of the number 36 is 8
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is 1 1/2 a rational number?
Answers
yes. It would be an irrational number if it didn't repeat in a pattern.
hope it helps comment if u have any questions
Answer:
Yes.
Step-by-step explanation:
Yes 1 \(\frac{1}{2}\) is a rational number because because it can be converted to a decimal, which is 1.5
[(3 x 8) + 2?] + 6 - 2 Write out the steps Jayden will have to take in the yellow box? what are the steps?
Answers
Answer:
[(3*8)+2]+6-2
PEMDAS
There are parentheses so solve what is in them
3*8=24
[24+2]
26+6-2
Do the addition
32-2
30 is your answer
30 steps
Consider the whole numbers from 0 to 9. You may only use each digit ONCE.
Sketch one digit in each of the blank squares to find the SMALLEST possible result.
Answers
Answer:
8 ÷ 0 (2+3)^7 x 1 - 9
Step-by-step explanation:
I think this is correct because the result would be zero as 9 ÷ 0 is 0 and 0 anything is zero. I could be wrong tho
PLEASE HELP! Select the equation that is true.
A.6,714 ÷ 10^3 = 6.714
B.6,714 ÷ 10^3 = 67.14
C.6,714 ÷ 10^3 = 671.4
D.6,714 ÷ 10^3 = 6,714
Answers
the easy way to think about it is that by dividing by 10^3 you are actually multipling by 1/10^3 which you can write as 10^-3 and the negative means that the decimal place moves to the left. so we move the decimal places (which is to the right of the 4 in the number above) 3 places to the left giving us: 6.714
2x-3\(\geq\) 0
Answers
Answer:
x ≥ 1.5
Step-by-step explanation:
2x - 3 ≥ 0 ( add 3 to both sides )
2x ≥ 3 ( divide both sides by 2 )
x ≥ 1.5
What is the circumference of the circle if the radius is 10 cm?
Answers
Answer for this question
The circumference of the circle is 62.8cm.
The Circumference of the circle is given by the formula,
Circumference = 2*\(\pi\)*r cm.........equation 1
Given, r = 10cm
On substituting the radius value in equation 1
Circumference = 2*\(\pi\)*10
Circumference = 62.8 cm
Therefore, the circumference of the circle is 62.8cm.
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The temperature inside my refrigerator is about 40 Celsius. That temperature in Kelvin is K.
I place a balloon in my fridge that initially has a temperature of 220 C. This is K.
If the original volume of the balloon is 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator? liters. (Round to two decimal places)
Answers
To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.
The law can be expressed mathematically as:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }\)
Where:
V₁ is the initial volumeT₁ is the initial temperatureV₂ is the final volumeT₂ is the final temperatureNow we obtain the data to continue solving:
V₁ = 0.5 LT₁ = 220 °CV₂ = ?T₂ = 40 °CNow, we will convert the temperatures to Kelvin:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }\)
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }\)
Now we solve for V₂:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }\)
Where:
V₁ is the initial volumeT₁ is the initial temperatureV₂ is the final volumeT₂ is the final temperatureNow, we substitute the values in the formula:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }\)
\(\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}\)
The final volume of the balloon, when completely cooled in the refrigerator, will be approximately 0.32 liters.solve for x
(look at photo)
Answers
By definition of proportion, the value of x is,
⇒ x = 80
We have to given that;
In a triangle,
Perpendicular = 60
Now, By Pythagoras theorem we get;
60² = 36² + y²
3600 = 1296 + y²
y² = 3600 - 1296
y² = 2304
y = 48
Hence, By definition of proportion;
⇒ x / 48 = 60 / 36
⇒ x = 80
Thus, By definition of proportion, the value of x is,
⇒ x = 80
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1)
Science 5
Measurement Assignment
Name each measurement instrument below. Then, indicate which
type of measurement is performed with each one. Remember,
some instruments can be used for more than one type of
measurement!
Instrument
Name of Instrument
Measurement Type
Answers
Answer: See below
Step-by-step explanation:
The first is a beaker, it's used to measure liquid volume
The second is a ruler, it's used to measure length.
Last is a thermometer, it's used to measure temperature.
What additional piece of information is needed to show that DEF = PQR by ASA?
Answers
Answer:
The sigle line between E and D shows that it is tje same as Q AND P. SO angle D and E is the same as angle Q and P
The triangles ΔDEF and ΔPQR are congruent with each other by ASA postulates because ∠F = ∠R. Then the correct option is A.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangles ΔDEF and ΔPQR,
∠DEF = ∠PRQ (Given)
DE = PQ (Given)
∠F = ∠R (Opposite sides are equal)
The triangles ΔDEF and ΔPQR are congruent with each other by ASA postulates because ∠F = ∠R. Then the correct option is A.
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PLEASE HELP!!! The sum of 2 consecutive itegers is 294. Write an equation for the integers.
Answers
Answer:
147
Step-by-step explanation:
Divide 294 by 2
Solve for x.
(Round to the nearest hundredth)
Answers
Answer:
x=26.44
rounded to the nearest hundredth.
Step-by-step explanation:
Soh Cah Toa
We need opposite for x and adjacent for 44
Length × Tan (Angle)
44 × Tan (31)=26.43786724
Petra jogs 6 miles in 42 minutes. At this rate, how long would it take her to jog 8 miles?
Answers
Distance 1 / Time 1 = Distance 2 / Time 2
Using the information given:
6 miles / 42 minutes = 8 miles / Time 2
To solve for Time 2, we can cross-multiply and then divide:
6 miles * Time 2 = 8 miles * 42 minutes
6 * Time 2 = 8 * 42
6 * Time 2 = 336
Now, we divide both sides by 6 to isolate Time 2:
Time 2 = 336 / 6
Time 2 = 56 minutes
Therefore, it would take Petra 56 minutes to jog 8 miles at the same rate.
Answer:
56 minutes
Step-by-step explanation:
We can use proportions to solve.
6 miles 8 miles
------------ = ------------------
42 minutes x minutes
Using cross products.
6x = 42 *8
Divide each side by 6
x = 42/6 * 8
x = 7*8
x = 56
Calculate the volume of this regular solid.
A sphere with radius of 8 centimeters.
What is the volume of the sphere?
Use the button on your calculator to complete this problem.
Round at the end to the nearest tenth.
Answers
Answer:
2144.7cm³
Step-by-step explanation:
volume = \(\frac{4}{3}\) pi 8³
Quadrilateral A'B'C'D' is the image of
quadrilateral ABCD under a dilation with a scale
factor of 3. What is the length of segment BC?
Answers
By using the concept of dilation factor, length of BC obtained is 3 units
What is dilation factor?
Dilation is a transformation which changes the size of a figure by a certain factor.
That factor is called the scale factor
In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3
A'B'C'D' is the dilated figure
Length of B'C' = 9 units
Length of BC = \(9 \div 3\) = 3 units
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Complete Question
The figure has been attached here
Which operation should be performed last in this
problem: 32 + 7 x 4? Why?
Answers
Find the sum of the complex numbers (3+3i)+(8+7i)
Answers
Answer:
11 + 10i
Step-by-step explanation:
Just treat i like any other variable, and combine like terms. Hope that helps!
what’s the solution?
Answers
Answer:
a> -21 1/3
Step-by-step explanation:
I hope it helped